LMFDB - Embedded newform 275.2.bm.c.7.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [275,2,Mod(7,275)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(275, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([5, 14]))

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

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

chi := DirichletCharacter("275.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 275 = 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	275.bm (of order $20$, degree $8$, 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:	$2.19588605559$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.6
Character	$\chi$	$=$	275.7
Dual form			275.2.bm.c.118.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.67541 - 0.265359i) q^{2} +(0.954428 + 1.87317i) q^{3} +(0.834479 - 0.271139i) q^{4} +(2.09612 + 2.88507i) q^{6} +(1.62781 + 0.829412i) q^{7} +(-1.69668 + 0.864500i) q^{8} +(-0.834479 + 1.14856i) q^{9} +O(q^{10})$	\(q+(1.67541 - 0.265359i) q^{2} +(0.954428 + 1.87317i) q^{3} +(0.834479 - 0.271139i) q^{4} +(2.09612 + 2.88507i) q^{6} +(1.62781 + 0.829412i) q^{7} +(-1.69668 + 0.864500i) q^{8} +(-0.834479 + 1.14856i) q^{9} +(-2.06203 - 2.59770i) q^{11} +(1.30434 + 1.30434i) q^{12} +(0.298426 + 1.88419i) q^{13} +(2.94735 + 0.957652i) q^{14} +(-4.03293 + 2.93009i) q^{16} +(1.20096 - 7.58255i) q^{17} +(-1.09331 + 2.14575i) q^{18} +(-0.306474 + 0.943229i) q^{19} +3.84078i q^{21} +(-4.14408 - 3.80504i) q^{22} +(4.45709 - 4.45709i) q^{23} +(-3.23871 - 2.35306i) q^{24} +(0.999975 + 3.07761i) q^{26} +(3.28137 + 0.519719i) q^{27} +(1.58326 + 0.250764i) q^{28} +(2.29883 + 7.07507i) q^{29} +(-5.01147 - 3.64105i) q^{31} +(-3.28631 + 3.28631i) q^{32} +(2.89787 - 6.34185i) q^{33} -13.0226i q^{34} +(-0.384935 + 1.18471i) q^{36} +(-2.97754 + 5.84374i) q^{37} +(-0.263175 + 1.66162i) q^{38} +(-3.24458 + 2.35733i) q^{39} +(-7.06579 - 2.29582i) q^{41} +(1.01919 + 6.43490i) q^{42} +(-4.91933 - 4.91933i) q^{43} +(-2.42506 - 1.60863i) q^{44} +(6.28474 - 8.65020i) q^{46} +(0.166573 - 0.0848732i) q^{47} +(-9.33771 - 4.75780i) q^{48} +(-2.15265 - 2.96286i) q^{49} +(15.3496 - 4.98740i) q^{51} +(0.759907 + 1.49140i) q^{52} +(3.64497 - 0.577307i) q^{53} +5.63557 q^{54} -3.47890 q^{56} +(-2.05934 + 0.326167i) q^{57} +(5.72892 + 11.2436i) q^{58} +(-5.05093 + 1.64115i) q^{59} +(3.27130 + 4.50255i) q^{61} +(-9.36247 - 4.77042i) q^{62} +(-2.31101 + 1.17752i) q^{63} +(1.22631 - 1.68787i) q^{64} +(3.17226 - 11.3942i) q^{66} +(5.99054 + 5.99054i) q^{67} +(-1.05375 - 6.65310i) q^{68} +(12.6029 + 4.09492i) q^{69} +(6.49654 - 4.72001i) q^{71} +(0.422909 - 2.67014i) q^{72} +(-3.85754 + 7.57085i) q^{73} +(-3.43791 + 10.5808i) q^{74} +0.870202i q^{76} +(-1.20204 - 5.93884i) q^{77} +(-4.81048 + 4.81048i) q^{78} +(-7.68588 - 5.58412i) q^{79} +(3.47445 + 10.6933i) q^{81} +(-12.4473 - 1.97146i) q^{82} +(-8.70250 - 1.37834i) q^{83} +(1.04138 + 3.20505i) q^{84} +(-9.54730 - 6.93652i) q^{86} +(-11.0587 + 11.0587i) q^{87} +(5.74431 + 2.62483i) q^{88} +12.0425i q^{89} +(-1.07699 + 3.31463i) q^{91} +(2.51086 - 4.92784i) q^{92} +(2.03721 - 12.8625i) q^{93} +(0.256557 - 0.186399i) q^{94} +(-9.29237 - 3.01928i) q^{96} +(0.226246 + 1.42846i) q^{97} +(-4.39279 - 4.39279i) q^{98} +(4.70434 - 0.200646i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 20 q^{6}+O(q^{10}) $ 64 * q + 20 * q^6	$ 64 q + 20 q^{6} + 44 q^{11} - 16 q^{16} - 120 q^{26} + 8 q^{31} - 228 q^{36} - 180 q^{41} + 40 q^{46} - 60 q^{51} + 240 q^{56} + 160 q^{61} + 460 q^{66} + 8 q^{71} - 140 q^{81} - 40 q^{86} - 200 q^{91} - 240 q^{96}+O(q^{100}) $ 64 * q + 20 * q^6 + 44 * q^11 - 16 * q^16 - 120 * q^26 + 8 * q^31 - 228 * q^36 - 180 * q^41 + 40 * q^46 - 60 * q^51 + 240 * q^56 + 160 * q^61 + 460 * q^66 + 8 * q^71 - 140 * q^81 - 40 * q^86 - 200 * q^91 - 240 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/275\mathbb{Z}\right)^\times$.

$n$	$101$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	1.67541	−	0.265359i	1.18470	−	0.187637i	0.467169	−	0.884168i	$-0.345274\pi$
$2$	1.67541	−	0.265359i	1.18470	−	0.187637i	0.717527	+	0.696531i	$0.245274\pi$
$3$	0.954428	+	1.87317i	0.551039	+	1.08148i	0.983683	+	0.179910i	$0.0575808\pi$
$3$	0.954428	+	1.87317i	0.551039	+	1.08148i	−0.432644	+	0.901565i	$0.642419\pi$
$4$	0.834479	−	0.271139i	0.417239	−	0.135569i
$5$		0			0
$5$		0			0
$6$	2.09612	+	2.88507i	0.855739	+	1.17782i
$7$	1.62781	+	0.829412i	0.615255	+	0.313488i	0.733701	−	0.679472i	$-0.237791\pi$
$7$	1.62781	+	0.829412i	0.615255	+	0.313488i	−0.118446	+	0.992961i	$0.537791\pi$
$8$	−1.69668	+	0.864500i	−0.599866	+	0.305647i
$9$	−0.834479	+	1.14856i	−0.278160	+	0.382854i
$10$		0			0
$11$	−2.06203	−	2.59770i	−0.621726	−	0.783235i
$11$	−2.06203	−	2.59770i	−0.621726	−	0.783235i
$12$	1.30434	+	1.30434i	0.376530	+	0.376530i
$13$	0.298426	+	1.88419i	0.0827686	+	0.522580i	0.993884	+	0.110429i	$0.0352225\pi$
$13$	0.298426	+	1.88419i	0.0827686	+	0.522580i	−0.911115	+	0.412151i	$0.864777\pi$
$14$	2.94735	+	0.957652i	0.787713	+	0.255943i
$15$		0			0
$16$	−4.03293	+	2.93009i	−1.00823	+	0.732524i
$17$	1.20096	−	7.58255i	0.291275	−	1.83904i	−0.214936	−	0.976628i	$-0.568954\pi$
$17$	1.20096	−	7.58255i	0.291275	−	1.83904i	0.506211	−	0.862409i	$-0.331046\pi$
$18$	−1.09331	+	2.14575i	−0.257697	+	0.505758i
$19$	−0.306474	+	0.943229i	−0.0703099	+	0.216392i	−0.980037	−	0.198815i	$-0.936291\pi$
$19$	−0.306474	+	0.943229i	−0.0703099	+	0.216392i	0.909727	+	0.415207i	$0.136291\pi$
$20$		0			0
$21$			3.84078i			0.838128i
$22$	−4.14408	−	3.80504i	−0.883520	−	0.811236i
$23$	4.45709	−	4.45709i	0.929368	−	0.929368i	−0.0682968	−	0.997665i	$-0.521756\pi$
$23$	4.45709	−	4.45709i	0.929368	−	0.929368i	0.997665	+	0.0682968i	$0.0217565\pi$
$24$	−3.23871	−	2.35306i	−0.661099	−	0.480316i
$25$		0			0
$26$	0.999975	+	3.07761i	0.196111	+	0.603568i
$27$	3.28137	+	0.519719i	0.631501	+	0.100020i
$28$	1.58326	+	0.250764i	0.299208	+	0.0473899i
$29$	2.29883	+	7.07507i	0.426882	+	1.31381i	0.901181	+	0.433443i	$0.142702\pi$
$29$	2.29883	+	7.07507i	0.426882	+	1.31381i	−0.474299	+	0.880364i	$0.657298\pi$
$30$		0			0
$31$	−5.01147	−	3.64105i	−0.900087	−	0.653952i	0.0384012	−	0.999262i	$-0.487774\pi$
$31$	−5.01147	−	3.64105i	−0.900087	−	0.653952i	−0.938488	+	0.345311i	$0.887774\pi$
$32$	−3.28631	+	3.28631i	−0.580944	+	0.580944i
$33$	2.89787	−	6.34185i	0.504454	−	1.10397i
$34$		−	13.0226i		−	2.23335i
$35$		0			0
$36$	−0.384935	+	1.18471i	−0.0641559	+	0.197452i
$37$	−2.97754	+	5.84374i	−0.489504	+	0.960706i	0.505684	+	0.862719i	$0.331240\pi$
$37$	−2.97754	+	5.84374i	−0.489504	+	0.960706i	−0.995188	+	0.0979867i	$0.968760\pi$
$38$	−0.263175	+	1.66162i	−0.0426927	+	0.269551i
$39$	−3.24458	+	2.35733i	−0.519549	+	0.377475i
$40$		0			0
$41$	−7.06579	−	2.29582i	−1.10349	−	0.358546i	−0.300046	−	0.953925i	$-0.597002\pi$
$41$	−7.06579	−	2.29582i	−1.10349	−	0.358546i	−0.803445	+	0.595379i	$0.797002\pi$
$42$	1.01919	+	6.43490i	0.157264	+	0.992927i
$43$	−4.91933	−	4.91933i	−0.750191	−	0.750191i	0.224324	−	0.974515i	$-0.427983\pi$
$43$	−4.91933	−	4.91933i	−0.750191	−	0.750191i	−0.974515	+	0.224324i	$0.927983\pi$
$44$	−2.42506	−	1.60863i	−0.365591	−	0.242510i
$45$		0			0
$46$	6.28474	−	8.65020i	0.926634	−	1.27540i
$47$	0.166573	−	0.0848732i	0.0242972	−	0.0123800i	−0.441800	−	0.897114i	$-0.645660\pi$
$47$	0.166573	−	0.0848732i	0.0242972	−	0.0123800i	0.466097	+	0.884734i	$0.345660\pi$
$48$	−9.33771	−	4.75780i	−1.34778	−	0.686729i
$49$	−2.15265	−	2.96286i	−0.307521	−	0.423266i
$50$		0			0
$51$	15.3496	−	4.98740i	2.14938	−	0.698375i
$52$	0.759907	+	1.49140i	0.105380	+	0.206820i
$53$	3.64497	−	0.577307i	0.500675	−	0.0792991i	0.0990112	−	0.995086i	$-0.468432\pi$
$53$	3.64497	−	0.577307i	0.500675	−	0.0792991i	0.401664	+	0.915787i	$0.368432\pi$
$54$	5.63557			0.766904
$55$		0			0
$56$	−3.47890			−0.464887
$57$	−2.05934	+	0.326167i	−0.272766	+	0.0432019i
$58$	5.72892	+	11.2436i	0.752244	+	1.47636i
$59$	−5.05093	+	1.64115i	−0.657576	+	0.213659i	−0.618751	−	0.785587i	$-0.712361\pi$
$59$	−5.05093	+	1.64115i	−0.657576	+	0.213659i	−0.0388241	+	0.999246i	$0.512361\pi$
$60$		0			0
$61$	3.27130	+	4.50255i	0.418847	+	0.576493i	0.965348	−	0.260965i	$-0.0840408\pi$
$61$	3.27130	+	4.50255i	0.418847	+	0.576493i	−0.546502	+	0.837458i	$0.684041\pi$
$62$	−9.36247	−	4.77042i	−1.18904	−	0.605844i
$63$	−2.31101	+	1.17752i	−0.291159	+	0.148353i
$64$	1.22631	−	1.68787i	0.153289	−	0.210984i
