LMFDB - Embedded newform 196.9.h.c.129.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [196,9,Mod(117,196)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("196.117"); S:= CuspForms(chi, 9); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(196, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 9, names="a")

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	196.h (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$79.8462075720$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			129.6
Character	$\chi$	$=$	196.129
Dual form			196.9.h.c.117.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-31.7145 - 18.3104i) q^{3} +(-917.948 + 529.978i) q^{5} +(-2609.96 - 4520.59i) q^{9} +(-87.7782 + 152.036i) q^{11} -463.876i q^{13} +38816.3 q^{15} +(-127008. - 73327.9i) q^{17} +(-7710.17 + 4451.47i) q^{19} +(-255214. - 442044. i) q^{23} +(366440. - 634693. i) q^{25} +431426. i q^{27} +406178. q^{29} +(-700595. - 404489. i) q^{31} +(5567.68 - 3214.50i) q^{33} +(-479821. - 831074. i) q^{37} +(-8493.73 + 14711.6i) q^{39} -1.28045e6i q^{41} -3.13224e6 q^{43} +(4.79162e6 + 2.76644e6i) q^{45} +(-6.80317e6 + 3.92781e6i) q^{47} +(2.68532e6 + 4.65111e6i) q^{51} +(-5.01639e6 + 8.68865e6i) q^{53} -186082. i q^{55} +326032. q^{57} +(1.49855e7 + 8.65189e6i) q^{59} +(7.40037e6 - 4.27260e6i) q^{61} +(245844. + 425814. i) q^{65} +(9.94850e6 - 1.72313e7i) q^{67} +1.86923e7i q^{69} +1.84731e7 q^{71} +(-1.63136e7 - 9.41869e6i) q^{73} +(-2.32429e7 + 1.34193e7i) q^{75} +(-3.02779e7 - 5.24429e7i) q^{79} +(-9.22439e6 + 1.59771e7i) q^{81} +4.13681e7i q^{83} +1.55449e8 q^{85} +(-1.28817e7 - 7.43727e6i) q^{87} +(3.73562e7 - 2.15676e7i) q^{89} +(1.48127e7 + 2.56563e7i) q^{93} +(4.71836e6 - 8.17243e6i) q^{95} +8.64109e7i q^{97} +916390. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 52264 q^{9} + 22776 q^{11} + 206064 q^{15} - 571560 q^{23} + 1030440 q^{25} - 5384256 q^{29} + 3376640 q^{37} + 10336136 q^{39} + 18525008 q^{43} + 16028856 q^{51} - 14106216 q^{53} - 4787360 q^{57}+ \cdots + 1119499328 q^{99}+O(q^{100}) $ 32 * q + 52264 * q^9 + 22776 * q^11 + 206064 * q^15 - 571560 * q^23 + 1030440 * q^25 - 5384256 * q^29 + 3376640 * q^37 + 10336136 * q^39 + 18525008 * q^43 + 16028856 * q^51 - 14106216 * q^53 - 4787360 * q^57 - 5623008 * q^65 - 82433680 * q^67 + 250685568 * q^71 + 138241200 * q^79 - 465637680 * q^81 + 880381104 * q^85 + 310654512 * q^93 - 811120872 * q^95 + 1119499328 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−31.7145	−	18.3104i	−0.391537	−	0.226054i	0.291289	−	0.956635i	$-0.405916\pi$
$3$	−31.7145	−	18.3104i	−0.391537	−	0.226054i	−0.682826	+	0.730581i	$0.739249\pi$
$4$		0			0
$5$	−917.948	+	529.978i	−1.46872	+	0.847964i	−0.999385	−	0.0350572i	$-0.988839\pi$
$5$	−917.948	+	529.978i	−1.46872	+	0.847964i	−0.469332	+	0.883022i	$0.655505\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	−2609.96	−	4520.59i	−0.397799	−	0.689009i
$10$		0			0
$11$	−87.7782	+	152.036i	−0.00599537	+	0.0103843i	−0.869008	−	0.494799i	$-0.835242\pi$
$11$	−87.7782	+	152.036i	−0.00599537	+	0.0103843i	0.863012	+	0.505183i	$0.168575\pi$
$12$		0			0
$13$		−	463.876i		−	0.0162416i	−0.999967	−	0.00812079i	$-0.997415\pi$
$13$		−	463.876i		−	0.0162416i	0.999967	−	0.00812079i	$-0.00258496\pi$
$14$		0			0
$15$	38816.3			0.766743
$16$		0			0
$17$	−127008.	−	73327.9i	−1.52067	−	0.877957i	−0.999703	−	0.0243787i	$-0.992239\pi$
$17$	−127008.	−	73327.9i	−1.52067	−	0.877957i	−0.520964	−	0.853579i	$-0.674427\pi$
$18$		0			0
$19$	−7710.17	+	4451.47i	−0.0591629	+	0.0341577i	−0.529290	−	0.848441i	$-0.677542\pi$
$19$	−7710.17	+	4451.47i	−0.0591629	+	0.0341577i	0.470127	+	0.882599i	$0.344208\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−255214.	−	442044.i	−0.911997	−	1.57962i	−0.811240	−	0.584714i	$-0.801207\pi$
$23$	−255214.	−	442044.i	−0.911997	−	1.57962i	−0.100757	−	0.994911i	$-0.532126\pi$
$24$		0			0
$25$	366440.	−	634693.i	0.938087	−	1.62482i
$26$		0			0
$27$			431426.i			0.811804i
$28$		0			0
$29$	406178.			0.574281			0.287140	−	0.957889i	$-0.407295\pi$
$29$	406178.			0.574281			0.287140	+	0.957889i	$0.407295\pi$
$30$		0			0
$31$	−700595.	−	404489.i	−0.758613	−	0.437986i	0.0701842	−	0.997534i	$-0.477641\pi$
$31$	−700595.	−	404489.i	−0.758613	−	0.437986i	−0.828798	+	0.559548i	$0.810975\pi$
$32$		0			0
$33$	5567.68	−	3214.50i	0.00469481	−	0.00271055i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−479821.	−	831074.i	−0.256019	−	0.443438i	0.709153	−	0.705055i	$-0.249078\pi$
$37$	−479821.	−	831074.i	−0.256019	−	0.443438i	−0.965172	+	0.261617i	$0.915744\pi$
$38$		0			0
$39$	−8493.73	+	14711.6i	−0.00367147	+	0.00635917i
$40$		0			0
$41$		−	1.28045e6i		−	0.453136i	−0.973995	−	0.226568i	$-0.927249\pi$
$41$		−	1.28045e6i		−	0.453136i	0.973995	−	0.226568i	$-0.0727506\pi$
$42$		0			0
$43$	−3.13224e6			−0.916182			−0.458091	−	0.888905i	$-0.651467\pi$
$43$	−3.13224e6			−0.916182			−0.458091	+	0.888905i	$0.651467\pi$
$44$		0			0
$45$	4.79162e6	+	2.76644e6i	1.16851	+	0.674639i
$46$		0			0
$47$	−6.80317e6	+	3.92781e6i	−1.39418	+	0.804932i	−0.993775	−	0.111405i	$-0.964465\pi$
$47$	−6.80317e6	+	3.92781e6i	−1.39418	+	0.804932i	−0.400408	+	0.916337i	$0.631131\pi$
$48$		0			0
$49$		0			0
$50$		0			0
$51$	2.68532e6	+	4.65111e6i	0.396931	+	0.687505i
$52$		0			0
$53$	−5.01639e6	+	8.68865e6i	−0.635753	+	1.10116i	0.350602	+	0.936524i	$0.385977\pi$
$53$	−5.01639e6	+	8.68865e6i	−0.635753	+	1.10116i	−0.986355	+	0.164632i	$0.947356\pi$
$54$		0			0
$55$		−	186082.i		−	0.0203354i
$56$		0			0
$57$	326032.			0.0308859
$58$		0			0
$59$	1.49855e7	+	8.65189e6i	1.23670	+	0.714008i	0.968418	−	0.249333i	$-0.0802113\pi$
$59$	1.49855e7	+	8.65189e6i	1.23670	+	0.714008i	0.268280	+	0.963341i	$0.413545\pi$
$60$		0			0
$61$	7.40037e6	−	4.27260e6i	0.534483	−	0.308584i	−0.208357	−	0.978053i	$-0.566812\pi$
$61$	7.40037e6	−	4.27260e6i	0.534483	−	0.308584i	0.742840	+	0.669469i	$0.233478\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	245844.	+	425814.i	0.0137723	+	0.0238543i
$66$		0			0
$67$	9.94850e6	−	1.72313e7i	0.493695	−	0.855104i	−0.506279	−	0.862370i	$-0.668979\pi$
$67$	9.94850e6	−	1.72313e7i	0.493695	−	0.855104i	0.999974	+	0.00726554i	$0.00231271\pi$
$68$		0			0
$69$			1.86923e7i			0.824642i
$70$		0			0
$71$	1.84731e7			0.726952			0.363476	−	0.931604i	$-0.381590\pi$
$71$	1.84731e7			0.726952			0.363476	+	0.931604i	$0.381590\pi$
$72$		0			0
$73$	−1.63136e7	−	9.41869e6i	−0.574460	−	0.331664i	0.184469	−	0.982838i	$-0.440944\pi$
