LMFDB - Embedded newform 867.2.h.j.688.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [867,2,Mod(688,867)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(867, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("867.688");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.h (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	16.0.1963501163244660295991296.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 1889x^{8} + 65536 $ x^16 + 1889*x^8 + 65536
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			688.4
Root			$-2.36657 + 0.980264i$ of defining polynomial
Character	$\chi$	$=$	867.688
Dual form			867.2.h.j.712.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.81129 - 1.81129i) q^{2} +(0.382683 - 0.923880i) q^{3} -4.56155i q^{4} +(-3.29045 - 1.36295i) q^{5} +(-0.980264 - 2.36657i) q^{6} +(-4.63972 - 4.63972i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(-8.42865 + 3.49126i) q^{10} +(0.597580 + 1.44269i) q^{11} +(-4.21433 - 1.74563i) q^{12} +0.438447i q^{13} +(-2.51840 + 2.51840i) q^{15} -7.68466 q^{16} -2.56155 q^{18} +(3.31255 - 3.31255i) q^{19} +(-6.21716 + 15.0095i) q^{20} +(3.69552 + 1.53073i) q^{22} +(0.933153 + 2.25283i) q^{23} +(-6.06208 + 2.51100i) q^{24} +(5.43387 + 5.43387i) q^{25} +(0.794156 + 0.794156i) q^{26} +(-0.923880 + 0.382683i) q^{27} +(-7.61851 - 3.15569i) q^{29} +9.12311i q^{30} +(1.19516 - 2.88537i) q^{31} +(-4.63972 + 4.63972i) q^{32} +1.56155 q^{33} +(-3.22550 + 3.22550i) q^{36} +(1.96053 - 4.73313i) q^{37} -12.0000i q^{38} +(0.405072 + 0.167786i) q^{39} +(8.94305 + 21.5904i) q^{40} +(3.29045 - 1.36295i) q^{41} +(-3.31255 - 3.31255i) q^{43} +(6.58089 - 2.72589i) q^{44} +(1.36295 + 3.29045i) q^{45} +(5.77075 + 2.39032i) q^{46} -11.1231i q^{47} +(-2.94079 + 7.09970i) q^{48} +(-4.94975 + 4.94975i) q^{49} +19.6847 q^{50} +2.00000 q^{52} +(-8.65938 + 8.65938i) q^{53} +(-0.980264 + 2.36657i) q^{54} -5.56155i q^{55} +(-1.79274 - 4.32806i) q^{57} +(-19.5152 + 8.08346i) q^{58} +(5.03680 + 5.03680i) q^{59} +(11.4878 + 11.4878i) q^{60} +(8.42865 - 3.49126i) q^{61} +(-3.06147 - 7.39104i) q^{62} +1.43845i q^{64} +(0.597580 - 1.44269i) q^{65} +(2.82843 - 2.82843i) q^{66} -4.00000 q^{67} +2.43845 q^{69} +(2.39032 - 5.77075i) q^{71} +6.56155i q^{72} +(11.3140 + 4.68642i) q^{73} +(-5.02200 - 12.1242i) q^{74} +(7.09970 - 2.94079i) q^{75} +(-15.1104 - 15.1104i) q^{76} +(1.03761 - 0.429794i) q^{78} +(-3.58548 - 8.65612i) q^{79} +(25.2860 + 10.4738i) q^{80} +1.00000i q^{81} +(3.49126 - 8.42865i) q^{82} +(-0.620058 + 0.620058i) q^{83} -12.0000 q^{86} +(-5.83095 + 5.83095i) q^{87} +(3.92106 - 9.46626i) q^{88} +1.12311i q^{89} +(8.42865 + 3.49126i) q^{90} +(10.2764 - 4.25663i) q^{92} +(-2.20837 - 2.20837i) q^{93} +(-20.1472 - 20.1472i) q^{94} +(-15.4146 + 6.38494i) q^{95} +(2.51100 + 6.06208i) q^{96} +(-2.65790 - 1.10094i) q^{97} +17.9309i q^{98} +(0.597580 - 1.44269i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 24 q^{16} - 8 q^{18} - 8 q^{33} + 216 q^{50} + 32 q^{52} - 64 q^{67} + 72 q^{69} - 192 q^{86}+O(q^{100}) $ 16 * q - 24 * q^16 - 8 * q^18 - 8 * q^33 + 216 * q^50 + 32 * q^52 - 64 * q^67 + 72 * q^69 - 192 * q^86

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{5}{8}\right)$

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 $

$2$	1.81129	−	1.81129i	1.28078	−	1.28078i	0.340550	−	0.940226i	$-0.389387\pi$
$2$	1.81129	−	1.81129i	1.28078	−	1.28078i	0.940226	−	0.340550i	$-0.110613\pi$
$3$	0.382683	−	0.923880i	0.220942	−	0.533402i
$3$	0.382683	−	0.923880i	0.220942	−	0.533402i
$4$		−	4.56155i		−	2.28078i
$5$	−3.29045	−	1.36295i	−1.47153	−	0.609529i	−0.504324	−	0.863514i	$-0.668258\pi$
$5$	−3.29045	−	1.36295i	−1.47153	−	0.609529i	−0.967208	+	0.253986i	$0.918258\pi$
$6$	−0.980264	−	2.36657i	−0.400191	−	0.966147i
$7$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$7$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$8$	−4.63972	−	4.63972i	−1.64039	−	1.64039i
$9$	−0.707107	−	0.707107i	−0.235702	−	0.235702i
$10$	−8.42865	+	3.49126i	−2.66537	+	1.10403i
$11$	0.597580	+	1.44269i	0.180177	+	0.434986i	0.988003	−	0.154435i	$-0.0493557\pi$
$11$	0.597580	+	1.44269i	0.180177	+	0.434986i	−0.807826	+	0.589421i	$0.799356\pi$
$12$	−4.21433	−	1.74563i	−1.21657	−	0.503920i
$13$			0.438447i			0.121603i	0.998150	+	0.0608017i	$0.0193657\pi$
$13$			0.438447i			0.121603i	−0.998150	+	0.0608017i	$0.980634\pi$
$14$		0			0
$15$	−2.51840	+	2.51840i	−0.650248	+	0.650248i
$16$	−7.68466			−1.92116
$17$		0			0
$17$		0			0
$18$	−2.56155			−0.603764
$19$	3.31255	−	3.31255i	0.759952	−	0.759952i	−0.216361	−	0.976313i	$-0.569419\pi$
$19$	3.31255	−	3.31255i	0.759952	−	0.759952i	0.976313	+	0.216361i	$0.0694189\pi$
$20$	−6.21716	+	15.0095i	−1.39020	+	3.35624i
$21$		0			0
$22$	3.69552	+	1.53073i	0.787887	+	0.326354i
$23$	0.933153	+	2.25283i	0.194576	+	0.469748i	0.990813	−	0.135236i	$-0.0431794\pi$
$23$	0.933153	+	2.25283i	0.194576	+	0.469748i	−0.796237	+	0.604984i	$0.793179\pi$
$24$	−6.06208	+	2.51100i	−1.23742	+	0.512555i
$25$	5.43387	+	5.43387i	1.08677	+	1.08677i
$26$	0.794156	+	0.794156i	0.155747	+	0.155747i
$27$	−0.923880	+	0.382683i	−0.177801	+	0.0736475i
$28$		0			0
$29$	−7.61851	−	3.15569i	−1.41472	−	0.585997i	−0.461193	−	0.887300i	$-0.652578\pi$
$29$	−7.61851	−	3.15569i	−1.41472	−	0.585997i	−0.953528	+	0.301303i	$0.902578\pi$
$30$			9.12311i			1.66564i
$31$	1.19516	−	2.88537i	0.214657	−	0.518228i	−0.779471	−	0.626439i	$-0.784512\pi$
$31$	1.19516	−	2.88537i	0.214657	−	0.518228i	0.994128	+	0.108210i	$0.0345119\pi$
$32$	−4.63972	+	4.63972i	−0.820194	+	0.820194i
$33$	1.56155			0.271831
$34$		0			0
$35$		0			0
$36$	−3.22550	+	3.22550i	−0.537584	+	0.537584i
$37$	1.96053	−	4.73313i	0.322309	−	0.778122i	−0.676810	−	0.736157i	$-0.736638\pi$
$37$	1.96053	−	4.73313i	0.322309	−	0.778122i	0.999119	−	0.0419647i	$-0.0133617\pi$
$38$		−	12.0000i		−	1.94666i
$39$	0.405072	+	0.167786i	0.0648635	+	0.0268673i
$40$	8.94305	+	21.5904i	1.41402	+	3.41375i
$41$	3.29045	−	1.36295i	0.513881	−	0.212857i	−0.110646	−	0.993860i	$-0.535292\pi$
$41$	3.29045	−	1.36295i	0.513881	−	0.212857i	0.624527	+	0.781003i	$0.285292\pi$
$42$		0			0
$43$	−3.31255	−	3.31255i	−0.505160	−	0.505160i	0.407877	−	0.913037i	$-0.366269\pi$
$43$	−3.31255	−	3.31255i	−0.505160	−	0.505160i	−0.913037	+	0.407877i	$0.866269\pi$
$44$	6.58089	−	2.72589i	0.992107	−	0.410944i
$45$	1.36295	+	3.29045i	0.203176	+	0.490511i
$46$	5.77075	+	2.39032i	0.850850	+	0.352434i
$47$		−	11.1231i		−	1.62247i	−0.584719	−	0.811236i	$-0.698795\pi$
$47$		−	11.1231i		−	1.62247i	0.584719	−	0.811236i	$-0.301205\pi$
$48$	−2.94079	+	7.09970i	−0.424467	+	1.02475i
$49$	−4.94975	+	4.94975i	−0.707107	+	0.707107i
$50$	19.6847			2.78383
$51$		0			0
$52$	2.00000			0.277350
$53$	−8.65938	+	8.65938i	−1.18946	+	1.18946i	−0.212240	+	0.977218i	$0.568076\pi$
$53$	−8.65938	+	8.65938i	−1.18946	+	1.18946i	−0.977218	+	0.212240i	$0.931924\pi$
$54$	−0.980264	+	2.36657i	−0.133397	+	0.322049i
$55$		−	5.56155i		−	0.749920i
$56$		0			0
$57$	−1.79274	−	4.32806i	−0.237454	−	0.573266i
$58$	−19.5152	+	8.08346i	−2.56247	+	1.06141i
$59$	5.03680	+	5.03680i	0.655735	+	0.655735i	0.954368	−	0.298633i	$-0.0965306\pi$
$59$	5.03680	+	5.03680i	0.655735	+	0.655735i	−0.298633	+	0.954368i	$0.596531\pi$
$60$	11.4878	+	11.4878i	1.48307	+	1.48307i
$61$	8.42865	−	3.49126i	1.07918	−	0.447010i	0.228957	−	0.973436i	$-0.426468\pi$
$61$	8.42865	−	3.49126i	1.07918	−	0.447010i	0.850221	+	0.526426i	$0.176468\pi$
$62$	−3.06147	−	7.39104i	−0.388807	−	0.938663i
$63$		0			0
$64$			1.43845i			0.179806i
$65$	0.597580	−	1.44269i	0.0741207	−	0.178943i
$66$	2.82843	−	2.82843i	0.348155	−	0.348155i
$67$	−4.00000			−0.488678			−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000			−0.488678			−0.244339	+	0.969690i	$0.578571\pi$
$68$		0			0
$69$	2.43845			0.293555
$70$		0			0
$71$	2.39032	−	5.77075i	0.283679	−	0.684862i	−0.716237	−	0.697858i	$-0.754137\pi$
$71$	2.39032	−	5.77075i	0.283679	−	0.684862i	0.999916	+	0.0129959i	$0.00413685\pi$
$72$			6.56155i			0.773286i
$73$	11.3140	+	4.68642i	1.32421	+	0.548504i	0.928997	−	0.370087i	$-0.120672\pi$
$73$	11.3140	+	4.68642i	1.32421	+	0.548504i	0.395209	+	0.918591i	$0.370672\pi$
