LMFDB - Embedded newform 14.15.d.a.5.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [14,15,Mod(3,14)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(14, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 15, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("14.3");

S:= CuspForms(chi, 15);

N := Newforms(S);

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 15 $
Character orbit:	$[\chi]$	$=$	14.d (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$17.4060555413$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 5366534 x^{18} + 786490608 x^{17} + 19826027932115 x^{16} + \cdots + 13\!\cdots\!24 $ x^20 - 4x^19 + 5366534x^18 + 786490608x^17 + 19826027932115x^16 + 3116508483645696x^15 + 38794655189396647126x^14 + 6995731541198679243060x^13 + 54561557157067963809187457x^12 + 6630233353755658208901796272x^11 + 34794459335155646904361009621528x^10 - 507937593458729410665953593711872x^9 + 15479722701777718863087638126396034896x^8 - 883719083612311978219332637069278729984x^7 + 3763299771642320209476548571825975912308608x^6 - 633899212255257611286599422411160802422874624x^5 + 597491591633081375797803556549613553954788912384x^4 - 42265294259314426139494021682209240856866274451456x^3 + 11534106439702605092537039760142524539554443571202048x^2 + 525642005044107600688521330249536141111741609738240000*x + 136102482846251121074713416730051821278073355281841537024
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{76}\cdot 3^{12}\cdot 7^{14} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.5
Root			$-727.640 + 1260.31i$ of defining polynomial
Character	$\chi$	$=$	14.5
Dual form			14.15.d.a.3.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-45.2548 + 78.3837i) q^{2} +(2710.52 - 1564.92i) q^{3} +(-4096.00 - 7094.48i) q^{4} +(10170.7 + 5872.03i) q^{5} +283280. i q^{6} +(552858. + 610386. i) q^{7} +741455. q^{8} +(2.50645e6 - 4.34129e6i) q^{9} +O(q^{10})$	\(q+(-45.2548 + 78.3837i) q^{2} +(2710.52 - 1564.92i) q^{3} +(-4096.00 - 7094.48i) q^{4} +(10170.7 + 5872.03i) q^{5} +283280. i q^{6} +(552858. + 610386. i) q^{7} +741455. q^{8} +(2.50645e6 - 4.34129e6i) q^{9} +(-920543. + 531476. i) q^{10} +(777792. + 1.34718e6i) q^{11} +(-2.22045e7 - 1.28198e7i) q^{12} -7.67305e7i q^{13} +(-7.28638e7 + 1.57121e7i) q^{14} +3.67570e7 q^{15} +(-3.35544e7 + 5.81180e7i) q^{16} +(3.82953e8 - 2.21098e8i) q^{17} +(2.26858e8 + 3.92929e8i) q^{18} +(1.50144e9 + 8.66859e8i) q^{19} -9.62074e7i q^{20} +(2.45373e9 + 7.89284e8i) q^{21} -1.40795e8 q^{22} +(-4.17226e8 + 7.22657e8i) q^{23} +(2.00973e9 - 1.16032e9i) q^{24} +(-2.98280e9 - 5.16635e9i) q^{25} +(6.01442e9 + 3.47243e9i) q^{26} -7.19630e8i q^{27} +(2.06586e9 - 6.42238e9i) q^{28} +1.93832e10 q^{29} +(-1.66343e9 + 2.88115e9i) q^{30} +(3.04677e9 - 1.75905e9i) q^{31} +(-3.03700e9 - 5.26024e9i) q^{32} +(4.21644e9 + 2.43436e9i) q^{33} +4.00230e10i q^{34} +(2.03872e9 + 9.45443e9i) q^{35} -4.10656e10 q^{36} +(-1.22953e9 + 2.12961e9i) q^{37} +(-1.35895e11 + 7.84591e10i) q^{38} +(-1.20077e11 - 2.07979e11i) q^{39} +(7.54109e9 + 4.35385e9i) q^{40} -6.79703e10i q^{41} +(-1.72910e11 + 1.56614e11i) q^{42} +8.78392e10 q^{43} +(6.37167e9 - 1.10361e10i) q^{44} +(5.09844e10 - 2.94359e10i) q^{45} +(-3.77630e10 - 6.54075e10i) q^{46} +(-2.20796e11 - 1.27476e11i) q^{47} +2.10040e11i q^{48} +(-6.69190e10 + 6.74914e11i) q^{49} +5.39944e11 q^{50} +(6.92000e11 - 1.19858e12i) q^{51} +(-5.44363e11 + 3.14288e11i) q^{52} +(-6.20215e11 - 1.07424e12i) q^{53} +(5.64072e10 + 3.25667e10i) q^{54} +1.82689e10i q^{55} +(4.09919e11 + 4.52574e11i) q^{56} +5.42625e12 q^{57} +(-8.77185e11 + 1.51933e12i) q^{58} +(-2.99509e12 + 1.72922e12i) q^{59} +(-1.50557e11 - 2.60772e11i) q^{60} +(3.34859e12 + 1.93331e12i) q^{61} +3.18423e11i q^{62} +(4.03557e12 - 8.70219e11i) q^{63} +5.49756e11 q^{64} +(4.50564e11 - 7.80400e11i) q^{65} +(-3.81628e11 + 2.20333e11i) q^{66} +(-4.13868e12 - 7.16841e12i) q^{67} +(-3.13715e12 - 1.81124e12i) q^{68} +2.61170e12i q^{69} +(-8.33335e11 - 2.68056e11i) q^{70} -1.12049e13 q^{71} +(1.85842e12 - 3.21888e12i) q^{72} +(-1.24939e13 + 7.21337e12i) q^{73} +(-1.11284e11 - 1.92750e11i) q^{74} +(-1.61698e13 - 9.33566e12i) q^{75} -1.42026e13i q^{76} +(-3.92288e11 + 1.21955e12i) q^{77} +2.17362e13 q^{78} +(-8.80870e12 + 1.52571e13i) q^{79} +(-6.82541e11 + 3.94065e11i) q^{80} +(1.08621e13 + 1.88137e13i) q^{81} +(5.32776e12 + 3.07599e12i) q^{82} +5.05290e13i q^{83} +(-4.45094e12 - 2.06409e13i) q^{84} +5.19318e12 q^{85} +(-3.97515e12 + 6.88516e12i) q^{86} +(5.25386e13 - 3.03332e13i) q^{87} +(5.76698e11 + 9.98870e11i) q^{88} +(-6.21834e13 - 3.59016e13i) q^{89} +5.32846e12i q^{90} +(4.68352e13 - 4.24211e13i) q^{91} +6.83584e12 q^{92} +(5.50554e12 - 9.53588e12i) q^{93} +(1.99841e13 - 1.15378e13i) q^{94} +(1.01804e13 + 1.76331e13i) q^{95} +(-1.64637e13 - 9.50531e12i) q^{96} +6.76473e13i q^{97} +(-4.98738e13 - 3.57885e13i) q^{98} +7.79798e12 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4374 q^{3} - 81920 q^{4} + 3354 q^{5} + 1455616 q^{7} + 17547432 q^{9}+O(q^{10}) $ 20 * q - 4374 * q^3 - 81920 * q^4 + 3354 * q^5 + 1455616 * q^7 + 17547432 * q^9	\( 20 q - 4374 q^{3} - 81920 q^{4} + 3354 q^{5} + 1455616 q^{7} + 17547432 q^{9} - 3933696 q^{10} + 8400426 q^{11} + 35831808 q^{12} - 114693888 q^{14} + 562720524 q^{15} - 671088640 q^{16} + 2180481042 q^{17} - 251755008 q^{18} - 3919727442 q^{19} + 7585509006 q^{21} + 5394565632 q^{22} - 6905098386 q^{23} - 2371878912 q^{24} + 14165082644 q^{25} + 12652202496 q^{26} - 17334943744 q^{28} + 27884908704 q^{29} + 54103511808 q^{30} + 45638710782 q^{31} - 37041090498 q^{33} - 18274367202 q^{35} - 287497125888 q^{36} - 27026027926 q^{37} - 354043974912 q^{38} - 126125404380 q^{39} + 32224837632 q^{40} - 298475364864 q^{42} + 726682953656 q^{43} + 68816289792 q^{44} + 498861631944 q^{45} - 286664984832 q^{46} - 2044625353338 q^{47} + 2939974016204 q^{49} + 1161106642944 q^{50} - 2419609945602 q^{51} + 1314350333952 q^{52} + 1546271487546 q^{53} - 5213176950528 q^{54} + 1720927125504 q^{56} + 14789884876092 q^{57} - 2365863040512 q^{58} - 6798944731566 q^{59} - 2304903266304 q^{60} - 2214453865554 q^{61} - 4417730390688 q^{63} + 10995116277760 q^{64} + 7516703932836 q^{65} - 8476063570944 q^{66} - 4655820763226 q^{67} - 17862500696064 q^{68} + 20497461621504 q^{70} + 96606137494152 q^{71} - 2062377025536 q^{72} - 65348368908666 q^{73} - 566532483072 q^{74} - 186663280957308 q^{75} + 77525241691422 q^{77} + 88663911671808 q^{78} - 60517474082978 q^{79} - 225083129856 q^{80} - 107180264511342 q^{81} - 43979002397184 q^{82} + 18842436550656 q^{84} + 416326699526124 q^{85} + 2363335174656 q^{86} - 126768392660088 q^{87} - 22096140828672 q^{88} - 237147002561826 q^{89} + 203506111374408 q^{91} + 113133131956224 q^{92} - 94175068190130 q^{93} - 221058962902272 q^{94} + 25202514515490 q^{95} + 19430432047104 q^{96} + 165606984015360 q^{98} + 10\!\cdots\!68 q^{99}+O(q^{100}) \) 20 * q - 4374 * q^3 - 81920 * q^4 + 3354 * q^5 + 1455616 * q^7 + 17547432 * q^9 - 3933696 * q^10 + 8400426 * q^11 + 35831808 * q^12 - 114693888 * q^14 + 562720524 * q^15 - 671088640 * q^16 + 2180481042 * q^17 - 251755008 * q^18 - 3919727442 * q^19 + 7585509006 * q^21 + 5394565632 * q^22 - 6905098386 * q^23 - 2371878912 * q^24 + 14165082644 * q^25 + 12652202496 * q^26 - 17334943744 * q^28 + 27884908704 * q^29 + 54103511808 * q^30 + 45638710782 * q^31 - 37041090498 * q^33 - 18274367202 * q^35 - 287497125888 * q^36 - 27026027926 * q^37 - 354043974912 * q^38 - 126125404380 * q^39 + 32224837632 * q^40 - 298475364864 * q^42 + 726682953656 * q^43 + 68816289792 * q^44 + 498861631944 * q^45 - 286664984832 * q^46 - 2044625353338 * q^47 + 2939974016204 * q^49 + 1161106642944 * q^50 - 2419609945602 * q^51 + 1314350333952 * q^52 + 1546271487546 * q^53 - 5213176950528 * q^54 + 1720927125504 * q^56 + 14789884876092 * q^57 - 2365863040512 * q^58 - 6798944731566 * q^59 - 2304903266304 * q^60 - 2214453865554 * q^61 - 4417730390688 * q^63 + 10995116277760 * q^64 + 7516703932836 * q^65 - 8476063570944 * q^66 - 4655820763226 * q^67 - 17862500696064 * q^68 + 20497461621504 * q^70 + 96606137494152 * q^71 - 2062377025536 * q^72 - 65348368908666 * q^73 - 566532483072 * q^74 - 186663280957308 * q^75 + 77525241691422 * q^77 + 88663911671808 * q^78 - 60517474082978 * q^79 - 225083129856 * q^80 - 107180264511342 * q^81 - 43979002397184 * q^82 + 18842436550656 * q^84 + 416326699526124 * q^85 + 2363335174656 * q^86 - 126768392660088 * q^87 - 22096140828672 * q^88 - 237147002561826 * q^89 + 203506111374408 * q^91 + 113133131956224 * q^92 - 94175068190130 * q^93 - 221058962902272 * q^94 + 25202514515490 * q^95 + 19430432047104 * q^96 + 165606984015360 * q^98 + 1056686373672768 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−45.2548	+	78.3837i	−0.353553	+	0.612372i
$2$	−45.2548	+	78.3837i	−0.353553	+	0.612372i
$3$	2710.52	−	1564.92i	1.23938	−	0.715554i	0.270410	−	0.962745i	$-0.412841\pi$
$3$	2710.52	−	1564.92i	1.23938	−	0.715554i	0.968967	+	0.247191i	$0.0795075\pi$
$4$	−4096.00	−	7094.48i	−0.250000	−	0.433013i
$5$	10170.7	+	5872.03i	0.130184	+	0.0751620i	0.563678	−	0.825995i	$-0.309386\pi$
$5$	10170.7	+	5872.03i	0.130184	+	0.0751620i	−0.433493	+	0.901157i	$0.642719\pi$
$6$			283280.i			1.01195i
$7$	552858.	+	610386.i	0.671317	+	0.741171i
$7$	552858.	+	610386.i	0.671317	+	0.741171i
$8$	741455.			0.353553
$9$	2.50645e6	−	4.34129e6i	0.524036	−	0.907657i
$10$	−920543.	+	531476.i	−0.0920543	+	0.0531476i
$11$	777792.	+	1.34718e6i	0.0399130	+	0.0691314i	0.885292	−	0.465036i	$-0.153959\pi$
$11$	777792.	+	1.34718e6i	0.0399130	+	0.0691314i	−0.845379	+	0.534167i	$0.820625\pi$
$12$	−2.22045e7	−	1.28198e7i	−0.619688	−	0.357777i
$13$		−	7.67305e7i		−	1.22283i	−0.791312	−	0.611413i	$-0.790601\pi$
$13$		−	7.67305e7i		−	1.22283i	0.791312	−	0.611413i	$-0.209399\pi$
$14$	−7.28638e7	+	1.57121e7i	−0.691219	+	0.149052i
$15$	3.67570e7			0.215130
$16$	−3.35544e7	+	5.81180e7i	−0.125000	+	0.216506i
$17$	3.82953e8	−	2.21098e8i	0.933261	−	0.538818i	0.0454195	−	0.998968i	$-0.485538\pi$
$17$	3.82953e8	−	2.21098e8i	0.933261	−	0.538818i	0.887841	+	0.460150i	$0.152204\pi$
$18$	2.26858e8	+	3.92929e8i	0.370549	+	0.641810i
$19$	1.50144e9	+	8.66859e8i	1.67971	+	0.969780i	0.961845	+	0.273595i	$0.0882129\pi$
$19$	1.50144e9	+	8.66859e8i	1.67971	+	0.969780i	0.717863	+	0.696184i	$0.245120\pi$
$20$		−	9.62074e7i		−	0.0751620i
$21$	2.45373e9	+	7.89284e8i	1.36236	+	0.438226i
$22$	−1.40795e8			−0.0564455
