LMFDB - Embedded newform 128.12.e.b.33.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,12,Mod(33,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("128.33");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	128.e (of order $4$, degree $2$, not 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:	$98.3479271116$
Analytic rank:	$0$
Dimension:	$42$
Relative dimension:	$21$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 16)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			33.4
Character	$\chi$	$=$	128.33
Dual form			128.12.e.b.97.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-396.720 - 396.720i) q^{3} +(-7616.23 + 7616.23i) q^{5} +16490.4i q^{7} +137626. i q^{9} +O(q^{10})$	\(q+(-396.720 - 396.720i) q^{3} +(-7616.23 + 7616.23i) q^{5} +16490.4i q^{7} +137626. i q^{9} +(-568615. + 568615. i) q^{11} +(1.11150e6 + 1.11150e6i) q^{13} +6.04302e6 q^{15} +6.34711e6 q^{17} +(-3.59606e6 - 3.59606e6i) q^{19} +(6.54205e6 - 6.54205e6i) q^{21} +4.79362e7i q^{23} -6.71858e7i q^{25} +(-1.56787e7 + 1.56787e7i) q^{27} +(2.69107e7 + 2.69107e7i) q^{29} +1.46392e8 q^{31} +4.51162e8 q^{33} +(-1.25594e8 - 1.25594e8i) q^{35} +(4.69927e8 - 4.69927e8i) q^{37} -8.81907e8i q^{39} +3.61263e8i q^{41} +(-5.36452e8 + 5.36452e8i) q^{43} +(-1.04819e9 - 1.04819e9i) q^{45} -1.46204e9 q^{47} +1.70539e9 q^{49} +(-2.51802e9 - 2.51802e9i) q^{51} +(2.55876e8 - 2.55876e8i) q^{53} -8.66141e9i q^{55} +2.85325e9i q^{57} +(2.13617e9 - 2.13617e9i) q^{59} +(4.43007e9 + 4.43007e9i) q^{61} -2.26951e9 q^{63} -1.69309e10 q^{65} +(7.43238e9 + 7.43238e9i) q^{67} +(1.90172e10 - 1.90172e10i) q^{69} +8.28036e9i q^{71} +1.36040e10i q^{73} +(-2.66539e10 + 2.66539e10i) q^{75} +(-9.37667e9 - 9.37667e9i) q^{77} -6.96390e8 q^{79} +3.68202e10 q^{81} +(3.69451e10 + 3.69451e10i) q^{83} +(-4.83410e10 + 4.83410e10i) q^{85} -2.13520e10i q^{87} +9.40272e10i q^{89} +(-1.83290e10 + 1.83290e10i) q^{91} +(-5.80768e10 - 5.80768e10i) q^{93} +5.47768e10 q^{95} -1.46969e11 q^{97} +(-7.82564e10 - 7.82564e10i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 42 q + 2 q^{3} + 2 q^{5}+O(q^{10}) $ 42 * q + 2 * q^3 + 2 * q^5	$ 42 q + 2 q^{3} + 2 q^{5} + 540846 q^{11} + 2 q^{13} - 6075004 q^{15} - 4 q^{17} + 11291290 q^{19} - 354292 q^{21} + 66463304 q^{27} - 77673206 q^{29} + 343549808 q^{31} - 4 q^{33} + 434731684 q^{35} + 522762058 q^{37} - 3824193658 q^{43} - 97301954 q^{45} - 4586900144 q^{47} - 8474257474 q^{49} - 7074245796 q^{51} + 2100608058 q^{53} - 955824746 q^{59} - 2150827022 q^{61} + 27758037828 q^{63} - 1884965292 q^{65} + 3186519018 q^{67} + 16193060732 q^{69} - 28890034486 q^{75} + 22711870540 q^{77} + 48011833792 q^{79} - 90656394430 q^{81} - 55713221118 q^{83} + 84575506252 q^{85} + 147369662716 q^{91} + 69689773328 q^{93} + 375702304500 q^{95} - 4 q^{97} + 286271331106 q^{99}+O(q^{100}) $ 42 * q + 2 * q^3 + 2 * q^5 + 540846 * q^11 + 2 * q^13 - 6075004 * q^15 - 4 * q^17 + 11291290 * q^19 - 354292 * q^21 + 66463304 * q^27 - 77673206 * q^29 + 343549808 * q^31 - 4 * q^33 + 434731684 * q^35 + 522762058 * q^37 - 3824193658 * q^43 - 97301954 * q^45 - 4586900144 * q^47 - 8474257474 * q^49 - 7074245796 * q^51 + 2100608058 * q^53 - 955824746 * q^59 - 2150827022 * q^61 + 27758037828 * q^63 - 1884965292 * q^65 + 3186519018 * q^67 + 16193060732 * q^69 - 28890034486 * q^75 + 22711870540 * q^77 + 48011833792 * q^79 - 90656394430 * q^81 - 55713221118 * q^83 + 84575506252 * q^85 + 147369662716 * q^91 + 69689773328 * q^93 + 375702304500 * q^95 - 4 * q^97 + 286271331106 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−396.720	−	396.720i	−0.942577	−	0.942577i	0.0558611	−	0.998439i	$-0.482210\pi$
$3$	−396.720	−	396.720i	−0.942577	−	0.942577i	−0.998439	+	0.0558611i	$0.982210\pi$
$4$		0			0
$5$	−7616.23	+	7616.23i	−1.08995	+	1.08995i	−0.0944131	+	0.995533i	$0.530097\pi$
$5$	−7616.23	+	7616.23i	−1.08995	+	1.08995i	−0.995533	+	0.0944131i	$0.969903\pi$
$6$		0			0
$7$			16490.4i			0.370844i	0.982659	+	0.185422i	$0.0593651\pi$
$7$			16490.4i			0.370844i	−0.982659	+	0.185422i	$0.940635\pi$
$8$		0			0
$9$			137626.i			0.776904i
$10$		0			0
$11$	−568615.	+	568615.i	−1.06453	+	1.06453i	−0.0667634	+	0.997769i	$0.521267\pi$
$11$	−568615.	+	568615.i	−1.06453	+	1.06453i	−0.997769	+	0.0667634i	$0.978733\pi$
$12$		0			0
$13$	1.11150e6	+	1.11150e6i	0.830272	+	0.830272i	0.987554	−	0.157282i	$-0.0502731\pi$
$13$	1.11150e6	+	1.11150e6i	0.830272	+	0.830272i	−0.157282	+	0.987554i	$0.550273\pi$
$14$		0			0
$15$	6.04302e6			2.05472
$16$		0			0
$17$	6.34711e6			1.08419			0.542097	−	0.840316i	$-0.317631\pi$
$17$	6.34711e6			1.08419			0.542097	+	0.840316i	$0.317631\pi$
$18$		0			0
$19$	−3.59606e6	−	3.59606e6i	−0.333182	−	0.333182i	0.520611	−	0.853794i	$-0.325704\pi$
$19$	−3.59606e6	−	3.59606e6i	−0.333182	−	0.333182i	−0.853794	+	0.520611i	$0.825704\pi$
$20$		0			0
$21$	6.54205e6	−	6.54205e6i	0.349549	−	0.349549i
$22$		0			0
$23$			4.79362e7i			1.55296i	0.630141	+	0.776480i	$0.282997\pi$
$23$			4.79362e7i			1.55296i	−0.630141	+	0.776480i	$0.717003\pi$
$24$		0			0
$25$		−	6.71858e7i		−	1.37597i
$26$		0			0
$27$	−1.56787e7	+	1.56787e7i	−0.210285	+	0.210285i
$28$		0			0
$29$	2.69107e7	+	2.69107e7i	0.243633	+	0.243633i	0.818351	−	0.574719i	$-0.194888\pi$
$29$	2.69107e7	+	2.69107e7i	0.243633	+	0.243633i	−0.574719	+	0.818351i	$0.694888\pi$
$30$		0			0
$31$	1.46392e8			0.918395			0.459197	−	0.888334i	$-0.348137\pi$
$31$	1.46392e8			0.918395			0.459197	+	0.888334i	$0.348137\pi$
$32$		0			0
$33$	4.51162e8			2.00681
$34$		0			0
$35$	−1.25594e8	−	1.25594e8i	−0.404200	−	0.404200i
$36$		0			0
$37$	4.69927e8	−	4.69927e8i	1.11409	−	1.11409i	0.121501	−	0.992591i	$-0.461229\pi$
$37$	4.69927e8	−	4.69927e8i	1.11409	−	1.11409i	0.992591	−	0.121501i	$-0.0387707\pi$
$38$		0			0
$39$		−	8.81907e8i		−	1.56519i
$40$		0			0
$41$			3.61263e8i			0.486981i	0.969903	+	0.243491i	$0.0782925\pi$
$41$			3.61263e8i			0.486981i	−0.969903	+	0.243491i	$0.921707\pi$
$42$		0			0
$43$	−5.36452e8	+	5.36452e8i	−0.556486	+	0.556486i	−0.928305	−	0.371819i	$-0.878734\pi$
$43$	−5.36452e8	+	5.36452e8i	−0.556486	+	0.556486i	0.371819	+	0.928305i	$0.378734\pi$
$44$		0			0
$45$	−1.04819e9	−	1.04819e9i	−0.846784	−	0.846784i
$46$		0			0
$47$	−1.46204e9			−0.929866			−0.464933	−	0.885346i	$-0.653922\pi$
$47$	−1.46204e9			−0.929866			−0.464933	+	0.885346i	$0.653922\pi$
$48$		0			0
$49$	1.70539e9			0.862475
$50$		0			0
$51$	−2.51802e9	−	2.51802e9i	−1.02194	−	1.02194i
$52$		0			0
$53$	2.55876e8	−	2.55876e8i	0.0840450	−	0.0840450i	−0.663835	−	0.747879i	$-0.731072\pi$
$53$	2.55876e8	−	2.55876e8i	0.0840450	−	0.0840450i	0.747879	+	0.663835i	$0.231072\pi$
$54$		0			0
$55$		−	8.66141e9i		−	2.32057i
$56$		0			0
$57$			2.85325e9i			0.628100i
$58$		0			0
$59$	2.13617e9	−	2.13617e9i	0.389000	−	0.389000i	−0.485331	−	0.874331i	$-0.661301\pi$