$65$		0			0
$66$	3.17226	−	11.3942i	0.390478	−	1.40253i
$67$	5.99054	+	5.99054i	0.731861	+	0.731861i	0.970988	−	0.239128i	$-0.0768614\pi$
$67$	5.99054	+	5.99054i	0.731861	+	0.731861i	−0.239128	+	0.970988i	$0.576861\pi$
$68$	−1.05375	−	6.65310i	−0.127786	−	0.806807i
$69$	12.6029	+	4.09492i	1.51721	+	0.492971i
$70$		0			0
$71$	6.49654	−	4.72001i	0.770997	−	0.560162i	−0.131267	−	0.991347i	$-0.541904\pi$
$71$	6.49654	−	4.72001i	0.770997	−	0.560162i	0.902264	+	0.431185i	$0.141904\pi$
$72$	0.422909	−	2.67014i	0.0498403	−	0.314679i
$73$	−3.85754	+	7.57085i	−0.451491	+	0.886101i	0.547300	+	0.836937i	$0.315656\pi$
$73$	−3.85754	+	7.57085i	−0.451491	+	0.886101i	−0.998791	+	0.0491643i	$0.984344\pi$
$74$	−3.43791	+	10.5808i	−0.399649	+	1.22999i
$75$		0			0
$76$			0.870202i			0.0998190i
$77$	−1.20204	−	5.93884i	−0.136985	−	0.676793i
$78$	−4.81048	+	4.81048i	−0.544679	+	0.544679i
$79$	−7.68588	−	5.58412i	−0.864729	−	0.628262i	0.0644385	−	0.997922i	$-0.479474\pi$
$79$	−7.68588	−	5.58412i	−0.864729	−	0.628262i	−0.929167	+	0.369659i	$0.879474\pi$
$80$		0			0
$81$	3.47445	+	10.6933i	0.386050	+	1.18814i
$82$	−12.4473	−	1.97146i	−1.37458	−	0.217712i
$83$	−8.70250	−	1.37834i	−0.955223	−	0.151292i	−0.340683	−	0.940178i	$-0.610658\pi$
$83$	−8.70250	−	1.37834i	−0.955223	−	0.151292i	−0.614540	+	0.788886i	$0.710658\pi$
$84$	1.04138	+	3.20505i	0.113624	+	0.349700i
$85$		0			0
$86$	−9.54730	−	6.93652i	−1.02951	−	0.747984i
$87$	−11.0587	+	11.0587i	−1.18562	+	1.18562i
$88$	5.74431	+	2.62483i	0.612345	+	0.279807i
$89$			12.0425i			1.27651i	0.769826	+	0.638253i	$0.220343\pi$
$89$			12.0425i			1.27651i	−0.769826	+	0.638253i	$0.779657\pi$
$90$		0			0
$91$	−1.07699	+	3.31463i	−0.112899	+	0.347467i
$92$	2.51086	−	4.92784i	0.261775	−	0.513763i
$93$	2.03721	−	12.8625i	0.211249	−	1.33378i
$94$	0.256557	−	0.186399i	0.0264618	−	0.0192256i
$95$		0			0
$96$	−9.29237	−	3.01928i	−0.948399	−	0.308154i
$97$	0.226246	+	1.42846i	0.0229718	+	0.145038i	0.996508	−	0.0834932i	$-0.0266077\pi$
$97$	0.226246	+	1.42846i	0.0229718	+	0.145038i	−0.973537	+	0.228531i	$0.926608\pi$
$98$	−4.39279	−	4.39279i	−0.443739	−	0.443739i
$99$	4.70434	−	0.200646i	0.472803	−	0.0201657i
$100$		0			0
$101$	0.671747	−	0.924580i	0.0668413	−	0.0919991i	−0.774288	−	0.632834i	$-0.781892\pi$
$101$	0.671747	−	0.924580i	0.0668413	−	0.0919991i	0.841129	+	0.540835i	$0.181892\pi$
$102$	24.3935	−	12.4291i	2.41532	−	1.23067i
$103$	9.26333	+	4.71990i	0.912743	+	0.465066i	0.846289	−	0.532723i	$-0.178831\pi$
$103$	9.26333	+	4.71990i	0.912743	+	0.465066i	0.0664541	+	0.997789i	$0.478831\pi$
$104$	−2.13522	−	2.93887i	−0.209375	−	0.288180i
$105$		0			0
$106$	5.95363	−	1.93445i	0.578268	−	0.187891i
$107$	4.83164	+	9.48263i	0.467092	+	0.916720i	0.997613	+	0.0690483i	$0.0219963\pi$
$107$	4.83164	+	9.48263i	0.467092	+	0.916720i	−0.530521	+	0.847672i	$0.678004\pi$
$108$	2.87915	−	0.456013i	0.277047	−	0.0438799i
$109$	−8.68844			−0.832202			−0.416101	−	0.909318i	$-0.636604\pi$
$109$	−8.68844			−0.832202			−0.416101	+	0.909318i	$0.636604\pi$
$110$		0			0
$111$	−13.7882			−1.30872
$112$	−8.99511	+	1.42469i	−0.849958	+	0.134620i
$113$	8.90205	+	17.4713i	0.837434	+	1.64356i	0.763061	+	0.646327i	$0.223696\pi$
$113$	8.90205	+	17.4713i	0.837434	+	1.64356i	0.0743735	+	0.997230i	$0.476304\pi$
$114$	−3.36369	+	1.09293i	−0.315038	+	0.102362i
$115$		0			0
$116$	3.83665	+	5.28069i	0.356224	+	0.490300i
$117$	−2.41314	−	1.22956i	−0.223095	−	0.113672i
$118$	−8.02690	+	4.08991i	−0.738936	+	0.376507i
$119$	8.24399	−	11.3469i	0.755725	−	1.04017i
$120$		0			0
$121$	−2.49606	+	10.7131i	−0.226915	+	0.973915i
$122$	6.67557	+	6.67557i	0.604377	+	0.604377i
$123$	−2.44334	−	15.4266i	−0.220308	−	1.39097i
$124$	−5.16920	−	1.67957i	−0.464208	−	0.150830i
$125$		0			0
$126$	−3.55942	+	2.58607i	−0.317099	+	0.230386i
$127$	0.919553	−	5.80583i	0.0815971	−	0.515184i	−0.912708	−	0.408612i	$-0.866013\pi$
$127$	0.919553	−	5.80583i	0.0815971	−	0.515184i	0.994305	−	0.106571i	$-0.0339872\pi$
$128$	5.82657	−	11.4353i	0.515001	−	1.01075i
$129$	4.51960	−	13.9099i	0.397929	−	1.22470i
$130$		0			0
$131$			7.99047i			0.698131i	0.937098	+	0.349065i	$0.113501\pi$
$131$			7.99047i			0.698131i	−0.937098	+	0.349065i	$0.886499\pi$
$132$	0.698690	−	6.07786i	0.0608132	−	0.529010i
$133$	−1.28121	+	1.28121i	−0.111095	+	0.111095i
$134$	11.6263	+	8.44698i	1.00436	+	0.729708i
$135$		0			0
$136$	4.51747	+	13.9034i	0.387370	+	1.19220i
$137$	8.58986	+	1.36050i	0.733882	+	0.116235i	0.512179	−	0.858879i	$-0.328839\pi$
$137$	8.58986	+	1.36050i	0.733882	+	0.116235i	0.221703	+	0.975114i	$0.428839\pi$
$138$	22.2016	+	3.51639i	1.88993	+	0.299335i
$139$	−3.74767	−	11.5341i	−0.317873	−	0.978313i	−0.974556	−	0.224146i	$-0.928041\pi$
$139$	−3.74767	−	11.5341i	−0.317873	−	0.978313i	0.656682	−	0.754167i	$-0.271959\pi$
$140$		0			0
$141$	0.317964	+	0.231014i	0.0267774	+	0.0194549i
$142$	9.63188	−	9.63188i	0.808289	−	0.808289i
$143$	4.27919	−	4.66048i	0.357844	−	0.389729i
$144$		−	7.07717i		−	0.589764i
$145$		0			0
$146$	−4.45398	+	13.7079i	−0.368614	+	1.13448i
$147$	3.49540	−	6.86011i	0.288296	−	0.565813i
$148$	−0.900226	+	5.68380i	−0.0739981	+	0.467206i
$149$	2.97274	−	2.15982i	0.243536	−	0.176940i	−0.459321	−	0.888270i	$-0.651907\pi$
$149$	2.97274	−	2.15982i	0.243536	−	0.176940i	0.702857	+	0.711331i	$0.251907\pi$
$150$		0			0
$151$	−7.79816	−	2.53377i	−0.634605	−	0.206196i	−0.0259910	−	0.999662i	$-0.508274\pi$
$151$	−7.79816	−	2.53377i	−0.634605	−	0.206196i	−0.608614	+	0.793467i	$0.708274\pi$
$152$	−0.295435	−	1.86530i	−0.0239629	−	0.151296i
$153$	7.70685	+	7.70685i	0.623062	+	0.623062i
$154$	−3.58984	−	9.63103i	−0.289277	−	0.776091i
$155$		0			0
$156$	−2.06837	+	2.84687i	−0.165602	+	0.227932i
$157$	12.6987	−	6.47032i	1.01347	−	0.516388i	0.133313	−	0.991074i	$-0.457438\pi$
$157$	12.6987	−	6.47032i	1.01347	−	0.516388i	0.880155	+	0.474686i	$0.157438\pi$
$158$	−14.3588	−	7.31618i	−1.14233	−	0.582044i
$159$	4.56025	+	6.27665i	0.361652	+	0.497771i
$160$		0			0
$161$	10.9521	−	3.55855i	0.863145	−	0.280453i
$162$	8.65869	+	16.9936i	0.680291	+	1.33515i
$163$	−15.1117	+	2.39345i	−1.18364	+	0.187470i	−0.717061	−	0.697011i	$-0.754513\pi$
$163$	−15.1117	+	2.39345i	−1.18364	+	0.187470i	−0.466577	+	0.884481i	$0.654513\pi$
$164$	−6.51874			−0.509028
$165$		0			0
$166$	−14.9460			−1.16004
$167$	−3.80999	+	0.603443i	−0.294826	+	0.0466959i	−0.302095	−	0.953278i	$-0.597686\pi$
$167$	−3.80999	+	0.603443i	−0.294826	+	0.0466959i	0.00726928	+	0.999974i	$0.497686\pi$
$168$	−3.32036	−	6.51657i	−0.256171	−	0.502764i
$169$	8.90262	−	2.89264i	0.684817	−	0.222510i
$170$		0			0
$171$	−0.827611	−	1.13911i	−0.0632890	−	0.0871098i
$172$	−5.43890	−	2.77126i	−0.414712	−	0.211306i
$173$	1.31437	−	0.669703i	0.0999295	−	0.0509166i	−0.403311	−	0.915063i	$-0.632141\pi$
$173$	1.31437	−	0.669703i	0.0999295	−	0.0509166i	0.503241	+	0.864146i	$0.332141\pi$
$174$	−15.5934	+	21.4625i	−1.18213	+	1.62707i
$175$		0			0
$176$	15.9275	+	4.43438i	1.20058	+	0.334254i
$177$	−7.89490	−	7.89490i	−0.593417	−	0.593417i
$178$	3.19560	+	20.1762i	0.239520	+	1.51227i
$179$	3.27043	+	1.06263i	0.244444	+	0.0794246i	0.428677	−	0.903458i	$-0.358980\pi$
$179$	3.27043	+	1.06263i	0.244444	+	0.0794246i	−0.184233	+	0.982883i	$0.558980\pi$
$180$		0			0
$181$	0.807847	−	0.586935i	0.0600468	−	0.0436265i	−0.557357	−	0.830273i	$-0.688185\pi$
$181$	0.807847	−	0.586935i	0.0600468	−	0.0436265i	0.617404	+	0.786646i	$0.288185\pi$
$182$	−0.924832	+	5.83916i	−0.0685531	+	0.432827i
$183$	−5.31183	+	10.4251i	−0.392662	+	0.770643i
$184$	−3.70909	+	11.4154i	−0.273438	+	0.841554i
$185$		0			0
$186$		−	22.0905i		−	1.61976i
$187$	−22.1736	+	12.5157i	−1.62149	+	0.915240i
$188$	0.115989	−	0.115989i	0.00845938	−	0.00845938i
$189$	4.91040	+	3.56762i	0.357179	+	0.259506i
$190$		0			0
$191$	−7.77655	−	23.9338i	−0.562691	−	1.73179i	−0.674713	−	0.738080i	$-0.735733\pi$
$191$	−7.77655	−	23.9338i	−0.562691	−	1.73179i	0.112022	−	0.993706i	$-0.464267\pi$
$192$	4.33210	+	0.686138i	0.312643	+	0.0495177i
$193$	−1.56221	−	0.247430i	−0.112450	−	0.0178104i	0.0999556	−	0.994992i	$-0.468130\pi$
$193$	−1.56221	−	0.247430i	−0.112450	−	0.0178104i	−0.212406	+	0.977182i	$0.568130\pi$
$194$	0.758110	+	2.33322i	0.0544291	+	0.167516i
$195$		0			0
$196$	−2.59968	−	1.88878i	−0.185692	−	0.134913i
$197$	9.20446	−	9.20446i	0.655791	−	0.655791i	−0.298591	−	0.954381i	$-0.596516\pi$
$197$	9.20446	−	9.20446i	0.655791	−	0.655791i	0.954381	+	0.298591i	$0.0965165\pi$
