LMFDB - Embedded newform 975.2.bn.d.407.13

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(218,975)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("975.218"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(975, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([6, 9, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.bn (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [96,0,2,0,0,-12,12,0,0,0,0,12,24,0,0,16,0,0,0,0,0,-20,0,0,0,0, 32,36,0,0,0,0,-30,0,0,-4,84,0,0,0,0,48,-8,0,0,0,0,28,0,0,-16,-28,0,0,0, 0,0,-84,0,0,-32,0,-90,0,0,0,-36,0,0,0,0,-90,0,0,0,72] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(76)] == traces)

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			407.13
Character	$\chi$	$=$	975.407
Dual form			975.2.bn.d.218.13

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.107570 - 0.0288234i) q^{2} +(-0.836177 + 1.51684i) q^{3} +(-1.72131 + 0.993799i) q^{4} +(-0.0462274 + 0.187269i) q^{6} +(3.86093 + 1.03453i) q^{7} +(-0.314011 + 0.314011i) q^{8} +(-1.60161 - 2.53670i) q^{9} +(2.60494 - 4.51189i) q^{11} +(-0.0681144 - 3.44195i) q^{12} +(1.36091 - 3.33885i) q^{13} +0.445140 q^{14} +(1.96287 - 3.39979i) q^{16} +(-3.27708 - 0.878092i) q^{17} +(-0.245402 - 0.226709i) q^{18} +(-0.210416 - 0.364452i) q^{19} +(-4.79764 + 4.99136i) q^{21} +(0.150166 - 0.560429i) q^{22} +(2.63136 - 0.705071i) q^{23} +(-0.213736 - 0.738874i) q^{24} +(0.0501565 - 0.398387i) q^{26} +(5.18700 - 0.308267i) q^{27} +(-7.67398 + 2.05624i) q^{28} +(2.52506 - 4.37354i) q^{29} -4.23553i q^{31} +(0.343025 - 1.28019i) q^{32} +(4.66563 + 7.72402i) q^{33} -0.377826 q^{34} +(5.27784 + 2.77476i) q^{36} +(1.53863 + 5.74223i) q^{37} +(-0.0331393 - 0.0331393i) q^{38} +(3.92655 + 4.85615i) q^{39} +(-0.973131 + 1.68551i) q^{41} +(-0.372216 + 0.675207i) q^{42} +(-0.905224 - 0.242554i) q^{43} +10.3551i q^{44} +(0.262734 - 0.151689i) q^{46} +(1.29449 + 1.29449i) q^{47} +(3.51564 + 5.82019i) q^{48} +(7.77434 + 4.48852i) q^{49} +(4.07215 - 4.23657i) q^{51} +(0.975600 + 7.09967i) q^{52} +(2.45762 + 2.45762i) q^{53} +(0.549082 - 0.182667i) q^{54} +(-1.53723 + 0.887520i) q^{56} +(0.728761 - 0.0144218i) q^{57} +(0.145562 - 0.543244i) q^{58} +(7.83433 - 4.52315i) q^{59} +(2.65934 + 4.60611i) q^{61} +(-0.122082 - 0.455618i) q^{62} +(-3.55942 - 11.4509i) q^{63} +7.70388i q^{64} +(0.724516 + 0.696396i) q^{66} +(-1.98691 - 7.41523i) q^{67} +(6.51352 - 1.74529i) q^{68} +(-1.13080 + 4.58092i) q^{69} +(-6.09876 - 10.5634i) q^{71} +(1.29948 + 0.293626i) q^{72} +(1.29733 + 1.29733i) q^{73} +(0.331021 + 0.573345i) q^{74} +(0.724384 + 0.418223i) q^{76} +(14.7252 - 14.7252i) q^{77} +(0.562351 + 0.409202i) q^{78} -2.49102i q^{79} +(-3.86966 + 8.12562i) q^{81} +(-0.0560979 + 0.209360i) q^{82} +(-9.55183 + 9.55183i) q^{83} +(3.29782 - 13.3596i) q^{84} -0.104367 q^{86} +(4.52256 + 7.48717i) q^{87} +(0.598803 + 2.23476i) q^{88} +(-3.74597 - 2.16273i) q^{89} +(8.70853 - 11.4832i) q^{91} +(-3.82869 + 3.82869i) q^{92} +(6.42463 + 3.54166i) q^{93} +(0.176560 + 0.101937i) q^{94} +(1.65501 + 1.59078i) q^{96} +(2.76392 + 0.740590i) q^{97} +(0.965663 + 0.258749i) q^{98} +(-15.6174 + 0.618364i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 2 q^{3} - 12 q^{6} + 12 q^{7} + 12 q^{12} + 24 q^{13} + 16 q^{16} - 20 q^{22} + 32 q^{27} + 36 q^{28} - 30 q^{33} - 4 q^{36} + 84 q^{37} + 48 q^{42} - 8 q^{43} + 28 q^{48} - 16 q^{51} - 28 q^{52}+ \cdots + 48 q^{97}+O(q^{100}) $ 96 * q + 2 * q^3 - 12 * q^6 + 12 * q^7 + 12 * q^12 + 24 * q^13 + 16 * q^16 - 20 * q^22 + 32 * q^27 + 36 * q^28 - 30 * q^33 - 4 * q^36 + 84 * q^37 + 48 * q^42 - 8 * q^43 + 28 * q^48 - 16 * q^51 - 28 * q^52 - 84 * q^58 - 32 * q^61 - 90 * q^63 - 36 * q^67 - 90 * q^72 + 72 * q^76 - 60 * q^78 + 32 * q^81 + 68 * q^82 + 26 * q^87 + 108 * q^88 - 80 * q^91 - 48 * q^93 + 48 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	0.107570	−	0.0288234i	0.0760637	−	0.0203812i	−0.220586	−	0.975367i	$-0.570797\pi$
$2$	0.107570	−	0.0288234i	0.0760637	−	0.0203812i	0.296650	+	0.954986i	$0.404130\pi$
$3$	−0.836177	+	1.51684i	−0.482767	+	0.875749i
$3$	−0.836177	+	1.51684i	−0.482767	+	0.875749i
$4$	−1.72131	+	0.993799i	−0.860655	+	0.496899i
$5$		0			0
$5$		0			0
$6$	−0.0462274	+	0.187269i	−0.0188723	+	0.0764521i
$7$	3.86093	+	1.03453i	1.45929	+	0.391017i	0.899246	−	0.437443i	$-0.144116\pi$
$7$	3.86093	+	1.03453i	1.45929	+	0.391017i	0.560048	+	0.828460i	$0.310783\pi$
$8$	−0.314011	+	0.314011i	−0.111020	+	0.111020i
$9$	−1.60161	−	2.53670i	−0.533872	−	0.845566i
$10$		0			0
$11$	2.60494	−	4.51189i	0.785419	−	1.36039i	−0.143329	−	0.989675i	$-0.545781\pi$
$11$	2.60494	−	4.51189i	0.785419	−	1.36039i	0.928748	−	0.370711i	$-0.120886\pi$
$12$	−0.0681144	−	3.44195i	−0.0196629	−	0.993604i
$13$	1.36091	−	3.33885i	0.377448	−	0.926031i
$13$	1.36091	−	3.33885i	0.377448	−	0.926031i
$14$	0.445140			0.118969
$15$		0			0
$16$	1.96287	−	3.39979i	0.490718	−	0.849948i
$17$	−3.27708	−	0.878092i	−0.794809	−	0.212969i	−0.161506	−	0.986872i	$-0.551635\pi$
$17$	−3.27708	−	0.878092i	−0.794809	−	0.212969i	−0.633304	+	0.773903i	$0.718302\pi$
$18$	−0.245402	−	0.226709i	−0.0578419	−	0.0534359i
$19$	−0.210416	−	0.364452i	−0.0482728	−	0.0836110i	0.840879	−	0.541223i	$-0.182038\pi$
$19$	−0.210416	−	0.364452i	−0.0482728	−	0.0836110i	−0.889152	+	0.457612i	$0.848705\pi$
$20$		0			0
$21$	−4.79764	+	4.99136i	−1.04693	+	1.08920i
$22$	0.150166	−	0.560429i	0.0320156	−	0.119484i
$23$	2.63136	−	0.705071i	0.548676	−	0.147017i	0.0261774	−	0.999657i	$-0.491667\pi$
$23$	2.63136	−	0.705071i	0.548676	−	0.147017i	0.522499	+	0.852640i	$0.325000\pi$
$24$	−0.213736	−	0.738874i	−0.0436287	−	0.150822i
$25$		0			0
$26$	0.0501565	−	0.398387i	0.00983649	−	0.0781302i
$27$	5.18700	−	0.308267i	0.998239	−	0.0593259i
$28$	−7.67398	+	2.05624i	−1.45024	+	0.388592i
$29$	2.52506	−	4.37354i	0.468892	−	0.812146i	−0.530475	−	0.847700i	$-0.677987\pi$
$29$	2.52506	−	4.37354i	0.468892	−	0.812146i	0.999368	+	0.0355548i	$0.0113198\pi$
$30$		0			0
$31$		−	4.23553i		−	0.760724i	−0.924838	−	0.380362i	$-0.875799\pi$
$31$		−	4.23553i		−	0.760724i	0.924838	−	0.380362i	$-0.124201\pi$
$32$	0.343025	−	1.28019i	0.0606389	−	0.226307i
$33$	4.66563	+	7.72402i	0.812181	+	1.34458i
$34$	−0.377826			−0.0647967
$35$		0			0
$36$	5.27784	+	2.77476i	0.879640	+	0.462460i
$37$	1.53863	+	5.74223i	0.252949	+	0.944017i	0.969220	+	0.246195i	$0.0791805\pi$
$37$	1.53863	+	5.74223i	0.252949	+	0.944017i	−0.716272	+	0.697822i	$0.754153\pi$
$38$	−0.0331393	−	0.0331393i	−0.00537590	−	0.00537590i
$39$	3.92655	+	4.85615i	0.628751	+	0.777607i
$40$		0			0
$41$	−0.973131	+	1.68551i	−0.151978	+	0.263233i	−0.931954	−	0.362576i	$-0.881897\pi$
$41$	−0.973131	+	1.68551i	−0.151978	+	0.263233i	0.779977	+	0.625808i	$0.215231\pi$
$42$	−0.372216	+	0.675207i	−0.0574342	+	0.104187i
$43$	−0.905224	−	0.242554i	−0.138045	−	0.0369892i	0.189135	−	0.981951i	$-0.439432\pi$
$43$	−0.905224	−	0.242554i	−0.138045	−	0.0369892i	−0.327180	+	0.944962i	$0.606098\pi$
$44$			10.3551i			1.56110i
$45$		0			0
$46$	0.262734	−	0.151689i	0.0387380	−	0.0223654i
$47$	1.29449	+	1.29449i	0.188821	+	0.188821i	0.795186	−	0.606365i	$-0.207373\pi$
$47$	1.29449	+	1.29449i	0.188821	+	0.188821i	−0.606365	+	0.795186i	$0.707373\pi$
$48$	3.51564	+	5.82019i	0.507438	+	0.840072i
$49$	7.77434	+	4.48852i	1.11062	+	0.641217i
$50$		0			0
$51$	4.07215	−	4.23657i	0.570215	−	0.593239i
$52$	0.975600	+	7.09967i	0.135291	+	0.984547i
$53$	2.45762	+	2.45762i	0.337580	+	0.337580i	0.855456	−	0.517876i	$-0.173277\pi$
$53$	2.45762	+	2.45762i	0.337580	+	0.337580i	−0.517876	+	0.855456i	$0.673277\pi$
$54$	0.549082	−	0.182667i	0.0747206	−	0.0248579i
$55$		0			0
$56$	−1.53723	+	0.887520i	−0.205421	+	0.118600i
$57$	0.728761	−	0.0144218i	0.0965268	−	0.00191022i
$58$	0.145562	−	0.543244i	0.0191132	−	0.0713314i
$59$	7.83433	−	4.52315i	1.01994	−	0.588865i	0.105856	−	0.994381i	$-0.466242\pi$
$59$	7.83433	−	4.52315i	1.01994	−	0.588865i	0.914088	+	0.405517i	$0.132908\pi$
$60$		0			0
$61$	2.65934	+	4.60611i	0.340493	+	0.589752i	0.984524	−	0.175248i	$-0.0560726\pi$
$61$	2.65934	+	4.60611i	0.340493	+	0.589752i	−0.644031	+	0.764999i	$0.722739\pi$
$62$	−0.122082	−	0.455618i	−0.0155045	−	0.0578635i
$63$	−3.55942	−	11.4509i	−0.448445	−	1.44268i
$64$			7.70388i			0.962986i
$65$		0			0
$66$	0.724516	+	0.696396i	0.0891817	+	0.0857205i
$67$	−1.98691	−	7.41523i	−0.242739	−	0.905915i	−0.974506	−	0.224360i	$-0.927971\pi$
$67$	−1.98691	−	7.41523i	−0.242739	−	0.905915i	0.731767	−	0.681555i	$-0.238696\pi$