$59$	2.13617e9	−	2.13617e9i	0.389000	−	0.389000i	0.874331	+	0.485331i	$0.161301\pi$
$60$		0			0
$61$	4.43007e9	+	4.43007e9i	0.671578	+	0.671578i	0.958080	−	0.286502i	$-0.0924924\pi$
$61$	4.43007e9	+	4.43007e9i	0.671578	+	0.671578i	−0.286502	+	0.958080i	$0.592492\pi$
$62$		0			0
$63$	−2.26951e9			−0.288110
$64$		0			0
$65$	−1.69309e10			−1.80990
$66$		0			0
$67$	7.43238e9	+	7.43238e9i	0.672537	+	0.672537i	0.958300	−	0.285763i	$-0.0922470\pi$
$67$	7.43238e9	+	7.43238e9i	0.672537	+	0.672537i	−0.285763	+	0.958300i	$0.592247\pi$
$68$		0			0
$69$	1.90172e10	−	1.90172e10i	1.46379	−	1.46379i
$70$		0			0
$71$			8.28036e9i			0.544664i	0.962203	+	0.272332i	$0.0877948\pi$
$71$			8.28036e9i			0.544664i	−0.962203	+	0.272332i	$0.912205\pi$
$72$		0			0
$73$			1.36040e10i			0.768050i	0.923323	+	0.384025i	$0.125462\pi$
$73$			1.36040e10i			0.768050i	−0.923323	+	0.384025i	$0.874538\pi$
$74$		0			0
$75$	−2.66539e10	+	2.66539e10i	−1.29695	+	1.29695i
$76$		0			0
$77$	−9.37667e9	−	9.37667e9i	−0.394775	−	0.394775i
$78$		0			0
$79$	−6.96390e8			−0.0254626			−0.0127313	−	0.999919i	$-0.504053\pi$
$79$	−6.96390e8			−0.0254626			−0.0127313	+	0.999919i	$0.504053\pi$
$80$		0			0
$81$	3.68202e10			1.17332
$82$		0			0
$83$	3.69451e10	+	3.69451e10i	1.02950	+	1.02950i	0.999551	+	0.0299513i	$0.00953524\pi$
$83$	3.69451e10	+	3.69451e10i	1.02950	+	1.02950i	0.0299513	+	0.999551i	$0.490465\pi$
$84$		0			0
$85$	−4.83410e10	+	4.83410e10i	−1.18171	+	1.18171i
$86$		0			0
$87$		−	2.13520e10i		−	0.459285i
$88$		0			0
$89$			9.40272e10i			1.78488i	0.451168	+	0.892439i	$0.351007\pi$
$89$			9.40272e10i			1.78488i	−0.451168	+	0.892439i	$0.648993\pi$
$90$		0			0
$91$	−1.83290e10	+	1.83290e10i	−0.307901	+	0.307901i
$92$		0			0
$93$	−5.80768e10	−	5.80768e10i	−0.865658	−	0.865658i
$94$		0			0
$95$	5.47768e10			0.726301
$96$		0			0
$97$	−1.46969e11			−1.73772			−0.868860	−	0.495057i	$-0.835147\pi$
$97$	−1.46969e11			−1.73772			−0.868860	+	0.495057i	$0.835147\pi$
$98$		0			0
$99$	−7.82564e10	−	7.82564e10i	−0.827040	−	0.827040i
$100$		0			0
$101$	−7.59323e10	+	7.59323e10i	−0.718884	+	0.718884i	−0.968377	−	0.249492i	$-0.919736\pi$
$101$	−7.59323e10	+	7.59323e10i	−0.718884	+	0.718884i	0.249492	+	0.968377i	$0.419736\pi$
$102$		0			0
$103$		−	3.25333e10i		−	0.276518i	−0.990396	−	0.138259i	$-0.955849\pi$
$103$		−	3.25333e10i		−	0.276518i	0.990396	−	0.138259i	$-0.0441506\pi$
$104$		0			0
$105$			9.96515e10i			0.761979i
$106$		0			0
$107$	−3.22092e10	+	3.22092e10i	−0.222008	+	0.222008i	−0.809344	−	0.587336i	$-0.800177\pi$
$107$	−3.22092e10	+	3.22092e10i	−0.222008	+	0.222008i	0.587336	+	0.809344i	$0.300177\pi$
$108$		0			0
$109$	2.01916e11	+	2.01916e11i	1.25697	+	1.25697i	0.952531	+	0.304442i	$0.0984700\pi$
$109$	2.01916e11	+	2.01916e11i	1.25697	+	1.25697i	0.304442	+	0.952531i	$0.401530\pi$
$110$		0			0
$111$	−3.72859e11			−2.10024
$112$		0			0
$113$	3.70572e10			0.189209			0.0946044	−	0.995515i	$-0.469841\pi$
$113$	3.70572e10			0.189209			0.0946044	+	0.995515i	$0.469841\pi$
$114$		0			0
$115$	−3.65093e11	−	3.65093e11i	−1.69264	−	1.69264i
$116$		0			0
$117$	−1.52971e11	+	1.52971e11i	−0.645042	+	0.645042i
$118$		0			0
$119$			1.04666e11i			0.402066i
$120$		0			0
$121$		−	3.61335e11i		−	1.26646i
$122$		0			0
$123$	1.43320e11	−	1.43320e11i	0.459018	−	0.459018i
$124$		0			0
$125$	1.39816e11	+	1.39816e11i	0.409782	+	0.409782i
$126$		0			0
$127$	−2.32003e11			−0.623123			−0.311562	−	0.950226i	$-0.600852\pi$
$127$	−2.32003e11			−0.623123			−0.311562	+	0.950226i	$0.600852\pi$
$128$		0			0
$129$	4.25642e11			1.04906
$130$		0			0
$131$	9.04781e9	+	9.04781e9i	0.0204904	+	0.0204904i	0.717278	−	0.696787i	$-0.245388\pi$
$131$	9.04781e9	+	9.04781e9i	0.0204904	+	0.0204904i	−0.696787	+	0.717278i	$0.745388\pi$
$132$		0			0
$133$	5.93003e10	−	5.93003e10i	0.123558	−	0.123558i
$134$		0			0
$135$		−	2.38825e11i		−	0.458399i
$136$		0			0
$137$			5.75403e11i			1.01861i	0.860585	+	0.509306i	$0.170098\pi$
$137$			5.75403e11i			1.01861i	−0.860585	+	0.509306i	$0.829902\pi$
$138$		0			0
$139$	1.59606e11	−	1.59606e11i	0.260895	−	0.260895i	−0.564522	−	0.825418i	$-0.690940\pi$
$139$	1.59606e11	−	1.59606e11i	0.260895	−	0.260895i	0.825418	+	0.564522i	$0.190940\pi$
$140$		0			0
$141$	5.80020e11	+	5.80020e11i	0.876471	+	0.876471i
$142$		0			0
$143$	−1.26403e12			−1.76770
$144$		0			0
$145$	−4.09916e11			−0.531093
$146$		0			0
$147$	−6.76564e11	−	6.76564e11i	−0.812949	−	0.812949i
$148$		0			0
$149$	−2.37904e11	+	2.37904e11i	−0.265386	+	0.265386i	−0.827238	−	0.561852i	$-0.810089\pi$
$149$	−2.37904e11	+	2.37904e11i	−0.265386	+	0.265386i	0.561852	+	0.827238i	$0.310089\pi$
$150$		0			0
$151$			3.54158e10i			0.0367133i	0.999832	+	0.0183567i	$0.00584343\pi$
$151$			3.54158e10i			0.0367133i	−0.999832	+	0.0183567i	$0.994157\pi$
$152$		0			0
$153$			8.73529e11i			0.842315i
$154$		0			0
$155$	−1.11496e12	+	1.11496e12i	−1.00100	+	1.00100i
$156$		0			0
$157$	−2.32853e11	−	2.32853e11i	−0.194820	−	0.194820i	0.602955	−	0.797775i	$-0.293990\pi$
$157$	−2.32853e11	−	2.32853e11i	−0.194820	−	0.194820i	−0.797775	+	0.602955i	$0.793990\pi$
$158$		0			0
$159$	−2.03022e11			−0.158438
$160$		0			0
$161$	−7.90485e11			−0.575906
$162$		0			0
$163$	−2.77021e11	−	2.77021e11i	−0.188574	−	0.188574i	0.606506	−	0.795079i	$-0.292571\pi$
$163$	−2.77021e11	−	2.77021e11i	−0.188574	−	0.188574i	−0.795079	+	0.606506i	$0.792571\pi$
$164$		0			0
$165$	−3.43615e12	+	3.43615e12i	−2.18731	+	2.18731i
$166$		0			0
$167$			8.77341e11i			0.522670i	0.965248	+	0.261335i	$0.0841628\pi$
$167$			8.77341e11i			0.522670i	−0.965248	+	0.261335i	$0.915837\pi$
$168$		0			0
$169$			6.78697e11i			0.378703i
$170$		0			0
$171$	4.94912e11	−	4.94912e11i	0.258851	−	0.258851i
$172$		0			0
$173$	−3.22621e11	−	3.22621e11i	−0.158285	−	0.158285i	0.623522	−	0.781806i	$-0.285701\pi$
$173$	−3.22621e11	−	3.22621e11i	−0.158285	−	0.158285i	−0.781806	+	0.623522i	$0.785701\pi$
$174$		0			0
$175$	1.10792e12			0.510268
$176$		0			0
$177$	−1.69492e12			−0.733325
$178$		0			0
$179$	−2.68966e12	−	2.68966e12i	−1.09397	−	1.09397i	−0.995100	−	0.0988710i	$-0.968477\pi$
$179$	−2.68966e12	−	2.68966e12i	−1.09397	−	1.09397i	−0.0988710	−	0.995100i	$-0.531523\pi$
$180$		0			0
$181$	8.92753e10	−	8.92753e10i	0.0341585	−	0.0341585i	−0.689821	−	0.723980i	$-0.742311\pi$
$181$	8.92753e10	−	8.92753e10i	0.0341585	−	0.0341585i	0.723980	+	0.689821i	$0.242311\pi$
$182$		0			0
$183$		−	3.51499e12i		−	1.26603i
$184$		0			0
$185$			7.15815e12i			2.42860i
$186$		0			0
$187$	−3.60906e12	+	3.60906e12i	−1.15416	+	1.15416i
$188$		0			0
$189$	−2.58547e11	−	2.58547e11i	−0.0779828	−	0.0779828i
$190$		0			0
$191$	4.67234e11			0.133000			0.0664998	−	0.997786i	$-0.478817\pi$
$191$	4.67234e11			0.133000			0.0664998	+	0.997786i	$0.478817\pi$
$192$		0			0