$198$	7.82846	−	1.58450i	0.556344	−	0.112606i
$199$			26.6701i			1.89059i	0.326213	+	0.945296i	$0.394227\pi$
$199$			26.6701i			1.89059i	−0.326213	+	0.945296i	$0.605773\pi$
$200$		0			0
$201$	−5.50376	+	16.9388i	−0.388205	+	1.19477i
$202$	0.880107	−	1.72731i	0.0619241	−	0.121533i
$203$	−2.12608	+	13.4236i	−0.149222	+	0.942149i
$204$	11.4567	−	8.32375i	0.802127	−	0.582779i
$205$		0			0
$206$	16.7724	+	5.44968i	1.16859	+	0.379697i
$207$	1.39990	+	8.83860i	0.0972995	+	0.614325i
$208$	−6.72439	−	6.72439i	−0.466253	−	0.466253i
$209$	3.08218	−	1.14884i	0.213199	−	0.0794671i
$210$		0			0
$211$	6.76218	−	9.30735i	0.465528	−	0.640744i	−0.510116	−	0.860106i	$-0.670397\pi$
$211$	6.76218	−	9.30735i	0.465528	−	0.640744i	0.975644	+	0.219362i	$0.0703974\pi$
$212$	2.88512	−	1.47004i	0.198151	−	0.100963i
$213$	15.0419	+	7.66421i	1.03065	+	0.525143i
$214$	10.6113	+	14.6052i	0.725373	+	0.998390i
$215$		0			0
$216$	−6.01673	+	1.95495i	−0.409386	+	0.133018i
$217$	−5.13781	−	10.0835i	−0.348777	−	0.684514i
$218$	−14.5567	+	2.30556i	−0.985906	+	0.156152i
$219$	−17.8632			−1.20709
$220$		0			0
$221$	14.6454			0.985153
$222$	−23.1009	+	3.65882i	−1.55043	+	0.245564i
$223$	−4.36971	−	8.57604i	−0.292617	−	0.574294i	0.697160	−	0.716916i	$-0.254447\pi$
$223$	−4.36971	−	8.57604i	−0.292617	−	0.574294i	−0.989777	+	0.142622i	$0.954447\pi$
$224$	−8.07521	+	2.62380i	−0.539548	+	0.175310i
$225$		0			0
$226$	19.5508	+	26.9093i	1.30050	+	1.78998i
$227$	5.93906	+	3.02610i	0.394189	+	0.200849i	0.639839	−	0.768509i	$-0.279001\pi$
$227$	5.93906	+	3.02610i	0.394189	+	0.200849i	−0.245649	+	0.969359i	$0.579001\pi$
$228$	−1.63004	+	0.830545i	−0.107952	+	0.0550042i
$229$	6.52603	−	8.98231i	0.431252	−	0.593567i	−0.536988	−	0.843590i	$-0.680438\pi$
$229$	6.52603	−	8.98231i	0.431252	−	0.593567i	0.968240	+	0.250022i	$0.0804380\pi$
$230$		0			0
$231$	9.97720	−	7.91982i	0.656451	−	0.521086i
$232$	−10.0168	−	10.0168i	−0.657633	−	0.657633i
$233$	−0.384230	−	2.42593i	−0.0251717	−	0.158928i	0.971901	−	0.235391i	$-0.0756372\pi$
$233$	−0.384230	−	2.42593i	−0.0251717	−	0.158928i	−0.997072	+	0.0764634i	$0.975637\pi$
$234$	−4.36928	−	1.41966i	−0.285629	−	0.0928064i
$235$		0			0
$236$	−3.76992	+	2.73901i	−0.245401	+	0.178294i
$237$	3.12439	−	19.7266i	0.202951	−	1.28138i
$238$	10.8011	−	21.1983i	0.700130	−	1.37408i
$239$	4.66589	−	14.3601i	0.301811	−	0.928879i	−0.679037	−	0.734104i	$-0.737602\pi$
$239$	4.66589	−	14.3601i	0.301811	−	0.928879i	0.980848	−	0.194775i	$-0.0623976\pi$
$240$		0			0
$241$		−	19.2391i		−	1.23930i	−0.784878	−	0.619650i	$-0.787275\pi$
$241$		−	19.2391i		−	1.23930i	0.784878	−	0.619650i	$-0.212725\pi$
$242$	−1.33912	+	18.6112i	−0.0860818	+	1.19637i
$243$	−9.66656	+	9.66656i	−0.620110	+	0.620110i
$244$	3.95064	+	2.87031i	0.252914	+	0.183753i
$245$		0			0
$246$	−8.18720	−	25.1976i	−0.521996	−	1.60654i
$247$	−1.86868	−	0.295970i	−0.118902	−	0.0188321i
$248$	11.6505	+	1.84526i	0.739810	+	0.117174i
$249$	−5.72404	−	17.6168i	−0.362746	−	1.11642i
$250$		0			0
$251$	−4.40349	−	3.19932i	−0.277946	−	0.201939i	0.440075	−	0.897961i	$-0.354952\pi$
$251$	−4.40349	−	3.19932i	−0.277946	−	0.201939i	−0.718021	+	0.696022i	$0.754952\pi$
$252$	−1.60922	+	1.60922i	−0.101371	+	0.101371i
$253$	−20.7688	−	2.38752i	−1.30573	−	0.150102i
$254$		−	9.97117i		−	0.625647i
$255$		0			0
$256$	5.43803	−	16.7365i	0.339877	−	1.04603i
$257$	−3.94812	+	7.74863i	−0.246277	+	0.483346i	−0.980744	−	0.195299i	$-0.937432\pi$
$257$	−3.94812	+	7.74863i	−0.246277	+	0.483346i	0.734467	+	0.678645i	$0.237432\pi$
$258$	3.88107	−	24.5041i	0.241625	−	1.52556i
$259$	−9.69374	+	7.04292i	−0.602340	+	0.437626i
$260$		0			0
$261$	−10.0445	−	3.26365i	−0.621737	−	0.202015i
$262$	2.12035	+	13.3873i	0.130995	+	0.827072i
$263$	0.777404	+	0.777404i	0.0479368	+	0.0479368i	0.730669	−	0.682732i	$-0.239208\pi$
$263$	0.777404	+	0.777404i	0.0479368	+	0.0479368i	−0.682732	+	0.730669i	$0.739208\pi$
$264$	0.565781	+	13.2653i	0.0348214	+	0.816421i
$265$		0			0
$266$	−1.80657	+	2.48653i	−0.110768	+	0.152459i
$267$	−22.5577	+	11.4937i	−1.38051	+	0.703405i
$268$	6.62324	+	3.37471i	0.404579	+	0.206143i
$269$	−18.0692	−	24.8702i	−1.10170	−	1.51636i	−0.833110	−	0.553108i	$-0.813442\pi$
$269$	−18.0692	−	24.8702i	−1.10170	−	1.51636i	−0.268592	−	0.963254i	$-0.586558\pi$
$270$		0			0
$271$	−26.6152	+	8.64779i	−1.61676	+	0.525316i	−0.971173	−	0.238374i	$-0.923386\pi$
$271$	−26.6152	+	8.64779i	−1.61676	+	0.525316i	−0.645583	+	0.763690i	$0.723386\pi$
$272$	17.3742	+	34.0988i	1.05347	+	2.06754i
$273$	−7.23677	+	1.14619i	−0.437989	+	0.0693707i
$274$	14.7526			0.891236
$275$		0			0
$276$	11.6271			0.699870
$277$	12.9114	−	2.04496i	0.775769	−	0.122870i	0.244018	−	0.969771i	$-0.421534\pi$
$277$	12.9114	−	2.04496i	0.775769	−	0.122870i	0.531751	+	0.846901i	$0.321534\pi$
$278$	−9.33959	−	18.3300i	−0.560151	−	1.09936i
$279$	8.36394	−	2.71761i	0.500736	−	0.162699i
$280$		0			0
$281$	3.92934	+	5.40827i	0.234405	+	0.322630i	0.909973	−	0.414667i	$-0.136102\pi$
$281$	3.92934	+	5.40827i	0.234405	+	0.322630i	−0.675569	+	0.737297i	$0.736102\pi$
$282$	0.594022	+	0.302670i	0.0353735	+	0.0180237i
$283$	−3.87364	+	1.97372i	−0.230264	+	0.117325i	−0.565316	−	0.824874i	$-0.691246\pi$
$283$	−3.87364	+	1.97372i	−0.230264	+	0.117325i	0.335053	+	0.942199i	$0.391246\pi$
$284$	4.14144	−	5.70021i	0.245750	−	0.338245i
$285$		0			0
$286$	5.93271	−	8.94375i	0.350808	−	0.528855i
$287$	−9.59761	−	9.59761i	−0.566529	−	0.566529i
$288$	−1.03217	−	6.51689i	−0.0608214	−	0.384012i
$289$	−39.8847	−	12.9593i	−2.34616	−	0.762314i
$290$		0			0
$291$	−2.45981	+	1.78716i	−0.144197	+	0.104765i
$292$	−1.16629	+	7.36364i	−0.0682517	+	0.430925i
$293$	10.2400	−	20.0971i	0.598226	−	1.17408i	−0.371166	−	0.928567i	$-0.621042\pi$
$293$	10.2400	−	20.0971i	0.598226	−	1.17408i	0.969392	−	0.245518i	$-0.0789581\pi$
$294$	4.03585	−	12.4211i	0.235375	−	0.724411i
$295$		0			0
$296$		−	12.4890i		−	0.725909i
$297$	−5.41622	−	9.59569i	−0.314281	−	0.556799i
$298$	4.40744	−	4.40744i	0.255316	−	0.255316i
$299$	9.72813	+	7.06790i	0.562592	+	0.408747i
$300$		0			0
$301$	−3.92760	−	12.0879i	−0.226383	−	0.696735i
$302$	−13.7375	−	2.17580i	−0.790504	−	0.125203i
$303$	2.37303	+	0.375851i	0.136327	+	0.0215921i
$304$	−1.52776	−	4.70198i	−0.0876233	−	0.269677i
$305$		0			0
$306$	14.9572	+	10.8671i	0.855048	+	0.621229i
$307$	−9.37539	+	9.37539i	−0.535082	+	0.535082i	−0.922080	−	0.386998i	$-0.873512\pi$
$307$	−9.37539	+	9.37539i	−0.535082	+	0.535082i	0.386998	+	0.922080i	$0.373512\pi$
$308$	−2.61332	−	4.62991i	−0.148908	−	0.263814i
$309$			21.8566i			1.24338i
$310$		0			0
$311$	−1.62851	+	5.01205i	−0.0923445	+	0.284207i	−0.986553	−	0.163444i	$-0.947740\pi$
$311$	−1.62851	+	5.01205i	−0.0923445	+	0.284207i	0.894208	+	0.447652i	$0.147740\pi$
$312$	3.46710	−	6.80456i	0.196286	−	0.385232i
$313$	−2.96299	+	18.7076i	−0.167478	+	1.05741i	0.750525	+	0.660842i	$0.229800\pi$
$313$	−2.96299	+	18.7076i	−0.167478	+	1.05741i	−0.918003	+	0.396573i	$0.870200\pi$
$314$	19.5586	−	14.2102i	1.10376	−	0.801927i
$315$		0			0
$316$	−7.92777	−	2.57589i	−0.445972	−	0.144905i
$317$	0.0412836	+	0.260655i	0.00231872	+	0.0146398i	0.988821	−	0.149110i	$-0.0476409\pi$
$317$	0.0412836	+	0.260655i	0.00231872	+	0.0146398i	−0.986502	+	0.163750i	$0.947641\pi$
$318$	9.30588	+	9.30588i	0.521848	+	0.521848i
$319$	13.6386	−	20.5607i	0.763616	−	1.15118i
$320$		0			0
$321$	−13.1511	+	18.1010i	−0.734024	+	1.01030i
$322$	17.4050	−	8.86827i	0.969941	−	0.494209i
$323$	6.78402	+	3.45663i	0.377473	+	0.192332i
$324$	5.79871	+	7.98124i	0.322150	+	0.443402i
$325$		0			0
$326$	−24.6832	+	8.02005i	−1.36707	+	0.444189i
$327$	−8.29249	−	16.2749i	−0.458576	−	0.900006i
$328$	13.9731	−	2.21312i	0.771535	−	0.122199i
$329$	0.341545			0.0188300
$330$		0			0
$331$	6.20281			0.340937			0.170469	−	0.985363i	$-0.445472\pi$
$331$	6.20281			0.340937			0.170469	+	0.985363i	$0.445472\pi$
$332$	−7.63577	+	1.20939i	−0.419067	+	0.0663737i
$333$	−4.22721	−	8.29636i	−0.231650	−	0.454638i
$334$	−6.22318	+	2.02203i	−0.340517	+	0.110641i
$335$		0			0
$336$	−11.2539	−	15.4896i	−0.613949	−	0.845028i
$337$	−7.42329	−	3.78235i	−0.404372	−	0.206038i	0.239961	−	0.970782i	$-0.422865\pi$
$337$	−7.42329	−	3.78235i	−0.404372	−	0.206038i	−0.644334	+	0.764744i	$0.722865\pi$
$338$	14.1480	−	7.20875i	0.769548	−	0.392104i
$339$	−24.2303	+	33.3501i	−1.31601	+	1.81133i
$340$		0			0
$341$	0.875471	+	20.5262i	0.0474094	+	1.11156i
