LMFDB - Embedded newform 867.2.h.j.688.1

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			688.1
Root			$-1.44269 + 0.597580i$ of defining polynomial
Character	$\chi$	$=$	867.688
Dual form			867.2.h.j.712.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.10418 + 1.10418i) q^{2} +(-0.382683 + 0.923880i) q^{3} -0.438447i q^{4} +(-0.518807 - 0.214897i) q^{5} +(-0.597580 - 1.44269i) q^{6} +(-1.72424 - 1.72424i) q^{8} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})$	\(q+(-1.10418 + 1.10418i) q^{2} +(-0.382683 + 0.923880i) q^{3} -0.438447i q^{4} +(-0.518807 - 0.214897i) q^{5} +(-0.597580 - 1.44269i) q^{6} +(-1.72424 - 1.72424i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(0.810145 - 0.335573i) q^{10} +(0.980264 + 2.36657i) q^{11} +(0.405072 + 0.167786i) q^{12} +4.56155i q^{13} +(0.397078 - 0.397078i) q^{15} +4.68466 q^{16} +1.56155 q^{18} +(-5.43387 + 5.43387i) q^{19} +(-0.0942210 + 0.227470i) q^{20} +(-3.69552 - 1.53073i) q^{22} +(-2.51100 - 6.06208i) q^{23} +(2.25283 - 0.933153i) q^{24} +(-3.31255 - 3.31255i) q^{25} +(-5.03680 - 5.03680i) q^{26} +(0.923880 - 0.382683i) q^{27} +(-7.61851 - 3.15569i) q^{29} +0.876894i q^{30} +(1.96053 - 4.73313i) q^{31} +(-1.72424 + 1.72424i) q^{32} -2.56155 q^{33} +(-0.310029 + 0.310029i) q^{36} +(1.19516 - 2.88537i) q^{37} -12.0000i q^{38} +(-4.21433 - 1.74563i) q^{39} +(0.524015 + 1.26508i) q^{40} +(0.518807 - 0.214897i) q^{41} +(5.43387 + 5.43387i) q^{43} +(1.03761 - 0.429794i) q^{44} +(0.214897 + 0.518807i) q^{45} +(9.46626 + 3.92106i) q^{46} -2.87689i q^{47} +(-1.79274 + 4.32806i) q^{48} +(-4.94975 + 4.94975i) q^{49} +7.31534 q^{50} +2.00000 q^{52} +(3.00252 - 3.00252i) q^{53} +(-0.597580 + 1.44269i) q^{54} -1.43845i q^{55} +(-2.94079 - 7.09970i) q^{57} +(11.8967 - 4.92777i) q^{58} +(-0.794156 - 0.794156i) q^{59} +(-0.174098 - 0.174098i) q^{60} +(-0.810145 + 0.335573i) q^{61} +(3.06147 + 7.39104i) q^{62} +5.56155i q^{64} +(0.980264 - 2.36657i) q^{65} +(2.82843 - 2.82843i) q^{66} -4.00000 q^{67} +6.56155 q^{69} +(3.92106 - 9.46626i) q^{71} +2.43845i q^{72} +(3.92299 + 1.62495i) q^{73} +(1.86631 + 4.50566i) q^{74} +(4.32806 - 1.79274i) q^{75} +(2.38247 + 2.38247i) q^{76} +(6.58089 - 2.72589i) q^{78} +(-5.88158 - 14.1994i) q^{79} +(-2.43043 - 1.00672i) q^{80} +1.00000i q^{81} +(-0.335573 + 0.810145i) q^{82} +(-6.45101 + 6.45101i) q^{83} -12.0000 q^{86} +(5.83095 - 5.83095i) q^{87} +(2.39032 - 5.77075i) q^{88} -7.12311i q^{89} +(-0.810145 - 0.335573i) q^{90} +(-2.65790 + 1.10094i) q^{92} +(3.62258 + 3.62258i) q^{93} +(3.17662 + 3.17662i) q^{94} +(3.98686 - 1.65141i) q^{95} +(-0.933153 - 2.25283i) q^{96} +(10.2764 + 4.25663i) q^{97} -10.9309i q^{98} +(0.980264 - 2.36657i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q+O(q^{10}) $ 16 * 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

Display 100 coefficients 10 coefficients

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 $

$2$	−1.10418	+	1.10418i	−0.780776	+	0.780776i	−0.979962	−	0.199185i	$-0.936170\pi$
$2$	−1.10418	+	1.10418i	−0.780776	+	0.780776i	0.199185	+	0.979962i	$0.436170\pi$
$3$	−0.382683	+	0.923880i	−0.220942	+	0.533402i
$3$	−0.382683	+	0.923880i	−0.220942	+	0.533402i
$4$		−	0.438447i		−	0.219224i
$5$	−0.518807	−	0.214897i	−0.232018	−	0.0961048i	0.263646	−	0.964620i	$-0.415075\pi$
$5$	−0.518807	−	0.214897i	−0.232018	−	0.0961048i	−0.495663	+	0.868515i	$0.665075\pi$
$6$	−0.597580	−	1.44269i	−0.243961	−	0.588974i
$7$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$7$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$8$	−1.72424	−	1.72424i	−0.609612	−	0.609612i
$9$	−0.707107	−	0.707107i	−0.235702	−	0.235702i
$10$	0.810145	−	0.335573i	0.256190	−	0.106117i
$11$	0.980264	+	2.36657i	0.295561	+	0.713547i	0.999993	+	0.00377529i	$0.00120171\pi$
$11$	0.980264	+	2.36657i	0.295561	+	0.713547i	−0.704432	+	0.709771i	$0.748798\pi$
$12$	0.405072	+	0.167786i	0.116934	+	0.0484358i
$13$			4.56155i			1.26515i	0.774500	+	0.632574i	$0.218001\pi$
$13$			4.56155i			1.26515i	−0.774500	+	0.632574i	$0.781999\pi$
$14$		0			0
$15$	0.397078	−	0.397078i	0.102525	−	0.102525i
$16$	4.68466			1.17116
$17$		0			0
$17$		0			0
$18$	1.56155			0.368062
$19$	−5.43387	+	5.43387i	−1.24662	+	1.24662i	−0.289411	+	0.957205i	$0.593460\pi$
$19$	−5.43387	+	5.43387i	−1.24662	+	1.24662i	−0.957205	+	0.289411i	$0.906540\pi$
$20$	−0.0942210	+	0.227470i	−0.0210684	+	0.0508637i
$21$		0			0
$22$	−3.69552	−	1.53073i	−0.787887	−	0.326354i
$23$	−2.51100	−	6.06208i	−0.523579	−	1.26403i	−0.935666	−	0.352887i	$-0.885200\pi$
$23$	−2.51100	−	6.06208i	−0.523579	−	1.26403i	0.412087	−	0.911145i	$-0.364800\pi$
$24$	2.25283	−	0.933153i	0.459857	−	0.190479i
$25$	−3.31255	−	3.31255i	−0.662511	−	0.662511i
$26$	−5.03680	−	5.03680i	−0.987797	−	0.987797i
$27$	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	$0.902578\pi$
$30$			0.876894i			0.160098i
$31$	1.96053	−	4.73313i	0.352121	−	0.850096i	−0.644237	−	0.764826i	$-0.722825\pi$
$31$	1.96053	−	4.73313i	0.352121	−	0.850096i	0.996358	−	0.0852696i	$-0.0271751\pi$
$32$	−1.72424	+	1.72424i	−0.304806	+	0.304806i
$33$	−2.56155			−0.445909
$34$		0			0
$35$		0			0
$36$	−0.310029	+	0.310029i	−0.0516715	+	0.0516715i
$37$	1.19516	−	2.88537i	0.196483	−	0.474352i	−0.794675	−	0.607035i	$-0.792359\pi$
$37$	1.19516	−	2.88537i	0.196483	−	0.474352i	0.991159	+	0.132682i	$0.0423589\pi$
$38$		−	12.0000i		−	1.94666i
$39$	−4.21433	−	1.74563i	−0.674832	−	0.279525i
$40$	0.524015	+	1.26508i	0.0828540	+	0.200027i
$41$	0.518807	−	0.214897i	0.0810241	−	0.0335613i	−0.341803	−	0.939772i	$-0.611038\pi$
$41$	0.518807	−	0.214897i	0.0810241	−	0.0335613i	0.422827	+	0.906210i	$0.361038\pi$
$42$		0			0
$43$	5.43387	+	5.43387i	0.828658	+	0.828658i	0.987331	−	0.158673i	$-0.0507216\pi$
$43$	5.43387	+	5.43387i	0.828658	+	0.828658i	−0.158673	+	0.987331i	$0.550722\pi$
$44$	1.03761	−	0.429794i	0.156426	−	0.0647939i
$45$	0.214897	+	0.518807i	0.0320349	+	0.0773392i
$46$	9.46626	+	3.92106i	1.39572	+	0.578128i
$47$		−	2.87689i		−	0.419638i	−0.977740	−	0.209819i	$-0.932712\pi$
$47$		−	2.87689i		−	0.419638i	0.977740	−	0.209819i	$-0.0672875\pi$
$48$	−1.79274	+	4.32806i	−0.258760	+	0.624702i
$49$	−4.94975	+	4.94975i	−0.707107	+	0.707107i
$50$	7.31534			1.03455
$51$		0			0
$52$	2.00000			0.277350
$53$	3.00252	−	3.00252i	0.412428	−	0.412428i	−0.470155	−	0.882584i	$-0.655802\pi$
$53$	3.00252	−	3.00252i	0.412428	−	0.412428i	0.882584	+	0.470155i	$0.155802\pi$
$54$	−0.597580	+	1.44269i	−0.0813204	+	0.196325i
$55$		−	1.43845i		−	0.193960i
$56$		0			0
$57$	−2.94079	−	7.09970i	−0.389517	−	0.940378i
$58$	11.8967	−	4.92777i	1.56211	−	0.647048i
$59$	−0.794156	−	0.794156i	−0.103390	−	0.103390i	0.653519	−	0.756910i	$-0.273292\pi$
$59$	−0.794156	−	0.794156i	−0.103390	−	0.103390i	−0.756910	+	0.653519i	$0.773292\pi$
$60$	−0.174098	−	0.174098i	−0.0224759	−	0.0224759i
$61$	−0.810145	+	0.335573i	−0.103728	+	0.0429657i	−0.433944	−	0.900940i	$-0.642878\pi$
$61$	−0.810145	+	0.335573i	−0.103728	+	0.0429657i	0.330216	+	0.943905i	$0.392878\pi$
$62$	3.06147	+	7.39104i	0.388807	+	0.938663i
$63$		0			0
$64$			5.56155i			0.695194i
$65$	0.980264	−	2.36657i	0.121587	−	0.293536i
$66$	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
$69$	6.56155			0.789918
$70$		0			0
$71$	3.92106	−	9.46626i	0.465344	−	1.12344i	−0.500830	−	0.865546i	$-0.666972\pi$
$71$	3.92106	−	9.46626i	0.465344	−	1.12344i	0.966173	−	0.257893i	$-0.0830283\pi$
$72$			2.43845i			0.287374i
$73$	3.92299	+	1.62495i	0.459151	+	0.190187i	0.600256	−	0.799808i	$-0.295065\pi$
$73$	3.92299	+	1.62495i	0.459151	+	0.190187i	−0.141105	+	0.989995i	$0.545065\pi$
$74$	1.86631	+	4.50566i	0.216954	+	0.523773i
$75$	4.32806	−	1.79274i	0.499761	−	0.207008i
$76$	2.38247	+	2.38247i	0.273288	+	0.273288i
$77$		0			0
$78$	6.58089	−	2.72589i	0.745139	−	0.308647i
$79$	−5.88158	−	14.1994i	−0.661730	−	1.59756i	−0.795091	−	0.606490i	$-0.792577\pi$
$79$	−5.88158	−	14.1994i	−0.661730	−	1.59756i	0.133362	−	0.991067i	$-0.457423\pi$
$80$	−2.43043	−	1.00672i	−0.271731	−	0.112555i
$81$			1.00000i			0.111111i