$74$	−5.02200	−	12.1242i	−0.583795	−	1.40941i
$75$	7.09970	−	2.94079i	0.819803	−	0.339573i
$76$	−15.1104	−	15.1104i	−1.73328	−	1.73328i
$77$		0			0
$78$	1.03761	−	0.429794i	0.117487	−	0.0486646i
$79$	−3.58548	−	8.65612i	−0.403398	−	0.973890i	−0.986835	−	0.161731i	$-0.948292\pi$
$79$	−3.58548	−	8.65612i	−0.403398	−	0.973890i	0.583437	−	0.812159i	$-0.301708\pi$
$80$	25.2860	+	10.4738i	2.82706	+	1.17100i
$81$			1.00000i			0.111111i
$82$	3.49126	−	8.42865i	0.385545	−	0.930789i
$83$	−0.620058	+	0.620058i	−0.0680602	+	0.0680602i	−0.740318	−	0.672257i	$-0.765325\pi$
$83$	−0.620058	+	0.620058i	−0.0680602	+	0.0680602i	0.672257	+	0.740318i	$0.265325\pi$
$84$		0			0
$85$		0			0
$86$	−12.0000			−1.29399
$87$	−5.83095	+	5.83095i	−0.625144	+	0.625144i
$88$	3.92106	−	9.46626i	0.417986	−	1.00911i
$89$			1.12311i			0.119049i	0.998227	+	0.0595245i	$0.0189584\pi$
$89$			1.12311i			0.119049i	−0.998227	+	0.0595245i	$0.981042\pi$
$90$	8.42865	+	3.49126i	0.888458	+	0.368011i
$91$		0			0
$92$	10.2764	−	4.25663i	1.07139	−	0.443784i
$93$	−2.20837	−	2.20837i	−0.228997	−	0.228997i
$94$	−20.1472	−	20.1472i	−2.07802	−	2.07802i
$95$	−15.4146	+	6.38494i	−1.58151	+	0.655081i
$96$	2.51100	+	6.06208i	0.256278	+	0.618709i
$97$	−2.65790	−	1.10094i	−0.269869	−	0.111784i	0.243645	−	0.969864i	$-0.421657\pi$
$97$	−2.65790	−	1.10094i	−0.269869	−	0.111784i	−0.513514	+	0.858081i	$0.671657\pi$
$98$			17.9309i			1.81129i
$99$	0.597580	−	1.44269i	0.0600591	−	0.144995i
$100$	24.7869	−	24.7869i	2.47869	−	2.47869i
$101$	−10.8769			−1.08229			−0.541146	−	0.840929i	$-0.682009\pi$
$101$	−10.8769			−1.08229			−0.541146	+	0.840929i	$0.682009\pi$
$102$		0			0
$103$	16.6847			1.64399			0.821994	−	0.569496i	$-0.192862\pi$
$103$	16.6847			1.64399			0.821994	+	0.569496i	$0.192862\pi$
$104$	2.03427	−	2.03427i	0.199477	−	0.199477i
$105$		0			0
$106$			31.3693i			3.04686i
$107$	4.32806	+	1.79274i	0.418409	+	0.173311i	0.581948	−	0.813226i	$-0.302291\pi$
$107$	4.32806	+	1.79274i	0.418409	+	0.173311i	−0.163538	+	0.986537i	$0.552291\pi$
$108$	1.74563	+	4.21433i	0.167973	+	0.405524i
$109$	6.35342	−	2.63167i	0.608547	−	0.252069i	−0.0570599	−	0.998371i	$-0.518173\pi$
$109$	6.35342	−	2.63167i	0.608547	−	0.252069i	0.665607	+	0.746302i	$0.268173\pi$
$110$	−10.0736	−	10.0736i	−0.960479	−	0.960479i
$111$	−3.62258	−	3.62258i	−0.343840	−	0.343840i
$112$		0			0
$113$	−0.167786	−	0.405072i	−0.0157840	−	0.0381060i	0.915791	−	0.401655i	$-0.131565\pi$
$113$	−0.167786	−	0.405072i	−0.0157840	−	0.0381060i	−0.931575	+	0.363549i	$0.881565\pi$
$114$	−11.0866	−	4.59220i	−1.03835	−	0.430099i
$115$		−	8.68466i		−	0.809849i
$116$	−14.3948	+	34.7522i	−1.33653	+	3.22666i
$117$	0.310029	−	0.310029i	0.0286622	−	0.0286622i
$118$	18.2462			1.67970
$119$		0			0
$120$	23.3693			2.13332
$121$	6.05393	−	6.05393i	0.550357	−	0.550357i
$122$	8.94305	−	21.5904i	0.809666	−	1.95471i
$123$		−	3.56155i		−	0.321134i
$124$	−13.1618	−	5.45179i	−1.18196	−	0.489585i
$125$	−3.65905	−	8.83372i	−0.327275	−	0.790112i
$126$		0			0
$127$	14.0062	+	14.0062i	1.24285	+	1.24285i	0.958814	+	0.284036i	$0.0916735\pi$
$127$	14.0062	+	14.0062i	1.24285	+	1.24285i	0.284036	+	0.958814i	$0.408326\pi$
$128$	−6.67399	−	6.67399i	−0.589903	−	0.589903i
$129$	−4.32806	+	1.79274i	−0.381064	+	0.157842i
$130$	−1.53073	−	3.69552i	−0.134254	−	0.324118i
$131$	13.3394	+	5.52535i	1.16547	+	0.482752i	0.879692	−	0.475544i	$-0.157749\pi$
$131$	13.3394	+	5.52535i	1.16547	+	0.482752i	0.285776	+	0.958297i	$0.407749\pi$
$132$		−	7.12311i		−	0.619987i
$133$		0			0
$134$	−7.24517	+	7.24517i	−0.625887	+	0.625887i
$135$	3.56155			0.306530
$136$		0			0
$137$	0.246211			0.0210352			0.0105176	−	0.999945i	$-0.496652\pi$
$137$	0.246211			0.0210352			0.0105176	+	0.999945i	$0.496652\pi$
$138$	4.41674	−	4.41674i	0.375978	−	0.375978i
$139$	0.335573	−	0.810145i	0.0284629	−	0.0687156i	−0.909009	−	0.416777i	$-0.863160\pi$
$139$	0.335573	−	0.810145i	0.0284629	−	0.0687156i	0.937472	+	0.348061i	$0.113160\pi$
$140$		0			0
$141$	−10.2764	−	4.25663i	−0.865430	−	0.358473i
$142$	−6.12293	−	14.7821i	−0.513825	−	1.24048i
$143$	−0.632542	+	0.262007i	−0.0528958	+	0.0219102i
$144$	5.43387	+	5.43387i	0.452823	+	0.452823i
$145$	20.7672	+	20.7672i	1.72463	+	1.72463i
$146$	28.9815	−	12.0045i	2.39852	−	0.993501i
$147$	2.67878	+	6.46716i	0.220942	+	0.533402i
$148$	−21.5904	−	8.94305i	−1.77472	−	0.735114i
$149$			12.2462i			1.00325i	0.865086	+	0.501624i	$0.167264\pi$
$149$			12.2462i			1.00325i	−0.865086	+	0.501624i	$0.832736\pi$
$150$	7.53299	−	18.1863i	0.615066	−	1.48490i
$151$	5.65685	−	5.65685i	0.460348	−	0.460348i	−0.438421	−	0.898770i	$-0.644462\pi$
$151$	5.65685	−	5.65685i	0.460348	−	0.460348i	0.898770	+	0.438421i	$0.144462\pi$
$152$	−30.7386			−2.49323
$153$		0			0
$154$		0			0
$155$	−7.86522	+	7.86522i	−0.631750	+	0.631750i
$156$	0.765367	−	1.84776i	0.0612784	−	0.147939i
$157$		−	6.68466i		−	0.533494i	−0.963767	−	0.266747i	$-0.914051\pi$
$157$		−	6.68466i		−	0.533494i	0.963767	−	0.266747i	$-0.0859488\pi$
$158$	−22.1731	−	9.18440i	−1.76400	−	0.730672i
$159$	4.68642	+	11.3140i	0.371657	+	0.897260i
$160$	21.5904	−	8.94305i	1.70687	−	0.707010i
$161$		0			0
$162$	1.81129	+	1.81129i	0.142308	+	0.142308i
$163$	−13.9719	+	5.78736i	−1.09437	+	0.453301i	−0.855527	−	0.517758i	$-0.826767\pi$
$163$	−13.9719	+	5.78736i	−1.09437	+	0.453301i	−0.238839	+	0.971059i	$0.576767\pi$
$164$	−6.21716	−	15.0095i	−0.485478	−	1.17205i
$165$	−5.13820	−	2.12831i	−0.400009	−	0.165689i
$166$			2.24621i			0.174340i
$167$	7.58010	−	18.3000i	0.586566	−	1.41610i	−0.300200	−	0.953876i	$-0.597053\pi$
$167$	7.58010	−	18.3000i	0.586566	−	1.41610i	0.886766	−	0.462219i	$-0.152947\pi$
$168$		0			0
$169$	12.8078			0.985213
$170$		0			0
$171$	−4.68466			−0.358245
$172$	−15.1104	+	15.1104i	−1.15216	+	1.15216i
$173$	−0.691801	+	1.67016i	−0.0525967	+	0.126980i	−0.947994	−	0.318289i	$-0.896892\pi$
$173$	−0.691801	+	1.67016i	−0.0525967	+	0.126980i	0.895397	+	0.445269i	$0.146892\pi$
$174$			21.1231i			1.60134i
$175$		0			0
$176$	−4.59220	−	11.0866i	−0.346150	−	0.835680i
$177$	6.58089	−	2.72589i	0.494650	−	0.204891i
$178$	2.03427	+	2.03427i	0.152475	+	0.152475i
$179$	0.620058	+	0.620058i	0.0463453	+	0.0463453i	0.729900	−	0.683554i	$-0.239567\pi$
$179$	0.620058	+	0.620058i	0.0463453	+	0.0463453i	−0.683554	+	0.729900i	$0.739567\pi$
$180$	15.0095	−	6.21716i	1.11875	−	0.463399i
$181$	2.29610	+	5.54328i	0.170668	+	0.412029i	0.985951	−	0.167034i	$-0.0534188\pi$
$181$	2.29610	+	5.54328i	0.170668	+	0.412029i	−0.815283	+	0.579062i	$0.803419\pi$
$182$		0			0
$183$		−	9.12311i		−	0.674399i
$184$	6.12293	−	14.7821i	0.451389	−	1.08975i
$185$	−12.9020	+	12.9020i	−0.948575	+	0.948575i
$186$	−8.00000			−0.586588
$187$		0			0
$188$	−50.7386			−3.70050
$189$		0			0
$190$	−16.3554	+	39.4853i	−1.18654	+	2.86457i
$191$			4.87689i			0.352880i	0.984311	+	0.176440i	$0.0564581\pi$
$191$			4.87689i			0.352880i	−0.984311	+	0.176440i	$0.943542\pi$
$192$	1.32895	+	0.550470i	0.0959088	+	0.0397267i
$193$	2.96725	+	7.16357i	0.213587	+	0.515645i	0.993969	−	0.109658i	$-0.0349755\pi$
$193$	2.96725	+	7.16357i	0.213587	+	0.515645i	−0.780382	+	0.625303i	$0.784976\pi$
$194$	−6.80836	+	2.82012i	−0.488812	+	0.202472i
$195$	−1.10418	−	1.10418i	−0.0790723	−	0.0790723i
$196$	22.5785	+	22.5785i	1.61275	+	1.61275i
$197$	−8.25105	+	3.41770i	−0.587863	+	0.243501i	−0.656731	−	0.754125i	$-0.728061\pi$
$197$	−8.25105	+	3.41770i	−0.587863	+	0.243501i	0.0688681	+	0.997626i	$0.478061\pi$
$198$	−1.53073	−	3.69552i	−0.108785	−	0.262629i
$199$	14.7821	+	6.12293i	1.04787	+	0.434043i	0.839132	−	0.543928i	$-0.183063\pi$
$199$	14.7821	+	6.12293i	1.04787	+	0.434043i	0.208741	+	0.977971i	$0.433063\pi$
$200$		−	50.4233i		−	3.56547i
$201$	−1.53073	+	3.69552i	−0.107970	+	0.260662i
$202$	−19.7012	+	19.7012i	−1.38617	+	1.38617i
$203$		0			0
$204$		0			0
$205$	−12.6847			−0.885935
$206$	30.2208	−	30.2208i	2.10558	−	2.10558i
$207$	0.933153	−	2.25283i	0.0648586	−	0.156583i
$208$		−	3.36932i		−	0.233620i
$209$	6.75849	+	2.79946i	0.467495	+	0.193643i
$210$		0			0
$211$	−12.3516	+	5.11622i	−0.850322	+	0.352215i	−0.764915	−	0.644131i	$-0.777219\pi$
