LMFDB - Embedded newform 855.2.be.d.334.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(64,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("855.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.be (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6x^{10} + 29x^{8} - 40x^{6} + 43x^{4} - 7x^{2} + 1 $ x^12 - 6x^10 + 29x^8 - 40x^6 + 43x^4 - 7*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 95)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			334.4
Root			$1.83525 + 1.05958i$ of defining polynomial
Character	$\chi$	$=$	855.334
Dual form			855.2.be.d.64.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.408663 + 0.235942i) q^{2} +(-0.888663 - 1.53921i) q^{4} +(2.19202 + 0.441641i) q^{5} -1.17540i q^{7} -1.78246i q^{8} +O(q^{10})$	\(q+(0.408663 + 0.235942i) q^{2} +(-0.888663 - 1.53921i) q^{4} +(2.19202 + 0.441641i) q^{5} -1.17540i q^{7} -1.78246i q^{8} +(0.791597 + 0.697672i) q^{10} -0.713538 q^{11} +(3.55344 - 2.05158i) q^{13} +(0.277326 - 0.480342i) q^{14} +(-1.35677 + 2.34999i) q^{16} +(-2.21038 - 1.27616i) q^{17} +(-1.57031 - 4.06622i) q^{19} +(-1.26819 - 3.76645i) q^{20} +(-0.291597 - 0.168353i) q^{22} +(0.525730 - 0.303530i) q^{23} +(4.60991 + 1.93617i) q^{25} +1.93621 q^{26} +(-1.80918 + 1.04453i) q^{28} +(0.429693 + 0.744250i) q^{29} +2.50914 q^{31} +(-4.19623 + 2.42270i) q^{32} +(-0.602201 - 1.04304i) q^{34} +(0.519104 - 2.57650i) q^{35} -9.38171i q^{37} +(0.317665 - 2.03222i) q^{38} +(0.787207 - 3.90719i) q^{40} +(-2.06117 + 3.57005i) q^{41} +(-8.76759 - 5.06197i) q^{43} +(0.634095 + 1.09828i) q^{44} +0.286462 q^{46} +(9.10919 - 5.25919i) q^{47} +5.61844 q^{49} +(1.42708 + 1.87891i) q^{50} +(-6.31561 - 3.64632i) q^{52} +(-4.31330 + 2.49028i) q^{53} +(-1.56409 - 0.315128i) q^{55} -2.09510 q^{56} +0.405530i q^{58} +(3.12496 - 5.41259i) q^{59} +(2.27733 + 3.94444i) q^{61} +(1.02539 + 0.592010i) q^{62} +3.14061 q^{64} +(8.69527 - 2.92776i) q^{65} +(4.48783 - 2.59105i) q^{67} +4.53632i q^{68} +(0.820042 - 0.930441i) q^{70} +(-6.58393 + 11.4037i) q^{71} +(10.7199 + 6.18914i) q^{73} +(2.21354 - 3.83396i) q^{74} +(-4.86329 + 6.03053i) q^{76} +0.838691i q^{77} +(-2.98173 + 5.16450i) q^{79} +(-4.01192 + 4.55203i) q^{80} +(-1.68465 + 0.972633i) q^{82} -13.8603i q^{83} +(-4.28159 - 3.77357i) q^{85} +(-2.38866 - 4.13729i) q^{86} +1.27185i q^{88} +(-7.98173 - 13.8248i) q^{89} +(-2.41142 - 4.17670i) q^{91} +(-0.934393 - 0.539472i) q^{92} +4.96345 q^{94} +(-1.64634 - 9.60675i) q^{95} +(14.4643 + 8.35099i) q^{97} +(2.29605 + 1.32563i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{4} + 2 q^{5}+O(q^{10}) $ 12 * q + 2 * q^4 + 2 * q^5	$ 12 q + 2 q^{4} + 2 q^{5} + 6 q^{10} - 4 q^{11} - 22 q^{14} - 14 q^{16} - 12 q^{19} + 40 q^{20} - 6 q^{25} + 44 q^{26} + 12 q^{29} + 60 q^{31} + 10 q^{34} + 10 q^{40} + 12 q^{41} - 20 q^{44} + 8 q^{46} - 4 q^{49} + 8 q^{50} - 18 q^{55} - 92 q^{56} - 20 q^{59} + 2 q^{61} + 24 q^{64} + 40 q^{65} + 46 q^{70} - 2 q^{71} + 22 q^{74} - 70 q^{76} + 24 q^{79} + 22 q^{80} + 2 q^{85} - 16 q^{86} - 36 q^{89} + 24 q^{91} - 60 q^{94} - 46 q^{95}+O(q^{100}) $ 12 * q + 2 * q^4 + 2 * q^5 + 6 * q^10 - 4 * q^11 - 22 * q^14 - 14 * q^16 - 12 * q^19 + 40 * q^20 - 6 * q^25 + 44 * q^26 + 12 * q^29 + 60 * q^31 + 10 * q^34 + 10 * q^40 + 12 * q^41 - 20 * q^44 + 8 * q^46 - 4 * q^49 + 8 * q^50 - 18 * q^55 - 92 * q^56 - 20 * q^59 + 2 * q^61 + 24 * q^64 + 40 * q^65 + 46 * q^70 - 2 * q^71 + 22 * q^74 - 70 * q^76 + 24 * q^79 + 22 * q^80 + 2 * q^85 - 16 * q^86 - 36 * q^89 + 24 * q^91 - 60 * q^94 - 46 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.408663	+	0.235942i	0.288969	+	0.166836i	0.637477	−	0.770470i	$-0.279978\pi$
$2$	0.408663	+	0.235942i	0.288969	+	0.166836i	−0.348508	+	0.937306i	$0.613312\pi$
$3$		0			0
$3$		0			0
$4$	−0.888663	−	1.53921i	−0.444331	−	0.769605i
$5$	2.19202	+	0.441641i	0.980301	+	0.197508i
$5$	2.19202	+	0.441641i	0.980301	+	0.197508i
$6$		0			0
$7$		−	1.17540i		−	0.444259i	−0.975017	−	0.222129i	$-0.928699\pi$
$7$		−	1.17540i		−	0.444259i	0.975017	−	0.222129i	$-0.0713007\pi$
$8$		−	1.78246i		−	0.630194i
$9$		0			0
$10$	0.791597	+	0.697672i	0.250325	+	0.220623i
$11$	−0.713538			−0.215140			−0.107570	−	0.994198i	$-0.534307\pi$
$11$	−0.713538			−0.215140			−0.107570	+	0.994198i	$0.534307\pi$
$12$		0			0
$13$	3.55344	−	2.05158i	0.985546	−	0.569005i	0.0816060	−	0.996665i	$-0.473995\pi$
$13$	3.55344	−	2.05158i	0.985546	−	0.569005i	0.903940	+	0.427659i	$0.140662\pi$
$14$	0.277326	−	0.480342i	0.0741184	−	0.128377i
$15$		0			0
$16$	−1.35677	+	2.34999i	−0.339192	+	0.587498i
$17$	−2.21038	−	1.27616i	−0.536096	−	0.309515i	0.207399	−	0.978256i	$-0.433500\pi$
$17$	−2.21038	−	1.27616i	−0.536096	−	0.309515i	−0.743495	+	0.668741i	$0.766833\pi$
$18$		0			0
$19$	−1.57031	−	4.06622i	−0.360253	−	0.932855i
$19$	−1.57031	−	4.06622i	−0.360253	−	0.932855i
$20$	−1.26819	−	3.76645i	−0.283576	−	0.842203i
$21$		0			0
$22$	−0.291597	−	0.168353i	−0.0621686	−	0.0358931i
$23$	0.525730	−	0.303530i	0.109622	−	0.0632904i	−0.444186	−	0.895934i	$-0.646507\pi$
$23$	0.525730	−	0.303530i	0.109622	−	0.0632904i	0.553809	+	0.832644i	$0.313174\pi$
$24$		0			0
$25$	4.60991	+	1.93617i	0.921981	+	0.387234i
$26$	1.93621			0.379722
$27$		0			0
$28$	−1.80918	+	1.04453i	−0.341904	+	0.197398i
$29$	0.429693	+	0.744250i	0.0797920	+	0.138204i	0.903160	−	0.429304i	$-0.141241\pi$
$29$	0.429693	+	0.744250i	0.0797920	+	0.138204i	−0.823368	+	0.567508i	$0.807908\pi$
$30$		0			0
$31$	2.50914			0.450654			0.225327	−	0.974283i	$-0.427655\pi$
$31$	2.50914			0.450654			0.225327	+	0.974283i	$0.427655\pi$
$32$	−4.19623	+	2.42270i	−0.741796	+	0.428276i
$33$		0			0
$34$	−0.602201	−	1.04304i	−0.103277	−	0.178880i
$35$	0.519104	−	2.57650i	0.0877446	−	0.435507i
$36$		0			0
$37$		−	9.38171i		−	1.54234i	−0.636627	−	0.771172i	$-0.719671\pi$
$37$		−	9.38171i		−	1.54234i	0.636627	−	0.771172i	$-0.280329\pi$
$38$	0.317665	−	2.03222i	0.0515320	−	0.329669i
$39$		0			0
$40$	0.787207	−	3.90719i	0.124468	−	0.617780i
$41$	−2.06117	+	3.57005i	−0.321901	+	0.557548i	−0.980880	−	0.194612i	$-0.937655\pi$
$41$	−2.06117	+	3.57005i	−0.321901	+	0.557548i	0.658979	+	0.752161i	$0.270988\pi$
$42$		0			0
$43$	−8.76759	−	5.06197i	−1.33705	−	0.771944i	−0.350677	−	0.936496i	$-0.614049\pi$
$43$	−8.76759	−	5.06197i	−1.33705	−	0.771944i	−0.986368	+	0.164553i	$0.947382\pi$
$44$	0.634095	+	1.09828i	0.0955934	+	0.165573i
$45$		0			0
$46$	0.286462			0.0422365
$47$	9.10919	−	5.25919i	1.32871	−	0.767132i	0.343611	−	0.939112i	$-0.388350\pi$
$47$	9.10919	−	5.25919i	1.32871	−	0.767132i	0.985100	+	0.171980i	$0.0550165\pi$
$48$		0			0
$49$	5.61844			0.802634
$50$	1.42708	+	1.87891i	0.201819	+	0.265718i
$51$		0			0
$52$	−6.31561	−	3.64632i	−0.875818	−	0.505654i
$53$	−4.31330	+	2.49028i	−0.592477	+	0.342067i	−0.766076	−	0.642750i	$-0.777794\pi$
$53$	−4.31330	+	2.49028i	−0.592477	+	0.342067i	0.173599	+	0.984816i	$0.444460\pi$
$54$		0			0
$55$	−1.56409	−	0.315128i	−0.210902	−	0.0424918i
$56$	−2.09510			−0.279969
$57$		0			0
$58$			0.405530i			0.0532488i
$59$	3.12496	−	5.41259i	0.406835	−	0.704659i	−0.587698	−	0.809080i	$-0.699966\pi$
$59$	3.12496	−	5.41259i	0.406835	−	0.704659i	0.994533	+	0.104421i	$0.0332991\pi$
$60$		0			0
$61$	2.27733	+	3.94444i	0.291582	+	0.505034i	0.974184	−	0.225756i	$-0.0724852\pi$
$61$	2.27733	+	3.94444i	0.291582	+	0.505034i	−0.682602	+	0.730790i	$0.739152\pi$
$62$	1.02539	+	0.592010i	0.130225	+	0.0751854i
$63$		0			0
$64$	3.14061			0.392577
$65$	8.69527	−	2.92776i	1.07851	−	0.363144i
$66$		0			0
