LMFDB - Embedded newform 867.2.h.j.757.3

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			757.3
Root			$0.597580 + 1.44269i$ of defining polynomial
Character	$\chi$	$=$	867.757
Dual form			867.2.h.j.733.3

$q$-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} +(-0.923880 - 0.382683i) q^{3} -0.438447i q^{4} +(0.214897 - 0.518807i) q^{5} +(-1.44269 + 0.597580i) q^{6} +(1.72424 + 1.72424i) q^{8} +(0.707107 + 0.707107i) q^{9} +(-0.335573 - 0.810145i) q^{10} +(2.36657 - 0.980264i) q^{11} +(-0.167786 + 0.405072i) 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} +(-0.227470 - 0.0942210i) q^{20} +(1.53073 - 3.69552i) q^{22} +(-6.06208 + 2.51100i) q^{23} +(-0.933153 - 2.25283i) q^{24} +(3.31255 + 3.31255i) q^{25} +(5.03680 + 5.03680i) q^{26} +(-0.382683 - 0.923880i) q^{27} +(3.15569 - 7.61851i) q^{29} +0.876894i q^{30} +(4.73313 + 1.96053i) q^{31} +(1.72424 - 1.72424i) q^{32} -2.56155 q^{33} +(0.310029 - 0.310029i) q^{36} +(2.88537 + 1.19516i) q^{37} -12.0000i q^{38} +(1.74563 - 4.21433i) q^{39} +(1.26508 - 0.524015i) q^{40} +(-0.214897 - 0.518807i) q^{41} +(-5.43387 - 5.43387i) q^{43} +(-0.429794 - 1.03761i) q^{44} +(0.518807 - 0.214897i) q^{45} +(-3.92106 + 9.46626i) q^{46} -2.87689i q^{47} +(-4.32806 - 1.79274i) q^{48} +(4.94975 - 4.94975i) q^{49} +7.31534 q^{50} +2.00000 q^{52} +(-3.00252 + 3.00252i) q^{53} +(-1.44269 - 0.597580i) q^{54} -1.43845i q^{55} +(-7.09970 + 2.94079i) q^{57} +(-4.92777 - 11.8967i) q^{58} +(0.794156 + 0.794156i) q^{59} +(0.174098 + 0.174098i) q^{60} +(0.335573 + 0.810145i) q^{61} +(7.39104 - 3.06147i) q^{62} +5.56155i q^{64} +(2.36657 + 0.980264i) q^{65} +(-2.82843 + 2.82843i) q^{66} -4.00000 q^{67} +6.56155 q^{69} +(9.46626 + 3.92106i) q^{71} +2.43845i q^{72} +(-1.62495 + 3.92299i) q^{73} +(4.50566 - 1.86631i) q^{74} +(-1.79274 - 4.32806i) q^{75} +(-2.38247 - 2.38247i) q^{76} +(-2.72589 - 6.58089i) q^{78} +(-14.1994 + 5.88158i) q^{79} +(1.00672 - 2.43043i) q^{80} +1.00000i q^{81} +(-0.810145 - 0.335573i) q^{82} +(6.45101 - 6.45101i) q^{83} -12.0000 q^{86} +(-5.83095 + 5.83095i) q^{87} +(5.77075 + 2.39032i) q^{88} -7.12311i q^{89} +(0.335573 - 0.810145i) q^{90} +(1.10094 + 2.65790i) q^{92} +(-3.62258 - 3.62258i) q^{93} +(-3.17662 - 3.17662i) q^{94} +(-1.65141 - 3.98686i) q^{95} +(-2.25283 + 0.933153i) q^{96} +(-4.25663 + 10.2764i) q^{97} -10.9309i q^{98} +(2.36657 + 0.980264i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 24 q^{16} - 8 q^{18} - 8 q^{33} + 216 q^{50} + 32 q^{52} - 64 q^{67} + 72 q^{69} - 192 q^{86}+O(q^{100}) $ 16 * q - 24 * q^16 - 8 * q^18 - 8 * q^33 + 216 * q^50 + 32 * q^52 - 64 * q^67 + 72 * q^69 - 192 * q^86

Character values

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

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

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	$-0.563830\pi$
$2$	1.10418	−	1.10418i	0.780776	−	0.780776i	0.979962	+	0.199185i	$0.0638296\pi$
$3$	−0.923880	−	0.382683i	−0.533402	−	0.220942i
$3$	−0.923880	−	0.382683i	−0.533402	−	0.220942i
$4$		−	0.438447i		−	0.219224i
$5$	0.214897	−	0.518807i	0.0961048	−	0.232018i	−0.868515	−	0.495663i	$-0.834925\pi$
$5$	0.214897	−	0.518807i	0.0961048	−	0.232018i	0.964620	+	0.263646i	$0.0849250\pi$
$6$	−1.44269	+	0.597580i	−0.588974	+	0.243961i
$7$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$7$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$8$	1.72424	+	1.72424i	0.609612	+	0.609612i
$9$	0.707107	+	0.707107i	0.235702	+	0.235702i
$10$	−0.335573	−	0.810145i	−0.106117	−	0.256190i
$11$	2.36657	−	0.980264i	0.713547	−	0.295561i	0.00377529	−	0.999993i	$-0.498798\pi$
$11$	2.36657	−	0.980264i	0.713547	−	0.295561i	0.709771	+	0.704432i	$0.248798\pi$
$12$	−0.167786	+	0.405072i	−0.0484358	+	0.116934i
$13$			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	$-0.406540\pi$
$19$	5.43387	−	5.43387i	1.24662	−	1.24662i	0.957205	−	0.289411i	$-0.0934596\pi$
$20$	−0.227470	−	0.0942210i	−0.0508637	−	0.0210684i
$21$		0			0
$22$	1.53073	−	3.69552i	0.326354	−	0.787887i
$23$	−6.06208	+	2.51100i	−1.26403	+	0.523579i	−0.911145	−	0.412087i	$-0.864800\pi$
$23$	−6.06208	+	2.51100i	−1.26403	+	0.523579i	−0.352887	+	0.935666i	$0.614800\pi$
$24$	−0.933153	−	2.25283i	−0.190479	−	0.459857i
$25$	3.31255	+	3.31255i	0.662511	+	0.662511i
$26$	5.03680	+	5.03680i	0.987797	+	0.987797i
$27$	−0.382683	−	0.923880i	−0.0736475	−	0.177801i
$28$		0			0
$29$	3.15569	−	7.61851i	0.585997	−	1.41472i	−0.301303	−	0.953528i	$-0.597422\pi$
$29$	3.15569	−	7.61851i	0.585997	−	1.41472i	0.887300	−	0.461193i	$-0.152578\pi$
$30$			0.876894i			0.160098i
$31$	4.73313	+	1.96053i	0.850096	+	0.352121i	0.764826	−	0.644237i	$-0.222825\pi$
$31$	4.73313	+	1.96053i	0.850096	+	0.352121i	0.0852696	+	0.996358i	$0.472825\pi$
$32$	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
$37$	2.88537	+	1.19516i	0.474352	+	0.196483i	0.607035	−	0.794675i	$-0.292359\pi$
$37$	2.88537	+	1.19516i	0.474352	+	0.196483i	−0.132682	+	0.991159i	$0.542359\pi$
$38$		−	12.0000i		−	1.94666i
$39$	1.74563	−	4.21433i	0.279525	−	0.674832i
$40$	1.26508	−	0.524015i	0.200027	−	0.0828540i
$41$	−0.214897	−	0.518807i	−0.0335613	−	0.0810241i	0.906210	−	0.422827i	$-0.138962\pi$
$41$	−0.214897	−	0.518807i	−0.0335613	−	0.0810241i	−0.939772	+	0.341803i	$0.888962\pi$
$42$		0			0
$43$	−5.43387	−	5.43387i	−0.828658	−	0.828658i	0.158673	−	0.987331i	$-0.449278\pi$
$43$	−5.43387	−	5.43387i	−0.828658	−	0.828658i	−0.987331	+	0.158673i	$0.949278\pi$
$44$	−0.429794	−	1.03761i	−0.0647939	−	0.156426i
$45$	0.518807	−	0.214897i	0.0773392	−	0.0320349i
$46$	−3.92106	+	9.46626i	−0.578128	+	1.39572i
$47$		−	2.87689i		−	0.419638i	−0.977740	−	0.209819i	$-0.932712\pi$
$47$		−	2.87689i		−	0.419638i	0.977740	−	0.209819i	$-0.0672875\pi$
$48$	−4.32806	−	1.79274i	−0.624702	−	0.258760i
$49$	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	$-0.844198\pi$
$53$	−3.00252	+	3.00252i	−0.412428	+	0.412428i	0.470155	+	0.882584i	$0.344198\pi$
$54$	−1.44269	−	0.597580i	−0.196325	−	0.0813204i
$55$		−	1.43845i		−	0.193960i
$56$		0			0
$57$	−7.09970	+	2.94079i	−0.940378	+	0.389517i
$58$	−4.92777	−	11.8967i	−0.647048	−	1.56211i
$59$	0.794156	+	0.794156i	0.103390	+	0.103390i	0.756910	−	0.653519i	$-0.226708\pi$
$59$	0.794156	+	0.794156i	0.103390	+	0.103390i	−0.653519	+	0.756910i	$0.726708\pi$
$60$	0.174098	+	0.174098i	0.0224759	+	0.0224759i
$61$	0.335573	+	0.810145i	0.0429657	+	0.103728i	0.943905	−	0.330216i	$-0.107122\pi$
$61$	0.335573	+	0.810145i	0.0429657	+	0.103728i	−0.900940	+	0.433944i	$0.857122\pi$
$62$	7.39104	−	3.06147i	0.938663	−	0.388807i
$63$		0			0
$64$			5.56155i			0.695194i
$65$	2.36657	+	0.980264i	0.293536	+	0.121587i
$66$	−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
$71$	9.46626	+	3.92106i	1.12344	+	0.465344i	0.865546	−	0.500830i	$-0.166972\pi$
$71$	9.46626	+	3.92106i	1.12344	+	0.465344i	0.257893	+	0.966173i	$0.416972\pi$
$72$			2.43845i			0.287374i
$73$	−1.62495	+	3.92299i	−0.190187	+	0.459151i	−0.989995	−	0.141105i	$-0.954935\pi$
$73$	−1.62495	+	3.92299i	−0.190187	+	0.459151i	0.799808	+	0.600256i	$0.204935\pi$
$74$	4.50566	−	1.86631i	0.523773	−	0.216954i
$75$	−1.79274	−	4.32806i	−0.207008	−	0.499761i
$76$	−2.38247	−	2.38247i	−0.273288	−	0.273288i
$77$		0			0
