LMFDB - Embedded newform 875.2.bb.c.507.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [875,2,Mod(82,875)] 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("875.82"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(875, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([27, 50])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not minimal)

Newform invariants

comment:select newform

sage:traces = [288,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			507.14
Character	$\chi$	$=$	875.507
Dual form			875.2.bb.c.768.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.32236 + 0.858753i) q^{2} +(0.119873 + 0.0460148i) q^{3} +(0.197716 + 0.444077i) q^{4} +(0.119000 + 0.163789i) q^{6} +(0.202552 - 2.63799i) q^{7} +(0.373412 - 2.35763i) q^{8} +(-2.21718 - 1.99636i) q^{9} +(2.39345 + 2.65820i) q^{11} +(0.00326660 + 0.0623305i) q^{12} +(0.403536 - 0.791984i) q^{13} +(2.53323 - 3.31444i) q^{14} +(3.16894 - 3.51947i) q^{16} +(-5.12118 - 4.14705i) q^{17} +(-1.21754 - 4.54393i) q^{18} +(-0.939710 - 0.418386i) q^{19} +(0.145667 - 0.306902i) q^{21} +(0.882278 + 5.57049i) q^{22} +(1.46557 - 2.25678i) q^{23} +(0.153248 - 0.265433i) q^{24} +(1.21374 - 0.700753i) q^{26} +(-0.348796 - 0.684551i) q^{27} +(1.21152 - 0.431623i) q^{28} +(-0.242693 + 0.334038i) q^{29} +(4.38248 - 0.460617i) q^{31} +(2.60148 - 0.697064i) q^{32} +(0.164593 + 0.428779i) q^{33} +(-3.21077 - 9.88174i) q^{34} +(0.448165 - 1.37931i) q^{36} +(10.4129 - 0.545719i) q^{37} +(-0.883348 - 1.36024i) q^{38} +(0.0848159 - 0.0763686i) q^{39} +(0.884011 - 0.287233i) q^{41} +(0.456178 - 0.280744i) q^{42} +(-3.39602 + 3.39602i) q^{43} +(-0.707220 + 1.58844i) q^{44} +(3.87603 - 1.72572i) q^{46} +(4.26766 + 5.27013i) q^{47} +(0.541817 - 0.276070i) q^{48} +(-6.91795 - 1.06866i) q^{49} +(-0.423064 - 0.732768i) q^{51} +(0.431487 + 0.0226133i) q^{52} +(2.94467 - 7.67112i) q^{53} +(0.126625 - 1.20475i) q^{54} +(-6.14376 - 1.46260i) q^{56} +(-0.0933936 - 0.0933936i) q^{57} +(-0.607784 + 0.233306i) q^{58} +(5.60265 + 1.19088i) q^{59} +(1.11752 + 5.25754i) q^{61} +(6.19079 + 3.15437i) q^{62} +(-5.71547 + 5.44453i) q^{63} +(-4.96953 - 1.61470i) q^{64} +(-0.150564 + 0.708347i) q^{66} +(-6.86033 + 8.47180i) q^{67} +(0.829071 - 3.09413i) q^{68} +(0.279527 - 0.203088i) q^{69} +(5.23629 + 3.80439i) q^{71} +(-5.53460 + 4.48183i) q^{72} +(-0.600604 + 11.4602i) q^{73} +(14.2383 + 8.22050i) q^{74} -0.500025i q^{76} +(7.49709 - 5.77547i) q^{77} +(0.177739 - 0.0281511i) q^{78} +(13.2858 + 1.39640i) q^{79} +(0.925274 + 8.80340i) q^{81} +(1.41565 + 0.379321i) q^{82} +(-10.5884 - 1.67704i) q^{83} +(0.165089 + 0.00400790i) q^{84} +(-7.40711 + 1.57443i) q^{86} +(-0.0444629 + 0.0288746i) q^{87} +(7.16079 - 4.65027i) q^{88} +(5.11164 - 1.08651i) q^{89} +(-2.00751 - 1.22494i) q^{91} +(1.29195 + 0.204625i) q^{92} +(0.546535 + 0.146444i) q^{93} +(1.11767 + 10.6339i) q^{94} +(0.343922 + 0.0361476i) q^{96} +(-14.9519 + 2.36815i) q^{97} +(-8.23033 - 7.35396i) q^{98} -10.6719i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) $ 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.32236	+	0.858753i	0.935052	+	0.607230i	0.919687	−	0.392652i	$-0.128442\pi$