$342$	−1.68886	−	1.68886i	−0.0913233	−	0.0913233i
$343$	−3.04724	−	19.2395i	−0.164536	−	1.03884i
$344$	12.5993	+	4.09375i	0.679307	+	0.220720i
$345$		0			0
$346$	2.02439	−	1.47081i	0.108832	−	0.0790712i
$347$	3.93024	−	24.8146i	0.210986	−	1.33212i	−0.623818	−	0.781570i	$-0.714419\pi$
$347$	3.93024	−	24.8146i	0.210986	−	1.33212i	0.834805	−	0.550546i	$-0.185581\pi$
$348$	−6.22983	+	12.2267i	−0.333954	+	0.655422i
$349$	−10.1484	+	31.2335i	−0.543231	+	1.67189i	0.181929	+	0.983312i	$0.441766\pi$
$349$	−10.1484	+	31.2335i	−0.543231	+	1.67189i	−0.725160	+	0.688580i	$0.758234\pi$
$350$		0			0
$351$			6.33783i			0.338289i
$352$	15.3133	+	1.76037i	0.816203	+	0.0938279i
$353$	0.877338	−	0.877338i	0.0466960	−	0.0466960i	−0.683373	−	0.730069i	$-0.739488\pi$
$353$	0.877338	−	0.877338i	0.0466960	−	0.0466960i	0.730069	+	0.683373i	$0.239488\pi$
$354$	−15.3222	−	11.1322i	−0.814366	−	0.591671i
$355$		0			0
$356$	3.26520	+	10.0492i	0.173055	+	0.532609i
$357$	29.1229	+	4.61262i	1.54135	+	0.244126i
$358$	5.76131	+	0.912501i	0.304494	+	0.0482272i
$359$	−3.90630	−	12.0224i	−0.206167	−	0.634516i	−0.999663	−	0.0259412i	$-0.991742\pi$
$359$	−3.90630	−	12.0224i	−0.206167	−	0.634516i	0.793497	−	0.608574i	$-0.208258\pi$
$360$		0			0
$361$	14.5756	+	10.5898i	0.767135	+	0.557356i
$362$	1.19773	−	1.19773i	0.0629512	−	0.0629512i
$363$	−22.4497	+	5.54930i	−1.17830	+	0.291263i
$364$			3.05800i			0.160283i
$365$		0			0
$366$	−6.13313	+	18.8758i	−0.320584	+	0.986655i
$367$	−4.49225	+	8.81653i	−0.234493	+	0.460219i	−0.978027	−	0.208480i	$-0.933148\pi$
$367$	−4.49225	+	8.81653i	−0.234493	+	0.460219i	0.743533	+	0.668699i	$0.233148\pi$
$368$	−4.91544	+	31.0348i	−0.256235	+	1.61780i
$369$	8.53314	−	6.19969i	0.444217	−	0.322743i
$370$		0			0
$371$	6.41215	+	2.08344i	0.332902	+	0.108167i
$372$	−1.78750	−	11.2858i	−0.0926775	−	0.585142i
$373$	4.69763	+	4.69763i	0.243234	+	0.243234i	0.818187	−	0.574953i	$-0.194980\pi$
$373$	4.69763	+	4.69763i	0.243234	+	0.243234i	−0.574953	+	0.818187i	$0.694980\pi$
$374$	−33.8287	+	26.8530i	−1.74924	+	1.38853i
$375$		0			0
$376$	−0.209248	+	0.288005i	−0.0107911	+	0.0148527i
$377$	−12.6447	+	6.44282i	−0.651237	+	0.331822i
$378$	9.17365	+	4.67421i	0.471842	+	0.240415i
$379$	16.9556	+	23.3374i	0.870951	+	1.19876i	0.978846	+	0.204599i	$0.0655889\pi$
$379$	16.9556	+	23.3374i	0.870951	+	1.19876i	−0.107895	+	0.994162i	$0.534411\pi$
$380$		0			0
$381$	11.7529	−	3.81876i	0.602122	−	0.195641i
$382$	−19.3800	−	38.0353i	−0.991566	−	1.94606i
$383$	6.29331	−	0.996762i	0.321573	−	0.0509322i	0.00643884	−	0.999979i	$-0.497950\pi$
$383$	6.29331	−	0.996762i	0.321573	−	0.0509322i	0.315134	+	0.949047i	$0.397950\pi$
$384$	26.9813			1.37688
$385$		0			0
$386$	−2.68300			−0.136561
$387$	9.75523	−	1.54508i	0.495886	−	0.0785407i
$388$	0.576107	+	1.13067i	0.0292474	+	0.0574013i
$389$	22.9077	−	7.44317i	1.16147	−	0.377384i	0.336016	−	0.941856i	$-0.390920\pi$
$389$	22.9077	−	7.44317i	1.16147	−	0.377384i	0.825452	+	0.564473i	$0.190920\pi$
$390$		0			0
$391$	−28.4433	−	39.1489i	−1.43844	−	1.97984i
$392$	6.21374	+	3.16606i	0.313841	+	0.159910i
$393$	−14.9675	+	7.62633i	−0.755011	+	0.384697i
$394$	12.9788	−	17.8638i	0.653862	−	0.899963i
$395$		0			0
$396$	3.87127	−	1.44296i	0.194538	−	0.0725115i
$397$	18.7789	+	18.7789i	0.942488	+	0.942488i	0.998434	−	0.0559459i	$-0.0178174\pi$
$397$	18.7789	+	18.7789i	0.942488	+	0.942488i	−0.0559459	+	0.998434i	$0.517817\pi$
$398$	7.07716	+	44.6834i	0.354746	+	2.23978i
$399$	−3.62274	−	1.17710i	−0.181364	−	0.0589287i
$400$		0			0
$401$	23.5567	−	17.1150i	1.17637	−	0.854680i	0.184609	−	0.982812i	$-0.440898\pi$
$401$	23.5567	−	17.1150i	1.17637	−	0.854680i	0.991757	+	0.128132i	$0.0408981\pi$
$402$	−4.72619	+	29.8400i	−0.235721	+	1.48828i
$403$	5.36487	−	10.5292i	0.267243	−	0.524495i
$404$	0.309869	−	0.953679i	0.0154166	−	0.0474473i
$405$		0			0
$406$			23.0542i			1.14416i
$407$	21.3200	−	4.31524i	1.05680	−	0.213899i
$408$	−21.7317	+	21.7317i	−1.07588	+	1.07588i
$409$	−1.43337	−	1.04140i	−0.0708754	−	0.0514940i	0.551783	−	0.833987i	$-0.313948\pi$
$409$	−1.43337	−	1.04140i	−0.0708754	−	0.0514940i	−0.622659	+	0.782493i	$0.713948\pi$
$410$		0			0
$411$	5.64996	+	17.3888i	0.278692	+	0.857725i
$412$	9.00980	+	1.42701i	0.443881	+	0.0703039i
$413$	−9.58316	−	1.51782i	−0.471557	−	0.0746872i
$414$	4.69081	+	14.4368i	0.230541	+	0.709531i
$415$		0			0
$416$	−7.17276	−	5.21132i	−0.351674	−	0.255506i
$417$	18.0285	−	18.0285i	0.882861	−	0.882861i
$418$	4.85907	−	2.74267i	0.237665	−	0.134148i
$419$		−	2.42901i		−	0.118665i	−0.998238	−	0.0593325i	$-0.981103\pi$
$419$		−	2.42901i		−	0.118665i	0.998238	−	0.0593325i	$-0.0188972\pi$
$420$		0			0
$421$	−3.71954	+	11.4476i	−0.181279	+	0.557920i	−0.999864	−	0.0164648i	$-0.994759\pi$
$421$	−3.71954	+	11.4476i	−0.181279	+	0.557920i	0.818585	+	0.574385i	$0.194759\pi$
$422$	8.85966	−	17.3881i	0.431281	−	0.846437i
$423$	−0.0415196	+	0.262144i	−0.00201875	+	0.0127459i
$424$	−5.68525	+	4.13058i	−0.276100	+	0.200599i
$425$		0			0
$426$	27.2351	+	8.84922i	1.31954	+	0.428746i
$427$	1.59059	+	10.0426i	0.0769739	+	0.485994i
$428$	6.60301	+	6.60301i	0.319168	+	0.319168i
$429$	12.8141	+	3.56756i	0.618668	+	0.172244i
$430$		0			0
$431$	7.72737	−	10.6358i	0.372214	−	0.512309i	−0.581287	−	0.813699i	$-0.697451\pi$
$431$	7.72737	−	10.6358i	0.372214	−	0.512309i	0.953501	+	0.301390i	$0.0974506\pi$
$432$	−14.7564	+	7.51875i	−0.709967	+	0.361746i
$433$	1.64539	+	0.838369i	0.0790724	+	0.0402894i	0.493080	−	0.869984i	$-0.335871\pi$
$433$	1.64539	+	0.838369i	0.0790724	+	0.0402894i	−0.414007	+	0.910274i	$0.635871\pi$
$434$	−11.2837	−	15.5307i	−0.541635	−	0.745497i
$435$		0			0
$436$	−7.25032	+	2.35577i	−0.347227	+	0.112821i
$437$	2.83808	+	5.57004i	0.135764	+	0.266451i
$438$	−29.9283	+	4.74018i	−1.43003	+	0.226494i
$439$	22.4529			1.07162			0.535809	−	0.844339i	$-0.320007\pi$
$439$	22.4529			1.07162			0.535809	+	0.844339i	$0.320007\pi$
$440$		0			0
$441$	5.19937			0.247589
$442$	24.5370	−	3.88628i	1.16711	−	0.184852i
$443$	10.3470	+	20.3071i	0.491600	+	0.964820i	0.994915	+	0.100717i	$0.0321137\pi$
$443$	10.3470	+	20.3071i	0.491600	+	0.964820i	−0.503315	+	0.864103i	$0.667886\pi$
$444$	−11.5059	+	3.73851i	−0.546048	+	0.177422i
$445$		0			0
$446$	−9.59680	−	13.2089i	−0.454421	−	0.625458i
$447$	6.88298	+	3.50705i	0.325554	+	0.165878i
$448$	3.39615	−	1.73042i	0.160453	−	0.0817549i
$449$	−0.523394	+	0.720390i	−0.0247005	+	0.0339973i	−0.821189	−	0.570657i	$-0.806689\pi$
$449$	−0.523394	+	0.720390i	−0.0247005	+	0.0339973i	0.796488	+	0.604654i	$0.206689\pi$
$450$		0			0
$451$	8.60605	+	23.0888i	0.405243	+	1.08721i
$452$	12.1657	+	12.1657i	0.572226	+	0.572226i
$453$	−2.69659	−	17.0256i	−0.126697	−	0.799931i
$454$	10.7534	+	3.49399i	0.504681	+	0.163981i
$455$		0			0
$456$	3.21206	−	2.33370i	0.150418	−	0.109285i
$457$	−3.98316	+	25.1487i	−0.186324	+	1.17641i	0.700277	+	0.713871i	$0.253060\pi$
$457$	−3.98316	+	25.1487i	−0.186324	+	1.17641i	−0.886601	+	0.462535i	$0.846940\pi$
$458$	8.55025	−	16.7808i	0.399527	−	0.784116i
$459$	7.88158	−	24.2570i	0.367881	−	1.13222i
$460$		0			0
$461$			18.6821i			0.870112i	0.900403	+	0.435056i	$0.143271\pi$
$461$			18.6821i			0.870112i	−0.900403	+	0.435056i	$0.856729\pi$
$462$	14.6143	−	15.9165i	0.679920	−	0.740503i
$463$	10.6534	−	10.6534i	0.495103	−	0.495103i	−0.414806	−	0.909910i	$-0.636151\pi$
$463$	10.6534	−	10.6534i	0.495103	−	0.495103i	0.909910	+	0.414806i	$0.136151\pi$
$464$	−30.0016	−	21.7975i	−1.39279	−	1.01192i
$465$		0			0
$466$	−1.28749	−	3.96247i	−0.0596416	−	0.183558i
$467$	−30.9301	−	4.89884i	−1.43127	−	0.226691i	−0.607820	−	0.794075i	$-0.707956\pi$
$467$	−30.9301	−	4.89884i	−1.43127	−	0.226691i	−0.823453	+	0.567384i	$0.807956\pi$
$468$	−2.34709	−	0.371743i	−0.108494	−	0.0171838i
$469$	4.78285	+	14.7201i	0.220851	+	0.679711i
$470$		0			0
$471$	24.2400	+	17.6114i	1.11692	+	0.811491i
$472$	7.15103	−	7.15103i	0.329153	−	0.329153i
$473$	−2.63512	+	22.9227i	−0.121163	+	1.05399i
$474$		−	33.8793i		−	1.55613i
$475$		0			0
$476$	3.80286	−	11.7040i	0.174304	−	0.536452i
$477$	−2.37858	+	4.66822i	−0.108908	+	0.213743i
$478$	4.00669	−	25.2973i	0.183262	−	1.15707i
$479$	−21.4322	+	15.5714i	−0.979262	+	0.711475i	−0.957544	−	0.288289i	$-0.906914\pi$
$479$	−21.4322	+	15.5714i	−0.979262	+	0.711475i	−0.0217183	+	0.999764i	$0.506914\pi$
$480$		0			0
$481$	−11.8993	−	3.86632i	−0.542561	−	0.176289i
$482$	−5.10528	−	32.2334i	−0.232539	−	1.46819i