$82$	−0.335573	+	0.810145i	−0.0370578	+	0.0894655i
$83$	−6.45101	+	6.45101i	−0.708090	+	0.708090i	−0.966133	−	0.258043i	$-0.916922\pi$
$83$	−6.45101	+	6.45101i	−0.708090	+	0.708090i	0.258043	+	0.966133i	$0.416922\pi$
$84$		0			0
$85$		0			0
$86$	−12.0000			−1.29399
$87$	5.83095	−	5.83095i	0.625144	−	0.625144i
$88$	2.39032	−	5.77075i	0.254809	−	0.615164i
$89$		−	7.12311i		−	0.755048i	−0.926000	−	0.377524i	$-0.876776\pi$
$89$		−	7.12311i		−	0.755048i	0.926000	−	0.377524i	$-0.123224\pi$
$90$	−0.810145	−	0.335573i	−0.0853968	−	0.0353725i
$91$		0			0
$92$	−2.65790	+	1.10094i	−0.277106	+	0.114781i
$93$	3.62258	+	3.62258i	0.375644	+	0.375644i
$94$	3.17662	+	3.17662i	0.327644	+	0.327644i
$95$	3.98686	−	1.65141i	0.409043	−	0.169431i
$96$	−0.933153	−	2.25283i	−0.0952396	−	0.229929i
$97$	10.2764	+	4.25663i	1.04341	+	0.432195i	0.837535	−	0.546383i	$-0.183996\pi$
$97$	10.2764	+	4.25663i	1.04341	+	0.432195i	0.205876	+	0.978578i	$0.433996\pi$
$98$		−	10.9309i		−	1.10418i
$99$	0.980264	−	2.36657i	0.0985202	−	0.237849i
$100$	−1.45238	+	1.45238i	−0.145238	+	0.145238i
$101$	−19.1231			−1.90282			−0.951410	−	0.307927i	$-0.900365\pi$
$101$	−19.1231			−1.90282			−0.951410	+	0.307927i	$0.900365\pi$
$102$		0			0
$103$	4.31534			0.425203			0.212602	−	0.977139i	$-0.431806\pi$
$103$	4.31534			0.425203			0.212602	+	0.977139i	$0.431806\pi$
$104$	7.86522	−	7.86522i	0.771249	−	0.771249i
$105$		0			0
$106$			6.63068i			0.644029i
$107$	7.09970	+	2.94079i	0.686354	+	0.284297i	0.698480	−	0.715629i	$-0.253860\pi$
$107$	7.09970	+	2.94079i	0.686354	+	0.284297i	−0.0121264	+	0.999926i	$0.503860\pi$
$108$	−0.167786	−	0.405072i	−0.0161453	−	0.0389781i
$109$	−13.9719	+	5.78736i	−1.33827	+	0.554329i	−0.933002	−	0.359870i	$-0.882821\pi$
$109$	−13.9719	+	5.78736i	−1.33827	+	0.554329i	−0.405266	+	0.914199i	$0.632821\pi$
$110$	1.58831	+	1.58831i	0.151440	+	0.151440i
$111$	2.20837	+	2.20837i	0.209609	+	0.209609i
$112$		0			0
$113$	1.74563	+	4.21433i	0.164215	+	0.396450i	0.984471	−	0.175546i	$-0.0561691\pi$
$113$	1.74563	+	4.21433i	0.164215	+	0.396450i	−0.820256	+	0.571996i	$0.806169\pi$
$114$	11.0866	+	4.59220i	1.03835	+	0.430099i
$115$			3.68466i			0.343596i
$116$	−1.38360	+	3.34031i	−0.128464	+	0.310140i
$117$	3.22550	−	3.22550i	0.298198	−	0.298198i
$118$	1.75379			0.161449
$119$		0			0
$120$	−1.36932			−0.125001
$121$	3.13846	−	3.13846i	0.285314	−	0.285314i
$122$	0.524015	−	1.26508i	0.0474421	−	0.114535i
$123$			0.561553i			0.0506335i
$124$	−2.07523	−	0.859588i	−0.186361	−	0.0771933i
$125$	2.08120	+	5.02447i	0.186149	+	0.449402i
$126$		0			0
$127$	−0.571175	−	0.571175i	−0.0506836	−	0.0506836i	0.681311	−	0.731994i	$-0.261410\pi$
$127$	−0.571175	−	0.571175i	−0.0506836	−	0.0506836i	−0.731994	+	0.681311i	$0.761410\pi$
$128$	−9.58947	−	9.58947i	−0.847597	−	0.847597i
$129$	−7.09970	+	2.94079i	−0.625094	+	0.258922i
$130$	1.53073	+	3.69552i	0.134254	+	0.324118i
$131$	−17.1486	−	7.10320i	−1.49828	−	0.620609i	−0.525183	−	0.850989i	$-0.676003\pi$
$131$	−17.1486	−	7.10320i	−1.49828	−	0.620609i	−0.973101	+	0.230380i	$0.926003\pi$
$132$			1.12311i			0.0977538i
$133$		0			0
$134$	4.41674	−	4.41674i	0.381548	−	0.381548i
$135$	−0.561553			−0.0483308
$136$		0			0
$137$	−16.2462			−1.38801			−0.694004	−	0.719971i	$-0.744155\pi$
$137$	−16.2462			−1.38801			−0.694004	+	0.719971i	$0.744155\pi$
$138$	−7.24517	+	7.24517i	−0.616749	+	0.616749i
$139$	−3.49126	+	8.42865i	−0.296125	+	0.714909i	0.703865	+	0.710334i	$0.251456\pi$
$139$	−3.49126	+	8.42865i	−0.296125	+	0.714909i	−0.999990	+	0.00457466i	$0.998544\pi$
$140$		0			0
$141$	2.65790	+	1.10094i	0.223836	+	0.0927159i
$142$	6.12293	+	14.7821i	0.513825	+	1.24048i
$143$	−10.7952	+	4.47153i	−0.902741	+	0.373928i
$144$	−3.31255	−	3.31255i	−0.276046	−	0.276046i
$145$	3.27439	+	3.27439i	0.271923	+	0.271923i
$146$	−6.12595	+	2.53745i	−0.506987	+	0.210001i
$147$	−2.67878	−	6.46716i	−0.220942	−	0.533402i
$148$	−1.26508	−	0.524015i	−0.103989	−	0.0430738i
$149$		−	4.24621i		−	0.347863i	−0.984758	−	0.173932i	$-0.944353\pi$
$149$		−	4.24621i		−	0.347863i	0.984758	−	0.173932i	$-0.0556472\pi$
$150$	−2.79946	+	6.75849i	−0.228575	+	0.551829i
$151$	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	$0.144462\pi$
$152$	18.7386			1.51990
$153$		0			0
$154$		0			0
$155$	−2.03427	+	2.03427i	−0.163397	+	0.163397i
$156$	−0.765367	+	1.84776i	−0.0612784	+	0.147939i
$157$			5.68466i			0.453685i	0.973931	+	0.226843i	$0.0728403\pi$
$157$			5.68466i			0.453685i	−0.973931	+	0.226843i	$0.927160\pi$
$158$	22.1731	+	9.18440i	1.76400	+	0.730672i
$159$	1.62495	+	3.92299i	0.128867	+	0.311113i
$160$	1.26508	−	0.524015i	0.100014	−	0.0414270i
$161$		0			0
$162$	−1.10418	−	1.10418i	−0.0867529	−	0.0867529i
$163$	6.35342	−	2.63167i	0.497638	−	0.206129i	−0.119724	−	0.992807i	$-0.538201\pi$
$163$	6.35342	−	2.63167i	0.497638	−	0.206129i	0.617363	+	0.786679i	$0.288201\pi$
$164$	−0.0942210	−	0.227470i	−0.00735742	−	0.0177624i
$165$	1.32895	+	0.550470i	0.103459	+	0.0428540i
$166$		−	14.2462i		−	1.10572i
$167$	0.309118	−	0.746277i	0.0239203	−	0.0577486i	−0.911468	−	0.411371i	$-0.865050\pi$
$167$	0.309118	−	0.746277i	0.0239203	−	0.0577486i	0.935388	+	0.353622i	$0.115050\pi$
$168$		0			0
$169$	−7.80776			−0.600597
$170$		0			0
$171$	7.68466			0.587661
$172$	2.38247	−	2.38247i	0.181661	−	0.181661i
$173$	−7.19742	+	17.3761i	−0.547210	+	1.32108i	0.372336	+	0.928098i	$0.378557\pi$
$173$	−7.19742	+	17.3761i	−0.547210	+	1.32108i	−0.919546	+	0.392983i	$0.871443\pi$
$174$			12.8769i			0.976195i
$175$		0			0
$176$	4.59220	+	11.0866i	0.346150	+	0.835680i
$177$	1.03761	−	0.429794i	0.0779919	−	0.0323053i
$178$	7.86522	+	7.86522i	0.589523	+	0.589523i
$179$	6.45101	+	6.45101i	0.482171	+	0.482171i	0.905824	−	0.423653i	$-0.139253\pi$
$179$	6.45101	+	6.45101i	0.482171	+	0.482171i	−0.423653	+	0.905824i	$0.639253\pi$
$180$	0.227470	−	0.0942210i	0.0169546	−	0.00702282i
$181$	−2.29610	−	5.54328i	−0.170668	−	0.412029i	0.815283	−	0.579062i	$-0.196581\pi$
$181$	−2.29610	−	5.54328i	−0.170668	−	0.412029i	−0.985951	+	0.167034i	$0.946581\pi$
$182$		0			0
$183$		−	0.876894i		−	0.0648219i
$184$	−6.12293	+	14.7821i	−0.451389	+	1.08975i
$185$	−1.24012	+	1.24012i	−0.0911751	+	0.0911751i
$186$	−8.00000			−0.586588
$187$		0			0
$188$	−1.26137			−0.0919946
$189$		0			0
$190$	−2.57876	+	6.22569i	−0.187083	+	0.451659i
$191$			13.1231i			0.949555i	0.880106	+	0.474777i	$0.157471\pi$
$191$			13.1231i			0.949555i	−0.880106	+	0.474777i	$0.842529\pi$
$192$	−5.13820	−	2.12831i	−0.370818	−	0.153598i
$193$	−9.27862	−	22.4006i	−0.667890	−	1.61243i	−0.785134	−	0.619326i	$-0.787406\pi$
$193$	−9.27862	−	22.4006i	−0.667890	−	1.61243i	0.117244	−	0.993103i	$-0.462594\pi$
$194$	−16.0472	+	6.64695i	−1.15212	+	0.477223i
$195$	1.81129	+	1.81129i	0.129709	+	0.129709i
$196$	2.17020	+	2.17020i	0.155014	+	0.155014i
$197$	−18.4137	+	7.62721i	−1.31192	+	0.543416i	−0.925445	−	0.378882i	$-0.876309\pi$
$197$	−18.4137	+	7.62721i	−1.31192	+	0.543416i	−0.386478	+	0.922298i	$0.626309\pi$
$198$	1.53073	+	3.69552i	0.108785	+	0.262629i
$199$	−14.7821	−	6.12293i	−1.04787	−	0.434043i	−0.208741	−	0.977971i	$-0.566937\pi$
$199$	−14.7821	−	6.12293i	−1.04787	−	0.434043i	−0.839132	+	0.543928i	$0.816937\pi$
$200$			11.4233i			0.807749i
$201$	1.53073	−	3.69552i	0.107970	−	0.260662i
$202$	21.1154	−	21.1154i	1.48568	−	1.48568i
$203$		0			0
$204$		0			0
$205$	−0.315342			−0.0220244
$206$	−4.76493	+	4.76493i	−0.331989	+	0.331989i
$207$	−2.51100	+	6.06208i	−0.174526	+	0.421344i
$208$			21.3693i			1.48170i
$209$	−18.1863	−	7.53299i	−1.25797	−	0.521068i
$210$		0			0
$211$	−10.5039	+	4.35085i	−0.723117	+	0.299525i	−0.713720	−	0.700431i	$-0.752991\pi$
$211$	−10.5039	+	4.35085i	−0.723117	+	0.299525i	−0.00939678	+	0.999956i	$0.502991\pi$
$212$	−1.31645	−	1.31645i	−0.0904141	−	0.0904141i
$213$	7.24517	+	7.24517i	0.496431	+	0.496431i
$214$	−11.0866	+	4.59220i	−0.757861	+	0.313916i
$215$	−1.65141	−	3.98686i	−0.112625	−	0.271901i
$216$	−2.25283	−	0.933153i	−0.153286	−	0.0634930i
$217$		0			0
$218$	9.03727	−	21.8179i	0.612081	−	1.47769i