$68$	6.51352	−	1.74529i	0.789881	−	0.211648i
$69$	−1.13080	+	4.58092i	−0.136133	+	0.551478i
$70$		0			0
$71$	−6.09876	−	10.5634i	−0.723789	−	1.25364i	−0.959470	−	0.281809i	$-0.909065\pi$
$71$	−6.09876	−	10.5634i	−0.723789	−	1.25364i	0.235681	−	0.971830i	$-0.424268\pi$
$72$	1.29948	+	0.293626i	0.153145	+	0.0346042i
$73$	1.29733	+	1.29733i	0.151841	+	0.151841i	0.778940	−	0.627099i	$-0.215758\pi$
$73$	1.29733	+	1.29733i	0.151841	+	0.151841i	−0.627099	+	0.778940i	$0.715758\pi$
$74$	0.331021	+	0.573345i	0.0384804	+	0.0666500i
$75$		0			0
$76$	0.724384	+	0.418223i	0.0830925	+	0.0479735i
$77$	14.7252	−	14.7252i	1.67809	−	1.67809i
$78$	0.562351	+	0.409202i	0.0636737	+	0.0463330i
$79$		−	2.49102i		−	0.280262i	−0.990133	−	0.140131i	$-0.955248\pi$
$79$		−	2.49102i		−	0.280262i	0.990133	−	0.140131i	$-0.0447523\pi$
$80$		0			0
$81$	−3.86966	+	8.12562i	−0.429962	+	0.902847i
$82$	−0.0560979	+	0.209360i	−0.00619497	+	0.0231200i
$83$	−9.55183	+	9.55183i	−1.04845	+	1.04845i	−0.0496844	+	0.998765i	$0.515822\pi$
$83$	−9.55183	+	9.55183i	−1.04845	+	1.04845i	−0.998765	+	0.0496844i	$0.984178\pi$
$84$	3.29782	−	13.3596i	0.359822	−	1.45765i
$85$		0			0
$86$	−0.104367			−0.0112541
$87$	4.52256	+	7.48717i	0.484870	+	0.802709i
$88$	0.598803	+	2.23476i	0.0638326	+	0.238227i
$89$	−3.74597	−	2.16273i	−0.397072	−	0.229249i	0.288148	−	0.957586i	$-0.406960\pi$
$89$	−3.74597	−	2.16273i	−0.397072	−	0.229249i	−0.685220	+	0.728336i	$0.740294\pi$
$90$		0			0
$91$	8.70853	−	11.4832i	0.912901	−	1.20376i
$92$	−3.82869	+	3.82869i	−0.399168	+	0.399168i
$93$	6.42463	+	3.54166i	0.666203	+	0.367253i
$94$	0.176560	+	0.101937i	0.0182108	+	0.0105140i
$95$		0			0
$96$	1.65501	+	1.59078i	0.168914	+	0.162358i
$97$	2.76392	+	0.740590i	0.280633	+	0.0751955i	0.396390	−	0.918082i	$-0.370263\pi$
$97$	2.76392	+	0.740590i	0.280633	+	0.0751955i	−0.115757	+	0.993278i	$0.536929\pi$
$98$	0.965663	+	0.258749i	0.0975467	+	0.0261376i
$99$	−15.6174	+	0.618364i	−1.56961	+	0.0621479i
$100$		0			0
$101$	2.39453	+	1.38248i	0.238265	+	0.137562i	0.614379	−	0.789011i	$-0.289407\pi$
$101$	2.39453	+	1.38248i	0.238265	+	0.137562i	−0.376114	+	0.926573i	$0.622740\pi$
$102$	0.315930	−	0.573103i	0.0312817	−	0.0567456i
$103$	−0.0455864	+	0.0455864i	−0.00449176	+	0.00449176i	−0.709349	−	0.704857i	$-0.751011\pi$
$103$	−0.0455864	+	0.0455864i	−0.00449176	+	0.00449176i	0.704857	+	0.709349i	$0.251011\pi$
$104$	0.621096	+	1.47578i	0.0609035	+	0.144712i
$105$		0			0
$106$	0.335204	+	0.193530i	0.0325579	+	0.0187973i
$107$	4.39639	+	16.4075i	0.425015	+	1.58618i	0.763890	+	0.645346i	$0.223287\pi$
$107$	4.39639	+	16.4075i	0.425015	+	1.58618i	−0.338875	+	0.940831i	$0.610046\pi$
$108$	−8.62208	+	5.68546i	−0.829660	+	0.547083i
$109$	−4.73152			−0.453198			−0.226599	−	0.973988i	$-0.572761\pi$
$109$	−4.73152			−0.453198			−0.226599	+	0.973988i	$0.572761\pi$
$110$		0			0
$111$	−9.99662	−	2.46767i	−0.948837	−	0.234221i
$112$	11.0957	−	11.0957i	1.04845	−	1.04845i
$113$	0.729762	−	2.72351i	0.0686502	−	0.256206i	−0.923068	−	0.384636i	$-0.874327\pi$
$113$	0.729762	−	2.72351i	0.0686502	−	0.256206i	0.991719	+	0.128430i	$0.0409937\pi$
$114$	0.0779774	−	0.0225567i	0.00730325	−	0.00211263i
$115$		0			0
$116$			10.0376i			0.931970i
$117$	−10.6493	+	1.89534i	−0.984529	+	0.175224i
$118$	0.712369	−	0.712369i	0.0655789	−	0.0655789i
$119$	−11.7442	−	6.78050i	−1.07659	−	0.621567i
$120$		0			0
$121$	−8.07143	−	13.9801i	−0.733766	−	1.27092i
$122$	0.418829	+	0.418829i	0.0379190	+	0.0379190i
$123$	−1.74294	−	2.88547i	−0.157156	−	0.260174i
$124$	4.20927	+	7.29067i	0.378003	+	0.654721i
$125$		0			0
$126$	−0.712943	−	1.12919i	−0.0635140	−	0.100596i
$127$	1.74999	−	0.468909i	0.155287	−	0.0416089i	−0.180338	−	0.983605i	$-0.557719\pi$
$127$	1.74999	−	0.468909i	0.155287	−	0.0416089i	0.335625	+	0.941996i	$0.391053\pi$
$128$	0.908103	+	3.38909i	0.0802657	+	0.299556i
$129$	1.12484	−	1.17026i	0.0990370	−	0.103036i
$130$		0			0
$131$			20.2873i			1.77251i	0.463200	+	0.886254i	$0.346701\pi$
$131$			20.2873i			1.77251i	−0.463200	+	0.886254i	$0.653299\pi$
$132$	−15.7071	−	8.65874i	−1.36713	−	0.753647i
$133$	−0.435365	−	1.62481i	−0.0377510	−	0.140889i
$134$	−0.427464	−	0.740390i	−0.0369273	−	0.0639599i
$135$		0			0
$136$	1.30477	−	0.753310i	0.111883	−	0.0645958i
$137$	3.45972	−	12.9118i	0.295584	−	1.10313i	−0.645169	−	0.764040i	$-0.723213\pi$
$137$	3.45972	−	12.9118i	0.295584	−	1.10313i	0.940753	−	0.339093i	$-0.110120\pi$
$138$	0.0103967	+	0.525365i	0.000885026	+	0.0447220i
$139$	17.9438	−	10.3598i	1.52197	−	0.878710i	0.522307	−	0.852758i	$-0.325072\pi$
$139$	17.9438	−	10.3598i	1.52197	−	0.878710i	0.999663	−	0.0259523i	$-0.00826180\pi$
$140$		0			0
$141$	−3.04596	+	0.881112i	−0.256516	+	0.0742030i
$142$	−0.960517	−	0.960517i	−0.0806048	−	0.0806048i
$143$	−11.5194	−	14.8378i	−0.963304	−	1.24080i
$144$	−11.7680	+	0.465948i	−0.980667	+	0.0388290i
$145$		0			0
$146$	0.176948	+	0.102161i	0.0146443	+	0.00845490i
$147$	−13.3091	+	8.03924i	−1.09772	+	0.663066i
$148$	−8.35507	−	8.35507i	−0.686783	−	0.686783i
$149$	−7.82540	+	4.51800i	−0.641082	+	0.370129i	−0.785031	−	0.619456i	$-0.787353\pi$
$149$	−7.82540	+	4.51800i	−0.641082	+	0.370129i	0.143949	+	0.989585i	$0.454020\pi$
$150$		0			0
$151$			11.7129i			0.953180i	0.879126	+	0.476590i	$0.158127\pi$
$151$			11.7129i			0.953180i	−0.879126	+	0.476590i	$0.841873\pi$
$152$	0.180515	+	0.0483689i	0.0146417	+	0.00392323i
$153$	3.02117	+	9.71933i	0.244247	+	0.785761i
$154$	1.15956	−	2.00842i	0.0934403	−	0.161843i
$155$		0			0
$156$	−11.5848	−	4.45675i	−0.927530	−	0.356826i
$157$	−11.2708	−	11.2708i	−0.899508	−	0.899508i	0.0958846	−	0.995392i	$-0.469432\pi$
$157$	−11.2708	−	11.2708i	−0.899508	−	0.899508i	−0.995392	+	0.0958846i	$0.969432\pi$
$158$	−0.0717997	−	0.267960i	−0.00571207	−	0.0213177i
$159$	−5.78282	+	1.67281i	−0.458608	+	0.132663i
$160$		0			0
$161$	10.8889			0.858167
$162$	−0.182053	+	0.985613i	−0.0143034	+	0.0774370i
$163$	3.31744	−	12.3808i	0.259842	−	0.969742i	−0.705491	−	0.708719i	$-0.749273\pi$
$163$	3.31744	−	12.3808i	0.259842	−	0.969742i	0.965333	−	0.261023i	$-0.0840599\pi$
$164$		−	3.86839i		−	0.302070i
$165$		0			0
$166$	−0.752177	+	1.30281i	−0.0583803	+	0.101118i
$167$	−21.7842	+	5.83706i	−1.68571	+	0.451685i	−0.969278	−	0.245968i	$-0.920894\pi$
$167$	−21.7842	+	5.83706i	−1.68571	+	0.451685i	−0.716435	+	0.697654i	$0.754227\pi$
$168$	−0.0608301	−	3.07386i	−0.00469315	−	0.237153i
$169$	−9.29585	−	9.08774i	−0.715066	−	0.699057i
$170$		0			0
$171$	−0.587498	+	1.11747i	−0.0449271	+	0.0854554i
$172$	1.79922	−	0.482100i	0.137189	−	0.0367598i
$173$	0.936524	−	3.49516i	0.0712026	−	0.265732i	−0.921143	−	0.389225i	$-0.872743\pi$
$173$	0.936524	−	3.49516i	0.0712026	−	0.265732i	0.992345	+	0.123493i	$0.0394096\pi$
$174$	0.702299	+	0.675042i	0.0532412	+	0.0511748i
$175$		0			0
$176$	−10.2263	−	17.7125i	−0.770838	−	1.33513i
$177$	0.310014	+	15.6656i	0.0233021	+	1.17750i
$178$	−0.465292	−	0.124675i	−0.0348751	−	0.00934476i
$179$	−2.91155	+	5.04296i	−0.217620	+	0.376928i	−0.954080	−	0.299553i	$-0.903163\pi$
$179$	−2.91155	+	5.04296i	−0.217620	+	0.376928i	0.736460	+	0.676481i	$0.236496\pi$
$180$		0			0
$181$	9.95426			0.739894			0.369947	−	0.929053i	$-0.379376\pi$
$181$	9.95426			0.739894			0.369947	+	0.929053i	$0.379376\pi$
$182$	0.605795	−	1.48626i	0.0449045	−	0.110169i
$183$	−9.21041	+	0.182270i	−0.680853	+	0.0134738i
$184$	−0.604876	+	1.04768i	−0.0445921	+	0.0772357i
$185$		0			0
$186$	0.793182	+	0.195798i	0.0581590	+	0.0143566i
$187$	−12.4985	+	12.4985i	−0.913978	+	0.913978i
$188$	−3.51468	−	0.941755i	−0.256334	−	0.0686846i
$189$	20.3456	+	4.17593i	1.47992	+	0.303754i
$190$		0			0
$191$	19.8105	−	11.4376i	1.43343	−	0.827594i	0.436053	−	0.899921i	$-0.356376\pi$
$191$	19.8105	−	11.4376i	1.43343	−	0.827594i	0.997381	+	0.0723271i	$0.0230425\pi$
$192$	−11.6856	−	6.44181i	−0.843333	−	0.464898i
$193$	16.5328	−	4.42994i	1.19005	−	0.318874i	0.391147	−	0.920328i	$-0.372078\pi$
$193$	16.5328	−	4.42994i	1.19005	−	0.318874i	0.798908	+	0.601454i	$0.205412\pi$
$194$	0.318662			0.0228786
$195$		0			0
$196$	−17.8427			−1.27448
$197$	1.42911	−	0.382929i	0.101820	−	0.0272826i	−0.207549	−	0.978225i	$-0.566549\pi$
$197$	1.42911	−	0.382929i	0.101820	−	0.0272826i	0.309369	+	0.950942i	$0.399882\pi$
$198$	−1.66215	+	0.516664i	−0.118124	+	0.0367177i
$199$	20.6928	−	11.9470i	1.46687	−	0.846899i	0.467558	−	0.883962i	$-0.345134\pi$
$199$	20.6928	−	11.9470i	1.46687	−	0.846899i	0.999313	+	0.0370636i	$0.0118004\pi$
$200$		0			0
$201$	12.9091	+	3.18663i	0.910540	+	0.224768i