$483$	17.1187	+	17.1187i	0.778930	+	0.778930i
$484$	0.821816	+	9.61660i	0.0373553	+	0.437118i
$485$		0			0
$486$	−13.6304	+	18.7606i	−0.618286	+	0.850997i
$487$	9.91008	−	5.04944i	0.449068	−	0.228812i	−0.214805	−	0.976657i	$-0.568911\pi$
$487$	9.91008	−	5.04944i	0.449068	−	0.228812i	0.663873	+	0.747845i	$0.268911\pi$
$488$	−9.44279	−	4.81134i	−0.427455	−	0.217799i
$489$	−18.9064	−	26.0224i	−0.854975	−	1.17677i
$490$		0			0
$491$	−11.5128	+	3.74073i	−0.519565	+	0.168817i	−0.557048	−	0.830480i	$-0.688066\pi$
$491$	−11.5128	+	3.74073i	−0.519565	+	0.168817i	0.0374828	+	0.999297i	$0.488066\pi$
$492$	−6.22167	−	12.2107i	−0.280494	−	0.550501i
$493$	56.4078	−	8.93412i	2.54048	−	0.402373i
$494$	−3.20936			−0.144396
$495$		0			0
$496$	30.8795			1.38653
$497$	14.4900	−	2.29499i	0.649964	−	0.102944i
$498$	−14.2649	−	27.9965i	−0.639226	−	1.25455i
$499$	14.9943	−	4.87193i	0.671235	−	0.218098i	0.0464812	−	0.998919i	$-0.485199\pi$
$499$	14.9943	−	4.87193i	0.671235	−	0.218098i	0.624754	+	0.780822i	$0.285199\pi$
$500$		0			0
$501$	−4.76672	−	6.56082i	−0.212961	−	0.293116i
$502$	−8.22663	−	4.19168i	−0.367173	−	0.187084i
$503$	23.4296	−	11.9380i	1.04468	−	0.532289i	0.154541	−	0.987986i	$-0.450610\pi$
$503$	23.4296	−	11.9380i	1.04468	−	0.532289i	0.890135	+	0.455697i	$0.150610\pi$
$504$	2.90307	−	3.99573i	0.129313	−	0.177984i
$505$		0			0
$506$	−35.4299	+	1.51113i	−1.57505	+	0.0671780i
$507$	13.9153	+	13.9153i	0.618001	+	0.618001i
$508$	−0.806836	−	5.09417i	−0.0357976	−	0.226017i
$509$	13.8254	+	4.49215i	0.612800	+	0.199111i	0.598941	−	0.800793i	$-0.295588\pi$
$509$	13.8254	+	4.49215i	0.612800	+	0.199111i	0.0138592	+	0.999904i	$0.495588\pi$
$510$		0			0
$511$	−12.5587	+	9.12444i	−0.555565	+	0.403641i
$512$	0.654349	−	4.13140i	0.0289184	−	0.182584i
$513$	−1.49587	+	2.93581i	−0.0660443	+	0.129619i
$514$	−4.55857	+	14.0298i	−0.201070	+	0.618829i
$515$		0			0
$516$		−	12.8330i		−	0.564939i
$517$	−0.563953	−	0.257695i	−0.0248026	−	0.0113334i
$518$	−14.3721	+	14.3721i	−0.631475	+	0.631475i
$519$	2.50894	+	1.82285i	0.110130	+	0.0800142i
$520$		0			0
$521$	−2.48594	−	7.65095i	−0.108911	−	0.335194i	0.881717	−	0.471778i	$-0.156388\pi$
$521$	−2.48594	−	7.65095i	−0.108911	−	0.335194i	−0.990629	+	0.136584i	$0.956388\pi$
$522$	−17.6947	−	2.80256i	−0.774475	−	0.122665i
$523$	−22.1131	−	3.50238i	−0.966940	−	0.153148i	−0.347058	−	0.937844i	$-0.612819\pi$
$523$	−22.1131	−	3.50238i	−0.966940	−	0.153148i	−0.619882	+	0.784695i	$0.712819\pi$
$524$	2.16653	+	6.66788i	0.0946451	+	0.291288i
$525$		0			0
$526$	1.50876	+	1.09618i	0.0657852	+	0.0477958i
$527$	−33.6270	+	33.6270i	−1.46481	+	1.46481i
$528$	6.89532	+	34.0673i	0.300080	+	1.48259i
$529$		−	16.7314i		−	0.727451i
$530$		0			0
$531$	2.32994	−	7.17081i	0.101111	−	0.311187i
$532$	−0.721756	+	1.41653i	−0.0312921	+	0.0614142i
$533$	2.21713	−	13.9984i	0.0960347	−	0.606339i
$534$	−34.7435	+	25.2427i	−1.50350	+	1.09236i
$535$		0			0
$536$	−15.3428	−	4.98518i	−0.662709	−	0.215327i
$537$	1.13091	+	7.14028i	0.0488024	+	0.308126i
$538$	−36.8730	−	36.8730i	−1.58971	−	1.58971i
$539$	−3.25780	+	11.7014i	−0.140323	+	0.504017i
$540$		0			0
$541$	9.36221	−	12.8860i	0.402513	−	0.554011i	−0.558860	−	0.829262i	$-0.688761\pi$
$541$	9.36221	−	12.8860i	0.402513	−	0.554011i	0.961372	+	0.275251i	$0.0887609\pi$
$542$	−42.2966	+	21.5512i	−1.81680	+	0.925703i
$543$	1.87046	+	0.953047i	0.0802691	+	0.0408992i
$544$	20.9719	+	28.8653i	0.899163	+	1.23759i
$545$		0			0
$546$	−11.8204	+	3.84069i	−0.505867	+	0.164366i
$547$	−3.77957	−	7.41782i	−0.161603	−	0.317163i	0.795979	−	0.605324i	$-0.206956\pi$
$547$	−3.77957	−	7.41782i	−0.161603	−	0.317163i	−0.957582	+	0.288161i	$0.906956\pi$
$548$	7.53694	−	1.19373i	0.321962	−	0.0509938i
$549$	−7.90129			−0.337219
$550$		0			0
$551$	−7.37794			−0.314311
$552$	−24.9230	+	3.94742i	−1.06080	+	0.168013i
$553$	−7.87964	−	15.4647i	−0.335076	−	0.657624i
$554$	21.0892	−	6.85230i	0.895995	−	0.291126i
$555$		0			0
$556$	−6.25470	−	8.60886i	−0.265259	−	0.365097i
$557$	−10.2017	−	5.19803i	−0.432260	−	0.220247i	0.224302	−	0.974520i	$-0.427990\pi$
$557$	−10.2017	−	5.19803i	−0.432260	−	0.220247i	−0.656562	+	0.754272i	$0.727990\pi$
$558$	13.2919	−	6.77256i	0.562691	−	0.286705i
$559$	7.80090	−	10.7370i	0.329943	−	0.454127i
$560$		0			0
$561$	−44.6071	−	29.5895i	−1.88332	−	1.24927i
$562$	8.01840	+	8.01840i	0.338236	+	0.338236i
$563$	−2.46585	−	15.5688i	−0.103923	−	0.656146i	−0.983571	−	0.180521i	$-0.942222\pi$
$563$	−2.46585	−	15.5688i	−0.103923	−	0.656146i	0.879648	−	0.475625i	$-0.157778\pi$
$564$	0.327971	+	0.106564i	0.0138101	+	0.00448716i
$565$		0			0
$566$	−5.96620	+	4.33470i	−0.250778	+	0.182201i
$567$	−3.21336	+	20.2884i	−0.134948	+	0.852031i
$568$	−6.94207	+	13.6246i	−0.291283	+	0.571675i
$569$	−4.29082	+	13.2058i	−0.179881	+	0.553615i	−0.999823	−	0.0188311i	$-0.994006\pi$
$569$	−4.29082	+	13.2058i	−0.179881	+	0.553615i	0.819942	+	0.572446i	$0.194006\pi$
$570$		0			0
$571$		−	17.7667i		−	0.743512i	−0.928330	−	0.371756i	$-0.878756\pi$
$571$		−	17.7667i		−	0.743512i	0.928330	−	0.371756i	$-0.121244\pi$
$572$	2.30726	−	5.04933i	0.0964713	−	0.211123i
$573$	37.4098	−	37.4098i	1.56282	−	1.56282i
$574$	−18.6268	−	13.5331i	−0.777466	−	0.564862i
$575$		0			0
$576$	0.915296	+	2.81699i	0.0381373	+	0.117375i
$577$	−12.7957	−	2.02665i	−0.532694	−	0.0843704i	−0.115708	−	0.993283i	$-0.536914\pi$
$577$	−12.7957	−	2.02665i	−0.532694	−	0.0843704i	−0.416986	+	0.908913i	$0.636914\pi$
$578$	−70.2623	−	11.1285i	−2.92253	−	0.462883i
$579$	−1.02754	−	3.16244i	−0.0427031	−	0.131427i
$580$		0			0
$581$	−13.0228	−	9.46164i	−0.540278	−	0.392535i
$582$	−3.64696	+	3.64696i	−0.151171	+	0.151171i
$583$	−9.01571	−	8.27810i	−0.373392	−	0.342844i
$584$		−	16.1801i		−	0.669538i
$585$		0			0
$586$	11.8232	−	36.3882i	0.488414	−	1.50318i
$587$	6.55945	−	12.8737i	0.270738	−	0.531352i	−0.715107	−	0.699015i	$-0.753622\pi$
$587$	6.55945	−	12.8737i	0.270738	−	0.531352i	0.985844	+	0.167663i	$0.0536220\pi$
$588$	1.05680	−	6.67236i	0.0435816	−	0.275163i
$589$	4.97023	−	3.61108i	0.204795	−	0.148792i
$590$		0			0
$591$	26.0265	+	8.45653i	1.07059	+	0.347855i
$592$	−5.11453	−	32.2919i	−0.210206	−	1.32719i
$593$	25.8204	+	25.8204i	1.06032	+	1.06032i	0.998060	+	0.0622556i	$0.0198294\pi$
$593$	25.8204	+	25.8204i	1.06032	+	1.06032i	0.0622556	+	0.998060i	$0.480171\pi$
$594$	−11.6207	−	14.6395i	−0.476804	−	0.600666i
$595$		0			0
$596$	1.89508	−	2.60835i	0.0776254	−	0.106842i
$597$	−49.9576	+	25.4547i	−2.04463	+	1.04179i
$598$	18.1742	+	9.26020i	0.743197	+	0.378678i
$599$	−3.34912	−	4.60967i	−0.136841	−	0.188346i	0.735097	−	0.677962i	$-0.237137\pi$
$599$	−3.34912	−	4.60967i	−0.136841	−	0.188346i	−0.871938	+	0.489616i	$0.837137\pi$
$600$		0			0
$601$	0.135724	−	0.0440995i	0.00553631	−	0.00179886i	−0.306248	−	0.951952i	$-0.599074\pi$
$601$	0.135724	−	0.0440995i	0.00553631	−	0.00179886i	0.311784	+	0.950153i	$0.399074\pi$
$602$	−9.78799	−	19.2100i	−0.398929	−	0.782941i
$603$	−11.8795	+	1.88152i	−0.483770	+	0.0766216i
$604$	−7.19440			−0.292736
$605$		0			0
$606$	4.07554			0.165557
$607$	44.7648	−	7.09004i	1.81695	−	0.287776i	0.847089	−	0.531452i	$-0.178353\pi$
$607$	44.7648	−	7.09004i	1.81695	−	0.287776i	0.969857	+	0.243676i	$0.0783534\pi$
$608$	−2.09258	−	4.10692i	−0.0848653	−	0.166557i
$609$	−27.1738	+	8.82931i	−1.10114	+	0.357782i
$610$		0			0
$611$	0.209627	+	0.288527i	0.00848060	+	0.0116725i
$612$	8.52082	+	4.34158i	0.344434	+	0.175498i
$613$	−27.3175	+	13.9190i	−1.10334	+	0.562181i	−0.908176	−	0.418589i	$-0.862525\pi$
$613$	−27.3175	+	13.9190i	−1.10334	+	0.562181i	−0.195167	+	0.980770i	$0.562525\pi$
$614$	−13.2198	+	18.1955i	−0.533508	+	0.734311i
$615$		0			0
$616$	7.17359	+	9.03712i	0.289032	+	0.364116i
$617$	−16.4102	−	16.4102i	−0.660651	−	0.660651i	0.294883	−	0.955533i	$-0.404719\pi$
$617$	−16.4102	−	16.4102i	−0.660651	−	0.660651i	−0.955533	+	0.294883i	$0.904719\pi$
$618$	5.79986	+	36.6188i	0.233304	+	1.47303i
$619$	8.65803	+	2.81316i	0.347995	+	0.113071i	0.477799	−	0.878469i	$-0.341435\pi$
$619$	8.65803	+	2.81316i	0.347995	+	0.113071i	−0.129804	+	0.991540i	$0.541435\pi$
$620$		0			0
$621$	16.9418	−	12.3090i	0.679852	−	0.493942i
$622$	−1.39844	+	8.82939i	−0.0560722	+	0.354026i
$623$	−9.98823	+	19.6030i	−0.400170	+	0.785378i
$624$	6.17798	−	19.0139i	0.247317	−	0.761164i
$625$		0			0
$626$			32.1291i			1.28414i
$627$	5.09370	+	4.67697i	0.203423	+	0.186780i
