LMFDB - Embedded newform 975.2.bo.h.626.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [975,2,Mod(176,975)] 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("975.176"); 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, 0, 11])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [96,0,0,24,0,0,0,0,4,0,0,0,0,0,0,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(19)] == 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			626.8
Character	$\chi$	$=$	975.626
Dual form			975.2.bo.h.176.8

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.335598 + 1.25247i) q^{2} +(-0.518148 + 1.65273i) q^{3} +(0.276000 + 0.159349i) q^{4} +(-1.89610 - 1.20362i) q^{6} +(2.20132 - 0.589843i) q^{7} +(-2.12594 + 2.12594i) q^{8} +(-2.46304 - 1.71272i) q^{9} +(2.74441 + 0.735363i) q^{11} +(-0.406369 + 0.373587i) q^{12} +(-2.40830 + 2.68330i) q^{13} +2.95504i q^{14} +(-1.63052 - 2.82414i) q^{16} +(-2.27079 + 3.93313i) q^{17} +(2.97172 - 2.51010i) q^{18} +(-0.775797 - 2.89531i) q^{19} +(-0.165760 + 3.94382i) q^{21} +(-1.84204 + 3.19050i) q^{22} +(-0.223746 - 0.387540i) q^{23} +(-2.41206 - 4.61517i) q^{24} +(-2.55253 - 3.91682i) q^{26} +(4.10689 - 3.18331i) q^{27} +(0.701555 + 0.187981i) q^{28} +(-4.98037 + 2.87542i) q^{29} +(-4.62601 + 4.62601i) q^{31} +(-1.72384 + 0.461902i) q^{32} +(-2.63737 + 4.15475i) q^{33} +(-4.16405 - 4.16405i) q^{34} +(-0.406880 - 0.865193i) q^{36} +(-2.75740 + 10.2908i) q^{37} +3.88664 q^{38} +(-3.18693 - 5.37061i) q^{39} +(-0.217322 + 0.811058i) q^{41} +(-4.88389 - 1.53115i) q^{42} +(4.12924 + 2.38402i) q^{43} +(0.640278 + 0.640278i) q^{44} +(0.560470 - 0.150177i) q^{46} +(3.06335 - 3.06335i) q^{47} +(5.51240 - 1.23149i) q^{48} +(-1.56426 + 0.903128i) q^{49} +(-5.32380 - 5.79096i) q^{51} +(-1.09227 + 0.356833i) q^{52} -8.28713i q^{53} +(2.60873 + 6.21206i) q^{54} +(-3.42592 + 5.93387i) q^{56} +(5.18715 + 0.218017i) q^{57} +(-1.92997 - 7.20275i) q^{58} +(1.67660 + 6.25715i) q^{59} +(5.66303 - 9.80865i) q^{61} +(-4.24145 - 7.34641i) q^{62} +(-6.43220 - 2.31744i) q^{63} -8.83615i q^{64} +(-4.31860 - 4.69755i) q^{66} +(-8.96003 - 2.40083i) q^{67} +(-1.25348 + 0.723695i) q^{68} +(0.756433 - 0.168989i) q^{69} +(12.8138 - 3.43344i) q^{71} +(8.87745 - 1.59515i) q^{72} +(1.56653 + 1.56653i) q^{73} +(-11.9635 - 6.90712i) q^{74} +(0.247244 - 0.922728i) q^{76} +6.47509 q^{77} +(7.79605 - 2.18916i) q^{78} +9.74173 q^{79} +(3.13318 + 8.43701i) q^{81} +(-0.942892 - 0.544379i) q^{82} +(-0.856250 - 0.856250i) q^{83} +(-0.674192 + 1.06208i) q^{84} +(-4.37167 + 4.37167i) q^{86} +(-2.17173 - 9.72112i) q^{87} +(-7.39781 + 4.27113i) q^{88} +(1.64453 + 0.440650i) q^{89} +(-3.71871 + 7.32734i) q^{91} -0.142614i q^{92} +(-5.24860 - 10.0425i) q^{93} +(2.80869 + 4.86480i) q^{94} +(0.129806 - 3.08838i) q^{96} +(-2.62855 - 9.80988i) q^{97} +(-0.606176 - 2.26228i) q^{98} +(-5.50014 - 6.51164i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 24 q^{4} + 4 q^{9} - 16 q^{21} + 28 q^{24} - 40 q^{31} + 32 q^{34} - 60 q^{36} + 4 q^{39} - 128 q^{46} - 60 q^{54} - 48 q^{61} - 8 q^{66} - 72 q^{69} - 80 q^{76} + 80 q^{79} + 48 q^{81} + 132 q^{84}+ \cdots + 48 q^{99}+O(q^{100}) $ 96 * q + 24 * q^4 + 4 * q^9 - 16 * q^21 + 28 * q^24 - 40 * q^31 + 32 * q^34 - 60 * q^36 + 4 * q^39 - 128 * q^46 - 60 * q^54 - 48 * q^61 - 8 * q^66 - 72 * q^69 - 80 * q^76 + 80 * q^79 + 48 * q^81 + 132 * q^84 - 56 * q^91 - 72 * q^94 + 204 * q^96 + 48 * q^99

Character values

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

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$-1$	$1$

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 $

$2$	−0.335598	+	1.25247i	−0.237304	+	0.885629i	0.739793	+	0.672834i	$0.234923\pi$
$2$	−0.335598	+	1.25247i	−0.237304	+	0.885629i	−0.977097	+	0.212795i	$0.931743\pi$
$3$	−0.518148	+	1.65273i	−0.299153	+	0.954205i
$3$	−0.518148	+	1.65273i	−0.299153	+	0.954205i
$4$	0.276000	+	0.159349i	0.138000	+	0.0796743i
$5$		0			0
$5$		0			0
$6$	−1.89610	−	1.20362i	−0.774082	−	0.491375i
$7$	2.20132	−	0.589843i	0.832022	−	0.222940i	0.182427	−	0.983219i	$-0.441605\pi$
$7$	2.20132	−	0.589843i	0.832022	−	0.222940i	0.649596	+	0.760280i	$0.274938\pi$
$8$	−2.12594	+	2.12594i	−0.751635	+	0.751635i
$9$	−2.46304	−	1.71272i	−0.821015	−	0.570907i
$10$		0			0
$11$	2.74441	+	0.735363i	0.827472	+	0.221720i	0.647610	−	0.761972i	$-0.275768\pi$
$11$	2.74441	+	0.735363i	0.827472	+	0.221720i	0.179861	+	0.983692i	$0.442435\pi$
$12$	−0.406369	+	0.373587i	−0.117309	+	0.107845i
$13$	−2.40830	+	2.68330i	−0.667941	+	0.744214i
$13$	−2.40830	+	2.68330i	−0.667941	+	0.744214i
$14$			2.95504i			0.789767i
$15$		0			0
$16$	−1.63052	−	2.82414i	−0.407630	−	0.706035i
$17$	−2.27079	+	3.93313i	−0.550748	+	0.953924i	0.447473	+	0.894298i	$0.352324\pi$
$17$	−2.27079	+	3.93313i	−0.550748	+	0.953924i	−0.998221	+	0.0596262i	$0.981009\pi$
$18$	2.97172	−	2.51010i	0.700441	−	0.591636i
$19$	−0.775797	−	2.89531i	−0.177980	−	0.664230i	−0.996025	−	0.0890759i	$-0.971609\pi$
$19$	−0.775797	−	2.89531i	−0.177980	−	0.664230i	0.818045	−	0.575154i	$-0.195058\pi$
$20$		0			0
$21$	−0.165760	+	3.94382i	−0.0361718	+	0.860613i
$22$	−1.84204	+	3.19050i	−0.392724	+	0.680218i
$23$	−0.223746	−	0.387540i	−0.0466543	−	0.0808076i	0.841755	−	0.539859i	$-0.181523\pi$
$23$	−0.223746	−	0.387540i	−0.0466543	−	0.0808076i	−0.888410	+	0.459052i	$0.848189\pi$
$24$	−2.41206	−	4.61517i	−0.492360	−	0.942068i
$25$		0			0
$26$	−2.55253	−	3.91682i	−0.500593	−	0.768152i
$27$	4.10689	−	3.18331i	0.790371	−	0.612628i
$28$	0.701555	+	0.187981i	0.132582	+	0.0355251i
$29$	−4.98037	+	2.87542i	−0.924832	+	0.533952i	−0.885173	−	0.465261i	$-0.845960\pi$
$29$	−4.98037	+	2.87542i	−0.924832	+	0.533952i	−0.0396587	+	0.999213i	$0.512627\pi$
$30$		0			0
$31$	−4.62601	+	4.62601i	−0.830856	+	0.830856i	−0.987634	−	0.156778i	$-0.949889\pi$
$31$	−4.62601	+	4.62601i	−0.830856	+	0.830856i	0.156778	+	0.987634i	$0.449889\pi$
$32$	−1.72384	+	0.461902i	−0.304735	+	0.0816535i
$33$	−2.63737	+	4.15475i	−0.459107	+	0.723249i
$34$	−4.16405	−	4.16405i	−0.714128	−	0.714128i
$35$		0			0
$36$	−0.406880	−	0.865193i	−0.0678134	−	0.144199i
$37$	−2.75740	+	10.2908i	−0.453315	+	1.69179i	0.239682	+	0.970852i	$0.422957\pi$
$37$	−2.75740	+	10.2908i	−0.453315	+	1.69179i	−0.692996	+	0.720941i	$0.743710\pi$
$38$	3.88664			0.630497
$39$	−3.18693	−	5.37061i	−0.510317	−	0.859987i
$40$		0			0
$41$	−0.217322	+	0.811058i	−0.0339401	+	0.126666i	−0.980817	−	0.194929i	$-0.937552\pi$
$41$	−0.217322	+	0.811058i	−0.0339401	+	0.126666i	0.946877	+	0.321595i	$0.104219\pi$
$42$	−4.88389	−	1.53115i	−0.753600	−	0.236261i
$43$	4.12924	+	2.38402i	0.629703	+	0.363559i	0.780637	−	0.624985i	$-0.214895\pi$
$43$	4.12924	+	2.38402i	0.629703	+	0.363559i	−0.150934	+	0.988544i	$0.548228\pi$
$44$	0.640278	+	0.640278i	0.0965256	+	0.0965256i
$45$		0			0
$46$	0.560470	−	0.150177i	0.0826368	−	0.0221425i
$47$	3.06335	−	3.06335i	0.446835	−	0.446835i	−0.447466	−	0.894301i	$-0.647673\pi$
$47$	3.06335	−	3.06335i	0.446835	−	0.446835i	0.894301	+	0.447466i	$0.147673\pi$
$48$	5.51240	−	1.23149i	0.795646	−	0.177750i
$49$	−1.56426	+	0.903128i	−0.223466	+	0.129018i
$50$		0			0
$51$	−5.32380	−	5.79096i	−0.745481	−	0.810896i
$52$	−1.09227	+	0.356833i	−0.151470	+	0.0494838i
$53$		−	8.28713i		−	1.13832i	−0.822225	−	0.569162i	$-0.807268\pi$
$53$		−	8.28713i		−	1.13832i	0.822225	−	0.569162i	$-0.192732\pi$
$54$	2.60873	+	6.21206i	0.355003	+	0.845354i
$55$		0			0
$56$	−3.42592	+	5.93387i	−0.457808	+	0.792946i
$57$	5.18715	+	0.218017i	0.687055	+	0.0288771i
$58$	−1.92997	−	7.20275i	−0.253417	−	0.945767i
$59$	1.67660	+	6.25715i	0.218275	+	0.814612i	0.984988	+	0.172622i	$0.0552240\pi$
$59$	1.67660	+	6.25715i	0.218275	+	0.814612i	−0.766714	+	0.641989i	$0.778109\pi$
$60$		0			0
$61$	5.66303	−	9.80865i	0.725077	−	1.25587i	−0.233866	−	0.972269i	$-0.575138\pi$
$61$	5.66303	−	9.80865i	0.725077	−	1.25587i	0.958942	−	0.283601i	$-0.0915290\pi$
$62$	−4.24145	−	7.34641i	−0.538665	−	0.932995i
$63$	−6.43220	−	2.31744i	−0.810381	−	0.291970i
$64$		−	8.83615i		−	1.10452i
$65$		0			0
$66$	−4.31860	−	4.69755i	−0.531583	−	0.578228i
$67$	−8.96003	−	2.40083i	−1.09464	−	0.293308i	−0.334061	−	0.942552i	$-0.608419\pi$
$67$	−8.96003	−	2.40083i	−1.09464	−	0.293308i	−0.760581	+	0.649243i	$0.775086\pi$
$68$	−1.25348	+	0.723695i	−0.152006	+	0.0877609i
$69$	0.756433	−	0.168989i	0.0910638	−	0.0203439i
$70$		0			0
