LMFDB - Embedded newform 14.15.d.a.3.9

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			3.9
Root			$319.863 + 554.019i$ of defining polynomial
Character	$\chi$	$=$	14.3
Dual form			14.15.d.a.5.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(45.2548 + 78.3837i) q^{2} +(1298.66 + 749.784i) q^{3} +(-4096.00 + 7094.48i) q^{4} +(-67507.4 + 38975.4i) q^{5} +135725. i q^{6} +(-346065. - 747303. i) q^{7} -741455. q^{8} +(-1.26713e6 - 2.19474e6i) q^{9} +O(q^{10})$	\(q+(45.2548 + 78.3837i) q^{2} +(1298.66 + 749.784i) q^{3} +(-4096.00 + 7094.48i) q^{4} +(-67507.4 + 38975.4i) q^{5} +135725. i q^{6} +(-346065. - 747303. i) q^{7} -741455. q^{8} +(-1.26713e6 - 2.19474e6i) q^{9} +(-6.11007e6 - 3.52765e6i) q^{10} +(-4.94890e6 + 8.57174e6i) q^{11} +(-1.06387e7 + 6.14223e6i) q^{12} +1.06948e7i q^{13} +(4.29153e7 - 6.09449e7i) q^{14} -1.16892e8 q^{15} +(-3.35544e7 - 5.81180e7i) q^{16} +(-2.56175e8 - 1.47903e8i) q^{17} +(1.14688e8 - 1.98645e8i) q^{18} +(3.85399e8 - 2.22510e8i) q^{19} -6.38573e8i q^{20} +(1.10894e8 - 1.22997e9i) q^{21} -8.95846e8 q^{22} +(-1.70339e9 - 2.95036e9i) q^{23} +(-9.62901e8 - 5.55931e8i) q^{24} +(-1.35959e7 + 2.35488e7i) q^{25} +(-8.38298e8 + 4.83992e8i) q^{26} -1.09727e10i q^{27} +(6.71921e9 + 6.05806e8i) q^{28} -2.75528e10 q^{29} +(-5.28995e9 - 9.16246e9i) q^{30} +(-5.44700e9 - 3.14483e9i) q^{31} +(3.03700e9 - 5.26024e9i) q^{32} +(-1.28539e10 + 7.42121e9i) q^{33} -2.67733e10i q^{34} +(5.24883e10 + 3.69605e10i) q^{35} +2.07607e10 q^{36} +(9.12395e10 + 1.58031e11i) q^{37} +(3.48824e10 + 2.01393e10i) q^{38} +(-8.01880e9 + 1.38890e10i) q^{39} +(5.00537e10 - 2.88985e10i) q^{40} +1.84110e11i q^{41} +(1.01428e11 - 4.69698e10i) q^{42} -1.16902e11 q^{43} +(-4.05414e10 - 7.02197e10i) q^{44} +(1.71081e11 + 9.87739e10i) q^{45} +(1.54174e11 - 2.67036e11i) q^{46} +(-6.76112e11 + 3.90353e11i) q^{47} -1.00634e11i q^{48} +(-4.38702e11 + 5.17231e11i) q^{49} -2.46112e9 q^{50} +(-2.21790e11 - 3.84152e11i) q^{51} +(-7.58741e10 - 4.38059e10i) q^{52} +(6.00003e11 - 1.03923e12i) q^{53} +(8.60080e11 - 4.96567e11i) q^{54} -7.71541e11i q^{55} +(2.56591e11 + 5.54092e11i) q^{56} +6.67339e11 q^{57} +(-1.24690e12 - 2.15969e12i) q^{58} +(-3.90985e11 - 2.25735e11i) q^{59} +(4.78792e11 - 8.29292e11i) q^{60} +(-2.34687e12 + 1.35497e12i) q^{61} -5.69275e11i q^{62} +(-1.20163e12 + 1.70645e12i) q^{63} +5.49756e11 q^{64} +(-4.16834e11 - 7.21978e11i) q^{65} +(-1.16340e12 - 6.71691e11i) q^{66} +(-7.27991e11 + 1.26092e12i) q^{67} +(2.09859e12 - 1.21162e12i) q^{68} -5.10871e12i q^{69} +(-5.21746e11 + 5.78687e12i) q^{70} +3.35864e12 q^{71} +(9.39522e11 + 1.62730e12i) q^{72} +(9.10071e12 + 5.25430e12i) q^{73} +(-8.25805e12 + 1.43034e13i) q^{74} +(-3.53130e10 + 2.03880e10i) q^{75} +3.64561e12i q^{76} +(8.11833e12 + 7.31951e11i) q^{77} -1.45156e12 q^{78} +(1.16407e13 + 2.01623e13i) q^{79} +(4.53034e12 + 2.61559e12i) q^{80} +(2.16649e12 - 3.75248e12i) q^{81} +(-1.44312e13 + 8.33188e12i) q^{82} -5.19742e13i q^{83} +(8.27177e12 + 5.82469e12i) q^{84} +2.30583e13 q^{85} +(-5.29038e12 - 9.16321e12i) q^{86} +(-3.57818e13 - 2.06586e13i) q^{87} +(3.66939e12 - 6.35556e12i) q^{88} +(-2.25113e13 + 1.29969e13i) q^{89} +1.78800e13i q^{90} +(7.99227e12 - 3.70109e12i) q^{91} +2.79084e13 q^{92} +(-4.71589e12 - 8.16815e12i) q^{93} +(-6.11947e13 - 3.53308e13i) q^{94} +(-1.73449e13 + 3.00422e13i) q^{95} +(7.88809e12 - 4.55419e12i) q^{96} -5.20028e13i q^{97} +(-6.03958e13 - 1.09799e13i) q^{98} +2.50836e13 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 $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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
$3$	1298.66	+	749.784i	0.593811	+	0.342837i	0.766603	−	0.642122i	$-0.221946\pi$
$3$	1298.66	+	749.784i	0.593811	+	0.342837i	−0.172792	+	0.984958i	$0.555279\pi$
$4$	−4096.00	+	7094.48i	−0.250000	+	0.433013i
$5$	−67507.4	+	38975.4i	−0.864094	+	0.498885i	−0.865381	−	0.501114i	$-0.832924\pi$
$5$	−67507.4	+	38975.4i	−0.864094	+	0.498885i	0.00128703	+	0.999999i	$0.499590\pi$
$6$			135725.i			0.484844i
$7$	−346065.	−	747303.i	−0.420214	−	0.907425i
$7$	−346065.	−	747303.i	−0.420214	−	0.907425i
$8$	−741455.			−0.353553
$9$	−1.26713e6	−	2.19474e6i	−0.264926	−	0.458865i
$10$	−6.11007e6	−	3.52765e6i	−0.611007	−	0.352765i
$11$	−4.94890e6	+	8.57174e6i	−0.253957	+	0.439866i	−0.964612	−	0.263675i	$-0.915065\pi$
$11$	−4.94890e6	+	8.57174e6i	−0.253957	+	0.439866i	0.710655	+	0.703541i	$0.248399\pi$
$12$	−1.06387e7	+	6.14223e6i	−0.296905	+	0.171418i
$13$			1.06948e7i			0.170439i	0.996362	+	0.0852196i	$0.0271592\pi$
$13$			1.06948e7i			0.170439i	−0.996362	+	0.0852196i	$0.972841\pi$
$14$	4.29153e7	−	6.09449e7i	0.407114	−	0.578151i
$15$	−1.16892e8			−0.684144
$16$	−3.35544e7	−	5.81180e7i	−0.125000	−	0.216506i
$17$	−2.56175e8	−	1.47903e8i	−0.624302	−	0.360441i	0.154240	−	0.988033i	$-0.450707\pi$
$17$	−2.56175e8	−	1.47903e8i	−0.624302	−	0.360441i	−0.778542	+	0.627593i	$0.784040\pi$
$18$	1.14688e8	−	1.98645e8i	0.187331	−	0.324467i
$19$	3.85399e8	−	2.22510e8i	0.431157	−	0.248929i	−0.268682	−	0.963229i	$-0.586588\pi$
$19$	3.85399e8	−	2.22510e8i	0.431157	−	0.248929i	0.699839	+	0.714300i	$0.253255\pi$
$20$		−	6.38573e8i		−	0.498885i
$21$	1.10894e8	−	1.22997e9i	0.0615708	−	0.682904i
$22$	−8.95846e8			−0.359149
$23$	−1.70339e9	−	2.95036e9i	−0.500288	−	0.866524i	−1.00000		0.000332535i	$-0.999894\pi$
$23$	−1.70339e9	−	2.95036e9i	−0.500288	−	0.866524i	0.499712	−	0.866192i	$-0.333439\pi$
$24$	−9.62901e8	−	5.55931e8i	−0.209944	−	0.121211i
$25$	−1.35959e7	+	2.35488e7i	−0.00222755	+	0.00385823i
$26$	−8.38298e8	+	4.83992e8i	−0.104372	+	0.0602594i
$27$		−	1.09727e10i		−	1.04898i
$28$	6.71921e9	+	6.05806e8i	0.497980	+	0.0448980i
$29$	−2.75528e10			−1.59727			−0.798636	−	0.601814i	$-0.794445\pi$
$29$	−2.75528e10			−1.59727			−0.798636	+	0.601814i	$0.794445\pi$
$30$	−5.28995e9	−	9.16246e9i	−0.241882	−	0.418951i
$31$	−5.44700e9	−	3.14483e9i	−0.197982	−	0.114305i	0.397732	−	0.917502i	$-0.369797\pi$
$31$	−5.44700e9	−	3.14483e9i	−0.197982	−	0.114305i	−0.595714	+	0.803197i	$0.703131\pi$
$32$	3.03700e9	−	5.26024e9i	0.0883883	−	0.153093i
$33$	−1.28539e10	+	7.42121e9i	−0.301604	+	0.174131i
$34$		−	2.67733e10i		−	0.509740i
$35$	5.24883e10	+	3.69605e10i	0.815805	+	0.574462i
$36$	2.07607e10			0.264926
$37$	9.12395e10	+	1.58031e11i	0.961105	+	1.66468i	0.719735	+	0.694249i	$0.244263\pi$
$37$	9.12395e10	+	1.58031e11i	0.961105	+	1.66468i	0.241370	+	0.970433i	$0.422403\pi$
$38$	3.48824e10	+	2.01393e10i	0.304874	+	0.176019i
$39$	−8.01880e9	+	1.38890e10i	−0.0584328	+	0.101209i
$40$	5.00537e10	−	2.88985e10i	0.305503	−	0.176382i
$41$			1.84110e11i			0.945347i	0.881238	+	0.472673i	$0.156711\pi$
$41$			1.84110e11i			0.945347i	−0.881238	+	0.472673i	$0.843289\pi$
$42$	1.01428e11	−	4.69698e10i	0.439960	−	0.203739i
$43$	−1.16902e11			−0.430074			−0.215037	−	0.976606i	$-0.568987\pi$
$43$	−1.16902e11			−0.430074			−0.215037	+	0.976606i	$0.568987\pi$
$44$	−4.05414e10	−	7.02197e10i	−0.126978	−	0.219933i
$45$	1.71081e11	+	9.87739e10i	0.457842	+	0.264335i
$46$	1.54174e11	−	2.67036e11i	0.353757	−	0.612725i
$47$	−6.76112e11	+	3.90353e11i	−1.33455	+	0.770501i	−0.985993	−	0.166788i	$-0.946660\pi$
$47$	−6.76112e11	+	3.90353e11i	−1.33455	+	0.770501i	−0.348553	+	0.937289i	$0.613327\pi$
$48$		−	1.00634e11i		−	0.171418i
$49$	−4.38702e11	+	5.17231e11i	−0.646840	+	0.762626i
$50$	−2.46112e9			−0.00315023
$51$	−2.21790e11	−	3.84152e11i	−0.247145	−	0.428067i
$52$	−7.58741e10	−	4.38059e10i	−0.0738023	−	0.0426098i
$53$	6.00003e11	−	1.03923e12i	0.510766	−	0.884673i	−0.489156	−	0.872196i	$-0.662695\pi$
$53$	6.00003e11	−	1.03923e12i	0.510766	−	0.884673i	0.999922	−	0.0124765i	$-0.00397149\pi$
$54$	8.60080e11	−	4.96567e11i	0.642366	−	0.370870i
$55$		−	7.71541e11i		−	0.506781i
$56$	2.56591e11	+	5.54092e11i	0.148568	+	0.320823i
$57$	6.67339e11			0.341368
$58$	−1.24690e12	−	2.15969e12i	−0.564721	−	0.978126i
$59$	−3.90985e11	−	2.25735e11i	−0.157107	−	0.0907058i	0.419385	−	0.907808i	$-0.362246\pi$
$59$	−3.90985e11	−	2.25735e11i	−0.157107	−	0.0907058i	−0.576492	+	0.817103i	$0.695579\pi$
$60$	4.78792e11	−	8.29292e11i	0.171036	−	0.296243i
$61$	−2.34687e12	+	1.35497e12i	−0.746758	+	0.431141i	−0.824521	−	0.565831i	$-0.808556\pi$
$61$	−2.34687e12	+	1.35497e12i	−0.746758	+	0.431141i	0.0777631	+	0.996972i	$0.475222\pi$
$62$		−	5.69275e11i		−	0.161652i
$63$	−1.20163e12	+	1.70645e12i	−0.305060	+	0.433222i
$64$	5.49756e11			0.125000
$65$	−4.16834e11	−	7.21978e11i	−0.0850296	−	0.147276i
$66$	−1.16340e12	−	6.71691e11i	−0.213267	−	0.123130i
$67$	−7.27991e11	+	1.26092e12i	−0.120116	+	0.208048i	−0.919813	−	0.392356i	$-0.871660\pi$
$67$	−7.27991e11	+	1.26092e12i	−0.120116	+	0.208048i	0.799697	+	0.600404i	$0.204993\pi$
$68$	2.09859e12	−	1.21162e12i	0.312151	−	0.180220i
$69$		−	5.10871e12i		−	0.686068i
$70$	−5.21746e11	+	5.78687e12i	−0.0633538	+	0.702680i
$71$	3.35864e12			0.369279			0.184640	−	0.982806i	$-0.440888\pi$
$71$	3.35864e12			0.369279			0.184640	+	0.982806i	$0.440888\pi$
$72$	9.39522e11	+	1.62730e12i	0.0936654	+	0.162233i
$73$	9.10071e12	+	5.25430e12i	0.823787	+	0.475614i	0.851721	−	0.523996i	$-0.175559\pi$
$73$	9.10071e12	+	5.25430e12i	0.823787	+	0.475614i	−0.0279334	+	0.999610i	$0.508893\pi$
$74$	−8.25805e12	+	1.43034e13i	−0.679604	+	1.17711i
$75$	−3.53130e10	+	2.03880e10i	−0.00264549	+	0.00152737i
$76$			3.64561e12i			0.248929i
$77$	8.11833e12	+	7.31951e11i	0.505862	+	0.0456086i