$73$	−1.63136e7	−	9.41869e6i	−0.574460	−	0.331664i	−0.758929	+	0.651174i	$0.774277\pi$
$74$		0			0
$75$	−2.32429e7	+	1.34193e7i	−0.734591	+	0.424117i
$76$		0			0
$77$		0			0
$78$		0			0
$79$	−3.02779e7	−	5.24429e7i	−0.777353	−	1.34641i	−0.933463	−	0.358675i	$-0.883229\pi$
$79$	−3.02779e7	−	5.24429e7i	−0.777353	−	1.34641i	0.156110	−	0.987740i	$-0.450105\pi$
$80$		0			0
$81$	−9.22439e6	+	1.59771e7i	−0.214288	+	0.371157i
$82$		0			0
$83$			4.13681e7i			0.871673i	0.900026	+	0.435837i	$0.143547\pi$
$83$			4.13681e7i			0.871673i	−0.900026	+	0.435837i	$0.856453\pi$
$84$		0			0
$85$	1.55449e8			2.97791
$86$		0			0
$87$	−1.28817e7	−	7.43727e6i	−0.224852	−	0.129818i
$88$		0			0
$89$	3.73562e7	−	2.15676e7i	0.595392	−	0.343750i	−0.171835	−	0.985126i	$-0.554969\pi$
$89$	3.73562e7	−	2.15676e7i	0.595392	−	0.343750i	0.767227	+	0.641376i	$0.221636\pi$
$90$		0			0
$91$		0			0
$92$		0			0
$93$	1.48127e7	+	2.56563e7i	0.198017	+	0.342975i
$94$		0			0
$95$	4.71836e6	−	8.17243e6i	0.0579291	−	0.100336i
$96$		0			0
$97$			8.64109e7i			0.976071i	0.872824	+	0.488036i	$0.162286\pi$
$97$			8.64109e7i			0.976071i	−0.872824	+	0.488036i	$0.837714\pi$
$98$		0			0
$99$	916390.			0.00953981
$100$		0			0
$101$	1.20417e8	+	6.95230e7i	1.15719	+	0.668103i	0.950628	−	0.310332i	$-0.100440\pi$
$101$	1.20417e8	+	6.95230e7i	1.15719	+	0.668103i	0.206559	+	0.978434i	$0.433773\pi$
$102$		0			0
$103$	−1.52953e8	+	8.83075e7i	−1.35897	+	0.784600i	−0.989485	−	0.144637i	$-0.953799\pi$
$103$	−1.52953e8	+	8.83075e7i	−1.35897	+	0.784600i	−0.369483	+	0.929238i	$0.620465\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−2.60336e7	−	4.50915e7i	−0.198609	−	0.344001i	0.749469	−	0.662040i	$-0.230309\pi$
$107$	−2.60336e7	−	4.50915e7i	−0.198609	−	0.344001i	−0.948078	+	0.318039i	$0.896976\pi$
$108$		0			0
$109$	−6.74506e7	+	1.16828e8i	−0.477837	+	0.827639i	−0.999677	−	0.0254049i	$-0.991913\pi$
$109$	−6.74506e7	+	1.16828e8i	−0.477837	+	0.827639i	0.521840	+	0.853043i	$0.325246\pi$
$110$		0			0
$111$			3.51428e7i			0.231496i
$112$		0			0
$113$	1.53723e8			0.942813			0.471406	−	0.881916i	$-0.343747\pi$
$113$	1.53723e8			0.942813			0.471406	+	0.881916i	$0.343747\pi$
$114$		0			0
$115$	4.68547e8	+	2.70516e8i	2.67893	+	1.54668i
$116$		0			0
$117$	−2.09699e6	+	1.21070e6i	−0.0111906	+	0.00646089i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.07164e8	+	1.85614e8i	0.499928	+	0.865901i
$122$		0			0
$123$	−2.34456e7	+	4.06089e7i	−0.102433	+	0.177419i
$124$		0			0
$125$			3.62776e8i			1.48593i
$126$		0			0
$127$	2.59200e8			0.996370			0.498185	−	0.867071i	$-0.334000\pi$
$127$	2.59200e8			0.996370			0.498185	+	0.867071i	$0.334000\pi$
$128$		0			0
$129$	9.93375e7	+	5.73525e7i	0.358719	+	0.207107i
$130$		0			0
$131$	−4.39996e8	+	2.54032e8i	−1.49405	+	0.862587i	−0.999977	−	0.00683548i	$-0.997824\pi$
$131$	−4.39996e8	+	2.54032e8i	−1.49405	+	0.862587i	−0.494069	+	0.869423i	$0.664491\pi$
$132$		0			0
$133$		0			0
$134$		0			0
$135$	−2.28646e8	−	3.96027e8i	−0.688381	−	1.19231i
$136$		0			0
$137$	−1.21484e8	+	2.10417e8i	−0.344855	+	0.597307i	−0.985327	−	0.170674i	$-0.945405\pi$
$137$	−1.21484e8	+	2.10417e8i	−0.344855	+	0.597307i	0.640472	+	0.767981i	$0.278739\pi$
$138$		0			0
$139$		−	1.11438e8i		−	0.298520i	−0.988798	−	0.149260i	$-0.952311\pi$
$139$		−	1.11438e8i		−	0.298520i	0.988798	−	0.149260i	$-0.0476891\pi$
$140$		0			0
$141$	2.87679e8			0.727832
$142$		0			0
$143$	70525.9	+	40718.1i	0.000168657	+	9.73742e-5i
$144$		0			0
$145$	−3.72850e8	+	2.15265e8i	−0.843456	+	0.486970i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−4.30617e8	−	7.45851e8i	−0.873668	−	1.51324i	−0.858175	−	0.513358i	$-0.828401\pi$
$149$	−4.30617e8	−	7.45851e8i	−0.873668	−	1.51324i	−0.0154936	−	0.999880i	$-0.504932\pi$
$150$		0			0
$151$	4.39335e8	−	7.60950e8i	0.845060	−	1.46369i	−0.0405083	−	0.999179i	$-0.512898\pi$
$151$	4.39335e8	−	7.60950e8i	0.845060	−	1.46369i	0.885569	−	0.464508i	$-0.153769\pi$
$152$		0			0
$153$			7.65532e8i			1.39700i
$154$		0			0
$155$	8.57481e8			1.48559
$156$		0			0
$157$	7.07634e7	+	4.08553e7i	0.116469	+	0.0672434i	0.557103	−	0.830444i	$-0.311913\pi$
$157$	7.07634e7	+	4.08553e7i	0.116469	+	0.0672434i	−0.440634	+	0.897687i	$0.645246\pi$
$158$		0			0
$159$	3.18185e8	−	1.83704e8i	0.497841	−	0.287429i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	2.07541e8	+	3.59471e8i	0.294004	+	0.509229i	0.974753	−	0.223288i	$-0.0716789\pi$
$163$	2.07541e8	+	3.59471e8i	0.294004	+	0.509229i	−0.680749	+	0.732517i	$0.738346\pi$
$164$		0			0
$165$	−3.40723e6	+	5.90149e6i	−0.00459690	+	0.00796207i
$166$		0			0
$167$			1.05689e9i			1.35883i	0.733754	+	0.679416i	$0.237767\pi$
$167$			1.05689e9i			1.35883i	−0.733754	+	0.679416i	$0.762233\pi$
$168$		0			0
$169$	8.15516e8			0.999736
$170$		0			0
$171$	4.02465e7	+	2.32363e7i	0.0470699	+	0.0271758i
$172$		0			0
$173$	−2.55913e7	+	1.47752e7i	−0.0285699	+	0.0164948i	−0.514217	−	0.857660i	$-0.671917\pi$
$173$	−2.55913e7	+	1.47752e7i	−0.0285699	+	0.0164948i	0.485647	+	0.874155i	$0.338584\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.16839e8	−	5.48781e8i	−0.322809	−	0.559121i
$178$		0			0
$179$	−4.54211e8	+	7.86717e8i	−0.442431	+	0.766314i	−0.997869	−	0.0652444i	$-0.979217\pi$
$179$	−4.54211e8	+	7.86717e8i	−0.442431	+	0.766314i	0.555438	+	0.831558i	$0.312551\pi$
$180$		0			0
$181$		−	1.44603e9i		−	1.34729i	−0.739053	−	0.673647i	$-0.764727\pi$
$181$		−	1.44603e9i		−	1.34729i	0.739053	−	0.673647i	$-0.235273\pi$
$182$		0			0
$183$	−3.12932e8			−0.279026
$184$		0			0
$185$	8.80902e8	+	5.08589e8i	0.752039	+	0.434190i
$186$		0			0
$187$	2.22970e7	−	1.28732e7i	0.0182339	−	0.0105274i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	1.03683e9	+	1.79585e9i	0.779069	+	1.34939i	0.932479	+	0.361224i	$0.117641\pi$
$191$	1.03683e9	+	1.79585e9i	0.779069	+	1.34939i	−0.153410	+	0.988163i	$0.549026\pi$
$192$		0			0
$193$	−6.32668e7	+	1.09581e8i	−0.0455981	+	0.0789782i	−0.887924	−	0.459991i	$-0.847853\pi$
$193$	−6.32668e7	+	1.09581e8i	−0.0455981	+	0.0789782i	0.842326	+	0.538969i	$0.181186\pi$
$194$		0			0
$195$		−	1.80060e7i		−	0.0124531i
$196$		0			0
$197$	−2.58795e9			−1.71827			−0.859133	−	0.511752i	$-0.828997\pi$
$197$	−2.58795e9			−1.71827			−0.859133	+	0.511752i	$0.828997\pi$
$198$		0			0
$199$	3.30529e8	+	1.90831e8i	0.210764	+	0.121685i	0.601667	−	0.798747i	$-0.294504\pi$
$199$	3.30529e8	+	1.90831e8i	0.210764	+	0.121685i	−0.390902	+	0.920432i	$0.627837\pi$
$200$		0			0
$201$	−6.31023e8	+	3.64321e8i	−0.386599	+	0.223203i
$202$		0			0
$203$		0			0
$204$		0			0
