LMFDB - Embedded newform 14.15.d.a.5.6

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			5.6
Root			$-728.515 + 1261.82i$ of defining polynomial
Character	$\chi$	$=$	14.5
Dual form			14.15.d.a.3.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(45.2548 - 78.3837i) q^{2} +(-3149.23 + 1818.21i) q^{3} +(-4096.00 - 7094.48i) q^{4} +(-112471. - 64935.4i) q^{5} +329131. i q^{6} +(-629509. - 530982. i) q^{7} -741455. q^{8} +(4.22027e6 - 7.30973e6i) q^{9} +O(q^{10})$	\(q+(45.2548 - 78.3837i) q^{2} +(-3149.23 + 1818.21i) q^{3} +(-4096.00 - 7094.48i) q^{4} +(-112471. - 64935.4i) q^{5} +329131. i q^{6} +(-629509. - 530982. i) q^{7} -741455. q^{8} +(4.22027e6 - 7.30973e6i) q^{9} +(-1.01797e7 + 5.87728e6i) q^{10} +(8.48266e6 + 1.46924e7i) q^{11} +(2.57985e7 + 1.48948e7i) q^{12} +7.99021e7i q^{13} +(-7.01086e7 + 2.53137e7i) q^{14} +4.72264e8 q^{15} +(-3.35544e7 + 5.81180e7i) q^{16} +(1.21978e8 - 7.04238e7i) q^{17} +(-3.81976e8 - 6.61601e8i) q^{18} +(-1.12792e9 - 6.51204e8i) q^{19} +1.06390e9i q^{20} +(2.94790e9 + 5.27605e8i) q^{21} +1.53552e9 q^{22} +(2.23845e9 - 3.87711e9i) q^{23} +(2.33501e9 - 1.34812e9i) q^{24} +(5.38144e9 + 9.32093e9i) q^{25} +(6.26302e9 + 3.61596e9i) q^{26} +1.33005e10i q^{27} +(-1.18857e9 + 6.64094e9i) q^{28} -1.38120e10 q^{29} +(2.13722e10 - 3.70178e10i) q^{30} +(1.21075e10 - 6.99029e9i) q^{31} +(3.03700e9 + 5.26024e9i) q^{32} +(-5.34276e10 - 3.08465e10i) q^{33} -1.27481e10i q^{34} +(3.63222e10 + 1.00598e11i) q^{35} -6.91450e10 q^{36} +(1.37498e10 - 2.38153e10i) q^{37} +(-1.02087e11 + 5.89402e10i) q^{38} +(-1.45279e11 - 2.51630e11i) q^{39} +(8.33925e10 + 4.81467e10i) q^{40} +1.39237e11i q^{41} +(1.74762e11 - 2.07191e11i) q^{42} +1.05402e11 q^{43} +(6.94899e10 - 1.20360e11i) q^{44} +(-9.49320e11 + 5.48090e11i) q^{45} +(-2.02601e11 - 3.50916e11i) q^{46} +(-2.06363e11 - 1.19144e11i) q^{47} -2.44036e11i q^{48} +(1.14340e11 + 6.68516e11i) q^{49} +9.74145e11 q^{50} +(-2.56090e11 + 4.43561e11i) q^{51} +(5.66864e11 - 3.27279e11i) q^{52} +(3.56937e11 + 6.18232e11i) q^{53} +(1.04254e12 + 6.01911e11i) q^{54} -2.20330e12i q^{55} +(4.66753e11 + 3.93699e11i) q^{56} +4.73609e12 q^{57} +(-6.25059e11 + 1.08263e12i) q^{58} +(-2.66660e12 + 1.53956e12i) q^{59} +(-1.93439e12 - 3.35047e12i) q^{60} +(2.59390e12 + 1.49759e12i) q^{61} -1.26538e12i q^{62} +(-6.53803e12 + 2.36065e12i) q^{63} +5.49756e11 q^{64} +(5.18847e12 - 8.98670e12i) q^{65} +(-4.83572e12 + 2.79190e12i) q^{66} +(-2.00851e12 - 3.47885e12i) q^{67} +(-9.99241e11 - 5.76912e11i) q^{68} +1.62799e13i q^{69} +(9.52897e12 + 1.70546e12i) q^{70} +1.48607e13 q^{71} +(-3.12914e12 + 5.41984e12i) q^{72} +(-3.42177e12 + 1.97556e12i) q^{73} +(-1.24449e12 - 2.15552e12i) q^{74} +(-3.38948e13 - 1.95692e13i) q^{75} +1.06693e13i q^{76} +(2.46149e12 - 1.37531e13i) q^{77} -2.62983e13 q^{78} +(-3.03988e12 + 5.26522e12i) q^{79} +(7.54782e12 - 4.35774e12i) q^{80} +(-3.99758e12 - 6.92402e12i) q^{81} +(1.09139e13 + 6.30115e12i) q^{82} -9.40181e12i q^{83} +(-8.33152e12 - 2.30749e13i) q^{84} -1.82920e13 q^{85} +(4.76995e12 - 8.26179e12i) q^{86} +(4.34971e13 - 2.51131e13i) q^{87} +(-6.28951e12 - 1.08937e13i) q^{88} +(6.63468e13 + 3.83054e13i) q^{89} +9.92149e13i q^{90} +(4.24266e13 - 5.02991e13i) q^{91} -3.66748e13 q^{92} +(-2.54196e13 + 4.40280e13i) q^{93} +(-1.86779e13 + 1.07837e13i) q^{94} +(8.45723e13 + 1.46483e14i) q^{95} +(-1.91284e13 - 1.10438e13i) q^{96} -8.19781e13i q^{97} +(5.75751e13 + 2.12912e13i) q^{98} +1.43197e14 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
$3$	−3149.23	+	1818.21i	−1.43998	+	0.831371i	−0.997847	−	0.0655808i	$-0.979110\pi$
$3$	−3149.23	+	1818.21i	−1.43998	+	0.831371i	−0.442129	+	0.896951i	$0.645777\pi$
$4$	−4096.00	−	7094.48i	−0.250000	−	0.433013i
$5$	−112471.	−	64935.4i	−1.43963	−	0.831173i	−0.441809	−	0.897109i	$-0.645663\pi$
$5$	−112471.	−	64935.4i	−1.43963	−	0.831173i	−0.997824	+	0.0659365i	$0.978997\pi$
$6$			329131.i			1.17574i
$7$	−629509.	−	530982.i	−0.764391	−	0.644753i
$7$	−629509.	−	530982.i	−0.764391	−	0.644753i
$8$	−741455.			−0.353553
$9$	4.22027e6	−	7.30973e6i	0.882354	−	1.52828i
$10$	−1.01797e7	+	5.87728e6i	−1.01797	+	0.587728i
$11$	8.48266e6	+	1.46924e7i	0.435294	+	0.753952i	0.997320	−	0.0731681i	$-0.0233110\pi$
$11$	8.48266e6	+	1.46924e7i	0.435294	+	0.753952i	−0.562025	+	0.827120i	$0.689978\pi$
$12$	2.57985e7	+	1.48948e7i	0.719988	+	0.415685i
$13$			7.99021e7i			1.27337i	0.771124	+	0.636686i	$0.219695\pi$
$13$			7.99021e7i			1.27337i	−0.771124	+	0.636686i	$0.780305\pi$
$14$	−7.01086e7	+	2.53137e7i	−0.665082	+	0.240137i
$15$	4.72264e8			2.76405
$16$	−3.35544e7	+	5.81180e7i	−0.125000	+	0.216506i
$17$	1.21978e8	−	7.04238e7i	0.297261	−	0.171624i	−0.343951	−	0.938988i	$-0.611765\pi$
$17$	1.21978e8	−	7.04238e7i	0.297261	−	0.171624i	0.641212	+	0.767364i	$0.278432\pi$
$18$	−3.81976e8	−	6.61601e8i	−0.623919	−	1.08066i
$19$	−1.12792e9	−	6.51204e8i	−1.26183	−	0.728520i	−0.288405	−	0.957509i	$-0.593125\pi$
$19$	−1.12792e9	−	6.51204e8i	−1.26183	−	0.728520i	−0.973429	+	0.228988i	$0.926458\pi$
$20$			1.06390e9i			0.831173i
$21$	2.94790e9	+	5.27605e8i	1.63673	+	0.292937i
$22$	1.53552e9			0.615599
$23$	2.23845e9	−	3.87711e9i	0.657434	−	1.13871i	−0.323843	−	0.946111i	$-0.604975\pi$
$23$	2.23845e9	−	3.87711e9i	0.657434	−	1.13871i	0.981278	−	0.192599i	$-0.0616916\pi$
$24$	2.33501e9	−	1.34812e9i	0.509108	−	0.293934i
$25$	5.38144e9	+	9.32093e9i	0.881695	+	1.52714i
$26$	6.26302e9	+	3.61596e9i	0.779777	+	0.450205i
$27$			1.33005e10i			1.27151i
$28$	−1.18857e9	+	6.64094e9i	−0.0880885	+	0.492179i
$29$	−1.38120e10			−0.800701			−0.400350	−	0.916362i	$-0.631112\pi$
$29$	−1.38120e10			−0.800701			−0.400350	+	0.916362i	$0.631112\pi$
$30$	2.13722e10	−	3.70178e10i	0.977239	−	1.69263i
$31$	1.21075e10	−	6.99029e9i	0.440072	−	0.254076i	−0.263556	−	0.964644i	$-0.584895\pi$
$31$	1.21075e10	−	6.99029e9i	0.440072	−	0.254076i	0.703628	+	0.710568i	$0.251562\pi$
$32$	3.03700e9	+	5.26024e9i	0.0883883	+	0.153093i
$33$	−5.34276e10	−	3.08465e10i	−1.25363	−	0.723782i
$34$		−	1.27481e10i		−	0.242712i
$35$	3.63222e10	+	1.00598e11i	0.564541	+	1.56355i
$36$	−6.91450e10			−0.882354
$37$	1.37498e10	−	2.38153e10i	0.144838	−	0.250867i	−0.784474	−	0.620161i	$-0.787067\pi$
$37$	1.37498e10	−	2.38153e10i	0.144838	−	0.250867i	0.929313	+	0.369294i	$0.120400\pi$
$38$	−1.02087e11	+	5.89402e10i	−0.892251	+	0.515142i
$39$	−1.45279e11	−	2.51630e11i	−1.05864	−	1.83362i
$40$	8.33925e10	+	4.81467e10i	0.508987	+	0.293864i
$41$			1.39237e11i			0.714937i	0.933925	+	0.357468i	$0.116360\pi$
$41$			1.39237e11i			0.714937i	−0.933925	+	0.357468i	$0.883640\pi$
$42$	1.74762e11	−	2.07191e11i	0.758059	−	0.898722i
$43$	1.05402e11			0.387766			0.193883	−	0.981025i	$-0.437892\pi$
$43$	1.05402e11			0.387766			0.193883	+	0.981025i	$0.437892\pi$
$44$	6.94899e10	−	1.20360e11i	0.217647	−	0.376976i
$45$	−9.49320e11	+	5.48090e11i	−2.54053	+	1.46678i
$46$	−2.02601e11	−	3.50916e11i	−0.464876	−	0.805189i
$47$	−2.06363e11	−	1.19144e11i	−0.407331	−	0.235173i	0.282311	−	0.959323i	$-0.408899\pi$
$47$	−2.06363e11	−	1.19144e11i	−0.407331	−	0.235173i	−0.689642	+	0.724150i	$0.742232\pi$
$48$		−	2.44036e11i		−	0.415685i
$49$	1.14340e11	+	6.68516e11i	0.168587	+	0.985687i
$50$	9.74145e11			1.24691
$51$	−2.56090e11	+	4.43561e11i	−0.285366	+	0.494268i
$52$	5.66864e11	−	3.27279e11i	0.551386	−	0.318343i
$53$	3.56937e11	+	6.18232e11i	0.303851	+	0.526285i	0.977005	−	0.213218i	$-0.0683943\pi$
$53$	3.56937e11	+	6.18232e11i	0.303851	+	0.526285i	−0.673154	+	0.739502i	$0.735061\pi$
$54$	1.04254e12	+	6.01911e11i	0.778639	+	0.449548i
$55$		−	2.20330e12i		−	1.44722i
$56$	4.66753e11	+	3.93699e11i	0.270253	+	0.227955i
$57$	4.73609e12			2.42268
$58$	−6.25059e11	+	1.08263e12i	−0.283090	+	0.490327i
$59$	−2.66660e12	+	1.53956e12i	−1.07151	+	0.618634i	−0.928592	−	0.371101i	$-0.878980\pi$
$59$	−2.66660e12	+	1.53956e12i	−1.07151	+	0.618634i	−0.142913	+	0.989735i	$0.545647\pi$
$60$	−1.93439e12	−	3.35047e12i	−0.691012	−	1.19687i
$61$	2.59390e12	+	1.49759e12i	0.825363	+	0.476523i	0.852262	−	0.523115i	$-0.175230\pi$
$61$	2.59390e12	+	1.49759e12i	0.825363	+	0.476523i	−0.0268996	+	0.999638i	$0.508563\pi$
$62$		−	1.26538e12i		−	0.359318i
$63$	−6.53803e12	+	2.36065e12i	−1.65983	+	0.599305i
$64$	5.49756e11			0.125000
$65$	5.18847e12	−	8.98670e12i	1.05839	−	1.83319i
$66$	−4.83572e12	+	2.79190e12i	−0.886448	+	0.511791i
$67$	−2.00851e12	−	3.47885e12i	−0.331399	−	0.574000i	0.651387	−	0.758745i	$-0.274187\pi$
$67$	−2.00851e12	−	3.47885e12i	−0.331399	−	0.574000i	−0.982786	+	0.184745i	$0.940854\pi$
$68$	−9.99241e11	−	5.76912e11i	−0.148630	−	0.0858118i
$69$			1.62799e13i			2.18629i
$70$	9.52897e12	+	1.70546e12i	1.15707	+	0.207088i
$71$	1.48607e13			1.63392			0.816958	−	0.576698i	$-0.195659\pi$
$71$	1.48607e13			1.63392			0.816958	+	0.576698i	$0.195659\pi$
$72$	−3.12914e12	+	5.41984e12i	−0.311959	+	0.540329i
$73$	−3.42177e12	+	1.97556e12i	−0.309735	+	0.178826i	−0.646808	−	0.762653i	$-0.723896\pi$
$73$	−3.42177e12	+	1.97556e12i	−0.309735	+	0.178826i	0.337073	+	0.941479i	$0.390563\pi$
$74$	−1.24449e12	−	2.15552e12i	−0.102416	−	0.177390i
$75$	−3.38948e13	−	1.95692e13i	−2.53924	−	1.46603i
$76$			1.06693e13i			0.728520i
$77$	2.46149e12	−	1.37531e13i	0.153378	−	0.856971i
$78$	−2.62983e13			−1.49715
$79$	−3.03988e12	+	5.26522e12i	−0.158295	+	0.274174i	−0.934254	−	0.356609i	$-0.883933\pi$