$78$	−1.45156e12			−0.0826365
$79$	1.16407e13	+	2.01623e13i	0.606162	+	1.04990i	0.991867	+	0.127281i	$0.0406251\pi$
$79$	1.16407e13	+	2.01623e13i	0.606162	+	1.04990i	−0.385705	+	0.922622i	$0.626042\pi$
$80$	4.53034e12	+	2.61559e12i	0.216024	+	0.124721i
$81$	2.16649e12	−	3.75248e12i	0.0947027	−	0.164030i
$82$	−1.44312e13	+	8.33188e12i	−0.578904	+	0.334231i
$83$		−	5.19742e13i		−	1.91532i	−0.287900	−	0.957660i	$-0.592957\pi$
$83$		−	5.19742e13i		−	1.91532i	0.287900	−	0.957660i	$-0.407043\pi$
$84$	8.27177e12	+	5.82469e12i	0.280313	+	0.197387i
$85$	2.30583e13			0.719274
$86$	−5.29038e12	−	9.16321e12i	−0.152054	−	0.263365i
$87$	−3.57818e13	−	2.06586e13i	−0.948478	−	0.547604i
$88$	3.66939e12	−	6.35556e12i	0.0897873	−	0.155516i
$89$	−2.25113e13	+	1.29969e13i	−0.508945	+	0.293839i	−0.732400	−	0.680875i	$-0.761600\pi$
$89$	−2.25113e13	+	1.29969e13i	−0.508945	+	0.293839i	0.223455	+	0.974714i	$0.428266\pi$
$90$			1.78800e13i			0.373826i
$91$	7.99227e12	−	3.70109e12i	0.154661	−	0.0716210i
$92$	2.79084e13			0.500288
$93$	−4.71589e12	−	8.16815e12i	−0.0783759	−	0.135751i
$94$	−6.11947e13	−	3.53308e13i	−0.943667	−	0.544826i
$95$	−1.73449e13	+	3.00422e13i	−0.248374	+	0.430196i
$96$	7.88809e12	−	4.55419e12i	0.104972	−	0.0606056i
$97$		−	5.20028e13i		−	0.643613i	−0.946805	−	0.321807i	$-0.895710\pi$
$97$		−	5.20028e13i		−	0.643613i	0.946805	−	0.321807i	$-0.104290\pi$
$98$	−6.03958e13	−	1.09799e13i	−0.695704	−	0.126478i
$99$	2.50836e13			0.269119
$100$	−1.11378e11	−	1.92912e11i	−0.00111378	−	0.00192912i
$101$	−1.56899e14	−	9.05856e13i	−1.46342	−	0.844908i	−0.464256	−	0.885701i	$-0.653678\pi$
$101$	−1.56899e14	−	9.05856e13i	−1.46342	−	0.844908i	−0.999168	+	0.0407932i	$0.987012\pi$
$102$	2.00742e13	−	3.47695e13i	0.174758	−	0.302689i
$103$	9.44788e13	−	5.45473e13i	0.768199	−	0.443520i	−0.0640328	−	0.997948i	$-0.520396\pi$
$103$	9.44788e13	−	5.45473e13i	0.768199	−	0.443520i	0.832232	+	0.554428i	$0.187063\pi$
$104$		−	7.92972e12i		−	0.0602594i
$105$	4.04524e13	+	8.73542e13i	0.287487	+	0.620810i
$106$	1.08612e14			0.722332
$107$	4.11220e13	+	7.12255e13i	0.256087	+	0.443556i	0.965190	−	0.261549i	$-0.0842332\pi$
$107$	4.11220e13	+	7.12255e13i	0.256087	+	0.443556i	−0.709103	+	0.705105i	$0.750900\pi$
$108$	7.78455e13	+	4.49441e13i	0.454221	+	0.262245i
$109$	−3.29414e13	+	5.70562e13i	−0.180201	+	0.312117i	−0.941949	−	0.335757i	$-0.891008\pi$
$109$	−3.29414e13	+	5.70562e13i	−0.180201	+	0.312117i	0.761748	+	0.647873i	$0.224341\pi$
$110$	6.04762e13	−	3.49160e13i	0.310339	−	0.179174i
$111$			2.73640e14i			1.31801i
$112$	−3.18198e13	+	4.51879e13i	−0.143936	+	0.204407i
$113$	−1.48098e14			−0.629506			−0.314753	−	0.949174i	$-0.601922\pi$
$113$	−1.48098e14			−0.629506			−0.314753	+	0.949174i	$0.601922\pi$
$114$	3.02003e13	+	5.23085e13i	0.120692	+	0.209044i
$115$	2.29983e14	+	1.32781e14i	0.864592	+	0.499172i
$116$	1.12856e14	−	1.95473e14i	0.399318	−	0.691639i
$117$	2.34723e13	−	1.35517e13i	0.0782086	−	0.0451538i
$118$		−	4.08624e13i		−	0.128277i
$119$	−2.18751e13	+	2.42624e14i	−0.0647323	+	0.717969i
$120$	8.66706e13			0.241882
$121$	1.40892e14	+	2.44032e14i	0.371012	+	0.642612i
$122$	−2.12414e14	−	1.22637e14i	−0.528038	−	0.304863i
$123$	−1.38043e14	+	2.39097e14i	−0.324100	+	0.561357i
$124$	4.46219e13	−	2.57624e13i	0.0989910	−	0.0571525i
$125$		−	4.77893e14i		−	1.00222i
$126$	−1.88137e14	−	1.69625e13i	−0.373148	−	0.0336431i
$127$	−8.03620e14			−1.50808			−0.754041	−	0.656827i	$-0.771898\pi$
$127$	−8.03620e14			−1.50808			−0.754041	+	0.656827i	$0.771898\pi$
$128$	2.48791e13	+	4.30919e13i	0.0441942	+	0.0765466i
$129$	−1.51816e14	−	8.76513e13i	−0.255382	−	0.147445i
$130$	3.77275e13	−	6.53460e13i	0.0601250	−	0.104140i
$131$	5.53433e14	−	3.19525e14i	0.835922	−	0.482620i	−0.0199539	−	0.999801i	$-0.506352\pi$
$131$	5.53433e14	−	3.19525e14i	0.835922	−	0.482620i	0.855876	+	0.517181i	$0.173019\pi$
$132$		−	1.21589e14i		−	0.174131i
$133$	−2.99656e14	−	2.11007e14i	−0.407063	−	0.286639i
$134$	−1.31780e14			−0.169870
$135$	4.27665e14	+	7.40737e14i	0.523320	+	0.906417i
$136$	1.89942e14	+	1.09663e14i	0.220724	+	0.127435i
$137$	5.13837e14	−	8.89992e14i	0.567259	−	0.982521i	−0.429577	−	0.903030i	$-0.641337\pi$
$137$	5.13837e14	−	8.89992e14i	0.567259	−	0.982521i	0.996836	−	0.0794909i	$-0.0253295\pi$
$138$	4.00439e14	−	2.31194e14i	0.420129	−	0.242562i
$139$		−	1.22498e15i		−	1.22187i	−0.791681	−	0.610935i	$-0.790794\pi$
$139$		−	1.22498e15i		−	1.22187i	0.791681	−	0.610935i	$-0.209206\pi$
$140$	−4.77208e14	+	2.20987e14i	−0.452701	+	0.209639i
$141$	−1.17072e15			−1.05662
$142$	1.51995e14	+	2.63263e14i	0.130560	+	0.226136i
$143$	−9.16732e13	−	5.29275e13i	−0.0749704	−	0.0432842i
$144$	−8.50358e13	+	1.47286e14i	−0.0662315	+	0.114716i
$145$	1.86001e15	−	1.07388e15i	1.38019	−	0.796855i
$146$			9.51129e14i			0.672620i
$147$	−9.57537e14	+	3.42777e14i	−0.645557	+	0.231095i
$148$	−1.49487e15			−0.961105
$149$	4.16513e14	+	7.21422e14i	0.255461	+	0.442472i	0.965021	−	0.262174i	$-0.0844394\pi$
$149$	4.16513e14	+	7.21422e14i	0.255461	+	0.442472i	−0.709560	+	0.704645i	$0.751106\pi$
$150$	−3.19617e12	−	1.84531e12i	−0.00187064	−	0.00108002i
$151$	9.62670e14	−	1.66739e15i	0.537822	−	0.931535i	−0.461199	−	0.887297i	$-0.652580\pi$
$151$	9.62670e14	−	1.66739e15i	0.537822	−	0.931535i	0.999021	−	0.0442386i	$-0.0140862\pi$
$152$	−2.85756e14	+	1.64981e14i	−0.152437	+	0.0880096i
$153$			7.49649e14i			0.381960i
$154$	3.10021e14	+	6.69469e14i	0.150920	+	0.325901i
$155$	4.90284e14			0.228100
$156$	−6.56900e13	−	1.13778e14i	−0.0292164	−	0.0506043i
$157$	−3.17325e15	−	1.83208e15i	−1.34961	−	0.779195i	−0.361412	−	0.932406i	$-0.617705\pi$
$157$	−3.17325e15	−	1.83208e15i	−1.34961	−	0.779195i	−0.988194	+	0.153211i	$0.951039\pi$
$158$	−1.05359e15	+	1.82488e15i	−0.428621	+	0.742394i
$159$	1.55840e15	−	8.99745e14i	0.606597	−	0.350219i
$160$			4.73473e14i			0.176382i
$161$	−1.61533e15	+	2.29397e15i	−0.576077	+	0.818100i
$162$	3.92177e14			0.133930
$163$	2.88932e15	+	5.00445e15i	0.945111	+	1.63698i	0.755529	+	0.655115i	$0.227380\pi$
$163$	2.88932e15	+	5.00445e15i	0.945111	+	1.63698i	0.189581	+	0.981865i	$0.439287\pi$
$164$	−1.30617e15	−	7.54116e14i	−0.409347	−	0.236337i
$165$	5.78489e14	−	1.00197e15i	0.173743	−	0.300932i
$166$	4.07393e15	−	2.35209e15i	1.17289	−	0.677168i
$167$			5.18360e15i			1.43092i	0.698652	+	0.715461i	$0.253783\pi$
$167$			5.18360e15i			1.43092i	−0.698652	+	0.715461i	$0.746217\pi$
$168$	−8.22232e13	+	9.11967e14i	−0.0217686	+	0.241443i
$169$	3.82300e15			0.970950
$170$	1.04350e15	+	1.80739e15i	0.254302	+	0.440463i
$171$	−9.76704e14	−	5.63900e14i	−0.228449	−	0.131895i
$172$	4.78831e14	−	8.29359e14i	0.107518	−	0.186227i
$173$	1.89953e15	−	1.09669e15i	0.409565	−	0.236462i	−0.281038	−	0.959697i	$-0.590679\pi$
$173$	1.89953e15	−	1.09669e15i	0.409565	−	0.236462i	0.690603	+	0.723234i	$0.257345\pi$
$174$		−	3.73961e15i		−	0.774429i
$175$	2.23031e13	+	2.01086e12i	0.00443710	+	0.000400051i
$176$	6.64230e14			0.126978
$177$	−3.38505e14	−	5.86308e14i	−0.0621946	−	0.107724i
$178$	−2.03749e15	−	1.17635e15i	−0.359878	−	0.207776i
$179$	−2.78595e15	+	4.82541e15i	−0.473154	+	0.819527i	−0.999528	−	0.0307266i	$-0.990218\pi$
$179$	−2.78595e15	+	4.82541e15i	−0.473154	+	0.819527i	0.526374	+	0.850253i	$0.323551\pi$
$180$	−1.40150e15	+	8.09156e14i	−0.228921	+	0.132168i
$181$		−	1.15526e16i		−	1.81523i	−0.419807	−	0.907613i	$-0.637902\pi$
$181$		−	1.15526e16i		−	1.81523i	0.419807	−	0.907613i	$-0.362098\pi$
$182$	6.51794e14	+	4.58971e14i	0.0985396	+	0.0693881i
$183$	−4.06373e15			−0.591244
$184$	1.26299e15	+	2.18756e15i	0.176879	+	0.306363i
$185$	−1.23187e16	−	7.11219e15i	−1.66097	−	0.958961i
$186$	4.26833e14	−	7.39297e14i	0.0554201	−	0.0959905i
$187$	2.53557e15	−	1.46391e15i	0.317091	−	0.183073i
$188$		−	6.39555e15i		−	0.770501i
$189$	−8.19993e15	+	3.79726e15i	−0.951870	+	0.440796i
$190$	−3.13975e15			−0.351253
$191$	7.14355e15	+	1.23730e16i	0.770337	+	1.33426i	0.937378	+	0.348313i	$0.113245\pi$
$191$	7.14355e15	+	1.23730e16i	0.770337	+	1.33426i	−0.167041	+	0.985950i	$0.553421\pi$
$192$	7.13948e14	+	4.12198e14i	0.0742263	+	0.0428546i
$193$	4.06583e15	−	7.04222e15i	0.407613	−	0.706006i	−0.587009	−	0.809580i	$-0.699695\pi$
$193$	4.06583e15	−	7.04222e15i	0.407613	−	0.706006i	0.994622	+	0.103574i	$0.0330280\pi$
$194$	4.07617e15	−	2.35338e15i	0.394131	−	0.227552i
$195$		−	1.25014e15i		−	0.116605i
$196$	−1.87256e15	−	5.23094e15i	−0.168517	−	0.470746i
$197$	−6.50117e15			−0.564583			−0.282291	−	0.959329i	$-0.591094\pi$
$197$	−6.50117e15			−0.564583			−0.282291	+	0.959329i	$0.591094\pi$
$198$	1.13516e15	+	1.96615e15i	0.0951479	+	0.164801i
$199$	−2.52113e15	−	1.45558e15i	−0.203997	−	0.117778i	0.394521	−	0.918887i	$-0.370910\pi$
$199$	−2.52113e15	−	1.45558e15i	−0.203997	−	0.117778i	−0.598519	+	0.801109i	$0.704244\pi$
$200$	1.00807e13	−	1.74604e13i	0.000787558	−	0.00136409i
$201$	−1.89083e15	+	1.09167e15i	−0.142653	+	0.0823606i
$202$		−	1.63977e16i		−	1.19488i
$203$	9.53504e15	+	2.05903e16i	0.671197	+	1.44941i
$204$	3.63381e15			0.247145
$205$	−7.17577e15	−	1.24288e16i	−0.471619	−	0.816869i
$206$	8.55124e15	+	4.93706e15i	0.543199	+	0.313616i
$207$	−4.31685e15	+	7.47700e15i	−0.265078	+	0.459129i
$208$	6.21561e14	−	3.58858e14i	0.0369012	−	0.0213049i
$209$			4.40472e15i			0.252869i
$210$	−5.01647e15	+	7.12400e15i	−0.278525	+	0.395539i
$211$	2.34044e16			1.25696			0.628479	−	0.777826i	$-0.283678\pi$