$205$	6.78612e8	+	1.17539e9i	0.384243	+	0.665529i
$206$		0			0
$207$	−1.33220e9	+	2.30743e9i	−0.725583	+	1.25675i
$208$		0			0
$209$		−	1.56297e6i		−	0.000819152i
$210$		0			0
$211$	2.82056e9			1.42300			0.711501	−	0.702685i	$-0.248016\pi$
$211$	2.82056e9			1.42300			0.711501	+	0.702685i	$0.248016\pi$
$212$		0			0
$213$	−5.85864e8	−	3.38249e8i	−0.284628	−	0.164330i
$214$		0			0
$215$	2.87524e9	−	1.66002e9i	1.34561	−	0.776890i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	3.44919e8	+	5.97418e8i	0.149948	+	0.259718i
$220$		0			0
$221$	−3.40150e7	+	5.89157e7i	−0.0142594	+	0.0246980i
$222$		0			0
$223$		−	3.79033e9i		−	1.53270i	−0.642423	−	0.766350i	$-0.722071\pi$
$223$		−	3.79033e9i		−	1.53270i	0.642423	−	0.766350i	$-0.277929\pi$
$224$		0			0
$225$	−3.82558e9			−1.49268
$226$		0			0
$227$	−1.92233e9	−	1.10986e9i	−0.723978	−	0.417989i	0.0922373	−	0.995737i	$-0.470598\pi$
$227$	−1.92233e9	−	1.10986e9i	−0.723978	−	0.417989i	−0.816215	+	0.577748i	$0.803931\pi$
$228$		0			0
$229$	−9.72765e8	+	5.61626e8i	−0.353725	+	0.204223i	−0.666325	−	0.745662i	$-0.732134\pi$
$229$	−9.72765e8	+	5.61626e8i	−0.353725	+	0.204223i	0.312600	+	0.949885i	$0.398800\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.64247e9	−	2.84485e9i	−0.557281	−	0.965240i	−0.997722	−	0.0674579i	$-0.978511\pi$
$233$	−1.64247e9	−	2.84485e9i	−0.557281	−	0.965240i	0.440441	−	0.897782i	$-0.354822\pi$
$234$		0			0
$235$	4.16330e9	−	7.21105e9i	1.36511	−	2.36443i
$236$		0			0
$237$			2.21760e9i			0.702894i
$238$		0			0
$239$	−5.37385e9			−1.64700			−0.823500	−	0.567316i	$-0.807982\pi$
$239$	−5.37385e9			−1.64700			−0.823500	+	0.567316i	$0.807982\pi$
$240$		0			0
$241$	−4.35723e9	−	2.51565e9i	−1.29164	−	0.745730i	−0.312696	−	0.949853i	$-0.601232\pi$
$241$	−4.35723e9	−	2.51565e9i	−1.29164	−	0.745730i	−0.978945	+	0.204124i	$0.934566\pi$
$242$		0			0
$243$	3.03645e9	−	1.75310e9i	0.870846	−	0.502783i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	2.06493e6	+	3.57656e6i	0.000554775	+	0.000960898i
$248$		0			0
$249$	7.57466e8	−	1.31197e9i	0.197045	−	0.341292i
$250$		0			0
$251$		−	1.11941e9i		−	0.282030i	−0.990007	−	0.141015i	$-0.954963\pi$
$251$		−	1.11941e9i		−	0.282030i	0.990007	−	0.141015i	$-0.0450366\pi$
$252$		0			0
$253$	8.96089e7			0.0218710
$254$		0			0
$255$	−4.92997e9	−	2.84632e9i	−1.16596	−	0.673167i
$256$		0			0
$257$	1.23912e8	−	7.15406e7i	0.0284041	−	0.0163991i	−0.485731	−	0.874108i	$-0.661446\pi$
$257$	1.23912e8	−	7.15406e7i	0.0284041	−	0.0163991i	0.514135	+	0.857709i	$0.328113\pi$
$258$		0			0
$259$		0			0
$260$		0			0
$261$	−1.06011e9	−	1.83616e9i	−0.228449	−	0.395684i
$262$		0			0
$263$	−1.57178e9	+	2.72240e9i	−0.328525	+	0.569022i	−0.982219	−	0.187737i	$-0.939885\pi$
$263$	−1.57178e9	+	2.72240e9i	−0.328525	+	0.569022i	0.653695	+	0.756759i	$0.273218\pi$
$264$		0			0
$265$		−	1.06343e10i		−	2.15638i
$266$		0			0
$267$	−1.57964e9			−0.310824
$268$		0			0
$269$	−5.65624e9	−	3.26563e9i	−1.08024	−	0.623675i	−0.149276	−	0.988796i	$-0.547694\pi$
$269$	−5.65624e9	−	3.26563e9i	−1.08024	−	0.623675i	−0.930960	+	0.365121i	$0.881028\pi$
$270$		0			0
$271$	1.01079e9	−	5.83581e8i	0.187407	−	0.108199i	−0.403361	−	0.915041i	$-0.632158\pi$
$271$	1.01079e9	−	5.83581e8i	0.187407	−	0.108199i	0.590768	+	0.806842i	$0.298825\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	6.43309e7	+	1.11424e8i	0.0112484	+	0.0194827i
$276$		0			0
$277$	−5.20413e8	+	9.01382e8i	−0.0883953	+	0.153105i	−0.906833	−	0.421490i	$-0.861507\pi$
$277$	−5.20413e8	+	9.01382e8i	−0.0883953	+	0.153105i	0.818438	+	0.574595i	$0.194841\pi$
$278$		0			0
$279$			4.22280e9i			0.696922i
$280$		0			0
$281$	−6.19245e9			−0.993201			−0.496601	−	0.867979i	$-0.665419\pi$
$281$	−6.19245e9			−0.993201			−0.496601	+	0.867979i	$0.665419\pi$
$282$		0			0
$283$	6.32245e9	+	3.65027e9i	0.985688	+	0.569088i	0.903983	−	0.427569i	$-0.140630\pi$
$283$	6.32245e9	+	3.65027e9i	0.985688	+	0.569088i	0.0817058	+	0.996656i	$0.473963\pi$
$284$		0			0
$285$	−2.99281e8	+	1.72790e8i	−0.0453627	+	0.0261902i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	7.26608e9	+	1.25852e10i	1.04162	+	1.80414i
$290$		0			0
$291$	1.58221e9	−	2.74048e9i	0.220645	−	0.382168i
$292$		0			0
$293$		−	5.25584e9i		−	0.713134i	−0.934270	−	0.356567i	$-0.883947\pi$
$293$		−	5.25584e9i		−	0.713134i	0.934270	−	0.356567i	$-0.116053\pi$
$294$		0			0
$295$	−1.83412e10			−2.42181
$296$		0			0
$297$	−6.55924e7	−	3.78698e7i	−0.00843000	−	0.00486706i
$298$		0			0
$299$	−2.05053e8	+	1.18388e8i	−0.0256556	+	0.0148123i
$300$		0			0
$301$		0			0
$302$		0			0
$303$	−2.54598e9	−	4.40977e9i	−0.302054	−	0.523173i
$304$		0			0
$305$	−4.52877e9	+	7.84406e9i	−0.523336	+	0.906445i
$306$		0			0
$307$		−	9.63110e9i		−	1.08423i	−0.840304	−	0.542116i	$-0.817623\pi$
$307$		−	9.63110e9i		−	1.08423i	0.840304	−	0.542116i	$-0.182377\pi$
$308$		0			0
$309$	6.46777e9			0.709448
$310$		0			0
$311$	4.65131e9	+	2.68543e9i	0.497203	+	0.287060i	0.727558	−	0.686046i	$-0.240655\pi$
$311$	4.65131e9	+	2.68543e9i	0.497203	+	0.287060i	−0.230355	+	0.973107i	$0.573989\pi$
$312$		0			0
$313$	8.35072e9	−	4.82129e9i	0.870055	−	0.502326i	0.00268847	−	0.999996i	$-0.499144\pi$
$313$	8.35072e9	−	4.82129e9i	0.870055	−	0.502326i	0.867367	+	0.497670i	$0.165811\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	5.64399e9	+	9.77568e9i	0.558919	+	0.968077i	0.997587	+	0.0694273i	$0.0221172\pi$
$317$	5.64399e9	+	9.77568e9i	0.558919	+	0.968077i	−0.438668	+	0.898649i	$0.644549\pi$
$318$		0			0
$319$	−3.56536e7	+	6.17538e7i	−0.00344302	+	0.00596349i
$320$		0			0
$321$			1.90674e9i			0.179585i
$322$		0			0
$323$	1.30567e9			0.119956
$324$		0			0
$325$	−2.94419e8	−	1.69983e8i	−0.0263896	−	0.0152360i
$326$		0			0
$327$	4.27832e9	−	2.47009e9i	0.374182	−	0.216034i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	2.78992e9	+	4.83228e9i	0.232423	+	0.402568i	0.958521	−	0.285023i	$-0.0920013\pi$
$331$	2.78992e9	+	4.83228e9i	0.232423	+	0.402568i	−0.726098	+	0.687592i	$0.758668\pi$
$332$		0			0
$333$	−2.50463e9	+	4.33814e9i	−0.203688	+	0.352799i
$334$		0			0
$335$			2.10899e10i			1.67454i
$336$		0			0
$337$	2.12480e10			1.64740			0.823701	−	0.567025i	$-0.191906\pi$
$337$	2.12480e10			1.64740			0.823701	+	0.567025i	$0.191906\pi$
$338$		0			0
$339$	−4.87525e9	−	2.81473e9i	−0.369146	−	0.213126i
$340$		0			0
$341$	1.22994e8	−	7.10106e7i	0.00909633	−	0.00525177i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−9.90648e9	−	1.71585e10i	−0.699267	−	1.21117i
$346$		0			0
$347$	1.11294e10	−	1.92767e10i	0.767635	−	1.32958i	−0.171208	−	0.985235i	$-0.554767\pi$