$628$	8.84246	−	8.84246i	0.352853	−	0.352853i
$629$	40.7346	+	29.5954i	1.62419	+	1.18005i
$630$		0			0
$631$	12.8374	+	39.5094i	0.511048	+	1.57284i	0.790360	+	0.612643i	$0.209894\pi$
$631$	12.8374	+	39.5094i	0.511048	+	1.57284i	−0.279312	+	0.960200i	$0.590106\pi$
$632$	17.8679	+	2.83000i	0.710747	+	0.112571i
$633$	23.8883	+	3.78353i	0.949473	+	0.150382i
$634$	0.138334	+	0.425749i	0.00549396	+	0.0169087i
$635$		0			0
$636$	5.50728	+	4.00127i	0.218378	+	0.158661i
$637$	4.94019	−	4.94019i	0.195738	−	0.195738i
$638$	17.3944	−	38.0667i	0.688649	−	1.50708i
$639$			11.4004i			0.450994i
$640$		0			0
$641$	8.12688	−	25.0120i	0.320993	−	0.987914i	−0.652224	−	0.758026i	$-0.726164\pi$
$641$	8.12688	−	25.0120i	0.320993	−	0.987914i	0.973217	−	0.229888i	$-0.0738360\pi$
$642$	−17.2303	+	33.8164i	−0.680026	+	1.33463i
$643$	4.39302	−	27.7364i	0.173244	−	1.09382i	−0.735825	−	0.677172i	$-0.763205\pi$
$643$	4.39302	−	27.7364i	0.173244	−	1.09382i	0.909069	−	0.416646i	$-0.136795\pi$
$644$	8.17442	−	5.93906i	0.322117	−	0.234032i
$645$		0			0
$646$	12.2833	+	3.99108i	0.483279	+	0.157027i
$647$	−4.39069	−	27.7217i	−0.172616	−	1.08985i	−0.910070	−	0.414455i	$-0.863972\pi$
$647$	−4.39069	−	27.7217i	−0.172616	−	1.08985i	0.737454	−	0.675397i	$-0.236028\pi$
$648$	−15.1393	−	15.1393i	−0.594729	−	0.594729i
$649$	14.6784	+	9.73670i	0.576177	+	0.382199i
$650$		0			0
$651$	13.9845	−	19.2480i	0.548095	−	0.754388i
$652$	−11.9614	+	6.09465i	−0.468445	+	0.238685i
$653$	−39.9239	−	20.3422i	−1.56234	−	0.796053i	−0.562807	−	0.826588i	$-0.690279\pi$
$653$	−39.9239	−	20.3422i	−1.56234	−	0.796053i	−0.999534	+	0.0305355i	$0.990279\pi$
$654$	−18.2120	−	25.0667i	−0.712147	−	0.980187i
$655$		0			0
$656$	35.2228	−	11.4446i	1.37522	−	0.446836i
$657$	−5.47655	−	10.7483i	−0.213661	−	0.419333i
$658$	0.572228	−	0.0906320i	0.0223078	−	0.00353320i
$659$	−22.7487			−0.886165			−0.443083	−	0.896481i	$-0.646115\pi$
$659$	−22.7487			−0.886165			−0.443083	+	0.896481i	$0.646115\pi$
$660$		0			0
$661$	9.96766			0.387697			0.193849	−	0.981031i	$-0.437903\pi$
$661$	9.96766			0.387697			0.193849	+	0.981031i	$0.437903\pi$
$662$	10.3923	−	1.64597i	0.403907	−	0.0639725i
$663$	13.9779	+	27.4333i	0.542858	+	1.06542i
$664$	15.9569	−	5.18471i	0.619248	−	0.201206i
$665$		0			0
$666$	−9.28383	−	12.7781i	−0.359741	−	0.495141i
$667$	41.7803	+	21.2881i	1.61774	+	0.824280i
$668$	−3.01574	+	1.53660i	−0.116683	+	0.0594527i
$669$	11.8938	−	16.3704i	0.459841	−	0.632917i
$670$		0			0
$671$	4.95076	−	17.7822i	0.191122	−	0.686476i
$672$	−12.6220	−	12.6220i	−0.486905	−	0.486905i
$673$	0.529639	+	3.34401i	0.0204161	+	0.128902i	0.995791	−	0.0916500i	$-0.0292141\pi$
$673$	0.529639	+	3.34401i	0.0204161	+	0.128902i	−0.975375	+	0.220552i	$0.929214\pi$
$674$	−13.4408	−	4.36716i	−0.517718	−	0.168217i
$675$		0			0
$676$	6.64474	−	4.82769i	0.255567	−	0.185680i
$677$	−1.12038	+	7.07380i	−0.0430597	+	0.271868i	−0.999819	−	0.0190116i	$-0.993948\pi$
$677$	−1.12038	+	7.07380i	−0.0430597	+	0.271868i	0.956760	+	0.290880i	$0.0939480\pi$
$678$	−31.7459	+	62.3049i	−1.21920	+	2.39281i
$679$	−0.816495	+	2.51291i	−0.0313342	+	0.0964368i
$680$		0			0
$681$			14.0131i			0.536982i
$682$	6.91360	+	34.1576i	0.264736	+	1.30796i
$683$	16.3474	−	16.3474i	0.625515	−	0.625515i	−0.321421	−	0.946936i	$-0.604160\pi$
$683$	16.3474	−	16.3474i	0.625515	−	0.625515i	0.946936	+	0.321421i	$0.104160\pi$
$684$	−0.999480	−	0.726165i	−0.0382161	−	0.0277656i
$685$		0			0
$686$	−10.2108	−	31.4255i	−0.389849	−	1.19983i
$687$	23.0540	+	3.65140i	0.879565	+	0.139309i
$688$	34.2534	+	5.42521i	1.30590	+	0.206834i
$689$	2.17551	+	6.69553i	0.0828804	+	0.255080i
$690$		0			0
$691$	1.85902	+	1.35066i	0.0707205	+	0.0513814i	0.622584	−	0.782553i	$-0.286083\pi$
$691$	1.85902	+	1.35066i	0.0707205	+	0.0513814i	−0.551863	+	0.833935i	$0.686083\pi$
$692$	0.915229	−	0.915229i	0.0347918	−	0.0347918i
$693$	7.82420	+	3.57522i	0.297217	+	0.135811i
$694$		−	42.6176i		−	1.61774i
$695$		0			0
$696$	9.20282	−	28.3234i	0.348832	−	1.07359i
$697$	−25.8938	+	50.8195i	−0.980799	+	1.92493i
$698$	−8.71463	+	55.0220i	−0.329854	+	2.08261i
$699$	4.17746	−	3.03510i	0.158006	−	0.114798i
$700$		0			0
$701$	33.6723	+	10.9408i	1.27179	+	0.413228i	0.865680	−	0.500598i	$-0.166886\pi$
$701$	33.6723	+	10.9408i	1.27179	+	0.413228i	0.406106	+	0.913826i	$0.366886\pi$
$702$	1.68180	+	10.6185i	0.0634756	+	0.400769i
$703$	−4.59945	−	4.59945i	−0.173472	−	0.173472i
$704$	−6.91328	+	0.294860i	−0.260554	+	0.0111130i
$705$		0			0
$706$	1.23709	−	1.70271i	0.0465586	−	0.0640825i
$707$	1.86034	−	0.947888i	0.0699651	−	0.0356490i
$708$	−8.72874	−	4.44752i	−0.328046	−	0.167148i
$709$	28.6797	+	39.4742i	1.07709	+	1.48248i	0.862688	+	0.505737i	$0.168779\pi$
$709$	28.6797	+	39.4742i	1.07709	+	1.48248i	0.214399	+	0.976746i	$0.431221\pi$
$710$		0			0
$711$	12.8274	−	4.16788i	0.481065	−	0.156308i
$712$	−10.4108	−	20.4323i	−0.390160	−	0.765732i
$713$	−38.5651	+	6.10811i	−1.44427	+	0.228751i
$714$	50.0169			1.87184
$715$		0			0
$716$	3.01723			0.112759
$717$	31.3522	−	4.96570i	1.17087	−	0.185447i
$718$	−9.73491	−	19.1058i	−0.363303	−	0.713023i
$719$	−50.6600	+	16.4604i	−1.88930	+	0.613871i	−0.908842	+	0.417140i	$0.863032\pi$
$719$	−50.6600	+	16.4604i	−1.88930	+	0.613871i	−0.980458	+	0.196731i	$0.936968\pi$
$720$		0			0
$721$	11.1642	+	15.3662i	0.415778	+	0.572269i
$722$	27.2302	+	13.8745i	1.01340	+	0.516354i
$723$	36.0381	−	18.3623i	1.34027	−	0.682903i
$724$	0.514990	−	0.708823i	0.0191395	−	0.0263432i
$725$		0			0
$726$	−36.1399	+	15.2546i	−1.34128	+	0.566151i
$727$	−0.275456	−	0.275456i	−0.0102161	−	0.0102161i	0.701980	−	0.712196i	$-0.252299\pi$
$727$	−0.275456	−	0.275456i	−0.0102161	−	0.0102161i	−0.712196	+	0.701980i	$0.752299\pi$
$728$	−1.03820	−	6.55491i	−0.0384781	−	0.242941i
$729$	4.74661	+	1.54227i	0.175800	+	0.0571210i
$730$		0			0
$731$	−43.2090	+	31.3932i	−1.59814	+	1.16112i
$732$	−1.60598	+	10.1397i	−0.0593586	+	0.374775i
$733$	−15.1359	+	29.7058i	−0.559056	+	1.09721i	0.422559	+	0.906335i	$0.361132\pi$
$733$	−15.1359	+	29.7058i	−0.559056	+	1.09721i	−0.981615	+	0.190873i	$0.938868\pi$
$734$	−5.18682	+	15.9634i	−0.191449	+	0.589219i
$735$		0			0
$736$			29.2948i			1.07982i
$737$	3.20893	−	27.9143i	0.118202	−	1.02824i
$738$	12.6514	−	12.6514i	0.465704	−	0.465704i
$739$	4.17028	+	3.02989i	0.153406	+	0.111456i	0.661841	−	0.749645i	$-0.269776\pi$
$739$	4.17028	+	3.02989i	0.153406	+	0.111456i	−0.508434	+	0.861101i	$0.669776\pi$
$740$		0			0
$741$	−1.22912	−	3.78285i	−0.0451529	−	0.138966i
$742$	11.2959	+	1.78909i	0.414684	+	0.0656795i
$743$	−15.0763	−	2.38785i	−0.553095	−	0.0876016i	−0.126370	−	0.991983i	$-0.540333\pi$
$743$	−15.0763	−	2.38785i	−0.553095	−	0.0876016i	−0.426725	+	0.904382i	$0.640333\pi$
$744$	7.66310	+	23.5846i	0.280943	+	0.864653i
$745$		0			0
$746$	9.11702	+	6.62390i	0.333798	+	0.242518i
$747$	8.84516	−	8.84516i	0.323627	−	0.323627i
$748$	−15.1099	+	16.4562i	−0.552472	+	0.601699i
$749$			19.4434i			0.710445i
$750$		0			0
$751$	14.4619	−	44.5092i	0.527723	−	1.62416i	−0.231144	−	0.972919i	$-0.574247\pi$
$751$	14.4619	−	44.5092i	0.527723	−	1.62416i	0.758867	−	0.651245i	$-0.225753\pi$
$752$	−0.423091	+	0.830362i	−0.0154285	+	0.0302802i
$753$	1.79006	−	11.3020i	0.0652335	−	0.411868i
$754$	−19.4755	+	14.1498i	−0.709256	+	0.515305i
$755$		0			0
$756$	5.06495	+	1.64570i	0.184210	+	0.0598536i
$757$	4.29624	+	27.1254i	0.156149	+	0.985889i	0.933957	+	0.357386i	$0.116332\pi$
$757$	4.29624	+	27.1254i	0.156149	+	0.985889i	−0.777807	+	0.628503i	$0.783668\pi$
$758$	34.6004	+	34.6004i	1.25674	+	1.25674i
$759$	−15.3501	−	41.1823i	−0.557175	−	1.49482i
$760$		0			0
$761$	−18.2024	+	25.0534i	−0.659835	+	0.908185i	−0.999476	−	0.0323699i	$-0.989695\pi$
$761$	−18.2024	+	25.0534i	−0.659835	+	0.908185i	0.339641	+	0.940555i	$0.389695\pi$
$762$	18.6777	−	9.51676i	0.676621	−	0.344756i
$763$	−14.1432	−	7.20630i	−0.512017	−	0.260885i
$764$	−12.9787	−	17.8637i	−0.469554	−	0.646286i
$765$		0			0
$766$	10.2794	−	3.33998i	0.371409	−	0.120678i
$767$	−4.59957	−	9.02716i	−0.166081	−	0.325952i
$768$	36.5406	−	5.78746i	1.31855	−	0.208837i
$769$	−48.2925			−1.74147			−0.870735	−	0.491752i	$-0.836357\pi$
$769$	−48.2925			−1.74147			−0.870735	+	0.491752i	$0.836357\pi$
$770$		0			0
$771$	−18.2827			−0.658435
$772$	−1.37072	+	0.217101i	−0.0493333	+	0.00781362i
$773$	−3.45656	−	6.78388i	−0.124324	−	0.243999i	0.820453	−	0.571714i	$-0.193721\pi$
$773$	−3.45656	−	6.78388i	−0.124324	−	0.243999i	−0.944777	+	0.327715i	$0.893721\pi$