$202$	0.297429	+	0.0796957i	0.0209270	+	0.00560737i
$203$	14.2737	−	14.2737i	1.00181	−	1.00181i
$204$	−2.79913	+	11.3394i	−0.195978	+	0.793914i
$205$		0			0
$206$	−0.00358979	+	0.00621770i	−0.000250113	+	0.000433208i
$207$	−6.00297	−	5.54571i	−0.417236	−	0.385453i
$208$	−8.68011	−	11.1805i	−0.601857	−	0.775231i
$209$	−2.19249			−0.151658
$210$		0			0
$211$	1.53923	−	2.66603i	0.105965	−	0.183537i	−0.808167	−	0.588953i	$-0.799540\pi$
$211$	1.53923	−	2.66603i	0.105965	−	0.183537i	0.914132	+	0.405416i	$0.132873\pi$
$212$	−6.67270	−	1.78795i	−0.458283	−	0.122797i
$213$	21.1226	−	0.418005i	1.44730	−	0.0286413i
$214$	0.945842	+	1.63825i	0.0646565	+	0.111988i
$215$		0			0
$216$	−1.53198	+	1.72558i	−0.104238	+	0.117411i
$217$	4.38180	−	16.3531i	0.297456	−	1.11012i
$218$	−0.508972	+	0.136379i	−0.0344719	+	0.00923672i
$219$	−3.05264	+	0.883046i	−0.206279	+	0.0596707i
$220$		0			0
$221$	−7.39163	+	9.74669i	−0.497215	+	0.655633i
$222$	−1.14647	+	0.0226880i	−0.0769458	+	0.00152272i
$223$	5.58375	−	1.49616i	0.373916	−	0.100190i	−0.0669668	−	0.997755i	$-0.521332\pi$
$223$	5.58375	−	1.49616i	0.373916	−	0.100190i	0.440883	+	0.897565i	$0.354666\pi$
$224$	2.64879	−	4.58784i	0.176980	−	0.306538i
$225$		0			0
$226$		−	0.314003i		−	0.0208872i
$227$	−3.79984	+	14.1812i	−0.252204	+	0.941238i	0.717421	+	0.696640i	$0.245323\pi$
$227$	−3.79984	+	14.1812i	−0.252204	+	0.941238i	−0.969625	+	0.244598i	$0.921344\pi$
$228$	−1.24009	+	0.749066i	−0.0821271	+	0.0496081i
$229$	−3.60574			−0.238274			−0.119137	−	0.992878i	$-0.538013\pi$
$229$	−3.60574			−0.238274			−0.119137	+	0.992878i	$0.538013\pi$
$230$		0			0
$231$	10.0229	+	34.6486i	0.659459	+	2.27971i
$232$	0.580442	+	2.16624i	0.0381079	+	0.142220i
$233$	7.88221	+	7.88221i	0.516381	+	0.516381i	0.916474	−	0.400093i	$-0.131022\pi$
$233$	7.88221	+	7.88221i	0.516381	+	0.516381i	−0.400093	+	0.916474i	$0.631022\pi$
$234$	−1.09092	+	0.510831i	−0.0713156	+	0.0333941i
$235$		0			0
$236$	−8.99021	+	15.5715i	−0.585213	+	1.01362i
$237$	3.77848	+	2.08294i	0.245439	+	0.135301i
$238$	−1.45876	−	0.390874i	−0.0945575	−	0.0253366i
$239$		−	0.0947772i		−	0.00613063i	−0.999995	−	0.00306532i	$-0.999024\pi$
$239$		−	0.0947772i		−	0.00613063i	0.999995	−	0.00306532i	$-0.000975722\pi$
$240$		0			0
$241$	9.34499	−	5.39533i	0.601964	−	0.347544i	−0.167850	−	0.985813i	$-0.553682\pi$
$241$	9.34499	−	5.39533i	0.601964	−	0.347544i	0.769814	+	0.638269i	$0.220349\pi$
$242$	−1.27120	−	1.27120i	−0.0817159	−	0.0817159i
$243$	−9.08955	−	12.6641i	−0.583095	−	0.812404i
$244$	−9.15509	−	5.28569i	−0.586095	−	0.338382i
$245$		0			0
$246$	−0.270658	−	0.260154i	−0.0172565	−	0.0165868i
$247$	−1.50321	+	0.206563i	−0.0956468	+	0.0131433i
$248$	1.33000	+	1.33000i	0.0844554	+	0.0844554i
$249$	−6.50158	−	22.4756i	−0.412021	−	1.42434i
$250$		0			0
$251$	−18.5242	+	10.6949i	−1.16923	+	0.675058i	−0.953500	−	0.301394i	$-0.902548\pi$
$251$	−18.5242	+	10.6949i	−1.16923	+	0.675058i	−0.215735	+	0.976452i	$0.569215\pi$
$252$	17.5068	+	16.1733i	1.10282	+	1.01882i
$253$	3.67333	−	13.7091i	0.230941	−	0.861882i
$254$	0.174732	−	0.100881i	0.0109636	−	0.00632986i
$255$		0			0
$256$	−7.50851	−	13.0051i	−0.469282	−	0.812821i
$257$	4.19954	+	15.6729i	0.261960	+	0.977648i	0.964085	+	0.265594i	$0.0855681\pi$
$257$	4.19954	+	15.6729i	0.261960	+	0.977648i	−0.702125	+	0.712054i	$0.747765\pi$
$258$	0.0872689	−	0.158307i	0.00543313	−	0.00985579i
$259$			23.7621i			1.47651i
$260$		0			0
$261$	−15.1385	+	0.599402i	−0.937051	+	0.0371021i
$262$	0.584748	+	2.18231i	0.0361259	+	0.134824i
$263$	−22.1701	+	5.94046i	−1.36707	+	0.366304i	−0.866406	−	0.499340i	$-0.833576\pi$
$263$	−22.1701	+	5.94046i	−1.36707	+	0.366304i	−0.500660	+	0.865644i	$0.666909\pi$
$264$	−3.89049	−	0.960370i	−0.239443	−	0.0591067i
$265$		0			0
$266$	−0.0936648	−	0.162232i	−0.00574296	−	0.00994709i
$267$	6.41282	−	3.87361i	0.392458	−	0.237061i
$268$	10.7893	+	10.7893i	0.659063	+	0.659063i
$269$	−1.73455	−	3.00433i	−0.105758	−	0.183177i	0.808290	−	0.588785i	$-0.200393\pi$
$269$	−1.73455	−	3.00433i	−0.105758	−	0.183177i	−0.914047	+	0.405607i	$0.867060\pi$
$270$		0			0
$271$	10.2881	+	5.93984i	0.624958	+	0.360819i	0.778797	−	0.627277i	$-0.215830\pi$
$271$	10.2881	+	5.93984i	0.624958	+	0.360819i	−0.153839	+	0.988096i	$0.549164\pi$
$272$	−9.41782	+	9.41782i	−0.571039	+	0.571039i
$273$	10.1363	+	22.8114i	0.613475	+	1.38061i
$274$		−	1.48865i		−	0.0899328i
$275$		0			0
$276$	−2.60605	−	9.00897i	−0.156866	−	0.542276i
$277$	4.44872	−	16.6029i	0.267298	−	0.997570i	−0.693531	−	0.720427i	$-0.743946\pi$
$277$	4.44872	−	16.6029i	0.267298	−	0.997570i	0.960829	−	0.277143i	$-0.0893875\pi$
$278$	1.63161	−	1.63161i	0.0978575	−	0.0978575i
$279$	−10.7443	+	6.78369i	−0.643242	+	0.406129i
$280$		0			0
$281$	22.1387			1.32068			0.660341	−	0.750966i	$-0.270412\pi$
$281$	22.1387			1.32068			0.660341	+	0.750966i	$0.270412\pi$
$282$	−0.302258	+	0.182576i	−0.0179992	+	0.0108723i
$283$	0.732387	+	2.73331i	0.0435359	+	0.162478i	0.984271	−	0.176663i	$-0.0565303\pi$
$283$	0.732387	+	2.73331i	0.0435359	+	0.162478i	−0.940736	+	0.339141i	$0.889864\pi$
$284$	20.9957	+	12.1219i	1.24587	+	0.719301i
$285$		0			0
$286$	−1.66682	−	1.26408i	−0.0985614	−	0.0747464i
$287$	−5.50091	+	5.50091i	−0.324708	+	0.324708i
$288$	−3.79684	+	1.18022i	−0.223731	+	0.0695449i
$289$	−4.75421	−	2.74484i	−0.279659	−	0.161461i
$290$		0			0
$291$	−3.43448	+	3.57316i	−0.201333	+	0.209462i
$292$	−3.52240	−	0.943823i	−0.206133	−	0.0552331i
$293$	−7.63862	−	2.04676i	−0.446253	−	0.119573i	0.0286927	−	0.999588i	$-0.490866\pi$
$293$	−7.63862	−	2.04676i	−0.446253	−	0.119573i	−0.474946	+	0.880015i	$0.657532\pi$
$294$	−1.19995	+	1.24840i	−0.0699823	+	0.0728080i
$295$		0			0
$296$	−2.28627	−	1.31998i	−0.132887	−	0.0767222i
$297$	12.1210	−	24.2062i	0.703329	−	1.40459i
$298$	−0.711557	+	0.711557i	−0.0412194	+	0.0412194i
$299$	1.22691	−	9.74525i	0.0709543	−	0.563583i
$300$		0			0
$301$	−3.24408	−	1.87297i	−0.186985	−	0.107956i
$302$	0.337605	+	1.25996i	0.0194270	+	0.0725024i
$303$	−4.09926	+	2.47612i	−0.235496	+	0.142250i
$304$	−1.65208			−0.0947533
$305$		0			0
$306$	0.605132	+	0.958431i	0.0345931	+	0.0547899i
$307$	−10.6962	+	10.6962i	−0.610465	+	0.610465i	−0.943067	−	0.332602i	$-0.892073\pi$
$307$	−10.6962	+	10.6962i	−0.610465	+	0.610465i	0.332602	+	0.943067i	$0.392073\pi$
$308$	−10.7127	+	39.9805i	−0.610415	+	2.27810i
$309$	−0.0310290	−	0.107266i	−0.00176518	−	0.00610213i
$310$		0			0
$311$		−	12.0194i		−	0.681560i	−0.940143	−	0.340780i	$-0.889309\pi$
$311$		−	12.0194i		−	0.681560i	0.940143	−	0.340780i	$-0.110691\pi$
$312$	−2.75787	−	0.291908i	−0.156133	−	0.0165260i
$313$	−16.5079	+	16.5079i	−0.933082	+	0.933082i	−0.997897	−	0.0648148i	$-0.979354\pi$
$313$	−16.5079	+	16.5079i	−0.933082	+	0.933082i	0.0648148	+	0.997897i	$0.479354\pi$
$314$	−1.53727	−	0.887541i	−0.0867530	−	0.0500869i
$315$		0			0
$316$	2.47557	+	4.28782i	0.139262	+	0.241209i
$317$	0.778692	+	0.778692i	0.0437357	+	0.0437357i	0.728636	−	0.684901i	$-0.240154\pi$
$317$	0.778692	+	0.778692i	0.0437357	+	0.0437357i	−0.684901	+	0.728636i	$0.740154\pi$
$318$	−0.573844	+	0.346626i	−0.0321796	+	0.0194378i
$319$	−13.1553	−	22.7856i	−0.736554	−	1.27575i
$320$		0			0
$321$	−28.5638	−	7.05100i	−1.59428	−	0.393548i
$322$	1.17132	−	0.313855i	0.0652753	−	0.0174905i
$323$	0.369530	+	1.37910i	0.0205612	+	0.0767354i
$324$	−1.41435	−	17.8324i	−0.0785748	−	0.990688i
$325$		0			0
$326$		−	1.42743i		−	0.0790581i
$327$	3.95639	−	7.17697i	0.218789	−	0.396887i
$328$	−0.223696	−	0.834844i	−0.0123515	−	0.0460965i
$329$	3.65874	+	6.33712i	0.201713	+	0.349377i
$330$		0			0
$331$	−24.3850	+	14.0787i	−1.34032	+	0.773834i	−0.986854	−	0.161614i	$-0.948330\pi$
$331$	−24.3850	+	14.0787i	−1.34032	+	0.773834i	−0.353466	+	0.935448i	$0.614997\pi$
$332$	6.94906	−	25.9343i	0.381379	−	1.42333i
$333$	12.1020	−	13.0999i	0.663186	−	0.717868i
$334$	−2.17509	+	1.25579i	−0.119016	+	0.0687138i
$335$		0			0
$336$	7.55244	+	26.1084i	0.412019	+	1.42433i
$337$	17.9435	+	17.9435i	0.977446	+	0.977446i	0.999751	−	0.0223051i	$-0.00710052\pi$
$337$	17.9435	+	17.9435i	0.977446	+	0.977446i	−0.0223051	+	0.999751i	$0.507101\pi$
$338$	−1.26190	−	0.709634i	−0.0686382	−	0.0385990i
$339$	3.52092	+	3.38427i	0.191230	+	0.183808i
$340$		0			0
$341$	−19.1103	−	11.0333i	−1.03488	−	0.597487i
$342$	−0.0309880	+	0.137141i	−0.00167564	+	0.00741572i
$343$	5.58789	+	5.58789i	0.301717	+	0.301717i
$344$	0.360415	−	0.208086i	0.0194323	−	0.0112192i
$345$		0			0
$346$		−	0.402969i		−	0.0216637i