$23$	−4.17226e8	+	7.22657e8i	−0.122540	+	0.212245i	−0.920769	−	0.390109i	$-0.872437\pi$
$23$	−4.17226e8	+	7.22657e8i	−0.122540	+	0.212245i	0.798229	+	0.602354i	$0.205771\pi$
$24$	2.00973e9	−	1.16032e9i	0.438186	−	0.252987i
$25$	−2.98280e9	−	5.16635e9i	−0.488701	−	0.846456i
$26$	6.01442e9	+	3.47243e9i	0.748825	+	0.432334i
$27$		−	7.19630e8i		−	0.0687960i
$28$	2.06586e9	−	6.42238e9i	0.153107	−	0.475981i
$29$	1.93832e10			1.12367			0.561837	−	0.827248i	$-0.310095\pi$
$29$	1.93832e10			1.12367			0.561837	+	0.827248i	$0.310095\pi$
$30$	−1.66343e9	+	2.88115e9i	−0.0760600	+	0.131740i
$31$	3.04677e9	−	1.75905e9i	0.110741	−	0.0639362i	−0.443607	−	0.896222i	$-0.646301\pi$
$31$	3.04677e9	−	1.75905e9i	0.110741	−	0.0639362i	0.554347	+	0.832285i	$0.312968\pi$
$32$	−3.03700e9	−	5.26024e9i	−0.0883883	−	0.153093i
$33$	4.21644e9	+	2.43436e9i	0.0989345	+	0.0571199i
$34$			4.00230e10i			0.762004i
$35$	2.03872e9	+	9.45443e9i	0.0316871	+	0.146946i
$36$	−4.10656e10			−0.524036
$37$	−1.22953e9	+	2.12961e9i	−0.0129517	+	0.0224330i	−0.872429	−	0.488742i	$-0.837456\pi$
$37$	−1.22953e9	+	2.12961e9i	−0.0129517	+	0.0224330i	0.859477	+	0.511175i	$0.170789\pi$
$38$	−1.35895e11	+	7.84591e10i	−1.18773	+	0.685738i
$39$	−1.20077e11	−	2.07979e11i	−0.874998	−	1.51554i
$40$	7.54109e9	+	4.35385e9i	0.0460272	+	0.0265738i
$41$		−	6.79703e10i		−	0.349006i	−0.984657	−	0.174503i	$-0.944168\pi$
$41$		−	6.79703e10i		−	0.349006i	0.984657	−	0.174503i	$-0.0558318\pi$
$42$	−1.72910e11	+	1.56614e11i	−0.750025	+	0.679336i
$43$	8.78392e10			0.323154			0.161577	−	0.986860i	$-0.448342\pi$
$43$	8.78392e10			0.323154			0.161577	+	0.986860i	$0.448342\pi$
$44$	6.37167e9	−	1.10361e10i	0.0199565	−	0.0345657i
$45$	5.09844e10	−	2.94359e10i	0.136443	−	0.0787752i
$46$	−3.77630e10	−	6.54075e10i	−0.0866487	−	0.150080i
$47$	−2.20796e11	−	1.27476e11i	−0.435818	−	0.251620i	0.266004	−	0.963972i	$-0.414297\pi$
$47$	−2.20796e11	−	1.27476e11i	−0.435818	−	0.251620i	−0.701822	+	0.712352i	$0.747630\pi$
$48$			2.10040e11i			0.357777i
$49$	−6.69190e10	+	6.74914e11i	−0.0986682	+	0.995120i
$50$	5.39944e11			0.691128
$51$	6.92000e11	−	1.19858e12i	0.771108	−	1.33560i
$52$	−5.44363e11	+	3.14288e11i	−0.529499	+	0.305706i
$53$	−6.20215e11	−	1.07424e12i	−0.527972	−	0.914474i	−0.999468	−	0.0326063i	$-0.989619\pi$
$53$	−6.20215e11	−	1.07424e12i	−0.527972	−	0.914474i	0.471496	−	0.881868i	$-0.343714\pi$
$54$	5.64072e10	+	3.25667e10i	0.0421287	+	0.0243230i
$55$			1.82689e10i			0.0119998i
$56$	4.09919e11	+	4.52574e11i	0.237346	+	0.262043i
$57$	5.42625e12			2.77572
$58$	−8.77185e11	+	1.51933e12i	−0.397279	+	0.688107i
$59$	−2.99509e12	+	1.72922e12i	−1.20350	+	0.694841i	−0.961332	−	0.275393i	$-0.911192\pi$
$59$	−2.99509e12	+	1.72922e12i	−1.20350	+	0.694841i	−0.242168	+	0.970234i	$0.577859\pi$
$60$	−1.50557e11	−	2.60772e11i	−0.0537825	−	0.0931540i
$61$	3.34859e12	+	1.93331e12i	1.06550	+	0.615166i	0.926948	−	0.375189i	$-0.122422\pi$
$61$	3.34859e12	+	1.93331e12i	1.06550	+	0.615166i	0.138551	+	0.990355i	$0.455756\pi$
$62$			3.18423e11i			0.0904195i
$63$	4.03557e12	−	8.70219e11i	1.02452	−	0.220925i
$64$	5.49756e11			0.125000
$65$	4.50564e11	−	7.80400e11i	0.0919101	−	0.159193i
$66$	−3.81628e11	+	2.20333e11i	−0.0699573	+	0.0403899i
$67$	−4.13868e12	−	7.16841e12i	−0.682871	−	1.18277i	−0.974101	−	0.226114i	$-0.927398\pi$
$67$	−4.13868e12	−	7.16841e12i	−0.682871	−	1.18277i	0.291230	−	0.956653i	$-0.405936\pi$
$68$	−3.13715e12	−	1.81124e12i	−0.466630	−	0.269409i
$69$			2.61170e12i			0.350735i
$70$	−8.33335e11	−	2.68056e11i	−0.101189	−	0.0325491i
$71$	−1.12049e13			−1.23196			−0.615982	−	0.787760i	$-0.711241\pi$
$71$	−1.12049e13			−1.23196			−0.615982	+	0.787760i	$0.711241\pi$
$72$	1.85842e12	−	3.21888e12i	0.185275	−	0.320905i
$73$	−1.24939e13	+	7.21337e12i	−1.13094	+	0.652947i	−0.944171	−	0.329457i	$-0.893134\pi$
$73$	−1.24939e13	+	7.21337e12i	−1.13094	+	0.652947i	−0.186767	+	0.982404i	$0.559801\pi$
$74$	−1.11284e11	−	1.92750e11i	−0.00915825	−	0.0158625i
$75$	−1.61698e13	−	9.33566e12i	−1.21137	−	0.699385i
$76$		−	1.42026e13i		−	0.969780i
$77$	−3.92288e11	+	1.21955e12i	−0.0244439	+	0.0759914i
$78$	2.17362e13			1.23743
$79$	−8.80870e12	+	1.52571e13i	−0.458693	+	0.794480i	−0.998892	−	0.0470572i	$-0.985016\pi$
$79$	−8.80870e12	+	1.52571e13i	−0.458693	+	0.794480i	0.540199	+	0.841537i	$0.318349\pi$
$80$	−6.82541e11	+	3.94065e11i	−0.0325461	+	0.0187905i
$81$	1.08621e13	+	1.88137e13i	0.474809	+	0.822393i
$82$	5.32776e12	+	3.07599e12i	0.213721	+	0.123392i
$83$			5.05290e13i			1.86206i	0.364939	+	0.931032i	$0.381090\pi$
$83$			5.05290e13i			1.86206i	−0.364939	+	0.931032i	$0.618910\pi$
$84$	−4.45094e12	−	2.06409e13i	−0.150833	−	0.699476i
$85$	5.19318e12			0.161995
$86$	−3.97515e12	+	6.88516e12i	−0.114252	+	0.197890i
$87$	5.25386e13	−	3.03332e13i	1.39266	−	0.804050i
$88$	5.76698e11	+	9.98870e11i	0.0141114	+	0.0244416i
$89$	−6.21834e13	−	3.59016e13i	−1.40587	−	0.811678i	−0.410881	−	0.911689i	$-0.634779\pi$
$89$	−6.21834e13	−	3.59016e13i	−1.40587	−	0.811678i	−0.994986	+	0.100011i	$0.968112\pi$
$90$			5.32846e12i			0.111405i
$91$	4.68352e13	−	4.24211e13i	0.906323	−	0.820903i
$92$	6.83584e12			0.122540
$93$	5.50554e12	−	9.53588e12i	0.0914997	−	0.158482i
$94$	1.99841e13	−	1.15378e13i	0.308170	−	0.177922i
$95$	1.01804e13	+	1.76331e13i	0.145781	+	0.252500i
$96$	−1.64637e13	−	9.50531e12i	−0.219093	−	0.126493i
$97$			6.76473e13i			0.837237i	0.908162	+	0.418618i	$0.137485\pi$
$97$			6.76473e13i			0.837237i	−0.908162	+	0.418618i	$0.862515\pi$
$98$	−4.98738e13	−	3.57885e13i	−0.574500	−	0.412250i
$99$	7.79798e12			0.0836634
$100$	−2.44351e13	+	4.23228e13i	−0.244351	+	0.423228i
$101$	1.09522e14	−	6.32324e13i	1.02153	−	0.589780i	0.106983	−	0.994261i	$-0.465881\pi$
$101$	1.09522e14	−	6.32324e13i	1.02153	−	0.589780i	0.914547	+	0.404480i	$0.132548\pi$
$102$	6.26327e13	+	1.08483e14i	0.545255	+	0.944410i
$103$	5.66973e13	+	3.27342e13i	0.461001	+	0.266159i	0.712465	−	0.701708i	$-0.247579\pi$
$103$	5.66973e13	+	3.27342e13i	0.461001	+	0.266159i	−0.251464	+	0.967867i	$0.580912\pi$
$104$		−	5.68922e13i		−	0.432334i
$105$	2.03214e13	+	2.24359e13i	0.144420	+	0.159448i
$106$	1.12271e14			0.746665
$107$	−4.47522e13	+	7.75130e13i	−0.278694	+	0.482712i	−0.971060	−	0.238834i	$-0.923235\pi$
$107$	−4.47522e13	+	7.75130e13i	−0.278694	+	0.482712i	0.692366	+	0.721546i	$0.256568\pi$
$108$	−5.10540e12	+	2.94760e12i	−0.0297895	+	0.0171990i
$109$	−9.85912e13	−	1.70765e14i	−0.539328	−	0.934143i	−0.998940	−	0.0460235i	$-0.985345\pi$
$109$	−9.85912e13	−	1.70765e14i	−0.539328	−	0.934143i	0.459613	−	0.888119i	$-0.347988\pi$
$110$	−1.43198e12	−	8.26755e11i	−0.00734833	−	0.00424256i
$111$			7.69646e12i			0.0370706i
$112$	−5.40252e13	+	1.16498e13i	−0.244383	+	0.0526980i
$113$	−4.15591e14			−1.76651			−0.883257	−	0.468889i	$-0.844654\pi$
$113$	−4.15591e14			−1.76651			−0.883257	+	0.468889i	$0.844654\pi$
$114$	−2.45564e14	+	4.25329e14i	−0.981365	+	1.69977i
$115$	−8.48693e12	+	4.89993e12i	−0.0319055	+	0.0184207i
$116$	−7.93938e13	−	1.37514e14i	−0.280919	−	0.486565i
$117$	−3.33110e14	−	1.92321e14i	−1.10991	−	0.640805i
$118$		−	3.13022e14i		−	0.982654i
$119$	3.46674e14	+	1.11513e14i	1.02587	+	0.329988i
$120$	2.72537e13			0.0760600
$121$	1.88665e14	−	3.26777e14i	0.496814	−	0.860507i
$122$	−3.03080e14	+	1.74983e14i	−0.753421	+	0.434988i
$123$	−1.06368e14	−	1.84235e14i	−0.249732	−	0.432549i
$124$	−2.49591e13	−	1.44102e13i	−0.0553704	−	0.0319681i
$125$		−	1.41740e14i		−	0.297251i
$126$	−1.14418e14	+	3.55705e14i	−0.226935	+	0.705498i
$127$	7.86509e14			1.47597			0.737985	−	0.674817i	$-0.235777\pi$
$127$	7.86509e14			1.47597			0.737985	+	0.674817i	$0.235777\pi$
$128$	−2.48791e13	+	4.30919e13i	−0.0441942	+	0.0765466i
$129$	2.38090e14	−	1.37461e14i	0.400509	−	0.231234i
$130$	4.07804e13	+	7.06337e13i	0.0649902	+	0.112566i
$131$	−1.80083e14	−	1.03971e14i	−0.272002	−	0.157041i	0.357795	−	0.933800i	$-0.383529\pi$
$131$	−1.80083e14	−	1.03971e14i	−0.272002	−	0.157041i	−0.629797	+	0.776760i	$0.716862\pi$
$132$		−	3.98846e13i		−	0.0571199i
$133$	3.00967e14	+	1.39571e15i	0.408843	+	1.89598i
$134$	7.49182e14			0.965725
$135$	4.22569e12	−	7.31911e12i	0.00517084	−	0.00895616i
$136$	2.83943e14	−	1.63934e14i	0.329958	−	0.190501i
$137$	7.55822e13	+	1.30912e14i	0.0834402	+	0.144523i	0.904726	−	0.425995i	$-0.140076\pi$
$137$	7.55822e13	+	1.30912e14i	0.0834402	+	0.144523i	−0.821285	+	0.570518i	$0.806743\pi$
$138$	−2.04715e14	−	1.18192e14i	−0.214781	−	0.124004i
$139$		−	5.80700e14i		−	0.579226i	−0.957144	−	0.289613i	$-0.906473\pi$
$139$		−	5.80700e14i		−	0.579226i	0.957144	−	0.289613i	$-0.0935266\pi$
$140$	5.87236e13	−	5.31890e13i	0.0557079	−	0.0504575i
$141$	−7.97960e14			−0.720190
$142$	5.07074e14	−	8.78278e14i	0.435565	−	0.754420i
$143$	1.03369e14	−	5.96804e13i	0.0845356	−	0.0488067i
$144$	1.68205e14	+	2.91339e14i	0.131009	+	0.226914i
$145$	1.97140e14	+	1.13819e14i	0.146285	+	0.0844576i
$146$		−	1.30576e15i		−	0.923407i
$147$	8.74799e14	+	1.93409e15i	0.589776	+	1.30393i
$148$	2.01446e13			0.0129517
$149$	−1.55172e15	+	2.68766e15i	−0.951723	+	1.64843i	−0.210026	+	0.977696i	$0.567355\pi$
$149$	−1.55172e15	+	2.68766e15i	−0.951723	+	1.64843i	−0.741696	+	0.670736i	$0.765978\pi$
$150$	1.46353e15	−	8.44967e14i	0.856568	−	0.494540i
$151$	−5.86936e14	−	1.01660e15i	−0.327908	−	0.567953i	0.654189	−	0.756331i	$-0.273010\pi$
$151$	−5.86936e14	−	1.01660e15i	−0.327908	−	0.567953i	−0.982097	+	0.188378i	$0.939677\pi$
$152$	1.11325e15	+	6.42737e14i	0.593866	+	0.342869i
$153$		−	2.21668e15i		−	1.12944i
$154$	−7.78399e13	−	8.59395e13i	−0.0378928	−	0.0418358i
$155$	4.13169e13			0.0192223
$156$	−9.83670e14	+	1.70377e15i	−0.437499	+	0.757771i
$157$	1.09181e15	−	6.30356e14i	0.464354	−	0.268095i	−0.249519	−	0.968370i	$-0.580273\pi$
$157$	1.09181e15	−	6.30356e14i	0.464354	−	0.268095i	0.713873	+	0.700275i	$0.246939\pi$
$158$	−7.97273e14	−	1.38092e15i	−0.324345	−	0.561782i
$159$	−3.36220e15	−	1.94117e15i	−1.30871	−	0.755585i
$160$		−	7.13335e13i		−	0.0265738i
$161$	−6.71767e14	+	1.44858e14i	−0.239573	+	0.0516607i
$162$	−1.96625e15			−0.671481
$163$	−1.74178e15	+	3.01686e15i	−0.569745	+	0.986828i	0.426846	+	0.904325i	$0.359625\pi$
$163$	−1.74178e15	+	3.01686e15i	−0.569745	+	0.986828i	−0.996591	+	0.0825031i	$0.973709\pi$
$164$	−4.82214e14	+	2.78406e14i	−0.151124	+	0.0872514i
$165$	2.85893e13	+	4.95181e13i	0.00858649	+	0.0148722i
$166$	−3.96065e15	−	2.28668e15i	−1.14028	−	0.658339i
$167$			1.68802e15i			0.465976i	0.972480	+	0.232988i	$0.0748502\pi$
$167$			1.68802e15i			0.465976i	−0.972480	+	0.232988i	$0.925150\pi$
$168$	1.81933e15	+	5.85219e14i	0.481668	+	0.154936i