$79$	−3.03988e12	+	5.26522e12i	−0.158295	+	0.274174i	0.775959	+	0.630783i	$0.217266\pi$
$80$	7.54782e12	−	4.35774e12i	0.359908	−	0.207793i
$81$	−3.99758e12	−	6.92402e12i	−0.174744	−	0.302666i
$82$	1.09139e13	+	6.30115e12i	0.437808	+	0.252768i
$83$		−	9.40181e12i		−	0.346469i	−0.984881	−	0.173235i	$-0.944578\pi$
$83$		−	9.40181e12i		−	0.346469i	0.984881	−	0.173235i	$-0.0554219\pi$
$84$	−8.33152e12	−	2.30749e13i	−0.282338	−	0.781961i
$85$	−1.82920e13			−0.570595
$86$	4.76995e12	−	8.26179e12i	0.137096	−	0.237457i
$87$	4.34971e13	−	2.51131e13i	1.15299	−	0.665679i
$88$	−6.28951e12	−	1.08937e13i	−0.153900	−	0.266562i
$89$	6.63468e13	+	3.83054e13i	1.50000	+	0.866023i	1.00000		4.82638e-6i	$-1.53628e-6\pi$
$89$	6.63468e13	+	3.83054e13i	1.50000	+	0.866023i	0.499996	+	0.866028i	$0.333335\pi$
$90$			9.92149e13i			2.07434i
$91$	4.24266e13	−	5.02991e13i	0.821010	−	0.973353i
$92$	−3.66748e13			−0.657434
$93$	−2.54196e13	+	4.40280e13i	−0.422462	+	0.731726i
$94$	−1.86779e13	+	1.07837e13i	−0.288027	+	0.166292i
$95$	8.45723e13	+	1.46483e14i	1.21105	+	2.09760i
$96$	−1.91284e13	−	1.10438e13i	−0.254554	−	0.146967i
$97$		−	8.19781e13i		−	1.01460i	−0.861769	−	0.507301i	$-0.830643\pi$
$97$		−	8.19781e13i		−	1.01460i	0.861769	−	0.507301i	$-0.169357\pi$
$98$	5.75751e13	+	2.12912e13i	0.663212	+	0.245255i
$99$	1.43197e14			1.53634
$100$	4.40848e13	−	7.63571e13i	0.440848	−	0.763571i
$101$	−3.22909e13	+	1.86432e13i	−0.301183	+	0.173888i	−0.642974	−	0.765888i	$-0.722300\pi$
$101$	−3.22909e13	+	1.86432e13i	−0.301183	+	0.173888i	0.341791	+	0.939776i	$0.388967\pi$
$102$	2.31786e13	+	4.01466e13i	0.201784	+	0.349500i
$103$	−1.33011e14	−	7.67940e13i	−1.08150	−	0.624405i	−0.150201	−	0.988656i	$-0.547992\pi$
$103$	−1.33011e14	−	7.67940e13i	−1.08150	−	0.624405i	−0.931301	+	0.364250i	$0.881325\pi$
$104$		−	5.92439e13i		−	0.450205i
$105$	−2.97294e14	−	2.50764e14i	−2.11281	−	1.78213i
$106$	6.46124e13			0.429710
$107$	−1.12949e14	+	1.95634e14i	−0.703393	+	1.21831i	0.263876	+	0.964557i	$0.414999\pi$
$107$	−1.12949e14	+	1.95634e14i	−0.703393	+	1.21831i	−0.967269	+	0.253755i	$0.918334\pi$
$108$	9.43599e13	−	5.44787e13i	0.550581	−	0.317878i
$109$	1.37676e13	+	2.38462e13i	0.0753136	+	0.130447i	0.901223	−	0.433356i	$-0.142671\pi$
$109$	1.37676e13	+	2.38462e13i	0.0753136	+	0.130447i	−0.825909	+	0.563803i	$0.809338\pi$
$110$	−1.72703e14	−	9.97098e13i	−0.886237	−	0.511669i
$111$			9.99998e13i			0.481658i
$112$	5.19824e13	−	1.87690e13i	0.235142	−	0.0849014i
$113$	−8.40248e13			−0.357156			−0.178578	−	0.983926i	$-0.557150\pi$
$113$	−8.40248e13			−0.357156			−0.178578	+	0.983926i	$0.557150\pi$
$114$	2.14331e14	−	3.71232e14i	0.856547	−	1.48358i
$115$	−5.03523e14	+	2.90709e14i	−1.89293	+	1.09288i
$116$	5.65739e13	+	9.79889e13i	0.200175	+	0.346714i
$117$	5.84063e14	+	3.37209e14i	1.94607	+	1.12356i
$118$			2.78691e14i			0.874880i
$119$	−1.14180e14	−	2.04355e13i	−0.337878	−	0.0604723i
$120$	−3.50162e14			−0.977239
$121$	4.59640e13	−	7.96120e13i	0.121038	−	0.209643i
$122$	2.34773e14	−	1.35546e14i	0.583619	−	0.336953i
$123$	−2.53162e14	−	4.38489e14i	−0.594378	−	1.02949i
$124$	−9.91850e13	−	5.72645e13i	−0.220036	−	0.127038i
$125$		−	6.05116e14i		−	1.26902i
$126$	−1.10841e14	+	6.19306e14i	−0.219840	+	1.22832i
$127$	−9.54897e13			−0.179197			−0.0895984	−	0.995978i	$-0.528558\pi$
$127$	−9.54897e13			−0.179197			−0.0895984	+	0.995978i	$0.528558\pi$
$128$	2.48791e13	−	4.30919e13i	0.0441942	−	0.0765466i
$129$	−3.31935e14	+	1.91643e14i	−0.558373	+	0.322377i
$130$	−4.69607e14	−	8.13383e14i	−0.748395	−	1.29626i
$131$	8.50764e14	+	4.91189e14i	1.28502	+	0.741907i	0.977762	−	0.209719i	$-0.0672548\pi$
$131$	8.50764e14	+	4.91189e14i	1.28502	+	0.741907i	0.307259	+	0.951626i	$0.400588\pi$
$132$			5.05388e14i			0.723782i
$133$	3.64257e14	+	1.00884e15i	0.494819	+	1.37045i
$134$	−3.63580e14			−0.468669
$135$	8.63671e14	−	1.49592e15i	1.05685	−	1.83051i
$136$	−9.04409e13	+	5.22161e13i	−0.105098	+	0.0606781i
$137$	−2.18382e13	−	3.78248e13i	−0.0241086	−	0.0417573i	0.853719	−	0.520733i	$-0.174341\pi$
$137$	−2.18382e13	−	3.78248e13i	−0.0241086	−	0.0417573i	−0.877828	+	0.478976i	$0.841008\pi$
$138$	1.27608e15	+	7.36742e14i	1.33882	+	0.772969i
$139$			4.44295e14i			0.443167i	0.975141	+	0.221584i	$0.0711225\pi$
$139$			4.44295e14i			0.443167i	−0.975141	+	0.221584i	$0.928877\pi$
$140$	5.64912e14	−	6.69735e14i	0.535901	−	0.635341i
$141$	8.66514e14			0.782063
$142$	6.72516e14	−	1.16483e15i	0.577676	−	1.00056i
$143$	−1.17395e15	+	6.77782e14i	−0.960061	+	0.554291i
$144$	2.83218e14	+	4.90548e14i	0.220589	+	0.382071i
$145$	1.55345e15	+	8.96886e14i	1.15272	+	0.665520i
$146$			3.57614e14i			0.252898i
$147$	−1.57558e15	−	1.89741e15i	−1.06223	−	1.27921i
$148$	−2.25276e14			−0.144838
$149$	1.16454e14	−	2.01705e14i	0.0714252	−	0.123712i	−0.828101	−	0.560579i	$-0.810579\pi$
$149$	1.16454e14	−	2.01705e14i	0.0714252	−	0.123712i	0.899526	+	0.436867i	$0.143912\pi$
$150$	−3.06781e15	+	1.77120e15i	−1.79551	+	1.03664i
$151$	1.31134e14	+	2.27131e14i	0.0732617	+	0.126893i	0.900329	−	0.435210i	$-0.143326\pi$
$151$	1.31134e14	+	2.27131e14i	0.0732617	+	0.126893i	−0.827067	+	0.562103i	$0.809993\pi$
$152$	8.36300e14	+	4.82838e14i	0.446126	+	0.257571i
$153$		−	1.18883e15i		−	0.605731i
$154$	−9.66626e14	−	8.15336e14i	−0.470558	−	0.396909i
$155$	−1.81567e15			−0.844724
$156$	−1.19012e15	+	2.06135e15i	−0.529322	+	0.916812i
$157$	3.88243e15	−	2.24152e15i	1.65122	−	0.953334i	0.674653	−	0.738135i	$-0.264293\pi$
$157$	3.88243e15	−	2.24152e15i	1.65122	−	0.953334i	0.976570	−	0.215199i	$-0.0690399\pi$
$158$	2.75138e14	+	4.76554e14i	0.111931	+	0.193871i
$159$	−2.24815e15	−	1.29797e15i	−0.875075	−	0.505225i
$160$		−	7.88835e14i		−	0.293864i
$161$	−3.46780e15	+	1.25210e15i	−1.23672	+	0.446537i
$162$	−7.23640e14			−0.247125
$163$	2.50924e15	−	4.34613e15i	0.820785	−	1.42164i	−0.0843142	−	0.996439i	$-0.526870\pi$
$163$	2.50924e15	−	4.34613e15i	0.820785	−	1.42164i	0.905099	−	0.425201i	$-0.139797\pi$
$164$	9.87814e14	−	5.70315e14i	0.309577	−	0.178734i
$165$	4.00605e15	+	6.93868e15i	1.20318	+	2.08396i
$166$	−7.36948e14	−	4.25477e14i	−0.212168	−	0.122495i
$167$			1.01232e15i			0.279449i	0.990190	+	0.139724i	$0.0446217\pi$
$167$			1.01232e15i			0.279449i	−0.990190	+	0.139724i	$0.955378\pi$
$168$	−2.18574e15	−	3.91196e14i	−0.578673	−	0.103569i
$169$	−2.44698e15			−0.621474
$170$	−8.27800e14	+	1.43379e15i	−0.201736	+	0.349417i
$171$	−9.52024e15	+	5.49651e15i	−2.22677	+	1.28563i
$172$	−4.31726e14	−	7.47772e14i	−0.0969414	−	0.167907i
$173$	4.04033e15	+	2.33269e15i	0.871153	+	0.502960i	0.867731	−	0.497034i	$-0.165578\pi$
$173$	4.04033e15	+	2.33269e15i	0.871153	+	0.502960i	0.00342158	+	0.999994i	$0.498911\pi$
$174$		−	4.54595e15i		−	0.941412i
$175$	1.56158e15	−	8.72506e15i	0.310669	−	1.73581i
$176$	−1.13852e15			−0.217647
$177$	5.59849e15	−	9.69688e15i	1.02863	−	1.78164i
$178$	6.00503e15	−	3.46700e15i	1.06066	−	0.612371i
$179$	1.92746e14	+	3.33846e14i	0.0327351	+	0.0566989i	0.881929	−	0.471383i	$-0.156245\pi$
$179$	1.92746e14	+	3.33846e14i	0.0327351	+	0.0566989i	−0.849194	+	0.528081i	$0.822912\pi$
$180$	7.77683e15	+	4.48995e15i	1.27027	+	0.733389i
$181$			8.71500e15i			1.36936i	0.728844	+	0.684679i	$0.240058\pi$
$181$			8.71500e15i			1.36936i	−0.728844	+	0.684679i	$0.759942\pi$
$182$	−2.02262e15	−	5.60183e15i	−0.305784	−	0.846896i
$183$	−1.08917e16			−1.58467
$184$	−1.65971e15	+	2.87470e15i	−0.232438	+	0.402595i
$185$	−3.09291e15	+	1.78569e15i	−0.417028	+	0.240771i
$186$	2.30072e15	+	3.98496e15i	0.298726	+	0.517409i
$187$	2.06939e15	+	1.19476e15i	0.258792	+	0.149414i
$188$			1.95206e15i			0.235173i
$189$	7.06231e15	−	8.37277e15i	0.819812	−	0.971933i
$190$	1.53092e16			1.71269
$191$	−4.71114e15	+	8.15994e15i	−0.508034	+	0.879941i	0.491923	+	0.870639i	$0.336294\pi$
$191$	−4.71114e15	+	8.15994e15i	−0.508034	+	0.879941i	−0.999957	+	0.00930193i	$0.997039\pi$
$192$	−1.73131e15	+	9.99570e14i	−0.179997	+	0.103921i
$193$	−2.46625e14	−	4.27167e14i	−0.0247250	−	0.0428249i	0.853398	−	0.521260i	$-0.174538\pi$
$193$	−2.46625e14	−	4.27167e14i	−0.0247250	−	0.0428249i	−0.878123	+	0.478435i	$0.841204\pi$
$194$	−6.42574e15	−	3.70990e15i	−0.621314	−	0.358716i
$195$			3.77349e16i			3.51966i
$196$	4.27443e15	−	3.54942e15i	0.384668	−	0.319422i
$197$	−2.80815e15			−0.243869			−0.121935	−	0.992538i	$-0.538910\pi$
$197$	−2.80815e15			−0.243869			−0.121935	+	0.992538i	$0.538910\pi$
$198$	6.48033e15	−	1.12243e16i	0.543177	−	0.940810i
$199$	1.74602e16	−	1.00807e16i	1.41279	−	0.815675i	0.417140	−	0.908842i	$-0.363032\pi$
$199$	1.74602e16	−	1.00807e16i	1.41279	−	0.815675i	0.995650	+	0.0931674i	$0.0296992\pi$
$200$	−3.99010e15	−	6.91105e15i	−0.311726	−	0.539926i
$201$	1.26505e16	+	7.30379e15i	0.954413	+	0.551031i
$202$			3.37478e15i			0.245915i
$203$	8.69477e15	+	7.33392e15i	0.612048	+	0.516254i
$204$	4.19578e15			0.285366
$205$	9.04140e15	−	1.56602e16i	0.594236	−	1.02925i
$206$	−1.20388e16	+	6.95060e15i	−0.764737	+	0.441521i
$207$	−1.88937e16	−	3.27249e16i	−1.16018	−	2.00949i
$208$	−4.64375e15	−	2.68107e15i	−0.275693	−	0.159171i
$209$		−	2.20957e16i		−	1.26848i
$210$	−3.31098e16	+	1.19548e16i	−1.83832	+	0.663752i
$211$	−1.54901e16			−0.831913			−0.415956	−	0.909385i	$-0.636553\pi$
$211$	−1.54901e16			−0.831913			−0.415956	+	0.909385i	$0.636553\pi$