$211$	−12.3516	+	5.11622i	−0.850322	+	0.352215i	−0.0854069	+	0.996346i	$0.527219\pi$
$212$	39.5002	+	39.5002i	2.71289	+	2.71289i
$213$	−4.41674	−	4.41674i	−0.302630	−	0.302630i
$214$	11.0866	−	4.59220i	0.757861	−	0.313916i
$215$	6.38494	+	15.4146i	0.435449	+	1.05127i
$216$	6.06208	+	2.51100i	0.412473	+	0.170852i
$217$		0			0
$218$	6.74117	−	16.2746i	0.456570	−	1.10226i
$219$	8.65938	−	8.65938i	0.585147	−	0.585147i
$220$	−25.3693			−1.71040
$221$		0			0
$222$	−13.1231			−0.880765
$223$	10.5577	−	10.5577i	0.706997	−	0.706997i	−0.258905	−	0.965903i	$-0.583362\pi$
$223$	10.5577	−	10.5577i	0.706997	−	0.706997i	0.965903	+	0.258905i	$0.0833618\pi$
$224$		0			0
$225$		−	7.68466i		−	0.512311i
$226$	−1.03761	−	0.429794i	−0.0690211	−	0.0285895i
$227$	5.37822	+	12.9842i	0.356965	+	0.861790i	0.995724	+	0.0923829i	$0.0294484\pi$
$227$	5.37822	+	12.9842i	0.356965	+	0.861790i	−0.638758	+	0.769407i	$0.720552\pi$
$228$	−19.7427	+	8.17768i	−1.30749	+	0.541580i
$229$	4.24264	+	4.24264i	0.280362	+	0.280362i	0.833253	−	0.552892i	$-0.186476\pi$
$229$	4.24264	+	4.24264i	0.280362	+	0.280362i	−0.552892	+	0.833253i	$0.686476\pi$
$230$	−15.7304	−	15.7304i	−1.03723	−	1.03723i
$231$		0			0
$232$	20.7062	+	49.9892i	1.35943	+	3.28195i
$233$	−3.29045	−	1.36295i	−0.215564	−	0.0892896i	0.272288	−	0.962216i	$-0.412220\pi$
$233$	−3.29045	−	1.36295i	−0.215564	−	0.0892896i	−0.487852	+	0.872926i	$0.662220\pi$
$234$		−	1.12311i		−	0.0734197i
$235$	−15.1602	+	36.6000i	−0.988943	+	2.38752i
$236$	22.9756	−	22.9756i	1.49558	−	1.49558i
$237$	−9.36932			−0.608603
$238$		0			0
$239$	−6.24621			−0.404034			−0.202017	−	0.979382i	$-0.564750\pi$
$239$	−6.24621			−0.404034			−0.202017	+	0.979382i	$0.564750\pi$
$240$	19.3530	−	19.3530i	1.24923	−	1.24923i
$241$	−1.28938	+	3.11284i	−0.0830564	+	0.200516i	−0.959952	−	0.280166i	$-0.909611\pi$
$241$	−1.28938	+	3.11284i	−0.0830564	+	0.200516i	0.876895	+	0.480681i	$0.159611\pi$
$242$		−	21.9309i		−	1.40977i
$243$	0.923880	+	0.382683i	0.0592669	+	0.0245492i
$244$	−15.9256	−	38.4477i	−1.01953	−	2.46136i
$245$	23.0331	−	9.54063i	1.47153	−	0.609529i
$246$	−6.45101	−	6.45101i	−0.411301	−	0.411301i
$247$	1.45238	+	1.45238i	0.0924127	+	0.0924127i
$248$	−18.9325	+	7.84211i	−1.20222	+	0.497975i
$249$	0.335573	+	0.810145i	0.0212661	+	0.0513408i
$250$	−22.6280	−	9.37284i	−1.43112	−	0.592791i
$251$			8.49242i			0.536037i	0.963414	+	0.268018i	$0.0863688\pi$
$251$			8.49242i			0.536037i	−0.963414	+	0.268018i	$0.913631\pi$
$252$		0			0
$253$	−2.69250	+	2.69250i	−0.169276	+	0.169276i
$254$	50.7386			3.18363
$255$		0			0
$256$	−27.0540			−1.69087
$257$	10.8677	−	10.8677i	0.677912	−	0.677912i	−0.281616	−	0.959527i	$-0.590870\pi$
$257$	10.8677	−	10.8677i	0.677912	−	0.677912i	0.959527	+	0.281616i	$0.0908703\pi$
$258$	−4.59220	+	11.0866i	−0.285898	+	0.690219i
$259$		0			0
$260$	−6.58089	−	2.72589i	−0.408130	−	0.169053i
$261$	3.15569	+	7.61851i	0.195332	+	0.471574i
$262$	34.1695	−	14.1535i	2.11100	−	0.874405i
$263$	−14.4903	−	14.4903i	−0.893512	−	0.893512i	0.101340	−	0.994852i	$-0.467687\pi$
$263$	−14.4903	−	14.4903i	−0.893512	−	0.893512i	−0.994852	+	0.101340i	$0.967687\pi$
$264$	−7.24517	−	7.24517i	−0.445909	−	0.445909i
$265$	40.2955	−	16.6909i	2.47533	−	1.02532i
$266$		0			0
$267$	1.03761	+	0.429794i	0.0635010	+	0.0263030i
$268$			18.2462i			1.11456i
$269$	6.29072	−	15.1871i	0.383552	−	0.925977i	−0.607721	−	0.794151i	$-0.707916\pi$
$269$	6.29072	−	15.1871i	0.383552	−	0.925977i	0.991273	−	0.131826i	$-0.0420840\pi$
$270$	6.45101	−	6.45101i	0.392596	−	0.392596i
$271$	−19.8078			−1.20324			−0.601618	−	0.798784i	$-0.705477\pi$
$271$	−19.8078			−1.20324			−0.601618	+	0.798784i	$0.705477\pi$
$272$		0			0
$273$		0			0
$274$	0.445960	−	0.445960i	0.0269414	−	0.0269414i
$275$	−4.59220	+	11.0866i	−0.276920	+	0.668544i
$276$		−	11.1231i		−	0.669532i
$277$	−5.54328	−	2.29610i	−0.333063	−	0.137959i	0.209884	−	0.977726i	$-0.432691\pi$
$277$	−5.54328	−	2.29610i	−0.333063	−	0.137959i	−0.542947	+	0.839767i	$0.682691\pi$
$278$	−0.859588	−	2.07523i	−0.0515547	−	0.124464i
$279$	−2.88537	+	1.19516i	−0.172743	+	0.0715524i
$280$		0			0
$281$	7.69113	+	7.69113i	0.458814	+	0.458814i	0.898266	−	0.439452i	$-0.144827\pi$
$281$	7.69113	+	7.69113i	0.458814	+	0.458814i	−0.439452	+	0.898266i	$0.644827\pi$
$282$	−26.3236	+	10.9036i	−1.56755	+	0.649299i
$283$	8.17768	+	19.7427i	0.486113	+	1.17358i	0.956660	+	0.291206i	$0.0940564\pi$
$283$	8.17768	+	19.7427i	0.486113	+	1.17358i	−0.470548	+	0.882375i	$0.655944\pi$
$284$	−26.3236	−	10.9036i	−1.56202	−	0.647008i
$285$			16.6847i			0.988314i
$286$	−0.671146	+	1.62029i	−0.0396857	+	0.0958097i
$287$		0			0
$288$	6.56155			0.386643
$289$		0			0
$290$	75.2311			4.41772
$291$	−2.03427	+	2.03427i	−0.119251	+	0.119251i
$292$	21.3774	−	51.6095i	1.25102	−	3.02022i
$293$		−	1.12311i		−	0.0656125i	−0.999462	−	0.0328063i	$-0.989556\pi$
$293$		−	1.12311i		−	0.0656125i	0.999462	−	0.0328063i	$-0.0104444\pi$
$294$	16.5660	+	6.86185i	0.966147	+	0.400191i
$295$	−9.70842	−	23.4382i	−0.565246	−	1.36462i
$296$	−31.0567	+	12.8641i	−1.80513	+	0.747711i
$297$	−1.10418	−	1.10418i	−0.0640713	−	0.0640713i
$298$	22.1815	+	22.1815i	1.28494	+	1.28494i
$299$	−0.987748	+	0.409138i	−0.0571229	+	0.0236611i
$300$	−13.4146	−	32.3857i	−0.774491	−	1.86979i
$301$		0			0
$302$		−	20.4924i		−	1.17921i
$303$	−4.16241	+	10.0489i	−0.239124	+	0.577297i
$304$	−25.4558	+	25.4558i	−1.45999	+	1.45999i
$305$	−32.4924			−1.86051
$306$		0			0
$307$	32.4924			1.85444			0.927220	−	0.374516i	$-0.122191\pi$
$307$	32.4924			1.85444			0.927220	+	0.374516i	$0.122191\pi$
$308$		0			0
$309$	6.38494	−	15.4146i	0.363227	−	0.876907i
$310$			28.4924i			1.61826i
$311$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$311$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$312$	−1.10094	−	2.65790i	−0.0623284	−	0.150474i
$313$	−31.0567	+	12.8641i	−1.75543	+	0.727122i	−0.758257	+	0.651955i	$0.773949\pi$
$313$	−31.0567	+	12.8641i	−1.75543	+	0.727122i	−0.997171	+	0.0751670i	$0.976051\pi$
$314$	−12.1079	−	12.1079i	−0.683286	−	0.683286i
$315$		0			0
$316$	−39.4853	+	16.3554i	−2.22122	+	0.920061i
$317$	−6.88830	−	16.6298i	−0.386886	−	0.934024i	−0.990596	−	0.136821i	$-0.956312\pi$
$317$	−6.88830	−	16.6298i	−0.386886	−	0.934024i	0.603710	−	0.797204i	$-0.293688\pi$
$318$	28.9815	+	12.0045i	1.62520	+	0.673180i
$319$		−	12.8769i		−	0.720968i
$320$	1.96053	−	4.73313i	0.109597	−	0.264590i
$321$	3.31255	−	3.31255i	0.184889	−	0.184889i
$322$		0			0
$323$		0			0
$324$	4.56155			0.253420
$325$	−2.38247	+	2.38247i	−0.132155	+	0.132155i
$326$	−14.8246	+	35.7898i	−0.821061	+	1.98222i
$327$		−	6.87689i		−	0.380293i
$328$	−21.5904	−	8.94305i	−1.19213	−	0.493797i
$329$		0			0
$330$	−13.1618	+	5.45179i	−0.724532	+	0.300111i
$331$	−24.6999	−	24.6999i	−1.35763	−	1.35763i	−0.876835	−	0.480792i	$-0.840349\pi$
$331$	−24.6999	−	24.6999i	−1.35763	−	1.35763i	−0.480792	−	0.876835i	$-0.659651\pi$
$332$	2.82843	+	2.82843i	0.155230	+	0.155230i
$333$	−4.73313	+	1.96053i	−0.259374	+	0.107436i
$334$	−19.4168	−	46.8764i	−1.06244	−	2.56496i
$335$	13.1618	+	5.45179i	0.719105	+	0.297863i
$336$		0			0
$337$	−6.40560	+	15.4645i	−0.348935	+	0.842404i	0.647811	+	0.761801i	$0.275685\pi$
$337$	−6.40560	+	15.4645i	−0.348935	+	0.842404i	−0.996746	+	0.0806030i	$0.974315\pi$
$338$	23.1986	−	23.1986i	1.26184	−	1.26184i
$339$	−0.438447			−0.0238132
$340$		0			0
$341$	4.87689			0.264099
$342$	−8.48528	+	8.48528i	−0.458831	+	0.458831i
$343$		0			0
$344$			30.7386i			1.65732i
$345$	−8.02358	−	3.32347i	−0.431975	−	0.178930i
$346$	1.77209	+	4.27819i	0.0952679	+	0.229997i
$347$	7.84598	−	3.24991i	0.421194	−	0.174464i	−0.162012	−	0.986789i	$-0.551798\pi$
$347$	7.84598	−	3.24991i	0.421194	−	0.174464i	0.583206	+	0.812325i	$0.301798\pi$
$348$	26.5982	+	26.5982i	1.42581	+	1.42581i
$349$	−8.17525	−	8.17525i	−0.437611	−	0.437611i	0.453596	−	0.891207i	$-0.350141\pi$
$349$	−8.17525	−	8.17525i	−0.437611	−	0.437611i	−0.891207	+	0.453596i	$0.850141\pi$
$350$		0			0
$351$	−0.167786	−	0.405072i	−0.00895578	−	0.0216212i
$352$	−9.46626	−	3.92106i	−0.504554	−	0.208993i
$353$		−	10.4924i		−	0.558455i	−0.960225	−	0.279228i	$-0.909922\pi$