$219$	−3.00252	+	3.00252i	−0.202892	+	0.202892i
$220$	−0.630683			−0.0425206
$221$		0			0
$222$	−4.87689			−0.327316
$223$	−9.85061	+	9.85061i	−0.659646	+	0.659646i	−0.955296	−	0.295650i	$-0.904464\pi$
$223$	−9.85061	+	9.85061i	−0.659646	+	0.659646i	0.295650	+	0.955296i	$0.404464\pi$
$224$		0			0
$225$			4.68466i			0.312311i
$226$	−6.58089	−	2.72589i	−0.437754	−	0.181324i
$227$	8.82237	+	21.2991i	0.585562	+	1.41367i	0.887707	+	0.460409i	$0.152297\pi$
$227$	8.82237	+	21.2991i	0.585562	+	1.41367i	−0.302145	+	0.953262i	$0.597703\pi$
$228$	−3.11284	+	1.28938i	−0.206153	+	0.0853914i
$229$	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	$0.686476\pi$
$230$	−4.06854	−	4.06854i	−0.268272	−	0.268272i
$231$		0			0
$232$	7.69498	+	18.5773i	0.505200	+	1.21966i
$233$	−0.518807	−	0.214897i	−0.0339882	−	0.0140784i	0.365625	−	0.930762i	$-0.380855\pi$
$233$	−0.518807	−	0.214897i	−0.0339882	−	0.0140784i	−0.399613	+	0.916684i	$0.630855\pi$
$234$			7.12311i			0.465652i
$235$	−0.618236	+	1.49255i	−0.0403293	+	0.0973634i
$236$	−0.348195	+	0.348195i	−0.0226656	+	0.0226656i
$237$	15.3693			0.998344
$238$		0			0
$239$	10.2462			0.662772			0.331386	−	0.943495i	$-0.392484\pi$
$239$	10.2462			0.662772			0.331386	+	0.943495i	$0.392484\pi$
$240$	1.86017	−	1.86017i	0.120074	−	0.120074i
$241$	−8.17768	+	19.7427i	−0.526771	+	1.27174i	0.406857	+	0.913492i	$0.366625\pi$
$241$	−8.17768	+	19.7427i	−0.526771	+	1.27174i	−0.933627	+	0.358245i	$0.883375\pi$
$242$			6.93087i			0.445533i
$243$	−0.923880	−	0.382683i	−0.0592669	−	0.0245492i
$244$	0.147131	+	0.355206i	0.00941910	+	0.0227397i
$245$	3.63165	−	1.50428i	0.232018	−	0.0961048i
$246$	−0.620058	−	0.620058i	−0.0395335	−	0.0395335i
$247$	−24.7869	−	24.7869i	−1.57715	−	1.57715i
$248$	−11.5415	+	4.78064i	−0.732886	+	0.303571i
$249$	−3.49126	−	8.42865i	−0.221250	−	0.534144i
$250$	−7.84598	−	3.24991i	−0.496223	−	0.205542i
$251$		−	24.4924i		−	1.54595i	−0.634438	−	0.772974i	$-0.718768\pi$
$251$		−	24.4924i		−	1.54595i	0.634438	−	0.772974i	$-0.281232\pi$
$252$		0			0
$253$	11.8849	−	11.8849i	0.747196	−	0.747196i
$254$	1.26137			0.0791452
$255$		0			0
$256$	10.0540			0.628373
$257$	−6.62511	+	6.62511i	−0.413263	+	0.413263i	−0.882874	−	0.469611i	$-0.844394\pi$
$257$	−6.62511	+	6.62511i	−0.413263	+	0.413263i	0.469611	+	0.882874i	$0.344394\pi$
$258$	4.59220	−	11.0866i	0.285898	−	0.690219i
$259$		0			0
$260$	−1.03761	−	0.429794i	−0.0643501	−	0.0266547i
$261$	3.15569	+	7.61851i	0.195332	+	0.471574i
$262$	26.7785	−	11.0920i	1.65438	−	0.685267i
$263$	8.83348	+	8.83348i	0.544696	+	0.544696i	0.924902	−	0.380206i	$-0.124147\pi$
$263$	8.83348	+	8.83348i	0.544696	+	0.544696i	−0.380206	+	0.924902i	$0.624147\pi$
$264$	4.41674	+	4.41674i	0.271831	+	0.271831i
$265$	−2.20296	+	0.912498i	−0.135327	+	0.0560543i
$266$		0			0
$267$	6.58089	+	2.72589i	0.402744	+	0.166822i
$268$			1.75379i			0.107130i
$269$	−7.86857	+	18.9964i	−0.479755	+	1.15823i	0.479969	+	0.877286i	$0.340648\pi$
$269$	−7.86857	+	18.9964i	−0.479755	+	1.15823i	−0.959724	+	0.280945i	$0.909352\pi$
$270$	0.620058	−	0.620058i	0.0377355	−	0.0377355i
$271$	0.807764			0.0490682			0.0245341	−	0.999699i	$-0.492190\pi$
$271$	0.807764			0.0490682			0.0245341	+	0.999699i	$0.492190\pi$
$272$		0			0
$273$		0			0
$274$	17.9388	−	17.9388i	1.08372	−	1.08372i
$275$	4.59220	−	11.0866i	0.276920	−	0.668544i
$276$		−	2.87689i		−	0.173169i
$277$	5.54328	+	2.29610i	0.333063	+	0.137959i	0.542947	−	0.839767i	$-0.317309\pi$
$277$	5.54328	+	2.29610i	0.333063	+	0.137959i	−0.209884	+	0.977726i	$0.567309\pi$
$278$	−5.45179	−	13.1618i	−0.326977	−	0.789391i
$279$	−4.73313	+	1.96053i	−0.283365	+	0.117374i
$280$		0			0
$281$	13.5221	+	13.5221i	0.806660	+	0.806660i	0.984127	−	0.177467i	$-0.0567904\pi$
$281$	13.5221	+	13.5221i	0.806660	+	0.806660i	−0.177467	+	0.984127i	$0.556790\pi$
$282$	−4.15046	+	1.71918i	−0.247156	+	0.102375i
$283$	1.28938	+	3.11284i	0.0766458	+	0.185039i	0.957558	−	0.288240i	$-0.0930701\pi$
$283$	1.28938	+	3.11284i	0.0766458	+	0.185039i	−0.880912	+	0.473279i	$0.843070\pi$
$284$	−4.15046	−	1.71918i	−0.246284	−	0.102014i
$285$			4.31534i			0.255619i
$286$	6.98252	−	16.8573i	0.412885	−	0.996793i
$287$		0			0
$288$	2.43845			0.143687
$289$		0			0
$290$	−7.23106			−0.424622
$291$	−7.86522	+	7.86522i	−0.461068	+	0.461068i
$292$	0.712457	−	1.72002i	0.0416934	−	0.100657i
$293$			7.12311i			0.416136i	0.978114	+	0.208068i	$0.0667176\pi$
$293$			7.12311i			0.416136i	−0.978114	+	0.208068i	$0.933282\pi$
$294$	10.0988	+	4.18306i	0.588974	+	0.243961i
$295$	0.241352	+	0.582675i	0.0140521	+	0.0339247i
$296$	−7.03583	+	2.91434i	−0.408949	+	0.169392i
$297$	1.81129	+	1.81129i	0.105102	+	0.105102i
$298$	4.68860	+	4.68860i	0.271603	+	0.271603i
$299$	27.6525	−	11.4540i	1.59919	−	0.662405i
$300$	−0.786022	−	1.89763i	−0.0453810	−	0.109559i
$301$		0			0
$302$			12.4924i			0.718858i
$303$	7.31810	−	17.6674i	0.420414	−	1.01497i
$304$	−25.4558	+	25.4558i	−1.45999	+	1.45999i
$305$	0.492423			0.0281960
$306$		0			0
$307$	−0.492423			−0.0281040			−0.0140520	−	0.999901i	$-0.504473\pi$
$307$	−0.492423			−0.0281040			−0.0140520	+	0.999901i	$0.504473\pi$
$308$		0			0
$309$	−1.65141	+	3.98686i	−0.0939454	+	0.226804i
$310$		−	4.49242i		−	0.255152i
$311$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$311$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$312$	4.25663	+	10.2764i	0.240984	+	0.581787i
$313$	−7.03583	+	2.91434i	−0.397689	+	0.164728i	−0.572559	−	0.819863i	$-0.694049\pi$
$313$	−7.03583	+	2.91434i	−0.397689	+	0.164728i	0.174871	+	0.984591i	$0.444049\pi$
$314$	−6.27691	−	6.27691i	−0.354227	−	0.354227i
$315$		0			0
$316$	−6.22569	+	2.57876i	−0.350222	+	0.145067i
$317$	6.88830	+	16.6298i	0.386886	+	0.934024i	0.990596	+	0.136821i	$0.0436884\pi$
$317$	6.88830	+	16.6298i	0.386886	+	0.934024i	−0.603710	+	0.797204i	$0.706312\pi$
$318$	−6.12595	−	2.53745i	−0.343526	−	0.142293i
$319$		−	21.1231i		−	1.18267i
$320$	1.19516	−	2.88537i	0.0668115	−	0.161297i
$321$	−5.43387	+	5.43387i	−0.303289	+	0.303289i
$322$		0			0
$323$		0			0
$324$	0.438447			0.0243582
$325$	15.1104	−	15.1104i	0.838174	−	0.838174i
$326$	−4.10950	+	9.92120i	−0.227604	+	0.549485i
$327$		−	15.1231i		−	0.836310i
$328$	−1.26508	−	0.524015i	−0.0698526	−	0.0289339i
$329$		0			0
$330$	−2.07523	+	0.859588i	−0.114238	+	0.0473188i
$331$	−4.29152	−	4.29152i	−0.235883	−	0.235883i	0.579260	−	0.815143i	$-0.303342\pi$
$331$	−4.29152	−	4.29152i	−0.235883	−	0.235883i	−0.815143	+	0.579260i	$0.803342\pi$
$332$	2.82843	+	2.82843i	0.155230	+	0.155230i
$333$	−2.88537	+	1.19516i	−0.158117	+	0.0654944i
$334$	0.482704	+	1.16535i	0.0264124	+	0.0637651i
$335$	2.07523	+	0.859588i	0.113382	+	0.0469643i
$336$		0			0
$337$	−12.5285	+	30.2466i	−0.682473	+	1.64763i	0.0769482	+	0.997035i	$0.475482\pi$
$337$	−12.5285	+	30.2466i	−0.682473	+	1.64763i	−0.759421	+	0.650600i	$0.774518\pi$
$338$	8.62121	−	8.62121i	0.468932	−	0.468932i
$339$	−4.56155			−0.247750
$340$		0			0
$341$	13.1231			0.710656
$342$	−8.48528	+	8.48528i	−0.458831	+	0.458831i
$343$		0			0
$344$		−	18.7386i		−	1.01032i
$345$	−3.40418	−	1.41006i	−0.183275	−	0.0759150i
$346$	−11.2392	−	27.1337i	−0.604221	−	1.45872i
$347$	22.6280	−	9.37284i	1.21474	−	0.503161i	0.319004	−	0.947753i	$-0.396652\pi$
$347$	22.6280	−	9.37284i	1.21474	−	0.503161i	0.895733	+	0.444593i	$0.146652\pi$
$348$	−2.55656	−	2.55656i	−0.137046	−	0.137046i
$349$	−5.25978	−	5.25978i	−0.281549	−	0.281549i	0.552177	−	0.833727i	$-0.313797\pi$
$349$	−5.25978	−	5.25978i	−0.281549	−	0.281549i	−0.833727	+	0.552177i	$0.813797\pi$
$350$		0			0
$351$	1.74563	+	4.21433i	0.0931749	+	0.224944i
$352$	−5.77075	−	2.39032i	−0.307582	−	0.127405i
$353$			22.4924i			1.19715i	0.801066	+	0.598575i	$0.204266\pi$
$353$			22.4924i			1.19715i	−0.801066	+	0.598575i	$0.795734\pi$
$354$	−0.671146	+	1.62029i	−0.0356710	+	0.0861174i
$355$	−4.06854	+	4.06854i	−0.215936	+	0.215936i
$356$	−3.12311			−0.165524
$357$		0			0
$358$	−14.2462			−0.752936
$359$	1.58831	−	1.58831i	0.0838279	−	0.0838279i	−0.663950	−	0.747777i	$-0.731121\pi$
