LMFDB - Embedded newform 975.2.bn.d.407.18

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			407.18
Character	$\chi$	$=$	975.407
Dual form			975.2.bn.d.218.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.42342 - 0.381405i) q^{2} +(0.323695 - 1.70154i) q^{3} +(0.148609 - 0.0857994i) q^{4} +(-0.188219 - 2.54546i) q^{6} +(-3.97287 - 1.06453i) q^{7} +(-1.90523 + 1.90523i) q^{8} +(-2.79044 - 1.10156i) q^{9} +(-2.13830 + 3.70364i) q^{11} +(-0.0978867 - 0.280636i) q^{12} +(3.59901 + 0.217053i) q^{13} -6.06108 q^{14} +(-2.15688 + 3.73582i) q^{16} +(-2.26413 - 0.606673i) q^{17} +(-4.39212 - 0.503692i) q^{18} +(-2.42558 - 4.20123i) q^{19} +(-3.09733 + 6.41539i) q^{21} +(-1.63112 + 6.08741i) q^{22} +(-2.72722 + 0.730756i) q^{23} +(2.62510 + 3.85852i) q^{24} +(5.20570 - 1.06372i) q^{26} +(-2.77759 + 4.39147i) q^{27} +(-0.681739 + 0.182671i) q^{28} +(-0.553990 + 0.959539i) q^{29} -2.59652i q^{31} +(-0.250564 + 0.935116i) q^{32} +(5.60972 + 4.83724i) q^{33} -3.45421 q^{34} +(-0.509198 + 0.0757171i) q^{36} +(0.255918 + 0.955101i) q^{37} +(-5.05499 - 5.05499i) q^{38} +(1.53431 - 6.05359i) q^{39} +(-0.575209 + 0.996292i) q^{41} +(-1.96194 + 10.3131i) q^{42} +(-9.84550 - 2.63809i) q^{43} +0.733860i q^{44} +(-3.60327 + 2.08035i) q^{46} +(3.07931 + 3.07931i) q^{47} +(5.65846 + 4.87927i) q^{48} +(8.58827 + 4.95844i) q^{49} +(-1.76516 + 3.65613i) q^{51} +(0.553469 - 0.276537i) q^{52} +(-2.89463 - 2.89463i) q^{53} +(-2.27876 + 7.31030i) q^{54} +(9.59737 - 5.54104i) q^{56} +(-7.93368 + 2.76729i) q^{57} +(-0.422589 + 1.57712i) q^{58} +(7.54722 - 4.35739i) q^{59} +(1.64416 + 2.84776i) q^{61} +(-0.990323 - 3.69594i) q^{62} +(9.91342 + 7.34684i) q^{63} -7.20087i q^{64} +(9.82995 + 4.74586i) q^{66} +(-1.59596 - 5.95621i) q^{67} +(-0.388523 + 0.104104i) q^{68} +(0.360619 + 4.87700i) q^{69} +(-4.38783 - 7.59994i) q^{71} +(7.41514 - 3.21771i) q^{72} +(-8.00201 - 8.00201i) q^{73} +(0.728560 + 1.26190i) q^{74} +(-0.720926 - 0.416227i) q^{76} +(12.4378 - 12.4378i) q^{77} +(-0.124901 - 9.20200i) q^{78} +2.06111i q^{79} +(6.57314 + 6.14767i) q^{81} +(-0.438775 + 1.63753i) q^{82} +(6.21215 - 6.21215i) q^{83} +(0.0901463 + 1.21913i) q^{84} -15.0205 q^{86} +(1.45336 + 1.25323i) q^{87} +(-2.98233 - 11.1302i) q^{88} +(-3.27478 - 1.89069i) q^{89} +(-14.0673 - 4.69357i) q^{91} +(-0.342591 + 0.342591i) q^{92} +(-4.41806 - 0.840480i) q^{93} +(5.55763 + 3.20870i) q^{94} +(1.51003 + 0.729035i) q^{96} +(-4.91400 - 1.31670i) q^{97} +(14.1159 + 3.78234i) q^{98} +(10.0466 - 7.97935i) 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 $

$2$	1.42342	−	0.381405i	1.00651	−	0.269694i	0.282340	−	0.959314i	$-0.408889\pi$
$2$	1.42342	−	0.381405i	1.00651	−	0.269694i	0.724171	+	0.689621i	$0.242223\pi$
$3$	0.323695	−	1.70154i	0.186885	−	0.982382i
$3$	0.323695	−	1.70154i	0.186885	−	0.982382i
$4$	0.148609	−	0.0857994i	0.0743045	−	0.0428997i
$5$		0			0
$5$		0			0
$6$	−0.188219	−	2.54546i	−0.0768400	−	1.03918i
$7$	−3.97287	−	1.06453i	−1.50160	−	0.402353i	−0.587966	−	0.808886i	$-0.700071\pi$
$7$	−3.97287	−	1.06453i	−1.50160	−	0.402353i	−0.913636	+	0.406533i	$0.866738\pi$
$8$	−1.90523	+	1.90523i	−0.673599	+	0.673599i
$9$	−2.79044	−	1.10156i	−0.930148	−	0.367186i
$10$		0			0
$11$	−2.13830	+	3.70364i	−0.644722	+	1.11669i	0.339644	+	0.940554i	$0.389693\pi$
$11$	−2.13830	+	3.70364i	−0.644722	+	1.11669i	−0.984366	+	0.176137i	$0.943640\pi$
$12$	−0.0978867	−	0.280636i	−0.0282575	−	0.0810127i
$13$	3.59901	+	0.217053i	0.998186	+	0.0601997i
$13$	3.59901	+	0.217053i	0.998186	+	0.0601997i
$14$	−6.06108			−1.61989
$15$		0			0
$16$	−2.15688	+	3.73582i	−0.539219	+	0.933955i
$17$	−2.26413	−	0.606673i	−0.549133	−	0.147140i	−0.0264240	−	0.999651i	$-0.508412\pi$
$17$	−2.26413	−	0.606673i	−0.549133	−	0.147140i	−0.522709	+	0.852511i	$0.675079\pi$
$18$	−4.39212	−	0.503692i	−1.03523	−	0.118721i
$19$	−2.42558	−	4.20123i	−0.556466	−	0.963827i	−0.997788	−	0.0664784i	$-0.978824\pi$
$19$	−2.42558	−	4.20123i	−0.556466	−	0.963827i	0.441322	−	0.897349i	$-0.354510\pi$
$20$		0			0
$21$	−3.09733	+	6.41539i	−0.675892	+	1.39995i
$22$	−1.63112	+	6.08741i	−0.347755	+	1.29784i
$23$	−2.72722	+	0.730756i	−0.568664	+	0.152373i	−0.531684	−	0.846943i	$-0.678441\pi$
$23$	−2.72722	+	0.730756i	−0.568664	+	0.152373i	−0.0369803	+	0.999316i	$0.511774\pi$
$24$	2.62510	+	3.85852i	0.535845	+	0.787617i
$25$		0			0
$26$	5.20570	−	1.06372i	1.02092	−	0.208613i
$27$	−2.77759	+	4.39147i	−0.534548	+	0.845138i
$28$	−0.681739	+	0.182671i	−0.128837	+	0.0345217i
$29$	−0.553990	+	0.959539i	−0.102873	+	0.178182i	−0.912867	−	0.408256i	$-0.866137\pi$
$29$	−0.553990	+	0.959539i	−0.102873	+	0.178182i	0.809994	+	0.586438i	$0.199470\pi$
$30$		0			0
$31$		−	2.59652i		−	0.466348i	−0.972435	−	0.233174i	$-0.925089\pi$
$31$		−	2.59652i		−	0.466348i	0.972435	−	0.233174i	$-0.0749112\pi$
$32$	−0.250564	+	0.935116i	−0.0442938	+	0.165307i
$33$	5.60972	+	4.83724i	0.976528	+	0.842056i
$34$	−3.45421			−0.592391
$35$		0			0
$36$	−0.509198	+	0.0757171i	−0.0848663	+	0.0126195i
$37$	0.255918	+	0.955101i	0.0420727	+	0.157018i	0.983766	−	0.179454i	$-0.0574331\pi$
$37$	0.255918	+	0.955101i	0.0420727	+	0.157018i	−0.941694	+	0.336472i	$0.890766\pi$
$38$	−5.05499	−	5.05499i	−0.820027	−	0.820027i
$39$	1.53431	−	6.05359i	0.245686	−	0.969350i
$40$		0			0
$41$	−0.575209	+	0.996292i	−0.0898326	+	0.155595i	−0.907440	−	0.420181i	$-0.861967\pi$
$41$	−0.575209	+	0.996292i	−0.0898326	+	0.155595i	0.817608	+	0.575776i	$0.195300\pi$
$42$	−1.96194	+	10.3131i	−0.302734	+	1.59135i
$43$	−9.84550	−	2.63809i	−1.50142	−	0.402305i	−0.587847	−	0.808972i	$-0.700024\pi$
$43$	−9.84550	−	2.63809i	−1.50142	−	0.402305i	−0.913577	+	0.406666i	$0.866691\pi$
$44$			0.733860i			0.110634i
$45$		0			0
$46$	−3.60327	+	2.08035i	−0.531273	+	0.306730i
$47$	3.07931	+	3.07931i	0.449164	+	0.449164i	0.895077	−	0.445913i	$-0.147121\pi$
$47$	3.07931	+	3.07931i	0.449164	+	0.449164i	−0.445913	+	0.895077i	$0.647121\pi$
$48$	5.65846	+	4.87927i	0.816728	+	0.704261i
$49$	8.58827	+	4.95844i	1.22690	+	0.708349i
$50$		0			0
$51$	−1.76516	+	3.65613i	−0.247172	+	0.511960i
$52$	0.553469	−	0.276537i	0.0767523	−	0.0383488i
$53$	−2.89463	−	2.89463i	−0.397608	−	0.397608i	0.479780	−	0.877389i	$-0.340716\pi$
$53$	−2.89463	−	2.89463i	−0.397608	−	0.397608i	−0.877389	+	0.479780i	$0.840716\pi$
$54$	−2.27876	+	7.31030i	−0.310100	+	0.994805i
$55$		0			0
$56$	9.59737	−	5.54104i	1.28250	−	0.740453i
$57$	−7.93368	+	2.76729i	−1.05084	+	0.366537i
$58$	−0.422589	+	1.57712i	−0.0554886	+	0.207086i
$59$	7.54722	−	4.35739i	0.982564	−	0.567284i	0.0795208	−	0.996833i	$-0.474661\pi$
$59$	7.54722	−	4.35739i	0.982564	−	0.567284i	0.903043	+	0.429550i	$0.141328\pi$
$60$		0			0
$61$	1.64416	+	2.84776i	0.210513	+	0.364619i	0.951875	−	0.306486i	$-0.0991534\pi$
$61$	1.64416	+	2.84776i	0.210513	+	0.364619i	−0.741362	+	0.671105i	$0.765820\pi$
$62$	−0.990323	−	3.69594i	−0.125771	−	0.469385i
$63$	9.91342	+	7.34684i	1.24897	+	0.925615i
$64$		−	7.20087i		−	0.900109i
$65$		0			0
$66$	9.82995	+	4.74586i	1.20998	+	0.584175i
$67$	−1.59596	−	5.95621i	−0.194978	−	0.727667i	−0.992273	−	0.124077i	$-0.960403\pi$
$67$	−1.59596	−	5.95621i	−0.194978	−	0.727667i	0.797295	−	0.603590i	$-0.206264\pi$
$68$	−0.388523	+	0.104104i	−0.0471153	+	0.0126245i
$69$	0.360619	+	4.87700i	0.0434135	+	0.587122i
$70$		0			0
$71$	−4.38783	−	7.59994i	−0.520739	−	0.901947i	−0.999709	−	0.0241156i	$-0.992323\pi$
$71$	−4.38783	−	7.59994i	−0.520739	−	0.901947i	0.478970	−	0.877831i	$-0.341010\pi$
$72$	7.41514	−	3.21771i	0.873882	−	0.379210i
$73$	−8.00201	−	8.00201i	−0.936565	−	0.936565i	0.0615398	−	0.998105i	$-0.480399\pi$
$73$	−8.00201	−	8.00201i	−0.936565	−	0.936565i	−0.998105	+	0.0615398i	$0.980399\pi$
$74$	0.728560	+	1.26190i	0.0846934	+	0.146693i
$75$		0			0
$76$	−0.720926	−	0.416227i	−0.0826958	−	0.0477445i
$77$	12.4378	−	12.4378i	1.41742	−	1.41742i
$78$	−0.124901	−	9.20200i	−0.0141423	−	1.04192i
$79$			2.06111i			0.231893i	0.993255	+	0.115946i	$0.0369901\pi$
$79$			2.06111i			0.231893i	−0.993255	+	0.115946i	$0.963010\pi$
$80$		0			0
$81$	6.57314	+	6.14767i	0.730349	+	0.683074i
$82$	−0.438775	+	1.63753i	−0.0484546	+	0.180835i
$83$	6.21215	−	6.21215i	0.681872	−	0.681872i	−0.278550	−	0.960422i	$-0.589854\pi$