$212$	2.92402e15	−	5.06456e15i	0.151925	−	0.263142i
$213$	−4.67996e16	+	2.70198e16i	−2.35280	+	1.35839i
$214$	1.02230e16	+	1.77068e16i	0.497374	+	0.861476i
$215$	−1.18547e16	−	6.84431e15i	−0.558240	−	0.322300i
$216$		−	9.86170e15i		−	0.449548i
$217$	−1.13335e16	−	2.02843e15i	−0.500204	−	0.0895247i
$218$	2.49220e15			0.106509
$219$	7.18395e15	−	1.24430e16i	0.297341	−	0.515009i
$220$	−1.56312e16	+	9.02470e15i	−0.626664	+	0.361805i
$221$	5.62701e15	+	9.74627e15i	0.218541	+	0.378523i
$222$	7.83835e15	+	4.52548e15i	0.294954	+	0.170292i
$223$		−	5.24150e16i		−	1.91127i	−0.294556	−	0.955634i	$-0.595172\pi$
$223$		−	5.24150e16i		−	1.91127i	0.294556	−	0.955634i	$-0.404828\pi$
$224$	8.81273e14	−	4.92396e15i	0.0311440	−	0.174012i
$225$	9.08446e16			3.11187
$226$	−3.80253e15	+	6.58617e15i	−0.126274	+	0.218713i
$227$	−2.03450e16	+	1.17462e16i	−0.655052	+	0.378194i	−0.790389	−	0.612605i	$-0.790122\pi$
$227$	−2.03450e16	+	1.17462e16i	−0.655052	+	0.378194i	0.135337	+	0.990800i	$0.456788\pi$
$228$	−1.93990e16	−	3.36001e16i	−0.605670	−	1.04905i
$229$	7.44016e14	+	4.29558e14i	0.0225286	+	0.0130069i	0.511222	−	0.859449i	$-0.329193\pi$
$229$	7.44016e14	+	4.29558e14i	0.0225286	+	0.0130069i	−0.488693	+	0.872456i	$0.662526\pi$
$230$			5.26239e16i			1.54557i
$231$	1.72543e16	+	4.77872e16i	0.491601	+	1.36153i
$232$	1.02410e16			0.283090
$233$	−3.26450e16	+	5.65428e16i	−0.875639	+	1.51665i	−0.0195593	+	0.999809i	$0.506226\pi$
$233$	−3.26450e16	+	5.65428e16i	−0.875639	+	1.51665i	−0.856080	+	0.516843i	$0.827107\pi$
$234$	5.28633e16	−	3.05207e16i	1.37608	−	0.794480i
$235$	1.54733e16	+	2.68006e16i	0.390938	+	0.677125i
$236$	2.18448e16	+	1.26121e16i	0.535753	+	0.309317i
$237$		−	2.21085e16i		−	0.526406i
$238$	−6.76899e15	+	8.02502e15i	−0.156490	+	0.185527i
$239$	−4.12185e16			−0.925352			−0.462676	−	0.886527i	$-0.653111\pi$
$239$	−4.12185e16			−0.925352			−0.462676	+	0.886527i	$0.653111\pi$
$240$	−1.58465e16	+	2.74470e16i	−0.345506	+	0.598434i
$241$	1.05388e16	−	6.08460e15i	0.223189	−	0.128858i	−0.384237	−	0.923235i	$-0.625535\pi$
$241$	1.05388e16	−	6.08460e15i	0.223189	−	0.128858i	0.607426	+	0.794376i	$0.292202\pi$
$242$	−4.16019e15	−	7.20566e15i	−0.0855865	−	0.148240i
$243$	−2.99142e16	−	1.72710e16i	−0.597908	−	0.345202i
$244$		−	2.45365e16i		−	0.476523i
$245$	3.05504e16	−	8.26135e16i	0.576572	−	1.55915i
$246$	−4.58272e16			−0.840577
$247$	5.20326e16	−	9.01231e16i	0.927677	−	1.60678i
$248$	−8.97720e15	+	5.18299e15i	−0.155589	+	0.0898294i
$249$	1.70944e16	+	2.96084e16i	0.288044	+	0.498907i
$250$	−4.74312e16	−	2.73844e16i	−0.777112	−	0.448666i
$251$			4.02896e15i			0.0641914i	0.999485	+	0.0320957i	$0.0102181\pi$
$251$			4.02896e15i			0.0641914i	−0.999485	+	0.0320957i	$0.989782\pi$
$252$	4.35274e16	+	3.67147e16i	0.674464	+	0.568901i
$253$	7.59520e16			1.14471
$254$	−4.32137e15	+	7.48483e15i	−0.0633557	+	0.109735i
$255$	5.76056e16	−	3.32586e16i	0.821644	−	0.474376i
$256$	−2.25180e15	−	3.90023e15i	−0.0312500	−	0.0541266i
$257$	7.10918e16	+	4.10449e16i	0.960036	+	0.554277i	0.896184	−	0.443682i	$-0.146328\pi$
$257$	7.10918e16	+	4.10449e16i	0.960036	+	0.554277i	0.0638519	+	0.997959i	$0.479661\pi$
$258$			3.46910e16i			0.455910i
$259$	−2.13011e16	+	7.69107e15i	−0.272461	+	0.0983758i
$260$	−8.50080e16			−1.05839
$261$	−5.82904e16	+	1.00962e17i	−0.706502	+	1.22370i
$262$	7.70024e16	−	4.44574e16i	0.908647	−	0.524608i
$263$	5.44597e16	+	9.43270e16i	0.625727	+	1.08379i	0.988400	+	0.151875i	$0.0485310\pi$
$263$	5.44597e16	+	9.43270e16i	0.625727	+	1.08379i	−0.362673	+	0.931917i	$0.618136\pi$
$264$	3.96142e16	+	2.28713e16i	0.443224	+	0.255896i
$265$		−	9.27112e16i		−	1.01021i
$266$	9.55611e16	+	1.71032e16i	1.01417	+	0.181512i
$267$	−2.78588e17			−2.87994
$268$	−1.64537e16	+	2.84987e16i	−0.165699	+	0.287000i
$269$	8.61321e16	−	4.97284e16i	0.845082	−	0.487908i	−0.0139064	−	0.999903i	$-0.504427\pi$
$269$	8.61321e16	−	4.97284e16i	0.845082	−	0.487908i	0.858988	+	0.511995i	$0.171093\pi$
$270$	−7.81706e16	−	1.35395e17i	−0.747303	−	1.29437i
$271$	−1.29914e17	−	7.50058e16i	−1.21024	−	0.698731i	−0.247426	−	0.968907i	$-0.579585\pi$
$271$	−1.29914e17	−	7.50058e16i	−1.21024	−	0.698731i	−0.962811	+	0.270176i	$0.912918\pi$
$272$			9.45212e15i			0.0858118i
$273$	−4.21568e16	+	2.35544e17i	−0.373017	+	2.08417i
$274$	−3.95313e15			−0.0340947
$275$	−9.12978e16	+	1.58133e17i	−0.767594	+	1.32951i
$276$	1.15497e17	−	6.66823e16i	0.946690	−	0.546572i
$277$	4.83334e16	+	8.37159e16i	0.386268	+	0.669036i	0.991944	−	0.126675i	$-0.0404306\pi$
$277$	4.83334e16	+	8.37159e16i	0.386268	+	0.669036i	−0.605676	+	0.795711i	$0.707097\pi$
$278$	3.48254e16	+	2.01065e16i	0.271383	+	0.156683i
$279$		−	1.18004e17i		−	0.896740i
$280$	−2.69313e16	−	7.45886e16i	−0.199596	−	0.552798i
$281$	−3.07269e16			−0.222113			−0.111057	−	0.993814i	$-0.535423\pi$
$281$	−3.07269e16			−0.222113			−0.111057	+	0.993814i	$0.535423\pi$
$282$	3.92140e16	−	6.79206e16i	0.276501	−	0.478914i
$283$	3.98315e16	−	2.29967e16i	0.273982	−	0.158184i	−0.356714	−	0.934214i	$-0.616103\pi$
$283$	3.98315e16	−	2.29967e16i	0.273982	−	0.158184i	0.630696	+	0.776030i	$0.282770\pi$
$284$	−6.08692e16	−	1.05429e17i	−0.408479	−	0.707506i
$285$	−5.32675e17	−	3.07540e17i	−3.48777	−	2.01367i
$286$			1.22692e17i			0.783886i
$287$	7.39323e16	−	8.76509e16i	0.460958	−	0.546491i
$288$	5.12679e16			0.311959
$289$	−7.42699e16	+	1.28639e17i	−0.441091	+	0.763991i
$290$	1.40602e17	−	8.11769e16i	0.815093	−	0.470594i
$291$	1.49053e17	+	2.58168e17i	0.843510	+	1.46100i
$292$	2.80311e16	+	1.61838e16i	0.154868	+	0.0894128i
$293$		−	2.45541e17i		−	1.32450i	−0.749284	−	0.662249i	$-0.769602\pi$
$293$		−	2.45541e17i		−	1.32450i	0.749284	−	0.662249i	$-0.230398\pi$
$294$	−2.20029e17	+	3.76327e16i	−1.15891	+	0.198214i
$295$	3.99888e17			2.05677
$296$	−1.01948e16	+	1.76580e16i	−0.0512081	+	0.0886950i
$297$	−1.95416e17	+	1.12823e17i	−0.958660	+	0.553482i
$298$	−1.05402e16	−	1.82562e16i	−0.0505052	−	0.0874776i
$299$	3.09789e17	+	1.78857e17i	1.45000	+	0.837158i
$300$			3.20621e17i			1.46603i
$301$	−6.63515e16	−	5.59665e16i	−0.296405	−	0.250013i
$302$	2.37378e16			0.103608
$303$	6.77943e16	−	1.17423e17i	0.289131	−	0.500790i
$304$	7.56933e16	−	4.37015e16i	0.315459	−	0.182130i
$305$	−1.94493e17	−	3.36872e17i	−0.792146	−	1.37204i
$306$	−9.31849e16	−	5.38003e16i	−0.370933	−	0.214158i
$307$			2.12101e17i			0.825230i	0.910906	+	0.412615i	$0.135384\pi$
$307$			2.12101e17i			0.825230i	−0.910906	+	0.412615i	$0.864616\pi$
$308$	−1.07654e17	+	3.88698e16i	−0.409424	+	0.147828i
$309$	5.58510e17			2.07645
$310$	−8.21678e16	+	1.42319e17i	−0.298655	+	0.517285i
$311$	1.08941e17	−	6.28969e16i	0.387139	−	0.223515i	−0.293781	−	0.955873i	$-0.594914\pi$
$311$	1.08941e17	−	6.28969e16i	0.387139	−	0.223515i	0.680920	+	0.732358i	$0.261580\pi$
$312$	1.07718e17	+	1.86572e17i	0.374287	+	0.648284i
$313$	1.08572e17	+	6.26838e16i	0.368898	+	0.212983i	0.672977	−	0.739664i	$-0.265015\pi$
$313$	1.08572e17	+	6.26838e16i	0.368898	+	0.212983i	−0.304079	+	0.952647i	$0.598349\pi$
$314$		−	4.05758e17i		−	1.34822i
$315$	8.88631e17	+	1.59044e17i	2.88767	+	0.516825i
$316$	4.98054e16			0.158295
$317$	−2.40290e17	+	4.16195e17i	−0.747001	+	1.29384i	0.202254	+	0.979333i	$0.435173\pi$
$317$	−2.40290e17	+	4.16195e17i	−0.747001	+	1.29384i	−0.949254	+	0.314510i	$0.898160\pi$
$318$	−2.03479e17	+	1.17479e17i	−0.618772	+	0.357248i
$319$	−1.17162e17	−	2.02931e17i	−0.348541	−	0.603690i
$320$	−6.18318e16	−	3.56986e16i	−0.179954	−	0.103897i
$321$		−	8.21462e17i		−	2.33912i
$322$	−5.87906e16	+	3.28482e17i	−0.163801	+	0.915210i
$323$	−1.83441e17			−0.500125
$324$	−3.27482e16	+	5.67216e16i	−0.0873720	+	0.151333i
$325$	−7.44762e17	+	4.29989e17i	−1.94462	+	1.12273i
$326$	−2.27111e17	−	3.93367e17i	−0.580382	−	1.00525i
$327$	−8.67147e16	−	5.00648e16i	−0.216899	−	0.125227i
$328$		−	1.03238e17i		−	0.252768i
$329$	6.66443e16	+	1.84577e17i	0.159732	+	0.442392i
$330$	7.25173e17			1.70155
$331$	8.28231e16	−	1.43454e17i	0.190264	−	0.329546i	−0.755074	−	0.655640i	$-0.772399\pi$
$331$	8.28231e16	−	1.43454e17i	0.190264	−	0.329546i	0.945338	+	0.326093i	$0.105732\pi$
$332$	−6.67009e16	+	3.85098e16i	−0.150026	+	0.0866173i
$333$	−1.16056e17	−	2.01014e17i	−0.255598	−	0.442708i
$334$	7.93493e16	+	4.58123e16i	0.171127	+	0.0988001i
$335$			5.21694e17i			1.10180i
$336$	−1.29579e17	+	1.53623e17i	−0.268014	+	0.317746i
$337$	−7.54004e17			−1.52744			−0.763721	−	0.645547i	$-0.776629\pi$
$337$	−7.54004e17			−1.52744			−0.763721	+	0.645547i	$0.776629\pi$
$338$	−1.10738e17	+	1.91803e17i	−0.219724	+	0.380573i
$339$	2.64613e17	−	1.52775e17i	0.514297	−	0.296929i
$340$	7.49239e16	+	1.29772e17i	0.142649	+	0.247075i
$341$	2.05408e17	+	1.18592e17i	0.383122	+	0.221196i
$342$			9.94975e17i			1.81815i
$343$	2.82992e17	−	4.81549e17i	0.506658	−	0.862147i
$344$	−7.81508e16			−0.137096
$345$	1.05714e18	−	1.83102e18i	1.81718	−	3.14745i
$346$	3.65689e17	−	2.11131e17i	0.615998	−	0.355647i
$347$	9.65027e16	+	1.67148e17i	0.159306	+	0.275927i	0.934619	−	0.355651i	$-0.115741\pi$
$347$	9.65027e16	+	1.67148e17i	0.159306	+	0.275927i	−0.775312	+	0.631578i	$0.782408\pi$
$348$	−3.56328e17	−	2.05726e17i	−0.576495	−	0.332840i
$349$			1.07803e18i			1.70943i	0.519095	+	0.854716i	$0.326269\pi$
$349$			1.07803e18i			1.70943i	−0.519095	+	0.854716i	$0.673731\pi$