$359$	1.58831	−	1.58831i	0.0838279	−	0.0838279i	0.747777	+	0.663950i	$0.231121\pi$
$360$	0.524015	−	1.26508i	0.0276180	−	0.0666758i
$361$		−	40.0540i		−	2.10810i
$362$	8.65612	+	3.58548i	0.454956	+	0.188449i
$363$	1.69852	+	4.10059i	0.0891492	+	0.215225i
$364$		0			0
$365$	−1.68608	−	1.68608i	−0.0882533	−	0.0882533i
$366$	0.968253	+	0.968253i	0.0506114	+	0.0506114i
$367$	16.8573	−	6.98252i	0.879944	−	0.364485i	0.103469	−	0.994633i	$-0.467006\pi$
$367$	16.8573	−	6.98252i	0.879944	−	0.364485i	0.776475	+	0.630148i	$0.217006\pi$
$368$	−11.7632	−	28.3988i	−0.613197	−	1.48039i
$369$	−0.518807	−	0.214897i	−0.0270080	−	0.0111871i
$370$		−	2.73863i		−	0.142375i
$371$		0			0
$372$	1.58831	−	1.58831i	0.0823501	−	0.0823501i
$373$	−16.2462			−0.841197			−0.420598	−	0.907247i	$-0.638180\pi$
$373$	−16.2462			−0.841197			−0.420598	+	0.907247i	$0.638180\pi$
$374$		0			0
$375$	−5.43845			−0.280840
$376$	−4.96046	+	4.96046i	−0.255816	+	0.255816i
$377$	14.3948	−	34.7522i	0.741372	−	1.78983i
$378$		0			0
$379$	−11.0866	−	4.59220i	−0.569478	−	0.235886i	0.0793161	−	0.996850i	$-0.474726\pi$
$379$	−11.0866	−	4.59220i	−0.569478	−	0.235886i	−0.648794	+	0.760964i	$0.724726\pi$
$380$	−0.724056	−	1.74803i	−0.0371433	−	0.0896718i
$381$	0.746277	−	0.309118i	0.0382329	−	0.0158366i
$382$	−14.4903	−	14.4903i	−0.741390	−	0.741390i
$383$	7.24517	+	7.24517i	0.370211	+	0.370211i	0.867554	−	0.497343i	$-0.165691\pi$
$383$	7.24517	+	7.24517i	0.370211	+	0.370211i	−0.497343	+	0.867554i	$0.665691\pi$
$384$	12.5292	−	5.18978i	0.639380	−	0.264840i
$385$		0			0
$386$	34.9797	+	14.4891i	1.78042	+	0.737474i
$387$		−	7.68466i		−	0.390633i
$388$	1.86631	−	4.50566i	0.0947474	−	0.228740i
$389$	−15.4586	+	15.4586i	−0.783781	+	0.783781i	−0.980467	−	0.196685i	$-0.936982\pi$
$389$	−15.4586	+	15.4586i	−0.783781	+	0.783781i	0.196685	+	0.980467i	$0.436982\pi$
$390$	−4.00000			−0.202548
$391$		0			0
$392$	17.0691			0.862121
$393$	13.1250	−	13.1250i	0.662069	−	0.662069i
$394$	11.9103	−	28.7540i	0.600032	−	1.44861i
$395$			8.63068i			0.434257i
$396$	−1.03761	−	0.429794i	−0.0521421	−	0.0215980i
$397$	2.05475	+	4.96060i	0.103125	+	0.248965i	0.967017	−	0.254711i	$-0.0819804\pi$
$397$	2.05475	+	4.96060i	0.103125	+	0.248965i	−0.863892	+	0.503677i	$0.831980\pi$
$398$	23.0830	−	9.56129i	1.15705	−	0.479264i
$399$		0			0
$400$	−15.5182	−	15.5182i	−0.775909	−	0.775909i
$401$	5.70688	−	2.36387i	0.284988	−	0.118046i	−0.235610	−	0.971848i	$-0.575709\pi$
$401$	5.70688	−	2.36387i	0.284988	−	0.118046i	0.520598	+	0.853802i	$0.325709\pi$
$402$	2.39032	+	5.77075i	0.119218	+	0.287819i
$403$	21.5904	+	8.94305i	1.07550	+	0.445485i
$404$			8.38447i			0.417143i
$405$	0.214897	−	0.518807i	0.0106783	−	0.0257797i
$406$		0			0
$407$	8.00000			0.396545
$408$		0			0
$409$	−2.31534			−0.114486			−0.0572431	−	0.998360i	$-0.518231\pi$
$409$	−2.31534			−0.114486			−0.0572431	+	0.998360i	$0.518231\pi$
$410$	0.348195	−	0.348195i	0.0171961	−	0.0171961i
$411$	6.21716	−	15.0095i	0.306670	−	0.740366i
$412$		−	1.89205i		−	0.0932146i
$413$		0			0
$414$	−3.92106	−	9.46626i	−0.192709	−	0.465242i
$415$	4.73313	−	1.96053i	0.232340	−	0.0962385i
$416$	−7.86522	−	7.86522i	−0.385624	−	0.385624i
$417$	−6.45101	−	6.45101i	−0.315907	−	0.315907i
$418$	28.3988	−	11.7632i	1.38903	−	0.575355i
$419$	−12.4343	−	30.0191i	−0.607456	−	1.46653i	−0.865757	−	0.500464i	$-0.833163\pi$
$419$	−12.4343	−	30.0191i	−0.607456	−	1.46653i	0.258302	−	0.966064i	$-0.416837\pi$
$420$		0			0
$421$			28.5616i			1.39200i	0.718039	+	0.696002i	$0.245040\pi$
$421$			28.5616i			1.39200i	−0.718039	+	0.696002i	$0.754960\pi$
$422$	6.79408	−	16.4024i	0.330731	−	0.798454i
$423$	−2.03427	+	2.03427i	−0.0989097	+	0.0989097i
$424$	−10.3542			−0.502843
$425$		0			0
$426$	−16.0000			−0.775203
$427$		0			0
$428$	1.28938	−	3.11284i	0.0623246	−	0.150465i
$429$		−	11.6847i		−	0.564141i
$430$	6.22569	+	2.57876i	0.300229	+	0.124359i
$431$	−9.18440	−	22.1731i	−0.442397	−	1.06804i	−0.975105	−	0.221742i	$-0.928826\pi$
$431$	−9.18440	−	22.1731i	−0.442397	−	1.06804i	0.532708	−	0.846299i	$-0.321174\pi$
$432$	4.32806	−	1.79274i	0.208234	−	0.0862533i
$433$	10.1225	+	10.1225i	0.486455	+	0.486455i	0.907186	−	0.420731i	$-0.138226\pi$
$433$	10.1225	+	10.1225i	0.486455	+	0.486455i	−0.420731	+	0.907186i	$0.638226\pi$
$434$		0			0
$435$	−4.27819	+	1.77209i	−0.205124	+	0.0849650i
$436$	2.53745	+	6.12595i	0.121522	+	0.293380i
$437$	46.5850	+	19.2962i	2.22847	+	0.923060i
$438$		−	6.63068i		−	0.316826i
$439$	2.20188	−	5.31581i	0.105090	−	0.253710i	−0.862584	−	0.505914i	$-0.831155\pi$
$439$	2.20188	−	5.31581i	0.105090	−	0.253710i	0.967674	+	0.252204i	$0.0811554\pi$
$440$	−2.48023	+	2.48023i	−0.118240	+	0.118240i
$441$	7.00000			0.333333
$442$		0			0
$443$	−22.8769			−1.08691			−0.543457	−	0.839437i	$-0.682885\pi$
$443$	−22.8769			−1.08691			−0.543457	+	0.839437i	$0.682885\pi$
$444$	0.968253	−	0.968253i	0.0459513	−	0.0459513i
$445$	−1.53073	+	3.69552i	−0.0725637	+	0.175184i
$446$		−	21.7538i		−	1.03007i
$447$	3.92299	+	1.62495i	0.185551	+	0.0768577i
$448$		0			0
$449$	−11.7690	+	4.87486i	−0.555412	+	0.230059i	−0.642692	−	0.766125i	$-0.722182\pi$
$449$	−11.7690	+	4.87486i	−0.555412	+	0.230059i	0.0872802	+	0.996184i	$0.472182\pi$
$450$	−5.17273	−	5.17273i	−0.243845	−	0.243845i
$451$	1.01714	+	1.01714i	0.0478951	+	0.0478951i
$452$	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
$456$	−7.17096	+	17.3122i	−0.335811	+	0.810720i
$457$	−4.81382	+	4.81382i	−0.225181	+	0.225181i	−0.810676	−	0.585495i	$-0.800900\pi$
$457$	−4.81382	+	4.81382i	−0.225181	+	0.225181i	0.585495	+	0.810676i	$0.300900\pi$
$458$	−9.36932			−0.437799
$459$		0			0
$460$	1.61553			0.0753244
$461$	−5.83095	+	5.83095i	−0.271575	+	0.271575i	−0.829734	−	0.558159i	$-0.811508\pi$
$461$	−5.83095	+	5.83095i	−0.271575	+	0.271575i	0.558159	+	0.829734i	$0.311508\pi$
$462$		0			0
$463$		−	24.9848i		−	1.16114i	−0.814209	−	0.580572i	$-0.802829\pi$
$463$		−	24.9848i		−	1.16114i	0.814209	−	0.580572i	$-0.197171\pi$
$464$	−35.6901	−	14.7833i	−1.65687	−	0.686299i
$465$	−1.10094	−	2.65790i	−0.0510549	−	0.123257i
$466$	0.810145	−	0.335573i	0.0375292	−	0.0155451i
$467$	−2.38247	−	2.38247i	−0.110247	−	0.110247i	0.649831	−	0.760079i	$-0.274840\pi$
$467$	−2.38247	−	2.38247i	−0.110247	−	0.110247i	−0.760079	+	0.649831i	$0.774840\pi$
$468$	−1.41421	−	1.41421i	−0.0653720	−	0.0653720i
$469$		0			0
$470$	−0.965408	−	2.33070i	−0.0445309	−	0.107507i
$471$	−5.25194	−	2.17542i	−0.241997	−	0.100238i
$472$			2.73863i			0.126056i
$473$	−7.53299	+	18.1863i	−0.346367	+	0.836205i
$474$	−16.9706	+	16.9706i	−0.779484	+	0.779484i
$475$	36.0000			1.65179
$476$		0			0
$477$	−4.24621			−0.194421
$478$	−11.3137	+	11.3137i	−0.517477	+	0.517477i
$479$	−11.2127	+	27.0698i	−0.512321	+	1.23685i	0.430208	+	0.902730i	$0.358440\pi$
$479$	−11.2127	+	27.0698i	−0.512321	+	1.23685i	−0.942529	+	0.334123i	$0.891560\pi$
$480$			1.36932i			0.0625005i
$481$	13.1618	+	5.45179i	0.600126	+	0.248580i
$482$	−12.7699	−	30.8292i	−0.581652	−	1.40423i
$483$		0			0
$484$	−1.37605	−	1.37605i	−0.0625476	−	0.0625476i
$485$	−4.41674	−	4.41674i	−0.200554	−	0.200554i
$486$	1.44269	−	0.597580i	0.0654416	−	0.0271068i
$487$	2.82012	+	6.80836i	0.127792	+	0.308516i	0.974806	−	0.223053i	$-0.0716024\pi$
$487$	2.82012	+	6.80836i	0.127792	+	0.308516i	−0.847015	+	0.531570i	$0.821602\pi$
$488$	1.97550	+	0.818277i	0.0894265	+	0.0370417i
$489$			6.87689i			0.310984i
$490$	−2.34901	+	5.67101i	−0.106117	+	0.256190i
$491$	2.38247	−	2.38247i	0.107519	−	0.107519i	−0.651301	−	0.758820i	$-0.725776\pi$
$491$	2.38247	−	2.38247i	0.107519	−	0.107519i	0.758820	+	0.651301i	$0.225776\pi$
$492$	0.246211			0.0111001
$493$		0			0
$494$	54.7386			2.46281
$495$	−1.01714	+	1.01714i	−0.0457169	+	0.0457169i
$496$	9.18440	−	22.1731i	0.412392	−	0.995602i
$497$		0			0
$498$	13.1618	+	5.45179i	0.589794	+	0.244301i
$499$	−4.35085	−	10.5039i	−0.194771	−	0.470218i	0.796078	−	0.605194i	$-0.206904\pi$
$499$	−4.35085	−	10.5039i	−0.194771	−	0.470218i	−0.990849	+	0.134976i	$0.956904\pi$