$169$	−1.95019e15			−0.495303
$170$	−2.35016e14	+	4.07061e14i	−0.0572738	+	0.0992011i
$171$	7.52658e15	−	4.34547e15i	1.76045	−	1.01640i
$172$	−3.59789e14	−	6.23173e14i	−0.0807884	−	0.139930i
$173$	−4.03099e15	−	2.32730e15i	−0.869139	−	0.501798i	−0.00207721	−	0.999998i	$-0.500661\pi$
$173$	−4.03099e15	−	2.32730e15i	−0.869139	−	0.501798i	−0.867062	+	0.498200i	$0.833995\pi$
$174$			5.49089e15i			1.13710i
$175$	1.50441e15	−	4.67692e15i	0.299295	−	0.930451i
$176$	−1.04393e14			−0.0199565
$177$	−5.41216e15	+	9.37414e15i	−0.994393	+	1.72234i
$178$	5.62820e15	−	3.24944e15i	0.994098	−	0.573943i
$179$	4.98799e15	+	8.63945e15i	0.847138	+	1.46729i	0.883752	+	0.467956i	$0.155009\pi$
$179$	4.98799e15	+	8.63945e15i	0.847138	+	1.46729i	−0.0366140	+	0.999329i	$0.511657\pi$
$180$	−4.17665e14	−	2.41139e14i	−0.0682213	−	0.0393876i
$181$		−	9.96483e15i		−	1.56574i	−0.622185	−	0.782871i	$-0.713755\pi$
$181$		−	9.96483e15i		−	1.56574i	0.622185	−	0.782871i	$-0.286245\pi$
$182$	1.20560e15	+	5.59088e15i	0.182265	+	0.845240i
$183$	1.21019e16			1.76074
$184$	−3.09355e14	+	5.35818e14i	−0.0433243	+	0.0750399i
$185$	−2.50103e13	+	1.44397e13i	−0.00337222	+	0.00194695i
$186$	4.98305e14	+	8.63090e14i	0.0647000	+	0.112064i
$187$	5.95716e14	+	3.43937e14i	0.0744985	+	0.0430118i
$188$			2.08857e15i			0.251620i
$189$	4.39252e14	−	3.97853e14i	0.0509895	−	0.0461839i
$190$	−1.84286e15			−0.206166
$191$	2.85930e15	−	4.95246e15i	0.308337	−	0.534056i	−0.669661	−	0.742667i	$-0.733561\pi$
$191$	2.85930e15	−	4.95246e15i	0.308337	−	0.534056i	0.977999	+	0.208610i	$0.0668941\pi$
$192$	1.49012e15	−	8.60322e14i	0.154922	−	0.0894443i
$193$	−2.65225e15	−	4.59383e15i	−0.265897	−	0.460547i	0.701901	−	0.712274i	$-0.252335\pi$
$193$	−2.65225e15	−	4.59383e15i	−0.265897	−	0.460547i	−0.967798	+	0.251727i	$0.919001\pi$
$194$	−5.30244e15	−	3.06137e15i	−0.512701	−	0.296008i
$195$		−	2.82038e15i		−	0.263067i
$196$	5.06226e15	−	2.28969e15i	0.455567	−	0.206056i
$197$	3.94755e15			0.342818			0.171409	−	0.985200i	$-0.445168\pi$
$197$	3.94755e15			0.342818			0.171409	+	0.985200i	$0.445168\pi$
$198$	−3.52896e14	+	6.11234e14i	−0.0295795	+	0.0512332i
$199$	6.41240e15	−	3.70220e15i	0.518859	−	0.299563i	−0.217609	−	0.976036i	$-0.569826\pi$
$199$	6.41240e15	−	3.70220e15i	0.518859	−	0.299563i	0.736468	+	0.676473i	$0.236492\pi$
$200$	−2.21161e15	−	3.83062e15i	−0.172782	−	0.299267i
$201$	−2.24359e16	−	1.29534e16i	−1.69267	−	0.977262i
$202$			1.14463e16i			0.834075i
$203$	1.07162e16	+	1.18313e16i	0.754341	+	0.832835i
$204$	−1.13377e16			−0.771108
$205$	3.99124e14	−	6.91303e14i	0.0262320	−	0.0454351i
$206$	−5.13165e15	+	2.96276e15i	−0.325977	+	0.188203i
$207$	2.09151e15	+	3.62260e15i	0.128430	+	0.222448i
$208$	4.45942e15	+	2.57465e15i	0.264750	+	0.152853i
$209$			2.69694e15i			0.154827i
$210$	−2.67825e15	+	5.77530e14i	−0.148702	+	0.0320656i
$211$	3.53705e16			1.89961			0.949804	−	0.312845i	$-0.101282\pi$
$211$	3.53705e16			1.89961			0.949804	+	0.312845i	$0.101282\pi$
$212$	−5.08080e15	+	8.80020e15i	−0.263986	+	0.457237i
$213$	−3.03709e16	+	1.75347e16i	−1.52687	+	0.881537i
$214$	−4.05050e15	−	7.01568e15i	−0.197066	−	0.341329i
$215$	8.93382e14	+	5.15795e14i	0.0420696	+	0.0242889i
$216$		−	5.33573e14i		−	0.0243230i
$217$	2.75813e15	+	8.87199e14i	0.121730	+	0.0391564i
$218$	1.78469e16			0.762725
$219$	−2.25766e16	+	3.91039e16i	−0.934438	+	1.61849i
$220$	1.29608e14	−	7.48293e13i	0.00519606	−	0.00299994i
$221$	−1.69650e16	−	2.93842e16i	−0.658881	−	1.14122i
$222$	−6.03276e14	−	3.48302e14i	−0.0227010	−	0.0131064i
$223$		−	3.63840e16i		−	1.32671i	−0.748304	−	0.663356i	$-0.769131\pi$
$223$		−	3.63840e16i		−	1.32671i	0.748304	−	0.663356i	$-0.230869\pi$
$224$	1.53175e15	−	4.76191e15i	0.0541316	−	0.168285i
$225$	−2.99049e16			−1.02439
$226$	1.88075e16	−	3.25756e16i	0.624557	−	1.08176i
$227$	−3.79559e16	+	2.19138e16i	−1.22208	+	0.705566i	−0.965360	−	0.260921i	$-0.915974\pi$
$227$	−3.79559e16	+	2.19138e16i	−1.22208	+	0.705566i	−0.256716	+	0.966487i	$0.582640\pi$
$228$	−2.22259e16	−	3.84964e16i	−0.693930	−	1.20192i
$229$	1.90401e15	+	1.09928e15i	0.0576529	+	0.0332859i	0.528549	−	0.848903i	$-0.322736\pi$
$229$	1.90401e15	+	1.09928e15i	0.0576529	+	0.0332859i	−0.470897	+	0.882188i	$0.656069\pi$
$230$		−	8.86983e14i		−	0.0260508i
$231$	8.45191e14	+	3.91951e15i	0.0240808	+	0.111673i
$232$	1.43718e16			0.397279
$233$	5.39661e15	−	9.34720e15i	0.144754	−	0.250721i	−0.784527	−	0.620094i	$-0.787094\pi$
$233$	5.39661e15	−	9.34720e15i	0.144754	−	0.250721i	0.929281	+	0.369374i	$0.120428\pi$
$234$	3.01496e16	−	1.74069e16i	0.784822	−	0.453117i
$235$	−1.49709e15	−	2.59304e15i	−0.0378245	−	0.0655139i
$236$	2.45358e16	+	1.41657e16i	0.601750	+	0.347421i
$237$			5.51396e16i			1.31288i
$238$	−2.44295e16	+	2.21270e16i	−0.564775	+	0.511546i
$239$	−2.88401e16			−0.647458			−0.323729	−	0.946150i	$-0.604937\pi$
$239$	−2.88401e16			−0.647458			−0.323729	+	0.946150i	$0.604937\pi$
$240$	−1.23336e15	+	2.13624e15i	−0.0268913	+	0.0465770i
$241$	3.23296e16	−	1.86655e16i	0.684669	−	0.395294i	−0.116943	−	0.993139i	$-0.537310\pi$
$241$	3.23296e16	−	1.86655e16i	0.684669	−	0.395294i	0.801612	+	0.597845i	$0.203976\pi$
$242$	1.70760e16	+	2.95765e16i	0.351300	+	0.608470i
$243$	6.18646e16	+	3.57176e16i	1.23651	+	0.713901i
$244$		−	3.16753e16i		−	0.615166i
$245$	−4.64373e15	+	6.47137e15i	−0.0876403	+	0.122133i
$246$	1.92547e16			0.353175
$247$	6.65145e16	−	1.15207e17i	1.18587	−	2.05399i
$248$	2.25904e15	−	1.30426e15i	0.0391528	−	0.0226049i
$249$	7.90738e16	+	1.36960e17i	1.33241	+	2.30780i
$250$	1.11101e16	+	6.41444e15i	0.182028	+	0.105094i
$251$			6.80346e15i			0.108396i	0.998530	+	0.0541980i	$0.0172602\pi$
$251$			6.80346e15i			0.108396i	−0.998530	+	0.0541980i	$0.982740\pi$
$252$	−2.27035e16	−	2.50659e16i	−0.351794	−	0.388400i
$253$	−1.29806e15			−0.0195637
$254$	−3.55933e16	+	6.16495e16i	−0.521834	+	0.903843i
$255$	1.40762e16	−	8.12690e15i	0.200772	−	0.115916i
$256$	−2.25180e15	−	3.90023e15i	−0.0312500	−	0.0541266i
$257$	−9.49863e15	−	5.48403e15i	−0.128271	−	0.0740574i	0.434491	−	0.900676i	$-0.356928\pi$
$257$	−9.49863e15	−	5.48403e15i	−0.128271	−	0.0740574i	−0.562763	+	0.826619i	$0.690261\pi$
$258$			2.48831e16i			0.327014i
$259$	−1.97964e15	+	4.26884e14i	−0.0253214	+	0.00546023i
$260$	−7.38204e15			−0.0919101
$261$	4.85831e16	−	8.41484e16i	0.588846	−	1.01991i
$262$	1.62992e16	−	9.41036e15i	0.192335	−	0.111045i
$263$	−2.67370e16	−	4.63099e16i	−0.307201	−	0.532088i	0.670548	−	0.741866i	$-0.266059\pi$
$263$	−2.67370e16	−	4.63099e16i	−0.307201	−	0.532088i	−0.977749	+	0.209779i	$0.932726\pi$
$264$	3.12630e15	+	1.80497e15i	0.0349786	+	0.0201949i
$265$		−	1.45677e16i		−	0.158734i
$266$	−1.23021e17	−	3.95717e16i	−1.30559	−	0.419966i
$267$	−2.24732e17			−2.32320
$268$	−3.39041e16	+	5.87236e16i	−0.341435	+	0.591384i
$269$	−3.87224e16	+	2.23564e16i	−0.379924	+	0.219349i	−0.677785	−	0.735260i	$-0.737060\pi$
$269$	−3.87224e16	+	2.23564e16i	−0.379924	+	0.219349i	0.297861	+	0.954609i	$0.403727\pi$
$270$	3.82466e14	+	6.62450e14i	0.00365634	+	0.00633296i
$271$	2.43696e16	+	1.40698e16i	0.227020	+	0.131070i	0.609197	−	0.793019i	$-0.291492\pi$
$271$	2.43696e16	+	1.40698e16i	0.227020	+	0.131070i	−0.382177	+	0.924089i	$0.624825\pi$
$272$			2.96753e16i			0.269409i
$273$	6.05622e16	−	1.88276e17i	0.535874	−	1.66593i
$274$	−1.36818e16			−0.118002
$275$	4.63999e15	−	8.03670e15i	0.0390111	−	0.0675692i
$276$	1.85286e16	−	1.06975e16i	0.151873	−	0.0876838i
$277$	2.72208e16	+	4.71479e16i	0.217542	+	0.376794i	0.954056	−	0.299629i	$-0.0968628\pi$
$277$	2.72208e16	+	4.71479e16i	0.217542	+	0.376794i	−0.736514	+	0.676422i	$0.763529\pi$
$278$	4.55174e16	+	2.62795e16i	0.354702	+	0.204787i
$279$		−	1.76359e16i		−	0.134020i
$280$	1.51162e15	+	7.01004e15i	0.0112031	+	0.0519534i
$281$	−1.28039e17			−0.925548			−0.462774	−	0.886476i	$-0.653146\pi$
$281$	−1.28039e17			−0.925548			−0.462774	+	0.886476i	$0.653146\pi$
$282$	3.61115e16	−	6.25470e16i	0.254626	−	0.441025i
$283$	−1.53408e17	+	8.85701e16i	−1.05522	+	0.609231i	−0.924106	−	0.382136i	$-0.875189\pi$
$283$	−1.53408e17	+	8.85701e16i	−1.05522	+	0.609231i	−0.131113	+	0.991367i	$0.541855\pi$
$284$	4.58951e16	+	7.94926e16i	0.307991	+	0.533456i
$285$	5.51885e16	+	3.18631e16i	0.361356	+	0.208629i
$286$			1.08033e16i			0.0690231i
$287$	4.14881e16	−	3.75779e16i	0.258673	−	0.234293i
$288$	−3.04483e16			−0.185275
$289$	1.35798e16	−	2.35208e16i	0.0806506	−	0.139691i
$290$	−1.78431e16	+	1.03017e16i	−0.103439	+	0.0597206i
$291$	1.05862e17	+	1.83359e17i	0.599088	+	1.03765i
$292$	1.02350e17	+	5.90919e16i	0.565469	+	0.326474i
$293$		−	1.06391e17i		−	0.573893i	−0.957947	−	0.286947i	$-0.907360\pi$
$293$		−	1.06391e17i		−	0.573893i	0.957947	−	0.286947i	$-0.0926402\pi$
$294$	−1.91190e17	−	1.89568e16i	−1.00701	−	0.0998469i
$295$	−4.06161e16			−0.208903
$296$	−9.11642e14	+	1.57901e15i	−0.00457912	+	0.00793127i
$297$	9.69468e14	−	5.59722e14i	0.00475596	−	0.00274585i
$298$	−1.40446e17	−	2.43260e17i	−0.672969	−	1.16562i
$299$	5.54498e16	+	3.20140e16i	0.259539	+	0.149845i
$300$			1.52955e17i			0.699385i
$301$	4.85626e16	+	5.36158e16i	0.216938	+	0.239512i
$302$	1.06247e17			0.463732
$303$	1.97907e17	−	3.42785e17i	0.844040	−	1.46192i
$304$	−1.00760e17	+	5.81739e16i	−0.419927	+	0.242445i
$305$	2.27049e16	+	3.93260e16i	0.0924742	+	0.160170i
$306$	1.73752e17	+	1.00316e17i	0.691638	+	0.399318i
$307$			1.38159e16i			0.0537539i	0.999639	+	0.0268770i	$0.00855624\pi$
$307$			1.38159e16i			0.0537539i	−0.999639	+	0.0268770i	$0.991444\pi$
$308$	1.02589e16	−	2.21220e15i	0.0390162	−	0.00841334i
$309$	2.04905e17			0.761805
$310$	−1.86979e15	+	3.23857e15i	−0.00679611	+	0.0117712i
$311$	−3.47282e17	+	2.00504e17i	−1.23413	+	0.712524i	−0.967888	−	0.251383i	$-0.919115\pi$
$311$	−3.47282e17	+	2.00504e17i	−1.23413	+	0.712524i	−0.266240	+	0.963907i	$0.585781\pi$
$312$	−8.90316e16	−	1.54207e17i	−0.309359	−	0.535825i
$313$	2.39978e17	+	1.38551e17i	0.815381	+	0.470760i	0.848821	−	0.528680i	$-0.177313\pi$
$313$	2.39978e17	+	1.38551e17i	0.815381	+	0.470760i	−0.0334402	+	0.999441i	$0.510646\pi$
$314$			1.14107e17i			0.379143i
$315$	4.61544e16	+	1.48463e16i	0.149982	+	0.0482442i
$316$	1.44322e17			0.458693
$317$	1.06322e17	−	1.84155e17i	0.330527	−	0.572490i	−0.652088	−	0.758143i	$-0.726107\pi$
$317$	1.06322e17	−	1.84155e17i	0.330527	−	0.572490i	0.982615	+	0.185653i	$0.0594401\pi$
$318$	3.04312e17	−	1.75695e17i	0.925399	−	0.534279i
$319$	1.50761e16	+	2.61126e16i	0.0448492	+	0.0776812i
$320$	5.59138e15	+	3.22818e15i	0.0162731	+	0.00939525i