$83$	6.21215	−	6.21215i	0.681872	−	0.681872i	0.960422	+	0.278550i	$0.0898538\pi$
$84$	0.0901463	+	1.21913i	0.00983576	+	0.133018i
$85$		0			0
$86$	−15.0205			−1.61970
$87$	1.45336	+	1.25323i	0.155817	+	0.134360i
$88$	−2.98233	−	11.1302i	−0.317918	−	1.18649i
$89$	−3.27478	−	1.89069i	−0.347126	−	0.200413i	0.316293	−	0.948662i	$-0.397562\pi$
$89$	−3.27478	−	1.89069i	−0.347126	−	0.200413i	−0.663419	+	0.748248i	$0.730895\pi$
$90$		0			0
$91$	−14.0673	−	4.69357i	−1.47466	−	0.492019i
$92$	−0.342591	+	0.342591i	−0.0357175	+	0.0357175i
$93$	−4.41806	−	0.840480i	−0.458132	−	0.0871537i
$94$	5.55763	+	3.20870i	0.573225	+	0.330952i
$95$		0			0
$96$	1.51003	+	0.729035i	0.154116	+	0.0744068i
$97$	−4.91400	−	1.31670i	−0.498941	−	0.133691i	0.000567486	−	1.00000i	$-0.499819\pi$
$97$	−4.91400	−	1.31670i	−0.498941	−	0.133691i	−0.499508	+	0.866309i	$0.666486\pi$
$98$	14.1159	+	3.78234i	1.42592	+	0.382075i
$99$	10.0466	−	7.97935i	1.00972	−	0.801955i
$100$		0			0
$101$	16.9579	+	9.79064i	1.68737	+	0.974205i	0.956518	+	0.291673i	$0.0942119\pi$
$101$	16.9579	+	9.79064i	1.68737	+	0.974205i	0.730855	+	0.682533i	$0.239121\pi$
$102$	−1.11811	+	5.87745i	−0.110709	+	0.581954i
$103$	−11.6815	+	11.6815i	−1.15101	+	1.15101i	−0.164663	+	0.986350i	$0.552654\pi$
$103$	−11.6815	+	11.6815i	−1.15101	+	1.15101i	−0.986350	+	0.164663i	$0.947346\pi$
$104$	−7.27046	+	6.44339i	−0.712928	+	0.631827i
$105$		0			0
$106$	−5.22431	−	3.01626i	−0.507430	−	0.292965i
$107$	2.39707	+	8.94599i	0.231734	+	0.864841i	0.979594	+	0.200986i	$0.0644145\pi$
$107$	2.39707	+	8.94599i	0.231734	+	0.864841i	−0.747861	+	0.663856i	$0.768919\pi$
$108$	−0.0359895	+	0.890927i	−0.00346309	+	0.0857295i
$109$	−13.8177			−1.32349			−0.661746	−	0.749728i	$-0.730184\pi$
$109$	−13.8177			−1.32349			−0.661746	+	0.749728i	$0.730184\pi$
$110$		0			0
$111$	1.70798	−	0.126293i	0.162114	−	0.0119872i
$112$	12.5459	−	12.5459i	1.18547	−	1.18547i
$113$	−0.372017	+	1.38839i	−0.0349964	+	0.130608i	−0.981214	−	0.192923i	$-0.938203\pi$
$113$	−0.372017	+	1.38839i	−0.0349964	+	0.130608i	0.946218	+	0.323531i	$0.104870\pi$
$114$	−10.2375	+	6.96497i	−0.958831	+	0.652329i
$115$		0			0
$116$			0.190128i			0.0176529i
$117$	−9.80374	−	4.57019i	−0.906356	−	0.422514i
$118$	9.08095	−	9.08095i	0.835969	−	0.835969i
$119$	8.34928	+	4.82046i	0.765377	+	0.441891i
$120$		0			0
$121$	−3.64466	−	6.31273i	−0.331332	−	0.573884i
$122$	3.42648	+	3.42648i	0.310219	+	0.310219i
$123$	1.50903	+	1.30123i	0.136065	+	0.117328i
$124$	−0.222780	−	0.385866i	−0.0200062	−	0.0346518i
$125$		0			0
$126$	16.9131	+	6.67663i	1.50674	+	0.594801i
$127$	−2.87595	+	0.770609i	−0.255199	+	0.0683805i	−0.384150	−	0.923270i	$-0.625506\pi$
$127$	−2.87595	+	0.770609i	−0.255199	+	0.0683805i	0.128951	+	0.991651i	$0.458839\pi$
$128$	−3.24757	−	12.1201i	−0.287048	−	1.07128i
$129$	−7.67575	+	15.8985i	−0.675812	+	1.39979i
$130$		0			0
$131$		−	2.62072i		−	0.228973i	−0.993425	−	0.114487i	$-0.963478\pi$
$131$		−	2.62072i		−	0.228973i	0.993425	−	0.114487i	$-0.0365223\pi$
$132$	1.24869	+	0.237547i	0.108684	+	0.0206758i
$133$	5.16418	+	19.2730i	0.447792	+	1.67118i
$134$	−4.54345	−	7.86949i	−0.392494	−	0.679820i
$135$		0			0
$136$	5.46953	−	3.15784i	0.469009	−	0.270782i
$137$	−2.68583	+	10.0236i	−0.229466	+	0.856377i	0.751100	+	0.660188i	$0.229523\pi$
$137$	−2.68583	+	10.0236i	−0.229466	+	0.856377i	−0.980566	+	0.196189i	$0.937143\pi$
$138$	2.37342	+	6.80448i	0.202039	+	0.579236i
$139$	−1.68558	+	0.973168i	−0.142969	+	0.0825431i	−0.569778	−	0.821799i	$-0.692971\pi$
$139$	−1.68558	+	0.973168i	−0.142969	+	0.0825431i	0.426809	+	0.904342i	$0.359638\pi$
$140$		0			0
$141$	6.23632	−	4.24280i	0.525193	−	0.357308i
$142$	−9.14438	−	9.14438i	−0.767379	−	0.767379i
$143$	−8.49966	+	12.8653i	−0.710777	+	1.07585i
$144$	10.1339	−	8.04867i	0.844488	−	0.670722i
$145$		0			0
$146$	−14.4422	−	8.33823i	−1.19525	−	0.690077i
$147$	11.2169	−	13.0082i	0.925158	−	1.07290i
$148$	0.119979	+	0.119979i	0.00986220	+	0.00986220i
$149$	−8.56121	+	4.94282i	−0.701362	+	0.404931i	−0.807854	−	0.589382i	$-0.799371\pi$
$149$	−8.56121	+	4.94282i	−0.701362	+	0.404931i	0.106493	+	0.994313i	$0.466038\pi$
$150$		0			0
$151$		−	20.0349i		−	1.63042i	−0.579165	−	0.815210i	$-0.696621\pi$
$151$		−	20.0349i		−	1.63042i	0.579165	−	0.815210i	$-0.303379\pi$
$152$	12.6256	+	3.38301i	1.02407	+	0.274398i
$153$	5.64965	+	4.18696i	0.456747	+	0.338496i
$154$	12.9604	−	22.4481i	1.04438	−	1.80892i
$155$		0			0
$156$	−0.291383	−	1.03126i	−0.0233293	−	0.0825669i
$157$	5.41204	+	5.41204i	0.431928	+	0.431928i	0.889284	−	0.457356i	$-0.151203\pi$
$157$	5.41204	+	5.41204i	0.431928	+	0.431928i	−0.457356	+	0.889284i	$0.651203\pi$
$158$	0.786117	+	2.93383i	0.0625401	+	0.233403i
$159$	−5.86230	+	3.98834i	−0.464910	+	0.316296i
$160$		0			0
$161$	11.6128			0.915215
$162$	11.7011	+	6.24369i	0.919325	+	0.490551i
$163$	−1.81388	+	6.76947i	−0.142074	+	0.530226i	0.857795	+	0.513993i	$0.171834\pi$
$163$	−1.81388	+	6.76947i	−0.142074	+	0.530226i	−0.999868	+	0.0162335i	$0.994833\pi$
$164$			0.197410i			0.0154152i
$165$		0			0
$166$	6.47316	−	11.2118i	0.502415	−	0.870208i
$167$	−24.5943	+	6.59002i	−1.90316	+	0.509951i	−0.907143	+	0.420822i	$0.861742\pi$
$167$	−24.5943	+	6.59002i	−1.90316	+	0.509951i	−0.996020	+	0.0891292i	$0.971592\pi$
$168$	−6.32166	−	18.1239i	−0.487726	−	1.39829i
$169$	12.9058	+	1.56235i	0.992752	+	0.120181i
$170$		0			0
$171$	2.14055	+	14.3952i	0.163692	+	1.10083i
$172$	−1.68948	+	0.452694i	−0.128821	+	0.0345176i
$173$	4.95717	−	18.5004i	0.376887	−	1.40656i	−0.473681	−	0.880696i	$-0.657075\pi$
$173$	4.95717	−	18.5004i	0.376887	−	1.40656i	0.850568	−	0.525865i	$-0.176258\pi$
$174$	2.54674	+	1.22956i	0.193068	+	0.0932124i
$175$		0			0
$176$	−9.22410	−	15.9766i	−0.695292	−	1.20428i
$177$	−4.97125	−	14.2523i	−0.373662	−	1.07127i
$178$	−5.38251	−	1.44224i	−0.403436	−	0.108100i
$179$	3.01935	−	5.22967i	0.225677	−	0.390884i	−0.730845	−	0.682543i	$-0.760874\pi$
$179$	3.01935	−	5.22967i	0.225677	−	0.390884i	0.956522	+	0.291659i	$0.0942072\pi$
$180$		0			0
$181$	5.56311			0.413503			0.206751	−	0.978394i	$-0.433711\pi$
$181$	5.56311			0.413503			0.206751	+	0.978394i	$0.433711\pi$
$182$	−21.8139	−	1.31558i	−1.61695	−	0.0975170i
$183$	5.37777	−	1.87578i	0.397536	−	0.138662i
$184$	3.80371	−	6.58822i	0.280413	−	0.485690i
$185$		0			0
$186$	−6.60933	+	0.488713i	−0.484620	+	0.0358342i
$187$	7.08830	−	7.08830i	0.518348	−	0.518348i
$188$	0.721817	+	0.193410i	0.0526439	+	0.0141059i
$189$	15.7098	−	14.4899i	1.14272	−	1.05398i
$190$		0			0
$191$	2.61637	−	1.51056i	0.189314	−	0.109300i	−0.402348	−	0.915487i	$-0.631806\pi$
$191$	2.61637	−	1.51056i	0.189314	−	0.109300i	0.591661	+	0.806187i	$0.298472\pi$
$192$	−12.2525	−	2.33089i	−0.884251	−	0.168217i
$193$	3.38290	−	0.906445i	0.243506	−	0.0652473i	−0.135002	−	0.990845i	$-0.543104\pi$
$193$	3.38290	−	0.906445i	0.243506	−	0.0652473i	0.378508	+	0.925598i	$0.376437\pi$
$194$	−7.49689			−0.538245
$195$		0			0
$196$	1.70173			0.121552
$197$	4.48363	−	1.20138i	0.319445	−	0.0855951i	−0.0955335	−	0.995426i	$-0.530456\pi$
$197$	4.48363	−	1.20138i	0.319445	−	0.0855951i	0.414979	+	0.909831i	$0.363789\pi$
$198$	11.2572	−	15.1898i	0.800012	−	1.07949i
$199$	−3.93217	+	2.27024i	−0.278744	+	0.160933i	−0.632855	−	0.774271i	$-0.718117\pi$
$199$	−3.93217	+	2.27024i	−0.278744	+	0.160933i	0.354111	+	0.935204i	$0.384784\pi$
$200$		0			0
$201$	−10.6513	+	0.787588i	−0.751285	+	0.0555522i
$202$	27.8724	+	7.46839i	1.96110	+	0.525474i
$203$	3.22238	−	3.22238i	0.226167	−	0.226167i
$204$	0.0513743	+	0.694783i	0.00359692	+	0.0486446i
$205$		0			0
$206$	−12.1723	+	21.0831i	−0.848086	+	1.46893i
$207$	8.41511	+	0.965054i	0.584891	+	0.0670759i
$208$	−8.57349	+	12.9771i	−0.594465	+	0.899800i
$209$	20.7465			1.43506
$210$		0			0
$211$	−6.07034	+	10.5141i	−0.417899	+	0.723823i	−0.995728	−	0.0923352i	$-0.970567\pi$
$211$	−6.07034	+	10.5141i	−0.417899	+	0.723823i	0.577829	+	0.816158i	$0.303900\pi$
$212$	−0.678526	−	0.181811i	−0.0466014	−	0.0124868i
$213$	−14.3519	+	5.00598i	−0.983375	+	0.343004i
$214$	6.82408	+	11.8197i	0.466485	+	0.807975i
$215$		0			0
$216$	−3.07480	−	13.6587i	−0.209214	−	0.929355i