$211$	2.34044e16			1.25696			0.628479	+	0.777826i	$0.283678\pi$
$212$	4.91522e15	+	8.51341e15i	0.255383	+	0.442336i
$213$	4.36174e15	+	2.51825e15i	0.219282	+	0.126603i
$214$	−3.72194e15	+	6.44659e15i	−0.181081	+	0.313642i
$215$	7.89175e15	−	4.55630e15i	0.371624	−	0.214557i
$216$			8.13576e15i			0.370870i
$217$	−4.65126e14	+	5.15888e15i	−0.0205283	+	0.227686i
$218$	−5.96303e15			−0.254842
$219$	7.87917e15	+	1.36471e16i	0.326116	+	0.564849i
$220$	5.47368e15	+	3.16023e15i	0.219443	+	0.126695i
$221$	1.58179e15	−	2.73974e15i	0.0614332	−	0.106405i
$222$	−2.14489e16	+	1.23835e16i	−0.807112	+	0.465986i
$223$		−	5.99930e15i		−	0.218759i	−0.994000	−	0.109380i	$-0.965114\pi$
$223$		−	5.99930e15i		−	0.218759i	0.994000	−	0.109380i	$-0.0348864\pi$
$224$	−4.98199e15	−	4.49178e14i	−0.176063	−	0.0158738i
$225$	6.89112e13			0.00236054
$226$	−6.70215e15	−	1.16085e16i	−0.222564	−	0.385492i
$227$	−4.94190e15	−	2.85320e15i	−0.159116	−	0.0918654i	0.418328	−	0.908296i	$-0.362616\pi$
$227$	−4.94190e15	−	2.85320e15i	−0.159116	−	0.0918654i	−0.577443	+	0.816431i	$0.695950\pi$
$228$	−2.73342e15	+	4.73442e15i	−0.0853419	+	0.147817i
$229$	1.67924e16	−	9.69509e15i	0.508469	−	0.293564i	−0.223735	−	0.974650i	$-0.571825\pi$
$229$	1.67924e16	−	9.69509e15i	0.508469	−	0.293564i	0.732204	+	0.681085i	$0.238492\pi$
$230$			2.40359e16i			0.705936i
$231$	9.99418e15	+	7.03755e15i	0.284750	+	0.200511i
$232$	2.04291e16			0.564721
$233$	−2.37422e16	−	4.11226e16i	−0.636837	−	1.10303i	−0.986123	−	0.166018i	$-0.946909\pi$
$233$	−2.37422e16	−	4.11226e16i	−0.636837	−	1.10303i	0.349285	−	0.937016i	$-0.386424\pi$
$234$	2.12447e15	+	1.22656e15i	0.0553018	+	0.0319285i
$235$	3.04283e16	−	5.27034e16i	0.768782	−	1.33157i
$236$	3.20295e15	−	1.84922e15i	0.0785535	−	0.0453529i
$237$			3.49120e16i			0.831259i
$238$	−2.00077e16	+	9.26528e15i	−0.462551	+	0.214200i
$239$	−5.97167e16			−1.34063			−0.670317	−	0.742074i	$-0.733842\pi$
$239$	−5.97167e16			−1.34063			−0.670317	+	0.742074i	$0.733842\pi$
$240$	3.92226e15	+	6.79356e15i	0.0855181	+	0.148122i
$241$	−1.71508e16	−	9.90203e15i	−0.363216	−	0.209703i	0.307274	−	0.951621i	$-0.400583\pi$
$241$	−1.71508e16	−	9.90203e15i	−0.363216	−	0.209703i	−0.670491	+	0.741918i	$0.733916\pi$
$242$	−1.27521e16	+	2.20872e16i	−0.262345	+	0.454395i
$243$	−3.98237e16	+	2.29922e16i	−0.795971	+	0.459554i
$244$		−	2.21998e16i		−	0.431141i
$245$	9.45632e15	−	5.20154e16i	0.178468	−	0.981679i
$246$	−2.49884e16			−0.458346
$247$	2.37971e15	+	4.12177e15i	0.0424272	+	0.0734861i
$248$	4.03871e15	+	2.33175e15i	0.0699972	+	0.0404129i
$249$	3.89695e16	−	6.74971e16i	0.656642	−	1.13734i
$250$	3.74590e16	−	2.16270e16i	0.613729	−	0.354337i
$251$			4.39475e15i			0.0700194i	0.999387	+	0.0350097i	$0.0111462\pi$
$251$			4.39475e15i			0.0700194i	−0.999387	+	0.0350097i	$0.988854\pi$
$252$	−7.18454e15	−	1.55145e16i	−0.111326	−	0.240400i
$253$	3.37197e16			0.508206
$254$	−3.63677e16	−	6.29907e16i	−0.533187	−	0.923508i
$255$	2.99449e16	+	1.72887e16i	0.427112	+	0.246593i
$256$	−2.25180e15	+	3.90023e15i	−0.0312500	+	0.0541266i
$257$	−5.01427e16	+	2.89499e16i	−0.677135	+	0.390944i	−0.798775	−	0.601630i	$-0.794518\pi$
$257$	−5.01427e16	+	2.89499e16i	−0.677135	+	0.390944i	0.121639	+	0.992574i	$0.461185\pi$
$258$		−	1.58666e16i		−	0.208519i
$259$	8.65226e16	−	1.22873e17i	1.10670	−	1.57165i
$260$	6.82941e15			0.0850296
$261$	3.49130e16	+	6.04711e16i	0.423159	+	0.732933i
$262$	5.00910e16	+	2.89201e16i	0.591086	+	0.341264i
$263$	−7.61427e16	+	1.31883e17i	−0.874859	+	1.51530i	−0.0179466	+	0.999839i	$0.505713\pi$
$263$	−7.61427e16	+	1.31883e17i	−0.874859	+	1.51530i	−0.856913	+	0.515462i	$0.827620\pi$
$264$	9.53060e15	−	5.50250e15i	0.106633	−	0.0615648i
$265$			9.35413e16i			1.01925i
$266$	2.97864e15	−	3.30372e16i	0.0316116	−	0.350616i
$267$	−3.89795e16			−0.402956
$268$	−5.96370e15	−	1.03294e16i	−0.0600582	−	0.104024i
$269$	6.59727e15	+	3.80894e15i	0.0647290	+	0.0373713i	0.532015	−	0.846735i	$-0.321435\pi$
$269$	6.59727e15	+	3.80894e15i	0.0647290	+	0.0373713i	−0.467286	+	0.884106i	$0.654768\pi$
$270$	−3.87078e16	+	6.70439e16i	−0.370043	+	0.640933i
$271$	−1.32983e17	+	7.67780e16i	−1.23883	+	0.715240i	−0.968855	−	0.247627i	$-0.920349\pi$
$271$	−1.32983e17	+	7.67780e16i	−1.23883	+	0.715240i	−0.269977	+	0.962867i	$0.587016\pi$
$272$			1.98512e16i			0.180220i
$273$	1.31543e16	+	1.18599e15i	0.116394	+	0.0104941i
$274$	9.30144e16			0.802225
$275$	−1.34569e14	−	2.33081e14i	−0.00113140	−	0.00195965i
$276$	3.62436e16	+	2.09253e16i	0.297076	+	0.171517i
$277$	−1.78804e16	+	3.09697e16i	−0.142895	+	0.247502i	−0.928586	−	0.371118i	$-0.878975\pi$
$277$	−1.78804e16	+	3.09697e16i	−0.142895	+	0.247502i	0.785690	+	0.618620i	$0.212308\pi$
$278$	9.60184e16	−	5.54362e16i	0.748240	−	0.431996i
$279$			1.59397e16i			0.121129i
$280$	−3.89178e16	−	2.74045e16i	−0.288431	−	0.203103i
$281$	−2.57762e16			−0.186327			−0.0931634	−	0.995651i	$-0.529698\pi$
$281$	−2.57762e16			−0.186327			−0.0931634	+	0.995651i	$0.529698\pi$
$282$	−5.29809e16	−	9.17656e16i	−0.373573	−	0.647047i
$283$	5.83377e16	+	3.36813e16i	0.401277	+	0.231677i	0.687035	−	0.726624i	$-0.258912\pi$
$283$	5.83377e16	+	3.36813e16i	0.401277	+	0.231677i	−0.285758	+	0.958302i	$0.592245\pi$
$284$	−1.37570e16	+	2.38278e16i	−0.0923198	+	0.159903i
$285$	−4.50503e16	+	2.60098e16i	−0.294974	+	0.170303i
$286$		−	9.58090e15i		−	0.0612131i
$287$	1.37586e17	−	6.37141e16i	0.857831	−	0.397248i
$288$	−1.53931e16			−0.0936654
$289$	−4.04385e16	−	7.00415e16i	−0.240165	−	0.415978i
$290$	1.68349e17	+	9.71965e16i	0.975945	+	0.563462i
$291$	3.89909e16	−	6.75342e16i	0.220654	−	0.382184i
$292$	−7.45530e16	+	4.30432e16i	−0.411894	+	0.237807i
$293$			3.06340e17i			1.65246i	0.563334	+	0.826229i	$0.309518\pi$
$293$			3.06340e17i			1.65246i	−0.563334	+	0.826229i	$0.690482\pi$
$294$	−7.02013e16	−	5.95430e16i	−0.369755	−	0.313617i
$295$	3.51925e16			0.181007
$296$	−6.76500e16	−	1.17173e17i	−0.339802	−	0.588554i
$297$	9.40551e16	+	5.43027e16i	0.461410	+	0.266395i
$298$	−3.76985e16	+	6.52957e16i	−0.180638	+	0.312875i
$299$	3.15536e16	−	1.82175e16i	0.147690	−	0.0852687i
$300$		−	3.34036e14i		−	0.00152737i
$301$	4.04557e16	+	8.73613e16i	0.180723	+	0.390260i
$302$	1.74262e17			0.760596
$303$	−1.35839e17	−	2.35280e17i	−0.579331	−	1.00343i
$304$	−2.58637e16	−	1.49324e16i	−0.107789	−	0.0622322i
$305$	1.05621e17	−	1.82940e17i	0.430180	−	0.745093i
$306$	−5.87603e16	+	3.39253e16i	−0.233902	+	0.135043i
$307$		−	1.36311e17i		−	0.530348i	−0.964201	−	0.265174i	$-0.914571\pi$
$307$		−	1.36311e17i		−	0.530348i	0.964201	−	0.265174i	$-0.0854294\pi$
$308$	−3.84455e16	+	5.45973e16i	−0.146215	+	0.207642i
$309$	1.63595e17			0.608220
$310$	2.21877e16	+	3.84302e16i	0.0806456	+	0.139682i
$311$	−3.57294e17	−	2.06284e17i	−1.26971	−	0.733065i	−0.294774	−	0.955567i	$-0.595244\pi$
$311$	−3.57294e17	−	2.06284e17i	−1.26971	−	0.733065i	−0.974932	+	0.222502i	$0.928578\pi$
$312$	5.94558e15	−	1.02980e16i	0.0206591	−	0.0357827i
$313$	−3.36075e17	+	1.94033e17i	−1.14189	+	0.659273i	−0.946899	−	0.321532i	$-0.895802\pi$
$313$	−3.36075e17	+	1.94033e17i	−1.14189	+	0.659273i	−0.194995	+	0.980804i	$0.562469\pi$
$314$		−	3.31642e17i		−	1.10195i
$315$	1.46088e16	−	1.62032e17i	0.0474725	−	0.526534i
$316$	−1.90721e17			−0.606162
$317$	−2.02786e17	−	3.51235e17i	−0.630409	−	1.09190i	−0.987468	−	0.157819i	$-0.949554\pi$
$317$	−2.02786e17	−	3.51235e17i	−0.630409	−	1.09190i	0.357059	−	0.934082i	$-0.383780\pi$
$318$	1.41051e17	+	8.14356e16i	0.428929	+	0.247642i
$319$	1.36356e17	−	2.36175e17i	0.405638	−	0.702586i
$320$	−3.71126e16	+	2.14269e16i	−0.108012	+	0.0623606i
$321$			1.23331e17i			0.351185i
$322$	−2.52911e17	−	2.28025e16i	−0.704656	−	0.0635320i
$323$	−1.31640e17			−0.358896
$324$	1.77479e16	+	3.07403e16i	0.0473513	+	0.0820149i
$325$	−2.51850e14	−	1.45405e14i	−0.000657594	−	0.000379662i
$326$	−2.61512e17	+	4.52951e17i	−0.668294	+	1.15752i
$327$	−8.55596e16	+	4.93978e16i	−0.214010	+	0.123559i
$328$		−	1.36510e17i		−	0.334231i
$329$	5.25691e17	+	3.70173e17i	1.25997	+	0.887225i
$330$	1.04718e17			0.245710
$331$	9.82038e16	+	1.70094e17i	0.225596	+	0.390744i	0.956498	−	0.291738i	$-0.0942336\pi$
$331$	9.82038e16	+	1.70094e17i	0.225596	+	0.390744i	−0.730902	+	0.682483i	$0.760900\pi$
$332$	3.68730e17	+	2.12887e17i	0.829358	+	0.478830i
$333$	2.31225e17	−	4.00493e17i	0.509243	−	0.882035i
$334$	−4.06310e17	+	2.34583e17i	−0.876258	+	0.505908i
$335$		−	1.13495e17i		−	0.239697i
$336$	−7.52044e16	+	3.48260e16i	−0.155549	+	0.0720325i
$337$	3.36134e17			0.680931			0.340465	−	0.940257i	$-0.389415\pi$
$337$	3.36134e17			0.680931			0.340465	+	0.940257i	$0.389415\pi$
$338$	1.73009e17	+	2.99661e17i	0.343283	+	0.594583i
$339$	−1.92330e17	−	1.11042e17i	−0.373808	−	0.215818i
$340$	−9.44467e16	+	1.63586e17i	−0.179818	+	0.311455i
$341$	5.39134e16	−	3.11269e16i	0.100558	−	0.0580571i
$342$		−	1.02077e17i		−	0.186528i
$343$	5.38347e17	+	1.48848e17i	0.963837	+	0.266492i
$344$	8.66776e16			0.152054
$345$	1.99114e17	+	3.44875e17i	0.342269	+	0.592828i
$346$	1.71926e17	+	9.92613e16i	0.289606	+	0.167204i
$347$	4.92888e15	−	8.53708e15i	0.00813659	−	0.0140930i	−0.861928	−	0.507030i	$-0.830743\pi$
$347$	4.92888e15	−	8.53708e15i	0.00813659	−	0.0140930i	0.870065	+	0.492937i	$0.164077\pi$
$348$	2.93124e17	−	1.69235e17i	0.474239	−	0.273802i
$349$			3.37354e17i			0.534944i	0.963566	+	0.267472i	$0.0861883\pi$
