LMFDB - Embedded newform 975.2.bn.d.218.7

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)

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")

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);

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			218.7
Character	$\chi$	$=$	975.218
Dual form			975.2.bn.d.407.7

$q$-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} +(-1.13110 + 1.31172i) q^{3} +(0.148609 + 0.0857994i) q^{4} +(2.11032 - 1.43573i) q^{6} +(-3.97287 + 1.06453i) q^{7} +(1.90523 + 1.90523i) q^{8} +(-0.441245 - 2.96737i) q^{9} +(2.13830 + 3.70364i) q^{11} +(-0.280636 + 0.0978867i) q^{12} +(3.59901 - 0.217053i) q^{13} +6.06108 q^{14} +(-2.15688 - 3.73582i) q^{16} +(2.26413 - 0.606673i) q^{17} +(-0.503692 + 4.39212i) 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} +(-4.65412 + 0.344139i) q^{24} +(-5.20570 - 1.06372i) q^{26} +(4.39147 + 2.77759i) q^{27} +(-0.681739 - 0.182671i) q^{28} +(0.553990 + 0.959539i) q^{29} +2.59652i q^{31} +(0.250564 + 0.935116i) q^{32} +(-7.27679 - 1.38431i) q^{33} -3.45421 q^{34} +(0.189026 - 0.478837i) q^{36} +(0.255918 - 0.955101i) q^{37} +(5.05499 - 5.05499i) q^{38} +(-3.78611 + 4.96642i) q^{39} +(0.575209 + 0.996292i) q^{41} +(-6.85566 + 7.95047i) q^{42} +(-9.84550 + 2.63809i) q^{43} +0.733860i q^{44} +(-3.60327 - 2.08035i) q^{46} +(-3.07931 + 3.07931i) q^{47} +(7.34000 + 1.39634i) 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} +(-5.19152 - 5.62861i) q^{54} +(-9.59737 - 5.54104i) q^{56} +(-2.76729 - 7.93368i) 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} +(4.91185 + 11.3193i) q^{63} +7.20087i q^{64} +(9.82995 + 4.74586i) q^{66} +(-1.59596 + 5.95621i) q^{67} +(0.388523 + 0.104104i) q^{68} +(-4.04329 + 2.75080i) q^{69} +(4.38783 - 7.59994i) q^{71} +(4.81284 - 6.49418i) 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} +(7.28345 - 5.62527i) q^{78} -2.06111i q^{79} +(-8.61061 + 2.61868i) q^{81} +(-0.438775 - 1.63753i) q^{82} +(-6.21215 - 6.21215i) q^{83} +(1.01073 - 0.687636i) q^{84} +15.0205 q^{86} +(-1.88527 - 0.358648i) 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} +(-3.40592 - 2.93691i) 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 $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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	$-0.591111\pi$
$2$	−1.42342	−	0.381405i	−1.00651	−	0.269694i	−0.724171	+	0.689621i	$0.757777\pi$
$3$	−1.13110	+	1.31172i	−0.653038	+	0.757325i
$3$	−1.13110	+	1.31172i	−0.653038	+	0.757325i
$4$	0.148609	+	0.0857994i	0.0743045	+	0.0428997i
$5$		0			0
$5$		0			0
$6$	2.11032	−	1.43573i	0.861536	−	0.586135i
$7$	−3.97287	+	1.06453i	−1.50160	+	0.402353i	−0.913636	−	0.406533i	$-0.866738\pi$
$7$	−3.97287	+	1.06453i	−1.50160	+	0.402353i	−0.587966	+	0.808886i	$0.700071\pi$
$8$	1.90523	+	1.90523i	0.673599	+	0.673599i
$9$	−0.441245	−	2.96737i	−0.147082	−	0.989124i
$10$		0			0
$11$	2.13830	+	3.70364i	0.644722	+	1.11669i	0.984366	+	0.176137i	$0.0563601\pi$
$11$	2.13830	+	3.70364i	0.644722	+	1.11669i	−0.339644	+	0.940554i	$0.610307\pi$
$12$	−0.280636	+	0.0978867i	−0.0810127	+	0.0282575i
$13$	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	$-0.491588\pi$
$17$	2.26413	−	0.606673i	0.549133	−	0.147140i	0.522709	+	0.852511i	$0.324921\pi$
$18$	−0.503692	+	4.39212i	−0.118721	+	1.03523i
$19$	−2.42558	+	4.20123i	−0.556466	+	0.963827i	0.441322	+	0.897349i	$0.354510\pi$
$19$	−2.42558	+	4.20123i	−0.556466	+	0.963827i	−0.997788	+	0.0664784i	$0.978824\pi$
$20$		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	$-0.321559\pi$
$23$	2.72722	+	0.730756i	0.568664	+	0.152373i	0.0369803	+	0.999316i	$0.488226\pi$
$24$	−4.65412	+	0.344139i	−0.950019	+	0.0702472i
$25$		0			0
$26$	−5.20570	−	1.06372i	−1.02092	−	0.208613i
$27$	4.39147	+	2.77759i	0.845138	+	0.534548i
$28$	−0.681739	−	0.182671i	−0.128837	−	0.0345217i
$29$	0.553990	+	0.959539i	0.102873	+	0.178182i	0.912867	−	0.408256i	$-0.133863\pi$
$29$	0.553990	+	0.959539i	0.102873	+	0.178182i	−0.809994	+	0.586438i	$0.800530\pi$
$30$		0			0
$31$			2.59652i			0.466348i	0.972435	+	0.233174i	$0.0749112\pi$
$31$			2.59652i			0.466348i	−0.972435	+	0.233174i	$0.925089\pi$
$32$	0.250564	+	0.935116i	0.0442938	+	0.165307i
$33$	−7.27679	−	1.38431i	−1.26673	−	0.240978i
$34$	−3.45421			−0.592391
$35$		0			0
$36$	0.189026	−	0.478837i	0.0315043	−	0.0798061i
$37$	0.255918	−	0.955101i	0.0420727	−	0.157018i	−0.941694	−	0.336472i	$-0.890766\pi$
$37$	0.255918	−	0.955101i	0.0420727	−	0.157018i	0.983766	+	0.179454i	$0.0574331\pi$
$38$	5.05499	−	5.05499i	0.820027	−	0.820027i
$39$	−3.78611	+	4.96642i	−0.606263	+	0.795264i
$40$		0			0
$41$	0.575209	+	0.996292i	0.0898326	+	0.155595i	0.907440	−	0.420181i	$-0.138033\pi$
$41$	0.575209	+	0.996292i	0.0898326	+	0.155595i	−0.817608	+	0.575776i	$0.804700\pi$
$42$	−6.85566	+	7.95047i	−1.05785	+	1.22678i
$43$	−9.84550	+	2.63809i	−1.50142	+	0.402305i	−0.913577	−	0.406666i	$-0.866691\pi$
$43$	−9.84550	+	2.63809i	−1.50142	+	0.402305i	−0.587847	+	0.808972i	$0.700024\pi$
$44$			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	$-0.852879\pi$
$47$	−3.07931	+	3.07931i	−0.449164	+	0.449164i	0.445913	+	0.895077i	$0.352879\pi$
$48$	7.34000	+	1.39634i	1.05944	+	0.201544i
$49$	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	$-0.659284\pi$
$53$	2.89463	−	2.89463i	0.397608	−	0.397608i	0.877389	+	0.479780i	$0.159284\pi$
$54$	−5.19152	−	5.62861i	−0.706477	−	0.765957i
$55$		0			0
$56$	−9.59737	−	5.54104i	−1.28250	−	0.740453i
$57$	−2.76729	−	7.93368i	−0.366537	−	1.05084i
$58$	−0.422589	−	1.57712i	−0.0554886	−	0.207086i
$59$	−7.54722	−	4.35739i	−0.982564	−	0.567284i	−0.0795208	−	0.996833i	$-0.525339\pi$
$59$	−7.54722	−	4.35739i	−0.982564	−	0.567284i	−0.903043	+	0.429550i	$0.858672\pi$
$60$		0			0
$61$	1.64416	−	2.84776i	0.210513	−	0.364619i	−0.741362	−	0.671105i	$-0.765820\pi$
$61$	1.64416	−	2.84776i	0.210513	−	0.364619i	0.951875	+	0.306486i	$0.0991534\pi$
$62$	0.990323	−	3.69594i	0.125771	−	0.469385i
$63$	4.91185	+	11.3193i	0.618835	+	1.42609i
$64$			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	0.797295	+	0.603590i	$0.206264\pi$
$67$	−1.59596	+	5.95621i	−0.194978	+	0.727667i	−0.992273	+	0.124077i	$0.960403\pi$
$68$	0.388523	+	0.104104i	0.0471153	+	0.0126245i
$69$	−4.04329	+	2.75080i	−0.486755	+	0.331158i
$70$		0			0
$71$	4.38783	−	7.59994i	0.520739	−	0.901947i	−0.478970	−	0.877831i	$-0.658990\pi$
$71$	4.38783	−	7.59994i	0.520739	−	0.901947i	0.999709	−	0.0241156i	$-0.00767696\pi$
$72$	4.81284	−	6.49418i	0.567199	−	0.765347i
$73$	−8.00201	+	8.00201i	−0.936565	+	0.936565i	−0.998105	−	0.0615398i	$-0.980399\pi$
$73$	−8.00201	+	8.00201i	−0.936565	+	0.936565i	0.0615398	+	0.998105i	$0.480399\pi$
$74$	−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