$217$	−2.76406	+	10.3156i	−0.187637	+	0.700269i
$218$	−19.6684	+	5.27012i	−1.33211	+	0.356938i
$219$	−16.2059	+	11.0255i	−1.09509	+	0.745034i
$220$		0			0
$221$	−8.01697	−	2.67486i	−0.539279	−	0.179931i
$222$	2.38300	−	0.831198i	0.159937	−	0.0557864i
$223$	16.8709	−	4.52055i	1.12976	−	0.302718i	0.354933	−	0.934892i	$-0.384504\pi$
$223$	16.8709	−	4.52055i	1.12976	−	0.302718i	0.774827	+	0.632174i	$0.217837\pi$
$224$	1.99091	−	3.44836i	0.133023	−	0.230403i
$225$		0			0
$226$			2.11815i			0.140897i
$227$	2.48265	−	9.26536i	0.164779	−	0.614964i	−0.833289	−	0.552837i	$-0.813545\pi$
$227$	2.48265	−	9.26536i	0.164779	−	0.614964i	0.998068	−	0.0621264i	$-0.0197882\pi$
$228$	−0.941584	+	1.09195i	−0.0623579	+	0.0723161i
$229$	5.60158			0.370163			0.185081	−	0.982723i	$-0.440745\pi$
$229$	5.60158			0.370163			0.185081	+	0.982723i	$0.440745\pi$
$230$		0			0
$231$	−17.1373	−	25.1894i	−1.12755	−	1.65734i
$232$	−0.772662	−	2.88361i	−0.0507277	−	0.189318i
$233$	19.2843	+	19.2843i	1.26336	+	1.26336i	0.949456	+	0.313900i	$0.101636\pi$
$233$	19.2843	+	19.2843i	1.26336	+	1.26336i	0.313900	+	0.949456i	$0.398364\pi$
$234$	−15.6980	−	2.76612i	−1.02621	−	0.180827i
$235$		0			0
$236$	0.747723	−	1.29509i	0.0486726	−	0.0843034i
$237$	3.50705	+	0.667171i	0.227807	+	0.0433374i
$238$	13.7231	+	3.67709i	0.889536	+	0.238351i
$239$		−	17.3432i		−	1.12184i	−0.827870	−	0.560921i	$-0.810447\pi$
$239$		−	17.3432i		−	1.12184i	0.827870	−	0.560921i	$-0.189553\pi$
$240$		0			0
$241$	−1.44789	+	0.835937i	−0.0932665	+	0.0538475i	−0.545908	−	0.837845i	$-0.683815\pi$
$241$	−1.44789	+	0.835937i	−0.0932665	+	0.0538475i	0.452641	+	0.891693i	$0.350482\pi$
$242$	−7.59559	−	7.59559i	−0.488263	−	0.488263i
$243$	12.5882	−	9.19446i	0.807531	−	0.589825i
$244$	0.488673	+	0.282135i	0.0312841	+	0.0180619i
$245$		0			0
$246$	2.64429	+	1.27665i	0.168594	+	0.0813963i
$247$	−7.81780	−	15.6467i	−0.497435	−	0.995578i
$248$	4.94695	+	4.94695i	0.314131	+	0.314131i
$249$	−8.55934	−	12.5810i	−0.542426	−	0.797290i
$250$		0			0
$251$	6.81314	−	3.93357i	0.430042	−	0.248285i	−0.269323	−	0.963050i	$-0.586800\pi$
$251$	6.81314	−	3.93357i	0.430042	−	0.248285i	0.699364	+	0.714765i	$0.253466\pi$
$252$	2.10358	+	0.241240i	0.132513	+	0.0151967i
$253$	3.12515	−	11.6632i	0.196477	−	0.733260i
$254$	−3.79978	+	2.19380i	−0.238419	+	0.137651i
$255$		0			0
$256$	−2.04446	−	3.54111i	−0.127779	−	0.221319i
$257$	−2.46492	−	9.19920i	−0.153757	−	0.573830i	−0.999209	−	0.0397776i	$-0.987335\pi$
$257$	−2.46492	−	9.19920i	−0.153757	−	0.573830i	0.845451	−	0.534053i	$-0.179332\pi$
$258$	−4.86205	+	25.5579i	−0.302698	+	1.59116i
$259$		−	4.06692i		−	0.252706i
$260$		0			0
$261$	2.60286	−	2.06729i	0.161113	−	0.127962i
$262$	−0.999554	−	3.73039i	−0.0617526	−	0.230464i
$263$	−22.7323	+	6.09110i	−1.40173	+	0.375593i	−0.878967	−	0.476883i	$-0.841767\pi$
$263$	−22.7323	+	6.09110i	−1.40173	+	0.375593i	−0.522766	+	0.852476i	$0.675100\pi$
$264$	−19.9038	+	1.47175i	−1.22500	+	0.0905798i
$265$		0			0
$266$	14.7016	+	25.4640i	0.901414	+	1.56130i
$267$	−4.27711	+	4.96014i	−0.261755	+	0.303556i
$268$	−0.748213	−	0.748213i	−0.0457044	−	0.0457044i
$269$	5.95253	+	10.3101i	0.362932	+	0.628617i	0.988442	−	0.151599i	$-0.0484424\pi$
$269$	5.95253	+	10.3101i	0.362932	+	0.628617i	−0.625510	+	0.780216i	$0.715109\pi$
$270$		0			0
$271$	−17.4412	−	10.0697i	−1.05947	−	0.611688i	−0.134188	−	0.990956i	$-0.542843\pi$
$271$	−17.4412	−	10.0697i	−1.05947	−	0.611688i	−0.925287	+	0.379268i	$0.876176\pi$
$272$	7.14988	−	7.14988i	0.433525	−	0.433525i
$273$	−12.5398	+	22.4168i	−0.758943	+	1.35673i
$274$			15.2923i			0.923839i
$275$		0			0
$276$	0.472035	+	0.693825i	0.0284132	+	0.0417633i
$277$	1.13875	−	4.24989i	0.0684211	−	0.255351i	−0.923240	−	0.384224i	$-0.874469\pi$
$277$	1.13875	−	4.24989i	0.0684211	−	0.255351i	0.991661	+	0.128873i	$0.0411358\pi$
$278$	−2.02812	+	2.02812i	−0.121638	+	0.121638i
$279$	−2.86021	+	7.24543i	−0.171236	+	0.433773i
$280$		0			0
$281$	−23.0139			−1.37290			−0.686448	−	0.727179i	$-0.740831\pi$
$281$	−23.0139			−1.37290			−0.686448	+	0.727179i	$0.740831\pi$
$282$	7.25869	−	8.41785i	0.432248	−	0.501276i
$283$	3.53515	+	13.1933i	0.210143	+	0.784263i	0.987820	+	0.155600i	$0.0497309\pi$
$283$	3.53515	+	13.1933i	0.210143	+	0.784263i	−0.777678	+	0.628663i	$0.783602\pi$
$284$	−1.30414	−	0.752946i	−0.0773865	−	0.0446791i
$285$		0			0
$286$	−7.19170	+	21.5546i	−0.425254	+	1.27455i
$287$	3.34581	−	3.34581i	0.197497	−	0.197497i
$288$	1.72927	−	2.33338i	0.101898	−	0.137496i
$289$	−9.96418	−	5.75282i	−0.586128	−	0.338401i
$290$		0			0
$291$	−3.83105	+	7.93513i	−0.224580	+	0.465166i
$292$	−1.87574	−	0.502603i	−0.109769	−	0.0294126i
$293$	23.4342	+	6.27918i	1.36904	+	0.366834i	0.867129	−	0.498084i	$-0.165963\pi$
$293$	23.4342	+	6.27918i	1.36904	+	0.366834i	0.501914	+	0.864918i	$0.332630\pi$
$294$	11.0050	−	22.7944i	0.641827	−	1.32940i
$295$		0			0
$296$	−2.30726	−	1.33210i	−0.134107	−	0.0774267i
$297$	−10.3251	−	19.6775i	−0.599124	−	1.14180i
$298$	−10.3010	+	10.3010i	−0.596721	+	0.596721i
$299$	−9.97390	+	2.03805i	−0.576806	+	0.117863i
$300$		0			0
$301$	36.3065	+	20.9616i	2.09267	+	1.20821i
$302$	−7.64142	−	28.5182i	−0.439714	−	1.64104i
$303$	22.1483	−	25.6853i	1.27239	−	1.47558i
$304$	20.9267			1.20023
$305$		0			0
$306$	9.63876	+	3.80501i	0.551011	+	0.217518i
$307$	−12.8951	+	12.8951i	−0.735962	+	0.735962i	−0.971794	−	0.235832i	$-0.924219\pi$
$307$	−12.8951	+	12.8951i	−0.735962	+	0.735962i	0.235832	+	0.971794i	$0.424219\pi$
$308$	0.781213	−	2.91553i	0.0445137	−	0.166128i
$309$	16.0952	+	23.6577i	0.915626	+	1.34584i
$310$		0			0
$311$			8.39481i			0.476026i	0.971262	+	0.238013i	$0.0764960\pi$
$311$			8.39481i			0.476026i	−0.971262	+	0.238013i	$0.923504\pi$
$312$	8.61024	+	14.4566i	0.487459	+	0.818446i
$313$	0.445796	−	0.445796i	0.0251979	−	0.0251979i	−0.694396	−	0.719593i	$-0.744328\pi$
$313$	0.445796	−	0.445796i	0.0251979	−	0.0251979i	0.719593	+	0.694396i	$0.244328\pi$
$314$	9.76780	+	5.63944i	0.551229	+	0.318252i
$315$		0			0
$316$	0.176842	+	0.306299i	0.00994814	+	0.0172307i
$317$	12.5839	+	12.5839i	0.706781	+	0.706781i	0.965857	−	0.259076i	$-0.0834179\pi$
$317$	12.5839	+	12.5839i	0.706781	+	0.706781i	−0.259076	+	0.965857i	$0.583418\pi$
$318$	−6.82335	+	7.91300i	−0.382634	+	0.443739i
$319$	−2.36919	−	4.10356i	−0.132649	−	0.229755i
$320$		0			0
$321$	15.9978	−	1.18293i	0.892912	−	0.0660245i
$322$	16.5299	−	4.42917i	0.921174	−	0.246828i
$323$	2.94307	+	10.9837i	0.163757	+	0.611148i
$324$	1.50429	+	0.349626i	0.0835719	+	0.0194237i
$325$		0			0
$326$			10.3276i			0.571995i
$327$	−4.47271	+	23.5112i	−0.247341	+	1.30017i
$328$	−0.802257	−	2.99406i	−0.0442972	−	0.165319i
$329$	−8.95569	−	15.5117i	−0.493743	−	0.855188i
$330$		0			0
$331$	−12.2822	+	7.09113i	−0.675091	+	0.389764i	−0.798003	−	0.602654i	$-0.794110\pi$
$331$	−12.2822	+	7.09113i	−0.675091	+	0.389764i	0.122912	+	0.992418i	$0.460777\pi$
$332$	0.390182	−	1.45618i	0.0214140	−	0.0799182i
$333$	0.337972	−	2.94706i	0.0185208	−	0.161498i
$334$	−32.4946	+	18.7608i	−1.77802	+	1.02654i
$335$		0			0
$336$	−17.2862	−	25.4082i	−0.943038	−	1.38613i
$337$	5.88105	+	5.88105i	0.320361	+	0.320361i	0.848906	−	0.528544i	$-0.177262\pi$
$337$	5.88105	+	5.88105i	0.320361	+	0.320361i	−0.528544	+	0.848906i	$0.677262\pi$
$338$	18.9663	−	2.69843i	1.03163	−	0.146775i
$339$	2.24197	+	1.08241i	0.121767	+	0.0587886i
$340$		0			0
$341$	9.61657	+	5.55213i	0.520767	+	0.300665i
$342$	8.53730	+	19.6740i	0.461644	+	1.06385i
$343$	−8.48328	−	8.48328i	−0.458054	−	0.458054i
$344$	23.7840	−	13.7317i	1.28235	−	0.740365i
$345$		0			0
$346$		−	28.2246i		−	1.51736i
$347$	4.71314	+	1.26288i	0.253014	+	0.0677950i	0.383097	−	0.923708i	$-0.374858\pi$
$347$	4.71314	+	1.26288i	0.253014	+	0.0677950i	−0.130082	+	0.991503i	$0.541524\pi$
$348$	0.323510	+	0.0615435i	0.0173419	+	0.00329908i
$349$	6.13414	−	10.6246i	0.328353	−	0.568724i	−0.653832	−	0.756640i	$-0.726840\pi$
$349$	6.13414	−	10.6246i	0.328353	−	0.568724i	0.982185	+	0.187916i	$0.0601731\pi$
$350$		0			0
$351$	−10.9498	+	15.2021i	−0.584455	+	0.811426i
$352$	−2.92756	−	2.92756i	−0.156039	−	0.156039i
$353$	2.79817	+	10.4429i	0.148932	+	0.555820i	0.999549	+	0.0300349i	$0.00956184\pi$