$67$	4.48783	−	2.59105i	0.548276	−	0.316547i	−0.200151	−	0.979765i	$-0.564143\pi$
$67$	4.48783	−	2.59105i	0.548276	−	0.316547i	0.748426	+	0.663218i	$0.230810\pi$
$68$			4.53632i			0.550109i
$69$		0			0
$70$	0.820042	−	0.930441i	0.0980138	−	0.111209i
$71$	−6.58393	+	11.4037i	−0.781368	+	1.35337i	0.149776	+	0.988720i	$0.452145\pi$
$71$	−6.58393	+	11.4037i	−0.781368	+	1.35337i	−0.931145	+	0.364650i	$0.881189\pi$
$72$		0			0
$73$	10.7199	+	6.18914i	1.25467	+	0.724384i	0.972033	−	0.234842i	$-0.0754574\pi$
$73$	10.7199	+	6.18914i	1.25467	+	0.724384i	0.282637	+	0.959227i	$0.408791\pi$
$74$	2.21354	−	3.83396i	0.257319	−	0.445689i
$75$		0			0
$76$	−4.86329	+	6.03053i	−0.557857	+	0.691749i
$77$			0.838691i			0.0955777i
$78$		0			0
$79$	−2.98173	+	5.16450i	−0.335471	+	0.581052i	−0.983575	−	0.180499i	$-0.942229\pi$
$79$	−2.98173	+	5.16450i	−0.335471	+	0.581052i	0.648105	+	0.761551i	$0.275562\pi$
$80$	−4.01192	+	4.55203i	−0.448546	+	0.508932i
$81$		0			0
$82$	−1.68465	+	0.972633i	−0.186038	+	0.107409i
$83$		−	13.8603i		−	1.52136i	−0.649124	−	0.760682i	$-0.724864\pi$
$83$		−	13.8603i		−	1.52136i	0.649124	−	0.760682i	$-0.275136\pi$
$84$		0			0
$85$	−4.28159	−	3.77357i	−0.464404	−	0.409301i
$86$	−2.38866	−	4.13729i	−0.257576	−	0.446135i
$87$		0			0
$88$			1.27185i			0.135580i
$89$	−7.98173	−	13.8248i	−0.846061	−	1.46542i	−0.884696	−	0.466168i	$-0.845634\pi$
$89$	−7.98173	−	13.8248i	−0.846061	−	1.46542i	0.0386349	−	0.999253i	$-0.487699\pi$
$90$		0			0
$91$	−2.41142	−	4.17670i	−0.252786	−	0.437837i
$92$	−0.934393	−	0.539472i	−0.0974172	−	0.0562439i
$93$		0			0
$94$	4.96345			0.511941
$95$	−1.64634	−	9.60675i	−0.168911	−	0.985631i
$96$		0			0
$97$	14.4643	+	8.35099i	1.46863	+	0.847915i	0.999382	−	0.0351512i	$-0.0111913\pi$
$97$	14.4643	+	8.35099i	1.46863	+	0.847915i	0.469249	+	0.883066i	$0.344525\pi$
$98$	2.29605	+	1.32563i	0.231936	+	0.133908i
$99$		0			0
$100$	−1.11648	−	8.81621i	−0.111648	−	0.881621i
$101$	7.01362	+	12.1479i	0.697881	+	1.20877i	0.969200	+	0.246276i	$0.0792071\pi$
$101$	7.01362	+	12.1479i	0.697881	+	1.20877i	−0.271318	+	0.962490i	$0.587460\pi$
$102$		0			0
$103$			3.55382i			0.350169i	0.984553	+	0.175084i	$0.0560198\pi$
$103$			3.55382i			0.350169i	−0.984553	+	0.175084i	$0.943980\pi$
$104$	−3.65685	−	6.33385i	−0.358584	−	0.621085i
$105$		0			0
$106$	−2.35025			−0.228276
$107$			3.63127i			0.351048i	0.984475	+	0.175524i	$0.0561620\pi$
$107$			3.63127i			0.351048i	−0.984475	+	0.175524i	$0.943838\pi$
$108$		0			0
$109$	−3.11134	+	5.38899i	−0.298012	+	0.516172i	−0.975681	−	0.219195i	$-0.929657\pi$
$109$	−3.11134	+	5.38899i	−0.298012	+	0.516172i	0.677669	+	0.735367i	$0.262990\pi$
$110$	−0.564834	−	0.497815i	−0.0538548	−	0.0474648i
$111$		0			0
$112$	2.76218	+	1.59474i	0.261001	+	0.150689i
$113$			12.2707i			1.15433i	0.816626	+	0.577167i	$0.195842\pi$
$113$			12.2707i			1.15433i	−0.816626	+	0.577167i	$0.804158\pi$
$114$		0			0
$115$	1.28646	−	0.433161i	0.119963	−	0.0403925i
$116$	0.763705	−	1.32278i	0.0709082	−	0.122817i
$117$		0			0
$118$	2.55411	−	1.47462i	0.235125	−	0.135750i
$119$	−1.50000	+	2.59808i	−0.137505	+	0.238165i
$120$		0			0
$121$	−10.4909			−0.953715
$122$			2.14927i			0.194585i
$123$		0			0
$124$	−2.22978	−	3.86209i	−0.200240	−	0.346826i
$125$	9.24992	+	6.28005i	0.827338	+	0.561705i
$126$		0			0
$127$	−1.86879	+	1.07894i	−0.165828	+	0.0957408i	−0.580617	−	0.814177i	$-0.697189\pi$
$127$	−1.86879	+	1.07894i	−0.165828	+	0.0957408i	0.414789	+	0.909918i	$0.363855\pi$
$128$	9.67592	+	5.58639i	0.855239	+	0.493772i
$129$		0			0
$130$	4.24422	+	0.855111i	0.372242	+	0.0749982i
$131$	−8.77471	+	15.1982i	−0.766650	+	1.32788i	0.172720	+	0.984971i	$0.444744\pi$
$131$	−8.77471	+	15.1982i	−0.766650	+	1.32788i	−0.939370	+	0.342906i	$0.888589\pi$
$132$		0			0
$133$	−4.77943	+	1.84574i	−0.414429	+	0.160046i
$134$	2.44535			0.211246
$135$		0			0
$136$	−2.27471	+	3.93991i	−0.195055	+	0.337845i
$137$	4.39469	−	2.53728i	0.375464	−	0.216774i	−0.300379	−	0.953820i	$-0.597113\pi$
$137$	4.39469	−	2.53728i	0.375464	−	0.216774i	0.675843	+	0.737046i	$0.263780\pi$
$138$		0			0
$139$	2.99086	+	5.18033i	0.253682	+	0.439390i	0.964537	−	0.263949i	$-0.0850251\pi$
$139$	2.99086	+	5.18033i	0.253682	+	0.439390i	−0.710855	+	0.703339i	$0.751692\pi$
$140$	−4.42708	+	1.49063i	−0.374156	+	0.125981i
$141$		0			0
$142$	−5.38122	+	3.10685i	−0.451582	+	0.260721i
$143$	−2.53551	+	1.46388i	−0.212030	+	0.122416i
$144$		0			0
$145$	0.613205	+	1.82118i	0.0509239	+	0.151241i
$146$	2.92056	+	5.05855i	0.241707	+	0.418649i
$147$		0			0
$148$	−14.4404	+	8.33718i	−1.18699	+	0.685312i
$149$	−4.80008	+	8.31399i	−0.393238	+	0.681108i	−0.992875	−	0.119164i	$-0.961979\pi$
$149$	−4.80008	+	8.31399i	−0.393238	+	0.681108i	0.599636	+	0.800273i	$0.295312\pi$
$150$		0			0
$151$	7.53638			0.613302			0.306651	−	0.951822i	$-0.400792\pi$
$151$	7.53638			0.613302			0.306651	+	0.951822i	$0.400792\pi$
$152$	−7.24787	+	2.79901i	−0.587880	+	0.227029i
$153$		0			0
$154$	−0.197882	+	0.342742i	−0.0159458	+	0.0276190i
$155$	5.50008	+	1.10814i	0.441777	+	0.0890077i
$156$		0			0
$157$	−8.53560	−	4.92803i	−0.681215	−	0.393300i	0.119098	−	0.992883i	$-0.462000\pi$
$157$	−8.53560	−	4.92803i	−0.681215	−	0.393300i	−0.800313	+	0.599583i	$0.795333\pi$
$158$	−2.43705	+	1.40703i	−0.193881	+	0.111937i
$159$		0			0
$160$	−10.2682	+	3.45737i	−0.811772	+	0.273329i
$161$	−0.356769	−	0.617942i	−0.0281173	−	0.0487007i
$162$		0			0
$163$		−	0.0688234i		−	0.00539067i	−0.999996	−	0.00269533i	$-0.999142\pi$
$163$		−	0.0688234i		−	0.00539067i	0.999996	−	0.00269533i	$-0.000857952\pi$
$164$	7.32674			0.572122
$165$		0			0
$166$	3.27022	−	5.66419i	0.253819	−	0.439627i
$167$	−14.4143	+	8.32212i	−1.11542	+	0.643985i	−0.940227	−	0.340550i	$-0.889387\pi$
$167$	−14.4143	+	8.32212i	−1.11542	+	0.643985i	−0.175189	+	0.984535i	$0.556054\pi$
$168$		0			0
$169$	1.91794	−	3.32197i	0.147534	−	0.255536i
$170$	−0.859386	−	2.55233i	−0.0659119	−	0.195755i
$171$		0			0
$172$			17.9935i			1.37200i
$173$	10.5097	+	6.06778i	0.799038	+	0.461325i	0.843135	−	0.537702i	$-0.180708\pi$
$173$	10.5097	+	6.06778i	0.799038	+	0.461325i	−0.0440965	+	0.999027i	$0.514041\pi$
$174$		0			0
$175$	2.27577	−	5.41848i	0.172032	−	0.409598i
$176$	0.968106	−	1.67681i	0.0729737	−	0.126394i
$177$		0			0
$178$		−	7.53290i		−	0.564614i
$179$	11.7538			0.878522			0.439261	−	0.898360i	$-0.355240\pi$
$179$	11.7538			0.878522			0.439261	+	0.898360i	$0.355240\pi$
$180$		0			0
$181$	4.41794	+	7.65210i	0.328383	+	0.568776i	0.982191	−	0.187884i	$-0.0601631\pi$
$181$	4.41794	+	7.65210i	0.328383	+	0.568776i	−0.653808	+	0.756660i	$0.726830\pi$
$182$		−	2.27582i		−	0.168695i
$183$		0			0
$184$	−0.541030	−	0.937092i	−0.0398853	−	0.0690833i
$185$	4.14335	−	20.5649i	0.304625	−	1.51196i
$186$		0			0
$187$	1.57719	+	0.910591i	0.115336	+	0.0665890i
$188$	−16.1900	−	9.34730i	−1.18078	−	0.681722i
$189$		0			0
$190$	1.59384	−	4.31436i	0.115629	−	0.312997i
$191$	−14.2447			−1.03071			−0.515355	−	0.856977i	$-0.672340\pi$
$191$	−14.2447			−1.03071			−0.515355	+	0.856977i	$0.672340\pi$
$192$		0			0
$193$	16.8924	+	9.75283i	1.21594	+	0.702024i	0.964047	−	0.265731i	$-0.0856133\pi$
$193$	16.8924	+	9.75283i	1.21594	+	0.702024i	0.251894	+	0.967755i	$0.418947\pi$
$194$	3.94070	+	6.82549i	0.282926	+	0.490041i
$195$		0			0
$196$	−4.99290	−	8.64795i	−0.356636	−	0.617711i
$197$			4.33232i			0.308665i	0.988019	+	0.154332i	$0.0493226\pi$
$197$			4.33232i			0.308665i	−0.988019	+	0.154332i	$0.950677\pi$
$198$		0			0
$199$	−6.31574	−	10.9392i	−0.447711	−	0.775458i	0.550526	−	0.834818i	$-0.314427\pi$