$347$	−0.484424	−	0.129801i	−0.0260052	−	0.00696808i	0.245793	−	0.969322i	$-0.420952\pi$
$347$	−0.484424	−	0.129801i	−0.0260052	−	0.00696808i	−0.271798	+	0.962354i	$0.587618\pi$
$348$	−15.2255	−	8.39323i	−0.816171	−	0.449924i
$349$	−4.63210	+	8.02304i	−0.247951	+	0.429463i	−0.962957	−	0.269655i	$-0.913090\pi$
$349$	−4.63210	+	8.02304i	−0.247951	+	0.429463i	0.715006	+	0.699118i	$0.246424\pi$
$350$		0			0
$351$	6.02978	−	17.7381i	0.321846	−	0.946792i
$352$	−4.88250	−	4.88250i	−0.260238	−	0.260238i
$353$	−5.48087	−	20.4549i	−0.291717	−	1.08870i	−0.943790	−	0.330547i	$-0.892767\pi$
$353$	−5.48087	−	20.4549i	−0.291717	−	1.08870i	0.652072	−	0.758157i	$-0.273900\pi$
$354$	0.484884	+	1.67622i	0.0257713	+	0.0890900i
$355$		0			0
$356$	8.59729			0.455656
$357$	20.1052	−	12.1443i	1.06408	−	0.642747i
$358$	−0.167842	+	0.626394i	−0.00887071	+	0.0331059i
$359$			17.7610i			0.937391i	0.883360	+	0.468695i	$0.155276\pi$
$359$			17.7610i			0.937391i	−0.883360	+	0.468695i	$0.844724\pi$
$360$		0			0
$361$	9.41145	−	16.3011i	0.495339	−	0.857953i
$362$	1.07078	−	0.286915i	0.0562791	−	0.0150799i
$363$	27.9548	−	0.553211i	1.46724	−	0.0290361i
$364$	−3.57812	+	28.4206i	−0.187544	+	1.48964i
$365$		0			0
$366$	−0.985514	+	0.285082i	−0.0515136	+	0.0149015i
$367$	−1.08991	+	0.292041i	−0.0568929	+	0.0152444i	−0.287153	−	0.957885i	$-0.592709\pi$
$367$	−1.08991	+	0.292041i	−0.0568929	+	0.0152444i	0.230260	+	0.973129i	$0.426042\pi$
$368$	2.76792	−	10.3300i	0.144288	−	0.538490i
$369$	5.83421	−	0.231003i	0.303717	−	0.0120255i
$370$		0			0
$371$	6.94621	+	12.0312i	0.360629	+	0.624628i
$372$	−14.5785	+	0.288501i	−0.755859	+	0.0149581i
$373$	−17.2256	−	4.61559i	−0.891908	−	0.238986i	−0.216370	−	0.976311i	$-0.569422\pi$
$373$	−17.2256	−	4.61559i	−0.891908	−	0.238986i	−0.675538	+	0.737325i	$0.736088\pi$
$374$	−0.984215	+	1.70471i	−0.0508926	+	0.0881485i
$375$		0			0
$376$	−0.812968			−0.0419256
$377$	−11.1662	−	14.3828i	−0.575089	−	0.740752i
$378$	2.30894	−	0.137222i	0.118759	−	0.00705793i
$379$	5.17481	−	8.96303i	0.265812	−	0.460400i	−0.701964	−	0.712212i	$-0.747693\pi$
$379$	5.17481	−	8.96303i	0.265812	−	0.460400i	0.967776	+	0.251813i	$0.0810267\pi$
$380$		0			0
$381$	−0.752043	+	3.04655i	−0.0385283	+	0.156079i
$382$	1.80135	−	1.80135i	0.0921650	−	0.0921650i
$383$	16.0474	+	4.29989i	0.819985	+	0.219714i	0.644340	−	0.764739i	$-0.277132\pi$
$383$	16.0474	+	4.29989i	0.819985	+	0.219714i	0.175645	+	0.984454i	$0.443799\pi$
$384$	−5.90004	−	1.45643i	−0.301085	−	0.0743231i
$385$		0			0
$386$	1.65075	−	0.953061i	0.0840210	−	0.0485095i
$387$	0.834534	+	2.68476i	0.0424218	+	0.136474i
$388$	−5.49356	+	1.47199i	−0.278893	+	0.0747292i
$389$	24.1762			1.22578			0.612891	−	0.790167i	$-0.290006\pi$
$389$	24.1762			1.22578			0.612891	+	0.790167i	$0.290006\pi$
$390$		0			0
$391$	−9.24230			−0.467403
$392$	−3.85068	+	1.03179i	−0.194488	+	0.0521130i
$393$	−30.7726	−	16.9638i	−1.55227	−	0.855709i
$394$	0.142693	−	0.0823836i	0.00718875	−	0.00415043i
$395$		0			0
$396$	26.2679	−	16.5850i	1.32001	−	0.833425i
$397$	−8.25936	−	2.21309i	−0.414525	−	0.111072i	0.0455279	−	0.998963i	$-0.485503\pi$
$397$	−8.25936	−	2.21309i	−0.414525	−	0.111072i	−0.460053	+	0.887891i	$0.652170\pi$
$398$	1.88158	−	1.88158i	0.0943149	−	0.0943149i
$399$	2.82861	+	0.698246i	0.141608	+	0.0349560i
$400$		0			0
$401$	13.7400	−	23.7983i	0.686142	−	1.18843i	−0.286935	−	0.957950i	$-0.592636\pi$
$401$	13.7400	−	23.7983i	0.686142	−	1.18843i	0.973076	−	0.230482i	$-0.0740304\pi$
$402$	1.48049	−	0.0292982i	0.0738401	−	0.00146126i
$403$	−14.1418	−	5.76418i	−0.704454	−	0.287134i
$404$	−5.49564			−0.273418
$405$		0			0
$406$	1.12401	−	1.94684i	0.0557835	−	0.0966199i
$407$	29.9163	+	8.01606i	1.48290	+	0.397341i
$408$	0.0516315	+	2.60903i	0.00255614	+	0.129166i
$409$	18.6648	+	32.3284i	0.922916	+	1.59854i	0.794878	+	0.606769i	$0.207535\pi$
$409$	18.6648	+	32.3284i	0.922916	+	1.59854i	0.128038	+	0.991769i	$0.459132\pi$
$410$		0			0
$411$	16.6923	+	16.0444i	0.823369	+	0.791414i
$412$	0.0331646	−	0.123772i	0.00163390	−	0.00609781i
$413$	34.9272	−	9.35870i	1.71865	−	0.460512i
$414$	−0.805588	−	0.423528i	−0.0395925	−	0.0208153i
$415$		0			0
$416$	−3.80753	−	2.88753i	−0.186680	−	0.141573i
$417$	0.710057	+	35.8805i	0.0347717	+	1.75708i
$418$	−0.235847	+	0.0631949i	−0.0115356	+	0.00309097i
$419$	−14.8413	+	25.7059i	−0.725046	+	1.25582i	0.233909	+	0.972259i	$0.424848\pi$
$419$	−14.8413	+	25.7059i	−0.725046	+	1.25582i	−0.958955	+	0.283558i	$0.908485\pi$
$420$		0			0
$421$			21.3437i			1.04023i	0.854097	+	0.520114i	$0.174111\pi$
$421$			21.3437i			1.04023i	−0.854097	+	0.520114i	$0.825889\pi$
$422$	0.0887317	−	0.331151i	0.00431939	−	0.0161202i
$423$	1.21045	−	5.35700i	0.0588543	−	0.260466i
$424$	−1.54344			−0.0749561
$425$		0			0
$426$	2.26011	−	0.653789i	0.109503	−	0.0316762i
$427$	5.50234	+	20.5350i	0.266277	+	0.993760i
$428$	−23.8734	−	23.8734i	−1.15396	−	1.15396i
$429$	32.1388	−	5.06614i	1.55168	−	0.244596i
$430$		0			0
$431$	1.45407	−	2.51852i	0.0700400	−	0.121313i	−0.828879	−	0.559429i	$-0.811021\pi$
$431$	1.45407	−	2.51852i	0.0700400	−	0.121313i	0.898919	+	0.438116i	$0.144354\pi$
$432$	9.13337	−	18.2398i	0.439429	−	0.877563i
$433$	25.5439	+	6.84446i	1.22756	+	0.328924i	0.813629	−	0.581384i	$-0.197489\pi$
$433$	25.5439	+	6.84446i	1.22756	+	0.328924i	0.413932	+	0.910308i	$0.364155\pi$
$434$		−	1.88541i		−	0.0905024i
$435$		0			0
$436$	8.14442	−	4.70218i	0.390047	−	0.225194i
$437$	−0.810645	−	0.810645i	−0.0387784	−	0.0387784i
$438$	−0.302922	+	0.182977i	−0.0144742	+	0.00874299i
$439$	−23.2175	−	13.4046i	−1.10811	−	0.639768i	−0.169771	−	0.985484i	$-0.554303\pi$
$439$	−23.2175	−	13.4046i	−1.10811	−	0.639768i	−0.938339	+	0.345716i	$0.887636\pi$
$440$		0			0
$441$	−1.06549	−	26.9100i	−0.0507376	−	1.28143i
$442$	−0.514187	+	1.26151i	−0.0244574	+	0.0600037i
$443$	19.3624	+	19.3624i	0.919937	+	0.919937i	0.997024	−	0.0770872i	$-0.0245620\pi$
$443$	19.3624	+	19.3624i	0.919937	+	0.919937i	−0.0770872	+	0.997024i	$0.524562\pi$
$444$	19.6596	−	5.68700i	0.933006	−	0.269893i
$445$		0			0
$446$	0.557522	−	0.321885i	0.0263994	−	0.0152417i
$447$	−0.309661	−	15.6477i	−0.0146465	−	0.740113i
$448$	−7.96992	+	29.7442i	−0.376543	+	1.40528i
$449$	3.02917	−	1.74889i	0.142956	−	0.0825354i	−0.426816	−	0.904338i	$-0.640365\pi$
$449$	3.02917	−	1.74889i	0.142956	−	0.0825354i	0.569772	+	0.821803i	$0.307032\pi$
$450$		0			0
$451$	5.06990	+	8.78132i	0.238732	+	0.413496i
$452$	1.45047	+	5.41324i	0.0682245	+	0.254617i
$453$	−17.7666	−	9.79404i	−0.834746	−	0.460164i
$454$			1.63500i			0.0767343i
$455$		0			0
$456$	−0.224311	+	0.233368i	−0.0105043	+	0.0109284i
$457$	9.02853	+	33.6949i	0.422337	+	1.57618i	0.769671	+	0.638441i	$0.220420\pi$
$457$	9.02853	+	33.6949i	0.422337	+	1.57618i	−0.347334	+	0.937742i	$0.612913\pi$
$458$	−0.387870	+	0.103930i	−0.0181240	+	0.00485631i
$459$	−17.2689	−	3.54445i	−0.806044	−	0.165441i
$460$		0			0
$461$	−5.43399	−	9.41194i	−0.253086	−	0.438358i	0.711288	−	0.702901i	$-0.248112\pi$
$461$	−5.43399	−	9.41194i	−0.253086	−	0.438358i	−0.964374	+	0.264543i	$0.914779\pi$
$462$	2.07686	+	3.43827i	0.0966242	+	0.159963i
$463$	6.69797	+	6.69797i	0.311281	+	0.311281i	0.845406	−	0.534125i	$-0.179359\pi$
$463$	6.69797	+	6.69797i	0.311281	+	0.311281i	−0.534125	+	0.845406i	$0.679359\pi$
$464$	−9.91274	−	17.1694i	−0.460188	−	0.797068i
$465$		0			0
$466$	1.07508	+	0.620700i	0.0498023	+	0.0287534i
$467$	4.56632	−	4.56632i	0.211304	−	0.211304i	−0.593517	−	0.804821i	$-0.702261\pi$
$467$	4.56632	−	4.56632i	0.211304	−	0.211304i	0.804821	+	0.593517i	$0.202261\pi$
$468$	16.4472	−	13.8457i	0.760271	−	0.640019i
$469$		−	30.6852i		−	1.41691i
$470$		0			0
$471$	26.5204	−	7.67163i	1.22200	−	0.353490i
$472$	−1.03975	+	3.88039i	−0.0478582	+	0.178609i
$473$	−3.45243	+	3.45243i	−0.158743	+	0.158743i
$474$	0.466490	+	0.115153i	0.0214266	+	0.00528917i
$475$		0			0
$476$	26.9538			1.23543
$477$	2.29808	−	10.1704i	0.105222	−	0.465670i
$478$	−0.00273180	−	0.0101952i	−0.000124950	−	0.000466319i
$479$	−13.8170	−	7.97728i	−0.631317	−	0.364491i	0.149945	−	0.988694i	$-0.452090\pi$
$479$	−13.8170	−	7.97728i	−0.631317	−	0.364491i	−0.781262	+	0.624203i	$0.785424\pi$
$480$		0			0
$481$	21.2664	+	2.67741i	0.969664	+	0.122079i
$482$	0.849732	−	0.849732i	0.0387042	−	0.0387042i
$483$	−9.10506	+	16.5168i	−0.414295	+	0.751538i
$484$	27.7869	+	16.0427i	1.26304	+	0.729216i
$485$		0			0
$486$	−1.34279	−	1.10029i	−0.0609102	−	0.0499103i
$487$	−31.7115	−	8.49708i	−1.43699	−	0.385040i	−0.545510	−	0.838104i	$-0.683664\pi$