$321$			2.80134e17i			0.797683i
$322$	1.90462e16	−	5.92111e16i	0.0530661	−	0.164973i
$323$	7.66643e17			2.09014
$324$	8.89823e16	−	1.54122e17i	0.237404	−	0.411196i
$325$	−3.96417e17	+	2.28871e17i	−1.03507	+	0.597597i
$326$	−1.57648e17	−	2.73055e17i	−0.402871	−	0.697793i
$327$	−5.34466e17	−	3.08574e17i	−1.33686	−	0.771836i
$328$		−	5.03969e16i		−	0.123392i
$329$	−4.42588e16	−	2.05247e17i	−0.106079	−	0.491932i
$330$	−5.17521e15			−0.0121431
$331$	−2.42199e17	+	4.19501e17i	−0.556386	+	0.963688i	0.441409	+	0.897306i	$0.354479\pi$
$331$	−2.42199e17	+	4.19501e17i	−0.556386	+	0.963688i	−0.997794	+	0.0663820i	$0.978854\pi$
$332$	3.58477e17	−	2.06967e17i	0.806297	−	0.465516i
$333$	6.16351e15	+	1.06755e16i	0.0135743	+	0.0235114i
$334$	−1.32313e17	−	7.63912e16i	−0.285351	−	0.164747i
$335$		−	9.72099e16i		−	0.205304i
$336$	−1.28205e17	+	1.16122e17i	−0.265174	+	0.240182i
$337$	−2.40526e17			−0.487252			−0.243626	−	0.969869i	$-0.578337\pi$
$337$	−2.40526e17			−0.487252			−0.243626	+	0.969869i	$0.578337\pi$
$338$	8.82557e16	−	1.52863e17i	0.175116	−	0.303310i
$339$	−1.12647e18	+	6.50366e17i	−2.18938	+	1.26404i
$340$	−2.12713e16	−	3.68429e16i	−0.0404987	−	0.0701458i
$341$	4.73951e15	+	2.73635e15i	0.00884000	+	0.00510378i
$342$			7.86614e17i			1.43740i
$343$	−4.48955e17	+	3.32285e17i	−0.803792	+	0.594911i
$344$	6.51288e16			0.114252
$345$	−1.53360e16	+	2.65627e16i	−0.0263620	+	0.0456603i
$346$	3.64844e17	−	2.10643e17i	0.614574	−	0.354825i
$347$	−2.80637e17	−	4.86077e17i	−0.463274	−	0.802414i	0.535848	−	0.844315i	$-0.319992\pi$
$347$	−2.80637e17	−	4.86077e17i	−0.463274	−	0.802414i	−0.999122	+	0.0419004i	$0.986659\pi$
$348$	−4.30396e17	−	2.48489e17i	−0.696328	−	0.402025i
$349$		−	5.33826e17i		−	0.846490i	−0.906015	−	0.423245i	$-0.860891\pi$
$349$		−	5.33826e17i		−	0.846490i	0.906015	−	0.423245i	$-0.139109\pi$
$350$	2.98512e17	+	3.29574e17i	0.463966	+	0.512244i
$351$	−5.52176e16			−0.0841255
$352$	4.72431e15	−	8.18274e15i	0.00705569	−	0.0122208i
$353$	7.68669e17	−	4.43791e17i	1.12542	−	0.649764i	0.182644	−	0.983179i	$-0.441534\pi$
$353$	7.68669e17	−	4.43791e17i	1.12542	−	0.649764i	0.942780	+	0.333415i	$0.108201\pi$
$354$	−4.89853e17	−	8.48451e17i	−0.703142	−	1.21788i
$355$	−1.13961e17	−	6.57953e16i	−0.160382	−	0.0925969i
$356$			5.88212e17i			0.811678i
$357$	1.11417e18	−	2.40257e17i	1.50756	−	0.325086i
$358$	−9.02922e17			−1.19803
$359$	−1.34413e17	+	2.32811e17i	−0.174896	+	0.302929i	−0.940125	−	0.340829i	$-0.889292\pi$
$359$	−1.34413e17	+	2.32811e17i	−0.174896	+	0.302929i	0.765229	+	0.643758i	$0.222626\pi$
$360$	3.78027e16	−	2.18254e16i	0.0482398	−	0.0278512i
$361$	1.10338e18	+	1.91112e18i	1.38095	+	2.39187i
$362$	7.81080e17	+	4.50957e17i	0.958817	+	0.553573i
$363$		−	1.18098e18i		−	1.42199i
$364$	−4.92793e17	−	1.58515e17i	−0.582042	−	0.187223i
$365$	−1.69429e17			−0.196307
$366$	−5.47668e17	+	9.48589e17i	−0.622515	+	1.07823i
$367$	2.58584e17	−	1.49294e17i	0.288363	−	0.166486i	−0.348840	−	0.937182i	$-0.613424\pi$
$367$	2.58584e17	−	1.49294e17i	0.288363	−	0.166486i	0.637203	+	0.770696i	$0.280091\pi$
$368$	−2.79996e16	−	4.84967e16i	−0.0306349	−	0.0530613i
$369$	−2.95079e17	−	1.70364e17i	−0.316777	−	0.182891i
$370$		−	2.61386e15i		−	0.00275341i
$371$	3.12812e17	−	9.72474e17i	0.323345	−	1.00522i
$372$	−9.02028e16			−0.0914997
$373$	−6.53893e17	+	1.13258e18i	−0.650946	+	1.12747i	0.331947	+	0.943298i	$0.392294\pi$
$373$	−6.53893e17	+	1.13258e18i	−0.650946	+	1.12747i	−0.982894	+	0.184174i	$0.941039\pi$
$374$	−5.39180e16	+	3.11296e16i	−0.0526784	+	0.0304139i
$375$	−2.21812e17	−	3.84190e17i	−0.212699	−	0.368406i
$376$	−1.63710e17	−	9.45180e16i	−0.154085	−	0.0889610i
$377$		−	1.48729e18i		−	1.37406i
$378$	1.13069e16	+	5.24350e16i	0.0102542	+	0.0475531i
$379$	5.12346e17			0.456130			0.228065	−	0.973646i	$-0.426760\pi$
$379$	5.12346e17			0.456130			0.228065	+	0.973646i	$0.426760\pi$
$380$	8.33982e16	−	1.44450e17i	0.0728906	−	0.126250i
$381$	2.13185e18	−	1.23082e18i	1.82928	−	1.05614i
$382$	2.58794e17	+	4.48245e17i	0.218028	+	0.377635i
$383$	−9.11308e17	−	5.26144e17i	−0.753831	−	0.435224i	0.0732456	−	0.997314i	$-0.476664\pi$
$383$	−9.11308e17	−	5.26144e17i	−0.753831	−	0.435224i	−0.827076	+	0.562090i	$0.809998\pi$
$384$			1.55735e17i			0.126493i
$385$	−1.11511e16	+	1.01001e16i	−0.00889388	+	0.00805565i
$386$	4.80109e17			0.376035
$387$	2.20164e17	−	3.81336e17i	0.169344	−	0.293313i
$388$	4.79922e17	−	2.77083e17i	0.362534	−	0.209309i
$389$	1.12756e18	+	1.95299e18i	0.836551	+	1.44895i	0.892761	+	0.450530i	$0.148765\pi$
$389$	1.12756e18	+	1.95299e18i	0.836551	+	1.44895i	−0.0562104	+	0.998419i	$0.517902\pi$
$390$	2.21072e17	+	1.27636e17i	0.161095	+	0.0930081i
$391$			3.68992e17i			0.264107i
$392$	−4.96175e16	+	5.00418e17i	−0.0348845	+	0.351828i
$393$	−6.50822e17			−0.449484
$394$	−1.78646e17	+	3.09424e17i	−0.121205	+	0.209933i
$395$	−1.79181e17	+	1.03450e17i	−0.119429	+	0.0689526i
$396$	−3.19405e16	−	5.53226e16i	−0.0209159	−	0.0362273i
$397$	−1.63187e18	−	9.42159e17i	−1.04991	−	0.606165i	−0.127285	−	0.991866i	$-0.540626\pi$
$397$	−1.63187e18	−	9.42159e17i	−1.04991	−	0.606165i	−0.922624	+	0.385701i	$0.873960\pi$
$398$			6.70170e17i			0.423647i
$399$	2.99995e18	+	3.31211e18i	1.86339	+	2.05728i
$400$	4.00344e17			0.244351
$401$	−5.49536e17	+	9.51824e17i	−0.329599	+	0.570882i	−0.982432	−	0.186620i	$-0.940247\pi$
$401$	−5.49536e17	+	9.51824e17i	−0.329599	+	0.570882i	0.652833	+	0.757501i	$0.273580\pi$
$402$	2.03067e18	−	1.17241e18i	1.19690	−	0.691029i
$403$	−1.34973e17	−	2.33780e17i	−0.0781829	−	0.135417i
$404$	−8.97203e17	−	5.18000e17i	−0.510765	−	0.294890i
$405$			2.55130e17i			0.142750i
$406$	−1.41234e18	+	3.04552e17i	−0.776705	+	0.167486i
$407$	−3.82528e15			−0.00206777
$408$	5.13087e17	−	8.88693e17i	0.272628	−	0.472205i
$409$	−2.94670e16	+	1.70128e16i	−0.0153912	+	0.00888613i	−0.507676	−	0.861548i	$-0.669495\pi$
$409$	−2.94670e16	+	1.70128e16i	−0.0153912	+	0.00888613i	0.492285	+	0.870434i	$0.336162\pi$
$410$	3.61246e16	+	6.25696e16i	0.0185488	+	0.0321275i
$411$	4.09734e17	+	2.36560e17i	0.206828	+	0.119412i
$412$		−	5.36317e17i		−	0.266159i
$413$	−2.71135e18	−	8.72151e17i	−1.32293	−	0.425541i
$414$	−3.78604e17			−0.181628
$415$	−2.96708e17	+	5.13914e17i	−0.139956	+	0.242412i
$416$	−4.03621e17	+	2.33031e17i	−0.187206	+	0.108084i
$417$	−9.08748e17	−	1.57400e18i	−0.414468	−	0.717879i
$418$	−2.11396e17	−	1.22050e17i	−0.0948120	−	0.0547398i
$419$		−	3.82746e18i		−	1.68815i	−0.536222	−	0.844077i	$-0.680149\pi$
$419$		−	3.82746e18i		−	1.68815i	0.536222	−	0.844077i	$-0.319851\pi$
$420$	7.59350e16	−	2.36067e17i	0.0329380	−	0.102398i
$421$	−2.80445e18			−1.19639			−0.598195	−	0.801351i	$-0.704115\pi$
$421$	−2.80445e18			−1.19639			−0.598195	+	0.801351i	$0.704115\pi$
$422$	−1.60069e18	+	2.77247e18i	−0.671613	+	1.16327i
$423$	−1.10682e18	+	6.39026e17i	−0.456769	+	0.263716i
$424$	−4.59861e17	−	7.96503e17i	−0.186666	−	0.323316i
$425$	−2.28454e18	−	1.31898e18i	−0.912172	−	0.526643i
$426$		−	3.17411e18i		−	1.24668i
$427$	6.71230e17	+	3.11278e18i	0.259344	+	1.20269i
$428$	7.33219e17			0.278694
$429$	1.86790e17	−	3.23529e17i	0.0698477	−	0.120980i
$430$	−8.08597e16	+	4.66844e16i	−0.0297477	+	0.0171748i
$431$	−1.29679e18	−	2.24611e18i	−0.469384	−	0.812997i	0.530003	−	0.847996i	$-0.322191\pi$
$431$	−1.29679e18	−	2.24611e18i	−0.469384	−	0.812997i	−0.999387	+	0.0349983i	$0.988857\pi$
$432$	4.18234e16	+	2.41468e16i	0.0148948	+	0.00859949i
$433$			5.49392e17i			0.192516i	0.995356	+	0.0962580i	$0.0306874\pi$
$433$			5.49392e17i			0.192516i	−0.995356	+	0.0962580i	$0.969313\pi$
$434$	−1.94361e17	+	1.76042e17i	−0.0670163	+	0.0607001i
$435$	7.12470e17			0.241736
$436$	−8.07659e17	+	1.39891e18i	−0.269664	+	0.467071i
$437$	−1.25288e18	+	7.23353e17i	−0.411662	+	0.237673i
$438$	−2.04340e18	−	3.53928e18i	−0.660748	−	1.14445i
$439$	4.93669e18	+	2.85020e18i	1.57103	+	0.907034i	0.996043	+	0.0888703i	$0.0283257\pi$
$439$	4.93669e18	+	2.85020e18i	1.57103	+	0.907034i	0.574986	+	0.818164i	$0.305008\pi$
$440$			1.35456e16i			0.00424256i
$441$	2.76227e18	+	1.98215e18i	0.851522	+	0.611036i
$442$	3.07099e18			0.931798
$443$	1.30439e18	−	2.25926e18i	0.389565	−	0.674747i	−0.602826	−	0.797873i	$-0.705959\pi$
$443$	1.30439e18	−	2.25926e18i	0.389565	−	0.674747i	0.992391	+	0.123126i	$0.0392920\pi$
$444$	5.46024e16	−	3.15247e16i	0.0160521	−	0.00926766i
$445$	−4.21631e17	−	7.30286e17i	−0.122015	−	0.211336i
$446$	2.85192e18	+	1.64655e18i	0.812442	+	0.469064i
$447$			9.71327e18i			2.72404i
$448$	3.03937e17	+	3.35563e17i	0.0839146	+	0.0926463i
$449$	−2.99121e17			−0.0813059			−0.0406529	−	0.999173i	$-0.512944\pi$
$449$	−2.99121e17			−0.0813059			−0.0406529	+	0.999173i	$0.512944\pi$
$450$	1.35334e18	−	2.34405e18i	0.362176	−	0.627307i
$451$	9.15679e16	−	5.28668e16i	0.0241272	−	0.0139299i
$452$	1.70226e18	+	2.94840e18i	0.441629	+	0.764923i
$453$	−3.18180e18	−	1.83701e18i	−0.812802	−	0.469272i
$454$		−	3.96683e18i		−	0.997821i
$455$	7.25443e17	−	1.56432e17i	0.179690	−	0.0387478i
$456$	4.02332e18			0.981365
$457$	−1.32599e18	+	2.29669e18i	−0.318513	+	0.551682i	−0.980178	−	0.198118i	$-0.936517\pi$
$457$	−1.32599e18	+	2.29669e18i	−0.318513	+	0.551682i	0.661665	+	0.749800i	$0.269850\pi$
$458$	−1.72331e17	+	9.94955e16i	−0.0407667	+	0.0235367i
$459$	−1.59109e17	−	2.75584e17i	−0.0370685	−	0.0642046i
$460$	6.95250e16	+	4.01403e16i	0.0159528	+	0.00921033i
$461$			1.30316e18i			0.294505i	0.989099	+	0.147252i	$0.0470430\pi$
$461$			1.30316e18i			0.294505i	−0.989099	+	0.147252i	$0.952957\pi$
$462$	−3.45474e17	−	1.11128e17i	−0.0768993	−	0.0247359i
$463$	6.41399e18			1.40625			0.703123	−	0.711069i	$-0.251788\pi$
$463$	6.41399e18			1.40625			0.703123	+	0.711069i	$0.251788\pi$
$464$	−6.50394e17	+	1.12651e18i	−0.140459	+	0.243283i
$465$	1.11990e17	−	6.46575e16i	0.0238237	−	0.0137546i
$466$	4.88445e17	+	8.46012e17i	0.102356	+	0.177286i
$467$	−2.53890e16	−	1.46583e16i	−0.00524116	−	0.00302598i	0.497377	−	0.867534i	$-0.334297\pi$
$467$	−2.53890e16	−	1.46583e16i	−0.00524116	−	0.00302598i	−0.502618	+	0.864508i	$0.667630\pi$
$468$			3.15099e18i			0.640805i
$469$	2.08739e18	−	6.48931e18i	0.418210	−	1.30014i
$470$	2.71002e17			0.0534919
$471$	1.97291e18	−	3.41718e18i	0.383673	−	0.664541i
$472$	−2.22073e18	+	1.28214e18i	−0.425502	+	0.245663i
$473$	6.83206e16	+	1.18335e17i	0.0128980	+	0.0223401i
$474$	−4.32204e18	−	2.49533e18i	−0.803971	−	0.464173i
$475$		−	1.03427e19i		−	1.89573i
$476$	−6.28847e17	−	2.91623e18i	−0.113579	−	0.526712i
$477$	−6.21814e18			−1.10671
$478$	1.30515e18	−	2.26059e18i	0.228911	−	0.396485i