$2$	1.32236	+	0.858753i	0.935052	+	0.607230i	0.0153652	+	0.999882i	$0.495109\pi$
$3$	0.119873	+	0.0460148i	0.0692085	+	0.0265667i	0.392726	−	0.919656i	$-0.371532\pi$
$3$	0.119873	+	0.0460148i	0.0692085	+	0.0265667i	−0.323517	+	0.946222i	$0.604865\pi$
$4$	0.197716	+	0.444077i	0.0988579	+	0.222038i
$5$		0			0
$5$		0			0
$6$	0.119000	+	0.163789i	0.0485815	+	0.0668667i
$7$	0.202552	−	2.63799i	0.0765574	−	0.997065i
$7$	0.202552	−	2.63799i	0.0765574	−	0.997065i
$8$	0.373412	−	2.35763i	0.132021	−	0.833549i
$9$	−2.21718	−	1.99636i	−0.739061	−	0.665453i
$10$		0			0
$11$	2.39345	+	2.65820i	0.721653	+	0.801476i	0.986664	−	0.162769i	$-0.0520424\pi$
$11$	2.39345	+	2.65820i	0.721653	+	0.801476i	−0.265012	+	0.964245i	$0.585376\pi$
$12$	0.00326660	+	0.0623305i	0.000942988	+	0.0179933i
$13$	0.403536	−	0.791984i	0.111921	−	0.219657i	−0.828251	−	0.560357i	$-0.810664\pi$
$13$	0.403536	−	0.791984i	0.111921	−	0.219657i	0.940172	+	0.340700i	$0.110664\pi$
$14$	2.53323	−	3.31444i	0.677033	−	0.885820i
$15$		0			0
$16$	3.16894	−	3.51947i	0.792235	−	0.879867i
$17$	−5.12118	−	4.14705i	−1.24207	−	1.00581i	−0.999362	−	0.0357074i	$-0.988632\pi$
$17$	−5.12118	−	4.14705i	−1.24207	−	1.00581i	−0.242706	−	0.970100i	$-0.578035\pi$
$18$	−1.21754	−	4.54393i	−0.286977	−	1.07101i
$19$	−0.939710	−	0.418386i	−0.215584	−	0.0959842i	0.296103	−	0.955156i	$-0.404313\pi$
$19$	−0.939710	−	0.418386i	−0.215584	−	0.0959842i	−0.511687	+	0.859172i	$0.670979\pi$
$20$		0			0
$21$	0.145667	−	0.306902i	0.0317871	−	0.0669715i
$22$	0.882278	+	5.57049i	0.188102	+	1.18763i
$23$	1.46557	−	2.25678i	0.305592	−	0.470571i	−0.652194	−	0.758052i	$-0.726151\pi$
$23$	1.46557	−	2.25678i	0.305592	−	0.470571i	0.957786	+	0.287481i	$0.0928179\pi$
$24$	0.153248	−	0.265433i	0.0312816	−	0.0541813i
$25$		0			0
$26$	1.21374	−	0.700753i	0.238034	−	0.137429i
$27$	−0.348796	−	0.684551i	−0.0671258	−	0.131742i
$28$	1.21152	−	0.431623i	0.228955	−	0.0815690i
$29$	−0.242693	+	0.334038i	−0.0450669	+	0.0620293i	−0.830956	−	0.556339i	$-0.812206\pi$
$29$	−0.242693	+	0.334038i	−0.0450669	+	0.0620293i	0.785889	+	0.618368i	$0.212206\pi$
$30$		0			0
$31$	4.38248	−	0.460617i	0.787117	−	0.0827293i	0.297563	−	0.954702i	$-0.403826\pi$
$31$	4.38248	−	0.460617i	0.787117	−	0.0827293i	0.489554	+	0.871973i	$0.337160\pi$
$32$	2.60148	−	0.697064i	0.459881	−	0.123225i
$33$	0.164593	+	0.428779i	0.0286520	+	0.0746409i
$34$	−3.21077	−	9.88174i	−0.550643	−	1.69470i
$35$		0			0
$36$	0.448165	−	1.37931i	0.0746942	−	0.229885i
$37$	10.4129	−	0.545719i	1.71188	−	0.0897156i	0.828978	−	0.559281i	$-0.188923\pi$
$37$	10.4129	−	0.545719i	1.71188	−	0.0897156i	0.882898	+	0.469565i	$0.155589\pi$
$38$	−0.883348	−	1.36024i	−0.143298	−	0.220659i
$39$	0.0848159	−	0.0763686i	0.0135814	−	0.0122288i
$40$		0			0
$41$	0.884011	−	0.287233i	0.138059	−	0.0448582i	−0.239172	−	0.970977i	$-0.576876\pi$
$41$	0.884011	−	0.287233i	0.138059	−	0.0448582i	0.377232	+	0.926119i	$0.376876\pi$
$42$	0.456178	−	0.280744i	0.0703898	−	0.0433198i
$43$	−3.39602	+	3.39602i	−0.517888	+	0.517888i	−0.916932	−	0.399044i	$-0.869342\pi$
