LMFDB - Embedded newform 867.2.h.j.712.2

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			712.2
Root			$1.44269 + 0.597580i$ of defining polynomial
Character	$\chi$	$=$	867.712
Dual form			867.2.h.j.688.2

$q$-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 $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

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	0.199185	−	0.979962i	$-0.436170\pi$
$2$	−1.10418	−	1.10418i	−0.780776	−	0.780776i	−0.979962	+	0.199185i	$0.936170\pi$
$3$	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	$-0.584925\pi$
$5$	0.518807	−	0.214897i	0.232018	−	0.0961048i	0.495663	+	0.868515i	$0.334925\pi$
$6$	0.597580	−	1.44269i	0.243961	−	0.588974i
$7$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$7$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$8$	−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	0.704432	+	0.709771i	$0.251202\pi$
$11$	−0.980264	+	2.36657i	−0.295561	+	0.713547i	−0.999993	+	0.00377529i	$0.998798\pi$
$12$	−0.405072	+	0.167786i	−0.116934	+	0.0484358i
$13$		−	4.56155i		−	1.26515i	−0.774500	−	0.632574i	$-0.781999\pi$
$13$		−	4.56155i		−	1.26515i	0.774500	−	0.632574i	$-0.218001\pi$
$14$		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	−0.957205	−	0.289411i	$-0.906540\pi$
$19$	−5.43387	−	5.43387i	−1.24662	−	1.24662i	−0.289411	−	0.957205i	$-0.593460\pi$
$20$	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	−0.412087	−	0.911145i	$-0.635200\pi$
$23$	2.51100	−	6.06208i	0.523579	−	1.26403i	0.935666	−	0.352887i	$-0.114800\pi$
$24$	−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	$-0.347422\pi$
$29$	7.61851	−	3.15569i	1.41472	−	0.585997i	0.953528	+	0.301303i	$0.0974217\pi$
$30$		−	0.876894i		−	0.160098i
$31$	−1.96053	−	4.73313i	−0.352121	−	0.850096i	−0.996358	−	0.0852696i	$-0.972825\pi$
$31$	−1.96053	−	4.73313i	−0.352121	−	0.850096i	0.644237	−	0.764826i	$-0.277175\pi$
$32$	−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	$-0.207641\pi$
$37$	−1.19516	−	2.88537i	−0.196483	−	0.474352i	−0.991159	+	0.132682i	$0.957641\pi$
$38$			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	$-0.388962\pi$
$41$	−0.518807	−	0.214897i	−0.0810241	−	0.0335613i	−0.422827	+	0.906210i	$0.638962\pi$
$42$		0			0
$43$	5.43387	−	5.43387i	0.828658	−	0.828658i	−0.158673	−	0.987331i	$-0.550722\pi$
$43$	5.43387	−	5.43387i	0.828658	−	0.828658i	0.987331	+	0.158673i	$0.0507216\pi$
$44$	−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	$0.0672875\pi$
$47$			2.87689i			0.419638i	−0.977740	+	0.209819i	$0.932712\pi$
$48$	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	0.882584	−	0.470155i	$-0.155802\pi$
$53$	3.00252	+	3.00252i	0.412428	+	0.412428i	−0.470155	+	0.882584i	$0.655802\pi$
$54$	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	−0.756910	−	0.653519i	$-0.773292\pi$
$59$	−0.794156	+	0.794156i	−0.103390	+	0.103390i	0.653519	+	0.756910i	$0.273292\pi$
$60$	−0.174098	+	0.174098i	−0.0224759	+	0.0224759i
$61$	0.810145	+	0.335573i	0.103728	+	0.0429657i	0.433944	−	0.900940i	$-0.357122\pi$
$61$	0.810145	+	0.335573i	0.103728	+	0.0429657i	−0.330216	+	0.943905i	$0.607122\pi$
$62$	−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	−0.966173	−	0.257893i	$-0.916972\pi$
$71$	−3.92106	−	9.46626i	−0.465344	−	1.12344i	0.500830	−	0.865546i	$-0.333028\pi$
$72$		−	2.43845i		−	0.287374i
$73$	−3.92299	+	1.62495i	−0.459151	+	0.190187i	−0.600256	−	0.799808i	$-0.704935\pi$
$73$	−3.92299	+	1.62495i	−0.459151	+	0.190187i	0.141105	+	0.989995i	$0.454935\pi$
$74$	−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	−0.133362	−	0.991067i	$-0.542577\pi$