$350$	−6.13233e17	−	5.17253e17i	−0.953123	−	0.803946i
$351$	−1.06274e18			−1.61911
$352$	−5.15237e16	+	8.92416e16i	−0.0769499	+	0.133281i
$353$	−8.88856e17	+	5.13181e17i	−1.30139	+	0.751359i	−0.980643	−	0.195805i	$-0.937268\pi$
$353$	−8.88856e17	+	5.13181e17i	−1.30139	+	0.751359i	−0.320750	+	0.947164i	$0.603935\pi$
$354$	−5.06718e17	−	8.77661e17i	−0.727350	−	1.25981i
$355$	−1.67140e18	−	9.64982e17i	−2.35224	−	1.35807i
$356$		−	6.27595e17i		−	0.866023i
$357$	3.96734e17	−	1.43246e17i	0.536812	−	0.193823i
$358$	3.48908e16			0.0462945
$359$	−2.95665e17	+	5.12107e17i	−0.384715	+	0.666346i	−0.991730	−	0.128345i	$-0.959034\pi$
$359$	−2.95665e17	+	5.12107e17i	−0.384715	+	0.666346i	0.607015	+	0.794691i	$0.292367\pi$
$360$	7.03878e17	−	4.06384e17i	0.898214	−	0.518584i
$361$	4.48629e17	+	7.77048e17i	0.561483	+	0.972518i
$362$	6.83114e17	+	3.94396e17i	0.838558	+	0.484141i
$363$			3.34289e17i			0.402509i
$364$	−5.30625e17	−	9.49695e16i	−0.626727	−	0.112169i
$365$	5.13134e17			0.594540
$366$	−4.92903e17	+	8.53733e17i	−0.560265	+	0.970408i
$367$	1.64369e17	−	9.48985e16i	0.183298	−	0.105827i	−0.405543	−	0.914076i	$-0.632918\pi$
$367$	1.64369e17	−	9.48985e16i	0.183298	−	0.105827i	0.588841	+	0.808249i	$0.299584\pi$
$368$	1.50220e17	+	2.60188e17i	0.164359	+	0.284677i
$369$	1.01778e18	+	5.87618e17i	1.09263	+	0.630828i
$370$			3.23245e17i			0.340502i
$371$	1.03575e17	−	5.78710e17i	0.107063	−	0.598196i
$372$	4.16475e17			0.422462
$373$	−5.43247e16	+	9.40932e16i	−0.0540799	+	0.0936691i	−0.891798	−	0.452434i	$-0.850556\pi$
$373$	−5.43247e16	+	9.40932e16i	−0.0540799	+	0.0936691i	0.837718	+	0.546103i	$0.183889\pi$
$374$	1.87300e17	−	1.08137e17i	0.182994	−	0.105651i
$375$	1.10023e18	+	1.90565e18i	1.05503	+	1.82736i
$376$	1.53009e17	+	8.83399e16i	0.144013	+	0.0831462i
$377$		−	1.10361e18i		−	1.01959i
$378$	−3.36684e17	−	9.32478e17i	−0.305338	−	0.845660i
$379$	7.18652e17			0.639800			0.319900	−	0.947451i	$-0.396351\pi$
$379$	7.18652e17			0.639800			0.319900	+	0.947451i	$0.396351\pi$
$380$	6.92816e17	−	1.19999e18i	0.605526	−	1.04880i
$381$	3.00719e17	−	1.73620e17i	0.258039	−	0.148979i
$382$	4.26404e17	+	7.38554e17i	0.359234	+	0.622212i
$383$	1.02256e18	+	5.90373e17i	0.845855	+	0.488355i	0.859250	−	0.511556i	$-0.170931\pi$
$383$	1.02256e18	+	5.90373e17i	0.845855	+	0.488355i	−0.0133950	+	0.999910i	$0.504264\pi$
$384$			1.80942e17i			0.146967i
$385$	−1.16991e18	+	1.38699e18i	−0.933099	+	1.10624i
$386$	−4.46438e16			−0.0349664
$387$	4.44825e17	−	7.70460e17i	0.342147	−	0.592616i
$388$	−5.81592e17	+	3.35782e17i	−0.439335	+	0.253650i
$389$	1.78611e17	+	3.09363e17i	0.132514	+	0.229521i	0.924645	−	0.380830i	$-0.124362\pi$
$389$	1.78611e17	+	3.09363e17i	0.132514	+	0.229521i	−0.792131	+	0.610351i	$0.791028\pi$
$390$	2.95780e18	+	1.70769e18i	2.15534	+	1.24439i
$391$		−	6.30560e17i		−	0.451325i
$392$	−8.47777e16	−	4.95674e17i	−0.0596045	−	0.348493i
$393$	−3.57233e18			−2.46720
$394$	−1.27083e17	+	2.20113e17i	−0.0862208	+	0.149339i
$395$	6.83798e17	−	3.94791e17i	0.455773	−	0.263140i
$396$	−5.86533e17	−	1.01590e18i	−0.384084	−	0.665253i
$397$	1.59849e17	+	9.22890e16i	0.102844	+	0.0593768i	0.550540	−	0.834809i	$-0.314422\pi$
$397$	1.59849e17	+	9.22890e16i	0.102844	+	0.0593768i	−0.447696	+	0.894186i	$0.647755\pi$
$398$		−	1.82479e18i		−	1.15354i
$399$	−2.98141e18	−	2.51478e18i	−1.85188	−	1.56203i
$400$	−7.22285e17			−0.440848
$401$	3.14634e17	−	5.44962e17i	0.188710	−	0.326855i	−0.756110	−	0.654444i	$-0.772903\pi$
$401$	3.14634e17	−	5.44962e17i	0.188710	−	0.326855i	0.944820	+	0.327589i	$0.106236\pi$
$402$	1.14500e18	−	6.61063e17i	0.674872	−	0.389638i
$403$	5.58539e17	+	9.67418e17i	0.323533	+	0.560375i
$404$	2.64527e17	+	1.52725e17i	0.150592	+	0.0869442i
$405$			1.03834e18i			0.580970i
$406$	9.68340e17	−	3.49633e17i	0.532532	−	0.192278i
$407$	4.66539e17			0.252189
$408$	1.89879e17	−	3.28881e17i	0.100892	−	0.174750i
$409$	−2.26527e18	+	1.30786e18i	−1.18320	+	0.683120i	−0.956752	−	0.290904i	$-0.906044\pi$
$409$	−2.26527e18	+	1.30786e18i	−1.18320	+	0.683120i	−0.226446	+	0.974024i	$0.572711\pi$
$410$	−8.18334e17	−	1.41740e18i	−0.420188	−	0.727787i
$411$	1.37547e17	+	7.94126e16i	0.0694316	+	0.0400864i
$412$			1.25819e18i			0.624405i
$413$	2.49613e18	+	4.46749e17i	1.21791	+	0.217978i
$414$	−3.42013e18			−1.64074
$415$	−6.10510e17	+	1.05743e18i	−0.287976	+	0.498788i
$416$	−4.20304e17	+	2.42663e17i	−0.194944	+	0.112551i
$417$	−8.07820e17	−	1.39919e18i	−0.368436	−	0.638150i
$418$	−1.73195e18	−	9.99939e17i	−0.776784	−	0.448476i
$419$		−	1.58195e18i		−	0.697741i	−0.937171	−	0.348870i	$-0.886565\pi$
$419$		−	1.58195e18i		−	0.697741i	0.937171	−	0.348870i	$-0.113435\pi$
$420$	−5.61320e17	+	3.13628e18i	−0.243481	+	1.36041i
$421$	4.17707e18			1.78196			0.890978	−	0.454046i	$-0.150020\pi$
$421$	4.17707e18			1.78196			0.890978	+	0.454046i	$0.150020\pi$
$422$	−7.01003e17	+	1.21417e18i	−0.294126	+	0.509440i
$423$	−1.74182e18	+	1.00564e18i	−0.718821	+	0.415012i
$424$	−2.64653e17	−	4.58392e17i	−0.107427	−	0.186070i
$425$	1.31283e18	+	7.57963e17i	0.524187	+	0.302640i
$426$			4.89110e18i			1.92105i
$427$	−8.37691e17	−	2.32006e18i	−0.323660	−	0.896405i
$428$	1.85056e18			0.703393
$429$	2.46470e18	−	4.26898e18i	0.921643	−	1.59633i
$430$	−1.07296e18	+	6.19476e17i	−0.394736	+	0.227901i
$431$	2.37383e18	+	4.11160e18i	0.859229	+	1.48823i	0.872665	+	0.488319i	$0.162390\pi$
$431$	2.37383e18	+	4.11160e18i	0.859229	+	1.48823i	−0.0134357	+	0.999910i	$0.504277\pi$
$432$	−7.72997e17	−	4.46290e17i	−0.275291	−	0.158939i
$433$		−	4.60551e18i		−	1.61385i	−0.590656	−	0.806923i	$-0.701131\pi$
$433$		−	4.60551e18i		−	1.61385i	0.590656	−	0.806923i	$-0.298869\pi$
$434$	−6.71893e17	+	7.96567e17i	−0.231671	+	0.274659i
$435$	−6.52290e18			−2.21318
$436$	1.12784e17	−	1.95348e17i	0.0376568	−	0.0652235i
$437$	−5.04957e18	+	2.91537e18i	−1.65915	+	0.957908i
$438$	−6.50217e17	−	1.12621e18i	−0.210252	−	0.364167i
$439$	4.37423e18	+	2.52546e18i	1.39204	+	0.803692i	0.993540	−	0.113478i	$-0.0361993\pi$
$439$	4.37423e18	+	2.52546e18i	1.39204	+	0.803692i	0.398495	+	0.917170i	$0.369533\pi$
$440$			1.63365e18i			0.511669i
$441$	5.36921e18	+	1.98553e18i	1.65516	+	0.612076i
$442$	1.01860e18			0.309063
$443$	2.58483e18	−	4.47706e18i	0.771979	−	1.33711i	−0.164497	−	0.986378i	$-0.552600\pi$
$443$	2.58483e18	−	4.47706e18i	0.771979	−	1.33711i	0.936477	−	0.350730i	$-0.114067\pi$
$444$	7.09447e17	−	4.09599e17i	0.208564	−	0.120414i
$445$	−4.97474e18	−	8.61651e18i	−1.43963	−	2.49351i
$446$	−4.10848e18	−	2.37203e18i	−1.17041	−	0.675735i
$447$			8.46951e17i			0.237523i
$448$	−3.46076e17	−	2.91910e17i	−0.0955489	−	0.0805941i
$449$	6.72832e18			1.82887			0.914434	−	0.404735i	$-0.132636\pi$
$449$	6.72832e18			1.82887			0.914434	+	0.404735i	$0.132636\pi$
$450$	4.11116e18	−	7.12074e18i	1.10021	−	1.90562i
$451$	−2.04572e18	+	1.18110e18i	−0.539028	+	0.311208i
$452$	3.44166e17	+	5.96112e17i	0.0892891	+	0.154653i
$453$	−8.25942e17	−	4.76858e17i	−0.210990	−	0.121815i
$454$			2.12628e18i			0.534848i
$455$	−8.03797e18	+	2.90222e18i	−1.99098	+	0.718871i
$456$	−3.51160e18			−0.856547
$457$	−1.57796e17	+	2.73311e17i	−0.0379038	+	0.0656513i	−0.884355	−	0.466815i	$-0.845401\pi$
$457$	−1.57796e17	+	2.73311e17i	−0.0379038	+	0.0656513i	0.846451	+	0.532466i	$0.178735\pi$
$458$	6.73406e16	−	3.88791e16i	0.0159301	−	0.00919725i
$459$	9.36670e17	+	1.62236e18i	0.218222	+	0.377971i
$460$	4.12486e18	+	2.38149e18i	0.946464	+	0.546441i
$461$			6.43896e18i			1.45515i	0.686026	+	0.727577i	$0.259354\pi$
$461$			6.43896e18i			1.45515i	−0.686026	+	0.727577i	$0.740646\pi$
$462$	4.52658e18	+	8.10151e17i	1.00757	+	0.180332i
$463$	5.23938e18			1.14872			0.574358	−	0.818604i	$-0.305252\pi$
$463$	5.23938e18			1.14872			0.574358	+	0.818604i	$0.305252\pi$
$464$	4.63453e17	−	8.02725e17i	0.100088	−	0.173357i
$465$	5.71795e18	−	3.30126e18i	1.21638	−	0.702278i
$466$	2.95469e18	+	5.11767e18i	0.619171	+	1.07243i
$467$	−5.72374e17	−	3.30460e17i	−0.118158	−	0.0682183i	0.439756	−	0.898117i	$-0.355065\pi$
$467$	−5.72374e17	−	3.30460e17i	−0.118158	−	0.0682183i	−0.557914	+	0.829899i	$0.688398\pi$
$468$		−	5.52483e18i		−	1.12356i
$469$	−5.82828e17	+	3.25645e18i	−0.116770	+	0.652431i
$470$	2.80097e18			0.552870
$471$	−8.15110e18	+	1.41181e19i	−1.58515	+	2.74556i
$472$	1.97717e18	−	1.14152e18i	0.378834	−	0.218720i
$473$	8.94088e17	+	1.54861e18i	0.168792	+	0.292357i
$474$	−1.73295e18	−	1.00052e18i	−0.322357	−	0.186113i
$475$		−	1.40177e19i		−	2.56933i
$476$	3.22701e17	+	8.93750e17i	0.0582843	+	0.161424i
$477$	6.02548e18			1.07242
$478$	−1.86534e18	+	3.23086e18i	−0.327161	+	0.566660i
$479$	7.42334e18	−	4.28586e18i	1.28307	−	0.740781i	0.305662	−	0.952140i	$-0.401122\pi$
$479$	7.42334e18	−	4.28586e18i	1.28307	−	0.740781i	0.977408	+	0.211359i	$0.0677889\pi$
$480$	1.43427e18	+	2.48422e18i	0.244310	+	0.423157i
$481$	1.90289e18	+	1.09864e18i	0.319447	+	0.184433i
$482$		−	1.10143e18i		−	0.182233i
$483$	8.64431e18	−	1.02483e19i	1.40961	−	1.67118i
$484$	−7.53075e17			−0.121038
$485$	−5.32328e18	+	9.22018e18i	−0.843309	+	1.46065i
$486$	−2.70753e18	+	1.56319e18i	−0.422785	+	0.244095i
$487$	−2.35544e18	−	4.07974e18i	−0.362551	−	0.627956i	0.625829	−	0.779960i	$-0.284761\pi$
$487$	−2.35544e18	−	4.07974e18i	−0.362551	−	0.627956i	−0.988380	+	0.152004i	$0.951427\pi$
$488$	−1.92326e18	−	1.11040e18i	−0.291810	−	0.168476i