$479$	−7.65230e17	+	4.41806e17i	−0.132265	+	0.0763630i	−0.564672	−	0.825315i	$-0.690997\pi$
$479$	−7.65230e17	+	4.41806e17i	−0.132265	+	0.0763630i	0.432408	+	0.901678i	$0.357664\pi$
$480$	−1.11631e17	−	1.93351e17i	−0.0190150	−	0.0329349i
$481$	1.63406e17	+	9.43425e16i	0.0274317	+	0.0158377i
$482$			3.37881e18i			0.559030i
$483$	−1.59414e18	+	1.44390e18i	−0.259955	+	0.235454i
$484$	−3.09109e18			−0.496814
$485$	−3.97227e17	+	6.88017e17i	−0.0629284	+	0.108995i
$486$	−5.59935e18	+	3.23278e18i	−0.874346	+	0.504804i
$487$	−2.06286e17	−	3.57297e17i	−0.0317516	−	0.0549954i	0.849713	−	0.527246i	$-0.176775\pi$
$487$	−2.06286e17	−	3.57297e17i	−0.0317516	−	0.0549954i	−0.881465	+	0.472250i	$0.843442\pi$
$488$	2.48283e18	+	1.43346e18i	0.376711	+	0.217494i
$489$			1.09030e19i			1.63073i
$490$	−2.97098e17	−	6.56853e17i	−0.0438054	−	0.0968491i
$491$	6.93636e18			1.00823			0.504117	−	0.863635i	$-0.331818\pi$
$491$	6.93636e18			1.00823			0.504117	+	0.863635i	$0.331818\pi$
$492$	−8.71366e17	+	1.50925e18i	−0.124866	+	0.216275i
$493$	7.42287e18	−	4.28560e18i	1.04868	−	0.605456i
$494$	6.02021e18	+	1.04273e19i	0.838538	+	1.45239i
$495$	7.93106e16	+	4.57900e16i	0.0108917	+	0.00628831i
$496$			2.36096e17i			0.0319681i
$497$	−6.19469e18	−	6.83929e18i	−0.827037	−	0.913095i
$498$	−1.43139e19			−1.88431
$499$	3.10871e18	−	5.38444e18i	0.403531	−	0.698936i	−0.590619	−	0.806951i	$-0.701116\pi$
$499$	3.10871e18	−	5.38444e18i	0.403531	−	0.698936i	0.994149	+	0.108015i	$0.0344496\pi$
$500$	−1.00557e18	+	5.80569e17i	−0.128714	+	0.0743128i
$501$	2.64162e18	+	4.57542e18i	0.333431	+	0.577519i
$502$	−5.33280e17	−	3.07889e17i	−0.0663788	−	0.0383238i
$503$		−	8.53767e17i		−	0.104801i	−0.998626	−	0.0524003i	$-0.983313\pi$
$503$		−	8.53767e17i		−	0.104801i	0.998626	−	0.0524003i	$-0.0166872\pi$
$504$	2.99220e18	−	6.45228e17i	0.362223	−	0.0781088i
$505$	1.48521e18			0.177316
$506$	5.87435e16	−	1.01747e17i	0.00691682	−	0.0119803i
$507$	−5.28603e18	+	3.05189e18i	−0.613867	+	0.354416i
$508$	−3.22154e18	−	5.57987e18i	−0.368993	−	0.639114i
$509$	5.25065e17	+	3.03146e17i	0.0593182	+	0.0342474i	0.529366	−	0.848394i	$-0.322430\pi$
$509$	5.25065e17	+	3.03146e17i	0.0593182	+	0.0342474i	−0.470048	+	0.882641i	$0.655763\pi$
$510$			1.47113e18i			0.163930i
$511$	−1.13103e19	−	3.63814e18i	−1.24316	−	0.399884i
$512$	4.07619e17			0.0441942
$513$	6.23818e17	−	1.08048e18i	0.0667169	−	0.115557i
$514$	8.59717e17	−	4.96358e17i	0.0907014	−	0.0523665i
$515$	3.84432e17	+	6.65857e17i	0.0400101	+	0.0692995i
$516$	−1.95043e18	−	1.12608e18i	−0.200255	−	0.115617i
$517$		−	3.96600e17i		−	0.0401716i
$518$	5.61276e16	−	1.74490e17i	0.00560877	−	0.0174366i
$519$	−1.45681e19			−1.43625
$520$	3.34073e17	−	5.78631e17i	0.0324951	−	0.0562832i
$521$	−3.04939e18	+	1.76057e18i	−0.292650	+	0.168962i	−0.639136	−	0.769093i	$-0.720708\pi$
$521$	−3.04939e18	+	1.76057e18i	−0.292650	+	0.168962i	0.346486	+	0.938055i	$0.387375\pi$
$522$	4.39724e18	+	7.61624e18i	0.416377	+	0.721186i
$523$	6.23636e17	+	3.60056e17i	0.0582666	+	0.0336402i	0.528850	−	0.848715i	$-0.322623\pi$
$523$	6.23636e17	+	3.60056e17i	0.0582666	+	0.0336402i	−0.470584	+	0.882355i	$0.655957\pi$
$524$			1.70346e18i			0.157041i
$525$	−3.24127e18	−	1.50311e19i	−0.294849	−	1.36734i
$526$	4.83992e18			0.434448
$527$	7.77846e17	−	1.34727e18i	0.0689000	−	0.119338i
$528$	−2.82960e17	+	1.63367e17i	−0.0247336	+	0.0142800i
$529$	5.44826e18	+	9.43667e18i	0.469968	+	0.814009i
$530$	1.14187e18	+	6.59258e17i	0.0972042	+	0.0561209i
$531$			1.73368e19i			1.45649i
$532$	8.66908e18	−	7.85203e18i	0.718772	−	0.651029i
$533$	−5.21540e18			−0.426773
$534$	1.01702e19	−	1.76153e19i	0.821375	−	1.42266i
$535$	−9.10318e17	+	5.25572e17i	−0.0725632	+	0.0418944i
$536$	−3.06865e18	−	5.31505e18i	−0.241431	−	0.418171i
$537$	2.70400e19	+	1.56116e19i	2.09984	+	1.21235i
$538$		−	4.04694e18i		−	0.310206i
$539$	−9.61276e17	+	4.34791e17i	−0.0727322	+	0.0328972i
$540$	−6.92337e16			−0.00517084
$541$	−5.45379e18	+	9.44625e18i	−0.402085	+	0.696432i	−0.993977	−	0.109585i	$-0.965048\pi$
$541$	−5.45379e18	+	9.44625e18i	−0.402085	+	0.696432i	0.591892	+	0.806017i	$0.298381\pi$
$542$	−2.20569e18	+	1.27345e18i	−0.160527	+	0.0926805i
$543$	−1.55941e19	−	2.70098e19i	−1.12037	−	1.94054i
$544$	−2.32606e18	−	1.34295e18i	−0.164979	−	0.0952505i
$545$		−	2.31572e18i		−	0.162148i
$546$	1.20171e19	+	1.32675e19i	0.830710	+	0.917150i
$547$	1.98358e19			1.35375			0.676877	−	0.736097i	$-0.263333\pi$
$547$	1.98358e19			1.35375			0.676877	+	0.736097i	$0.263333\pi$
$548$	6.19169e17	−	1.07243e18i	0.0417201	−	0.0722614i
$549$	1.67861e19	−	9.69147e18i	1.11672	−	0.644738i
$550$	4.19964e17	+	7.27399e17i	0.0275850	+	0.0477786i
$551$	2.91028e19	+	1.68025e19i	1.88744	+	1.08972i
$552$			1.93646e18i			0.124004i
$553$	−1.41827e19	+	3.05831e18i	−0.896774	+	0.193378i
$554$	−4.92750e18			−0.307651
$555$	−4.51938e16	+	7.82780e16i	−0.00278630	+	0.00482602i
$556$	−4.11976e18	+	2.37855e18i	−0.250812	+	0.144807i
$557$	−1.13555e18	−	1.96683e18i	−0.0682685	−	0.118245i	0.829871	−	0.557956i	$-0.188414\pi$
$557$	−1.13555e18	−	1.96683e18i	−0.0682685	−	0.118245i	−0.898139	+	0.439711i	$0.855081\pi$
$558$	1.38237e18	+	7.98109e17i	0.0820699	+	0.0473831i
$559$		−	6.73994e18i		−	0.395161i
$560$	−6.17881e17	−	1.98751e17i	−0.0357757	−	0.0115078i
$561$	2.15293e18			0.123109
$562$	5.79439e18	−	1.00362e19i	0.327231	−	0.566780i
$563$	−2.41291e19	+	1.39309e19i	−1.34581	+	0.777002i	−0.987652	−	0.156661i	$-0.949927\pi$
$563$	−2.41291e19	+	1.39309e19i	−1.34581	+	0.777002i	−0.358154	+	0.933663i	$0.616594\pi$
$564$	3.26844e18	+	5.66111e18i	0.180048	+	0.311852i
$565$	−4.22684e18	−	2.44036e18i	−0.229973	−	0.132775i
$566$		−	1.60329e19i		−	0.861583i
$567$	−5.47842e18	+	1.70314e19i	−0.290787	+	0.904000i
$568$	−8.30790e18			−0.435565
$569$	5.09020e18	−	8.81648e18i	0.263602	−	0.456572i	−0.703594	−	0.710602i	$-0.748423\pi$
$569$	5.09020e18	−	8.81648e18i	0.263602	−	0.456572i	0.967196	+	0.254030i	$0.0817561\pi$
$570$	−4.99510e18	+	2.88392e18i	−0.255517	+	0.147523i
$571$	5.61251e18	+	9.72116e18i	0.283599	+	0.491208i	0.972268	−	0.233868i	$-0.0751382\pi$
$571$	5.61251e18	+	9.72116e18i	0.283599	+	0.491208i	−0.688669	+	0.725075i	$0.741805\pi$
$572$	−8.46802e17	−	4.88902e17i	−0.0422678	−	0.0244033i
$573$		−	1.78983e19i		−	0.882529i
$574$	1.06796e18	+	4.95258e18i	0.0520201	+	0.241239i
$575$	4.97800e18			0.239541
$576$	1.37793e18	−	2.38665e18i	0.0655045	−	0.113457i
$577$	−4.62442e18	+	2.66991e18i	−0.217183	+	0.125391i	−0.604645	−	0.796495i	$-0.706685\pi$
$577$	−4.62442e18	+	2.66991e18i	−0.217183	+	0.125391i	0.387462	+	0.921886i	$0.373352\pi$
$578$	1.22910e18	+	2.12886e18i	0.0570286	+	0.0987764i
$579$	−1.43779e19	−	8.30111e18i	−0.659093	−	0.380528i
$580$		−	1.86481e18i		−	0.0844576i
$581$	−3.08422e19	+	2.79354e19i	−1.38011	+	1.25003i
$582$	−1.91631e19			−0.847239
$583$	9.64796e17	−	1.67108e18i	0.0421459	−	0.0729989i
$584$	−9.26368e18	+	5.34839e18i	−0.399847	+	0.230852i
$585$	−2.25863e18	−	3.91206e18i	−0.0963283	−	0.166846i
$586$	8.33931e18	+	4.81470e18i	0.351436	+	0.202902i
$587$			1.30546e19i			0.543620i	0.962351	+	0.271810i	$0.0876222\pi$
$587$			1.30546e19i			0.543620i	−0.962351	+	0.271810i	$0.912378\pi$
$588$	1.01382e19	−	1.41283e19i	0.417175	−	0.581363i
$589$	6.09940e18			0.248016
$590$	1.83807e18	−	3.18364e18i	0.0738582	−	0.127926i
$591$	1.06999e19	−	6.17759e18i	0.424881	−	0.245305i
$592$	−8.25124e16	−	1.42916e17i	−0.00323793	−	0.00560826i
$593$	−8.44767e18	−	4.87726e18i	−0.327608	−	0.189144i	0.327171	−	0.944965i	$-0.393905\pi$
$593$	−8.44767e18	−	4.87726e18i	−0.327608	−	0.189144i	−0.654778	+	0.755821i	$0.727238\pi$
$594$			1.01321e17i			0.00388323i
$595$	2.87109e18	+	3.16984e18i	0.108750	+	0.120066i
$596$	2.54234e19			0.951723
$597$	1.15873e19	−	2.00698e19i	0.428708	−	0.742544i
$598$	−5.01875e18	+	2.89758e18i	−0.183522	+	0.105956i
$599$	−1.62887e19	−	2.82128e19i	−0.588706	−	1.01967i	−0.994402	−	0.105661i	$-0.966304\pi$
$599$	−1.62887e19	−	2.82128e19i	−0.588706	−	1.01967i	0.405696	−	0.914008i	$-0.367029\pi$
$600$	−1.19892e19	−	6.92197e18i	−0.428284	−	0.247270i
$601$			1.01386e19i			0.357980i	0.983851	+	0.178990i	$0.0572830\pi$
$601$			1.01386e19i			0.357980i	−0.983851	+	0.178990i	$0.942717\pi$
$602$	−6.40030e18	+	1.38014e18i	−0.223370	+	0.0481668i
$603$	−4.14936e19			−1.43140
$604$	−4.80818e18	+	8.32800e18i	−0.163954	+	0.283976i
$605$	3.83769e18	−	2.21569e18i	0.129355	−	0.0746831i
$606$	1.79125e19	+	3.10254e19i	0.596826	+	1.03373i
$607$	−1.81268e19	−	1.04655e19i	−0.597034	−	0.344698i	0.170840	−	0.985299i	$-0.445352\pi$
$607$	−1.81268e19	−	1.04655e19i	−0.597034	−	0.344698i	−0.767874	+	0.640601i	$0.778685\pi$
$608$		−	1.05306e19i		−	0.342869i
$609$	4.75613e19	+	1.52989e19i	1.53085	+	0.492423i
$610$	−4.11003e18			−0.130778
$611$	−9.78133e18	+	1.69418e19i	−0.307687	+	0.532930i
$612$	−1.57262e19	+	9.07953e18i	−0.489062	+	0.282360i
$613$	−1.97521e19	−	3.42117e19i	−0.607282	−	1.05184i	−0.991686	−	0.128678i	$-0.958927\pi$
$613$	−1.97521e19	−	3.42117e19i	−0.607282	−	1.05184i	0.384405	−	0.923165i	$-0.374407\pi$
$614$	−1.08294e18	−	6.25236e17i	−0.0329174	−	0.0190049i
$615$		−	2.49838e18i		−	0.0750816i
$616$	−2.90864e17	+	9.04242e17i	−0.00864222	+	0.0268670i
$617$	1.76100e19			0.517325			0.258662	−	0.965968i	$-0.416718\pi$
$617$	1.76100e19			0.517325			0.258662	+	0.965968i	$0.416718\pi$
$618$	−9.27295e18	+	1.60612e19i	−0.269339	+	0.466508i
$619$	2.51091e18	−	1.44968e18i	0.0721103	−	0.0416329i	−0.463511	−	0.886091i	$-0.653411\pi$
$619$	2.51091e18	−	1.44968e18i	0.0721103	−	0.0416329i	0.535622	+	0.844458i	$0.320077\pi$
$620$	−1.69234e17	−	2.93122e17i	−0.00480558	−	0.00832350i
$621$	5.20046e17	+	3.00249e17i	0.0146016	+	0.00843024i
$622$		−	3.62950e19i		−	1.00766i
$623$	−1.24648e19	−	5.78044e19i	−0.342190	−	1.58688i
$624$	1.61164e19			0.437499
$625$	−1.73732e19	+	3.00913e19i	−0.466359	+	0.807758i
$626$	−2.17203e19	+	1.25402e19i	−0.576561	+	0.332878i
$627$	4.22049e18	+	7.31011e18i	0.110787	+	0.191889i
$628$	−8.94410e18	−	5.16388e18i	−0.232177	−	0.134047i
$629$			1.08739e18i			0.0279145i
$630$	−3.25242e18	+	2.94588e18i	−0.0825701	+	0.0747880i
$631$	3.37231e19			0.846686			0.423343	−	0.905969i	$-0.360856\pi$
$631$	3.37231e19			0.846686			0.423343	+	0.905969i	$0.360856\pi$
$632$	−6.53126e18	+	1.13125e19i	−0.162173	+	0.280891i
$633$	9.58723e19	−	5.53519e19i	2.35433	−	1.35927i
$634$	9.62315e18	+	1.66678e19i	0.233718	+	0.404812i
$635$	7.99931e18	+	4.61841e18i	0.192148	+	0.110937i
$636$			3.18041e19i			0.755585i
$637$	5.17865e19	+	5.13473e18i	1.21686	+	0.120654i