$71$	12.8138	−	3.43344i	1.52072	−	0.407474i	0.600738	−	0.799446i	$-0.294873\pi$
$71$	12.8138	−	3.43344i	1.52072	−	0.407474i	0.919977	+	0.391971i	$0.128207\pi$
$72$	8.87745	−	1.59515i	1.04622	−	0.187990i
$73$	1.56653	+	1.56653i	0.183349	+	0.183349i	0.792813	−	0.609464i	$-0.208615\pi$
$73$	1.56653	+	1.56653i	0.183349	+	0.183349i	−0.609464	+	0.792813i	$0.708615\pi$
$74$	−11.9635	−	6.90712i	−1.39073	−	0.802937i
$75$		0			0
$76$	0.247244	−	0.922728i	0.0283608	−	0.105844i
$77$	6.47509			0.737905
$78$	7.79605	−	2.18916i	0.882729	−	0.247873i
$79$	9.74173			1.09603			0.548015	−	0.836468i	$-0.315384\pi$
$79$	9.74173			1.09603			0.548015	+	0.836468i	$0.315384\pi$
$80$		0			0
$81$	3.13318	+	8.43701i	0.348131	+	0.937446i
$82$	−0.942892	−	0.544379i	−0.104125	−	0.0601166i
$83$	−0.856250	−	0.856250i	−0.0939856	−	0.0939856i	0.658551	−	0.752536i	$-0.271170\pi$
$83$	−0.856250	−	0.856250i	−0.0939856	−	0.0939856i	−0.752536	+	0.658551i	$0.771170\pi$
$84$	−0.674192	+	1.06208i	−0.0735604	+	0.115883i
$85$		0			0
$86$	−4.37167	+	4.37167i	−0.471409	+	0.471409i
$87$	−2.17173	−	9.72112i	−0.232833	−	1.04221i
$88$	−7.39781	+	4.27113i	−0.788609	+	0.455304i
$89$	1.64453	+	0.440650i	0.174320	+	0.0467088i	0.344923	−	0.938631i	$-0.387905\pi$
$89$	1.64453	+	0.440650i	0.174320	+	0.0467088i	−0.170603	+	0.985340i	$0.554572\pi$
$90$		0			0
$91$	−3.71871	+	7.32734i	−0.389827	+	0.768114i
$92$		−	0.142614i		−	0.0148686i
$93$	−5.24860	−	10.0425i	−0.544254	−	1.04136i
$94$	2.80869	+	4.86480i	0.289695	+	0.501766i
$95$		0			0
$96$	0.129806	−	3.08838i	0.0132482	−	0.315207i
$97$	−2.62855	−	9.80988i	−0.266889	−	0.996042i	−0.961084	−	0.276256i	$-0.910906\pi$
$97$	−2.62855	−	9.80988i	−0.266889	−	0.996042i	0.694195	−	0.719787i	$-0.255760\pi$
$98$	−0.606176	−	2.26228i	−0.0612330	−	0.228525i
$99$	−5.50014	−	6.51164i	−0.552785	−	0.654445i
$100$		0			0
$101$	6.55756	+	11.3580i	0.652502	+	1.13017i	0.982514	+	0.186189i	$0.0596138\pi$
$101$	6.55756	+	11.3580i	0.652502	+	1.13017i	−0.330012	+	0.943977i	$0.607053\pi$
$102$	9.03965	−	4.72446i	0.895058	−	0.467791i
$103$			5.12642i			0.505122i	0.967581	+	0.252561i	$0.0812728\pi$
$103$			5.12642i			0.505122i	−0.967581	+	0.252561i	$0.918727\pi$
$104$	−0.584652	−	10.8245i	−0.0573298	−	1.06143i
$105$		0			0
$106$	10.3794	+	2.78114i	1.00813	+	0.270129i
$107$	5.95164	−	3.43618i	0.575367	−	0.332188i	−0.183923	−	0.982941i	$-0.558880\pi$
$107$	5.95164	−	3.43618i	0.575367	−	0.332188i	0.759290	+	0.650752i	$0.225546\pi$
$108$	1.64076	−	0.224166i	0.157882	−	0.0215704i
$109$	0.716943	−	0.716943i	0.0686706	−	0.0686706i	−0.671937	−	0.740608i	$-0.734538\pi$
$109$	0.716943	−	0.716943i	0.0686706	−	0.0686706i	0.740608	+	0.671937i	$0.234538\pi$
$110$		0			0
$111$	−15.5791	−	9.88940i	−1.47871	−	0.938660i
$112$	−5.25510	−	5.25510i	−0.496560	−	0.496560i
$113$	5.13301	+	2.96354i	0.482873	+	0.278787i	0.721613	−	0.692297i	$-0.243401\pi$
$113$	5.13301	+	2.96354i	0.482873	+	0.278787i	−0.238740	+	0.971083i	$0.576734\pi$
$114$	−2.01386	+	6.42358i	−0.188615	+	0.601623i
$115$		0			0
$116$	−1.83278			−0.170169
$117$	10.5275	−	2.48436i	0.973266	−	0.229679i
$118$	−8.39955			−0.773241
$119$	−2.67882	+	9.99750i	−0.245567	+	0.916470i
$120$		0			0
$121$	−2.53524	−	1.46372i	−0.230476	−	0.133065i
$122$	10.3845	+	10.3845i	0.940171	+	0.940171i
$123$	−1.22786	−	0.779424i	−0.110712	−	0.0702783i
$124$	−2.01393	+	0.539630i	−0.180856	+	0.0484602i
$125$		0			0
$126$	5.06116	−	7.27839i	0.450884	−	0.648411i
$127$	−10.6342	+	6.13964i	−0.943630	+	0.544805i	−0.891096	−	0.453814i	$-0.850063\pi$
$127$	−10.6342	+	6.13964i	−0.943630	+	0.544805i	−0.0525335	+	0.998619i	$0.516730\pi$
$128$	7.61931	+	2.04159i	0.673458	+	0.180453i
$129$	−6.07970	+	5.58925i	−0.535287	+	0.492106i
$130$		0			0
$131$			0.875714i			0.0765115i	0.999268	+	0.0382557i	$0.0121802\pi$
$131$			0.875714i			0.0765115i	−0.999268	+	0.0382557i	$0.987820\pi$
$132$	−1.38997	+	0.726449i	−0.120981	+	0.0632293i
$133$	−3.41556	−	5.91592i	−0.296167	−	0.512976i
$134$	6.01393	−	10.4164i	0.519525	−	0.899843i
$135$		0			0
$136$	−3.53403	−	13.1892i	−0.303041	−	1.13096i
$137$	−1.62972	−	6.08218i	−0.139236	−	0.519636i	−0.999944	−	0.0105378i	$-0.996646\pi$
$137$	−1.62972	−	6.08218i	−0.139236	−	0.519636i	0.860708	−	0.509098i	$-0.170021\pi$
$138$	−0.0422035	+	1.00412i	−0.00359260	+	0.0854764i
$139$	−8.67597	+	15.0272i	−0.735886	+	1.27459i	0.218447	+	0.975849i	$0.429901\pi$
$139$	−8.67597	+	15.0272i	−0.735886	+	1.27459i	−0.954333	+	0.298744i	$0.903432\pi$
$140$		0			0
$141$	3.47562	+	6.65016i	0.292700	+	0.560044i
$142$			17.2011i			1.44348i
$143$	−8.58256	+	5.59312i	−0.717710	+	0.467720i
$144$	−0.820923	+	9.74861i	−0.0684103	+	0.812384i
$145$		0			0
$146$	−2.48776	+	1.43631i	−0.205889	+	0.118870i
$147$	−0.682108	−	3.05326i	−0.0562593	−	0.251829i
$148$	−2.40086	+	2.40086i	−0.197350	+	0.197350i
$149$	21.4260	−	5.74107i	1.75528	−	0.470327i	0.769543	−	0.638595i	$-0.220484\pi$
$149$	21.4260	−	5.74107i	1.75528	−	0.470327i	0.985741	+	0.168269i	$0.0538176\pi$
$150$		0			0
$151$	−0.495344	−	0.495344i	−0.0403105	−	0.0403105i	0.686664	−	0.726975i	$-0.259074\pi$
$151$	−0.495344	−	0.495344i	−0.0403105	−	0.0403105i	−0.726975	+	0.686664i	$0.759074\pi$
$152$	7.80458	+	4.50597i	0.633035	+	0.365483i
$153$	12.3294	−	5.79824i	0.996774	−	0.468760i
$154$	−2.17303	+	8.10985i	−0.175108	+	0.653510i
$155$		0			0
$156$	−0.0237913	−	1.99012i	−0.00190483	−	0.159337i
$157$	21.4749			1.71388			0.856941	−	0.515414i	$-0.172362\pi$
$157$	21.4749			1.71388			0.856941	+	0.515414i	$0.172362\pi$
$158$	−3.26930	+	12.2012i	−0.260092	+	0.970676i
$159$	13.6964	+	4.29396i	1.08620	+	0.340533i
$160$		0			0
$161$	−0.721125	−	0.721125i	−0.0568326	−	0.0568326i
$162$	−11.6186	+	1.09276i	−0.912842	+	0.0858556i
$163$	10.6985	−	2.86667i	0.837975	−	0.224535i	0.185785	−	0.982590i	$-0.440517\pi$
$163$	10.6985	−	2.86667i	0.837975	−	0.224535i	0.652190	+	0.758056i	$0.273851\pi$
$164$	−0.189222	+	0.189222i	−0.0147757	+	0.0147757i
$165$		0			0
$166$	1.35978	−	0.785070i	0.105539	−	0.0609333i
$167$	−23.3283	−	6.25081i	−1.80520	−	0.483702i	−0.810430	−	0.585835i	$-0.800767\pi$
$167$	−23.3283	−	6.25081i	−1.80520	−	0.483702i	−0.994771	+	0.102133i	$0.967433\pi$
$168$	−8.03196	−	8.73675i	−0.619679	−	0.674055i
$169$	−1.40023	−	12.9244i	−0.107710	−	0.994182i
$170$		0			0
$171$	−3.04804	+	8.46001i	−0.233089	+	0.646953i
$172$	0.759779	+	1.31598i	0.0579326	+	0.100342i
$173$	−1.46268	+	2.53344i	−0.111206	+	0.192614i	−0.916257	−	0.400592i	$-0.868805\pi$
$173$	−1.46268	+	2.53344i	−0.111206	+	0.192614i	0.805051	+	0.593206i	$0.202138\pi$
$174$	12.9042	+	0.542368i	0.978266	+	0.0411168i
$175$		0			0
$176$	−2.39805	−	8.94964i	−0.180760	−	0.674604i
$177$	−11.2101	−	0.471164i	−0.842604	−	0.0354149i
$178$	−1.10380	+	1.91184i	−0.0827333	+	0.143298i
$179$	3.43112	+	5.94288i	0.256454	+	0.444192i	0.965290	−	0.261182i	$-0.0841124\pi$
$179$	3.43112	+	5.94288i	0.256454	+	0.444192i	−0.708835	+	0.705374i	$0.750779\pi$
$180$		0			0
$181$			22.0007i			1.63530i	0.575717	+	0.817649i	$0.304723\pi$
$181$			22.0007i			1.63530i	−0.575717	+	0.817649i	$0.695277\pi$
$182$	−7.92927	−	7.11661i	−0.587756	−	0.527518i
$183$	13.2768	+	14.4418i	0.981448	+	1.06757i
$184$	1.29956	+	0.348216i	0.0958048	+	0.0256708i
$185$		0			0
$186$	14.3394	−	3.20345i	1.05141	−	0.234889i
$187$	−9.12427	+	9.12427i	−0.667233	+	0.667233i
$188$	1.33362	−	0.357343i	0.0972644	−	0.0260619i
$189$	7.16294	−	9.42992i	0.521027	−	0.685925i
$190$		0			0
$191$	14.4065	+	8.31762i	1.04242	+	0.601842i	0.920518	−	0.390700i	$-0.127767\pi$
$191$	14.4065	+	8.31762i	1.04242	+	0.601842i	0.121903	+	0.992542i	$0.461100\pi$
$192$	14.6038	+	4.57843i	1.05394	+	0.330420i
$193$	−1.72615	+	6.44208i	−0.124251	+	0.463711i	−0.999812	−	0.0193966i	$-0.993825\pi$
$193$	−1.72615	+	6.44208i	−0.124251	+	0.463711i	0.875561	+	0.483108i	$0.160492\pi$
$194$	13.1687			0.945457
$195$		0			0
$196$	−0.575649			−0.0411178
$197$	−2.97372	+	11.0981i	−0.211869	+	0.790706i	0.775376	+	0.631499i	$0.217560\pi$
$197$	−2.97372	+	11.0981i	−0.211869	+	0.790706i	−0.987245	+	0.159206i	$0.949106\pi$
$198$	10.0015	−	4.70346i	0.710773	−	0.334260i
$199$	0.252420	+	0.145735i	0.0178936	+	0.0103309i	0.508920	−	0.860814i	$-0.330045\pi$
$199$	0.252420	+	0.145735i	0.0178936	+	0.0103309i	−0.491027	+	0.871145i	$0.663378\pi$
$200$		0			0
$201$	8.61055	−	13.5645i	0.607342	−	0.956768i
$202$	−16.4263	+	4.40141i	−1.15575	+	0.309682i
$203$	−9.26737	+	9.26737i	−0.650442	+	0.650442i