$79$	5.88158	−	14.1994i	0.661730	−	1.59756i	0.795091	−	0.606490i	$-0.207423\pi$
$80$	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	0.258043	−	0.966133i	$-0.416922\pi$
$83$	−6.45101	−	6.45101i	−0.708090	−	0.708090i	−0.966133	+	0.258043i	$0.916922\pi$
$84$		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	$0.123224\pi$
$89$			7.12311i			0.755048i	−0.926000	+	0.377524i	$0.876776\pi$
$90$	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	$-0.816004\pi$
$97$	−10.2764	+	4.25663i	−1.04341	+	0.432195i	−0.205876	+	0.978578i	$0.566004\pi$
$98$			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	$-0.746140\pi$
$107$	−7.09970	+	2.94079i	−0.686354	+	0.284297i	0.0121264	+	0.999926i	$0.496140\pi$
$108$	0.167786	−	0.405072i	0.0161453	−	0.0389781i
$109$	13.9719	+	5.78736i	1.33827	+	0.554329i	0.933002	−	0.359870i	$-0.117179\pi$
$109$	13.9719	+	5.78736i	1.33827	+	0.554329i	0.405266	+	0.914199i	$0.367179\pi$
$110$	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	$-0.943831\pi$
$113$	−1.74563	+	4.21433i	−0.164215	+	0.396450i	0.820256	+	0.571996i	$0.193831\pi$
$114$	−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	−0.731994	−	0.681311i	$-0.761410\pi$
$127$	−0.571175	+	0.571175i	−0.0506836	+	0.0506836i	0.681311	+	0.731994i	$0.261410\pi$
$128$	−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	$-0.323997\pi$
$131$	17.1486	−	7.10320i	1.49828	−	0.620609i	0.973101	+	0.230380i	$0.0739969\pi$
$132$		−	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	0.999990	+	0.00457466i	$0.00145616\pi$
$139$	3.49126	+	8.42865i	0.296125	+	0.714909i	−0.703865	+	0.710334i	$0.748544\pi$
$140$		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	$0.0556472\pi$
$149$			4.24621i			0.347863i	−0.984758	+	0.173932i	$0.944353\pi$
$150$	2.79946	+	6.75849i	0.228575	+	0.551829i
$151$	5.65685	+	5.65685i	0.460348	+	0.460348i	0.898770	−	0.438421i	$-0.144462\pi$
$151$	5.65685	+	5.65685i	0.460348	+	0.460348i	−0.438421	+	0.898770i	$0.644462\pi$
$152$	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	$-0.927160\pi$
$157$		−	5.68466i		−	0.453685i	0.973931	−	0.226843i	$-0.0728403\pi$
$158$	−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	$-0.461799\pi$
$163$	−6.35342	−	2.63167i	−0.497638	−	0.206129i	−0.617363	+	0.786679i	$0.711799\pi$
$164$	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	$-0.134950\pi$
$167$	−0.309118	−	0.746277i	−0.0239203	−	0.0577486i	−0.935388	+	0.353622i	$0.884950\pi$
$168$		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	0.919546	+	0.392983i	$0.128557\pi$
$173$	7.19742	+	17.3761i	0.547210	+	1.32108i	−0.372336	+	0.928098i	$0.621443\pi$
$174$		−	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	−0.423653	−	0.905824i	$-0.639253\pi$
$179$	6.45101	−	6.45101i	0.482171	−	0.482171i	0.905824	+	0.423653i	$0.139253\pi$
$180$	−0.227470	−	0.0942210i	−0.0169546	−	0.00702282i
$181$	2.29610	−	5.54328i	0.170668	−	0.412029i	−0.815283	−	0.579062i	$-0.803419\pi$
$181$	2.29610	−	5.54328i	0.170668	−	0.412029i	0.985951	+	0.167034i	$0.0534188\pi$
$182$		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	$-0.842529\pi$
$191$		−	13.1231i		−	0.949555i	0.880106	−	0.474777i	$-0.157471\pi$
$192$	5.13820	−	2.12831i	0.370818	−	0.153598i
$193$	9.27862	−	22.4006i	0.667890	−	1.61243i	−0.117244	−	0.993103i	$-0.537406\pi$
$193$	9.27862	−	22.4006i	0.667890	−	1.61243i	0.785134	−	0.619326i	$-0.212594\pi$
$194$	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	$-0.123691\pi$
$197$	18.4137	+	7.62721i	1.31192	+	0.543416i	0.386478	+	0.922298i	$0.373691\pi$
$198$	−1.53073	+	3.69552i	−0.108785	+	0.262629i