$487$	−31.7115	−	8.49708i	−1.43699	−	0.385040i	−0.891478	+	0.453065i	$0.850331\pi$
$488$	−2.28143	−	0.611308i	−0.103276	−	0.0276726i
$489$	16.0058	+	15.3846i	0.723807	+	0.695716i
$490$		0			0
$491$	−25.2561	−	14.5816i	−1.13979	−	0.658058i	−0.193412	−	0.981118i	$-0.561955\pi$
$491$	−25.2561	−	14.5816i	−1.13979	−	0.658058i	−0.946379	+	0.323059i	$0.895289\pi$
$492$	5.86773	+	3.23466i	0.264538	+	0.145830i
$493$	−12.1152	+	12.1152i	−0.545642	+	0.545642i
$494$	−0.155747	+	0.0655476i	−0.00700738	+	0.00294913i
$495$		0			0
$496$	−14.3999	−	8.31380i	−0.646576	−	0.373301i
$497$	−12.6187	−	47.0937i	−0.566027	−	2.11244i
$498$	−1.34720	−	2.23031i	−0.0603695	−	0.0999427i
$499$	−16.7557			−0.750087			−0.375044	−	0.927007i	$-0.622372\pi$
$499$	−16.7557			−0.750087			−0.375044	+	0.927007i	$0.622372\pi$
$500$		0			0
$501$	9.36157	−	37.9240i	0.418244	−	1.69432i
$502$	−1.68439	+	1.68439i	−0.0751778	+	0.0751778i
$503$	2.38495	−	8.90077i	0.106340	−	0.396866i	−0.892154	−	0.451732i	$-0.850806\pi$
$503$	2.38495	−	8.90077i	0.106340	−	0.396866i	0.998494	+	0.0548660i	$0.0174732\pi$
$504$	4.71342	+	2.47802i	0.209952	+	0.110380i
$505$		0			0
$506$		−	1.58057i		−	0.0702648i
$507$	21.5576	−	6.50137i	0.957409	−	0.288736i
$508$	−2.54628	+	2.54628i	−0.112973	+	0.112973i
$509$	0.476859	+	0.275315i	0.0211364	+	0.0122031i	0.510531	−	0.859859i	$-0.329449\pi$
$509$	0.476859	+	0.275315i	0.0211364	+	0.0122031i	−0.489395	+	0.872062i	$0.662782\pi$
$510$		0			0
$511$	3.66677	+	6.35104i	0.162208	+	0.280953i
$512$	−6.14451	−	6.14451i	−0.271552	−	0.271552i
$513$	−1.20378	−	1.82555i	−0.0531481	−	0.0805999i
$514$	0.903491	+	1.56489i	0.0398513	+	0.0690245i
$515$		0			0
$516$	−0.773199	+	3.13225i	−0.0340382	+	0.137890i
$517$	9.21266	−	2.46852i	0.405172	−	0.108566i
$518$	0.684904	+	2.55610i	0.0300930	+	0.112308i
$519$	4.51850	+	4.34313i	0.198340	+	0.190642i
$520$		0			0
$521$			32.2002i			1.41072i	0.708852	+	0.705358i	$0.249214\pi$
$521$			32.2002i			1.41072i	−0.708852	+	0.705358i	$0.750786\pi$
$522$	−1.61118	+	0.500821i	−0.0705194	+	0.0219204i
$523$	3.65245	+	13.6311i	0.159711	+	0.596048i	0.998656	+	0.0518323i	$0.0165061\pi$
$523$	3.65245	+	13.6311i	0.159711	+	0.596048i	−0.838945	+	0.544216i	$0.816827\pi$
$524$	−20.1615	−	34.9207i	−0.880758	−	1.52552i
$525$		0			0
$526$	−2.21362	+	1.27803i	−0.0965184	+	0.0557249i
$527$	−3.71919	+	13.8802i	−0.162010	+	0.604631i
$528$	35.4181	−	0.700906i	1.54137	−	0.0305030i
$529$	−13.4917	+	7.78941i	−0.586594	+	0.338670i
$530$		0			0
$531$	−24.0215	−	12.6290i	−1.04244	−	0.548051i
$532$	2.36413	+	2.36413i	0.102498	+	0.102498i
$533$	4.30333	+	5.54297i	0.186398	+	0.240093i
$534$	0.578179	−	0.601524i	0.0250202	−	0.0260305i
$535$		0			0
$536$	2.95238	+	1.70456i	0.127523	+	0.0736256i
$537$	−5.21479	−	8.63317i	−0.225035	−	0.372549i
$538$	−0.273182	−	0.273182i	−0.0117777	−	0.0117777i
$539$	40.5034	−	23.3846i	1.74460	−	1.00725i
$540$		0			0
$541$			22.8149i			0.980890i	0.871472	+	0.490445i	$0.163166\pi$
$541$			22.8149i			0.980890i	−0.871472	+	0.490445i	$0.836834\pi$
$542$	1.27790	+	0.342412i	0.0548905	+	0.0147079i
$543$	−8.32353	+	15.0990i	−0.357197	+	0.647961i
$544$	−2.24824	+	3.89407i	−0.0963927	+	0.166957i
$545$		0			0
$546$	1.74786	+	2.16167i	0.0748017	+	0.0925109i
$547$	−10.0470	−	10.0470i	−0.429577	−	0.429577i	0.458907	−	0.888484i	$-0.348241\pi$
$547$	−10.0470	−	10.0470i	−0.429577	−	0.429577i	−0.888484	+	0.458907i	$0.848241\pi$
$548$	6.87653	+	25.6636i	0.293751	+	1.09629i
$549$	7.42506	−	14.1231i	0.316894	−	0.602761i
$550$		0			0
$551$	−2.12526			−0.0905391
$552$	−1.08337	−	1.79354i	−0.0461115	−	0.0763383i
$553$	2.57704	−	9.61765i	0.109587	−	0.408984i
$554$		−	1.91420i		−	0.0813267i
$555$		0			0
$556$	−20.5912	+	35.6650i	−0.873261	+	1.51253i
$557$	25.4378	−	6.81604i	1.07783	−	0.288805i	0.324126	−	0.946014i	$-0.394930\pi$
$557$	25.4378	−	6.81604i	1.07783	−	0.288805i	0.753708	+	0.657209i	$0.228263\pi$
$558$	−0.960235	+	1.03941i	−0.0406500	+	0.0440017i
$559$	−2.04178	+	2.69231i	−0.0863581	+	0.113873i
$560$		0			0
$561$	−8.50725	−	29.4091i	−0.359176	−	1.24165i
$562$	2.38146	−	0.638111i	0.100456	−	0.0269171i
$563$	−5.06546	+	18.9045i	−0.213484	+	0.796732i	0.773211	+	0.634149i	$0.218649\pi$
$563$	−5.06546	+	18.9045i	−0.213484	+	0.796732i	−0.986695	+	0.162583i	$0.948017\pi$
$564$	4.36739	−	4.54374i	0.183900	−	0.191326i
$565$		0			0
$566$	0.157566	+	0.272913i	0.00662300	+	0.0114714i
$567$	−23.3467	+	27.3692i	−0.980470	+	1.14940i
$568$	5.23209	+	1.40193i	0.219534	+	0.0588239i
$569$	2.45559	−	4.25321i	0.102944	−	0.178304i	−0.809952	−	0.586495i	$-0.800507\pi$
$569$	2.45559	−	4.25321i	0.102944	−	0.178304i	0.912896	+	0.408192i	$0.133841\pi$
$570$		0			0
$571$	−17.2440			−0.721639			−0.360819	−	0.932636i	$-0.617503\pi$
$571$	−17.2440			−0.721639			−0.360819	+	0.932636i	$0.617503\pi$
$572$	34.5743	+	14.0924i	1.44562	+	0.589233i
$573$	0.783925	+	39.6132i	0.0327489	+	1.65486i
$574$	−0.433180	+	0.750289i	−0.0180806	+	0.0313165i
$575$		0			0
$576$	19.5424	−	12.3387i	0.814267	−	0.514111i
$577$	16.3463	−	16.3463i	0.680507	−	0.680507i	−0.279607	−	0.960114i	$-0.590204\pi$
$577$	16.3463	−	16.3463i	0.680507	−	0.680507i	0.960114	+	0.279607i	$0.0902043\pi$
$578$	−0.590527	−	0.158231i	−0.0245627	−	0.00658156i
$579$	−7.10481	+	28.7818i	−0.295266	+	1.19613i
$580$		0			0
$581$	−46.7606	+	26.9973i	−1.93996	+	1.12003i
$582$	−0.266458	+	0.483360i	−0.0110450	+	0.0200359i
$583$	17.4905	−	4.68655i	0.724381	−	0.194097i
$584$	−0.814753			−0.0337147
$585$		0			0
$586$	−0.880683			−0.0363807
$587$	−1.29527	+	0.347066i	−0.0534615	+	0.0143250i	−0.285451	−	0.958393i	$-0.592143\pi$
$587$	−1.29527	+	0.347066i	−0.0534615	+	0.0143250i	0.231989	+	0.972718i	$0.425477\pi$
$588$	14.9197	−	27.0646i	0.615278	−	1.11613i
$589$	−1.54365	+	0.891226i	−0.0636049	+	0.0367223i
$590$		0			0
$591$	−0.614148	+	2.48793i	−0.0252627	+	0.102340i
$592$	22.5425	+	6.04025i	0.926491	+	0.248253i
$593$	−16.7430	+	16.7430i	−0.687552	+	0.687552i	−0.961690	−	0.274138i	$-0.911607\pi$
$593$	−16.7430	+	16.7430i	−0.687552	+	0.687552i	0.274138	+	0.961690i	$0.411607\pi$
$594$	0.606152	−	2.95323i	0.0248707	−	0.121173i
$595$		0			0
$596$	8.97996	−	15.5537i	0.367834	−	0.637106i
$597$	0.818839	+	41.3774i	0.0335129	+	1.69347i
$598$	−0.148912	−	1.08366i	−0.00608945	−	0.0443143i
$599$	−29.1006			−1.18902			−0.594509	−	0.804089i	$-0.702653\pi$
$599$	−29.1006			−1.18902			−0.594509	+	0.804089i	$0.702653\pi$
$600$		0			0
$601$	15.9418	−	27.6120i	0.650280	−	1.12632i	−0.332775	−	0.943006i	$-0.607985\pi$
$601$	15.9418	−	27.6120i	0.650280	−	1.12632i	0.983055	−	0.183311i	$-0.0586816\pi$
$602$	−0.402952	−	0.107971i	−0.0164231	−	0.00440055i
$603$	−15.6279	+	16.9165i	−0.636419	+	0.688894i
$604$	−11.6402	−	20.1615i	−0.473635	−	0.820359i
$605$		0			0
$606$	−0.369589	+	0.384512i	−0.0150135	+	0.0156197i
$607$	−3.79661	+	14.1691i	−0.154100	+	0.575107i	0.845081	+	0.534638i	$0.179552\pi$
$607$	−3.79661	+	14.1691i	−0.154100	+	0.575107i	−0.999181	+	0.0404693i	$0.987115\pi$
$608$	−0.538745	+	0.144356i	−0.0218490	+	0.00585442i
$609$	9.71556	+	33.5862i	0.393695	+	1.36098i
$610$		0			0
$611$	6.08379	−	2.56042i	0.246124	−	0.103584i
$612$	−14.8594	−	13.7275i	−0.600657	−	0.554903i
$613$	−20.0772	+	5.37967i	−0.810911	+	0.217283i	−0.640369	−	0.768067i	$-0.721219\pi$
$613$	−20.0772	+	5.37967i	−0.810911	+	0.217283i	−0.170542	+	0.985350i	$0.554552\pi$
$614$	−0.842294	+	1.45890i	−0.0339922	+	0.0588762i
$615$		0			0
$616$			9.24775i			0.372602i
$617$	10.5157	−	39.2451i	0.423345	−	1.57995i	−0.344164	−	0.938909i	$-0.611838\pi$
$617$	10.5157	−	39.2451i	0.423345	−	1.57995i	0.767510	−	0.641037i	$-0.221496\pi$
$618$	−0.00642956	−	0.0106442i	−0.000258635	−	0.000428174i
$619$	−21.9052			−0.880445			−0.440222	−	0.897889i	$-0.645100\pi$
$619$	−21.9052			−0.880445			−0.440222	+	0.897889i	$0.645100\pi$
$620$		0			0
$621$	13.4315	−	4.46836i	0.538988	−	0.179309i
$622$	−0.346441	−	1.29293i	−0.0138910	−	0.0518420i
$623$	−12.2255	−	12.2255i	−0.489804	−	0.489804i
$624$	24.2172	−	3.81743i	0.969464	−	0.152820i
$625$		0			0
$626$	−1.29995	+	2.25158i	−0.0519564	+	0.0899911i
$627$	1.83331	−	3.32566i	0.0732153	−	0.132814i
$628$	30.6015	+	8.19964i	1.22113	+	0.327201i
$629$		−	20.1688i		−	0.804183i
$630$		0			0
$631$	16.2845	−	9.40185i	0.648275	−	0.374282i	−0.139520	−	0.990219i	$-0.544556\pi$
$631$	16.2845	−	9.40185i	0.648275	−	0.374282i	0.787795	+	0.615937i	$0.211223\pi$
$632$	0.782208	+	0.782208i	0.0311146	+	0.0311146i
$633$	2.75687	+	4.56404i	0.109576	+	0.181404i