$78$	−2.72589	−	6.58089i	−0.308647	−	0.745139i
$79$	−14.1994	+	5.88158i	−1.59756	+	0.661730i	−0.991067	−	0.133362i	$-0.957423\pi$
$79$	−14.1994	+	5.88158i	−1.59756	+	0.661730i	−0.606490	+	0.795091i	$0.707423\pi$
$80$	1.00672	−	2.43043i	0.112555	−	0.271731i
$81$			1.00000i			0.111111i
$82$	−0.810145	−	0.335573i	−0.0894655	−	0.0370578i
$83$	6.45101	−	6.45101i	0.708090	−	0.708090i	−0.258043	−	0.966133i	$-0.583078\pi$
$83$	6.45101	−	6.45101i	0.708090	−	0.708090i	0.966133	+	0.258043i	$0.0830777\pi$
$84$		0			0
$85$		0			0
$86$	−12.0000			−1.29399
$87$	−5.83095	+	5.83095i	−0.625144	+	0.625144i
$88$	5.77075	+	2.39032i	0.615164	+	0.254809i
$89$		−	7.12311i		−	0.755048i	−0.926000	−	0.377524i	$-0.876776\pi$
$89$		−	7.12311i		−	0.755048i	0.926000	−	0.377524i	$-0.123224\pi$
$90$	0.335573	−	0.810145i	0.0353725	−	0.0853968i
$91$		0			0
$92$	1.10094	+	2.65790i	0.114781	+	0.277106i
$93$	−3.62258	−	3.62258i	−0.375644	−	0.375644i
$94$	−3.17662	−	3.17662i	−0.327644	−	0.327644i
$95$	−1.65141	−	3.98686i	−0.169431	−	0.409043i
$96$	−2.25283	+	0.933153i	−0.229929	+	0.0952396i
$97$	−4.25663	+	10.2764i	−0.432195	+	1.04341i	0.546383	+	0.837535i	$0.316004\pi$
$97$	−4.25663	+	10.2764i	−0.432195	+	1.04341i	−0.978578	+	0.205876i	$0.933996\pi$
$98$		−	10.9309i		−	1.10418i
$99$	2.36657	+	0.980264i	0.237849	+	0.0985202i
$100$	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
$107$	−2.94079	+	7.09970i	−0.284297	+	0.686354i	−0.999926	−	0.0121264i	$-0.996140\pi$
$107$	−2.94079	+	7.09970i	−0.284297	+	0.686354i	0.715629	+	0.698480i	$0.246140\pi$
$108$	−0.405072	+	0.167786i	−0.0389781	+	0.0161453i
$109$	5.78736	+	13.9719i	0.554329	+	1.33827i	0.914199	+	0.405266i	$0.132821\pi$
$109$	5.78736	+	13.9719i	0.554329	+	1.33827i	−0.359870	+	0.933002i	$0.617179\pi$
$110$	−1.58831	−	1.58831i	−0.151440	−	0.151440i
$111$	−2.20837	−	2.20837i	−0.209609	−	0.209609i
$112$		0			0
$113$	4.21433	−	1.74563i	0.396450	−	0.164215i	−0.175546	−	0.984471i	$-0.556169\pi$
$113$	4.21433	−	1.74563i	0.396450	−	0.164215i	0.571996	+	0.820256i	$0.306169\pi$
$114$	−4.59220	+	11.0866i	−0.430099	+	1.03835i
$115$			3.68466i			0.343596i
$116$	−3.34031	−	1.38360i	−0.310140	−	0.128464i
$117$	−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
$122$	1.26508	+	0.524015i	0.114535	+	0.0474421i
$123$			0.561553i			0.0506335i
$124$	0.859588	−	2.07523i	0.0771933	−	0.186361i
$125$	5.02447	−	2.08120i	0.449402	−	0.186149i
$126$		0			0
$127$	0.571175	+	0.571175i	0.0506836	+	0.0506836i	0.731994	−	0.681311i	$-0.238590\pi$
$127$	0.571175	+	0.571175i	0.0506836	+	0.0506836i	−0.681311	+	0.731994i	$0.738590\pi$
$128$	9.58947	+	9.58947i	0.847597	+	0.847597i
$129$	2.94079	+	7.09970i	0.258922	+	0.625094i
$130$	3.69552	−	1.53073i	0.324118	−	0.134254i
$131$	7.10320	−	17.1486i	0.620609	−	1.49828i	−0.230380	−	0.973101i	$-0.573997\pi$
$131$	7.10320	−	17.1486i	0.620609	−	1.49828i	0.850989	−	0.525183i	$-0.176003\pi$
$132$			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
$139$	−8.42865	−	3.49126i	−0.714909	−	0.296125i	−0.00457466	−	0.999990i	$-0.501456\pi$
$139$	−8.42865	−	3.49126i	−0.714909	−	0.296125i	−0.710334	+	0.703865i	$0.751456\pi$
$140$		0			0
$141$	−1.10094	+	2.65790i	−0.0927159	+	0.223836i
$142$	14.7821	−	6.12293i	1.24048	−	0.513825i
$143$	4.47153	+	10.7952i	0.373928	+	0.902741i
$144$	3.31255	+	3.31255i	0.276046	+	0.276046i
$145$	−3.27439	−	3.27439i	−0.271923	−	0.271923i
$146$	2.53745	+	6.12595i	0.210001	+	0.506987i
$147$	−6.46716	+	2.67878i	−0.533402	+	0.220942i
$148$	0.524015	−	1.26508i	0.0430738	−	0.103989i
$149$		−	4.24621i		−	0.347863i	−0.984758	−	0.173932i	$-0.944353\pi$
$149$		−	4.24621i		−	0.347863i	0.984758	−	0.173932i	$-0.0556472\pi$
$150$	−6.75849	−	2.79946i	−0.551829	−	0.228575i
$151$	−5.65685	+	5.65685i	−0.460348	+	0.460348i	−0.898770	−	0.438421i	$-0.855538\pi$
$151$	−5.65685	+	5.65685i	−0.460348	+	0.460348i	0.438421	+	0.898770i	$0.355538\pi$
$152$	18.7386			1.51990
$153$		0			0
$154$		0			0
$155$	2.03427	−	2.03427i	0.163397	−	0.163397i
$156$	−1.84776	−	0.765367i	−0.147939	−	0.0612784i
$157$			5.68466i			0.453685i	0.973931	+	0.226843i	$0.0728403\pi$
$157$			5.68466i			0.453685i	−0.973931	+	0.226843i	$0.927160\pi$
$158$	−9.18440	+	22.1731i	−0.730672	+	1.76400i
$159$	3.92299	−	1.62495i	0.311113	−	0.128867i
$160$	−0.524015	−	1.26508i	−0.0414270	−	0.100014i
$161$		0			0
$162$	1.10418	+	1.10418i	0.0867529	+	0.0867529i
$163$	−2.63167	−	6.35342i	−0.206129	−	0.497638i	0.786679	−	0.617363i	$-0.211799\pi$
$163$	−2.63167	−	6.35342i	−0.206129	−	0.497638i	−0.992807	+	0.119724i	$0.961799\pi$
$164$	−0.227470	+	0.0942210i	−0.0177624	+	0.00735742i
$165$	−0.550470	+	1.32895i	−0.0428540	+	0.103459i
$166$		−	14.2462i		−	1.10572i
$167$	0.746277	+	0.309118i	0.0577486	+	0.0239203i	0.411371	−	0.911468i	$-0.365050\pi$
$167$	0.746277	+	0.309118i	0.0577486	+	0.0239203i	−0.353622	+	0.935388i	$0.615050\pi$
$168$		0			0
$169$	−7.80776			−0.600597
$170$		0			0
$171$	7.68466			0.587661
$172$	−2.38247	+	2.38247i	−0.181661	+	0.181661i
$173$	−17.3761	−	7.19742i	−1.32108	−	0.547210i	−0.392983	−	0.919546i	$-0.628557\pi$
$173$	−17.3761	−	7.19742i	−1.32108	−	0.547210i	−0.928098	+	0.372336i	$0.878557\pi$
$174$			12.8769i			0.976195i
$175$		0			0
$176$	11.0866	−	4.59220i	0.835680	−	0.346150i
$177$	−0.429794	−	1.03761i	−0.0323053	−	0.0779919i
$178$	−7.86522	−	7.86522i	−0.589523	−	0.589523i
$179$	−6.45101	−	6.45101i	−0.482171	−	0.482171i	0.423653	−	0.905824i	$-0.360747\pi$
$179$	−6.45101	−	6.45101i	−0.482171	−	0.482171i	−0.905824	+	0.423653i	$0.860747\pi$
$180$	−0.0942210	−	0.227470i	−0.00702282	−	0.0169546i
$181$	−5.54328	+	2.29610i	−0.412029	+	0.170668i	−0.579062	−	0.815283i	$-0.696581\pi$
$181$	−5.54328	+	2.29610i	−0.412029	+	0.170668i	0.167034	+	0.985951i	$0.446581\pi$
$182$		0			0
$183$		−	0.876894i		−	0.0648219i
$184$	−14.7821	−	6.12293i	−1.08975	−	0.451389i
$185$	1.24012	−	1.24012i	0.0911751	−	0.0911751i
$186$	−8.00000			−0.586588
$187$		0			0
$188$	−1.26137			−0.0919946
$189$		0			0
$190$	−6.22569	−	2.57876i	−0.451659	−	0.187083i
$191$			13.1231i			0.949555i	0.880106	+	0.474777i	$0.157471\pi$
$191$			13.1231i			0.949555i	−0.880106	+	0.474777i	$0.842529\pi$
$192$	2.12831	−	5.13820i	0.153598	−	0.370818i
$193$	−22.4006	+	9.27862i	−1.61243	+	0.667890i	−0.993103	−	0.117244i	$-0.962594\pi$
$193$	−22.4006	+	9.27862i	−1.61243	+	0.667890i	−0.619326	+	0.785134i	$0.712594\pi$
$194$	6.64695	+	16.0472i	0.477223	+	1.15212i
$195$	−1.81129	−	1.81129i	−0.129709	−	0.129709i
$196$	−2.17020	−	2.17020i	−0.155014	−	0.155014i
$197$	7.62721	+	18.4137i	0.543416	+	1.31192i	0.922298	+	0.386478i	$0.126309\pi$
$197$	7.62721	+	18.4137i	0.543416	+	1.31192i	−0.378882	+	0.925445i	$0.623691\pi$
$198$	3.69552	−	1.53073i	0.262629	−	0.108785i
$199$	6.12293	−	14.7821i	0.434043	−	1.04787i	−0.543928	−	0.839132i	$-0.683063\pi$
$199$	6.12293	−	14.7821i	0.434043	−	1.04787i	0.977971	−	0.208741i	$-0.0669366\pi$
$200$			11.4233i			0.807749i
$201$	3.69552	+	1.53073i	0.260662	+	0.107970i
$202$	−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
$207$	−6.06208	−	2.51100i	−0.421344	−	0.174526i
$208$			21.3693i			1.48170i
$209$	7.53299	−	18.1863i	0.521068	−	1.25797i
$210$		0			0
$211$	4.35085	+	10.5039i	0.299525	+	0.723117i	0.999956	+	0.00939678i	$0.00299113\pi$