$349$			3.37354e17i			0.534944i	−0.963566	+	0.267472i	$0.913812\pi$
$350$	8.51706e14	+	1.83920e15i	0.00132377	+	0.00285860i
$351$	1.17351e17			0.178787
$352$	3.00596e16	+	5.20648e16i	0.0448936	+	0.0777581i
$353$	1.19183e17	+	6.88102e16i	0.174498	+	0.100746i	0.584705	−	0.811246i	$-0.301210\pi$
$353$	1.19183e17	+	6.88102e16i	0.174498	+	0.100746i	−0.410207	+	0.911992i	$0.634544\pi$
$354$	3.06380e16	−	5.30666e16i	0.0439782	−	0.0761725i
$355$	−2.26733e17	+	1.30904e17i	−0.319092	+	0.184228i
$356$		−	2.12941e17i		−	0.293839i
$357$	−2.10324e17	+	2.98686e17i	−0.284585	+	0.404145i
$358$	−5.04311e17			−0.669141
$359$	5.44235e16	+	9.42643e16i	0.0708150	+	0.122655i	0.899259	−	0.437417i	$-0.144107\pi$
$359$	5.44235e16	+	9.42643e16i	0.0708150	+	0.122655i	−0.828444	+	0.560072i	$0.810773\pi$
$360$	−1.26849e17	−	7.32365e16i	−0.161872	−	0.0934566i
$361$	−3.00482e17	+	5.20449e17i	−0.376069	+	0.651371i
$362$	9.05538e17	−	5.22812e17i	1.11159	−	0.641780i
$363$			4.22553e17i			0.508786i
$364$	−6.47898e15	+	7.18607e16i	−0.00765238	+	0.0848753i
$365$	−8.19153e17			−0.949106
$366$	−1.83903e17	−	3.18530e17i	−0.209036	−	0.362062i
$367$	−1.30597e18	−	7.54003e17i	−1.45637	−	0.840835i	−0.457539	−	0.889190i	$-0.651269\pi$
$367$	−1.30597e18	−	7.54003e17i	−1.45637	−	0.840835i	−0.998830	+	0.0483544i	$0.984602\pi$
$368$	−1.14313e17	+	1.97996e17i	−0.125072	+	0.216631i
$369$	4.04074e17	−	2.33292e17i	0.433787	−	0.250447i
$370$		−	1.28744e18i		−	1.35618i
$371$	−9.84263e17	−	8.87415e16i	−1.01741	−	0.0917295i
$372$	7.72651e16			0.0783759
$373$	6.58177e17	+	1.14000e18i	0.655210	+	1.13486i	0.981841	+	0.189706i	$0.0607534\pi$
$373$	6.58177e17	+	1.14000e18i	0.655210	+	1.13486i	−0.326631	+	0.945152i	$0.605913\pi$
$374$	2.29493e17	+	1.32498e17i	0.224217	+	0.129452i
$375$	3.58317e17	−	6.20623e17i	0.343596	−	0.595126i
$376$	5.01307e17	−	2.89430e17i	0.471833	−	0.272413i
$377$		−	2.94671e17i		−	0.272238i
$378$	−6.68730e17	−	4.70896e17i	−0.606468	−	0.427054i
$379$	1.12046e17			0.0997522			0.0498761	−	0.998755i	$-0.484117\pi$
$379$	1.12046e17			0.0997522			0.0498761	+	0.998755i	$0.484117\pi$
$380$	−1.42089e17	−	2.46105e17i	−0.124187	−	0.215098i
$381$	−1.04363e18	−	6.02542e17i	−0.895515	−	0.517026i
$382$	−6.46561e17	+	1.11988e18i	−0.544711	+	0.943466i
$383$	1.09263e18	−	6.30830e17i	0.903819	−	0.521820i	0.0253820	−	0.999678i	$-0.491920\pi$
$383$	1.09263e18	−	6.30830e17i	0.903819	−	0.521820i	0.878437	+	0.477857i	$0.158586\pi$
$384$			7.46158e16i			0.0606056i
$385$	−5.76575e17	+	2.67003e17i	−0.459866	+	0.212957i
$386$	7.35994e17			0.576452
$387$	1.48130e17	+	2.56569e17i	0.113938	+	0.197346i
$388$	3.68933e17	+	2.13004e17i	0.278693	+	0.160903i
$389$	6.57817e17	−	1.13937e18i	0.488043	−	0.845314i	−0.511863	−	0.859067i	$-0.671044\pi$
$389$	6.57817e17	−	1.13937e18i	0.488043	−	0.845314i	0.999905	+	0.0137527i	$0.00437776\pi$
$390$	9.79908e16	−	5.65750e16i	0.0714057	−	0.0412261i
$391$			1.00775e18i			0.721296i
$392$	3.25278e17	−	3.83503e17i	0.228692	−	0.269629i
$393$	9.58298e17			0.661839
$394$	−2.94209e17	−	5.09585e17i	−0.199610	−	0.345735i
$395$	−1.57166e18	−	9.07400e17i	−1.04756	−	0.604810i
$396$	−1.02743e17	+	1.77955e17i	−0.0672797	+	0.116532i
$397$	−1.05783e17	+	6.10740e16i	−0.0680587	+	0.0392937i	−0.533643	−	0.845710i	$-0.679177\pi$
$397$	−1.05783e17	+	6.10740e16i	−0.0680587	+	0.0392937i	0.465585	+	0.885003i	$0.345844\pi$
$398$		−	2.63488e17i		−	0.166563i
$399$	−2.30942e17	−	4.98704e17i	−0.143448	−	0.309765i
$400$	1.82481e15			0.00111378
$401$	4.00051e17	+	6.92909e17i	0.239941	+	0.415590i	0.960697	−	0.277599i	$-0.0895385\pi$
$401$	4.00051e17	+	6.92909e17i	0.239941	+	0.415590i	−0.720756	+	0.693189i	$0.756205\pi$
$402$	−1.71139e17	−	9.88069e16i	−0.100871	−	0.0582378i
$403$	3.36333e16	−	5.82547e16i	0.0194821	−	0.0337439i
$404$	1.28531e18	−	7.42077e17i	0.731712	−	0.422454i
$405$			3.37760e17i			0.188983i
$406$	−1.18243e18	+	1.67920e18i	−0.650272	+	0.923465i
$407$	−1.80614e18			−0.976316
$408$	1.64448e17	+	2.84831e17i	0.0873788	+	0.151345i
$409$	6.74457e17	+	3.89398e17i	0.352282	+	0.203390i	0.665690	−	0.746228i	$-0.268137\pi$
$409$	6.74457e17	+	3.89398e17i	0.352282	+	0.203390i	−0.313408	+	0.949619i	$0.601471\pi$
$410$	6.49477e17	−	1.12493e18i	0.333485	−	0.577613i
$411$	1.33460e18	−	7.70533e17i	0.673689	−	0.388954i
$412$			8.93704e17i			0.443520i
$413$	−3.33866e16	+	3.70303e17i	−0.0162900	+	0.180679i
$414$	−7.81433e17			−0.374878
$415$	2.02572e18	+	3.50864e18i	0.955525	+	1.65502i
$416$	5.62572e16	+	3.24801e16i	0.0260931	+	0.0150648i
$417$	9.18470e17	−	1.59084e18i	0.418902	−	0.725560i
$418$	−3.45258e17	+	1.99335e17i	−0.154850	+	0.0894025i
$419$			1.10427e18i			0.487054i	0.969894	+	0.243527i	$0.0783044\pi$
$419$			1.10427e18i			0.487054i	−0.969894	+	0.243527i	$0.921696\pi$
$420$	−7.85425e17	−	7.08141e16i	−0.340690	−	0.0307167i
$421$	−4.05832e18			−1.73130			−0.865649	−	0.500651i	$-0.833094\pi$
$421$	−4.05832e18			−1.73130			−0.865649	+	0.500651i	$0.833094\pi$
$422$	1.05916e18	+	1.83452e18i	0.444402	+	0.769727i
$423$	1.71345e18	+	9.89259e17i	0.707112	+	0.408251i
$424$	−4.44875e17	+	7.70546e17i	−0.180583	+	0.312779i
$425$	6.96586e15	−	4.02174e15i	0.00278133	−	0.00160580i
$426$			4.55853e17i			0.179043i
$427$	1.82474e18	+	1.28492e18i	0.705027	+	0.496455i
$428$	−6.73743e17			−0.256087
$429$	−7.93684e16	−	1.37470e17i	−0.0296788	−	0.0514052i
$430$	7.14279e17	+	4.12389e17i	0.262778	+	0.151715i
$431$	−2.03737e17	+	3.52883e17i	−0.0737445	+	0.127729i	−0.900540	−	0.434774i	$-0.856828\pi$
$431$	−2.03737e17	+	3.52883e17i	−0.0737445	+	0.127729i	0.826795	+	0.562503i	$0.190162\pi$
$432$	−6.37711e17	+	3.68182e17i	−0.227111	+	0.131122i
$433$		−	4.58610e18i		−	1.60705i	−0.595274	−	0.803523i	$-0.702956\pi$
$433$		−	4.58610e18i		−	1.60705i	0.595274	−	0.803523i	$-0.297044\pi$
$434$	−4.25421e17	+	1.97006e17i	−0.146687	+	0.0679284i
$435$	3.22071e18			1.09277
$436$	−2.69856e17	−	4.67404e17i	−0.0901003	−	0.156058i
$437$	−1.31297e18	−	7.58045e17i	−0.431405	−	0.249072i
$438$	−7.13141e17	+	1.23520e18i	−0.230599	+	0.399409i
$439$	1.52050e18	−	8.77860e17i	0.483876	−	0.279366i	−0.238154	−	0.971227i	$-0.576542\pi$
$439$	1.52050e18	−	8.77860e17i	0.483876	−	0.279366i	0.722030	+	0.691861i	$0.243209\pi$
$440$			5.72063e17i			0.179174i
$441$	1.69108e18	+	3.07435e17i	0.521307	+	0.0947728i
$442$	2.86335e17			0.0868797
$443$	2.07751e17	+	3.59836e17i	0.0620465	+	0.107468i	0.895380	−	0.445303i	$-0.146904\pi$
$443$	2.07751e17	+	3.59836e17i	0.0620465	+	0.107468i	−0.833334	+	0.552770i	$0.813571\pi$
$444$	−1.94133e18	−	1.12083e18i	−0.570714	−	0.329502i
$445$	1.01312e18	−	1.75477e18i	0.293184	−	0.507810i
$446$	4.70247e17	−	2.71498e17i	0.133962	−	0.0773431i
$447$			1.24918e18i			0.350326i
$448$	−1.90251e17	−	4.10834e17i	−0.0525268	−	0.113428i
$449$	−6.86642e18			−1.86641			−0.933203	−	0.359350i	$-0.882999\pi$
$449$	−6.86642e18			−1.86641			−0.933203	+	0.359350i	$0.882999\pi$
$450$	3.11856e15	+	5.40151e15i	0.000834578	+	0.00144553i
$451$	−1.57815e18	−	9.11143e17i	−0.415826	−	0.240077i
$452$	6.06610e17	−	1.05068e18i	0.157377	−	0.272584i
$453$	2.50037e18	−	1.44359e18i	0.638729	−	0.368770i
$454$		−	5.16485e17i		−	0.129917i
$455$	−3.95285e17	+	5.61353e17i	−0.0979108	+	0.139045i
$456$	−4.94802e17			−0.120692
$457$	−2.71084e18	−	4.69531e18i	−0.651164	−	1.12785i	−0.982841	−	0.184456i	$-0.940948\pi$
$457$	−2.71084e18	−	4.69531e18i	−0.651164	−	1.12785i	0.331677	−	0.943393i	$-0.392385\pi$
$458$	1.51987e18	+	8.77499e17i	0.359542	+	0.207581i
$459$	−1.62289e18	+	2.81093e18i	−0.378095	+	0.654879i
$460$	−1.88402e18	+	1.08774e18i	−0.432296	+	0.249586i
$461$		−	5.61041e18i		−	1.26791i	−0.773370	−	0.633955i	$-0.781430\pi$
$461$		−	5.61041e18i		−	1.26791i	0.773370	−	0.633955i	$-0.218570\pi$
$462$	−9.93444e16	+	1.10186e18i	−0.0221131	+	0.245264i
$463$	8.48778e18			1.86092			0.930459	−	0.366396i	$-0.119408\pi$
$463$	8.48778e18			1.86092			0.930459	+	0.366396i	$0.119408\pi$
$464$	9.24517e17	+	1.60131e18i	0.199659	+	0.345820i
$465$	6.36714e17	+	3.67607e17i	0.135448	+	0.0782011i
$466$	2.14889e18	−	3.72199e18i	0.450312	−	0.779963i
$467$	−5.56099e18	+	3.21064e18i	−1.14798	+	0.662786i	−0.948394	−	0.317095i	$-0.897293\pi$
$467$	−5.56099e18	+	3.21064e18i	−1.14798	+	0.662786i	−0.199585	+	0.979881i	$0.563959\pi$
$468$			2.22032e17i			0.0451538i
$469$	1.19422e18	+	1.07671e17i	0.239262	+	0.0215720i
$470$	5.50812e18			1.08722
$471$	−2.74733e18	−	4.75851e18i	−0.534274	−	0.925389i
$472$	2.89898e17	+	1.67373e17i	0.0555457	+	0.0320693i
$473$	5.78536e17	−	1.00205e18i	0.109220	−	0.189175i
$474$	−2.73653e18	+	1.57994e18i	−0.509040	+	0.293894i
$475$			1.21009e16i			0.00221801i
$476$	−1.63169e18	−	1.14898e18i	−0.294707	−	0.207522i
$477$	−3.04113e18			−0.541261
$478$	−2.70247e18	−	4.68081e18i	−0.473986	−	0.820968i
$479$	−3.52204e17	−	2.03345e17i	−0.0608759	−	0.0351467i	0.469253	−	0.883064i	$-0.344523\pi$
$479$	−3.52204e17	−	2.03345e17i	−0.0608759	−	0.0351467i	−0.530129	+	0.847917i	$0.677857\pi$
$480$	−3.55003e17	+	6.14882e17i	−0.0604704	+	0.104738i
$481$	−1.69012e18	+	9.75789e17i	−0.283727	+	0.163810i
$482$		−	1.79246e18i		−	0.296565i
$483$	−3.81775e18	+	1.76794e18i	−0.622556	+	0.288296i
$484$	−2.30837e18			−0.371012
$485$	2.02683e18	+	3.51057e18i	0.321089	+	0.556142i
$486$	−3.60443e18	−	2.08102e18i	−0.562837	−	0.324954i
$487$	−3.65518e18	+	6.33096e18i	−0.562609	+	0.974467i	0.434659	+	0.900595i	$0.356869\pi$