$78$	7.28345	−	5.62527i	0.824689	−	0.636937i
$79$		−	2.06111i		−	0.231893i	−0.993255	−	0.115946i	$-0.963010\pi$
$79$		−	2.06111i		−	0.231893i	0.993255	−	0.115946i	$-0.0369901\pi$
$80$		0			0
$81$	−8.61061	+	2.61868i	−0.956734	+	0.290964i
$82$	−0.438775	−	1.63753i	−0.0484546	−	0.180835i
$83$	−6.21215	−	6.21215i	−0.681872	−	0.681872i	0.278550	−	0.960422i	$-0.410146\pi$
$83$	−6.21215	−	6.21215i	−0.681872	−	0.681872i	−0.960422	+	0.278550i	$0.910146\pi$
$84$	1.01073	−	0.687636i	0.110279	−	0.0750272i
$85$		0			0
$86$	15.0205			1.61970
$87$	−1.88527	−	0.358648i	−0.202122	−	0.0384511i
$88$	−2.98233	+	11.1302i	−0.317918	+	1.18649i
$89$	3.27478	−	1.89069i	0.347126	−	0.200413i	−0.316293	−	0.948662i	$-0.602438\pi$
$89$	3.27478	−	1.89069i	0.347126	−	0.200413i	0.663419	+	0.748248i	$0.269105\pi$
$90$		0			0
$91$	−14.0673	+	4.69357i	−1.47466	+	0.492019i
$92$	0.342591	+	0.342591i	0.0357175	+	0.0357175i
$93$	−3.40592	−	2.93691i	−0.353177	−	0.304543i
$94$	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	−0.499508	−	0.866309i	$-0.666486\pi$
$97$	−4.91400	+	1.31670i	−0.498941	+	0.133691i	0.000567486		1.00000i	$0.499819\pi$
$98$	−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	−0.730855	+	0.682533i	$0.760879\pi$
$101$	−16.9579	+	9.79064i	−1.68737	+	0.974205i	−0.956518	+	0.291673i	$0.905788\pi$
$102$	3.90704	−	4.53097i	0.386854	−	0.448633i
$103$	−11.6815	−	11.6815i	−1.15101	−	1.15101i	−0.986350	−	0.164663i	$-0.947346\pi$
$103$	−11.6815	−	11.6815i	−1.15101	−	1.15101i	−0.164663	−	0.986350i	$-0.552654\pi$
$104$	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	0.747861	+	0.663856i	$0.231081\pi$
$107$	−2.39707	+	8.94599i	−0.231734	+	0.864841i	−0.979594	+	0.200986i	$0.935586\pi$
$108$	0.414296	+	0.789560i	0.0398656	+	0.0759755i
$109$	−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
$111$	0.963361	+	1.41600i	0.0914382	+	0.134401i
$112$	12.5459	+	12.5459i	1.18547	+	1.18547i
$113$	0.372017	+	1.38839i	0.0349964	+	0.130608i	0.981214	−	0.192923i	$-0.0617967\pi$
$113$	0.372017	+	1.38839i	0.0349964	+	0.130608i	−0.946218	+	0.323531i	$0.895130\pi$
$114$	0.913079	+	12.3484i	0.0855177	+	1.15654i
$115$		0			0
$116$			0.190128i			0.0176529i
$117$	−2.23212	−	10.5838i	−0.206360	−	0.978476i
$118$	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
$123$	−1.95748	−	0.372385i	−0.176500	−	0.0335768i
$124$	−0.222780	+	0.385866i	−0.0200062	+	0.0346518i
$125$		0			0
$126$	−2.67442	−	17.9855i	−0.238256	−	1.60227i
$127$	−2.87595	−	0.770609i	−0.255199	−	0.0683805i	0.128951	−	0.991651i	$-0.458839\pi$
$127$	−2.87595	−	0.770609i	−0.255199	−	0.0683805i	−0.384150	+	0.923270i	$0.625506\pi$
$128$	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	$-0.0365223\pi$
$132$	−0.962622	−	0.830066i	−0.0837855	−	0.0722479i
$133$	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	0.980566	+	0.196189i	$0.0628567\pi$
$137$	2.68583	+	10.0236i	0.229466	+	0.856377i	−0.751100	+	0.660188i	$0.770477\pi$
$138$	6.80448	−	2.37342i	0.579236	−	0.202039i
$139$	−1.68558	−	0.973168i	−0.142969	−	0.0825431i	0.426809	−	0.904342i	$-0.359638\pi$
$139$	−1.68558	−	0.973168i	−0.142969	−	0.0825431i	−0.569778	+	0.821799i	$0.692971\pi$
$140$		0			0
$141$	−0.556214	−	7.52221i	−0.0468417	−	0.633484i
$142$	−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
$147$	−3.21005	+	16.8739i	−0.264760	+	1.39174i
$148$	0.119979	−	0.119979i	0.00986220	−	0.00986220i
$149$	8.56121	+	4.94282i	0.701362	+	0.404931i	0.807854	−	0.589382i	$-0.200629\pi$
$149$	8.56121	+	4.94282i	0.701362	+	0.404931i	−0.106493	+	0.994313i	$0.533962\pi$
$150$		0			0
$151$			20.0349i			1.63042i	0.579165	+	0.815210i	$0.303379\pi$
$151$			20.0349i			1.63042i	−0.579165	+	0.815210i	$0.696621\pi$
$152$	−12.6256	+	3.38301i	−1.02407	+	0.274398i
$153$	−2.79926	−	6.45084i	−0.226307	−	0.521519i
$154$	12.9604	+	22.4481i	1.04438	+	1.80892i
$155$		0			0
$156$	−0.988767	+	0.413209i	−0.0791647	+	0.0330832i
$157$	5.41204	−	5.41204i	0.431928	−	0.431928i	−0.457356	−	0.889284i	$-0.651203\pi$
$157$	5.41204	−	5.41204i	0.431928	−	0.431928i	0.889284	+	0.457356i	$0.151203\pi$
$158$	−0.786117	+	2.93383i	−0.0625401	+	0.233403i
$159$	0.522855	+	7.07107i	0.0414651	+	0.560772i
$160$		0			0
$161$	−11.6128			−0.915215
$162$	13.2553	−	0.443356i	1.04143	−	0.0348333i
$163$	−1.81388	−	6.76947i	−0.142074	−	0.530226i	−0.999868	−	0.0162335i	$-0.994833\pi$
$163$	−1.81388	−	6.76947i	−0.142074	−	0.530226i	0.857795	−	0.513993i	$-0.171834\pi$
$164$			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	0.996020	+	0.0891292i	$0.0284084\pi$
$167$	24.5943	+	6.59002i	1.90316	+	0.509951i	0.907143	+	0.420822i	$0.138258\pi$
$168$	18.1239	−	6.32166i	1.39829	−	0.487726i
$169$	12.9058	−	1.56235i	0.992752	−	0.120181i
$170$		0			0
$171$	13.5369	+	5.34383i	1.03519	+	0.408653i
$172$	−1.68948	−	0.452694i	−0.128821	−	0.0345176i
$173$	−4.95717	−	18.5004i	−0.376887	−	1.40656i	−0.850568	−	0.525865i	$-0.823742\pi$
$173$	−4.95717	−	18.5004i	−0.376887	−	1.40656i	0.473681	−	0.880696i	$-0.342925\pi$
$174$	2.54674	+	1.22956i	0.193068	+	0.0932124i
$175$		0			0
$176$	9.22410	−	15.9766i	0.695292	−	1.20428i
$177$	14.2523	−	4.97125i	1.07127	−	0.373662i
$178$	−5.38251	+	1.44224i	−0.403436	+	0.108100i
$179$	−3.01935	−	5.22967i	−0.225677	−	0.390884i	0.730845	−	0.682543i	$-0.239126\pi$
$179$	−3.01935	−	5.22967i	−0.225677	−	0.390884i	−0.956522	+	0.291659i	$0.905793\pi$
$180$		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
$183$	1.87578	+	5.37777i	0.138662	+	0.397536i
$184$	3.80371	+	6.58822i	0.280413	+	0.485690i
$185$		0			0
$186$	3.72790	+	5.47949i	0.273343	+	0.401776i
$187$	7.08830	+	7.08830i	0.518348	+	0.518348i
$188$	−0.721817	+	0.193410i	−0.0526439	+	0.0141059i
$189$	−20.4035	−	6.36016i	−1.48414	−	0.462634i
$190$		0			0
$191$	−2.61637	−	1.51056i	−0.189314	−	0.109300i	0.402348	−	0.915487i	$-0.368194\pi$
$191$	−2.61637	−	1.51056i	−0.189314	−	0.109300i	−0.591661	+	0.806187i	$0.701528\pi$
$192$	−9.44556	−	8.14488i	−0.681675	−	0.587806i
$193$	3.38290	+	0.906445i	0.243506	+	0.0652473i	0.378508	−	0.925598i	$-0.376437\pi$
$193$	3.38290	+	0.906445i	0.243506	+	0.0652473i	−0.135002	+	0.990845i	$0.543104\pi$
$194$	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	$-0.469544\pi$
$197$	−4.48363	−	1.20138i	−0.319445	−	0.0855951i	−0.414979	+	0.909831i	$0.636211\pi$
$198$	−17.3439	+	7.52617i	−1.23258	+	0.534861i
$199$	−3.93217	−	2.27024i	−0.278744	−	0.160933i	0.354111	−	0.935204i	$-0.384784\pi$
$199$	−3.93217	−	2.27024i	−0.278744	−	0.160933i	−0.632855	+	0.774271i	$0.718117\pi$
$200$		0			0
$201$	−6.00772	−	8.83050i	−0.423752	−	0.622856i
$202$	27.8724	−	7.46839i	1.96110	−	0.525474i
$203$	−3.22238	−	3.22238i	−0.226167	−	0.226167i
$204$	−0.576013	+	0.391883i	−0.0403290	+	0.0274373i
$205$		0			0
$206$	12.1723	+	21.0831i	0.848086	+	1.46893i