$634$	0.106209	+	0.0613196i	0.00421809	+	0.00243531i
$635$		0			0
$636$	8.29159	−	8.62639i	0.328783	−	0.342059i
$637$	25.5667	−	19.8489i	1.01299	−	0.786442i
$638$	−2.07188	−	2.07188i	−0.0820264	−	0.0820264i
$639$	−17.0282	+	32.3891i	−0.673624	+	1.28129i
$640$		0			0
$641$	−18.6204	+	10.7505i	−0.735461	+	0.424619i	−0.820417	−	0.571766i	$-0.806258\pi$
$641$	−18.6204	+	10.7505i	−0.735461	+	0.424619i	0.0849557	+	0.996385i	$0.472925\pi$
$642$	−3.27585	+	0.0648275i	−0.129288	+	0.00255854i
$643$	−0.707671	+	2.64106i	−0.0279078	+	0.104153i	−0.978475	−	0.206366i	$-0.933836\pi$
$643$	−0.707671	+	2.64106i	−0.0279078	+	0.104153i	0.950567	+	0.310519i	$0.100503\pi$
$644$	−18.7432	+	10.8214i	−0.738585	+	0.426422i
$645$		0			0
$646$	0.0795009	+	0.137700i	0.00312792	+	0.00541772i
$647$	10.6764	+	39.8449i	0.419733	+	1.56647i	0.775162	+	0.631762i	$0.217668\pi$
$647$	10.6764	+	39.8449i	0.419733	+	1.56647i	−0.355429	+	0.934703i	$0.615665\pi$
$648$	−1.33642	−	3.76665i	−0.0524995	−	0.147968i
$649$		−	47.1302i		−	1.85002i
$650$		0			0
$651$	21.1411	+	20.3206i	0.828585	+	0.796426i
$652$	6.59373	+	24.6081i	0.258230	+	0.963729i
$653$	16.7866	−	4.49795i	0.656909	−	0.176018i	0.0850584	−	0.996376i	$-0.472892\pi$
$653$	16.7866	−	4.49795i	0.656909	−	0.176018i	0.571851	+	0.820358i	$0.306226\pi$
$654$	0.218726	−	0.886066i	0.00855286	−	0.0346479i
$655$		0			0
$656$	3.82026	+	6.61688i	0.149156	+	0.258346i
$657$	1.21311	−	5.36876i	0.0473280	−	0.209455i
$658$	0.576229	+	0.576229i	0.0224638	+	0.0224638i
$659$	9.34358	+	16.1835i	0.363974	+	0.630422i	0.988611	−	0.150494i	$-0.0480863\pi$
$659$	9.34358	+	16.1835i	0.363974	+	0.630422i	−0.624637	+	0.780915i	$0.714753\pi$
$660$		0			0
$661$	36.7989	+	21.2459i	1.43131	+	0.826368i	0.997221	−	0.0745005i	$-0.0237362\pi$
$661$	36.7989	+	21.2459i	1.43131	+	0.826368i	0.434091	+	0.900869i	$0.357070\pi$
$662$	−2.21731	+	2.21731i	−0.0861780	+	0.0861780i
$663$	−8.60347	−	19.3619i	−0.334131	−	0.751953i
$664$		−	5.99876i		−	0.232797i
$665$		0			0
$666$	0.924235	−	1.75798i	0.0358134	−	0.0681203i
$667$	3.56070	−	13.2887i	0.137871	−	0.514540i
$668$	31.6965	−	31.6965i	1.22638	−	1.22638i
$669$	−2.39957	+	9.72072i	−0.0927727	+	0.375825i
$670$		0			0
$671$	27.7097			1.06972
$672$	4.74417	+	7.85405i	0.183010	+	0.302977i
$673$	−0.262737	−	0.980547i	−0.0101278	−	0.0377973i	0.960677	−	0.277668i	$-0.0895616\pi$
$673$	−0.262737	−	0.980547i	−0.0101278	−	0.0377973i	−0.970805	+	0.239871i	$0.922895\pi$
$674$	2.44738	+	1.41300i	0.0942697	+	0.0544267i
$675$		0			0
$676$	25.0324	+	6.40462i	0.962786	+	0.246331i
$677$	2.15255	−	2.15255i	0.0827291	−	0.0827291i	−0.664531	−	0.747260i	$-0.731369\pi$
$677$	2.15255	−	2.15255i	0.0827291	−	0.0827291i	0.747260	+	0.664531i	$0.231369\pi$
$678$	0.476293	+	0.262562i	0.0182919	+	0.0100836i
$679$	9.90513	+	5.71873i	0.380124	+	0.219465i
$680$		0			0
$681$	−18.3333	−	17.6217i	−0.702532	−	0.675266i
$682$	−2.37371	−	0.636035i	−0.0908942	−	0.0243550i
$683$	−31.0697	−	8.32509i	−1.18885	−	0.318551i	−0.390418	−	0.920638i	$-0.627669\pi$
$683$	−31.0697	−	8.32509i	−1.18885	−	0.318551i	−0.798430	+	0.602087i	$0.794336\pi$
$684$	−0.0992783	−	2.50737i	−0.00379600	−	0.0958718i
$685$		0			0
$686$	0.762153	+	0.440029i	0.0290991	+	0.0168004i
$687$	3.01504	−	5.46933i	0.115031	−	0.208668i
$688$	−2.60147	+	2.60147i	−0.0991802	+	0.0991802i
$689$	11.5502	−	4.86103i	0.440028	−	0.185190i
$690$		0			0
$691$	−15.5777	−	8.99379i	−0.592603	−	0.342140i	0.173523	−	0.984830i	$-0.444485\pi$
$691$	−15.5777	−	8.99379i	−0.592603	−	0.342140i	−0.766126	+	0.642690i	$0.777818\pi$
$692$	1.86143	+	6.94696i	0.0707611	+	0.264084i
$693$	−60.9374	−	13.7693i	−2.31482	−	0.523051i
$694$	−0.0558510			−0.00212007
$695$		0			0
$696$	−3.77119	−	0.930921i	−0.142947	−	0.0352865i
$697$	4.66906	−	4.66906i	0.176853	−	0.176853i
$698$	−0.267026	+	0.996554i	−0.0101071	+	0.0377201i
$699$	−18.5470	+	5.36514i	−0.701512	+	0.202928i
$700$		0			0
$701$		−	36.5117i		−	1.37903i	−0.724272	−	0.689515i	$-0.757824\pi$
$701$		−	36.5117i		−	1.37903i	0.724272	−	0.689515i	$-0.242176\pi$
$702$	0.137352	−	2.08190i	0.00518402	−	0.0785761i
$703$	1.76901	−	1.76901i	0.0667196	−	0.0667196i
$704$	34.7591	+	20.0682i	1.31003	+	0.756347i
$705$		0			0
$706$	−1.17916	−	2.04236i	−0.0443782	−	0.0768653i
$707$	7.81490	+	7.81490i	0.293909	+	0.293909i
$708$	−16.1021	−	26.6573i	−0.605153	−	1.00184i
$709$	17.1761	+	29.7499i	0.645063	+	1.11728i	0.984287	+	0.176577i	$0.0565023\pi$
$709$	17.1761	+	29.7499i	0.645063	+	1.11728i	−0.339224	+	0.940706i	$0.610164\pi$
$710$		0			0
$711$	−6.31896	+	3.98965i	−0.236980	+	0.149624i
$712$	1.85540	−	0.497153i	0.0695340	−	0.0186316i
$713$	−2.98635	−	11.1452i	−0.111840	−	0.417391i
$714$	1.81268	−	1.88587i	0.0678377	−	0.0705769i
$715$		0			0
$716$		−	11.5740i		−	0.432540i
$717$	0.143762	+	0.0792506i	0.00536889	+	0.00295967i
$718$	0.511933	+	1.91056i	0.0191052	+	0.0713014i
$719$	5.50044	+	9.52704i	0.205132	+	0.355299i	0.950175	−	0.311718i	$-0.100904\pi$
$719$	5.50044	+	9.52704i	0.205132	+	0.355299i	−0.745043	+	0.667016i	$0.767571\pi$
$720$		0			0
$721$	−0.223167	+	0.128845i	−0.00831116	+	0.00479845i
$722$	0.542540	−	2.02479i	0.0201912	−	0.0753547i
$723$	0.369793	+	18.6863i	0.0137528	+	0.694952i
$724$	−17.1344	+	9.89253i	−0.636794	+	0.367653i
$725$		0			0
$726$	2.99116	−	0.865260i	0.111012	−	0.0321128i
$727$	−13.9424	−	13.9424i	−0.517094	−	0.517094i	0.399597	−	0.916691i	$-0.369150\pi$
$727$	−13.9424	−	13.9424i	−0.517094	−	0.517094i	−0.916691	+	0.399597i	$0.869150\pi$
$728$	0.871268	+	6.34042i	0.0322913	+	0.234991i
$729$	26.8099	−	3.19796i	0.992961	−	0.118443i
$730$		0			0
$731$	2.75351	+	1.58974i	0.101842	+	0.0587986i
$732$	15.6728	−	9.46704i	0.579285	−	0.349912i
$733$	10.0007	+	10.0007i	0.369383	+	0.369383i	0.867252	−	0.497869i	$-0.165884\pi$
$733$	10.0007	+	10.0007i	0.369383	+	0.369383i	−0.497869	+	0.867252i	$0.665884\pi$
$734$	−0.108825	+	0.0628299i	−0.00401679	+	0.00231909i
$735$		0			0
$736$		−	3.61049i		−	0.133084i
$737$	−38.6325	−	10.3515i	−1.42305	−	0.381304i
$738$	0.620930	−	0.193011i	0.0228568	−	0.00710483i
$739$	5.27257	−	9.13236i	0.193955	−	0.335939i	−0.752603	−	0.658475i	$-0.771202\pi$
$739$	5.27257	−	9.13236i	0.193955	−	0.335939i	0.946557	+	0.322536i	$0.104535\pi$
$740$		0			0
$741$	0.943625	−	2.45285i	0.0346649	−	0.0901077i
$742$	1.09399	+	1.09399i	0.0401615	+	0.0401615i
$743$	8.87832	+	33.1343i	0.325714	+	1.21558i	0.913592	+	0.406632i	$0.133297\pi$
$743$	8.87832	+	33.1343i	0.325714	+	1.21558i	−0.587878	+	0.808949i	$0.700037\pi$
$744$	−3.12953	+	0.905286i	−0.114734	+	0.0331894i
$745$		0			0
$746$	−1.98600			−0.0727127
$747$	39.5284	+	8.93174i	1.44627	+	0.326795i
$748$	9.09277	−	33.9347i	0.332465	−	1.24077i
$749$			67.8966i			2.48089i
$750$		0			0
$751$	−7.98474	+	13.8300i	−0.291367	+	0.504663i	−0.974133	−	0.225974i	$-0.927444\pi$
$751$	−7.98474	+	13.8300i	−0.291367	+	0.504663i	0.682766	+	0.730637i	$0.260777\pi$
$752$	6.94191	−	1.86008i	0.253145	−	0.0678301i
$753$	−0.733024	−	37.0411i	−0.0267129	−	1.34985i
$754$	−1.61571	−	1.22531i	−0.0588408	−	0.0446233i
$755$		0			0
$756$	−39.1710	+	13.0313i	−1.42464	+	0.473945i
$757$	−40.7211	+	10.9112i	−1.48003	+	0.396574i	−0.906358	−	0.422510i	$-0.861149\pi$
$757$	−40.7211	+	10.9112i	−1.48003	+	0.396574i	−0.573675	+	0.819083i	$0.694483\pi$
$758$	0.298311	−	1.11331i	0.0108351	−	0.0404373i
$759$	17.7229	+	17.0351i	0.643301	+	0.618334i
$760$		0			0
$761$	2.02411	+	3.50585i	0.0733738	+	0.127087i	0.900378	−	0.435109i	$-0.143290\pi$
$761$	2.02411	+	3.50585i	0.0733738	+	0.127087i	−0.827004	+	0.562196i	$0.809957\pi$
$762$	0.00691435	+	0.349395i	0.000250480	+	0.0126572i
$763$	−18.2681	−	4.89492i	−0.661349	−	0.177208i
$764$	−22.7333	+	39.3752i	−0.822462	+	1.42455i
$765$		0			0
$766$	1.85016			0.0668492
$767$	−4.44032	−	32.3133i	−0.160331	−	1.16676i
$768$	26.0052	−	0.514629i	0.938381	−	0.0185701i
$769$	9.59863	−	16.6253i	0.346135	−	0.599524i	−0.639424	−	0.768854i	$-0.720827\pi$
$769$	9.59863	−	16.6253i	0.346135	−	0.599524i	0.985559	+	0.169330i	$0.0541605\pi$
$770$		0			0
$771$	−27.2848	−	6.73528i	−0.982640	−	0.242565i
$772$	−24.0556	+	24.0556i	−0.865778	+	0.865778i
$773$	−3.32613	−	0.891235i	−0.119633	−	0.0320555i	0.198506	−	0.980100i	$-0.436391\pi$
$773$	−3.32613	−	0.891235i	−0.119633	−	0.0320555i	−0.318139	+	0.948044i	$0.603058\pi$
$774$	0.167155	+	0.264746i	0.00600826	+	0.00951611i
$775$		0			0
$776$	−1.10045	+	0.635348i	−0.0395040	+	0.0228077i
$777$	−36.0433	−	19.8693i	−1.29305	−	0.712808i
$778$	2.60064	−	0.696840i	0.0932375	−	0.0249829i
$779$	0.819051			0.0293455