$204$	−0.546587	−	2.44664i	−0.0382687	−	0.171299i
$205$		0			0
$206$	−6.42069	−	1.72042i	−0.447350	−	0.119867i
$207$	−0.112650	+	1.33774i	−0.00782974	+	0.0929795i
$208$	11.5048	+	2.42619i	0.797714	+	0.168226i
$209$		−	8.51643i		−	0.589094i
$210$		0			0
$211$	7.95121	+	13.7719i	0.547384	+	0.948096i	0.998453	+	0.0556073i	$0.0177095\pi$
$211$	7.95121	+	13.7719i	0.547384	+	0.948096i	−0.451069	+	0.892489i	$0.648957\pi$
$212$	1.32054	−	2.28725i	0.0906952	−	0.157089i
$213$	−0.964879	+	22.9568i	−0.0661124	+	1.57297i
$214$	2.30635	+	8.60742i	0.157659	+	0.588391i
$215$		0			0
$216$	−1.96348	+	15.4986i	−0.133598	+	1.05454i
$217$	−7.45473	+	12.9120i	−0.506060	+	0.876522i
$218$	0.657343	+	1.13855i	0.0445209	+	0.0771125i
$219$	−3.40076	+	1.77736i	−0.229802	+	0.120103i
$220$		0			0
$221$	−5.08504	−	15.5654i	−0.342057	−	1.04704i
$222$	17.6145	−	16.1935i	1.18221	−	1.08684i
$223$	−4.28509	−	1.14819i	−0.286951	−	0.0768882i	0.112473	−	0.993655i	$-0.464123\pi$
$223$	−4.28509	−	1.14819i	−0.286951	−	0.0768882i	−0.399423	+	0.916767i	$0.630790\pi$
$224$	−3.52229	+	2.03359i	−0.235343	+	0.135875i
$225$		0			0
$226$	−5.43437	+	5.43437i	−0.361489	+	0.361489i
$227$	−12.9846	+	3.47922i	−0.861820	+	0.230924i	−0.662547	−	0.749020i	$-0.730525\pi$
$227$	−12.9846	+	3.47922i	−0.861820	+	0.230924i	−0.199273	+	0.979944i	$0.563858\pi$
$228$	1.39691	+	0.886738i	0.0925128	+	0.0587257i
$229$	8.40317	+	8.40317i	0.555297	+	0.555297i	0.927965	−	0.372668i	$-0.121557\pi$
$229$	8.40317	+	8.40317i	0.555297	+	0.555297i	−0.372668	+	0.927965i	$0.621557\pi$
$230$		0			0
$231$	−3.35506	+	10.7016i	−0.220747	+	0.704113i
$232$	4.47502	−	16.7010i	0.293799	−	1.09647i
$233$	12.1684			0.797175			0.398588	−	0.917130i	$-0.369500\pi$
$233$	12.1684			0.797175			0.398588	+	0.917130i	$0.369500\pi$
$234$	−0.421420	+	14.0191i	−0.0275491	+	0.916457i
$235$		0			0
$236$	−0.534327	+	1.99414i	−0.0347817	+	0.129807i
$237$	−5.04766	+	16.1005i	−0.327881	+	1.04584i
$238$	−11.6226	−	6.71028i	−0.753378	−	0.434963i
$239$	15.4524	+	15.4524i	0.999531	+	0.999531i	1.00000		0.000468754i	$-0.000149209\pi$
$239$	15.4524	+	15.4524i	0.999531	+	0.999531i	−0.000468754		1.00000i	$0.500149\pi$
$240$		0			0
$241$	−24.0324	+	6.43947i	−1.54806	+	0.414803i	−0.928861	−	0.370428i	$-0.879211\pi$
$241$	−24.0324	+	6.43947i	−1.54806	+	0.414803i	−0.619203	+	0.785231i	$0.712544\pi$
$242$	2.68408	−	2.68408i	0.172539	−	0.172539i
$243$	−15.5676	+	0.806681i	−0.998660	+	0.0517486i
$244$	3.12599	−	1.80479i	0.200121	−	0.115540i
$245$		0			0
$246$	1.38827	−	1.27628i	0.0885129	−	0.0813726i
$247$	9.63735	+	4.89107i	0.613210	+	0.311211i
$248$		−	19.6693i		−	1.24900i
$249$	1.85882	−	0.971487i	0.117798	−	0.0615655i
$250$		0			0
$251$	1.55359	−	2.69089i	0.0980614	−	0.169847i	−0.812821	−	0.582514i	$-0.802069\pi$
$251$	1.55359	−	2.69089i	0.0980614	−	0.169847i	0.910882	+	0.412666i	$0.135402\pi$
$252$	−1.40600	−	1.66457i	−0.0885699	−	0.104858i
$253$	−0.329069	−	1.22810i	−0.0206884	−	0.0772102i
$254$	−4.12090	−	15.3794i	−0.258568	−	0.964990i
$255$		0			0
$256$	3.72210	−	6.44686i	0.232631	−	0.402929i
$257$	6.58997	+	11.4142i	0.411071	+	0.711996i	0.995007	−	0.0998036i	$-0.0318214\pi$
$257$	6.58997	+	11.4142i	0.411071	+	0.711996i	−0.583936	+	0.811800i	$0.698488\pi$
$258$	−4.96002	−	9.49037i	−0.308797	−	0.590844i
$259$			24.2798i			1.50867i
$260$		0			0
$261$	17.1917	+	1.44770i	1.06414	+	0.0896103i
$262$	−1.09680	−	0.293888i	−0.0677608	−	0.0181564i
$263$	2.74583	−	1.58530i	0.169315	−	0.0977540i	−0.412948	−	0.910755i	$-0.635501\pi$
$263$	2.74583	−	1.58530i	0.169315	−	0.0977540i	0.582263	+	0.813001i	$0.302167\pi$
$264$	−3.22587	−	14.4397i	−0.198538	−	0.888701i
$265$		0			0
$266$	8.55576	−	2.29251i	0.524588	−	0.140563i
$267$	−1.58038	+	2.48964i	−0.0967180	+	0.152364i
$268$	−2.09040	−	2.09040i	−0.127691	−	0.127691i
$269$	−8.98175	−	5.18562i	−0.547627	−	0.316173i	0.200537	−	0.979686i	$-0.435731\pi$
$269$	−8.98175	−	5.18562i	−0.547627	−	0.316173i	−0.748164	+	0.663513i	$0.769065\pi$
$270$		0			0
$271$	5.62575	−	20.9956i	0.341740	−	1.27539i	−0.554635	−	0.832094i	$-0.687142\pi$
$271$	5.62575	−	20.9956i	0.341740	−	1.27539i	0.896375	−	0.443297i	$-0.146191\pi$
$272$	14.8103			0.898005
$273$	−10.1833	−	9.94268i	−0.616320	−	0.601758i
$274$	8.16467			0.493246
$275$		0			0
$276$	0.235703	+	0.0738954i	0.0141877	+	0.00444798i
$277$	−2.06025	−	1.18949i	−0.123789	−	0.0714694i	0.436827	−	0.899546i	$-0.356102\pi$
$277$	−2.06025	−	1.18949i	−0.123789	−	0.0714694i	−0.560616	+	0.828076i	$0.689436\pi$
$278$	−15.9095	−	15.9095i	−0.954188	−	0.954188i
$279$	19.3171	−	3.47101i	1.15649	−	0.207804i
$280$		0			0
$281$	7.28271	−	7.28271i	0.434450	−	0.434450i	−0.455689	−	0.890139i	$-0.650607\pi$
$281$	7.28271	−	7.28271i	0.434450	−	0.434450i	0.890139	+	0.455689i	$0.150607\pi$
$282$	−9.49553	+	2.12133i	−0.565450	+	0.126323i
$283$	12.0763	−	6.97223i	0.717859	−	0.414456i	−0.0961049	−	0.995371i	$-0.530638\pi$
$283$	12.0763	−	6.97223i	0.717859	−	0.414456i	0.813964	+	0.580915i	$0.197305\pi$
$284$	4.08371	+	1.09423i	0.242324	+	0.0649305i
$285$		0			0
$286$	−4.12492	−	12.6264i	−0.243911	−	0.746616i
$287$			1.91359i			0.112956i
$288$	5.03701	+	1.81477i	0.296809	+	0.106937i
$289$	−1.81300	−	3.14021i	−0.106647	−	0.184718i
$290$		0			0
$291$	17.5751	+	0.738685i	1.03027	+	0.0433025i
$292$	0.182738	+	0.681988i	0.0106939	+	0.0399103i
$293$	−7.12679	−	26.5976i	−0.416352	−	1.55385i	−0.782113	−	0.623137i	$-0.785858\pi$
$293$	−7.12679	−	26.5976i	−0.416352	−	1.55385i	0.365761	−	0.930709i	$-0.380809\pi$
$294$	4.05303	+	0.170350i	0.236378	+	0.00993501i
$295$		0			0
$296$	−16.0155	−	27.7397i	−0.930884	−	1.61234i
$297$	13.6119	−	5.71626i	0.789842	−	0.331691i
$298$			28.7620i			1.66614i
$299$	1.57873	+	0.332931i	0.0913005	+	0.0192539i
$300$		0			0
$301$	10.4960	+	2.81239i	0.604978	+	0.162103i
$302$	0.786639	−	0.454166i	0.0452660	−	0.0261343i
$303$	−22.1696	+	4.95275i	−1.27361	+	0.284528i
$304$	−6.91182	+	6.91182i	−0.396420	+	0.396420i
$305$		0			0
$306$	3.12439	+	17.3881i	0.178609	+	0.994010i
$307$	11.4213	+	11.4213i	0.651847	+	0.651847i	0.953437	−	0.301591i	$-0.0975177\pi$
$307$	11.4213	+	11.4213i	0.651847	+	0.651847i	−0.301591	+	0.953437i	$0.597518\pi$
$308$	1.78712	+	1.03180i	0.101831	+	0.0587920i
$309$	−8.47261	−	2.65625i	−0.481990	−	0.151109i
$310$		0			0
$311$	−8.25099			−0.467871			−0.233935	−	0.972252i	$-0.575160\pi$
$311$	−8.25099			−0.467871			−0.233935	+	0.972252i	$0.575160\pi$
$312$	18.1929	+	4.64240i	1.02997	+	0.262824i
$313$	12.5949			0.711907			0.355954	−	0.934504i	$-0.384156\pi$
$313$	12.5949			0.711907			0.355954	+	0.934504i	$0.384156\pi$
$314$	−7.20693	+	26.8966i	−0.406710	+	1.51786i
$315$		0			0
$316$	2.68871	+	1.55233i	0.151252	+	0.0873254i
$317$	−4.02879	−	4.02879i	−0.226279	−	0.226279i	0.584857	−	0.811136i	$-0.301151\pi$
$317$	−4.02879	−	4.02879i	−0.226279	−	0.226279i	−0.811136	+	0.584857i	$0.801151\pi$
$318$	−9.97453	+	15.7133i	−0.559344	+	0.881156i
$319$	−15.7827	+	4.22896i	−0.883660	+	0.236776i
$320$		0			0
$321$	2.59526	+	11.6169i	0.144853	+	0.648393i
$322$	1.14520	−	0.661179i	0.0638192	−	0.0368460i
$323$	13.1493	+	3.52335i	0.731647	+	0.196044i
$324$	−0.479669	+	2.82788i	−0.0266483	+	0.157104i
$325$		0			0
$326$			14.3616i			0.795418i
$327$	0.813431	+	1.55640i	0.0449828	+	0.0860689i
$328$	−1.26225	−	2.18628i	−0.0696961	−	0.120717i
$329$	4.93653	−	8.55031i	0.272160	−	0.471394i
$330$		0			0
$331$	4.18246	+	15.6091i	0.229889	+	0.857956i	0.980387	+	0.197083i	$0.0631470\pi$
$331$	4.18246	+	15.6091i	0.229889	+	0.857956i	−0.750498	+	0.660873i	$0.770186\pi$
$332$	−0.0998825	−	0.372767i	−0.00548177	−	0.0204582i
$333$	24.4168	−	20.6240i	1.33803	−	1.13019i
$334$	15.6579	−	27.1202i	0.856761	−	1.48395i
$335$		0			0
$336$	11.4082	−	5.96235i	0.622368	−	0.325273i
$337$		−	7.02217i		−	0.382522i	−0.981539	−	0.191261i	$-0.938742\pi$
$337$		−	7.02217i		−	0.382522i	0.981539	−	0.191261i	$-0.0612577\pi$
$338$	16.6573	+	2.58365i	0.906037	+	0.140532i
$339$	−7.55760	+	6.94793i	−0.410473	+	0.377360i
$340$		0			0
$341$	−16.0975	+	9.29389i	−0.871728	+	0.503292i
$342$	−9.57298	−	6.65673i	−0.517647	−	0.359955i
$343$	−14.1911	+	14.1911i	−0.766248	+	0.766248i
$344$	−13.8468	+	3.71024i	−0.746570	+	0.200043i
$345$		0			0
$346$	−2.68218	−	2.68218i	−0.144195	−	0.144195i
$347$	28.1095	+	16.2290i	1.50900	+	0.871221i	0.999945	+	0.0104862i	$0.00333792\pi$
$347$	28.1095	+	16.2290i	1.50900	+	0.871221i	0.509054	+	0.860735i	$0.329995\pi$