$353$		−	10.4924i		−	0.558455i	0.960225	−	0.279228i	$-0.0900784\pi$
$354$	6.98252	−	16.8573i	0.371117	−	0.895955i
$355$	−15.7304	+	15.7304i	−0.834885	+	0.834885i
$356$	5.12311			0.271524
$357$		0			0
$358$	2.24621			0.118716
$359$	−10.0736	+	10.0736i	−0.531664	+	0.531664i	−0.921067	−	0.389403i	$-0.872681\pi$
$359$	−10.0736	+	10.0736i	−0.531664	+	0.531664i	0.389403	+	0.921067i	$0.372681\pi$
$360$	8.94305	−	21.5904i	0.471340	−	1.13792i
$361$		−	2.94602i		−	0.155054i
$362$	14.1994	+	5.88158i	0.746304	+	0.309129i
$363$	−3.27636	−	7.90984i	−0.171965	−	0.415159i
$364$		0			0
$365$	−30.8408	−	30.8408i	−1.61428	−	1.61428i
$366$	−16.5246	−	16.5246i	−0.863755	−	0.863755i
$367$	−1.62029	+	0.671146i	−0.0845784	+	0.0350335i	−0.424572	−	0.905394i	$-0.639575\pi$
$367$	−1.62029	+	0.671146i	−0.0845784	+	0.0350335i	0.339993	+	0.940428i	$0.389575\pi$
$368$	−7.17096	−	17.3122i	−0.373812	−	0.902463i
$369$	−3.29045	−	1.36295i	−0.171294	−	0.0709522i
$370$			46.7386i			2.42983i
$371$		0			0
$372$	−10.0736	+	10.0736i	−0.522291	+	0.522291i
$373$	0.246211			0.0127483			0.00637417	−	0.999980i	$-0.497971\pi$
$373$	0.246211			0.0127483			0.00637417	+	0.999980i	$0.497971\pi$
$374$		0			0
$375$	−9.56155			−0.493756
$376$	−51.6081	+	51.6081i	−2.66148	+	2.66148i
$377$	1.38360	−	3.34031i	0.0712592	−	0.172035i
$378$		0			0
$379$	11.0866	+	4.59220i	0.569478	+	0.235886i	0.648794	−	0.760964i	$-0.275274\pi$
$379$	11.0866	+	4.59220i	0.569478	+	0.235886i	−0.0793161	+	0.996850i	$0.525274\pi$
$380$	29.1253	+	70.3146i	1.49409	+	3.60706i
$381$	18.3000	−	7.58010i	0.937537	−	0.388340i
$382$	8.83348	+	8.83348i	0.451960	+	0.451960i
$383$	−4.41674	−	4.41674i	−0.225685	−	0.225685i	0.585202	−	0.810887i	$-0.301015\pi$
$383$	−4.41674	−	4.41674i	−0.225685	−	0.225685i	−0.810887	+	0.585202i	$0.801015\pi$
$384$	−8.71999	+	3.61194i	−0.444990	+	0.184321i
$385$		0			0
$386$	18.3499	+	7.60076i	0.933983	+	0.386868i
$387$			4.68466i			0.238135i
$388$	−5.02200	+	12.1242i	−0.254953	+	0.615511i
$389$	25.3581	−	25.3581i	1.28571	−	1.28571i	0.348336	−	0.937370i	$-0.386747\pi$
$389$	25.3581	−	25.3581i	1.28571	−	1.28571i	0.937370	−	0.348336i	$-0.113253\pi$
$390$	−4.00000			−0.202548
$391$		0			0
$392$	45.9309			2.31986
$393$	10.2095	−	10.2095i	0.515002	−	0.515002i
$394$	−8.75461	+	21.1355i	−0.441051	+	1.06479i
$395$			33.3693i			1.67899i
$396$	−6.58089	−	2.72589i	−0.330702	−	0.136981i
$397$	7.41232	+	17.8949i	0.372014	+	0.898120i	0.993409	+	0.114623i	$0.0365660\pi$
$397$	7.41232	+	17.8949i	0.372014	+	0.898120i	−0.621396	+	0.783497i	$0.713434\pi$
$398$	37.8651	−	15.6842i	1.89800	−	0.786179i
$399$		0			0
$400$	−41.7575	−	41.7575i	−2.08787	−	2.08787i
$401$	36.1949	−	14.9924i	1.80749	−	0.748686i	0.824283	−	0.566178i	$-0.191579\pi$
$401$	36.1949	−	14.9924i	1.80749	−	0.748686i	0.983204	−	0.182507i	$-0.0584213\pi$
$402$	3.92106	+	9.46626i	0.195564	+	0.472134i
$403$	1.26508	+	0.524015i	0.0630183	+	0.0261030i
$404$			49.6155i			2.46846i
$405$	1.36295	−	3.29045i	0.0677254	−	0.163504i
$406$		0			0
$407$	8.00000			0.396545
$408$		0			0
$409$	−14.6847			−0.726110			−0.363055	−	0.931768i	$-0.618266\pi$
$409$	−14.6847			−0.726110			−0.363055	+	0.931768i	$0.618266\pi$
$410$	−22.9756	+	22.9756i	−1.13468	+	1.13468i
$411$	0.0942210	−	0.227470i	0.00464758	−	0.0112202i
$412$		−	76.1080i		−	3.74957i
$413$		0			0
$414$	−2.39032	−	5.77075i	−0.117478	−	0.283617i
$415$	2.88537	−	1.19516i	0.141637	−	0.0586681i
$416$	−2.03427	−	2.03427i	−0.0997384	−	0.0997384i
$417$	−0.620058	−	0.620058i	−0.0303644	−	0.0303644i
$418$	17.3122	−	7.17096i	0.846769	−	0.350743i
$419$	−0.188442	−	0.454939i	−0.00920599	−	0.0222252i	0.919210	−	0.393768i	$-0.128829\pi$
$419$	−0.188442	−	0.454939i	−0.00920599	−	0.0222252i	−0.928416	+	0.371543i	$0.878829\pi$
$420$		0			0
$421$			24.4384i			1.19106i	0.803334	+	0.595529i	$0.203057\pi$
$421$			24.4384i			1.19106i	−0.803334	+	0.595529i	$0.796943\pi$
$422$	−13.1055	+	31.6394i	−0.637964	+	1.54018i
$423$	−7.86522	+	7.86522i	−0.382420	+	0.382420i
$424$	80.3542			3.90234
$425$		0			0
$426$	−16.0000			−0.775203
$427$		0			0
$428$	8.17768	−	19.7427i	0.395283	−	0.954298i
$429$			0.684658i			0.0330556i
$430$	39.4853	+	16.3554i	1.90415	+	0.788726i
$431$	9.18440	+	22.1731i	0.442397	+	1.06804i	0.975105	+	0.221742i	$0.0711743\pi$
$431$	9.18440	+	22.1731i	0.442397	+	1.06804i	−0.532708	+	0.846299i	$0.678826\pi$
$432$	7.09970	−	2.94079i	0.341584	−	0.141489i
$433$	18.8689	+	18.8689i	0.906782	+	0.906782i	0.996011	−	0.0892295i	$-0.0284405\pi$
$433$	18.8689	+	18.8689i	0.906782	+	0.906782i	−0.0892295	+	0.996011i	$0.528440\pi$
$434$		0			0
$435$	27.1337	−	11.2392i	1.30096	−	0.538876i
$436$	−12.0045	−	28.9815i	−0.574912	−	1.38796i
$437$	10.5537	+	4.37150i	0.504854	+	0.209117i
$438$		−	31.3693i		−	1.49888i
$439$	−8.51326	+	20.5528i	−0.406316	+	0.980933i	0.579783	+	0.814771i	$0.303137\pi$
$439$	−8.51326	+	20.5528i	−0.406316	+	0.980933i	−0.986099	+	0.166162i	$0.946863\pi$
$440$	−25.8040	+	25.8040i	−1.23016	+	1.23016i
$441$	7.00000			0.333333
$442$		0			0
$443$	−31.1231			−1.47870			−0.739352	−	0.673319i	$-0.764868\pi$
$443$	−31.1231			−1.47870			−0.739352	+	0.673319i	$0.764868\pi$
$444$	−16.5246	+	16.5246i	−0.784223	+	0.784223i
$445$	1.53073	−	3.69552i	0.0725637	−	0.175184i
$446$		−	38.2462i		−	1.81101i
$447$	11.3140	+	4.68642i	0.535135	+	0.221660i
$448$		0			0
$449$	−33.9421	+	14.0593i	−1.60183	+	0.663498i	−0.991672	−	0.128786i	$-0.958892\pi$
$449$	−33.9421	+	14.0593i	−1.60183	+	0.663498i	−0.610153	+	0.792284i	$0.708892\pi$
$450$	−13.9192	−	13.9192i	−0.656155	−	0.656155i
$451$	3.93261	+	3.93261i	0.185179	+	0.185179i
$452$	−1.84776	+	0.765367i	−0.0869113	+	0.0359998i
$453$	−3.06147	−	7.39104i	−0.143840	−	0.347261i
$454$	33.2597	+	13.7766i	1.56095	+	0.646568i
$455$		0			0
$456$	−11.7632	+	28.3988i	−0.550861	+	1.32990i
$457$	9.76356	−	9.76356i	0.456720	−	0.456720i	−0.440857	−	0.897577i	$-0.645325\pi$
$457$	9.76356	−	9.76356i	0.456720	−	0.456720i	0.897577	+	0.440857i	$0.145325\pi$
$458$	15.3693			0.718161
$459$		0			0
$460$	−39.6155			−1.84708
$461$	5.83095	−	5.83095i	0.271575	−	0.271575i	−0.558159	−	0.829734i	$-0.688492\pi$
$461$	5.83095	−	5.83095i	0.271575	−	0.271575i	0.829734	+	0.558159i	$0.188492\pi$
$462$		0			0
$463$			40.9848i			1.90473i	0.304965	+	0.952364i	$0.401355\pi$
$463$			40.9848i			1.90473i	−0.304965	+	0.952364i	$0.598645\pi$
$464$	58.5456	+	24.2504i	2.71791	+	1.12580i
$465$	4.25663	+	10.2764i	0.197396	+	0.476557i
$466$	−8.42865	+	3.49126i	−0.390450	+	0.161730i
$467$	15.1104	+	15.1104i	0.699225	+	0.699225i	0.964243	−	0.265018i	$-0.0853779\pi$
$467$	15.1104	+	15.1104i	0.699225	+	0.699225i	−0.265018	+	0.964243i	$0.585378\pi$
$468$	−1.41421	−	1.41421i	−0.0653720	−	0.0653720i
$469$		0			0
$470$	38.8337	+	93.7528i	1.79126	+	4.32449i
$471$	−6.17582	−	2.55811i	−0.284567	−	0.117871i
$472$		−	46.7386i		−	2.15132i
$473$	2.79946	−	6.75849i	0.128719	−	0.310756i
$474$	−16.9706	+	16.9706i	−0.779484	+	0.779484i
$475$	36.0000			1.65179
$476$		0			0
$477$	12.2462			0.560715
$478$	−11.3137	+	11.3137i	−0.517477	+	0.517477i
$479$	−9.29928	+	22.4504i	−0.424895	+	1.02579i	0.555988	+	0.831190i	$0.312340\pi$
$479$	−9.29928	+	22.4504i	−0.424895	+	1.02579i	−0.980883	+	0.194597i	$0.937660\pi$
$480$		−	23.3693i		−	1.06666i
$481$	2.07523	+	0.859588i	0.0946223	+	0.0391938i
$482$	3.30282	+	7.97371i	0.150439	+	0.363193i
$483$		0			0
$484$	−27.6153	−	27.6153i	−1.25524	−	1.25524i
$485$	7.24517	+	7.24517i	0.328986	+	0.328986i
$486$	2.36657	−	0.980264i	0.107350	−	0.0444657i
$487$	6.64695	+	16.0472i	0.301202	+	0.727166i	0.999931	+	0.0117792i	$0.00374952\pi$
$487$	6.64695	+	16.0472i	0.301202	+	0.727166i	−0.698729	+	0.715387i	$0.746250\pi$
$488$	−55.3050	−	22.9081i	−2.50354	−	1.03700i
$489$			15.1231i			0.683890i
$490$	24.4388	−	59.0006i	1.10403	−	2.66537i
$491$	−15.1104	+	15.1104i	−0.681922	+	0.681922i	−0.960433	−	0.278511i	$-0.910159\pi$
$491$	−15.1104	+	15.1104i	−0.681922	+	0.681922i	0.278511	+	0.960433i	$0.410159\pi$
$492$	−16.2462			−0.732436
$493$		0			0
$494$	5.26137			0.236720
$495$	−3.93261	+	3.93261i	−0.176758	+	0.176758i
$496$	−9.18440	+	22.1731i	−0.412392	+	0.995602i
$497$		0			0
