LMFDB - Embedded newform 756.2.bi.c.307.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [756,2,Mod(307,756)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(756, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("756.307"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 756 = 2^{2} \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	756.bi (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [80,6,0,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$6.03669039281$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 252)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			307.14
Character	$\chi$	$=$	756.307
Dual form			756.2.bi.c.559.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.648812 + 1.25660i) q^{2} +(-1.15809 - 1.63059i) q^{4} +(2.66647 + 1.53948i) q^{5} +(1.48111 + 2.19233i) q^{7} +(2.80038 - 0.397302i) q^{8} +(-3.66455 + 2.35184i) q^{10} +(-3.64870 + 2.10658i) q^{11} +(-2.97309 - 1.71651i) q^{13} +(-3.71584 + 0.438755i) q^{14} +(-1.31767 + 3.77674i) q^{16} +2.29127i q^{17} +1.70965 q^{19} +(-0.577723 - 6.13078i) q^{20} +(-0.279805 - 5.95173i) q^{22} +(4.68317 + 2.70383i) q^{23} +(2.24003 + 3.87984i) q^{25} +(4.08594 - 2.62229i) q^{26} +(1.85954 - 4.95400i) q^{28} +(4.76517 + 8.25352i) q^{29} +(3.22265 - 5.58179i) q^{31} +(-3.89093 - 4.10618i) q^{32} +(-2.87921 - 1.48660i) q^{34} +(0.574276 + 8.12592i) q^{35} -2.04135 q^{37} +(-1.10924 + 2.14835i) q^{38} +(8.07877 + 3.25176i) q^{40} +(-4.43693 - 2.56166i) q^{41} +(-2.89849 + 1.67344i) q^{43} +(7.66048 + 3.50995i) q^{44} +(-6.43612 + 4.13059i) q^{46} +(-2.20674 - 3.82219i) q^{47} +(-2.61262 + 6.49417i) q^{49} +(-6.32876 + 0.297531i) q^{50} +(0.644156 + 6.83577i) q^{52} -10.5744 q^{53} -12.9722 q^{55} +(5.01870 + 5.55091i) q^{56} +(-13.4631 + 0.632933i) q^{58} +(-4.44595 + 7.70061i) q^{59} +(3.57388 - 2.06338i) q^{61} +(4.92318 + 7.67111i) q^{62} +(7.68430 - 2.22520i) q^{64} +(-5.28509 - 9.15404i) q^{65} +(9.53591 + 5.50556i) q^{67} +(3.73613 - 2.65349i) q^{68} +(-10.5836 - 4.55056i) q^{70} +2.48841i q^{71} +3.46980i q^{73} +(1.32445 - 2.56517i) q^{74} +(-1.97992 - 2.78774i) q^{76} +(-10.0224 - 4.87907i) q^{77} +(8.87914 - 5.12638i) q^{79} +(-9.32776 + 8.04200i) q^{80} +(6.09771 - 3.91340i) q^{82} +(0.0572673 + 0.0991899i) q^{83} +(-3.52738 + 6.10959i) q^{85} +(-0.222275 - 4.72799i) q^{86} +(-9.38081 + 7.34886i) q^{88} +3.61933i q^{89} +(-0.640313 - 9.06033i) q^{91} +(-1.01467 - 10.7676i) q^{92} +(6.23472 - 0.293110i) q^{94} +(4.55872 + 2.63198i) q^{95} +(5.53677 - 3.19666i) q^{97} +(-6.46548 - 7.49651i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8} - 10 q^{14} - 18 q^{16} - 14 q^{22} + 32 q^{25} + 28 q^{28} - 8 q^{29} + 16 q^{32} - 16 q^{37} + 84 q^{44} + 24 q^{46} - 24 q^{49} + 12 q^{50} + 48 q^{53} - 32 q^{56}+ \cdots - 20 q^{98}+O(q^{100}) $ 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8 - 10 * q^14 - 18 * q^16 - 14 * q^22 + 32 * q^25 + 28 * q^28 - 8 * q^29 + 16 * q^32 - 16 * q^37 + 84 * q^44 + 24 * q^46 - 24 * q^49 + 12 * q^50 + 48 * q^53 - 32 * q^56 - 14 * q^58 - 8 * q^64 + 40 * q^65 - 22 * q^70 - 64 * q^74 + 12 * q^77 + 40 * q^85 + 52 * q^86 + 6 * q^88 - 30 * q^92 - 20 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/756\mathbb{Z}\right)^\times$.

$n$	$29$	$325$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$	$-1$

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 $

$2$	−0.648812	+	1.25660i	−0.458779	+	0.888550i
$2$	−0.648812	+	1.25660i	−0.458779	+	0.888550i
$3$		0			0
$3$		0			0
$4$	−1.15809	−	1.63059i	−0.579043	−	0.815297i
$5$	2.66647	+	1.53948i	1.19248	+	0.688479i	0.958868	−	0.283851i	$-0.0916123\pi$
$5$	2.66647	+	1.53948i	1.19248	+	0.688479i	0.233612	+	0.972330i	$0.424946\pi$
$6$		0			0
$7$	1.48111	+	2.19233i	0.559808	+	0.828623i
$7$	1.48111	+	2.19233i	0.559808	+	0.828623i
$8$	2.80038	−	0.397302i	0.990085	−	0.140468i
$9$		0			0
$10$	−3.66455	+	2.35184i	−1.15883	+	0.743719i
$11$	−3.64870	+	2.10658i	−1.10012	+	0.635157i	−0.936254	−	0.351325i	$-0.885731\pi$
$11$	−3.64870	+	2.10658i	−1.10012	+	0.635157i	−0.163870	+	0.986482i	$0.552398\pi$
$12$		0			0
$13$	−2.97309	−	1.71651i	−0.824586	−	0.476075i	0.0274094	−	0.999624i	$-0.491274\pi$
$13$	−2.97309	−	1.71651i	−0.824586	−	0.476075i	−0.851995	+	0.523549i	$0.824608\pi$
$14$	−3.71584	+	0.438755i	−0.993101	+	0.117262i
$15$		0			0
$16$	−1.31767	+	3.77674i	−0.329418	+	0.944184i
$17$			2.29127i			0.555715i	0.960622	+	0.277857i	$0.0896242\pi$
$17$			2.29127i			0.555715i	−0.960622	+	0.277857i	$0.910376\pi$
$18$		0			0
$19$	1.70965			0.392221			0.196110	−	0.980582i	$-0.437169\pi$
$19$	1.70965			0.392221			0.196110	+	0.980582i	$0.437169\pi$
$20$	−0.577723	−	6.13078i	−0.129183	−	1.37088i
$21$		0			0
$22$	−0.279805	−	5.95173i	−0.0596547	−	1.26891i
$23$	4.68317	+	2.70383i	0.976507	+	0.563787i	0.901214	−	0.433375i	$-0.142677\pi$
$23$	4.68317	+	2.70383i	0.976507	+	0.563787i	0.0752935	+	0.997161i	$0.476011\pi$
$24$		0			0
$25$	2.24003	+	3.87984i	0.448005	+	0.775968i
$26$	4.08594	−	2.62229i	0.801319	−	0.514273i
$27$		0			0
$28$	1.85954	−	4.95400i	0.351421	−	0.936218i
$29$	4.76517	+	8.25352i	0.884870	+	1.53264i	0.845862	+	0.533401i	$0.179086\pi$
$29$	4.76517	+	8.25352i	0.884870	+	1.53264i	0.0390079	+	0.999239i	$0.487580\pi$
$30$		0			0
$31$	3.22265	−	5.58179i	0.578805	−	1.00252i	−0.416812	−	0.908993i	$-0.636853\pi$
$31$	3.22265	−	5.58179i	0.578805	−	1.00252i	0.995617	−	0.0935263i	$-0.0298139\pi$
$32$	−3.89093	−	4.10618i	−0.687825	−	0.725877i
$33$		0			0
$34$	−2.87921	−	1.48660i	−0.493780	−	0.254950i
$35$	0.574276	+	8.12592i	0.0970704	+	1.37353i
$36$		0			0
$37$	−2.04135			−0.335597			−0.167798	−	0.985821i	$-0.553666\pi$
$37$	−2.04135			−0.335597			−0.167798	+	0.985821i	$0.553666\pi$
$38$	−1.10924	+	2.14835i	−0.179943	+	0.348508i
$39$		0			0
$40$	8.07877	+	3.25176i	1.27737	+	0.514148i
$41$	−4.43693	−	2.56166i	−0.692931	−	0.400064i	0.111778	−	0.993733i	$-0.464345\pi$
$41$	−4.43693	−	2.56166i	−0.692931	−	0.400064i	−0.804709	+	0.593669i	$0.797679\pi$
$42$		0			0
$43$	−2.89849	+	1.67344i	−0.442015	+	0.255198i	−0.704452	−	0.709752i	$-0.748807\pi$
$43$	−2.89849	+	1.67344i	−0.442015	+	0.255198i	0.262437	+	0.964949i	$0.415474\pi$
$44$	7.66048	+	3.50995i	1.15486	+	0.529144i
$45$		0			0
$46$	−6.43612	+	4.13059i	−0.948954	+	0.609022i
$47$	−2.20674	−	3.82219i	−0.321886	−	0.557524i	0.658991	−	0.752151i	$-0.270984\pi$
$47$	−2.20674	−	3.82219i	−0.321886	−	0.557524i	−0.980877	+	0.194627i	$0.937650\pi$
$48$		0			0
$49$	−2.61262	+	6.49417i	−0.373231	+	0.927738i
$50$	−6.32876	+	0.297531i	−0.895022	+	0.0420772i
$51$		0			0
$52$	0.644156	+	6.83577i	0.0893284	+	0.947950i
$53$	−10.5744			−1.45250			−0.726250	−	0.687431i	$-0.758738\pi$
$53$	−10.5744			−1.45250			−0.726250	+	0.687431i	$0.758738\pi$
$54$		0			0
$55$	−12.9722			−1.74917
$56$	5.01870	+	5.55091i	0.670652	+	0.741772i
$57$		0			0
$58$	−13.4631	+	0.632933i	−1.76779	+	0.0831081i
$59$	−4.44595	+	7.70061i	−0.578813	+	1.00253i	0.416802	+	0.908997i	$0.363151\pi$
$59$	−4.44595	+	7.70061i	−0.578813	+	1.00253i	−0.995616	+	0.0935372i	$0.970183\pi$
$60$		0			0
$61$	3.57388	−	2.06338i	0.457588	−	0.264189i	−0.253441	−	0.967351i	$-0.581563\pi$
$61$	3.57388	−	2.06338i	0.457588	−	0.264189i	0.711030	+	0.703162i	$0.248229\pi$
$62$	4.92318	+	7.67111i	0.625245	+	0.974232i
$63$		0			0
$64$	7.68430	−	2.22520i	0.960538	−	0.278150i
$65$	−5.28509	−	9.15404i	−0.655535	−	1.13542i
$66$		0			0
$67$	9.53591	+	5.50556i	1.16500	+	0.672611i	0.952496	−	0.304550i	$-0.0985061\pi$
$67$	9.53591	+	5.50556i	1.16500	+	0.672611i	0.212500	+	0.977161i	$0.431839\pi$
$68$	3.73613	−	2.65349i	0.453072	−	0.321783i