$347$	1.11294e10	−	1.92767e10i	0.767635	−	1.32958i	0.938842	−	0.344347i	$-0.111900\pi$
$348$		0			0
$349$			1.21543e9i			0.0819269i	0.999161	+	0.0409635i	$0.0130427\pi$
$349$			1.21543e9i			0.0819269i	−0.999161	+	0.0409635i	$0.986957\pi$
$350$		0			0
$351$	2.00128e8			0.0131850
$352$		0			0
$353$	−9.02354e9	−	5.20974e9i	−0.581136	−	0.335519i	0.180449	−	0.983584i	$-0.442245\pi$
$353$	−9.02354e9	−	5.20974e9i	−0.581136	−	0.335519i	−0.761585	+	0.648065i	$0.775578\pi$
$354$		0			0
$355$	−1.69573e10	+	9.79031e9i	−1.06769	+	0.616429i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−8.28368e9	−	1.43477e10i	−0.498707	−	0.863785i	0.501292	−	0.865278i	$-0.332858\pi$
$359$	−8.28368e9	−	1.43477e10i	−0.498707	−	0.863785i	−0.999999	+	0.00149264i	$0.999525\pi$
$360$		0			0
$361$	−8.45215e9	+	1.46396e10i	−0.497667	+	0.861984i
$362$		0			0
$363$		−	7.84885e9i		−	0.452043i
$364$		0			0
$365$	1.99668e10			1.12496
$366$		0			0
$367$	9.34056e8	+	5.39277e8i	0.0514883	+	0.0297268i	0.525523	−	0.850779i	$-0.323870\pi$
$367$	9.34056e8	+	5.39277e8i	0.0514883	+	0.0297268i	−0.474035	+	0.880506i	$0.657203\pi$
$368$		0			0
$369$	−5.78840e9	+	3.34194e9i	−0.312215	+	0.180257i
$370$		0			0
$371$		0			0
$372$		0			0
$373$	−1.02558e10	−	1.77636e10i	−0.529827	−	0.917687i	−0.999395	−	0.0347909i	$-0.988923\pi$
$373$	−1.02558e10	−	1.77636e10i	−0.529827	−	0.917687i	0.469567	−	0.882897i	$-0.344410\pi$
$374$		0			0
$375$	6.64256e9	−	1.15052e10i	0.335900	−	0.581796i
$376$		0			0
$377$		−	1.88416e8i		−	0.00932722i
$378$		0			0
$379$	1.71573e10			0.831557			0.415779	−	0.909466i	$-0.363509\pi$
$379$	1.71573e10			0.831557			0.415779	+	0.909466i	$0.363509\pi$
$380$		0			0
$381$	−8.22040e9	−	4.74605e9i	−0.390115	−	0.225233i
$382$		0			0
$383$	9.07510e9	−	5.23951e9i	0.421751	−	0.243498i	−0.274075	−	0.961708i	$-0.588372\pi$
$383$	9.07510e9	−	5.23951e9i	0.421751	−	0.243498i	0.695826	+	0.718210i	$0.255038\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	8.17504e9	+	1.41596e10i	0.364457	+	0.631257i
$388$		0			0
$389$	−3.00887e9	+	5.21151e9i	−0.131403	+	0.227596i	−0.924218	−	0.381866i	$-0.875281\pi$
$389$	−3.00887e9	+	5.21151e9i	−0.131403	+	0.227596i	0.792815	+	0.609463i	$0.208615\pi$
$390$		0			0
$391$			7.48572e10i			3.20278i
$392$		0			0
$393$	1.86057e10			0.779965
$394$		0			0
$395$	5.55872e10	+	3.20933e10i	2.28342	+	1.31833i
$396$		0			0
$397$	−2.22042e10	+	1.28196e10i	−0.893869	+	0.516075i	−0.875206	−	0.483751i	$-0.839274\pi$
$397$	−2.22042e10	+	1.28196e10i	−0.893869	+	0.516075i	−0.0186627	+	0.999826i	$0.505941\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.26709e10	+	2.19467e10i	0.490039	+	0.848772i	0.999934	−	0.0114645i	$-0.00364934\pi$
$401$	1.26709e10	+	2.19467e10i	0.490039	+	0.848772i	−0.509896	+	0.860236i	$0.670316\pi$
$402$		0			0
$403$	−1.87633e8	+	3.24989e8i	−0.00711358	+	0.0123211i
$404$		0			0
$405$		−	1.95549e10i		−	0.726834i
$406$		0			0
$407$	1.68471e8			0.00613971
$408$		0			0
$409$	3.77946e10	+	2.18207e10i	1.35063	+	0.779788i	0.988338	−	0.152276i	$-0.0486603\pi$
$409$	3.77946e10	+	2.18207e10i	1.35063	+	0.779788i	0.362294	+	0.932064i	$0.381994\pi$
$410$		0			0
$411$	7.70561e9	−	4.44883e9i	0.270047	−	0.155912i
$412$		0			0
$413$		0			0
$414$		0			0
$415$	−2.19242e10	−	3.79738e10i	−0.739148	−	1.28024i
$416$		0			0
$417$	−2.04046e9	+	3.53419e9i	−0.0674815	+	0.116881i
$418$		0			0
$419$		−	2.58977e10i		−	0.840244i	−0.907468	−	0.420122i	$-0.861987\pi$
$419$		−	2.58977e10i		−	0.840244i	0.907468	−	0.420122i	$-0.138013\pi$
$420$		0			0
$421$	−2.01494e10			−0.641406			−0.320703	−	0.947180i	$-0.603919\pi$
$421$	−2.01494e10			−0.641406			−0.320703	+	0.947180i	$0.603919\pi$
$422$		0			0
$423$	3.55120e10	+	2.05029e10i	1.10921	+	0.640403i
$424$		0			0
$425$	−9.30814e10	+	5.37406e10i	−2.85304	+	1.64720i
$426$		0			0
$427$		0			0
$428$		0			0
$429$	−1.49113e6	−	2.58271e6i	−4.40236e−5	−	7.62512e-5i
$430$		0			0
$431$	−1.63352e10	+	2.82934e10i	−0.473387	+	0.819930i	−0.999536	−	0.0304623i	$-0.990302\pi$
$431$	−1.63352e10	+	2.82934e10i	−0.473387	+	0.819930i	0.526149	+	0.850392i	$0.323635\pi$
$432$		0			0
$433$			1.85538e10i			0.527816i	0.964548	+	0.263908i	$0.0850115\pi$
$433$			1.85538e10i			0.527816i	−0.964548	+	0.263908i	$0.914989\pi$
$434$		0			0
$435$	1.57663e10			0.440326
$436$		0			0
$437$	3.93549e9	+	2.27215e9i	0.107913	+	0.0623034i
$438$		0			0
$439$	4.68257e10	−	2.70348e10i	1.26074	−	0.727889i	0.287523	−	0.957774i	$-0.407168\pi$
$439$	4.68257e10	−	2.70348e10i	1.26074	−	0.727889i	0.973218	+	0.229884i	$0.0738348\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	2.76361e10	+	4.78671e10i	0.717566	+	1.24286i	0.961962	+	0.273184i	$0.0880769\pi$
$443$	2.76361e10	+	4.78671e10i	0.717566	+	1.24286i	−0.244396	+	0.969675i	$0.578590\pi$
$444$		0			0
$445$	−2.28607e10	+	3.95959e10i	−0.582975	+	1.00974i
$446$		0			0
$447$			3.15390e10i			0.789984i
$448$		0			0
$449$	2.75787e10			0.678561			0.339281	−	0.940685i	$-0.389816\pi$
$449$	2.75787e10			0.678561			0.339281	+	0.940685i	$0.389816\pi$
$450$		0			0
$451$	1.94675e8	+	1.12396e8i	0.00470549	+	0.00271672i
$452$		0			0
$453$	−2.78665e10	+	1.60888e10i	−0.661745	+	0.382058i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−1.63233e10	−	2.82727e10i	−0.374233	−	0.648190i	0.615979	−	0.787763i	$-0.288761\pi$
$457$	−1.63233e10	−	2.82727e10i	−0.374233	−	0.648190i	−0.990212	+	0.139572i	$0.955427\pi$
$458$		0			0
$459$	3.16355e10	−	5.47944e10i	0.712729	−	1.23448i
$460$		0			0
$461$			1.05577e9i			0.0233758i	0.999932	+	0.0116879i	$0.00372046\pi$
$461$			1.05577e9i			0.0233758i	−0.999932	+	0.0116879i	$0.996280\pi$
$462$		0			0
$463$	1.69452e10			0.368742			0.184371	−	0.982857i	$-0.440975\pi$
$463$	1.69452e10			0.368742			0.184371	+	0.982857i	$0.440975\pi$
$464$		0			0
$465$	−2.71946e10	−	1.57008e10i	−0.581661	−	0.335822i
$466$		0			0
$467$	4.14846e10	−	2.39512e10i	0.872207	−	0.503569i	0.00412614	−	0.999991i	$-0.498687\pi$
$467$	4.14846e10	−	2.39512e10i	0.872207	−	0.503569i	0.868081	+	0.496422i	$0.165353\pi$
$468$		0			0
$469$		0			0
$470$		0			0
$471$	−1.49615e9	−	2.59141e9i	−0.0304013	−	0.0526565i
$472$		0			0
$473$	2.74943e8	−	4.76215e8i	0.00549285	−	0.00951389i
$474$		0			0
$475$			6.52479e9i			0.128172i
$476$		0			0
$477$	5.23704e10			1.01161
$478$		0			0
$479$	−1.07269e10	−	6.19316e9i	−0.203766	−	0.117644i	0.394645	−	0.918834i	$-0.370868\pi$
$479$	−1.07269e10	−	6.19316e9i	−0.203766	−	0.117644i	−0.598411	+	0.801190i	$0.704201\pi$
$480$		0			0