$638$	−2.72907e18			−0.0634264
$639$	−2.80844e19	+	4.86436e19i	−0.645593	+	1.11820i
$640$	−5.06074e17	+	2.92182e17i	−0.0115068	+	0.00664345i
$641$	3.86042e19	+	6.68644e19i	0.868217	+	1.50380i	0.863817	+	0.503806i	$0.168067\pi$
$641$	3.86042e19	+	6.68644e19i	0.868217	+	1.50380i	0.00439998	+	0.999990i	$0.498599\pi$
$642$	−2.19579e19	−	1.26774e19i	−0.488479	−	0.282023i
$643$			1.31637e19i			0.289669i	0.989456	+	0.144834i	$0.0462649\pi$
$643$			1.31637e19i			0.289669i	−0.989456	+	0.144834i	$0.953735\pi$
$644$	3.77925e18	+	4.17250e18i	0.0822629	+	0.0908229i
$645$	3.22870e18			0.0695201
$646$	−3.46943e19	+	6.00923e19i	−0.738976	+	1.27994i
$647$	8.17433e19	−	4.71945e19i	1.72235	−	0.994401i	0.808340	−	0.588716i	$-0.200366\pi$
$647$	8.17433e19	−	4.71945e19i	1.72235	−	0.994401i	0.914013	−	0.405685i	$-0.132967\pi$
$648$	8.05376e18	+	1.39495e19i	0.167870	+	0.290760i
$649$	−4.65912e18	−	2.68994e18i	−0.0960707	−	0.0554664i
$650$		−	4.14302e19i		−	0.845129i
$651$	8.86435e18	−	1.91148e18i	0.178888	−	0.0385748i
$652$	2.85374e19			0.569745
$653$	3.44004e19	−	5.95832e19i	0.679471	−	1.17688i	−0.295669	−	0.955291i	$-0.595542\pi$
$653$	3.44004e19	−	5.95832e19i	0.679471	−	1.17688i	0.975140	−	0.221589i	$-0.0711242\pi$
$654$	4.83744e19	−	2.79289e19i	0.945303	−	0.545771i
$655$	−1.22104e18	−	2.11490e18i	−0.0236070	−	0.0408885i
$656$	3.95030e18	+	2.28071e18i	0.0755619	+	0.0436257i
$657$			7.23197e19i			1.36867i
$658$	1.80909e19	+	5.81924e18i	0.338750	+	0.108965i
$659$	−6.39261e19			−1.18435			−0.592175	−	0.805809i	$-0.701731\pi$
$659$	−6.39261e19			−1.18435			−0.592175	+	0.805809i	$0.701731\pi$
$660$	2.34203e17	−	4.05652e17i	0.00429325	−	0.00743612i
$661$	−2.79220e19	+	1.61208e19i	−0.506451	+	0.292399i	−0.731373	−	0.681977i	$-0.761120\pi$
$661$	−2.79220e19	+	1.61208e19i	−0.506451	+	0.292399i	0.224923	+	0.974377i	$0.427787\pi$
$662$	−2.19213e19	−	3.79689e19i	−0.393424	−	0.681430i
$663$	−9.19676e19	−	5.30975e19i	−1.63320	−	0.942930i
$664$			3.74650e19i			0.658339i
$665$	−5.13463e18	+	1.59626e19i	−0.0892806	+	0.277557i
$666$	−1.11571e18			−0.0191970
$667$	−8.08720e18	+	1.40074e19i	−0.137695	+	0.238494i
$668$	1.19756e19	−	6.91414e18i	0.201773	−	0.116494i
$669$	−5.69380e19	−	9.86196e19i	−0.949335	−	1.64430i
$670$	7.61967e18	+	4.39922e18i	0.125722	+	0.0725859i
$671$			6.01485e18i			0.0982126i
$672$	−3.30017e18	−	1.53043e19i	−0.0533275	−	0.247302i
$673$	−1.73158e19			−0.276909			−0.138454	−	0.990369i	$-0.544213\pi$
$673$	−1.73158e19			−0.276909			−0.138454	+	0.990369i	$0.544213\pi$
$674$	1.08850e19	−	1.88533e19i	0.172270	−	0.298380i
$675$	−3.71786e18	+	2.14651e18i	−0.0582327	+	0.0336207i
$676$	7.98799e18	+	1.38356e19i	0.123826	+	0.214472i
$677$	−2.59457e19	−	1.49797e19i	−0.398056	−	0.229818i	0.287589	−	0.957754i	$-0.407146\pi$
$677$	−2.59457e19	−	1.49797e19i	−0.398056	−	0.229818i	−0.685645	+	0.727936i	$0.740480\pi$
$678$		−	1.17729e20i		−	1.78762i
$679$	−4.12910e19	+	3.73993e19i	−0.620535	+	0.562051i
$680$	3.85051e18			0.0572738
$681$	−6.85867e19	+	1.18796e20i	−1.00974	+	1.74892i
$682$	−4.28971e17	+	2.47667e17i	−0.00625083	+	0.00360892i
$683$	1.64509e19	+	2.84938e19i	0.237271	+	0.410966i	0.959930	−	0.280239i	$-0.0904137\pi$
$683$	1.64509e19	+	2.84938e19i	0.237271	+	0.410966i	−0.722659	+	0.691204i	$0.757080\pi$
$684$	−6.16577e19	−	3.55981e19i	−0.880227	−	0.508199i
$685$			1.77528e18i			0.0250861i
$686$	−5.72835e18	−	5.02282e19i	−0.0801237	−	0.702553i
$687$	6.88113e18			0.0952714
$688$	−2.94739e18	+	5.10504e18i	−0.0403942	+	0.0699648i
$689$	−8.24272e19	+	4.75894e19i	−1.11824	+	0.645618i
$690$	−1.38805e18	−	2.40418e18i	−0.0186407	−	0.0322867i
$691$	−6.61844e19	−	3.82116e19i	−0.879851	−	0.507982i	−0.00924184	−	0.999957i	$-0.502942\pi$
$691$	−6.61844e19	−	3.82116e19i	−0.879851	−	0.507982i	−0.870609	+	0.491975i	$0.836275\pi$
$692$			3.81304e19i			0.501798i
$693$	4.31118e18	+	4.75978e18i	0.0561647	+	0.0620089i
$694$	5.08007e19			0.655168
$695$	3.40989e18	−	5.90610e18i	0.0435358	−	0.0754063i
$696$	3.89550e19	−	2.24907e19i	0.492378	−	0.284275i
$697$	−1.50281e19	−	2.60294e19i	−0.188051	−	0.325713i
$698$	4.18433e19	+	2.41582e19i	0.518367	+	0.299279i
$699$		−	3.37810e19i		−	0.414316i
$700$	−3.93424e19	+	8.48367e18i	−0.477721	+	0.103014i
$701$	1.02806e20			1.23593			0.617964	−	0.786207i	$-0.287958\pi$
$701$	1.02806e20			1.23593			0.617964	+	0.786207i	$0.287958\pi$
$702$	2.49886e18	−	4.32816e18i	0.0297428	−	0.0515161i
$703$	−3.69214e18	+	2.13166e18i	−0.0435102	+	0.0251206i
$704$	4.27596e17	+	7.40617e17i	0.00498913	+	0.00864142i
$705$	−8.11578e18	−	4.68565e18i	−0.0937576	−	0.0541310i
$706$			8.03347e19i			0.918905i
$707$	9.91462e19	+	3.18920e19i	1.12290	+	0.361199i
$708$	8.86729e19			0.994393
$709$	−1.99783e19	+	3.46034e19i	−0.221837	+	0.384233i	−0.955366	−	0.295425i	$-0.904539\pi$
$709$	−1.99783e19	+	3.46034e19i	−0.221837	+	0.384233i	0.733529	+	0.679658i	$0.237872\pi$
$710$	1.03146e19	−	5.95511e18i	0.113408	−	0.0654759i
$711$	4.41571e19	+	7.64824e19i	0.480744	+	0.832672i
$712$	−4.61062e19	−	2.66194e19i	−0.497049	−	0.286971i
$713$			2.93569e18i			0.0313389i
$714$	−3.15895e19	+	9.82059e19i	−0.333930	+	1.03813i
$715$	1.40178e18			0.0146736
$716$	4.08616e19	−	7.07743e19i	0.423569	−	0.733643i
$717$	−7.81716e19	+	4.51324e19i	−0.802444	+	0.463291i
$718$	−1.21657e19	−	2.10716e19i	−0.123670	−	0.214203i
$719$	1.27856e20	+	7.38174e19i	1.28711	+	0.743116i	0.978139	−	0.207954i	$-0.0666803\pi$
$719$	1.27856e20	+	7.38174e19i	1.28711	+	0.743116i	0.308976	+	0.951070i	$0.400014\pi$
$720$			3.95082e18i			0.0393876i
$721$	1.13651e19	+	5.27046e19i	0.112208	+	0.520357i
$722$	−1.99734e20			−1.95295
$723$	5.84198e19	−	1.01186e20i	0.565708	−	0.979835i
$724$	−7.06953e19	+	4.08159e19i	−0.677986	+	0.391435i
$725$	−5.78163e19	−	1.00141e20i	−0.549141	−	0.951140i
$726$	9.25696e19	+	5.34451e19i	0.870787	+	0.502749i
$727$		−	2.44581e19i		−	0.227868i	−0.993488	−	0.113934i	$-0.963655\pi$
$727$		−	2.44581e19i		−	0.227868i	0.993488	−	0.113934i	$-0.0363452\pi$
$728$	3.47262e19	−	3.14533e19i	0.320433	−	0.290233i
$729$	1.19674e20			1.09372
$730$	7.66746e18	−	1.32804e19i	0.0694051	−	0.120213i
$731$	3.36383e19	−	1.94211e19i	0.301587	−	0.174121i
$732$	−4.95693e19	−	8.58565e19i	−0.440185	−	0.762422i
$733$	−1.20280e20	−	6.94439e19i	−1.05795	−	0.610810i	−0.133089	−	0.991104i	$-0.542490\pi$
$733$	−1.20280e20	−	6.94439e19i	−1.05795	−	0.610810i	−0.924866	+	0.380294i	$0.875823\pi$
$734$			2.70250e19i			0.235447i
$735$	−2.45974e18	+	2.48078e19i	−0.0212265	+	0.214080i
$736$	5.06847e18			0.0433243
$737$	6.43807e18	−	1.11511e19i	0.0545109	−	0.0944156i
$738$	2.67075e19	−	1.54196e19i	0.223995	−	0.129324i
$739$	5.51203e19	+	9.54711e19i	0.457931	+	0.793160i	0.998851	−	0.0479135i	$-0.0152572\pi$
$739$	5.51203e19	+	9.54711e19i	0.457931	+	0.793160i	−0.540920	+	0.841074i	$0.681924\pi$
$740$	2.04884e17	+	1.18290e17i	0.00168611	+	0.000973477i
$741$		−	4.16359e20i		−	3.39422i
$742$	6.20698e19	+	6.85285e19i	0.501249	+	0.553406i
$743$	1.42534e19			0.114024			0.0570119	−	0.998373i	$-0.481843\pi$
$743$	1.42534e19			0.114024			0.0570119	+	0.998373i	$0.481843\pi$
$744$	4.08211e18	−	7.07043e18i	0.0323500	−	0.0560319i
$745$	−3.15641e19	+	1.82235e19i	−0.247799	+	0.143067i
$746$	−5.91837e19	−	1.02509e20i	−0.460288	−	0.797243i
$747$	2.19361e20	+	1.26648e20i	1.69011	+	0.975788i
$748$		−	5.63506e18i		−	0.0430118i
$749$	−7.20544e19	+	1.55376e19i	−0.544864	+	0.117493i
$750$	4.01523e19			0.300802
$751$	5.13740e18	−	8.89824e18i	0.0381297	−	0.0660426i	−0.846331	−	0.532658i	$-0.821193\pi$
$751$	5.13740e18	−	8.89824e18i	0.0381297	−	0.0660426i	0.884460	+	0.466615i	$0.154527\pi$
$752$	1.48173e19	−	8.55479e18i	0.108955	−	0.0629049i
$753$	1.06468e19	+	1.84409e19i	0.0775633	+	0.134344i
$754$	1.16579e20	+	6.73069e19i	0.841435	+	0.485803i
$755$		−	1.37860e19i		−	0.0985849i
$756$	−4.62174e18	−	1.48666e18i	−0.0327456	−	0.0105332i
$757$	−2.03901e20			−1.43136			−0.715679	−	0.698430i	$-0.753883\pi$
$757$	−2.03901e20			−1.43136			−0.715679	+	0.698430i	$0.753883\pi$
$758$	−2.31861e19	+	4.01596e19i	−0.161266	+	0.279322i
$759$	−3.51842e18	+	2.03136e18i	−0.0242468	+	0.0139989i
$760$	7.54834e18	+	1.30741e19i	0.0515414	+	0.0892724i
$761$	1.46441e20	+	8.45476e19i	0.990762	+	0.572017i	0.905502	−	0.424342i	$-0.139495\pi$
$761$	1.46441e20	+	8.45476e19i	0.990762	+	0.572017i	0.0852602	+	0.996359i	$0.472828\pi$
$762$			2.22802e20i			1.49360i
$763$	4.97256e19	−	1.54587e20i	0.330300	−	1.02684i
$764$	−4.68468e19			−0.308337
$765$	1.30164e19	−	2.25451e19i	0.0848911	−	0.147036i
$766$	8.24822e19	−	4.76211e19i	0.533039	−	0.307750i
$767$	1.32684e20	+	2.29815e20i	0.849670	+	1.47167i
$768$	−1.22071e19	−	7.04776e18i	−0.0774610	−	0.0447221i
$769$			4.98905e19i			0.313713i	0.987621	+	0.156857i	$0.0501361\pi$
$769$			4.98905e19i			0.313713i	−0.987621	+	0.156857i	$0.949864\pi$
$770$	−2.87043e17	−	1.33114e18i	−0.00178859	−	0.00829447i
$771$	−3.43282e19			−0.211968
$772$	−2.17272e19	+	3.76327e19i	−0.132949	+	0.230274i
$773$	−2.69197e20	+	1.55421e20i	−1.63235	+	0.942439i	−0.648986	+	0.760800i	$0.724807\pi$
$773$	−2.69197e20	+	1.55421e20i	−1.63235	+	0.942439i	−0.983365	+	0.181638i	$0.941860\pi$
$774$	1.99270e19	+	3.45146e19i	0.119744	+	0.207403i
$775$	−1.81758e19	−	1.04938e19i	−0.108238	−	0.0624914i
$776$			5.01574e19i			0.296008i
$777$	−4.69781e18	+	4.25505e18i	−0.0274757	+	0.0248861i
$778$	−2.04110e20			−1.18306
$779$	5.89207e19	−	1.02054e20i	0.338458	−	0.586227i
$780$	−2.00091e19	+	1.15523e19i	−0.113911	+	0.0657666i
$781$	−8.71505e18	−	1.50949e19i	−0.0491714	−	0.0851674i
$782$	−2.89229e19	−	1.66987e19i	−0.161732	−	0.0933758i
$783$		−	1.39488e19i		−	0.0773042i
$784$	−3.69792e19	−	2.65355e19i	−0.203116	−	0.145752i
$785$	1.48059e19			0.0806022
$786$	2.94529e19	−	5.10139e19i	0.158917	−	0.275252i
$787$	1.73469e20	−	1.00153e20i	0.927683	−	0.535598i	0.0416050	−	0.999134i	$-0.486753\pi$
$787$	1.73469e20	−	1.00153e20i	0.927683	−	0.535598i	0.886078	+	0.463536i	$0.153420\pi$
$788$	−1.61692e19	−	2.80058e19i	−0.0857046	−	0.148445i
$789$	−1.44942e20	−	8.36824e19i	−0.761475	−	0.439638i
$790$		−	1.87265e19i		−	0.0975138i
$791$	−2.29763e20	−	2.53671e20i	−1.18589	−	1.30929i
$792$	5.78185e18			0.0295795
$793$	1.48344e20	−	2.56939e20i	0.752241	−	1.30292i
$794$	1.47700e20	−	8.52745e19i	0.742397	−	0.428623i
$795$	−2.27972e19	−	3.94859e19i	−0.113583	−	0.196731i
$796$	−5.25304e19	−	3.03284e19i	−0.259430	−	0.149782i
$797$			2.04554e20i			1.00138i	0.865627	+	0.500690i	$0.166920\pi$
$797$			2.04554e20i			1.00138i	−0.865627	+	0.500690i	$0.833080\pi$