$69$		0			0
$70$	−10.5836	−	4.55056i	−1.26499	−	0.543896i
$71$			2.48841i			0.295320i	0.989038	+	0.147660i	$0.0471741\pi$
$71$			2.48841i			0.295320i	−0.989038	+	0.147660i	$0.952826\pi$
$72$		0			0
$73$			3.46980i			0.406110i	0.979167	+	0.203055i	$0.0650870\pi$
$73$			3.46980i			0.406110i	−0.979167	+	0.203055i	$0.934913\pi$
$74$	1.32445	−	2.56517i	0.153965	−	0.298194i
$75$		0			0
$76$	−1.97992	−	2.78774i	−0.227113	−	0.319776i
$77$	−10.0224	−	4.87907i	−1.14216	−	0.556022i
$78$		0			0
$79$	8.87914	−	5.12638i	0.998982	−	0.576762i	0.0910349	−	0.995848i	$-0.470983\pi$
$79$	8.87914	−	5.12638i	0.998982	−	0.576762i	0.907947	+	0.419085i	$0.137649\pi$
$80$	−9.32776	+	8.04200i	−1.04287	+	0.899123i
$81$		0			0
$82$	6.09771	−	3.91340i	0.673380	−	0.432163i
$83$	0.0572673	+	0.0991899i	0.00628591	+	0.0108875i	0.869151	−	0.494546i	$-0.164666\pi$
$83$	0.0572673	+	0.0991899i	0.00628591	+	0.0108875i	−0.862865	+	0.505434i	$0.831332\pi$
$84$		0			0
$85$	−3.52738	+	6.10959i	−0.382598	+	0.662678i
$86$	−0.222275	−	4.72799i	−0.0239685	−	0.509832i
$87$		0			0
$88$	−9.38081	+	7.34886i	−0.999997	+	0.783391i
$89$			3.61933i			0.383648i	0.981429	+	0.191824i	$0.0614403\pi$
$89$			3.61933i			0.383648i	−0.981429	+	0.191824i	$0.938560\pi$
$90$		0			0
$91$	−0.640313	−	9.06033i	−0.0671230	−	0.949781i
$92$	−1.01467	−	10.7676i	−0.105786	−	1.12260i
$93$		0			0
$94$	6.23472	−	0.293110i	0.643063	−	0.0302320i
$95$	4.55872	+	2.63198i	0.467715	+	0.270035i
$96$		0			0
$97$	5.53677	−	3.19666i	0.562174	−	0.324571i	−0.191844	−	0.981426i	$-0.561447\pi$
$97$	5.53677	−	3.19666i	0.562174	−	0.324571i	0.754018	+	0.656854i	$0.228113\pi$
$98$	−6.46548	−	7.49651i	−0.653112	−	0.757262i
$99$		0			0
$100$	3.73230	−	8.14576i	0.373230	−	0.814576i
$101$	14.8206	−	8.55666i	1.47470	−	0.851420i	0.475109	−	0.879927i	$-0.342409\pi$
$101$	14.8206	−	8.55666i	1.47470	−	0.851420i	0.999594	+	0.0285076i	$0.00907547\pi$
$102$		0			0
$103$	−0.807160	+	1.39804i	−0.0795318	+	0.137753i	−0.903048	−	0.429540i	$-0.858676\pi$
$103$	−0.807160	+	1.39804i	−0.0795318	+	0.137753i	0.823516	+	0.567293i	$0.192009\pi$
$104$	−9.00776	−	3.62568i	−0.883283	−	0.355527i
$105$		0			0
$106$	6.86077	−	13.2877i	0.666377	−	1.29062i
$107$		−	1.84363i		−	0.178231i	−0.996021	−	0.0891153i	$-0.971596\pi$
$107$		−	1.84363i		−	0.178231i	0.996021	−	0.0891153i	$-0.0284040\pi$
$108$		0			0
$109$	−2.66853			−0.255599			−0.127800	−	0.991800i	$-0.540791\pi$
$109$	−2.66853			−0.255599			−0.127800	+	0.991800i	$0.540791\pi$
$110$	8.41650	−	16.3008i	0.802482	−	1.55422i
$111$		0			0
$112$	−10.2315	+	2.70500i	−0.966783	+	0.255598i
$113$	0.626681	−	1.08544i	0.0589532	−	0.102110i	−0.835043	−	0.550185i	$-0.814557\pi$
$113$	0.626681	−	1.08544i	0.0589532	−	0.102110i	0.893996	+	0.448075i	$0.147890\pi$
$114$		0			0
$115$	8.32500	+	14.4193i	0.776310	+	1.34461i
$116$	7.93966	−	17.3283i	0.737179	−	1.60890i
$117$		0			0
$118$	−6.79200	−	10.5830i	−0.625255	−	0.974247i
$119$	−5.02322	+	3.39363i	−0.460478	+	0.311093i
$120$		0			0
$121$	3.37533	−	5.84625i	0.306848	−	0.531477i
$122$	0.274068	+	5.82968i	0.0248129	+	0.527794i
$123$		0			0
$124$	−12.8337	+	1.20936i	−1.15250	+	0.108604i
$125$		−	1.60090i		−	0.143189i
$126$		0			0
$127$			10.6611i			0.946022i	0.881056	+	0.473011i	$0.156833\pi$
$127$			10.6611i			0.946022i	−0.881056	+	0.473011i	$0.843167\pi$
$128$	−2.18948	+	11.0998i	−0.193525	+	0.981095i
$129$		0			0
$130$	14.9320	−	0.701990i	1.30962	−	0.0615686i
$131$	4.50282	−	7.79911i	0.393413	−	0.681411i	−0.599484	−	0.800387i	$-0.704628\pi$
$131$	4.50282	−	7.79911i	0.393413	−	0.681411i	0.992897	+	0.118975i	$0.0379609\pi$
$132$		0			0
$133$	2.53218	+	3.74812i	0.219568	+	0.325003i
$134$	−13.1053	+	8.41075i	−1.13213	+	0.726578i
$135$		0			0
$136$	0.910327	+	6.41644i	0.0780599	+	0.550205i
$137$	−1.11722	−	1.93509i	−0.0954509	−	0.165326i	0.814346	−	0.580380i	$-0.197096\pi$
$137$	−1.11722	−	1.93509i	−0.0954509	−	0.165326i	−0.909797	+	0.415054i	$0.863763\pi$
$138$		0			0
$139$	5.09811	−	8.83019i	0.432416	−	0.748967i	−0.564665	−	0.825320i	$-0.690994\pi$
$139$	5.09811	−	8.83019i	0.432416	−	0.748967i	0.997081	+	0.0763537i	$0.0243278\pi$
$140$	12.5850	−	10.3469i	1.06363	−	0.874475i
$141$		0			0
$142$	−3.12693	−	1.61451i	−0.262406	−	0.135487i
$143$	14.4639			1.20953
$144$		0			0
$145$			29.3436i			2.43686i
$146$	−4.36016	−	2.25125i	−0.360849	−	0.186315i
$147$		0			0
$148$	2.36406	+	3.32862i	0.194325	+	0.273611i
$149$	−6.16913	+	10.6853i	−0.505395	+	0.875370i	0.494585	+	0.869129i	$0.335320\pi$
$149$	−6.16913	+	10.6853i	−0.505395	+	0.875370i	−0.999981	+	0.00624098i	$0.998013\pi$
$150$		0			0
$151$	9.36053	−	5.40430i	0.761749	−	0.439796i	−0.0681743	−	0.997673i	$-0.521717\pi$
$151$	9.36053	−	5.40430i	0.761749	−	0.439796i	0.829923	+	0.557877i	$0.188384\pi$
$152$	4.78768	−	0.679248i	0.388332	−	0.0550943i
$153$		0			0
$154$	12.6337	−	9.42860i	1.01805	−	0.759778i
$155$	17.1862	−	9.92243i	1.38043	−	0.796989i
$156$		0			0
$157$	−21.4858	−	12.4049i	−1.71476	−	0.990015i	−0.927860	−	0.372930i	$-0.878353\pi$
$157$	−21.4858	−	12.4049i	−1.71476	−	0.990015i	−0.786896	−	0.617085i	$-0.788313\pi$
$158$	0.680909	+	14.4836i	0.0541702	+	1.15225i
$159$		0			0
$160$	−4.05362	−	16.9390i	−0.320467	−	1.33915i
$161$	1.00861	+	14.2717i	0.0794898	+	1.12477i
$162$		0			0
$163$			10.9277i			0.855920i	0.903798	+	0.427960i	$0.140768\pi$
$163$			10.9277i			0.855920i	−0.903798	+	0.427960i	$0.859232\pi$
$164$	0.961316	+	10.2014i	0.0750661	+	0.796599i
$165$		0			0
$166$	−0.161798	+	0.00760652i	−0.0125579	+	0.000590380i
$167$	8.50615	−	14.7331i	0.658226	−	1.14008i	−0.322849	−	0.946451i	$-0.604641\pi$
$167$	8.50615	−	14.7331i	0.658226	−	1.14008i	0.981075	−	0.193630i	$-0.0620261\pi$
$168$		0			0
$169$	−0.607170	−	1.05165i	−0.0467054	−	0.0808961i
$170$	−5.38871	−	8.39648i	−0.413295	−	0.643980i
$171$		0			0
$172$	6.08540	+	2.78827i	0.464008	+	0.212603i
$173$	4.06899	−	2.34923i	0.309360	−	0.178609i	−0.337280	−	0.941404i	$-0.609507\pi$
$173$	4.06899	−	2.34923i	0.309360	−	0.178609i	0.646640	+	0.762795i	$0.276174\pi$
$174$		0			0
$175$	−5.18816	+	10.6574i	−0.392188	+	0.805620i
$176$	−3.14820	−	16.5559i	−0.237304	−	1.24795i
$177$		0			0
$178$	−4.54805	−	2.34826i	−0.340891	−	0.176010i
$179$		−	8.32224i		−	0.622034i	−0.950404	−	0.311017i	$-0.899330\pi$
$179$		−	8.32224i		−	0.622034i	0.950404	−	0.311017i	$-0.100670\pi$
$180$		0			0
$181$		−	9.07327i		−	0.674411i	−0.941431	−	0.337205i	$-0.890518\pi$
$181$		−	9.07327i		−	0.674411i	0.941431	−	0.337205i	$-0.109482\pi$
$182$	11.8007	+	5.07383i	0.874723	+	0.376098i
$183$		0			0
$184$	14.1889	+	5.71112i	1.04602	+	0.421029i
$185$	−5.44320	−	3.14263i	−0.400192	−	0.231051i
$186$		0			0
$187$	−4.82674	−	8.36015i	−0.352966	−	0.611355i
$188$	−3.67684	+	8.02473i	−0.268161	+	0.585263i
$189$		0			0
$190$	−6.26510	+	4.02083i	−0.454518	+	0.291702i
$191$	10.1929	−	5.88490i	0.737535	−	0.425816i	−0.0836373	−	0.996496i	$-0.526654\pi$
$191$	10.1929	−	5.88490i	0.737535	−	0.425816i	0.821172	+	0.570680i	$0.193320\pi$
$192$		0			0
$193$	10.6936	−	18.5218i	0.769742	−	1.33323i	−0.167961	−	0.985794i	$-0.553718\pi$
$193$	10.6936	−	18.5218i	0.769742	−	1.33323i	0.937703	−	0.347438i	$-0.112948\pi$
$194$	0.424595	+	9.03154i	0.0304841	+	0.648426i
$195$		0			0
$196$	13.6150	−	3.26069i	0.972499	−	0.232907i
$197$	10.7855			0.768436			0.384218	−	0.923242i	$-0.374471\pi$
$197$	10.7855			0.768436			0.384218	+	0.923242i	$0.374471\pi$
$198$		0			0
$199$	4.64957			0.329599			0.164800	−	0.986327i	$-0.447302\pi$
$199$	4.64957			0.329599			0.164800	+	0.986327i	$0.447302\pi$
$200$	7.81441	+	9.97507i	0.552562	+	0.705344i
$201$		0			0