$498$	2.07523	+	0.859588i	0.0929932	+	0.0385191i
$499$	−5.11622	−	12.3516i	−0.229033	−	0.552935i	0.767027	−	0.641615i	$-0.221735\pi$
$499$	−5.11622	−	12.3516i	−0.229033	−	0.552935i	−0.996060	+	0.0886797i	$0.971735\pi$
$500$	−40.2955	+	16.6909i	−1.80207	+	0.746442i
$501$	−14.0062	−	14.0062i	−0.625751	−	0.625751i
$502$	15.3823	+	15.3823i	0.686543	+	0.686543i
$503$	−27.3113	+	11.3127i	−1.21775	+	0.504409i	−0.896694	−	0.442651i	$-0.854038\pi$
$503$	−27.3113	+	11.3127i	−1.21775	+	0.504409i	−0.321057	+	0.947060i	$0.604038\pi$
$504$		0			0
$505$	35.7898	+	14.8246i	1.59263	+	0.659688i
$506$			9.75379i			0.433609i
$507$	4.90132	−	11.8328i	0.217675	−	0.525514i
$508$	63.8900	−	63.8900i	2.83466	−	2.83466i
$509$	−25.1231			−1.11356			−0.556781	−	0.830659i	$-0.687964\pi$
$509$	−25.1231			−1.11356			−0.556781	+	0.830659i	$0.687964\pi$
$510$		0			0
$511$		0			0
$512$	−35.6547	+	35.6547i	−1.57573	+	1.57573i
$513$	−1.79274	+	4.32806i	−0.0791515	+	0.191089i
$514$		−	39.3693i		−	1.73651i
$515$	−54.9000	−	22.7403i	−2.41918	−	1.00206i
$516$	8.17768	+	19.7427i	0.360002	+	0.869123i
$517$	16.0472	−	6.64695i	0.705753	−	0.292333i
$518$		0			0
$519$	1.27828	+	1.27828i	0.0561104	+	0.0561104i
$520$	−9.46626	+	3.92106i	−0.415123	+	0.171950i
$521$	−13.6088	−	32.8546i	−0.596213	−	1.43939i	−0.877413	−	0.479736i	$-0.840732\pi$
$521$	−13.6088	−	32.8546i	−0.596213	−	1.43939i	0.281200	−	0.959649i	$-0.409268\pi$
$522$	19.5152	+	8.08346i	0.854157	+	0.353804i
$523$		−	20.0000i		−	0.874539i	−0.899331	−	0.437269i	$-0.855946\pi$
$523$		−	20.0000i		−	0.874539i	0.899331	−	0.437269i	$-0.144054\pi$
$524$	25.2042	−	60.8483i	1.10105	−	2.65817i
$525$		0			0
$526$	−52.4924			−2.28878
$527$		0			0
$528$	−12.0000			−0.522233
$529$	12.0590	−	12.0590i	0.524304	−	0.524304i
$530$	42.7547	−	103.219i	1.85715	−	4.48355i
$531$		−	7.12311i		−	0.309116i
$532$		0			0
$533$	0.597580	+	1.44269i	0.0258841	+	0.0624897i
$534$	2.65790	−	1.10094i	0.115019	−	0.0476423i
$535$	−11.7978	−	11.7978i	−0.510065	−	0.510065i
$536$	18.5589	+	18.5589i	0.801621	+	0.801621i
$537$	0.810145	−	0.335573i	0.0349603	−	0.0144810i
$538$	−16.1140	−	38.9027i	−0.694725	−	1.67721i
$539$	−10.0988	−	4.18306i	−0.434986	−	0.180177i
$540$		−	16.2462i		−	0.699126i
$541$	13.0525	−	31.5116i	0.561173	−	1.35479i	−0.347656	−	0.937622i	$-0.613022\pi$
$541$	13.0525	−	31.5116i	0.561173	−	1.35479i	0.908829	−	0.417169i	$-0.136978\pi$
$542$	−35.8776	+	35.8776i	−1.54108	+	1.54108i
$543$	6.00000			0.257485
$544$		0			0
$545$	−24.4924			−1.04914
$546$		0			0
$547$	−10.7151	+	25.8686i	−0.458146	+	1.10606i	0.511001	+	0.859580i	$0.329275\pi$
$547$	−10.7151	+	25.8686i	−0.458146	+	1.10606i	−0.969147	+	0.246483i	$0.920725\pi$
$548$		−	1.12311i		−	0.0479767i
$549$	−8.42865	−	3.49126i	−0.359726	−	0.149003i
$550$	11.7632	+	28.3988i	0.501583	+	1.21093i
$551$	−35.6901	+	14.7833i	−1.52045	+	0.629791i
$552$	−11.3137	−	11.3137i	−0.481543	−	0.481543i
$553$		0			0
$554$	−14.1994	+	5.88158i	−0.603275	+	0.249885i
$555$	6.98252	+	16.8573i	0.296392	+	0.715553i
$556$	−3.69552	−	1.53073i	−0.156725	−	0.0649176i
$557$			26.4924i			1.12252i	0.827640	+	0.561260i	$0.189683\pi$
$557$			26.4924i			1.12252i	−0.827640	+	0.561260i	$0.810317\pi$
$558$	−3.06147	+	7.39104i	−0.129602	+	0.312888i
$559$	1.45238	−	1.45238i	0.0614291	−	0.0614291i
$560$		0			0
$561$		0			0
$562$	27.8617			1.17528
$563$	−22.0074	+	22.0074i	−0.927500	+	0.927500i	−0.997544	−	0.0700443i	$-0.977686\pi$
$563$	−22.0074	+	22.0074i	−0.927500	+	0.927500i	0.0700443	+	0.997544i	$0.477686\pi$
$564$	−19.4168	+	46.8764i	−0.817596	+	1.97385i
$565$			1.56155i			0.0656950i
$566$	50.5719	+	20.9476i	2.12570	+	0.880492i
$567$		0			0
$568$	−37.8651	+	15.6842i	−1.58878	+	0.658095i
$569$	14.9363	+	14.9363i	0.626162	+	0.626162i	0.947100	−	0.320938i	$-0.103998\pi$
$569$	14.9363	+	14.9363i	0.626162	+	0.626162i	−0.320938	+	0.947100i	$0.603998\pi$
$570$	30.2208	+	30.2208i	1.26581	+	1.26581i
$571$	−28.3988	+	11.7632i	−1.18845	+	0.492273i	−0.887251	−	0.461287i	$-0.847388\pi$
$571$	−28.3988	+	11.7632i	−1.18845	+	0.492273i	−0.301202	+	0.953560i	$0.597388\pi$
$572$	1.19516	+	2.88537i	0.0499722	+	0.120644i
$573$	4.50566	+	1.86631i	0.188227	+	0.0779661i
$574$		0			0
$575$	−7.17096	+	17.3122i	−0.299050	+	0.721970i
$576$	1.01714	−	1.01714i	0.0423807	−	0.0423807i
$577$	3.94602			0.164275			0.0821376	−	0.996621i	$-0.473825\pi$
$577$	3.94602			0.164275			0.0821376	+	0.996621i	$0.473825\pi$
$578$		0			0
$579$	7.75379			0.322236
$580$	94.7309	−	94.7309i	3.93349	−	3.93349i
$581$		0			0
$582$			7.36932i			0.305468i
$583$	−17.6674	−	7.31810i	−0.731711	−	0.303085i
$584$	−30.7502	−	74.2376i	−1.27245	−	3.07197i
$585$	−1.44269	+	0.597580i	−0.0596478	+	0.0247069i
$586$	−2.03427	−	2.03427i	−0.0840350	−	0.0840350i
$587$	20.4954	+	20.4954i	0.845935	+	0.845935i	0.989623	−	0.143688i	$-0.0458962\pi$
$587$	20.4954	+	20.4954i	0.845935	+	0.845935i	−0.143688	+	0.989623i	$0.545896\pi$
$588$	29.5003	−	12.2194i	1.21657	−	0.503920i
$589$	−5.59892	−	13.5170i	−0.230699	−	0.556958i
$590$	−60.0382	−	24.8686i	−2.47173	−	1.02383i
$591$			8.93087i			0.367367i
$592$	−15.0660	+	36.3725i	−0.619208	+	1.49490i
$593$	19.6249	−	19.6249i	0.805898	−	0.805898i	−0.178112	−	0.984010i	$-0.556999\pi$
$593$	19.6249	−	19.6249i	0.805898	−	0.805898i	0.984010	+	0.178112i	$0.0569991\pi$
$594$	−4.00000			−0.164122
$595$		0			0
$596$	55.8617			2.28819
$597$	11.3137	−	11.3137i	0.463039	−	0.463039i
$598$	−1.04803	+	2.53017i	−0.0428571	+	0.103466i
$599$			0.384472i			0.0157091i	0.999969	+	0.00785455i	$0.00250021\pi$
$599$			0.384472i			0.0157091i	−0.999969	+	0.00785455i	$0.997500\pi$
$600$	−46.5850	−	19.2962i	−1.90183	−	0.787762i
$601$	11.8574	+	28.6263i	0.483673	+	1.16769i	0.957852	+	0.287261i	$0.0927448\pi$
$601$	11.8574	+	28.6263i	0.483673	+	1.16769i	−0.474179	+	0.880428i	$0.657255\pi$
$602$		0			0
$603$	2.82843	+	2.82843i	0.115182	+	0.115182i
$604$	−25.8040	−	25.8040i	−1.04995	−	1.04995i
$605$	−28.1713	+	11.6689i	−1.14533	+	0.474410i
$606$	10.6622	+	25.7409i	0.433123	+	1.04565i
$607$	−8.65612	−	3.58548i	−0.351341	−	0.145530i	0.200031	−	0.979790i	$-0.435896\pi$
$607$	−8.65612	−	3.58548i	−0.351341	−	0.145530i	−0.551372	+	0.834259i	$0.685896\pi$
$608$			30.7386i			1.24662i
$609$		0			0
$610$	−58.8532	+	58.8532i	−2.38290	+	2.38290i
$611$	4.87689			0.197298
$612$		0			0
$613$	14.6847			0.593108			0.296554	−	0.955016i	$-0.404163\pi$
$613$	14.6847			0.593108			0.296554	+	0.955016i	$0.404163\pi$
$614$	58.8532	−	58.8532i	2.37512	−	2.37512i
$615$	−4.85421	+	11.7191i	−0.195741	+	0.472560i
$616$		0			0
$617$	40.8782	+	16.9323i	1.64569	+	0.681668i	0.996854	−	0.0792574i	$-0.0252549\pi$
$617$	40.8782	+	16.9323i	1.64569	+	0.681668i	0.648839	+	0.760926i	$0.275255\pi$
$618$	−16.3554	−	39.4853i	−0.657909	−	1.58833i
$619$	−4.96060	+	2.05475i	−0.199383	+	0.0825873i	−0.480141	−	0.877191i	$-0.659414\pi$
$619$	−4.96060	+	2.05475i	−0.199383	+	0.0825873i	0.280757	+	0.959779i	$0.409414\pi$
$620$	35.8776	+	35.8776i	1.44088	+	1.44088i
$621$	−1.72424	−	1.72424i	−0.0691915	−	0.0691915i
$622$		0			0
$623$		0			0
$624$	−3.11284	−	1.28938i	−0.124613	−	0.0516166i
$625$		−	4.36932i		−	0.174773i
$626$	−32.9521	+	79.5534i	−1.31703	+	3.17959i
$627$	5.17273	−	5.17273i	0.206579	−	0.206579i
$628$	−30.4924			−1.21678
$629$		0			0
$630$		0			0
$631$	0.484127	−	0.484127i	0.0192728	−	0.0192728i	−0.697405	−	0.716678i	$-0.745662\pi$
$631$	0.484127	−	0.484127i	0.0192728	−	0.0192728i	0.716678	+	0.697405i	$0.245662\pi$
$632$	−23.5263	+	56.7976i	−0.935827	+	2.25929i
$633$			13.3693i			0.531383i
$634$	−42.5982	−	17.6447i	−1.69179	−	0.700762i
$635$	−26.9969	−	65.1764i	−1.07134	−	2.58645i
$636$	51.6095	−	21.3774i	2.04645	−	0.847668i
$637$	−2.17020	−	2.17020i	−0.0859866	−	0.0859866i
$638$	−23.3238	−	23.3238i	−0.923398	−	0.923398i
$639$	−5.77075	+	2.39032i	−0.228287	+	0.0945597i
$640$	12.8641	+	31.0567i	0.508498	+	1.22762i
$641$	−26.7286	−	11.0714i	−1.05572	−	0.437293i	−0.213788	−	0.976880i	$-0.568580\pi$
$641$	−26.7286	−	11.0714i	−1.05572	−	0.437293i	−0.841930	+	0.539587i	$0.818580\pi$
$642$		−	12.0000i		−	0.473602i
$643$	−5.26335	+	12.7068i	−0.207566	+	0.501109i	−0.993039	−	0.117787i	$-0.962420\pi$