$199$	14.7821	−	6.12293i	1.04787	−	0.434043i	0.208741	−	0.977971i	$-0.433063\pi$
$199$	14.7821	−	6.12293i	1.04787	−	0.434043i	0.839132	+	0.543928i	$0.183063\pi$
$200$		−	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	$-0.247009\pi$
$211$	10.5039	+	4.35085i	0.723117	+	0.299525i	0.00939678	+	0.999956i	$0.497009\pi$
$212$	−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	0.295650	−	0.955296i	$-0.404464\pi$
$223$	−9.85061	−	9.85061i	−0.659646	−	0.659646i	−0.955296	+	0.295650i	$0.904464\pi$
$224$		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	0.302145	+	0.953262i	$0.402297\pi$
$227$	−8.82237	+	21.2991i	−0.585562	+	1.41367i	−0.887707	+	0.460409i	$0.847703\pi$
$228$	3.11284	+	1.28938i	0.206153	+	0.0853914i
$229$	4.24264	−	4.24264i	0.280362	−	0.280362i	−0.552892	−	0.833253i	$-0.686476\pi$
$229$	4.24264	−	4.24264i	0.280362	−	0.280362i	0.833253	+	0.552892i	$0.186476\pi$
$230$	−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	$-0.619145\pi$
$233$	0.518807	−	0.214897i	0.0339882	−	0.0140784i	0.399613	+	0.916684i	$0.369145\pi$
$234$		−	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	0.933627	+	0.358245i	$0.116625\pi$
$241$	8.17768	+	19.7427i	0.526771	+	1.27174i	−0.406857	+	0.913492i	$0.633375\pi$
$242$		−	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	$0.281232\pi$
$251$			24.4924i			1.54595i	−0.634438	+	0.772974i	$0.718768\pi$
$252$		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	0.469611	−	0.882874i	$-0.344394\pi$
$257$	−6.62511	−	6.62511i	−0.413263	−	0.413263i	−0.882874	+	0.469611i	$0.844394\pi$
$258$	−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	−0.380206	−	0.924902i	$-0.624147\pi$
$263$	8.83348	−	8.83348i	0.544696	−	0.544696i	0.924902	+	0.380206i	$0.124147\pi$
$264$	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	0.959724	+	0.280945i	$0.0906480\pi$
$269$	7.86857	+	18.9964i	0.479755	+	1.15823i	−0.479969	+	0.877286i	$0.659352\pi$
$270$	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	$-0.682691\pi$
$277$	−5.54328	+	2.29610i	−0.333063	+	0.137959i	0.209884	+	0.977726i	$0.432691\pi$
$278$	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	−0.177467	−	0.984127i	$-0.556790\pi$
$281$	13.5221	−	13.5221i	0.806660	−	0.806660i	0.984127	+	0.177467i	$0.0567904\pi$
$282$	4.15046	+	1.71918i	0.247156	+	0.102375i
$283$	−1.28938	+	3.11284i	−0.0766458	+	0.185039i	−0.957558	−	0.288240i	$-0.906930\pi$
$283$	−1.28938	+	3.11284i	−0.0766458	+	0.185039i	0.880912	+	0.473279i	$0.156930\pi$
$284$	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	$-0.933282\pi$
$293$		−	7.12311i		−	0.416136i	0.978114	−	0.208068i	$-0.0667176\pi$
$294$	−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	$-0.625000\pi$
$311$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$312$	−4.25663	+	10.2764i	−0.240984	+	0.581787i
$313$	7.03583	+	2.91434i	0.397689	+	0.164728i	0.572559	−	0.819863i	$-0.305951\pi$
$313$	7.03583	+	2.91434i	0.397689	+	0.164728i	−0.174871	+	0.984591i	$0.555951\pi$
$314$	−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	0.603710	+	0.797204i	$0.293688\pi$
$317$	−6.88830	+	16.6298i	−0.386886	+	0.934024i	−0.990596	+	0.136821i	$0.956312\pi$
$318$	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	−0.815143	−	0.579260i	$-0.803342\pi$
$331$	−4.29152	+	4.29152i	−0.235883	+	0.235883i	0.579260	+	0.815143i	$0.303342\pi$
$332$	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	0.759421	+	0.650600i	$0.225482\pi$
$337$	12.5285	+	30.2466i	0.682473	+	1.64763i	−0.0769482	+	0.997035i	$0.524518\pi$
$338$	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	$-0.603348\pi$