$193$	−1.08304e12			−0.291126			−0.145563	−	0.989349i	$-0.546499\pi$
$193$	−1.08304e12			−0.291126			−0.145563	+	0.989349i	$0.546499\pi$
$194$		0			0
$195$	6.71681e12	+	6.71681e12i	1.70597	+	1.70597i
$196$		0			0
$197$	5.21414e12	−	5.21414e12i	1.25204	−	1.25204i	0.297238	−	0.954803i	$-0.403935\pi$
$197$	5.21414e12	−	5.21414e12i	1.25204	−	1.25204i	0.954803	−	0.297238i	$-0.0960655\pi$
$198$		0			0
$199$			2.25210e12i			0.511559i	0.966735	+	0.255779i	$0.0823321\pi$
$199$			2.25210e12i			0.511559i	−0.966735	+	0.255779i	$0.917668\pi$
$200$		0			0
$201$		−	5.89714e12i		−	1.26784i
$202$		0			0
$203$	−4.43766e11	+	4.43766e11i	−0.0903496	+	0.0903496i
$204$		0			0
$205$	−2.75146e12	−	2.75146e12i	−0.530784	−	0.530784i
$206$		0			0
$207$	−6.59728e12			−1.20650
$208$		0			0
$209$	4.08955e12			0.709366
$210$		0			0
$211$	4.10170e12	+	4.10170e12i	0.675165	+	0.675165i	0.958902	−	0.283737i	$-0.0915742\pi$
$211$	4.10170e12	+	4.10170e12i	0.675165	+	0.675165i	−0.283737	+	0.958902i	$0.591574\pi$
$212$		0			0
$213$	3.28498e12	−	3.28498e12i	0.513388	−	0.513388i
$214$		0			0
$215$		−	8.17149e12i		−	1.21308i
$216$		0			0
$217$			2.41406e12i			0.340581i
$218$		0			0
$219$	5.39696e12	−	5.39696e12i	0.723947	−	0.723947i
$220$		0			0
$221$	7.05480e12	+	7.05480e12i	0.900175	+	0.900175i
$222$		0			0
$223$	7.90979e12			0.960479			0.480240	−	0.877137i	$-0.340550\pi$
$223$	7.90979e12			0.960479			0.480240	+	0.877137i	$0.340550\pi$
$224$		0			0
$225$	9.24653e12			1.06899
$226$		0			0
$227$	−7.63795e12	−	7.63795e12i	−0.841075	−	0.841075i	0.147924	−	0.988999i	$-0.452741\pi$
$227$	−7.63795e12	−	7.63795e12i	−0.841075	−	0.841075i	−0.988999	+	0.147924i	$0.952741\pi$
$228$		0			0
$229$	8.80754e12	−	8.80754e12i	0.924186	−	0.924186i	−0.0731355	−	0.997322i	$-0.523301\pi$
$229$	8.80754e12	−	8.80754e12i	0.924186	−	0.924186i	0.997322	+	0.0731355i	$0.0233006\pi$
$230$		0			0
$231$			7.43982e12i			0.744212i
$232$		0			0
$233$		−	1.24295e13i		−	1.18576i	−0.805291	−	0.592880i	$-0.797991\pi$
$233$		−	1.24295e13i		−	1.18576i	0.805291	−	0.592880i	$-0.202009\pi$
$234$		0			0
$235$	1.11352e13	−	1.11352e13i	1.01350	−	1.01350i
$236$		0			0
$237$	2.76272e11	+	2.76272e11i	0.0240005	+	0.0240005i
$238$		0			0
$239$	−3.64183e12			−0.302087			−0.151043	−	0.988527i	$-0.548263\pi$
$239$	−3.64183e12			−0.302087			−0.151043	+	0.988527i	$0.548263\pi$
$240$		0			0
$241$	−1.27249e13			−1.00824			−0.504118	−	0.863635i	$-0.668182\pi$
$241$	−1.27249e13			−1.00824			−0.504118	+	0.863635i	$0.668182\pi$
$242$		0			0
$243$	−1.18299e13	−	1.18299e13i	−0.895664	−	0.895664i
$244$		0			0
$245$	−1.29887e13	+	1.29887e13i	−0.940051	+	0.940051i
$246$		0			0
$247$		−	7.99402e12i		−	0.553264i
$248$		0			0
$249$		−	2.93137e13i		−	1.94077i
$250$		0			0
$251$	−2.09351e13	+	2.09351e13i	−1.32638	+	1.32638i	−0.417880	+	0.908502i	$0.637227\pi$
$251$	−2.09351e13	+	2.09351e13i	−1.32638	+	1.32638i	−0.908502	+	0.417880i	$0.862773\pi$
$252$		0			0
$253$	−2.72573e13	−	2.72573e13i	−1.65318	−	1.65318i
$254$		0			0
$255$	3.83557e13			2.22771
$256$		0			0
$257$	1.06673e13			0.593500			0.296750	−	0.954955i	$-0.404097\pi$
$257$	1.06673e13			0.593500			0.296750	+	0.954955i	$0.404097\pi$
$258$		0			0
$259$	7.74927e12	+	7.74927e12i	0.413154	+	0.413154i
$260$		0			0
$261$	−3.70361e12	+	3.70361e12i	−0.189279	+	0.189279i
$262$		0			0
$263$			3.68084e13i			1.80381i	0.431935	+	0.901905i	$0.357831\pi$
$263$			3.68084e13i			1.80381i	−0.431935	+	0.901905i	$0.642169\pi$
$264$		0			0
$265$			3.89762e12i			0.183209i
$266$		0			0
$267$	3.73025e13	−	3.73025e13i	1.68239	−	1.68239i
$268$		0			0
$269$	3.00347e13	+	3.00347e13i	1.30013	+	1.30013i	0.928303	+	0.371825i	$0.121268\pi$
$269$	3.00347e13	+	3.00347e13i	1.30013	+	1.30013i	0.371825	+	0.928303i	$0.378732\pi$
$270$		0			0
$271$	−9.23248e11			−0.0383696			−0.0191848	−	0.999816i	$-0.506107\pi$
$271$	−9.23248e11			−0.0383696			−0.0191848	+	0.999816i	$0.506107\pi$
$272$		0			0
$273$	1.45430e13			0.580441
$274$		0			0
$275$	3.82029e13	+	3.82029e13i	1.46476	+	1.46476i
$276$		0			0
$277$	7.75117e12	−	7.75117e12i	0.285580	−	0.285580i	−0.549749	−	0.835330i	$-0.685277\pi$
$277$	7.75117e12	−	7.75117e12i	0.285580	−	0.285580i	0.835330	+	0.549749i	$0.185277\pi$
$278$		0			0
$279$			2.01475e13i			0.713505i
$280$		0			0
$281$		−	7.71875e12i		−	0.262822i	−0.991328	−	0.131411i	$-0.958049\pi$
$281$		−	7.71875e12i		−	0.262822i	0.991328	−	0.131411i	$-0.0419508\pi$
$282$		0			0
$283$	1.29432e13	−	1.29432e13i	0.423854	−	0.423854i	−0.462674	−	0.886528i	$-0.653110\pi$
$283$	1.29432e13	−	1.29432e13i	0.423854	−	0.423854i	0.886528	+	0.462674i	$0.153110\pi$
$284$		0			0
$285$	−2.17310e13	−	2.17310e13i	−0.684595	−	0.684595i
$286$		0			0
$287$	−5.95736e12			−0.180594
$288$		0			0
$289$	6.01388e12			0.175475
$290$		0			0
$291$	5.83054e13	+	5.83054e13i	1.63794	+	1.63794i
$292$		0			0
$293$	2.08690e13	−	2.08690e13i	0.564586	−	0.564586i	−0.366021	−	0.930607i	$-0.619280\pi$
$293$	2.08690e13	−	2.08690e13i	0.564586	−	0.564586i	0.930607	+	0.366021i	$0.119280\pi$
$294$		0			0
$295$			3.25391e13i			0.847978i
$296$		0			0
$297$		−	1.78303e13i		−	0.447710i
$298$		0			0
$299$	−5.32810e13	+	5.32810e13i	−1.28938	+	1.28938i
$300$		0			0
$301$	−8.84629e12	−	8.84629e12i	−0.206369	−	0.206369i
$302$		0			0
$303$	6.02477e13			1.35521
$304$		0			0
$305$	−6.74809e13			−1.46397
$306$		0			0
$307$	−6.36815e13	−	6.36815e13i	−1.33276	−	1.33276i	−0.902891	−	0.429870i	$-0.858560\pi$
$307$	−6.36815e13	−	6.36815e13i	−1.33276	−	1.33276i	−0.429870	−	0.902891i	$-0.641440\pi$
$308$		0			0
$309$	−1.29066e13	+	1.29066e13i	−0.260639	+	0.260639i
$310$		0			0
$311$		−	3.17271e13i		−	0.618370i	−0.951002	−	0.309185i	$-0.899944\pi$
$311$		−	3.17271e13i		−	0.618370i	0.951002	−	0.309185i	$-0.100056\pi$
$312$		0			0
$313$		−	3.48621e12i		−	0.0655933i	−0.999462	−	0.0327966i	$-0.989559\pi$
$313$		−	3.48621e12i		−	0.0655933i	0.999462	−	0.0327966i	$-0.0104414\pi$
$314$		0			0
$315$	1.72851e13	−	1.72851e13i	0.314024	−	0.314024i
$316$		0			0
$317$	5.05740e11	+	5.05740e11i	0.00887362	+	0.00887362i	0.711530	−	0.702656i	$-0.248003\pi$
$317$	5.05740e11	+	5.05740e11i	0.00887362	+	0.00887362i	−0.702656	+	0.711530i	$0.748003\pi$
$318$		0			0
$319$	−3.06036e13			−0.518709
$320$		0			0
$321$	2.55560e13			0.418519
$322$		0			0
$323$	−2.28246e13	−	2.28246e13i	−0.361234	−	0.361234i
$324$		0			0
$325$	7.46769e13	−	7.46769e13i	1.14243	−	1.14243i
$326$		0			0
$327$		−	1.60209e14i		−	2.36959i
$328$		0			0
$329$		−	2.41095e13i		−	0.344835i
$330$		0			0
$331$	3.88311e13	−	3.88311e13i	0.537187	−	0.537187i	−0.385515	−	0.922702i	$-0.625976\pi$
$331$	3.88311e13	−	3.88311e13i	0.537187	−	0.537187i	0.922702	+	0.385515i	$0.125976\pi$
$332$		0			0
$333$	6.46743e13	+	6.46743e13i	0.865543	+	0.865543i
$334$		0			0
$335$	−1.13213e14			−1.46606
$336$		0			0