$643$	−5.26335	+	12.7068i	−0.207566	+	0.501109i	0.785473	+	0.618896i	$0.212420\pi$
$644$		0			0
$645$	16.6847			0.656958
$646$		0			0
$647$	−9.36932			−0.368346			−0.184173	−	0.982894i	$-0.558961\pi$
$647$	−9.36932			−0.368346			−0.184173	+	0.982894i	$0.558961\pi$
$648$	4.63972	−	4.63972i	0.182265	−	0.182265i
$649$	−4.25663	+	10.2764i	−0.167087	+	0.403384i
$650$			8.63068i			0.338523i
$651$		0			0
$652$	26.3994	+	63.7337i	1.03388	+	2.49600i
$653$	30.4242	−	12.6021i	1.19059	−	0.493158i	0.302642	−	0.953104i	$-0.402131\pi$
$653$	30.4242	−	12.6021i	1.19059	−	0.493158i	0.887947	+	0.459946i	$0.152131\pi$
$654$	−12.4561	−	12.4561i	−0.487070	−	0.487070i
$655$	−36.3618	−	36.3618i	−1.42077	−	1.42077i
$656$	−25.2860	+	10.4738i	−0.987251	+	0.408933i
$657$	−4.68642	−	11.3140i	−0.182835	−	0.441402i
$658$		0			0
$659$		−	9.86174i		−	0.384159i	−0.981379	−	0.192079i	$-0.938477\pi$
$659$		−	9.86174i		−	0.384159i	0.981379	−	0.192079i	$-0.0615231\pi$
$660$	−9.70842	+	23.4382i	−0.377900	+	0.912330i
$661$	9.41537	−	9.41537i	0.366215	−	0.366215i	−0.499880	−	0.866095i	$-0.666622\pi$
$661$	9.41537	−	9.41537i	0.366215	−	0.366215i	0.866095	+	0.499880i	$0.166622\pi$
$662$	−89.4773			−3.47763
$663$		0			0
$664$	5.75379			0.223290
$665$		0			0
$666$	−5.02200	+	12.1242i	−0.194598	+	0.469802i
$667$		−	20.1080i		−	0.778583i
$668$	−83.4764	−	34.5770i	−3.22980	−	1.33783i
$669$	−5.71380	−	13.7943i	−0.220908	−	0.533319i
$670$	33.7146	−	13.9650i	1.30251	−	0.539517i
$671$	10.0736	+	10.0736i	0.388887	+	0.388887i
$672$		0			0
$673$	−0.682409	+	0.282663i	−0.0263049	+	0.0108959i	−0.395797	−	0.918338i	$-0.629532\pi$
$673$	−0.682409	+	0.282663i	−0.0263049	+	0.0108959i	0.369492	+	0.929234i	$0.379532\pi$
$674$	16.4083	+	39.6131i	0.632023	+	1.52584i
$675$	−7.09970	−	2.94079i	−0.273268	−	0.113191i
$676$		−	58.4233i		−	2.24705i
$677$	−0.503359	+	1.21522i	−0.0193457	+	0.0467046i	−0.933257	−	0.359209i	$-0.883047\pi$
$677$	−0.503359	+	1.21522i	−0.0193457	+	0.0467046i	0.913912	+	0.405913i	$0.133047\pi$
$678$	−0.794156	+	0.794156i	−0.0304994	+	0.0304994i
$679$		0			0
$680$		0			0
$681$	14.0540			0.538550
$682$	8.83348	−	8.83348i	0.338251	−	0.338251i
$683$	3.65905	−	8.83372i	0.140010	−	0.338013i	−0.838285	−	0.545232i	$-0.816441\pi$
$683$	3.65905	−	8.83372i	0.140010	−	0.338013i	0.978294	+	0.207219i	$0.0664414\pi$
$684$			21.3693i			0.817076i
$685$	−0.810145	−	0.335573i	−0.0309540	−	0.0128216i
$686$		0			0
$687$	5.54328	−	2.29610i	0.211489	−	0.0876017i
$688$	25.4558	+	25.4558i	0.970495	+	0.970495i
$689$	−3.79668	−	3.79668i	−0.144642	−	0.144642i
$690$	−20.5528	+	8.51326i	−0.782432	+	0.324094i
$691$	−11.0920	−	26.7785i	−0.421960	−	1.01870i	−0.981769	−	0.190080i	$-0.939125\pi$
$691$	−11.0920	−	26.7785i	−0.421960	−	1.01870i	0.559808	−	0.828622i	$-0.310875\pi$
$692$	7.61851	+	3.15569i	0.289612	+	0.119961i
$693$		0			0
$694$	8.32481	−	20.0979i	0.316006	−	0.762905i
$695$	−2.20837	+	2.20837i	−0.0837682	+	0.0837682i
$696$	54.1080			2.05096
$697$		0			0
$698$	−29.6155			−1.12096
$699$	−2.51840	+	2.51840i	−0.0952546	+	0.0952546i
$700$		0			0
$701$		−	15.3693i		−	0.580491i	−0.956952	−	0.290246i	$-0.906263\pi$
$701$		−	15.3693i		−	0.580491i	0.956952	−	0.290246i	$-0.0937370\pi$
$702$	−1.03761	−	0.429794i	−0.0391622	−	0.0162215i
$703$	−9.18440	−	22.1731i	−0.346396	−	0.836275i
$704$	−2.07523	+	0.859588i	−0.0782131	+	0.0323969i
$705$	28.0124	+	28.0124i	1.05501	+	1.05501i
$706$	−19.0048	−	19.0048i	−0.715256	−	0.715256i
$707$		0			0
$708$	−12.4343	−	30.0191i	−0.467310	−	1.12819i
$709$	−41.3331	−	17.1207i	−1.55230	−	0.642983i	−0.568568	−	0.822637i	$-0.692502\pi$
$709$	−41.3331	−	17.1207i	−1.55230	−	0.642983i	−0.983730	+	0.179654i	$0.942502\pi$
$710$			56.9848i			2.13860i
$711$	−3.58548	+	8.65612i	−0.134466	+	0.324630i
$712$	5.21089	−	5.21089i	0.195287	−	0.195287i
$713$	7.61553			0.285204
$714$		0			0
$715$	2.43845			0.0911928
$716$	2.82843	−	2.82843i	0.105703	−	0.105703i
$717$	−2.39032	+	5.77075i	−0.0892682	+	0.215512i
$718$			36.4924i			1.36189i
$719$	10.9090	+	4.51864i	0.406835	+	0.168517i	0.576710	−	0.816949i	$-0.304336\pi$
$719$	10.9090	+	4.51864i	0.406835	+	0.168517i	−0.169875	+	0.985466i	$0.554336\pi$
$720$	−10.4738	−	25.2860i	−0.390335	−	0.942352i
$721$		0			0
$722$	−5.33611	−	5.33611i	−0.198589	−	0.198589i
$723$	2.38247	+	2.38247i	0.0886049	+	0.0886049i
$724$	25.2860	−	10.4738i	0.939745	−	0.389255i
$725$	−24.2504	−	58.5456i	−0.900637	−	2.17433i
$726$	−20.2615	−	8.39258i	−0.751974	−	0.311478i
$727$		−	8.00000i		−	0.296704i	−0.988935	−	0.148352i	$-0.952603\pi$
$727$		−	8.00000i		−	0.296704i	0.988935	−	0.148352i	$-0.0473968\pi$
$728$		0			0
$729$	0.707107	−	0.707107i	0.0261891	−	0.0261891i
$730$	−111.723			−4.13507
$731$		0			0
$732$	−41.6155			−1.53815
$733$	8.31118	−	8.31118i	0.306981	−	0.306981i	−0.536757	−	0.843737i	$-0.680351\pi$
$733$	8.31118	−	8.31118i	0.306981	−	0.306981i	0.843737	+	0.536757i	$0.180351\pi$
$734$	−1.71918	+	4.15046i	−0.0634559	+	0.153196i
$735$		−	24.9309i		−	0.919589i
$736$	−14.7821	−	6.12293i	−0.544874	−	0.225694i
$737$	−2.39032	−	5.77075i	−0.0880486	−	0.212568i
$738$	−8.42865	+	3.49126i	−0.310263	+	0.128515i
$739$	−14.6263	−	14.6263i	−0.538036	−	0.538036i	0.384916	−	0.922952i	$-0.374230\pi$
$739$	−14.6263	−	14.6263i	−0.538036	−	0.538036i	−0.922952	+	0.384916i	$0.874230\pi$
$740$	58.8532	+	58.8532i	2.16349	+	2.16349i
$741$	1.89763	−	0.786022i	0.0697110	−	0.0288753i
$742$		0			0
$743$	26.3236	+	10.9036i	0.965718	+	0.400013i	0.809116	−	0.587648i	$-0.199946\pi$
$743$	26.3236	+	10.9036i	0.965718	+	0.400013i	0.156602	+	0.987662i	$0.449946\pi$
$744$			20.4924i			0.751289i
$745$	16.6909	−	40.2955i	0.611509	−	1.47631i
$746$	0.445960	−	0.445960i	0.0163278	−	0.0163278i
$747$	0.876894			0.0320839
$748$		0			0
$749$		0			0
$750$	−17.3188	+	17.3188i	−0.632392	+	0.632392i
$751$	9.70842	−	23.4382i	0.354265	−	0.855272i	−0.641819	−	0.766857i	$-0.721820\pi$
$751$	9.70842	−	23.4382i	0.354265	−	0.855272i	0.996084	−	0.0884152i	$-0.0281802\pi$
$752$			85.4773i			3.11704i
$753$	7.84598	+	3.24991i	0.285923	+	0.118433i
$754$	−3.54417	−	8.55639i	−0.129071	−	0.311605i
$755$	−26.3236	+	10.9036i	−0.958013	+	0.396822i
$756$		0			0
$757$	−11.3519	−	11.3519i	−0.412591	−	0.412591i	0.470049	−	0.882640i	$-0.344236\pi$
$757$	−11.3519	−	11.3519i	−0.412591	−	0.412591i	−0.882640	+	0.470049i	$0.844236\pi$
$758$	28.3988	−	11.7632i	1.03149	−	0.427257i
$759$	1.45717	+	3.51792i	0.0528919	+	0.127692i
$760$	101.144	+	41.8951i	3.66887	+	1.51970i
$761$		−	15.7538i		−	0.571074i	−0.958368	−	0.285537i	$-0.907828\pi$
$761$		−	15.7538i		−	0.571074i	0.958368	−	0.285537i	$-0.0921720\pi$
$762$	19.4168	−	46.8764i	0.703398	−	1.69815i
$763$		0			0
$764$	22.2462			0.804840
$765$		0			0
$766$	−16.0000			−0.578103
$767$	−2.20837	+	2.20837i	−0.0797396	+	0.0797396i
$768$	−10.3531	+	24.9946i	−0.373586	+	0.901915i
$769$		−	40.5464i		−	1.46214i	−0.682302	−	0.731070i	$-0.739021\pi$
$769$		−	40.5464i		−	1.46214i	0.682302	−	0.731070i	$-0.260979\pi$
$770$		0			0
$771$	−5.88158	−	14.1994i	−0.211820	−	0.511379i
$772$	32.6770	−	13.5353i	1.17607	−	0.487144i
$773$	−6.10281	−	6.10281i	−0.219503	−	0.219503i	0.588786	−	0.808289i	$-0.299606\pi$
$773$	−6.10281	−	6.10281i	−0.219503	−	0.219503i	−0.808289	+	0.588786i	$0.799606\pi$
$774$	8.48528	+	8.48528i	0.304997	+	0.304997i
$775$	22.1731	−	9.18440i	0.796482	−	0.329913i
$776$	7.22387	+	17.4400i	0.259322	+	0.626059i
$777$		0			0
$778$		−	91.8617i		−	3.29340i
$779$	6.38494	−	15.4146i	0.228764	−	0.552286i
$780$	−5.03680	+	5.03680i	−0.180346	+	0.180346i
$781$	9.75379			0.349018
$782$		0			0
$783$	8.24621			0.294696
$784$	38.0371	−	38.0371i	1.35847	−	1.35847i
$785$	−9.11084	+	21.9955i	−0.325180	+	0.785053i
$786$		−	36.9848i		−	1.31921i
$787$	9.46626	+	3.92106i	0.337436	+	0.139771i	0.544966	−	0.838458i	$-0.316543\pi$
$787$	9.46626	+	3.92106i	0.337436	+	0.139771i	−0.207530	+	0.978229i	$0.566543\pi$
$788$	15.5900	+	37.6376i	0.555371	+	1.34078i
$789$	−18.9325	+	7.84211i	−0.674016	+	0.279187i
$790$	60.4416	+	60.4416i	2.15041	+	2.15041i
$791$		0			0
$792$	−9.46626	+	3.92106i	−0.336369	+	0.139329i
$793$	1.53073	+	3.69552i	0.0543579	+	0.131232i