$348$	0.949649	−	3.02909i	0.0509066	−	0.162376i
$349$	2.92829	−	10.9285i	0.156748	−	0.584990i	−0.842202	−	0.539162i	$-0.818741\pi$
$349$	2.92829	−	10.9285i	0.156748	−	0.584990i	0.998949	−	0.0458273i	$-0.0145924\pi$
$350$		0			0
$351$	−1.34882	+	18.6864i	−0.0719946	+	0.997405i
$352$	−5.07060			−0.270264
$353$	−3.66208	+	13.6671i	−0.194913	+	0.727425i	0.797376	+	0.603482i	$0.206221\pi$
$353$	−3.66208	+	13.6671i	−0.194913	+	0.727425i	−0.992289	+	0.123943i	$0.960446\pi$
$354$	4.35221	−	13.8822i	0.231317	−	0.737831i
$355$		0			0
$356$	0.383672	+	0.383672i	0.0203346	+	0.0203346i
$357$	−15.1352	−	9.60757i	−0.801038	−	0.508486i
$358$	−8.59475	+	2.30296i	−0.454247	+	0.121715i
$359$	−18.3546	+	18.3546i	−0.968720	+	0.968720i	−0.999525	−	0.0308058i	$-0.990193\pi$
$359$	−18.3546	+	18.3546i	−0.968720	+	0.968720i	0.0308058	+	0.999525i	$0.490193\pi$
$360$		0			0
$361$	8.67351	−	5.00765i	0.456500	−	0.263561i
$362$	−27.5552	−	7.38338i	−1.44827	−	0.388062i
$363$	3.73276	−	3.43164i	0.195919	−	0.180114i
$364$	−2.19396	+	1.42977i	−0.114995	+	0.0749404i
$365$		0			0
$366$	−22.5436	+	11.7821i	−1.17837	+	0.615861i
$367$	−6.60945	−	11.4479i	−0.345010	−	0.597575i	0.640345	−	0.768087i	$-0.278791\pi$
$367$	−6.60945	−	11.4479i	−0.345010	−	0.597575i	−0.985356	+	0.170512i	$0.945458\pi$
$368$	−0.729645	+	1.26378i	−0.0380354	+	0.0658792i
$369$	1.92439	−	1.62546i	0.100180	−	0.0846181i
$370$		0			0
$371$	−4.88811	−	18.2427i	−0.253778	−	0.947112i
$372$	0.151649	−	3.60809i	0.00786263	−	0.187071i
$373$	7.54312	−	13.0651i	0.390568	−	0.676483i	−0.601957	−	0.798529i	$-0.705612\pi$
$373$	7.54312	−	13.0651i	0.390568	−	0.676483i	0.992525	+	0.122045i	$0.0389453\pi$
$374$	−8.36578	−	14.4900i	−0.432584	−	0.749257i
$375$		0			0
$376$			13.0250i			0.671714i
$377$	4.27859	−	20.2887i	0.220358	−	1.04492i
$378$	9.40680	+	12.1360i	0.483834	+	0.624209i
$379$	4.41475	+	1.18293i	0.226771	+	0.0607630i	0.370415	−	0.928866i	$-0.379215\pi$
$379$	4.41475	+	1.18293i	0.226771	+	0.0607630i	−0.143644	+	0.989629i	$0.545882\pi$
$380$		0			0
$381$	−4.63710	−	20.7567i	−0.237566	−	1.06340i
$382$	−15.2524	+	15.2524i	−0.780379	+	0.780379i
$383$	−14.6214	+	3.91778i	−0.747117	+	0.200189i	−0.612239	−	0.790673i	$-0.709731\pi$
$383$	−14.6214	+	3.91778i	−0.747117	+	0.200189i	−0.134878	+	0.990862i	$0.543064\pi$
$384$	−7.32213	+	11.5348i	−0.373656	+	0.588634i
$385$		0			0
$386$	−7.48921	−	4.32390i	−0.381191	−	0.220081i
$387$	−6.08734	−	12.9442i	−0.309437	−	0.657989i
$388$	0.837711	−	3.12638i	0.0425283	−	0.158718i
$389$	−20.3601			−1.03230			−0.516150	−	0.856498i	$-0.672635\pi$
$389$	−20.3601			−1.03230			−0.516150	+	0.856498i	$0.672635\pi$
$390$		0			0
$391$	2.03232			0.102779
$392$	1.40554	−	5.24554i	0.0709904	−	0.264940i
$393$	−1.44732	−	0.453750i	−0.0730077	−	0.0228886i
$394$	−12.9020	−	7.44899i	−0.649995	−	0.375275i
$395$		0			0
$396$	−0.480416	−	2.67365i	−0.0241418	−	0.134356i
$397$	30.2688	−	8.11051i	1.51915	−	0.407055i	0.599688	−	0.800234i	$-0.295291\pi$
$397$	30.2688	−	8.11051i	1.51915	−	0.407055i	0.919462	+	0.393179i	$0.128625\pi$
$398$	−0.267240	+	0.267240i	−0.0133955	+	0.0133955i
$399$	11.5472	−	2.57968i	0.578083	−	0.129146i
$400$		0			0
$401$	−13.7202	−	3.67631i	−0.685154	−	0.183586i	−0.100582	−	0.994929i	$-0.532071\pi$
$401$	−13.7202	−	3.67631i	−0.685154	−	0.183586i	−0.584571	+	0.811342i	$0.698737\pi$
$402$	14.0995	+	15.3367i	0.703217	+	0.764924i
$403$	−1.27219	−	23.5538i	−0.0633723	−	1.17330i
$404$			4.17975i			0.207950i
$405$		0			0
$406$	−8.49698	−	14.7172i	−0.421698	−	0.730402i
$407$	−15.1349	+	26.2144i	−0.750210	+	1.29940i
$408$	23.6294	+	0.993148i	1.16983	+	0.0491682i
$409$	−5.33224	−	19.9002i	−0.263662	−	0.984001i	−0.963064	−	0.269273i	$-0.913217\pi$
$409$	−5.33224	−	19.9002i	−0.263662	−	0.984001i	0.699402	−	0.714729i	$-0.253450\pi$
$410$		0			0
$411$	10.8967	+	0.457989i	0.537492	+	0.0225909i
$412$	−0.816888	+	1.41489i	−0.0402452	+	0.0697067i
$413$	7.38148	+	12.7851i	0.363219	+	0.629113i
$414$	−1.63767	−	0.590034i	−0.0804873	−	0.0289986i
$415$		0			0
$416$	2.91210	−	5.73799i	0.142777	−	0.281328i
$417$	−20.3405	−	22.1254i	−0.996080	−	1.08348i
$418$	10.6666	+	2.85810i	0.521718	+	0.139794i
$419$	11.6759	−	6.74109i	0.570405	−	0.329324i	−0.186906	−	0.982378i	$-0.559846\pi$
$419$	11.6759	−	6.74109i	0.570405	−	0.329324i	0.757311	+	0.653054i	$0.226513\pi$
$420$		0			0
$421$	11.4321	−	11.4321i	0.557166	−	0.557166i	−0.371333	−	0.928500i	$-0.621099\pi$
$421$	11.4321	−	11.4321i	0.557166	−	0.557166i	0.928500	+	0.371333i	$0.121099\pi$
$422$	−19.9173	+	5.33682i	−0.969558	+	0.259792i
$423$	−12.7918	+	2.29850i	−0.621959	+	0.111757i
$424$	17.6180	+	17.6180i	0.855605	+	0.855605i
$425$		0			0
$426$	−28.4288	−	8.91272i	−1.37738	−	0.431823i
$427$	6.68060	−	24.9323i	0.323297	−	1.20656i
$428$	2.19020			0.105867
$429$	−4.79689	−	17.0827i	−0.231596	−	0.824762i
$430$		0			0
$431$	−3.16022	+	11.7941i	−0.152222	+	0.568102i	0.847105	+	0.531426i	$0.178344\pi$
$431$	−3.16022	+	11.7941i	−0.152222	+	0.568102i	−0.999327	+	0.0366759i	$0.988323\pi$
$432$	−15.6865	−	6.40799i	−0.754716	−	0.308305i
$433$	14.6584	+	8.46304i	0.704439	+	0.406708i	0.808999	−	0.587811i	$-0.200010\pi$
$433$	14.6584	+	8.46304i	0.704439	+	0.406708i	−0.104560	+	0.994519i	$0.533343\pi$
$434$	−13.6700	−	13.6700i	−0.656183	−	0.656183i
$435$		0			0
$436$	0.312120	−	0.0836322i	0.0149478	−	0.00400526i
$437$	−0.948467	+	0.948467i	−0.0453713	+	0.0453713i
$438$	−1.08481	−	4.85582i	−0.0518340	−	0.232020i
$439$	−2.43013	+	1.40303i	−0.115984	+	0.0669631i	−0.556870	−	0.830600i	$-0.687998\pi$
$439$	−2.43013	+	1.40303i	−0.115984	+	0.0669631i	0.440886	+	0.897563i	$0.354664\pi$
$440$		0			0
$441$	5.39966	+	0.454701i	0.257127	+	0.0216524i
$442$	21.2017	−	1.14515i	1.00846	−	0.0544690i
$443$		−	27.4864i		−	1.30592i	−0.757393	−	0.652960i	$-0.773527\pi$
$443$		−	27.4864i		−	1.30592i	0.757393	−	0.652960i	$-0.226473\pi$
$444$	−2.72398	−	5.21198i	−0.129274	−	0.247350i
$445$		0			0
$446$	2.87613	−	4.98160i	0.136189	−	0.235886i
$447$	−1.61338	+	38.3861i	−0.0763102	+	1.81560i
$448$	−5.21194	−	19.4512i	−0.246241	−	0.918984i
$449$	−1.90550	−	7.11141i	−0.0899260	−	0.335608i	0.906275	−	0.422688i	$-0.138913\pi$
$449$	−1.90550	−	7.11141i	−0.0899260	−	0.335608i	−0.996201	+	0.0870794i	$0.972247\pi$
$450$		0			0
$451$	−1.19285	+	2.06607i	−0.0561689	+	0.0972874i
$452$	0.944472	+	1.63587i	0.0444242	+	0.0769450i
$453$	1.07533	−	0.562009i	0.0505235	−	0.0264055i
$454$		−	17.4304i		−	0.818051i
$455$		0			0
$456$	−11.4911	+	10.5641i	−0.538120	+	0.494710i
$457$	0.231621	+	0.0620628i	0.0108348	+	0.00290317i	0.264232	−	0.964459i	$-0.414881\pi$
$457$	0.231621	+	0.0620628i	0.0108348	+	0.00290317i	−0.253398	+	0.967362i	$0.581548\pi$
$458$	−13.3448	+	7.70462i	−0.623561	+	0.360013i
$459$	3.19447	+	23.3816i	0.149105	+	1.09136i
$460$		0			0
$461$	−16.4008	+	4.39457i	−0.763860	+	0.204676i	−0.619657	−	0.784872i	$-0.712728\pi$
$461$	−16.4008	+	4.39457i	−0.763860	+	0.204676i	−0.144203	+	0.989548i	$0.546062\pi$
$462$	−12.2775	−	7.79353i	−0.571199	−	0.362588i
$463$	−13.0393	−	13.0393i	−0.605988	−	0.605988i	0.335907	−	0.941895i	$-0.390957\pi$
$463$	−13.0393	−	13.0393i	−0.605988	−	0.605988i	−0.941895	+	0.335907i	$0.890957\pi$
$464$	16.2412	+	9.37685i	0.753978	+	0.435310i
$465$		0			0
$466$	−4.08367	+	15.2405i	−0.189173	+	0.706002i
$467$	15.8095			0.731575			0.365788	−	0.930698i	$-0.380800\pi$
$467$	15.8095			0.731575			0.365788	+	0.930698i	$0.380800\pi$
$468$	3.30146	+	0.991857i	0.152610	+	0.0458486i
$469$	−21.1400			−0.976156
$470$		0			0
$471$	−11.1272	+	35.4922i	−0.512713	+	1.63540i
$472$	−16.8667	−	9.73800i	−0.776354	−	0.448228i
$473$	9.57921	+	9.57921i	0.440453	+	0.440453i
$474$	−18.4713	−	11.7253i	−0.848417	−	0.538562i
$475$		0			0
$476$	−2.33244	+	2.33244i	−0.106907	+	0.106907i
$477$	−14.1935	+	20.4116i	−0.649877	+	0.934582i
$478$	−24.5394	+	14.1678i	−1.12241	+	0.648021i
$479$	−4.26159	−	1.14189i	−0.194717	−	0.0521742i	0.160143	−	0.987094i	$-0.448805\pi$
$479$	−4.26159	−	1.14189i	−0.194717	−	0.0521742i	−0.354859	+	0.934920i	$0.615471\pi$
$480$		0			0
$481$	−20.9726	−	32.1822i	−0.956269	−	1.46738i
$482$		−	32.2609i		−	1.46944i
$483$	1.56548	−	0.818177i	0.0712317	−	0.0372283i
$484$	−0.466483	−	0.807972i	−0.0212038	−	0.0367260i
$485$		0			0
$486$	4.21410	−	19.7686i	0.191156	−	0.896722i
$487$	−10.3589	−	38.6598i	−0.469405	−	1.75184i	−0.641855	−	0.766826i	$-0.721835\pi$