$489$			1.82493e19i			2.72950i
$490$	−5.09300e18	−	6.13331e18i	−0.750933	−	0.904320i
$491$	−8.73975e18			−1.27037			−0.635183	−	0.772362i	$-0.719075\pi$
$491$	−8.73975e18			−1.27037			−0.635183	+	0.772362i	$0.719075\pi$
$492$	−2.07390e18	+	3.59210e18i	−0.297189	+	0.514746i
$493$	−1.68475e18	+	9.72693e17i	−0.238017	+	0.137419i
$494$	−4.70945e18	−	8.15701e18i	−0.655966	−	1.13617i
$495$	−1.61055e19	−	9.29852e18i	−2.21176	−	1.27696i
$496$			9.38221e17i			0.127038i
$497$	−9.35491e18	−	7.89074e18i	−1.24895	−	1.05347i
$498$	3.09442e18			0.407356
$499$	−6.97458e18	+	1.20803e19i	−0.905346	+	1.56811i	−0.0848937	+	0.996390i	$0.527055\pi$
$499$	−6.97458e18	+	1.20803e19i	−0.905346	+	1.56811i	−0.820452	+	0.571715i	$0.806278\pi$
$500$	−4.29298e18	+	2.47855e18i	−0.549501	+	0.317255i
$501$	−1.84061e18	−	3.18802e18i	−0.232326	−	0.402400i
$502$	3.15805e17	+	1.82330e17i	0.0393090	+	0.0226951i
$503$		−	2.62057e18i		−	0.321677i	−0.986981	−	0.160838i	$-0.948580\pi$
$503$		−	2.62057e18i		−	0.321677i	0.986981	−	0.160838i	$-0.0514198\pi$
$504$	4.84766e18	−	1.75032e18i	0.586838	−	0.211886i
$505$	4.84241e18			0.578125
$506$	3.43719e18	−	5.95339e18i	0.404716	−	0.700989i
$507$	7.70609e18	−	4.44911e18i	0.894908	−	0.516675i
$508$	3.91126e17	+	6.77450e17i	0.0447992	+	0.0775945i
$509$	−4.31622e18	−	2.49197e18i	−0.487617	−	0.281526i	0.235968	−	0.971761i	$-0.424174\pi$
$509$	−4.31622e18	−	2.49197e18i	−0.487617	−	0.281526i	−0.723585	+	0.690235i	$0.757507\pi$
$510$		−	6.02045e18i		−	0.670869i
$511$	3.20302e18	+	5.73265e17i	0.352057	+	0.0630099i
$512$	−4.07619e17			−0.0441942
$513$	8.66132e18	−	1.50018e19i	0.926323	−	1.60444i
$514$	6.43449e18	−	3.71496e18i	0.678848	−	0.391933i
$515$	9.97329e18	+	1.72742e19i	1.03798	+	1.79783i
$516$	2.71921e18	+	1.56994e18i	0.279187	+	0.161189i
$517$		−	4.04263e18i		−	0.409478i
$518$	−3.61124e17	+	2.01772e18i	−0.0360868	+	0.201629i
$519$	−1.69652e19			−1.67259
$520$	−3.84702e18	+	6.66324e18i	−0.374198	+	0.648130i
$521$	−1.60659e18	+	9.27564e17i	−0.154184	+	0.0890184i	−0.575107	−	0.818078i	$-0.695040\pi$
$521$	−1.60659e18	+	9.27564e17i	−0.154184	+	0.0890184i	0.420923	+	0.907096i	$0.361706\pi$
$522$	5.27584e18	+	9.13803e18i	0.499572	+	0.865284i
$523$	−1.01125e19	−	5.83848e18i	−0.944820	−	0.545492i	−0.0533517	−	0.998576i	$-0.516990\pi$
$523$	−1.01125e19	−	5.83848e18i	−0.944820	−	0.545492i	−0.891468	+	0.453084i	$0.850324\pi$
$524$		−	8.04764e18i		−	0.741907i
$525$	1.09462e19	+	3.03165e19i	0.995745	+	2.75780i
$526$	9.85826e18			0.884912
$527$	9.84566e17	−	1.70532e18i	0.0872108	−	0.151054i
$528$	3.58547e18	−	2.07007e18i	0.313407	−	0.180945i
$529$	−4.22489e18	−	7.31773e18i	−0.364440	−	0.631228i
$530$	−7.26705e18	−	4.19563e18i	−0.618624	−	0.357163i
$531$			2.59895e19i			2.18342i
$532$	5.66522e18	−	6.71643e18i	0.469716	−	0.556874i
$533$	−1.11253e19			−0.910380
$534$	−1.26075e19	+	2.18368e19i	−1.01821	+	1.76360i
$535$	2.54072e19	−	1.46688e19i	2.02525	−	1.16928i
$536$	1.48922e18	+	2.57941e18i	0.117167	+	0.202940i
$537$	−1.21400e18	−	7.00905e17i	−0.0942757	−	0.0544301i
$538$		−	9.00180e18i		−	0.690007i
$539$	−8.85219e18	+	7.35071e18i	−0.669775	+	0.556170i
$540$	−1.41504e19			−1.05685
$541$	8.75635e18	−	1.51664e19i	0.645569	−	1.11816i	−0.338601	−	0.940930i	$-0.609954\pi$
$541$	8.75635e18	−	1.51664e19i	0.645569	−	1.11816i	0.984170	−	0.177228i	$-0.0567129\pi$
$542$	−1.17585e19	+	6.78875e18i	−0.855767	+	0.494077i
$543$	−1.58457e19	−	2.74455e19i	−1.13844	−	1.97184i
$544$	7.40892e17	+	4.27754e17i	0.0525488	+	0.0303391i
$545$		−	3.57602e18i		−	0.250394i
$546$	1.65550e19	+	1.39639e19i	1.14441	+	0.965291i
$547$	1.84752e19			1.26089			0.630447	−	0.776232i	$-0.282871\pi$
$547$	1.84752e19			1.26089			0.630447	+	0.776232i	$0.282871\pi$
$548$	−1.78898e17	+	3.09861e17i	−0.0120543	+	0.0208787i
$549$	2.18940e19	−	1.26405e19i	1.45652	−	0.840925i
$550$	8.26334e18	+	1.43125e19i	0.542771	+	0.940107i
$551$	1.55788e19	+	8.99442e18i	1.01035	+	0.583327i
$552$		−	1.20708e19i		−	0.772969i
$553$	4.70937e18	−	1.70038e18i	0.297774	−	0.107516i
$554$	8.74928e18			0.546266
$555$	6.49352e18	−	1.12471e19i	0.400341	−	0.693410i
$556$	3.15204e18	−	1.81983e18i	0.191897	−	0.110792i
$557$	6.62715e18	+	1.14786e19i	0.398419	+	0.690082i	0.993531	−	0.113560i	$-0.0362256\pi$
$557$	6.62715e18	+	1.14786e19i	0.398419	+	0.690082i	−0.595112	+	0.803643i	$0.702892\pi$
$558$	−9.24957e18	−	5.34024e18i	−0.549139	−	0.317045i
$559$			8.42184e18i			0.493770i
$560$	−7.06530e18	−	1.26452e18i	−0.409086	−	0.0732167i
$561$	−8.68930e18			−0.496872
$562$	−1.39054e18	+	2.40849e18i	−0.0785288	+	0.136016i
$563$	−3.76620e18	+	2.17442e18i	−0.210060	+	0.121278i	−0.601340	−	0.798994i	$-0.705366\pi$
$563$	−3.76620e18	+	2.17442e18i	−0.210060	+	0.121278i	0.391279	+	0.920272i	$0.372033\pi$
$564$	−3.54924e18	−	6.14747e18i	−0.195516	−	0.338643i
$565$	9.45038e18	+	5.45618e18i	0.514174	+	0.296859i
$566$		−	4.16285e18i		−	0.223705i
$567$	−1.16001e18	+	6.48138e18i	−0.0615718	+	0.344022i
$568$	−1.10185e19			−0.577676
$569$	−7.74204e18	+	1.34096e19i	−0.400931	+	0.694433i	−0.993839	−	0.110838i	$-0.964647\pi$
$569$	−7.74204e18	+	1.34096e19i	−0.400931	+	0.694433i	0.592908	+	0.805270i	$0.297980\pi$
$570$	−4.82122e19	+	2.78353e19i	−2.46623	+	1.42388i
$571$	4.60112e18	+	7.96937e18i	0.232493	+	0.402690i	0.958541	−	0.284954i	$-0.0919783\pi$
$571$	4.60112e18	+	7.96937e18i	0.232493	+	0.402690i	−0.726048	+	0.687644i	$0.758645\pi$
$572$	9.61703e18	+	5.55239e18i	0.480030	+	0.277146i
$573$		−	3.42634e19i		−	1.68946i
$574$	−3.52461e18	−	9.76171e18i	−0.171683	−	0.475492i
$575$	4.81843e19			2.31863
$576$	2.32012e18	−	4.01857e18i	0.110294	−	0.191035i
$577$	−3.17461e19	+	1.83286e19i	−1.49094	+	0.860794i	−0.999946	−	0.0103706i	$-0.996699\pi$
$577$	−3.17461e19	+	1.83286e19i	−1.49094	+	0.860794i	−0.490992	+	0.871164i	$0.663366\pi$
$578$	6.72214e18	+	1.16431e19i	0.311898	+	0.540224i
$579$	1.55336e18	+	8.96830e17i	0.0712067	+	0.0411112i
$580$		−	1.46946e19i		−	0.665520i
$581$	−4.99219e18	+	5.91852e18i	−0.223387	+	0.264838i
$582$	2.69815e19			1.19290
$583$	−6.05554e18	+	1.04885e19i	−0.264529	+	0.458177i
$584$	2.53709e18	−	1.46479e18i	0.109508	−	0.0632244i
$585$	−4.37936e19	−	7.58527e19i	−1.86775	−	3.23504i
$586$	−1.92464e19	−	1.11119e19i	−0.811086	−	0.468281i
$587$		−	4.19471e18i		−	0.174677i	−0.996179	−	0.0873385i	$-0.972164\pi$
$587$		−	4.19471e18i		−	0.174677i	0.996179	−	0.0873385i	$-0.0278362\pi$
$588$	−7.00759e18	+	1.89497e19i	−0.288355	+	0.779762i
$589$	−1.82084e19			−0.740398
$590$	1.80969e19	−	3.13447e19i	0.727176	−	1.25951i
$591$	8.84352e18	−	5.10581e18i	0.351166	−	0.202746i
$592$	9.22732e17	+	1.59822e18i	0.0362096	+	0.0627169i
$593$	−2.52078e19	−	1.45538e19i	−0.977581	−	0.564407i	−0.0760422	−	0.997105i	$-0.524228\pi$
$593$	−2.52078e19	−	1.45538e19i	−0.977581	−	0.564407i	−0.901539	+	0.432698i	$0.857562\pi$
$594$			2.04232e19i			0.782742i
$595$	1.15150e19	+	9.71271e18i	0.436158	+	0.367893i
$596$	−1.90799e18			−0.0714252
$597$	−3.66574e19	+	6.34925e19i	−1.35626	+	2.34910i
$598$	2.80389e19	−	1.61883e19i	1.02530	−	0.591960i
$599$	−7.92133e18	−	1.37201e19i	−0.286293	−	0.495874i	0.686629	−	0.727008i	$-0.259090\pi$
$599$	−7.92133e18	−	1.37201e19i	−0.286293	−	0.495874i	−0.972922	+	0.231134i	$0.925756\pi$
$600$	2.51315e19	+	1.45097e19i	0.897757	+	0.518320i
$601$		−	2.81883e19i		−	0.995284i	−0.867383	−	0.497642i	$-0.834199\pi$
$601$		−	2.81883e19i		−	0.995284i	0.867383	−	0.497642i	$-0.165801\pi$
$602$	−7.38959e18	+	2.66812e18i	−0.257896	+	0.0931170i
$603$	−3.39059e19			−1.16965
$604$	1.07425e18	−	1.86066e18i	0.0366308	−	0.0634465i
$605$	−1.03393e19	+	5.96938e18i	−0.348500	+	0.201206i
$606$	−6.13604e18	−	1.06279e19i	−0.204447	−	0.354112i
$607$	4.59576e19	+	2.65337e19i	1.51369	+	0.873929i	0.999872	+	0.0160303i	$0.00510283\pi$
$607$	4.59576e19	+	2.65337e19i	1.51369	+	0.873929i	0.513818	+	0.857899i	$0.328231\pi$
$608$		−	7.91082e18i		−	0.257571i
$609$	−4.07164e19	−	7.28728e18i	−1.31053	−	0.234555i
$610$	−3.52070e19			−1.12026
$611$	9.51986e18	−	1.64889e19i	0.299462	−	0.518684i
$612$	−8.43414e18	+	4.86945e18i	−0.262289	+	0.151433i
$613$	1.44888e19	+	2.50954e19i	0.445462	+	0.771562i	0.998084	−	0.0618696i	$-0.0197063\pi$
$613$	1.44888e19	+	2.50954e19i	0.445462	+	0.771562i	−0.552623	+	0.833432i	$0.686373\pi$
$614$	1.66253e19	+	9.59861e18i	0.505348	+	0.291763i
$615$			6.57566e19i			1.97612i
$616$	−1.82508e18	+	1.01973e19i	−0.0542272	+	0.302985i
$617$	1.58310e19			0.465062			0.232531	−	0.972589i	$-0.425299\pi$
$617$	1.58310e19			0.465062			0.232531	+	0.972589i	$0.425299\pi$
$618$	2.52753e19	−	4.37780e19i	0.734136	−	1.27156i
$619$	−1.46006e19	+	8.42969e18i	−0.419312	+	0.242090i	−0.694783	−	0.719219i	$-0.744500\pi$
$619$	−1.46006e19	+	8.42969e18i	−0.419312	+	0.242090i	0.275471	+	0.961309i	$0.411166\pi$
$620$	7.43698e18	+	1.28812e19i	0.211181	+	0.365776i
$621$	5.15674e19	+	2.97724e19i	1.44788	+	0.835936i
$622$		−	1.13856e19i		−	0.316098i
$623$	−2.14265e19	−	5.93425e19i	−0.588212	−	1.62911i
$624$	1.94990e19			0.529322
$625$	−6.44767e18	+	1.11677e19i	−0.173078	+	0.299781i
$626$	9.82678e18	−	5.67349e18i	0.260850	−	0.150602i
$627$	4.01747e19	+	6.95845e19i	1.05458	+	1.82659i
$628$	−3.18048e19	−	1.83625e19i	−0.825611	−	0.476667i
$629$		−	3.87325e18i		−	0.0994308i
$630$	5.26813e19	−	6.24566e19i	1.33743	−	1.58560i