$487$	−3.65518e18	+	6.33096e18i	−0.562609	+	0.974467i	−0.997268	+	0.0738715i	$0.976465\pi$
$488$	1.74010e18	−	1.00465e18i	0.264019	−	0.152431i
$489$			8.66547e18i			1.29607i
$490$	4.50510e18	−	1.61273e18i	0.664251	−	0.237787i
$491$	3.97545e18			0.577851			0.288925	−	0.957352i	$-0.406702\pi$
$491$	3.97545e18			0.577851			0.288925	+	0.957352i	$0.406702\pi$
$492$	−1.13085e18	−	1.95869e18i	−0.162050	−	0.280679i
$493$	7.05833e18	+	4.07513e18i	0.997180	+	0.575722i
$494$	−2.15386e17	+	3.73060e17i	−0.0300006	+	0.0519625i
$495$	−1.69333e18	+	9.77645e17i	−0.232544	+	0.134259i
$496$			4.22092e17i			0.0571525i
$497$	−1.16231e18	−	2.50992e18i	−0.155177	−	0.335093i
$498$	7.05423e18			0.928633
$499$	−3.27595e17	−	5.67412e17i	−0.0425240	−	0.0736537i	0.843980	−	0.536375i	$-0.180207\pi$
$499$	−3.27595e17	−	5.67412e17i	−0.0425240	−	0.0736537i	−0.886504	+	0.462721i	$0.846873\pi$
$500$	3.39041e18	+	1.95745e18i	0.433972	+	0.250554i
$501$	−3.88658e18	+	6.73176e18i	−0.490573	+	0.849697i
$502$	−3.44477e17	+	1.98884e17i	−0.0428779	+	0.0247556i
$503$			2.50022e18i			0.306903i	0.988156	+	0.153452i	$0.0490390\pi$
$503$			2.50022e18i			0.306903i	−0.988156	+	0.153452i	$0.950961\pi$
$504$	8.90951e17	−	1.26526e18i	0.107855	−	0.153167i
$505$	1.41224e19			1.68605
$506$	1.52598e18	+	2.64307e18i	0.179678	+	0.311211i
$507$	4.96479e18	+	2.86642e18i	0.576561	+	0.332878i
$508$	3.29163e18	−	5.70127e18i	0.377020	−	0.653019i
$509$	−1.24044e19	+	7.16168e18i	−1.40136	+	0.809078i	−0.994533	−	0.104425i	$-0.966700\pi$
$509$	−1.24044e19	+	7.16168e18i	−1.40136	+	0.809078i	−0.406831	+	0.913503i	$0.633366\pi$
$510$			3.12959e18i			0.348736i
$511$	7.77120e17	−	8.61932e18i	0.0854165	−	0.947385i
$512$	−4.07619e17			−0.0441942
$513$	−2.44154e18	−	4.22887e18i	−0.261121	−	0.452275i
$514$	−4.53840e18	−	2.62024e18i	−0.478807	−	0.276439i
$515$	−4.25201e18	+	7.36469e18i	−0.442531	+	0.766486i
$516$	1.24368e18	−	7.18039e17i	0.127691	−	0.0737225i
$517$		−	7.72728e18i		−	0.782695i
$518$	1.35468e19	+	1.22138e18i	1.35372	+	0.122051i
$519$	3.28913e18			0.324272
$520$	3.09064e17	+	5.35314e17i	0.0300625	+	0.0520698i
$521$	5.69400e18	+	3.28743e18i	0.546454	+	0.315495i	0.747691	−	0.664047i	$-0.231163\pi$
$521$	5.69400e18	+	3.28743e18i	0.546454	+	0.315495i	−0.201237	+	0.979543i	$0.564496\pi$
$522$	−3.15996e18	+	5.47322e18i	−0.299219	+	0.518262i
$523$	9.39499e18	−	5.42420e18i	0.877778	−	0.506785i	0.00785283	−	0.999969i	$-0.497500\pi$
$523$	9.39499e18	−	5.42420e18i	0.877778	−	0.506785i	0.869925	+	0.493184i	$0.164167\pi$
$524$			5.23509e18i			0.482620i
$525$	2.74566e16	+	1.93340e16i	0.00249765	+	0.00175876i
$526$	−1.37833e19			−1.23724
$527$	9.30258e17	+	1.61125e18i	0.0824003	+	0.142722i
$528$	8.62612e17	+	4.98029e17i	0.0754011	+	0.0435329i
$529$	−6.67837e15	+	1.15673e16i	−0.000576078	+	0.000997796i
$530$	−7.33211e18	+	4.23320e18i	−0.624163	+	0.360361i
$531$			1.14415e18i			0.0961213i
$532$	2.72438e18	−	1.26162e18i	0.225884	−	0.104603i
$533$	−1.96902e18			−0.161124
$534$	−1.76401e18	−	3.05536e18i	−0.142466	−	0.246759i
$535$	−5.55208e18	−	3.20549e18i	−0.442567	−	0.255516i
$536$	5.39773e17	−	9.34914e17i	0.0424676	−	0.0735560i
$537$	−7.23603e18	+	4.17772e18i	−0.561928	+	0.324429i
$538$			6.89491e17i			0.0528510i
$539$	−2.26248e18	−	6.32016e18i	−0.171184	−	0.478197i
$540$	−7.00686e18			−0.523320
$541$	−1.24416e19	−	2.15495e19i	−0.917265	−	1.58875i	−0.803551	−	0.595236i	$-0.797058\pi$
$541$	−1.24416e19	−	2.15495e19i	−0.917265	−	1.58875i	−0.113715	−	0.993513i	$-0.536275\pi$
$542$	−1.20363e19	−	6.94915e18i	−0.875987	−	0.505751i
$543$	8.66198e18	−	1.50030e19i	0.622326	−	1.07790i
$544$	−1.55601e18	+	8.98361e17i	−0.110362	+	0.0637175i
$545$		−	5.13561e18i		−	0.359598i
$546$	5.02333e17	+	1.08475e18i	0.0347250	+	0.0749864i
$547$	−1.32156e19			−0.901937			−0.450968	−	0.892540i	$-0.648921\pi$
$547$	−1.32156e19			−0.901937			−0.450968	+	0.892540i	$0.648921\pi$
$548$	4.20935e18	+	7.29081e18i	0.283629	+	0.491261i
$549$	5.94759e18	+	3.43384e18i	0.395671	+	0.228441i
$550$	1.21798e16	−	2.10961e16i	0.000800023	−	0.00138568i
$551$	−1.06188e19	+	6.13077e18i	−0.688676	+	0.397607i
$552$			3.78788e18i			0.242562i
$553$	1.10389e19	−	1.56766e19i	0.697990	−	0.991231i
$554$	−3.23669e18			−0.202085
$555$	−1.06652e19	−	1.84727e19i	−0.657534	−	1.13888i
$556$	8.69059e18	+	5.01752e18i	0.529085	+	0.305468i
$557$	1.21140e18	−	2.09821e18i	0.0728286	−	0.126143i	−0.827311	−	0.561744i	$-0.810131\pi$
$557$	1.21140e18	−	2.09821e18i	0.0728286	−	0.126143i	0.900140	+	0.435601i	$0.143464\pi$
$558$	−1.24941e18	+	7.21347e17i	−0.0741763	+	0.0428257i
$559$		−	1.25024e18i		−	0.0733014i
$560$	3.86851e17	−	4.29070e18i	0.0223989	−	0.248435i
$561$	4.39047e18			0.251056
$562$	−1.16650e18	−	2.02044e18i	−0.0658765	−	0.114101i
$563$	2.37837e19	+	1.37316e19i	1.32654	+	0.765880i	0.984763	−	0.173900i	$-0.0556368\pi$
$563$	2.37837e19	+	1.37316e19i	1.32654	+	0.765880i	0.341780	+	0.939780i	$0.388970\pi$
$564$	4.79528e18	−	8.30567e18i	0.264156	−	0.457531i
$565$	9.99771e18	−	5.77218e18i	0.543953	−	0.314051i
$566$			6.09696e18i			0.327641i
$567$	−3.55398e18	−	3.20428e17i	−0.188640	−	0.0170078i
$568$	−2.49028e18			−0.130560
$569$	6.36025e18	+	1.10163e19i	0.329373	+	0.570491i	0.982388	−	0.186855i	$-0.0598293\pi$
$569$	6.36025e18	+	1.10163e19i	0.329373	+	0.570491i	−0.653015	+	0.757345i	$0.726496\pi$
$570$	−4.07749e18	−	2.35414e18i	−0.208578	−	0.120423i
$571$	−4.13724e18	+	7.16590e18i	−0.209054	+	0.362091i	−0.951417	−	0.307906i	$-0.900372\pi$
$571$	−4.13724e18	+	7.16590e18i	−0.209054	+	0.362091i	0.742363	+	0.669998i	$0.233705\pi$
$572$	7.50986e17	−	4.33582e17i	0.0374852	−	0.0216421i
$573$			2.14245e19i			1.05640i
$574$	1.12206e19	+	7.90115e18i	0.546553	+	0.384864i
$575$	9.26366e16			0.00445767
$576$	−6.96613e17	−	1.20657e18i	−0.0331157	−	0.0573581i
$577$	2.97960e19	+	1.72028e19i	1.39936	+	0.807918i	0.994325	−	0.106385i	$-0.0339277\pi$
$577$	2.97960e19	+	1.72028e19i	1.39936	+	0.807918i	0.405030	+	0.914303i	$0.367261\pi$
$578$	3.66007e18	−	6.33943e18i	0.169822	−	0.294141i
$579$	1.05603e19	−	6.09699e18i	0.484090	−	0.279489i
$580$			1.75944e19i			0.796855i
$581$	−3.88405e19	+	1.79864e19i	−1.73801	+	0.804845i
$582$	7.05811e18			0.312052
$583$	5.93870e18	+	1.02861e19i	0.259425	+	0.449337i
$584$	−6.74777e18	−	3.89583e18i	−0.291253	−	0.168155i
$585$	−1.05637e18	+	1.82968e18i	−0.0450531	+	0.0780342i
$586$	−2.40121e19	+	1.38634e19i	−1.01192	+	0.584232i
$587$		−	1.72472e19i		−	0.718213i	−0.933297	−	0.359106i	$-0.883082\pi$
$587$		−	1.72472e19i		−	0.718213i	0.933297	−	0.359106i	$-0.116918\pi$
$588$	1.49025e18	−	8.19724e18i	0.0613220	−	0.337308i
$589$	−2.79903e18			−0.113815
$590$	1.59263e18	+	2.75851e18i	0.0639957	+	0.110844i
$591$	−8.44283e18	−	4.87447e18i	−0.335255	−	0.193560i
$592$	6.12298e18	−	1.06053e19i	0.240276	−	0.416171i
$593$	3.97886e19	−	2.29719e19i	1.54303	−	0.890871i	0.544389	−	0.838833i	$-0.316762\pi$
$593$	3.97886e19	−	2.29719e19i	1.54303	−	0.890871i	0.998645	−	0.0520383i	$-0.0165718\pi$
$594$			9.82984e18i			0.376740i
$595$	−7.97965e18	−	1.72315e19i	−0.302249	−	0.652687i
$596$	−6.82415e18			−0.255461
$597$	−2.18274e18	−	3.78061e18i	−0.0807572	−	0.139876i
$598$	2.85590e18	+	1.64886e18i	0.104432	+	0.0602941i
$599$	−5.37158e18	+	9.30385e18i	−0.194140	+	0.336260i	−0.946618	−	0.322357i	$-0.895525\pi$
$599$	−5.37158e18	+	9.30385e18i	−0.194140	+	0.336260i	0.752479	+	0.658617i	$0.228858\pi$
$600$	2.61830e16	−	1.51168e16i	0.000935321	−	0.000540008i
$601$			2.74940e19i			0.970772i	0.874300	+	0.485386i	$0.161321\pi$
$601$			2.74940e19i			0.970772i	−0.874300	+	0.485386i	$0.838679\pi$
$602$	−5.01688e18	+	7.12458e18i	−0.175089	+	0.248647i
$603$	3.68984e18			0.127288
$604$	7.88619e18	+	1.36593e19i	0.268911	+	0.465768i
$605$	−1.90225e19	−	1.09826e19i	−0.641178	−	0.370185i
$606$	1.22948e19	−	2.12952e19i	0.409649	−	0.709533i
$607$	−8.27907e18	+	4.77992e18i	−0.272685	+	0.157435i	−0.630107	−	0.776508i	$-0.716989\pi$
$607$	−8.27907e18	+	4.77992e18i	−0.272685	+	0.157435i	0.357422	+	0.933943i	$0.383656\pi$
$608$		−	2.70306e18i		−	0.0880096i
$609$	−3.05545e18	+	3.38891e19i	−0.0983453	+	1.09078i
$610$	1.91194e19			0.608366
$611$	−4.17475e18	−	7.23089e18i	−0.131323	−	0.227459i
$612$	−5.31837e18	−	3.07056e18i	−0.165394	−	0.0954901i
$613$	−2.43865e19	+	4.22386e19i	−0.749766	+	1.29863i	0.198168	+	0.980168i	$0.436501\pi$
$613$	−2.43865e19	+	4.22386e19i	−0.749766	+	1.29863i	−0.947935	+	0.318465i	$0.896833\pi$
$614$	1.06845e19	−	6.16871e18i	0.324771	−	0.187506i
$615$		−	2.15211e19i		−	0.646754i
$616$	−6.01938e18	−	5.42709e17i	−0.178849	−	0.0161251i
$617$	6.60776e18			0.194114			0.0970572	−	0.995279i	$-0.469057\pi$
$617$	6.60776e18			0.194114			0.0970572	+	0.995279i	$0.469057\pi$
$618$	7.40346e18	+	1.28232e19i	0.215038	+	0.372457i
$619$	−7.83336e18	−	4.52259e18i	−0.224964	−	0.129883i	0.383283	−	0.923631i	$-0.374794\pi$
$619$	−7.83336e18	−	4.52259e18i	−0.224964	−	0.129883i	−0.608247	+	0.793748i	$0.708127\pi$
$620$	−2.00820e18	+	3.47831e18i	−0.0570251	+	0.0987703i
$621$	−3.23734e19	+	1.86908e19i	−0.908966	+	0.524792i
$622$		−	3.73414e19i		−	1.03671i
$623$	1.75030e19	+	1.23250e19i	0.480503	+	0.338354i
$624$	1.07626e18			0.0292164
$625$	1.85431e19	+	3.21176e19i	0.497763	+	0.862150i
$626$	−3.04180e19	−	1.75619e19i	−0.807441	−	0.466176i
$627$	−3.30259e18	+	5.72026e18i	−0.0866926	+	0.150156i
$628$	2.59953e19	−	1.50084e19i	0.674803	−	0.389598i
$629$		−	5.39783e19i		−	1.38568i