$487$	−10.3589	−	38.6598i	−0.469405	−	1.75184i	0.172450	−	0.985018i	$-0.444832\pi$
$488$	8.81337	+	32.8919i	0.398963	+	1.48895i
$489$	−0.805602	+	19.1672i	−0.0364306	+	0.866770i
$490$		0			0
$491$	7.03573	+	12.1862i	0.317518	+	0.549957i	0.979970	−	0.199147i	$-0.0638173\pi$
$491$	7.03573	+	12.1862i	0.317518	+	0.549957i	−0.662452	+	0.749105i	$0.730484\pi$
$492$	−0.214688	−	0.410778i	−0.00967888	−	0.0185193i
$493$		−	26.1179i		−	1.17629i
$494$	−9.36018	+	10.4290i	−0.421135	+	0.469225i
$495$		0			0
$496$	20.6073	+	5.52171i	0.925296	+	0.247932i
$497$	26.1821	−	15.1162i	1.17443	−	0.678056i
$498$	0.592942	+	2.65414i	0.0265704	+	0.118935i
$499$	12.8997	−	12.8997i	0.577470	−	0.577470i	−0.356735	−	0.934206i	$-0.616110\pi$
$499$	12.8997	−	12.8997i	0.577470	−	0.577470i	0.934206	+	0.356735i	$0.116110\pi$
$500$		0			0
$501$	22.4184	−	35.3166i	1.00158	−	1.57783i
$502$	2.84887	+	2.84887i	0.127151	+	0.127151i
$503$	20.0990	+	11.6042i	0.896172	+	0.517405i	0.875956	−	0.482391i	$-0.160231\pi$
$503$	20.0990	+	11.6042i	0.896172	+	0.517405i	0.0202156	+	0.999796i	$0.493565\pi$
$504$	18.6013	−	8.74774i	0.828566	−	0.389655i
$505$		0			0
$506$	1.64860			0.0732890
$507$	22.0860	+	4.38254i	0.980876	+	0.194635i
$508$	−3.91337			−0.173628
$509$	2.71529	−	10.1336i	0.120353	−	0.449165i	−0.879278	−	0.476308i	$-0.841975\pi$
$509$	2.71529	−	10.1336i	0.120353	−	0.449165i	0.999632	+	0.0271439i	$0.00864124\pi$
$510$		0			0
$511$	4.37246	+	2.52444i	0.193426	+	0.111675i
$512$	17.9808	+	17.9808i	0.794647	+	0.794647i
$513$	−12.4028	−	9.42113i	−0.547597	−	0.415953i
$514$	−16.5075	+	4.42316i	−0.728113	+	0.195097i
$515$		0			0
$516$	−2.56863	+	0.573840i	−0.113078	+	0.0252619i
$517$	10.6598	−	6.15442i	0.468816	−	0.270671i
$518$	−30.4096	−	8.14824i	−1.33612	−	0.358013i
$519$	−3.42921	−	3.73011i	−0.150525	−	0.163734i
$520$		0			0
$521$			28.1221i			1.23205i	0.787726	+	0.616026i	$0.211259\pi$
$521$			28.1221i			1.23205i	−0.787726	+	0.616026i	$0.788741\pi$
$522$	−7.58269	+	21.0462i	−0.331885	+	0.921166i
$523$	17.3704	+	30.0865i	0.759556	+	1.31559i	0.943077	+	0.332574i	$0.107917\pi$
$523$	17.3704	+	30.0865i	0.759556	+	1.31559i	−0.183521	+	0.983016i	$0.558749\pi$
$524$	−0.139544	+	0.241697i	−0.00609600	+	0.0105586i
$525$		0			0
$526$	1.06405	+	3.97109i	0.0463948	+	0.173148i
$527$	−7.68998	−	28.6994i	−0.334981	−	1.25017i
$528$	16.0339	+	0.673909i	0.697786	+	0.0293281i
$529$	11.3999	−	19.7452i	0.495647	−	0.858485i
$530$		0			0
$531$	6.58721	−	18.2832i	0.285861	−	0.793423i
$532$		−	2.17706i		−	0.0943874i
$533$	−1.65294	−	2.53641i	−0.0715967	−	0.109864i
$534$	−2.58782	−	2.81490i	−0.111986	−	0.121813i
$535$		0			0
$536$	24.1526	−	13.9445i	1.04323	−	0.602310i
$537$	−11.5998	+	2.59143i	−0.500569	+	0.111829i
$538$	9.50908	−	9.50908i	0.409965	−	0.409965i
$539$	−4.95711	+	1.32825i	−0.213518	+	0.0572120i
$540$		0			0
$541$	−17.6269	−	17.6269i	−0.757839	−	0.757839i	0.218090	−	0.975929i	$-0.430017\pi$
$541$	−17.6269	−	17.6269i	−0.757839	−	0.757839i	−0.975929	+	0.218090i	$0.930017\pi$
$542$	24.4083	+	14.0922i	1.04843	+	0.605310i
$543$	−36.3612	−	11.3996i	−1.56041	−	0.489204i
$544$	2.09777	−	7.82898i	0.0899411	−	0.335665i
$545$		0			0
$546$	15.8704	−	9.41749i	0.679189	−	0.403031i
$547$	7.60825			0.325305			0.162653	−	0.986683i	$-0.447995\pi$
$547$	7.60825			0.325305			0.162653	+	0.986683i	$0.447995\pi$
$548$	0.519386	−	1.93837i	0.0221871	−	0.0828032i
$549$	−30.7478	+	14.4600i	−1.31228	+	0.617136i
$550$		0			0
$551$	12.1890	+	12.1890i	0.519269	+	0.519269i
$552$	−1.24887	+	1.96740i	−0.0531555	+	0.0837380i
$553$	21.4447	−	5.74609i	0.911922	−	0.244349i
$554$	2.18121	−	2.18121i	0.0926709	−	0.0926709i
$555$		0			0
$556$	−4.78913	+	2.76501i	−0.203104	+	0.117262i
$557$	−3.10705	−	0.832532i	−0.131650	−	0.0352755i	0.192392	−	0.981318i	$-0.438375\pi$
$557$	−3.10705	−	0.832532i	−0.131650	−	0.0352755i	−0.324042	+	0.946043i	$0.605042\pi$
$558$	−2.13546	+	25.3590i	−0.0904012	+	1.07353i
$559$	−16.3415	+	5.33858i	−0.691170	+	0.225798i
$560$		0			0
$561$	−10.3522	−	19.8077i	−0.437072	−	0.836282i
$562$	6.67730	+	11.5654i	0.281665	+	0.487858i
$563$	9.27874	−	16.0712i	0.391052	−	0.677322i	−0.601536	−	0.798845i	$-0.705445\pi$
$563$	9.27874	−	16.0712i	0.391052	−	0.677322i	0.992589	+	0.121523i	$0.0387779\pi$
$564$	−0.100422	+	2.38928i	−0.00422853	+	0.100607i
$565$		0			0
$566$	4.67973	+	17.4650i	0.196704	+	0.734109i
$567$	11.8737	+	16.7245i	0.498647	+	0.702364i
$568$	−19.9421	+	34.5407i	−0.836751	+	1.44930i
$569$	10.2020	+	17.6703i	0.427688	+	0.740778i	0.996667	−	0.0815741i	$-0.0259947\pi$
$569$	10.2020	+	17.6703i	0.427688	+	0.740778i	−0.568979	+	0.822352i	$0.692661\pi$
$570$		0			0
$571$		−	0.850329i		−	0.0355852i	−0.999842	−	0.0177926i	$-0.994336\pi$
$571$		−	0.850329i		−	0.0355852i	0.999842	−	0.0177926i	$-0.00566385\pi$
$572$	−3.26004	+	0.176082i	−0.136309	+	0.00736234i
$573$	−21.2115	+	19.5004i	−0.886124	+	0.814640i
$574$	−2.39671	−	0.642196i	−0.100037	−	0.0268048i
$575$		0			0
$576$	−15.1338	+	21.7638i	−0.630577	+	0.906826i
$577$	−8.23663	+	8.23663i	−0.342896	+	0.342896i	−0.857455	−	0.514559i	$-0.827956\pi$
$577$	−8.23663	+	8.23663i	−0.342896	+	0.342896i	0.514559	+	0.857455i	$0.327956\pi$
$578$	4.54146	−	1.21688i	0.188900	−	0.0506155i
$579$	−9.75264	−	6.19082i	−0.405306	−	0.257282i
$580$		0			0
$581$	−2.38994	−	1.37983i	−0.0991513	−	0.0572450i
$582$	−6.82334	+	21.7643i	−0.282836	+	0.902160i
$583$	6.09405	−	22.7433i	0.252390	−	0.941932i
$584$	−6.66073			−0.275623
$585$		0			0
$586$	35.7043			1.47493
$587$	0.0218800	−	0.0816572i	0.000903083	−	0.00337035i	−0.965473	−	0.260504i	$-0.916111\pi$
$587$	0.0218800	−	0.0816572i	0.000903083	−	0.00337035i	0.966376	+	0.257133i	$0.0827780\pi$
$588$	0.298271	−	0.951393i	0.0123005	−	0.0392348i
$589$	16.9826	+	9.80491i	0.699756	+	0.404004i
$590$		0			0
$591$	−16.8013	−	10.6652i	−0.691114	−	0.438709i
$592$	33.5586	−	8.99200i	1.37925	−	0.369569i
$593$	−29.3266	+	29.3266i	−1.20430	+	1.20430i	−0.231451	+	0.972847i	$0.574347\pi$
$593$	−29.3266	+	29.3266i	−1.20430	+	1.20430i	−0.972847	+	0.231451i	$0.925653\pi$
$594$	2.59131	+	18.9668i	0.106323	+	0.778218i
$595$		0			0
$596$	6.82839	+	1.82966i	0.279702	+	0.0749459i
$597$	−0.371652	+	0.341671i	−0.0152107	+	0.0139837i
$598$	−0.946805	+	1.86558i	−0.0387178	+	0.0762893i
$599$		−	35.3223i		−	1.44323i	−0.692294	−	0.721615i	$-0.743400\pi$
$599$		−	35.3223i		−	1.44323i	0.692294	−	0.721615i	$-0.256600\pi$
$600$		0			0
$601$	−5.49445	−	9.51667i	−0.224123	−	0.388193i	0.731933	−	0.681377i	$-0.238619\pi$
$601$	−5.49445	−	9.51667i	−0.224123	−	0.388193i	−0.956056	+	0.293184i	$0.905285\pi$
$602$	−7.04486	+	12.2021i	−0.287127	+	0.497319i
$603$	17.9570	+	21.2594i	0.731265	+	0.865749i
$604$	−0.0577824	−	0.215647i	−0.00235113	−	0.00877455i
$605$		0			0
$606$	1.23690	−	29.4288i	0.0502456	−	1.19546i
$607$	7.49947	−	12.9895i	0.304394	−	0.527226i	−0.672732	−	0.739886i	$-0.734879\pi$
$607$	7.49947	−	12.9895i	0.304394	−	0.527226i	0.977126	+	0.212660i	$0.0682127\pi$
$608$	2.67470	+	4.63272i	0.108474	+	0.187882i
$609$	−10.5146	−	20.1184i	−0.426073	−	0.815237i
$610$		0			0
$611$	0.842445	+	15.5973i	0.0340817	+	0.631001i
$612$	4.32686	+	0.364361i	0.174903	+	0.0147284i
$613$	6.71663	+	1.79972i	0.271282	+	0.0726898i	0.391895	−	0.920010i	$-0.371819\pi$
$613$	6.71663	+	1.79972i	0.271282	+	0.0726898i	−0.120613	+	0.992700i	$0.538486\pi$
$614$	−18.1377	+	10.4718i	−0.731980	+	0.422609i
$615$		0			0
$616$	−13.7657	+	13.7657i	−0.554635	+	0.554635i
$617$	3.80094	−	1.01846i	0.153020	−	0.0410017i	−0.181496	−	0.983392i	$-0.558094\pi$
$617$	3.80094	−	1.01846i	0.153020	−	0.0410017i	0.334516	+	0.942390i	$0.391427\pi$
$618$	6.17026	−	9.72024i	0.248204	−	0.391005i
$619$	−21.4563	−	21.4563i	−0.862401	−	0.862401i	0.129216	−	0.991617i	$-0.458754\pi$
$619$	−21.4563	−	21.4563i	−0.862401	−	0.862401i	−0.991617	+	0.129216i	$0.958754\pi$
$620$		0			0
$621$	−2.15256	−	0.879330i	−0.0863792	−	0.0352863i
$622$	2.76901	−	10.3341i	0.111027	−	0.414360i
$623$	3.88005			0.155451
$624$	−9.97103	+	17.7572i	−0.399161	+	0.710858i
$625$		0			0
$626$	−4.22683	+	15.7747i	−0.168938	+	0.630486i
$627$	14.0754	+	4.41277i	0.562116	+	0.176229i
$628$	5.92706	+	3.42199i	0.236516	+	0.136552i
$629$	−34.2134	−	34.2134i	−1.36418	−	1.36418i
$630$		0			0
$631$	−21.8951	+	5.86676i	−0.871628	+	0.233552i	−0.666792	−	0.745244i	$-0.732333\pi$
$631$	−21.8951	+	5.86676i	−0.871628	+	0.233552i	−0.204837	+	0.978796i	$0.565666\pi$
$632$	−20.7104	+	20.7104i	−0.823815	+	0.823815i