$780$		0			0
$781$	−63.5476			−2.27391
$782$	−0.994197	+	0.266394i	−0.0355524	+	0.00952624i
$783$	11.7493	−	23.4639i	0.419885	−	0.838533i
$784$	30.5200	−	17.6208i	1.09000	−	0.629313i
$785$		0			0
$786$	−3.79917	−	0.937828i	−0.135512	−	0.0334512i
$787$	−33.5033	−	8.97719i	−1.19426	−	0.320002i	−0.393694	−	0.919241i	$-0.628803\pi$
$787$	−33.5033	−	8.97719i	−1.19426	−	0.320002i	−0.800570	+	0.599239i	$0.795470\pi$
$788$	−2.07939	+	2.07939i	−0.0740752	+	0.0740752i
$789$	9.52740	−	38.5958i	0.339184	−	1.37405i
$790$		0			0
$791$	5.63512	−	9.76031i	0.200362	−	0.347037i
$792$	4.70987	−	5.09821i	0.167358	−	0.181157i
$793$	18.9982	−	2.61064i	0.674647	−	0.0927065i
$794$	−0.952251			−0.0337941
$795$		0			0
$796$	−23.7458	+	41.1289i	−0.841647	+	1.45778i
$797$	−29.7594	−	7.97400i	−1.05413	−	0.282454i	−0.310173	−	0.950680i	$-0.600387\pi$
$797$	−29.7594	−	7.97400i	−1.05413	−	0.282454i	−0.743958	+	0.668226i	$0.767054\pi$
$798$	0.324401	−	0.00641973i	0.0114837	−	0.000227256i
$799$	−3.10547	−	5.37883i	−0.109864	−	0.190289i
$800$		0			0
$801$	0.513392	+	12.9662i	0.0181398	+	0.458140i
$802$	0.792066	−	2.95603i	0.0279688	−	0.104381i
$803$	9.23288	−	2.47394i	0.325821	−	0.0873036i
$804$	−25.3875	+	7.34391i	−0.895348	+	0.259000i
$805$		0			0
$806$	−1.68738	−	0.212439i	−0.0594355	−	0.00748286i
$807$	6.00749	−	0.118885i	0.211474	−	0.00418496i
$808$	−1.18603	+	0.317795i	−0.0417242	+	0.0111800i
$809$	18.8982	−	32.7327i	0.664427	−	1.15082i	−0.315013	−	0.949087i	$-0.602009\pi$
$809$	18.8982	−	32.7327i	0.664427	−	1.15082i	0.979440	−	0.201734i	$-0.0646576\pi$
$810$		0			0
$811$			11.6051i			0.407512i	0.979022	+	0.203756i	$0.0653148\pi$
$811$			11.6051i			0.407512i	−0.979022	+	0.203756i	$0.934685\pi$
$812$	−10.3842	+	38.7545i	−0.364416	+	1.36002i
$813$	−17.6125	+	10.6387i	−0.617696	+	0.373114i
$814$	3.44916			0.120893
$815$		0			0
$816$	−6.41037	−	22.1603i	−0.224408	−	0.775766i
$817$	0.102075	+	0.380948i	0.00357114	+	0.0133277i
$818$	2.93960	+	2.93960i	0.102781	+	0.102781i
$819$	−43.0770	−	3.69928i	−1.50523	−	0.129263i
$820$		0			0
$821$	−21.9513	+	38.0208i	−0.766107	+	1.32694i	0.173553	+	0.984825i	$0.444475\pi$
$821$	−21.9513	+	38.0208i	−0.766107	+	1.32694i	−0.939659	+	0.342111i	$0.888858\pi$
$822$	2.25805	+	1.24478i	0.0787585	+	0.0434166i
$823$	−42.7695	−	11.4601i	−1.49085	−	0.399472i	−0.580827	−	0.814027i	$-0.697271\pi$
$823$	−42.7695	−	11.4601i	−1.49085	−	0.399472i	−0.910025	+	0.414554i	$0.863937\pi$
$824$		−	0.0286293i		−	0.000997349i
$825$		0			0
$826$	3.48738	−	2.01344i	0.121341	−	0.0700565i
$827$	6.22326	+	6.22326i	0.216404	+	0.216404i	0.806981	−	0.590577i	$-0.201100\pi$
$827$	6.22326	+	6.22326i	0.216404	+	0.216404i	−0.590577	+	0.806981i	$0.701100\pi$
$828$	15.8443	+	3.58014i	0.550628	+	0.124418i
$829$	−34.6858	−	20.0259i	−1.20469	−	0.695527i	−0.243094	−	0.970003i	$-0.578162\pi$
$829$	−34.6858	−	20.0259i	−1.20469	−	0.695527i	−0.961594	+	0.274475i	$0.911496\pi$
$830$		0			0
$831$	21.4640	+	20.6310i	0.744578	+	0.715680i
$832$	25.7221	+	10.4843i	0.891754	+	0.363477i
$833$	−21.5358	−	21.5358i	−0.746172	−	0.746172i
$834$	1.11058	+	3.83921i	0.0384562	+	0.132941i
$835$		0			0
$836$	3.77395	−	2.17889i	0.130525	−	0.0753586i
$837$	−1.30567	−	21.9697i	−0.0451307	−	0.759384i
$838$	−0.855555	+	3.19297i	−0.0295546	+	0.110299i
$839$	3.62533	−	2.09309i	0.125160	−	0.0722614i	−0.436113	−	0.899892i	$-0.643645\pi$
$839$	3.62533	−	2.09309i	0.125160	−	0.0722614i	0.561273	+	0.827631i	$0.310312\pi$
$840$		0			0
$841$	1.74811	+	3.02782i	0.0602797	+	0.104407i
$842$	0.615198	+	2.29595i	0.0212011	+	0.0791236i
$843$	−18.5119	+	33.5808i	−0.637582	+	1.15659i
$844$			6.11875i			0.210616i
$845$		0			0
$846$	−0.0241979	−	0.611144i	−0.000831942	−	0.0210116i
$847$	−16.7003	−	62.3264i	−0.573830	−	2.14156i
$848$	13.1794	−	3.53140i	0.452582	−	0.121269i
$849$	−4.75840	−	1.17461i	−0.163308	−	0.0403126i
$850$		0			0
$851$	8.09736	+	14.0250i	0.277574	+	0.480772i
$852$	−35.9431	+	21.7111i	−1.23139	+	0.743810i
$853$	−1.57958	−	1.57958i	−0.0540837	−	0.0540837i	0.679548	−	0.733631i	$-0.262176\pi$
$853$	−1.57958	−	1.57958i	−0.0540837	−	0.0540837i	−0.733631	+	0.679548i	$0.762176\pi$
$854$	1.18378	+	2.05036i	0.0405081	+	0.0701620i
$855$		0			0
$856$	−6.53267	−	3.77164i	−0.223282	−	0.128912i
$857$	−31.1740	+	31.1740i	−1.06488	+	1.06488i	−0.0671414	+	0.997743i	$0.521388\pi$
$857$	−31.1740	+	31.1740i	−1.06488	+	1.06488i	−0.997743	+	0.0671414i	$0.978612\pi$
$858$	3.31116	−	1.47132i	0.113041	−	0.0502299i
$859$			17.7932i			0.607095i	0.952816	+	0.303547i	$0.0981711\pi$
$859$			17.7932i			0.607095i	−0.952816	+	0.303547i	$0.901829\pi$
$860$		0			0
$861$	−3.74427	−	12.9437i	−0.127604	−	0.441121i
$862$	0.0838223	−	0.312829i	0.00285500	−	0.0106550i
$863$	4.49895	−	4.49895i	0.153146	−	0.153146i	−0.626375	−	0.779522i	$-0.715462\pi$
$863$	4.49895	−	4.49895i	0.153146	−	0.153146i	0.779522	+	0.626375i	$0.215462\pi$
$864$	1.38463	−	6.74608i	0.0471062	−	0.229506i
$865$		0			0
$866$	2.94505			0.100077
$867$	8.13885	−	4.91620i	0.276410	−	0.166963i
$868$	8.70925	+	32.5034i	0.295611	+	1.10324i
$869$	−11.2392	−	6.48896i	−0.381264	−	0.220123i
$870$		0			0
$871$	−27.4624	−	3.45747i	−0.930526	−	0.117152i
$872$	1.48575	−	1.48575i	0.0503139	−	0.0503139i
$873$	−2.54808	−	8.19736i	−0.0862395	−	0.277439i
$874$	−0.110567	−	0.0638359i	−0.00373998	−	0.00215928i
$875$		0			0
$876$	4.37698	−	4.55371i	0.147884	−	0.153856i
$877$	−5.92830	−	1.58848i	−0.200184	−	0.0536393i	0.157334	−	0.987546i	$-0.449710\pi$
$877$	−5.92830	−	1.58848i	−0.200184	−	0.0536393i	−0.357518	+	0.933906i	$0.616377\pi$
$878$	−2.88388	−	0.772733i	−0.0973262	−	0.0260785i
$879$	9.49185	−	9.87511i	0.320152	−	0.333079i
$880$		0			0
$881$	36.9093	+	21.3096i	1.24350	+	0.717938i	0.969806	−	0.243878i	$-0.0784195\pi$
$881$	36.9093	+	21.3096i	1.24350	+	0.717938i	0.273699	+	0.961815i	$0.411753\pi$
$882$	−0.890253	−	2.86401i	−0.0299764	−	0.0964362i
$883$	13.2826	−	13.2826i	0.446996	−	0.446996i	−0.447358	−	0.894355i	$-0.647635\pi$
$883$	13.2826	−	13.2826i	0.446996	−	0.446996i	0.894355	+	0.447358i	$0.147635\pi$
$884$	3.03704	−	24.1229i	0.102147	−	0.811340i
$885$		0			0
$886$	2.64092	+	1.52473i	0.0887233	+	0.0512244i
$887$	−0.0189788	−	0.0708297i	−0.000637244	−	0.00237823i	0.965606	−	0.260008i	$-0.0837252\pi$
$887$	−0.0189788	−	0.0708297i	−0.000637244	−	0.00237823i	−0.966244	+	0.257630i	$0.917059\pi$
$888$	3.91393	−	2.36417i	0.131343	−	0.0793364i
$889$	7.24169			0.242879
$890$		0			0
$891$	26.5817	+	38.6262i	0.890519	+	1.29403i
$892$	−8.12449	+	8.12449i	−0.272028	+	0.272028i
$893$	0.199397	−	0.744161i	0.00667257	−	0.0249024i
$894$	−0.484331	−	1.67431i	−0.0161985	−	0.0559972i
$895$		0			0
$896$			14.0245i			0.468525i
$897$	13.7561	+	10.0098i	0.459302	+	0.334217i
$898$	0.275440	−	0.275440i	0.00919156	−	0.00919156i
$899$	−18.5243	−	10.6950i	−0.617819	−	0.356698i
$900$		0			0
$901$	−5.89581	−	10.2118i	−0.196418	−	0.340206i
$902$	0.798478	+	0.798478i	0.0265864	+	0.0265864i
$903$	5.55362	−	3.35462i	0.184813	−	0.111635i
$904$	0.626059	+	1.08437i	0.0208224	+	0.0360655i
$905$		0			0
$906$	−2.19345	−	0.541456i	−0.0728726	−	0.0179887i
$907$	−12.8605	+	3.44596i	−0.427026	+	0.114421i	−0.465930	−	0.884822i	$-0.654280\pi$
$907$	−12.8605	+	3.44596i	−0.427026	+	0.114421i	0.0389038	+	0.999243i	$0.487613\pi$
$908$	−7.55255	−	28.1865i	−0.250640	−	0.935401i
$909$	−0.328176	−	8.28841i	−0.0108849	−	0.274909i
$910$		0			0
$911$		−	26.2784i		−	0.870641i	−0.900276	−	0.435321i	$-0.856635\pi$
$911$		−	26.2784i		−	0.870641i	0.900276	−	0.435321i	$-0.143365\pi$
$912$	1.38143	−	2.50594i	0.0457438	−	0.0829801i
$913$	18.2148	+	67.9787i	0.602823	+	2.24977i
$914$	1.94240	+	3.36434i	0.0642490	+	0.111283i
$915$		0			0
$916$	6.20659	−	3.58338i	0.205072	−	0.118398i
$917$	−20.9879	+	78.3277i	−0.693080	+	2.58661i
$918$	−1.95979	+	0.116471i	−0.0646826	+	0.00384412i
$919$	12.6380	−	7.29655i	0.416889	−	0.240691i	−0.276856	−	0.960911i	$-0.589293\pi$
$919$	12.6380	−	7.29655i	0.416889	−	0.240691i	0.693746	+	0.720220i	$0.255959\pi$
$920$		0			0
$921$	−7.28052	−	25.1684i	−0.239901	−	0.829326i
$922$	−0.855820	−	0.855820i	−0.0281849	−	0.0281849i
$923$	−43.5693	+	5.98707i	−1.43410	+	0.197067i
$924$	−51.6863	−	49.6803i	−1.70035	−	1.63436i
$925$		0			0
$926$	0.913562	+	0.527445i	0.0300215	+	0.0173329i
$927$	0.188651	+	0.0426271i	0.00619611	+	0.00140006i
$928$	−4.73279	−	4.73279i	−0.155361	−	0.155361i
$929$	−38.3045	+	22.1151i	−1.25673	+	0.725573i	−0.972437	−	0.233165i	$-0.925092\pi$
$929$	−38.3045	+	22.1151i	−1.25673	+	0.725573i	−0.284292	+	0.958738i	$0.591758\pi$