$199$	−6.31574	−	10.9392i	−0.447711	−	0.775458i	−0.998237	+	0.0593602i	$0.981094\pi$
$200$	3.45115	−	8.21697i	0.244033	−	0.581027i
$201$		0			0
$202$			6.61923i			0.465727i
$203$	0.874790	−	0.505060i	0.0613983	−	0.0354483i
$204$		0			0
$205$	−6.09481	+	6.91533i	−0.425680	+	0.482988i
$206$	−0.838496	+	1.45232i	−0.0584208	+	0.101188i
$207$		0			0
$208$			11.1341i			0.772009i
$209$	1.12047	+	2.90140i	0.0775048	+	0.200694i
$210$		0			0
$211$	−11.1223	+	19.2645i	−0.765694	+	1.32622i	0.174186	+	0.984713i	$0.444271\pi$
$211$	−11.1223	+	19.2645i	−0.765694	+	1.32622i	−0.939879	+	0.341507i	$0.889063\pi$
$212$	7.66614	+	4.42605i	0.526512	+	0.303982i
$213$		0			0
$214$	−0.856769	+	1.48397i	−0.0585675	+	0.101442i
$215$	−16.9832	−	14.9681i	−1.15824	−	1.02081i
$216$		0			0
$217$		−	2.94923i		−	0.200207i
$218$	−2.54298	+	1.46819i	−0.172232	+	0.0994383i
$219$		0			0
$220$	0.904901	+	2.68750i	0.0610084	+	0.181191i
$221$	−10.4726			−0.704463
$222$		0			0
$223$	11.7974	+	6.81125i	0.790015	+	0.456115i	0.839968	−	0.542636i	$-0.182574\pi$
$223$	11.7974	+	6.81125i	0.790015	+	0.456115i	−0.0499529	+	0.998752i	$0.515907\pi$
$224$	2.84763	+	4.93224i	0.190265	+	0.329549i
$225$		0			0
$226$	−2.89518	+	5.01460i	−0.192585	+	0.333566i
$227$		−	6.58913i		−	0.437336i	−0.975799	−	0.218668i	$-0.929829\pi$
$227$		−	6.58913i		−	0.437336i	0.975799	−	0.218668i	$-0.0701711\pi$
$228$		0			0
$229$	0.585962			0.0387215			0.0193607	−	0.999813i	$-0.493837\pi$
$229$	0.585962			0.0387215			0.0193607	+	0.999813i	$0.493837\pi$
$230$	0.627931	+	0.126513i	0.0414045	+	0.00834204i
$231$		0			0
$232$	1.32660	−	0.765910i	0.0870953	−	0.0502845i
$233$	−6.19855	−	3.57873i	−0.406080	−	0.234451i	0.283024	−	0.959113i	$-0.408662\pi$
$233$	−6.19855	−	3.57873i	−0.406080	−	0.234451i	−0.689104	+	0.724662i	$0.741996\pi$
$234$		0			0
$235$	22.2902	−	7.50527i	1.45405	−	0.489590i
$236$	−11.1081			−0.723078
$237$		0			0
$238$	−1.22599	+	0.707826i	−0.0794691	+	0.0458815i
$239$	3.65498			0.236421			0.118211	−	0.992989i	$-0.462284\pi$
$239$	3.65498			0.236421			0.118211	+	0.992989i	$0.462284\pi$
$240$		0			0
$241$	−8.63148	−	14.9502i	−0.556002	−	0.963024i	−0.997825	−	0.0659218i	$-0.979001\pi$
$241$	−8.63148	−	14.9502i	−0.556002	−	0.963024i	0.441822	−	0.897103i	$-0.354332\pi$
$242$	−4.28723	−	2.47523i	−0.275594	−	0.159114i
$243$		0			0
$244$	4.04755	−	7.01056i	0.259118	−	0.448805i
$245$	12.3157	+	2.48133i	0.786823	+	0.158527i
$246$		0			0
$247$	−13.9221	−	11.2274i	−0.885845	−	0.714385i
$248$		−	4.47243i		−	0.284000i
$249$		0			0
$250$	2.29837	+	4.74887i	0.145362	+	0.300345i
$251$	−9.70702	−	16.8130i	−0.612702	−	1.06123i	−0.990783	−	0.135458i	$-0.956749\pi$
$251$	−9.70702	−	16.8130i	−0.612702	−	1.06123i	0.378082	−	0.925772i	$-0.376584\pi$
$252$		0			0
$253$	−0.375128	+	0.216580i	−0.0235841	+	0.0136163i
$254$	−1.01827			−0.0638921
$255$		0			0
$256$	−0.504485	−	0.873793i	−0.0315303	−	0.0546121i
$257$	12.0316	−	6.94643i	0.750509	−	0.433306i	−0.0753689	−	0.997156i	$-0.524013\pi$
$257$	12.0316	−	6.94643i	0.750509	−	0.433306i	0.825878	+	0.563849i	$0.190680\pi$
$258$		0			0
$259$	−11.0272			−0.685199
$260$	−12.2336	−	10.7820i	−0.758695	−	0.668674i
$261$		0			0
$262$	−7.17180	+	4.14064i	−0.443076	+	0.255810i
$263$	12.9803	+	7.49417i	0.800399	+	0.462110i	0.843611	−	0.536955i	$-0.180426\pi$
$263$	12.9803	+	7.49417i	0.800399	+	0.462110i	−0.0432118	+	0.999066i	$0.513759\pi$
$264$		0			0
$265$	−10.5547	+	3.55382i	−0.648367	+	0.218310i
$266$	−2.38866	−	0.373382i	−0.146458	−	0.0228935i
$267$		0			0
$268$	−7.97633	−	4.60514i	−0.487232	−	0.281304i
$269$	−9.68613	+	16.7769i	−0.590574	+	1.02290i	0.403582	+	0.914944i	$0.367765\pi$
$269$	−9.68613	+	16.7769i	−0.590574	+	1.02290i	−0.994155	+	0.107960i	$0.965568\pi$
$270$		0			0
$271$	−5.95897	+	10.3212i	−0.361982	+	0.626971i	−0.988287	−	0.152607i	$-0.951233\pi$
$271$	−5.95897	+	10.3212i	−0.361982	+	0.626971i	0.626305	+	0.779578i	$0.284566\pi$
$272$	5.99795	−	3.46292i	0.363679	−	0.209970i
$273$		0			0
$274$	2.39460			0.144663
$275$	−3.28934	−	1.38153i	−0.198355	−	0.0833095i
$276$		0			0
$277$			10.9824i			0.659866i	0.944004	+	0.329933i	$0.107026\pi$
$277$			10.9824i			0.659866i	−0.944004	+	0.329933i	$0.892974\pi$
$278$			2.82268i			0.169293i
$279$		0			0
$280$	−4.59250	−	0.925281i	−0.274454	−	0.0552961i
$281$	7.32488	+	12.6871i	0.436965	+	0.756846i	0.997454	−	0.0713160i	$-0.0227199\pi$
$281$	7.32488	+	12.6871i	0.436965	+	0.756846i	−0.560488	+	0.828162i	$0.689387\pi$
$282$		0			0
$283$	−16.3927	−	9.46435i	−0.974447	−	0.562597i	−0.0738576	−	0.997269i	$-0.523531\pi$
$283$	−16.3927	−	9.46435i	−0.974447	−	0.562597i	−0.900589	+	0.434672i	$0.856864\pi$
$284$	23.4036			1.38875
$285$		0			0
$286$	−1.38156			−0.0816934
$287$	4.19623	+	2.42270i	0.247696	+	0.143007i
$288$		0			0
$289$	−5.24281	−	9.08082i	−0.308401	−	0.534166i
$290$	−0.179099	+	0.888931i	−0.0105170	+	0.0521998i
$291$		0			0
$292$		−	22.0002i		−	1.28747i
$293$			5.59625i			0.326937i	0.986549	+	0.163468i	$0.0522681\pi$
$293$			5.59625i			0.326937i	−0.986549	+	0.163468i	$0.947732\pi$
$294$		0			0
$295$	9.24039	−	10.4844i	0.537996	−	0.610425i
$296$	−16.7225			−0.971976
$297$		0			0
$298$	−3.92324	+	2.26508i	−0.227267	+	0.131213i
$299$	1.24543	−	2.15715i	0.0720252	−	0.124751i
$300$		0			0
$301$	−5.94983	+	10.3054i	−0.342943	+	0.593994i
$302$	3.07984	+	1.77815i	0.177225	+	0.102321i
$303$		0			0
$304$	11.6861	+	1.82671i	0.670245	+	0.104769i
$305$	3.24992	+	9.65206i	0.186090	+	0.552675i
$306$		0			0
$307$	17.8678	+	10.3160i	1.01977	+	0.588764i	0.914037	−	0.405631i	$-0.132948\pi$
$307$	17.8678	+	10.3160i	1.01977	+	0.588764i	0.105732	+	0.994395i	$0.466282\pi$
$308$	1.29092	−	0.745314i	0.0735571	−	0.0424682i
$309$		0			0
$310$	1.98622	+	1.75055i	0.112810	+	0.0994248i
$311$	24.6587			1.39827			0.699134	−	0.714991i	$-0.253569\pi$
$311$	24.6587			1.39827			0.699134	+	0.714991i	$0.253569\pi$
$312$		0			0
$313$	3.02985	−	1.74928i	0.171257	−	0.0988753i	−0.411921	−	0.911219i	$-0.635142\pi$
$313$	3.02985	−	1.74928i	0.171257	−	0.0988753i	0.583178	+	0.812344i	$0.301809\pi$
$314$	−2.32546	−	4.02781i	−0.131233	−	0.227303i
$315$		0			0
$316$	10.5990			0.596240
$317$	27.1680	−	15.6854i	1.52590	−	0.880982i	0.526377	−	0.850251i	$-0.323550\pi$
$317$	27.1680	−	15.6854i	1.52590	−	0.880982i	0.999528	−	0.0307305i	$-0.00978335\pi$
$318$		0			0
$319$	−0.306602	−	0.531051i	−0.0171664	−	0.0297331i
$320$	6.88429	+	1.38702i	0.384843	+	0.0775370i
$321$		0			0
$322$		−	0.336707i		−	0.0187639i
$323$	−1.71818	+	10.9919i	−0.0956024	+	0.611603i
$324$		0			0
$325$	20.3532	−	2.57752i	1.12899	−	0.142975i
$326$	0.0162383	−	0.0281256i	0.000899358	−	0.00155773i
$327$		0			0
$328$	6.36347	+	3.67395i	0.351364	+	0.202860i
$329$	−6.18164	−	10.7069i	−0.340805	−	0.590292i
$330$		0			0
$331$	35.7497			1.96498			0.982492	−	0.186305i	$-0.0596512\pi$
$331$	35.7497			1.96498			0.982492	+	0.186305i	$0.0596512\pi$
$332$	−21.3339	+	12.3171i	−1.17085	+	0.675990i
$333$		0			0
$334$	−7.85415			−0.429760
$335$	10.9817	−	3.69762i	0.599996	−	0.202023i
$336$		0			0
$337$	22.9403	+	13.2446i	1.24964	+	0.721480i	0.971038	−	0.238927i	$-0.0767956\pi$
$337$	22.9403	+	13.2446i	1.24964	+	0.721480i	0.278602	+	0.960407i	$0.410129\pi$
$338$	1.56758	−	0.905045i	0.0852653	−	0.0492279i
$339$		0			0
$340$	−2.00342	+	9.94370i	−0.108651	+	0.539273i
$341$	−1.79036			−0.0969536
$342$		0			0
$343$		−	14.8317i		−	0.800836i
$344$	−9.02276	+	15.6279i	−0.486474	+	0.842599i
$345$		0			0
$346$	2.86329	+	4.95936i	0.153931	+	0.266617i
$347$	−29.7392	−	17.1699i	−1.59648	−	0.921729i	−0.992158	−	0.124990i	$-0.960110\pi$