$500$	2.20296	−	0.912498i	0.0985196	−	0.0408081i
$501$	0.571175	+	0.571175i	0.0255182	+	0.0255182i
$502$	27.0442	+	27.0442i	1.20704	+	1.20704i
$503$	23.5021	−	9.73487i	1.04791	−	0.434057i	0.208762	−	0.977967i	$-0.433057\pi$
$503$	23.5021	−	9.73487i	1.04791	−	0.434057i	0.839144	+	0.543910i	$0.183057\pi$
$504$		0			0
$505$	9.92120	+	4.10950i	0.441488	+	0.182870i
$506$			26.2462i			1.16679i
$507$	2.98790	−	7.21343i	0.132697	−	0.320360i
$508$	−0.250430	+	0.250430i	−0.0111110	+	0.0111110i
$509$	−16.8769			−0.748055			−0.374028	−	0.927418i	$-0.622023\pi$
$509$	−16.8769			−0.748055			−0.374028	+	0.927418i	$0.622023\pi$
$510$		0			0
$511$		0			0
$512$	8.07749	−	8.07749i	0.356978	−	0.356978i
$513$	−2.94079	+	7.09970i	−0.129839	+	0.313459i
$514$		−	14.6307i		−	0.645332i
$515$	−2.23883	−	0.927354i	−0.0986546	−	0.0408641i
$516$	1.28938	+	3.11284i	0.0567619	+	0.137035i
$517$	6.80836	−	2.82012i	0.299431	−	0.124029i
$518$		0			0
$519$	−13.2991	−	13.2991i	−0.583766	−	0.583766i
$520$	−5.77075	+	2.39032i	−0.253064	+	0.104823i
$521$	12.0310	+	29.0453i	0.527086	+	1.27250i	0.933424	+	0.358776i	$0.116806\pi$
$521$	12.0310	+	29.0453i	0.527086	+	1.27250i	−0.406337	+	0.913723i	$0.633194\pi$
$522$	−11.8967	−	4.92777i	−0.520704	−	0.215683i
$523$		−	20.0000i		−	0.874539i	−0.899331	−	0.437269i	$-0.855946\pi$
$523$		−	20.0000i		−	0.874539i	0.899331	−	0.437269i	$-0.144054\pi$
$524$	−3.11438	+	7.51877i	−0.136052	+	0.328459i
$525$		0			0
$526$	−19.5076			−0.850571
$527$		0			0
$528$	−12.0000			−0.522233
$529$	−14.1803	+	14.1803i	−0.616535	+	0.616535i
$530$	1.42491	−	3.44005i	0.0618943	−	0.149426i
$531$			1.12311i			0.0487386i
$532$		0			0
$533$	0.980264	+	2.36657i	0.0424599	+	0.102507i
$534$	−10.2764	+	4.25663i	−0.444704	+	0.184202i
$535$	−3.05141	−	3.05141i	−0.131924	−	0.131924i
$536$	6.89697	+	6.89697i	0.297904	+	0.297904i
$537$	−8.42865	+	3.49126i	−0.363723	+	0.150659i
$538$	−12.2872	−	29.6639i	−0.529738	−	1.27890i
$539$	−16.5660	−	6.86185i	−0.713547	−	0.295561i
$540$			0.246211i			0.0105952i
$541$	15.3486	−	37.0549i	0.659890	−	1.59312i	−0.138082	−	0.990421i	$-0.544094\pi$
$541$	15.3486	−	37.0549i	0.659890	−	1.59312i	0.797972	−	0.602694i	$-0.205906\pi$
$542$	−0.891921	+	0.891921i	−0.0383113	+	0.0383113i
$543$	6.00000			0.257485
$544$		0			0
$545$	8.49242			0.363775
$546$		0			0
$547$	10.7151	−	25.8686i	0.458146	−	1.10606i	−0.511001	−	0.859580i	$-0.670725\pi$
$547$	10.7151	−	25.8686i	0.458146	−	1.10606i	0.969147	−	0.246483i	$-0.0792748\pi$
$548$			7.12311i			0.304284i
$549$	0.810145	+	0.335573i	0.0345761	+	0.0143219i
$550$	7.17096	+	17.3122i	0.305771	+	0.738196i
$551$	58.5456	−	24.2504i	2.49413	−	1.03310i
$552$	−11.3137	−	11.3137i	−0.481543	−	0.481543i
$553$		0			0
$554$	−8.65612	+	3.58548i	−0.367763	+	0.152333i
$555$	−0.671146	−	1.62029i	−0.0284886	−	0.0687775i
$556$	3.69552	+	1.53073i	0.156725	+	0.0649176i
$557$		−	6.49242i		−	0.275093i	−0.990495	−	0.137546i	$-0.956078\pi$
$557$		−	6.49242i		−	0.275093i	0.990495	−	0.137546i	$-0.0439216\pi$
$558$	3.06147	−	7.39104i	0.129602	−	0.312888i
$559$	−24.7869	+	24.7869i	−1.04837	+	1.04837i
$560$		0			0
$561$		0			0
$562$	−29.8617			−1.25964
$563$	−16.1764	+	16.1764i	−0.681754	+	0.681754i	−0.960395	−	0.278641i	$-0.910116\pi$
$563$	−16.1764	+	16.1764i	−0.681754	+	0.681754i	0.278641	+	0.960395i	$0.410116\pi$
$564$	0.482704	−	1.16535i	0.0203255	−	0.0490701i
$565$		−	2.56155i		−	0.107765i
$566$	−4.86087	−	2.01344i	−0.204318	−	0.0846311i
$567$		0			0
$568$	−23.0830	+	9.56129i	−0.968541	+	0.401183i
$569$	9.10534	+	9.10534i	0.381716	+	0.381716i	0.871720	−	0.490004i	$-0.163005\pi$
$569$	9.10534	+	9.10534i	0.381716	+	0.381716i	−0.490004	+	0.871720i	$0.663005\pi$
$570$	−4.76493	−	4.76493i	−0.199581	−	0.199581i
$571$	−17.3122	+	7.17096i	−0.724495	+	0.300096i	−0.714288	−	0.699852i	$-0.753249\pi$
$571$	−17.3122	+	7.17096i	−0.724495	+	0.300096i	−0.0102072	+	0.999948i	$0.503249\pi$
$572$	1.96053	+	4.73313i	0.0819738	+	0.197902i
$573$	−12.1242	−	5.02200i	−0.506494	−	0.209797i
$574$		0			0
$575$	−11.7632	+	28.3988i	−0.490558	+	1.18431i
$576$	3.93261	−	3.93261i	0.163859	−	0.163859i
$577$	41.0540			1.70910			0.854550	−	0.519370i	$-0.173833\pi$
$577$	41.0540			1.70910			0.854550	+	0.519370i	$0.173833\pi$
$578$		0			0
$579$	24.2462			1.00764
$580$	1.43565	−	1.43565i	0.0596120	−	0.0596120i
$581$		0			0
$582$		−	17.3693i		−	0.719981i
$583$	10.0489	+	4.16241i	0.416185	+	0.172389i
$584$	−3.96237	−	9.56600i	−0.163964	−	0.395844i
$585$	−2.36657	+	0.980264i	−0.0978455	+	0.0405289i
$586$	−7.86522	−	7.86522i	−0.324909	−	0.324909i
$587$	−26.1522	−	26.1522i	−1.07942	−	1.07942i	−0.996561	−	0.0828568i	$-0.973596\pi$
$587$	−26.1522	−	26.1522i	−1.07942	−	1.07942i	−0.0828568	−	0.996561i	$-0.526404\pi$
$588$	−2.83551	+	1.17451i	−0.116934	+	0.0484358i
$589$	15.0660	+	36.3725i	0.620783	+	1.49870i
$590$	−0.909878	−	0.376884i	−0.0374591	−	0.0155161i
$591$		−	19.9309i		−	0.819846i
$592$	5.59892	−	13.5170i	0.230114	−	0.555545i
$593$	31.2868	−	31.2868i	1.28479	−	1.28479i	0.346888	−	0.937906i	$-0.387238\pi$
$593$	31.2868	−	31.2868i	1.28479	−	1.28479i	0.937906	−	0.346888i	$-0.112762\pi$
$594$	−4.00000			−0.164122
$595$		0			0
$596$	−1.86174			−0.0762598
$597$	11.3137	−	11.3137i	0.463039	−	0.463039i
$598$	−17.8861	+	43.1809i	−0.731417	+	1.76580i
$599$			41.6155i			1.70036i	0.526489	+	0.850182i	$0.323508\pi$
$599$			41.6155i			1.70036i	−0.526489	+	0.850182i	$0.676492\pi$
$600$	−10.5537	−	4.37150i	−0.430855	−	0.178466i
$601$	13.3881	+	32.3218i	0.546113	+	1.31843i	0.920348	+	0.391099i	$0.127905\pi$
$601$	13.3881	+	32.3218i	0.546113	+	1.31843i	−0.374236	+	0.927334i	$0.622095\pi$
$602$		0			0
$603$	2.82843	+	2.82843i	0.115182	+	0.115182i
$604$	−2.48023	−	2.48023i	−0.100919	−	0.100919i
$605$	−2.30270	+	0.953809i	−0.0936180	+	0.0387778i
$606$	11.4276	+	27.5886i	0.464214	+	1.12071i
$607$	−14.1994	−	5.88158i	−0.576336	−	0.238726i	0.0754240	−	0.997152i	$-0.475969\pi$
$607$	−14.1994	−	5.88158i	−0.576336	−	0.238726i	−0.651760	+	0.758425i	$0.725969\pi$
$608$		−	18.7386i		−	0.759952i
$609$		0			0
$610$	−0.543725	+	0.543725i	−0.0220148	+	0.0220148i
$611$	13.1231			0.530904
$612$		0			0
$613$	2.31534			0.0935158			0.0467579	−	0.998906i	$-0.485111\pi$
$613$	2.31534			0.0935158			0.0467579	+	0.998906i	$0.485111\pi$
$614$	0.543725	−	0.543725i	0.0219430	−	0.0219430i
$615$	0.120676	−	0.291338i	0.00486613	−	0.0117479i
$616$		0			0
$617$	−25.6412	−	10.6209i	−1.03227	−	0.427582i	−0.198741	−	0.980052i	$-0.563685\pi$
$617$	−25.6412	−	10.6209i	−1.03227	−	0.427582i	−0.833533	+	0.552470i	$0.813685\pi$
$618$	−2.57876	−	6.22569i	−0.103733	−	0.250434i
$619$	−17.8949	+	7.41232i	−0.719257	+	0.297926i	−0.712129	−	0.702048i	$-0.752269\pi$
$619$	−17.8949	+	7.41232i	−0.719257	+	0.297926i	−0.00712818	+	0.999975i	$0.502269\pi$
$620$	0.891921	+	0.891921i	0.0358204	+	0.0358204i
$621$	−4.63972	−	4.63972i	−0.186185	−	0.186185i
$622$		0			0
$623$		0			0
$624$	−19.7427	−	8.17768i	−0.790340	−	0.327369i
$625$			20.3693i			0.814773i
$626$	4.55089	−	10.9868i	0.181890	−	0.439122i
$627$	13.9192	−	13.9192i	0.555878	−	0.555878i
$628$	2.49242			0.0994585
$629$		0			0
$630$		0			0
$631$	−8.26230	+	8.26230i	−0.328917	+	0.328917i	−0.852175	−	0.523258i	$-0.824717\pi$
$631$	−8.26230	+	8.26230i	−0.328917	+	0.328917i	0.523258	+	0.852175i	$0.324717\pi$
$632$	−14.3419	+	34.6245i	−0.570491	+	1.37729i
$633$		−	11.3693i		−	0.451890i
$634$	−25.9684	−	10.7564i	−1.03134	−	0.427193i
$635$	0.173586	+	0.419074i	0.00688855	+	0.0166304i
$636$	1.72002	−	0.712457i	0.0682033	−	0.0282508i
$637$	−22.5785	−	22.5785i	−0.894594	−	0.894594i
$638$	23.3238	+	23.3238i	0.923398	+	0.923398i
$639$	−9.46626	+	3.92106i	−0.374480	+	0.155115i
$640$	2.91434	+	7.03583i	0.115199	+	0.278116i
$641$	0.0638681	+	0.0264550i	0.00252264	+	0.00104491i	0.383944	−	0.923356i	$-0.374565\pi$
$641$	0.0638681	+	0.0264550i	0.00252264	+	0.00104491i	−0.381422	+	0.924401i	$0.624565\pi$
$642$		−	12.0000i		−	0.473602i
$643$	11.5747	−	27.9439i	0.456463	−	1.10200i	−0.513357	−	0.858175i	$-0.671598\pi$
$643$	11.5747	−	27.9439i	0.456463	−	1.10200i	0.969820	−	0.243823i	$-0.0784016\pi$