$630$	1.33618e19	−	6.18763e18i	0.339219	−	0.157087i
$631$	−5.48595e19			−1.37736			−0.688678	−	0.725067i	$-0.741809\pi$
$631$	−5.48595e19			−1.37736			−0.688678	+	0.725067i	$0.741809\pi$
$632$	−8.63104e18	−	1.49494e19i	−0.214311	−	0.371197i
$633$	3.03945e19	+	1.75483e19i	0.746395	+	0.430931i
$634$	1.83541e19	−	3.17902e19i	0.445767	−	0.772090i
$635$	5.42503e19	−	3.13214e19i	1.30312	−	0.752359i
$636$			1.47414e19i			0.350219i
$637$	−5.53168e18	−	4.69183e18i	−0.129981	−	0.110247i
$638$	2.46830e19			0.573659
$639$	−4.25584e18	−	7.37133e18i	−0.0978317	−	0.169449i
$640$	−3.35905e18	−	1.93935e18i	−0.0763759	−	0.0440956i
$641$	4.55332e18	−	7.88659e18i	0.102405	−	0.177371i	−0.810270	−	0.586057i	$-0.800679\pi$
$641$	4.55332e18	−	7.88659e18i	0.102405	−	0.177371i	0.912675	+	0.408686i	$0.134013\pi$
$642$	−9.66710e18	+	5.58131e18i	−0.215056	+	0.124163i
$643$		−	4.79964e19i		−	1.05617i	−0.849193	−	0.528083i	$-0.822911\pi$
$643$		−	4.79964e19i		−	1.05617i	0.849193	−	0.528083i	$-0.177089\pi$
$644$	−9.65811e18	−	2.08560e19i	−0.210228	−	0.453974i
$645$	1.36650e19			0.294233
$646$	−5.95733e18	−	1.03184e19i	−0.126889	−	0.219778i
$647$	−5.25281e19	−	3.03271e19i	−1.10678	−	0.639001i	−0.168788	−	0.985652i	$-0.553985\pi$
$647$	−5.25281e19	−	3.03271e19i	−1.10678	−	0.639001i	−0.937994	+	0.346652i	$0.887319\pi$
$648$	−1.60636e18	+	2.78229e18i	−0.0334824	+	0.0579933i
$649$	3.86989e18	−	2.23428e18i	0.0797968	−	0.0460707i
$650$		−	2.63212e16i		−	0.000536923i
$651$	−4.47209e18	+	6.35091e18i	−0.0902492	+	0.128165i
$652$	−4.73386e19			−0.945111
$653$	1.95657e19	+	3.38888e19i	0.386459	+	0.669367i	0.991970	−	0.126470i	$-0.0403647\pi$
$653$	1.95657e19	+	3.38888e19i	0.386459	+	0.669367i	−0.605511	+	0.795837i	$0.707031\pi$
$654$	−7.74397e18	−	4.47098e18i	−0.151328	−	0.0873693i
$655$	−2.49072e19	+	4.31405e19i	−0.481544	+	0.834058i
$656$	1.07001e19	−	6.17772e18i	0.204674	−	0.118168i
$657$		−	2.66316e19i		−	0.504010i
$658$	−5.22548e18	+	5.79577e19i	−0.0978465	+	1.08525i
$659$	−2.98014e19			−0.552127			−0.276064	−	0.961139i	$-0.589030\pi$
$659$	−2.98014e19			−0.552127			−0.276064	+	0.961139i	$0.589030\pi$
$660$	4.73898e18	+	8.20816e18i	0.0868716	+	0.150466i
$661$	−8.37369e19	−	4.83455e19i	−1.51882	−	0.876891i	−0.999754	−	0.0221573i	$-0.992947\pi$
$661$	−8.37369e19	−	4.83455e19i	−1.51882	−	0.876891i	−0.519066	−	0.854734i	$-0.673720\pi$
$662$	−8.88839e18	+	1.53951e19i	−0.159521	+	0.276298i
$663$	4.10843e18	−	2.37200e18i	0.0729594	−	0.0421231i
$664$			3.85366e19i			0.677168i
$665$	2.84531e19	+	2.56533e18i	0.494740	+	0.0446059i
$666$	4.18562e19			0.720178
$667$	4.69332e19	+	8.12907e19i	0.799096	+	1.38408i
$668$	−3.67750e19	−	2.12320e19i	−0.619608	−	0.357731i
$669$	4.49818e18	−	7.79108e18i	0.0749988	−	0.129902i
$670$	8.89615e18	−	5.13619e18i	0.146784	−	0.0847457i
$671$		−	2.68224e19i		−	0.437965i
$672$	−6.13315e18	−	4.31875e18i	−0.0991057	−	0.0697868i
$673$	9.26340e19			1.48137			0.740687	−	0.671850i	$-0.234500\pi$
$673$	9.26340e19			1.48137			0.740687	+	0.671850i	$0.234500\pi$
$674$	1.52117e19	+	2.63474e19i	0.240745	+	0.416983i
$675$	2.58393e17	+	1.49184e17i	0.00404720	+	0.00233665i
$676$	−1.56590e19	+	2.71222e19i	−0.242738	+	0.420434i
$677$	1.89152e19	−	1.09207e19i	0.290195	−	0.167544i	−0.347835	−	0.937556i	$-0.613083\pi$
$677$	1.89152e19	−	1.09207e19i	0.290195	−	0.167544i	0.638030	+	0.770012i	$0.279750\pi$
$678$		−	2.01007e19i		−	0.305213i
$679$	−3.88619e19	+	1.79963e19i	−0.584031	+	0.270456i
$680$	−1.70967e19			−0.254302
$681$	−4.27857e18	−	7.41071e18i	−0.0629897	−	0.109101i
$682$	4.87968e18	+	2.81728e18i	0.0711051	+	0.0410525i
$683$	4.69498e19	−	8.13195e19i	0.677156	−	1.17287i	−0.298677	−	0.954354i	$-0.596545\pi$
$683$	4.69498e19	−	8.13195e19i	0.677156	−	1.17287i	0.975834	−	0.218515i	$-0.0701212\pi$
$684$	8.00116e18	−	4.61947e18i	0.114225	−	0.0659477i
$685$			8.01080e19i			1.13199i
$686$	1.26956e19	+	4.89337e19i	0.177576	+	0.684446i
$687$	2.90769e19			0.402579
$688$	3.92258e18	+	6.79411e18i	0.0537592	+	0.0931137i
$689$	1.11144e19	+	6.41691e18i	0.150783	+	0.0870546i
$690$	−1.80217e19	+	3.12146e19i	−0.242021	+	0.419192i
$691$	−7.47944e19	+	4.31826e19i	−0.994312	+	0.574066i	−0.906560	−	0.422076i	$-0.861302\pi$
$691$	−7.47944e19	+	4.31826e19i	−0.994312	+	0.574066i	−0.0877517	+	0.996142i	$0.527968\pi$
$692$			1.79682e19i			0.236462i
$693$	−8.68056e18	−	1.87451e19i	−0.113088	−	0.244205i
$694$	8.92223e17			0.0115069
$695$	4.77441e19	+	8.26951e19i	0.609573	+	1.05581i
$696$	2.65306e19	+	1.53174e19i	0.335338	+	0.193607i
$697$	2.72304e19	−	4.71645e19i	0.340741	−	0.590181i
$698$	−2.64431e19	+	1.52669e19i	−0.327585	+	0.189131i
$699$		−	7.12059e19i		−	0.873325i
$700$	−1.05620e17	+	1.49993e17i	−0.00128250	+	0.00182131i
$701$	−1.70829e19			−0.205369			−0.102684	−	0.994714i	$-0.532743\pi$
$701$	−1.70829e19			−0.205369			−0.102684	+	0.994714i	$0.532743\pi$
$702$	5.31069e18	+	9.19839e18i	0.0632108	+	0.109484i
$703$	7.03272e19	+	4.06034e19i	0.828774	+	0.478493i
$704$	−2.72069e18	+	4.71237e18i	−0.0317446	+	0.0549833i
$705$	7.90324e19	−	4.56294e19i	0.913022	−	0.527134i
$706$			1.24560e19i			0.142477i
$707$	−1.33978e19	+	1.48599e20i	−0.151739	+	1.68299i
$708$	5.54607e18			0.0621946
$709$	−4.57744e19	−	7.92835e19i	−0.508275	−	0.880358i	−0.999954	−	0.00958151i	$-0.996950\pi$
$709$	−4.57744e19	−	7.92835e19i	−0.508275	−	0.880358i	0.491679	−	0.870776i	$-0.336383\pi$
$710$	−2.05215e19	−	1.18481e19i	−0.225632	−	0.130269i
$711$	2.95006e19	−	5.10965e19i	0.321176	−	0.556293i
$712$	1.66911e19	−	9.63663e18i	0.179939	−	0.103888i
$713$			2.14275e19i			0.228742i
$714$	−3.29303e19	−	2.96900e18i	−0.348103	−	0.0313851i
$715$	8.25148e18			0.0863753
$716$	−2.28225e19	−	3.95298e19i	−0.236577	−	0.409763i
$717$	−7.75519e19	−	4.47746e19i	−0.796083	−	0.459619i
$718$	−4.92585e18	+	8.53183e18i	−0.0500738	+	0.0867304i
$719$	1.23257e20	−	7.11622e19i	1.24082	−	0.716386i	0.271557	−	0.962422i	$-0.412462\pi$
$719$	1.23257e20	−	7.11622e19i	1.24082	−	0.716386i	0.969261	+	0.246036i	$0.0791282\pi$
$720$		−	1.32572e19i		−	0.132168i
$721$	−7.34592e19	−	5.17274e19i	−0.725269	−	0.510709i
$722$	−5.43930e19			−0.531842
$723$	−1.48488e19	−	2.57188e19i	−0.143788	−	0.249048i
$724$	8.19599e19	+	4.73196e19i	0.786016	+	0.453807i
$725$	3.74604e17	−	6.48834e17i	0.00355801	−	0.00616265i
$726$	−3.31213e19	+	1.91226e19i	−0.311567	+	0.179883i
$727$			6.69549e19i			0.623795i	0.950116	+	0.311897i	$0.100964\pi$
$727$			6.69549e19i			0.623795i	−0.950116	+	0.311897i	$0.899036\pi$
$728$	−5.92591e18	+	2.74420e18i	−0.0546808	+	0.0253219i
$729$	−8.96813e19			−0.819614
$730$	−3.70706e19	−	6.42082e19i	−0.335560	−	0.581207i
$731$	2.99474e19	+	1.72901e19i	0.268496	+	0.155016i
$732$	1.66450e19	−	2.88300e19i	0.147811	−	0.256016i
$733$	−1.21753e20	+	7.02942e19i	−1.07091	+	0.618289i	−0.928429	−	0.371509i	$-0.878841\pi$
$733$	−1.21753e20	+	7.02942e19i	−1.07091	+	0.618289i	−0.142479	+	0.989798i	$0.545507\pi$
$734$		−	1.36489e20i		−	1.18912i
$735$	5.12809e19	−	6.04604e19i	0.442532	−	0.521746i
$736$	−2.06928e19			−0.176879
$737$	−7.20551e18	−	1.24803e19i	−0.0610087	−	0.105670i
$738$	3.65726e19	+	2.11152e19i	0.306733	+	0.177093i
$739$	8.48650e18	−	1.46991e19i	0.0705047	−	0.122118i	−0.828618	−	0.559815i	$-0.810872\pi$
$739$	8.48650e18	−	1.46991e19i	0.0705047	−	0.122118i	0.899123	+	0.437697i	$0.144206\pi$
$740$	1.00915e20	−	5.82630e19i	0.830485	−	0.479481i
$741$			7.13706e18i			0.0581824i
$742$	−3.75868e19	−	8.11662e19i	−0.303534	−	0.655462i
$743$	−2.94222e19			−0.235371			−0.117686	−	0.993051i	$-0.537548\pi$
$743$	−2.94222e19			−0.235371			−0.117686	+	0.993051i	$0.537548\pi$
$744$	3.49662e18	+	6.05632e18i	0.0277101	+	0.0479953i
$745$	−5.62354e19	−	3.24675e19i	−0.441485	−	0.254891i
$746$	−5.95714e19	+	1.03181e20i	−0.463304	+	0.802466i
$747$	−1.14070e20	+	6.58582e19i	−0.878874	+	0.507418i
$748$			2.39847e19i			0.183073i
$749$	3.89961e19	−	5.53792e19i	0.294882	−	0.418769i
$750$	6.48623e19			0.485918
$751$	−5.54318e19	−	9.60106e19i	−0.411414	−	0.712590i	0.583631	−	0.812019i	$-0.301632\pi$
$751$	−5.54318e19	−	9.60106e19i	−0.411414	−	0.712590i	−0.995045	+	0.0994292i	$0.968298\pi$
$752$	4.53731e19	+	2.61962e19i	0.333637	+	0.192625i
$753$	−3.29511e18	+	5.70731e18i	−0.0240052	+	0.0415783i
$754$	2.30974e19	−	1.33353e19i	0.166711	−	0.0962506i
$755$			1.50082e20i			1.07325i
$756$	6.64732e18	−	7.37278e19i	0.0470971	−	0.522371i
$757$	−1.67563e20			−1.17627			−0.588137	−	0.808762i	$-0.700138\pi$
$757$	−1.67563e20			−1.17627			−0.588137	+	0.808762i	$0.700138\pi$
$758$	5.07063e18	+	8.78259e18i	0.0352677	+	0.0610855i
$759$	4.37905e19	+	2.52825e19i	0.301778	+	0.174232i
$760$	1.28604e19	−	2.22749e19i	0.0878133	−	0.152097i
$761$	6.92283e19	−	3.99690e19i	0.468372	−	0.270415i	−0.247186	−	0.968968i	$-0.579506\pi$
$761$	6.92283e19	−	3.99690e19i	0.468372	−	0.270415i	0.715558	+	0.698553i	$0.246172\pi$
$762$		−	1.09072e20i		−	0.731185i
$763$	5.40381e19	+	4.87209e18i	0.358945	+	0.0323626i
$764$	−1.17040e20			−0.770337
$765$	−2.92179e19	−	5.06068e19i	−0.190554	−	0.330050i
$766$	9.88936e19	+	5.70962e19i	0.639097	+	0.368983i
$767$	2.41419e18	−	4.18151e18i	0.0154598	−	0.0267772i
$768$	−5.84866e18	+	3.37673e18i	−0.0371132	+	0.0214273i
$769$			1.28830e19i			0.0810091i	0.999179	+	0.0405045i	$0.0128965\pi$
$769$			1.28830e19i			0.0810091i	−0.999179	+	0.0405045i	$0.987103\pi$
$770$	−4.70215e19	−	3.31109e19i	−0.292996	−	0.206317i
$771$	−8.68246e19			−0.536120