$347$	−22.6280	−	9.37284i	−1.21474	−	0.503161i	−0.895733	+	0.444593i	$0.853348\pi$
$348$	−2.55656	+	2.55656i	−0.137046	+	0.137046i
$349$	−5.25978	+	5.25978i	−0.281549	+	0.281549i	−0.833727	−	0.552177i	$-0.813797\pi$
$349$	−5.25978	+	5.25978i	−0.281549	+	0.281549i	0.552177	+	0.833727i	$0.313797\pi$
$350$		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	$-0.795734\pi$
$353$		−	22.4924i		−	1.19715i	0.801066	−	0.598575i	$-0.204266\pi$
$354$	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	0.747777	−	0.663950i	$-0.231121\pi$
$359$	1.58831	+	1.58831i	0.0838279	+	0.0838279i	−0.663950	+	0.747777i	$0.731121\pi$
$360$	−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	$-0.532994\pi$
$367$	−16.8573	−	6.98252i	−0.879944	−	0.364485i	−0.776475	+	0.630148i	$0.782994\pi$
$368$	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	$-0.525274\pi$
$379$	11.0866	−	4.59220i	0.569478	−	0.235886i	0.648794	+	0.760964i	$0.275274\pi$
$380$	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	−0.497343	−	0.867554i	$-0.665691\pi$
$383$	7.24517	−	7.24517i	0.370211	−	0.370211i	0.867554	+	0.497343i	$0.165691\pi$
$384$	−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	0.196685	−	0.980467i	$-0.436982\pi$
$389$	−15.4586	−	15.4586i	−0.783781	−	0.783781i	−0.980467	+	0.196685i	$0.936982\pi$
$390$	−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	$-0.918020\pi$
$397$	−2.05475	+	4.96060i	−0.103125	+	0.248965i	0.863892	+	0.503677i	$0.168020\pi$
$398$	−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	$-0.424291\pi$
$401$	−5.70688	−	2.36387i	−0.284988	−	0.118046i	−0.520598	+	0.853802i	$0.674291\pi$
$402$	−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	−0.258302	−	0.966064i	$-0.583163\pi$
$419$	12.4343	−	30.0191i	0.607456	−	1.46653i	0.865757	−	0.500464i	$-0.166837\pi$
$420$		0			0
$421$		−	28.5616i		−	1.39200i	−0.718039	−	0.696002i	$-0.754960\pi$
$421$		−	28.5616i		−	1.39200i	0.718039	−	0.696002i	$-0.245040\pi$
$422$	−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	−0.532708	−	0.846299i	$-0.678826\pi$
$431$	9.18440	−	22.1731i	0.442397	−	1.06804i	0.975105	−	0.221742i	$-0.0711743\pi$
$432$	−4.32806	−	1.79274i	−0.208234	−	0.0862533i
$433$	10.1225	−	10.1225i	0.486455	−	0.486455i	−0.420731	−	0.907186i	$-0.638226\pi$
$433$	10.1225	−	10.1225i	0.486455	−	0.486455i	0.907186	+	0.420731i	$0.138226\pi$
$434$		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	$-0.168845\pi$
$439$	−2.20188	−	5.31581i	−0.105090	−	0.253710i	−0.967674	+	0.252204i	$0.918845\pi$
$440$	−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	$-0.277818\pi$
$449$	11.7690	+	4.87486i	0.555412	+	0.230059i	−0.0872802	+	0.996184i	$0.527818\pi$
$450$	−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	0.585495	−	0.810676i	$-0.300900\pi$
$457$	−4.81382	−	4.81382i	−0.225181	−	0.225181i	−0.810676	+	0.585495i	$0.800900\pi$
$458$	−9.36932			−0.437799
$459$		0			0
$460$	1.61553			0.0753244
$461$	−5.83095	−	5.83095i	−0.271575	−	0.271575i	0.558159	−	0.829734i	$-0.311508\pi$
$461$	−5.83095	−	5.83095i	−0.271575	−	0.271575i	−0.829734	+	0.558159i	$0.811508\pi$
$462$		0			0
$463$			24.9848i			1.16114i	0.814209	+	0.580572i	$0.197171\pi$
$463$			24.9848i			1.16114i	−0.814209	+	0.580572i	$0.802829\pi$
$464$	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	−0.760079	−	0.649831i	$-0.774840\pi$
$467$	−2.38247	+	2.38247i	−0.110247	+	0.110247i	0.649831	+	0.760079i	$0.274840\pi$
$468$	−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	0.942529	+	0.334123i	$0.108440\pi$
$479$	11.2127	+	27.0698i	0.512321	+	1.23685i	−0.430208	+	0.902730i	$0.641560\pi$