$337$	−1.68879e13			−0.211647			−0.105823	−	0.994385i	$-0.533748\pi$
$337$	−1.68879e13			−0.211647			−0.105823	+	0.994385i	$0.533748\pi$
$338$		0			0
$339$	−1.47013e13	−	1.47013e13i	−0.178344	−	0.178344i
$340$		0			0
$341$	−8.32410e13	+	8.32410e13i	−0.977661	+	0.977661i
$342$		0			0
$343$			6.07294e13i			0.690687i
$344$		0			0
$345$			2.89679e14i			3.19090i
$346$		0			0
$347$	−3.90511e13	+	3.90511e13i	−0.416698	+	0.416698i	−0.884064	−	0.467366i	$-0.845203\pi$
$347$	−3.90511e13	+	3.90511e13i	−0.416698	+	0.416698i	0.467366	+	0.884064i	$0.345203\pi$
$348$		0			0
$349$	−4.76750e13	−	4.76750e13i	−0.492891	−	0.492891i	0.416325	−	0.909216i	$-0.363318\pi$
$349$	−4.76750e13	−	4.76750e13i	−0.492891	−	0.492891i	−0.909216	+	0.416325i	$0.863318\pi$
$350$		0			0
$351$	−3.48536e13			−0.349187
$352$		0			0
$353$	1.10675e14			1.07470			0.537352	−	0.843358i	$-0.319425\pi$
$353$	1.10675e14			1.07470			0.537352	+	0.843358i	$0.319425\pi$
$354$		0			0
$355$	−6.30651e13	−	6.30651e13i	−0.593654	−	0.593654i
$356$		0			0
$357$	4.15231e13	−	4.15231e13i	0.378979	−	0.378979i
$358$		0			0
$359$		−	1.55145e14i		−	1.37315i	−0.727059	−	0.686574i	$-0.759114\pi$
$359$		−	1.55145e14i		−	1.37315i	0.727059	−	0.686574i	$-0.240886\pi$
$360$		0			0
$361$		−	9.06270e13i		−	0.777979i
$362$		0			0
$363$	−1.43349e14	+	1.43349e14i	−1.19373	+	1.19373i
$364$		0			0
$365$	−1.03611e14	−	1.03611e14i	−0.837133	−	0.837133i
$366$		0			0
$367$	2.60665e13			0.204371			0.102186	−	0.994765i	$-0.467416\pi$
$367$	2.60665e13			0.204371			0.102186	+	0.994765i	$0.467416\pi$
$368$		0			0
$369$	−4.97193e13			−0.378338
$370$		0			0
$371$	4.21948e12	+	4.21948e12i	0.0311675	+	0.0311675i
$372$		0			0
$373$	−4.15009e13	+	4.15009e13i	−0.297618	+	0.297618i	−0.840080	−	0.542462i	$-0.817492\pi$
$373$	−4.15009e13	+	4.15009e13i	−0.297618	+	0.297618i	0.542462	+	0.840080i	$0.317492\pi$
$374$		0			0
$375$		−	1.10936e14i		−	0.772502i
$376$		0			0
$377$			5.98223e13i			0.404563i
$378$		0			0
$379$	−2.23013e13	+	2.23013e13i	−0.146492	+	0.146492i	−0.776549	−	0.630057i	$-0.783032\pi$
$379$	−2.23013e13	+	2.23013e13i	−0.146492	+	0.146492i	0.630057	+	0.776549i	$0.283032\pi$
$380$		0			0
$381$	9.20404e13	+	9.20404e13i	0.587342	+	0.587342i
$382$		0			0
$383$	3.42745e13			0.212509			0.106254	−	0.994339i	$-0.466114\pi$
$383$	3.42745e13			0.212509			0.106254	+	0.994339i	$0.466114\pi$
$384$		0			0
$385$	1.42830e14			0.860567
$386$		0			0
$387$	−7.38299e13	−	7.38299e13i	−0.432337	−	0.432337i
$388$		0			0
$389$	−3.40257e13	+	3.40257e13i	−0.193680	+	0.193680i	−0.797284	−	0.603604i	$-0.793731\pi$
$389$	−3.40257e13	+	3.40257e13i	−0.193680	+	0.193680i	0.603604	+	0.797284i	$0.293731\pi$
$390$		0			0
$391$			3.04256e14i			1.68371i
$392$		0			0
$393$		−	7.17889e12i		−	0.0386277i
$394$		0			0
$395$	5.30387e12	−	5.30387e12i	0.0277529	−	0.0277529i
$396$		0			0
$397$	1.49091e14	+	1.49091e14i	0.758759	+	0.758759i	0.976097	−	0.217337i	$-0.0697371\pi$
$397$	1.49091e14	+	1.49091e14i	0.758759	+	0.758759i	−0.217337	+	0.976097i	$0.569737\pi$
$398$		0			0
$399$	−4.70512e13			−0.232927
$400$		0			0
$401$	−3.22674e14			−1.55407			−0.777034	−	0.629459i	$-0.783276\pi$
$401$	−3.22674e14			−1.55407			−0.777034	+	0.629459i	$0.783276\pi$
$402$		0			0
$403$	1.62715e14	+	1.62715e14i	0.762518	+	0.762518i
$404$		0			0
$405$	−2.80431e14	+	2.80431e14i	−1.27886	+	1.27886i
$406$		0			0
$407$			5.34416e14i			2.37197i
$408$		0			0
$409$			2.49725e14i			1.07891i	0.842015	+	0.539454i	$0.181369\pi$
$409$			2.49725e14i			1.07891i	−0.842015	+	0.539454i	$0.818631\pi$
$410$		0			0
$411$	2.28274e14	−	2.28274e14i	0.960121	−	0.960121i
$412$		0			0
$413$	3.52262e13	+	3.52262e13i	0.144258	+	0.144258i
$414$		0			0
$415$	−5.62765e14			−2.24421
$416$		0			0
$417$	−1.26637e14			−0.491828
$418$		0			0
$419$	−3.13887e14	−	3.13887e14i	−1.18740	−	1.18740i	−0.977784	−	0.209613i	$-0.932779\pi$
$419$	−3.13887e14	−	3.13887e14i	−1.18740	−	1.18740i	−0.209613	−	0.977784i	$-0.567221\pi$
$420$		0			0
$421$	−2.84805e14	+	2.84805e14i	−1.04953	+	1.04953i	−0.0508239	+	0.998708i	$0.516185\pi$
$421$	−2.84805e14	+	2.84805e14i	−1.04953	+	1.04953i	−0.998708	+	0.0508239i	$0.983815\pi$
$422$		0			0
$423$		−	2.01215e14i		−	0.722417i
$424$		0			0
$425$		−	4.26436e14i		−	1.49181i
$426$		0			0
$427$	−7.30534e13	+	7.30534e13i	−0.249050	+	0.249050i
$428$		0			0
$429$	5.01466e14	+	5.01466e14i	1.66620	+	1.66620i
$430$		0			0
$431$	1.79355e14			0.580884			0.290442	−	0.956893i	$-0.406198\pi$
$431$	1.79355e14			0.580884			0.290442	+	0.956893i	$0.406198\pi$
$432$		0			0
$433$	−4.08904e14			−1.29103			−0.645517	−	0.763746i	$-0.723358\pi$
$433$	−4.08904e14			−1.29103			−0.645517	+	0.763746i	$0.723358\pi$
$434$		0			0
$435$	1.62622e14	+	1.62622e14i	0.500596	+	0.500596i
$436$		0			0
$437$	1.72381e14	−	1.72381e14i	0.517419	−	0.517419i
$438$		0			0
$439$		−	2.94454e14i		−	0.861912i	−0.902373	−	0.430956i	$-0.858176\pi$
$439$		−	2.94454e14i		−	0.861912i	0.902373	−	0.430956i	$-0.141824\pi$
$440$		0			0
$441$			2.34707e14i			0.670061i
$442$		0			0
$443$	1.47611e14	−	1.47611e14i	0.411052	−	0.411052i	−0.471053	−	0.882105i	$-0.656126\pi$
$443$	1.47611e14	−	1.47611e14i	0.411052	−	0.411052i	0.882105	+	0.471053i	$0.156126\pi$
$444$		0			0
$445$	−7.16133e14	−	7.16133e14i	−1.94542	−	1.94542i
$446$		0			0
$447$	1.88763e14			0.500293
$448$		0			0
$449$	2.53852e13			0.0656486			0.0328243	−	0.999461i	$-0.489550\pi$
$449$	2.53852e13			0.0656486			0.0328243	+	0.999461i	$0.489550\pi$
$450$		0			0
$451$	−2.05420e14	−	2.05420e14i	−0.518407	−	0.518407i
$452$		0			0
$453$	1.40501e13	−	1.40501e13i	0.0346051	−	0.0346051i
$454$		0			0
$455$		−	2.79196e14i		−	0.671191i
$456$		0			0
$457$			1.90513e14i			0.447080i	0.974695	+	0.223540i	$0.0717613\pi$
$457$			1.90513e14i			0.447080i	−0.974695	+	0.223540i	$0.928239\pi$
$458$		0			0
$459$	−9.95141e13	+	9.95141e13i	−0.227990	+	0.227990i
$460$		0			0
$461$	−7.44533e13	−	7.44533e13i	−0.166544	−	0.166544i	0.618914	−	0.785458i	$-0.287573\pi$
$461$	−7.44533e13	−	7.44533e13i	−0.166544	−	0.166544i	−0.785458	+	0.618914i	$0.787573\pi$
$462$		0			0
$463$	−2.05938e14			−0.449821			−0.224911	−	0.974379i	$-0.572209\pi$
$463$	−2.05938e14			−0.449821			−0.224911	+	0.974379i	$0.572209\pi$
$464$		0			0
$465$	8.84653e14			1.88704
$466$		0			0
$467$	−1.31003e14	−	1.31003e14i	−0.272922	−	0.272922i	0.557353	−	0.830276i	$-0.311817\pi$
$467$	−1.31003e14	−	1.31003e14i	−0.272922	−	0.272922i	−0.830276	+	0.557353i	$0.811817\pi$
$468$		0			0
$469$	−1.22563e14	+	1.22563e14i	−0.249406	+	0.249406i
$470$		0			0
$471$			1.84755e14i			0.367266i
$472$		0			0
$473$		−	6.10070e14i		−	1.18480i
$474$		0			0
$475$	−2.41604e14	+	2.41604e14i	−0.458447	+	0.458447i
$476$		0			0
$477$	3.52152e13	+	3.52152e13i	0.0652949	+	0.0652949i
$478$		0			0
$479$	2.24204e14			0.406255			0.203127	−	0.979152i	$-0.434889\pi$