$207$	0.965054	−	8.41511i	0.0670759	−	0.584891i
$208$	−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	0.577829	−	0.816158i	$-0.303900\pi$
$211$	−6.07034	−	10.5141i	−0.417899	−	0.723823i	−0.995728	+	0.0923352i	$0.970567\pi$
$212$	0.678526	−	0.181811i	0.0466014	−	0.0124868i
$213$	5.00598	+	14.3519i	0.343004	+	0.983375i
$214$	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
$219$	−1.44540	−	19.5475i	−0.0976709	−	1.32090i
$220$		0			0
$221$	8.01697	−	2.67486i	0.539279	−	0.179931i
$222$	−0.831198	−	2.38300i	−0.0557864	−	0.159937i
$223$	16.8709	+	4.52055i	1.12976	+	0.302718i	0.774827	−	0.632174i	$-0.217837\pi$
$223$	16.8709	+	4.52055i	1.12976	+	0.302718i	0.354933	+	0.934892i	$0.384504\pi$
$224$	−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	−0.998068	−	0.0621264i	$-0.980212\pi$
$227$	−2.48265	−	9.26536i	−0.164779	−	0.614964i	0.833289	−	0.552837i	$-0.186455\pi$
$228$	0.269461	−	1.41645i	0.0178455	−	0.0938066i
$229$	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
$231$	30.3833	−	2.24663i	1.99908	−	0.147818i
$232$	−0.772662	+	2.88361i	−0.0507277	+	0.189318i
$233$	−19.2843	+	19.2843i	−1.26336	+	1.26336i	−0.313900	+	0.949456i	$0.601636\pi$
$233$	−19.2843	+	19.2843i	−1.26336	+	1.26336i	−0.949456	+	0.313900i	$0.898364\pi$
$234$	−0.859472	+	15.9166i	−0.0561854	+	1.04050i
$235$		0			0
$236$	−0.747723	−	1.29509i	−0.0486726	−	0.0843034i
$237$	2.70361	+	2.33131i	0.175618	+	0.151435i
$238$	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	0.452641	−	0.891693i	$-0.350482\pi$
$241$	−1.44789	−	0.835937i	−0.0932665	−	0.0538475i	−0.545908	+	0.837845i	$0.683815\pi$
$242$	7.59559	−	7.59559i	0.488263	−	0.488263i
$243$	6.30444	−	14.2567i	0.404430	−	0.914569i
$244$	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
$249$	15.1752	−	1.12210i	0.961687	−	0.0711099i
$250$		0			0
$251$	−6.81314	−	3.93357i	−0.430042	−	0.248285i	0.269323	−	0.963050i	$-0.413200\pi$
$251$	−6.81314	−	3.93357i	−0.430042	−	0.248285i	−0.699364	+	0.714765i	$0.746534\pi$
$252$	−0.241240	+	2.10358i	−0.0151967	+	0.132513i
$253$	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	−0.845451	−	0.534053i	$-0.820668\pi$
$257$	2.46492	−	9.19920i	0.153757	−	0.573830i	0.999209	−	0.0397776i	$-0.0126649\pi$
$258$	−16.9896	+	19.7027i	−1.05773	+	1.22664i
$259$			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	$-0.158233\pi$
$263$	22.7323	+	6.09110i	1.40173	+	0.375593i	0.522766	+	0.852476i	$0.324900\pi$
$264$	−11.2265	−	16.5013i	−0.690942	−	1.01559i
$265$		0			0
$266$	−14.7016	+	25.4640i	−0.901414	+	1.56130i
$267$	−1.22402	+	6.43416i	−0.0749086	+	0.393764i
$268$	−0.748213	+	0.748213i	−0.0457044	+	0.0457044i
$269$	−5.95253	+	10.3101i	−0.362932	+	0.628617i	−0.988442	−	0.151599i	$-0.951558\pi$
$269$	−5.95253	+	10.3101i	−0.362932	+	0.628617i	0.625510	+	0.780216i	$0.284891\pi$
$270$		0			0
$271$	−17.4412	+	10.0697i	−1.05947	+	0.611688i	−0.925287	−	0.379268i	$-0.876176\pi$
$271$	−17.4412	+	10.0697i	−1.05947	+	0.611688i	−0.134188	+	0.990956i	$0.542843\pi$
$272$	−7.14988	−	7.14988i	−0.433525	−	0.433525i
$273$	9.75483	−	23.7613i	0.590389	−	1.43810i
$274$		−	15.2923i		−	0.923839i
$275$		0			0
$276$	−0.836887	+	0.0618819i	−0.0503747	+	0.00372485i
$277$	1.13875	+	4.24989i	0.0684211	+	0.255351i	0.991661	−	0.128873i	$-0.0411358\pi$
$277$	1.13875	+	4.24989i	0.0684211	+	0.255351i	−0.923240	+	0.384224i	$0.874469\pi$
$278$	2.02812	+	2.02812i	0.121638	+	0.121638i
$279$	7.70483	−	1.14570i	0.461276	−	0.0685912i
$280$		0			0
$281$	23.0139			1.37290			0.686448	−	0.727179i	$-0.259169\pi$
$281$	23.0139			1.37290			0.686448	+	0.727179i	$0.259169\pi$
$282$	−2.07728	+	10.9194i	−0.123700	+	0.650242i
$283$	3.53515	−	13.1933i	0.210143	−	0.784263i	−0.777678	−	0.628663i	$-0.783602\pi$
$283$	3.53515	−	13.1933i	0.210143	−	0.784263i	0.987820	−	0.155600i	$-0.0497309\pi$
$284$	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
$288$	2.66428	−	1.15613i	0.156994	−	0.0681257i
$289$	−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	$-0.834037\pi$
$293$	−23.4342	+	6.27918i	−1.36904	+	0.366834i	−0.501914	+	0.864918i	$0.667370\pi$
$294$	11.0050	−	22.7944i	0.641827	−	1.32940i
$295$		0			0
$296$	2.30726	−	1.33210i	0.134107	−	0.0774267i
$297$	−0.896933	+	22.2038i	−0.0520454	+	1.28839i
$298$	−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
$303$	6.33837	−	33.3182i	0.364130	−	1.91408i
$304$	20.9267			1.20023
$305$		0			0
$306$	1.52415	+	10.2499i	0.0871299	+	0.585949i
$307$	−12.8951	−	12.8951i	−0.735962	−	0.735962i	0.235832	−	0.971794i	$-0.424219\pi$
$307$	−12.8951	−	12.8951i	−0.735962	−	0.735962i	−0.971794	+	0.235832i	$0.924219\pi$
$308$	−0.781213	−	2.91553i	−0.0445137	−	0.166128i
$309$	28.5358	−	2.11002i	1.62335	−	0.120035i
$310$		0			0
$311$			8.39481i			0.476026i	0.971262	+	0.238013i	$0.0764960\pi$
$311$			8.39481i			0.476026i	−0.971262	+	0.238013i	$0.923504\pi$
$312$	−16.6755	+	2.24875i	−0.944067	+	0.127311i
$313$	0.445796	+	0.445796i	0.0251979	+	0.0251979i	0.719593	−	0.694396i	$-0.244328\pi$
$313$	0.445796	+	0.445796i	0.0251979	+	0.0251979i	−0.694396	+	0.719593i	$0.744328\pi$
$314$	−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	$-0.916582\pi$
$317$	−12.5839	+	12.5839i	−0.706781	+	0.706781i	0.259076	+	0.965857i	$0.416582\pi$
$318$	1.95269	−	10.2645i	0.109502	−	0.575606i
$319$	−2.36919	+	4.10356i	−0.132649	+	0.229755i
$320$		0			0
$321$	−9.02336	−	13.2631i	−0.503635	−	0.740272i
$322$	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
$327$	15.6291	−	18.1250i	0.864291	−	1.00231i
$328$	−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	0.122912	−	0.992418i	$-0.460777\pi$
$331$	−12.2822	−	7.09113i	−0.675091	−	0.389764i	−0.798003	+	0.602654i	$0.794110\pi$
$332$	−0.390182	−	1.45618i	−0.0214140	−	0.0799182i
$333$	−2.94706	−	0.337972i	−0.161498	−	0.0185208i
$334$	−32.4946	−	18.7608i	−1.77802	−	1.02654i
$335$		0			0
$336$	−30.6473	+	2.26615i	−1.67195	+	0.123629i
$337$	5.88105	−	5.88105i	0.320361	−	0.320361i	−0.528544	−	0.848906i	$-0.677262\pi$
$337$	5.88105	−	5.88105i	0.320361	−	0.320361i	0.848906	+	0.528544i	$0.177262\pi$
$338$	−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
$342$	−17.2305	−	12.7695i	−0.931720	−	0.690498i
$343$	−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	$-0.625142\pi$
$347$	−4.71314	+	1.26288i	−0.253014	+	0.0677950i	0.130082	+	0.991503i	$0.458476\pi$
$348$	−0.249396	−	0.215053i	−0.0133690	−	0.0115281i
$349$	6.13414	+	10.6246i	0.328353	+	0.568724i	0.982185	−	0.187916i	$-0.0601731\pi$
$349$	6.13414	+	10.6246i	0.328353	+	0.568724i	−0.653832	+	0.756640i	$0.726840\pi$
$350$		0			0
$351$	16.4078	+	9.04340i	0.875785	+	0.482701i
$352$	−2.92756	+	2.92756i	−0.156039	+	0.156039i
$353$	−2.79817	+	10.4429i	−0.148932	+	0.555820i	0.850617	+	0.525785i	$0.176229\pi$