$644$		0			0
$645$	4.31534			0.169916
$646$		0			0
$647$	15.3693			0.604230			0.302115	−	0.953271i	$-0.402307\pi$
$647$	15.3693			0.604230			0.302115	+	0.953271i	$0.402307\pi$
$648$	1.72424	−	1.72424i	0.0677346	−	0.0677346i
$649$	1.10094	−	2.65790i	0.0432157	−	0.104332i
$650$			33.3693i			1.30885i
$651$		0			0
$652$	−1.15385	−	2.78564i	−0.0451882	−	0.109094i
$653$	−3.75939	+	1.55719i	−0.147116	+	0.0609375i	−0.455027	−	0.890478i	$-0.650370\pi$
$653$	−3.75939	+	1.55719i	−0.147116	+	0.0609375i	0.307910	+	0.951415i	$0.400370\pi$
$654$	16.6987	+	16.6987i	0.652971	+	0.652971i
$655$	7.37038	+	7.37038i	0.287985	+	0.287985i
$656$	2.43043	−	1.00672i	0.0948925	−	0.0393058i
$657$	−1.62495	−	3.92299i	−0.0633955	−	0.153050i
$658$		0			0
$659$			47.8617i			1.86443i	0.361907	+	0.932214i	$0.382126\pi$
$659$			47.8617i			1.86443i	−0.361907	+	0.932214i	$0.617874\pi$
$660$	0.241352	−	0.582675i	0.00939461	−	0.0226806i
$661$	18.1618	−	18.1618i	0.706412	−	0.706412i	−0.259367	−	0.965779i	$-0.583514\pi$
$661$	18.1618	−	18.1618i	0.706412	−	0.706412i	0.965779	+	0.259367i	$0.0835139\pi$
$662$	9.47727			0.368344
$663$		0			0
$664$	22.2462			0.863320
$665$		0			0
$666$	1.86631	−	4.50566i	0.0723179	−	0.174591i
$667$			54.1080i			2.09507i
$668$	−0.327203	−	0.135532i	−0.0126599	−	0.00524389i
$669$	−5.33111	−	12.8704i	−0.206113	−	0.497600i
$670$	−3.24058	+	1.34229i	−0.125194	+	0.0518573i
$671$	−1.58831	−	1.58831i	−0.0613161	−	0.0613161i
$672$		0			0
$673$	−45.0286	+	18.6515i	−1.73573	+	0.718961i	−0.736637	+	0.676288i	$0.763587\pi$
$673$	−45.0286	+	18.6515i	−1.73573	+	0.718961i	−0.999089	+	0.0426728i	$0.986413\pi$
$674$	−19.5640	−	47.2316i	−0.753576	−	1.81929i
$675$	−4.32806	−	1.79274i	−0.166587	−	0.0690026i
$676$			3.42329i			0.131665i
$677$	5.23689	−	12.6430i	0.201270	−	0.485909i	−0.790727	−	0.612169i	$-0.790297\pi$
$677$	5.23689	−	12.6430i	0.201270	−	0.485909i	0.991997	+	0.126260i	$0.0402973\pi$
$678$	5.03680	−	5.03680i	0.193437	−	0.193437i
$679$		0			0
$680$		0			0
$681$	−23.0540			−0.883430
$682$	−14.4903	+	14.4903i	−0.554863	+	0.554863i
$683$	−2.08120	+	5.02447i	−0.0796350	+	0.192256i	−0.958682	−	0.284478i	$-0.908180\pi$
$683$	−2.08120	+	5.02447i	−0.0796350	+	0.192256i	0.879047	+	0.476734i	$0.158180\pi$
$684$		−	3.36932i		−	0.128829i
$685$	8.42865	+	3.49126i	0.322042	+	0.133394i
$686$		0			0
$687$	−5.54328	+	2.29610i	−0.211489	+	0.0876017i
$688$	25.4558	+	25.4558i	0.970495	+	0.970495i
$689$	13.6962	+	13.6962i	0.521783	+	0.521783i
$690$	5.31581	−	2.20188i	0.202369	−	0.0838241i
$691$	−14.1535	−	34.1695i	−0.538424	−	1.29987i	−0.925823	−	0.377958i	$-0.876626\pi$
$691$	−14.1535	−	34.1695i	−0.538424	−	1.29987i	0.387399	−	0.921912i	$-0.373374\pi$
$692$	7.61851	+	3.15569i	0.289612	+	0.119961i
$693$		0			0
$694$	−14.6362	+	35.3349i	−0.555582	+	1.34129i
$695$	3.62258	−	3.62258i	0.137412	−	0.137412i
$696$	−20.1080			−0.762190
$697$		0			0
$698$	11.6155			0.439654
$699$	0.397078	−	0.397078i	0.0150189	−	0.0150189i
$700$		0			0
$701$			9.36932i			0.353874i	0.984222	+	0.176937i	$0.0566189\pi$
$701$			9.36932i			0.353874i	−0.984222	+	0.176937i	$0.943381\pi$
$702$	−6.58089	−	2.72589i	−0.248380	−	0.102882i
$703$	9.18440	+	22.1731i	0.346396	+	0.836275i
$704$	−13.1618	+	5.45179i	−0.496053	+	0.205472i
$705$	−1.14235	−	1.14235i	−0.0430234	−	0.0430234i
$706$	−24.8358	−	24.8358i	−0.934707	−	0.934707i
$707$		0			0
$708$	−0.188442	−	0.454939i	−0.00708208	−	0.0170977i
$709$	−4.37793	−	1.81340i	−0.164416	−	0.0681035i	0.298957	−	0.954267i	$-0.403361\pi$
$709$	−4.37793	−	1.81340i	−0.164416	−	0.0681035i	−0.463374	+	0.886163i	$0.653361\pi$
$710$		−	8.98485i		−	0.337195i
$711$	−5.88158	+	14.1994i	−0.220577	+	0.532519i
$712$	−12.2820	+	12.2820i	−0.460286	+	0.460286i
$713$	−33.6155			−1.25891
$714$		0			0
$715$	6.56155			0.245388
$716$	2.82843	−	2.82843i	0.105703	−	0.105703i
$717$	−3.92106	+	9.46626i	−0.146434	+	0.353524i
$718$			3.50758i			0.130902i
$719$	8.13731	+	3.37059i	0.303471	+	0.125702i	0.529222	−	0.848483i	$-0.322484\pi$
$719$	8.13731	+	3.37059i	0.303471	+	0.125702i	−0.225752	+	0.974185i	$0.572484\pi$
$720$	1.00672	+	2.43043i	0.0375182	+	0.0905769i
$721$		0			0
$722$	44.2270	+	44.2270i	1.64596	+	1.64596i
$723$	−15.1104	−	15.1104i	−0.561961	−	0.561961i
$724$	−2.43043	+	1.00672i	−0.0903264	+	0.0374144i
$725$	14.7833	+	35.6901i	0.549039	+	1.32550i
$726$	−6.40329	−	2.65233i	−0.237648	−	0.0984372i
$727$		−	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
$730$	3.72348			0.137812
$731$		0			0
$732$	−0.384472			−0.0142105
$733$	19.9731	−	19.9731i	0.737723	−	0.737723i	−0.234414	−	0.972137i	$-0.575317\pi$
$733$	19.9731	−	19.9731i	0.737723	−	0.737723i	0.972137	+	0.234414i	$0.0753171\pi$
$734$	−10.9036	+	26.3236i	−0.402458	+	0.971621i
$735$			3.93087i			0.144992i
$736$	14.7821	+	6.12293i	0.544874	+	0.225694i
$737$	−3.92106	−	9.46626i	−0.144434	−	0.348694i
$738$	0.810145	−	0.335573i	0.0298218	−	0.0123526i
$739$	−5.87983	−	5.87983i	−0.216293	−	0.216293i	0.590641	−	0.806934i	$-0.298875\pi$
$739$	−5.87983	−	5.87983i	−0.216293	−	0.216293i	−0.806934	+	0.590641i	$0.798875\pi$
$740$	0.543725	+	0.543725i	0.0199877	+	0.0199877i
$741$	32.3857	−	13.4146i	1.18972	−	0.492797i
$742$		0			0
$743$	4.15046	+	1.71918i	0.152266	+	0.0630704i	0.457515	−	0.889202i	$-0.348740\pi$
$743$	4.15046	+	1.71918i	0.152266	+	0.0630704i	−0.305249	+	0.952273i	$0.598740\pi$
$744$		−	12.4924i		−	0.457994i
$745$	−0.912498	+	2.20296i	−0.0334313	+	0.0807104i
$746$	17.9388	−	17.9388i	0.656787	−	0.656787i
$747$	9.12311			0.333797
$748$		0			0
$749$		0			0
$750$	6.00505	−	6.00505i	0.219273	−	0.219273i
$751$	−0.241352	+	0.582675i	−0.00880706	+	0.0212621i	−0.928222	−	0.372027i	$-0.878663\pi$
$751$	−0.241352	+	0.582675i	−0.00880706	+	0.0212621i	0.919415	+	0.393289i	$0.128663\pi$
$752$		−	13.4773i		−	0.491465i
$753$	22.6280	+	9.37284i	0.824612	+	0.341565i
$754$	22.4783	+	54.2674i	0.818611	+	1.97630i
$755$	−4.15046	+	1.71918i	−0.151051	+	0.0625672i
$756$		0			0
$757$	14.8874	+	14.8874i	0.541092	+	0.541092i	0.923849	−	0.382757i	$-0.125025\pi$
$757$	14.8874	+	14.8874i	0.541092	+	0.541092i	−0.382757	+	0.923849i	$0.625025\pi$
$758$	17.3122	−	7.17096i	0.628809	−	0.260461i
$759$	6.43205	+	15.5283i	0.233469	+	0.563643i
$760$	−9.72174	−	4.02688i	−0.352644	−	0.146070i
$761$		−	32.2462i		−	1.16892i	−0.811421	−	0.584462i	$-0.801306\pi$
$761$		−	32.2462i		−	1.16892i	0.811421	−	0.584462i	$-0.198694\pi$
$762$	−0.482704	+	1.16535i	−0.0174865	+	0.0422162i
$763$		0			0
$764$	5.75379			0.208165
$765$		0			0
$766$	−16.0000			−0.578103
$767$	3.62258	−	3.62258i	0.130804	−	0.130804i
$768$	−3.84749	+	9.28866i	−0.138834	+	0.335176i
$769$			29.5464i			1.06547i	0.846282	+	0.532735i	$0.178836\pi$
$769$			29.5464i			1.06547i	−0.846282	+	0.532735i	$0.821164\pi$
$770$		0			0
$771$	−3.58548	−	8.65612i	−0.129128	−	0.311743i
$772$	−9.82147	+	4.06819i	−0.353482	+	0.146417i
$773$	−23.5957	−	23.5957i	−0.848677	−	0.848677i	0.141291	−	0.989968i	$-0.454875\pi$
$773$	−23.5957	−	23.5957i	−0.848677	−	0.848677i	−0.989968	+	0.141291i	$0.954875\pi$
$774$	8.48528	+	8.48528i	0.304997	+	0.304997i
$775$	−22.1731	+	9.18440i	−0.796482	+	0.329913i
$776$	−10.3796	−	25.0585i	−0.372605	−	0.899547i
$777$		0			0
$778$		−	34.1383i		−	1.22392i
$779$	−1.65141	+	3.98686i	−0.0591679	+	0.142844i
$780$	0.794156	−	0.794156i	0.0284353	−	0.0284353i
$781$	26.2462			0.939163
$782$		0			0
$783$	−8.24621			−0.294696
$784$	−23.1879	+	23.1879i	−0.828138	+	0.828138i
$785$	1.22162	−	2.94924i	0.0436013	−	0.105263i
$786$			28.9848i			1.03386i
$787$	5.77075	+	2.39032i	0.205705	+	0.0852058i	0.483157	−	0.875534i	$-0.339490\pi$
$787$	5.77075	+	2.39032i	0.205705	+	0.0852058i	−0.277452	+	0.960739i	$0.589490\pi$
$788$	3.34413	+	8.07344i	0.119130	+	0.287605i
$789$	−11.5415	+	4.78064i	−0.410888	+	0.170195i
$790$	−9.52987	−	9.52987i	−0.339057	−	0.339057i
$791$		0			0
$792$	−5.77075	+	2.39032i	−0.205055	+	0.0849364i
$793$	−1.53073	−	3.69552i	−0.0543579	−	0.131232i
$794$	−7.74624	−	3.20860i	−0.274904	−	0.113869i