$347$	−29.7392	−	17.1699i	−1.59648	−	0.921729i	−0.604323	−	0.796739i	$-0.706556\pi$
$348$		0			0
$349$	21.4308			1.14717			0.573583	−	0.819148i	$-0.305553\pi$
$349$	21.4308			1.14717			0.573583	+	0.819148i	$0.305553\pi$
$350$	2.20847	−	1.67738i	0.118048	−	0.0896599i
$351$		0			0
$352$	2.99417	−	1.72869i	0.159590	−	0.0921393i
$353$		−	19.5659i		−	1.04139i	−0.853744	−	0.520693i	$-0.825674\pi$
$353$		−	19.5659i		−	1.04139i	0.853744	−	0.520693i	$-0.174326\pi$
$354$		0			0
$355$	−19.4684	+	22.0894i	−1.03328	+	1.17238i
$356$	−14.1861	+	24.5711i	−0.751863	+	1.30227i
$357$		0			0
$358$	4.80335	+	2.77322i	0.253865	+	0.146569i
$359$	8.23630	−	14.2657i	0.434695	−	0.752914i	−0.562576	−	0.826746i	$-0.690189\pi$
$359$	8.23630	−	14.2657i	0.434695	−	0.752914i	0.997271	+	0.0738319i	$0.0235228\pi$
$360$		0			0
$361$	−14.0683	+	12.7704i	−0.740435	+	0.672128i
$362$			4.16951i			0.219144i
$363$		0			0
$364$	−4.28588	+	7.42336i	−0.224641	+	0.389090i
$365$	20.7649	+	18.3011i	1.08688	+	0.957922i
$366$		0			0
$367$	−11.0286	+	6.36735i	−0.575687	+	0.332373i	−0.759418	−	0.650603i	$-0.774516\pi$
$367$	−11.0286	+	6.36735i	−0.575687	+	0.332373i	0.183730	+	0.982977i	$0.441183\pi$
$368$			1.64728i			0.0858705i
$369$		0			0
$370$	6.54535	−	7.42653i	0.340277	−	0.386087i
$371$	2.92708	+	5.06984i	0.151966	+	0.263213i
$372$		0			0
$373$		−	19.3342i		−	1.00109i	−0.865711	−	0.500544i	$-0.833133\pi$
$373$		−	19.3342i		−	1.00109i	0.865711	−	0.500544i	$-0.166867\pi$
$374$	0.429693	+	0.744250i	0.0222189	+	0.0384843i
$375$		0			0
$376$	−9.37429	−	16.2368i	−0.483442	−	0.837346i
$377$	3.05377	+	1.76310i	0.157277	+	0.0908041i
$378$		0			0
$379$	−9.85789			−0.506366			−0.253183	−	0.967418i	$-0.581477\pi$
$379$	−9.85789			−0.506366			−0.253183	+	0.967418i	$0.581477\pi$
$380$	−13.3238	+	11.0712i	−0.683494	+	0.567941i
$381$		0			0
$382$	−5.82128	−	3.36092i	−0.297843	−	0.171959i
$383$	−17.6091	−	10.1666i	−0.899784	−	0.519490i	−0.0226536	−	0.999743i	$-0.507211\pi$
$383$	−17.6091	−	10.1666i	−0.899784	−	0.519490i	−0.877130	+	0.480253i	$0.840545\pi$
$384$		0			0
$385$	−0.370400	+	1.83843i	−0.0188773	+	0.0936950i
$386$	4.60220	+	7.97125i	0.234246	+	0.405726i
$387$		0			0
$388$		−	29.6849i		−	1.50702i
$389$	0.502617	+	0.870559i	0.0254837	+	0.0441391i	0.878486	−	0.477768i	$-0.158554\pi$
$389$	0.502617	+	0.870559i	0.0254837	+	0.0441391i	−0.853002	+	0.521907i	$0.825221\pi$
$390$		0			0
$391$	−1.54942			−0.0783574
$392$		−	10.0146i		−	0.505816i
$393$		0			0
$394$	−1.02217	+	1.77046i	−0.0514964	+	0.0891944i
$395$	−8.81686	+	10.0038i	−0.443625	+	0.503348i
$396$		0			0
$397$	−8.54093	−	4.93111i	−0.428657	−	0.247485i	0.270117	−	0.962827i	$-0.412937\pi$
$397$	−8.54093	−	4.93111i	−0.428657	−	0.247485i	−0.698774	+	0.715342i	$0.746271\pi$
$398$		−	5.96059i		−	0.298777i
$399$		0			0
$400$	−10.8046	+	8.20631i	−0.540228	+	0.410315i
$401$	14.9159	−	25.8351i	0.744865	−	1.29014i	−0.205393	−	0.978680i	$-0.565847\pi$
$401$	14.9159	−	25.8351i	0.744865	−	1.29014i	0.950258	−	0.311464i	$-0.100819\pi$
$402$		0			0
$403$	8.91606	−	5.14769i	0.444140	−	0.256425i
$404$	12.4655	−	21.5909i	0.620181	−	1.07419i
$405$		0			0
$406$	0.476660			0.0236562
$407$			6.69420i			0.331819i
$408$		0			0
$409$	13.8221	+	23.9406i	0.683458	+	1.18378i	0.973919	+	0.226898i	$0.0728583\pi$
$409$	13.8221	+	23.9406i	0.683458	+	1.18378i	−0.290460	+	0.956887i	$0.593808\pi$
$410$	−4.12234	+	1.38802i	−0.203588	+	0.0685495i
$411$		0			0
$412$	5.47008	−	3.15815i	0.269491	−	0.155591i
$413$	−6.36194	−	3.67307i	−0.313051	−	0.180740i
$414$		0			0
$415$	6.12127	−	30.3820i	0.300481	−	1.49140i
$416$	−9.94070	+	17.2178i	−0.487383	+	0.844172i
$417$		0			0
$418$	−0.226666	+	1.45006i	−0.0110866	+	0.0709249i
$419$	−11.2902			−0.551562			−0.275781	−	0.961220i	$-0.588936\pi$
$419$	−11.2902			−0.551562			−0.275781	+	0.961220i	$0.588936\pi$
$420$		0			0
$421$	−2.27471	+	3.93991i	−0.110863	+	0.192019i	−0.916118	−	0.400908i	$-0.868695\pi$
$421$	−2.27471	+	3.93991i	−0.110863	+	0.192019i	0.805256	+	0.592928i	$0.202028\pi$
$422$	−9.09059	+	5.24845i	−0.442523	+	0.255491i
$423$		0			0
$424$	4.43883	+	7.68828i	0.215569	+	0.373376i
$425$	−7.71877	−	10.1627i	−0.374415	−	0.492962i
$426$		0			0
$427$	4.63629	−	2.67676i	0.224366	−	0.129538i
$428$	5.58929	−	3.22698i	0.270168	−	0.155982i
$429$		0			0
$430$	−3.40880	−	10.1239i	−0.164387	−	0.488220i
$431$	16.4517	+	28.4952i	0.792451	+	1.37256i	0.924445	+	0.381314i	$0.124528\pi$
$431$	16.4517	+	28.4952i	0.792451	+	1.37256i	−0.131995	+	0.991250i	$0.542138\pi$
$432$		0			0
$433$	−19.3204	+	11.1547i	−0.928481	+	0.536059i	−0.886331	−	0.463052i	$-0.846754\pi$
$433$	−19.3204	+	11.1547i	−0.928481	+	0.536059i	−0.0421503	+	0.999111i	$0.513421\pi$
$434$	0.695848	−	1.20524i	0.0334018	−	0.0578536i
$435$		0			0
$436$	11.0597			0.529664
$437$	−2.05978	−	1.66110i	−0.0985325	−	0.0794611i
$438$		0			0
$439$	2.85287	−	4.94131i	0.136160	−	0.235836i	−0.789880	−	0.613261i	$-0.789857\pi$
$439$	2.85287	−	4.94131i	0.136160	−	0.235836i	0.926040	+	0.377425i	$0.123191\pi$
$440$	−0.561702	+	2.78793i	−0.0267781	+	0.132909i
$441$		0			0
$442$	−4.27976	−	2.47092i	−0.203568	−	0.117530i
$443$	10.0265	−	5.78881i	0.476374	−	0.275034i	−0.242530	−	0.970144i	$-0.577977\pi$
$443$	10.0265	−	5.78881i	0.476374	−	0.275034i	0.718904	+	0.695109i	$0.244644\pi$
$444$		0			0
$445$	−11.3905	−	33.8292i	−0.539963	−	1.60366i
$446$	3.21412	+	5.56702i	0.152193	+	0.263606i
$447$		0			0
$448$		−	3.69147i		−	0.174406i
$449$	−25.4726			−1.20213			−0.601063	−	0.799202i	$-0.705256\pi$
$449$	−25.4726			−1.20213			−0.601063	+	0.799202i	$0.705256\pi$
$450$		0			0
$451$	1.47072	−	2.54737i	0.0692537	−	0.119951i
$452$	18.8872	−	10.9046i	0.888381	−	0.512907i
$453$		0			0
$454$	1.55465	−	2.69274i	0.0729634	−	0.126376i
$455$	−3.44128	−	10.2204i	−0.161330	−	0.479140i
$456$		0			0
$457$		−	6.92830i		−	0.324092i	−0.986783	−	0.162046i	$-0.948191\pi$
$457$		−	6.92830i		−	0.324092i	0.986783	−	0.162046i	$-0.0518094\pi$
$458$	0.239461	+	0.138253i	0.0111893	+	0.00646014i
$459$		0			0
$460$	−1.80996	−	1.59520i	−0.0843896	−	0.0743766i
$461$	16.2473	−	28.1411i	0.756712	−	1.31066i	−0.187806	−	0.982206i	$-0.560138\pi$
$461$	16.2473	−	28.1411i	0.756712	−	1.31066i	0.944519	−	0.328458i	$-0.106529\pi$
$462$		0			0
$463$		−	21.5062i		−	0.999477i	−0.866176	−	0.499738i	$-0.833429\pi$
$463$		−	21.5062i		−	0.999477i	0.866176	−	0.499738i	$-0.166571\pi$
$464$	−2.33198			−0.108259
$465$		0			0
$466$	−1.68875	−	2.92499i	−0.0782296	−	0.135498i
$467$			16.9509i			0.784392i	0.919882	+	0.392196i	$0.128285\pi$
$467$			16.9509i			0.784392i	−0.919882	+	0.392196i	$0.871715\pi$
$468$		0			0
$469$	−3.04551	−	5.27499i	−0.140629	−	0.243576i
$470$	10.8800	+	2.19206i	0.501857	+	0.101112i
$471$		0			0
$472$	−9.64771	−	5.57011i	−0.444072	−	0.256385i
$473$	6.25601	+	3.61191i	0.287652	+	0.166076i
$474$		0			0
$475$	0.633930	−	21.7853i	0.0290867	−	0.999577i
$476$	5.33198			0.244391
$477$		0			0
$478$	1.49366	+	0.862364i	0.0683183	+	0.0394436i
$479$	−4.42894	−	7.67115i	−0.202364	−	0.350504i	0.746926	−	0.664907i	$-0.231529\pi$
$479$	−4.42894	−	7.67115i	−0.202364	−	0.350504i	−0.949290	+	0.314403i	$0.898196\pi$
$480$		0			0
$481$	−19.2473	−	33.3373i	−0.877601	−	1.52005i
$482$		−	8.14611i		−	0.371045i
$483$		0			0
$484$	9.32284	+	16.1476i	0.423765	+	0.733983i
$485$	28.0180	+	24.6936i	1.27223	+	1.12128i
$486$		0			0
$487$		−	30.0628i		−	1.36227i	−0.732156	−	0.681137i	$-0.761486\pi$
$487$		−	30.0628i		−	1.36227i	0.732156	−	0.681137i	$-0.238514\pi$
$488$	7.03081	−	4.05924i	0.318270	−	0.183753i