$353$	2.79817	+	10.4429i	0.148932	+	0.555820i	−0.850617	+	0.525785i	$0.823771\pi$
$354$	−12.5121	−	18.3910i	−0.665010	−	0.977471i
$355$		0			0
$356$	−0.648882			−0.0343907
$357$	10.9048	−	12.6462i	0.577143	−	0.669310i
$358$	2.30319	−	8.59563i	0.121727	−	0.454293i
$359$			37.2979i			1.96851i	0.176755	+	0.984255i	$0.443440\pi$
$359$			37.2979i			1.96851i	−0.176755	+	0.984255i	$0.556560\pi$
$360$		0			0
$361$	−2.26687	+	3.92633i	−0.119309	+	0.206649i
$362$	7.91865	−	2.12180i	0.416195	−	0.111519i
$363$	−11.9211	+	4.15811i	−0.625695	+	0.218244i
$364$	−2.49324	+	0.509463i	−0.130681	+	0.0267031i
$365$		0			0
$366$	6.93940	−	4.72114i	0.362728	−	0.246778i
$367$	−0.634359	+	0.169976i	−0.0331133	+	0.00887268i	−0.275338	−	0.961348i	$-0.588790\pi$
$367$	−0.634359	+	0.169976i	−0.0331133	+	0.00887268i	0.242224	+	0.970220i	$0.422123\pi$
$368$	3.15230	−	11.7645i	0.164325	−	0.613269i
$369$	2.70256	−	2.14647i	0.140690	−	0.111741i
$370$		0			0
$371$	8.41857	+	14.5814i	0.437071	+	0.757028i
$372$	−0.728677	+	0.254165i	−0.0377801	+	0.0131778i
$373$	−32.4088	−	8.68391i	−1.67806	−	0.449636i	−0.710796	−	0.703398i	$-0.751665\pi$
$373$	−32.4088	−	8.68391i	−1.67806	−	0.449636i	−0.967267	+	0.253762i	$0.918332\pi$
$374$	7.38613	−	12.7932i	0.381928	−	0.661518i
$375$		0			0
$376$	−11.7336			−0.605113
$377$	−2.20209	+	3.33315i	−0.113413	+	0.171666i
$378$	16.8352	−	26.6170i	0.865909	−	1.36903i
$379$	−8.79891	+	15.2402i	−0.451969	+	0.782834i	−0.998508	−	0.0545997i	$-0.982612\pi$
$379$	−8.79891	+	15.2402i	−0.451969	+	0.782834i	0.546539	+	0.837434i	$0.315945\pi$
$380$		0			0
$381$	0.380286	+	5.14297i	0.0194827	+	0.263482i
$382$	3.14806	−	3.14806i	0.161069	−	0.161069i
$383$	−20.2110	−	5.41553i	−1.03274	−	0.276721i	−0.297635	−	0.954680i	$-0.596198\pi$
$383$	−20.2110	−	5.41553i	−1.03274	−	0.276721i	−0.735100	+	0.677959i	$0.762865\pi$
$384$	−21.6740	+	1.60264i	−1.10605	+	0.0817844i
$385$		0			0
$386$	4.46957	−	2.58051i	0.227495	−	0.131344i
$387$	24.5673	+	18.2068i	1.24883	+	0.925505i
$388$	−0.843237	+	0.225945i	−0.0428089	+	0.0114706i
$389$	9.74450			0.494066			0.247033	−	0.969007i	$-0.420544\pi$
$389$	9.74450			0.494066			0.247033	+	0.969007i	$0.420544\pi$
$390$		0			0
$391$	6.61812			0.334693
$392$	−25.8095	+	6.91564i	−1.30358	+	0.349293i
$393$	−4.45924	−	0.848313i	−0.224939	−	0.0427918i
$394$	5.92388	−	3.42015i	0.298441	−	0.172305i
$395$		0			0
$396$	0.808389	−	2.04779i	0.0406231	−	0.102906i
$397$	−2.79246	−	0.748237i	−0.140150	−	0.0375530i	0.188062	−	0.982157i	$-0.439779\pi$
$397$	−2.79246	−	0.748237i	−0.140150	−	0.0375530i	−0.328212	+	0.944604i	$0.606446\pi$
$398$	−4.73125	+	4.73125i	−0.237156	+	0.237156i
$399$	34.4653	−	2.54847i	1.72542	−	0.127583i
$400$		0			0
$401$	0.557130	−	0.964978i	0.0278218	−	0.0481887i	−0.851779	−	0.523901i	$-0.824476\pi$
$401$	0.557130	−	0.964978i	0.0278218	−	0.0481887i	0.879601	+	0.475712i	$0.157810\pi$
$402$	−14.8609	+	5.18353i	−0.741194	+	0.258531i
$403$	0.563582	−	9.34489i	0.0280740	−	0.465502i
$404$	3.36013			0.167173
$405$		0			0
$406$	3.35778	−	5.81584i	0.166644	−	0.288635i
$407$	−4.08458	−	1.09446i	−0.202465	−	0.0542504i
$408$	−3.60271	−	10.3288i	−0.178361	−	0.511351i
$409$	−6.17475	−	10.6950i	−0.305322	−	0.528833i	0.672011	−	0.740541i	$-0.265431\pi$
$409$	−6.17475	−	10.6950i	−0.305322	−	0.528833i	−0.977333	+	0.211708i	$0.932097\pi$
$410$		0			0
$411$	16.1862	+	7.81463i	0.798406	+	0.385467i
$412$	−0.733710	+	2.73824i	−0.0361473	+	0.134904i
$413$	−34.6226	+	9.27711i	−1.70367	+	0.456497i
$414$	12.3463	−	1.83589i	0.606789	−	0.0902288i
$415$		0			0
$416$	−1.10475	+	3.31111i	−0.0541649	+	0.162340i
$417$	1.11027	+	3.18308i	0.0543700	+	0.155876i
$418$	29.5310	−	7.91280i	1.44441	−	0.387028i
$419$	−9.48656	+	16.4312i	−0.463449	+	0.802717i	−0.999130	−	0.0417034i	$-0.986722\pi$
$419$	−9.48656	+	16.4312i	−0.463449	+	0.802717i	0.535681	+	0.844420i	$0.320055\pi$
$420$		0			0
$421$		−	30.3717i		−	1.48022i	−0.672484	−	0.740112i	$-0.734772\pi$
$421$		−	30.3717i		−	1.48022i	0.672484	−	0.740112i	$-0.265228\pi$
$422$	−4.63051	+	17.2813i	−0.225410	+	0.841241i
$423$	−5.20061	−	11.9847i	−0.252862	−	0.582715i
$424$	11.0299			0.535657
$425$		0			0
$426$	−18.5195	+	12.5995i	−0.897272	+	0.610447i
$427$	−3.50049	−	13.0640i	−0.169401	−	0.632212i
$428$	1.12379	+	1.12379i	0.0543203	+	0.0543203i
$429$	19.1395	+	18.6269i	0.924065	+	0.899316i
$430$		0			0
$431$	13.0681	−	22.6347i	0.629469	−	1.09027i	−0.358189	−	0.933649i	$-0.616606\pi$
$431$	13.0681	−	22.6347i	0.629469	−	1.09027i	0.987658	−	0.156624i	$-0.0500611\pi$
$432$	−10.4148	−	19.8484i	−0.501083	−	0.954958i
$433$	8.65818	+	2.31995i	0.416086	+	0.111490i	0.460787	−	0.887511i	$-0.347567\pi$
$433$	8.65818	+	2.31995i	0.416086	+	0.111490i	−0.0447016	+	0.999000i	$0.514234\pi$
$434$			15.7377i			0.755433i
$435$		0			0
$436$	−2.05343	+	1.18555i	−0.0983414	+	0.0567774i
$437$	9.68515	+	9.68515i	0.463304	+	0.463304i
$438$	−18.8627	+	21.8749i	−0.901294	+	1.04523i
$439$	−14.8493	−	8.57324i	−0.708718	−	0.409179i	0.101868	−	0.994798i	$-0.467518\pi$
$439$	−14.8493	−	8.57324i	−0.708718	−	0.409179i	−0.810586	+	0.585619i	$0.800851\pi$
$440$		0			0
$441$	−18.5031	−	23.2967i	−0.881099	−	1.10937i
$442$	−12.4317	−	0.749747i	−0.591317	−	0.0356618i
$443$	16.8516	+	16.8516i	0.800642	+	0.800642i	0.983196	−	0.182554i	$-0.0584364\pi$
$443$	16.8516	+	16.8516i	0.800642	+	0.800642i	−0.182554	+	0.983196i	$0.558436\pi$
$444$	0.242985	−	0.165312i	0.0115315	−	0.00784535i
$445$		0			0
$446$	22.2903	−	12.8693i	1.05547	−	0.609378i
$447$	5.63915	+	16.1672i	0.266723	+	0.764681i
$448$	−7.66552	+	28.6081i	−0.362162	+	1.35161i
$449$	−5.80271	+	3.35020i	−0.273847	+	0.158105i	−0.630634	−	0.776080i	$-0.717205\pi$
$449$	−5.80271	+	3.35020i	−0.273847	+	0.158105i	0.356788	+	0.934185i	$0.383872\pi$
$450$		0			0
$451$	−2.45994	−	4.26074i	−0.115834	−	0.200630i
$452$	0.0638377	+	0.238245i	0.00300267	+	0.0112061i
$453$	−34.0901	−	6.48521i	−1.60169	−	0.304702i
$454$		−	14.1354i		−	0.663407i
$455$		0			0
$456$	9.84314	−	20.3878i	0.460947	−	0.954744i
$457$	9.62717	+	35.9291i	0.450340	+	1.68069i	0.701438	+	0.712731i	$0.252542\pi$
$457$	9.62717	+	35.9291i	0.450340	+	1.68069i	−0.251097	+	0.967962i	$0.580791\pi$
$458$	7.97341	−	2.13647i	0.372573	−	0.0998306i
$459$	8.95302	−	8.25778i	0.417891	−	0.385440i
$460$		0			0
$461$	−4.19385	−	7.26397i	−0.195327	−	0.338317i	0.751681	−	0.659527i	$-0.229244\pi$
$461$	−4.19385	−	7.26397i	−0.195327	−	0.338317i	−0.947008	+	0.321211i	$0.895910\pi$
$462$	−34.0010	−	29.3189i	−1.58187	−	1.36404i
$463$	−7.19262	−	7.19262i	−0.334269	−	0.334269i	0.519936	−	0.854205i	$-0.325956\pi$
$463$	−7.19262	−	7.19262i	−0.334269	−	0.334269i	−0.854205	+	0.519936i	$0.825956\pi$
$464$	−2.38977	−	4.13921i	−0.110942	−	0.192158i
$465$		0			0
$466$	34.8048	+	20.0946i	1.61230	+	0.930863i
$467$	−20.1687	+	20.1687i	−0.933297	+	0.933297i	−0.997910	−	0.0646132i	$-0.979419\pi$
$467$	−20.1687	+	20.1687i	−0.933297	+	0.933297i	0.0646132	+	0.997910i	$0.479419\pi$
$468$	−1.84904	+	0.161984i	−0.0854721	+	0.00748770i
$469$			25.3622i			1.17112i
$470$		0			0
$471$	10.9606	−	7.45693i	0.505039	−	0.343597i
$472$	−6.07734	+	22.6810i	−0.279732	+	1.04398i
$473$	30.8232	−	30.8232i	1.41725	−	1.41725i
$474$	5.24647	−	0.387939i	0.240978	−	0.0178186i
$475$		0			0
$476$	1.65437			0.0758280
$477$	4.88870	+	11.2659i	0.223838	+	0.515831i
$478$	−6.61480	−	24.6868i	−0.302554	−	1.12915i
$479$	10.4307	+	6.02217i	0.476591	+	0.275160i	0.718995	−	0.695016i	$-0.244603\pi$
$479$	10.4307	+	6.02217i	0.476591	+	0.275160i	−0.242404	+	0.970175i	$0.577936\pi$
$480$		0			0
$481$	0.713746	+	3.49297i	0.0325440	+	0.159266i
$482$	−1.74212	+	1.74212i	−0.0793515	+	0.0793515i
$483$	3.75900	−	19.7596i	0.171040	−	0.899091i
$484$	−1.08326	−	0.625419i	−0.0492390	−	0.0284281i
$485$		0			0
$486$	14.4115	−	17.8888i	0.653717	−	0.811452i
$487$	−38.7327	−	10.3784i	−1.75515	−	0.470290i	−0.769434	−	0.638726i	$-0.779462\pi$
$487$	−38.7327	−	10.3784i	−1.75515	−	0.470290i	−0.985713	+	0.168435i	$0.946129\pi$
$488$	−8.55811	−	2.29314i	−0.387408	−	0.103806i
$489$	10.9314	+	5.27762i	0.494333	+	0.238662i
$490$		0			0
$491$	−16.8964	−	9.75516i	−0.762525	−	0.440244i	0.0676765	−	0.997707i	$-0.478441\pi$