$930$		0			0
$931$		−	3.77783i		−	0.123813i
$932$	−21.4011	−	5.73440i	−0.701015	−	0.187836i
$933$	18.2316	+	10.0504i	0.596875	+	0.329035i
$934$	0.359584	−	0.622817i	0.0117659	−	0.0203792i
$935$		0			0
$936$	2.74884	−	3.93916i	0.0898488	−	0.128755i
$937$	−22.4956	−	22.4956i	−0.734898	−	0.734898i	0.236688	−	0.971586i	$-0.423938\pi$
$937$	−22.4956	−	22.4956i	−0.734898	−	0.734898i	−0.971586	+	0.236688i	$0.923938\pi$
$938$	−0.884452	−	3.30082i	−0.0288784	−	0.107776i
$939$	−11.2363	−	38.8434i	−0.366684	−	1.26761i
$940$		0			0
$941$	37.4186			1.21981			0.609905	−	0.792474i	$-0.291207\pi$
$941$	37.4186			1.21981			0.609905	+	0.792474i	$0.291207\pi$
$942$	2.63169	−	1.58965i	0.0857450	−	0.0517935i
$943$	−1.37225	+	5.12131i	−0.0446867	+	0.166773i
$944$		−	35.5135i		−	1.15586i
$945$		0			0
$946$	−0.271869	+	0.470890i	−0.00883921	+	0.0153100i
$947$	−3.34143	+	0.895335i	−0.108582	+	0.0290945i	−0.312701	−	0.949852i	$-0.601234\pi$
$947$	−3.34143	+	0.895335i	−0.108582	+	0.0290945i	0.204119	+	0.978946i	$0.434567\pi$
$948$	−8.57396	+	0.169674i	−0.278469	+	0.00551077i
$949$	6.09715	−	2.56605i	0.197922	−	0.0832974i
$950$		0			0
$951$	−1.83228	+	0.530028i	−0.0594157	+	0.0171873i
$952$	5.81695	−	1.55865i	0.188529	−	0.0505161i
$953$	−7.66352	+	28.6007i	−0.248246	+	0.926466i	0.723478	+	0.690347i	$0.242542\pi$
$953$	−7.66352	+	28.6007i	−0.248246	+	0.926466i	−0.971724	+	0.236119i	$0.924124\pi$
$954$	−0.0459404	−	1.16027i	−0.00148737	−	0.0375652i
$955$		0			0
$956$	0.0941895	+	0.163141i	0.00304631	+	0.00527636i
$957$	45.5623	−	0.901655i	1.47282	−	0.0291464i
$958$	−1.71624	−	0.459864i	−0.0554491	−	0.0148575i
$959$	26.7155	−	46.2725i	0.862687	−	1.49422i
$960$		0			0
$961$	13.0603			0.421299
$962$	2.36480	−	0.324959i	0.0762443	−	0.0104771i
$963$	34.5797	−	37.4309i	1.11431	−	1.20619i
$964$	−10.7238	+	18.5741i	−0.345389	+	0.598231i
$965$		0			0
$966$	−0.503366	+	2.03915i	−0.0161955	+	0.0656086i
$967$	18.5880	−	18.5880i	0.597750	−	0.597750i	−0.341963	−	0.939713i	$-0.611092\pi$
$967$	18.5880	−	18.5880i	0.597750	−	0.597750i	0.939713	+	0.341963i	$0.111092\pi$
$968$	6.92443	+	1.85540i	0.222560	+	0.0596347i
$969$	−2.40087	−	0.592657i	−0.0771272	−	0.0190389i
$970$		0			0
$971$	−6.10879	+	3.52691i	−0.196040	+	0.113184i	−0.594807	−	0.803868i	$-0.702772\pi$
$971$	−6.10879	+	3.52691i	−0.196040	+	0.113184i	0.398767	+	0.917052i	$0.369438\pi$
$972$	28.2315	+	12.7657i	0.905527	+	0.409460i
$973$	79.9972	−	21.4352i	2.56459	−	0.687180i
$974$	−3.65614			−0.117150
$975$		0			0
$976$	20.8797			0.668344
$977$	−19.7099	+	5.28126i	−0.630577	+	0.168963i	−0.559932	−	0.828539i	$-0.689173\pi$
$977$	−19.7099	+	5.28126i	−0.630577	+	0.168963i	−0.0706455	+	0.997501i	$0.522506\pi$
$978$	2.16519	+	1.19359i	0.0692350	+	0.0381667i
$979$	−19.5160	+	11.2676i	−0.623735	+	0.360114i
$980$		0			0
$981$	7.57808	+	12.0024i	0.241949	+	0.383208i
$982$	−3.13710	−	0.840582i	−0.100109	−	0.0268241i
$983$	30.8727	−	30.8727i	0.984687	−	0.984687i	−0.0151975	−	0.999885i	$-0.504838\pi$
$983$	30.8727	−	30.8727i	0.984687	−	0.984687i	0.999885	+	0.0151975i	$0.00483769\pi$
$984$	1.45337	+	0.358767i	0.0463319	+	0.0114371i
$985$		0			0
$986$	−0.954036	+	1.65244i	−0.0303827	+	0.0526244i
$987$	−12.6718	+	0.250768i	−0.403347	+	0.00798203i
$988$	2.38221	−	1.84945i	0.0757880	−	0.0588387i
$989$	−2.55299			−0.0811803
$990$		0			0
$991$	−6.36105	+	11.0177i	−0.202065	+	0.349988i	−0.949194	−	0.314692i	$-0.898099\pi$
$991$	−6.36105	+	11.0177i	−0.202065	+	0.349988i	0.747128	+	0.664680i	$0.231432\pi$
$992$	−5.42228	−	1.45290i	−0.172158	−	0.0461295i
$993$	−0.964945	−	48.7604i	−0.0306216	−	1.54736i
$994$	−2.71480	−	4.70218i	−0.0861083	−	0.149144i
$995$		0			0
$996$	33.5275	+	32.2263i	1.06236	+	1.02113i
$997$	−2.34514	+	8.75218i	−0.0742713	+	0.277184i	−0.993067	−	0.117549i	$-0.962496\pi$
$997$	−2.34514	+	8.75218i	−0.0742713	+	0.277184i	0.918796	+	0.394733i	$0.129163\pi$
$998$	−1.80241	+	0.482956i	−0.0570544	+	0.0152877i
$999$	9.75099	+	29.3106i	0.308508	+	0.927348i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bn.d.407.13		96
3.2	odd	2	inner	975.2.bn.d.407.12		96
5.2	odd	4		195.2.bf.a.173.13	yes	96
5.3	odd	4	inner	975.2.bn.d.368.12		96
5.4	even	2		195.2.bf.a.17.12	✓	96
13.10	even	6	inner	975.2.bn.d.257.13		96
15.2	even	4		195.2.bf.a.173.12	yes	96
15.8	even	4	inner	975.2.bn.d.368.13		96
15.14	odd	2		195.2.bf.a.17.13	yes	96
39.23	odd	6	inner	975.2.bn.d.257.12		96
65.23	odd	12	inner	975.2.bn.d.218.12		96
65.49	even	6		195.2.bf.a.62.12	yes	96
65.62	odd	12		195.2.bf.a.23.13	yes	96
195.23	even	12	inner	975.2.bn.d.218.13		96
195.62	even	12		195.2.bf.a.23.12	yes	96
195.179	odd	6		195.2.bf.a.62.13	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.12	✓	96	5.4	even	2
195.2.bf.a.17.13	yes	96	15.14	odd	2
195.2.bf.a.23.12	yes	96	195.62	even	12
195.2.bf.a.23.13	yes	96	65.62	odd	12
195.2.bf.a.62.12	yes	96	65.49	even	6
195.2.bf.a.62.13	yes	96	195.179	odd	6
195.2.bf.a.173.12	yes	96	15.2	even	4
195.2.bf.a.173.13	yes	96	5.2	odd	4
975.2.bn.d.218.12		96	65.23	odd	12	inner
975.2.bn.d.218.13		96	195.23	even	12	inner
975.2.bn.d.257.12		96	39.23	odd	6	inner
975.2.bn.d.257.13		96	13.10	even	6	inner
975.2.bn.d.368.12		96	5.3	odd	4	inner
975.2.bn.d.368.13		96	15.8	even	4	inner
975.2.bn.d.407.12		96	3.2	odd	2	inner
975.2.bn.d.407.13		96	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.bn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.107570 - 0.0288234i) q^{2} +(-0.836177 + 1.51684i) q^{3} +(-1.72131 + 0.993799i) q^{4} +(-0.0462274 + 0.187269i) q^{6} +(3.86093 + 1.03453i) q^{7} +(-0.314011 + 0.314011i) q^{8} +(-1.60161 - 2.53670i) q^{9} +(2.60494 - 4.51189i) q^{11} +(-0.0681144 - 3.44195i) q^{12} +(1.36091 - 3.33885i) q^{13} +0.445140 q^{14} +(1.96287 - 3.39979i) q^{16} +(-3.27708 - 0.878092i) q^{17} +(-0.245402 - 0.226709i) q^{18} +(-0.210416 - 0.364452i) q^{19} +(-4.79764 + 4.99136i) q^{21} +(0.150166 - 0.560429i) q^{22} +(2.63136 - 0.705071i) q^{23} +(-0.213736 - 0.738874i) q^{24} +(0.0501565 - 0.398387i) q^{26} +(5.18700 - 0.308267i) q^{27} +(-7.67398 + 2.05624i) q^{28} +(2.52506 - 4.37354i) q^{29} -4.23553i q^{31} +(0.343025 - 1.28019i) q^{32} +(4.66563 + 7.72402i) q^{33} -0.377826 q^{34} +(5.27784 + 2.77476i) q^{36} +(1.53863 + 5.74223i) q^{37} +(-0.0331393 - 0.0331393i) q^{38} +(3.92655 + 4.85615i) q^{39} +(-0.973131 + 1.68551i) q^{41} +(-0.372216 + 0.675207i) q^{42} +(-0.905224 - 0.242554i) q^{43} +10.3551i q^{44} +(0.262734 - 0.151689i) q^{46} +(1.29449 + 1.29449i) q^{47} +(3.51564 + 5.82019i) q^{48} +(7.77434 + 4.48852i) q^{49} +(4.07215 - 4.23657i) q^{51} +(0.975600 + 7.09967i) q^{52} +(2.45762 + 2.45762i) q^{53} +(0.549082 - 0.182667i) q^{54} +(-1.53723 + 0.887520i) q^{56} +(0.728761 - 0.0144218i) q^{57} +(0.145562 - 0.543244i) q^{58} +(7.83433 - 4.52315i) q^{59} +(2.65934 + 4.60611i) q^{61} +(-0.122082 - 0.455618i) q^{62} +(-3.55942 - 11.4509i) q^{63} +7.70388i q^{64} +(0.724516 + 0.696396i) q^{66} +(-1.98691 - 7.41523i) q^{67} +(6.51352 - 1.74529i) q^{68} +(-1.13080 + 4.58092i) q^{69} +(-6.09876 - 10.5634i) q^{71} +(1.29948 + 0.293626i) q^{72} +(1.29733 + 1.29733i) q^{73} +(0.331021 + 0.573345i) q^{74} +(0.724384 + 0.418223i) q^{76} +(14.7252 - 14.7252i) q^{77} +(0.562351 + 0.409202i) q^{78} -2.49102i q^{79} +(-3.86966 + 8.12562i) q^{81} +(-0.0560979 + 0.209360i) q^{82} +(-9.55183 + 9.55183i) q^{83} +(3.29782 - 13.3596i) q^{84} -0.104367 q^{86} +(4.52256 + 7.48717i) q^{87} +(0.598803 + 2.23476i) q^{88} +(-3.74597 - 2.16273i) q^{89} +(8.70853 - 11.4832i) q^{91} +(-3.82869 + 3.82869i) q^{92} +(6.42463 + 3.54166i) q^{93} +(0.176560 + 0.101937i) q^{94} +(1.65501 + 1.59078i) q^{96} +(2.76392 + 0.740590i) q^{97} +(0.965663 + 0.258749i) q^{98} +(-15.6174 + 0.618364i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 2 q^{3} - 12 q^{6} + 12 q^{7} + 12 q^{12} + 24 q^{13} + 16 q^{16} - 20 q^{22} + 32 q^{27} + 36 q^{28} - 30 q^{33} - 4 q^{36} + 84 q^{37} + 48 q^{42} - 8 q^{43} + 28 q^{48} - 16 q^{51} - 28 q^{52}+ \cdots + 48 q^{97}+O(q^{100}) \) 96 * q + 2 * q^3 - 12 * q^6 + 12 * q^7 + 12 * q^12 + 24 * q^13 + 16 * q^16 - 20 * q^22 + 32 * q^27 + 36 * q^28 - 30 * q^33 - 4 * q^36 + 84 * q^37 + 48 * q^42 - 8 * q^43 + 28 * q^48 - 16 * q^51 - 28 * q^52 - 84 * q^58 - 32 * q^61 - 90 * q^63 - 36 * q^67 - 90 * q^72 + 72 * q^76 - 60 * q^78 + 32 * q^81 + 68 * q^82 + 26 * q^87 + 108 * q^88 - 80 * q^91 - 48 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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