$489$		0			0
$490$	4.44754	+	3.91983i	0.200919	+	0.177080i
$491$	1.55017	−	2.68497i	0.0699580	−	0.121171i	−0.828925	−	0.559360i	$-0.811047\pi$
$491$	1.55017	−	2.68497i	0.0699580	−	0.121171i	0.898883	+	0.438190i	$0.144380\pi$
$492$		0			0
$493$		−	2.19343i		−	0.0987873i
$494$	−3.04045	−	7.87306i	−0.136796	−	0.354226i
$495$		0			0
$496$	−3.40432	+	5.89645i	−0.152858	+	0.264759i
$497$	13.4039	+	7.73874i	0.601246	+	0.347130i
$498$		0			0
$499$	16.0696	−	27.8333i	0.719372	−	1.24599i	−0.241877	−	0.970307i	$-0.577763\pi$
$499$	16.0696	−	27.8333i	0.719372	−	1.24599i	0.961249	−	0.275682i	$-0.0889037\pi$
$500$	1.44626	−	19.8184i	0.0646785	−	0.886306i
$501$		0			0
$502$		−	9.16117i		−	0.408883i
$503$	−7.29040	+	4.20911i	−0.325063	+	0.187675i	−0.653647	−	0.756800i	$-0.726762\pi$
$503$	−7.29040	+	4.20911i	−0.325063	+	0.187675i	0.328584	+	0.944475i	$0.393429\pi$
$504$		0			0
$505$	10.0090	+	29.7261i	0.445393	+	1.32279i
$506$	−0.204402			−0.00908676
$507$		0			0
$508$	3.32144	+	1.91764i	0.147365	+	0.0850813i
$509$	−10.1725	−	17.6193i	−0.450888	−	0.780962i	0.547553	−	0.836771i	$-0.315559\pi$
$509$	−10.1725	−	17.6193i	−0.450888	−	0.780962i	−0.998441	+	0.0558093i	$0.982226\pi$
$510$		0			0
$511$	7.27471	−	12.6002i	0.321814	−	0.557398i
$512$		−	22.8217i		−	1.00859i
$513$		0			0
$514$	6.55582			0.289165
$515$	−1.56951	+	7.79006i	−0.0691611	+	0.343271i
$516$		0			0
$517$	−6.49975	+	3.75263i	−0.285859	+	0.165041i
$518$	−4.50643	−	2.60179i	−0.198001	−	0.114316i
$519$		0			0
$520$	−5.21861	−	15.4990i	−0.228851	−	0.679674i
$521$	−15.3502			−0.672507			−0.336253	−	0.941772i	$-0.609160\pi$
$521$	−15.3502			−0.672507			−0.336253	+	0.941772i	$0.609160\pi$
$522$		0			0
$523$	11.4633	−	6.61835i	0.501256	−	0.289400i	−0.227976	−	0.973667i	$-0.573211\pi$
$523$	11.4633	−	6.61835i	0.501256	−	0.289400i	0.729232	+	0.684267i	$0.239878\pi$
$524$	31.1910			1.36259
$525$		0			0
$526$	3.53638	+	6.12519i	0.154193	+	0.267071i
$527$	−5.54614	−	3.20207i	−0.241594	−	0.139484i
$528$		0			0
$529$	−11.3157	+	19.5994i	−0.491989	+	0.852149i
$530$	−5.15180	−	1.03797i	−0.223780	−	0.0450864i
$531$		0			0
$532$	7.08827	+	5.71630i	0.307316	+	0.247833i
$533$			16.9146i			0.732653i
$534$		0			0
$535$	−1.60372	+	7.95982i	−0.0693348	+	0.344133i
$536$	−4.61844	−	7.99937i	−0.199486	−	0.345520i
$537$		0			0
$538$	−7.91673	+	4.57073i	−0.341315	+	0.197058i
$539$	−4.00897			−0.172679
$540$		0			0
$541$	13.8704	+	24.0242i	0.596335	+	1.03288i	0.993357	+	0.115073i	$0.0367102\pi$
$541$	13.8704	+	24.0242i	0.596335	+	1.03288i	−0.397022	+	0.917809i	$0.629956\pi$
$542$	−4.87043	+	2.81194i	−0.209203	+	0.120783i
$543$		0			0
$544$	12.3670			0.530232
$545$	−9.20011	+	10.4387i	−0.394090	+	0.447144i
$546$		0			0
$547$	−14.7745	+	8.53008i	−0.631714	+	0.364720i	−0.781415	−	0.624011i	$-0.785502\pi$
$547$	−14.7745	+	8.53008i	−0.631714	+	0.364720i	0.149702	+	0.988731i	$0.452169\pi$
$548$	−7.81080	−	4.50957i	−0.333661	−	0.192639i
$549$		0			0
$550$	−1.01827	−	1.34068i	−0.0434193	−	0.0571666i
$551$	2.35153	−	2.91593i	0.100179	−	0.124223i
$552$		0			0
$553$	6.07035	+	3.50472i	0.258137	+	0.149036i
$554$	−2.59120	+	4.48808i	−0.110089	+	0.190680i
$555$		0			0
$556$	5.31574	−	9.20713i	0.225438	−	0.390469i
$557$	−22.9856	+	13.2708i	−0.973932	+	0.562300i	−0.900433	−	0.434995i	$-0.856750\pi$
$557$	−22.9856	+	13.2708i	−0.973932	+	0.562300i	−0.0734992	+	0.997295i	$0.523417\pi$
$558$		0			0
$559$	−41.5401			−1.75696
$560$	5.35044	+	4.71560i	0.226098	+	0.199271i
$561$		0			0
$562$			6.91298i			0.291606i
$563$		−	35.5594i		−	1.49865i	−0.662203	−	0.749325i	$-0.730378\pi$
$563$		−	35.5594i		−	1.49865i	0.662203	−	0.749325i	$-0.269622\pi$
$564$		0			0
$565$	−5.41926	+	26.8977i	−0.227990	+	1.13160i
$566$	−4.46607	−	7.73546i	−0.187723	−	0.325146i
$567$		0			0
$568$	20.3266	+	11.7356i	0.852886	+	0.492414i
$569$	−14.9713			−0.627628			−0.313814	−	0.949485i	$-0.601607\pi$
$569$	−14.9713			−0.627628			−0.313814	+	0.949485i	$0.601607\pi$
$570$		0			0
$571$	5.92724			0.248047			0.124024	−	0.992279i	$-0.460420\pi$
$571$	5.92724			0.248047			0.124024	+	0.992279i	$0.460420\pi$
$572$	4.50643	+	2.60179i	0.188423	+	0.108786i
$573$		0			0
$574$	1.14323	+	1.98013i	0.0477175	+	0.0826492i
$575$	3.01125	−	0.381343i	0.125578	−	0.0159031i
$576$		0			0
$577$		−	14.5559i		−	0.605970i	−0.952995	−	0.302985i	$-0.902017\pi$
$577$		−	14.5559i		−	0.605970i	0.952995	−	0.302985i	$-0.0979832\pi$
$578$		−	4.94800i		−	0.205810i
$579$		0			0
$580$	2.25825	−	2.56227i	0.0937686	−	0.106392i
$581$	−16.2914			−0.675880
$582$		0			0
$583$	3.07770	−	1.77691i	0.127465	−	0.0735922i
$584$	11.0319	−	19.1078i	0.456503	−	0.790686i
$585$		0			0
$586$	−1.32039	+	2.28698i	−0.0545448	+	0.0944744i
$587$	17.8262	+	10.2919i	0.735765	+	0.424794i	0.820527	−	0.571607i	$-0.193680\pi$
$587$	17.8262	+	10.2919i	0.735765	+	0.424794i	−0.0847626	+	0.996401i	$0.527013\pi$
$588$		0			0
$589$	−3.94011	−	10.2027i	−0.162350	−	0.420395i
$590$	6.24992	−	2.10439i	0.257305	−	0.0866364i
$591$		0			0
$592$	22.0469	+	12.7288i	0.906124	+	0.523151i
$593$	12.4120	−	7.16609i	0.509701	−	0.294276i	−0.223010	−	0.974816i	$-0.571588\pi$
$593$	12.4120	−	7.16609i	0.509701	−	0.294276i	0.732711	+	0.680540i	$0.238255\pi$
$594$		0			0
$595$	−4.43545	+	5.03257i	−0.181836	+	0.206315i
$596$	17.0626			0.698912
$597$		0			0
$598$	1.01792	−	0.587699i	0.0416260	−	0.0240328i
$599$	−1.25008	−	2.16521i	−0.0510770	−	0.0884680i	0.839356	−	0.543581i	$-0.182932\pi$
$599$	−1.25008	−	2.16521i	−0.0510770	−	0.0884680i	−0.890434	+	0.455113i	$0.849599\pi$
$600$		0			0
$601$	14.5259			0.592524			0.296262	−	0.955107i	$-0.404260\pi$
$601$	14.5259			0.592524			0.296262	+	0.955107i	$0.404260\pi$
$602$	−4.86296	+	2.80763i	−0.198199	+	0.114430i
$603$		0			0
$604$	−6.69730	−	11.6001i	−0.272509	−	0.472000i
$605$	−22.9962	−	4.63319i	−0.934928	−	0.188366i
$606$		0			0
$607$			31.8704i			1.29358i	0.762669	+	0.646789i	$0.223889\pi$
$607$			31.8704i			1.29358i	−0.762669	+	0.646789i	$0.776111\pi$
$608$	16.4406	+	13.2584i	0.666754	+	0.537700i
$609$		0			0
$610$	−0.949204	+	4.71124i	−0.0384321	+	0.190752i
$611$	21.5793	−	37.3764i	0.873004	−	1.51209i
$612$		0			0
$613$	−17.3628	−	10.0244i	−0.701277	−	0.404882i	0.106546	−	0.994308i	$-0.466021\pi$
$613$	−17.3628	−	10.0244i	−0.701277	−	0.404882i	−0.807823	+	0.589425i	$0.799354\pi$
$614$	4.86794	+	8.43152i	0.196454	+	0.340268i
$615$		0			0
$616$	1.49493			0.0602325
$617$	−17.3914	+	10.0410i	−0.700153	+	0.404234i	−0.807404	−	0.589998i	$-0.799128\pi$
$617$	−17.3914	+	10.0410i	−0.700153	+	0.404234i	0.107251	+	0.994232i	$0.465795\pi$
$618$		0			0
$619$	−5.62217			−0.225974			−0.112987	−	0.993596i	$-0.536042\pi$
$619$	−5.62217			−0.225974			−0.112987	+	0.993596i	$0.536042\pi$
$620$	−3.18206	−	9.45053i	−0.127795	−	0.379542i
$621$		0			0
$622$	10.0771	+	5.81803i	0.404056	+	0.233282i
$623$	−16.2496	+	9.38171i	−0.651026	+	0.375870i
$624$		0			0
$625$	17.5025	+	17.8511i	0.700099	+	0.714046i
$626$	1.65092			0.0659839
$627$		0			0
$628$			17.5174i			0.699022i
$629$	−11.9726	+	20.7371i	−0.477378	+	0.826844i
$630$		0			0
$631$	2.42184	+	4.19475i	0.0964120	+	0.166990i	0.910197	−	0.414176i	$-0.135930\pi$
$631$	2.42184	+	4.19475i	0.0964120	+	0.166990i	−0.813785	+	0.581166i	$0.802597\pi$
$632$	9.20551	+	5.31481i	0.366176	+	0.211412i
$633$		0			0
$634$	14.8034			0.587918
$635$	−4.57292	+	1.53974i	−0.181471	+	0.0611025i
$636$		0			0
$637$	19.9648	−	11.5267i	0.791033	−	0.456703i
$638$		−	0.289361i		−	0.0114559i
$639$		0			0
$640$	18.7426	+	16.5188i	0.740868	+	0.652962i