$481$	−3.85515e8	+	2.22577e8i	−0.00720213	+	0.00415815i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.57958e10	−	7.93207e10i	−0.827674	−	1.43357i
$486$		0			0
$487$	−9.17764e9	+	1.58961e10i	−0.163160	+	0.282602i	−0.936001	−	0.351999i	$-0.885502\pi$
$487$	−9.17764e9	+	1.58961e10i	−0.163160	+	0.282602i	0.772840	+	0.634601i	$0.218835\pi$
$488$		0			0
$489$		−	1.52006e10i		−	0.265843i
$490$		0			0
$491$	7.15516e10			1.23110			0.615550	−	0.788098i	$-0.288934\pi$
$491$	7.15516e10			1.23110			0.615550	+	0.788098i	$0.288934\pi$
$492$		0			0
$493$	−5.15877e10	−	2.97842e10i	−0.873290	−	0.504194i
$494$		0			0
$495$	−8.41199e8	+	4.85667e8i	−0.0140113	+	0.00808942i
$496$		0			0
$497$		0			0
$498$		0			0
$499$	1.20718e10	+	2.09089e10i	0.194701	+	0.337232i	0.946803	−	0.321815i	$-0.104293\pi$
$499$	1.20718e10	+	2.09089e10i	0.194701	+	0.337232i	−0.752101	+	0.659047i	$0.770960\pi$
$500$		0			0
$501$	1.93521e10	−	3.35188e10i	0.307169	−	0.532032i
$502$		0			0
$503$			5.32847e10i			0.832397i	0.909274	+	0.416198i	$0.136638\pi$
$503$			5.32847e10i			0.832397i	−0.909274	+	0.416198i	$0.863362\pi$
$504$		0			0
$505$	−1.47383e11			−2.26611
$506$		0			0
$507$	−2.58637e10	−	1.49324e10i	−0.391434	−	0.225994i
$508$		0			0
$509$	1.60975e10	−	9.29392e9i	0.239822	−	0.138461i	−0.375273	−	0.926914i	$-0.622451\pi$
$509$	1.60975e10	−	9.29392e9i	0.239822	−	0.138461i	0.615095	+	0.788453i	$0.289118\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	−1.92048e9	−	3.32637e9i	−0.0277294	−	0.0480287i
$514$		0			0
$515$	9.36020e10	−	1.62123e11i	1.33063	−	2.30471i
$516$		0			0
$517$		−	1.37910e9i		−	0.0193034i
$518$		0			0
$519$	1.08215e9			0.0149149
$520$		0			0
$521$	−6.43174e10	−	3.71337e10i	−0.872927	−	0.503985i	−0.00460708	−	0.999989i	$-0.501466\pi$
$521$	−6.43174e10	−	3.71337e10i	−0.872927	−	0.503985i	−0.868320	+	0.496005i	$0.834800\pi$
$522$		0			0
$523$	1.11694e11	−	6.44867e10i	1.49288	−	0.861914i	0.492911	−	0.870080i	$-0.335933\pi$
$523$	1.11694e11	−	6.44867e10i	1.49288	−	0.861914i	0.999967	+	0.00816598i	$0.00259934\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	5.93206e10	+	1.02746e11i	0.769066	+	1.33206i
$528$		0			0
$529$	−9.11130e10	+	1.57812e11i	−1.16348	+	2.01520i
$530$		0			0
$531$		−	9.03244e10i		−	1.13613i
$532$		0			0
$533$	−5.93971e8			−0.00735964
$534$		0			0
$535$	4.77950e10	+	2.75945e10i	0.583401	+	0.336827i
$536$		0			0
$537$	2.88102e10	−	1.66336e10i	0.346456	−	0.200027i
$538$		0			0
$539$		0			0
$540$		0			0
$541$	2.00584e10	+	3.47422e10i	0.234157	+	0.405572i	0.959027	−	0.283314i	$-0.0914337\pi$
$541$	2.00584e10	+	3.47422e10i	0.234157	+	0.405572i	−0.724870	+	0.688885i	$0.758100\pi$
$542$		0			0
$543$	−2.64773e10	+	4.58600e10i	−0.304561	+	0.527515i
$544$		0			0
$545$		−	1.42989e11i		−	1.62076i
$546$		0			0
$547$	−1.09122e11			−1.21889			−0.609444	−	0.792829i	$-0.708607\pi$
$547$	−1.09122e11			−1.21889			−0.609444	+	0.792829i	$0.708607\pi$
$548$		0			0
$549$	−3.86293e10	−	2.23027e10i	−0.425234	−	0.245509i
$550$		0			0
$551$	−3.13170e9	+	1.80809e9i	−0.0339761	+	0.0196161i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	−1.86249e10	−	3.22593e10i	−0.196301	−	0.340003i
$556$		0			0
$557$	−6.00697e10	+	1.04044e11i	−0.624072	+	1.08092i	0.364648	+	0.931145i	$0.381189\pi$
$557$	−6.00697e10	+	1.04044e11i	−0.624072	+	1.08092i	−0.988720	+	0.149778i	$0.952144\pi$
$558$		0			0
$559$			1.45297e9i			0.0148802i
$560$		0			0
$561$	−9.42850e8			−0.00951900
$562$		0			0
$563$	9.79690e9	+	5.65624e9i	0.0975113	+	0.0562982i	0.547963	−	0.836503i	$-0.315404\pi$
$563$	9.79690e9	+	5.65624e9i	0.0975113	+	0.0562982i	−0.450451	+	0.892801i	$0.648737\pi$
$564$		0			0
$565$	−1.41110e11	+	8.14698e10i	−1.38473	+	0.799472i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	7.03143e10	+	1.21788e11i	0.670802	+	1.16186i	0.977677	+	0.210113i	$0.0673833\pi$
$569$	7.03143e10	+	1.21788e11i	0.670802	+	1.16186i	−0.306875	+	0.951750i	$0.599283\pi$
$570$		0			0
$571$	4.57449e10	−	7.92324e10i	0.430326	−	0.745347i	−0.566575	−	0.824010i	$-0.691732\pi$
$571$	4.57449e10	−	7.92324e10i	0.430326	−	0.745347i	0.996901	+	0.0786632i	$0.0250652\pi$
$572$		0			0
$573$		−	7.59392e10i		−	0.704446i
$574$		0			0
$575$	−3.74083e11			−3.42213
$576$		0			0
$577$	−7.14434e9	−	4.12479e9i	−0.0644554	−	0.0372133i	0.467426	−	0.884032i	$-0.345181\pi$
$577$	−7.14434e9	−	4.12479e9i	−0.0644554	−	0.0372133i	−0.531881	+	0.846819i	$0.678515\pi$
$578$		0			0
$579$	4.01295e9	−	2.31688e9i	0.0357067	−	0.0206153i
$580$		0			0
$581$		0			0
$582$		0			0
$583$	−8.80660e8	−	1.52535e9i	−0.00762314	−	0.0132037i
$584$		0			0
$585$	1.28329e9	−	2.22272e9i	0.0109572	−	0.0189784i
$586$		0			0
$587$			4.08974e9i			0.0344463i	0.999852	+	0.0172232i	$0.00548258\pi$
$587$			4.08974e9i			0.0344463i	−0.999852	+	0.0172232i	$0.994517\pi$
$588$		0			0
$589$	7.20228e9			0.0598424
$590$		0			0
$591$	8.20754e10	+	4.73863e10i	0.672765	+	0.388421i
$592$		0			0
$593$	7.98177e10	−	4.60828e10i	0.645477	−	0.372666i	−0.141244	−	0.989975i	$-0.545110\pi$
$593$	7.98177e10	−	4.60828e10i	0.645477	−	0.372666i	0.786721	+	0.617309i	$0.211777\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−6.98837e9	−	1.21042e10i	−0.0550147	−	0.0952882i
$598$		0			0
$599$	8.48489e10	−	1.46963e11i	0.659081	−	1.14156i	−0.321773	−	0.946817i	$-0.604279\pi$
$599$	8.48489e10	−	1.46963e11i	0.659081	−	1.14156i	0.980854	−	0.194745i	$-0.0623879\pi$
$600$		0			0
$601$		−	1.48134e11i		−	1.13542i	−0.823229	−	0.567709i	$-0.807830\pi$
$601$		−	1.48134e11i		−	1.13542i	0.823229	−	0.567709i	$-0.192170\pi$
$602$		0			0
$603$	−1.03861e11			−0.785566
$604$		0			0
$605$	−1.96742e11	−	1.13589e11i	−1.46851	−	0.847843i
$606$		0			0
$607$	1.30753e11	−	7.54902e10i	0.963155	−	0.556078i	0.0660126	−	0.997819i	$-0.478972\pi$
$607$	1.30753e11	−	7.54902e10i	0.963155	−	0.556078i	0.897143	+	0.441741i	$0.145639\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	1.82202e9	+	3.15582e9i	0.0130734	+	0.0226437i
$612$		0			0
$613$	1.32080e10	−	2.28770e10i	0.0935398	−	0.162016i	−0.815458	−	0.578816i	$-0.803515\pi$
$613$	1.32080e10	−	2.28770e10i	0.0935398	−	0.162016i	0.908998	+	0.416800i	$0.136848\pi$
$614$		0			0
$615$		−	4.97025e10i		−	0.347439i
$616$		0			0
$617$	3.03709e10			0.209564			0.104782	−	0.994495i	$-0.466586\pi$
$617$	3.03709e10			0.209564			0.104782	+	0.994495i	$0.466586\pi$
$618$		0			0
$619$	−1.10401e11	−	6.37398e10i	−0.751984	−	0.434158i	0.0744264	−	0.997227i	$-0.476287\pi$
$619$	−1.10401e11	−	6.37398e10i	−0.751984	−	0.434158i	−0.826410	+	0.563068i	$0.809621\pi$
$620$		0			0