$211$	4.35085	+	10.5039i	0.299525	+	0.723117i	−0.700431	+	0.713720i	$0.747009\pi$
$212$	1.31645	+	1.31645i	0.0904141	+	0.0904141i
$213$	−7.24517	−	7.24517i	−0.496431	−	0.496431i
$214$	4.59220	+	11.0866i	0.313916	+	0.757861i
$215$	−3.98686	+	1.65141i	−0.271901	+	0.112625i
$216$	0.933153	−	2.25283i	0.0634930	−	0.153286i
$217$		0			0
$218$	21.8179	+	9.03727i	1.47769	+	0.612081i
$219$	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	$-0.595536\pi$
$223$	9.85061	−	9.85061i	0.659646	−	0.659646i	0.955296	+	0.295650i	$0.0955363\pi$
$224$		0			0
$225$			4.68466i			0.312311i
$226$	2.72589	−	6.58089i	0.181324	−	0.437754i
$227$	21.2991	−	8.82237i	1.41367	−	0.585562i	0.460409	−	0.887707i	$-0.347703\pi$
$227$	21.2991	−	8.82237i	1.41367	−	0.585562i	0.953262	+	0.302145i	$0.0977028\pi$
$228$	1.28938	+	3.11284i	0.0853914	+	0.206153i
$229$	−4.24264	−	4.24264i	−0.280362	−	0.280362i	0.552892	−	0.833253i	$-0.313524\pi$
$229$	−4.24264	−	4.24264i	−0.280362	−	0.280362i	−0.833253	+	0.552892i	$0.813524\pi$
$230$	4.06854	+	4.06854i	0.268272	+	0.268272i
$231$		0			0
$232$	18.5773	−	7.69498i	1.21966	−	0.505200i
$233$	0.214897	−	0.518807i	0.0140784	−	0.0339882i	−0.916684	−	0.399613i	$-0.869145\pi$
$233$	0.214897	−	0.518807i	0.0140784	−	0.0339882i	0.930762	+	0.365625i	$0.119145\pi$
$234$			7.12311i			0.465652i
$235$	−1.49255	−	0.618236i	−0.0973634	−	0.0403293i
$236$	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
$241$	−19.7427	−	8.17768i	−1.27174	−	0.526771i	−0.358245	−	0.933627i	$-0.616625\pi$
$241$	−19.7427	−	8.17768i	−1.27174	−	0.526771i	−0.913492	+	0.406857i	$0.866625\pi$
$242$			6.93087i			0.445533i
$243$	0.382683	−	0.923880i	0.0245492	−	0.0592669i
$244$	0.355206	−	0.147131i	0.0227397	−	0.00941910i
$245$	−1.50428	−	3.63165i	−0.0961048	−	0.232018i
$246$	0.620058	+	0.620058i	0.0395335	+	0.0395335i
$247$	24.7869	+	24.7869i	1.57715	+	1.57715i
$248$	4.78064	+	11.5415i	0.303571	+	0.732886i
$249$	−8.42865	+	3.49126i	−0.534144	+	0.221250i
$250$	3.24991	−	7.84598i	0.205542	−	0.496223i
$251$		−	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	−0.469611	−	0.882874i	$-0.655606\pi$
$257$	6.62511	−	6.62511i	0.413263	−	0.413263i	0.882874	+	0.469611i	$0.155606\pi$
$258$	11.0866	+	4.59220i	0.690219	+	0.285898i
$259$		0			0
$260$	0.429794	−	1.03761i	0.0266547	−	0.0643501i
$261$	7.61851	−	3.15569i	0.471574	−	0.195332i
$262$	−11.0920	−	26.7785i	−0.685267	−	1.65438i
$263$	−8.83348	−	8.83348i	−0.544696	−	0.544696i	0.380206	−	0.924902i	$-0.375853\pi$
$263$	−8.83348	−	8.83348i	−0.544696	−	0.544696i	−0.924902	+	0.380206i	$0.875853\pi$
$264$	−4.41674	−	4.41674i	−0.271831	−	0.271831i
$265$	0.912498	+	2.20296i	0.0560543	+	0.135327i
$266$		0			0
$267$	−2.72589	+	6.58089i	−0.166822	+	0.402744i
$268$			1.75379i			0.107130i
$269$	−18.9964	−	7.86857i	−1.15823	−	0.479755i	−0.280945	−	0.959724i	$-0.590648\pi$
$269$	−18.9964	−	7.86857i	−1.15823	−	0.479755i	−0.877286	+	0.479969i	$0.840648\pi$
$270$	−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
$275$	11.0866	+	4.59220i	0.668544	+	0.276920i
$276$		−	2.87689i		−	0.173169i
$277$	−2.29610	+	5.54328i	−0.137959	+	0.333063i	−0.977726	−	0.209884i	$-0.932691\pi$
$277$	−2.29610	+	5.54328i	−0.137959	+	0.333063i	0.839767	+	0.542947i	$0.182691\pi$
$278$	−13.1618	+	5.45179i	−0.789391	+	0.326977i
$279$	1.96053	+	4.73313i	0.117374	+	0.283365i
$280$		0			0
$281$	−13.5221	−	13.5221i	−0.806660	−	0.806660i	0.177467	−	0.984127i	$-0.443210\pi$
$281$	−13.5221	−	13.5221i	−0.806660	−	0.806660i	−0.984127	+	0.177467i	$0.943210\pi$
$282$	1.71918	+	4.15046i	0.102375	+	0.247156i
$283$	3.11284	−	1.28938i	0.185039	−	0.0766458i	−0.288240	−	0.957558i	$-0.593070\pi$
$283$	3.11284	−	1.28938i	0.185039	−	0.0766458i	0.473279	+	0.880912i	$0.343070\pi$
$284$	1.71918	−	4.15046i	0.102014	−	0.246284i
$285$			4.31534i			0.255619i
$286$	16.8573	+	6.98252i	0.996793	+	0.412885i
$287$		0			0
$288$	2.43845			0.143687
$289$		0			0
$290$	−7.23106			−0.424622
$291$	7.86522	−	7.86522i	0.461068	−	0.461068i
$292$	1.72002	+	0.712457i	0.100657	+	0.0416934i
$293$			7.12311i			0.416136i	0.978114	+	0.208068i	$0.0667176\pi$
$293$			7.12311i			0.416136i	−0.978114	+	0.208068i	$0.933282\pi$
$294$	−4.18306	+	10.0988i	−0.243961	+	0.588974i
$295$	0.582675	−	0.241352i	0.0339247	−	0.0140521i
$296$	2.91434	+	7.03583i	0.169392	+	0.408949i
$297$	−1.81129	−	1.81129i	−0.105102	−	0.105102i
$298$	−4.68860	−	4.68860i	−0.271603	−	0.271603i
$299$	−11.4540	−	27.6525i	−0.662405	−	1.59919i
$300$	−1.89763	+	0.786022i	−0.109559	+	0.0453810i
$301$		0			0
$302$			12.4924i			0.718858i
$303$	17.6674	+	7.31810i	1.01497	+	0.420414i
$304$	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
$309$	−3.98686	−	1.65141i	−0.226804	−	0.0939454i
$310$		−	4.49242i		−	0.255152i
$311$		0			0		−0.923880	−	0.382683i	$-0.875000\pi$
$311$		0			0		0.923880	+	0.382683i	$0.125000\pi$
$312$	10.2764	−	4.25663i	0.581787	−	0.240984i
$313$	2.91434	+	7.03583i	0.164728	+	0.397689i	0.984591	−	0.174871i	$-0.0559507\pi$
$313$	2.91434	+	7.03583i	0.164728	+	0.397689i	−0.819863	+	0.572559i	$0.805951\pi$
$314$	6.27691	+	6.27691i	0.354227	+	0.354227i
$315$		0			0
$316$	2.57876	+	6.22569i	0.145067	+	0.350222i
$317$	16.6298	−	6.88830i	0.934024	−	0.386886i	0.136821	−	0.990596i	$-0.456312\pi$
$317$	16.6298	−	6.88830i	0.934024	−	0.386886i	0.797204	+	0.603710i	$0.206312\pi$
$318$	2.53745	−	6.12595i	0.142293	−	0.343526i
$319$		−	21.1231i		−	1.18267i
$320$	2.88537	+	1.19516i	0.161297	+	0.0668115i
$321$	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
$326$	−9.92120	−	4.10950i	−0.549485	−	0.227604i
$327$		−	15.1231i		−	0.836310i
$328$	0.524015	−	1.26508i	0.0289339	−	0.0698526i
$329$		0			0
$330$	0.859588	+	2.07523i	0.0473188	+	0.114238i
$331$	4.29152	+	4.29152i	0.235883	+	0.235883i	0.815143	−	0.579260i	$-0.196658\pi$
$331$	4.29152	+	4.29152i	0.235883	+	0.235883i	−0.579260	+	0.815143i	$0.696658\pi$
$332$	−2.82843	−	2.82843i	−0.155230	−	0.155230i
$333$	1.19516	+	2.88537i	0.0654944	+	0.158117i
$334$	1.16535	−	0.482704i	0.0637651	−	0.0264124i
$335$	−0.859588	+	2.07523i	−0.0469643	+	0.113382i
$336$		0			0
$337$	−30.2466	−	12.5285i	−1.64763	−	0.682473i	−0.650600	−	0.759421i	$-0.725482\pi$
$337$	−30.2466	−	12.5285i	−1.64763	−	0.682473i	−0.997035	+	0.0769482i	$0.975482\pi$
$338$	−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
$345$	1.41006	−	3.40418i	0.0759150	−	0.183275i
$346$	−27.1337	+	11.2392i	−1.45872	+	0.604221i
$347$	−9.37284	−	22.6280i	−0.503161	−	1.21474i	−0.947753	−	0.319004i	$-0.896652\pi$
$347$	−9.37284	−	22.6280i	−0.503161	−	1.21474i	0.444593	−	0.895733i	$-0.353348\pi$
$348$	2.55656	+	2.55656i	0.137046	+	0.137046i
$349$	5.25978	+	5.25978i	0.281549	+	0.281549i	0.833727	−	0.552177i	$-0.186203\pi$
$349$	5.25978	+	5.25978i	0.281549	+	0.281549i	−0.552177	+	0.833727i	$0.686203\pi$
$350$		0			0
$351$	4.21433	−	1.74563i	0.224944	−	0.0931749i
$352$	2.39032	−	5.77075i	0.127405	−	0.307582i
$353$			22.4924i			1.19715i	0.801066	+	0.598575i	$0.204266\pi$
$353$			22.4924i			1.19715i	−0.801066	+	0.598575i	$0.795734\pi$
$354$	−1.62029	−	0.671146i	−0.0861174	−	0.0356710i
$355$	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	$-0.768879\pi$
$359$	−1.58831	+	1.58831i	−0.0838279	+	0.0838279i	0.663950	+	0.747777i	$0.268879\pi$