$479$	2.24204e14			0.406255			0.203127	+	0.979152i	$0.434889\pi$
$480$		0			0
$481$	1.04465e15			1.85000
$482$		0			0
$483$	3.13601e14	+	3.13601e14i	0.542836	+	0.542836i
$484$		0			0
$485$	1.11935e15	−	1.11935e15i	1.89402	−	1.89402i
$486$		0			0
$487$		−	1.28230e14i		−	0.212119i	−0.994360	−	0.106059i	$-0.966177\pi$
$487$		−	1.28230e14i		−	0.212119i	0.994360	−	0.106059i	$-0.0338234\pi$
$488$		0			0
$489$			2.19799e14i			0.355490i
$490$		0			0
$491$	2.56345e14	−	2.56345e14i	0.405394	−	0.405394i	−0.474735	−	0.880129i	$-0.657456\pi$
$491$	2.56345e14	−	2.56345e14i	0.405394	−	0.405394i	0.880129	+	0.474735i	$0.157456\pi$
$492$		0			0
$493$	1.70805e14	+	1.70805e14i	0.264145	+	0.264145i
$494$		0			0
$495$	1.19204e15			1.80286
$496$		0			0
$497$	−1.36546e14			−0.201985
$498$		0			0
$499$	3.65085e14	+	3.65085e14i	0.528251	+	0.528251i	0.920051	−	0.391799i	$-0.128147\pi$
$499$	3.65085e14	+	3.65085e14i	0.528251	+	0.528251i	−0.391799	+	0.920051i	$0.628147\pi$
$500$		0			0
$501$	3.48059e14	−	3.48059e14i	0.492657	−	0.492657i
$502$		0			0
$503$			5.75270e12i			0.00796614i	0.999992	+	0.00398307i	$0.00126785\pi$
$503$			5.75270e12i			0.00796614i	−0.999992	+	0.00398307i	$0.998732\pi$
$504$		0			0
$505$		−	1.15664e15i		−	1.56709i
$506$		0			0
$507$	2.69253e14	−	2.69253e14i	0.356957	−	0.356957i
$508$		0			0
$509$	−2.46291e14	−	2.46291e14i	−0.319522	−	0.319522i	0.529061	−	0.848584i	$-0.322544\pi$
$509$	−2.46291e14	−	2.46291e14i	−0.319522	−	0.319522i	−0.848584	+	0.529061i	$0.822544\pi$
$510$		0			0
$511$	−2.24334e14			−0.284826
$512$		0			0
$513$	1.12763e14			0.140126
$514$		0			0
$515$	2.47781e14	+	2.47781e14i	0.301389	+	0.301389i
$516$		0			0
$517$	8.31337e14	−	8.31337e14i	0.989873	−	0.989873i
$518$		0			0
$519$			2.55980e14i			0.298391i
$520$		0			0
$521$		−	6.95866e14i		−	0.794179i	−0.917780	−	0.397089i	$-0.870020\pi$
$521$		−	6.95866e14i		−	0.794179i	0.917780	−	0.397089i	$-0.129980\pi$
$522$		0			0
$523$	−5.50584e14	+	5.50584e14i	−0.615268	+	0.615268i	−0.944314	−	0.329046i	$-0.893273\pi$
$523$	−5.50584e14	+	5.50584e14i	−0.615268	+	0.615268i	0.329046	+	0.944314i	$0.393273\pi$
$524$		0			0
$525$	−4.39533e14	−	4.39533e14i	−0.480967	−	0.480967i
$526$		0			0
$527$	9.29169e14			0.995718
$528$		0			0
$529$	−1.34507e15			−1.41169
$530$		0			0
$531$	2.93993e14	+	2.93993e14i	0.302216	+	0.302216i
$532$		0			0
$533$	−4.01543e14	+	4.01543e14i	−0.404327	+	0.404327i
$534$		0			0
$535$		−	4.90625e14i		−	0.483954i
$536$		0			0
$537$			2.13408e15i			2.06231i
$538$		0			0
$539$	−9.69714e14	+	9.69714e14i	−0.918132	+	0.918132i
$540$		0			0
$541$	1.77650e14	+	1.77650e14i	0.164808	+	0.164808i	0.784693	−	0.619885i	$-0.212821\pi$
$541$	1.77650e14	+	1.77650e14i	0.164808	+	0.164808i	−0.619885	+	0.784693i	$0.712821\pi$
$542$		0			0
$543$	−7.08346e13			−0.0643941
$544$		0			0
$545$	−3.07568e15			−2.74007
$546$		0			0
$547$	1.13722e15	+	1.13722e15i	0.992921	+	0.992921i	0.999975	−	0.00705383i	$-0.00224532\pi$
$547$	1.13722e15	+	1.13722e15i	0.992921	+	0.992921i	−0.00705383	+	0.999975i	$0.502245\pi$
$548$		0			0
$549$	−6.09694e14	+	6.09694e14i	−0.521752	+	0.521752i
$550$		0			0
$551$		−	1.93545e14i		−	0.162348i
$552$		0			0
$553$		−	1.14837e13i		−	0.00944266i
$554$		0			0
$555$	2.83978e15	−	2.83978e15i	2.28914	−	2.28914i
$556$		0			0
$557$	−7.54908e14	−	7.54908e14i	−0.596610	−	0.596610i	0.342799	−	0.939409i	$-0.388625\pi$
$557$	−7.54908e14	−	7.54908e14i	−0.596610	−	0.596610i	−0.939409	+	0.342799i	$0.888625\pi$
$558$		0			0
$559$	−1.19253e15			−0.924070
$560$		0			0
$561$	2.86357e15			2.17577
$562$		0			0
$563$	2.41426e14	+	2.41426e14i	0.179882	+	0.179882i	0.791304	−	0.611422i	$-0.209402\pi$
$563$	2.41426e14	+	2.41426e14i	0.179882	+	0.179882i	−0.611422	+	0.791304i	$0.709402\pi$
$564$		0			0
$565$	−2.82236e14	+	2.82236e14i	−0.206227	+	0.206227i
$566$		0			0
$567$			6.07177e14i			0.435120i
$568$		0			0
$569$			2.70660e14i			0.190242i	0.995466	+	0.0951212i	$0.0303239\pi$
$569$			2.70660e14i			0.190242i	−0.995466	+	0.0951212i	$0.969676\pi$
$570$		0			0
$571$	3.17050e13	−	3.17050e13i	0.0218590	−	0.0218590i	−0.696093	−	0.717952i	$-0.745080\pi$
$571$	3.17050e13	−	3.17050e13i	0.0218590	−	0.0218590i	0.717952	+	0.696093i	$0.245080\pi$
$572$		0			0
$573$	−1.85361e14	−	1.85361e14i	−0.125362	−	0.125362i
$574$		0			0
$575$	3.22063e15			2.13682
$576$		0			0
$577$	1.36724e15			0.889974			0.444987	−	0.895537i	$-0.353208\pi$
$577$	1.36724e15			0.889974			0.444987	+	0.895537i	$0.353208\pi$
$578$		0			0
$579$	4.29665e14	+	4.29665e14i	0.274408	+	0.274408i
$580$		0			0
$581$	−6.09238e14	+	6.09238e14i	−0.381785	+	0.381785i
$582$		0			0
$583$			2.90990e14i			0.178937i
$584$		0			0
$585$		−	2.33013e15i		−	1.40612i
$586$		0			0
$587$	−1.72013e15	+	1.72013e15i	−1.01871	+	1.01871i	−0.0188901	+	0.999822i	$0.506013\pi$
$587$	−1.72013e15	+	1.72013e15i	−1.01871	+	1.01871i	−0.999822	+	0.0188901i	$0.993987\pi$
$588$		0			0
$589$	−5.26436e14	−	5.26436e14i	−0.305993	−	0.305993i
$590$		0			0
$591$	−4.13711e15			−2.36029
$592$		0			0
$593$	−1.53052e15			−0.857112			−0.428556	−	0.903515i	$-0.640978\pi$
$593$	−1.53052e15			−0.857112			−0.428556	+	0.903515i	$0.640978\pi$
$594$		0			0
$595$	−7.97161e14	−	7.97161e14i	−0.438231	−	0.438231i
$596$		0			0
$597$	8.93453e14	−	8.93453e14i	0.482184	−	0.482184i
$598$		0			0
$599$			1.99443e15i			1.05675i	0.849012	+	0.528374i	$0.177198\pi$
$599$			1.99443e15i			1.05675i	−0.849012	+	0.528374i	$0.822802\pi$
$600$		0			0
$601$		−	2.41177e15i		−	1.25466i	−0.778753	−	0.627331i	$-0.784147\pi$
$601$		−	2.41177e15i		−	1.25466i	0.778753	−	0.627331i	$-0.215853\pi$
$602$		0			0
$603$	−1.02289e15	+	1.02289e15i	−0.522497	+	0.522497i
$604$		0			0
$605$	2.75201e15	+	2.75201e15i	1.38037	+	1.38037i
$606$		0			0
$607$	3.38451e15			1.66708			0.833542	−	0.552456i	$-0.186309\pi$
$607$	3.38451e15			1.66708			0.833542	+	0.552456i	$0.186309\pi$
$608$		0			0
$609$	3.52102e14			0.170323
$610$		0			0
$611$	−1.62505e15	−	1.62505e15i	−0.772042	−	0.772042i
$612$		0			0
$613$	−1.49201e15	+	1.49201e15i	−0.696206	+	0.696206i	−0.963590	−	0.267384i	$-0.913841\pi$
$613$	−1.49201e15	+	1.49201e15i	−0.696206	+	0.696206i	0.267384	+	0.963590i	$0.413841\pi$
$614$		0			0
$615$			2.18312e15i			1.00061i
$616$		0			0
$617$			3.12865e15i			1.40860i	0.709901	+	0.704301i	$0.248740\pi$
$617$			3.12865e15i			1.40860i	−0.709901	+	0.704301i	$0.751260\pi$
$618$		0			0
$619$	1.29237e15	−	1.29237e15i	0.571595	−	0.571595i	−0.360979	−	0.932574i	$-0.617557\pi$
$619$	1.29237e15	−	1.29237e15i	0.571595	−	0.571595i	0.932574	+	0.360979i	$0.117557\pi$
$620$		0			0
$621$	−7.51575e14	−	7.51575e14i	−0.326564	−	0.326564i
$622$		0			0
$623$	−1.55054e15			−0.661910
$624$		0			0
$625$	1.15081e15			0.482685
$626$		0			0
$627$	−1.62240e15	−	1.62240e15i	−0.668633	−	0.668633i
$628$		0			0