$641$	−12.6503	+	21.9110i	−0.499658	+	0.865433i	−1.00000		0.000394734i	$-0.999874\pi$
$641$	−12.6503	+	21.9110i	−0.499658	+	0.865433i	0.500342	+	0.865828i	$0.333208\pi$
$642$		0			0
$643$	−12.0773	−	6.97283i	−0.476282	−	0.274981i	0.242584	−	0.970130i	$-0.422005\pi$
$643$	−12.0773	−	6.97283i	−0.476282	−	0.274981i	−0.718866	+	0.695149i	$0.755338\pi$
$644$	−0.634095	+	1.09828i	−0.0249868	+	0.0432785i
$645$		0			0
$646$	−3.29560	+	4.08658i	−0.129664	+	0.160784i
$647$		−	2.51360i		−	0.0988200i	−0.998779	−	0.0494100i	$-0.984266\pi$
$647$		−	2.51360i		−	0.0988200i	0.998779	−	0.0494100i	$-0.0157341\pi$
$648$		0			0
$649$	−2.22978	+	3.86209i	−0.0875264	+	0.151600i
$650$	8.92576	+	3.74884i	0.350097	+	0.147042i
$651$		0			0
$652$	−0.105934	+	0.0611608i	−0.00414868	+	0.00239524i
$653$		−	1.92873i		−	0.0754770i	−0.999288	−	0.0377385i	$-0.987985\pi$
$653$		−	1.92873i		−	0.0754770i	0.999288	−	0.0377385i	$-0.0120154\pi$
$654$		0			0
$655$	−25.9465	+	29.4396i	−1.01381	+	1.15030i
$656$	−5.59306	−	9.68747i	−0.218372	−	0.378232i
$657$		0			0
$658$		−	5.83404i		−	0.227434i
$659$	−7.90042	−	13.6839i	−0.307757	−	0.533050i	0.670115	−	0.742258i	$-0.266245\pi$
$659$	−7.90042	−	13.6839i	−0.307757	−	0.533050i	−0.977871	+	0.209208i	$0.932912\pi$
$660$		0			0
$661$	−8.20178	−	14.2059i	−0.319012	−	0.552546i	0.661270	−	0.750148i	$-0.270018\pi$
$661$	−8.20178	−	14.2059i	−0.319012	−	0.552546i	−0.980282	+	0.197602i	$0.936685\pi$
$662$	14.6096	+	8.43486i	0.567819	+	0.327830i
$663$		0			0
$664$	−24.7054			−0.958755
$665$	−11.2918	+	1.93510i	−0.437875	+	0.0750400i
$666$		0			0
$667$	0.451805	+	0.260850i	0.0174940	+	0.0101001i
$668$	25.6190	+	14.7911i	0.991228	+	0.572286i
$669$		0			0
$670$	5.36025	+	1.07997i	0.207085	+	0.0417227i
$671$	−1.62496	−	2.81451i	−0.0627308	−	0.108653i
$672$		0			0
$673$			17.0878i			0.658686i	0.944210	+	0.329343i	$0.106827\pi$
$673$			17.0878i			0.658686i	−0.944210	+	0.329343i	$0.893173\pi$
$674$	6.24992	+	10.8252i	0.240738	+	0.416970i
$675$		0			0
$676$	−6.81761			−0.262216
$677$		−	4.57680i		−	0.175901i	−0.996125	−	0.0879504i	$-0.971968\pi$
$677$		−	4.57680i		−	0.175901i	0.996125	−	0.0879504i	$-0.0280317\pi$
$678$		0			0
$679$	9.81574	−	17.0014i	0.376693	−	0.652452i
$680$	−6.72623	+	7.63176i	−0.257939	+	0.292665i
$681$		0			0
$682$	−0.731656	−	0.422422i	−0.0280166	−	0.0161754i
$683$			29.0692i			1.11230i	0.831082	+	0.556151i	$0.187722\pi$
$683$			29.0692i			1.11230i	−0.831082	+	0.556151i	$0.812278\pi$
$684$		0			0
$685$	10.7538	−	3.62089i	0.410882	−	0.138347i
$686$	3.49942	−	6.06117i	0.133608	−	0.231416i
$687$		0			0
$688$	23.7912	−	13.7359i	0.907031	−	0.523675i
$689$	−10.2180	+	17.6981i	−0.389276	+	0.674245i
$690$		0			0
$691$	−6.07833			−0.231230			−0.115615	−	0.993294i	$-0.536884\pi$
$691$	−6.07833			−0.231230			−0.115615	+	0.993294i	$0.536884\pi$
$692$		−	21.5689i		−	0.819925i
$693$		0			0
$694$	−8.10220	−	14.0334i	−0.307555	−	0.532701i
$695$	4.26819	+	12.6763i	0.161902	+	0.480838i
$696$		0			0
$697$	9.11194	−	5.26078i	0.345139	−	0.199266i
$698$	8.75799	+	5.05643i	0.331495	+	0.191389i
$699$		0			0
$700$	−10.3626	+	1.31231i	−0.391668	+	0.0496006i
$701$	5.20569	−	9.01651i	0.196616	−	0.340549i	−0.750813	−	0.660515i	$-0.770338\pi$
$701$	5.20569	−	9.01651i	0.196616	−	0.340549i	0.947429	+	0.319966i	$0.103671\pi$
$702$		0			0
$703$	−38.1481	+	14.7322i	−1.43878	+	0.555634i
$704$	−2.24095			−0.0844589
$705$		0			0
$706$	4.61640	−	7.99585i	0.173741	−	0.300928i
$707$	14.2787	−	8.24380i	0.537005	−	0.310040i
$708$		0			0
$709$	−0.265572	−	0.459984i	−0.00997377	−	0.0172751i	0.860995	−	0.508613i	$-0.169841\pi$
$709$	−0.265572	−	0.459984i	−0.00997377	−	0.0172751i	−0.870969	+	0.491338i	$0.836508\pi$
$710$	−13.1679	+	4.43371i	−0.494181	+	0.166394i
$711$		0			0
$712$	−24.6421	+	14.2271i	−0.923500	+	0.533183i
$713$	1.31913	−	0.761599i	0.0494017	−	0.0285221i
$714$		0			0
$715$	−6.20440	+	2.08907i	−0.232031	+	0.0781266i
$716$	−10.4452	−	18.0916i	−0.390355	−	0.676114i
$717$		0			0
$718$	6.73174	−	3.88657i	0.251226	−	0.145046i
$719$	−11.2135	+	19.4224i	−0.418194	+	0.724334i	−0.995758	−	0.0920118i	$-0.970670\pi$
$719$	−11.2135	+	19.4224i	−0.418194	+	0.724334i	0.577564	+	0.816346i	$0.304004\pi$
$720$		0			0
$721$	4.17716			0.155566
$722$	−8.76227	+	1.89951i	−0.326098	+	0.0706924i
$723$		0			0
$724$	7.85212	−	13.6003i	0.291822	−	0.505450i
$725$	0.539849	+	4.26288i	0.0200495	+	0.158320i
$726$		0			0
$727$	−39.8141	−	22.9867i	−1.47662	−	0.852529i	−0.476972	−	0.878918i	$-0.658266\pi$
$727$	−39.8141	−	22.9867i	−1.47662	−	0.852529i	−0.999652	+	0.0263888i	$0.991599\pi$
$728$	−7.44480	+	4.29826i	−0.275923	+	0.159304i
$729$		0			0
$730$	4.16786	+	12.3783i	0.154259	+	0.458141i
$731$	12.9198	+	22.3778i	0.477856	+	0.827671i
$732$		0			0
$733$			42.5178i			1.57043i	0.619223	+	0.785215i	$0.287448\pi$
$733$			42.5178i			1.57043i	−0.619223	+	0.785215i	$0.712552\pi$
$734$	−6.00930			−0.221807
$735$		0			0
$736$	−1.47072	+	2.54737i	−0.0542116	+	0.0938972i
$737$	−3.20224	+	1.84881i	−0.117956	+	0.0681019i
$738$		0			0
$739$	−1.70889	+	2.95988i	−0.0628624	+	0.108881i	−0.895744	−	0.444571i	$-0.853356\pi$
$739$	−1.70889	+	2.95988i	−0.0628624	+	0.108881i	0.832881	+	0.553452i	$0.186690\pi$
$740$	−35.3357	+	11.8978i	−1.29897	+	0.437371i
$741$		0			0
$742$			2.76248i			0.101414i
$743$	−8.41853	−	4.86044i	−0.308846	−	0.178312i	0.337564	−	0.941303i	$-0.390397\pi$
$743$	−8.41853	−	4.86044i	−0.308846	−	0.178312i	−0.646410	+	0.762990i	$0.723730\pi$
$744$		0			0
$745$	−14.1937	+	16.1045i	−0.520016	+	0.590024i
$746$	4.56175	−	7.90119i	0.167018	−	0.289283i
$747$		0			0
$748$		−	3.23683i		−	0.118350i
$749$	4.26819			0.155956
$750$		0			0
$751$	5.69265	+	9.85996i	0.207728	+	0.359795i	0.950998	−	0.309196i	$-0.100060\pi$
$751$	5.69265	+	9.85996i	0.207728	+	0.359795i	−0.743271	+	0.668991i	$0.766727\pi$
$752$			28.5420i			1.04082i
$753$		0			0
$754$	0.831977	+	1.44103i	0.0302988	+	0.0524791i
$755$	16.5199	+	3.32837i	0.601221	+	0.121132i
$756$		0			0
$757$	19.7317	+	11.3921i	0.717160	+	0.414053i	0.813707	−	0.581276i	$-0.197446\pi$
$757$	19.7317	+	11.3921i	0.717160	+	0.414053i	−0.0965464	+	0.995328i	$0.530780\pi$
$758$	−4.02856	−	2.32589i	−0.146324	−	0.0844801i
$759$		0			0
$760$	−17.1236	+	2.93453i	−0.621139	+	0.106446i
$761$	36.7665			1.33279			0.666393	−	0.745601i	$-0.267837\pi$
$761$	36.7665			1.33279			0.666393	+	0.745601i	$0.267837\pi$
$762$		0			0
$763$	6.33421	+	3.65706i	0.229314	+	0.132394i
$764$	12.6587	+	21.9255i	0.457976	+	0.793238i
$765$		0			0
$766$	−4.79747	−	8.30945i	−0.173339	−	0.300233i
$767$		−	25.6444i		−	0.925965i
$768$		0			0
$769$	−10.4004	−	18.0140i	−0.375049	−	0.649603i	0.615286	−	0.788304i	$-0.289041\pi$
$769$	−10.4004	−	18.0140i	−0.375049	−	0.649603i	−0.990334	+	0.138701i	$0.955707\pi$
$770$	−0.585131	+	0.663905i	−0.0210867	+	0.0239255i
$771$		0			0
$772$		−	34.6679i		−	1.24772i
$773$	−18.1944	+	10.5046i	−0.654409	+	0.377823i	−0.790143	−	0.612922i	$-0.789994\pi$
$773$	−18.1944	+	10.5046i	−0.654409	+	0.377823i	0.135735	+	0.990745i	$0.456661\pi$
$774$		0			0
$775$	11.5669	+	4.85812i	0.415495	+	0.174509i
$776$	14.8853	−	25.7821i	0.534351	−	0.925523i
$777$		0			0
$778$			0.474354i			0.0170064i
$779$	17.7533	+	2.77509i	0.636077	+	0.0994280i
$780$		0			0
$781$	4.69788	−	8.13697i	0.168103	−	0.291164i
$782$	−0.633190	−	0.365572i	−0.0226428	−	0.0130728i
$783$		0			0
$784$	−7.62292	+	13.2033i	−0.272247	+	0.471546i
$785$	−16.5338	−	14.5720i	−0.590116	−	0.520097i
$786$		0			0
$787$			18.0606i			0.643791i	0.946775	+	0.321896i	$0.104320\pi$
$787$			18.0606i			0.643791i	−0.946775	+	0.321896i	$0.895680\pi$