$621$	1.90709e11	−	1.10106e11i	1.28235	−	0.740363i
$622$		0			0
$623$		0			0
$624$		0			0
$625$	−4.91224e10	−	8.50825e10i	−0.321929	−	0.557597i
$626$		0			0
$627$	−2.86185e7	+	4.95687e7i	−0.000185172	+	0.000320728i
$628$		0			0
$629$			1.40737e11i			0.899095i
$630$		0			0
$631$	1.33173e11			0.840039			0.420019	−	0.907515i	$-0.362023\pi$
$631$	1.33173e11			0.840039			0.420019	+	0.907515i	$0.362023\pi$
$632$		0			0
$633$	−8.94525e10	−	5.16454e10i	−0.557157	−	0.321675i
$634$		0			0
$635$	−2.37932e11	+	1.37370e11i	−1.46339	+	0.844886i
$636$		0			0
$637$		0			0
$638$		0			0
$639$	−4.82140e10	−	8.35091e10i	−0.289181	−	0.500876i
$640$		0			0
$641$	−5.22192e10	+	9.04464e10i	−0.309313	+	0.535746i	−0.978212	−	0.207607i	$-0.933432\pi$
$641$	−5.22192e10	+	9.04464e10i	−0.309313	+	0.535746i	0.668899	+	0.743353i	$0.266766\pi$
$642$		0			0
$643$		−	1.80997e10i		−	0.105883i	−0.998598	−	0.0529415i	$-0.983140\pi$
$643$		−	1.80997e10i		−	0.105883i	0.998598	−	0.0529415i	$-0.0168597\pi$
$644$		0			0
$645$	−1.21582e11			−0.702476
$646$		0			0
$647$	−1.01442e11	−	5.85677e10i	−0.578897	−	0.334226i	0.181798	−	0.983336i	$-0.441808\pi$
$647$	−1.01442e11	−	5.85677e10i	−0.578897	−	0.334226i	−0.760695	+	0.649109i	$0.775142\pi$
$648$		0			0
$649$	−2.63080e9	+	1.51889e9i	−0.0148289	+	0.00856148i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	6.71936e9	+	1.16383e10i	0.0369552	+	0.0640082i	0.883911	−	0.467654i	$-0.154901\pi$
$653$	6.71936e9	+	1.16383e10i	0.0369552	+	0.0640082i	−0.846956	+	0.531663i	$0.821567\pi$
$654$		0			0
$655$	2.69263e11	−	4.66376e11i	1.46289	−	2.53379i
$656$		0			0
$657$			9.83296e10i			0.527744i
$658$		0			0
$659$	3.08932e10			0.163803			0.0819015	−	0.996640i	$-0.473901\pi$
$659$	3.08932e10			0.163803			0.0819015	+	0.996640i	$0.473901\pi$
$660$		0			0
$661$	−1.40945e11	−	8.13745e10i	−0.738317	−	0.426268i	0.0831399	−	0.996538i	$-0.473505\pi$
$661$	−1.40945e11	−	8.13745e10i	−0.738317	−	0.426268i	−0.821457	+	0.570270i	$0.806838\pi$
$662$		0			0
$663$	2.15754e9	−	1.24565e9i	0.0111662	−	0.00644679i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−1.03662e11	−	1.79548e11i	−0.523742	−	0.907148i
$668$		0			0
$669$	−6.94022e10	+	1.20208e11i	−0.346473	+	0.600108i
$670$		0			0
$671$			1.50017e9i			0.00740030i
$672$		0			0
$673$	1.99851e11			0.974195			0.487098	−	0.873347i	$-0.338056\pi$
$673$	1.99851e11			0.974195			0.487098	+	0.873347i	$0.338056\pi$
$674$		0			0
$675$	2.73823e11	+	1.58092e11i	1.31903	+	0.761543i
$676$		0			0
$677$	−2.91620e10	+	1.68367e10i	−0.138823	+	0.0801497i	−0.567803	−	0.823164i	$-0.692207\pi$
$677$	−2.91620e10	+	1.68367e10i	−0.138823	+	0.0801497i	0.428980	+	0.903314i	$0.358873\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	4.06439e10	+	7.03972e10i	0.188976	+	0.327316i
$682$		0			0
$683$	−1.84745e11	+	3.19987e11i	−0.848964	+	1.47045i	0.0331691	+	0.999450i	$0.489440\pi$
$683$	−1.84745e11	+	3.19987e11i	−0.848964	+	1.47045i	−0.882133	+	0.471000i	$0.843893\pi$
$684$		0			0
$685$		−	2.57535e11i		−	1.16970i
$686$		0			0
$687$	4.11343e10			0.184662
$688$		0			0
$689$	4.03045e9	+	2.32698e9i	0.0178845	+	0.0103256i
$690$		0			0
$691$	2.31360e11	−	1.33576e11i	1.01479	−	0.585889i	0.102199	−	0.994764i	$-0.467412\pi$
$691$	2.31360e11	−	1.33576e11i	1.01479	−	0.585889i	0.912590	+	0.408875i	$0.134079\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	5.90595e10	+	1.02294e11i	0.253134	+	0.438441i
$696$		0			0
$697$	−9.38930e10	+	1.62627e11i	−0.397834	+	0.689069i
$698$		0			0
$699$			1.20297e11i			0.503902i
$700$		0			0
$701$	1.51180e11			0.626071			0.313035	−	0.949741i	$-0.398654\pi$
$701$	1.51180e11			0.626071			0.313035	+	0.949741i	$0.398654\pi$
$702$		0			0
$703$	7.39900e9	+	4.27181e9i	0.0302936	+	0.0174900i
$704$		0			0
$705$	−2.64074e11	+	1.52463e11i	−1.06898	+	0.617175i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	1.70255e11	+	2.94890e11i	0.673774	+	1.16701i	0.976826	+	0.214036i	$0.0686611\pi$
$709$	1.70255e11	+	2.94890e11i	0.673774	+	1.16701i	−0.303052	+	0.952974i	$0.598006\pi$
$710$		0			0
$711$	−1.58049e11	+	2.73748e11i	−0.618461	+	1.07121i
$712$		0			0
$713$			4.12925e11i			1.59777i
$714$		0			0
$715$	−8.63188e7			−0.000330279
$716$		0			0
$717$	1.70429e11	+	9.83971e10i	0.644861	+	0.372311i
$718$		0			0
$719$	1.13379e11	−	6.54596e10i	0.424247	−	0.244939i	−0.272646	−	0.962114i	$-0.587899\pi$
$719$	1.13379e11	−	6.54596e10i	0.424247	−	0.244939i	0.696893	+	0.717175i	$0.254565\pi$
$720$		0			0
$721$		0			0
$722$		0			0
$723$	9.21248e10	+	1.59565e11i	0.337150	+	0.583961i
$724$		0			0
$725$	1.48840e11	−	2.57798e11i	0.538726	−	0.933100i
$726$		0			0
$727$		−	2.05407e11i		−	0.735321i	−0.929960	−	0.367660i	$-0.880159\pi$
$727$		−	2.05407e11i		−	0.735321i	0.929960	−	0.367660i	$-0.119841\pi$
$728$		0			0
$729$	−7.35692e9			−0.0260487
$730$		0			0
$731$	3.97819e11	+	2.29681e11i	1.39321	+	0.804369i
$732$		0			0
$733$	−2.00313e11	+	1.15651e11i	−0.693894	+	0.400620i	−0.805069	−	0.593181i	$-0.797872\pi$
$733$	−2.00313e11	+	1.15651e11i	−0.693894	+	0.400620i	0.111175	+	0.993801i	$0.464538\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	1.74652e9	+	3.02507e9i	0.00591976	+	0.0102533i
$738$		0			0
$739$	−2.38828e10	+	4.13663e10i	−0.0800770	+	0.138697i	−0.903283	−	0.429046i	$-0.858850\pi$
$739$	−2.38828e10	+	4.13663e10i	−0.0800770	+	0.138697i	0.823206	+	0.567743i	$0.192183\pi$
$740$		0			0
$741$		−	1.51238e8i		−	0.000501636i
$742$		0			0
$743$	1.17658e11			0.386069			0.193034	−	0.981192i	$-0.438167\pi$
$743$	1.17658e11			0.386069			0.193034	+	0.981192i	$0.438167\pi$
$744$		0			0
$745$	7.90569e11	+	4.56435e11i	2.56634	+	1.48168i
$746$		0			0
$747$	1.87008e11	−	1.07969e11i	0.600590	−	0.346751i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−8.75286e9	−	1.51604e10i	−0.0275163	−	0.0476596i	0.851939	−	0.523640i	$-0.175426\pi$
$751$	−8.75286e9	−	1.51604e10i	−0.0275163	−	0.0476596i	−0.879456	+	0.475981i	$0.842093\pi$
$752$		0			0
$753$	−2.04969e10	+	3.55016e10i	−0.0637540	+	0.110425i
$754$		0			0
$755$			9.31351e11i			2.86632i
$756$		0			0
$757$	4.82314e11			1.46875			0.734373	−	0.678746i	$-0.237476\pi$
$757$	4.82314e11			1.46875			0.734373	+	0.678746i	$0.237476\pi$
$758$		0			0
$759$	−2.84190e9	−	1.64077e9i	−0.00856331	−	0.00494403i
$760$		0			0
$761$	−3.21337e11	+	1.85524e11i	−0.958124	+	0.553173i	−0.895595	−	0.444870i	$-0.853250\pi$
$761$	−3.21337e11	+	1.85524e11i	−0.958124	+	0.553173i	−0.0625288	+	0.998043i	$0.519917\pi$
$762$		0			0
$763$		0			0
$764$		0			0
$765$	−4.05715e11	−	7.02719e11i	−1.18461	−	2.05180i