$794$	45.8388	+	18.9870i	1.62676	+	0.673825i
$795$		−	43.6155i		−	1.54688i
$796$	27.9301	−	67.4292i	0.989956	−	2.38996i
$797$	−6.79921	+	6.79921i	−0.240840	+	0.240840i	−0.817198	−	0.576357i	$-0.804474\pi$
$797$	−6.79921	+	6.79921i	−0.240840	+	0.240840i	0.576357	+	0.817198i	$0.304474\pi$
$798$		0			0
$799$		0			0
$800$	−50.4233			−1.78273
$801$	0.794156	−	0.794156i	0.0280601	−	0.0280601i
$802$	38.4039	−	92.7152i	1.35609	−	3.27389i
$803$			19.1231i			0.674840i
$804$	16.8573	+	6.98252i	0.594511	+	0.246255i
$805$		0			0
$806$	3.24058	−	1.34229i	0.114145	−	0.0472802i
$807$	−11.6237	−	11.6237i	−0.409175	−	0.409175i
$808$	50.4657	+	50.4657i	1.77538	+	1.77538i
$809$	14.7322	−	6.10228i	0.517957	−	0.214545i	−0.108362	−	0.994111i	$-0.534561\pi$
$809$	14.7322	−	6.10228i	0.517957	−	0.214545i	0.626319	+	0.779567i	$0.284561\pi$
$810$	−3.49126	−	8.42865i	−0.122670	−	0.296153i
$811$	−41.9158	−	17.3621i	−1.47186	−	0.609665i	−0.504579	−	0.863365i	$-0.668352\pi$
$811$	−41.9158	−	17.3621i	−1.47186	−	0.609665i	−0.967283	+	0.253700i	$0.918352\pi$
$812$		0			0
$813$	−7.58010	+	18.3000i	−0.265846	+	0.641809i
$814$	14.4903	−	14.4903i	0.507886	−	0.507886i
$815$	53.8617			1.88669
$816$		0			0
$817$	−21.9460			−0.767794
$818$	−26.5982	+	26.5982i	−0.929984	+	0.929984i
$819$		0			0
$820$			57.8617i			2.02062i
$821$	11.4916	+	4.75999i	0.401061	+	0.166125i	0.574091	−	0.818792i	$-0.305356\pi$
$821$	11.4916	+	4.75999i	0.401061	+	0.166125i	−0.173030	+	0.984917i	$0.555356\pi$
$822$	−0.241352	−	0.582675i	−0.00841812	−	0.0203231i
$823$	−3.24058	+	1.34229i	−0.112959	+	0.0467894i	−0.438447	−	0.898757i	$-0.644471\pi$
$823$	−3.24058	+	1.34229i	−0.112959	+	0.0467894i	0.325488	+	0.945546i	$0.394471\pi$
$824$	−77.4121	−	77.4121i	−2.69678	−	2.69678i
$825$	8.48528	+	8.48528i	0.295420	+	0.295420i
$826$		0			0
$827$	18.1481	+	43.8134i	0.631072	+	1.52354i	0.838277	+	0.545244i	$0.183563\pi$
$827$	18.1481	+	43.8134i	0.631072	+	1.52354i	−0.207206	+	0.978297i	$0.566437\pi$
$828$	−10.2764	−	4.25663i	−0.357130	−	0.147928i
$829$			17.5076i			0.608063i	0.952662	+	0.304032i	$0.0983329\pi$
$829$			17.5076i			0.608063i	−0.952662	+	0.304032i	$0.901667\pi$
$830$	3.06147	−	7.39104i	0.106265	−	0.256547i
$831$	−4.24264	+	4.24264i	−0.147176	+	0.147176i
$832$	−0.630683			−0.0218650
$833$		0			0
$834$	−2.24621			−0.0777799
$835$	−49.8838	+	49.8838i	−1.72630	+	1.72630i
$836$	12.7699	−	30.8292i	0.441656	−	1.06625i
$837$			3.12311i			0.107950i
$838$	−1.16535	−	0.482704i	−0.0402564	−	0.0166747i
$839$	9.97042	+	24.0707i	0.344217	+	0.831014i	0.997280	+	0.0737100i	$0.0234839\pi$
$839$	9.97042	+	24.0707i	0.344217	+	0.831014i	−0.653062	+	0.757304i	$0.726516\pi$
$840$		0			0
$841$	27.5772	+	27.5772i	0.950937	+	0.950937i
$842$	44.2651	+	44.2651i	1.52548	+	1.52548i
$843$	10.0489	−	4.16241i	0.346104	−	0.143361i
$844$	23.3379	+	56.3427i	0.803323	+	1.93939i
$845$	−42.1433	−	17.4563i	−1.44977	−	0.600515i
$846$			28.4924i			0.979590i
$847$		0			0
$848$	66.5444	−	66.5444i	2.28514	−	2.28514i
$849$	21.3693			0.733393
$850$		0			0
$851$	12.4924			0.428235
$852$	−20.1472	+	20.1472i	−0.690231	+	0.690231i
$853$	10.9978	−	26.5510i	0.376557	−	0.909090i	−0.616048	−	0.787708i	$-0.711267\pi$
$853$	10.9978	−	26.5510i	0.376557	−	0.909090i	0.992606	−	0.121382i	$-0.0387326\pi$
$854$		0			0
$855$	15.4146	+	6.38494i	0.527169	+	0.218360i
$856$	−11.7632	−	28.3988i	−0.402057	−	0.970651i
$857$	5.54328	−	2.29610i	0.189355	−	0.0784333i	−0.285991	−	0.958232i	$-0.592323\pi$
$857$	5.54328	−	2.29610i	0.189355	−	0.0784333i	0.475346	+	0.879799i	$0.342323\pi$
$858$	1.24012	+	1.24012i	0.0423369	+	0.0423369i
$859$	−8.48528	−	8.48528i	−0.289514	−	0.289514i	0.547374	−	0.836888i	$-0.315628\pi$
$859$	−8.48528	−	8.48528i	−0.289514	−	0.289514i	−0.836888	+	0.547374i	$0.815628\pi$
$860$	70.3146	−	29.1253i	2.39771	−	0.993163i
$861$		0			0
$862$	56.7976	+	23.5263i	1.93453	+	0.801310i
$863$		−	9.75379i		−	0.332023i	−0.986124	−	0.166011i	$-0.946911\pi$
$863$		−	9.75379i		−	0.332023i	0.986124	−	0.166011i	$-0.0530889\pi$
$864$	2.51100	−	6.06208i	0.0854259	−	0.206236i
$865$	4.55267	−	4.55267i	0.154795	−	0.154795i
$866$	68.3542			2.32277
$867$		0			0
$868$		0			0
$869$	10.3455	−	10.3455i	0.350946	−	0.350946i
$870$	28.7897	−	69.5044i	0.976062	−	2.35642i
$871$		−	1.75379i		−	0.0594249i
$872$	−41.6883	−	17.2679i	−1.41174	−	0.584764i
$873$	1.10094	+	2.65790i	0.0372612	+	0.0899564i
$874$	27.0340	−	11.1978i	0.914438	−	0.378773i
$875$		0			0
$876$	−39.5002	−	39.5002i	−1.33459	−	1.33459i
$877$	−31.4119	+	13.0112i	−1.06070	+	0.439358i	−0.843701	−	0.536813i	$-0.819628\pi$
$877$	−31.4119	+	13.0112i	−1.06070	+	0.439358i	−0.217003	+	0.976171i	$0.569628\pi$
$878$	21.8072	+	52.6471i	0.735956	+	1.77675i
$879$	−1.03761	−	0.429794i	−0.0349979	−	0.0144966i
$880$			42.7386i			1.44072i
$881$	15.4016	−	37.1827i	0.518892	−	1.25272i	−0.419693	−	0.907666i	$-0.637862\pi$
$881$	15.4016	−	37.1827i	0.518892	−	1.25272i	0.938585	−	0.345049i	$-0.112138\pi$
$882$	12.6790	−	12.6790i	0.426925	−	0.426925i
$883$	23.4233			0.788257			0.394128	−	0.919055i	$-0.371047\pi$
$883$	23.4233			0.788257			0.394128	+	0.919055i	$0.371047\pi$
$884$		0			0
$885$	−25.3693			−0.852780
$886$	−56.3730	+	56.3730i	−1.89389	+	1.89389i
$887$	−7.05609	+	17.0349i	−0.236920	+	0.571976i	−0.996961	−	0.0778990i	$-0.975179\pi$
$887$	−7.05609	+	17.0349i	−0.236920	+	0.571976i	0.760041	+	0.649875i	$0.225179\pi$
$888$			33.6155i			1.12806i
$889$		0			0
$890$	−3.92106	−	9.46626i	−0.131434	−	0.317310i
$891$	−1.44269	+	0.597580i	−0.0483318	+	0.0200197i
$892$	−48.1596	−	48.1596i	−1.61250	−	1.61250i
$893$	−36.8459	−	36.8459i	−1.23300	−	1.23300i
$894$	28.9815	−	12.0045i	0.969285	−	0.401491i
$895$	−1.19516	−	2.88537i	−0.0399498	−	0.0964474i
$896$		0			0
$897$			1.06913i			0.0356972i
$898$	−36.0136	+	86.9444i	−1.20179	+	2.90137i
$899$	−18.2107	+	18.2107i	−0.607360	+	0.607360i
$900$	−35.0540			−1.16847
$901$		0			0
$902$	14.2462			0.474347
$903$		0			0
$904$	−1.10094	+	2.65790i	−0.0366167	+	0.0884006i
$905$		−	21.3693i		−	0.710340i
$906$	−18.9325	−	7.84211i	−0.628991	−	0.260537i
$907$	3.77392	+	9.11106i	0.125311	+	0.302528i	0.974068	−	0.226256i	$-0.0726484\pi$
$907$	3.77392	+	9.11106i	0.125311	+	0.302528i	−0.848757	+	0.528783i	$0.822648\pi$
$908$	59.2280	−	24.5331i	1.96555	−	0.814158i
$909$	7.69113	+	7.69113i	0.255099	+	0.255099i
$910$		0			0
$911$	22.4504	−	9.29928i	0.743816	−	0.308099i	0.0216007	−	0.999767i	$-0.493124\pi$
$911$	22.4504	−	9.29928i	0.743816	−	0.308099i	0.722216	+	0.691668i	$0.243124\pi$
$912$	13.7766	+	33.2597i	0.456189	+	1.10134i
$913$	−1.26508	−	0.524015i	−0.0418682	−	0.0173424i
$914$		−	35.3693i		−	1.16991i
$915$	−12.4343	+	30.0191i	−0.411066	+	0.992400i
$916$	19.3530	−	19.3530i	0.639442	−	0.639442i
$917$		0			0
$918$		0			0
$919$	−16.6847			−0.550376			−0.275188	−	0.961390i	$-0.588740\pi$
$919$	−16.6847			−0.550376			−0.275188	+	0.961390i	$0.588740\pi$
$920$	−40.2944	+	40.2944i	−1.32847	+	1.32847i
$921$	12.4343	−	30.0191i	0.409725	−	0.989162i
$922$		−	21.1231i		−	0.695652i
$923$	2.53017	+	1.04803i	0.0832815	+	0.0344963i
$924$		0			0
$925$	36.3725	−	15.0660i	1.19592	−	0.495367i
$926$	74.2355	+	74.2355i	2.43953	+	2.43953i
$927$	−11.7978	−	11.7978i	−0.387492	−	0.387492i
$928$	49.9892	−	20.7062i	1.64098	−	0.679715i
$929$	1.17451	+	2.83551i	0.0385343	+	0.0930300i	0.941975	−	0.335683i	$-0.108967\pi$
$929$	1.17451	+	2.83551i	0.0385343	+	0.0930300i	−0.903441	+	0.428713i	$0.858967\pi$
$930$	26.3236	+	10.9036i	0.863184	+	0.357542i
$931$			32.7926i			1.07473i
$932$	−6.21716	+	15.0095i	−0.203650	+	0.491654i
$933$		0			0
$934$	54.7386			1.79110
$935$		0			0
$936$	−2.87689			−0.0940342
$937$	15.5563	−	15.5563i	0.508204	−	0.508204i	−0.405771	−	0.913975i	$-0.632997\pi$
$937$	15.5563	−	15.5563i	0.508204	−	0.508204i	0.913975	+	0.405771i	$0.132997\pi$
$938$		0			0
$939$			33.6155i			1.09700i
$940$	166.953	+	69.1541i	5.44540	+	2.25556i
$941$	−11.4805	−	27.7164i	−0.374254	−	0.903528i	−0.993019	−	0.117953i	$-0.962367\pi$
$941$	−11.4805	−	27.7164i	−0.374254	−	0.903528i	0.618766	−	0.785576i	$-0.287633\pi$
$942$	−15.8197	+	6.55273i	−0.515433	+	0.213499i
$943$	6.14098	+	6.14098i	0.199978	+	0.199978i