$480$		−	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	$-0.928398\pi$
$487$	−2.82012	+	6.80836i	−0.127792	+	0.308516i	0.847015	+	0.531570i	$0.178398\pi$
$488$	−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	0.758820	−	0.651301i	$-0.225776\pi$
$491$	2.38247	+	2.38247i	0.107519	+	0.107519i	−0.651301	+	0.758820i	$0.725776\pi$
$492$	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	$-0.793096\pi$
$499$	4.35085	−	10.5039i	0.194771	−	0.470218i	0.990849	+	0.134976i	$0.0430956\pi$
$500$	−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	$-0.566943\pi$
$503$	−23.5021	−	9.73487i	−1.04791	−	0.434057i	−0.839144	+	0.543910i	$0.816943\pi$
$504$		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	0.406337	+	0.913723i	$0.366806\pi$
$521$	−12.0310	+	29.0453i	−0.527086	+	1.27250i	−0.933424	+	0.358776i	$0.883194\pi$
$522$	11.8967	−	4.92777i	0.520704	−	0.215683i
$523$			20.0000i			0.874539i	0.899331	+	0.437269i	$0.144054\pi$
$523$			20.0000i			0.874539i	−0.899331	+	0.437269i	$0.855946\pi$
$524$	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	−0.797972	−	0.602694i	$-0.794094\pi$
$541$	−15.3486	−	37.0549i	−0.659890	−	1.59312i	0.138082	−	0.990421i	$-0.455906\pi$
$542$	−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	−0.969147	−	0.246483i	$-0.920725\pi$
$547$	−10.7151	−	25.8686i	−0.458146	−	1.10606i	0.511001	−	0.859580i	$-0.329275\pi$
$548$		−	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	$0.0439216\pi$
$557$			6.49242i			0.275093i	−0.990495	+	0.137546i	$0.956078\pi$
$558$	−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	0.278641	−	0.960395i	$-0.410116\pi$
$563$	−16.1764	−	16.1764i	−0.681754	−	0.681754i	−0.960395	+	0.278641i	$0.910116\pi$
$564$	−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	−0.490004	−	0.871720i	$-0.663005\pi$
$569$	9.10534	−	9.10534i	0.381716	−	0.381716i	0.871720	+	0.490004i	$0.163005\pi$
$570$	−4.76493	+	4.76493i	−0.199581	+	0.199581i
$571$	17.3122	+	7.17096i	0.724495	+	0.300096i	0.714288	−	0.699852i	$-0.246751\pi$
$571$	17.3122	+	7.17096i	0.724495	+	0.300096i	0.0102072	+	0.999948i	$0.496751\pi$
$572$	−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	−0.0828568	+	0.996561i	$0.526404\pi$
$587$	−26.1522	+	26.1522i	−1.07942	+	1.07942i	−0.996561	+	0.0828568i	$0.973596\pi$
$588$	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	0.937906	+	0.346888i	$0.112762\pi$
$593$	31.2868	+	31.2868i	1.28479	+	1.28479i	0.346888	+	0.937906i	$0.387238\pi$
$594$	−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	$-0.676492\pi$
$599$		−	41.6155i		−	1.70036i	0.526489	−	0.850182i	$-0.323508\pi$
$600$	10.5537	−	4.37150i	0.430855	−	0.178466i
$601$	−13.3881	+	32.3218i	−0.546113	+	1.31843i	0.374236	+	0.927334i	$0.377905\pi$
$601$	−13.3881	+	32.3218i	−0.546113	+	1.31843i	−0.920348	+	0.391099i	$0.872095\pi$
$602$		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	$-0.524031\pi$
$607$	14.1994	−	5.88158i	0.576336	−	0.238726i	0.651760	+	0.758425i	$0.274031\pi$
$608$			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	$-0.436315\pi$
$617$	25.6412	−	10.6209i	1.03227	−	0.427582i	0.833533	+	0.552470i	$0.186315\pi$
$618$	2.57876	−	6.22569i	0.103733	−	0.250434i
$619$	17.8949	+	7.41232i	0.719257	+	0.297926i	0.712129	−	0.702048i	$-0.247731\pi$
$619$	17.8949	+	7.41232i	0.719257	+	0.297926i	0.00712818	+	0.999975i	$0.497731\pi$
$620$	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	0.523258	−	0.852175i	$-0.324717\pi$
$631$	−8.26230	−	8.26230i	−0.328917	−	0.328917i	−0.852175	+	0.523258i	$0.824717\pi$