$766$		0			0
$767$	4.01340e9	−	6.95142e9i	0.0115966	−	0.0200859i
$768$		0			0
$769$		−	6.12899e11i		−	1.75260i	−0.481762	−	0.876302i	$-0.660003\pi$
$769$		−	6.12899e11i		−	1.75260i	0.481762	−	0.876302i	$-0.339997\pi$
$770$		0			0
$771$	−5.23974e9			−0.0148283
$772$		0			0
$773$	−2.82531e11	−	1.63120e11i	−0.791314	−	0.456865i	0.0491110	−	0.998793i	$-0.484361\pi$
$773$	−2.82531e11	−	1.63120e11i	−0.791314	−	0.456865i	−0.840425	+	0.541928i	$0.817695\pi$
$774$		0			0
$775$	−5.13453e11	+	2.96442e11i	−1.42329	+	0.821738i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	5.69990e9	+	9.87252e9i	0.0154781	+	0.0268088i
$780$		0			0
$781$	−1.62153e9	+	2.80858e9i	−0.00435834	+	0.00754887i
$782$		0			0
$783$			1.75236e11i			0.466203i
$784$		0			0
$785$	−8.66096e10			−0.228080
$786$		0			0
$787$	−1.82211e11	−	1.05200e11i	−0.474981	−	0.274231i	0.243341	−	0.969941i	$-0.421757\pi$
$787$	−1.82211e11	−	1.05200e11i	−0.474981	−	0.274231i	−0.718323	+	0.695710i	$0.755090\pi$
$788$		0			0
$789$	9.96963e10	−	5.75597e10i	0.257259	−	0.148529i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−1.98196e9	−	3.43285e9i	−0.00501189	−	0.00868085i
$794$		0			0
$795$	−1.94718e11	+	3.37262e11i	−0.487459	+	0.844303i
$796$		0			0
$797$			3.28855e11i			0.815026i	0.913199	+	0.407513i	$0.133604\pi$
$797$			3.28855e11i			0.815026i	−0.913199	+	0.407513i	$0.866396\pi$
$798$		0			0
$799$	1.15207e12			2.82678
$800$		0			0
$801$	−1.94997e11	−	1.12581e11i	−0.473693	−	0.273487i
$802$		0			0
$803$	2.86396e9	−	1.65351e9i	0.00688819	−	0.00397690i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	1.19590e11	+	2.07136e11i	0.281968	+	0.488383i
$808$		0			0
$809$	2.79667e11	−	4.84397e11i	0.652900	−	1.13086i	−0.329516	−	0.944150i	$-0.606886\pi$
$809$	2.79667e11	−	4.84397e11i	0.652900	−	1.13086i	0.982416	−	0.186705i	$-0.0597810\pi$
$810$		0			0
$811$			4.12178e11i			0.952800i	0.879229	+	0.476400i	$0.158059\pi$
$811$			4.12178e11i			0.952800i	−0.879229	+	0.476400i	$0.841941\pi$
$812$		0			0
$813$	−4.27423e10			−0.0978354
$814$		0			0
$815$	−3.81023e11	−	2.19984e11i	−0.863616	−	0.498609i
$816$		0			0
$817$	2.41501e10	−	1.39431e10i	0.0542040	−	0.0312947i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−2.80835e11	−	4.86420e11i	−0.618128	−	1.07063i	−0.989827	−	0.142276i	$-0.954558\pi$
$821$	−2.80835e11	−	4.86420e11i	−0.618128	−	1.07063i	0.371699	−	0.928353i	$-0.378775\pi$
$822$		0			0
$823$	2.15505e11	−	3.73266e11i	0.469741	−	0.813615i	−0.529660	−	0.848210i	$-0.677681\pi$
$823$	2.15505e11	−	3.73266e11i	0.469741	−	0.813615i	0.999401	+	0.0345944i	$0.0110139\pi$
$824$		0			0
$825$		−	4.71169e9i		−	0.0101709i
$826$		0			0
$827$	1.77468e11			0.379402			0.189701	−	0.981842i	$-0.439248\pi$
$827$	1.77468e11			0.379402			0.189701	+	0.981842i	$0.439248\pi$
$828$		0			0
$829$	6.87102e11	+	3.96698e11i	1.45480	+	0.839928i	0.998748	−	0.0500256i	$-0.0159303\pi$
$829$	6.87102e11	+	3.96698e11i	1.45480	+	0.839928i	0.456050	+	0.889954i	$0.349264\pi$
$830$		0			0
$831$	3.30093e10	−	1.90579e10i	0.0692200	−	0.0399642i
$832$		0			0
$833$		0			0
$834$		0			0
$835$	−5.60130e11	−	9.70174e11i	−1.15224	−	1.99574i
$836$		0			0
$837$	1.74507e11	−	3.02255e11i	0.355559	−	0.615845i
$838$		0			0
$839$		−	3.05327e11i		−	0.616194i	−0.951355	−	0.308097i	$-0.900308\pi$
$839$		−	3.05327e11i		−	0.616194i	0.951355	−	0.308097i	$-0.0996921\pi$
$840$		0			0
$841$	−3.35266e11			−0.670202
$842$		0			0
$843$	1.96390e11	+	1.13386e11i	0.388875	+	0.224517i
$844$		0			0
$845$	−7.48601e11	+	4.32205e11i	−1.46833	+	0.847741i
$846$		0			0
$847$		0			0
$848$		0			0
$849$	−1.33675e11	−	2.31533e11i	−0.257289	−	0.445637i
$850$		0			0
$851$	−2.44914e11	+	4.24204e11i	−0.466977	+	0.808828i
$852$		0			0
$853$			5.62048e11i			1.06164i	0.847485	+	0.530820i	$0.178116\pi$
$853$			5.62048e11i			1.06164i	−0.847485	+	0.530820i	$0.821884\pi$
$854$		0			0
$855$	−4.92589e10			−0.0921765
$856$		0			0
$857$	−1.26700e11	−	7.31504e10i	−0.234884	−	0.135611i	0.377939	−	0.925831i	$-0.376633\pi$
$857$	−1.26700e11	−	7.31504e10i	−0.234884	−	0.135611i	−0.612823	+	0.790220i	$0.709966\pi$
$858$		0			0
$859$	3.28952e10	−	1.89920e10i	0.0604171	−	0.0348818i	−0.469487	−	0.882939i	$-0.655561\pi$
$859$	3.28952e10	−	1.89920e10i	0.0604171	−	0.0348818i	0.529904	+	0.848057i	$0.322228\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	5.41661e11	+	9.38184e11i	0.976526	+	1.69139i	0.674803	+	0.737998i	$0.264229\pi$
$863$	5.41661e11	+	9.38184e11i	0.976526	+	1.69139i	0.301723	+	0.953395i	$0.402438\pi$
$864$		0			0
$865$	1.56610e10	−	2.71257e10i	0.0279740	−	0.0484525i
$866$		0			0
$867$		−	5.32178e11i		−	0.941847i
$868$		0			0
$869$	1.06310e10			0.0186421
$870$		0			0
$871$	−7.99318e9	−	4.61487e9i	−0.0138882	−	0.00801838i
$872$		0			0
$873$	3.90628e11	−	2.25529e11i	0.672521	−	0.388280i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	2.89645e11	+	5.01680e11i	0.489629	+	0.848063i	0.999929	−	0.0119339i	$-0.00379877\pi$
$877$	2.89645e11	+	5.01680e11i	0.489629	+	0.848063i	−0.510299	+	0.859997i	$0.670465\pi$
$878$		0			0
$879$	−9.62363e10	+	1.66686e11i	−0.161207	+	0.279218i
$880$		0			0
$881$			8.23483e11i			1.36694i	0.729976	+	0.683472i	$0.239531\pi$
$881$			8.23483e11i			1.36694i	−0.729976	+	0.683472i	$0.760469\pi$
$882$		0			0
$883$	−4.34805e11			−0.715240			−0.357620	−	0.933867i	$-0.616412\pi$
$883$	−4.34805e11			−0.715240			−0.357620	+	0.933867i	$0.616412\pi$
$884$		0			0
$885$	5.81683e11	+	3.35835e11i	0.948229	+	0.547460i
$886$		0			0
$887$	−3.35092e11	+	1.93465e11i	−0.541339	+	0.312542i	−0.745622	−	0.666370i	$-0.767847\pi$
$887$	−3.35092e11	+	1.93465e11i	−0.541339	+	0.312542i	0.204282	+	0.978912i	$0.434514\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	−1.61940e9	−	2.80488e9i	−0.00256947	−	0.00445045i
$892$		0			0
$893$	3.49690e10	−	6.05681e10i	0.0549893	−	0.0952442i
$894$		0			0
$895$		−	9.62888e11i		−	1.50066i
$896$		0			0
$897$	8.67088e9			0.0133935
$898$		0			0
$899$	−2.84566e11	−	1.64294e11i	−0.435657	−	0.251527i
$900$		0			0
$901$	1.27424e12	−	7.35683e11i	1.93354	−	1.11633i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	7.66363e11	+	1.32738e12i	1.14246	+	1.97879i
$906$		0			0
$907$	−3.96953e11	+	6.87543e11i	−0.586557	+	1.01595i	0.408123	+	0.912927i	$0.366184\pi$
$907$	−3.96953e11	+	6.87543e11i	−0.586557	+	1.01595i	−0.994679	+	0.103019i	$0.967150\pi$
$908$		0			0
$909$		−	7.25809e11i		−	1.06308i
$910$		0			0
$911$	−4.91456e11			−0.713528			−0.356764	−	0.934195i	$-0.616120\pi$