$202$	1.13654	+	24.1752i	0.0799664	+	1.70096i
$203$	−11.0367	+	22.6712i	−0.774623	+	1.59121i
$204$		0			0
$205$	−7.88727	−	13.6612i	−0.550871	−	0.954137i
$206$	−1.23308	−	1.92134i	−0.0859130	−	0.133866i
$207$		0			0
$208$	10.4004	−	8.96676i	0.721136	−	0.621733i
$209$	−6.23800	+	3.60151i	−0.431491	+	0.249122i
$210$		0			0
$211$	2.23918	+	1.29279i	0.154151	+	0.0889993i	0.575092	−	0.818089i	$-0.304966\pi$
$211$	2.23918	+	1.29279i	0.154151	+	0.0889993i	−0.420940	+	0.907088i	$0.638300\pi$
$212$	12.2460	+	17.2425i	0.841060	+	1.18422i
$213$		0			0
$214$	2.31671	+	1.19617i	0.158367	+	0.0817685i
$215$	−10.3050			−0.702792
$216$		0			0
$217$	17.0102	−	1.20215i	1.15473	−	0.0816072i
$218$	1.73138	−	3.35328i	0.117264	−	0.227113i
$219$		0			0
$220$	15.0229	+	21.1523i	1.01284	+	1.42609i
$221$	3.93299	−	6.81214i	0.264562	−	0.458234i
$222$		0			0
$223$	0.326746	+	0.565940i	0.0218805	+	0.0378981i	0.876758	−	0.480931i	$-0.159701\pi$
$223$	0.326746	+	0.565940i	0.0218805	+	0.0378981i	−0.854878	+	0.518829i	$0.826368\pi$
$224$	3.23920	−	14.6119i	0.216428	−	0.976299i
$225$		0			0
$226$	0.957371	+	1.49174i	0.0636833	+	0.0992289i
$227$	2.88313	+	4.99372i	0.191360	+	0.331445i	0.945701	−	0.325037i	$-0.105377\pi$
$227$	2.88313	+	4.99372i	0.191360	+	0.331445i	−0.754341	+	0.656483i	$0.772044\pi$
$228$		0			0
$229$	24.2527	+	14.0023i	1.60267	+	0.925299i	0.990951	+	0.134220i	$0.0428530\pi$
$229$	24.2527	+	14.0023i	1.60267	+	0.925299i	0.611714	+	0.791079i	$0.290480\pi$
$230$	−23.5207	+	1.10577i	−1.55091	+	0.0729120i
$231$		0			0
$232$	16.6235	+	21.2198i	1.09138	+	1.39315i
$233$	8.45031			0.553598			0.276799	−	0.960928i	$-0.410726\pi$
$233$	8.45031			0.553598			0.276799	+	0.960928i	$0.410726\pi$
$234$		0			0
$235$		−	13.5890i		−	0.886448i
$236$	17.7054	−	1.66843i	1.15252	−	0.108606i
$237$		0			0
$238$	−1.00531	−	8.51400i	−0.0651644	−	0.551881i
$239$	−18.5973	−	10.7371i	−1.20296	−	0.694528i	−0.241746	−	0.970339i	$-0.577720\pi$
$239$	−18.5973	−	10.7371i	−1.20296	−	0.694528i	−0.961212	+	0.275811i	$0.911054\pi$
$240$		0			0
$241$	22.3544	−	12.9063i	1.43998	−	0.831371i	0.442129	−	0.896951i	$-0.354223\pi$
$241$	22.3544	−	12.9063i	1.43998	−	0.831371i	0.997847	+	0.0655806i	$0.0208899\pi$
$242$	5.15644	+	8.03455i	0.331468	+	0.516481i
$243$		0			0
$244$	−7.50339	−	3.43797i	−0.480355	−	0.220094i
$245$	−16.9641	+	13.2944i	−1.08380	+	0.849348i
$246$		0			0
$247$	−5.08294	−	2.93464i	−0.323420	−	0.186726i
$248$	6.80699	−	16.9115i	0.432244	−	1.07388i
$249$		0			0
$250$	2.01169	+	1.03868i	0.127230	+	0.0656920i
$251$	−14.3699			−0.907018			−0.453509	−	0.891252i	$-0.649828\pi$
$251$	−14.3699			−0.907018			−0.453509	+	0.891252i	$0.649828\pi$
$252$		0			0
$253$	−22.7833			−1.43237
$254$	−13.3968	−	6.91707i	−0.840588	−	0.434015i
$255$		0			0
$256$	−12.5275	−	9.95300i	−0.782967	−	0.622063i
$257$	14.8202	+	8.55644i	0.924458	+	0.533736i	0.885055	−	0.465487i	$-0.154121\pi$
$257$	14.8202	+	8.55644i	0.924458	+	0.533736i	0.0394034	+	0.999223i	$0.487454\pi$
$258$		0			0
$259$	−3.02347	−	4.47532i	−0.187870	−	0.278083i
$260$	−8.80594	+	19.2190i	−0.546121	+	1.19191i
$261$		0			0
$262$	6.87888	+	10.7184i	0.424979	+	0.662185i
$263$	−14.9410	+	8.62620i	−0.921302	+	0.531914i	−0.884050	−	0.467392i	$-0.845194\pi$
$263$	−14.9410	+	8.62620i	−0.921302	+	0.531914i	−0.0372520	+	0.999306i	$0.511860\pi$
$264$		0			0
$265$	−28.1962	−	16.2791i	−1.73208	−	1.00001i
$266$	−6.35279	+	0.750118i	−0.389515	+	0.0459927i
$267$		0			0
$268$	−2.06607	−	21.9251i	−0.126206	−	1.33929i
$269$		−	21.5478i		−	1.31379i	−0.753982	−	0.656895i	$-0.771869\pi$
$269$		−	21.5478i		−	1.31379i	0.753982	−	0.656895i	$-0.228131\pi$
$270$		0			0
$271$	−0.857294			−0.0520769			−0.0260384	−	0.999661i	$-0.508289\pi$
$271$	−0.857294			−0.0520769			−0.0260384	+	0.999661i	$0.508289\pi$
$272$	−8.65352	−	3.01914i	−0.524697	−	0.183062i
$273$		0			0
$274$	3.15650	−	0.148395i	0.190691	−	0.00896487i
$275$	−16.3464	−	9.43758i	−0.985723	−	0.569107i
$276$		0			0
$277$	8.94703	+	15.4967i	0.537575	+	0.931107i	0.999034	+	0.0439457i	$0.0139928\pi$
$277$	8.94703	+	15.4967i	0.537575	+	0.931107i	−0.461459	+	0.887162i	$0.652674\pi$
$278$	7.78830	+	12.1354i	0.467111	+	0.727834i
$279$		0			0
$280$	4.83664	+	22.5275i	0.289045	+	1.34628i
$281$	−10.8543	−	18.8002i	−0.647513	−	1.12153i	−0.983715	−	0.179735i	$-0.942476\pi$
$281$	−10.8543	−	18.8002i	−0.647513	−	1.12153i	0.336202	−	0.941790i	$-0.390857\pi$
$282$		0			0
$283$	11.7141	−	20.2894i	0.696331	−	1.20608i	−0.273399	−	0.961901i	$-0.588148\pi$
$283$	11.7141	−	20.2894i	0.696331	−	1.20608i	0.969730	−	0.244180i	$-0.0785186\pi$
$284$	4.05758	−	2.88179i	0.240773	−	0.171003i
$285$		0			0
$286$	−9.38432	+	18.1753i	−0.554907	+	1.07473i
$287$	−0.955580	−	13.5213i	−0.0564061	−	0.798138i
$288$		0			0
$289$	11.7501			0.691181
$290$	−36.8732	−	19.0385i	−2.16527	−	1.11798i
$291$		0			0
$292$	5.65784	−	4.01833i	0.331100	−	0.235155i
$293$	9.69068	+	5.59492i	0.566136	+	0.326859i	0.755605	−	0.655028i	$-0.227343\pi$
$293$	9.69068	+	5.59492i	0.566136	+	0.326859i	−0.189469	+	0.981887i	$0.560677\pi$
$294$		0			0
$295$	−23.7100	+	13.6889i	−1.38045	+	0.797001i
$296$	−5.71658	+	0.811035i	−0.332269	+	0.0471405i
$297$		0			0
$298$	−9.42448	−	14.6849i	−0.545945	−	0.850671i
$299$	−9.28230	−	16.0774i	−0.536809	−	0.929781i
$300$		0			0
$301$	−7.96172	−	3.87588i	−0.458906	−	0.223402i
$302$	0.717825	+	15.2688i	0.0413062	+	0.878622i
$303$		0			0
$304$	−2.25276	+	6.45690i	−0.129205	+	0.370329i
$305$	12.7062			0.727553
$306$		0			0
$307$	9.18388			0.524152			0.262076	−	0.965047i	$-0.415593\pi$
$307$	9.18388			0.524152			0.262076	+	0.965047i	$0.415593\pi$
$308$	3.65106	+	21.9929i	0.208039	+	1.25316i
$309$		0			0
$310$	1.31794	+	28.0339i	0.0748542	+	1.59222i
$311$	−3.81067	+	6.60027i	−0.216083	+	0.374267i	−0.953607	−	0.301054i	$-0.902662\pi$
$311$	−3.81067	+	6.60027i	−0.216083	+	0.374267i	0.737524	+	0.675321i	$0.235995\pi$
$312$		0			0
$313$	−5.36993	+	3.10033i	−0.303526	+	0.175241i	−0.644026	−	0.765004i	$-0.722737\pi$
$313$	−5.36993	+	3.10033i	−0.303526	+	0.175241i	0.340500	+	0.940245i	$0.389404\pi$
$314$	29.5282	−	18.9507i	1.66637	−	1.06945i
$315$		0			0
$316$	−18.6419	−	8.54149i	−1.04869	−	0.480496i
$317$	4.84502	+	8.39183i	0.272124	+	0.471332i	0.969405	−	0.245465i	$-0.0789407\pi$
$317$	4.84502	+	8.39183i	0.272124	+	0.471332i	−0.697282	+	0.716797i	$0.745607\pi$
$318$		0			0
$319$	−34.7733	−	20.0764i	−1.94693	−	1.12406i
$320$	23.9156	+	5.89645i	1.33692	+	0.329622i
$321$		0			0
$322$	−18.5882	−	7.99223i	−1.03588	−	0.445390i
$323$			3.91727i			0.217963i
$324$		0			0
$325$		−	15.3801i		−	0.853136i
$326$	−13.7317	−	7.08999i	−0.760528	−	0.392678i
$327$		0			0
$328$	−13.4429	−	5.41083i	−0.742257	−	0.298763i
$329$	5.11107	−	10.4990i	0.281782	−	0.578828i
$330$		0			0
$331$	−17.9174	+	10.3446i	−0.984827	+	0.568590i	−0.903724	−	0.428116i	$-0.859178\pi$
$331$	−17.9174	+	10.3446i	−0.984827	+	0.568590i	−0.0811031	+	0.996706i	$0.525844\pi$
$332$	0.0954180	−	0.208250i	0.00523674	−	0.0114292i
$333$		0			0
$334$	12.9947	+	20.2478i	0.711038	+	1.10791i
$335$	16.9514	+	29.3608i	0.926157	+	1.60415i
$336$		0			0
$337$	8.28764	−	14.3546i	0.451457	−	0.781946i	−0.547020	−	0.837119i	$-0.684238\pi$
$337$	8.28764	−	14.3546i	0.451457	−	0.781946i	0.998477	+	0.0551737i	$0.0175713\pi$
$338$	1.71544	−	0.0806472i	0.0933078	−	0.00438663i
$339$		0			0
$340$	14.0473	−	1.32372i	0.761820	−	0.0717888i
$341$			27.1550i			1.47053i
$342$		0			0
$343$	−18.1069	+	3.89087i	−0.977683	+	0.210087i
$344$	−7.45202	+	5.83786i	−0.401786	+	0.314756i
$345$		0			0
$346$	0.312036	+	6.63731i	0.0167752	+	0.356824i