$633$	−26.8812	+	6.00533i	−1.06843	+	0.238690i
$634$	6.39798	−	3.69388i	0.254096	−	0.146703i
$635$		0			0
$636$	3.09597	+	3.36763i	0.122763	+	0.133535i
$637$	1.34384	−	6.37239i	0.0532450	−	0.252483i
$638$		−	21.1865i		−	0.838783i
$639$	−37.4414	−	13.4897i	−1.48116	−	0.533644i
$640$		0			0
$641$	0.623490	−	1.07992i	0.0246264	−	0.0426542i	−0.853450	−	0.521175i	$-0.825494\pi$
$641$	0.623490	−	1.07992i	0.0246264	−	0.0426542i	0.878076	+	0.478521i	$0.158827\pi$
$642$	−15.4208	−	0.648140i	−0.608610	−	0.0255800i
$643$	0.781568	+	2.91685i	0.0308220	+	0.115029i	0.979623	−	0.200845i	$-0.0643688\pi$
$643$	0.781568	+	2.91685i	0.0308220	+	0.115029i	−0.948801	+	0.315875i	$0.897702\pi$
$644$	−0.0841202	−	0.313941i	−0.00331480	−	0.0123710i
$645$		0			0
$646$	−8.82576	+	15.2867i	−0.347245	+	0.601446i
$647$	−2.52686	−	4.37664i	−0.0993410	−	0.172064i	0.812071	−	0.583559i	$-0.198340\pi$
$647$	−2.52686	−	4.37664i	−0.0993410	−	0.172064i	−0.911412	+	0.411495i	$0.865007\pi$
$648$	−24.5976	−	11.2757i	−0.966285	−	0.442950i
$649$			18.4051i			0.722464i
$650$		0			0
$651$	−17.4774	−	19.0110i	−0.684992	−	0.745099i
$652$	3.40959	+	0.913598i	0.133530	+	0.0357793i
$653$	7.72146	−	4.45799i	0.302164	−	0.174454i	−0.341251	−	0.939972i	$-0.610850\pi$
$653$	7.72146	−	4.45799i	0.302164	−	0.174454i	0.643415	+	0.765518i	$0.277517\pi$
$654$	−2.22232	+	0.496474i	−0.0868997	+	0.0194137i
$655$		0			0
$656$	2.64489	−	0.708697i	0.103266	−	0.0276700i
$657$	−1.17541	−	6.54148i	−0.0458571	−	0.255208i
$658$	9.05231	+	9.05231i	0.352896	+	0.352896i
$659$	26.8813	+	15.5199i	1.04715	+	0.604570i	0.921849	−	0.387549i	$-0.126678\pi$
$659$	26.8813	+	15.5199i	1.04715	+	0.604570i	0.125297	+	0.992119i	$0.460012\pi$
$660$		0			0
$661$	−3.97807	+	14.8464i	−0.154729	+	0.577456i	0.844399	+	0.535714i	$0.179958\pi$
$661$	−3.97807	+	14.8464i	−0.154729	+	0.577456i	−0.999128	+	0.0417423i	$0.986709\pi$
$662$	−20.9536			−0.814384
$663$	28.3602	−	0.339038i	1.10142	−	0.0131671i
$664$	3.64068			0.141286
$665$		0			0
$666$	17.6366	+	37.5027i	0.683406	+	1.45320i
$667$	2.22868	+	1.28673i	0.0862948	+	0.0498223i
$668$	−5.44256	−	5.44256i	−0.210579	−	0.210579i
$669$	4.11795	−	6.48717i	0.159209	−	0.250808i
$670$		0			0
$671$	22.7546	−	22.7546i	0.878432	−	0.878432i
$672$	−1.53592	−	6.87510i	−0.0592493	−	0.265213i
$673$	9.13640	−	5.27490i	0.352182	−	0.203333i	−0.313464	−	0.949600i	$-0.601489\pi$
$673$	9.13640	−	5.27490i	0.352182	−	0.203333i	0.665646	+	0.746268i	$0.268156\pi$
$674$	8.79505	+	2.35663i	0.338773	+	0.0907739i
$675$		0			0
$676$	1.67302	−	3.79025i	0.0643468	−	0.145779i
$677$		−	39.8150i		−	1.53021i	−0.643904	−	0.765107i	$-0.722686\pi$
$677$		−	39.8150i		−	1.53021i	0.643904	−	0.765107i	$-0.277314\pi$
$678$	−6.16575	−	11.7974i	−0.236794	−	0.453075i
$679$	−11.5726	−	20.0443i	−0.444115	−	0.769229i
$680$		0			0
$681$	0.977744	−	23.2628i	0.0374672	−	0.891434i
$682$	−6.23802	−	23.2806i	−0.238866	−	0.891460i
$683$	−3.05980	−	11.4193i	−0.117080	−	0.436949i	0.882354	−	0.470586i	$-0.155958\pi$
$683$	−3.05980	−	11.4193i	−0.117080	−	0.436949i	−0.999434	+	0.0336375i	$0.989291\pi$
$684$	−2.18935	+	1.84926i	−0.0837118	+	0.0707082i
$685$		0			0
$686$	−13.0114	−	22.5364i	−0.496778	−	0.860445i
$687$	−18.2423	+	9.53410i	−0.695986	+	0.363748i
$688$		−	15.5487i		−	0.592790i
$689$	22.2369	+	19.9579i	0.847158	+	0.760334i
$690$		0			0
$691$	−13.1578	−	3.52563i	−0.500547	−	0.134121i	−0.000293354	−	1.00000i	$-0.500093\pi$
$691$	−13.1578	−	3.52563i	−0.500547	−	0.134121i	−0.500254	+	0.865879i	$0.666760\pi$
$692$	−0.807399	+	0.466152i	−0.0306927	+	0.0177204i
$693$	−15.9484	−	11.0900i	−0.605831	−	0.421275i
$694$	−29.7599	+	29.7599i	−1.12967	+	1.12967i
$695$		0			0
$696$	25.2835	+	16.0496i	0.958370	+	0.608358i
$697$	−2.69650	−	2.69650i	−0.102137	−	0.102137i
$698$	12.7049	+	7.33517i	0.480887	+	0.277640i
$699$	−6.30501	+	20.1110i	−0.238477	+	0.760669i
$700$		0			0
$701$	−30.0152			−1.13366			−0.566829	−	0.823836i	$-0.691830\pi$
$701$	−30.0152			−1.13366			−0.566829	+	0.823836i	$0.691830\pi$
$702$	−22.9514	−	7.96046i	−0.866246	−	0.300448i
$703$	31.9342			1.20442
$704$	6.49778	−	24.2500i	0.244894	−	0.913958i
$705$		0			0
$706$	−15.8886	−	9.17328i	−0.597975	−	0.345241i
$707$	21.1348	+	21.1348i	0.794855	+	0.794855i
$708$	−3.01891	−	1.91636i	−0.113458	−	0.0720211i
$709$	35.0441	−	9.39004i	1.31611	−	0.352650i	0.468590	−	0.883416i	$-0.344762\pi$
$709$	35.0441	−	9.39004i	1.31611	−	0.352650i	0.847519	+	0.530765i	$0.178095\pi$
$710$		0			0
$711$	−23.9943	−	16.6849i	−0.899857	−	0.625731i
$712$	−4.43297	+	2.55938i	−0.166133	+	0.0959167i
$713$	2.82782	+	0.757711i	0.105903	+	0.0283765i
$714$	17.1125	−	15.7320i	0.640419	−	0.588757i
$715$		0			0
$716$			2.18698i			0.0817312i
$717$	−33.5453	+	17.5320i	−1.25277	+	0.654745i
$718$	−16.8288	−	29.1483i	−0.628045	−	1.08781i
$719$	−23.2174	+	40.2137i	−0.865863	+	1.49972i	0.000324371		1.00000i	$0.499897\pi$
$719$	−23.2174	+	40.2137i	−0.865863	+	1.49972i	−0.866188	+	0.499719i	$0.833437\pi$
$720$		0			0
$721$	3.02379	+	11.2849i	0.112612	+	0.420273i
$722$	3.36111	+	12.5438i	0.125088	+	0.466834i
$723$	1.80964	−	43.0557i	0.0673014	−	1.60126i
$724$	−3.50578	+	6.07218i	−0.130291	+	0.225671i
$725$		0			0
$726$	3.04531	+	5.82682i	0.113022	+	0.216254i
$727$			51.6317i			1.91491i	0.288575	+	0.957457i	$0.406819\pi$
$727$			51.6317i			1.91491i	−0.288575	+	0.957457i	$0.593181\pi$
$728$	−7.67174	−	23.4833i	−0.284334	−	0.870348i
$729$	6.73308	−	26.1470i	0.249373	−	0.968407i
$730$		0			0
$731$	−18.7533	+	10.8272i	−0.693615	+	0.400459i
$732$	1.36311	+	6.10157i	0.0503820	+	0.225521i
$733$	6.10483	−	6.10483i	0.225487	−	0.225487i	−0.585317	−	0.810804i	$-0.699030\pi$
$733$	6.10483	−	6.10483i	0.225487	−	0.225487i	0.810804	+	0.585317i	$0.199030\pi$
$734$	16.5562	−	4.43623i	0.611102	−	0.163744i
$735$		0			0
$736$	0.564708	+	0.564708i	0.0208154	+	0.0208154i
$737$	−22.8245	−	13.1777i	−0.840752	−	0.485409i
$738$	1.39002	+	2.95574i	0.0511672	+	0.108802i
$739$	−4.11405	+	15.3538i	−0.151338	+	0.564800i	0.848054	+	0.529911i	$0.177775\pi$
$739$	−4.11405	+	15.3538i	−0.151338	+	0.564800i	−0.999391	+	0.0348893i	$0.988892\pi$
$740$		0			0
$741$	−13.0772	+	13.3937i	−0.480403	+	0.492028i
$742$	24.4888			0.899012
$743$	2.08870	−	7.79514i	0.0766270	−	0.285976i	−0.916970	−	0.398955i	$-0.869373\pi$
$743$	2.08870	−	7.79514i	0.0766270	−	0.285976i	0.993597	+	0.112980i	$0.0360395\pi$
$744$	32.5081	+	10.1916i	1.19180	+	0.373642i
$745$		0			0
$746$	13.8321	+	13.8321i	0.506430	+	0.506430i
$747$	0.642465	+	3.57550i	0.0235066	+	0.130821i
$748$	−3.97224	+	1.06436i	−0.145239	+	0.0389168i
$749$	11.0747	−	11.0747i	0.404660	−	0.404660i
$750$		0			0
$751$	26.3089	−	15.1894i	0.960025	−	0.554271i	0.0638441	−	0.997960i	$-0.479664\pi$
$751$	26.3089	−	15.1894i	0.960025	−	0.554271i	0.896181	+	0.443689i	$0.146331\pi$
$752$	−13.6462	−	3.65648i	−0.497625	−	0.133338i
$753$	3.64233	+	3.96194i	0.132734	+	0.144381i
$754$	23.9751	+	12.1676i	0.873121	+	0.443119i
$755$		0			0
$756$	3.47961	−	1.46125i	0.126552	−	0.0531451i
$757$	14.4995	+	25.1140i	0.526995	+	0.912782i	0.999505	+	0.0314569i	$0.0100147\pi$
$757$	14.4995	+	25.1140i	0.526995	+	0.912782i	−0.472510	+	0.881325i	$0.656652\pi$
$758$	−2.96316	+	5.13235i	−0.107627	+	0.186415i
$759$	2.20023	+	0.0924764i	0.0798634	+	0.00335668i
$760$		0			0
$761$	−1.91474	−	7.14590i	−0.0694092	−	0.259039i	0.922498	−	0.386001i	$-0.126144\pi$
$761$	−1.91474	−	7.14590i	−0.0694092	−	0.259039i	−0.991908	+	0.126962i	$0.959477\pi$
$762$	27.5533	+	1.15807i	0.998150	+	0.0419525i
$763$	1.15534	−	2.00111i	0.0418261	−	0.0724449i
$764$	2.65080	+	4.59132i	0.0959026	+	0.166108i
$765$		0			0
$766$		−	19.6276i		−	0.709174i
$767$	−20.8276	−	10.5702i	−0.752040	−	0.381669i
$768$	8.72634	+	9.49206i	0.314885	+	0.342515i
$769$	39.8453	+	10.6765i	1.43686	+	0.385005i	0.891433	−	0.453153i	$-0.149701\pi$
$769$	39.8453	+	10.6765i	1.43686	+	0.385005i	0.545427	+	0.838158i	$0.316368\pi$
$770$		0			0
$771$	−22.2791	+	4.97723i	−0.802364	+	0.179250i
$772$	−1.50295	+	1.50295i	−0.0540925	+	0.0540925i
$773$	20.0566	−	5.37414i	0.721385	−	0.193294i	0.120595	−	0.992702i	$-0.461520\pi$
$773$	20.0566	−	5.37414i	0.721385	−	0.193294i	0.600789	+	0.799407i	$0.294853\pi$
$774$	18.2551	−	3.28017i	0.656164	−	0.117903i
$775$		0			0
$776$	26.4434	+	15.2671i	0.949263	+	0.548057i
$777$	−40.1279	−	12.5805i	−1.43958	−	0.451324i
$778$	6.83282	−	25.5004i	0.244968	−	0.914235i