$360$	1.26508	+	0.524015i	0.0666758	+	0.0276180i
$361$		−	40.0540i		−	2.10810i
$362$	−3.58548	+	8.65612i	−0.188449	+	0.454956i
$363$	4.10059	−	1.69852i	0.215225	−	0.0891492i
$364$		0			0
$365$	1.68608	+	1.68608i	0.0882533	+	0.0882533i
$366$	−0.968253	−	0.968253i	−0.0506114	−	0.0506114i
$367$	−6.98252	−	16.8573i	−0.364485	−	0.879944i	−0.994633	−	0.103469i	$-0.967006\pi$
$367$	−6.98252	−	16.8573i	−0.364485	−	0.879944i	0.630148	−	0.776475i	$-0.282994\pi$
$368$	−28.3988	+	11.7632i	−1.48039	+	0.613197i
$369$	0.214897	−	0.518807i	0.0111871	−	0.0270080i
$370$		−	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
$377$	34.7522	+	14.3948i	1.78983	+	0.741372i
$378$		0			0
$379$	4.59220	−	11.0866i	0.235886	−	0.569478i	−0.760964	−	0.648794i	$-0.775274\pi$
$379$	4.59220	−	11.0866i	0.235886	−	0.569478i	0.996850	+	0.0793161i	$0.0252736\pi$
$380$	−1.74803	+	0.724056i	−0.0896718	+	0.0371433i
$381$	−0.309118	−	0.746277i	−0.0158366	−	0.0382329i
$382$	14.4903	+	14.4903i	0.741390	+	0.741390i
$383$	−7.24517	−	7.24517i	−0.370211	−	0.370211i	0.497343	−	0.867554i	$-0.334309\pi$
$383$	−7.24517	−	7.24517i	−0.370211	−	0.370211i	−0.867554	+	0.497343i	$0.834309\pi$
$384$	−5.18978	−	12.5292i	−0.264840	−	0.639380i
$385$		0			0
$386$	−14.4891	+	34.9797i	−0.737474	+	1.78042i
$387$		−	7.68466i		−	0.390633i
$388$	4.50566	+	1.86631i	0.228740	+	0.0947474i
$389$	15.4586	−	15.4586i	0.783781	−	0.783781i	−0.196685	−	0.980467i	$-0.563018\pi$
$389$	15.4586	−	15.4586i	0.783781	−	0.783781i	0.980467	+	0.196685i	$0.0630177\pi$
$390$	−4.00000			−0.202548
$391$		0			0
$392$	17.0691			0.862121
$393$	−13.1250	+	13.1250i	−0.662069	+	0.662069i
$394$	28.7540	+	11.9103i	1.44861	+	0.600032i
$395$			8.63068i			0.434257i
$396$	0.429794	−	1.03761i	0.0215980	−	0.0521421i
$397$	4.96060	−	2.05475i	0.248965	−	0.103125i	−0.254711	−	0.967017i	$-0.581980\pi$
$397$	4.96060	−	2.05475i	0.248965	−	0.103125i	0.503677	+	0.863892i	$0.331980\pi$
$398$	−9.56129	−	23.0830i	−0.479264	−	1.15705i
$399$		0			0
$400$	15.5182	+	15.5182i	0.775909	+	0.775909i
$401$	−2.36387	−	5.70688i	−0.118046	−	0.284988i	0.853802	−	0.520598i	$-0.174291\pi$
$401$	−2.36387	−	5.70688i	−0.118046	−	0.284988i	−0.971848	+	0.235610i	$0.924291\pi$
$402$	5.77075	−	2.39032i	0.287819	−	0.119218i
$403$	−8.94305	+	21.5904i	−0.445485	+	1.07550i
$404$			8.38447i			0.417143i
$405$	0.518807	+	0.214897i	0.0257797	+	0.0106783i
$406$		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
$411$	15.0095	+	6.21716i	0.740366	+	0.306670i
$412$		−	1.89205i		−	0.0932146i
$413$		0			0
$414$	−9.46626	+	3.92106i	−0.465242	+	0.192709i
$415$	−1.96053	−	4.73313i	−0.0962385	−	0.232340i
$416$	7.86522	+	7.86522i	0.385624	+	0.385624i
$417$	6.45101	+	6.45101i	0.315907	+	0.315907i
$418$	−11.7632	−	28.3988i	−0.575355	−	1.38903i
$419$	−30.0191	+	12.4343i	−1.46653	+	0.607456i	−0.966064	−	0.258302i	$-0.916837\pi$
$419$	−30.0191	+	12.4343i	−1.46653	+	0.607456i	−0.500464	+	0.865757i	$0.666837\pi$
$420$		0			0
$421$			28.5616i			1.39200i	0.718039	+	0.696002i	$0.245040\pi$
$421$			28.5616i			1.39200i	−0.718039	+	0.696002i	$0.754960\pi$
$422$	16.4024	+	6.79408i	0.798454	+	0.330731i
$423$	2.03427	−	2.03427i	0.0989097	−	0.0989097i
$424$	−10.3542			−0.502843
$425$		0			0
$426$	−16.0000			−0.775203
$427$		0			0
$428$	3.11284	+	1.28938i	0.150465	+	0.0623246i
$429$		−	11.6847i		−	0.564141i
$430$	−2.57876	+	6.22569i	−0.124359	+	0.300229i
$431$	−22.1731	+	9.18440i	−1.06804	+	0.442397i	−0.846299	−	0.532708i	$-0.821174\pi$
$431$	−22.1731	+	9.18440i	−1.06804	+	0.442397i	−0.221742	+	0.975105i	$0.571174\pi$
$432$	−1.79274	−	4.32806i	−0.0862533	−	0.208234i
$433$	−10.1225	−	10.1225i	−0.486455	−	0.486455i	0.420731	−	0.907186i	$-0.361774\pi$
$433$	−10.1225	−	10.1225i	−0.486455	−	0.486455i	−0.907186	+	0.420731i	$0.861774\pi$
$434$		0			0
$435$	1.77209	+	4.27819i	0.0849650	+	0.205124i
$436$	6.12595	−	2.53745i	0.293380	−	0.121522i
$437$	−19.2962	+	46.5850i	−0.923060	+	2.22847i
$438$		−	6.63068i		−	0.316826i
$439$	5.31581	+	2.20188i	0.253710	+	0.105090i	0.505914	−	0.862584i	$-0.331155\pi$
$439$	5.31581	+	2.20188i	0.253710	+	0.105090i	−0.252204	+	0.967674i	$0.581155\pi$
$440$	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
$445$	−3.69552	−	1.53073i	−0.175184	−	0.0725637i
$446$		−	21.7538i		−	1.03007i
$447$	−1.62495	+	3.92299i	−0.0768577	+	0.185551i
$448$		0			0
$449$	4.87486	+	11.7690i	0.230059	+	0.555412i	0.996184	−	0.0872802i	$-0.0278175\pi$
$449$	4.87486	+	11.7690i	0.230059	+	0.555412i	−0.766125	+	0.642692i	$0.777818\pi$
$450$	5.17273	+	5.17273i	0.243845	+	0.243845i
$451$	−1.01714	−	1.01714i	−0.0478951	−	0.0478951i
$452$	−0.765367	−	1.84776i	−0.0359998	−	0.0869113i
$453$	7.39104	−	3.06147i	0.347261	−	0.143840i
$454$	13.7766	−	33.2597i	0.646568	−	1.56095i
$455$		0			0
$456$	−17.3122	−	7.17096i	−0.810720	−	0.335811i
$457$	4.81382	−	4.81382i	0.225181	−	0.225181i	−0.585495	−	0.810676i	$-0.699100\pi$
$457$	4.81382	−	4.81382i	0.225181	−	0.225181i	0.810676	+	0.585495i	$0.199100\pi$
$458$	−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	$-0.688492\pi$
$461$	5.83095	−	5.83095i	0.271575	−	0.271575i	0.829734	+	0.558159i	$0.188492\pi$
$462$		0			0
$463$		−	24.9848i		−	1.16114i	−0.814209	−	0.580572i	$-0.802829\pi$
$463$		−	24.9848i		−	1.16114i	0.814209	−	0.580572i	$-0.197171\pi$
$464$	14.7833	−	35.6901i	0.686299	−	1.65687i
$465$	−2.65790	+	1.10094i	−0.123257	+	0.0510549i
$466$	−0.335573	−	0.810145i	−0.0155451	−	0.0375292i
$467$	2.38247	+	2.38247i	0.110247	+	0.110247i	0.760079	−	0.649831i	$-0.225160\pi$
$467$	2.38247	+	2.38247i	0.110247	+	0.110247i	−0.649831	+	0.760079i	$0.725160\pi$
$468$	1.41421	+	1.41421i	0.0653720	+	0.0653720i
$469$		0			0
$470$	−2.33070	+	0.965408i	−0.107507	+	0.0445309i
$471$	2.17542	−	5.25194i	0.100238	−	0.241997i
$472$			2.73863i			0.126056i
$473$	−18.1863	−	7.53299i	−0.836205	−	0.346367i
$474$	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
$479$	−27.0698	−	11.2127i	−1.23685	−	0.512321i	−0.334123	−	0.942529i	$-0.608440\pi$
$479$	−27.0698	−	11.2127i	−1.23685	−	0.512321i	−0.902730	+	0.430208i	$0.858440\pi$
$480$			1.36932i			0.0625005i
$481$	−5.45179	+	13.1618i	−0.248580	+	0.600126i
$482$	−30.8292	+	12.7699i	−1.40423	+	0.581652i
$483$		0			0
$484$	1.37605	+	1.37605i	0.0625476	+	0.0625476i
$485$	4.41674	+	4.41674i	0.200554	+	0.200554i
$486$	−0.597580	−	1.44269i	−0.0271068	−	0.0654416i
$487$	6.80836	−	2.82012i	0.308516	−	0.127792i	−0.223053	−	0.974806i	$-0.571602\pi$
$487$	6.80836	−	2.82012i	0.308516	−	0.127792i	0.531570	+	0.847015i	$0.321602\pi$
$488$	−0.818277	+	1.97550i	−0.0370417	+	0.0894265i
$489$			6.87689i			0.310984i
$490$	−5.67101	−	2.34901i	−0.256190	−	0.106117i
$491$	−2.38247	+	2.38247i	−0.107519	+	0.107519i	−0.758820	−	0.651301i	$-0.774224\pi$
$491$	−2.38247	+	2.38247i	−0.107519	+	0.107519i	0.651301	+	0.758820i	$0.274224\pi$
$492$	0.246211			0.0111001
$493$		0			0
$494$	54.7386			2.46281
$495$	1.01714	−	1.01714i	0.0457169	−	0.0457169i
$496$	22.1731	+	9.18440i	0.995602	+	0.412392i
$497$		0			0
$498$	−5.45179	+	13.1618i	−0.244301	+	0.589794i
$499$	−10.5039	+	4.35085i	−0.470218	+	0.194771i	−0.605194	−	0.796078i	$-0.706904\pi$
$499$	−10.5039	+	4.35085i	−0.470218	+	0.194771i	0.134976	+	0.990849i	$0.456904\pi$