$347$	8.93889	+	5.16087i	0.479865	+	0.277050i	0.720360	−	0.693600i	$-0.243977\pi$
$347$	8.93889	+	5.16087i	0.479865	+	0.277050i	−0.240495	+	0.970650i	$0.577310\pi$
$348$		0			0
$349$	8.33414	−	4.81172i	0.446116	−	0.257565i	−0.260072	−	0.965589i	$-0.583746\pi$
$349$	8.33414	−	4.81172i	0.446116	−	0.257565i	0.706189	+	0.708024i	$0.250413\pi$
$350$	−10.0259	−	13.4341i	−0.535906	−	0.718081i
$351$		0			0
$352$	22.8468	+	6.78567i	1.21774	+	0.361678i
$353$	20.3278	−	11.7363i	1.08194	−	0.624658i	0.150520	−	0.988607i	$-0.451905\pi$
$353$	20.3278	−	11.7363i	1.08194	−	0.624658i	0.931419	+	0.363949i	$0.118572\pi$
$354$		0			0
$355$	−3.83087	+	6.63526i	−0.203321	+	0.352163i
$356$	5.90165	−	4.19149i	0.312787	−	0.222149i
$357$		0			0
$358$	10.4577	+	5.39957i	0.552708	+	0.285376i
$359$		−	7.49888i		−	0.395776i	−0.980225	−	0.197888i	$-0.936592\pi$
$359$		−	7.49888i		−	0.395776i	0.980225	−	0.197888i	$-0.0634082\pi$
$360$		0			0
$361$	−16.0771			−0.846163
$362$	11.4015	+	5.88685i	0.599248	+	0.309406i
$363$		0			0
$364$	−14.0322	+	11.5367i	−0.735486	+	0.604689i
$365$	−5.34171	+	9.25211i	−0.279598	+	0.484278i
$366$		0			0
$367$	−2.39341	−	4.14551i	−0.124935	−	0.216394i	0.796772	−	0.604279i	$-0.206539\pi$
$367$	−2.39341	−	4.14551i	−0.124935	−	0.216394i	−0.921708	+	0.387885i	$0.873206\pi$
$368$	−16.3825	+	14.1243i	−0.853998	+	0.736281i
$369$		0			0
$370$	7.48065	−	4.80095i	0.388900	−	0.249589i
$371$	−15.6618	−	23.1825i	−0.813120	−	1.20357i
$372$		0			0
$373$	−13.8959	+	24.0683i	−0.719500	+	1.24621i	0.241698	+	0.970352i	$0.422296\pi$
$373$	−13.8959	+	24.0683i	−0.719500	+	1.24621i	−0.961198	+	0.275859i	$0.911038\pi$
$374$	13.6370	−	0.641110i	0.705153	−	0.0331510i
$375$		0			0
$376$	−7.69829	−	9.82685i	−0.397009	−	0.506781i
$377$		−	32.7179i		−	1.68506i
$378$		0			0
$379$		−	27.3958i		−	1.40723i	−0.710583	−	0.703613i	$-0.751569\pi$
$379$		−	27.3958i		−	1.40723i	0.710583	−	0.703613i	$-0.248431\pi$
$380$	−0.987705	−	10.4815i	−0.0506682	−	0.537689i
$381$		0			0
$382$	0.781659	+	16.6266i	0.0399932	+	0.850693i
$383$	7.36210	−	12.7515i	0.376185	−	0.651572i	−0.614318	−	0.789058i	$-0.710569\pi$
$383$	7.36210	−	12.7515i	0.376185	−	0.651572i	0.990504	+	0.137486i	$0.0439022\pi$
$384$		0			0
$385$	−19.2132	−	28.4393i	−0.979197	−	1.44940i
$386$	16.3364	+	25.4548i	0.831502	+	1.29561i
$387$		0			0
$388$	−11.6245	−	5.32622i	−0.590145	−	0.270398i
$389$	10.9505	+	18.9668i	0.555211	+	0.961653i	0.997887	+	0.0649717i	$0.0206957\pi$
$389$	10.9505	+	18.9668i	0.555211	+	0.961653i	−0.442676	+	0.896681i	$0.645971\pi$
$390$		0			0
$391$	−6.19520	+	10.7304i	−0.313305	+	0.542659i
$392$	−4.73618	+	19.2242i	−0.239213	+	0.970967i
$393$		0			0
$394$	−6.99777	+	13.5531i	−0.352542	+	0.682794i
$395$	31.5679			1.58835
$396$		0			0
$397$			34.9584i			1.75451i	0.480025	+	0.877255i	$0.340628\pi$
$397$			34.9584i			1.75451i	−0.480025	+	0.877255i	$0.659372\pi$
$398$	−3.01670	+	5.84265i	−0.151213	+	0.292865i
$399$		0			0
$400$	−17.6048	+	3.34763i	−0.880238	+	0.167382i
$401$	9.78297	−	16.9446i	0.488538	−	0.846173i	−0.511375	−	0.859358i	$-0.670864\pi$
$401$	9.78297	−	16.9446i	0.488538	−	0.846173i	0.999913	+	0.0131845i	$0.00419689\pi$
$402$		0			0
$403$	−19.1624	+	11.0634i	−0.954548	+	0.551109i
$404$	−31.1159	−	14.2570i	−1.54808	−	0.709311i
$405$		0			0
$406$	−21.3279	−	28.5780i	−1.05849	−	1.41830i
$407$	7.44829	−	4.30027i	0.369198	−	0.213156i
$408$		0			0
$409$	−2.97407	−	1.71708i	−0.147058	−	0.0849042i	0.424665	−	0.905350i	$-0.360392\pi$
$409$	−2.97407	−	1.71708i	−0.147058	−	0.0849042i	−0.571724	+	0.820446i	$0.693725\pi$
$410$	22.2840	−	1.04762i	1.10053	−	0.0517385i
$411$		0			0
$412$	3.21440	−	0.302903i	0.158362	−	0.0149230i
$413$	−23.4672	+	1.65848i	−1.15475	+	0.0816084i
$414$		0			0
$415$			0.352649i			0.0173108i
$416$	4.51975	+	18.8868i	0.221599	+	0.926004i
$417$		0			0
$418$	−0.478369	−	10.1754i	−0.0233978	−	0.497694i
$419$	−5.82364	+	10.0868i	−0.284503	+	0.492774i	−0.972489	−	0.232950i	$-0.925162\pi$
$419$	−5.82364	+	10.0868i	−0.284503	+	0.492774i	0.687985	+	0.725725i	$0.258495\pi$
$420$		0			0
$421$	−9.64312	−	16.7024i	−0.469977	−	0.814024i	0.529434	−	0.848351i	$-0.322404\pi$
$421$	−9.64312	−	16.7024i	−0.469977	−	0.814024i	−0.999411	+	0.0343274i	$0.989071\pi$
$422$	−3.07732	+	1.97497i	−0.149802	+	0.0961402i
$423$		0			0
$424$	−29.6123	+	4.20122i	−1.43810	+	0.204029i
$425$	−8.88976	+	5.13251i	−0.431217	+	0.248963i
$426$		0			0
$427$	9.81692	+	4.77902i	0.475074	+	0.231273i
$428$	−3.00621	+	2.13508i	−0.145311	+	0.103203i
$429$		0			0
$430$	6.68598	−	12.9492i	0.322427	−	0.624466i
$431$			1.73760i			0.0836971i	0.999124	+	0.0418485i	$0.0133247\pi$
$431$			1.73760i			0.0836971i	−0.999124	+	0.0418485i	$0.986675\pi$
$432$		0			0
$433$		−	5.95764i		−	0.286306i	−0.989701	−	0.143153i	$-0.954276\pi$
$433$		−	5.95764i		−	0.286306i	0.989701	−	0.143153i	$-0.0457241\pi$
$434$	−9.52581	+	22.1550i	−0.457254	+	1.06347i
$435$		0			0
$436$	3.09039	+	4.35130i	0.148003	+	0.208389i
$437$	8.00657	+	4.62260i	0.383006	+	0.221129i
$438$		0			0
$439$	10.6377	+	18.4250i	0.507708	+	0.879377i	0.999960	+	0.00892391i	$0.00284061\pi$
$439$	10.6377	+	18.4250i	0.507708	+	0.879377i	−0.492252	+	0.870453i	$0.663826\pi$
$440$	−36.3271	+	5.15388i	−1.73182	+	0.245701i
$441$		0			0
$442$	6.00837	+	9.36200i	0.285789	+	0.445305i
$443$	−30.1387	+	17.4006i	−1.43193	+	0.826726i	−0.997268	−	0.0738675i	$-0.976466\pi$
$443$	−30.1387	+	17.4006i	−1.43193	+	0.826726i	−0.434663	+	0.900593i	$0.643132\pi$
$444$		0			0
$445$	−5.57190	+	9.65081i	−0.264133	+	0.457492i
$446$	−0.923156	+	0.0433999i	−0.0437127	+	0.00205504i
$447$		0			0
$448$	16.2597	+	13.5508i	0.768198	+	0.640213i
$449$	−0.109498			−0.00516755			−0.00258377	−	0.999997i	$-0.500822\pi$
$449$	−0.109498			−0.00516755			−0.00258377	+	0.999997i	$0.500822\pi$
$450$		0			0
$451$	21.5853			1.01641
$452$	−2.49567	+	0.235175i	−0.117386	+	0.0110617i
$453$		0			0
$454$	−8.14572	+	0.382951i	−0.382298	+	0.0179728i
$455$	12.2409	−	25.1448i	0.573861	−	1.17881i
$456$		0			0
$457$	14.6591	+	25.3902i	0.685722	+	1.18770i	0.973209	+	0.229920i	$0.0738466\pi$
$457$	14.6591	+	25.3902i	0.685722	+	1.18770i	−0.287488	+	0.957784i	$0.592820\pi$
$458$	−33.3308	+	21.3911i	−1.55744	+	0.999541i
$459$		0			0
$460$	13.8710	−	30.2735i	0.646738	−	1.41151i
$461$	−28.8999	+	16.6853i	−1.34600	+	0.777114i	−0.987680	−	0.156485i	$-0.949984\pi$
$461$	−28.8999	+	16.6853i	−1.34600	+	0.777114i	−0.358320	+	0.933599i	$0.616650\pi$
$462$		0			0
$463$	8.98085	+	5.18510i	0.417376	+	0.240972i	0.693954	−	0.720019i	$-0.255867\pi$
$463$	8.98085	+	5.18510i	0.417376	+	0.240972i	−0.276578	+	0.960991i	$0.589200\pi$
$464$	−37.4503	+	7.12137i	−1.73859	+	0.330601i
$465$		0			0
$466$	−5.48266	+	10.6187i	−0.253979	+	0.491900i
$467$	−7.81904			−0.361822			−0.180911	−	0.983499i	$-0.557905\pi$
$467$	−7.81904			−0.361822			−0.180911	+	0.983499i	$0.557905\pi$
$468$		0			0
$469$	2.05375	+	29.0602i	0.0948332	+	1.34188i
$470$	17.0759	+	8.81669i	0.787653	+	0.406684i
$471$		0			0
$472$	−9.39090	+	23.3311i	−0.432251	+	1.07390i
$473$	7.05047	−	12.2118i	0.324181	−	0.561498i
$474$		0			0
$475$	3.82966	+	6.63317i	0.175717	+	0.304351i
$476$	11.3509	+	4.26072i	0.520270	+	0.195290i
$477$		0			0
$478$	25.5584	−	16.4030i	1.16902	−	0.750254i
$479$	2.78654	+	4.82643i	0.127320	+	0.220525i	0.922638	−	0.385668i	$-0.126029\pi$
$479$	2.78654	+	4.82643i	0.127320	+	0.220525i	−0.795317	+	0.606193i	$0.792696\pi$
$480$		0			0
$481$	6.06912	+	3.50401i	0.276728	+	0.159769i
$482$	1.71428	+	36.4644i	0.0780834	+	1.66091i
$483$		0			0
$484$	−13.4418	+	1.26666i	−0.610990	+	0.0575756i
$485$	19.6848			0.893842
$486$		0			0