$491$	−16.8964	−	9.75516i	−0.762525	−	0.440244i	−0.830202	+	0.557463i	$0.811775\pi$
$492$	0.335901	+	0.0639008i	0.0151436	+	0.00288087i
$493$	1.83643	−	1.83643i	0.0827088	−	0.0827088i
$494$	−17.0958	−	19.2902i	−0.769175	−	0.867906i
$495$		0			0
$496$	9.70011	+	5.60036i	0.435548	+	0.251464i
$497$	9.34191	+	34.8645i	0.419042	+	1.56389i
$498$	−16.9820	−	14.6435i	−0.760982	−	0.656192i
$499$	−7.54758			−0.337876			−0.168938	−	0.985627i	$-0.554034\pi$
$499$	−7.54758			−0.337876			−0.168938	+	0.985627i	$0.554034\pi$
$500$		0			0
$501$	3.25210	+	43.9812i	0.145293	+	1.96494i
$502$	8.19769	−	8.19769i	0.365881	−	0.365881i
$503$	8.24963	−	30.7880i	0.367833	−	1.37277i	−0.495707	−	0.868490i	$-0.665091\pi$
$503$	8.24963	−	30.7880i	0.367833	−	1.37277i	0.863540	−	0.504281i	$-0.168242\pi$
$504$	−32.8847	+	4.88991i	−1.46480	+	0.217814i
$505$		0			0
$506$		−	17.7936i		−	0.791023i
$507$	6.83594	−	21.4539i	0.303595	−	0.952801i
$508$	−0.361274	+	0.361274i	−0.0160290	+	0.0160290i
$509$	−8.77183	−	5.06442i	−0.388804	−	0.224476i	0.292838	−	0.956162i	$-0.405400\pi$
$509$	−8.77183	−	5.06442i	−0.388804	−	0.224476i	−0.681642	+	0.731686i	$0.738734\pi$
$510$		0			0
$511$	23.2726	+	40.3093i	1.02952	+	1.78318i
$512$	13.4843	+	13.4843i	0.595930	+	0.595930i
$513$	25.1868	+	1.01744i	1.11202	+	0.0449209i
$514$	−7.01724	−	12.1542i	−0.309517	−	0.536099i
$515$		0			0
$516$	0.223399	+	3.02124i	0.00983460	+	0.133003i
$517$	−17.9892	+	4.82019i	−0.791163	+	0.211992i
$518$	−1.55114	−	5.78894i	−0.0681533	−	0.254351i
$519$	−29.8745	−	14.4233i	−1.31135	−	0.633113i
$520$		0			0
$521$		−	27.9873i		−	1.22615i	−0.790026	−	0.613074i	$-0.789933\pi$
$521$		−	27.9873i		−	1.22615i	0.790026	−	0.613074i	$-0.210067\pi$
$522$	2.91650	−	3.93536i	0.127652	−	0.172246i
$523$	−4.22208	−	15.7570i	−0.184619	−	0.689007i	−0.994712	−	0.102705i	$-0.967250\pi$
$523$	−4.22208	−	15.7570i	−0.184619	−	0.689007i	0.810093	−	0.586301i	$-0.199417\pi$
$524$	−0.224856	−	0.389462i	−0.00982288	−	0.0170137i
$525$		0			0
$526$	−30.0345	+	17.3404i	−1.30956	+	0.756078i
$527$	−1.57524	+	5.87886i	−0.0686184	+	0.256087i
$528$	−30.1705	+	10.5236i	−1.31300	+	0.457980i
$529$	−13.0149	+	7.51414i	−0.565864	+	0.326702i
$530$		0			0
$531$	−25.8600	+	3.84535i	−1.12223	+	0.166874i
$532$	2.42106	+	2.42106i	0.104966	+	0.104966i
$533$	−2.28643	+	3.46081i	−0.0990364	+	0.149905i
$534$	−4.19631	+	8.69168i	−0.181592	+	0.376126i
$535$		0			0
$536$	14.3886	+	8.30725i	0.621492	+	0.358819i
$537$	−7.92112	−	6.83036i	−0.341822	−	0.294752i
$538$	12.4053	+	12.4053i	0.534829	+	0.534829i
$539$	−36.7286	+	21.2053i	−1.58201	+	0.913376i
$540$		0			0
$541$			1.73534i			0.0746081i	0.999304	+	0.0373041i	$0.0118770\pi$
$541$			1.73534i			0.0746081i	−0.999304	+	0.0373041i	$0.988123\pi$
$542$	−28.6667	−	7.68123i	−1.23134	−	0.329937i
$543$	1.80075	−	9.46582i	0.0772776	−	0.406217i
$544$	1.13462	−	1.96522i	0.0486464	−	0.0842580i
$545$		0			0
$546$	−9.29955	+	36.6913i	−0.397984	+	1.57024i
$547$	11.2029	+	11.2029i	0.479001	+	0.479001i	0.904812	−	0.425811i	$-0.140011\pi$
$547$	11.2029	+	11.2029i	0.479001	+	0.479001i	−0.425811	+	0.904812i	$0.640011\pi$
$548$	0.460885	+	1.72005i	0.0196880	+	0.0734767i
$549$	−1.45095	−	9.75765i	−0.0619251	−	0.416446i
$550$		0			0
$551$	5.37498			0.228982
$552$	−9.97884	−	8.60472i	−0.424728	−	0.366241i
$553$	2.19410	−	8.18851i	0.0933028	−	0.348211i
$554$		−	6.48371i		−	0.275466i
$555$		0			0
$556$	−0.166995	+	0.289243i	−0.00708215	+	0.0122666i
$557$	40.6785	−	10.8998i	1.72360	−	0.461838i	0.744909	−	0.667166i	$-0.232493\pi$
$557$	40.6785	−	10.8998i	1.72360	−	0.461838i	0.978693	+	0.205328i	$0.0658262\pi$
$558$	−1.30785	+	11.4042i	−0.0553655	+	0.482778i
$559$	−34.8615	−	11.6315i	−1.47448	−	0.491961i
$560$		0			0
$561$	−9.76654	−	14.3554i	−0.412344	−	0.606087i
$562$	−32.7585	+	8.77762i	−1.38184	+	0.370262i
$563$	−0.695238	+	2.59466i	−0.0293008	+	0.109352i	−0.979028	−	0.203728i	$-0.934694\pi$
$563$	−0.695238	+	2.59466i	−0.0293008	+	0.109352i	0.949727	+	0.313080i	$0.101361\pi$
$564$	0.562743	−	1.16559i	0.0236958	−	0.0490802i
$565$		0			0
$566$	10.0640	+	17.4314i	0.423022	+	0.732695i
$567$	−19.5699	−	31.4211i	−0.821857	−	1.31956i
$568$	22.8394	+	6.11980i	0.958320	+	0.256781i
$569$	5.33657	−	9.24321i	0.223721	−	0.387496i	−0.732214	−	0.681074i	$-0.761513\pi$
$569$	5.33657	−	9.24321i	0.223721	−	0.387496i	0.955935	+	0.293579i	$0.0948463\pi$
$570$		0			0
$571$	−22.6560			−0.948123			−0.474061	−	0.880492i	$-0.657213\pi$
$571$	−22.6560			−0.948123			−0.474061	+	0.880492i	$0.657213\pi$
$572$	−0.159287	+	2.64117i	−0.00666011	+	0.110433i
$573$	−1.72337	−	4.94080i	−0.0719946	−	0.206405i
$574$	3.48639	−	6.03860i	0.145519	−	0.252046i
$575$		0			0
$576$	−7.93217	+	20.0936i	−0.330507	+	0.837234i
$577$	−6.87604	+	6.87604i	−0.286253	+	0.286253i	−0.835597	−	0.549343i	$-0.814878\pi$
$577$	−6.87604	+	6.87604i	−0.286253	+	0.286253i	0.549343	+	0.835597i	$0.314878\pi$
$578$	−16.3774	−	4.38831i	−0.681209	−	0.182529i
$579$	−0.447320	−	6.04953i	−0.0185900	−	0.251410i
$580$		0			0
$581$	−31.2930	+	18.0670i	−1.29825	+	0.749547i
$582$	−2.42671	+	12.7562i	−0.100590	+	0.528762i
$583$	16.9103	−	4.53110i	0.700352	−	0.187659i
$584$	30.4913			1.26174
$585$		0			0
$586$	35.7517			1.47689
$587$	35.3085	−	9.46089i	1.45734	−	0.390493i	0.558769	−	0.829323i	$-0.311274\pi$
$587$	35.3085	−	9.46089i	1.45734	−	0.390493i	0.898570	+	0.438830i	$0.144607\pi$
$588$	0.550840	−	2.89555i	0.0227163	−	0.119410i
$589$	−10.9086	+	6.29805i	−0.449479	+	0.259507i
$590$		0			0
$591$	−0.592869	−	8.01793i	−0.0243874	−	0.329814i
$592$	−4.12007	−	1.10397i	−0.169334	−	0.0453728i
$593$	−28.7633	+	28.7633i	−1.18117	+	1.18117i	−0.201727	+	0.979442i	$0.564655\pi$
$593$	−28.7633	+	28.7633i	−1.18117	+	1.18117i	−0.979442	+	0.201727i	$0.935345\pi$
$594$	−22.2021	−	24.0713i	−0.910962	−	0.987658i
$595$		0			0
$596$	−0.848182	+	1.46909i	−0.0347429	+	0.0601764i
$597$	2.59007	+	7.42559i	0.106004	+	0.303909i
$598$	−13.4197	+	6.70509i	−0.548774	+	0.274192i
$599$	10.0471			0.410513			0.205256	−	0.978708i	$-0.434197\pi$
$599$	10.0471			0.410513			0.205256	+	0.978708i	$0.434197\pi$
$600$		0			0
$601$	−17.9309	+	31.0572i	−0.731415	+	1.26685i	0.224864	+	0.974390i	$0.427806\pi$
$601$	−17.9309	+	31.0572i	−0.731415	+	1.26685i	−0.956279	+	0.292458i	$0.905527\pi$
$602$	59.6743	+	15.9897i	2.43214	+	0.651691i
$603$	−2.10767	+	18.3785i	−0.0858308	+	0.748430i
$604$	−1.71899	−	2.97737i	−0.0699446	−	0.121148i
$605$		0			0
$606$	21.7299	−	45.0084i	0.882717	−	1.82834i
$607$	2.93149	−	10.9405i	0.118985	−	0.444060i	−0.880569	−	0.473919i	$-0.842839\pi$
$607$	2.93149	−	10.9405i	0.118985	−	0.444060i	0.999554	+	0.0298588i	$0.00950577\pi$
$608$	4.53639	−	1.21552i	0.183975	−	0.0492960i
$609$	−4.43993	−	6.52606i	−0.179915	−	0.264449i
$610$		0			0
$611$	10.4141	+	11.7509i	0.421310	+	0.475389i
$612$	1.19883	+	0.137483i	0.0484597	+	0.00555741i
$613$	19.2626	−	5.16141i	0.778011	−	0.208467i	0.152103	−	0.988365i	$-0.451395\pi$
$613$	19.2626	−	5.16141i	0.778011	−	0.208467i	0.625908	+	0.779897i	$0.284729\pi$
$614$	−13.4369	+	23.2734i	−0.542270	+	0.939239i
$615$		0			0
$616$			47.3936i			1.90954i
$617$	4.81611	−	17.9740i	0.193889	−	0.723605i	−0.798662	−	0.601780i	$-0.794459\pi$
$617$	4.81611	−	17.9740i	0.193889	−	0.723605i	0.992552	−	0.121825i	$-0.0388748\pi$
$618$	31.9335	+	27.5361i	1.28455	+	1.10767i
$619$	36.0310			1.44821			0.724104	−	0.689691i	$-0.242254\pi$
$619$	36.0310			1.44821			0.724104	+	0.689691i	$0.242254\pi$
$620$		0			0
$621$	4.36600	−	14.0062i	0.175202	−	0.562051i
$622$	3.20182	+	11.9493i	0.128381	+	0.479125i
$623$	10.9976	+	10.9976i	0.440608	+	0.440608i
$624$	19.3058	+	18.7887i	0.772850	+	0.752151i
$625$		0			0
$626$	0.464527	−	0.804584i	0.0185662	−	0.0321576i
$627$	6.71553	−	35.3008i	0.268192	−	1.40978i
$628$	1.26863	+	0.339928i	0.0506238	+	0.0135646i
$629$		−	2.31773i		−	0.0924141i
$630$		0			0
$631$	28.1867	−	16.2736i	1.12209	−	0.647841i	0.180159	−	0.983637i	$-0.442339\pi$
$631$	28.1867	−	16.2736i	1.12209	−	0.647841i	0.941935	+	0.335796i	$0.109005\pi$
$632$	−3.92688	−	3.92688i	−0.156203	−	0.156203i
$633$	15.9252	+	13.7323i	0.632971	+	0.545809i
$634$	22.7117	+	13.1126i	0.901998	+	0.520769i
$635$		0			0