$772$	3.33073e19	+	5.76899e19i	0.203806	+	0.353003i
$773$	−1.28249e19	−	7.40446e18i	−0.0777674	−	0.0448991i	0.460612	−	0.887602i	$-0.347630\pi$
$773$	−1.28249e19	−	7.40446e18i	−0.0777674	−	0.0448991i	−0.538379	+	0.842703i	$0.680963\pi$
$774$	−1.34072e19	+	2.32220e19i	−0.0805661	+	0.139545i
$775$	1.48114e17	−	8.55135e16i	0.000882030	−	0.000509240i
$776$			3.85578e19i			0.227552i
$777$	2.04492e20	−	9.46970e19i	1.19599	−	0.553846i
$778$	1.19078e20			0.690196
$779$	4.09664e19	+	7.09560e19i	0.235324	+	0.407593i
$780$	8.86911e18	+	5.12058e18i	0.0504915	+	0.0291513i
$781$	−1.66216e19	+	2.87894e19i	−0.0937810	+	0.162433i
$782$	−7.89908e19	+	4.56054e19i	−0.441702	+	0.255017i
$783$			3.02328e20i			1.67551i
$784$	4.47808e19	+	8.14107e18i	0.245968	+	0.0447166i
$785$	2.85624e20			1.55492
$786$	4.33676e19	+	7.51149e19i	0.233996	+	0.405292i
$787$	1.53142e20	+	8.84166e19i	0.818976	+	0.472836i	0.850063	−	0.526680i	$-0.176564\pi$
$787$	1.53142e20	+	8.84166e19i	0.818976	+	0.472836i	−0.0310870	+	0.999517i	$0.509897\pi$
$788$	2.66288e19	−	4.61224e19i	0.141146	−	0.244472i
$789$	−1.97768e20	+	1.14181e20i	−1.03900	+	0.599868i
$790$		−	1.64257e20i		−	0.855331i
$791$	5.12515e19	+	1.10674e20i	0.264528	+	0.571230i
$792$	−1.85984e19			−0.0951479
$793$	−1.44911e19	−	2.50993e19i	−0.0734834	−	0.127277i
$794$	−9.57441e18	−	5.52779e18i	−0.0481247	−	0.0277848i
$795$	−7.01358e19	+	1.21479e20i	−0.349438	+	0.605244i
$796$	2.06531e19	−	1.19241e19i	0.101999	−	0.0588890i
$797$			1.54278e20i			0.755259i	0.925957	+	0.377629i	$0.123261\pi$
$797$			1.54278e20i			0.755259i	−0.925957	+	0.377629i	$0.876739\pi$
$798$	2.86390e19	−	4.06709e19i	0.138975	−	0.197362i
$799$	2.30937e20			1.11088
$800$	8.25815e16	+	1.43035e17i	0.000393779	+	0.000682045i
$801$	5.70496e19	+	3.29376e19i	0.269665	+	0.155691i
$802$	−3.62085e19	+	6.27149e19i	−0.169664	+	0.293867i
$803$	−9.00770e19	+	5.20060e19i	−0.418413	+	0.241571i
$804$		−	1.78860e19i		−	0.0823606i
$805$	1.96385e19	−	2.17818e20i	0.0896474	−	0.994311i
$806$	6.08829e18			0.0275518
$807$	5.71176e18	+	9.89306e18i	0.0256245	+	0.0443829i
$808$	1.16333e20	+	6.71651e19i	0.517398	+	0.298720i
$809$	4.14065e19	−	7.17182e19i	0.182570	−	0.316220i	−0.760185	−	0.649707i	$-0.774892\pi$
$809$	4.14065e19	−	7.17182e19i	0.182570	−	0.316220i	0.942755	+	0.333486i	$0.108225\pi$
$810$	−2.64748e19	+	1.52853e19i	−0.115728	+	0.0668156i
$811$			1.22037e20i			0.528868i	0.964404	+	0.264434i	$0.0851851\pi$
$811$			1.22037e20i			0.528868i	−0.964404	+	0.264434i	$0.914815\pi$
$812$	−1.85133e20	−	1.66916e19i	−0.795410	−	0.0717144i
$813$	−2.30268e20			−0.980842
$814$	−8.17366e19	−	1.41572e20i	−0.345180	−	0.597869i
$815$	−3.90101e20	−	2.25225e20i	−1.63333	−	0.943003i
$816$	−1.48841e19	+	2.57800e19i	−0.0617862	+	0.107017i
$817$	−4.50539e19	+	2.60119e19i	−0.185429	+	0.107058i
$818$			7.04885e19i			0.287637i
$819$	−1.82502e19	−	1.28511e19i	−0.0738380	−	0.0519942i
$820$	1.17568e20			0.471619
$821$	−1.04812e20	−	1.81540e20i	−0.416879	−	0.722056i	0.578744	−	0.815509i	$-0.303543\pi$
$821$	−1.04812e20	−	1.81540e20i	−0.416879	−	0.722056i	−0.995624	+	0.0934527i	$0.970210\pi$
$822$	1.20794e20	+	6.97407e19i	0.476370	+	0.275032i
$823$	1.46097e20	−	2.53047e20i	0.571271	−	0.989471i	−0.425164	−	0.905116i	$-0.639784\pi$
$823$	1.46097e20	−	2.53047e20i	0.571271	−	0.989471i	0.996436	−	0.0843549i	$-0.0268829\pi$
$824$	−7.00518e19	+	4.04444e19i	−0.271599	+	0.156808i
$825$		−	4.03592e17i		−	0.00155155i
$826$	−3.05366e19	+	1.41410e19i	−0.116402	+	0.0539040i
$827$	−3.25414e17			−0.00122998			−0.000614989	−	1.00000i	$-0.500196\pi$
$827$	−3.25414e17			−0.00122998			−0.000614989		1.00000i	$0.500196\pi$
$828$	−3.53636e19	−	6.12516e19i	−0.132539	−	0.229565i
$829$	−3.06875e19	−	1.77174e19i	−0.114046	−	0.0658445i	0.441892	−	0.897068i	$-0.354307\pi$
$829$	−3.06875e19	−	1.77174e19i	−0.114046	−	0.0658445i	−0.555938	+	0.831224i	$0.687641\pi$
$830$	−1.83347e20	+	3.17566e20i	−0.675658	+	1.17027i
$831$	−4.64412e19	+	2.68128e19i	−0.169706	+	0.0979795i
$832$			5.87953e18i			0.0213049i
$833$	1.88884e20	−	6.76164e19i	0.678704	−	0.242961i
$834$	1.66261e20			0.592417
$835$	−2.02033e20	−	3.49931e20i	−0.713866	−	1.23645i
$836$	−3.12492e19	−	1.80418e19i	−0.109495	−	0.0632171i
$837$	−3.45072e19	+	5.97683e19i	−0.119904	+	0.207679i
$838$	−8.65567e19	+	4.99735e19i	−0.298258	+	0.172199i
$839$		−	3.67704e19i		−	0.125651i	−0.998025	−	0.0628253i	$-0.979989\pi$
$839$		−	3.67704e19i		−	0.125651i	0.998025	−	0.0628253i	$-0.0200111\pi$
$840$	−2.99936e19	−	6.47692e19i	−0.101642	−	0.219489i
$841$	4.61596e20			1.55128
$842$	−1.83659e20	−	3.18106e20i	−0.612106	−	1.06020i
$843$	−3.34747e19	−	1.93266e19i	−0.110643	−	0.0638797i
$844$	−9.58645e19	+	1.66042e20i	−0.314240	+	0.544279i
$845$	−2.58080e20	+	1.49003e20i	−0.838993	+	0.484393i
$846$			1.79075e20i			0.577354i
$847$	1.33608e20	−	1.89740e20i	0.427217	−	0.606700i
$848$	−8.05310e19			−0.255383
$849$	5.05074e19	+	8.74813e19i	0.158855	+	0.275145i
$850$	6.30477e17	+	3.64006e17i	0.00196670	+	0.00113547i
$851$	3.10833e20	−	5.38379e20i	0.961658	−	1.66564i
$852$	−3.57314e19	+	2.06295e19i	−0.109641	+	0.0633013i
$853$		−	4.14427e20i		−	1.26126i	−0.776083	−	0.630631i	$-0.782796\pi$
$853$		−	4.14427e20i		−	1.26126i	0.776083	−	0.630631i	$-0.217204\pi$
$854$	−1.81383e19	+	2.01178e20i	−0.0547509	+	0.607262i
$855$	8.79129e19			0.263202
$856$	−3.04901e19	−	5.28105e19i	−0.0905406	−	0.156821i
$857$	1.60214e20	+	9.24998e19i	0.471884	+	0.272443i	0.717028	−	0.697044i	$-0.245502\pi$
$857$	1.60214e20	+	9.24998e19i	0.471884	+	0.272443i	−0.245144	+	0.969487i	$0.578835\pi$
$858$	7.18361e18	−	1.24424e19i	0.0209861	−	0.0363490i
$859$	1.26235e20	−	7.28820e19i	0.365787	−	0.211187i	−0.305829	−	0.952086i	$-0.598934\pi$
$859$	1.26235e20	−	7.28820e19i	0.365787	−	0.211187i	0.671616	+	0.740899i	$0.265600\pi$
$860$			7.46505e19i			0.214557i
$861$	2.26450e20	+	2.04168e19i	0.645581	+	0.0582057i
$862$	−3.68804e19			−0.104290
$863$	4.09474e19	+	7.09229e19i	0.114855	+	0.198935i	0.917722	−	0.397224i	$-0.130026\pi$
$863$	4.09474e19	+	7.09229e19i	0.114855	+	0.198935i	−0.802867	+	0.596159i	$0.796693\pi$
$864$	−5.77190e19	−	3.33241e19i	−0.160591	−	0.0927175i
$865$	−8.54880e19	+	1.48070e20i	−0.235935	+	0.408652i
$866$	3.59475e20	−	2.07543e20i	0.984110	−	0.568176i
$867$		−	1.21280e20i		−	0.329350i
$868$	−3.46944e19	−	2.44306e19i	−0.0934591	−	0.0658106i
$869$	−2.30434e20			−0.615756
$870$	1.45753e20	+	2.52451e20i	0.386351	+	0.669179i
$871$	−1.34853e19	−	7.78572e18i	−0.0354595	−	0.0204725i
$872$	2.44246e19	−	4.23046e19i	0.0637106	−	0.110350i
$873$	−1.14133e20	+	6.58945e19i	−0.295332	+	0.170510i
$874$		−	1.37221e20i		−	0.352241i
$875$	−3.57131e20	+	1.65382e20i	−0.909435	+	0.421145i
$876$	−1.29092e20			−0.326116
$877$	3.88575e19	+	6.73032e19i	0.0973819	+	0.168670i	0.910600	−	0.413288i	$-0.135620\pi$
$877$	3.88575e19	+	6.73032e19i	0.0973819	+	0.168670i	−0.813218	+	0.581959i	$0.802287\pi$
$878$	1.37620e20	+	7.94548e19i	0.342152	+	0.197542i
$879$	−2.29689e20	+	3.97833e20i	−0.566523	+	0.981247i
$880$	−4.48404e19	+	2.58886e19i	−0.109721	+	0.0633476i
$881$		−	1.94272e20i		−	0.471606i	−0.971801	−	0.235803i	$-0.924228\pi$
$881$		−	1.94272e20i		−	0.471606i	0.971801	−	0.235803i	$-0.0757720\pi$
$882$	5.24316e19	+	1.46466e20i	0.126274	+	0.352741i
$883$	−3.31822e20			−0.792830			−0.396415	−	0.918071i	$-0.629746\pi$
$883$	−3.31822e20			−0.792830			−0.396415	+	0.918071i	$0.629746\pi$
$884$	1.29580e19	+	2.24440e19i	0.0307166	+	0.0532027i
$885$	4.57032e19	+	2.63867e19i	0.107484	+	0.0620559i
$886$	−1.88035e19	+	3.25686e19i	−0.0438735	+	0.0759911i
$887$	−1.92743e20	+	1.11280e20i	−0.446184	+	0.257604i	−0.706217	−	0.707995i	$-0.749600\pi$
$887$	−1.92743e20	+	1.11280e20i	−0.446184	+	0.257604i	0.260033	+	0.965600i	$0.416266\pi$
$888$		−	2.02891e20i		−	0.465986i
$889$	2.78105e20	+	6.00548e20i	0.633718	+	1.36847i
$890$	1.83394e20			0.414625
$891$	2.14435e19	+	3.71412e19i	0.0481008	+	0.0833130i
$892$	4.25619e19	+	2.45731e19i	0.0947256	+	0.0546899i
$893$	−1.73715e20	+	3.00884e20i	−0.383599	+	0.664414i
$894$	−9.79153e19	+	5.65314e19i	−0.214530	+	0.123859i
$895$		−	4.34334e20i		−	0.944197i
$896$	2.35929e19	−	3.35048e19i	0.0508892	−	0.0722689i
$897$	5.46366e19			0.116933
$898$	−3.10739e20	−	5.38215e20i	−0.659874	−	1.14294i
$899$	1.50080e20	+	8.66487e19i	0.316231	+	0.182576i
$900$	−2.82260e17	+	4.88889e17i	−0.000590136	+	0.00102215i
$901$	−3.07411e20	+	1.77484e20i	−0.637744	+	0.368202i
$902$		−	1.64935e20i		−	0.339520i
$903$	−1.29638e19	+	1.43786e20i	−0.0264800	+	0.293699i
$904$	1.09808e20			0.222564
$905$	4.50268e20	+	7.79888e20i	0.905589	+	1.56853i
$906$	2.26308e20	+	1.30659e20i	0.451650	+	0.260760i
$907$	2.11304e20	−	3.65990e20i	0.418463	−	0.724800i	−0.577322	−	0.816517i	$-0.695902\pi$
$907$	2.11304e20	−	3.65990e20i	0.418463	−	0.724800i	0.995785	+	0.0917170i	$0.0292355\pi$
$908$	4.04840e19	−	2.33735e19i	0.0795578	−	0.0459327i
$909$			4.59136e20i			0.895352i
$910$	−6.18895e19	−	5.57997e18i	−0.119764	−	0.0107980i
$911$	−1.01733e20			−0.195359			−0.0976793	−	0.995218i	$-0.531142\pi$
$911$	−1.01733e20			−0.195359			−0.0976793	+	0.995218i	$0.531142\pi$
$912$	−2.23922e19	−	3.87844e19i	−0.0426710	−	0.0739083i
$913$	4.45510e20	+	2.57215e20i	0.842485	+	0.486409i
$914$	2.45357e20	−	4.24971e20i	0.460442	−	0.797509i
$915$	2.74331e20	−	1.58385e20i	0.510891	−	0.294963i
$916$			1.58844e20i			0.293564i
$917$	−4.30305e20	−	3.03006e20i	−0.789208	−	0.555733i