$632$	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	$-0.625435\pi$
$641$	−0.0638681	+	0.0264550i	−0.00252264	+	0.00104491i	0.381422	+	0.924401i	$0.375435\pi$
$642$			12.0000i			0.473602i
$643$	−11.5747	−	27.9439i	−0.456463	−	1.10200i	−0.969820	−	0.243823i	$-0.921598\pi$
$643$	−11.5747	−	27.9439i	−0.456463	−	1.10200i	0.513357	−	0.858175i	$-0.328402\pi$
$644$		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	$-0.349630\pi$
$653$	3.75939	+	1.55719i	0.147116	+	0.0609375i	−0.307910	+	0.951415i	$0.599630\pi$
$654$	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	$-0.617874\pi$
$659$		−	47.8617i		−	1.86443i	0.361907	−	0.932214i	$-0.382126\pi$
$660$	−0.241352	−	0.582675i	−0.00939461	−	0.0226806i
$661$	18.1618	+	18.1618i	0.706412	+	0.706412i	0.965779	−	0.259367i	$-0.0835139\pi$
$661$	18.1618	+	18.1618i	0.706412	+	0.706412i	−0.259367	+	0.965779i	$0.583514\pi$
$662$	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	0.999089	+	0.0426728i	$0.0135873\pi$
$673$	45.0286	+	18.6515i	1.73573	+	0.718961i	0.736637	+	0.676288i	$0.236413\pi$
$674$	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	$-0.209703\pi$
$677$	−5.23689	−	12.6430i	−0.201270	−	0.485909i	−0.991997	+	0.126260i	$0.959703\pi$
$678$	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	$-0.0918204\pi$
$683$	2.08120	+	5.02447i	0.0796350	+	0.192256i	−0.879047	+	0.476734i	$0.841820\pi$
$684$			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	−0.387399	−	0.921912i	$-0.626626\pi$
$691$	14.1535	−	34.1695i	0.538424	−	1.29987i	0.925823	−	0.377958i	$-0.123374\pi$
$692$	−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	$-0.943381\pi$
$701$		−	9.36932i		−	0.353874i	0.984222	−	0.176937i	$-0.0566189\pi$
$702$	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	$-0.596639\pi$
$709$	4.37793	−	1.81340i	0.164416	−	0.0681035i	0.463374	+	0.886163i	$0.346639\pi$
$710$			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	$-0.677516\pi$
$719$	−8.13731	+	3.37059i	−0.303471	+	0.125702i	0.225752	+	0.974185i	$0.427516\pi$
$720$	−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	$0.0473968\pi$
$727$			8.00000i			0.296704i	−0.988935	+	0.148352i	$0.952603\pi$
$728$		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	0.972137	−	0.234414i	$-0.0753171\pi$
$733$	19.9731	+	19.9731i	0.737723	+	0.737723i	−0.234414	+	0.972137i	$0.575317\pi$
$734$	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	−0.806934	−	0.590641i	$-0.798875\pi$
$739$	−5.87983	+	5.87983i	−0.216293	+	0.216293i	0.590641	+	0.806934i	$0.298875\pi$
$740$	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	$-0.651260\pi$
$743$	−4.15046	+	1.71918i	−0.152266	+	0.0630704i	0.305249	+	0.952273i	$0.401260\pi$
$744$			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	$-0.121337\pi$
$751$	0.241352	+	0.582675i	0.00880706	+	0.0212621i	−0.919415	+	0.393289i	$0.871337\pi$
$752$			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	−0.382757	−	0.923849i	$-0.625025\pi$
$757$	14.8874	−	14.8874i	0.541092	−	0.541092i	0.923849	+	0.382757i	$0.125025\pi$
$758$	−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	$0.198694\pi$
$761$			32.2462i			1.16892i	−0.811421	+	0.584462i	$0.801306\pi$
$762$	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	$-0.821164\pi$
$769$		−	29.5464i		−	1.06547i	0.846282	−	0.532735i	$-0.178836\pi$
$770$		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	−0.989968	−	0.141291i	$-0.954875\pi$
$773$	−23.5957	+	23.5957i	−0.848677	+	0.848677i	0.141291	+	0.989968i	$0.454875\pi$
$774$	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	$-0.660510\pi$