$788$	6.66834	−	3.84997i	0.237550	−	0.137149i
$789$		0			0
$790$	−5.96345	+	2.00794i	−0.212170	+	0.0714392i
$791$	14.4230			0.512823
$792$		0			0
$793$	16.1847	+	9.34422i	0.574734	+	0.331823i
$794$	−2.32691	−	4.03033i	−0.0825789	−	0.143031i
$795$		0			0
$796$	−11.2251	+	19.4425i	−0.397864	+	0.689121i
$797$			24.2571i			0.859229i	0.903012	+	0.429615i	$0.141351\pi$
$797$			24.2571i			0.859229i	−0.903012	+	0.429615i	$0.858649\pi$
$798$		0			0
$799$	−26.8463			−0.949756
$800$	−24.0350	+	3.04378i	−0.849765	+	0.107614i
$801$		0			0
$802$	12.1912	−	7.03857i	0.430485	−	0.248541i
$803$	−7.64906	−	4.41619i	−0.269930	−	0.155844i
$804$		0			0
$805$	−0.509136	−	1.51211i	−0.0179447	−	0.0532947i
$806$	4.85822			0.171124
$807$		0			0
$808$	21.6532	−	12.5015i	0.761758	−	0.439801i
$809$	−4.27192			−0.150193			−0.0750964	−	0.997176i	$-0.523926\pi$
$809$	−4.27192			−0.150193			−0.0750964	+	0.997176i	$0.523926\pi$
$810$		0			0
$811$	−5.09120	−	8.81821i	−0.178776	−	0.309649i	0.762685	−	0.646770i	$-0.223880\pi$
$811$	−5.09120	−	8.81821i	−0.178776	−	0.309649i	−0.941462	+	0.337120i	$0.890547\pi$
$812$	−1.55479	−	0.897657i	−0.0545623	−	0.0315016i
$813$		0			0
$814$	−1.57944	+	2.73568i	−0.0553595	+	0.0958854i
$815$	0.0303952	−	0.150862i	0.00106470	−	0.00528448i
$816$		0			0
$817$	−6.81528	+	43.5998i	−0.238436	+	1.52536i
$818$			13.0448i			0.456102i
$819$		0			0
$820$	16.0604	+	3.23579i	0.560852	+	0.112999i
$821$	−28.0108	−	48.5162i	−0.977585	−	1.69323i	−0.671127	−	0.741343i	$-0.734189\pi$
$821$	−28.0108	−	48.5162i	−0.977585	−	1.69323i	−0.306458	−	0.951884i	$-0.599144\pi$
$822$		0			0
$823$	−29.0479	+	16.7708i	−1.01255	+	0.584593i	−0.911936	−	0.410333i	$-0.865413\pi$
$823$	−29.0479	+	16.7708i	−1.01255	+	0.584593i	−0.100610	+	0.994926i	$0.532079\pi$
$824$	6.33455			0.220674
$825$		0			0
$826$	−1.73326	−	3.00210i	−0.0603079	−	0.104456i
$827$	0.0313960	−	0.0181265i	0.00109175	−	0.000630320i	−0.499454	−	0.866340i	$-0.666466\pi$
$827$	0.0313960	−	0.0181265i	0.00109175	−	0.000630320i	0.500546	+	0.865710i	$0.333133\pi$
$828$		0			0
$829$	−39.5662			−1.37419			−0.687095	−	0.726567i	$-0.741115\pi$
$829$	−39.5662			−1.37419			−0.687095	+	0.726567i	$0.741115\pi$
$830$	9.66994	−	10.9718i	0.335648	−	0.380835i
$831$		0			0
$832$	11.1600	−	6.44321i	0.386902	−	0.223378i
$833$	−12.4189	−	7.17005i	−0.430289	−	0.248427i
$834$		0			0
$835$	−35.2719	+	11.8763i	−1.22064	+	0.410996i
$836$	3.47014	−	4.30301i	0.120017	−	0.148823i
$837$		0			0
$838$	−4.61389	−	2.66383i	−0.159384	−	0.0920205i
$839$	−20.0811	+	34.7816i	−0.693278	+	1.20079i	0.277480	+	0.960732i	$0.410501\pi$
$839$	−20.0811	+	34.7816i	−0.693278	+	1.20079i	−0.970758	+	0.240061i	$0.922832\pi$
$840$		0			0
$841$	14.1307	−	24.4751i	0.487266	−	0.843970i
$842$	−1.85918	+	1.07340i	−0.0640716	+	0.0369917i
$843$		0			0
$844$	39.5360			1.36089
$845$	5.67128	−	6.43478i	0.195098	−	0.221363i
$846$		0			0
$847$			12.3309i			0.423696i
$848$		−	13.5150i		−	0.464106i
$849$		0			0
$850$	−0.756580	−	5.97429i	−0.0259505	−	0.204917i
$851$	−2.84763	−	4.93224i	−0.0976156	−	0.169075i
$852$		0			0
$853$	14.2563	+	8.23086i	0.488126	+	0.281819i	0.723796	−	0.690014i	$-0.242395\pi$
$853$	14.2563	+	8.23086i	0.488126	+	0.281819i	−0.235671	+	0.971833i	$0.575729\pi$
$854$	2.52624			0.0864463
$855$		0			0
$856$	6.47259			0.221229
$857$	4.85549	+	2.80332i	0.165860	+	0.0957595i	0.580632	−	0.814166i	$-0.302805\pi$
$857$	4.85549	+	2.80332i	0.165860	+	0.0957595i	−0.414772	+	0.909925i	$0.636139\pi$
$858$		0			0
$859$	12.5149	+	21.6765i	0.427003	+	0.739591i	0.996605	−	0.0823296i	$-0.0262360\pi$
$859$	12.5149	+	21.6765i	0.427003	+	0.739591i	−0.569602	+	0.821921i	$0.692903\pi$
$860$	−7.94669	+	39.4422i	−0.270980	+	1.34497i
$861$		0			0
$862$			15.5266i			0.528837i
$863$		−	42.4307i		−	1.44436i	−0.691707	−	0.722178i	$-0.743141\pi$
$863$		−	42.4307i		−	1.44436i	0.691707	−	0.722178i	$-0.256859\pi$
$864$		0			0
$865$	20.3577	+	17.9422i	0.692183	+	0.610054i
$866$	−10.5274			−0.357736
$867$		0			0
$868$	−4.53949	+	2.62087i	−0.154080	+	0.0889583i
$869$	2.12758	−	3.68507i	0.0721731	−	0.125007i
$870$		0			0
$871$	10.6315	−	18.4143i	0.360234	−	0.623943i
$872$	9.60566	+	5.54583i	0.325289	+	0.187806i
$873$		0			0
$874$	−0.449833	−	1.16482i	−0.0152158	−	0.0394005i
$875$	7.38156	−	10.8723i	0.249542	−	0.367552i
$876$		0			0
$877$	−0.482588	−	0.278622i	−0.0162958	−	0.00940841i	0.491830	−	0.870691i	$-0.336328\pi$
$877$	−0.482588	−	0.278622i	−0.0162958	−	0.00940841i	−0.508126	+	0.861283i	$0.669662\pi$
$878$	2.33172	−	1.34622i	0.0786919	−	0.0454328i
$879$		0			0
$880$	2.86266	−	3.24804i	0.0965001	−	0.109492i
$881$	−8.35432			−0.281464			−0.140732	−	0.990048i	$-0.544946\pi$
$881$	−8.35432			−0.281464			−0.140732	+	0.990048i	$0.544946\pi$
$882$		0			0
$883$	−16.8738	+	9.74209i	−0.567848	+	0.327847i	−0.756289	−	0.654237i	$-0.772990\pi$
$883$	−16.8738	+	9.74209i	−0.567848	+	0.327847i	0.188441	+	0.982084i	$0.439657\pi$
$884$	9.30660	+	16.1195i	0.313015	+	0.542158i
$885$		0			0
$886$	5.46329			0.183543
$887$	−31.1226	+	17.9686i	−1.04499	+	0.603328i	−0.921244	−	0.388985i	$-0.872826\pi$
$887$	−31.1226	+	17.9686i	−1.04499	+	0.603328i	−0.123751	+	0.992313i	$0.539492\pi$
$888$		0			0
$889$	1.26819	+	2.19657i	0.0425337	+	0.0736705i
$890$	3.32683	−	16.5123i	0.111516	−	0.553492i
$891$		0			0
$892$		−	24.2116i		−	0.810666i
$893$	−35.6892	−	28.7814i	−1.19429	−	0.963133i
$894$		0			0
$895$	25.7646	+	5.19097i	0.861216	+	0.173515i
$896$	6.56624	−	11.3731i	0.219363	−	0.379947i
$897$		0			0
$898$	−10.4097	−	6.01005i	−0.347377	−	0.200558i
$899$	1.07816	+	1.86743i	0.0359586	+	0.0622821i
$900$		0			0
$901$	12.7120			0.423499
$902$	1.20206	−	0.694011i	0.0400243	−	0.0231080i
$903$		0			0
$904$	21.8721			0.727455
$905$	6.30473	+	18.7247i	0.209576	+	0.622430i
$906$		0			0
$907$	−42.3922	−	24.4751i	−1.40761	−	0.812683i	−0.412452	−	0.910980i	$-0.635327\pi$
$907$	−42.3922	−	24.4751i	−1.40761	−	0.812683i	−0.995157	+	0.0982962i	$0.968661\pi$
$908$	−10.1420	+	5.85551i	−0.336576	+	0.194322i
$909$		0			0
$910$	1.00510	−	4.98864i	0.0333186	−	0.165372i
$911$	19.7811			0.655376			0.327688	−	0.944786i	$-0.393731\pi$
$911$	19.7811			0.655376			0.327688	+	0.944786i	$0.393731\pi$
$912$		0			0
$913$			9.88984i			0.327306i
$914$	1.63468	−	2.83134i	0.0540703	−	0.0936525i
$915$		0			0
$916$	−0.520723	−	0.901919i	−0.0172052	−	0.0298002i
$917$	17.8640	+	10.3138i	0.589921	+	0.340591i
$918$		0			0
$919$	−26.0582			−0.859581			−0.429791	−	0.902929i	$-0.641413\pi$
$919$	−26.0582			−0.859581			−0.429791	+	0.902929i	$0.641413\pi$
$920$	−0.772091	−	2.29307i	−0.0254551	−	0.0756001i
$921$		0			0
$922$	13.2794	−	7.66684i	0.437332	−	0.252494i
$923$			54.0298i			1.77841i
$924$		0			0
$925$	18.1646	−	43.2488i	0.597248	−	1.42201i
$926$	5.07421	−	8.78879i	0.166749	−	0.288817i
$927$		0			0
$928$	−3.60618	−	2.08203i	−0.118379	−	0.0683460i
$929$	3.98900	−	6.90914i	0.130875	−	0.226682i	−0.793139	−	0.609040i	$-0.791555\pi$
$929$	3.98900	−	6.90914i	0.130875	−	0.226682i	0.924014	+	0.382359i	$0.124888\pi$
$930$		0			0
$931$	−8.82267	−	22.8458i	−0.289151	−	0.748741i
$932$			12.7211i			0.416695i
$933$		0			0
$934$	−3.99942	+	6.92719i	−0.130865	+	0.226665i
$935$	3.05508	+	2.69259i	0.0999117	+	0.0880570i
$936$		0			0
$937$	−40.4037	+	23.3271i	−1.31993	+	0.762063i	−0.983717	−	0.179722i	$-0.942480\pi$
$937$	−40.4037	+	23.3271i	−1.31993	+	0.762063i	−0.336215	+	0.941785i	$0.609147\pi$
$938$		−	2.87426i		−	0.0938479i
$939$		0			0
$940$	−31.3606	−	27.6396i	−1.02287	−	0.901505i