$798$	−3.95377e20	+	8.52579e19i	−1.91863	+	0.413728i
$799$	−1.12739e20			−0.542309
$800$	−1.81175e19	+	3.13804e19i	−0.0863910	+	0.149634i
$801$	−3.11719e20	+	1.79971e20i	−1.47345	+	0.850697i
$802$	−4.97383e19	−	8.61493e19i	−0.233062	−	0.403674i
$803$	−1.94353e19	−	1.12210e19i	−0.0902783	−	0.0521222i
$804$			2.12228e20i			0.977262i
$805$	−7.68292e18	−	2.47134e18i	−0.0350716	−	0.0112813i
$806$	2.44327e19			0.110567
$807$	−6.99718e19	+	1.21195e20i	−0.313912	+	0.543712i
$808$	8.12055e19	−	4.68840e19i	0.361165	−	0.208519i
$809$	1.08893e20	+	1.88608e20i	0.480131	+	0.831612i	0.999740	−	0.0227923i	$-0.00725565\pi$
$809$	1.08893e20	+	1.88608e20i	0.480131	+	0.831612i	−0.519609	+	0.854404i	$0.673922\pi$
$810$	−1.99981e19	−	1.15459e19i	−0.0874164	−	0.0504699i
$811$		−	1.44901e20i		−	0.627951i	−0.949431	−	0.313976i	$-0.898339\pi$
$811$		−	1.44901e20i		−	0.627951i	0.949431	−	0.313976i	$-0.101661\pi$
$812$	4.00432e19	−	1.24487e20i	0.172043	−	0.534848i
$813$	8.80724e19			0.375151
$814$	1.73112e17	−	2.99839e17i	0.000731067	−	0.00126624i
$815$	−3.54302e19	+	2.04556e19i	−0.148344	+	0.0856464i
$816$	4.64394e19	+	8.04353e19i	0.192777	+	0.333899i
$817$	1.31886e20	+	7.61442e19i	0.542804	+	0.313388i
$818$		−	3.07965e18i		−	0.0125669i
$819$	−6.67723e19	−	3.09652e20i	−0.270153	−	1.25281i
$820$	−6.53925e18			−0.0262320
$821$	1.34375e20	−	2.32745e20i	0.534463	−	0.925717i	−0.464726	−	0.885454i	$-0.653847\pi$
$821$	1.34375e20	−	2.32745e20i	0.534463	−	0.925717i	0.999189	−	0.0402625i	$-0.0128194\pi$
$822$	−3.70848e19	+	2.14109e19i	−0.146249	+	0.0844371i
$823$	1.88574e20	+	3.26620e20i	0.737366	+	1.27716i	0.953677	+	0.300831i	$0.0972640\pi$
$823$	1.88574e20	+	3.26620e20i	0.737366	+	1.27716i	−0.216311	+	0.976324i	$0.569403\pi$
$824$	4.20385e19	+	2.42709e19i	0.162988	+	0.0941014i
$825$		−	2.90448e19i		−	0.111658i
$826$	1.91064e20	−	1.73057e20i	0.728314	−	0.659672i
$827$	−3.97549e20			−1.50263			−0.751316	−	0.659943i	$-0.770580\pi$
$827$	−3.97549e20			−1.50263			−0.751316	+	0.659943i	$0.770580\pi$
$828$	1.71337e19	−	2.96764e19i	0.0642152	−	0.111224i
$829$	4.28679e20	−	2.47498e20i	1.59313	−	0.919792i	0.600361	−	0.799729i	$-0.295024\pi$
$829$	4.28679e20	−	2.47498e20i	1.59313	−	0.919792i	0.992766	−	0.120063i	$-0.0383096\pi$
$830$	−2.68550e19	−	4.65142e19i	−0.0989641	−	0.171411i
$831$	1.47565e20	+	8.51967e19i	0.539233	+	0.311326i
$832$		−	4.21830e19i		−	0.152853i
$833$	1.23595e20	+	2.73256e20i	0.444106	+	0.981871i
$834$	1.64501e20			0.586146
$835$	−9.91213e18	+	1.71683e19i	−0.0350237	+	0.0606628i
$836$	1.91334e19	−	1.10467e19i	0.0670422	−	0.0387068i
$837$	−1.26587e18	−	2.19255e18i	−0.00439855	−	0.00761852i
$838$	3.00010e20	+	1.73211e20i	1.03378	+	0.596853i
$839$			4.82121e20i			1.64749i	0.566962	+	0.823744i	$0.308118\pi$
$839$			4.82121e20i			1.64749i	−0.566962	+	0.823744i	$0.691882\pi$
$840$	1.50674e19	+	1.66352e19i	0.0510603	+	0.0563734i
$841$	7.81519e19			0.262644
$842$	1.26915e20	−	2.19823e20i	0.422987	−	0.732636i
$843$	−3.47052e20	+	2.00371e20i	−1.14710	+	0.662280i
$844$	−1.44878e20	−	2.50935e20i	−0.474902	−	0.822555i
$845$	−1.98348e19	−	1.14516e19i	−0.0644807	−	0.0372280i
$846$		−	1.15676e20i		−	0.372950i
$847$	3.03765e20	−	6.55030e19i	0.971302	−	0.209449i
$848$	8.32438e19			0.263986
$849$	−2.77210e20	+	4.80142e20i	−0.871876	+	1.51013i
$850$	2.06773e20	−	1.19381e20i	0.645003	−	0.372393i
$851$	−1.02599e18	−	1.77706e18i	−0.00317420	−	0.00549787i
$852$	2.48799e20	+	1.43644e20i	0.763433	+	0.440768i
$853$		−	1.91455e19i		−	0.0582670i	−0.999576	−	0.0291335i	$-0.990725\pi$
$853$		−	1.91455e19i		−	0.0582670i	0.999576	−	0.0291335i	$-0.00927480\pi$
$854$	−2.74367e20	−	8.82547e19i	−0.828185	−	0.266399i
$855$	1.02067e20			0.305578
$856$	−3.31817e19	+	5.74724e19i	−0.0985332	+	0.170664i
$857$	−1.21819e20	+	7.03320e19i	−0.358796	+	0.207151i	−0.668553	−	0.743665i	$-0.733086\pi$
$857$	−1.21819e20	+	7.03320e19i	−0.358796	+	0.207151i	0.309756	+	0.950816i	$0.399752\pi$
$858$	1.69063e19	+	2.92825e19i	0.0493898	+	0.0855456i
$859$	−3.07862e20	−	1.77744e20i	−0.892080	−	0.515043i	−0.0174577	−	0.999848i	$-0.505557\pi$
$859$	−3.07862e20	−	1.77744e20i	−0.892080	−	0.515043i	−0.874622	+	0.484805i	$0.838891\pi$
$860$		−	8.45078e18i		−	0.0242889i
$861$	5.36479e19	−	1.66781e20i	0.152943	−	0.475472i
$862$	2.34744e20			0.663810
$863$	1.56575e20	−	2.71197e20i	0.439186	−	0.760692i	−0.558441	−	0.829544i	$-0.688600\pi$
$863$	1.56575e20	−	2.71197e20i	0.439186	−	0.760692i	0.997627	+	0.0688523i	$0.0219337\pi$
$864$	−3.78543e18	+	2.18552e18i	−0.0105322	+	0.00608076i
$865$	−2.73319e19	−	4.73403e19i	−0.0754323	−	0.130653i
$866$	−4.30634e19	−	2.48626e19i	−0.117892	−	0.0680647i
$867$		−	8.50048e19i		−	0.230839i
$868$	−5.00310e18	−	2.32015e19i	−0.0134772	−	0.0624996i
$869$	−2.74054e19			−0.0732314
$870$	−3.22427e19	+	5.58460e19i	−0.0854666	+	0.148033i
$871$	−5.50036e20	+	3.17563e20i	−1.44632	+	0.835032i
$872$	−7.31010e19	−	1.26615e20i	−0.190681	−	0.330269i
$873$	2.93677e20	+	1.69554e20i	0.759923	+	0.438742i
$874$		−	1.30941e20i		−	0.336120i
$875$	8.65164e19	−	7.83623e19i	0.220314	−	0.199550i
$876$	3.69896e20			0.934438
$877$	2.31062e20	−	4.00211e20i	0.579070	−	1.00298i	−0.416516	−	0.909128i	$-0.636749\pi$
$877$	2.31062e20	−	4.00211e20i	0.579070	−	1.00298i	0.995586	−	0.0938506i	$-0.0299176\pi$
$878$	−4.46818e20	+	2.57971e20i	−1.11089	+	0.641370i
$879$	−1.66493e20	−	2.88374e20i	−0.410652	−	0.711270i
$880$	−1.06175e18	−	6.13002e17i	−0.00259803	−	0.00149997i
$881$			2.44137e20i			0.592656i	0.955086	+	0.296328i	$0.0957621\pi$
$881$			2.44137e20i			0.592656i	−0.955086	+	0.296328i	$0.904238\pi$
$882$	−2.80374e20	+	1.26815e20i	−0.675240	+	0.305415i
$883$	3.53080e20			0.843624			0.421812	−	0.906683i	$-0.361394\pi$
$883$	3.53080e20			0.843624			0.421812	+	0.906683i	$0.361394\pi$
$884$	−1.38977e20	+	2.40715e20i	−0.329441	+	0.570608i
$885$	−1.10091e20	+	6.35608e19i	−0.258909	+	0.149481i
$886$	1.18060e20	+	2.04485e20i	0.275464	+	0.477118i
$887$	−1.39144e20	−	8.03348e19i	−0.322106	−	0.185968i	0.330225	−	0.943902i	$-0.392875\pi$
$887$	−1.39144e20	−	8.03348e19i	−0.322106	−	0.185968i	−0.652331	+	0.757934i	$0.726209\pi$
$888$			5.70658e18i			0.0131064i
$889$	4.34828e20	+	4.80074e20i	0.990843	+	1.09395i
$890$	7.63233e19			0.172555
$891$	−1.68969e19	+	2.92663e19i	−0.0379021	+	0.0656484i
$892$	−2.58126e20	+	1.49029e20i	−0.574484	+	0.331678i
$893$	−2.21008e20	−	3.82797e20i	−0.488031	−	0.845295i
$894$	−7.61362e20	−	4.39573e20i	−1.66812	−	0.963092i
$895$			1.17158e20i			0.254690i
$896$	−4.00573e19	+	8.63783e18i	−0.0864023	+	0.0186315i
$897$	2.00397e20			0.428888
$898$	1.35367e19	−	2.34462e19i	0.0287460	−	0.0497895i
$899$	5.90563e19	−	3.40961e19i	0.124437	−	0.0718435i
$900$	1.22490e20	+	2.12160e20i	0.256097	+	0.443573i
$901$	−4.75026e20	−	2.74256e20i	−0.985471	−	0.568962i
$902$			9.56991e18i			0.0196998i
$903$	2.15534e20	+	6.93301e19i	0.440252	+	0.141614i
$904$	−3.08142e20			−0.624557
$905$	5.85138e19	−	1.01349e20i	0.117684	−	0.203835i
$906$	2.87983e20	−	1.66267e20i	0.574738	−	0.331825i
$907$	−2.84539e20	−	4.92837e20i	−0.563497	−	0.976005i	−0.997188	−	0.0749434i	$-0.976122\pi$
$907$	−2.84539e20	−	4.92837e20i	−0.563497	−	0.976005i	0.433691	−	0.901062i	$-0.357211\pi$
$908$	3.10935e20	+	1.79518e20i	0.611038	+	0.352783i
$909$		−	6.33955e20i		−	1.23626i
$910$	−2.05681e19	+	6.39422e19i	−0.0398019	+	0.123737i
$911$	−7.89377e20			−1.51585			−0.757924	−	0.652343i	$-0.773786\pi$
$911$	−7.89377e20			−1.51585			−0.757924	+	0.652343i	$0.773786\pi$
$912$	−1.82075e20	+	3.15363e20i	−0.346965	+	0.600961i
$913$	−6.80715e19	+	3.93011e19i	−0.128727	+	0.0743206i
$914$	−1.20015e20	−	2.07872e20i	−0.225223	−	0.390098i
$915$	1.23084e20	+	7.10626e19i	0.229221	+	0.132341i
$916$		−	1.80106e19i		−	0.0332859i
$917$	−3.60978e19	−	1.67401e20i	−0.0662058	−	0.307024i
$918$	2.88018e19			0.0524228
$919$	4.64859e20	−	8.05160e20i	0.839678	−	1.45437i	−0.0504854	−	0.998725i	$-0.516077\pi$
$919$	4.64859e20	−	8.05160e20i	0.839678	−	1.45437i	0.890164	−	0.455641i	$-0.150590\pi$
$920$	−6.29268e18	+	3.63308e18i	−0.0112803	+	0.00651269i
$921$	2.16207e19	+	3.74482e19i	0.0384639	+	0.0666214i
$922$	−1.02147e20	−	5.89745e19i	−0.180347	−	0.104123i
$923$			8.59754e20i			1.50648i
$924$	2.43450e19	−	2.20505e19i	0.0423356	−	0.0383455i
$925$	1.46698e19			0.0253181
$926$	−2.90264e20	+	5.02752e20i	−0.497183	+	0.861146i
$927$	2.84217e20	−	1.64093e20i	0.483162	−	0.278954i
$928$	−5.88669e19	−	1.01960e20i	−0.0993197	−	0.172027i
$929$	−2.52528e20	−	1.45797e20i	−0.422863	−	0.244140i	0.273439	−	0.961889i	$-0.411839\pi$
$929$	−2.52528e20	−	1.45797e20i	−0.422863	−	0.244140i	−0.696301	+	0.717749i	$0.745172\pi$
$930$			1.17043e19i			0.0194519i
$931$	−6.85530e20	+	9.55335e20i	−1.13078	+	1.57583i
$932$	−8.84180e19			−0.144754
$933$	−6.27543e20	+	1.08694e21i	−1.01970	+	1.76617i
$934$	2.29795e18	−	1.32672e18i	0.00370606	−	0.00213969i
$935$	4.03921e18	+	6.99612e18i	0.00646570	+	0.0111989i
$936$	−2.46986e20	−	1.42597e20i	−0.392411	−	0.226559i
$937$		−	8.43905e20i		−	1.33081i	−0.746482	−	0.665406i	$-0.768259\pi$
$937$		−	8.43905e20i		−	1.33081i	0.746482	−	0.665406i	$-0.231741\pi$
$938$	4.14191e20	+	4.57290e20i	0.648307	+	0.715767i
$939$	8.67285e20			1.34742
$940$	−1.22642e19	+	2.12422e19i	−0.0189122	+	0.0327570i
$941$	9.82812e20	−	5.67427e20i	1.50433	−	0.868525i	0.504342	−	0.863504i	$-0.331735\pi$
$941$	9.82812e20	−	5.67427e20i	1.50433	−	0.868525i	0.999987	−	0.00502153i	$-0.00159841\pi$
$942$	1.78567e20	+	3.09288e20i	0.271298	+	0.469901i
$943$	4.91192e19	+	2.83590e19i	0.0740747	+	0.0427670i
$944$		−	2.32092e20i		−	0.347421i
$945$	6.80369e18	−	1.46713e18i	0.0101093	−	0.00217994i
$946$	−1.23674e19			−0.0182406
$947$	3.90765e19	−	6.76824e19i	0.0572092	−	0.0990892i	−0.836002	−	0.548726i	$-0.815113\pi$
$947$	3.90765e19	−	6.76824e19i	0.0572092	−	0.0990892i	0.893212	+	0.449637i	$0.148446\pi$
$948$	3.91187e20	−	2.25852e20i	0.568494	−	0.328220i
$949$	5.53485e20	+	9.58665e20i	0.798440	+	1.38294i
$950$	8.10695e20	+	4.68055e20i	1.16089	+	0.670242i
$951$		−	6.65539e20i		−	0.946041i
$952$	2.57043e20	+	8.26821e19i	0.362700	+	0.116668i
$953$	6.51481e20			0.912540			0.456270	−	0.889841i	$-0.349185\pi$
$953$	6.51481e20			0.912540			0.456270	+	0.889841i	$0.349185\pi$
$954$	2.81401e20	−	4.87401e20i	0.391279	−	0.677716i
$955$	5.81620e19	−	3.35798e19i	0.0802815	−	0.0463505i
$956$	1.18129e20	+	2.04606e20i	0.161865	+	0.280358i
$957$	8.17282e19	+	4.71858e19i	0.111170	+	0.0641841i
$958$		−	7.99754e19i		−	0.107994i
$959$	−3.81207e19	+	1.18510e20i	−0.0511012	+	0.158864i
$960$	2.02074e19			0.0268913