$774$	15.9340	−	5.17728i	0.572737	−	0.186094i
$775$		0			0
$776$	−1.61877	−	2.22804i	−0.0581104	−	0.0799821i
$777$	−22.4446	−	11.4361i	−0.805194	−	0.410267i
$778$	36.4048	−	18.5492i	1.30517	−	0.665019i
$779$	4.33096	−	5.96106i	0.155173	−	0.213577i
$780$		0			0
$781$	−25.6572	−	7.14323i	−0.918087	−	0.255605i
$782$	−58.0428	−	58.0428i	−2.07561	−	2.07561i
$783$	3.86627	+	24.4107i	0.138169	+	0.872367i
$784$	17.3629	+	5.64156i	0.620105	+	0.201484i
$785$		0			0
$786$	−23.0530	+	16.7490i	−0.822275	+	0.597418i
$787$	5.06129	−	31.9557i	0.180415	−	1.13910i	−0.716726	−	0.697355i	$-0.754360\pi$
$787$	5.06129	−	31.9557i	0.180415	−	1.13910i	0.897141	−	0.441743i	$-0.145640\pi$
$788$	5.18524	−	10.1766i	0.184717	−	0.362527i
$789$	−0.714234	+	2.19819i	−0.0254274	+	0.0782575i
$790$		0			0
$791$			35.8234i			1.27373i
$792$	−7.80827	+	4.40733i	−0.277455	+	0.156608i
$793$	−7.50743	+	7.50743i	−0.266597	+	0.266597i
$794$	36.4456	+	26.4793i	1.29341	+	0.939715i
$795$		0			0
$796$	7.23129	+	22.2556i	0.256306	+	0.788830i
$797$	14.8168	+	2.34675i	0.524837	+	0.0831260i	0.413230	−	0.910627i	$-0.364400\pi$
$797$	14.8168	+	2.34675i	0.524837	+	0.0831260i	0.111606	+	0.993752i	$0.464400\pi$
$798$	−6.38194	−	1.01080i	−0.225918	−	0.0357819i
$799$	−0.443508	−	1.36498i	−0.0156902	−	0.0482894i
$800$		0			0
$801$	−13.8316	−	10.0492i	−0.488715	−	0.355073i
$802$	34.9256	−	34.9256i	1.23327	−	1.23327i
$803$	27.6211	−	5.59060i	0.974729	−	0.197288i
$804$			15.6274i			0.551135i
$805$		0			0
$806$	6.19437	−	19.0643i	0.218187	−	0.671511i
$807$	29.3403	−	57.5836i	1.03283	−	2.02704i
$808$	−0.340437	+	2.14944i	−0.0119765	+	0.0756169i
$809$	23.3789	−	16.9858i	0.821958	−	0.597188i	−0.0953145	−	0.995447i	$-0.530386\pi$
$809$	23.3789	−	16.9858i	0.821958	−	0.597188i	0.917273	+	0.398260i	$0.130386\pi$
$810$		0			0
$811$	15.5203	+	5.04286i	0.544993	+	0.177079i	0.568558	−	0.822643i	$-0.307502\pi$
$811$	15.5203	+	5.04286i	0.544993	+	0.177079i	−0.0235648	+	0.999722i	$0.507502\pi$
$812$	1.86547	+	11.7781i	0.0654653	+	0.413332i
$813$	−41.6011	−	41.6011i	−1.45901	−	1.45901i
$814$	34.5748	−	12.8873i	1.21185	−	0.451699i
$815$		0			0
$816$	−47.2904	+	65.0897i	−1.65550	+	2.27859i
$817$	6.14771	−	3.13241i	0.215081	−	0.109589i
$818$	−2.67783	−	1.36442i	−0.0936280	−	0.0477058i
$819$	−2.90833	−	4.00297i	−0.101625	−	0.139875i
$820$		0			0
$821$	−49.7344	+	16.1597i	−1.73574	+	0.563977i	−0.994260	−	0.106994i	$-0.965877\pi$
$821$	−49.7344	+	16.1597i	−1.73574	+	0.563977i	−0.741484	+	0.670971i	$0.765877\pi$
$822$	14.0803	+	27.6341i	0.491106	+	0.963850i
$823$	32.1097	−	5.08568i	1.11927	−	0.177276i	0.430738	−	0.902477i	$-0.358253\pi$
$823$	32.1097	−	5.08568i	1.11927	−	0.177276i	0.688537	+	0.725201i	$0.258253\pi$
$824$	−19.7972			−0.689669
$825$		0			0
$826$	−16.4585			−0.572665
$827$	−12.6781	+	2.00802i	−0.440862	+	0.0698256i	−0.372920	−	0.927864i	$-0.621643\pi$
$827$	−12.6781	+	2.00802i	−0.440862	+	0.0698256i	−0.0679420	+	0.997689i	$0.521643\pi$
$828$	3.56467	+	6.99605i	0.123881	+	0.243130i
$829$	−41.2091	+	13.3897i	−1.43125	+	0.465042i	−0.919159	−	0.393888i	$-0.871130\pi$
$829$	−41.2091	+	13.3897i	−1.43125	+	0.465042i	−0.512094	+	0.858930i	$0.671130\pi$
$830$		0			0
$831$	16.1535	+	22.2334i	0.560360	+	0.771269i
$832$	3.54624	+	1.80690i	0.122944	+	0.0626430i
$833$	−25.0513	+	12.7643i	−0.867976	+	0.442256i
$834$	25.4212	−	34.9893i	0.880264	−	1.21158i
$835$		0			0
$836$	2.26052	−	1.79438i	0.0781817	−	0.0620600i
$837$	−14.5522	−	14.5522i	−0.502998	−	0.502998i
$838$	−0.644561	−	4.06960i	−0.0222660	−	0.140582i
$839$	−21.0060	−	6.82528i	−0.725209	−	0.235635i	−0.0769291	−	0.997037i	$-0.524511\pi$
$839$	−21.0060	−	6.82528i	−0.725209	−	0.235635i	−0.648280	+	0.761402i	$0.724511\pi$
$840$		0			0
$841$	−21.3105	+	15.4830i	−0.734844	+	0.533895i
$842$	−3.19405	+	20.1664i	−0.110074	+	0.694981i
$843$	−6.38034	+	12.5221i	−0.219751	+	0.431285i
$844$	3.11932	−	9.60027i	0.107371	−	0.330455i
$845$		0			0
$846$			0.450217i			0.0154788i
$847$	−12.9487	+	15.3686i	−0.444921	+	0.528071i
$848$	−13.0083	+	13.0083i	−0.446708	+	0.446708i
$849$	−7.39422	−	5.37221i	−0.253769	−	0.184374i
$850$		0			0
$851$	12.7750	+	39.3173i	0.437920	+	1.34778i
$852$	14.6302	+	2.31719i	0.501222	+	0.0793857i
$853$	−10.4999	−	1.66302i	−0.359509	−	0.0569406i	−0.0259323	−	0.999664i	$-0.508255\pi$
$853$	−10.4999	−	1.66302i	−0.359509	−	0.0569406i	−0.333576	+	0.942723i	$0.608255\pi$
$854$	5.32978	+	16.4034i	0.182381	+	0.561312i
$855$		0			0
$856$	−16.3955	−	11.9120i	−0.560385	−	0.407144i
$857$	−22.8695	+	22.8695i	−0.781207	+	0.781207i	−0.980034	−	0.198828i	$-0.936287\pi$
$857$	−22.8695	+	22.8695i	−0.781207	+	0.781207i	0.198828	+	0.980034i	$0.436287\pi$
$858$	22.4155	+	2.57681i	0.765253	+	0.0879709i
$859$		−	6.71300i		−	0.229045i	−0.993421	−	0.114522i	$-0.963466\pi$
$859$		−	6.71300i		−	0.229045i	0.993421	−	0.114522i	$-0.0365337\pi$
$860$		0			0
$861$	8.81773	−	27.1382i	0.300507	−	0.924867i
$862$	10.1242	−	19.8699i	0.344832	−	0.676771i
$863$	−1.79816	+	11.3531i	−0.0612099	+	0.386464i	0.937997	+	0.346644i	$0.112679\pi$
$863$	−1.79816	+	11.3531i	−0.0612099	+	0.386464i	−0.999207	+	0.0398207i	$0.987321\pi$
$864$	−12.4916	+	9.07567i	−0.424972	+	0.308760i
$865$		0			0
$866$	2.97918	+	0.967993i	0.101237	+	0.0328938i
$867$	−13.7921	−	87.0797i	−0.468403	−	2.95738i
$868$	−7.02143	−	7.02143i	−0.238323	−	0.238323i
$869$	1.34267	+	31.4802i	0.0455470	+	1.06789i
$870$		0			0
$871$	−9.49958	+	13.0750i	−0.321881	+	0.443031i
$872$	14.7415	−	7.51115i	0.499209	−	0.254360i
$873$	−1.82947	−	0.932161i	−0.0619182	−	0.0315489i
$874$	6.23302	+	8.57901i	0.210835	+	0.290189i
$875$		0			0
$876$	−14.9065	+	4.84341i	−0.503644	+	0.163644i
$877$	0.789791	+	1.55005i	0.0266694	+	0.0523416i	0.903957	−	0.427624i	$-0.140649\pi$
$877$	0.789791	+	1.55005i	0.0266694	+	0.0523416i	−0.877287	+	0.479965i	$0.840649\pi$
$878$	37.6178	−	5.95808i	1.26954	−	0.201075i
$879$	47.4186			1.59939
$880$		0			0
$881$	−16.2459			−0.547338			−0.273669	−	0.961824i	$-0.588237\pi$
$881$	−16.2459			−0.547338			−0.273669	+	0.961824i	$0.588237\pi$
$882$	8.71109	−	1.37970i	0.293318	−	0.0464569i
$883$	3.24587	+	6.37038i	0.109232	+	0.214380i	0.939152	−	0.343503i	$-0.111614\pi$
$883$	3.24587	+	6.37038i	0.109232	+	0.214380i	−0.829919	+	0.557884i	$0.811614\pi$
$884$	12.2212	−	3.97092i	0.411045	−	0.133557i
$885$		0			0
$886$	22.7242	+	31.2771i	0.763433	+	1.05078i
$887$	26.5197	+	13.5125i	0.890445	+	0.453704i	0.838472	−	0.544944i	$-0.183449\pi$
$887$	26.5197	+	13.5125i	0.890445	+	0.453704i	0.0519724	+	0.998649i	$0.483449\pi$
$888$	23.3941	−	11.9199i	0.785053	−	0.400005i
$889$	6.31228	−	8.68811i	0.211707	−	0.291390i
$890$		0			0
$891$	20.6134	−	31.0754i	0.690575	−	1.04106i
$892$	−5.97172	−	5.97172i	−0.199948	−	0.199948i
$893$	0.0290046	+	0.183128i	0.000970603	+	0.00612814i
$894$	12.4625	+	4.04930i	0.416807	+	0.135429i
$895$		0			0
$896$	18.9691	−	13.7819i	0.633714	−	0.460420i
$897$	−3.95458	+	24.9682i	−0.132040	+	0.833665i
$898$	−0.685739	+	1.34584i	−0.0228834	+	0.0449112i
$899$	14.2401	−	43.8267i	0.474935	−	1.46170i
$900$		0			0
$901$		−	28.3315i		−	0.943858i
$902$	20.5455	+	36.3996i	0.684091	+	1.21197i
$903$	18.8941	−	18.8941i	0.628756	−	0.628756i
$904$	−30.2078	−	21.9472i	−1.00470	−	0.729954i
$905$		0			0
$906$	−9.03579	−	27.8093i	−0.300194	−	0.923902i
$907$	−8.28271	−	1.31185i	−0.275023	−	0.0435593i	0.0173995	−	0.999849i	$-0.494461\pi$
$907$	−8.28271	−	1.31185i	−0.275023	−	0.0435593i	−0.292422	+	0.956289i	$0.594461\pi$
$908$	5.77651	+	0.914910i	0.191700	+	0.0303623i
$909$	0.501379	+	1.54308i	0.0166297	+	0.0511809i
$910$		0			0
$911$	−0.388360	−	0.282160i	−0.0128670	−	0.00934839i	0.581333	−	0.813666i	$-0.302531\pi$
$911$	−0.388360	−	0.282160i	−0.0128670	−	0.00934839i	−0.594200	+	0.804317i	$0.702531\pi$
$912$	7.34946	−	7.34946i	0.243365	−	0.243365i
$913$	14.3643	+	25.4486i	0.475389	+	0.842227i
$914$			43.1914i			1.42864i
$915$		0			0
$916$	3.01038	−	9.26500i	0.0994658	−	0.306124i
$917$	−6.62739	+	13.0070i	−0.218856	+	0.429529i
$918$	6.76808	−	42.7320i	0.223380	−	1.41036i
$919$	−8.81813	+	6.40674i	−0.290883	+	0.211339i	−0.723650	−	0.690167i	$-0.757537\pi$
$919$	−8.81813	+	6.40674i	−0.290883	+	0.211339i	0.432767	+	0.901506i	$0.357537\pi$
$920$		0			0
$921$	−26.5098	−	8.61357i	−0.873529	−	0.283827i
$922$	4.95747	+	31.3002i	0.163265	+	1.03082i
$923$	10.8321	+	10.8321i	0.356544	+	0.356544i