$353$	−2.79817	+	10.4429i	−0.148932	+	0.555820i	−0.999549	+	0.0300349i	$0.990438\pi$
$354$	−22.1831	+	1.64028i	−1.17902	+	0.0871801i
$355$		0			0
$356$	0.648882			0.0343907
$357$	3.12072	−	16.4044i	0.165166	−	0.868211i
$358$	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
$363$	−4.15811	−	11.9211i	−0.218244	−	0.625695i
$364$	−2.49324	−	0.509463i	−0.130681	−	0.0267031i
$365$		0			0
$366$	−0.618922	−	8.37027i	−0.0323516	−	0.437521i
$367$	−0.634359	−	0.169976i	−0.0331133	−	0.00887268i	0.242224	−	0.970220i	$-0.422123\pi$
$367$	−0.634359	−	0.169976i	−0.0331133	−	0.00887268i	−0.275338	+	0.961348i	$0.588790\pi$
$368$	−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
$372$	−0.254165	−	0.728677i	−0.0131778	−	0.0377801i
$373$	−32.4088	+	8.68391i	−1.67806	+	0.449636i	−0.967267	−	0.253762i	$-0.918332\pi$
$373$	−32.4088	+	8.68391i	−1.67806	+	0.449636i	−0.710796	+	0.703398i	$0.751665\pi$
$374$	−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
$378$	26.6170	+	16.8352i	1.36903	+	0.865909i
$379$	−8.79891	−	15.2402i	−0.451969	−	0.782834i	0.546539	−	0.837434i	$-0.315945\pi$
$379$	−8.79891	−	15.2402i	−0.451969	−	0.782834i	−0.998508	+	0.0545997i	$0.982612\pi$
$380$		0			0
$381$	4.26380	−	2.90082i	0.218441	−	0.148614i
$382$	3.14806	+	3.14806i	0.161069	+	0.161069i
$383$	20.2110	−	5.41553i	1.03274	−	0.276721i	0.297635	−	0.954680i	$-0.403802\pi$
$383$	20.2110	−	5.41553i	1.03274	−	0.276721i	0.735100	+	0.677959i	$0.237135\pi$
$384$	12.2249	+	17.9689i	0.623851	+	0.916973i
$385$		0			0
$386$	−4.46957	−	2.58051i	−0.227495	−	0.131344i
$387$	12.1725	+	28.0512i	0.618762	+	1.42592i
$388$	−0.843237	−	0.225945i	−0.0428089	−	0.0114706i
$389$	−9.74450			−0.494066			−0.247033	−	0.969007i	$-0.579456\pi$
$389$	−9.74450			−0.494066			−0.247033	+	0.969007i	$0.579456\pi$
$390$		0			0
$391$	6.61812			0.334693
$392$	25.8095	+	6.91564i	1.30358	+	0.349293i
$393$	3.43766	+	2.96428i	0.173407	+	0.149528i
$394$	5.92388	+	3.42015i	0.298441	+	0.172305i
$395$		0			0
$396$	2.17764	−	0.323812i	0.109430	−	0.0162722i
$397$	−2.79246	+	0.748237i	−0.140150	+	0.0375530i	−0.328212	−	0.944604i	$-0.606446\pi$
$397$	−2.79246	+	0.748237i	−0.140150	+	0.0375530i	0.188062	+	0.982157i	$0.439779\pi$
$398$	4.73125	+	4.73125i	0.237156	+	0.237156i
$399$	19.4397	+	28.5736i	0.973202	+	1.43047i
$400$		0			0
$401$	−0.557130	−	0.964978i	−0.0278218	−	0.0481887i	0.851779	−	0.523901i	$-0.175524\pi$
$401$	−0.557130	−	0.964978i	−0.0278218	−	0.0481887i	−0.879601	+	0.475712i	$0.842190\pi$
$402$	5.18353	+	14.8609i	0.258531	+	0.741194i
$403$	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
$408$	−10.3288	+	3.60271i	−0.511351	+	0.178361i
$409$	−6.17475	+	10.6950i	−0.305322	+	0.528833i	−0.977333	−	0.211708i	$-0.932097\pi$
$409$	−6.17475	+	10.6950i	−0.305322	+	0.528833i	0.672011	+	0.740541i	$0.265431\pi$
$410$		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
$414$	−4.58324	+	11.6102i	−0.225254	+	0.570609i
$415$		0			0
$416$	1.10475	+	3.31111i	0.0541649	+	0.162340i
$417$	3.18308	−	1.11027i	0.155876	−	0.0543700i
$418$	29.5310	+	7.91280i	1.44441	+	0.387028i
$419$	9.48656	+	16.4312i	0.463449	+	0.802717i	0.999130	−	0.0417034i	$-0.0132785\pi$
$419$	9.48656	+	16.4312i	0.463449	+	0.802717i	−0.535681	+	0.844420i	$0.679945\pi$
$420$		0			0
$421$			30.3717i			1.48022i	0.672484	+	0.740112i	$0.265228\pi$
$421$			30.3717i			1.48022i	−0.672484	+	0.740112i	$0.734772\pi$
$422$	4.63051	+	17.2813i	0.225410	+	0.841241i
$423$	10.4962	+	7.77874i	0.510343	+	0.378215i
$424$	11.0299			0.535657
$425$		0			0
$426$	−1.65174	−	22.3381i	−0.0800272	−	1.08228i
$427$	−3.50049	+	13.0640i	−0.169401	+	0.632212i
$428$	−1.12379	+	1.12379i	−0.0543203	+	0.0543203i
$429$	−26.4897	−	3.40272i	−1.27894	−	0.164285i
$430$		0			0
$431$	−13.0681	−	22.6347i	−0.629469	−	1.09027i	−0.987658	−	0.156624i	$-0.949939\pi$
$431$	−13.0681	−	22.6347i	−0.629469	−	1.09027i	0.358189	−	0.933649i	$-0.383394\pi$
$432$	0.904725	−	22.3966i	0.0435286	−	1.07756i
$433$	8.65818	−	2.31995i	0.416086	−	0.111490i	−0.0447016	−	0.999000i	$-0.514234\pi$
$433$	8.65818	−	2.31995i	0.416086	−	0.111490i	0.460787	+	0.887511i	$0.347567\pi$
$434$			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
$438$	−5.39809	+	28.3756i	−0.257931	+	1.35584i
$439$	−14.8493	+	8.57324i	−0.708718	+	0.409179i	−0.810586	−	0.585619i	$-0.800851\pi$
$439$	−14.8493	+	8.57324i	−0.708718	+	0.409179i	0.101868	+	0.994798i	$0.467518\pi$
$440$		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	$-0.941564\pi$
$443$	−16.8516	+	16.8516i	−0.800642	+	0.800642i	0.182554	+	0.983196i	$0.441564\pi$
$444$	0.0216717	+	0.293087i	0.00102849	+	0.0139093i
$445$		0			0
$446$	−22.2903	−	12.8693i	−1.05547	−	0.609378i
$447$	−16.1672	+	5.63915i	−0.764681	+	0.266723i
$448$	−7.66552	−	28.6081i	−0.362162	−	1.35161i
$449$	5.80271	+	3.35020i	0.273847	+	0.158105i	0.630634	−	0.776080i	$-0.282795\pi$
$449$	5.80271	+	3.35020i	0.273847	+	0.158105i	−0.356788	+	0.934185i	$0.616128\pi$
$450$		0			0
$451$	−2.45994	+	4.26074i	−0.115834	+	0.200630i
$452$	−0.0638377	+	0.238245i	−0.00300267	+	0.0112061i
$453$	−26.2803	−	22.6614i	−1.23476	−	1.06473i
$454$			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	−0.251097	−	0.967962i	$-0.580791\pi$
$457$	9.62717	−	35.9291i	0.450340	−	1.68069i	0.701438	−	0.712731i	$-0.252542\pi$
$458$	−7.97341	−	2.13647i	−0.372573	−	0.0998306i
$459$	11.6280	+	3.62465i	0.542747	+	0.169184i
$460$		0			0
$461$	4.19385	−	7.26397i	0.195327	−	0.338317i	−0.751681	−	0.659527i	$-0.770756\pi$
$461$	4.19385	−	7.26397i	0.195327	−	0.338317i	0.947008	+	0.321211i	$0.104090\pi$
$462$	−44.1052	−	8.39044i	−2.05196	−	0.390359i
$463$	−7.19262	+	7.19262i	−0.334269	+	0.334269i	−0.854205	−	0.519936i	$-0.825956\pi$
$463$	−7.19262	+	7.19262i	−0.334269	+	0.334269i	0.519936	+	0.854205i	$0.325956\pi$
$464$	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	$-0.0205814\pi$
$467$	20.1687	+	20.1687i	0.933297	+	0.933297i	−0.0646132	+	0.997910i	$0.520581\pi$
$468$	0.576374	−	1.76437i	0.0266429	−	0.0815580i
$469$		−	25.3622i		−	1.17112i
$470$		0			0
$471$	0.977574	+	13.2207i	0.0450442	+	0.609175i
$472$	−6.07734	−	22.6810i	−0.279732	−	1.04398i
$473$	−30.8232	−	30.8232i	−1.41725	−	1.41725i
$474$	−2.95920	−	4.34961i	−0.135921	−	0.199784i
$475$		0			0
$476$	−1.65437			−0.0758280
$477$	−9.86670	−	7.31221i	−0.451765	−	0.334803i
$478$	−6.61480	+	24.6868i	−0.302554	+	1.12915i
$479$	−10.4307	+	6.02217i	−0.476591	+	0.275160i	−0.718995	−	0.695016i	$-0.755397\pi$
$479$	−10.4307	+	6.02217i	−0.476591	+	0.275160i	0.242404	+	0.970175i	$0.422064\pi$
$480$		0			0
$481$	0.713746	−	3.49297i	0.0325440	−	0.159266i
$482$	1.74212	+	1.74212i	0.0793515	+	0.0793515i
$483$	13.1352	−	15.2328i	0.597671	−	0.693115i