$487$			22.6868i			1.02804i	0.857780	+	0.514018i	$0.171843\pi$
$487$			22.6868i			1.02804i	−0.857780	+	0.514018i	$0.828157\pi$
$488$	9.18844	−	7.19816i	0.415941	−	0.325846i
$489$		0			0
$490$	−5.69921	−	29.9427i	−0.257464	−	1.35267i
$491$	−5.38821	−	3.11089i	−0.243167	−	0.140392i	0.373465	−	0.927644i	$-0.378170\pi$
$491$	−5.38821	−	3.11089i	−0.243167	−	0.140392i	−0.616631	+	0.787252i	$0.711503\pi$
$492$		0			0
$493$	−18.9110	+	10.9183i	−0.851711	+	0.491735i
$494$	6.98553	−	4.48319i	0.314294	−	0.201708i
$495$		0			0
$496$	16.8346	+	19.5261i	0.755894	+	0.876746i
$497$	−5.45541	+	3.68561i	−0.244709	+	0.165322i
$498$		0			0
$499$	−35.4214	−	20.4505i	−1.58568	−	0.915491i	−0.994008	−	0.109311i	$-0.965135\pi$
$499$	−35.4214	−	20.4505i	−1.58568	−	0.915491i	−0.591670	−	0.806180i	$-0.701531\pi$
$500$	−2.61042	+	1.85398i	−0.116741	+	0.0829125i
$501$		0			0
$502$	9.32334	−	18.0572i	0.416121	−	0.805931i
$503$	−8.58006			−0.382566			−0.191283	−	0.981535i	$-0.561265\pi$
$503$	−8.58006			−0.382566			−0.191283	+	0.981535i	$0.561265\pi$
$504$		0			0
$505$	52.6914			2.34474
$506$	14.7821	−	28.6295i	0.657143	−	1.27273i
$507$		0			0
$508$	17.3840	−	12.3465i	0.771289	−	0.547788i
$509$	−5.48332	−	3.16579i	−0.243044	−	0.140321i	0.373531	−	0.927618i	$-0.378147\pi$
$509$	−5.48332	−	3.16579i	−0.243044	−	0.140321i	−0.616575	+	0.787296i	$0.711480\pi$
$510$		0			0
$511$	−7.60695	+	5.13917i	−0.336512	+	0.227343i
$512$	20.6349	−	9.28440i	0.911943	−	0.410317i
$513$		0			0
$514$	−20.3675	+	13.0715i	−0.898373	+	0.576560i
$515$	−4.30453	+	2.48522i	−0.189680	+	0.109512i
$516$		0			0
$517$	16.1035	+	9.29734i	0.708230	+	0.408897i
$518$	7.58535	−	0.895655i	0.333281	−	0.0393528i
$519$		0			0
$520$	−18.4372	−	23.5351i	−0.808525	−	1.03208i
$521$		−	19.8412i		−	0.869261i	−0.900609	−	0.434630i	$-0.856879\pi$
$521$		−	19.8412i		−	0.869261i	0.900609	−	0.434630i	$-0.143121\pi$
$522$		0			0
$523$	−39.5715			−1.73034			−0.865171	−	0.501476i	$-0.832790\pi$
$523$	−39.5715			−1.73034			−0.865171	+	0.501476i	$0.832790\pi$
$524$	−17.9318	+	1.68977i	−0.783356	+	0.0738182i
$525$		0			0
$526$	−1.14577	−	24.3717i	−0.0499580	−	1.06265i
$527$	12.7894	+	7.38396i	0.557114	+	0.321650i
$528$		0			0
$529$	3.12136	+	5.40635i	0.135711	+	0.235059i
$530$	38.7503	−	24.8692i	1.68320	−	1.08025i
$531$		0			0
$532$	3.17917	−	8.46960i	0.137834	−	0.367204i
$533$	8.79424	+	15.2321i	0.380921	+	0.659774i
$534$		0			0
$535$	2.83824	−	4.91598i	0.122708	−	0.212536i
$536$	28.8916	+	11.6290i	1.24793	+	0.502298i
$537$		0			0
$538$	27.0769	+	13.9805i	1.16737	+	0.602740i
$539$	−4.14782	−	29.1989i	−0.178659	−	1.25769i
$540$		0			0
$541$	−14.8643			−0.639068			−0.319534	−	0.947575i	$-0.603526\pi$
$541$	−14.8643			−0.639068			−0.319534	+	0.947575i	$0.603526\pi$
$542$	0.556222	−	1.07727i	0.0238918	−	0.0462729i
$543$		0			0
$544$	9.40836	−	8.91516i	0.403380	−	0.382234i
$545$	−7.11556	−	4.10817i	−0.304797	−	0.175975i
$546$		0			0
$547$	17.5001	−	10.1037i	0.748252	−	0.432003i	−0.0768102	−	0.997046i	$-0.524474\pi$
$547$	17.5001	−	10.1037i	0.748252	−	0.432003i	0.825062	+	0.565042i	$0.191140\pi$
$548$	−1.86150	+	4.06274i	−0.0795194	+	0.173552i
$549$		0			0
$550$	22.4650	−	14.4176i	0.957910	−	0.614770i
$551$	8.14678	+	14.1106i	0.347064	+	0.601133i
$552$		0			0
$553$	24.3897	+	11.8733i	1.03716	+	0.504903i
$554$	−25.2781	+	1.18839i	−1.07396	+	0.0504897i
$555$		0			0
$556$	−20.3025	+	1.91317i	−0.861018	+	0.0811365i
$557$	−12.0437			−0.510308			−0.255154	−	0.966900i	$-0.582126\pi$
$557$	−12.0437			−0.510308			−0.255154	+	0.966900i	$0.582126\pi$
$558$		0			0
$559$	11.4899			0.485973
$560$	−31.4462	−	8.53841i	−1.32884	−	0.360814i
$561$		0			0
$562$	30.6667	−	1.44172i	1.29360	−	0.0608152i
$563$	19.3253	−	33.4724i	0.814463	−	1.41069i	−0.0952496	−	0.995453i	$-0.530365\pi$
$563$	19.3253	−	33.4724i	0.814463	−	1.41069i	0.909713	−	0.415238i	$-0.136302\pi$
$564$		0			0
$565$	3.34205	−	1.92953i	0.140601	−	0.0811761i
$566$	17.8954	+	27.8839i	0.752201	+	1.17205i
$567$		0			0
$568$	0.988651	+	6.96850i	0.0414829	+	0.292392i
$569$	6.96304	+	12.0603i	0.291906	+	0.505596i	0.974260	−	0.225426i	$-0.0723773\pi$
$569$	6.96304	+	12.0603i	0.291906	+	0.505596i	−0.682355	+	0.731021i	$0.739044\pi$
$570$		0			0
$571$	21.6359	+	12.4915i	0.905436	+	0.522754i	0.878960	−	0.476896i	$-0.158238\pi$
$571$	21.6359	+	12.4915i	0.905436	+	0.522754i	0.0264762	+	0.999649i	$0.491571\pi$
$572$	−16.7504	−	23.5847i	−0.700369	−	0.986125i
$573$		0			0
$574$	17.6109	+	7.57200i	0.735063	+	0.316049i
$575$			24.2266i			1.01032i
$576$		0			0
$577$		−	41.9153i		−	1.74495i	−0.488654	−	0.872477i	$-0.662512\pi$
$577$		−	41.9153i		−	1.74495i	0.488654	−	0.872477i	$-0.337488\pi$
$578$	−7.62359	+	14.7652i	−0.317100	+	0.614149i
$579$		0			0
$580$	47.8476	−	33.9825i	1.98676	−	1.41105i
$581$	−0.132638	+	0.272460i	−0.00550274	+	0.0113036i
$582$		0			0
$583$	38.5826	−	22.2757i	1.59793	−	0.922565i
$584$	1.37856	+	9.71678i	0.0570453	+	0.402083i
$585$		0			0
$586$	−13.3180	+	8.54726i	−0.550162	+	0.353084i
$587$	13.1495	+	22.7757i	0.542740	+	0.940053i	0.998745	+	0.0500760i	$0.0159464\pi$
$587$	13.1495	+	22.7757i	0.542740	+	0.940053i	−0.456006	+	0.889977i	$0.650720\pi$
$588$		0			0
$589$	5.50960	−	9.54291i	0.227019	−	0.393209i
$590$	−1.81823	−	38.6755i	−0.0748554	−	1.59224i
$591$		0			0
$592$	2.68984	−	7.70966i	0.110552	−	0.316865i
$593$		−	14.9954i		−	0.615786i	−0.951421	−	0.307893i	$-0.900376\pi$
$593$		−	14.9954i		−	0.615786i	0.951421	−	0.307893i	$-0.0996239\pi$
$594$		0			0
$595$	−18.6187	+	1.31582i	−0.763291	+	0.0539434i
$596$	24.5677	−	2.31509i	1.00633	−	0.0948299i
$597$		0			0
$598$	26.2254	−	1.23292i	1.07243	−	0.0504178i
$599$	11.6301	+	6.71463i	0.475192	+	0.274352i	0.718411	−	0.695619i	$-0.244870\pi$
$599$	11.6301	+	6.71463i	0.475192	+	0.274352i	−0.243219	+	0.969972i	$0.578203\pi$
$600$		0			0
$601$	−11.6714	+	6.73847i	−0.476086	+	0.274868i	−0.718784	−	0.695234i	$-0.755301\pi$
$601$	−11.6714	+	6.73847i	−0.476086	+	0.274868i	0.242698	+	0.970102i	$0.421968\pi$
$602$	10.0361	−	7.48998i	0.409041	−	0.305269i
$603$		0			0
$604$	−19.6525	−	9.00457i	−0.799650	−	0.366391i
$605$	18.0004	−	10.3925i	0.731821	−	0.422517i
$606$		0			0
$607$	17.3550	−	30.0598i	0.704419	−	1.22009i	−0.262482	−	0.964937i	$-0.584541\pi$
$607$	17.3550	−	30.0598i	0.704419	−	1.22009i	0.966901	−	0.255153i	$-0.0821257\pi$
$608$	−6.65212	−	7.02013i	−0.269779	−	0.284704i
$609$		0			0
$610$	−8.24391	+	15.9666i	−0.333786	+	0.646467i
$611$			15.1516i			0.612968i
$612$		0			0
$613$	−27.2426			−1.10032			−0.550159	−	0.835060i	$-0.685433\pi$
$613$	−27.2426			−1.10032			−0.550159	+	0.835060i	$0.685433\pi$
$614$	−5.95861	+	11.5405i	−0.240470	+	0.465735i
$615$		0			0
$616$	−30.0051	−	9.68134i	−1.20894	−	0.390072i
$617$	3.19357	−	5.53142i	0.128568	−	0.222687i	−0.794554	−	0.607194i	$-0.792295\pi$
$617$	3.19357	−	5.53142i	0.128568	−	0.222687i	0.923122	+	0.384507i	$0.125629\pi$
$618$		0			0
$619$	−13.4240	−	23.2510i	−0.539554	−	0.934536i	−0.998928	−	0.0462924i	$-0.985259\pi$
$619$	−13.4240	−	23.2510i	−0.539554	−	0.934536i	0.459374	−	0.888243i	$-0.348074\pi$
$620$	−36.0825	−	16.5326i	−1.44911	−	0.663966i
$621$		0			0
$622$	−5.82149	−	9.07082i	−0.233421	−	0.363707i
$623$	−7.93476	+	5.36063i	−0.317899	+	0.214769i
$624$		0			0
$625$	13.6647	−	23.6679i	0.546588	−	0.946718i
$626$	−0.411800	−	8.75938i	−0.0164588	−	0.350095i
$627$		0			0
$628$	4.65517	+	49.4005i	0.185762	+	1.97130i
$629$		−	4.67729i		−	0.186496i
$630$		0			0
$631$		−	24.9328i		−	0.992557i	−0.868163	−	0.496279i	$-0.834699\pi$
$631$		−	24.9328i		−	0.992557i	0.868163	−	0.496279i	$-0.165301\pi$