$629$	2.98268e15	−	2.98268e15i	1.20789	−	1.20789i
$630$		0			0
$631$		−	1.68624e15i		−	0.671053i	−0.942031	−	0.335526i	$-0.891086\pi$
$631$		−	1.68624e15i		−	0.671053i	0.942031	−	0.335526i	$-0.108914\pi$
$632$		0			0
$633$		−	3.25445e15i		−	1.27279i
$634$		0			0
$635$	1.76699e15	−	1.76699e15i	0.679171	−	0.679171i
$636$		0			0
$637$	1.89554e15	+	1.89554e15i	0.716089	+	0.716089i
$638$		0			0
$639$	−1.13960e15			−0.423151
$640$		0			0
$641$	4.46079e15			1.62814			0.814072	−	0.580764i	$-0.197246\pi$
$641$	4.46079e15			1.62814			0.814072	+	0.580764i	$0.197246\pi$
$642$		0			0
$643$	−1.45584e15	−	1.45584e15i	−0.522341	−	0.522341i	0.395937	−	0.918278i	$-0.370420\pi$
$643$	−1.45584e15	−	1.45584e15i	−0.522341	−	0.522341i	−0.918278	+	0.395937i	$0.870420\pi$
$644$		0			0
$645$	−3.24179e15	+	3.24179e15i	−1.14342	+	1.14342i
$646$		0			0
$647$		−	8.08350e14i		−	0.280302i	−0.990130	−	0.140151i	$-0.955241\pi$
$647$		−	8.08350e14i		−	0.280302i	0.990130	−	0.140151i	$-0.0447588\pi$
$648$		0			0
$649$			2.42932e15i			0.828206i
$650$		0			0
$651$	9.57707e14	−	9.57707e14i	0.321024	−	0.321024i
$652$		0			0
$653$	2.55968e15	+	2.55968e15i	0.843651	+	0.843651i	0.989332	−	0.145681i	$-0.0465372\pi$
$653$	2.55968e15	+	2.55968e15i	0.843651	+	0.843651i	−0.145681	+	0.989332i	$0.546537\pi$
$654$		0			0
$655$	−1.37820e14			−0.0446670
$656$		0			0
$657$	−1.87226e15			−0.596701
$658$		0			0
$659$	−3.34914e15	−	3.34914e15i	−1.04969	−	1.04969i	−0.998699	−	0.0509959i	$-0.983760\pi$
$659$	−3.34914e15	−	3.34914e15i	−1.04969	−	1.04969i	−0.0509959	−	0.998699i	$-0.516240\pi$
$660$		0			0
$661$	−2.53860e15	+	2.53860e15i	−0.782505	+	0.782505i	−0.980253	−	0.197748i	$-0.936637\pi$
$661$	−2.53860e15	+	2.53860e15i	−0.782505	+	0.782505i	0.197748	+	0.980253i	$0.436637\pi$
$662$		0			0
$663$		−	5.59756e15i		−	1.69697i
$664$		0			0
$665$			9.03289e14i			0.269344i
$666$		0			0
$667$	−1.28999e15	+	1.28999e15i	−0.378352	+	0.378352i
$668$		0			0
$669$	−3.13797e15	−	3.13797e15i	−0.905326	−	0.905326i
$670$		0			0
$671$	−5.03801e15			−1.42983
$672$		0			0
$673$	−4.21609e15			−1.17714			−0.588568	−	0.808448i	$-0.700308\pi$
$673$	−4.21609e15			−1.17714			−0.588568	+	0.808448i	$0.700308\pi$
$674$		0			0
$675$	1.05338e15	+	1.05338e15i	0.289345	+	0.289345i
$676$		0			0
$677$	−1.11815e15	+	1.11815e15i	−0.302177	+	0.302177i	−0.841865	−	0.539688i	$-0.818542\pi$
$677$	−1.11815e15	+	1.11815e15i	−0.302177	+	0.302177i	0.539688	+	0.841865i	$0.318542\pi$
$678$		0			0
$679$		−	2.42356e15i		−	0.644423i
$680$		0			0
$681$			6.06026e15i			1.58556i
$682$		0			0
$683$	−4.70621e15	+	4.70621e15i	−1.21159	+	1.21159i	−0.241093	+	0.970502i	$0.577506\pi$
$683$	−4.70621e15	+	4.70621e15i	−1.21159	+	1.21159i	−0.970502	+	0.241093i	$0.922494\pi$
$684$		0			0
$685$	−4.38240e15	−	4.38240e15i	−1.11023	−	1.11023i
$686$		0			0
$687$	−6.98825e15			−1.74223
$688$		0			0
$689$	5.68811e14			0.139560
$690$		0			0
$691$	2.60319e15	+	2.60319e15i	0.628602	+	0.628602i	0.947716	−	0.319114i	$-0.103385\pi$
$691$	2.60319e15	+	2.60319e15i	0.628602	+	0.628602i	−0.319114	+	0.947716i	$0.603385\pi$
$692$		0			0
$693$	1.29048e15	−	1.29048e15i	0.306702	−	0.306702i
$694$		0			0
$695$			2.43119e15i			0.568724i
$696$		0			0
$697$			2.29298e15i			0.527982i
$698$		0			0
$699$	−4.93104e15	+	4.93104e15i	−1.11767	+	1.11767i
$700$		0			0
$701$	5.24078e15	+	5.24078e15i	1.16936	+	1.16936i	0.982361	+	0.186996i	$0.0598753\pi$
$701$	5.24078e15	+	5.24078e15i	1.16936	+	1.16936i	0.186996	+	0.982361i	$0.440125\pi$
$702$		0			0
$703$	−3.37977e15			−0.742391
$704$		0			0
$705$	−8.83512e15			−1.91061
$706$		0			0
$707$	−1.25215e15	−	1.25215e15i	−0.266594	−	0.266594i
$708$		0			0
$709$	1.92644e15	−	1.92644e15i	0.403832	−	0.403832i	−0.475749	−	0.879581i	$-0.657823\pi$
$709$	1.92644e15	−	1.92644e15i	0.403832	−	0.403832i	0.879581	+	0.475749i	$0.157823\pi$
$710$		0			0
$711$		−	9.58416e13i		−	0.0197820i
$712$		0			0
$713$			7.01750e15i			1.42623i
$714$		0			0
$715$	9.62714e15	−	9.62714e15i	1.92670	−	1.92670i
$716$		0			0
$717$	1.44479e15	+	1.44479e15i	0.284740	+	0.284740i
$718$		0			0
$719$	5.69406e15			1.10513			0.552564	−	0.833470i	$-0.313649\pi$
$719$	5.69406e15			1.10513			0.552564	+	0.833470i	$0.313649\pi$
$720$		0			0
$721$	5.36485e14			0.102545
$722$		0			0
$723$	5.04824e15	+	5.04824e15i	0.950340	+	0.950340i
$724$		0			0
$725$	1.80801e15	−	1.80801e15i	0.335230	−	0.335230i
$726$		0			0
$727$		−	5.41605e15i		−	0.989107i	−0.869147	−	0.494554i	$-0.835332\pi$
$727$		−	5.41605e15i		−	0.989107i	0.869147	−	0.494554i	$-0.164668\pi$
$728$		0			0
$729$			2.86370e15i			0.515141i
$730$		0			0
$731$	−3.40492e15	+	3.40492e15i	−0.603339	+	0.603339i
$732$		0			0
$733$	−5.58948e14	−	5.58948e14i	−0.0975663	−	0.0975663i	0.656639	−	0.754205i	$-0.271978\pi$
$733$	−5.58948e14	−	5.58948e14i	−0.0975663	−	0.0975663i	−0.754205	+	0.656639i	$0.771978\pi$
$734$		0			0
$735$	1.03057e16			1.77214
$736$		0			0
$737$	−8.45233e15			−1.43188
$738$		0			0
$739$	7.72823e14	+	7.72823e14i	0.128984	+	0.128984i	0.768652	−	0.639668i	$-0.220928\pi$
$739$	7.72823e14	+	7.72823e14i	0.128984	+	0.128984i	−0.639668	+	0.768652i	$0.720928\pi$
$740$		0			0
$741$	−3.17139e15	+	3.17139e15i	−0.521494	+	0.521494i
$742$		0			0
$743$			2.58158e15i			0.418261i	0.977888	+	0.209131i	$0.0670634\pi$
$743$			2.58158e15i			0.418261i	−0.977888	+	0.209131i	$0.932937\pi$
$744$		0			0
$745$		−	3.62386e15i		−	0.578512i
$746$		0			0
$747$	−5.08462e15	+	5.08462e15i	−0.799825	+	0.799825i
$748$		0			0
$749$	−5.31141e14	−	5.31141e14i	−0.0823303	−	0.0823303i
$750$		0			0
$751$	1.74701e15			0.266856			0.133428	−	0.991059i	$-0.457402\pi$
$751$	1.74701e15			0.266856			0.133428	+	0.991059i	$0.457402\pi$
$752$		0			0
$753$	1.66107e16			2.50044
$754$		0			0
$755$	−2.69735e14	−	2.69735e14i	−0.0400155	−	0.0400155i
$756$		0			0
$757$	−7.44756e15	+	7.44756e15i	−1.08890	+	1.08890i	−0.0932537	+	0.995642i	$0.529727\pi$
$757$	−7.44756e15	+	7.44756e15i	−1.08890	+	1.08890i	−0.995642	+	0.0932537i	$0.970273\pi$
$758$		0			0
$759$			2.16270e16i			3.11649i
$760$		0			0
$761$		−	9.46000e15i		−	1.34362i	−0.740725	−	0.671809i	$-0.765518\pi$
$761$		−	9.46000e15i		−	1.34362i	0.740725	−	0.671809i	$-0.234482\pi$
$762$		0			0
$763$	−3.32967e15	+	3.32967e15i	−0.466140	+	0.466140i
$764$		0			0
$765$	−6.65300e15	−	6.65300e15i	−0.918078	−	0.918078i
$766$		0			0
$767$	4.74870e15			0.645952
$768$		0			0
$769$	6.92966e15			0.929217			0.464609	−	0.885516i	$-0.346195\pi$
$769$	6.92966e15			0.929217			0.464609	+	0.885516i	$0.346195\pi$
$770$		0			0
$771$	−4.23192e15	−	4.23192e15i	−0.559420	−	0.559420i
$772$		0			0
$773$	2.22531e13	−	2.22531e13i	0.00290003	−	0.00290003i	−0.705655	−	0.708555i	$-0.749347\pi$
$773$	2.22531e13	−	2.22531e13i	0.00290003	−	0.00290003i	0.708555	+	0.705655i	$0.249347\pi$
$774$		0			0
$775$		−	9.83550e15i		−	1.26368i