$484$	−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	−0.985713	−	0.168435i	$-0.946129\pi$
$487$	−38.7327	+	10.3784i	−1.75515	+	0.470290i	−0.769434	+	0.638726i	$0.779462\pi$
$488$	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	$-0.521559\pi$
$491$	16.8964	−	9.75516i	0.762525	−	0.440244i	0.830202	+	0.557463i	$0.188225\pi$
$492$	−0.258948	−	0.223290i	−0.0116743	−	0.0100667i
$493$	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
$498$	−22.0286	−	4.19066i	−0.987126	−	0.187788i
$499$	−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
$501$	−36.4628	+	24.8070i	−1.62904	+	1.10830i
$502$	8.19769	+	8.19769i	0.365881	+	0.365881i
$503$	−8.24963	−	30.7880i	−0.367833	−	1.37277i	−0.863540	−	0.504281i	$-0.831758\pi$
$503$	−8.24963	−	30.7880i	−0.367833	−	1.37277i	0.495707	−	0.868490i	$-0.334909\pi$
$504$	−12.2075	+	30.9239i	−0.543767	+	1.37746i
$505$		0			0
$506$		−	17.7936i		−	0.791023i
$507$	−12.5483	+	18.6960i	−0.557289	+	0.830319i
$508$	−0.361274	−	0.361274i	−0.0160290	−	0.0160290i
$509$	8.77183	−	5.06442i	0.388804	−	0.224476i	−0.292838	−	0.956162i	$-0.594600\pi$
$509$	8.77183	−	5.06442i	0.388804	−	0.224476i	0.681642	+	0.731686i	$0.261266\pi$
$510$		0			0
$511$	23.2726	−	40.3093i	1.02952	−	1.78318i
$512$	−13.4843	+	13.4843i	−0.595930	+	0.595930i
$513$	−22.3211	+	11.7123i	−0.985502	+	0.517110i
$514$	−7.01724	+	12.1542i	−0.309517	+	0.536099i
$515$		0			0
$516$	2.50477	−	1.70409i	0.110266	−	0.0750183i
$517$	−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	$-0.210067\pi$
$522$	−4.49345	+	1.94988i	−0.196673	+	0.0853437i
$523$	−4.22208	+	15.7570i	−0.184619	+	0.689007i	0.810093	+	0.586301i	$0.199417\pi$
$523$	−4.22208	+	15.7570i	−0.184619	+	0.689007i	−0.994712	+	0.102705i	$0.967250\pi$
$524$	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
$528$	10.5236	+	30.1705i	0.457980	+	1.31300i
$529$	−13.0149	−	7.51414i	−0.565864	−	0.326702i
$530$		0			0
$531$	−9.59983	+	24.3181i	−0.416597	+	1.05532i
$532$	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
$537$	10.2751	+	1.95470i	0.443402	+	0.0843516i
$538$	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	$-0.988123\pi$
$541$		−	1.73534i		−	0.0746081i	0.999304	−	0.0373041i	$-0.0118770\pi$
$542$	28.6667	−	7.68123i	1.23134	−	0.329937i
$543$	−6.29241	+	7.29727i	−0.270033	+	0.313156i
$544$	1.13462	+	1.96522i	0.0486464	+	0.0842580i
$545$		0			0
$546$	−22.9479	+	30.1019i	−0.982081	+	1.28824i
$547$	11.2029	−	11.2029i	0.479001	−	0.479001i	−0.425811	−	0.904812i	$-0.640011\pi$
$547$	11.2029	−	11.2029i	0.479001	−	0.479001i	0.904812	+	0.425811i	$0.140011\pi$
$548$	−0.460885	+	1.72005i	−0.0196880	+	0.0734767i
$549$	−9.17585	−	3.62226i	−0.391616	−	0.154594i
$550$		0			0
$551$	−5.37498			−0.228982
$552$	−12.9443	−	2.46248i	−0.550946	−	0.104810i
$553$	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	$-0.767507\pi$
$557$	−40.6785	−	10.8998i	−1.72360	−	0.461838i	−0.978693	+	0.205328i	$0.934174\pi$
$558$	−11.4042	−	1.30785i	−0.482778	−	0.0553655i
$559$	−34.8615	+	11.6315i	−1.47448	+	0.491961i
$560$		0			0
$561$	−17.3154	+	1.28035i	−0.731059	+	0.0540566i
$562$	−32.7585	−	8.77762i	−1.38184	−	0.370262i
$563$	0.695238	+	2.59466i	0.0293008	+	0.109352i	0.979028	−	0.203728i	$-0.0653058\pi$
$563$	0.695238	+	2.59466i	0.0293008	+	0.109352i	−0.949727	+	0.313080i	$0.898639\pi$
$564$	0.562743	−	1.16559i	0.0236958	−	0.0490802i
$565$		0			0
$566$	−10.0640	+	17.4314i	−0.423022	+	0.732695i
$567$	31.4211	−	19.5699i	1.31956	−	0.821857i
$568$	22.8394	−	6.11980i	0.958320	−	0.256781i
$569$	−5.33657	−	9.24321i	−0.223721	−	0.387496i	0.732214	−	0.681074i	$-0.238487\pi$
$569$	−5.33657	−	9.24321i	−0.223721	−	0.387496i	−0.955935	+	0.293579i	$0.905154\pi$
$570$		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
$573$	4.94080	−	1.72337i	0.206405	−	0.0719946i
$574$	3.48639	+	6.03860i	0.145519	+	0.252046i
$575$		0			0
$576$	21.3677	−	3.17735i	0.890320	−	0.132390i
$577$	−6.87604	−	6.87604i	−0.286253	−	0.286253i	0.549343	−	0.835597i	$-0.314878\pi$
$577$	−6.87604	−	6.87604i	−0.286253	−	0.286253i	−0.835597	+	0.549343i	$0.814878\pi$
$578$	16.3774	−	4.38831i	0.681209	−	0.182529i
$579$	−5.01539	+	3.41216i	−0.208432	+	0.141804i
$580$		0			0
$581$	31.2930	+	18.0670i	1.29825	+	0.749547i
$582$	−8.47970	+	9.83386i	−0.351495	+	0.407626i
$583$	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	$-0.688726\pi$
$587$	−35.3085	−	9.46089i	−1.45734	−	0.390493i	−0.898570	+	0.438830i	$0.855393\pi$
$588$	−1.92481	+	2.23220i	−0.0793780	+	0.0920542i
$589$	−10.9086	−	6.29805i	−0.449479	−	0.259507i
$590$		0			0
$591$	6.64730	−	4.52241i	0.273433	−	0.186027i
$592$	−4.12007	+	1.10397i	−0.169334	+	0.0453728i
$593$	28.7633	+	28.7633i	1.18117	+	1.18117i	0.979442	+	0.201727i	$0.0646553\pi$
$593$	28.7633	+	28.7633i	1.18117	+	1.18117i	0.201727	+	0.979442i	$0.435345\pi$
$594$	9.74533	−	31.2632i	0.399856	−	1.28275i
$595$		0			0
$596$	0.848182	+	1.46909i	0.0347429	+	0.0601764i
$597$	7.42559	−	2.59007i	0.303909	−	0.106004i
$598$	−13.4197	−	6.70509i	−0.548774	−	0.274192i
$599$	−10.0471			−0.410513			−0.205256	−	0.978708i	$-0.565803\pi$
$599$	−10.0471			−0.410513			−0.205256	+	0.978708i	$0.565803\pi$
$600$		0			0
$601$	−17.9309	−	31.0572i	−0.731415	−	1.26685i	−0.956279	−	0.292458i	$-0.905527\pi$
$601$	−17.9309	−	31.0572i	−0.731415	−	1.26685i	0.224864	−	0.974390i	$-0.427806\pi$
$602$	−59.6743	+	15.9897i	−2.43214	+	0.651691i
$603$	18.3785	+	2.10767i	0.748430	+	0.0858308i
$604$	−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	0.999554	−	0.0298588i	$-0.00950577\pi$
$607$	2.93149	+	10.9405i	0.118985	+	0.444060i	−0.880569	+	0.473919i	$0.842839\pi$
$608$	−4.53639	−	1.21552i	−0.183975	−	0.0492960i
$609$	7.87170	−	0.582056i	0.318977	−	0.0235861i
$610$		0			0
$611$	−10.4141	+	11.7509i	−0.421310	+	0.475389i
$612$	0.137483	−	1.19883i	0.00555741	−	0.0484597i
$613$	19.2626	+	5.16141i	0.778011	+	0.208467i	0.625908	−	0.779897i	$-0.284729\pi$
$613$	19.2626	+	5.16141i	0.778011	+	0.208467i	0.152103	+	0.988365i	$0.451395\pi$
$614$	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	−0.992552	−	0.121825i	$-0.961125\pi$
$617$	−4.81611	−	17.9740i	−0.193889	−	0.723605i	0.798662	−	0.601780i	$-0.205541\pi$
$618$	−41.4233	−	7.88025i	−1.66629	−	0.316990i
$619$	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
$621$	9.94675	+	10.7842i	0.399149	+	0.432754i
$622$	3.20182	−	11.9493i	0.128381	−	0.479125i
$623$	−10.9976	+	10.9976i	−0.440608	+	0.440608i
$624$	26.7198	+	3.43228i	1.06965	+	0.137401i
$625$		0			0
$626$	−0.464527	−	0.804584i	−0.0185662	−	0.0321576i
$627$	23.4662	−	27.2137i	0.937151	−	1.08681i
$628$	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	0.941935	−	0.335796i	$-0.109005\pi$
$631$	28.1867	+	16.2736i	1.12209	+	0.647841i	0.180159	+	0.983637i	$0.442339\pi$
$632$	3.92688	−	3.92688i	0.156203	−	0.156203i