$636$	−0.528993	+	1.09568i	−0.0209759	+	0.0434467i
$637$	29.8330	+	19.7096i	1.18203	+	0.780923i
$638$	−4.93748	−	4.93748i	−0.195477	−	0.195477i
$639$	3.87221	+	26.0406i	0.153182	+	1.03015i
$640$		0			0
$641$	−5.53230	+	3.19407i	−0.218513	+	0.126158i	−0.605261	−	0.796027i	$-0.706931\pi$
$641$	−5.53230	+	3.19407i	−0.218513	+	0.126158i	0.386749	+	0.922185i	$0.373598\pi$
$642$	22.3205	−	7.78545i	0.880919	−	0.307267i
$643$	−8.33296	+	31.0990i	−0.328620	+	1.22643i	0.582003	+	0.813187i	$0.302269\pi$
$643$	−8.33296	+	31.0990i	−0.328620	+	1.22643i	−0.910623	+	0.413239i	$0.864398\pi$
$644$	1.72576	−	0.996370i	0.0680046	−	0.0392625i
$645$		0			0
$646$	8.37845	+	14.5119i	0.329646	+	0.570963i
$647$	−4.45875	−	16.6403i	−0.175291	−	0.654196i	−0.996502	−	0.0835709i	$-0.973367\pi$
$647$	−4.45875	−	16.6403i	−0.175291	−	0.654196i	0.821210	−	0.570625i	$-0.193299\pi$
$648$	−24.2360	+	0.810632i	−0.952080	+	0.0318446i
$649$			37.2696i			1.46296i
$650$		0			0
$651$	16.6577	+	8.04226i	0.652865	+	0.315201i
$652$	0.311259	+	1.16163i	0.0121898	+	0.0454931i
$653$	−22.6354	+	6.06514i	−0.885791	+	0.237347i	−0.672904	−	0.739730i	$-0.734953\pi$
$653$	−22.6354	+	6.06514i	−0.885791	+	0.237347i	−0.212887	+	0.977077i	$0.568287\pi$
$654$	2.60074	+	35.1723i	0.101697	+	1.37535i
$655$		0			0
$656$	−2.48131	−	4.29775i	−0.0968789	−	0.167799i
$657$	13.5145	+	31.1438i	0.527250	+	1.21504i
$658$	−18.6640	−	18.6640i	−0.727597	−	0.727597i
$659$	−6.20035	−	10.7393i	−0.241532	−	0.418345i	0.719619	−	0.694369i	$-0.244316\pi$
$659$	−6.20035	−	10.7393i	−0.241532	−	0.418345i	−0.961151	+	0.276024i	$0.910983\pi$
$660$		0			0
$661$	−19.8030	−	11.4332i	−0.770246	−	0.444702i	0.0627164	−	0.998031i	$-0.480024\pi$
$661$	−19.8030	−	11.4332i	−0.770246	−	0.444702i	−0.832962	+	0.553330i	$0.813357\pi$
$662$	−14.7782	+	14.7782i	−0.574370	+	0.574370i
$663$	−7.14642	+	12.7753i	−0.277544	+	0.496152i
$664$			23.6711i			0.918616i
$665$		0			0
$666$	−0.642947	−	4.32382i	−0.0249137	−	0.167545i
$667$	0.809663	−	3.02170i	0.0313503	−	0.117001i
$668$	−3.08951	+	3.08951i	−0.119537	+	0.119537i
$669$	−2.23084	−	30.1697i	−0.0862491	−	1.16643i
$670$		0			0
$671$	−14.0628			−0.542888
$672$	−5.22305	−	4.50382i	−0.201484	−	0.173739i
$673$	−1.81967	−	6.79109i	−0.0701431	−	0.261777i	0.921945	−	0.387321i	$-0.126599\pi$
$673$	−1.81967	−	6.79109i	−0.0701431	−	0.261777i	−0.992088	+	0.125543i	$0.959933\pi$
$674$	10.6143	+	6.12816i	0.408847	+	0.236048i
$675$		0			0
$676$	2.05196	−	0.875128i	0.0789217	−	0.0336588i
$677$	−26.7622	+	26.7622i	−1.02856	+	1.02856i	−0.0289760	+	0.999580i	$0.509225\pi$
$677$	−26.7622	+	26.7622i	−1.02856	+	1.02856i	−0.999580	+	0.0289760i	$0.990775\pi$
$678$	3.60410	+	0.685634i	0.138415	+	0.0263316i
$679$	18.1210	+	10.4622i	0.695420	+	0.401501i
$680$		0			0
$681$	−14.9617	−	7.22346i	−0.573334	−	0.276804i
$682$	15.8060	+	4.23522i	0.605245	+	0.162175i
$683$	−9.97129	−	2.67180i	−0.381541	−	0.102234i	0.0629506	−	0.998017i	$-0.479949\pi$
$683$	−9.97129	−	2.67180i	−0.381541	−	0.102234i	−0.444491	+	0.895783i	$0.646616\pi$
$684$	1.55320	+	1.95560i	0.0593883	+	0.0747741i
$685$		0			0
$686$	−15.3108	−	8.83972i	−0.584571	−	0.337502i
$687$	1.81320	−	9.53128i	0.0691780	−	0.363641i
$688$	31.0909	−	31.0909i	1.18533	−	1.18533i
$689$	−9.78953	−	11.0461i	−0.372951	−	0.420823i
$690$		0			0
$691$	−21.8645	−	12.6235i	−0.831765	−	0.480220i	0.0226915	−	0.999743i	$-0.492776\pi$
$691$	−21.8645	−	12.6235i	−0.831765	−	0.480220i	−0.854457	+	0.519523i	$0.826110\pi$
$692$	−0.850645	−	3.17465i	−0.0323367	−	0.120682i
$693$	−48.4079	+	21.0060i	−1.83887	+	0.797953i
$694$	7.19045			0.272946
$695$		0			0
$696$	−5.15667	+	0.381299i	−0.195463	+	0.0144531i
$697$	1.90677	−	1.90677i	0.0722242	−	0.0722242i
$698$	4.67918	−	17.4629i	0.177110	−	0.660982i
$699$	39.0551	−	26.5707i	1.47720	−	1.00499i
$700$		0			0
$701$		−	5.83428i		−	0.220358i	−0.993912	−	0.110179i	$-0.964858\pi$
$701$		−	5.83428i		−	0.220358i	0.993912	−	0.110179i	$-0.0351424\pi$
$702$	−9.78800	+	25.8152i	−0.369424	+	0.974333i
$703$	3.39184	−	3.39184i	0.127926	−	0.127926i
$704$	26.6695	+	15.3976i	1.00514	+	0.580320i
$705$		0			0
$706$	7.96595	+	13.7974i	0.299803	+	0.519273i
$707$	−56.9490	−	56.9490i	−2.14179	−	2.14179i
$708$	−1.96161	−	1.69149i	−0.0737220	−	0.0635702i
$709$	−9.66759	−	16.7448i	−0.363074	−	0.628863i	0.625391	−	0.780311i	$-0.284939\pi$
$709$	−9.66759	−	16.7448i	−0.363074	−	0.628863i	−0.988465	+	0.151449i	$0.951606\pi$
$710$		0			0
$711$	2.27043	−	5.75141i	0.0851478	−	0.215695i
$712$	9.84138	−	2.63699i	0.368821	−	0.0988254i
$713$	1.89742	+	7.08126i	0.0710589	+	0.265195i
$714$	10.6988	−	22.1601i	0.400393	−	0.829320i
$715$		0			0
$716$		−	1.03624i		−	0.0387259i
$717$	−29.5101	−	5.61392i	−1.10208	−	0.209656i
$718$	14.2256	+	53.0907i	0.530895	+	1.98133i
$719$	−19.2268	−	33.3018i	−0.717038	−	1.24195i	−0.962168	−	0.272456i	$-0.912164\pi$
$719$	−19.2268	−	33.3018i	−0.717038	−	1.24195i	0.245130	−	0.969490i	$-0.421169\pi$
$720$		0			0
$721$	58.8443	−	33.9738i	2.19148	−	1.26525i
$722$	−1.72919	+	6.45341i	−0.0643537	+	0.240171i
$723$	0.953703	+	2.73422i	0.0354686	+	0.101687i
$724$	0.826728	−	0.477312i	0.0307251	−	0.0177391i
$725$		0			0
$726$	−15.3828	+	10.4655i	−0.570910	+	0.388411i
$727$	−24.8141	−	24.8141i	−0.920304	−	0.920304i	0.0767466	−	0.997051i	$-0.475547\pi$
$727$	−24.8141	−	24.8141i	−0.920304	−	0.920304i	−0.997051	+	0.0767466i	$0.975547\pi$
$728$	35.7437	−	17.8591i	1.32475	−	0.661904i
$729$	−11.5700	−	24.3954i	−0.428518	−	0.903533i
$730$		0			0
$731$	20.6911	+	11.9460i	0.765287	+	0.441838i
$732$	0.638244	−	0.740168i	0.0235902	−	0.0273574i
$733$	−28.6087	−	28.6087i	−1.05668	−	1.05668i	−0.998294	−	0.0583912i	$-0.981403\pi$
$733$	−28.6087	−	28.6087i	−1.05668	−	1.05668i	−0.0583912	−	0.998294i	$-0.518597\pi$
$734$	−0.838131	+	0.483895i	−0.0309360	+	0.0178609i
$735$		0			0
$736$		−	2.73337i		−	0.100753i
$737$	25.4723	+	6.82529i	0.938285	+	0.251413i
$738$	3.02821	−	4.08610i	0.111470	−	0.150411i
$739$	7.80807	−	13.5240i	0.287225	−	0.497488i	−0.685922	−	0.727675i	$-0.740601\pi$
$739$	7.80807	−	13.5240i	0.287225	−	0.497488i	0.973146	+	0.230188i	$0.0739340\pi$
$740$		0			0
$741$	−29.1541	+	8.23748i	−1.07100	+	0.302611i
$742$	17.5446	+	17.5446i	0.644082	+	0.644082i
$743$	−2.10721	−	7.86421i	−0.0773060	−	0.288510i	0.916440	−	0.400171i	$-0.131049\pi$
$743$	−2.10721	−	7.86421i	−0.0773060	−	0.288510i	−0.993746	+	0.111661i	$0.964383\pi$
$744$	10.0187	−	6.81610i	0.367304	−	0.249890i
$745$		0			0
$746$	−49.4434			−1.81025
$747$	−24.1777	+	10.4916i	−0.884615	+	0.383868i
$748$	0.445213	−	1.66156i	0.0162786	−	0.0607525i
$749$		−	38.0930i		−	1.39189i
$750$		0			0
$751$	−5.93245	+	10.2753i	−0.216478	+	0.374951i	−0.953729	−	0.300668i	$-0.902790\pi$
$751$	−5.93245	+	10.2753i	−0.216478	+	0.374951i	0.737251	+	0.675619i	$0.236124\pi$
$752$	−18.1454	+	4.86206i	−0.661696	+	0.177301i
$753$	−4.48772	−	12.8661i	−0.163542	−	0.468866i
$754$	−1.86322	+	5.58436i	−0.0678545	+	0.203370i
$755$		0			0
$756$	1.09140	−	3.50122i	0.0396937	−	0.127338i
$757$	8.51775	−	2.28233i	0.309583	−	0.0829525i	−0.100683	−	0.994919i	$-0.532103\pi$
$757$	8.51775	−	2.28233i	0.309583	−	0.0829525i	0.410266	+	0.911966i	$0.365436\pi$
$758$	−6.71189	+	25.0491i	−0.243787	+	0.909825i
$759$	−18.8338	−	9.09288i	−0.683623	−	0.330051i
$760$		0			0
$761$	−6.00928	−	10.4084i	−0.217836	−	0.377304i	0.736310	−	0.676645i	$-0.236567\pi$
$761$	−6.00928	−	10.4084i	−0.217836	−	0.377304i	−0.954146	+	0.299341i	$0.903233\pi$
$762$	2.50286	+	7.17558i	0.0906691	+	0.259944i
$763$	54.8957	+	14.7093i	1.98736	+	0.532511i
$764$	0.259210	−	0.448965i	0.00937790	−	0.0162430i
$765$		0			0
$766$	−30.8343			−1.11409
$767$	28.1083	−	14.0441i	1.01493	−	0.507105i
$768$	−6.68711	+	2.33248i	−0.241300	+	0.0841662i
$769$	−6.86300	+	11.8871i	−0.247486	+	0.428658i	−0.962828	−	0.270117i	$-0.912938\pi$
$769$	−6.86300	+	11.8871i	−0.247486	+	0.428658i	0.715342	+	0.698775i	$0.246271\pi$
$770$		0			0
$771$	−16.4506	+	1.21641i	−0.592455	+	0.0438079i
$772$	0.424956	−	0.424956i	0.0152945	−	0.0152945i
$773$	−20.8420	−	5.58461i	−0.749636	−	0.200864i	−0.136279	−	0.990670i	$-0.543514\pi$
$773$	−20.8420	−	5.58461i	−0.749636	−	0.200864i	−0.613357	+	0.789806i	$0.710181\pi$