$776$		0			0
$777$		−	6.14858e15i		−	0.778859i
$778$		0			0
$779$	1.29912e15	−	1.29912e15i	0.162254	−	0.162254i
$780$		0			0
$781$	−4.70834e15	−	4.70834e15i	−0.579812	−	0.579812i
$782$		0			0
$783$	−8.43846e14			−0.102465
$784$		0			0
$785$	3.54693e15			0.424687
$786$		0			0
$787$	7.87377e15	+	7.87377e15i	0.929654	+	0.929654i	0.997683	−	0.0680290i	$-0.0216710\pi$
$787$	7.87377e15	+	7.87377e15i	0.929654	+	0.929654i	−0.0680290	+	0.997683i	$0.521671\pi$
$788$		0			0
$789$	1.46026e16	−	1.46026e16i	1.70023	−	1.70023i
$790$		0			0
$791$			6.11086e14i			0.0701669i
$792$		0			0
$793$			9.84803e15i			1.11518i
$794$		0			0
$795$	1.54626e15	−	1.54626e15i	0.172689	−	0.172689i
$796$		0			0
$797$	1.06515e16	+	1.06515e16i	1.17325	+	1.17325i	0.981430	+	0.191823i	$0.0614400\pi$
$797$	1.06515e16	+	1.06515e16i	1.17325	+	1.17325i	0.191823	+	0.981430i	$0.438560\pi$
$798$		0			0
$799$	−9.27971e15			−1.00815
$800$		0			0
$801$	−1.29406e16			−1.38668
$802$		0			0
$803$	−7.73542e15	−	7.73542e15i	−0.817614	−	0.817614i
$804$		0			0
$805$	6.02052e15	−	6.02052e15i	0.627706	−	0.627706i
$806$		0			0
$807$		−	2.38307e16i		−	2.45094i
$808$		0			0
$809$			4.52575e15i			0.459170i	0.973289	+	0.229585i	$0.0737369\pi$
$809$			4.52575e15i			0.459170i	−0.973289	+	0.229585i	$0.926263\pi$
$810$		0			0
$811$	9.49504e15	−	9.49504e15i	0.950346	−	0.950346i	−0.0484778	−	0.998824i	$-0.515437\pi$
$811$	9.49504e15	−	9.49504e15i	0.950346	−	0.950346i	0.998824	+	0.0484778i	$0.0154370\pi$
$812$		0			0
$813$	3.66271e14	+	3.66271e14i	0.0361663	+	0.0361663i
$814$		0			0
$815$	4.21971e15			0.411070
$816$		0			0
$817$	3.85823e15			0.370823
$818$		0			0
$819$	−2.52255e15	−	2.52255e15i	−0.239210	−	0.239210i
$820$		0			0
$821$	−3.29306e15	+	3.29306e15i	−0.308115	+	0.308115i	−0.844178	−	0.536063i	$-0.819911\pi$
$821$	−3.29306e15	+	3.29306e15i	−0.308115	+	0.308115i	0.536063	+	0.844178i	$0.319911\pi$
$822$		0			0
$823$			6.74018e15i			0.622260i	0.950367	+	0.311130i	$0.100708\pi$
$823$			6.74018e15i			0.622260i	−0.950367	+	0.311130i	$0.899292\pi$
$824$		0			0
$825$		−	3.03117e16i		−	2.76130i
$826$		0			0
$827$	1.46330e16	−	1.46330e16i	1.31539	−	1.31539i	0.398005	−	0.917383i	$-0.369703\pi$
$827$	1.46330e16	−	1.46330e16i	1.31539	−	1.31539i	0.917383	−	0.398005i	$-0.130297\pi$
$828$		0			0
$829$	−4.13264e15	−	4.13264e15i	−0.366588	−	0.366588i	0.499643	−	0.866231i	$-0.333464\pi$
$829$	−4.13264e15	−	4.13264e15i	−0.366588	−	0.366588i	−0.866231	+	0.499643i	$0.833464\pi$
$830$		0			0
$831$	−6.15008e15			−0.538363
$832$		0			0
$833$	1.08243e16			0.935090
$834$		0			0
$835$	−6.68203e15	−	6.68203e15i	−0.569683	−	0.569683i
$836$		0			0
$837$	−2.29524e15	+	2.29524e15i	−0.193125	+	0.193125i
$838$		0			0
$839$			3.95045e15i			0.328061i	0.986455	+	0.164031i	$0.0524496\pi$
$839$			3.95045e15i			0.328061i	−0.986455	+	0.164031i	$0.947550\pi$
$840$		0			0
$841$		−	1.07521e16i		−	0.881286i
$842$		0			0
$843$	−3.06218e15	+	3.06218e15i	−0.247730	+	0.247730i
$844$		0			0
$845$	−5.16911e15	−	5.16911e15i	−0.412766	−	0.412766i
$846$		0			0
$847$	5.95855e15			0.469658
$848$		0			0
$849$	−1.02697e16			−0.799031
$850$		0			0
$851$	2.25265e16	+	2.25265e16i	1.73014	+	1.73014i
$852$		0			0
$853$	2.48039e14	−	2.48039e14i	0.0188062	−	0.0188062i	−0.697641	−	0.716447i	$-0.745767\pi$
$853$	2.48039e14	−	2.48039e14i	0.0188062	−	0.0188062i	0.716447	+	0.697641i	$0.245767\pi$
$854$		0			0
$855$			7.53873e15i			0.564267i
$856$		0			0
$857$			2.49832e14i			0.0184609i	0.999957	+	0.00923047i	$0.00293819\pi$
$857$			2.49832e14i			0.0184609i	−0.999957	+	0.00923047i	$0.997062\pi$
$858$		0			0
$859$	1.36021e16	−	1.36021e16i	0.992302	−	0.992302i	−0.00766861	−	0.999971i	$-0.502441\pi$
$859$	1.36021e16	−	1.36021e16i	0.992302	−	0.992302i	0.999971	+	0.00766861i	$0.00244102\pi$
$860$		0			0
$861$	2.36340e15	+	2.36340e15i	0.170224	+	0.170224i
$862$		0			0
$863$	1.02834e16			0.731266			0.365633	−	0.930759i	$-0.380852\pi$
$863$	1.02834e16			0.731266			0.365633	+	0.930759i	$0.380852\pi$
$864$		0			0
$865$	4.91431e15			0.345043
$866$		0			0
$867$	−2.38582e15	−	2.38582e15i	−0.165399	−	0.165399i
$868$		0			0
$869$	3.95978e14	−	3.95978e14i	0.0271058	−	0.0271058i
$870$		0			0
$871$			1.65221e16i			1.11678i
$872$		0			0
$873$		−	2.02267e16i		−	1.35004i
$874$		0			0
$875$	−2.30562e15	+	2.30562e15i	−0.151965	+	0.151965i
$876$		0			0
$877$	1.53378e16	+	1.53378e16i	0.998307	+	0.998307i	0.999999	−	0.00169149i	$-0.000538417\pi$
$877$	1.53378e16	+	1.53378e16i	0.998307	+	0.998307i	−0.00169149	+	0.999999i	$0.500538\pi$
$878$		0			0
$879$	−1.65583e16			−1.06433
$880$		0			0
$881$	−8.22761e15			−0.522283			−0.261142	−	0.965300i	$-0.584099\pi$
$881$	−8.22761e15			−0.522283			−0.261142	+	0.965300i	$0.584099\pi$
$882$		0			0
$883$	−4.89402e15	−	4.89402e15i	−0.306819	−	0.306819i	0.536856	−	0.843674i	$-0.319612\pi$
$883$	−4.89402e15	−	4.89402e15i	−0.306819	−	0.306819i	−0.843674	+	0.536856i	$0.819612\pi$
$884$		0			0
$885$	1.29089e16	−	1.29089e16i	0.799285	−	0.799285i
$886$		0			0
$887$			1.72925e16i			1.05750i	0.848779	+	0.528748i	$0.177338\pi$
$887$			1.72925e16i			1.05750i	−0.848779	+	0.528748i	$0.822662\pi$
$888$		0			0
$889$		−	3.82582e15i		−	0.231081i
$890$		0			0
$891$	−2.09365e16	+	2.09365e16i	−1.24904	+	1.24904i
$892$		0			0
$893$	5.25757e15	+	5.25757e15i	0.309815	+	0.309815i
$894$		0			0
$895$	4.09702e16			2.38474
$896$		0			0
$897$	4.22753e16			2.43068
$898$		0			0
$899$	3.93952e15	+	3.93952e15i	0.223751	+	0.223751i
$900$		0			0
$901$	1.62407e15	−	1.62407e15i	0.0911210	−	0.0911210i
$902$		0			0
$903$			7.01900e15i			0.389038i
$904$		0			0
$905$			1.35988e15i			0.0744619i
$906$		0			0
$907$	3.28180e15	−	3.28180e15i	0.177530	−	0.177530i	−0.612748	−	0.790278i	$-0.709936\pi$
$907$	3.28180e15	−	3.28180e15i	0.177530	−	0.177530i	0.790278	+	0.612748i	$0.209936\pi$
$908$		0			0
$909$	−1.04503e16	−	1.04503e16i	−0.558504	−	0.558504i
$910$		0			0
$911$	1.64549e16			0.868848			0.434424	−	0.900709i	$-0.356952\pi$
$911$	1.64549e16			0.868848			0.434424	+	0.900709i	$0.356952\pi$
$912$		0			0
$913$	−4.20151e16			−2.19188
$914$		0			0
$915$	2.67710e16	+	2.67710e16i	1.37990	+	1.37990i
$916$		0			0
$917$	−1.49202e14	+	1.49202e14i	−0.00759875	+	0.00759875i
$918$		0			0
$919$			1.41402e16i			0.711576i	0.934567	+	0.355788i	$0.115787\pi$
$919$			1.41402e16i			0.711576i	−0.934567	+	0.355788i	$0.884213\pi$
$920$		0			0
$921$			5.05274e16i			2.51246i
$922$		0			0
$923$	−9.20361e15	+	9.20361e15i	−0.452219	+	0.452219i
$924$		0			0
$925$	−3.15724e16	−	3.15724e16i	−1.53295	−	1.53295i
$926$		0			0
$927$	4.47743e15			0.214828
$928$		0			0
$929$	−8.54660e15			−0.405235			−0.202617	−	0.979258i	$-0.564945\pi$
$929$	−8.54660e15			−0.405235			−0.202617	+	0.979258i	$0.564945\pi$
$930$		0			0
$931$	−6.13270e15	−	6.13270e15i	−0.287361	−	0.287361i
$932$		0			0