$631$	−2.71554e19			−0.681791			−0.340895	−	0.940101i	$-0.610730\pi$
$631$	−2.71554e19			−0.681791			−0.340895	+	0.940101i	$0.610730\pi$
$632$	2.25393e18	−	3.90393e18i	0.0559656	−	0.0969353i
$633$	4.87819e19	−	2.81643e19i	1.19793	−	0.691628i
$634$	2.17486e19	+	3.76696e19i	0.528209	+	0.914885i
$635$	1.07399e19	+	6.20066e18i	0.257978	+	0.148944i
$636$			2.12659e19i			0.505225i
$637$	−5.34158e19	+	9.13598e18i	−1.25515	+	0.214674i
$638$	−2.12086e19			−0.492911
$639$	6.27160e19	−	1.08627e20i	1.44169	−	2.49708i
$640$	−5.59637e18	+	3.23107e18i	−0.127247	+	0.0734660i
$641$	1.37457e19	+	2.38083e19i	0.309144	+	0.535453i	0.978175	−	0.207781i	$-0.0666241\pi$
$641$	1.37457e19	+	2.38083e19i	0.309144	+	0.535453i	−0.669031	+	0.743234i	$0.733291\pi$
$642$	−6.43892e19	−	3.71751e19i	−1.43241	−	0.827004i
$643$			4.05690e19i			0.892724i	0.894852	+	0.446362i	$0.147281\pi$
$643$			4.05690e19i			0.892724i	−0.894852	+	0.446362i	$0.852719\pi$
$644$	2.30871e19	+	1.94736e19i	0.502537	+	0.423883i
$645$	4.97775e19			1.07180
$646$	−8.30159e18	+	1.43788e19i	−0.176821	+	0.306263i
$647$	2.71480e19	−	1.56739e19i	0.572016	−	0.330254i	−0.185938	−	0.982561i	$-0.559532\pi$
$647$	2.71480e19	−	1.56739e19i	0.572016	−	0.330254i	0.757954	+	0.652308i	$0.226199\pi$
$648$	2.96403e18	+	5.13385e18i	0.0617814	+	0.107008i
$649$	−4.52397e19	−	2.61192e19i	−0.932840	−	0.538576i
$650$			7.78363e19i			1.58777i
$651$	3.93800e19	−	1.42187e19i	0.794709	−	0.286941i
$652$	−4.11114e19			−0.820785
$653$	−1.04926e19	+	1.81738e19i	−0.207249	+	0.358966i	−0.950847	−	0.309661i	$-0.899784\pi$
$653$	−1.04926e19	+	1.81738e19i	−0.207249	+	0.358966i	0.743598	+	0.668627i	$0.233118\pi$
$654$	−7.84852e18	+	4.53135e18i	−0.153371	+	0.0885488i
$655$	−6.37911e19	−	1.10489e20i	−1.23331	−	2.13615i
$656$	−8.09217e18	−	4.67202e18i	−0.154788	−	0.0893671i
$657$			3.33496e19i			0.631150i
$658$	1.74838e19	+	3.12920e18i	0.327383	+	0.0585938i
$659$	−3.07340e19			−0.569404			−0.284702	−	0.958616i	$-0.591895\pi$
$659$	−3.07340e19			−0.569404			−0.284702	+	0.958616i	$0.591895\pi$
$660$	3.28176e19	−	5.68417e19i	0.601588	−	1.04198i
$661$	−2.14587e19	+	1.23892e19i	−0.389219	+	0.224716i	−0.681822	−	0.731518i	$-0.738812\pi$
$661$	−2.14587e19	+	1.23892e19i	−0.389219	+	0.224716i	0.292603	+	0.956234i	$0.405479\pi$
$662$	−7.49629e18	−	1.29840e19i	−0.134537	−	0.233024i
$663$	−3.54415e19	−	2.04622e19i	−0.629386	−	0.363376i
$664$			6.97102e18i			0.122495i
$665$	2.45411e19	−	1.37119e20i	0.426719	−	2.38422i
$666$	−2.10083e19			−0.361470
$667$	−3.09174e19	+	5.35506e19i	−0.526408	+	0.911766i
$668$	7.18188e18	−	4.14646e18i	0.121005	−	0.0698622i
$669$	9.53014e19	+	1.65067e20i	1.58897	+	2.75218i
$670$	4.08923e19	+	2.36092e19i	0.674711	+	0.389545i
$671$			5.08142e19i			0.829712i
$672$	6.17745e18	+	1.71090e19i	0.0998216	+	0.276465i
$673$	4.61683e19			0.738309			0.369154	−	0.929368i	$-0.379647\pi$
$673$	4.61683e19			0.738309			0.369154	+	0.929368i	$0.379647\pi$
$674$	−3.41223e19	+	5.91016e19i	−0.540032	+	0.935363i
$675$	−1.23973e20	+	7.15757e19i	−1.94178	+	1.12109i
$676$	1.00228e19	+	1.73600e19i	0.155368	+	0.269106i
$677$	8.58630e19	+	4.95730e19i	1.31730	+	0.760545i	0.983294	−	0.182026i	$-0.0582654\pi$
$677$	8.58630e19	+	4.95730e19i	1.31730	+	0.760545i	0.334008	+	0.942570i	$0.391599\pi$
$678$		−	2.76551e19i		−	0.419921i
$679$	−4.35289e19	+	5.16059e19i	−0.654167	+	0.775552i
$680$	1.35627e19			0.201736
$681$	4.27139e19	−	7.39827e19i	0.628839	−	1.08918i
$682$	1.85914e19	−	1.07338e19i	0.270908	−	0.156409i
$683$	−3.22343e19	−	5.58314e19i	−0.464915	−	0.805256i	0.534283	−	0.845306i	$-0.320582\pi$
$683$	−3.22343e19	−	5.58314e19i	−0.464915	−	0.805256i	−0.999198	+	0.0400498i	$0.987248\pi$
$684$	7.79898e19	+	4.50275e19i	1.11338	+	0.642813i
$685$			5.67227e18i			0.0801536i
$686$	−2.49388e19	−	4.39743e19i	−0.348824	−	0.615078i
$687$	−3.12410e18			−0.0432541
$688$	−3.53670e18	+	6.12575e18i	−0.0484707	+	0.0839537i
$689$	−4.93981e19	+	2.85200e19i	−0.670156	+	0.386914i
$690$	−9.56813e19	−	1.65725e20i	−1.28494	−	2.22558i
$691$	1.24395e19	+	7.18196e18i	0.165370	+	0.0954765i	0.580401	−	0.814331i	$-0.302896\pi$
$691$	1.24395e19	+	7.18196e18i	0.165370	+	0.0954765i	−0.415031	+	0.909807i	$0.636229\pi$
$692$		−	3.82187e19i		−	0.502960i
$693$	−9.01435e19	−	7.60347e19i	−1.17436	−	0.990557i
$694$	1.74688e19			0.225293
$695$	2.88504e19	−	4.99704e19i	0.368348	−	0.637998i
$696$	−3.22512e19	+	1.86202e19i	−0.407644	+	0.235353i
$697$	9.80560e18	+	1.69838e19i	0.122700	+	0.212523i
$698$	8.44998e19	+	4.87860e19i	1.04681	+	0.604376i
$699$		−	2.37422e20i		−	2.91192i
$700$	−6.82960e19	+	2.46592e19i	−0.829295	+	0.299429i
$701$	−1.02344e20			−1.23037			−0.615186	−	0.788382i	$-0.710919\pi$
$701$	−1.02344e20			−1.23037			−0.615186	+	0.788382i	$0.710919\pi$
$702$	−4.80940e19	+	8.33012e19i	−0.572441	+	0.991497i
$703$	−3.10172e19	+	1.79078e19i	−0.365524	+	0.211035i
$704$	4.66339e18	+	8.07723e18i	0.0544118	+	0.0942440i
$705$	−9.74580e19	−	5.62674e19i	−1.12588	−	0.650030i
$706$			9.28957e19i			1.06258i
$707$	3.02266e19	+	5.40985e18i	0.342337	+	0.0612702i
$708$	−9.17257e19			−1.02863
$709$	1.55870e19	−	2.69974e19i	0.173076	−	0.299777i	−0.766418	−	0.642343i	$-0.777963\pi$
$709$	1.55870e19	−	2.69974e19i	0.173076	−	0.299777i	0.939494	+	0.342566i	$0.111296\pi$
$710$	−1.51278e20	+	8.73402e19i	−1.66328	+	0.960297i
$711$	2.56582e19	+	4.44414e19i	0.279344	+	0.483838i
$712$	−4.91932e19	−	2.84017e19i	−0.530329	−	0.306185i
$713$		−	6.25897e19i		−	0.668153i
$714$	6.72595e18	−	3.75801e19i	0.0710994	−	0.397256i
$715$	1.76048e20			1.84285
$716$	1.57898e18	−	2.73487e18i	0.0163676	−	0.0283495i
$717$	1.29806e20	−	7.49438e19i	1.33248	−	0.769310i
$718$	2.67606e19	+	4.63507e19i	0.272035	+	0.471178i
$719$	8.37808e19	+	4.83709e19i	0.843417	+	0.486947i	0.858424	−	0.512941i	$-0.171444\pi$
$719$	8.37808e19	+	4.83709e19i	0.843417	+	0.486947i	−0.0150075	+	0.999887i	$0.504777\pi$
$720$		−	7.35634e19i		−	0.733389i
$721$	4.29554e19	+	1.18969e20i	0.424103	+	1.17459i
$722$	8.12105e19			0.794057
$723$	−2.21261e19	+	3.83236e19i	−0.214258	+	0.371106i
$724$	6.18284e19	−	3.56966e19i	0.592950	−	0.342340i
$725$	−7.43284e19	−	1.28741e20i	−0.705974	−	1.22278i
$726$	2.62028e19	+	1.51282e19i	0.246485	+	0.142308i
$727$			7.80294e18i			0.0726971i	0.999339	+	0.0363486i	$0.0115727\pi$
$727$			7.80294e18i			0.0726971i	−0.999339	+	0.0363486i	$0.988427\pi$
$728$	−3.14574e19	+	3.72945e19i	−0.290271	+	0.344132i
$729$	1.63850e20			1.49745
$730$	2.32218e19	−	4.02213e19i	0.210202	−	0.364080i
$731$	1.28567e19	−	7.42281e18i	0.115268	−	0.0665498i
$732$	4.46125e19	+	7.72711e19i	0.396168	+	0.686182i
$733$	−1.18263e19	−	6.82790e18i	−0.104021	−	0.0600564i	0.447087	−	0.894490i	$-0.352461\pi$
$733$	−1.18263e19	−	6.82790e18i	−0.104021	−	0.0600564i	−0.551108	+	0.834434i	$0.685795\pi$
$734$		−	1.71785e19i		−	0.149662i
$735$	5.39985e19	+	3.15716e20i	0.465983	+	2.72449i
$736$	2.71927e19			0.232438
$737$	3.40751e19	−	5.90197e19i	0.288512	−	0.499718i
$738$	9.21194e19	−	5.31851e19i	0.772603	−	0.446062i
$739$	1.20735e18	+	2.09119e18i	0.0100305	+	0.0173733i	0.870997	−	0.491288i	$-0.163474\pi$
$739$	1.20735e18	+	2.09119e18i	0.0100305	+	0.0173733i	−0.860967	+	0.508661i	$0.830140\pi$
$740$	2.53371e19	+	1.46284e19i	0.208514	+	0.120386i
$741$			3.78424e20i			3.08497i
$742$	−4.06741e19	−	3.43080e19i	−0.328466	−	0.277057i
$743$	−8.97332e19			−0.717846			−0.358923	−	0.933367i	$-0.616856\pi$
$743$	−8.97332e19			−0.717846			−0.358923	+	0.933367i	$0.616856\pi$
$744$	1.88475e19	−	3.26448e19i	0.149363	−	0.258704i
$745$	−2.61955e19	+	1.51240e19i	−0.205652	+	0.118733i
$746$	4.91691e18	+	8.51634e18i	0.0382402	+	0.0662340i
$747$	−6.87246e19	−	3.96782e19i	−0.529503	−	0.305709i
$748$		−	1.95750e19i		−	0.149414i
$749$	1.74981e20	−	6.31794e19i	1.32318	−	0.477752i
$750$	1.99162e20			1.49203
$751$	3.88512e19	−	6.72923e19i	0.288353	−	0.499443i	−0.685064	−	0.728483i	$-0.740226\pi$
$751$	3.88512e19	−	6.72923e19i	0.288353	−	0.499443i	0.973417	+	0.229041i	$0.0735589\pi$
$752$	1.38488e19	−	7.99562e18i	0.101833	−	0.0587932i
$753$	−7.32549e18	−	1.26881e19i	−0.0533668	−	0.0924341i
$754$	−8.65048e19	−	4.99436e19i	−0.624368	−	0.360479i
$755$		−	3.40609e19i		−	0.243572i
$756$	−8.83276e19	−	1.58086e19i	−0.625812	−	0.112006i
$757$	−1.71391e20			−1.20314			−0.601571	−	0.798819i	$-0.705458\pi$
$757$	−1.71391e20			−1.20314			−0.601571	+	0.798819i	$0.705458\pi$
$758$	3.25225e19	−	5.63305e19i	0.226203	−	0.391796i
$759$	−2.39190e20	+	1.38096e20i	−1.64836	+	0.951678i
$760$	−6.27066e19	−	1.08611e20i	−0.428172	−	0.741615i
$761$	5.11853e19	+	2.95519e19i	0.346300	+	0.199937i	0.663055	−	0.748571i	$-0.269260\pi$
$761$	5.11853e19	+	2.95519e19i	0.346300	+	0.199937i	−0.316754	+	0.948508i	$0.602593\pi$
$762$		−	3.14286e19i		−	0.210688i
$763$	3.99507e18	−	2.23218e19i	0.0265370	−	0.148271i
$764$	7.71874e19			0.508034
$765$	−7.71972e19	+	1.33709e20i	−0.503467	+	0.872031i
$766$	9.25513e19	−	5.34345e19i	0.598110	−	0.345319i
$767$	−1.23014e20	−	2.13067e20i	−0.787750	−	1.36442i
$768$	1.41829e19	+	8.18848e18i	0.0899985	+	0.0519607i
$769$		−	1.59565e20i		−	1.00335i	−0.865055	−	0.501676i	$-0.832717\pi$
$769$		−	1.59565e20i		−	1.00335i	0.865055	−	0.501676i	$-0.167283\pi$
$770$	5.57736e19	+	1.54470e20i	0.347531	+	0.962519i
$771$	−2.98512e20			−1.84324
$772$	−2.02035e18	+	3.49935e18i	−0.0123625	+	0.0214124i