$632$	22.8283	−	17.8835i	0.908061	−	0.711369i
$633$		0			0
$634$	−13.6887	+	0.643539i	−0.543647	+	0.0255582i
$635$	−16.4126	+	28.4275i	−0.651316	+	1.12811i
$636$		0			0
$637$	18.9149	−	14.8231i	0.749434	−	0.587314i
$638$	47.7894	−	30.6704i	1.89200	−	1.21425i
$639$		0			0
$640$	−22.9262	+	26.2266i	−0.906237	+	1.03670i
$641$	−12.1458	−	21.0372i	−0.479732	−	0.830920i	0.519998	−	0.854168i	$-0.325933\pi$
$641$	−12.1458	−	21.0372i	−0.479732	−	0.830920i	−0.999730	+	0.0232475i	$0.992599\pi$
$642$		0			0
$643$	−5.13144	+	8.88791i	−0.202364	+	0.350505i	−0.949290	−	0.314403i	$-0.898196\pi$
$643$	−5.13144	+	8.88791i	−0.202364	+	0.350505i	0.746926	+	0.664908i	$0.231529\pi$
$644$	22.1033	−	18.1725i	0.870992	−	0.716097i
$645$		0			0
$646$	−4.92244	−	2.54157i	−0.193671	−	0.0999968i
$647$	−44.3871			−1.74504			−0.872518	−	0.488581i	$-0.837515\pi$
$647$	−44.3871			−1.74504			−0.872518	+	0.488581i	$0.837515\pi$
$648$		0			0
$649$		−	37.4629i		−	1.47055i
$650$	19.3267	+	9.97881i	0.758055	+	0.391401i
$651$		0			0
$652$	17.8186	−	12.6552i	0.697829	−	0.495614i
$653$	−11.3840	+	19.7176i	−0.445489	+	0.771610i	−0.998086	−	0.0618385i	$-0.980304\pi$
$653$	−11.3840	+	19.7176i	−0.445489	+	0.771610i	0.552597	+	0.833449i	$0.313637\pi$
$654$		0			0
$655$	24.0132	−	13.8640i	0.938274	−	0.541713i
$656$	15.5211	−	13.3817i	0.605998	−	0.522466i
$657$		0			0
$658$	9.87692	+	13.2344i	0.385042	+	0.515932i
$659$	20.9713	−	12.1078i	0.816927	−	0.471653i	−0.0324284	−	0.999474i	$-0.510324\pi$
$659$	20.9713	−	12.1078i	0.816927	−	0.471653i	0.849356	+	0.527821i	$0.176991\pi$
$660$		0			0
$661$	−9.97746	−	5.76049i	−0.388078	−	0.224057i	0.293249	−	0.956036i	$-0.405264\pi$
$661$	−9.97746	−	5.76049i	−0.388078	−	0.224057i	−0.681327	+	0.731979i	$0.738597\pi$
$662$	−1.37402	−	29.2266i	−0.0534027	−	1.13593i
$663$		0			0
$664$	0.199779	+	0.255017i	0.00775293	+	0.00989660i
$665$	0.981811	+	13.8925i	0.0380730	+	0.538727i
$666$		0			0
$667$			51.5368i			1.99551i
$668$	−33.8745	+	3.19211i	−1.31065	+	0.123506i
$669$		0			0
$670$	−47.8930	+	2.25157i	−1.85027	+	0.0869858i
$671$	−8.69333	+	15.0573i	−0.335602	+	0.581280i
$672$		0			0
$673$	10.9799	+	19.0178i	0.423245	+	0.733083i	0.996255	−	0.0864662i	$-0.0275575\pi$
$673$	10.9799	+	19.0178i	0.423245	+	0.733083i	−0.573009	+	0.819549i	$0.694224\pi$
$674$	12.6609	+	19.7277i	0.487679	+	0.759882i
$675$		0			0
$676$	−1.01166	+	2.20795i	−0.0389099	+	0.0849211i
$677$	−38.3056	+	22.1157i	−1.47220	+	0.849977i	−0.999512	−	0.0312511i	$-0.990051\pi$
$677$	−38.3056	+	22.1157i	−1.47220	+	0.849977i	−0.472692	+	0.881228i	$0.656718\pi$
$678$		0			0
$679$	15.2087	+	7.40382i	0.583656	+	0.284133i
$680$	−7.45065	+	18.5106i	−0.285719	+	0.709851i
$681$		0			0
$682$	−34.1230	−	17.6185i	−1.30664	−	0.674647i
$683$		−	15.0761i		−	0.576872i	−0.957499	−	0.288436i	$-0.906865\pi$
$683$		−	15.0761i		−	0.576872i	0.957499	−	0.288436i	$-0.0931352\pi$
$684$		0			0
$685$		−	6.87980i		−	0.262864i
$686$	6.85872	−	25.2776i	0.261867	−	0.965104i
$687$		0			0
$688$	−2.50090	−	13.1519i	−0.0953458	−	0.501411i
$689$	31.4385	+	18.1510i	1.19771	+	0.691499i
$690$		0			0
$691$	11.3171	+	19.6017i	0.430522	+	0.745686i	0.996918	−	0.0784473i	$-0.0249962\pi$
$691$	11.3171	+	19.6017i	0.430522	+	0.745686i	−0.566396	+	0.824133i	$0.691663\pi$
$692$	−8.54289	−	3.91426i	−0.324752	−	0.148798i
$693$		0			0
$694$	−12.2848	+	7.88418i	−0.466325	+	0.299279i
$695$	27.1879	−	15.6969i	1.03130	−	0.595418i
$696$		0			0
$697$	5.86946	−	10.1662i	0.222321	−	0.385072i
$698$	0.639115	+	13.5946i	0.0241909	+	0.514563i
$699$		0			0
$700$	23.3861	−	3.88236i	0.883913	−	0.146739i
$701$	−8.62984			−0.325945			−0.162972	−	0.986631i	$-0.552108\pi$
$701$	−8.62984			−0.325945			−0.162972	+	0.986631i	$0.552108\pi$
$702$		0			0
$703$	−3.49000			−0.131628
$704$	−23.3501	+	24.3066i	−0.880042	+	0.916091i
$705$		0			0
$706$	1.55886	+	33.1585i	0.0586686	+	1.24794i
$707$	40.7099	+	19.8182i	1.53106	+	0.745340i
$708$		0			0
$709$	11.8717	+	20.5624i	0.445851	+	0.772237i	0.998111	−	0.0614349i	$-0.0195677\pi$
$709$	11.8717	+	20.5624i	0.445851	+	0.772237i	−0.552260	+	0.833672i	$0.686234\pi$
$710$	−5.85235	−	9.11890i	−0.219635	−	0.342226i
$711$		0			0
$712$	1.43797	+	10.1355i	0.0538901	+	0.379844i
$713$	30.1844	−	17.4270i	1.13041	−	0.652645i
$714$		0			0
$715$	38.5674	+	22.2669i	1.44234	+	0.832735i
$716$	−13.5702	+	9.63788i	−0.507142	+	0.360184i
$717$		0			0
$718$	9.42309	+	4.86536i	0.351667	+	0.181574i
$719$	−25.3519			−0.945467			−0.472734	−	0.881205i	$-0.656733\pi$
$719$	−25.3519			−0.945467			−0.472734	+	0.881205i	$0.656733\pi$
$720$		0			0
$721$	−4.26046	+	0.301096i	−0.158668	+	0.0112134i
$722$	10.4310	−	20.2025i	0.388202	−	0.751858i
$723$		0			0
$724$	−14.7948	+	10.5076i	−0.549845	+	0.390513i
$725$	−21.3482	+	36.9762i	−0.792853	+	1.37326i
$726$		0			0
$727$	5.16319	+	8.94291i	0.191492	+	0.331674i	0.945745	−	0.324910i	$-0.105334\pi$
$727$	5.16319	+	8.94291i	0.191492	+	0.331674i	−0.754253	+	0.656584i	$0.772001\pi$
$728$	−5.39281	−	25.1180i	−0.199871	−	0.930935i
$729$		0			0
$730$	−8.16044	−	12.7153i	−0.302031	−	0.470613i
$731$	−3.83431	−	6.64122i	−0.141817	−	0.245634i
$732$		0			0
$733$	−10.1555	−	5.86329i	−0.375102	−	0.216565i	0.300583	−	0.953756i	$-0.402819\pi$
$733$	−10.1555	−	5.86329i	−0.375102	−	0.216565i	−0.675685	+	0.737190i	$0.736152\pi$
$734$	6.76212	−	0.317904i	0.249595	−	0.0117341i
$735$		0			0
$736$	−7.11945	−	29.7503i	−0.262426	−	1.09661i
$737$	−46.3915			−1.70885
$738$		0			0
$739$		−	0.463561i		−	0.0170524i	−0.999964	−	0.00852618i	$-0.997286\pi$
$739$		−	0.463561i		−	0.0170524i	0.999964	−	0.00852618i	$-0.00271400\pi$
$740$	1.17934	+	12.5151i	0.0433533	+	0.460064i
$741$		0			0
$742$	39.2927	−	4.63956i	1.44248	−	0.170323i
$743$	−11.4461	−	6.60840i	−0.419916	−	0.242439i	0.275125	−	0.961408i	$-0.411281\pi$
$743$	−11.4461	−	6.60840i	−0.419916	−	0.242439i	−0.695041	+	0.718970i	$0.744614\pi$
$744$		0			0
$745$	−32.8996	+	18.9946i	−1.20535	+	0.695907i
$746$	−21.2285	−	33.0773i	−0.777229	−	1.21105i
$747$		0			0
$748$	−8.04224	+	17.5522i	−0.294053	+	0.641773i
$749$	4.04185	−	2.73062i	0.147686	−	0.0997748i
$750$		0			0
$751$	9.82352	+	5.67161i	0.358465	+	0.206960i	0.668407	−	0.743795i	$-0.266976\pi$
$751$	9.82352	+	5.67161i	0.358465	+	0.206960i	−0.309942	+	0.950755i	$0.600310\pi$
$752$	17.3432	−	3.29789i	0.632440	−	0.120262i
$753$		0			0
$754$	41.1133	+	21.2278i	1.49726	+	0.773070i
$755$	33.2794			1.21116
$756$		0			0
$757$	−21.1566			−0.768950			−0.384475	−	0.923135i	$-0.625618\pi$
$757$	−21.1566			−0.768950			−0.384475	+	0.923135i	$0.625618\pi$
$758$	34.4255	+	17.7747i	1.25039	+	0.645606i
$759$		0			0
$760$	13.8119	+	5.55936i	0.501009	+	0.201659i
$761$	7.75469	+	4.47717i	0.281107	+	0.162297i	0.633925	−	0.773395i	$-0.281443\pi$
$761$	7.75469	+	4.47717i	0.281107	+	0.162297i	−0.352817	+	0.935692i	$0.614776\pi$
$762$		0			0
$763$	−3.95240	−	5.85031i	−0.143086	−	0.211795i
$764$	−21.4002	−	9.80532i	−0.774231	−	0.354744i
$765$		0			0
$766$	11.2469	+	17.5245i	0.406369	+	0.633188i
$767$	26.4364	−	15.2631i	0.954563	−	0.551117i
$768$		0			0
$769$	7.27639	+	4.20103i	0.262393	+	0.151493i	0.625426	−	0.780284i	$-0.284925\pi$
$769$	7.27639	+	4.20103i	0.262393	+	0.151493i	−0.363033	+	0.931776i	$0.618259\pi$
$770$	48.2026	−	5.69161i	1.73710	−	0.205111i
$771$		0			0
$772$	−42.5857	+	4.01299i	−1.53269	+	0.144431i
$773$			5.75834i			0.207113i	0.994624	+	0.103556i	$0.0330223\pi$
$773$			5.75834i			0.207113i	−0.994624	+	0.103556i	$0.966978\pi$
$774$		0			0
$775$	28.8753			1.03723
$776$	14.2350	−	11.1516i	0.511008	−	0.400321i
$777$		0			0
$778$	−30.9384	+	1.45449i	−1.10920	+	0.0521461i