$933$	−1.25868e16	+	1.25868e16i	−0.582861	+	0.582861i
$934$		0			0
$935$		−	5.49749e16i		−	2.51594i
$936$		0			0
$937$			2.02990e16i			0.918134i	0.888402	+	0.459067i	$0.151816\pi$
$937$			2.02990e16i			0.918134i	−0.888402	+	0.459067i	$0.848184\pi$
$938$		0			0
$939$	−1.38305e15	+	1.38305e15i	−0.0618267	+	0.0618267i
$940$		0			0
$941$	−5.59019e15	−	5.59019e15i	−0.246993	−	0.246993i	0.572743	−	0.819735i	$-0.305879\pi$
$941$	−5.59019e15	−	5.59019e15i	−0.246993	−	0.246993i	−0.819735	+	0.572743i	$0.805879\pi$
$942$		0			0
$943$	−1.73176e16			−0.756263
$944$		0			0
$945$	3.93830e15			0.169994
$946$		0			0
$947$	1.42330e16	+	1.42330e16i	0.607255	+	0.607255i	0.942228	−	0.334973i	$-0.108727\pi$
$947$	1.42330e16	+	1.42330e16i	0.607255	+	0.607255i	−0.334973	+	0.942228i	$0.608727\pi$
$948$		0			0
$949$	−1.51208e16	+	1.51208e16i	−0.637690	+	0.637690i
$950$		0			0
$951$		−	4.01274e14i		−	0.0167282i
$952$		0			0
$953$		−	3.25717e16i		−	1.34224i	−0.741349	−	0.671120i	$-0.765814\pi$
$953$		−	3.25717e16i		−	1.34224i	0.741349	−	0.671120i	$-0.234186\pi$
$954$		0			0
$955$	−3.55856e15	+	3.55856e15i	−0.144962	+	0.144962i
$956$		0			0
$957$	1.21411e16	+	1.21411e16i	0.488924	+	0.488924i
$958$		0			0
$959$	−9.48860e15			−0.377746
$960$		0			0
$961$	−3.97772e15			−0.156551
$962$		0			0
$963$	−4.43283e15	−	4.43283e15i	−0.172479	−	0.172479i
$964$		0			0
$965$	8.24870e15	−	8.24870e15i	0.317311	−	0.317311i
$966$		0			0
$967$		−	3.44206e16i		−	1.30910i	−0.756018	−	0.654551i	$-0.772858\pi$
$967$		−	3.44206e16i		−	1.30910i	0.756018	−	0.654551i	$-0.227142\pi$
$968$		0			0
$969$			1.81099e16i			0.680982i
$970$		0			0
$971$	−7.00330e15	+	7.00330e15i	−0.260374	+	0.260374i	−0.825206	−	0.564832i	$-0.808941\pi$
$971$	−7.00330e15	+	7.00330e15i	−0.260374	+	0.260374i	0.564832	+	0.825206i	$0.308941\pi$
$972$		0			0
$973$	2.63195e15	+	2.63195e15i	0.0967514	+	0.0967514i
$974$		0			0
$975$	−5.92516e16			−2.15365
$976$		0			0
$977$	2.76987e16			0.995495			0.497747	−	0.867322i	$-0.334161\pi$
$977$	2.76987e16			0.995495			0.497747	+	0.867322i	$0.334161\pi$
$978$		0			0
$979$	−5.34653e16	−	5.34653e16i	−1.90006	−	1.90006i
$980$		0			0
$981$	−2.77890e16	+	2.77890e16i	−0.976548	+	0.976548i
$982$		0			0
$983$		−	1.63980e16i		−	0.569832i	−0.958553	−	0.284916i	$-0.908034\pi$
$983$		−	1.63980e16i		−	0.569832i	0.958553	−	0.284916i	$-0.0919657\pi$
$984$		0			0
$985$			7.94242e16i			2.72932i
$986$		0			0
$987$	−9.56473e15	+	9.56473e15i	−0.325034	+	0.325034i
$988$		0			0
$989$	−2.57155e16	−	2.57155e16i	−0.864202	−	0.864202i
$990$		0			0
$991$	−1.22246e16			−0.406285			−0.203142	−	0.979149i	$-0.565115\pi$
$991$	−1.22246e16			−0.406285			−0.203142	+	0.979149i	$0.565115\pi$
$992$		0			0
$993$	−3.08101e16			−1.01268
$994$		0			0
$995$	−1.71525e16	−	1.71525e16i	−0.557572	−	0.557572i
$996$		0			0
$997$	2.70942e16	−	2.70942e16i	0.871071	−	0.871071i	−0.121519	−	0.992589i	$-0.538776\pi$
$997$	2.70942e16	−	2.70942e16i	0.871071	−	0.871071i	0.992589	+	0.121519i	$0.0387764\pi$
$998$		0			0
$999$			1.47357e16i			0.468554i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.12.e.b.33.4		42
4.3	odd	2		128.12.e.a.33.18		42
8.3	odd	2		64.12.e.a.17.4		42
8.5	even	2		16.12.e.a.13.2	yes	42
16.3	odd	4		64.12.e.a.49.4		42
16.5	even	4	inner	128.12.e.b.97.4		42
16.11	odd	4		128.12.e.a.97.18		42
16.13	even	4		16.12.e.a.5.2	✓	42

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.12.e.a.5.2	✓	42	16.13	even	4
16.12.e.a.13.2	yes	42	8.5	even	2
64.12.e.a.17.4		42	8.3	odd	2
64.12.e.a.49.4		42	16.3	odd	4
128.12.e.a.33.18		42	4.3	odd	2
128.12.e.a.97.18		42	16.11	odd	4
128.12.e.b.33.4		42	1.1	even	1	trivial
128.12.e.b.97.4		42	16.5	even	4	inner

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	128.e (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-396.720 - 396.720i) q^{3} +(-7616.23 + 7616.23i) q^{5} +16490.4i q^{7} +137626. i q^{9} +O(q^{10})\)	\(q+(-396.720 - 396.720i) q^{3} +(-7616.23 + 7616.23i) q^{5} +16490.4i q^{7} +137626. i q^{9} +(-568615. + 568615. i) q^{11} +(1.11150e6 + 1.11150e6i) q^{13} +6.04302e6 q^{15} +6.34711e6 q^{17} +(-3.59606e6 - 3.59606e6i) q^{19} +(6.54205e6 - 6.54205e6i) q^{21} +4.79362e7i q^{23} -6.71858e7i q^{25} +(-1.56787e7 + 1.56787e7i) q^{27} +(2.69107e7 + 2.69107e7i) q^{29} +1.46392e8 q^{31} +4.51162e8 q^{33} +(-1.25594e8 - 1.25594e8i) q^{35} +(4.69927e8 - 4.69927e8i) q^{37} -8.81907e8i q^{39} +3.61263e8i q^{41} +(-5.36452e8 + 5.36452e8i) q^{43} +(-1.04819e9 - 1.04819e9i) q^{45} -1.46204e9 q^{47} +1.70539e9 q^{49} +(-2.51802e9 - 2.51802e9i) q^{51} +(2.55876e8 - 2.55876e8i) q^{53} -8.66141e9i q^{55} +2.85325e9i q^{57} +(2.13617e9 - 2.13617e9i) q^{59} +(4.43007e9 + 4.43007e9i) q^{61} -2.26951e9 q^{63} -1.69309e10 q^{65} +(7.43238e9 + 7.43238e9i) q^{67} +(1.90172e10 - 1.90172e10i) q^{69} +8.28036e9i q^{71} +1.36040e10i q^{73} +(-2.66539e10 + 2.66539e10i) q^{75} +(-9.37667e9 - 9.37667e9i) q^{77} -6.96390e8 q^{79} +3.68202e10 q^{81} +(3.69451e10 + 3.69451e10i) q^{83} +(-4.83410e10 + 4.83410e10i) q^{85} -2.13520e10i q^{87} +9.40272e10i q^{89} +(-1.83290e10 + 1.83290e10i) q^{91} +(-5.80768e10 - 5.80768e10i) q^{93} +5.47768e10 q^{95} -1.46969e11 q^{97} +(-7.82564e10 - 7.82564e10i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 42 q + 2 q^{3} + 2 q^{5}+O(q^{10}) \) 42 * q + 2 * q^3 + 2 * q^5	\( 42 q + 2 q^{3} + 2 q^{5} + 540846 q^{11} + 2 q^{13} - 6075004 q^{15} - 4 q^{17} + 11291290 q^{19} - 354292 q^{21} + 66463304 q^{27} - 77673206 q^{29} + 343549808 q^{31} - 4 q^{33} + 434731684 q^{35} + 522762058 q^{37} - 3824193658 q^{43} - 97301954 q^{45} - 4586900144 q^{47} - 8474257474 q^{49} - 7074245796 q^{51} + 2100608058 q^{53} - 955824746 q^{59} - 2150827022 q^{61} + 27758037828 q^{63} - 1884965292 q^{65} + 3186519018 q^{67} + 16193060732 q^{69} - 28890034486 q^{75} + 22711870540 q^{77} + 48011833792 q^{79} - 90656394430 q^{81} - 55713221118 q^{83} + 84575506252 q^{85} + 147369662716 q^{91} + 69689773328 q^{93} + 375702304500 q^{95} - 4 q^{97} + 286271331106 q^{99}+O(q^{100}) \) 42 * q + 2 * q^3 + 2 * q^5 + 540846 * q^11 + 2 * q^13 - 6075004 * q^15 - 4 * q^17 + 11291290 * q^19 - 354292 * q^21 + 66463304 * q^27 - 77673206 * q^29 + 343549808 * q^31 - 4 * q^33 + 434731684 * q^35 + 522762058 * q^37 - 3824193658 * q^43 - 97301954 * q^45 - 4586900144 * q^47 - 8474257474 * q^49 - 7074245796 * q^51 + 2100608058 * q^53 - 955824746 * q^59 - 2150827022 * q^61 + 27758037828 * q^63 - 1884965292 * q^65 + 3186519018 * q^67 + 16193060732 * q^69 - 28890034486 * q^75 + 22711870540 * q^77 + 48011833792 * q^79 - 90656394430 * q^81 - 55713221118 * q^83 + 84575506252 * q^85 + 147369662716 * q^91 + 69689773328 * q^93 + 375702304500 * q^95 - 4 * q^97 + 286271331106 * q^99

Introduction

L-functions

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