$500$	−0.912498	−	2.20296i	−0.0408081	−	0.0985196i
$501$	−0.571175	−	0.571175i	−0.0255182	−	0.0255182i
$502$	−27.0442	−	27.0442i	−1.20704	−	1.20704i
$503$	−9.73487	−	23.5021i	−0.434057	−	1.04791i	−0.977967	−	0.208762i	$-0.933057\pi$
$503$	−9.73487	−	23.5021i	−0.434057	−	1.04791i	0.543910	−	0.839144i	$-0.316943\pi$
$504$		0			0
$505$	−4.10950	+	9.92120i	−0.182870	+	0.441488i
$506$			26.2462i			1.16679i
$507$	7.21343	+	2.98790i	0.320360	+	0.132697i
$508$	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
$513$	−7.09970	−	2.94079i	−0.313459	−	0.129839i
$514$		−	14.6307i		−	0.645332i
$515$	0.927354	−	2.23883i	0.0408641	−	0.0986546i
$516$	3.11284	−	1.28938i	0.137035	−	0.0567619i
$517$	−2.82012	−	6.80836i	−0.124029	−	0.299431i
$518$		0			0
$519$	13.2991	+	13.2991i	0.583766	+	0.583766i
$520$	2.39032	+	5.77075i	0.104823	+	0.253064i
$521$	29.0453	−	12.0310i	1.27250	−	0.527086i	0.358776	−	0.933424i	$-0.383194\pi$
$521$	29.0453	−	12.0310i	1.27250	−	0.527086i	0.913723	+	0.406337i	$0.133194\pi$
$522$	4.92777	−	11.8967i	0.215683	−	0.520704i
$523$		−	20.0000i		−	0.874539i	−0.899331	−	0.437269i	$-0.855946\pi$
$523$		−	20.0000i		−	0.874539i	0.899331	−	0.437269i	$-0.144054\pi$
$524$	−7.51877	−	3.11438i	−0.328459	−	0.136052i
$525$		0			0
$526$	−19.5076			−0.850571
$527$		0			0
$528$	−12.0000			−0.522233
$529$	14.1803	−	14.1803i	0.616535	−	0.616535i
$530$	3.44005	+	1.42491i	0.149426	+	0.0618943i
$531$			1.12311i			0.0487386i
$532$		0			0
$533$	2.36657	−	0.980264i	0.102507	−	0.0424599i
$534$	4.25663	+	10.2764i	0.184202	+	0.444704i
$535$	3.05141	+	3.05141i	0.131924	+	0.131924i
$536$	−6.89697	−	6.89697i	−0.297904	−	0.297904i
$537$	3.49126	+	8.42865i	0.150659	+	0.363723i
$538$	−29.6639	+	12.2872i	−1.27890	+	0.529738i
$539$	6.86185	−	16.5660i	0.295561	−	0.713547i
$540$			0.246211i			0.0105952i
$541$	37.0549	+	15.3486i	1.59312	+	0.659890i	0.990421	−	0.138082i	$-0.0440938\pi$
$541$	37.0549	+	15.3486i	1.59312	+	0.659890i	0.602694	+	0.797972i	$0.294094\pi$
$542$	0.891921	−	0.891921i	0.0383113	−	0.0383113i
$543$	6.00000			0.257485
$544$		0			0
$545$	8.49242			0.363775
$546$		0			0
$547$	25.8686	+	10.7151i	1.10606	+	0.458146i	0.859580	−	0.511001i	$-0.170725\pi$
$547$	25.8686	+	10.7151i	1.10606	+	0.458146i	0.246483	+	0.969147i	$0.420725\pi$
$548$			7.12311i			0.304284i
$549$	−0.335573	+	0.810145i	−0.0143219	+	0.0345761i
$550$	17.3122	−	7.17096i	0.738196	−	0.305771i
$551$	−24.2504	−	58.5456i	−1.03310	−	2.49413i
$552$	11.3137	+	11.3137i	0.481543	+	0.481543i
$553$		0			0
$554$	3.58548	+	8.65612i	0.152333	+	0.367763i
$555$	−1.62029	+	0.671146i	−0.0687775	+	0.0284886i
$556$	−1.53073	+	3.69552i	−0.0649176	+	0.156725i
$557$		−	6.49242i		−	0.275093i	−0.990495	−	0.137546i	$-0.956078\pi$
$557$		−	6.49242i		−	0.275093i	0.990495	−	0.137546i	$-0.0439216\pi$
$558$	7.39104	+	3.06147i	0.312888	+	0.129602i
$559$	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	$-0.589884\pi$
$563$	16.1764	−	16.1764i	0.681754	−	0.681754i	0.960395	+	0.278641i	$0.0898840\pi$
$564$	1.16535	+	0.482704i	0.0490701	+	0.0203255i
$565$		−	2.56155i		−	0.107765i
$566$	2.01344	−	4.86087i	0.0846311	−	0.204318i
$567$		0			0
$568$	9.56129	+	23.0830i	0.401183	+	0.968541i
$569$	−9.10534	−	9.10534i	−0.381716	−	0.381716i	0.490004	−	0.871720i	$-0.336995\pi$
$569$	−9.10534	−	9.10534i	−0.381716	−	0.381716i	−0.871720	+	0.490004i	$0.836995\pi$
$570$	4.76493	+	4.76493i	0.199581	+	0.199581i
$571$	7.17096	+	17.3122i	0.300096	+	0.724495i	0.999948	+	0.0102072i	$0.00324911\pi$
$571$	7.17096	+	17.3122i	0.300096	+	0.724495i	−0.699852	+	0.714288i	$0.746751\pi$
$572$	4.73313	−	1.96053i	0.197902	−	0.0819738i
$573$	5.02200	−	12.1242i	0.209797	−	0.506494i
$574$		0			0
$575$	−28.3988	−	11.7632i	−1.18431	−	0.490558i
$576$	−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
$583$	−4.16241	+	10.0489i	−0.172389	+	0.416185i
$584$	−9.56600	+	3.96237i	−0.395844	+	0.163964i
$585$	0.980264	+	2.36657i	0.0405289	+	0.0978455i
$586$	7.86522	+	7.86522i	0.324909	+	0.324909i
$587$	26.1522	+	26.1522i	1.07942	+	1.07942i	0.996561	+	0.0828568i	$0.0264044\pi$
$587$	26.1522	+	26.1522i	1.07942	+	1.07942i	0.0828568	+	0.996561i	$0.473596\pi$
$588$	1.17451	+	2.83551i	0.0484358	+	0.116934i
$589$	36.3725	−	15.0660i	1.49870	−	0.620783i
$590$	0.376884	−	0.909878i	0.0155161	−	0.0374591i
$591$		−	19.9309i		−	0.819846i
$592$	13.5170	+	5.59892i	0.555545	+	0.230114i
$593$	−31.2868	+	31.2868i	−1.28479	+	1.28479i	−0.346888	+	0.937906i	$0.612762\pi$
$593$	−31.2868	+	31.2868i	−1.28479	+	1.28479i	−0.937906	+	0.346888i	$0.887238\pi$
$594$	−4.00000			−0.164122
$595$		0			0
$596$	−1.86174			−0.0762598
$597$	−11.3137	+	11.3137i	−0.463039	+	0.463039i
$598$	−43.1809	−	17.8861i	−1.76580	−	0.731417i
$599$			41.6155i			1.70036i	0.526489	+	0.850182i	$0.323508\pi$
$599$			41.6155i			1.70036i	−0.526489	+	0.850182i	$0.676492\pi$
$600$	4.37150	−	10.5537i	0.178466	−	0.430855i
$601$	32.3218	−	13.3881i	1.31843	−	0.546113i	0.391099	−	0.920348i	$-0.372095\pi$
$601$	32.3218	−	13.3881i	1.31843	−	0.546113i	0.927334	+	0.374236i	$0.122095\pi$
$602$		0			0
$603$	−2.82843	−	2.82843i	−0.115182	−	0.115182i
$604$	2.48023	+	2.48023i	0.100919	+	0.100919i
$605$	0.953809	+	2.30270i	0.0387778	+	0.0936180i
$606$	27.5886	−	11.4276i	1.12071	−	0.464214i
$607$	5.88158	−	14.1994i	0.238726	−	0.576336i	−0.758425	−	0.651760i	$-0.774031\pi$
$607$	5.88158	−	14.1994i	0.238726	−	0.576336i	0.997152	+	0.0754240i	$0.0240310\pi$
$608$		−	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
$615$	0.291338	+	0.120676i	0.0117479	+	0.00486613i
$616$		0			0
$617$	10.6209	−	25.6412i	0.427582	−	1.03227i	−0.552470	−	0.833533i	$-0.686315\pi$
$617$	10.6209	−	25.6412i	0.427582	−	1.03227i	0.980052	−	0.198741i	$-0.0636854\pi$
$618$	−6.22569	+	2.57876i	−0.250434	+	0.103733i
$619$	7.41232	+	17.8949i	0.297926	+	0.719257i	0.999975	+	0.00712818i	$0.00226899\pi$
$619$	7.41232	+	17.8949i	0.297926	+	0.719257i	−0.702048	+	0.712129i	$0.747731\pi$
$620$	−0.891921	−	0.891921i	−0.0358204	−	0.0358204i
$621$	4.63972	+	4.63972i	0.186185	+	0.186185i
$622$		0			0
$623$		0			0
$624$	8.17768	−	19.7427i	0.327369	−	0.790340i
$625$			20.3693i			0.814773i
$626$	10.9868	+	4.55089i	0.439122	+	0.181890i
$627$	−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	$-0.675283\pi$
$631$	8.26230	−	8.26230i	0.328917	−	0.328917i	0.852175	+	0.523258i	$0.175283\pi$
$632$	−34.6245	−	14.3419i	−1.37729	−	0.570491i
$633$		−	11.3693i		−	0.451890i
$634$	10.7564	−	25.9684i	0.427193	−	1.03134i
$635$	0.419074	−	0.173586i	0.0166304	−	0.00688855i
$636$	−0.712457	−	1.72002i	−0.0282508	−	0.0682033i
$637$	22.5785	+	22.5785i	0.894594	+	0.894594i
$638$	−23.3238	−	23.3238i	−0.923398	−	0.923398i
$639$	3.92106	+	9.46626i	0.155115	+	0.374480i
$640$	7.03583	−	2.91434i	0.278116	−	0.115199i
$641$	−0.0264550	+	0.0638681i	−0.00104491	+	0.00252264i	−0.924401	−	0.381422i	$-0.875435\pi$
$641$	−0.0264550	+	0.0638681i	−0.00104491	+	0.00252264i	0.923356	+	0.383944i	$0.125435\pi$
$642$		−	12.0000i		−	0.473602i
$643$	27.9439	+	11.5747i	1.10200	+	0.456463i	0.858175	−	0.513357i	$-0.171598\pi$
$643$	27.9439	+	11.5747i	1.10200	+	0.456463i	0.243823	+	0.969820i	$0.421598\pi$
$644$		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
$649$	2.65790	+	1.10094i	0.104332	+	0.0432157i