$779$	2.51687			0.0901761
$780$		0			0
$781$	37.6911			1.34869
$782$	−0.682044	+	2.54542i	−0.0243898	+	0.0910241i
$783$	−11.3005	+	27.6631i	−0.403847	+	0.988599i
$784$	5.10113	+	2.94514i	0.182183	+	0.105183i
$785$		0			0
$786$	1.05402	−	1.66045i	0.0375958	−	0.0592261i
$787$	−14.5265	+	3.89237i	−0.517815	+	0.138748i	−0.508256	−	0.861206i	$-0.669710\pi$
$787$	−14.5265	+	3.89237i	−0.517815	+	0.138748i	−0.00955922	+	0.999954i	$0.503043\pi$
$788$	−2.58921	+	2.58921i	−0.0922368	+	0.0922368i
$789$	1.19734	+	5.35954i	0.0426263	+	0.190805i
$790$		0			0
$791$	13.0474	+	3.49605i	0.463913	+	0.124305i
$792$	25.5364	+	2.15040i	0.907396	+	0.0764112i
$793$	12.6813	+	38.8178i	0.450328	+	1.37846i
$794$			40.6326i			1.44200i
$795$		0			0
$796$	0.0464453	+	0.0804456i	0.00164621	+	0.00285132i
$797$	−14.4534	+	25.0339i	−0.511964	+	0.886748i	0.487940	+	0.872877i	$0.337749\pi$
$797$	−14.4534	+	25.0339i	−0.511964	+	0.886748i	−0.999904	+	0.0138705i	$0.995585\pi$
$798$	−0.644250	+	15.3282i	−0.0228062	+	0.542614i
$799$	5.09231	+	19.0048i	0.180153	+	0.672340i
$800$		0			0
$801$	−3.29583	−	3.90195i	−0.116453	−	0.137869i
$802$	9.20894	−	15.9503i	0.325179	−	0.563226i
$803$	3.14725	+	5.45119i	0.111064	+	0.192368i
$804$	4.53800	−	2.37173i	0.160043	−	0.0836444i
$805$		0			0
$806$	29.9273	+	6.31122i	1.05414	+	0.222303i
$807$	13.2243	−	12.1575i	0.465518	−	0.427964i
$808$	−38.0875	−	10.2055i	−1.33992	−	0.359029i
$809$	6.32927	−	3.65421i	0.222525	−	0.128475i	−0.384594	−	0.923086i	$-0.625658\pi$
$809$	6.32927	−	3.65421i	0.222525	−	0.128475i	0.607119	+	0.794611i	$0.292325\pi$
$810$		0			0
$811$	−21.0431	+	21.0431i	−0.738922	+	0.738922i	−0.972369	−	0.233447i	$-0.924999\pi$
$811$	−21.0431	+	21.0431i	−0.738922	+	0.738922i	0.233447	+	0.972369i	$0.424999\pi$
$812$	−4.03453	+	1.08105i	−0.141584	+	0.0379374i
$813$	31.7851	+	20.1767i	1.11475	+	0.707627i
$814$	−27.7535	−	27.7535i	−0.972760	−	0.972760i
$815$		0			0
$816$	−7.67392	+	24.4774i	−0.268641	+	0.856881i
$817$	3.69902	−	13.8049i	0.129412	−	0.482974i
$818$	26.7139			0.934028
$819$	21.7090	−	11.6784i	0.758575	−	0.408078i
$820$		0			0
$821$	13.1364	−	49.0257i	0.458464	−	1.71101i	−0.219236	−	0.975672i	$-0.570357\pi$
$821$	13.1364	−	49.0257i	0.458464	−	1.71101i	0.677700	−	0.735339i	$-0.262977\pi$
$822$	−4.23051	+	13.4940i	−0.147556	+	0.470658i
$823$	−35.7712	−	20.6525i	−1.24690	−	0.719901i	−0.276414	−	0.961039i	$-0.589146\pi$
$823$	−35.7712	−	20.6525i	−1.24690	−	0.719901i	−0.970491	+	0.241138i	$0.922479\pi$
$824$	−10.8985	−	10.8985i	−0.379667	−	0.379667i
$825$		0			0
$826$	−18.4901	+	4.95442i	−0.643354	+	0.172386i
$827$	1.56771	−	1.56771i	0.0545146	−	0.0545146i	−0.679324	−	0.733839i	$-0.737727\pi$
$827$	1.56771	−	1.56771i	0.0545146	−	0.0545146i	0.733839	+	0.679324i	$0.237727\pi$
$828$	−0.244259	+	0.351266i	−0.00848858	+	0.0122073i
$829$	40.6816	−	23.4875i	1.41293	−	0.815756i	0.417267	−	0.908784i	$-0.362988\pi$
$829$	40.6816	−	23.4875i	1.41293	−	0.815756i	0.995663	+	0.0930281i	$0.0296546\pi$
$830$		0			0
$831$	3.03342	−	2.78872i	0.105228	−	0.0967395i
$832$	23.7101	+	21.2801i	0.821998	+	0.737753i
$833$		−	8.20327i		−	0.284226i
$834$	34.5376	−	18.0506i	1.19594	−	0.625043i
$835$		0			0
$836$	1.35708	−	2.35053i	0.0469356	−	0.0812948i
$837$	−4.27249	+	33.7245i	−0.147679	+	1.16569i
$838$	4.52459	+	16.8860i	0.156299	+	0.583317i
$839$	2.91462	+	10.8775i	0.100624	+	0.375534i	0.997812	−	0.0661149i	$-0.0210604\pi$
$839$	2.91462	+	10.8775i	0.100624	+	0.375534i	−0.897188	+	0.441649i	$0.854394\pi$
$840$		0			0
$841$	2.03608	−	3.52660i	0.0702097	−	0.121607i
$842$	10.4818	+	18.1549i	0.361225	+	0.625660i
$843$	8.26284	+	15.8099i	0.284587	+	0.544521i
$844$			5.06805i			0.174450i
$845$		0			0
$846$	1.41410	−	16.7927i	0.0486179	−	0.577346i
$847$	−6.44424	−	1.72673i	−0.221427	−	0.0593311i
$848$	−23.4040	+	13.5123i	−0.803698	+	0.464015i
$849$	5.26594	+	23.5715i	0.180727	+	0.808971i
$850$		0			0
$851$	4.60504	−	1.23392i	0.157859	−	0.0422981i
$852$	−3.92443	+	6.18231i	−0.134449	+	0.211802i
$853$	21.6293	+	21.6293i	0.740573	+	0.740573i	0.972688	−	0.232115i	$-0.0745646\pi$
$853$	21.6293	+	21.6293i	0.740573	+	0.740573i	−0.232115	+	0.972688i	$0.574565\pi$
$854$	28.9850	+	16.7345i	0.991845	+	0.572642i
$855$		0			0
$856$	−5.34773	+	19.9580i	−0.182782	+	0.682151i
$857$	27.4580			0.937948			0.468974	−	0.883212i	$-0.344624\pi$
$857$	27.4580			0.937948			0.468974	+	0.883212i	$0.344624\pi$
$858$	23.0054	−	0.275023i	0.785392	−	0.00938914i
$859$	−27.6237			−0.942508			−0.471254	−	0.881998i	$-0.656198\pi$
$859$	−27.6237			−0.942508			−0.471254	+	0.881998i	$0.656198\pi$
$860$		0			0
$861$	−3.16265	−	0.991523i	−0.107783	−	0.0337910i
$862$	−13.7112	−	7.91615i	−0.467004	−	0.269625i
$863$	−14.7595	−	14.7595i	−0.502418	−	0.502418i	0.409771	−	0.912188i	$-0.365609\pi$
$863$	−14.7595	−	14.7595i	−0.502418	−	0.502418i	−0.912188	+	0.409771i	$0.865609\pi$
$864$	−5.60925	+	7.38450i	−0.190831	+	0.251226i
$865$		0			0
$866$	−15.5190	+	15.5190i	−0.527358	+	0.527358i
$867$	6.12933	−	1.36931i	0.208163	−	0.0465042i
$868$	−4.11501	+	2.37580i	−0.139672	+	0.0806399i
$869$	26.7353	+	7.16371i	0.906934	+	0.243012i
$870$		0			0
$871$	28.0205	−	18.2606i	0.949440	−	0.618735i
$872$			3.04836i			0.103231i
$873$	−10.3273	+	28.6641i	−0.349528	+	0.970134i
$874$	−0.869622	−	1.50623i	−0.0294154	−	0.0509490i
$875$		0			0
$876$	−1.22183	−	0.0513538i	−0.0412818	−	0.00173508i
$877$	−3.75997	−	14.0324i	−0.126965	−	0.473841i	0.872937	−	0.487833i	$-0.162213\pi$
$877$	−3.75997	−	14.0324i	−0.126965	−	0.473841i	−0.999902	+	0.0139924i	$0.995546\pi$
$878$	−0.941710	−	3.51451i	−0.0317812	−	0.118609i
$879$	47.6514	+	2.00280i	1.60724	+	0.0675527i
$880$		0			0
$881$	19.4302	+	33.6541i	0.654619	+	1.13383i	0.981989	+	0.188938i	$0.0605045\pi$
$881$	19.4302	+	33.6541i	0.654619	+	1.13383i	−0.327370	+	0.944896i	$0.606162\pi$
$882$	−2.38161	+	6.61031i	−0.0801931	+	0.222581i
$883$			8.78225i			0.295546i	0.989021	+	0.147773i	$0.0472106\pi$
$883$			8.78225i			0.295546i	−0.989021	+	0.147773i	$0.952789\pi$
$884$	1.07685	−	5.10633i	0.0362183	−	0.171744i
$885$		0			0
$886$	34.4259	+	9.22439i	1.15656	+	0.309899i
$887$	−29.4578	+	17.0075i	−0.989097	+	0.571055i	−0.905004	−	0.425403i	$-0.860132\pi$
$887$	−29.4578	+	17.0075i	−0.989097	+	0.571055i	−0.0840926	+	0.996458i	$0.526799\pi$
$888$	54.1447	−	12.0961i	1.81698	−	0.405918i
$889$	−19.7878	+	19.7878i	−0.663662	+	0.663662i
$890$		0			0
$891$	2.39447	+	25.4587i	0.0802177	+	0.852898i
$892$	−0.999721	−	0.999721i	−0.0334731	−	0.0334731i
$893$	−11.2459	−	6.49281i	−0.376329	−	0.217274i
$894$	−47.5359	−	14.9030i	−1.58984	−	0.498431i
$895$		0			0
$896$	17.9768			0.600562
$897$	−1.36826	+	2.43671i	−0.0456850	+	0.0813595i
$898$	9.54630			0.318564
$899$	9.73754	−	36.3410i	0.324765	−	1.21204i
$900$		0			0
$901$	32.5943	+	18.8184i	1.08588	+	0.626930i
$902$	−2.18737	−	2.18737i	−0.0728314	−	0.0728314i
$903$	−10.0866	+	15.8898i	−0.335661	+	0.528780i
$904$	−17.2128	+	4.61216i	−0.572490	+	0.153398i
$905$		0			0
$906$	0.343019	+	1.53543i	0.0113961	+	0.0510112i
$907$	33.7449	−	19.4826i	1.12048	−	0.646911i	0.178958	−	0.983857i	$-0.442727\pi$
$907$	33.7449	−	19.4826i	1.12048	−	0.646911i	0.941524	+	0.336946i	$0.109394\pi$
$908$	−4.13816	−	1.10882i	−0.137330	−	0.0367974i
$909$	3.30156	−	39.2066i	0.109506	−	1.30040i
$910$		0			0
$911$		−	54.4600i		−	1.80434i	−0.431379	−	0.902171i	$-0.641973\pi$
$911$		−	54.4600i		−	1.80434i	0.431379	−	0.902171i	$-0.358027\pi$
$912$	−7.84204	−	15.0047i	−0.259676	−	0.496857i
$913$	−1.72025	−	2.97956i	−0.0569319	−	0.0986090i
$914$	−0.155463	+	0.269270i	−0.00514227	+	0.00890667i
$915$		0			0
$916$	0.980240	+	3.65830i	0.0323880	+	0.120874i
$917$	0.516534	+	1.92773i	0.0170574	+	0.0636593i
$918$	−30.3567	−	3.84583i	−1.00192	−	0.126931i
$919$	−15.1481	+	26.2373i	−0.499690	+	0.865488i	−1.00000		0.000358010i	$-0.999886\pi$
$919$	−15.1481	+	26.2373i	−0.499690	+	0.865488i	0.500310	+	0.865846i	$0.333219\pi$
$920$		0			0
$921$	−24.7942	+	12.9584i	−0.816997	+	0.426993i
$922$		−	22.0163i		−	0.725067i
$923$	−21.6464	+	42.6520i	−0.712500	+	1.40391i
$924$	−2.63128	+	2.41901i	−0.0865627	+	0.0795797i
$925$		0			0
$926$	20.7073	−	11.9553i	0.680483	−	0.392877i
$927$	8.78013	−	12.6266i	0.288377	−	0.414712i
$928$	7.25722	−	7.25722i	0.238230	−	0.238230i
$929$	−47.5492	+	12.7408i	−1.56004	+	0.418011i	−0.932675	−	0.360717i	$-0.882532\pi$
$929$	−47.5492	+	12.7408i	−1.56004	+	0.418011i	−0.627362	+	0.778728i	$0.715865\pi$