$779$	−7.58559	−	4.37954i	−0.271782	−	0.156913i
$780$		0			0
$781$	−5.24202	−	9.07945i	−0.187574	−	0.324888i
$782$	−9.46430	−	14.7469i	−0.338443	−	0.527348i
$783$		0			0
$784$	−21.0842	−	18.4244i	−0.753007	−	0.658013i
$785$	−38.1942	−	66.1542i	−1.36321	−	2.36115i
$786$		0			0
$787$	−18.4924	+	32.0297i	−0.659181	+	1.14174i	0.321647	+	0.946860i	$0.395764\pi$
$787$	−18.4924	+	32.0297i	−0.659181	+	1.14174i	−0.980828	+	0.194876i	$0.937570\pi$
$788$	−12.4906	−	17.5868i	−0.444957	−	0.626503i
$789$		0			0
$790$	−20.4816	+	39.6682i	−0.728704	+	1.41133i
$791$	3.30784	−	0.233772i	0.117613	−	0.00831197i
$792$		0			0
$793$	−14.1673			−0.503094
$794$	−43.9287	−	22.6814i	−1.55897	−	0.804933i
$795$		0			0
$796$	−5.38460	−	7.58156i	−0.190852	−	0.268721i
$797$	20.0024	+	11.5484i	0.708522	+	0.409065i	0.810513	−	0.585720i	$-0.199188\pi$
$797$	20.0024	+	11.5484i	0.708522	+	0.409065i	−0.101992	+	0.994785i	$0.532522\pi$
$798$		0			0
$799$	8.75767	−	5.05624i	0.309824	−	0.178877i
$800$	7.21554	−	24.2941i	0.255108	−	0.858927i
$801$		0			0
$802$	14.9453	+	23.2871i	0.527736	+	0.822298i
$803$	−7.30941	−	12.6603i	−0.257943	−	0.446771i
$804$		0			0
$805$	−19.2817	+	39.6078i	−0.679589	+	1.39599i
$806$	−1.46950	−	31.2576i	−0.0517608	−	1.10100i
$807$		0			0
$808$	38.1037	−	29.8502i	1.34048	−	1.05013i
$809$	22.9976			0.808553			0.404277	−	0.914637i	$-0.367523\pi$
$809$	22.9976			0.808553			0.404277	+	0.914637i	$0.367523\pi$
$810$		0			0
$811$	27.1173			0.952216			0.476108	−	0.879387i	$-0.342047\pi$
$811$	27.1173			0.952216			0.476108	+	0.879387i	$0.342047\pi$
$812$	49.7490	−	8.25887i	1.74585	−	0.289830i
$813$		0			0
$814$	0.571182	+	12.1496i	0.0200199	+	0.425843i
$815$	−16.8230	+	29.1382i	−0.589282	+	1.02067i
$816$		0			0
$817$	−4.95540	+	2.86100i	−0.173368	+	0.100094i
$818$	4.08730	−	2.62315i	0.142909	−	0.0917165i
$819$		0			0
$820$	−13.1417	+	28.6817i	−0.458927	+	1.00161i
$821$	2.27415	+	3.93894i	0.0793682	+	0.137470i	0.902978	−	0.429688i	$-0.141376\pi$
$821$	2.27415	+	3.93894i	0.0793682	+	0.137470i	−0.823609	+	0.567158i	$0.808043\pi$
$822$		0			0
$823$	20.0197	+	11.5584i	0.697844	+	0.402900i	0.806544	−	0.591174i	$-0.201335\pi$
$823$	20.0197	+	11.5584i	0.697844	+	0.402900i	−0.108700	+	0.994075i	$0.534669\pi$
$824$	−1.70491	+	4.23574i	−0.0593934	+	0.147559i
$825$		0			0
$826$	13.1418	−	30.5650i	0.457261	−	1.06349i
$827$			51.8058i			1.80146i	0.434376	+	0.900732i	$0.356969\pi$
$827$			51.8058i			1.80146i	−0.434376	+	0.900732i	$0.643031\pi$
$828$		0			0
$829$		−	13.9412i		−	0.484197i	−0.970252	−	0.242098i	$-0.922164\pi$
$829$		−	13.9412i		−	0.484197i	0.970252	−	0.242098i	$-0.0778357\pi$
$830$	−0.443138	−	0.228803i	−0.0153816	−	0.00794186i
$831$		0			0
$832$	−26.6657	−	6.57449i	−0.924466	−	0.227929i
$833$	−14.8799	−	5.98621i	−0.515558	−	0.207410i
$834$		0			0
$835$	45.3627	−	26.1902i	1.56984	−	0.906349i
$836$	13.0967	+	6.00078i	0.452960	+	0.207541i
$837$		0			0
$838$	−8.89667	−	13.8624i	−0.307330	−	0.478870i
$839$	−24.6769	−	42.7416i	−0.851941	−	1.47561i	−0.879454	−	0.475984i	$-0.842092\pi$
$839$	−24.6769	−	42.7416i	−0.851941	−	1.47561i	0.0275127	−	0.999621i	$-0.491241\pi$
$840$		0			0
$841$	−30.9137	+	53.5441i	−1.06599	+	1.84635i
$842$	27.2448	−	1.28084i	0.938917	−	0.0441408i
$843$		0			0
$844$	−0.485146	−	5.14835i	−0.0166994	−	0.177214i
$845$		−	3.73892i		−	0.128623i
$846$		0			0
$847$	17.8161	−	1.25910i	0.612170	−	0.0432633i
$848$	13.9335	−	39.9366i	0.478480	−	1.37143i
$849$		0			0
$850$	−0.681724	−	14.5009i	−0.0233829	−	0.497377i
$851$	−9.56000	−	5.51947i	−0.327713	−	0.189205i
$852$		0			0
$853$	−24.2685	+	14.0114i	−0.830939	+	0.479743i	−0.854174	−	0.519987i	$-0.825937\pi$
$853$	−24.2685	+	14.0114i	−0.830939	+	0.479743i	0.0232350	+	0.999730i	$0.492603\pi$
$854$	−12.3746	+	9.23525i	−0.423452	+	0.316024i
$855$		0			0
$856$	−0.732479	−	5.16288i	−0.0250356	−	0.176463i
$857$	−9.87736	+	5.70269i	−0.337404	+	0.194800i	−0.659123	−	0.752035i	$-0.729073\pi$
$857$	−9.87736	+	5.70269i	−0.337404	+	0.194800i	0.321719	+	0.946835i	$0.395739\pi$
$858$		0			0
$859$	−20.0438	+	34.7168i	−0.683884	+	1.18452i	0.289902	+	0.957056i	$0.406377\pi$
$859$	−20.0438	+	34.7168i	−0.683884	+	1.18452i	−0.973786	+	0.227466i	$0.926956\pi$
$860$	11.9340	+	16.8032i	0.406947	+	0.572984i
$861$		0			0
$862$	−2.18346	−	1.12737i	−0.0743691	−	0.0383985i
$863$			45.2430i			1.54009i	0.637989	+	0.770045i	$0.279766\pi$
$863$			45.2430i			1.54009i	−0.637989	+	0.770045i	$0.720234\pi$
$864$		0			0
$865$	14.4664			0.491874
$866$	7.48638	+	3.86539i	0.254397	+	0.131351i
$867$		0			0
$868$	−21.6595	−	26.3446i	−0.735172	−	0.894193i
$869$	−21.5982	+	37.4092i	−0.732669	+	1.26902i
$870$		0			0
$871$	−18.9007	−	32.7370i	−0.640426	−	1.10925i
$872$	−7.47292	+	1.06022i	−0.253065	+	0.0359034i
$873$		0			0
$874$	−11.0035	+	7.06186i	−0.372199	+	0.238871i
$875$	3.50970	−	2.37111i	0.118649	−	0.0801581i
$876$		0			0
$877$	6.89651	−	11.9451i	0.232878	−	0.403357i	−0.725776	−	0.687932i	$-0.758519\pi$
$877$	6.89651	−	11.9451i	0.232878	−	0.403357i	0.958654	+	0.284574i	$0.0918522\pi$
$878$	−30.0547	+	1.41295i	−1.01430	+	0.0476846i
$879$		0			0
$880$	17.0931	−	48.9925i	0.576207	−	1.65154i
$881$			46.4443i			1.56475i	0.622808	+	0.782375i	$0.285992\pi$
$881$			46.4443i			1.56475i	−0.622808	+	0.782375i	$0.714008\pi$
$882$		0			0
$883$		−	22.9737i		−	0.773127i	−0.922263	−	0.386564i	$-0.873662\pi$
$883$		−	22.9737i		−	0.773127i	0.922263	−	0.386564i	$-0.126338\pi$
$884$	−15.6626	+	1.47594i	−0.526790	+	0.0496411i
$885$		0			0
$886$	−2.31122	−	49.1619i	−0.0776471	−	1.65163i
$887$	10.6026	−	18.3642i	0.356000	−	0.616610i	−0.631289	−	0.775548i	$-0.717474\pi$
$887$	10.6026	−	18.3642i	0.356000	−	0.616610i	0.987289	+	0.158938i	$0.0508071\pi$
$888$		0			0
$889$	−23.3727	+	15.7903i	−0.783895	+	0.529590i
$890$	−8.51210	−	13.2632i	−0.285326	−	0.444584i
$891$		0			0
$892$	0.544418	−	1.18820i	0.0182285	−	0.0397838i
$893$	−3.77276	−	6.53461i	−0.126251	−	0.218672i
$894$		0			0
$895$	12.8120	−	22.1910i	0.428257	−	0.741763i
$896$	−27.5773	+	11.6400i	−0.921294	+	0.388866i
$897$		0			0
$898$	0.0710438	−	0.137596i	0.00237076	−	0.00459162i
$899$	61.4259			2.04867
$900$		0			0
$901$		−	24.2287i		−	0.807175i
$902$	−14.0048	+	27.1241i	−0.466310	+	0.903135i
$903$		0			0
$904$	1.32370	−	3.28864i	0.0440256	−	0.109379i
$905$	13.9682	−	24.1936i	0.464317	−	0.804221i
$906$		0			0
$907$	−18.6114	+	10.7453i	−0.617981	+	0.356791i	−0.776082	−	0.630632i	$-0.782796\pi$
$907$	−18.6114	+	10.7453i	−0.617981	+	0.356791i	0.158102	+	0.987423i	$0.449463\pi$
$908$	4.80383	−	10.4844i	0.159421	−	0.347936i
$909$		0			0
$910$	23.6550	+	31.6961i	0.784154	+	1.05072i
$911$	−44.5039	+	25.6943i	−1.47448	+	0.851291i	−0.999587	−	0.0287535i	$-0.990846\pi$
$911$	−44.5039	+	25.6943i	−1.47448	+	0.851291i	−0.474892	+	0.880044i	$0.657513\pi$
$912$		0			0
$913$	−0.417902	−	0.241276i	−0.0138306	−	0.00798507i
$914$	−41.4163	+	1.94708i	−1.36993	+	0.0644038i
$915$		0			0
$916$	−5.25466	−	55.7622i	−0.173619	−	1.84244i
$917$	23.7674	−	1.67969i	0.784869	−	0.0554683i
$918$		0			0
$919$		−	33.2245i		−	1.09597i	−0.836487	−	0.547987i	$-0.815394\pi$
$919$		−	33.2245i		−	1.09597i	0.836487	−	0.547987i	$-0.184606\pi$
$920$	29.0420	+	37.0721i	0.957487	+	1.22223i
$921$		0			0
$922$	−2.21623	−	47.1412i	−0.0729875	−	1.55251i
$923$	4.27138	−	7.39825i	0.140594	−	0.243516i
$924$		0			0
$925$	−4.57269	−	7.92013i	−0.150349	−	0.260412i
$926$	−12.3425	+	7.92118i	−0.405599	+	0.260306i
$927$		0			0
$928$	15.3495	−	51.6805i	0.503872	−	1.69649i
$929$	−23.4631	+	13.5464i	−0.769800	+	0.444444i	−0.832803	−	0.553569i	$-0.813265\pi$