$774$	41.9138	+	16.5459i	1.50656	+	0.594730i
$775$		0			0
$776$	11.8709	−	6.85366i	0.426140	−	0.246032i
$777$	−6.92000	−	1.31644i	−0.248254	−	0.0472271i
$778$	13.8705	−	3.71660i	0.497283	−	0.133247i
$779$	5.58086			0.199955
$780$		0			0
$781$	37.5300			1.34293
$782$	9.42037	−	2.52418i	0.336872	−	0.0902645i
$783$	−2.67503	−	5.09803i	−0.0955976	−	0.182189i
$784$	−37.0477	+	21.3895i	−1.32313	+	0.763910i
$785$		0			0
$786$	−6.67093	+	0.493268i	−0.237944	+	0.0175943i
$787$	−16.6307	−	4.45618i	−0.592820	−	0.158846i	−0.0500781	−	0.998745i	$-0.515947\pi$
$787$	−16.6307	−	4.45618i	−0.592820	−	0.158846i	−0.542742	+	0.839900i	$0.682614\pi$
$788$	0.563229	−	0.563229i	0.0200642	−	0.0200642i
$789$	3.00589	+	40.6515i	0.107012	+	1.44723i
$790$		0			0
$791$	2.95595	−	5.11985i	0.105101	−	0.182041i
$792$	−3.93854	+	34.3435i	−0.139950	+	1.22034i
$793$	5.29922	+	10.6060i	0.188181	+	0.376630i
$794$	−4.26023			−0.151190
$795$		0			0
$796$	−0.389570	+	0.674755i	−0.0138080	+	0.0239161i
$797$	−44.6186	−	11.9555i	−1.58047	−	0.423486i	−0.641400	−	0.767207i	$-0.721646\pi$
$797$	−44.6186	−	11.9555i	−1.58047	−	0.423486i	−0.939072	+	0.343721i	$0.888313\pi$
$798$	48.0867	−	16.7728i	1.70225	−	0.593750i
$799$	−5.10384	−	8.84011i	−0.180561	−	0.312741i
$800$		0			0
$801$	7.05537	+	8.88323i	0.249289	+	0.313873i
$802$	0.424984	−	1.58606i	0.0150067	−	0.0560058i
$803$	46.7473	−	12.5259i	1.64968	−	0.442030i
$804$	−1.51530	+	1.03092i	−0.0534407	+	0.0363577i
$805$		0			0
$806$	−2.76197	−	13.5167i	−0.0972863	−	0.476105i
$807$	19.4698	−	6.79111i	0.685368	−	0.239058i
$808$	−50.9620	+	13.6552i	−1.79284	+	0.480389i
$809$	−6.99405	+	12.1140i	−0.245898	+	0.425907i	−0.962384	−	0.271694i	$-0.912416\pi$
$809$	−6.99405	+	12.1140i	−0.245898	+	0.425907i	0.716486	+	0.697602i	$0.245749\pi$
$810$		0			0
$811$		−	19.5998i		−	0.688243i	−0.938925	−	0.344122i	$-0.888177\pi$
$811$		−	19.5998i		−	0.688243i	0.938925	−	0.344122i	$-0.111823\pi$
$812$	0.202396	−	0.755353i	0.00710272	−	0.0265077i
$813$	−22.7795	+	26.4172i	−0.798912	+	0.926493i
$814$	−6.23152			−0.218415
$815$		0			0
$816$	−9.85138	−	14.4801i	−0.344867	−	0.506906i
$817$	12.7978	+	47.7621i	0.447738	+	1.67098i
$818$	−12.8684	−	12.8684i	−0.449933	−	0.449933i
$819$	34.0839	+	28.5931i	1.19099	+	0.999124i
$820$		0			0
$821$	−4.61577	+	7.99475i	−0.161091	+	0.279019i	−0.935260	−	0.353960i	$-0.884835\pi$
$821$	−4.61577	+	7.99475i	−0.161091	+	0.279019i	0.774169	+	0.632979i	$0.218168\pi$
$822$	26.0203	+	4.95003i	0.907562	+	0.172652i
$823$	44.5620	+	11.9403i	1.55333	+	0.416214i	0.930545	−	0.366177i	$-0.119333\pi$
$823$	44.5620	+	11.9403i	1.55333	+	0.416214i	0.622788	+	0.782391i	$0.286000\pi$
$824$		−	44.5118i		−	1.55064i
$825$		0			0
$826$	−45.7443	+	26.4105i	−1.59165	+	0.918938i
$827$	−31.7914	−	31.7914i	−1.10549	−	1.10549i	−0.993735	−	0.111759i	$-0.964351\pi$
$827$	−31.7914	−	31.7914i	−1.10549	−	1.10549i	−0.111759	−	0.993735i	$-0.535649\pi$
$828$	1.33336	−	0.578596i	0.0463376	−	0.0201076i
$829$	−21.8064	−	12.5900i	−0.757369	−	0.437267i	0.0709813	−	0.997478i	$-0.477387\pi$
$829$	−21.8064	−	12.5900i	−0.757369	−	0.437267i	−0.828350	+	0.560210i	$0.810720\pi$
$830$		0			0
$831$	−6.86273	−	3.31330i	−0.238065	−	0.114937i
$832$	1.56297	−	25.9160i	0.0541863	−	0.898477i
$833$	−16.4368	−	16.4368i	−0.569503	−	0.569503i
$834$	2.79442	+	4.10740i	0.0967628	+	0.142228i
$835$		0			0
$836$	3.08311	−	1.78003i	0.106632	−	0.0615638i
$837$	11.4025	+	7.21206i	0.394129	+	0.249285i
$838$	−7.23644	+	27.0068i	−0.249979	+	0.932933i
$839$	−39.9358	+	23.0569i	−1.37874	+	0.796014i	−0.992008	−	0.126179i	$-0.959729\pi$
$839$	−39.9358	+	23.0569i	−1.37874	+	0.796014i	−0.386730	+	0.922193i	$0.626395\pi$
$840$		0			0
$841$	13.8862	+	24.0516i	0.478834	+	0.829365i
$842$	−11.5839	−	43.2317i	−0.399207	−	1.48986i
$843$	−7.44950	+	39.1590i	−0.256574	+	1.34871i
$844$			2.08333i			0.0717110i
$845$		0			0
$846$	−11.9737	−	15.0757i	−0.411663	−	0.518314i
$847$	7.75966	+	28.9595i	0.266625	+	0.995059i
$848$	17.0572	−	4.57046i	0.585746	−	0.156950i
$849$	23.5932	−	1.74455i	0.809718	−	0.0598729i
$850$		0			0
$851$	−1.39589	−	2.41775i	−0.0478505	−	0.0828795i
$852$	−1.70331	+	1.97532i	−0.0583544	+	0.0676732i
$853$	−29.1777	−	29.1777i	−0.999026	−	0.999026i	0.000973237	−	1.00000i	$-0.499690\pi$
$853$	−29.1777	−	29.1777i	−0.999026	−	0.999026i	−1.00000		0.000973237i	$0.999690\pi$
$854$	−9.96536	−	17.2605i	−0.341008	−	0.590642i
$855$		0			0
$856$	−21.6111	−	12.4772i	−0.738652	−	0.426461i
$857$	27.5270	−	27.5270i	0.940305	−	0.940305i	−0.0580111	−	0.998316i	$-0.518476\pi$
$857$	27.5270	−	27.5270i	0.940305	−	0.940305i	0.998316	+	0.0580111i	$0.0184759\pi$
$858$	34.3480	+	19.2140i	1.17262	+	0.655957i
$859$		−	40.5927i		−	1.38500i	−0.721416	−	0.692502i	$-0.756508\pi$
$859$		−	40.5927i		−	1.38500i	0.721416	−	0.692502i	$-0.243492\pi$
$860$		0			0
$861$	−4.60999	−	6.77603i	−0.157108	−	0.230926i
$862$	9.96849	−	37.2029i	0.339528	−	1.26714i
$863$	−28.4894	+	28.4894i	−0.969792	+	0.969792i	−0.999557	−	0.0297651i	$-0.990524\pi$
$863$	−28.4894	+	28.4894i	−0.969792	+	0.969792i	0.0297651	+	0.999557i	$0.490524\pi$
$864$	−3.41057	−	3.69771i	−0.116030	−	0.125799i
$865$		0			0
$866$	13.2091			0.448863
$867$	−13.0140	+	15.0922i	−0.441978	+	0.512559i
$868$	0.474310	+	1.77015i	0.0160991	+	0.0600827i
$869$	−7.63362	−	4.40727i	−0.258953	−	0.149506i
$870$		0			0
$871$	−4.45107	−	21.7829i	−0.150819	−	0.738084i
$872$	26.3258	−	26.3258i	0.891503	−	0.891503i
$873$	12.2618	+	9.08723i	0.414999	+	0.307556i
$874$	17.4800	+	10.0921i	0.591270	+	0.341370i
$875$		0			0
$876$	−1.46236	+	3.02895i	−0.0494087	+	0.102339i
$877$	17.0059	+	4.55671i	0.574248	+	0.153869i	0.534244	−	0.845330i	$-0.320596\pi$
$877$	17.0059	+	4.55671i	0.574248	+	0.153869i	0.0400039	+	0.999200i	$0.487263\pi$
$878$	−24.4067	−	6.53975i	−0.823686	−	0.220706i
$879$	18.2698	−	37.8416i	0.616225	−	1.27637i
$880$		0			0
$881$	34.8199	+	20.1033i	1.17311	+	0.677297i	0.954411	−	0.298495i	$-0.0964847\pi$
$881$	34.8199	+	20.1033i	1.17311	+	0.677297i	0.218701	+	0.975792i	$0.429818\pi$
$882$	−35.2232	−	26.1039i	−1.18603	−	0.878964i
$883$	1.83119	−	1.83119i	0.0616243	−	0.0616243i	−0.675623	−	0.737247i	$-0.736125\pi$
$883$	1.83119	−	1.83119i	0.0616243	−	0.0616243i	0.737247	+	0.675623i	$0.236125\pi$
$884$	−1.42089	+	0.290343i	−0.0477899	+	0.00976528i
$885$		0			0
$886$	30.4142	+	17.5596i	1.02178	+	0.589927i
$887$	10.1790	+	37.9885i	0.341777	+	1.27553i	0.896333	+	0.443381i	$0.146221\pi$
$887$	10.1790	+	37.9885i	0.341777	+	1.27553i	−0.554557	+	0.832146i	$0.687112\pi$
$888$	−3.01346	+	3.49470i	−0.101125	+	0.117274i
$889$	12.2461			0.410721
$890$		0			0
$891$	−36.8241	+	11.1990i	−1.23365	+	0.375182i
$892$	2.11931	−	2.11931i	0.0709597	−	0.0709597i
$893$	5.46777	−	20.4060i	0.182972	−	0.682861i
$894$	14.1931	+	20.8619i	0.474689	+	0.697726i
$895$		0			0
$896$			51.6087i			1.72413i
$897$	0.239305	+	17.6306i	0.00799018	+	0.588670i
$898$	−6.98192	+	6.98192i	−0.232990	+	0.232990i
$899$	2.49146	+	1.43844i	0.0830948	+	0.0479748i
$900$		0			0
$901$	4.79774	+	8.30993i	0.159836	+	0.276844i
$902$	−5.12660	−	5.12660i	−0.170697	−	0.170697i
$903$	47.4191	−	54.9917i	1.57801	−	1.83001i
$904$	−1.93641	−	3.35396i	−0.0644041	−	0.111551i
$905$		0			0
$906$	−50.9981	+	3.77095i	−1.69430	+	0.125281i
$907$	45.1184	−	12.0894i	1.49813	−	0.401423i	0.585658	−	0.810559i	$-0.300836\pi$
$907$	45.1184	−	12.0894i	1.49813	−	0.401423i	0.912474	+	0.409135i	$0.134170\pi$
$908$	−0.426019	−	1.58993i	−0.0141379	−	0.0527635i
$909$	−36.5351	−	46.0003i	−1.21179	−	1.52573i
$910$		0			0
$911$			17.5547i			0.581613i	0.956782	+	0.290807i	$0.0939236\pi$
$911$			17.5547i			0.581613i	−0.956782	+	0.290807i	$0.906076\pi$
$912$	6.77387	−	35.6075i	0.224305	−	1.17908i
$913$	9.72415	+	36.2910i	0.321822	+	1.20106i
$914$	27.4071	+	47.4704i	0.906545	+	1.57018i
$915$		0			0
$916$	0.832445	−	0.480612i	0.0275048	−	0.0158799i
$917$	−2.78982	+	10.4118i	−0.0921281	+	0.343827i
$918$	9.59437	−	15.1690i	0.316661	−	0.500653i
$919$	28.1500	−	16.2524i	0.928583	−	0.536118i	0.0422199	−	0.999108i	$-0.486557\pi$
$919$	28.1500	−	16.2524i	0.928583	−	0.536118i	0.886363	+	0.462991i	$0.153224\pi$
$920$		0			0
$921$	17.7674	+	26.1155i	0.585455	+	0.860536i