$773$	5.86691e19	−	3.38726e19i	0.355757	−	0.205396i	−0.311461	−	0.950259i	$-0.600818\pi$
$773$	5.86691e19	−	3.38726e19i	0.355757	−	0.205396i	0.667218	+	0.744863i	$0.267485\pi$
$774$	−4.02610e19	−	6.97340e19i	−0.241934	−	0.419043i
$775$	1.30312e20	+	7.52357e19i	0.776020	+	0.448035i
$776$			6.07831e19i			0.358716i
$777$	5.30981e19	−	6.29508e19i	0.310550	−	0.368175i
$778$	3.23321e19			0.187403
$779$	9.06716e19	−	1.57048e20i	0.520846	−	0.902132i
$780$	2.67709e20	−	1.54562e20i	1.52406	−	0.879915i
$781$	1.26058e20	+	2.18339e20i	0.711234	+	1.23189i
$782$	−4.94256e19	−	2.85359e19i	−0.276379	−	0.159568i
$783$		−	1.83706e20i		−	1.01810i
$784$	−4.26894e19	−	1.57865e19i	−0.234481	−	0.0867107i
$785$	−5.82216e20			−3.16954
$786$	−1.61665e20	+	2.80013e20i	−0.872287	+	1.51085i
$787$	1.01723e20	−	5.87299e19i	0.543997	−	0.314077i	−0.202700	−	0.979241i	$-0.564972\pi$
$787$	1.01723e20	−	5.87299e19i	0.543997	−	0.314077i	0.746697	+	0.665164i	$0.231638\pi$
$788$	1.15022e19	+	1.99224e19i	0.0609673	+	0.105599i
$789$	−3.43012e20	−	1.98038e20i	−1.80206	−	1.04042i
$790$		−	7.14648e19i		−	0.372137i
$791$	5.28944e19	+	4.46156e19i	0.273007	+	0.230278i
$792$	−1.06174e20			−0.543177
$793$	−1.19661e20	+	2.07258e20i	−0.606791	+	1.05099i
$794$	1.44679e19	−	8.35305e18i	0.0727214	−	0.0419857i
$795$	1.68568e20	+	2.91969e20i	0.839858	+	1.45468i
$796$	−1.43034e20	−	8.25807e19i	−0.706395	−	0.407837i
$797$		−	6.59263e19i		−	0.322738i	−0.986894	−	0.161369i	$-0.948409\pi$
$797$		−	6.59263e19i		−	0.322738i	0.986894	−	0.161369i	$-0.0515909\pi$
$798$	−3.32041e20	+	1.19888e20i	−1.61128	+	0.581776i
$799$	−3.35623e19			−0.161445
$800$	−3.26869e19	+	5.66153e19i	−0.155863	+	0.269963i
$801$	5.60003e20	−	3.23318e20i	2.64706	−	1.52828i
$802$	−2.84774e19	−	4.93243e19i	−0.133438	−	0.231122i
$803$	−5.80513e19	−	3.35159e19i	−0.269652	−	0.155684i
$804$		−	1.19665e20i		−	0.551031i
$805$	4.71333e20	+	8.43576e19i	2.15158	+	0.385082i
$806$	1.01106e20			0.457545
$807$	−1.80833e20	+	3.13212e20i	−0.811265	+	1.40515i
$808$	2.39423e19	−	1.38231e19i	0.106484	−	0.0614788i
$809$	2.16102e20	+	3.74299e20i	0.952836	+	1.65036i	0.739244	+	0.673438i	$0.235183\pi$
$809$	2.16102e20	+	3.74299e20i	0.952836	+	1.65036i	0.213592	+	0.976923i	$0.431484\pi$
$810$	8.13888e19	+	4.69898e19i	0.355770	+	0.205404i
$811$			5.89898e19i			0.255641i	0.991797	+	0.127821i	$0.0407982\pi$
$811$			5.89898e19i			0.255641i	−0.991797	+	0.127821i	$0.959202\pi$
$812$	1.64165e19	−	9.17246e19i	0.0705325	−	0.394088i
$813$	5.45504e20			2.32362
$814$	2.11131e19	−	3.65690e19i	0.0891624	−	0.154434i
$815$	−5.64435e20	+	3.25877e20i	−2.36326	+	1.36443i
$816$	−1.71859e19	−	2.97669e19i	−0.0713414	−	0.123567i
$817$	−1.18885e20	−	6.86381e19i	−0.489296	−	0.282495i
$818$			2.36747e20i			0.966077i
$819$	−1.88621e20	−	5.22403e20i	−0.763137	−	2.11358i
$820$	−1.48134e20			−0.594236
$821$	−1.39130e20	+	2.40981e20i	−0.553375	+	0.958474i	0.444653	+	0.895703i	$0.353327\pi$
$821$	−1.39130e20	+	2.40981e20i	−0.553375	+	0.958474i	−0.998028	+	0.0627706i	$0.980006\pi$
$822$	1.24493e19	−	7.18761e18i	0.0490956	−	0.0283453i
$823$	−1.82964e20	−	3.16904e20i	−0.715431	−	1.23916i	−0.962793	−	0.270240i	$-0.912897\pi$
$823$	−1.82964e20	−	3.16904e20i	−0.715431	−	1.23916i	0.247362	−	0.968923i	$-0.420436\pi$
$824$	9.86218e19	+	5.69393e19i	0.382369	+	0.220761i
$825$		−	6.63994e20i		−	2.55262i
$826$	1.47980e20	−	1.75438e20i	0.564082	−	0.668751i
$827$	2.98112e20			1.12678			0.563392	−	0.826189i	$-0.309496\pi$
$827$	2.98112e20			1.12678			0.563392	+	0.826189i	$0.309496\pi$
$828$	−1.54777e20	+	2.68082e20i	−0.580090	+	1.00475i
$829$	1.54349e20	−	8.91134e19i	0.573617	−	0.331178i	−0.184976	−	0.982743i	$-0.559221\pi$
$829$	1.54349e20	−	8.91134e19i	0.573617	−	0.331178i	0.758593	+	0.651565i	$0.225887\pi$
$830$	5.52570e19	+	9.57080e19i	0.203630	+	0.352697i
$831$	−3.04426e20	−	1.75760e20i	−1.11243	−	0.642264i
$832$			4.39267e19i			0.159171i
$833$	6.10263e19	+	7.34917e19i	0.219281	+	0.264073i
$834$	−1.46231e20			−0.521047
$835$	6.57353e19	−	1.13857e20i	0.232270	−	0.402304i
$836$	−1.56758e20	+	9.05042e19i	−0.549269	+	0.317121i
$837$	9.29742e19	+	1.61036e20i	0.323061	+	0.559558i
$838$	−1.23999e20	−	7.15908e19i	−0.427277	−	0.246689i
$839$			2.04910e20i			0.700211i	0.936710	+	0.350106i	$0.113854\pi$
$839$			2.04910e20i			0.700211i	−0.936710	+	0.350106i	$0.886146\pi$
$840$	2.20430e20	+	1.85930e20i	0.746993	+	0.630078i
$841$	−1.06787e20			−0.358878
$842$	1.89033e20	−	3.27414e20i	0.630017	−	1.09122i
$843$	9.67659e19	−	5.58678e19i	0.319838	−	0.184658i
$844$	6.34476e19	+	1.09894e20i	0.207978	+	0.360229i
$845$	2.75215e20	+	1.58895e20i	0.894694	+	0.516552i
$846$			1.82040e20i			0.586915i
$847$	−7.12073e19	+	2.57104e19i	−0.227688	+	0.0822101i
$848$	−4.79072e19			−0.151925
$849$	−8.36257e19	+	1.44844e20i	−0.263018	+	0.455561i
$850$	1.18824e20	−	6.86030e19i	0.370656	−	0.213998i
$851$	−6.15564e19	−	1.06619e20i	−0.190443	−	0.329858i
$852$	3.83382e20	+	2.21346e20i	1.17640	+	0.679195i
$853$			5.10267e20i			1.55294i	0.630155	+	0.776469i	$0.282991\pi$
$853$			5.10267e20i			1.55294i	−0.630155	+	0.776469i	$0.717009\pi$
$854$	−2.19765e20	−	3.93327e19i	−0.663365	−	0.118727i
$855$	1.42767e21			4.27431
$856$	8.37470e19	−	1.45054e20i	0.248687	−	0.430738i
$857$	2.14939e20	−	1.24095e20i	0.633066	−	0.365501i	−0.148872	−	0.988856i	$-0.547564\pi$
$857$	2.14939e20	−	1.24095e20i	0.633066	−	0.365501i	0.781939	+	0.623355i	$0.214231\pi$
$858$	−2.23079e20	−	3.86384e20i	−0.651700	−	1.12878i
$859$	−2.77482e20	−	1.60204e20i	−0.804048	−	0.464217i	0.0408365	−	0.999166i	$-0.486998\pi$
$859$	−2.77482e20	−	1.60204e20i	−0.804048	−	0.464217i	−0.844885	+	0.534948i	$0.820331\pi$
$860$			1.12137e20i			0.322300i
$861$	−7.34622e19	+	4.10457e20i	−0.209431	+	1.17016i
$862$	4.29710e20			1.21513
$863$	8.09310e19	−	1.40177e20i	0.227007	−	0.393188i	−0.729913	−	0.683540i	$-0.760439\pi$
$863$	8.09310e19	−	1.40177e20i	0.227007	−	0.393188i	0.956920	+	0.290353i	$0.0937727\pi$
$864$	−6.99637e19	+	4.03935e19i	−0.194660	+	0.112387i
$865$	−3.02948e20	−	5.24721e20i	−0.836093	−	1.44816i
$866$	−3.60997e20	−	2.08421e20i	−0.988275	−	0.570581i
$867$		−	5.40152e20i		−	1.46684i
$868$	3.20314e19	+	8.87139e19i	0.0862856	+	0.238976i
$869$	−1.03145e20			−0.275619
$870$	−2.95193e20	+	5.11289e20i	−0.782476	+	1.35529i
$871$	2.77967e20	−	1.60485e20i	0.730915	−	0.421994i
$872$	−1.02081e19	−	1.76809e19i	−0.0266274	−	0.0461200i
$873$	−5.99237e20	−	3.45970e20i	−1.55060	−	0.895238i
$874$			5.27739e20i			1.35469i
$875$	−3.21305e20	+	3.80926e20i	−0.818204	+	0.970027i
$876$	−1.17702e20			−0.297341
$877$	1.33797e20	−	2.31744e20i	0.335313	−	0.580780i	−0.648232	−	0.761443i	$-0.724491\pi$
$877$	1.33797e20	−	2.31744e20i	0.335313	−	0.580780i	0.983545	+	0.180664i	$0.0578245\pi$
$878$	3.95910e20	−	2.28579e20i	0.984318	−	0.568296i
$879$	4.46445e20	+	7.73265e20i	1.10115	+	1.90724i
$880$	1.28051e20	+	7.39304e19i	0.313332	+	0.180902i
$881$		−	2.81911e20i		−	0.684354i	−0.939635	−	0.342177i	$-0.888836\pi$
$881$		−	2.81911e20i		−	0.684354i	0.939635	−	0.342177i	$-0.111164\pi$
$882$	3.98616e20	−	3.31004e20i	0.960007	−	0.797174i
$883$	−2.77433e19			−0.0662876			−0.0331438	−	0.999451i	$-0.510552\pi$
$883$	−2.77433e19			−0.0662876			−0.0331438	+	0.999451i	$0.510552\pi$
$884$	4.60965e19	−	7.98415e19i	0.109270	−	0.189262i
$885$	−1.25934e21	+	7.27080e20i	−2.96169	+	1.70993i
$886$	−2.33952e20	−	4.05217e20i	−0.545872	−	0.945478i
$887$	1.56646e20	+	9.04399e19i	0.362623	+	0.209360i	0.670231	−	0.742153i	$-0.266195\pi$
$887$	1.56646e20	+	9.04399e19i	0.362623	+	0.209360i	−0.307608	+	0.951513i	$0.599528\pi$
$888$		−	7.41454e19i		−	0.170292i
$889$	6.01116e19	+	5.07033e19i	0.136976	+	0.115538i
$890$	−9.00525e20			−2.03594
$891$	6.78203e19	−	1.17468e20i	0.152130	−	0.263497i
$892$	−3.71857e20	+	2.14692e20i	−0.827603	+	0.477817i
$893$	1.55174e20	+	2.68769e20i	0.342656	+	0.593498i
$894$	6.63872e19	+	3.83286e19i	0.145453	+	0.0839771i
$895$		−	5.00641e19i		−	0.108834i
$896$	−3.85426e19	+	1.39164e19i	−0.0831352	+	0.0300172i
$897$	−1.30080e21			−2.78395
$898$	3.04489e20	−	5.27391e20i	0.646603	−	1.11995i
$899$	−1.67229e20	+	9.65498e19i	−0.352366	+	0.203439i
$900$	−3.72100e20	−	6.44495e20i	−0.777968	−	1.34748i
$901$	8.70766e19	+	5.02737e19i	0.180646	+	0.104296i
$902$			2.13802e20i			0.440115i
$903$	3.10715e20	+	5.56106e19i	0.634669	+	0.113591i
$904$	6.23006e19			0.126274
$905$	5.65911e20	−	9.80187e20i	1.13817	−	1.97137i
$906$	−7.47557e19	+	4.31602e19i	−0.149193	+	0.0861364i
$907$	−2.40716e20	−	4.16932e20i	−0.476709	−	0.825685i	0.522935	−	0.852373i	$-0.324837\pi$
$907$	−2.40716e20	−	4.16932e20i	−0.476709	−	0.825685i	−0.999644	+	0.0266882i	$0.991504\pi$
$908$	1.66666e20	+	9.62246e19i	0.327526	+	0.189097i
$909$			3.14717e20i			0.613724i
$910$	−1.36270e20	+	7.61385e20i	−0.263700	+	1.47338i
$911$	3.50358e20			0.672795			0.336398	−	0.941720i	$-0.390791\pi$
$911$	3.50358e20			0.672795			0.336398	+	0.941720i	$0.390791\pi$
$912$	−1.58917e20	+	2.75252e20i	−0.302835	+	0.524526i
$913$	1.38135e20	−	7.97523e19i	0.261221	−	0.150816i
$914$	1.42821e19	+	2.47373e19i	0.0268020	+	0.0464225i
$915$	1.22501e21	+	7.07258e20i	2.28134	+	1.31713i
$916$		−	7.03787e18i		−	0.0130069i
$917$	−2.74751e20	−	7.60948e20i	−0.503912	−	1.39563i
$918$	1.69555e20			0.308612
$919$	−2.95775e20	+	5.12297e20i	−0.534260	+	0.925365i	0.464939	+	0.885343i	$0.346076\pi$