$787$	−5.77075	+	2.39032i	−0.205705	+	0.0852058i	0.277452	+	0.960739i	$0.410510\pi$
$788$	−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	0.981799	−	0.189924i	$-0.0608243\pi$
$797$	22.3556	+	22.3556i	0.791874	+	0.791874i	−0.189924	+	0.981799i	$0.560824\pi$
$798$		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	0.999722	+	0.0235603i	$0.00750017\pi$
$809$	49.0155	+	20.3029i	1.72329	+	0.713811i	0.723570	+	0.690251i	$0.242500\pi$
$810$	−0.335573	+	0.810145i	−0.0117908	+	0.0284656i
$811$	−19.0603	+	7.89502i	−0.669296	+	0.277232i	−0.691345	−	0.722525i	$-0.742981\pi$
$811$	−19.0603	+	7.89502i	−0.669296	+	0.277232i	0.0220481	+	0.999757i	$0.492981\pi$
$812$		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	$-0.531677\pi$
$821$	15.3009	−	6.33783i	0.534004	−	0.221192i	0.633356	+	0.773861i	$0.281677\pi$
$822$	−9.70842	+	23.4382i	−0.338620	+	0.817501i
$823$	−33.7146	−	13.9650i	−1.17522	−	0.486791i	−0.292303	−	0.956326i	$-0.594422\pi$
$823$	−33.7146	−	13.9650i	−1.17522	−	0.486791i	−0.882914	+	0.469535i	$0.844422\pi$
$824$	−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	$-0.955685\pi$
$827$	−5.51955	+	13.3254i	−0.191934	+	0.463369i	0.798391	+	0.602140i	$0.205685\pi$
$828$	−2.65790	+	1.10094i	−0.0923685	+	0.0382603i
$829$		−	50.4924i		−	1.75367i	−0.480787	−	0.876837i	$-0.659649\pi$
$829$		−	50.4924i		−	1.75367i	0.480787	−	0.876837i	$-0.340351\pi$
$830$	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	$-0.936112\pi$
$839$	−4.23017	+	10.2125i	−0.146042	+	0.352576i	0.833884	+	0.551940i	$0.186112\pi$
$840$		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	$-0.240532\pi$
$853$	−7.93633	−	19.1600i	−0.271735	−	0.656026i	−0.999558	+	0.0297393i	$0.990532\pi$
$854$		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	$-0.342323\pi$
$857$	5.54328	+	2.29610i	0.189355	+	0.0784333i	−0.285991	+	0.958232i	$0.592323\pi$
$858$	12.9020	−	12.9020i	0.440468	−	0.440468i
$859$	−8.48528	+	8.48528i	−0.289514	+	0.289514i	−0.836888	−	0.547374i	$-0.815628\pi$
$859$	−8.48528	+	8.48528i	−0.289514	+	0.289514i	0.547374	+	0.836888i	$0.315628\pi$
$860$	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	$0.147406\pi$
$863$			26.2462i			0.893431i	−0.894676	+	0.446716i	$0.852594\pi$
$864$	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	$-0.569628\pi$
$877$	−31.4119	−	13.0112i	−1.06070	−	0.439358i	−0.843701	+	0.536813i	$0.819628\pi$
$878$	−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	0.999820	+	0.0189724i	$0.00603946\pi$
$881$	9.09018	+	21.9456i	0.306256	+	0.739367i	−0.693564	+	0.720395i	$0.743961\pi$
$882$	−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	$-0.248653\pi$
$887$	−8.63393	−	20.8442i	−0.289899	−	0.699878i	−0.999991	+	0.00423064i	$0.998653\pi$
$888$			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	0.256819	+	0.966459i	$0.417325\pi$
$907$	−18.3159	+	44.2185i	−0.608169	+	1.46825i	−0.864989	+	0.501791i	$0.832675\pi$
$908$	−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	$-0.536318\pi$
$911$	−27.0698	−	11.2127i	−0.896864	−	0.371493i	−0.783013	+	0.622005i	$0.786318\pi$
$912$	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	−0.586541	−	0.809920i	$-0.699511\pi$
$929$	12.2194	−	29.5003i	0.400906	−	0.967873i	0.987447	−	0.157953i	$-0.0504894\pi$
$930$	−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	0.913975	−	0.405771i	$-0.132997\pi$
$937$	15.5563	+	15.5563i	0.508204	+	0.508204i	−0.405771	+	0.913975i	$0.632997\pi$
$938$		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	0.618766	+	0.785576i	$0.287633\pi$
$941$	−11.4805	+	27.7164i	−0.374254	+	0.903528i	−0.993019	+	0.117953i	$0.962367\pi$