$918$	−2.93775e20			−0.534707
$919$	2.52902e20	+	4.38039e20i	0.456819	+	0.791233i	0.998791	−	0.0491634i	$-0.0156555\pi$
$919$	2.52902e20	+	4.38039e20i	0.456819	+	0.791233i	−0.541972	+	0.840396i	$0.682322\pi$
$920$	−1.70522e20	−	9.84510e19i	−0.305679	−	0.176484i
$921$	1.02204e20	−	1.77022e20i	0.181823	−	0.314926i
$922$	4.39765e20	−	2.53898e20i	0.776433	−	0.448274i
$923$			3.59200e19i			0.0629397i
$924$	−9.08640e19	+	4.20777e19i	−0.158011	+	0.0731725i
$925$	−4.96193e18			−0.00856364
$926$	3.84113e20	+	6.65303e20i	0.657934	+	1.13957i
$927$	−2.39434e20	−	1.38237e20i	−0.407032	−	0.235000i
$928$	−8.36777e19	+	1.44934e20i	−0.141180	+	0.244531i
$929$	2.67492e20	−	1.54436e20i	0.447920	−	0.258606i	−0.259032	−	0.965869i	$-0.583403\pi$
$929$	2.67492e20	−	1.54436e20i	0.447920	−	0.258606i	0.706951	+	0.707262i	$0.250070\pi$
$930$			6.65440e19i			0.110593i
$931$	−5.39861e19	+	2.96956e20i	−0.0890500	+	0.489829i
$932$	3.88991e20			0.636837
$933$	−3.09337e20	−	5.35787e20i	−0.502643	−	0.870604i
$934$	−5.03323e20	−	2.90594e20i	−0.811743	−	0.468660i
$935$	−1.14113e20	+	1.97650e20i	−0.182664	+	0.316384i
$936$	−1.74037e19	+	1.00480e19i	−0.0276509	+	0.0159643i
$937$			5.06993e20i			0.799512i	0.916621	+	0.399756i	$0.130905\pi$
$937$			5.06993e20i			0.799512i	−0.916621	+	0.399756i	$0.869095\pi$
$938$	4.56045e19	+	9.84800e19i	0.0713819	+	0.154144i
$939$	−5.81931e20			−0.904092
$940$	2.49269e20	+	4.31747e20i	0.384391	+	0.665785i
$941$	−3.86232e20	−	2.22991e20i	−0.591181	−	0.341319i	0.174383	−	0.984678i	$-0.444207\pi$
$941$	−3.86232e20	−	2.22991e20i	−0.591181	−	0.341319i	−0.765564	+	0.643359i	$0.777540\pi$
$942$	2.48660e20	−	4.30691e20i	0.377789	−	0.654349i
$943$	5.43192e20	−	3.13612e20i	0.819166	−	0.472946i
$944$			3.02977e19i			0.0453529i
$945$	4.05556e20	−	5.75938e20i	0.602598	−	0.855763i
$946$	1.04726e20			0.154461
$947$	3.01223e20	+	5.21734e20i	0.441000	+	0.763835i	0.997764	−	0.0668361i	$-0.0212905\pi$
$947$	3.01223e20	+	5.21734e20i	0.441000	+	0.763835i	−0.556764	+	0.830671i	$0.687957\pi$
$948$	−2.47682e20	−	1.43000e20i	−0.359946	−	0.207815i
$949$	−5.61937e19	+	9.73303e19i	−0.0810632	+	0.140406i
$950$	−9.48513e17	+	5.47624e17i	−0.00135825	+	0.000784183i
$951$		−	6.08182e20i		−	0.864510i
$952$	1.62194e19	−	1.79895e20i	0.0228863	−	0.253840i
$953$	−4.32972e20			−0.606470			−0.303235	−	0.952916i	$-0.598067\pi$
$953$	−4.32972e20			−0.606470			−0.303235	+	0.952916i	$0.598067\pi$
$954$	−1.37626e20	−	2.38375e20i	−0.191365	−	0.331453i
$955$	−9.64485e20	−	5.56846e20i	−1.33129	−	0.768619i
$956$	2.44600e20	−	4.23659e20i	0.335159	−	0.580512i
$957$	3.54161e20	−	2.04475e20i	0.481745	−	0.278135i
$958$		−	3.68094e19i		−	0.0497050i
$959$	−8.42915e20	−	7.59974e19i	−1.12993	−	0.101875i
$960$	−6.42623e19			−0.0855181
$961$	−3.58692e20	−	6.21273e20i	−0.473869	−	0.820765i
$962$	−1.52972e20	−	8.83183e19i	−0.200625	−	0.115831i
$963$	1.04214e20	−	1.80504e20i	0.135688	−	0.235019i
$964$	1.40499e20	−	8.11174e19i	0.181608	−	0.104852i
$965$			6.33869e20i			0.813408i
$966$	−3.11350e20	−	2.19242e20i	−0.396651	−	0.279308i
$967$	3.06464e20			0.387609			0.193804	−	0.981040i	$-0.437917\pi$
$967$	3.06464e20			0.387609			0.193804	+	0.981040i	$0.437917\pi$
$968$	−1.04465e20	−	1.80939e20i	−0.131173	−	0.227197i
$969$	−1.70956e20	−	9.87012e19i	−0.213116	−	0.123043i
$970$	−1.83448e20	+	3.17741e20i	−0.227044	+	0.393252i
$971$	8.91234e20	−	5.14554e20i	1.09511	−	0.632261i	0.160176	−	0.987088i	$-0.448794\pi$
$971$	8.91234e20	−	5.14554e20i	1.09511	−	0.632261i	0.934932	+	0.354827i	$0.115460\pi$
$972$		−	3.76704e20i		−	0.459554i
$973$	−9.15431e20	+	4.23922e20i	−1.10876	+	0.513448i
$974$	−6.61659e20			−0.795649
$975$	−2.18045e17	−	3.77666e17i	−0.000260324	−	0.000450895i
$976$	1.57496e20	+	9.09302e19i	0.186690	+	0.107785i
$977$	2.44710e20	−	4.23850e20i	0.287998	−	0.498828i	−0.685334	−	0.728229i	$-0.740344\pi$
$977$	2.44710e20	−	4.23850e20i	0.287998	−	0.498828i	0.973332	+	0.229402i	$0.0736769\pi$
$978$	−6.79231e20	+	3.92154e20i	−0.793680	+	0.458232i
$979$		−	2.57282e20i		−	0.298490i
$980$	3.30289e20	+	2.80143e20i	0.380463	+	0.322699i
$981$	1.66964e20			0.190959
$982$	1.79908e20	+	3.11610e20i	0.204301	+	0.353860i
$983$	−1.07196e21	−	6.18897e20i	−1.20866	−	0.697820i	−0.246194	−	0.969221i	$-0.579180\pi$
$983$	−1.07196e21	−	6.18897e20i	−1.20866	−	0.697820i	−0.962467	+	0.271400i	$0.912513\pi$
$984$	1.02353e20	−	1.77280e20i	0.114587	−	0.198470i
$985$	4.38876e20	−	2.53385e20i	0.487853	−	0.281662i
$986$			7.37677e20i			0.814194i
$987$	4.05146e20	+	8.74885e20i	0.444009	+	0.958807i
$988$	−3.89891e19			−0.0424272
$989$	1.99130e20	+	3.44904e20i	0.215161	+	0.372669i
$990$	−1.53263e20	−	8.84863e19i	−0.164433	−	0.0949357i
$991$	−6.13960e20	+	1.06341e21i	−0.654071	+	1.13288i	0.328055	+	0.944658i	$0.393607\pi$
$991$	−6.13960e20	+	1.06341e21i	−0.654071	+	1.13288i	−0.982126	+	0.188225i	$0.939727\pi$
$992$	−3.30851e19	+	1.91017e19i	−0.0349986	+	0.0202065i
$993$			2.94526e20i			0.309371i
$994$	1.44137e20	−	2.04692e20i	0.150339	−	0.213499i
$995$	2.26927e20			0.235031
$996$	3.19238e20	+	5.52936e20i	0.328321	+	0.568669i
$997$	1.62396e21	+	9.37592e20i	1.65847	+	0.957520i	0.973420	+	0.229026i	$0.0735542\pi$
$997$	1.62396e21	+	9.37592e20i	1.65847	+	0.957520i	0.685053	+	0.728493i	$0.259779\pi$
$998$	2.96505e19	−	5.13562e19i	0.0300690	−	0.0520810i
$999$	1.73403e21	−	1.00114e21i	1.74622	−	1.00818i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.15.d.a.3.9	✓	20
3.2	odd	2		126.15.n.b.73.4		20
7.2	even	3		98.15.d.b.19.7		20
7.3	odd	6		98.15.b.c.97.7		20
7.4	even	3		98.15.b.c.97.4		20
7.5	odd	6	inner	14.15.d.a.5.9	yes	20
7.6	odd	2		98.15.d.b.31.7		20
21.5	even	6		126.15.n.b.19.4		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.15.d.a.3.9	✓	20	1.1	even	1	trivial
14.15.d.a.5.9	yes	20	7.5	odd	6	inner
98.15.b.c.97.4		20	7.4	even	3
98.15.b.c.97.7		20	7.3	odd	6
98.15.d.b.19.7		20	7.2	even	3
98.15.d.b.31.7		20	7.6	odd	2
126.15.n.b.19.4		20	21.5	even	6
126.15.n.b.73.4		20	3.2	odd	2

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)

\(f(q)\)	\(=\)	\(q+(45.2548 + 78.3837i) q^{2} +(1298.66 + 749.784i) q^{3} +(-4096.00 + 7094.48i) q^{4} +(-67507.4 + 38975.4i) q^{5} +135725. i q^{6} +(-346065. - 747303. i) q^{7} -741455. q^{8} +(-1.26713e6 - 2.19474e6i) q^{9} +O(q^{10})\)	\(q+(45.2548 + 78.3837i) q^{2} +(1298.66 + 749.784i) q^{3} +(-4096.00 + 7094.48i) q^{4} +(-67507.4 + 38975.4i) q^{5} +135725. i q^{6} +(-346065. - 747303. i) q^{7} -741455. q^{8} +(-1.26713e6 - 2.19474e6i) q^{9} +(-6.11007e6 - 3.52765e6i) q^{10} +(-4.94890e6 + 8.57174e6i) q^{11} +(-1.06387e7 + 6.14223e6i) q^{12} +1.06948e7i q^{13} +(4.29153e7 - 6.09449e7i) q^{14} -1.16892e8 q^{15} +(-3.35544e7 - 5.81180e7i) q^{16} +(-2.56175e8 - 1.47903e8i) q^{17} +(1.14688e8 - 1.98645e8i) q^{18} +(3.85399e8 - 2.22510e8i) q^{19} -6.38573e8i q^{20} +(1.10894e8 - 1.22997e9i) q^{21} -8.95846e8 q^{22} +(-1.70339e9 - 2.95036e9i) q^{23} +(-9.62901e8 - 5.55931e8i) q^{24} +(-1.35959e7 + 2.35488e7i) q^{25} +(-8.38298e8 + 4.83992e8i) q^{26} -1.09727e10i q^{27} +(6.71921e9 + 6.05806e8i) q^{28} -2.75528e10 q^{29} +(-5.28995e9 - 9.16246e9i) q^{30} +(-5.44700e9 - 3.14483e9i) q^{31} +(3.03700e9 - 5.26024e9i) q^{32} +(-1.28539e10 + 7.42121e9i) q^{33} -2.67733e10i q^{34} +(5.24883e10 + 3.69605e10i) q^{35} +2.07607e10 q^{36} +(9.12395e10 + 1.58031e11i) q^{37} +(3.48824e10 + 2.01393e10i) q^{38} +(-8.01880e9 + 1.38890e10i) q^{39} +(5.00537e10 - 2.88985e10i) q^{40} +1.84110e11i q^{41} +(1.01428e11 - 4.69698e10i) q^{42} -1.16902e11 q^{43} +(-4.05414e10 - 7.02197e10i) q^{44} +(1.71081e11 + 9.87739e10i) q^{45} +(1.54174e11 - 2.67036e11i) q^{46} +(-6.76112e11 + 3.90353e11i) q^{47} -1.00634e11i q^{48} +(-4.38702e11 + 5.17231e11i) q^{49} -2.46112e9 q^{50} +(-2.21790e11 - 3.84152e11i) q^{51} +(-7.58741e10 - 4.38059e10i) q^{52} +(6.00003e11 - 1.03923e12i) q^{53} +(8.60080e11 - 4.96567e11i) q^{54} -7.71541e11i q^{55} +(2.56591e11 + 5.54092e11i) q^{56} +6.67339e11 q^{57} +(-1.24690e12 - 2.15969e12i) q^{58} +(-3.90985e11 - 2.25735e11i) q^{59} +(4.78792e11 - 8.29292e11i) q^{60} +(-2.34687e12 + 1.35497e12i) q^{61} -5.69275e11i q^{62} +(-1.20163e12 + 1.70645e12i) q^{63} +5.49756e11 q^{64} +(-4.16834e11 - 7.21978e11i) q^{65} +(-1.16340e12 - 6.71691e11i) q^{66} +(-7.27991e11 + 1.26092e12i) q^{67} +(2.09859e12 - 1.21162e12i) q^{68} -5.10871e12i q^{69} +(-5.21746e11 + 5.78687e12i) q^{70} +3.35864e12 q^{71} +(9.39522e11 + 1.62730e12i) q^{72} +(9.10071e12 + 5.25430e12i) q^{73} +(-8.25805e12 + 1.43034e13i) q^{74} +(-3.53130e10 + 2.03880e10i) q^{75} +3.64561e12i q^{76} +(8.11833e12 + 7.31951e11i) q^{77} -1.45156e12 q^{78} +(1.16407e13 + 2.01623e13i) q^{79} +(4.53034e12 + 2.61559e12i) q^{80} +(2.16649e12 - 3.75248e12i) q^{81} +(-1.44312e13 + 8.33188e12i) q^{82} -5.19742e13i q^{83} +(8.27177e12 + 5.82469e12i) q^{84} +2.30583e13 q^{85} +(-5.29038e12 - 9.16321e12i) q^{86} +(-3.57818e13 - 2.06586e13i) q^{87} +(3.66939e12 - 6.35556e12i) q^{88} +(-2.25113e13 + 1.29969e13i) q^{89} +1.78800e13i q^{90} +(7.99227e12 - 3.70109e12i) q^{91} +2.79084e13 q^{92} +(-4.71589e12 - 8.16815e12i) q^{93} +(-6.11947e13 - 3.53308e13i) q^{94} +(-1.73449e13 + 3.00422e13i) q^{95} +(7.88809e12 - 4.55419e12i) q^{96} -5.20028e13i q^{97} +(-6.03958e13 - 1.09799e13i) q^{98} +2.50836e13 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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