$650$			33.3693i			1.30885i
$651$		0			0
$652$	−2.78564	+	1.15385i	−0.109094	+	0.0451882i
$653$	1.55719	+	3.75939i	0.0609375	+	0.147116i	0.951415	−	0.307910i	$-0.0996297\pi$
$653$	1.55719	+	3.75939i	0.0609375	+	0.147116i	−0.890478	+	0.455027i	$0.849630\pi$
$654$	−16.6987	−	16.6987i	−0.652971	−	0.652971i
$655$	−7.37038	−	7.37038i	−0.287985	−	0.287985i
$656$	−1.00672	−	2.43043i	−0.0393058	−	0.0948925i
$657$	−3.92299	+	1.62495i	−0.153050	+	0.0633955i
$658$		0			0
$659$			47.8617i			1.86443i	0.361907	+	0.932214i	$0.382126\pi$
$659$			47.8617i			1.86443i	−0.361907	+	0.932214i	$0.617874\pi$
$660$	0.582675	+	0.241352i	0.0226806	+	0.00939461i
$661$	−18.1618	+	18.1618i	−0.706412	+	0.706412i	−0.965779	−	0.259367i	$-0.916486\pi$
$661$	−18.1618	+	18.1618i	−0.706412	+	0.706412i	0.259367	+	0.965779i	$0.416486\pi$
$662$	9.47727			0.368344
$663$		0			0
$664$	22.2462			0.863320
$665$		0			0
$666$	4.50566	+	1.86631i	0.174591	+	0.0723179i
$667$			54.1080i			2.09507i
$668$	0.135532	−	0.327203i	0.00524389	−	0.0126599i
$669$	−12.8704	+	5.33111i	−0.497600	+	0.206113i
$670$	1.34229	+	3.24058i	0.0518573	+	0.125194i
$671$	1.58831	+	1.58831i	0.0613161	+	0.0613161i
$672$		0			0
$673$	18.6515	+	45.0286i	0.718961	+	1.73573i	0.676288	+	0.736637i	$0.263587\pi$
$673$	18.6515	+	45.0286i	0.718961	+	1.73573i	0.0426728	+	0.999089i	$0.486413\pi$
$674$	−47.2316	+	19.5640i	−1.81929	+	0.753576i
$675$	1.79274	−	4.32806i	0.0690026	−	0.166587i
$676$			3.42329i			0.131665i
$677$	12.6430	+	5.23689i	0.485909	+	0.201270i	0.612169	−	0.790727i	$-0.290297\pi$
$677$	12.6430	+	5.23689i	0.485909	+	0.201270i	−0.126260	+	0.991997i	$0.540297\pi$
$678$	−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
$683$	−5.02447	−	2.08120i	−0.192256	−	0.0796350i	0.284478	−	0.958682i	$-0.408180\pi$
$683$	−5.02447	−	2.08120i	−0.192256	−	0.0796350i	−0.476734	+	0.879047i	$0.658180\pi$
$684$		−	3.36932i		−	0.128829i
$685$	−3.49126	+	8.42865i	−0.133394	+	0.322042i
$686$		0			0
$687$	2.29610	+	5.54328i	0.0876017	+	0.211489i
$688$	−25.4558	−	25.4558i	−0.970495	−	0.970495i
$689$	−13.6962	−	13.6962i	−0.521783	−	0.521783i
$690$	−2.20188	−	5.31581i	−0.0838241	−	0.202369i
$691$	−34.1695	+	14.1535i	−1.29987	+	0.538424i	−0.921912	−	0.387399i	$-0.873374\pi$
$691$	−34.1695	+	14.1535i	−1.29987	+	0.538424i	−0.377958	+	0.925823i	$0.623374\pi$
$692$	−3.15569	+	7.61851i	−0.119961	+	0.289612i
$693$		0			0
$694$	−35.3349	−	14.6362i	−1.34129	−	0.555582i
$695$	−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	$0.943381\pi$
$702$	2.72589	−	6.58089i	0.102882	−	0.248380i
$703$	22.1731	−	9.18440i	0.836275	−	0.346396i
$704$	5.45179	+	13.1618i	0.205472	+	0.496053i
$705$	1.14235	+	1.14235i	0.0430234	+	0.0430234i
$706$	24.8358	+	24.8358i	0.934707	+	0.934707i
$707$		0			0
$708$	−0.454939	+	0.188442i	−0.0170977	+	0.00708208i
$709$	1.81340	−	4.37793i	0.0681035	−	0.164416i	−0.886163	−	0.463374i	$-0.846639\pi$
$709$	1.81340	−	4.37793i	0.0681035	−	0.164416i	0.954267	+	0.298957i	$0.0966388\pi$
$710$		−	8.98485i		−	0.337195i
$711$	−14.1994	−	5.88158i	−0.532519	−	0.220577i
$712$	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
$717$	−9.46626	−	3.92106i	−0.353524	−	0.146434i
$718$			3.50758i			0.130902i
$719$	−3.37059	+	8.13731i	−0.125702	+	0.303471i	−0.974185	−	0.225752i	$-0.927516\pi$
$719$	−3.37059	+	8.13731i	−0.125702	+	0.303471i	0.848483	+	0.529222i	$0.177516\pi$
$720$	2.43043	−	1.00672i	0.0905769	−	0.0375182i
$721$		0			0
$722$	−44.2270	−	44.2270i	−1.64596	−	1.64596i
$723$	15.1104	+	15.1104i	0.561961	+	0.561961i
$724$	1.00672	+	2.43043i	0.0374144	+	0.0903264i
$725$	35.6901	−	14.7833i	1.32550	−	0.549039i
$726$	2.65233	−	6.40329i	0.0984372	−	0.237648i
$727$		−	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	−0.972137	−	0.234414i	$-0.924683\pi$
$733$	−19.9731	+	19.9731i	−0.737723	+	0.737723i	0.234414	+	0.972137i	$0.424683\pi$
$734$	−26.3236	−	10.9036i	−0.971621	−	0.402458i
$735$			3.93087i			0.144992i
$736$	−6.12293	+	14.7821i	−0.225694	+	0.544874i
$737$	−9.46626	+	3.92106i	−0.348694	+	0.144434i
$738$	−0.335573	−	0.810145i	−0.0123526	−	0.0298218i
$739$	5.87983	+	5.87983i	0.216293	+	0.216293i	0.806934	−	0.590641i	$-0.201125\pi$
$739$	5.87983	+	5.87983i	0.216293	+	0.216293i	−0.590641	+	0.806934i	$0.701125\pi$
$740$	−0.543725	−	0.543725i	−0.0199877	−	0.0199877i
$741$	−13.4146	−	32.3857i	−0.492797	−	1.18972i
$742$		0			0
$743$	−1.71918	+	4.15046i	−0.0630704	+	0.152266i	−0.952273	−	0.305249i	$-0.901260\pi$
$743$	−1.71918	+	4.15046i	−0.0630704	+	0.152266i	0.889202	+	0.457515i	$0.151260\pi$
$744$		−	12.4924i		−	0.457994i
$745$	−2.20296	−	0.912498i	−0.0807104	−	0.0334313i
$746$	−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
$751$	−0.582675	−	0.241352i	−0.0212621	−	0.00880706i	0.372027	−	0.928222i	$-0.378663\pi$
$751$	−0.582675	−	0.241352i	−0.0212621	−	0.00880706i	−0.393289	+	0.919415i	$0.628663\pi$
$752$		−	13.4773i		−	0.491465i
$753$	−9.37284	+	22.6280i	−0.341565	+	0.824612i
$754$	54.2674	−	22.4783i	1.97630	−	0.818611i
$755$	1.71918	+	4.15046i	0.0625672	+	0.151051i
$756$		0			0
$757$	−14.8874	−	14.8874i	−0.541092	−	0.541092i	0.382757	−	0.923849i	$-0.374975\pi$
$757$	−14.8874	−	14.8874i	−0.541092	−	0.541092i	−0.923849	+	0.382757i	$0.874975\pi$
$758$	−7.17096	−	17.3122i	−0.260461	−	0.628809i
$759$	15.5283	−	6.43205i	0.563643	−	0.233469i
$760$	4.02688	−	9.72174i	0.146070	−	0.352644i
$761$		−	32.2462i		−	1.16892i	−0.811421	−	0.584462i	$-0.801306\pi$
$761$		−	32.2462i		−	1.16892i	0.811421	−	0.584462i	$-0.198694\pi$
$762$	−1.16535	−	0.482704i	−0.0422162	−	0.0174865i
$763$		0			0
$764$	5.75379			0.208165
$765$		0			0
$766$	−16.0000			−0.578103
$767$	−3.62258	+	3.62258i	−0.130804	+	0.130804i
$768$	−9.28866	−	3.84749i	−0.335176	−	0.138834i
$769$			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
$771$	−8.65612	+	3.58548i	−0.311743	+	0.129128i
$772$	4.06819	+	9.82147i	0.146417	+	0.353482i
$773$	23.5957	+	23.5957i	0.848677	+	0.848677i	0.989968	−	0.141291i	$-0.0451253\pi$
$773$	23.5957	+	23.5957i	0.848677	+	0.848677i	−0.141291	+	0.989968i	$0.545125\pi$
$774$	−8.48528	−	8.48528i	−0.304997	−	0.304997i
$775$	9.18440	+	22.1731i	0.329913	+	0.796482i
$776$	−25.0585	+	10.3796i	−0.899547	+	0.372605i
$777$		0			0
$778$		−	34.1383i		−	1.22392i
$779$	−3.98686	−	1.65141i	−0.142844	−	0.0591679i
$780$	−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
$785$	2.94924	+	1.22162i	0.105263	+	0.0436013i
$786$			28.9848i			1.03386i
$787$	−2.39032	+	5.77075i	−0.0852058	+	0.205705i	−0.960739	−	0.277452i	$-0.910510\pi$
$787$	−2.39032	+	5.77075i	−0.0852058	+	0.205705i	0.875534	+	0.483157i	$0.160510\pi$
$788$	8.07344	−	3.34413i	0.287605	−	0.119130i
$789$	4.78064	+	11.5415i	0.170195	+	0.410888i
$790$	9.52987	+	9.52987i	0.339057	+	0.339057i
$791$		0			0
$792$	2.39032	+	5.77075i	0.0849364	+	0.205055i
$793$	−3.69552	+	1.53073i	−0.131232	+	0.0543579i
$794$	3.20860	−	7.74624i	0.113869	−	0.274904i
$795$		−	2.38447i		−	0.0845685i
$796$	−6.48116	−	2.68458i	−0.229719	−	0.0951525i
$797$	−22.3556	+	22.3556i	−0.791874	+	0.791874i	−0.981799	−	0.189924i	$-0.939176\pi$
$797$	−22.3556	+	22.3556i	−0.791874	+	0.791874i	0.189924	+	0.981799i	$0.439176\pi$
$798$		0			0
$799$		0			0
$800$	11.4233			0.403874