$929$	−23.4631	+	13.5464i	−0.769800	+	0.444444i	0.0630034	+	0.998013i	$0.479932\pi$
$930$		0			0
$931$	−4.46666	+	11.1028i	−0.146389	+	0.363878i
$932$	−9.78619	−	13.7790i	−0.320557	−	0.451347i
$933$		0			0
$934$	5.07309	−	9.82540i	0.165996	−	0.321497i
$935$		−	29.7227i		−	0.972038i
$936$		0			0
$937$			34.2337i			1.11837i	0.829044	+	0.559183i	$0.188885\pi$
$937$			34.2337i			1.11837i	−0.829044	+	0.559183i	$0.811115\pi$
$938$	−37.8495	−	16.2739i	−1.23583	−	0.531361i
$939$		0			0
$940$	−22.1581	+	15.7372i	−0.722718	+	0.513291i
$941$	−47.7364	−	27.5606i	−1.55616	−	0.898450i	−0.997618	−	0.0689741i	$-0.978027\pi$
$941$	−47.7364	−	27.5606i	−1.55616	−	0.898450i	−0.558543	−	0.829476i	$-0.688639\pi$
$942$		0			0
$943$	−13.8526	−	23.9934i	−0.451102	−	0.781331i
$944$	−23.2249	−	26.9381i	−0.755905	−	0.876759i
$945$		0			0
$946$	10.7709	+	16.7828i	0.350192	+	0.545655i
$947$	13.2348	−	7.64112i	0.430073	−	0.248303i	−0.269305	−	0.963055i	$-0.586794\pi$
$947$	13.2348	−	7.64112i	0.430073	−	0.248303i	0.699378	+	0.714752i	$0.253460\pi$
$948$		0			0
$949$	5.95596	−	10.3160i	0.193339	−	0.334872i
$950$	−10.8200	+	0.508674i	−0.351046	+	0.0165036i
$951$		0			0
$952$	−12.7186	+	11.4992i	−0.412214	+	0.372691i
$953$	−7.58109			−0.245576			−0.122788	−	0.992433i	$-0.539183\pi$
$953$	−7.58109			−0.245576			−0.122788	+	0.992433i	$0.539183\pi$
$954$		0			0
$955$	36.2388			1.17266
$956$	4.02933	+	42.7592i	0.130318	+	1.38293i
$957$		0			0
$958$	−7.87283	+	0.370121i	−0.254360	+	0.0119581i
$959$	2.58762	−	5.31541i	0.0835586	−	0.171643i
$960$		0			0
$961$	−5.27092	−	9.12949i	−0.170030	−	0.294500i
$962$	−8.34086	+	5.35302i	−0.268920	+	0.172588i
$963$		0			0
$964$	−46.9334	−	21.5044i	−1.51162	−	0.692609i
$965$	57.0282	−	32.9253i	1.83580	−	1.05990i
$966$		0			0
$967$	4.06638	+	2.34772i	0.130766	+	0.0754977i	0.563956	−	0.825805i	$-0.309279\pi$
$967$	4.06638	+	2.34772i	0.130766	+	0.0754977i	−0.433190	+	0.901303i	$0.642612\pi$
$968$	7.12950	−	17.7128i	0.229151	−	0.569310i
$969$		0			0
$970$	−12.7717	+	24.7359i	−0.410076	+	0.794223i
$971$	44.5685			1.43027			0.715135	−	0.698986i	$-0.246365\pi$
$971$	44.5685			1.43027			0.715135	+	0.698986i	$0.246365\pi$
$972$		0			0
$973$	26.9096	−	1.90176i	0.862681	−	0.0609675i
$974$	−28.5082	−	14.7194i	−0.913461	−	0.471641i
$975$		0			0
$976$	3.08364	+	16.2164i	0.0987049	+	0.519076i
$977$	4.78233	−	8.28324i	0.153000	−	0.265004i	−0.779329	−	0.626615i	$-0.784440\pi$
$977$	4.78233	−	8.28324i	0.153000	−	0.265004i	0.932329	+	0.361611i	$0.117773\pi$
$978$		0			0
$979$	−7.62439	−	13.2058i	−0.243677	−	0.422060i
$980$	41.3237	+	12.2655i	1.32004	+	0.391808i
$981$		0			0
$982$	7.40507	−	4.75245i	0.236305	−	0.151657i
$983$	26.0757	+	45.1644i	0.831685	+	1.44052i	0.896701	+	0.442637i	$0.145957\pi$
$983$	26.0757	+	45.1644i	0.831685	+	1.44052i	−0.0650157	+	0.997884i	$0.520710\pi$
$984$		0			0
$985$	28.7592	+	16.6041i	0.916344	+	0.529052i
$986$	−1.45022	−	30.8475i	−0.0461844	−	0.982386i
$987$		0			0
$988$	1.10128	+	11.6868i	0.0350365	+	0.371806i
$989$	−18.0988			−0.575508
$990$		0			0
$991$			41.3545i			1.31367i	0.754034	+	0.656835i	$0.228105\pi$
$991$			41.3545i			1.31367i	−0.754034	+	0.656835i	$0.771895\pi$
$992$	−35.4589	+	8.48556i	−1.12582	+	0.269417i
$993$		0			0
$994$	−1.09180	−	9.24654i	−0.0346299	−	0.293282i
$995$	12.3979	+	7.15794i	0.393040	+	0.226922i
$996$		0			0
$997$	45.7292	−	26.4017i	1.44826	−	0.836152i	0.449879	−	0.893089i	$-0.351467\pi$
$997$	45.7292	−	26.4017i	1.44826	−	0.836152i	0.998378	+	0.0569376i	$0.0181336\pi$
$998$	48.6799	−	31.2419i	1.54094	−	0.988946i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	756.2.bi.c.307.14		80
3.2	odd	2		252.2.bi.c.139.27	yes	80
4.3	odd	2	inner	756.2.bi.c.307.40		80
7.6	odd	2	inner	756.2.bi.c.307.13		80
9.2	odd	6		252.2.bi.c.223.1	yes	80
9.7	even	3	inner	756.2.bi.c.559.39		80
12.11	even	2		252.2.bi.c.139.2	yes	80
21.20	even	2		252.2.bi.c.139.28	yes	80
28.27	even	2	inner	756.2.bi.c.307.39		80
36.7	odd	6	inner	756.2.bi.c.559.13		80
36.11	even	6		252.2.bi.c.223.28	yes	80
63.20	even	6		252.2.bi.c.223.2	yes	80
63.34	odd	6	inner	756.2.bi.c.559.40		80
84.83	odd	2		252.2.bi.c.139.1	✓	80
252.83	odd	6		252.2.bi.c.223.27	yes	80
252.223	even	6	inner	756.2.bi.c.559.14		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.bi.c.139.1	✓	80	84.83	odd	2
252.2.bi.c.139.2	yes	80	12.11	even	2
252.2.bi.c.139.27	yes	80	3.2	odd	2
252.2.bi.c.139.28	yes	80	21.20	even	2
252.2.bi.c.223.1	yes	80	9.2	odd	6
252.2.bi.c.223.2	yes	80	63.20	even	6
252.2.bi.c.223.27	yes	80	252.83	odd	6
252.2.bi.c.223.28	yes	80	36.11	even	6
756.2.bi.c.307.13		80	7.6	odd	2	inner
756.2.bi.c.307.14		80	1.1	even	1	trivial
756.2.bi.c.307.39		80	28.27	even	2	inner
756.2.bi.c.307.40		80	4.3	odd	2	inner
756.2.bi.c.559.13		80	36.7	odd	6	inner
756.2.bi.c.559.14		80	252.223	even	6	inner
756.2.bi.c.559.39		80	9.7	even	3	inner
756.2.bi.c.559.40		80	63.34	odd	6	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:	\( N \)	\(=\)	\( 756 = 2^{2} \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	756.bi (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.648812 + 1.25660i) q^{2} +(-1.15809 - 1.63059i) q^{4} +(2.66647 + 1.53948i) q^{5} +(1.48111 + 2.19233i) q^{7} +(2.80038 - 0.397302i) q^{8} +(-3.66455 + 2.35184i) q^{10} +(-3.64870 + 2.10658i) q^{11} +(-2.97309 - 1.71651i) q^{13} +(-3.71584 + 0.438755i) q^{14} +(-1.31767 + 3.77674i) q^{16} +2.29127i q^{17} +1.70965 q^{19} +(-0.577723 - 6.13078i) q^{20} +(-0.279805 - 5.95173i) q^{22} +(4.68317 + 2.70383i) q^{23} +(2.24003 + 3.87984i) q^{25} +(4.08594 - 2.62229i) q^{26} +(1.85954 - 4.95400i) q^{28} +(4.76517 + 8.25352i) q^{29} +(3.22265 - 5.58179i) q^{31} +(-3.89093 - 4.10618i) q^{32} +(-2.87921 - 1.48660i) q^{34} +(0.574276 + 8.12592i) q^{35} -2.04135 q^{37} +(-1.10924 + 2.14835i) q^{38} +(8.07877 + 3.25176i) q^{40} +(-4.43693 - 2.56166i) q^{41} +(-2.89849 + 1.67344i) q^{43} +(7.66048 + 3.50995i) q^{44} +(-6.43612 + 4.13059i) q^{46} +(-2.20674 - 3.82219i) q^{47} +(-2.61262 + 6.49417i) q^{49} +(-6.32876 + 0.297531i) q^{50} +(0.644156 + 6.83577i) q^{52} -10.5744 q^{53} -12.9722 q^{55} +(5.01870 + 5.55091i) q^{56} +(-13.4631 + 0.632933i) q^{58} +(-4.44595 + 7.70061i) q^{59} +(3.57388 - 2.06338i) q^{61} +(4.92318 + 7.67111i) q^{62} +(7.68430 - 2.22520i) q^{64} +(-5.28509 - 9.15404i) q^{65} +(9.53591 + 5.50556i) q^{67} +(3.73613 - 2.65349i) q^{68} +(-10.5836 - 4.55056i) q^{70} +2.48841i q^{71} +3.46980i q^{73} +(1.32445 - 2.56517i) q^{74} +(-1.97992 - 2.78774i) q^{76} +(-10.0224 - 4.87907i) q^{77} +(8.87914 - 5.12638i) q^{79} +(-9.32776 + 8.04200i) q^{80} +(6.09771 - 3.91340i) q^{82} +(0.0572673 + 0.0991899i) q^{83} +(-3.52738 + 6.10959i) q^{85} +(-0.222275 - 4.72799i) q^{86} +(-9.38081 + 7.34886i) q^{88} +3.61933i q^{89} +(-0.640313 - 9.06033i) q^{91} +(-1.01467 - 10.7676i) q^{92} +(6.23472 - 0.293110i) q^{94} +(4.55872 + 2.63198i) q^{95} +(5.53677 - 3.19666i) q^{97} +(-6.46548 - 7.49651i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 6 q^{2} - 2 q^{4} + 24 q^{8} - 10 q^{14} - 18 q^{16} - 14 q^{22} + 32 q^{25} + 28 q^{28} - 8 q^{29} + 16 q^{32} - 16 q^{37} + 84 q^{44} + 24 q^{46} - 24 q^{49} + 12 q^{50} + 48 q^{53} - 32 q^{56}+ \cdots - 20 q^{98}+O(q^{100}) \) 80 * q + 6 * q^2 - 2 * q^4 + 24 * q^8 - 10 * q^14 - 18 * q^16 - 14 * q^22 + 32 * q^25 + 28 * q^28 - 8 * q^29 + 16 * q^32 - 16 * q^37 + 84 * q^44 + 24 * q^46 - 24 * q^49 + 12 * q^50 + 48 * q^53 - 32 * q^56 - 14 * q^58 - 8 * q^64 + 40 * q^65 - 22 * q^70 - 64 * q^74 + 12 * q^77 + 40 * q^85 + 52 * q^86 + 6 * q^88 - 30 * q^92 - 20 * q^98

Introduction

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