$911$	−4.91456e11			−0.713528			−0.356764	+	0.934195i	$0.616120\pi$
$912$		0			0
$913$	−6.28946e9	−	3.63122e9i	−0.00905170	−	0.00522600i
$914$		0			0
$915$	2.87255e11	−	1.65847e11i	0.409811	−	0.236604i
$916$		0			0
$917$		0			0
$918$		0			0
$919$	−1.39904e11	−	2.42320e11i	−0.196141	−	0.339725i	0.751133	−	0.660151i	$-0.229508\pi$
$919$	−1.39904e11	−	2.42320e11i	−0.196141	−	0.339725i	−0.947274	+	0.320425i	$0.896174\pi$
$920$		0			0
$921$	−1.76349e11	+	3.05445e11i	−0.245095	+	0.424517i
$922$		0			0
$923$		−	8.56920e9i		−	0.0118068i
$924$		0			0
$925$	−7.03303e11			−0.960673
$926$		0			0
$927$	7.98403e11	+	4.60958e11i	1.08119	+	0.624227i
$928$		0			0
$929$	−4.64262e10	+	2.68042e10i	−0.0623305	+	0.0359865i	−0.530841	−	0.847471i	$-0.678124\pi$
$929$	−4.64262e10	+	2.68042e10i	−0.0623305	+	0.0359865i	0.468511	+	0.883458i	$0.344791\pi$
$930$		0			0
$931$		0			0
$932$		0			0
$933$	−9.83426e10	−	1.70334e11i	−0.129782	−	0.224789i
$934$		0			0
$935$	−1.36450e10	+	2.36338e10i	−0.0178536	+	0.0309234i
$936$		0			0
$937$		−	3.98250e11i		−	0.516651i	−0.966058	−	0.258325i	$-0.916829\pi$
$937$		−	3.98250e11i		−	0.516651i	0.966058	−	0.258325i	$-0.0831707\pi$
$938$		0			0
$939$	−3.53118e11			−0.454211
$940$		0			0
$941$	−8.62807e11	−	4.98142e11i	−1.10041	−	0.635323i	−0.164082	−	0.986447i	$-0.552466\pi$
$941$	−8.62807e11	−	4.98142e11i	−1.10041	−	0.635323i	−0.936329	+	0.351124i	$0.885800\pi$
$942$		0			0
$943$	−5.66017e11	+	3.26790e11i	−0.715785	+	0.413259i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	5.86942e10	+	1.01661e11i	0.0729786	+	0.126403i	0.900205	−	0.435465i	$-0.143416\pi$
$947$	5.86942e10	+	1.01661e11i	0.0729786	+	0.126403i	−0.827227	+	0.561868i	$0.810083\pi$
$948$		0			0
$949$	−4.36910e9	+	7.56750e9i	−0.00538675	+	0.00933013i
$950$		0			0
$951$		−	4.13374e11i		−	0.505383i
$952$		0			0
$953$	−1.23547e11			−0.149782			−0.0748911	−	0.997192i	$-0.523861\pi$
$953$	−1.23547e11			−0.149782			−0.0748911	+	0.997192i	$0.523861\pi$
$954$		0			0
$955$	−1.90352e12	−	1.09900e12i	−2.28846	−	1.32125i
$956$		0			0
$957$	2.26147e9	−	1.30566e9i	0.00269614	−	0.00155662i
$958$		0			0
$959$		0			0
$960$		0			0
$961$	−9.92228e10	−	1.71859e11i	−0.116337	−	0.201502i
$962$		0			0
$963$	−1.35893e11	+	2.35374e11i	−0.158013	+	0.273687i
$964$		0			0
$965$		−	1.34120e11i		−	0.154662i
$966$		0			0
$967$	−4.03225e11			−0.461150			−0.230575	−	0.973055i	$-0.574061\pi$
$967$	−4.03225e11			−0.461150			−0.230575	+	0.973055i	$0.574061\pi$
$968$		0			0
$969$	−4.14085e10	−	2.39072e10i	−0.0469672	−	0.0271165i
$970$		0			0
$971$	−6.09791e11	+	3.52063e11i	−0.685968	+	0.396044i	−0.802100	−	0.597190i	$-0.796284\pi$
$971$	−6.09791e11	+	3.52063e11i	−0.685968	+	0.396044i	0.116132	+	0.993234i	$0.462951\pi$
$972$		0			0
$973$		0			0
$974$		0			0
$975$	6.22489e9	+	1.07818e10i	0.00688832	+	0.0119309i
$976$		0			0
$977$	6.25270e11	−	1.08300e12i	0.686261	−	1.18864i	−0.286777	−	0.957997i	$-0.592584\pi$
$977$	6.25270e11	−	1.08300e12i	0.686261	−	1.18864i	0.973039	−	0.230642i	$-0.0740826\pi$
$978$		0			0
$979$			7.57267e9i			0.00824362i
$980$		0			0
$981$	7.04174e11			0.760333
$982$		0			0
$983$	−2.98262e11	−	1.72202e11i	−0.319436	−	0.184426i	0.331705	−	0.943383i	$-0.392376\pi$
$983$	−2.98262e11	−	1.72202e11i	−0.319436	−	0.184426i	−0.651141	+	0.758957i	$0.725709\pi$
$984$		0			0
$985$	2.37560e12	−	1.37155e12i	2.52365	−	1.45703i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	7.99393e11	+	1.38459e12i	0.835555	+	1.44722i
$990$		0			0
$991$	2.51310e11	−	4.35281e11i	0.260564	−	0.451311i	−0.705828	−	0.708384i	$-0.749425\pi$
$991$	2.51310e11	−	4.35281e11i	0.260564	−	0.451311i	0.966392	+	0.257073i	$0.0827581\pi$
$992$		0			0
$993$		−	2.04338e11i		−	0.210161i
$994$		0			0
$995$	−4.04545e11			−0.412738
$996$		0			0
$997$	−7.94732e11	−	4.58838e11i	−0.804340	−	0.464386i	0.0406463	−	0.999174i	$-0.487058\pi$
$997$	−7.94732e11	−	4.58838e11i	−0.804340	−	0.464386i	−0.844987	+	0.534788i	$0.820392\pi$
$998$		0			0
$999$	3.58547e11	−	2.07007e11i	0.359985	−	0.207837i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.9.h.c.129.6		32
7.2	even	3	inner	196.9.h.c.117.11		32
7.3	odd	6		196.9.b.b.97.6	✓	16
7.4	even	3		196.9.b.b.97.11	yes	16
7.5	odd	6	inner	196.9.h.c.117.6		32
7.6	odd	2	inner	196.9.h.c.129.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.9.b.b.97.6	✓	16	7.3	odd	6
196.9.b.b.97.11	yes	16	7.4	even	3
196.9.h.c.117.6		32	7.5	odd	6	inner
196.9.h.c.117.11		32	7.2	even	3	inner
196.9.h.c.129.6		32	1.1	even	1	trivial
196.9.h.c.129.11		32	7.6	odd	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	196.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-31.7145 - 18.3104i) q^{3} +(-917.948 + 529.978i) q^{5} +(-2609.96 - 4520.59i) q^{9} +(-87.7782 + 152.036i) q^{11} -463.876i q^{13} +38816.3 q^{15} +(-127008. - 73327.9i) q^{17} +(-7710.17 + 4451.47i) q^{19} +(-255214. - 442044. i) q^{23} +(366440. - 634693. i) q^{25} +431426. i q^{27} +406178. q^{29} +(-700595. - 404489. i) q^{31} +(5567.68 - 3214.50i) q^{33} +(-479821. - 831074. i) q^{37} +(-8493.73 + 14711.6i) q^{39} -1.28045e6i q^{41} -3.13224e6 q^{43} +(4.79162e6 + 2.76644e6i) q^{45} +(-6.80317e6 + 3.92781e6i) q^{47} +(2.68532e6 + 4.65111e6i) q^{51} +(-5.01639e6 + 8.68865e6i) q^{53} -186082. i q^{55} +326032. q^{57} +(1.49855e7 + 8.65189e6i) q^{59} +(7.40037e6 - 4.27260e6i) q^{61} +(245844. + 425814. i) q^{65} +(9.94850e6 - 1.72313e7i) q^{67} +1.86923e7i q^{69} +1.84731e7 q^{71} +(-1.63136e7 - 9.41869e6i) q^{73} +(-2.32429e7 + 1.34193e7i) q^{75} +(-3.02779e7 - 5.24429e7i) q^{79} +(-9.22439e6 + 1.59771e7i) q^{81} +4.13681e7i q^{83} +1.55449e8 q^{85} +(-1.28817e7 - 7.43727e6i) q^{87} +(3.73562e7 - 2.15676e7i) q^{89} +(1.48127e7 + 2.56563e7i) q^{93} +(4.71836e6 - 8.17243e6i) q^{95} +8.64109e7i q^{97} +916390. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 52264 q^{9} + 22776 q^{11} + 206064 q^{15} - 571560 q^{23} + 1030440 q^{25} - 5384256 q^{29} + 3376640 q^{37} + 10336136 q^{39} + 18525008 q^{43} + 16028856 q^{51} - 14106216 q^{53} - 4787360 q^{57}+ \cdots + 1119499328 q^{99}+O(q^{100}) \) 32 * q + 52264 * q^9 + 22776 * q^11 + 206064 * q^15 - 571560 * q^23 + 1030440 * q^25 - 5384256 * q^29 + 3376640 * q^37 + 10336136 * q^39 + 18525008 * q^43 + 16028856 * q^51 - 14106216 * q^53 - 4787360 * q^57 - 5623008 * q^65 - 82433680 * q^67 + 250685568 * q^71 + 138241200 * q^79 - 465637680 * q^81 + 880381104 * q^85 + 310654512 * q^93 - 811120872 * q^95 + 1119499328 * q^99

Introduction

L-functions

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