$944$	−38.7061	−	38.7061i	−1.25977	−	1.25977i
$945$		0			0
$946$	−7.17096	−	17.3122i	−0.233148	−	0.562869i
$947$	11.0866	+	4.59220i	0.360265	+	0.149226i	0.555471	−	0.831536i	$-0.312538\pi$
$947$	11.0866	+	4.59220i	0.360265	+	0.149226i	−0.195207	+	0.980762i	$0.562538\pi$
$948$			42.7386i			1.38809i
$949$	−2.05475	+	4.96060i	−0.0667000	+	0.161028i
$950$	65.2065	−	65.2065i	2.11558	−	2.11558i
$951$	−18.0000			−0.583690
$952$		0			0
$953$	36.3542			1.17763			0.588813	−	0.808269i	$-0.299595\pi$
$953$	36.3542			1.17763			0.588813	+	0.808269i	$0.299595\pi$
$954$	22.1815	−	22.1815i	0.718151	−	0.718151i
$955$	6.64695	−	16.0472i	0.215090	−	0.519274i
$956$			28.4924i			0.921511i
$957$	−11.8967	−	4.92777i	−0.384566	−	0.159292i
$958$	23.8206	+	57.5080i	0.769608	+	1.85800i
$959$		0			0
$960$	−3.62258	−	3.62258i	−0.116918	−	0.116918i
$961$	15.0233	+	15.0233i	0.484624	+	0.484624i
$962$	5.31581	−	2.20188i	0.171389	−	0.0709914i
$963$	−1.79274	−	4.32806i	−0.0577703	−	0.139470i
$964$	14.1994	+	5.88158i	0.457332	+	0.189433i
$965$		−	27.6155i		−	0.888975i
$966$		0			0
$967$	30.0085	−	30.0085i	0.965009	−	0.965009i	−0.0343994	−	0.999408i	$-0.510952\pi$
$967$	30.0085	−	30.0085i	0.965009	−	0.965009i	0.999408	+	0.0343994i	$0.0109518\pi$
$968$	−56.1771			−1.80560
$969$		0			0
$970$	26.2462			0.842715
$971$	30.8408	−	30.8408i	0.989730	−	0.989730i	−0.0102183	−	0.999948i	$-0.503253\pi$
$971$	30.8408	−	30.8408i	0.989730	−	0.989730i	0.999948	+	0.0102183i	$0.00325263\pi$
$972$	1.74563	−	4.21433i	0.0559911	−	0.135175i
$973$		0			0
$974$	41.1056	+	17.0265i	1.31711	+	0.545565i
$975$	1.28938	+	3.11284i	0.0412933	+	0.0996908i
$976$	−64.7713	+	26.8292i	−2.07328	+	0.858780i
$977$	5.83095	+	5.83095i	0.186549	+	0.186549i	0.794202	−	0.607654i	$-0.207889\pi$
$977$	5.83095	+	5.83095i	0.186549	+	0.186549i	−0.607654	+	0.794202i	$0.707889\pi$
$978$	27.3924	+	27.3924i	0.875911	+	0.875911i
$979$	−1.62029	+	0.671146i	−0.0517847	+	0.0214499i
$980$	−43.5201	−	105.067i	−1.39020	−	3.35624i
$981$	−6.35342	−	2.63167i	−0.202849	−	0.0840229i
$982$			54.7386i			1.74678i
$983$	11.8367	−	28.5764i	0.377533	−	0.911446i	−0.614894	−	0.788610i	$-0.710801\pi$
$983$	11.8367	−	28.5764i	0.377533	−	0.911446i	0.992427	−	0.122836i	$-0.0391988\pi$
$984$	−16.5246	+	16.5246i	−0.526785	+	0.526785i
$985$	31.8078			1.01348
$986$		0			0
$987$		0			0
$988$	6.62511	−	6.62511i	0.210773	−	0.210773i
$989$	4.37150	−	10.5537i	0.139006	−	0.335590i
$990$			14.2462i			0.452774i
$991$	−39.4853	−	16.3554i	−1.25429	−	0.519545i	−0.346140	−	0.938183i	$-0.612508\pi$
$991$	−39.4853	−	16.3554i	−1.25429	−	0.519545i	−0.908153	+	0.418638i	$0.862508\pi$
$992$	7.84211	+	18.9325i	0.248987	+	0.601108i
$993$	−32.2719	+	13.3675i	−1.02412	+	0.424204i
$994$		0			0
$995$	−40.2944	−	40.2944i	−1.27742	−	1.27742i
$996$	3.69552	−	1.53073i	0.117097	−	0.0485032i
$997$	−3.82683	−	9.23880i	−0.121197	−	0.292596i	0.851624	−	0.524153i	$-0.175618\pi$
$997$	−3.82683	−	9.23880i	−0.121197	−	0.292596i	−0.972821	+	0.231557i	$0.925618\pi$
$998$	−31.6394	−	13.1055i	−1.00153	−	0.414846i
$999$			5.12311i			0.162088i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.h.j.688.4		16
17.2	even	8	inner	867.2.h.j.712.3		16
17.3	odd	16		867.2.e.f.616.2		8
17.4	even	4	inner	867.2.h.j.757.1		16
17.5	odd	16		867.2.e.f.829.4		8
17.6	odd	16		867.2.d.c.577.3		4
17.7	odd	16		51.2.a.b.1.1	✓	2
17.8	even	8	inner	867.2.h.j.733.1		16
17.9	even	8	inner	867.2.h.j.733.2		16
17.10	odd	16		867.2.a.f.1.1		2
17.11	odd	16		867.2.d.c.577.4		4
17.12	odd	16		867.2.e.f.829.3		8
17.13	even	4	inner	867.2.h.j.757.2		16
17.14	odd	16		867.2.e.f.616.1		8
17.15	even	8	inner	867.2.h.j.712.4		16
17.16	even	2	inner	867.2.h.j.688.3		16
51.41	even	16		153.2.a.e.1.2		2
51.44	even	16		2601.2.a.t.1.2		2
68.7	even	16		816.2.a.m.1.2		2
85.7	even	16		1275.2.b.d.1174.1		4
85.24	odd	16		1275.2.a.n.1.2		2
85.58	even	16		1275.2.b.d.1174.4		4
119.41	even	16		2499.2.a.o.1.1		2
136.75	even	16		3264.2.a.bg.1.1		2
136.109	odd	16		3264.2.a.bl.1.1		2
187.109	even	16		6171.2.a.p.1.2		2
204.143	odd	16		2448.2.a.v.1.1		2
221.194	odd	16		8619.2.a.q.1.2		2
255.194	even	16		3825.2.a.s.1.1		2
357.41	odd	16		7497.2.a.v.1.2		2
408.245	even	16		9792.2.a.cy.1.2		2
408.347	odd	16		9792.2.a.cz.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.a.b.1.1	✓	2	17.7	odd	16
153.2.a.e.1.2		2	51.41	even	16
816.2.a.m.1.2		2	68.7	even	16
867.2.a.f.1.1		2	17.10	odd	16
867.2.d.c.577.3		4	17.6	odd	16
867.2.d.c.577.4		4	17.11	odd	16
867.2.e.f.616.1		8	17.14	odd	16
867.2.e.f.616.2		8	17.3	odd	16
867.2.e.f.829.3		8	17.12	odd	16
867.2.e.f.829.4		8	17.5	odd	16
867.2.h.j.688.3		16	17.16	even	2	inner
867.2.h.j.688.4		16	1.1	even	1	trivial
867.2.h.j.712.3		16	17.2	even	8	inner
867.2.h.j.712.4		16	17.15	even	8	inner
867.2.h.j.733.1		16	17.8	even	8	inner
867.2.h.j.733.2		16	17.9	even	8	inner
867.2.h.j.757.1		16	17.4	even	4	inner
867.2.h.j.757.2		16	17.13	even	4	inner
1275.2.a.n.1.2		2	85.24	odd	16
1275.2.b.d.1174.1		4	85.7	even	16
1275.2.b.d.1174.4		4	85.58	even	16
2448.2.a.v.1.1		2	204.143	odd	16
2499.2.a.o.1.1		2	119.41	even	16
2601.2.a.t.1.2		2	51.44	even	16
3264.2.a.bg.1.1		2	136.75	even	16
3264.2.a.bl.1.1		2	136.109	odd	16
3825.2.a.s.1.1		2	255.194	even	16
6171.2.a.p.1.2		2	187.109	even	16
7497.2.a.v.1.2		2	357.41	odd	16
8619.2.a.q.1.2		2	221.194	odd	16
9792.2.a.cy.1.2		2	408.245	even	16
9792.2.a.cz.1.2		2	408.347	odd	16

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.81129 - 1.81129i) q^{2} +(0.382683 - 0.923880i) q^{3} -4.56155i q^{4} +(-3.29045 - 1.36295i) q^{5} +(-0.980264 - 2.36657i) q^{6} +(-4.63972 - 4.63972i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(-8.42865 + 3.49126i) q^{10} +(0.597580 + 1.44269i) q^{11} +(-4.21433 - 1.74563i) q^{12} +0.438447i q^{13} +(-2.51840 + 2.51840i) q^{15} -7.68466 q^{16} -2.56155 q^{18} +(3.31255 - 3.31255i) q^{19} +(-6.21716 + 15.0095i) q^{20} +(3.69552 + 1.53073i) q^{22} +(0.933153 + 2.25283i) q^{23} +(-6.06208 + 2.51100i) q^{24} +(5.43387 + 5.43387i) q^{25} +(0.794156 + 0.794156i) q^{26} +(-0.923880 + 0.382683i) q^{27} +(-7.61851 - 3.15569i) q^{29} +9.12311i q^{30} +(1.19516 - 2.88537i) q^{31} +(-4.63972 + 4.63972i) q^{32} +1.56155 q^{33} +(-3.22550 + 3.22550i) q^{36} +(1.96053 - 4.73313i) q^{37} -12.0000i q^{38} +(0.405072 + 0.167786i) q^{39} +(8.94305 + 21.5904i) q^{40} +(3.29045 - 1.36295i) q^{41} +(-3.31255 - 3.31255i) q^{43} +(6.58089 - 2.72589i) q^{44} +(1.36295 + 3.29045i) q^{45} +(5.77075 + 2.39032i) q^{46} -11.1231i q^{47} +(-2.94079 + 7.09970i) q^{48} +(-4.94975 + 4.94975i) q^{49} +19.6847 q^{50} +2.00000 q^{52} +(-8.65938 + 8.65938i) q^{53} +(-0.980264 + 2.36657i) q^{54} -5.56155i q^{55} +(-1.79274 - 4.32806i) q^{57} +(-19.5152 + 8.08346i) q^{58} +(5.03680 + 5.03680i) q^{59} +(11.4878 + 11.4878i) q^{60} +(8.42865 - 3.49126i) q^{61} +(-3.06147 - 7.39104i) q^{62} +1.43845i q^{64} +(0.597580 - 1.44269i) q^{65} +(2.82843 - 2.82843i) q^{66} -4.00000 q^{67} +2.43845 q^{69} +(2.39032 - 5.77075i) q^{71} +6.56155i q^{72} +(11.3140 + 4.68642i) q^{73} +(-5.02200 - 12.1242i) q^{74} +(7.09970 - 2.94079i) q^{75} +(-15.1104 - 15.1104i) q^{76} +(1.03761 - 0.429794i) q^{78} +(-3.58548 - 8.65612i) q^{79} +(25.2860 + 10.4738i) q^{80} +1.00000i q^{81} +(3.49126 - 8.42865i) q^{82} +(-0.620058 + 0.620058i) q^{83} -12.0000 q^{86} +(-5.83095 + 5.83095i) q^{87} +(3.92106 - 9.46626i) q^{88} +1.12311i q^{89} +(8.42865 + 3.49126i) q^{90} +(10.2764 - 4.25663i) q^{92} +(-2.20837 - 2.20837i) q^{93} +(-20.1472 - 20.1472i) q^{94} +(-15.4146 + 6.38494i) q^{95} +(2.51100 + 6.06208i) q^{96} +(-2.65790 - 1.10094i) q^{97} +17.9309i q^{98} +(0.597580 - 1.44269i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 24 q^{16} - 8 q^{18} - 8 q^{33} + 216 q^{50} + 32 q^{52} - 64 q^{67} + 72 q^{69} - 192 q^{86}+O(q^{100}) \) 16 * q - 24 * q^16 - 8 * q^18 - 8 * q^33 + 216 * q^50 + 32 * q^52 - 64 * q^67 + 72 * q^69 - 192 * q^86

Introduction

L-functions

Modular forms

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Representations

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Database

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