$930$		0			0
$931$	3.82839	+	3.82839i	0.125470	+	0.125470i
$932$	3.35846	+	1.93901i	0.110010	+	0.0635144i
$933$	4.27524	−	13.6367i	0.139965	−	0.446445i
$934$	−5.30563	+	19.8009i	−0.173605	+	0.647904i
$935$		0			0
$936$	−17.0992	+	27.6625i	−0.558906	+	0.904176i
$937$	36.4014			1.18918			0.594590	−	0.804029i	$-0.297314\pi$
$937$	36.4014			1.18918			0.594590	+	0.804029i	$0.297314\pi$
$938$	7.09455	−	26.4772i	0.231645	−	0.864512i
$939$	−6.52604	+	20.8160i	−0.212969	+	0.679306i
$940$		0			0
$941$	−0.425527	−	0.425527i	−0.0138718	−	0.0138718i	0.700137	−	0.714009i	$-0.253122\pi$
$941$	−0.425527	−	0.425527i	−0.0138718	−	0.0138718i	−0.714009	+	0.700137i	$0.753122\pi$
$942$	−40.7186	−	25.8476i	−1.32669	−	0.842159i
$943$	0.362942	−	0.0972501i	0.0118190	−	0.00316690i
$944$	14.9374	−	14.9374i	0.486170	−	0.486170i
$945$		0			0
$946$	−15.2124	+	8.78290i	−0.494599	+	0.285557i
$947$	33.3137	+	8.92637i	1.08255	+	0.290068i	0.755640	−	0.654988i	$-0.227326\pi$
$947$	33.3137	+	8.92637i	1.08255	+	0.290068i	0.326909	+	0.945056i	$0.393993\pi$
$948$	−3.95874	+	3.63939i	−0.128574	+	0.118202i
$949$	−7.97617	+	0.430810i	−0.258917	+	0.0139847i
$950$		0			0
$951$	8.74601	−	4.57100i	0.283609	−	0.148225i
$952$	−15.5591	−	26.9492i	−0.504274	−	0.873428i
$953$	−25.8040	+	44.6938i	−0.835873	+	1.44778i	0.0574438	+	0.998349i	$0.481705\pi$
$953$	−25.8040	+	44.6938i	−0.835873	+	1.44778i	−0.893317	+	0.449427i	$0.851628\pi$
$954$	−20.8015	−	24.6270i	−0.673474	−	0.797330i
$955$		0			0
$956$	1.80254	+	6.72716i	0.0582983	+	0.217572i
$957$	1.18844	−	28.2758i	0.0384167	−	0.914026i
$958$	2.86036	−	4.95429i	0.0924140	−	0.160066i
$959$	−7.17507	−	12.4276i	−0.231695	−	0.401308i
$960$		0			0
$961$		−	11.8000i		−	0.380644i
$962$	47.3455	−	15.4673i	1.52648	−	0.498685i
$963$	−20.5444	−	1.73003i	−0.662034	−	0.0557494i
$964$	−7.65906	−	2.05224i	−0.246682	−	0.0660982i
$965$		0			0
$966$	0.499370	+	2.23529i	0.0160670	+	0.0719192i
$967$	13.6221	−	13.6221i	0.438057	−	0.438057i	−0.453300	−	0.891358i	$-0.649754\pi$
$967$	13.6221	−	13.6221i	0.438057	−	0.438057i	0.891358	+	0.453300i	$0.149754\pi$
$968$	8.50156	−	2.27799i	0.273250	−	0.0732172i
$969$	−12.6364	+	19.9067i	−0.405941	+	0.639494i
$970$		0			0
$971$	−34.7333	−	20.0533i	−1.11465	−	0.643541i	−0.174617	−	0.984637i	$-0.555869\pi$
$971$	−34.7333	−	20.0533i	−1.11465	−	0.643541i	−0.940029	+	0.341096i	$0.889202\pi$
$972$	−4.42519	−	2.25803i	−0.141938	−	0.0724262i
$973$	−10.2349	+	38.1973i	−0.328117	+	1.22455i
$974$	51.8966			1.66288
$975$		0			0
$976$	−36.9347			−1.18225
$977$	−0.401205	+	1.49732i	−0.0128357	+	0.0479034i	−0.972047	−	0.234788i	$-0.924560\pi$
$977$	−0.401205	+	1.49732i	−0.0128357	+	0.0479034i	0.959211	+	0.282691i	$0.0912272\pi$
$978$	−23.7359	−	7.44146i	−0.758992	−	0.237952i
$979$	4.18922	+	2.41865i	0.133888	+	0.0773004i
$980$		0			0
$981$	−2.99378	+	0.537940i	−0.0955842	+	0.0171751i
$982$	−17.6241	+	4.72235i	−0.562406	+	0.150696i
$983$	7.26168	−	7.26168i	0.231611	−	0.231611i	−0.581754	−	0.813365i	$-0.697633\pi$
$983$	7.26168	−	7.26168i	0.231611	−	0.231611i	0.813365	+	0.581754i	$0.197633\pi$
$984$	4.26737	−	0.953343i	0.136039	−	0.0303915i
$985$		0			0
$986$	32.7119	+	8.76512i	1.04176	+	0.279138i
$987$	11.5735	+	12.5891i	0.368389	+	0.400715i
$988$	1.88052	+	2.88563i	0.0598273	+	0.0918042i
$989$		−	2.13366i		−	0.0678464i
$990$		0			0
$991$	−26.1268	−	45.2530i	−0.829946	−	1.43751i	−0.898080	−	0.439832i	$-0.855038\pi$
$991$	−26.1268	−	45.2530i	−0.829946	−	1.43751i	0.0681339	−	0.997676i	$-0.478295\pi$
$992$	5.83775	−	10.1113i	0.185349	−	0.321033i
$993$	−27.9649	−	1.17537i	−0.887438	−	0.0372992i
$994$	10.1460	+	37.8652i	0.321810	+	1.20101i
$995$		0			0
$996$	0.667837	+	0.0280694i	0.0211612	+	0.000889412i
$997$	−0.181069	+	0.313621i	−0.00573451	+	0.00993247i	−0.868878	−	0.495026i	$-0.835159\pi$
$997$	−0.181069	+	0.313621i	−0.00573451	+	0.00993247i	0.863144	+	0.504958i	$0.168492\pi$
$998$	11.8274	+	20.4856i	0.374389	+	0.648460i
$999$	21.4344	+	51.0407i	0.678153	+	1.61486i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bo.h.626.8		96
3.2	odd	2	inner	975.2.bo.h.626.18		96
5.2	odd	4		195.2.bh.a.119.8	yes	96
5.3	odd	4		195.2.bh.a.119.17	yes	96
5.4	even	2	inner	975.2.bo.h.626.17		96
13.7	odd	12	inner	975.2.bo.h.176.18		96
15.2	even	4		195.2.bh.a.119.18	yes	96
15.8	even	4		195.2.bh.a.119.7	yes	96
15.14	odd	2	inner	975.2.bo.h.626.7		96
39.20	even	12	inner	975.2.bo.h.176.8		96
65.7	even	12		195.2.bh.a.59.7	✓	96
65.33	even	12		195.2.bh.a.59.18	yes	96
65.59	odd	12	inner	975.2.bo.h.176.7		96
195.59	even	12	inner	975.2.bo.h.176.17		96
195.98	odd	12		195.2.bh.a.59.8	yes	96
195.137	odd	12		195.2.bh.a.59.17	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bh.a.59.7	✓	96	65.7	even	12
195.2.bh.a.59.8	yes	96	195.98	odd	12
195.2.bh.a.59.17	yes	96	195.137	odd	12
195.2.bh.a.59.18	yes	96	65.33	even	12
195.2.bh.a.119.7	yes	96	15.8	even	4
195.2.bh.a.119.8	yes	96	5.2	odd	4
195.2.bh.a.119.17	yes	96	5.3	odd	4
195.2.bh.a.119.18	yes	96	15.2	even	4
975.2.bo.h.176.7		96	65.59	odd	12	inner
975.2.bo.h.176.8		96	39.20	even	12	inner
975.2.bo.h.176.17		96	195.59	even	12	inner
975.2.bo.h.176.18		96	13.7	odd	12	inner
975.2.bo.h.626.7		96	15.14	odd	2	inner
975.2.bo.h.626.8		96	1.1	even	1	trivial
975.2.bo.h.626.17		96	5.4	even	2	inner
975.2.bo.h.626.18		96	3.2	odd	2	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 $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-0.335598 + 1.25247i) q^{2} +(-0.518148 + 1.65273i) q^{3} +(0.276000 + 0.159349i) q^{4} +(-1.89610 - 1.20362i) q^{6} +(2.20132 - 0.589843i) q^{7} +(-2.12594 + 2.12594i) q^{8} +(-2.46304 - 1.71272i) q^{9} +(2.74441 + 0.735363i) q^{11} +(-0.406369 + 0.373587i) q^{12} +(-2.40830 + 2.68330i) q^{13} +2.95504i q^{14} +(-1.63052 - 2.82414i) q^{16} +(-2.27079 + 3.93313i) q^{17} +(2.97172 - 2.51010i) q^{18} +(-0.775797 - 2.89531i) q^{19} +(-0.165760 + 3.94382i) q^{21} +(-1.84204 + 3.19050i) q^{22} +(-0.223746 - 0.387540i) q^{23} +(-2.41206 - 4.61517i) q^{24} +(-2.55253 - 3.91682i) q^{26} +(4.10689 - 3.18331i) q^{27} +(0.701555 + 0.187981i) q^{28} +(-4.98037 + 2.87542i) q^{29} +(-4.62601 + 4.62601i) q^{31} +(-1.72384 + 0.461902i) q^{32} +(-2.63737 + 4.15475i) q^{33} +(-4.16405 - 4.16405i) q^{34} +(-0.406880 - 0.865193i) q^{36} +(-2.75740 + 10.2908i) q^{37} +3.88664 q^{38} +(-3.18693 - 5.37061i) q^{39} +(-0.217322 + 0.811058i) q^{41} +(-4.88389 - 1.53115i) q^{42} +(4.12924 + 2.38402i) q^{43} +(0.640278 + 0.640278i) q^{44} +(0.560470 - 0.150177i) q^{46} +(3.06335 - 3.06335i) q^{47} +(5.51240 - 1.23149i) q^{48} +(-1.56426 + 0.903128i) q^{49} +(-5.32380 - 5.79096i) q^{51} +(-1.09227 + 0.356833i) q^{52} -8.28713i q^{53} +(2.60873 + 6.21206i) q^{54} +(-3.42592 + 5.93387i) q^{56} +(5.18715 + 0.218017i) q^{57} +(-1.92997 - 7.20275i) q^{58} +(1.67660 + 6.25715i) q^{59} +(5.66303 - 9.80865i) q^{61} +(-4.24145 - 7.34641i) q^{62} +(-6.43220 - 2.31744i) q^{63} -8.83615i q^{64} +(-4.31860 - 4.69755i) q^{66} +(-8.96003 - 2.40083i) q^{67} +(-1.25348 + 0.723695i) q^{68} +(0.756433 - 0.168989i) q^{69} +(12.8138 - 3.43344i) q^{71} +(8.87745 - 1.59515i) q^{72} +(1.56653 + 1.56653i) q^{73} +(-11.9635 - 6.90712i) q^{74} +(0.247244 - 0.922728i) q^{76} +6.47509 q^{77} +(7.79605 - 2.18916i) q^{78} +9.74173 q^{79} +(3.13318 + 8.43701i) q^{81} +(-0.942892 - 0.544379i) q^{82} +(-0.856250 - 0.856250i) q^{83} +(-0.674192 + 1.06208i) q^{84} +(-4.37167 + 4.37167i) q^{86} +(-2.17173 - 9.72112i) q^{87} +(-7.39781 + 4.27113i) q^{88} +(1.64453 + 0.440650i) q^{89} +(-3.71871 + 7.32734i) q^{91} -0.142614i q^{92} +(-5.24860 - 10.0425i) q^{93} +(2.80869 + 4.86480i) q^{94} +(0.129806 - 3.08838i) q^{96} +(-2.62855 - 9.80988i) q^{97} +(-0.606176 - 2.26228i) q^{98} +(-5.50014 - 6.51164i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 24 q^{4} + 4 q^{9} - 16 q^{21} + 28 q^{24} - 40 q^{31} + 32 q^{34} - 60 q^{36} + 4 q^{39} - 128 q^{46} - 60 q^{54} - 48 q^{61} - 8 q^{66} - 72 q^{69} - 80 q^{76} + 80 q^{79} + 48 q^{81} + 132 q^{84}+ \cdots + 48 q^{99}+O(q^{100}) \) 96 * q + 24 * q^4 + 4 * q^9 - 16 * q^21 + 28 * q^24 - 40 * q^31 + 32 * q^34 - 60 * q^36 + 4 * q^39 - 128 * q^46 - 60 * q^54 - 48 * q^61 - 8 * q^66 - 72 * q^69 - 80 * q^76 + 80 * q^79 + 48 * q^81 + 132 * q^84 - 56 * q^91 - 72 * q^94 + 204 * q^96 + 48 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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