$919$	−2.95775e20	+	5.12297e20i	−0.534260	+	0.925365i	−0.999199	+	0.0400224i	$0.987257\pi$
$920$	3.73340e20	−	2.15548e20i	0.669251	−	0.386392i
$921$	−3.85644e20	−	6.67956e20i	−0.686072	−	1.18831i
$922$	5.04709e20	+	2.91394e20i	0.891097	+	0.514475i
$923$			1.18740e21i			2.08058i
$924$	2.68352e20	−	3.18146e20i	0.466661	−	0.553252i
$925$	2.95975e20			0.510813
$926$	2.37107e20	−	4.10682e20i	0.406133	−	0.703442i
$927$	−1.12269e21	+	6.48183e20i	−1.90854	+	1.10189i
$928$	−4.19470e19	−	7.26544e19i	−0.0707726	−	0.122582i
$929$	−3.30954e20	−	1.91077e20i	−0.554189	−	0.319961i	0.196621	−	0.980480i	$-0.437003\pi$
$929$	−3.30954e20	−	1.91077e20i	−0.554189	−	0.319961i	−0.750810	+	0.660518i	$0.770337\pi$
$930$		−	5.97592e20i		−	0.993172i
$931$	3.06374e20	−	8.28489e20i	0.505364	−	1.36659i
$932$	5.34856e20			0.875639
$933$	−2.28719e20	+	3.96153e20i	−0.371647	+	0.643712i
$934$	−5.18054e19	+	2.99098e19i	−0.0835500	+	0.0482376i
$935$	−1.55165e20	−	2.68753e20i	−0.248377	−	0.430201i
$936$	−4.33057e20	−	2.50025e20i	−0.688040	−	0.397240i
$937$			9.81753e19i			0.154819i	0.996999	+	0.0774096i	$0.0246649\pi$
$937$			9.81753e19i			0.154819i	−0.996999	+	0.0774096i	$0.975335\pi$
$938$	2.28877e20	+	1.93054e20i	0.358246	+	0.302176i
$939$	−4.55889e20			−0.708272
$940$	1.26757e20	−	2.19550e20i	0.195469	−	0.338563i
$941$	−1.13729e20	+	6.56615e19i	−0.174078	+	0.100504i	−0.584507	−	0.811388i	$-0.698712\pi$
$941$	−1.13729e20	+	6.56615e19i	−0.174078	+	0.100504i	0.410429	+	0.911892i	$0.365379\pi$
$942$	7.37753e20	+	1.27783e21i	1.12087	+	1.94140i
$943$	5.39837e20	+	3.11675e20i	0.814106	+	0.470024i
$944$		−	2.06637e20i		−	0.309317i
$945$	−1.33800e21	+	4.83102e20i	−1.98807	+	0.717822i
$946$	1.61847e20			0.238708
$947$	−4.98699e20	+	8.63773e20i	−0.730111	+	1.26459i	0.226724	+	0.973959i	$0.427198\pi$
$947$	−4.98699e20	+	8.63773e20i	−0.730111	+	1.26459i	−0.956835	+	0.290631i	$0.906135\pi$
$948$	−1.56848e20	+	9.05565e19i	−0.227941	+	0.131602i
$949$	−1.57851e20	−	2.73406e20i	−0.227711	−	0.394408i
$950$	−1.09876e21	−	6.34367e20i	−1.57339	−	0.908396i
$951$		−	1.74759e21i		−	2.48414i
$952$	8.46592e19	+	1.51520e19i	0.119458	+	0.0213802i
$953$	1.14094e21			1.59813			0.799067	−	0.601242i	$-0.205327\pi$
$953$	1.14094e21			1.59813			0.799067	+	0.601242i	$0.205327\pi$
$954$	2.72682e20	−	4.72299e20i	0.379156	−	0.656718i
$955$	1.05974e21	−	6.11840e20i	1.46277	−	0.844528i
$956$	1.68831e20	+	2.92424e20i	0.231338	+	0.400689i
$957$	7.37942e20	+	4.26051e20i	1.00378	+	0.579533i
$958$		−	7.75824e20i		−	1.04762i
$959$	−6.33697e18	+	3.54067e19i	−0.00849476	+	0.0474630i
$960$	2.59630e20			0.345506
$961$	−2.80744e20	+	4.86262e20i	−0.370891	+	0.642402i
$962$	1.72230e20	−	9.94373e19i	0.225883	−	0.130414i
$963$	9.53355e20	+	1.65126e21i	1.24128	+	2.14997i
$964$	−8.63342e19	−	4.98451e19i	−0.111595	−	0.0644292i
$965$			6.40587e19i			0.0822028i
$966$	−4.12104e20	−	1.14136e21i	−0.525009	−	1.45406i
$967$	−1.37000e21			−1.73275			−0.866373	−	0.499397i	$-0.833555\pi$
$967$	−1.37000e21			−1.73275			−0.866373	+	0.499397i	$0.833555\pi$
$968$	−3.40803e19	+	5.90288e19i	−0.0427933	+	0.0741201i
$969$	5.77697e20	−	3.33534e20i	0.720168	−	0.415789i
$970$	4.81808e20	+	8.34516e20i	0.596310	+	1.03284i
$971$	4.90420e20	+	2.83144e20i	0.602607	+	0.347915i	0.770066	−	0.637964i	$-0.220223\pi$
$971$	4.90420e20	+	2.83144e20i	0.602607	+	0.347915i	−0.167460	+	0.985879i	$0.553556\pi$
$972$			2.82968e20i			0.345202i
$973$	2.35912e20	−	2.79687e20i	0.285733	−	0.338753i
$974$	−4.26380e20			−0.512724
$975$	1.56362e21	−	2.70827e21i	1.86680	−	3.23340i
$976$	−1.74074e20	+	1.00502e20i	−0.206341	+	0.119131i
$977$	2.94556e20	+	5.10186e20i	0.346662	+	0.600436i	0.985654	−	0.168777i	$-0.0539818\pi$
$977$	2.94556e20	+	5.10186e20i	0.346662	+	0.600436i	−0.638992	+	0.769213i	$0.720649\pi$
$978$	1.43045e21	+	8.25868e20i	1.67147	+	0.965026i
$979$			1.29972e21i			1.50790i
$980$	−7.11234e20	+	1.21646e20i	−0.819276	+	0.140125i
$981$	2.32412e20			0.265813
$982$	−3.95516e20	+	6.85054e20i	−0.449142	+	0.777937i
$983$	−5.28086e19	+	3.04891e19i	−0.0595429	+	0.0343771i	−0.529476	−	0.848325i	$-0.677611\pi$
$983$	−5.28086e19	+	3.04891e19i	−0.0595429	+	0.0343771i	0.469933	+	0.882702i	$0.344278\pi$
$984$	1.87708e20	+	3.25120e20i	0.210144	+	0.363980i
$985$	3.15837e20	+	1.82348e20i	0.351082	+	0.202698i
$986$			1.76076e20i			0.194340i
$987$	−5.45478e20	−	4.60103e20i	−0.597802	−	0.504238i
$988$	−8.52502e20			−0.927677
$989$	2.35937e20	−	4.08655e20i	0.254931	−	0.441553i
$990$	−1.45770e21	+	8.41606e20i	−1.56395	+	0.902947i
$991$	4.58557e20	+	7.94243e20i	0.488514	+	0.846132i	0.999913	−	0.0132119i	$-0.00420561\pi$
$991$	4.58557e20	+	7.94243e20i	0.488514	+	0.846132i	−0.511398	+	0.859344i	$0.670872\pi$
$992$	7.35412e19	+	4.24590e19i	0.0777945	+	0.0449147i
$993$			6.02359e20i			0.632718i
$994$	−1.04186e21	+	3.76178e20i	−1.08669	+	0.392364i
$995$	−2.61836e21			−2.71187
$996$	1.40038e20	−	2.42552e20i	0.144022	−	0.249454i
$997$	6.11875e20	−	3.53266e20i	0.624880	−	0.360775i	−0.153887	−	0.988089i	$-0.549179\pi$
$997$	6.11875e20	−	3.53266e20i	0.624880	−	0.360775i	0.778766	+	0.627314i	$0.215846\pi$
$998$	6.31267e20	+	1.09339e21i	0.640176	+	1.10882i
$999$	3.16755e20	+	1.82879e20i	0.318981	+	0.184164i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.15.d.a.5.6	yes	20
3.2	odd	2		126.15.n.b.19.5		20
7.2	even	3		98.15.b.c.97.2		20
7.3	odd	6	inner	14.15.d.a.3.6	✓	20
7.4	even	3		98.15.d.b.31.10		20
7.5	odd	6		98.15.b.c.97.9		20
7.6	odd	2		98.15.d.b.19.10		20
21.17	even	6		126.15.n.b.73.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.15.d.a.3.6	✓	20	7.3	odd	6	inner
14.15.d.a.5.6	yes	20	1.1	even	1	trivial
98.15.b.c.97.2		20	7.2	even	3
98.15.b.c.97.9		20	7.5	odd	6
98.15.d.b.19.10		20	7.6	odd	2
98.15.d.b.31.10		20	7.4	even	3
126.15.n.b.19.5		20	3.2	odd	2
126.15.n.b.73.5		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)

\(f(q)\)	\(=\)	\(q+(45.2548 - 78.3837i) q^{2} +(-3149.23 + 1818.21i) q^{3} +(-4096.00 - 7094.48i) q^{4} +(-112471. - 64935.4i) q^{5} +329131. i q^{6} +(-629509. - 530982. i) q^{7} -741455. q^{8} +(4.22027e6 - 7.30973e6i) q^{9} +O(q^{10})\)	\(q+(45.2548 - 78.3837i) q^{2} +(-3149.23 + 1818.21i) q^{3} +(-4096.00 - 7094.48i) q^{4} +(-112471. - 64935.4i) q^{5} +329131. i q^{6} +(-629509. - 530982. i) q^{7} -741455. q^{8} +(4.22027e6 - 7.30973e6i) q^{9} +(-1.01797e7 + 5.87728e6i) q^{10} +(8.48266e6 + 1.46924e7i) q^{11} +(2.57985e7 + 1.48948e7i) q^{12} +7.99021e7i q^{13} +(-7.01086e7 + 2.53137e7i) q^{14} +4.72264e8 q^{15} +(-3.35544e7 + 5.81180e7i) q^{16} +(1.21978e8 - 7.04238e7i) q^{17} +(-3.81976e8 - 6.61601e8i) q^{18} +(-1.12792e9 - 6.51204e8i) q^{19} +1.06390e9i q^{20} +(2.94790e9 + 5.27605e8i) q^{21} +1.53552e9 q^{22} +(2.23845e9 - 3.87711e9i) q^{23} +(2.33501e9 - 1.34812e9i) q^{24} +(5.38144e9 + 9.32093e9i) q^{25} +(6.26302e9 + 3.61596e9i) q^{26} +1.33005e10i q^{27} +(-1.18857e9 + 6.64094e9i) q^{28} -1.38120e10 q^{29} +(2.13722e10 - 3.70178e10i) q^{30} +(1.21075e10 - 6.99029e9i) q^{31} +(3.03700e9 + 5.26024e9i) q^{32} +(-5.34276e10 - 3.08465e10i) q^{33} -1.27481e10i q^{34} +(3.63222e10 + 1.00598e11i) q^{35} -6.91450e10 q^{36} +(1.37498e10 - 2.38153e10i) q^{37} +(-1.02087e11 + 5.89402e10i) q^{38} +(-1.45279e11 - 2.51630e11i) q^{39} +(8.33925e10 + 4.81467e10i) q^{40} +1.39237e11i q^{41} +(1.74762e11 - 2.07191e11i) q^{42} +1.05402e11 q^{43} +(6.94899e10 - 1.20360e11i) q^{44} +(-9.49320e11 + 5.48090e11i) q^{45} +(-2.02601e11 - 3.50916e11i) q^{46} +(-2.06363e11 - 1.19144e11i) q^{47} -2.44036e11i q^{48} +(1.14340e11 + 6.68516e11i) q^{49} +9.74145e11 q^{50} +(-2.56090e11 + 4.43561e11i) q^{51} +(5.66864e11 - 3.27279e11i) q^{52} +(3.56937e11 + 6.18232e11i) q^{53} +(1.04254e12 + 6.01911e11i) q^{54} -2.20330e12i q^{55} +(4.66753e11 + 3.93699e11i) q^{56} +4.73609e12 q^{57} +(-6.25059e11 + 1.08263e12i) q^{58} +(-2.66660e12 + 1.53956e12i) q^{59} +(-1.93439e12 - 3.35047e12i) q^{60} +(2.59390e12 + 1.49759e12i) q^{61} -1.26538e12i q^{62} +(-6.53803e12 + 2.36065e12i) q^{63} +5.49756e11 q^{64} +(5.18847e12 - 8.98670e12i) q^{65} +(-4.83572e12 + 2.79190e12i) q^{66} +(-2.00851e12 - 3.47885e12i) q^{67} +(-9.99241e11 - 5.76912e11i) q^{68} +1.62799e13i q^{69} +(9.52897e12 + 1.70546e12i) q^{70} +1.48607e13 q^{71} +(-3.12914e12 + 5.41984e12i) q^{72} +(-3.42177e12 + 1.97556e12i) q^{73} +(-1.24449e12 - 2.15552e12i) q^{74} +(-3.38948e13 - 1.95692e13i) q^{75} +1.06693e13i q^{76} +(2.46149e12 - 1.37531e13i) q^{77} -2.62983e13 q^{78} +(-3.03988e12 + 5.26522e12i) q^{79} +(7.54782e12 - 4.35774e12i) q^{80} +(-3.99758e12 - 6.92402e12i) q^{81} +(1.09139e13 + 6.30115e12i) q^{82} -9.40181e12i q^{83} +(-8.33152e12 - 2.30749e13i) q^{84} -1.82920e13 q^{85} +(4.76995e12 - 8.26179e12i) q^{86} +(4.34971e13 - 2.51131e13i) q^{87} +(-6.28951e12 - 1.08937e13i) q^{88} +(6.63468e13 + 3.83054e13i) q^{89} +9.92149e13i q^{90} +(4.24266e13 - 5.02991e13i) q^{91} -3.66748e13 q^{92} +(-2.54196e13 + 4.40280e13i) q^{93} +(-1.86779e13 + 1.07837e13i) q^{94} +(8.45723e13 + 1.46483e14i) q^{95} +(-1.91284e13 - 1.10438e13i) q^{96} -8.19781e13i q^{97} +(5.75751e13 + 2.12912e13i) q^{98} +1.43197e14 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

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Database

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