$922$	−8.74013	−	8.74013i	−0.287841	−	0.287841i
$923$	−14.1423	−	28.3047i	−0.465498	−	0.931659i
$924$	−4.70800	−	2.27300i	−0.154882	−	0.0747763i
$925$		0			0
$926$	−12.9814	−	7.49483i	−0.426596	−	0.246295i
$927$	45.4644	−	19.7287i	1.49325	−	0.647976i
$928$	−0.758470	−	0.758470i	−0.0248980	−	0.0248980i
$929$	−22.2780	+	12.8622i	−0.730916	+	0.421995i	−0.818757	−	0.574140i	$-0.805337\pi$
$929$	−22.2780	+	12.8622i	−0.730916	+	0.421995i	0.0878410	+	0.996135i	$0.472003\pi$
$930$		0			0
$931$		−	48.1084i		−	1.57669i
$932$	4.52040	+	1.21124i	0.148071	+	0.0396754i
$933$	14.2841	+	2.71736i	0.467639	+	0.0889623i
$934$	−21.0162	+	36.4010i	−0.687670	+	1.19108i
$935$		0			0
$936$	27.3856	−	9.97109i	0.895126	−	0.325915i
$937$	−19.2546	−	19.2546i	−0.629022	−	0.629022i	0.318800	−	0.947822i	$-0.396720\pi$
$937$	−19.2546	−	19.2546i	−0.629022	−	0.629022i	−0.947822	+	0.318800i	$0.896720\pi$
$938$	9.67325	+	36.1010i	0.315843	+	1.17874i
$939$	−0.614235	−	0.902839i	−0.0200448	−	0.0294630i
$940$		0			0
$941$	−27.3108			−0.890306			−0.445153	−	0.895455i	$-0.646851\pi$
$941$	−27.3108			−0.890306			−0.445153	+	0.895455i	$0.646851\pi$
$942$	12.7575	−	14.7948i	0.415662	−	0.482040i
$943$	0.840675	−	3.13744i	0.0273761	−	0.102169i
$944$			37.5934i			1.22356i
$945$		0			0
$946$	32.1183	−	55.6305i	1.04426	−	1.80870i
$947$	2.70642	−	0.725183i	0.0879469	−	0.0235653i	−0.214577	−	0.976707i	$-0.568837\pi$
$947$	2.70642	−	0.725183i	0.0879469	−	0.0235653i	0.302524	+	0.953142i	$0.402171\pi$
$948$	0.578422	−	0.201755i	0.0187863	−	0.00655271i
$949$	−27.0625	−	30.5362i	−0.878485	−	0.991247i
$950$		0			0
$951$	25.4853	−	17.3386i	0.826416	−	0.562242i
$952$	−25.0913	+	6.72320i	−0.813215	+	0.217900i
$953$	−0.742295	+	2.77028i	−0.0240453	+	0.0897382i	−0.976906	−	0.213671i	$-0.931458\pi$
$953$	−0.742295	+	2.77028i	−0.0240453	+	0.0897382i	0.952860	+	0.303409i	$0.0981248\pi$
$954$	11.2556	+	14.1716i	0.364412	+	0.458821i
$955$		0			0
$956$	−1.48804	−	2.57736i	−0.0481267	−	0.0833579i
$957$	−7.74925	+	2.70296i	−0.250498	+	0.0873743i
$958$	17.1442	+	4.59377i	0.553903	+	0.148418i
$959$	21.3409	−	36.9634i	0.689132	−	1.19361i
$960$		0			0
$961$	24.2581			0.782519
$962$	2.34820	+	4.69974i	0.0757089	+	0.151526i
$963$	3.16563	−	27.6038i	0.102011	−	0.889519i
$964$	−0.143446	+	0.248456i	−0.00462008	+	0.00800222i
$965$		0			0
$966$	−2.18574	−	29.5599i	−0.0703251	−	0.951073i
$967$	34.7663	−	34.7663i	1.11801	−	1.11801i	0.125975	−	0.992033i	$-0.459794\pi$
$967$	34.7663	−	34.7663i	1.11801	−	1.11801i	0.992033	−	0.125975i	$-0.0402058\pi$
$968$	18.9711	+	5.08328i	0.609753	+	0.163383i
$969$	19.6418	−	1.45237i	0.630984	−	0.0466568i
$970$		0			0
$971$	43.8854	−	25.3373i	1.40835	−	0.813112i	0.413121	−	0.910676i	$-0.364439\pi$
$971$	43.8854	−	25.3373i	1.40835	−	0.813112i	0.995229	+	0.0975644i	$0.0311052\pi$
$972$	1.08183	−	2.44644i	0.0346998	−	0.0784695i
$973$	7.73254	−	2.07193i	0.247894	−	0.0664229i
$974$	−59.0914			−1.89341
$975$		0			0
$976$	−14.1850			−0.454050
$977$	10.0876	−	2.70297i	0.322731	−	0.0864755i	−0.0938164	−	0.995590i	$-0.529907\pi$
$977$	10.0876	−	2.70297i	0.322731	−	0.0864755i	0.416547	+	0.909114i	$0.363240\pi$
$978$	17.5728	+	3.34301i	0.561917	+	0.106898i
$979$	14.0049	−	8.08574i	0.447599	−	0.258421i
$980$		0			0
$981$	38.5574	+	15.2209i	1.23104	+	0.485967i
$982$	−27.7714	−	7.44133i	−0.886221	−	0.237462i
$983$	15.8387	−	15.8387i	0.505176	−	0.505176i	−0.407866	−	0.913042i	$-0.633727\pi$
$983$	15.8387	−	15.8387i	0.505176	−	0.505176i	0.913042	+	0.407866i	$0.133727\pi$
$984$	−5.35419	+	0.395904i	−0.170685	+	0.0126210i
$985$		0			0
$986$	1.91359	−	3.31444i	0.0609413	−	0.105553i
$987$	−29.2926	+	10.2174i	−0.932395	+	0.325222i
$988$	−2.50428	−	1.65448i	−0.0796717	−	0.0526361i
$989$	28.7786			0.915107
$990$		0			0
$991$	12.4412	−	21.5489i	0.395209	−	0.684523i	−0.597919	−	0.801557i	$-0.704005\pi$
$991$	12.4412	−	21.5489i	0.395209	−	0.684523i	0.993128	+	0.117034i	$0.0373387\pi$
$992$	2.42804	+	0.650592i	0.0770905	+	0.0206563i
$993$	8.09012	+	23.1940i	0.256732	+	0.736038i
$994$	26.5950	+	46.0638i	0.843541	+	1.46106i
$995$		0			0
$996$	−2.35144	−	1.13527i	−0.0745082	−	0.0359723i
$997$	13.3731	−	49.9090i	0.423529	−	1.58063i	−0.343585	−	0.939122i	$-0.611641\pi$
$997$	13.3731	−	49.9090i	0.423529	−	1.58063i	0.767114	−	0.641511i	$-0.221692\pi$
$998$	−10.7434	+	2.87868i	−0.340076	+	0.0911231i
$999$	−4.90513	−	1.52902i	−0.155191	−	0.0483761i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bn.d.407.18		96
3.2	odd	2	inner	975.2.bn.d.407.7		96
5.2	odd	4		195.2.bf.a.173.18	yes	96
5.3	odd	4	inner	975.2.bn.d.368.7		96
5.4	even	2		195.2.bf.a.17.7	✓	96
13.10	even	6	inner	975.2.bn.d.257.18		96
15.2	even	4		195.2.bf.a.173.7	yes	96
15.8	even	4	inner	975.2.bn.d.368.18		96
15.14	odd	2		195.2.bf.a.17.18	yes	96
39.23	odd	6	inner	975.2.bn.d.257.7		96
65.23	odd	12	inner	975.2.bn.d.218.7		96
65.49	even	6		195.2.bf.a.62.7	yes	96
65.62	odd	12		195.2.bf.a.23.18	yes	96
195.23	even	12	inner	975.2.bn.d.218.18		96
195.62	even	12		195.2.bf.a.23.7	yes	96
195.179	odd	6		195.2.bf.a.62.18	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.7	✓	96	5.4	even	2
195.2.bf.a.17.18	yes	96	15.14	odd	2
195.2.bf.a.23.7	yes	96	195.62	even	12
195.2.bf.a.23.18	yes	96	65.62	odd	12
195.2.bf.a.62.7	yes	96	65.49	even	6
195.2.bf.a.62.18	yes	96	195.179	odd	6
195.2.bf.a.173.7	yes	96	15.2	even	4
195.2.bf.a.173.18	yes	96	5.2	odd	4
975.2.bn.d.218.7		96	65.23	odd	12	inner
975.2.bn.d.218.18		96	195.23	even	12	inner
975.2.bn.d.257.7		96	39.23	odd	6	inner
975.2.bn.d.257.18		96	13.10	even	6	inner
975.2.bn.d.368.7		96	5.3	odd	4	inner
975.2.bn.d.368.18		96	15.8	even	4	inner
975.2.bn.d.407.7		96	3.2	odd	2	inner
975.2.bn.d.407.18		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+(1.42342 - 0.381405i) q^{2} +(0.323695 - 1.70154i) q^{3} +(0.148609 - 0.0857994i) q^{4} +(-0.188219 - 2.54546i) q^{6} +(-3.97287 - 1.06453i) q^{7} +(-1.90523 + 1.90523i) q^{8} +(-2.79044 - 1.10156i) q^{9} +(-2.13830 + 3.70364i) q^{11} +(-0.0978867 - 0.280636i) q^{12} +(3.59901 + 0.217053i) q^{13} -6.06108 q^{14} +(-2.15688 + 3.73582i) q^{16} +(-2.26413 - 0.606673i) q^{17} +(-4.39212 - 0.503692i) q^{18} +(-2.42558 - 4.20123i) q^{19} +(-3.09733 + 6.41539i) q^{21} +(-1.63112 + 6.08741i) q^{22} +(-2.72722 + 0.730756i) q^{23} +(2.62510 + 3.85852i) q^{24} +(5.20570 - 1.06372i) q^{26} +(-2.77759 + 4.39147i) q^{27} +(-0.681739 + 0.182671i) q^{28} +(-0.553990 + 0.959539i) q^{29} -2.59652i q^{31} +(-0.250564 + 0.935116i) q^{32} +(5.60972 + 4.83724i) q^{33} -3.45421 q^{34} +(-0.509198 + 0.0757171i) q^{36} +(0.255918 + 0.955101i) q^{37} +(-5.05499 - 5.05499i) q^{38} +(1.53431 - 6.05359i) q^{39} +(-0.575209 + 0.996292i) q^{41} +(-1.96194 + 10.3131i) q^{42} +(-9.84550 - 2.63809i) q^{43} +0.733860i q^{44} +(-3.60327 + 2.08035i) q^{46} +(3.07931 + 3.07931i) q^{47} +(5.65846 + 4.87927i) q^{48} +(8.58827 + 4.95844i) q^{49} +(-1.76516 + 3.65613i) q^{51} +(0.553469 - 0.276537i) q^{52} +(-2.89463 - 2.89463i) q^{53} +(-2.27876 + 7.31030i) q^{54} +(9.59737 - 5.54104i) q^{56} +(-7.93368 + 2.76729i) q^{57} +(-0.422589 + 1.57712i) q^{58} +(7.54722 - 4.35739i) q^{59} +(1.64416 + 2.84776i) q^{61} +(-0.990323 - 3.69594i) q^{62} +(9.91342 + 7.34684i) q^{63} -7.20087i q^{64} +(9.82995 + 4.74586i) q^{66} +(-1.59596 - 5.95621i) q^{67} +(-0.388523 + 0.104104i) q^{68} +(0.360619 + 4.87700i) q^{69} +(-4.38783 - 7.59994i) q^{71} +(7.41514 - 3.21771i) q^{72} +(-8.00201 - 8.00201i) q^{73} +(0.728560 + 1.26190i) q^{74} +(-0.720926 - 0.416227i) q^{76} +(12.4378 - 12.4378i) q^{77} +(-0.124901 - 9.20200i) q^{78} +2.06111i q^{79} +(6.57314 + 6.14767i) q^{81} +(-0.438775 + 1.63753i) q^{82} +(6.21215 - 6.21215i) q^{83} +(0.0901463 + 1.21913i) q^{84} -15.0205 q^{86} +(1.45336 + 1.25323i) q^{87} +(-2.98233 - 11.1302i) q^{88} +(-3.27478 - 1.89069i) q^{89} +(-14.0673 - 4.69357i) q^{91} +(-0.342591 + 0.342591i) q^{92} +(-4.41806 - 0.840480i) q^{93} +(5.55763 + 3.20870i) q^{94} +(1.51003 + 0.729035i) q^{96} +(-4.91400 - 1.31670i) q^{97} +(14.1159 + 3.78234i) q^{98} +(10.0466 - 7.97935i) 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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