$795$		−	2.38447i		−	0.0845685i
$796$	−2.68458	+	6.48116i	−0.0951525	+	0.229719i
$797$	22.3556	−	22.3556i	0.791874	−	0.791874i	−0.189924	−	0.981799i	$-0.560824\pi$
$797$	22.3556	−	22.3556i	0.791874	−	0.791874i	0.981799	+	0.189924i	$0.0608243\pi$
$798$		0			0
$799$		0			0
$800$	11.4233			0.403874
$801$	−5.03680	+	5.03680i	−0.177966	+	0.177966i
$802$	−3.69130	+	8.91159i	−0.130344	+	0.314679i
$803$			10.8769i			0.383837i
$804$	−1.62029	−	0.671146i	−0.0571432	−	0.0236695i
$805$		0			0
$806$	−33.7146	+	13.9650i	−1.18755	+	0.491898i
$807$	−14.5392	−	14.5392i	−0.511805	−	0.511805i
$808$	32.9729	+	32.9729i	1.15998	+	1.15998i
$809$	−49.0155	+	20.3029i	−1.72329	+	0.713811i	−0.723570	+	0.690251i	$0.757500\pi$
$809$	−49.0155	+	20.3029i	−1.72329	+	0.713811i	−0.999722	+	0.0235603i	$0.992500\pi$
$810$	0.335573	+	0.810145i	0.0117908	+	0.0284656i
$811$	19.0603	+	7.89502i	0.669296	+	0.277232i	0.691345	−	0.722525i	$-0.257019\pi$
$811$	19.0603	+	7.89502i	0.669296	+	0.277232i	−0.0220481	+	0.999757i	$0.507019\pi$
$812$		0			0
$813$	−0.309118	+	0.746277i	−0.0108412	+	0.0261731i
$814$	−8.83348	+	8.83348i	−0.309613	+	0.309613i
$815$	−3.86174			−0.135271
$816$		0			0
$817$	−59.0540			−2.06604
$818$	2.55656	−	2.55656i	0.0893882	−	0.0893882i
$819$		0			0
$820$			0.138261i			0.00482827i
$821$	−15.3009	−	6.33783i	−0.534004	−	0.221192i	0.0993517	−	0.995052i	$-0.468323\pi$
$821$	−15.3009	−	6.33783i	−0.534004	−	0.221192i	−0.633356	+	0.773861i	$0.718323\pi$
$822$	9.70842	+	23.4382i	0.338620	+	0.817501i
$823$	33.7146	−	13.9650i	1.17522	−	0.486791i	0.292303	−	0.956326i	$-0.405578\pi$
$823$	33.7146	−	13.9650i	1.17522	−	0.486791i	0.882914	+	0.469535i	$0.155578\pi$
$824$	−7.44070	−	7.44070i	−0.259209	−	0.259209i
$825$	8.48528	+	8.48528i	0.295420	+	0.295420i
$826$		0			0
$827$	5.51955	+	13.3254i	0.191934	+	0.463369i	0.990325	−	0.138771i	$-0.0443151\pi$
$827$	5.51955	+	13.3254i	0.191934	+	0.463369i	−0.798391	+	0.602140i	$0.794315\pi$
$828$	2.65790	+	1.10094i	0.0923685	+	0.0382603i
$829$			50.4924i			1.75367i	0.480787	+	0.876837i	$0.340351\pi$
$829$			50.4924i			1.75367i	−0.480787	+	0.876837i	$0.659649\pi$
$830$	−3.06147	+	7.39104i	−0.106265	+	0.256547i
$831$	−4.24264	+	4.24264i	−0.147176	+	0.147176i
$832$	−25.3693			−0.879523
$833$		0			0
$834$	14.2462			0.493306
$835$	−0.320745	+	0.320745i	−0.0110998	+	0.0110998i
$836$	−3.30282	+	7.97371i	−0.114230	+	0.275777i
$837$		−	5.12311i		−	0.177080i
$838$	46.8764	+	19.4168i	1.61932	+	0.670743i
$839$	4.23017	+	10.2125i	0.146042	+	0.352576i	0.979925	−	0.199364i	$-0.0638877\pi$
$839$	4.23017	+	10.2125i	0.146042	+	0.352576i	−0.833884	+	0.551940i	$0.813888\pi$
$840$		0			0
$841$	27.5772	+	27.5772i	0.950937	+	0.950937i
$842$	−31.5372	−	31.5372i	−1.08684	−	1.08684i
$843$	−17.6674	+	7.31810i	−0.608499	+	0.252049i
$844$	1.90762	+	4.60540i	0.0656629	+	0.158524i
$845$	4.05072	+	1.67786i	0.139349	+	0.0577203i
$846$		−	4.49242i		−	0.154453i
$847$		0			0
$848$	14.0658	−	14.0658i	0.483022	−	0.483022i
$849$	−3.36932			−0.115635
$850$		0			0
$851$	−20.4924			−0.702471
$852$	3.17662	−	3.17662i	0.108829	−	0.108829i
$853$	7.93633	−	19.1600i	0.271735	−	0.656026i	−0.727823	−	0.685765i	$-0.759468\pi$
$853$	7.93633	−	19.1600i	0.271735	−	0.656026i	0.999558	+	0.0297393i	$0.00946771\pi$
$854$		0			0
$855$	−3.98686	−	1.65141i	−0.136348	−	0.0564770i
$856$	−7.17096	−	17.3122i	−0.245099	−	0.591720i
$857$	−5.54328	+	2.29610i	−0.189355	+	0.0784333i	−0.475346	−	0.879799i	$-0.657677\pi$
$857$	−5.54328	+	2.29610i	−0.189355	+	0.0784333i	0.285991	+	0.958232i	$0.407677\pi$
$858$	12.9020	+	12.9020i	0.440468	+	0.440468i
$859$	−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	$0.815628\pi$
$860$	−1.74803	+	0.724056i	−0.0596072	+	0.0246901i
$861$		0			0
$862$	34.6245	+	14.3419i	1.17931	+	0.488488i
$863$		−	26.2462i		−	0.893431i	−0.894676	−	0.446716i	$-0.852594\pi$
$863$		−	26.2462i		−	0.893431i	0.894676	−	0.446716i	$-0.147406\pi$
$864$	−0.933153	+	2.25283i	−0.0317465	+	0.0766429i
$865$	7.46815	−	7.46815i	0.253925	−	0.253925i
$866$	−22.3542			−0.759625
$867$		0			0
$868$		0			0
$869$	27.8383	−	27.8383i	0.944350	−	0.944350i
$870$	2.76721	−	6.68062i	0.0938171	−	0.226494i
$871$		−	18.2462i		−	0.618249i
$872$	34.0698	+	14.1122i	1.15375	+	0.477899i
$873$	−4.25663	−	10.2764i	−0.144065	−	0.347804i
$874$	−72.7450	+	30.1320i	−2.46064	+	1.01923i
$875$		0			0
$876$	1.31645	+	1.31645i	0.0444787	+	0.0444787i
$877$	31.4119	−	13.0112i	1.06070	−	0.439358i	0.217003	−	0.976171i	$-0.430372\pi$
$877$	31.4119	−	13.0112i	1.06070	−	0.439358i	0.843701	+	0.536813i	$0.180372\pi$
$878$	3.43835	+	8.30091i	0.116039	+	0.280142i
$879$	−6.58089	−	2.72589i	−0.221968	−	0.0919421i
$880$		−	6.73863i		−	0.227159i
$881$	−9.09018	+	21.9456i	−0.306256	+	0.739367i	0.693564	+	0.720395i	$0.256039\pi$
$881$	−9.09018	+	21.9456i	−0.306256	+	0.739367i	−0.999820	+	0.0189724i	$0.993961\pi$
$882$	−7.72929	+	7.72929i	−0.260259	+	0.260259i
$883$	−38.4233			−1.29305			−0.646523	−	0.762894i	$-0.723778\pi$
$883$	−38.4233			−1.29305			−0.646523	+	0.762894i	$0.723778\pi$
$884$		0			0
$885$	−0.630683			−0.0212002
$886$	25.2603	−	25.2603i	0.848637	−	0.848637i
$887$	8.63393	−	20.8442i	0.289899	−	0.699878i	−0.710092	−	0.704109i	$-0.751347\pi$
$887$	8.63393	−	20.8442i	0.289899	−	0.699878i	0.999991	+	0.00423064i	$0.00134666\pi$
$888$		−	7.61553i		−	0.255560i
$889$		0			0
$890$	−2.39032	−	5.77075i	−0.0801238	−	0.193436i
$891$	−2.36657	+	0.980264i	−0.0792830	+	0.0328401i
$892$	4.31897	+	4.31897i	0.144610	+	0.144610i
$893$	15.6327	+	15.6327i	0.523128	+	0.523128i
$894$	−6.12595	+	2.53745i	−0.204882	+	0.0848651i
$895$	−1.96053	−	4.73313i	−0.0655332	−	0.158211i
$896$		0			0
$897$			29.9309i			0.999363i
$898$	7.61236	−	18.3779i	0.254028	−	0.613277i
$899$	−29.8726	+	29.8726i	−0.996306	+	0.996306i
$900$	2.05398			0.0684658
$901$		0			0
$902$	−2.24621			−0.0747907
$903$		0			0
$904$	4.25663	−	10.2764i	0.141573	−	0.341788i
$905$			3.36932i			0.112000i
$906$	−11.5415	−	4.78064i	−0.383440	−	0.158826i
$907$	18.3159	+	44.2185i	0.608169	+	1.46825i	0.864989	+	0.501791i	$0.167325\pi$
$907$	18.3159	+	44.2185i	0.608169	+	1.46825i	−0.256819	+	0.966459i	$0.582675\pi$
$908$	9.33853	−	3.86815i	0.309910	−	0.128369i
$909$	13.5221	+	13.5221i	0.448499	+	0.448499i
$910$		0			0
$911$	27.0698	−	11.2127i	0.896864	−	0.371493i	0.113850	−	0.993498i	$-0.463682\pi$
$911$	27.0698	−	11.2127i	0.896864	−	0.371493i	0.783013	+	0.622005i	$0.213682\pi$
$912$	−13.7766	−	33.2597i	−0.456189	−	1.10134i
$913$	−21.5904	−	8.94305i	−0.714539	−	0.295972i
$914$		−	10.6307i		−	0.351632i
$915$	−0.188442	+	0.454939i	−0.00622970	+	0.0150398i
$916$	1.86017	−	1.86017i	0.0614619	−	0.0614619i
$917$		0			0
$918$		0			0
$919$	−4.31534			−0.142350			−0.0711750	−	0.997464i	$-0.522675\pi$
$919$	−4.31534			−0.142350			−0.0711750	+	0.997464i	$0.522675\pi$
$920$	6.35324	−	6.35324i	0.209460	−	0.209460i
$921$	0.188442	−	0.454939i	0.00620937	−	0.0149908i
$922$		−	12.8769i		−	0.424078i
$923$	43.1809	+	17.8861i	1.42132	+	0.588728i
$924$		0			0
$925$	−13.5170	+	5.59892i	−0.444436	+	0.184091i
$926$	27.5879	+	27.5879i	0.906594	+	0.906594i
$927$	−3.05141	−	3.05141i	−0.100221	−	0.100221i
$928$	18.5773	−	7.69498i	0.609831	−	0.252600i
$929$	−12.2194	−	29.5003i	−0.400906	−	0.967873i	−0.987447	−	0.157953i	$-0.949511\pi$
$929$	−12.2194	−	29.5003i	−0.400906	−	0.967873i	0.586541	−	0.809920i	$-0.300489\pi$
$930$	4.15046	+	1.71918i	0.136099	+	0.0563740i
$931$		−	53.7926i		−	1.76298i
$932$	−0.0942210	+	0.227470i	−0.00308631	+	0.00745101i
$933$		0			0
$934$	5.26137			0.172157
$935$		0			0
$936$	−11.1231			−0.363570
$937$	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
$939$		−	7.61553i		−	0.248523i
$940$	0.654406	+	0.271064i	0.0213444	+	0.00884113i
$941$	11.4805	+	27.7164i	0.374254	+	0.903528i	0.993019	+	0.117953i	$0.0376331\pi$
$941$	11.4805	+	27.7164i	0.374254	+	0.903528i	−0.618766	+	0.785576i	$0.712367\pi$
$942$	8.20118	−	3.39704i	0.267209	−	0.110682i
$943$	−2.60545	−	2.60545i	−0.0848450	−	0.0848450i
$944$	−3.72035	−	3.72035i	−0.121087	−	0.121087i
$945$		0			0