$633$	20.6578	+	3.92988i	0.821073	+	0.156199i
$634$	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
$639$	−24.4880	−	9.66689i	−0.968729	−	0.382416i
$640$		0			0
$641$	5.53230	+	3.19407i	0.218513	+	0.126158i	0.605261	−	0.796027i	$-0.293069\pi$
$641$	5.53230	+	3.19407i	0.218513	+	0.126158i	−0.386749	+	0.922185i	$0.626402\pi$
$642$	7.78545	+	22.3205i	0.307267	+	0.880919i
$643$	−8.33296	−	31.0990i	−0.328620	−	1.22643i	−0.910623	−	0.413239i	$-0.864398\pi$
$643$	−8.33296	−	31.0990i	−0.328620	−	1.22643i	0.582003	−	0.813187i	$-0.302269\pi$
$644$	−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	−0.821210	−	0.570625i	$-0.806701\pi$
$647$	4.45875	−	16.6403i	0.175291	−	0.654196i	0.996502	−	0.0835709i	$-0.0266325\pi$
$648$	−21.3943	−	11.4160i	−0.840448	−	0.448462i
$649$		−	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	$-0.265047\pi$
$653$	22.6354	+	6.06514i	0.885791	+	0.237347i	0.212887	+	0.977077i	$0.431713\pi$
$654$	−29.1597	+	19.8385i	−1.14024	+	0.775745i
$655$		0			0
$656$	2.48131	−	4.29775i	0.0968789	−	0.167799i
$657$	27.2758	+	20.2141i	1.06413	+	0.788628i
$658$	−18.6640	+	18.6640i	−0.727597	+	0.727597i
$659$	6.20035	−	10.7393i	0.241532	−	0.418345i	−0.719619	−	0.694369i	$-0.755684\pi$
$659$	6.20035	−	10.7393i	0.241532	−	0.418345i	0.961151	+	0.276024i	$0.0890169\pi$
$660$		0			0
$661$	−19.8030	+	11.4332i	−0.770246	+	0.444702i	−0.832962	−	0.553330i	$-0.813357\pi$
$661$	−19.8030	+	11.4332i	−0.770246	+	0.444702i	0.0627164	+	0.998031i	$0.480024\pi$
$662$	14.7782	+	14.7782i	0.574370	+	0.574370i
$663$	−5.55927	+	13.5416i	−0.215904	+	0.525911i
$664$		−	23.6711i		−	0.918616i
$665$		0			0
$666$	4.06601	+	1.60510i	0.157555	+	0.0621964i
$667$	0.809663	+	3.02170i	0.0313503	+	0.117001i
$668$	3.08951	+	3.08951i	0.119537	+	0.119537i
$669$	−25.0123	+	17.0168i	−0.967032	+	0.657908i
$670$		0			0
$671$	14.0628			0.542888
$672$	6.77521	+	1.28890i	0.261359	+	0.0497203i
$673$	−1.81967	+	6.79109i	−0.0701431	+	0.261777i	−0.992088	−	0.125543i	$-0.959933\pi$
$673$	−1.81967	+	6.79109i	−0.0701431	+	0.261777i	0.921945	+	0.387321i	$0.126599\pi$
$674$	−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	0.999580	+	0.0289760i	$0.00922463\pi$
$677$	26.7622	+	26.7622i	1.02856	+	1.02856i	0.0289760	+	0.999580i	$0.490775\pi$
$678$	2.77843	+	2.39583i	0.106705	+	0.0920112i
$679$	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	$-0.520051\pi$
$683$	9.97129	−	2.67180i	0.381541	−	0.102234i	0.444491	+	0.895783i	$0.353384\pi$
$684$	1.55320	+	1.95560i	0.0593883	+	0.0747741i
$685$		0			0
$686$	15.3108	−	8.83972i	0.584571	−	0.337502i
$687$	−6.33592	+	7.34773i	−0.241731	+	0.280333i
$688$	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	−0.854457	−	0.519523i	$-0.826110\pi$
$691$	−21.8645	+	12.6235i	−0.831765	+	0.480220i	0.0226915	+	0.999743i	$0.492776\pi$
$692$	0.850645	−	3.17465i	0.0323367	−	0.120682i
$693$	−31.4195	+	42.3957i	−1.19353	+	1.61048i
$694$	7.19045			0.272946
$695$		0			0
$696$	−2.90855	−	4.27516i	−0.110248	−	0.162050i
$697$	1.90677	+	1.90677i	0.0722242	+	0.0722242i
$698$	−4.67918	−	17.4629i	−0.177110	−	0.660982i
$699$	−3.48331	−	47.1081i	−0.131751	−	1.78179i
$700$		0			0
$701$		−	5.83428i		−	0.220358i	−0.993912	−	0.110179i	$-0.964858\pi$
$701$		−	5.83428i		−	0.220358i	0.993912	−	0.110179i	$-0.0351424\pi$
$702$	−19.9061	−	19.1306i	−0.751306	−	0.722038i
$703$	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
$708$	2.54455	+	0.484069i	0.0956302	+	0.0181924i
$709$	−9.66759	+	16.7448i	−0.363074	+	0.628863i	−0.988465	−	0.151449i	$-0.951606\pi$
$709$	−9.66759	+	16.7448i	−0.363074	+	0.628863i	0.625391	+	0.780311i	$0.284939\pi$
$710$		0			0
$711$	−6.11608	+	0.909454i	−0.229371	+	0.0341072i
$712$	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
$717$	22.7496	+	19.6169i	0.849598	+	0.732606i
$718$	14.2256	−	53.0907i	0.530895	−	1.98133i
$719$	19.2268	−	33.3018i	0.717038	−	1.24195i	−0.245130	−	0.969490i	$-0.578831\pi$
$719$	19.2268	−	33.3018i	0.717038	−	1.24195i	0.962168	−	0.272456i	$-0.0878359\pi$
$720$		0			0
$721$	58.8443	+	33.9738i	2.19148	+	1.26525i
$722$	1.72919	+	6.45341i	0.0643537	+	0.240171i
$723$	2.73422	−	0.953703i	0.101687	−	0.0354686i
$724$	0.826728	+	0.477312i	0.0307251	+	0.0177391i
$725$		0			0
$726$	1.37199	+	18.5547i	0.0509192	+	0.688628i
$727$	−24.8141	+	24.8141i	−0.920304	+	0.920304i	−0.997051	−	0.0767466i	$-0.975547\pi$
$727$	−24.8141	+	24.8141i	−0.920304	+	0.920304i	0.0767466	+	0.997051i	$0.475547\pi$
$728$	−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
$732$	−0.182652	+	0.960126i	−0.00675100	+	0.0354873i
$733$	−28.6087	+	28.6087i	−1.05668	+	1.05668i	−0.0583912	+	0.998294i	$0.518597\pi$
$733$	−28.6087	+	28.6087i	−1.05668	+	1.05668i	−0.998294	+	0.0583912i	$0.981403\pi$
$734$	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
$738$	−4.66556	+	2.02456i	−0.171742	+	0.0745251i
$739$	7.80807	+	13.5240i	0.287225	+	0.497488i	0.973146	−	0.230188i	$-0.0739340\pi$
$739$	7.80807	+	13.5240i	0.287225	+	0.497488i	−0.685922	+	0.727675i	$0.740601\pi$
$740$		0			0
$741$	−11.6815	−	27.9528i	−0.429132	−	1.02687i
$742$	17.5446	−	17.5446i	0.644082	−	0.644082i
$743$	2.10721	−	7.86421i	0.0773060	−	0.288510i	−0.916440	−	0.400171i	$-0.868951\pi$
$743$	2.10721	−	7.86421i	0.0773060	−	0.288510i	0.993746	+	0.111661i	$0.0356172\pi$
$744$	−0.893564	−	12.0845i	−0.0327596	−	0.443040i
$745$		0			0
$746$	49.4434			1.81025
$747$	−15.6927	+	21.1748i	−0.574165	+	0.774747i
$748$	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	0.737251	−	0.675619i	$-0.236124\pi$
$751$	−5.93245	−	10.2753i	−0.216478	−	0.374951i	−0.953729	+	0.300668i	$0.902790\pi$
$752$	18.1454	+	4.86206i	0.661696	+	0.177301i
$753$	12.8661	−	4.48772i	0.468866	−	0.163542i
$754$	−1.86322	−	5.58436i	−0.0678545	−	0.203370i
$755$		0			0
$756$	−2.48645	−	2.69579i	−0.0904313	−	0.0980449i
$757$	8.51775	+	2.28233i	0.309583	+	0.0829525i	0.410266	−	0.911966i	$-0.365436\pi$
$757$	8.51775	+	2.28233i	0.309583	+	0.0829525i	−0.100683	+	0.994919i	$0.532103\pi$
$758$	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	$-0.763433\pi$
$761$	6.00928	−	10.4084i	0.217836	−	0.377304i	0.954146	+	0.299341i	$0.0967667\pi$
$762$	−7.17558	+	2.50286i	−0.259944	+	0.0906691i
$763$	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
$768$	−2.33248	−	6.68711i	−0.0841662	−	0.241300i
$769$	−6.86300	−	11.8871i	−0.247486	−	0.428658i	0.715342	−	0.698775i	$-0.246271\pi$
$769$	−6.86300	−	11.8871i	−0.247486	−	0.428658i	−0.962828	+	0.270117i	$0.912938\pi$
$770$		0			0
$771$	9.27876	+	13.6385i	0.334166	+	0.491178i
$772$	0.424956	+	0.424956i	0.0152945	+	0.0152945i
$773$	20.8420	−	5.58461i	0.749636	−	0.200864i	0.136279	−	0.990670i	$-0.456486\pi$
$773$	20.8420	−	5.58461i	0.749636	−	0.200864i	0.613357	+	0.789806i	$0.289819\pi$