$942$	−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	$-0.562538\pi$
$947$	11.0866	−	4.59220i	0.360265	−	0.149226i	0.555471	+	0.831536i	$0.312538\pi$
$948$			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	0.998162	+	0.0606021i	$0.0193021\pi$
$967$	32.9240	+	32.9240i	1.05876	+	1.05876i	0.0606021	+	0.998162i	$0.480698\pi$
$968$	−10.8229			−0.347862
$969$		0			0
$970$	9.75379			0.313175
$971$	1.68608	+	1.68608i	0.0541088	+	0.0541088i	0.733643	−	0.679535i	$-0.237818\pi$
$971$	1.68608	+	1.68608i	0.0541088	+	0.0541088i	−0.679535	+	0.733643i	$0.737818\pi$
$972$	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	−0.794202	−	0.607654i	$-0.792111\pi$
$977$	−5.83095	+	5.83095i	−0.186549	+	0.186549i	0.607654	+	0.794202i	$0.292111\pi$
$978$	−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	$-0.114495\pi$
$983$	0.791822	+	1.91163i	0.0252552	+	0.0609714i	−0.910749	+	0.412961i	$0.864495\pi$
$984$	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	$-0.590866\pi$
$991$	6.22569	−	2.57876i	0.197765	−	0.0819171i	0.479368	+	0.877614i	$0.340866\pi$
$992$	−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	$-0.925618\pi$
$997$	−3.82683	+	9.23880i	−0.121197	+	0.292596i	0.851624	+	0.524153i	$0.175618\pi$
$998$	−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.712.2		16
17.2	even	8	inner	867.2.h.j.757.4		16
17.3	odd	16		867.2.d.c.577.2		4
17.4	even	4	inner	867.2.h.j.733.4		16
17.5	odd	16		51.2.a.b.1.2	✓	2
17.6	odd	16		867.2.e.f.829.2		8
17.7	odd	16		867.2.e.f.616.4		8
17.8	even	8	inner	867.2.h.j.688.2		16
17.9	even	8	inner	867.2.h.j.688.1		16
17.10	odd	16		867.2.e.f.616.3		8
17.11	odd	16		867.2.e.f.829.1		8
17.12	odd	16		867.2.a.f.1.2		2
17.13	even	4	inner	867.2.h.j.733.3		16
17.14	odd	16		867.2.d.c.577.1		4
17.15	even	8	inner	867.2.h.j.757.3		16
17.16	even	2	inner	867.2.h.j.712.1		16
51.5	even	16		153.2.a.e.1.1		2
51.29	even	16		2601.2.a.t.1.1		2
68.39	even	16		816.2.a.m.1.1		2
85.22	even	16		1275.2.b.d.1174.3		4
85.39	odd	16		1275.2.a.n.1.1		2
85.73	even	16		1275.2.b.d.1174.2		4
119.90	even	16		2499.2.a.o.1.2		2
136.5	odd	16		3264.2.a.bl.1.2		2
136.107	even	16		3264.2.a.bg.1.2		2
187.175	even	16		6171.2.a.p.1.1		2
204.107	odd	16		2448.2.a.v.1.2		2
221.90	odd	16		8619.2.a.q.1.1		2
255.209	even	16		3825.2.a.s.1.2		2
357.209	odd	16		7497.2.a.v.1.1		2
408.5	even	16		9792.2.a.cy.1.1		2
408.107	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	17.5	odd	16
153.2.a.e.1.1		2	51.5	even	16
816.2.a.m.1.1		2	68.39	even	16
867.2.a.f.1.2		2	17.12	odd	16
867.2.d.c.577.1		4	17.14	odd	16
867.2.d.c.577.2		4	17.3	odd	16
867.2.e.f.616.3		8	17.10	odd	16
867.2.e.f.616.4		8	17.7	odd	16
867.2.e.f.829.1		8	17.11	odd	16
867.2.e.f.829.2		8	17.6	odd	16
867.2.h.j.688.1		16	17.9	even	8	inner
867.2.h.j.688.2		16	17.8	even	8	inner
867.2.h.j.712.1		16	17.16	even	2	inner
867.2.h.j.712.2		16	1.1	even	1	trivial
867.2.h.j.733.3		16	17.13	even	4	inner
867.2.h.j.733.4		16	17.4	even	4	inner
867.2.h.j.757.3		16	17.15	even	8	inner
867.2.h.j.757.4		16	17.2	even	8	inner
1275.2.a.n.1.1		2	85.39	odd	16
1275.2.b.d.1174.2		4	85.73	even	16
1275.2.b.d.1174.3		4	85.22	even	16
2448.2.a.v.1.2		2	204.107	odd	16
2499.2.a.o.1.2		2	119.90	even	16
2601.2.a.t.1.1		2	51.29	even	16
3264.2.a.bg.1.2		2	136.107	even	16
3264.2.a.bl.1.2		2	136.5	odd	16
3825.2.a.s.1.2		2	255.209	even	16
6171.2.a.p.1.1		2	187.175	even	16
7497.2.a.v.1.1		2	357.209	odd	16
8619.2.a.q.1.1		2	221.90	odd	16
9792.2.a.cy.1.1		2	408.5	even	16
9792.2.a.cz.1.1		2	408.107	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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