$801$	5.03680	−	5.03680i	0.177966	−	0.177966i
$802$	−8.91159	−	3.69130i	−0.314679	−	0.130344i
$803$			10.8769i			0.383837i
$804$	0.671146	−	1.62029i	0.0236695	−	0.0571432i
$805$		0			0
$806$	13.9650	+	33.7146i	0.491898	+	1.18755i
$807$	14.5392	+	14.5392i	0.511805	+	0.511805i
$808$	−32.9729	−	32.9729i	−1.15998	−	1.15998i
$809$	20.3029	+	49.0155i	0.713811	+	1.72329i	0.690251	+	0.723570i	$0.257500\pi$
$809$	20.3029	+	49.0155i	0.713811	+	1.72329i	0.0235603	+	0.999722i	$0.492500\pi$
$810$	0.810145	−	0.335573i	0.0284656	−	0.0117908i
$811$	−7.89502	+	19.0603i	−0.277232	+	0.669296i	−0.999757	−	0.0220481i	$-0.992981\pi$
$811$	−7.89502	+	19.0603i	−0.277232	+	0.669296i	0.722525	+	0.691345i	$0.242981\pi$
$812$		0			0
$813$	−0.746277	−	0.309118i	−0.0261731	−	0.0108412i
$814$	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
$821$	6.33783	−	15.3009i	0.221192	−	0.534004i	−0.773861	−	0.633356i	$-0.781677\pi$
$821$	6.33783	−	15.3009i	0.221192	−	0.534004i	0.995052	+	0.0993517i	$0.0316769\pi$
$822$	23.4382	−	9.70842i	0.817501	−	0.338620i
$823$	−13.9650	−	33.7146i	−0.486791	−	1.17522i	−0.956326	−	0.292303i	$-0.905578\pi$
$823$	−13.9650	−	33.7146i	−0.486791	−	1.17522i	0.469535	−	0.882914i	$-0.344422\pi$
$824$	7.44070	+	7.44070i	0.259209	+	0.259209i
$825$	−8.48528	−	8.48528i	−0.295420	−	0.295420i
$826$		0			0
$827$	13.3254	−	5.51955i	0.463369	−	0.191934i	−0.138771	−	0.990325i	$-0.544315\pi$
$827$	13.3254	−	5.51955i	0.463369	−	0.191934i	0.602140	+	0.798391i	$0.294315\pi$
$828$	−1.10094	+	2.65790i	−0.0382603	+	0.0923685i
$829$			50.4924i			1.75367i	0.480787	+	0.876837i	$0.340351\pi$
$829$			50.4924i			1.75367i	−0.480787	+	0.876837i	$0.659649\pi$
$830$	−7.39104	−	3.06147i	−0.256547	−	0.106265i
$831$	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
$836$	−7.97371	−	3.30282i	−0.275777	−	0.114230i
$837$		−	5.12311i		−	0.177080i
$838$	−19.4168	+	46.8764i	−0.670743	+	1.61932i
$839$	10.2125	−	4.23017i	0.352576	−	0.146042i	−0.199364	−	0.979925i	$-0.563888\pi$
$839$	10.2125	−	4.23017i	0.352576	−	0.146042i	0.551940	+	0.833884i	$0.313888\pi$
$840$		0			0
$841$	−27.5772	−	27.5772i	−0.950937	−	0.950937i
$842$	31.5372	+	31.5372i	1.08684	+	1.08684i
$843$	7.31810	+	17.6674i	0.252049	+	0.608499i
$844$	4.60540	−	1.90762i	0.158524	−	0.0656629i
$845$	−1.67786	+	4.05072i	−0.0577203	+	0.139349i
$846$		−	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
$853$	19.1600	+	7.93633i	0.656026	+	0.271735i	0.685765	−	0.727823i	$-0.259468\pi$
$853$	19.1600	+	7.93633i	0.656026	+	0.271735i	−0.0297393	+	0.999558i	$0.509468\pi$
$854$		0			0
$855$	1.65141	−	3.98686i	0.0564770	−	0.136348i
$856$	−17.3122	+	7.17096i	−0.591720	+	0.245099i
$857$	2.29610	+	5.54328i	0.0784333	+	0.189355i	0.958232	−	0.285991i	$-0.0923229\pi$
$857$	2.29610	+	5.54328i	0.0784333	+	0.189355i	−0.879799	+	0.475346i	$0.842323\pi$
$858$	−12.9020	−	12.9020i	−0.440468	−	0.440468i
$859$	8.48528	+	8.48528i	0.289514	+	0.289514i	0.836888	−	0.547374i	$-0.184372\pi$
$859$	8.48528	+	8.48528i	0.289514	+	0.289514i	−0.547374	+	0.836888i	$0.684372\pi$
$860$	0.724056	+	1.74803i	0.0246901	+	0.0596072i
$861$		0			0
$862$	−14.3419	+	34.6245i	−0.488488	+	1.17931i
$863$		−	26.2462i		−	0.893431i	−0.894676	−	0.446716i	$-0.852594\pi$
$863$		−	26.2462i		−	0.893431i	0.894676	−	0.446716i	$-0.147406\pi$
$864$	−2.25283	−	0.933153i	−0.0766429	−	0.0317465i
$865$	−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
$870$	6.68062	+	2.76721i	0.226494	+	0.0938171i
$871$		−	18.2462i		−	0.618249i
$872$	−14.1122	+	34.0698i	−0.477899	+	1.15375i
$873$	−10.2764	+	4.25663i	−0.347804	+	0.144065i
$874$	30.1320	+	72.7450i	1.01923	+	2.46064i
$875$		0			0
$876$	−1.31645	−	1.31645i	−0.0444787	−	0.0444787i
$877$	−13.0112	−	31.4119i	−0.439358	−	1.06070i	−0.976171	−	0.217003i	$-0.930372\pi$
$877$	−13.0112	−	31.4119i	−0.439358	−	1.06070i	0.536813	−	0.843701i	$-0.319628\pi$
$878$	8.30091	−	3.43835i	0.280142	−	0.116039i
$879$	2.72589	−	6.58089i	0.0919421	−	0.221968i
$880$		−	6.73863i		−	0.227159i
$881$	−21.9456	−	9.09018i	−0.739367	−	0.306256i	−0.0189724	−	0.999820i	$-0.506039\pi$
$881$	−21.9456	−	9.09018i	−0.739367	−	0.306256i	−0.720395	+	0.693564i	$0.756039\pi$
$882$	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
$887$	20.8442	+	8.63393i	0.699878	+	0.289899i	0.704109	−	0.710092i	$-0.251347\pi$
$887$	20.8442	+	8.63393i	0.699878	+	0.289899i	−0.00423064	+	0.999991i	$0.501347\pi$
$888$		−	7.61553i		−	0.255560i
$889$		0			0
$890$	−5.77075	+	2.39032i	−0.193436	+	0.0801238i
$891$	0.980264	+	2.36657i	0.0328401	+	0.0792830i
$892$	−4.31897	−	4.31897i	−0.144610	−	0.144610i
$893$	−15.6327	−	15.6327i	−0.523128	−	0.523128i
$894$	2.53745	+	6.12595i	0.0848651	+	0.204882i
$895$	−4.73313	+	1.96053i	−0.158211	+	0.0655332i
$896$		0			0
$897$			29.9309i			0.999363i
$898$	18.3779	+	7.61236i	0.613277	+	0.254028i
$899$	29.8726	−	29.8726i	0.996306	−	0.996306i
$900$	2.05398			0.0684658
$901$		0			0
$902$	−2.24621			−0.0747907
$903$		0			0
$904$	10.2764	+	4.25663i	0.341788	+	0.141573i
$905$			3.36932i			0.112000i
$906$	4.78064	−	11.5415i	0.158826	−	0.383440i
$907$	44.2185	−	18.3159i	1.46825	−	0.608169i	0.501791	−	0.864989i	$-0.332675\pi$
$907$	44.2185	−	18.3159i	1.46825	−	0.608169i	0.966459	+	0.256819i	$0.0826746\pi$
$908$	−3.86815	−	9.33853i	−0.128369	−	0.309910i
$909$	−13.5221	−	13.5221i	−0.448499	−	0.448499i
$910$		0			0
$911$	−11.2127	−	27.0698i	−0.371493	−	0.896864i	−0.993498	−	0.113850i	$-0.963682\pi$
$911$	−11.2127	−	27.0698i	−0.371493	−	0.896864i	0.622005	−	0.783013i	$-0.286318\pi$
$912$	−33.2597	+	13.7766i	−1.10134	+	0.456189i
$913$	8.94305	−	21.5904i	0.295972	−	0.714539i
$914$		−	10.6307i		−	0.351632i
$915$	−0.454939	−	0.188442i	−0.0150398	−	0.00622970i
$916$	−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
$921$	0.454939	+	0.188442i	0.0149908	+	0.00620937i
$922$		−	12.8769i		−	0.424078i
$923$	−17.8861	+	43.1809i	−0.588728	+	1.42132i
$924$		0			0
$925$	5.59892	+	13.5170i	0.184091	+	0.444436i
$926$	−27.5879	−	27.5879i	−0.906594	−	0.906594i
$927$	3.05141	+	3.05141i	0.100221	+	0.100221i
$928$	−7.69498	−	18.5773i	−0.252600	−	0.609831i
$929$	−29.5003	+	12.2194i	−0.967873	+	0.400906i	−0.809920	−	0.586541i	$-0.800489\pi$
$929$	−29.5003	+	12.2194i	−0.967873	+	0.400906i	−0.157953	+	0.987447i	$0.550489\pi$
$930$	−1.71918	+	4.15046i	−0.0563740	+	0.136099i
$931$		−	53.7926i		−	1.76298i
$932$	−0.227470	−	0.0942210i	−0.00745101	−	0.00308631i
$933$		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	$-0.867003\pi$
$937$	−15.5563	+	15.5563i	−0.508204	+	0.508204i	0.405771	+	0.913975i	$0.367003\pi$
$938$		0			0
$939$		−	7.61553i		−	0.248523i
$940$	−0.271064	+	0.654406i	−0.00884113	+	0.0213444i
$941$	27.7164	−	11.4805i	0.903528	−	0.374254i	0.117953	−	0.993019i	$-0.462367\pi$
$941$	27.7164	−	11.4805i	0.903528	−	0.374254i	0.785576	+	0.618766i	$0.212367\pi$
$942$	−3.39704	−	8.20118i	−0.110682	−	0.267209i
$943$	2.60545	+	2.60545i	0.0848450	+	0.0848450i
$944$	3.72035	+	3.72035i	0.121087	+	0.121087i
$945$		0			0
$946$	−28.3988	+	11.7632i	−0.923324	+	0.382454i
$947$	4.59220	−	11.0866i	0.149226	−	0.360265i	−0.831536	−	0.555471i	$-0.812538\pi$
$947$	4.59220	−	11.0866i	0.149226	−	0.360265i	0.980762	+	0.195207i	$0.0625378\pi$
$948$		−	6.73863i		−	0.218861i