$774$	−6.62771	−	44.5713i	−0.238228	−	1.60208i
$775$		0			0
$776$	−11.8709	−	6.85366i	−0.426140	−	0.246032i
$777$	−5.33468	−	4.60007i	−0.191381	−	0.165027i
$778$	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
$783$	−0.232377	+	5.75254i	−0.00830448	+	0.205579i
$784$	−37.0477	−	21.3895i	−1.32313	−	0.763910i
$785$		0			0
$786$	−3.76265	−	5.53056i	−0.134209	−	0.197269i
$787$	−16.6307	+	4.45618i	−0.592820	+	0.158846i	−0.542742	−	0.839900i	$-0.682614\pi$
$787$	−16.6307	+	4.45618i	−0.592820	+	0.158846i	−0.0500781	+	0.998745i	$0.515947\pi$
$788$	−0.563229	−	0.563229i	−0.0200642	−	0.0200642i
$789$	−33.7022	+	22.9289i	−1.19983	+	0.816290i
$790$		0			0
$791$	−2.95595	−	5.11985i	−0.105101	−	0.182041i
$792$	34.3435	+	3.93854i	1.22034	+	0.139950i
$793$	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	$-0.278354\pi$
$797$	44.6186	−	11.9555i	1.58047	−	0.423486i	0.939072	+	0.343721i	$0.111687\pi$
$798$	−16.7728	−	48.0867i	−0.593750	−	1.70225i
$799$	−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
$804$	−0.135149	−	1.82775i	−0.00476635	−	0.0644598i
$805$		0			0
$806$	2.76197	−	13.5167i	0.0972863	−	0.476105i
$807$	−6.79111	−	19.4698i	−0.239058	−	0.685368i
$808$	−50.9620	−	13.6552i	−1.79284	−	0.480389i
$809$	6.99405	+	12.1140i	0.245898	+	0.425907i	0.962384	−	0.271694i	$-0.0875840\pi$
$809$	6.99405	+	12.1140i	0.245898	+	0.425907i	−0.716486	+	0.697602i	$0.754251\pi$
$810$		0			0
$811$			19.5998i			0.688243i	0.938925	+	0.344122i	$0.111823\pi$
$811$			19.5998i			0.688243i	−0.938925	+	0.344122i	$0.888177\pi$
$812$	−0.202396	−	0.755353i	−0.00710272	−	0.0265077i
$813$	6.51900	−	34.2677i	0.228631	−	1.20182i
$814$	−6.23152			−0.218415
$815$		0			0
$816$	17.4659	−	1.29148i	0.611428	−	0.0452107i
$817$	12.7978	−	47.7621i	0.447738	−	1.67098i
$818$	12.8684	−	12.8684i	0.449933	−	0.449933i
$819$	20.1347	+	39.6720i	0.703563	+	1.38625i
$820$		0			0
$821$	4.61577	+	7.99475i	0.161091	+	0.279019i	0.935260	−	0.353960i	$-0.115165\pi$
$821$	4.61577	+	7.99475i	0.161091	+	0.279019i	−0.774169	+	0.632979i	$0.781832\pi$
$822$	20.0592	+	17.2970i	0.699646	+	0.603302i
$823$	44.5620	−	11.9403i	1.55333	−	0.416214i	0.622788	−	0.782391i	$-0.286000\pi$
$823$	44.5620	−	11.9403i	1.55333	−	0.416214i	0.930545	+	0.366177i	$0.119333\pi$
$824$		−	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	0.111759	−	0.993735i	$-0.464351\pi$
$827$	31.7914	−	31.7914i	1.10549	−	1.10549i	0.993735	−	0.111759i	$-0.0356486\pi$
$828$	0.865428	−	1.16776i	0.0300757	−	0.0405825i
$829$	−21.8064	+	12.5900i	−0.757369	+	0.437267i	−0.828350	−	0.560210i	$-0.810720\pi$
$829$	−21.8064	+	12.5900i	−0.757369	+	0.437267i	0.0709813	+	0.997478i	$0.477387\pi$
$830$		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
$834$	−4.95432	+	0.366337i	−0.171554	+	0.0126852i
$835$		0			0
$836$	−3.08311	−	1.78003i	−0.106632	−	0.0615638i
$837$	−7.21206	+	11.4025i	−0.249285	+	0.394129i
$838$	−7.23644	−	27.0068i	−0.249979	−	0.932933i
$839$	39.9358	+	23.0569i	1.37874	+	0.796014i	0.992008	−	0.126179i	$-0.0402713\pi$
$839$	39.9358	+	23.0569i	1.37874	+	0.796014i	0.386730	+	0.922193i	$0.373605\pi$
$840$		0			0
$841$	13.8862	−	24.0516i	0.478834	−	0.829365i
$842$	11.5839	−	43.2317i	0.399207	−	1.48986i
$843$	−26.0310	+	30.1879i	−0.896554	+	1.03973i
$844$		−	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
$849$	13.3074	+	19.5601i	0.456710	+	0.671300i
$850$		0			0
$851$	1.39589	−	2.41775i	0.0478505	−	0.0828795i
$852$	−0.487450	+	2.56233i	−0.0166998	+	0.0877839i
$853$	−29.1777	+	29.1777i	−0.999026	+	0.999026i	−1.00000		0.000973237i	$-0.999690\pi$
$853$	−29.1777	+	29.1777i	−0.999026	+	0.999026i	0.000973237		1.00000i	$0.499690\pi$
$854$	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	$-0.481524\pi$
$857$	−27.5270	−	27.5270i	−0.940305	−	0.940305i	−0.998316	+	0.0580111i	$0.981524\pi$
$858$	36.4082	+	14.9468i	1.24296	+	0.510275i
$859$			40.5927i			1.38500i	0.721416	+	0.692502i	$0.243492\pi$
$859$			40.5927i			1.38500i	−0.721416	+	0.692502i	$0.756508\pi$
$860$		0			0
$861$	8.17321	−	0.604351i	0.278542	−	0.0205962i
$862$	9.96849	+	37.2029i	0.339528	+	1.26714i
$863$	28.4894	+	28.4894i	0.969792	+	0.969792i	0.999557	−	0.0297651i	$-0.00947594\pi$
$863$	28.4894	+	28.4894i	0.969792	+	0.969792i	−0.0297651	+	0.999557i	$0.509476\pi$
$864$	−1.49703	+	4.80249i	−0.0509299	+	0.163384i
$865$		0			0
$866$	−13.2091			−0.448863
$867$	3.72432	−	19.5773i	0.126485	−	0.664879i
$868$	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
$873$	6.07542	+	14.0007i	0.205622	+	0.473851i
$874$	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	0.0400039	−	0.999200i	$-0.487263\pi$
$877$	17.0059	−	4.55671i	0.574248	−	0.153869i	0.534244	+	0.845330i	$0.320596\pi$
$878$	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	$-0.903515\pi$
$881$	−34.8199	+	20.1033i	−1.17311	+	0.677297i	−0.218701	+	0.975792i	$0.570182\pi$
$882$	17.4522	+	40.2182i	0.587646	+	1.35422i
$883$	1.83119	+	1.83119i	0.0616243	+	0.0616243i	0.737247	−	0.675623i	$-0.236125\pi$
$883$	1.83119	+	1.83119i	0.0616243	+	0.0616243i	−0.675623	+	0.737247i	$0.736125\pi$
$884$	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	0.554557	+	0.832146i	$0.312888\pi$
$887$	−10.1790	+	37.9885i	−0.341777	+	1.27553i	−0.896333	+	0.443381i	$0.853779\pi$
$888$	−0.862388	+	4.53323i	−0.0289399	+	0.152125i
$889$	12.2461			0.410721
$890$		0			0
$891$	−28.1107	−	26.2911i	−0.941744	−	0.880785i
$892$	2.11931	+	2.11931i	0.0709597	+	0.0709597i
$893$	−5.46777	−	20.4060i	−0.182972	−	0.682861i
$894$	25.1635	−	1.86066i	0.841593	−	0.0622298i
$895$		0			0
$896$			51.6087i			1.72413i
$897$	−13.9548	+	10.7778i	−0.465937	+	0.359860i
$898$	−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
$903$	−13.5703	+	71.3337i	−0.451592	+	2.37384i
$904$	−1.93641	+	3.35396i	−0.0644041	+	0.111551i
$905$		0			0
$906$	28.7648	+	42.2802i	0.955647	+	1.40467i
$907$	45.1184	+	12.0894i	1.49813	+	0.401423i	0.912474	−	0.409135i	$-0.134170\pi$
$907$	45.1184	+	12.0894i	1.49813	+	0.401423i	0.585658	+	0.810559i	$0.300836\pi$
$908$	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	$0.906076\pi$
$912$	−23.6701	+	27.4501i	−0.783795	+	0.908962i
$913$	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
$918$	−15.1690	−	9.59437i	−0.500653	−	0.316661i
$919$	28.1500	+	16.2524i	0.928583	+	0.536118i	0.886363	−	0.462991i	$-0.153224\pi$
$919$	28.1500	+	16.2524i	0.928583	+	0.536118i	0.0422199	+	0.999108i	$0.486557\pi$
$920$		0			0
$921$	31.5004	−	2.32923i	1.03797	−	0.0767508i
$922$	−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
$927$	−29.5090	+	39.8178i	−0.969202	+	1.30779i
$928$	−0.758470	+	0.758470i	−0.0248980	+	0.0248980i
$929$	22.2780	+	12.8622i	0.730916	+	0.421995i	0.818757	−	0.574140i	$-0.194663\pi$