$941$	−0.700500	−	1.21330i	−0.0228356	−	0.0395525i	0.854382	−	0.519646i	$-0.173936\pi$
$941$	−0.700500	−	1.21330i	−0.0228356	−	0.0395525i	−0.877217	+	0.480093i	$0.840603\pi$
$942$		0			0
$943$			2.50251i			0.0814930i
$944$	8.47969	+	14.6873i	0.275990	+	0.478030i
$945$		0			0
$946$	1.70440	+	2.95211i	0.0554149	+	0.0959814i
$947$	−33.1255	−	19.1250i	−1.07643	−	0.621480i	−0.146502	−	0.989210i	$-0.546802\pi$
$947$	−33.1255	−	19.1250i	−1.07643	−	0.621480i	−0.929932	+	0.367730i	$0.880135\pi$
$948$		0			0
$949$	50.7900			1.64871
$950$	5.39912	−	8.75327i	0.175171	−	0.283994i
$951$		0			0
$952$	4.63096	+	2.67369i	0.150090	+	0.0866547i
$953$	47.1455	+	27.2195i	1.52719	+	0.881726i	0.999478	+	0.0323042i	$0.0102845\pi$
$953$	47.1455	+	27.2195i	1.52719	+	0.881726i	0.527715	+	0.849421i	$0.323049\pi$
$954$		0			0
$955$	−31.2246	−	6.29103i	−1.01041	−	0.203573i
$956$	−3.24805	−	5.62579i	−0.105049	−	0.181951i
$957$		0			0
$958$		−	4.17989i		−	0.135046i
$959$	−2.98231	−	5.16551i	−0.0963038	−	0.166803i
$960$		0			0
$961$	−24.7042			−0.796911
$962$		−	18.1650i		−	0.585662i
$963$		0			0
$964$	−15.3409	+	26.5713i	−0.494099	+	0.855804i
$965$	32.7212	+	28.8388i	1.05333	+	0.928353i
$966$		0			0
$967$	4.32077	+	2.49460i	0.138946	+	0.0802208i	0.567862	−	0.823124i	$-0.307771\pi$
$967$	4.32077	+	2.49460i	0.138946	+	0.0802208i	−0.428915	+	0.903345i	$0.641104\pi$
$968$			18.6995i			0.601026i
$969$		0			0
$970$	5.62367	+	16.7020i	0.180565	+	0.536268i
$971$	−7.27006	+	12.5921i	−0.233307	+	0.404100i	−0.958779	−	0.284152i	$-0.908288\pi$
$971$	−7.27006	+	12.5921i	−0.233307	+	0.404100i	0.725472	+	0.688252i	$0.241621\pi$
$972$		0			0
$973$	6.08895	−	3.51546i	0.195203	−	0.112700i
$974$	7.09306	−	12.2855i	0.227276	−	0.393654i
$975$		0			0
$976$	−12.3592			−0.395609
$977$			26.1353i			0.836141i	0.908415	+	0.418071i	$0.137294\pi$
$977$			26.1353i			0.836141i	−0.908415	+	0.418071i	$0.862706\pi$
$978$		0			0
$979$	5.69527	+	9.86449i	0.182021	+	0.315270i
$980$	−7.12524	−	21.1616i	−0.227608	−	0.675981i
$981$		0			0
$982$	1.26699	−	0.731499i	0.0404314	−	0.0233431i
$983$	39.9376	+	23.0580i	1.27381	+	0.735436i	0.975703	−	0.219096i	$-0.0703109\pi$
$983$	39.9376	+	23.0580i	1.27381	+	0.735436i	0.298109	+	0.954532i	$0.403644\pi$
$984$		0			0
$985$	−1.91333	+	9.49652i	−0.0609637	+	0.302584i
$986$	0.517523	−	0.896376i	0.0164813	−	0.0285464i
$987$		0			0
$988$	−4.90929	+	31.4065i	−0.156185	+	0.999174i
$989$	−6.14585			−0.195427
$990$		0			0
$991$	15.6640	−	27.1308i	0.497582	−	0.861837i	−0.502414	−	0.864627i	$-0.667555\pi$
$991$	15.6640	−	27.1308i	0.497582	−	0.861837i	0.999996	+	0.00278993i	$0.000888065\pi$
$992$	−10.5289	+	6.07887i	−0.334294	+	0.193004i
$993$		0			0
$994$	3.65178	+	6.32508i	0.115828	+	0.200619i
$995$	−9.01304	−	26.7682i	−0.285733	−	0.848609i
$996$		0			0
$997$	18.7186	−	10.8072i	0.592826	−	0.342268i	−0.173388	−	0.984854i	$-0.555472\pi$
$997$	18.7186	−	10.8072i	0.592826	−	0.342268i	0.766214	+	0.642586i	$0.222138\pi$
$998$	13.1341	−	7.58296i	0.415752	−	0.240035i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	855.2.be.d.334.4		12
3.2	odd	2		95.2.i.b.49.3	✓	12
5.4	even	2	inner	855.2.be.d.334.3		12
15.2	even	4		475.2.e.g.201.4		12
15.8	even	4		475.2.e.g.201.3		12
15.14	odd	2		95.2.i.b.49.4	yes	12
19.7	even	3	inner	855.2.be.d.64.3		12
57.8	even	6		1805.2.b.g.1084.3		6
57.11	odd	6		1805.2.b.f.1084.4		6
57.26	odd	6		95.2.i.b.64.4	yes	12
95.64	even	6	inner	855.2.be.d.64.4		12
285.8	odd	12		9025.2.a.bt.1.3		6
285.68	even	12		9025.2.a.bu.1.4		6
285.83	even	12		475.2.e.g.26.3		12
285.122	odd	12		9025.2.a.bt.1.4		6
285.179	even	6		1805.2.b.g.1084.4		6
285.182	even	12		9025.2.a.bu.1.3		6
285.197	even	12		475.2.e.g.26.4		12
285.239	odd	6		1805.2.b.f.1084.3		6
285.254	odd	6		95.2.i.b.64.3	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.i.b.49.3	✓	12	3.2	odd	2
95.2.i.b.49.4	yes	12	15.14	odd	2
95.2.i.b.64.3	yes	12	285.254	odd	6
95.2.i.b.64.4	yes	12	57.26	odd	6
475.2.e.g.26.3		12	285.83	even	12
475.2.e.g.26.4		12	285.197	even	12
475.2.e.g.201.3		12	15.8	even	4
475.2.e.g.201.4		12	15.2	even	4
855.2.be.d.64.3		12	19.7	even	3	inner
855.2.be.d.64.4		12	95.64	even	6	inner
855.2.be.d.334.3		12	5.4	even	2	inner
855.2.be.d.334.4		12	1.1	even	1	trivial
1805.2.b.f.1084.3		6	285.239	odd	6
1805.2.b.f.1084.4		6	57.11	odd	6
1805.2.b.g.1084.3		6	57.8	even	6
1805.2.b.g.1084.4		6	285.179	even	6
9025.2.a.bt.1.3		6	285.8	odd	12
9025.2.a.bt.1.4		6	285.122	odd	12
9025.2.a.bu.1.3		6	285.182	even	12
9025.2.a.bu.1.4		6	285.68	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.be (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.408663 + 0.235942i) q^{2} +(-0.888663 - 1.53921i) q^{4} +(2.19202 + 0.441641i) q^{5} -1.17540i q^{7} -1.78246i q^{8} +O(q^{10})\)	\(q+(0.408663 + 0.235942i) q^{2} +(-0.888663 - 1.53921i) q^{4} +(2.19202 + 0.441641i) q^{5} -1.17540i q^{7} -1.78246i q^{8} +(0.791597 + 0.697672i) q^{10} -0.713538 q^{11} +(3.55344 - 2.05158i) q^{13} +(0.277326 - 0.480342i) q^{14} +(-1.35677 + 2.34999i) q^{16} +(-2.21038 - 1.27616i) q^{17} +(-1.57031 - 4.06622i) q^{19} +(-1.26819 - 3.76645i) q^{20} +(-0.291597 - 0.168353i) q^{22} +(0.525730 - 0.303530i) q^{23} +(4.60991 + 1.93617i) q^{25} +1.93621 q^{26} +(-1.80918 + 1.04453i) q^{28} +(0.429693 + 0.744250i) q^{29} +2.50914 q^{31} +(-4.19623 + 2.42270i) q^{32} +(-0.602201 - 1.04304i) q^{34} +(0.519104 - 2.57650i) q^{35} -9.38171i q^{37} +(0.317665 - 2.03222i) q^{38} +(0.787207 - 3.90719i) q^{40} +(-2.06117 + 3.57005i) q^{41} +(-8.76759 - 5.06197i) q^{43} +(0.634095 + 1.09828i) q^{44} +0.286462 q^{46} +(9.10919 - 5.25919i) q^{47} +5.61844 q^{49} +(1.42708 + 1.87891i) q^{50} +(-6.31561 - 3.64632i) q^{52} +(-4.31330 + 2.49028i) q^{53} +(-1.56409 - 0.315128i) q^{55} -2.09510 q^{56} +0.405530i q^{58} +(3.12496 - 5.41259i) q^{59} +(2.27733 + 3.94444i) q^{61} +(1.02539 + 0.592010i) q^{62} +3.14061 q^{64} +(8.69527 - 2.92776i) q^{65} +(4.48783 - 2.59105i) q^{67} +4.53632i q^{68} +(0.820042 - 0.930441i) q^{70} +(-6.58393 + 11.4037i) q^{71} +(10.7199 + 6.18914i) q^{73} +(2.21354 - 3.83396i) q^{74} +(-4.86329 + 6.03053i) q^{76} +0.838691i q^{77} +(-2.98173 + 5.16450i) q^{79} +(-4.01192 + 4.55203i) q^{80} +(-1.68465 + 0.972633i) q^{82} -13.8603i q^{83} +(-4.28159 - 3.77357i) q^{85} +(-2.38866 - 4.13729i) q^{86} +1.27185i q^{88} +(-7.98173 - 13.8248i) q^{89} +(-2.41142 - 4.17670i) q^{91} +(-0.934393 - 0.539472i) q^{92} +4.96345 q^{94} +(-1.64634 - 9.60675i) q^{95} +(14.4643 + 8.35099i) q^{97} +(2.29605 + 1.32563i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{4} + 2 q^{5}+O(q^{10}) \) 12 * q + 2 * q^4 + 2 * q^5	\( 12 q + 2 q^{4} + 2 q^{5} + 6 q^{10} - 4 q^{11} - 22 q^{14} - 14 q^{16} - 12 q^{19} + 40 q^{20} - 6 q^{25} + 44 q^{26} + 12 q^{29} + 60 q^{31} + 10 q^{34} + 10 q^{40} + 12 q^{41} - 20 q^{44} + 8 q^{46} - 4 q^{49} + 8 q^{50} - 18 q^{55} - 92 q^{56} - 20 q^{59} + 2 q^{61} + 24 q^{64} + 40 q^{65} + 46 q^{70} - 2 q^{71} + 22 q^{74} - 70 q^{76} + 24 q^{79} + 22 q^{80} + 2 q^{85} - 16 q^{86} - 36 q^{89} + 24 q^{91} - 60 q^{94} - 46 q^{95}+O(q^{100}) \) 12 * q + 2 * q^4 + 2 * q^5 + 6 * q^10 - 4 * q^11 - 22 * q^14 - 14 * q^16 - 12 * q^19 + 40 * q^20 - 6 * q^25 + 44 * q^26 + 12 * q^29 + 60 * q^31 + 10 * q^34 + 10 * q^40 + 12 * q^41 - 20 * q^44 + 8 * q^46 - 4 * q^49 + 8 * q^50 - 18 * q^55 - 92 * q^56 - 20 * q^59 + 2 * q^61 + 24 * q^64 + 40 * q^65 + 46 * q^70 - 2 * q^71 + 22 * q^74 - 70 * q^76 + 24 * q^79 + 22 * q^80 + 2 * q^85 - 16 * q^86 - 36 * q^89 + 24 * q^91 - 60 * q^94 - 46 * q^95

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