$946$	−11.7632	−	28.3988i	−0.382454	−	0.923324i
$947$	−11.0866	−	4.59220i	−0.360265	−	0.149226i	0.195207	−	0.980762i	$-0.437462\pi$
$947$	−11.0866	−	4.59220i	−0.360265	−	0.149226i	−0.555471	+	0.831536i	$0.687462\pi$
$948$		−	6.73863i		−	0.218861i
$949$	−7.41232	+	17.8949i	−0.240614	+	0.580894i
$950$	−39.7506	+	39.7506i	−1.28968	+	1.28968i
$951$	−18.0000			−0.583690
$952$		0			0
$953$	−54.3542			−1.76070			−0.880352	−	0.474321i	$-0.842694\pi$
$953$	−54.3542			−1.76070			−0.880352	+	0.474321i	$0.842694\pi$
$954$	4.68860	−	4.68860i	0.151799	−	0.151799i
$955$	2.82012	−	6.80836i	0.0912568	−	0.220313i
$956$		−	4.49242i		−	0.145295i
$957$	19.5152	+	8.08346i	0.630837	+	0.261301i
$958$	−17.5092	−	42.2710i	−0.565697	−	1.36571i
$959$		0			0
$960$	2.20837	+	2.20837i	0.0712748	+	0.0712748i
$961$	3.36144	+	3.36144i	0.108433	+	0.108433i
$962$	−20.5528	+	8.51326i	−0.662649	+	0.274478i
$963$	−2.94079	−	7.09970i	−0.0947657	−	0.228785i
$964$	8.65612	+	3.58548i	0.278795	+	0.115481i
$965$			13.6155i			0.438299i
$966$		0			0
$967$	32.9240	−	32.9240i	1.05876	−	1.05876i	0.0606021	−	0.998162i	$-0.480698\pi$
$967$	32.9240	−	32.9240i	1.05876	−	1.05876i	0.998162	−	0.0606021i	$-0.0193021\pi$
$968$	−10.8229			−0.347862
$969$		0			0
$970$	9.75379			0.313175
$971$	1.68608	−	1.68608i	0.0541088	−	0.0541088i	−0.679535	−	0.733643i	$-0.737818\pi$
$971$	1.68608	−	1.68608i	0.0541088	−	0.0541088i	0.733643	+	0.679535i	$0.237818\pi$
$972$	−0.167786	+	0.405072i	−0.00538175	+	0.0129927i
$973$		0			0
$974$	−10.6316	−	4.40376i	−0.340659	−	0.141106i
$975$	8.17768	+	19.7427i	0.261895	+	0.632272i
$976$	−3.79525	+	1.57204i	−0.121483	+	0.0503199i
$977$	−5.83095	−	5.83095i	−0.186549	−	0.186549i	0.607654	−	0.794202i	$-0.292111\pi$
$977$	−5.83095	−	5.83095i	−0.186549	−	0.186549i	−0.794202	+	0.607654i	$0.792111\pi$
$978$	−7.59336	−	7.59336i	−0.242809	−	0.242809i
$979$	16.8573	−	6.98252i	0.538762	−	0.223162i
$980$	−0.659547	−	1.59229i	−0.0210684	−	0.0508637i
$981$	13.9719	+	5.78736i	0.446089	+	0.184776i
$982$			5.26137i			0.167897i
$983$	−0.791822	+	1.91163i	−0.0252552	+	0.0609714i	−0.936004	−	0.351989i	$-0.885505\pi$
$983$	−0.791822	+	1.91163i	−0.0252552	+	0.0609714i	0.910749	+	0.412961i	$0.135505\pi$
$984$	0.968253	−	0.968253i	0.0308668	−	0.0308668i
$985$	11.1922			0.356614
$986$		0			0
$987$		0			0
$988$	−10.8677	+	10.8677i	−0.345749	+	0.345749i
$989$	19.2962	−	46.5850i	0.613582	−	1.48132i
$990$		−	2.24621i		−	0.0713893i
$991$	−6.22569	−	2.57876i	−0.197765	−	0.0819171i	0.281603	−	0.959531i	$-0.409134\pi$
$991$	−6.22569	−	2.57876i	−0.197765	−	0.0819171i	−0.479368	+	0.877614i	$0.659134\pi$
$992$	4.78064	+	11.5415i	0.151786	+	0.366443i
$993$	5.60715	−	2.32256i	0.177937	−	0.0737041i
$994$		0			0
$995$	6.35324	+	6.35324i	0.201411	+	0.201411i
$996$	−3.69552	+	1.53073i	−0.117097	+	0.0485032i
$997$	3.82683	+	9.23880i	0.121197	+	0.292596i	0.972821	−	0.231557i	$-0.0743821\pi$
$997$	3.82683	+	9.23880i	0.121197	+	0.292596i	−0.851624	+	0.524153i	$0.824382\pi$
$998$	16.4024	+	6.79408i	0.519208	+	0.215063i
$999$		−	3.12311i		−	0.0988107i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.h.j.688.1		16
17.2	even	8	inner	867.2.h.j.712.2		16
17.3	odd	16		867.2.e.f.616.3		8
17.4	even	4	inner	867.2.h.j.757.4		16
17.5	odd	16		867.2.e.f.829.1		8
17.6	odd	16		867.2.d.c.577.2		4
17.7	odd	16		867.2.a.f.1.2		2
17.8	even	8	inner	867.2.h.j.733.4		16
17.9	even	8	inner	867.2.h.j.733.3		16
17.10	odd	16		51.2.a.b.1.2	✓	2
17.11	odd	16		867.2.d.c.577.1		4
17.12	odd	16		867.2.e.f.829.2		8
17.13	even	4	inner	867.2.h.j.757.3		16
17.14	odd	16		867.2.e.f.616.4		8
17.15	even	8	inner	867.2.h.j.712.1		16
17.16	even	2	inner	867.2.h.j.688.2		16
51.41	even	16		2601.2.a.t.1.1		2
51.44	even	16		153.2.a.e.1.1		2
68.27	even	16		816.2.a.m.1.1		2
85.27	even	16		1275.2.b.d.1174.3		4
85.44	odd	16		1275.2.a.n.1.1		2
85.78	even	16		1275.2.b.d.1174.2		4
119.27	even	16		2499.2.a.o.1.2		2
136.27	even	16		3264.2.a.bg.1.2		2
136.61	odd	16		3264.2.a.bl.1.2		2
187.10	even	16		6171.2.a.p.1.1		2
204.95	odd	16		2448.2.a.v.1.2		2
221.129	odd	16		8619.2.a.q.1.1		2
255.44	even	16		3825.2.a.s.1.2		2
357.146	odd	16		7497.2.a.v.1.1		2
408.197	even	16		9792.2.a.cy.1.1		2
408.299	odd	16		9792.2.a.cz.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.a.b.1.2	✓	2	17.10	odd	16
153.2.a.e.1.1		2	51.44	even	16
816.2.a.m.1.1		2	68.27	even	16
867.2.a.f.1.2		2	17.7	odd	16
867.2.d.c.577.1		4	17.11	odd	16
867.2.d.c.577.2		4	17.6	odd	16
867.2.e.f.616.3		8	17.3	odd	16
867.2.e.f.616.4		8	17.14	odd	16
867.2.e.f.829.1		8	17.5	odd	16
867.2.e.f.829.2		8	17.12	odd	16
867.2.h.j.688.1		16	1.1	even	1	trivial
867.2.h.j.688.2		16	17.16	even	2	inner
867.2.h.j.712.1		16	17.15	even	8	inner
867.2.h.j.712.2		16	17.2	even	8	inner
867.2.h.j.733.3		16	17.9	even	8	inner
867.2.h.j.733.4		16	17.8	even	8	inner
867.2.h.j.757.3		16	17.13	even	4	inner
867.2.h.j.757.4		16	17.4	even	4	inner
1275.2.a.n.1.1		2	85.44	odd	16
1275.2.b.d.1174.2		4	85.78	even	16
1275.2.b.d.1174.3		4	85.27	even	16
2448.2.a.v.1.2		2	204.95	odd	16
2499.2.a.o.1.2		2	119.27	even	16
2601.2.a.t.1.1		2	51.41	even	16
3264.2.a.bg.1.2		2	136.27	even	16
3264.2.a.bl.1.2		2	136.61	odd	16
3825.2.a.s.1.2		2	255.44	even	16
6171.2.a.p.1.1		2	187.10	even	16
7497.2.a.v.1.1		2	357.146	odd	16
8619.2.a.q.1.1		2	221.129	odd	16
9792.2.a.cy.1.1		2	408.197	even	16
9792.2.a.cz.1.1		2	408.299	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)

\(f(q)\)	\(=\)	\(q+(-1.10418 + 1.10418i) q^{2} +(-0.382683 + 0.923880i) q^{3} -0.438447i q^{4} +(-0.518807 - 0.214897i) q^{5} +(-0.597580 - 1.44269i) q^{6} +(-1.72424 - 1.72424i) q^{8} +(-0.707107 - 0.707107i) q^{9} +O(q^{10})\)	\(q+(-1.10418 + 1.10418i) q^{2} +(-0.382683 + 0.923880i) q^{3} -0.438447i q^{4} +(-0.518807 - 0.214897i) q^{5} +(-0.597580 - 1.44269i) q^{6} +(-1.72424 - 1.72424i) q^{8} +(-0.707107 - 0.707107i) q^{9} +(0.810145 - 0.335573i) q^{10} +(0.980264 + 2.36657i) q^{11} +(0.405072 + 0.167786i) q^{12} +4.56155i q^{13} +(0.397078 - 0.397078i) q^{15} +4.68466 q^{16} +1.56155 q^{18} +(-5.43387 + 5.43387i) q^{19} +(-0.0942210 + 0.227470i) q^{20} +(-3.69552 - 1.53073i) q^{22} +(-2.51100 - 6.06208i) q^{23} +(2.25283 - 0.933153i) q^{24} +(-3.31255 - 3.31255i) q^{25} +(-5.03680 - 5.03680i) q^{26} +(0.923880 - 0.382683i) q^{27} +(-7.61851 - 3.15569i) q^{29} +0.876894i q^{30} +(1.96053 - 4.73313i) q^{31} +(-1.72424 + 1.72424i) q^{32} -2.56155 q^{33} +(-0.310029 + 0.310029i) q^{36} +(1.19516 - 2.88537i) q^{37} -12.0000i q^{38} +(-4.21433 - 1.74563i) q^{39} +(0.524015 + 1.26508i) q^{40} +(0.518807 - 0.214897i) q^{41} +(5.43387 + 5.43387i) q^{43} +(1.03761 - 0.429794i) q^{44} +(0.214897 + 0.518807i) q^{45} +(9.46626 + 3.92106i) q^{46} -2.87689i q^{47} +(-1.79274 + 4.32806i) q^{48} +(-4.94975 + 4.94975i) q^{49} +7.31534 q^{50} +2.00000 q^{52} +(3.00252 - 3.00252i) q^{53} +(-0.597580 + 1.44269i) q^{54} -1.43845i q^{55} +(-2.94079 - 7.09970i) q^{57} +(11.8967 - 4.92777i) q^{58} +(-0.794156 - 0.794156i) q^{59} +(-0.174098 - 0.174098i) q^{60} +(-0.810145 + 0.335573i) q^{61} +(3.06147 + 7.39104i) q^{62} +5.56155i q^{64} +(0.980264 - 2.36657i) q^{65} +(2.82843 - 2.82843i) q^{66} -4.00000 q^{67} +6.56155 q^{69} +(3.92106 - 9.46626i) q^{71} +2.43845i q^{72} +(3.92299 + 1.62495i) q^{73} +(1.86631 + 4.50566i) q^{74} +(4.32806 - 1.79274i) q^{75} +(2.38247 + 2.38247i) q^{76} +(6.58089 - 2.72589i) q^{78} +(-5.88158 - 14.1994i) q^{79} +(-2.43043 - 1.00672i) q^{80} +1.00000i q^{81} +(-0.335573 + 0.810145i) q^{82} +(-6.45101 + 6.45101i) q^{83} -12.0000 q^{86} +(5.83095 - 5.83095i) q^{87} +(2.39032 - 5.77075i) q^{88} -7.12311i q^{89} +(-0.810145 - 0.335573i) q^{90} +(-2.65790 + 1.10094i) q^{92} +(3.62258 + 3.62258i) q^{93} +(3.17662 + 3.17662i) q^{94} +(3.98686 - 1.65141i) q^{95} +(-0.933153 - 2.25283i) q^{96} +(10.2764 + 4.25663i) q^{97} -10.9309i q^{98} +(0.980264 - 2.36657i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q+O(q^{10}) \) 16 * 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

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