$929$	22.2780	+	12.8622i	0.730916	+	0.421995i	−0.0878410	+	0.996135i	$0.527997\pi$
$930$		0			0
$931$			48.1084i			1.57669i
$932$	−4.52040	+	1.21124i	−0.148071	+	0.0396754i
$933$	−11.0117	−	9.49533i	−0.360506	−	0.310863i
$934$	−21.0162	−	36.4010i	−0.687670	−	1.19108i
$935$		0			0
$936$	15.9119	−	24.4173i	0.520097	−	0.798104i
$937$	−19.2546	+	19.2546i	−0.629022	+	0.629022i	−0.947822	−	0.318800i	$-0.896720\pi$
$937$	−19.2546	+	19.2546i	−0.629022	+	0.629022i	0.318800	+	0.947822i	$0.396720\pi$
$938$	−9.67325	+	36.1010i	−0.315843	+	1.17874i
$939$	−1.08900	+	0.0805238i	−0.0355381	+	0.00262779i
$940$		0			0
$941$	27.3108			0.890306			0.445153	−	0.895455i	$-0.353149\pi$
$941$	27.3108			0.890306			0.445153	+	0.895455i	$0.353149\pi$
$942$	3.65092	−	19.1914i	0.118953	−	0.625290i
$943$	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	$-0.431163\pi$
$947$	−2.70642	−	0.725183i	−0.0879469	−	0.0235653i	−0.302524	+	0.953142i	$0.597829\pi$
$948$	0.201755	+	0.578422i	0.00655271	+	0.0187863i
$949$	−27.0625	+	30.5362i	−0.878485	+	0.991247i
$950$		0			0
$951$	−2.27302	−	30.7402i	−0.0737077	−	0.996818i
$952$	−25.0913	−	6.72320i	−0.813215	−	0.217900i
$953$	0.742295	+	2.77028i	0.0240453	+	0.0897382i	0.976906	−	0.213671i	$-0.0685419\pi$
$953$	0.742295	+	2.77028i	0.0240453	+	0.0897382i	−0.952860	+	0.303409i	$0.901875\pi$
$954$	11.2556	+	14.1716i	0.364412	+	0.458821i
$955$		0			0
$956$	1.48804	−	2.57736i	0.0481267	−	0.0833579i
$957$	−2.70296	−	7.74925i	−0.0873743	−	0.250498i
$958$	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
$963$	27.6038	+	3.16563i	0.889519	+	0.102011i
$964$	−0.143446	−	0.248456i	−0.00462008	−	0.00800222i
$965$		0			0
$966$	−24.5067	+	16.6728i	−0.788491	+	0.536440i
$967$	34.7663	+	34.7663i	1.11801	+	1.11801i	0.992033	+	0.125975i	$0.0402058\pi$
$967$	34.7663	+	34.7663i	1.11801	+	1.11801i	0.125975	+	0.992033i	$0.459794\pi$
$968$	−18.9711	+	5.08328i	−0.609753	+	0.163383i
$969$	−11.0787	−	16.2841i	−0.355898	−	0.523120i
$970$		0			0
$971$	−43.8854	−	25.3373i	−1.40835	−	0.813112i	−0.413121	−	0.910676i	$-0.635561\pi$
$971$	−43.8854	−	25.3373i	−1.40835	−	0.813112i	−0.995229	+	0.0975644i	$0.968895\pi$
$972$	2.16011	−	1.57776i	0.0692857	−	0.0506067i
$973$	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	$-0.470093\pi$
$977$	−10.0876	−	2.70297i	−0.322731	−	0.0864755i	−0.416547	+	0.909114i	$0.636760\pi$
$978$	−13.5470	−	11.6815i	−0.433186	−	0.373535i
$979$	14.0049	+	8.08574i	0.447599	+	0.258421i
$980$		0			0
$981$	6.09697	+	41.0022i	0.194661	+	1.30910i
$982$	−27.7714	+	7.44133i	−0.886221	+	0.237462i
$983$	−15.8387	−	15.8387i	−0.505176	−	0.505176i	0.407866	−	0.913042i	$-0.366273\pi$
$983$	−15.8387	−	15.8387i	−0.505176	−	0.505176i	−0.913042	+	0.407866i	$0.866273\pi$
$984$	−3.01996	−	4.43891i	−0.0962727	−	0.141507i
$985$		0			0
$986$	−1.91359	−	3.31444i	−0.0609413	−	0.105553i
$987$	10.2174	+	29.2926i	0.325222	+	0.932395i
$988$	−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	0.993128	−	0.117034i	$-0.0373387\pi$
$991$	12.4412	+	21.5489i	0.395209	+	0.684523i	−0.597919	+	0.801557i	$0.704005\pi$
$992$	−2.42804	+	0.650592i	−0.0770905	+	0.0206563i
$993$	23.1940	−	8.09012i	0.736038	−	0.256732i
$994$	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	0.767114	+	0.641511i	$0.221692\pi$
$997$	13.3731	+	49.9090i	0.423529	+	1.58063i	−0.343585	+	0.939122i	$0.611641\pi$
$998$	10.7434	+	2.87868i	0.340076	+	0.0911231i
$999$	3.77674	−	3.48346i	0.119491	−	0.110212i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.bn.d.218.7		96
3.2	odd	2	inner	975.2.bn.d.218.18		96
5.2	odd	4	inner	975.2.bn.d.257.18		96
5.3	odd	4		195.2.bf.a.62.7	yes	96
5.4	even	2		195.2.bf.a.23.18	yes	96
13.4	even	6	inner	975.2.bn.d.368.7		96
15.2	even	4	inner	975.2.bn.d.257.7		96
15.8	even	4		195.2.bf.a.62.18	yes	96
15.14	odd	2		195.2.bf.a.23.7	yes	96
39.17	odd	6	inner	975.2.bn.d.368.18		96
65.4	even	6		195.2.bf.a.173.18	yes	96
65.17	odd	12	inner	975.2.bn.d.407.18		96
65.43	odd	12		195.2.bf.a.17.7	✓	96
195.17	even	12	inner	975.2.bn.d.407.7		96
195.134	odd	6		195.2.bf.a.173.7	yes	96
195.173	even	12		195.2.bf.a.17.18	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bf.a.17.7	✓	96	65.43	odd	12
195.2.bf.a.17.18	yes	96	195.173	even	12
195.2.bf.a.23.7	yes	96	15.14	odd	2
195.2.bf.a.23.18	yes	96	5.4	even	2
195.2.bf.a.62.7	yes	96	5.3	odd	4
195.2.bf.a.62.18	yes	96	15.8	even	4
195.2.bf.a.173.7	yes	96	195.134	odd	6
195.2.bf.a.173.18	yes	96	65.4	even	6
975.2.bn.d.218.7		96	1.1	even	1	trivial
975.2.bn.d.218.18		96	3.2	odd	2	inner
975.2.bn.d.257.7		96	15.2	even	4	inner
975.2.bn.d.257.18		96	5.2	odd	4	inner
975.2.bn.d.368.7		96	13.4	even	6	inner
975.2.bn.d.368.18		96	39.17	odd	6	inner
975.2.bn.d.407.7		96	195.17	even	12	inner
975.2.bn.d.407.18		96	65.17	odd	12	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.bn (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.42342 - 0.381405i) q^{2} +(-1.13110 + 1.31172i) q^{3} +(0.148609 + 0.0857994i) q^{4} +(2.11032 - 1.43573i) q^{6} +(-3.97287 + 1.06453i) q^{7} +(1.90523 + 1.90523i) q^{8} +(-0.441245 - 2.96737i) q^{9} +(2.13830 + 3.70364i) q^{11} +(-0.280636 + 0.0978867i) q^{12} +(3.59901 - 0.217053i) q^{13} +6.06108 q^{14} +(-2.15688 - 3.73582i) q^{16} +(2.26413 - 0.606673i) q^{17} +(-0.503692 + 4.39212i) 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} +(-4.65412 + 0.344139i) q^{24} +(-5.20570 - 1.06372i) q^{26} +(4.39147 + 2.77759i) q^{27} +(-0.681739 - 0.182671i) q^{28} +(0.553990 + 0.959539i) q^{29} +2.59652i q^{31} +(0.250564 + 0.935116i) q^{32} +(-7.27679 - 1.38431i) q^{33} -3.45421 q^{34} +(0.189026 - 0.478837i) q^{36} +(0.255918 - 0.955101i) q^{37} +(5.05499 - 5.05499i) q^{38} +(-3.78611 + 4.96642i) q^{39} +(0.575209 + 0.996292i) q^{41} +(-6.85566 + 7.95047i) q^{42} +(-9.84550 + 2.63809i) q^{43} +0.733860i q^{44} +(-3.60327 - 2.08035i) q^{46} +(-3.07931 + 3.07931i) q^{47} +(7.34000 + 1.39634i) 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} +(-5.19152 - 5.62861i) q^{54} +(-9.59737 - 5.54104i) q^{56} +(-2.76729 - 7.93368i) 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} +(4.91185 + 11.3193i) q^{63} +7.20087i q^{64} +(9.82995 + 4.74586i) q^{66} +(-1.59596 + 5.95621i) q^{67} +(0.388523 + 0.104104i) q^{68} +(-4.04329 + 2.75080i) q^{69} +(4.38783 - 7.59994i) q^{71} +(4.81284 - 6.49418i) 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} +(7.28345 - 5.62527i) q^{78} -2.06111i q^{79} +(-8.61061 + 2.61868i) q^{81} +(-0.438775 - 1.63753i) q^{82} +(-6.21215 - 6.21215i) q^{83} +(1.01073 - 0.687636i) q^{84} +15.0205 q^{86} +(-1.88527 - 0.358648i) 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} +(-3.40592 - 2.93691i) 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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