$949$	−17.8949	−	7.41232i	−0.580894	−	0.240614i
$950$	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
$955$	6.80836	+	2.82012i	0.220313	+	0.0912568i
$956$		−	4.49242i		−	0.145295i
$957$	−8.08346	+	19.5152i	−0.261301	+	0.630837i
$958$	−42.2710	+	17.5092i	−1.36571	+	0.565697i
$959$		0			0
$960$	−2.20837	−	2.20837i	−0.0712748	−	0.0712748i
$961$	−3.36144	−	3.36144i	−0.108433	−	0.108433i
$962$	8.51326	+	20.5528i	0.274478	+	0.662649i
$963$	−7.09970	+	2.94079i	−0.228785	+	0.0947657i
$964$	−3.58548	+	8.65612i	−0.115481	+	0.278795i
$965$			13.6155i			0.438299i
$966$		0			0
$967$	−32.9240	+	32.9240i	−1.05876	+	1.05876i	−0.0606021	+	0.998162i	$0.519302\pi$
$967$	−32.9240	+	32.9240i	−1.05876	+	1.05876i	−0.998162	+	0.0606021i	$0.980698\pi$
$968$	−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	$-0.762182\pi$
$971$	−1.68608	+	1.68608i	−0.0541088	+	0.0541088i	0.679535	+	0.733643i	$0.262182\pi$
$972$	−0.405072	−	0.167786i	−0.0129927	−	0.00538175i
$973$		0			0
$974$	4.40376	−	10.6316i	0.141106	−	0.340659i
$975$	19.7427	−	8.17768i	0.632272	−	0.261895i
$976$	1.57204	+	3.79525i	0.0503199	+	0.121483i
$977$	5.83095	+	5.83095i	0.186549	+	0.186549i	0.794202	−	0.607654i	$-0.207889\pi$
$977$	5.83095	+	5.83095i	0.186549	+	0.186549i	−0.607654	+	0.794202i	$0.707889\pi$
$978$	7.59336	+	7.59336i	0.242809	+	0.242809i
$979$	−6.98252	−	16.8573i	−0.223162	−	0.538762i
$980$	−1.59229	+	0.659547i	−0.0508637	+	0.0210684i
$981$	−5.78736	+	13.9719i	−0.184776	+	0.446089i
$982$			5.26137i			0.167897i
$983$	−1.91163	−	0.791822i	−0.0609714	−	0.0252552i	0.351989	−	0.936004i	$-0.385505\pi$
$983$	−1.91163	−	0.791822i	−0.0609714	−	0.0252552i	−0.412961	+	0.910749i	$0.635505\pi$
$984$	−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
$989$	46.5850	+	19.2962i	1.48132	+	0.613582i
$990$		−	2.24621i		−	0.0713893i
$991$	2.57876	−	6.22569i	0.0819171	−	0.197765i	−0.877614	−	0.479368i	$-0.840866\pi$
$991$	2.57876	−	6.22569i	0.0819171	−	0.197765i	0.959531	+	0.281603i	$0.0908659\pi$
$992$	11.5415	−	4.78064i	0.366443	−	0.151786i
$993$	−2.32256	−	5.60715i	−0.0737041	−	0.177937i
$994$		0			0
$995$	−6.35324	−	6.35324i	−0.201411	−	0.201411i
$996$	1.53073	+	3.69552i	0.0485032	+	0.117097i
$997$	9.23880	−	3.82683i	0.292596	−	0.121197i	−0.231557	−	0.972821i	$-0.574382\pi$
$997$	9.23880	−	3.82683i	0.292596	−	0.121197i	0.524153	+	0.851624i	$0.324382\pi$
$998$	−6.79408	+	16.4024i	−0.215063	+	0.519208i
$999$		−	3.12311i		−	0.0988107i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.h.j.757.3		16
17.2	even	8	inner	867.2.h.j.733.3		16
17.3	odd	16		867.2.e.f.829.1		8
17.4	even	4	inner	867.2.h.j.688.1		16
17.5	odd	16		867.2.e.f.616.4		8
17.6	odd	16		51.2.a.b.1.2	✓	2
17.7	odd	16		867.2.d.c.577.2		4
17.8	even	8	inner	867.2.h.j.712.2		16
17.9	even	8	inner	867.2.h.j.712.1		16
17.10	odd	16		867.2.d.c.577.1		4
17.11	odd	16		867.2.a.f.1.2		2
17.12	odd	16		867.2.e.f.616.3		8
17.13	even	4	inner	867.2.h.j.688.2		16
17.14	odd	16		867.2.e.f.829.2		8
17.15	even	8	inner	867.2.h.j.733.4		16
17.16	even	2	inner	867.2.h.j.757.4		16
51.11	even	16		2601.2.a.t.1.1		2
51.23	even	16		153.2.a.e.1.1		2
68.23	even	16		816.2.a.m.1.1		2
85.23	even	16		1275.2.b.d.1174.2		4
85.57	even	16		1275.2.b.d.1174.3		4
85.74	odd	16		1275.2.a.n.1.1		2
119.6	even	16		2499.2.a.o.1.2		2
136.91	even	16		3264.2.a.bg.1.2		2
136.125	odd	16		3264.2.a.bl.1.2		2
187.142	even	16		6171.2.a.p.1.1		2
204.23	odd	16		2448.2.a.v.1.2		2
221.142	odd	16		8619.2.a.q.1.1		2
255.74	even	16		3825.2.a.s.1.2		2
357.125	odd	16		7497.2.a.v.1.1		2
408.125	even	16		9792.2.a.cy.1.1		2
408.227	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	17.6	odd	16
153.2.a.e.1.1		2	51.23	even	16
816.2.a.m.1.1		2	68.23	even	16
867.2.a.f.1.2		2	17.11	odd	16
867.2.d.c.577.1		4	17.10	odd	16
867.2.d.c.577.2		4	17.7	odd	16
867.2.e.f.616.3		8	17.12	odd	16
867.2.e.f.616.4		8	17.5	odd	16
867.2.e.f.829.1		8	17.3	odd	16
867.2.e.f.829.2		8	17.14	odd	16
867.2.h.j.688.1		16	17.4	even	4	inner
867.2.h.j.688.2		16	17.13	even	4	inner
867.2.h.j.712.1		16	17.9	even	8	inner
867.2.h.j.712.2		16	17.8	even	8	inner
867.2.h.j.733.3		16	17.2	even	8	inner
867.2.h.j.733.4		16	17.15	even	8	inner
867.2.h.j.757.3		16	1.1	even	1	trivial
867.2.h.j.757.4		16	17.16	even	2	inner
1275.2.a.n.1.1		2	85.74	odd	16
1275.2.b.d.1174.2		4	85.23	even	16
1275.2.b.d.1174.3		4	85.57	even	16
2448.2.a.v.1.2		2	204.23	odd	16
2499.2.a.o.1.2		2	119.6	even	16
2601.2.a.t.1.1		2	51.11	even	16
3264.2.a.bg.1.2		2	136.91	even	16
3264.2.a.bl.1.2		2	136.125	odd	16
3825.2.a.s.1.2		2	255.74	even	16
6171.2.a.p.1.1		2	187.142	even	16
7497.2.a.v.1.1		2	357.125	odd	16
8619.2.a.q.1.1		2	221.142	odd	16
9792.2.a.cy.1.1		2	408.125	even	16
9792.2.a.cz.1.1		2	408.227	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} +(-0.923880 - 0.382683i) q^{3} -0.438447i q^{4} +(0.214897 - 0.518807i) q^{5} +(-1.44269 + 0.597580i) q^{6} +(1.72424 + 1.72424i) q^{8} +(0.707107 + 0.707107i) q^{9} +(-0.335573 - 0.810145i) q^{10} +(2.36657 - 0.980264i) q^{11} +(-0.167786 + 0.405072i) 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} +(-0.227470 - 0.0942210i) q^{20} +(1.53073 - 3.69552i) q^{22} +(-6.06208 + 2.51100i) q^{23} +(-0.933153 - 2.25283i) q^{24} +(3.31255 + 3.31255i) q^{25} +(5.03680 + 5.03680i) q^{26} +(-0.382683 - 0.923880i) q^{27} +(3.15569 - 7.61851i) q^{29} +0.876894i q^{30} +(4.73313 + 1.96053i) q^{31} +(1.72424 - 1.72424i) q^{32} -2.56155 q^{33} +(0.310029 - 0.310029i) q^{36} +(2.88537 + 1.19516i) q^{37} -12.0000i q^{38} +(1.74563 - 4.21433i) q^{39} +(1.26508 - 0.524015i) q^{40} +(-0.214897 - 0.518807i) q^{41} +(-5.43387 - 5.43387i) q^{43} +(-0.429794 - 1.03761i) q^{44} +(0.518807 - 0.214897i) q^{45} +(-3.92106 + 9.46626i) q^{46} -2.87689i q^{47} +(-4.32806 - 1.79274i) q^{48} +(4.94975 - 4.94975i) q^{49} +7.31534 q^{50} +2.00000 q^{52} +(-3.00252 + 3.00252i) q^{53} +(-1.44269 - 0.597580i) q^{54} -1.43845i q^{55} +(-7.09970 + 2.94079i) q^{57} +(-4.92777 - 11.8967i) q^{58} +(0.794156 + 0.794156i) q^{59} +(0.174098 + 0.174098i) q^{60} +(0.335573 + 0.810145i) q^{61} +(7.39104 - 3.06147i) q^{62} +5.56155i q^{64} +(2.36657 + 0.980264i) q^{65} +(-2.82843 + 2.82843i) q^{66} -4.00000 q^{67} +6.56155 q^{69} +(9.46626 + 3.92106i) q^{71} +2.43845i q^{72} +(-1.62495 + 3.92299i) q^{73} +(4.50566 - 1.86631i) q^{74} +(-1.79274 - 4.32806i) q^{75} +(-2.38247 - 2.38247i) q^{76} +(-2.72589 - 6.58089i) q^{78} +(-14.1994 + 5.88158i) q^{79} +(1.00672 - 2.43043i) q^{80} +1.00000i q^{81} +(-0.810145 - 0.335573i) q^{82} +(6.45101 - 6.45101i) q^{83} -12.0000 q^{86} +(-5.83095 + 5.83095i) q^{87} +(5.77075 + 2.39032i) q^{88} -7.12311i q^{89} +(0.335573 - 0.810145i) q^{90} +(1.10094 + 2.65790i) q^{92} +(-3.62258 - 3.62258i) q^{93} +(-3.17662 - 3.17662i) q^{94} +(-1.65141 - 3.98686i) q^{95} +(-2.25283 + 0.933153i) q^{96} +(-4.25663 + 10.2764i) q^{97} -10.9309i q^{98} +(2.36657 + 0.980264i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 24 q^{16} - 8 q^{18} - 8 q^{33} + 216 q^{50} + 32 q^{52} - 64 q^{67} + 72 q^{69} - 192 q^{86}+O(q^{100}) \) 16 * q - 24 * q^16 - 8 * q^18 - 8 * q^33 + 216 * q^50 + 32 * q^52 - 64 * q^67 + 72 * q^69 - 192 * q^86

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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