$961$	−3.72283e20	+	6.44814e20i	−0.491824	+	0.851865i
$962$	−1.47898e19	+	8.53891e18i	−0.0193971	+	0.0111989i
$963$	2.24338e20	+	3.88565e20i	0.292091	+	0.505917i
$964$	−2.64844e20	−	1.52908e20i	−0.342334	−	0.197647i
$965$		−	6.22964e19i		−	0.0799415i
$966$	−4.10353e19	−	1.90298e20i	−0.0522779	−	0.242435i
$967$	−7.51651e20			−0.950673			−0.475336	−	0.879804i	$-0.657674\pi$
$967$	−7.51651e20			−0.950673			−0.475336	+	0.879804i	$0.657674\pi$
$968$	1.39887e20	−	2.42291e20i	0.175650	−	0.304235i
$969$	2.07800e21	−	1.19973e21i	2.59047	−	1.49561i
$970$	−3.59529e19	−	6.22722e19i	−0.0444971	−	0.0770712i
$971$	−2.41126e20	−	1.39214e20i	−0.296284	−	0.171060i	0.344488	−	0.938791i	$-0.388052\pi$
$971$	−2.41126e20	−	1.39214e20i	−0.296284	−	0.171060i	−0.640773	+	0.767731i	$0.721386\pi$
$972$		−	5.85196e20i		−	0.713901i
$973$	3.54451e20	−	3.21045e20i	0.429306	−	0.388844i
$974$	3.73417e19			0.0449036
$975$	−7.16330e20	+	1.24072e21i	−0.855226	+	1.48129i
$976$	−2.24720e20	+	1.29742e20i	−0.266375	+	0.153791i
$977$	−3.47176e20	−	6.01326e20i	−0.408590	−	0.707698i	0.586142	−	0.810208i	$-0.300646\pi$
$977$	−3.47176e20	−	6.01326e20i	−0.408590	−	0.707698i	−0.994732	+	0.102510i	$0.967313\pi$
$978$	−8.54616e20	−	4.93413e20i	−0.998617	−	0.576552i
$979$		−	1.11696e20i		−	0.129586i
$980$	6.49317e19	+	6.43811e18i	0.0747953	+	0.00741610i
$981$	−9.88455e20			−1.13051
$982$	−3.13904e20	+	5.43698e20i	−0.356465	+	0.617415i
$983$	4.55803e20	−	2.63158e20i	0.513928	−	0.296717i	−0.220519	−	0.975383i	$-0.570775\pi$
$983$	4.55803e20	−	2.63158e20i	0.513928	−	0.296717i	0.734447	+	0.678666i	$0.237442\pi$
$984$	−7.88670e19	−	1.36602e20i	−0.0882937	−	0.152929i
$985$	4.01492e19	+	2.31801e19i	0.0446296	+	0.0257669i
$986$			7.75776e20i			0.856245i
$987$	−4.41159e20	−	4.87064e20i	−0.483476	−	0.533784i
$988$	−1.08977e21			−1.18587
$989$	−3.66488e19	+	6.34776e19i	−0.0395992	+	0.0685878i
$990$	−7.17838e18	+	4.14444e18i	−0.00770158	+	0.00444651i
$991$	−3.00117e20	−	5.19818e20i	−0.319724	−	0.553778i	0.660707	−	0.750644i	$-0.270257\pi$
$991$	−3.00117e20	−	5.19818e20i	−0.319724	−	0.553778i	−0.980430	+	0.196866i	$0.936923\pi$
$992$	−1.85061e19	−	1.06845e19i	−0.0195764	−	0.0113024i
$993$			1.51608e21i			1.59250i
$994$	8.16428e20	−	1.76052e20i	0.851556	−	0.183627i
$995$	8.69578e19			0.0900632
$996$	6.47772e20	−	1.12197e21i	0.666204	−	1.15390i
$997$	7.61879e19	−	4.39871e19i	0.0778072	−	0.0449220i	−0.460592	−	0.887612i	$-0.652363\pi$
$997$	7.61879e19	−	4.39871e19i	0.0778072	−	0.0449220i	0.538399	+	0.842690i	$0.319029\pi$
$998$	2.81368e20	+	4.87344e20i	0.285339	+	0.494222i
$999$	1.53253e18	+	8.84807e17i	0.00154330	+	0.000891026i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.15.d.a.5.5	yes	20
3.2	odd	2		126.15.n.b.19.8		20
7.2	even	3		98.15.b.c.97.19		20
7.3	odd	6	inner	14.15.d.a.3.5	✓	20
7.4	even	3		98.15.d.b.31.1		20
7.5	odd	6		98.15.b.c.97.12		20
7.6	odd	2		98.15.d.b.19.1		20
21.17	even	6		126.15.n.b.73.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.15.d.a.3.5	✓	20	7.3	odd	6	inner
14.15.d.a.5.5	yes	20	1.1	even	1	trivial
98.15.b.c.97.12		20	7.5	odd	6
98.15.b.c.97.19		20	7.2	even	3
98.15.d.b.19.1		20	7.6	odd	2
98.15.d.b.31.1		20	7.4	even	3
126.15.n.b.19.8		20	3.2	odd	2
126.15.n.b.73.8		20	21.17	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 15 \)
Character orbit:	\([\chi]\)	\(=\)	14.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-45.2548 + 78.3837i) q^{2} +(2710.52 - 1564.92i) q^{3} +(-4096.00 - 7094.48i) q^{4} +(10170.7 + 5872.03i) q^{5} +283280. i q^{6} +(552858. + 610386. i) q^{7} +741455. q^{8} +(2.50645e6 - 4.34129e6i) q^{9} +O(q^{10})\)	\(q+(-45.2548 + 78.3837i) q^{2} +(2710.52 - 1564.92i) q^{3} +(-4096.00 - 7094.48i) q^{4} +(10170.7 + 5872.03i) q^{5} +283280. i q^{6} +(552858. + 610386. i) q^{7} +741455. q^{8} +(2.50645e6 - 4.34129e6i) q^{9} +(-920543. + 531476. i) q^{10} +(777792. + 1.34718e6i) q^{11} +(-2.22045e7 - 1.28198e7i) q^{12} -7.67305e7i q^{13} +(-7.28638e7 + 1.57121e7i) q^{14} +3.67570e7 q^{15} +(-3.35544e7 + 5.81180e7i) q^{16} +(3.82953e8 - 2.21098e8i) q^{17} +(2.26858e8 + 3.92929e8i) q^{18} +(1.50144e9 + 8.66859e8i) q^{19} -9.62074e7i q^{20} +(2.45373e9 + 7.89284e8i) q^{21} -1.40795e8 q^{22} +(-4.17226e8 + 7.22657e8i) q^{23} +(2.00973e9 - 1.16032e9i) q^{24} +(-2.98280e9 - 5.16635e9i) q^{25} +(6.01442e9 + 3.47243e9i) q^{26} -7.19630e8i q^{27} +(2.06586e9 - 6.42238e9i) q^{28} +1.93832e10 q^{29} +(-1.66343e9 + 2.88115e9i) q^{30} +(3.04677e9 - 1.75905e9i) q^{31} +(-3.03700e9 - 5.26024e9i) q^{32} +(4.21644e9 + 2.43436e9i) q^{33} +4.00230e10i q^{34} +(2.03872e9 + 9.45443e9i) q^{35} -4.10656e10 q^{36} +(-1.22953e9 + 2.12961e9i) q^{37} +(-1.35895e11 + 7.84591e10i) q^{38} +(-1.20077e11 - 2.07979e11i) q^{39} +(7.54109e9 + 4.35385e9i) q^{40} -6.79703e10i q^{41} +(-1.72910e11 + 1.56614e11i) q^{42} +8.78392e10 q^{43} +(6.37167e9 - 1.10361e10i) q^{44} +(5.09844e10 - 2.94359e10i) q^{45} +(-3.77630e10 - 6.54075e10i) q^{46} +(-2.20796e11 - 1.27476e11i) q^{47} +2.10040e11i q^{48} +(-6.69190e10 + 6.74914e11i) q^{49} +5.39944e11 q^{50} +(6.92000e11 - 1.19858e12i) q^{51} +(-5.44363e11 + 3.14288e11i) q^{52} +(-6.20215e11 - 1.07424e12i) q^{53} +(5.64072e10 + 3.25667e10i) q^{54} +1.82689e10i q^{55} +(4.09919e11 + 4.52574e11i) q^{56} +5.42625e12 q^{57} +(-8.77185e11 + 1.51933e12i) q^{58} +(-2.99509e12 + 1.72922e12i) q^{59} +(-1.50557e11 - 2.60772e11i) q^{60} +(3.34859e12 + 1.93331e12i) q^{61} +3.18423e11i q^{62} +(4.03557e12 - 8.70219e11i) q^{63} +5.49756e11 q^{64} +(4.50564e11 - 7.80400e11i) q^{65} +(-3.81628e11 + 2.20333e11i) q^{66} +(-4.13868e12 - 7.16841e12i) q^{67} +(-3.13715e12 - 1.81124e12i) q^{68} +2.61170e12i q^{69} +(-8.33335e11 - 2.68056e11i) q^{70} -1.12049e13 q^{71} +(1.85842e12 - 3.21888e12i) q^{72} +(-1.24939e13 + 7.21337e12i) q^{73} +(-1.11284e11 - 1.92750e11i) q^{74} +(-1.61698e13 - 9.33566e12i) q^{75} -1.42026e13i q^{76} +(-3.92288e11 + 1.21955e12i) q^{77} +2.17362e13 q^{78} +(-8.80870e12 + 1.52571e13i) q^{79} +(-6.82541e11 + 3.94065e11i) q^{80} +(1.08621e13 + 1.88137e13i) q^{81} +(5.32776e12 + 3.07599e12i) q^{82} +5.05290e13i q^{83} +(-4.45094e12 - 2.06409e13i) q^{84} +5.19318e12 q^{85} +(-3.97515e12 + 6.88516e12i) q^{86} +(5.25386e13 - 3.03332e13i) q^{87} +(5.76698e11 + 9.98870e11i) q^{88} +(-6.21834e13 - 3.59016e13i) q^{89} +5.32846e12i q^{90} +(4.68352e13 - 4.24211e13i) q^{91} +6.83584e12 q^{92} +(5.50554e12 - 9.53588e12i) q^{93} +(1.99841e13 - 1.15378e13i) q^{94} +(1.01804e13 + 1.76331e13i) q^{95} +(-1.64637e13 - 9.50531e12i) q^{96} +6.76473e13i q^{97} +(-4.98738e13 - 3.57885e13i) q^{98} +7.79798e12 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4374 q^{3} - 81920 q^{4} + 3354 q^{5} + 1455616 q^{7} + 17547432 q^{9}+O(q^{10}) \) 20 * q - 4374 * q^3 - 81920 * q^4 + 3354 * q^5 + 1455616 * q^7 + 17547432 * q^9	\( 20 q - 4374 q^{3} - 81920 q^{4} + 3354 q^{5} + 1455616 q^{7} + 17547432 q^{9} - 3933696 q^{10} + 8400426 q^{11} + 35831808 q^{12} - 114693888 q^{14} + 562720524 q^{15} - 671088640 q^{16} + 2180481042 q^{17} - 251755008 q^{18} - 3919727442 q^{19} + 7585509006 q^{21} + 5394565632 q^{22} - 6905098386 q^{23} - 2371878912 q^{24} + 14165082644 q^{25} + 12652202496 q^{26} - 17334943744 q^{28} + 27884908704 q^{29} + 54103511808 q^{30} + 45638710782 q^{31} - 37041090498 q^{33} - 18274367202 q^{35} - 287497125888 q^{36} - 27026027926 q^{37} - 354043974912 q^{38} - 126125404380 q^{39} + 32224837632 q^{40} - 298475364864 q^{42} + 726682953656 q^{43} + 68816289792 q^{44} + 498861631944 q^{45} - 286664984832 q^{46} - 2044625353338 q^{47} + 2939974016204 q^{49} + 1161106642944 q^{50} - 2419609945602 q^{51} + 1314350333952 q^{52} + 1546271487546 q^{53} - 5213176950528 q^{54} + 1720927125504 q^{56} + 14789884876092 q^{57} - 2365863040512 q^{58} - 6798944731566 q^{59} - 2304903266304 q^{60} - 2214453865554 q^{61} - 4417730390688 q^{63} + 10995116277760 q^{64} + 7516703932836 q^{65} - 8476063570944 q^{66} - 4655820763226 q^{67} - 17862500696064 q^{68} + 20497461621504 q^{70} + 96606137494152 q^{71} - 2062377025536 q^{72} - 65348368908666 q^{73} - 566532483072 q^{74} - 186663280957308 q^{75} + 77525241691422 q^{77} + 88663911671808 q^{78} - 60517474082978 q^{79} - 225083129856 q^{80} - 107180264511342 q^{81} - 43979002397184 q^{82} + 18842436550656 q^{84} + 416326699526124 q^{85} + 2363335174656 q^{86} - 126768392660088 q^{87} - 22096140828672 q^{88} - 237147002561826 q^{89} + 203506111374408 q^{91} + 113133131956224 q^{92} - 94175068190130 q^{93} - 221058962902272 q^{94} + 25202514515490 q^{95} + 19430432047104 q^{96} + 165606984015360 q^{98} + 10\!\cdots\!68 q^{99}+O(q^{100}) \) 20 * q - 4374 * q^3 - 81920 * q^4 + 3354 * q^5 + 1455616 * q^7 + 17547432 * q^9 - 3933696 * q^10 + 8400426 * q^11 + 35831808 * q^12 - 114693888 * q^14 + 562720524 * q^15 - 671088640 * q^16 + 2180481042 * q^17 - 251755008 * q^18 - 3919727442 * q^19 + 7585509006 * q^21 + 5394565632 * q^22 - 6905098386 * q^23 - 2371878912 * q^24 + 14165082644 * q^25 + 12652202496 * q^26 - 17334943744 * q^28 + 27884908704 * q^29 + 54103511808 * q^30 + 45638710782 * q^31 - 37041090498 * q^33 - 18274367202 * q^35 - 287497125888 * q^36 - 27026027926 * q^37 - 354043974912 * q^38 - 126125404380 * q^39 + 32224837632 * q^40 - 298475364864 * q^42 + 726682953656 * q^43 + 68816289792 * q^44 + 498861631944 * q^45 - 286664984832 * q^46 - 2044625353338 * q^47 + 2939974016204 * q^49 + 1161106642944 * q^50 - 2419609945602 * q^51 + 1314350333952 * q^52 + 1546271487546 * q^53 - 5213176950528 * q^54 + 1720927125504 * q^56 + 14789884876092 * q^57 - 2365863040512 * q^58 - 6798944731566 * q^59 - 2304903266304 * q^60 - 2214453865554 * q^61 - 4417730390688 * q^63 + 10995116277760 * q^64 + 7516703932836 * q^65 - 8476063570944 * q^66 - 4655820763226 * q^67 - 17862500696064 * q^68 + 20497461621504 * q^70 + 96606137494152 * q^71 - 2062377025536 * q^72 - 65348368908666 * q^73 - 566532483072 * q^74 - 186663280957308 * q^75 + 77525241691422 * q^77 + 88663911671808 * q^78 - 60517474082978 * q^79 - 225083129856 * q^80 - 107180264511342 * q^81 - 43979002397184 * q^82 + 18842436550656 * q^84 + 416326699526124 * q^85 + 2363335174656 * q^86 - 126768392660088 * q^87 - 22096140828672 * q^88 - 237147002561826 * q^89 + 203506111374408 * q^91 + 113133131956224 * q^92 - 94175068190130 * q^93 - 221058962902272 * q^94 + 25202514515490 * q^95 + 19430432047104 * q^96 + 165606984015360 * q^98 + 1056686373672768 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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