$924$	6.17839	−	9.31412i	0.203254	−	0.306412i
$925$		0			0
$926$	15.0218	−	20.6757i	0.493647	−	0.679446i
$927$	−13.1512	+	6.70085i	−0.431941	+	0.220085i
$928$	−30.8056	−	15.6962i	−1.01124	−	0.515254i
$929$	−26.2134	−	36.0797i	−0.860035	−	1.18374i	−0.981561	−	0.191149i	$-0.938779\pi$
$929$	−26.2134	−	36.0797i	−0.860035	−	1.18374i	0.121526	−	0.992588i	$-0.461221\pi$
$930$		0			0
$931$	3.45439	−	1.12240i	0.113213	−	0.0367852i
$932$	−0.978395	−	1.92021i	−0.0320484	−	0.0628985i
$933$	−10.9427	+	1.73316i	−0.358248	+	0.0567410i
$934$	−53.1206			−1.73816
$935$		0			0
$936$	5.15727			0.168571
$937$	−56.2208	+	8.90450i	−1.83665	+	0.290897i	−0.975915	−	0.218150i	$-0.929998\pi$
$937$	−56.2208	+	8.90450i	−1.83665	+	0.290897i	−0.860738	+	0.509048i	$0.829998\pi$
$938$	11.9194	+	23.3931i	0.389181	+	0.763811i
$939$	−37.8704	+	12.3048i	−1.23585	+	0.401553i
$940$		0			0
$941$	−1.34552	−	1.85194i	−0.0438626	−	0.0603716i	0.786522	−	0.617562i	$-0.211879\pi$
$941$	−1.34552	−	1.85194i	−0.0438626	−	0.0603716i	−0.830385	+	0.557190i	$0.811879\pi$
$942$	45.2854	+	23.0741i	1.47548	+	0.751794i
$943$	−41.7256	+	21.2602i	−1.35877	+	0.692328i
$944$	15.5613	−	21.4183i	0.506478	−	0.697108i
$945$		0			0
$946$	1.66785	+	39.1043i	0.0542265	+	1.27139i
$947$	28.3884	+	28.3884i	0.922498	+	0.922498i	0.997206	−	0.0747071i	$-0.0238022\pi$
$947$	28.3884	+	28.3884i	0.922498	+	0.922498i	−0.0747071	+	0.997206i	$0.523802\pi$
$948$	−2.74141	−	17.3086i	−0.0890368	−	0.562156i
$949$	−15.4161	−	5.00900i	−0.500428	−	0.162599i
$950$		0			0
$951$	−0.448848	+	0.326107i	−0.0145549	+	0.0105748i
$952$	−4.17801	+	26.3789i	−0.135410	+	0.854945i
$953$	−5.49312	+	10.7809i	−0.177940	+	0.349226i	−0.962699	−	0.270574i	$-0.912786\pi$
$953$	−5.49312	+	10.7809i	−0.177940	+	0.349226i	0.784759	+	0.619800i	$0.212786\pi$
$954$	−2.74634	+	8.45238i	−0.0889161	+	0.273656i
$955$		0			0
$956$		−	13.2483i		−	0.428481i
$957$	51.5307	+	5.92380i	1.66575	+	0.191489i
$958$	−31.7757	+	31.7757i	−1.02663	+	1.02663i
$959$	12.8543	+	9.33918i	0.415086	+	0.301578i
$960$		0			0
$961$	2.27811	+	7.01129i	0.0734873	+	0.226171i
$962$	−20.9622	−	3.32009i	−0.675849	−	0.107044i
$963$	−14.9233	−	2.36362i	−0.480896	−	0.0761664i
$964$	−5.21646	−	16.0546i	−0.168011	−	0.517085i
$965$		0			0
$966$	33.2236	+	24.1383i	1.06895	+	0.776638i
$967$	21.8592	−	21.8592i	0.702945	−	0.702945i	−0.262097	−	0.965042i	$-0.584414\pi$
$967$	21.8592	−	21.8592i	0.702945	−	0.702945i	0.965042	+	0.262097i	$0.0844140\pi$
$968$	−5.02643	−	20.3344i	−0.161556	−	0.653574i
$969$			16.0067i			0.514210i
$970$		0			0
$971$	−3.76395	+	11.5843i	−0.120791	+	0.371756i	−0.993111	−	0.117179i	$-0.962615\pi$
$971$	−3.76395	+	11.5843i	−0.120791	+	0.371756i	0.872320	+	0.488936i	$0.162615\pi$
$972$	−5.44556	+	10.6875i	−0.174666	+	0.342802i
$973$	3.46605	−	21.8838i	0.111117	−	0.701562i
$974$	15.2636	−	11.0896i	0.489076	−	0.355334i
$975$		0			0
$976$	−26.3858	−	8.57327i	−0.844589	−	0.274424i
$977$	−0.444468	−	2.80626i	−0.0142198	−	0.0897802i	0.979558	−	0.201163i	$-0.0644721\pi$
$977$	−0.444468	−	2.80626i	−0.0142198	−	0.0897802i	−0.993778	+	0.111383i	$0.964472\pi$
$978$	−38.5812	−	38.5812i	−1.23369	−	1.23369i
$979$	31.2829	−	24.8321i	0.999805	−	0.793637i
$980$		0			0
$981$	7.25032	−	9.97921i	0.231485	−	0.318612i
$982$	−18.2960	+	9.32230i	−0.583850	+	0.297487i
$983$	10.1113	+	5.15196i	0.322500	+	0.164322i	0.607744	−	0.794133i	$-0.292075\pi$
$983$	10.1113	+	5.15196i	0.322500	+	0.164322i	−0.285244	+	0.958455i	$0.592075\pi$
$984$	17.4819	+	24.0617i	0.557301	+	0.767060i
$985$		0			0
$986$	92.1356	−	29.9367i	2.93420	−	0.953378i
$987$	0.325980	+	0.639771i	0.0103760	+	0.0203641i
$988$	−1.63963	+	0.259691i	−0.0521635	+	0.00826188i
$989$	−43.8518			−1.39441
$990$		0			0
$991$	12.4552			0.395654			0.197827	−	0.980237i	$-0.436612\pi$
$991$	12.4552			0.395654			0.197827	+	0.980237i	$0.436612\pi$
$992$	28.4349	−	4.50365i	0.902809	−	0.142991i
$993$	5.92013	+	11.6189i	0.187870	+	0.368715i
$994$	23.6677	−	7.69010i	0.750694	−	0.243915i
$995$		0			0
$996$	−9.55318	−	13.1488i	−0.302704	−	0.416636i
$997$	−49.2813	−	25.1101i	−1.56075	−	0.795244i	−0.561279	−	0.827627i	$-0.689690\pi$
$997$	−49.2813	−	25.1101i	−1.56075	−	0.795244i	−0.999476	+	0.0323827i	$0.989690\pi$
$998$	23.8288	−	12.1414i	0.754286	−	0.384328i
$999$	−12.8075	+	17.6280i	−0.405212	+	0.557726i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	275.2.bm.c.7.6	yes	64
5.2	odd	4	inner	275.2.bm.c.18.6	yes	64
5.3	odd	4	inner	275.2.bm.c.18.3	yes	64
5.4	even	2	inner	275.2.bm.c.7.3	✓	64
11.8	odd	10	inner	275.2.bm.c.107.3	yes	64
55.8	even	20	inner	275.2.bm.c.118.6	yes	64
55.19	odd	10	inner	275.2.bm.c.107.6	yes	64
55.52	even	20	inner	275.2.bm.c.118.3	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
275.2.bm.c.7.3	✓	64	5.4	even	2	inner
275.2.bm.c.7.6	yes	64	1.1	even	1	trivial
275.2.bm.c.18.3	yes	64	5.3	odd	4	inner
275.2.bm.c.18.6	yes	64	5.2	odd	4	inner
275.2.bm.c.107.3	yes	64	11.8	odd	10	inner
275.2.bm.c.107.6	yes	64	55.19	odd	10	inner
275.2.bm.c.118.3	yes	64	55.52	even	20	inner
275.2.bm.c.118.6	yes	64	55.8	even	20	inner

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:	\( N \)	\(=\)	\( 275 = 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	275.bm (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.67541 - 0.265359i) q^{2} +(0.954428 + 1.87317i) q^{3} +(0.834479 - 0.271139i) q^{4} +(2.09612 + 2.88507i) q^{6} +(1.62781 + 0.829412i) q^{7} +(-1.69668 + 0.864500i) q^{8} +(-0.834479 + 1.14856i) q^{9} +O(q^{10})\)	\(q+(1.67541 - 0.265359i) q^{2} +(0.954428 + 1.87317i) q^{3} +(0.834479 - 0.271139i) q^{4} +(2.09612 + 2.88507i) q^{6} +(1.62781 + 0.829412i) q^{7} +(-1.69668 + 0.864500i) q^{8} +(-0.834479 + 1.14856i) q^{9} +(-2.06203 - 2.59770i) q^{11} +(1.30434 + 1.30434i) q^{12} +(0.298426 + 1.88419i) q^{13} +(2.94735 + 0.957652i) q^{14} +(-4.03293 + 2.93009i) q^{16} +(1.20096 - 7.58255i) q^{17} +(-1.09331 + 2.14575i) q^{18} +(-0.306474 + 0.943229i) q^{19} +3.84078i q^{21} +(-4.14408 - 3.80504i) q^{22} +(4.45709 - 4.45709i) q^{23} +(-3.23871 - 2.35306i) q^{24} +(0.999975 + 3.07761i) q^{26} +(3.28137 + 0.519719i) q^{27} +(1.58326 + 0.250764i) q^{28} +(2.29883 + 7.07507i) q^{29} +(-5.01147 - 3.64105i) q^{31} +(-3.28631 + 3.28631i) q^{32} +(2.89787 - 6.34185i) q^{33} -13.0226i q^{34} +(-0.384935 + 1.18471i) q^{36} +(-2.97754 + 5.84374i) q^{37} +(-0.263175 + 1.66162i) q^{38} +(-3.24458 + 2.35733i) q^{39} +(-7.06579 - 2.29582i) q^{41} +(1.01919 + 6.43490i) q^{42} +(-4.91933 - 4.91933i) q^{43} +(-2.42506 - 1.60863i) q^{44} +(6.28474 - 8.65020i) q^{46} +(0.166573 - 0.0848732i) q^{47} +(-9.33771 - 4.75780i) q^{48} +(-2.15265 - 2.96286i) q^{49} +(15.3496 - 4.98740i) q^{51} +(0.759907 + 1.49140i) q^{52} +(3.64497 - 0.577307i) q^{53} +5.63557 q^{54} -3.47890 q^{56} +(-2.05934 + 0.326167i) q^{57} +(5.72892 + 11.2436i) q^{58} +(-5.05093 + 1.64115i) q^{59} +(3.27130 + 4.50255i) q^{61} +(-9.36247 - 4.77042i) q^{62} +(-2.31101 + 1.17752i) q^{63} +(1.22631 - 1.68787i) q^{64} +(3.17226 - 11.3942i) q^{66} +(5.99054 + 5.99054i) q^{67} +(-1.05375 - 6.65310i) q^{68} +(12.6029 + 4.09492i) q^{69} +(6.49654 - 4.72001i) q^{71} +(0.422909 - 2.67014i) q^{72} +(-3.85754 + 7.57085i) q^{73} +(-3.43791 + 10.5808i) q^{74} +0.870202i q^{76} +(-1.20204 - 5.93884i) q^{77} +(-4.81048 + 4.81048i) q^{78} +(-7.68588 - 5.58412i) q^{79} +(3.47445 + 10.6933i) q^{81} +(-12.4473 - 1.97146i) q^{82} +(-8.70250 - 1.37834i) q^{83} +(1.04138 + 3.20505i) q^{84} +(-9.54730 - 6.93652i) q^{86} +(-11.0587 + 11.0587i) q^{87} +(5.74431 + 2.62483i) q^{88} +12.0425i q^{89} +(-1.07699 + 3.31463i) q^{91} +(2.51086 - 4.92784i) q^{92} +(2.03721 - 12.8625i) q^{93} +(0.256557 - 0.186399i) q^{94} +(-9.29237 - 3.01928i) q^{96} +(0.226246 + 1.42846i) q^{97} +(-4.39279 - 4.39279i) q^{98} +(4.70434 - 0.200646i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 20 q^{6}+O(q^{10}) \) 64 * q + 20 * q^6	\( 64 q + 20 q^{6} + 44 q^{11} - 16 q^{16} - 120 q^{26} + 8 q^{31} - 228 q^{36} - 180 q^{41} + 40 q^{46} - 60 q^{51} + 240 q^{56} + 160 q^{61} + 460 q^{66} + 8 q^{71} - 140 q^{81} - 40 q^{86} - 200 q^{91} - 240 q^{96}+O(q^{100}) \) 64 * q + 20 * q^6 + 44 * q^11 - 16 * q^16 - 120 * q^26 + 8 * q^31 - 228 * q^36 - 180 * q^41 + 40 * q^46 - 60 * q^51 + 240 * q^56 + 160 * q^61 + 460 * q^66 + 8 * q^71 - 140 * q^81 - 40 * q^86 - 200 * q^91 - 240 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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