$43$	−3.39602	+	3.39602i	−0.517888	+	0.517888i	0.399044	+	0.916932i	$0.369342\pi$
$44$	−0.707220	+	1.58844i	−0.106618	+	0.239467i
$45$		0			0
$46$	3.87603	−	1.72572i	0.571489	−	0.254443i
$47$	4.26766	+	5.27013i	0.622503	+	0.768727i	0.986692	−	0.162598i	$-0.0519873\pi$
$47$	4.26766	+	5.27013i	0.622503	+	0.768727i	−0.364190	+	0.931325i	$0.618654\pi$
$48$	0.541817	−	0.276070i	0.0782046	−	0.0398472i
$49$	−6.91795	−	1.06866i	−0.988278	−	0.152665i
$50$		0			0
$51$	−0.423064	−	0.732768i	−0.0592408	−	0.102608i
$52$	0.431487	+	0.0226133i	0.0598365	+	0.00313590i
$53$	2.94467	−	7.67112i	0.404481	−	1.05371i	−0.568472	−	0.822703i	$-0.692465\pi$
$53$	2.94467	−	7.67112i	0.404481	−	1.05371i	0.972952	−	0.231006i	$-0.0742016\pi$
$54$	0.126625	−	1.20475i	0.0172315	−	0.163946i
$55$		0			0
$56$	−6.14376	−	1.46260i	−0.820995	−	0.195448i
$57$	−0.0933936	−	0.0933936i	−0.0123703	−	0.0123703i
$58$	−0.607784	+	0.233306i	−0.0798060	+	0.0306346i
$59$	5.60265	+	1.19088i	0.729403	+	0.155039i	0.557621	−	0.830096i	$-0.311714\pi$
$59$	5.60265	+	1.19088i	0.729403	+	0.155039i	0.171782	+	0.985135i	$0.445048\pi$
$60$		0			0
$61$	1.11752	+	5.25754i	0.143084	+	0.673159i	0.989958	+	0.141364i	$0.0451489\pi$
$61$	1.11752	+	5.25754i	0.143084	+	0.673159i	−0.846873	+	0.531795i	$0.821518\pi$
$62$	6.19079	+	3.15437i	0.786231	+	0.400605i
$63$	−5.71547	+	5.44453i	−0.720081	+	0.685946i
$64$	−4.96953	−	1.61470i	−0.621191	−	0.201837i
$65$		0			0
$66$	−0.150564	+	0.708347i	−0.0185331	+	0.0871915i
$67$	−6.86033	+	8.47180i	−0.838123	+	1.03500i	0.160725	+	0.986999i	$0.448617\pi$
$67$	−6.86033	+	8.47180i	−0.838123	+	1.03500i	−0.998848	+	0.0479959i	$0.984717\pi$
$68$	0.829071	−	3.09413i	0.100540	−	0.375219i
$69$	0.279527	−	0.203088i	0.0336511	−	0.0244489i
$70$		0			0
$71$	5.23629	+	3.80439i	0.621433	+	0.451498i	0.853422	−	0.521221i	$-0.174523\pi$
$71$	5.23629	+	3.80439i	0.621433	+	0.451498i	−0.231988	+	0.972719i	$0.574523\pi$
$72$	−5.53460	+	4.48183i	−0.652259	+	0.528189i
$73$	−0.600604	+	11.4602i	−0.0702954	+	1.34132i	0.704770	+	0.709436i	$0.251050\pi$
$73$	−0.600604	+	11.4602i	−0.0702954	+	1.34132i	−0.775066	+	0.631881i	$0.782283\pi$
$74$	14.2383	+	8.22050i	1.65517	+	0.955614i
$75$		0			0
$76$		−	0.500025i		−	0.0573567i
$77$	7.49709	−	5.77547i	0.854372	−	0.658176i
$78$	0.177739	−	0.0281511i	0.0201250	−	0.00318749i
$79$	13.2858	+	1.39640i	1.49477	+	0.157107i	0.816348	−	0.577561i	$-0.195995\pi$
$79$	13.2858	+	1.39640i	1.49477	+	0.157107i	0.678427	+	0.734668i	$0.262662\pi$
$80$		0			0
$81$	0.925274	+	8.80340i	0.102808	+	0.978155i
$82$	1.41565	+	0.379321i	0.156332	+	0.0418890i
$83$	−10.5884	−	1.67704i	−1.16223	−	0.184079i	−0.454621	−	0.890685i	$-0.650225\pi$
$83$	−10.5884	−	1.67704i	−1.16223	−	0.184079i	−0.707607	+	0.706606i	$0.750225\pi$
$84$	0.165089	+	0.00400790i	0.0180127	+	0.000437298i
$85$		0			0
$86$	−7.40711	+	1.57443i	−0.798729	+	0.169775i
$87$	−0.0444629	+	0.0288746i	−0.00476693	+	0.00309568i
$88$	7.16079	−	4.65027i	0.763343	−	0.495721i
$89$	5.11164	−	1.08651i	0.541833	−	0.115170i	0.0711385	−	0.997466i	$-0.477337\pi$
$89$	5.11164	−	1.08651i	0.541833	−	0.115170i	0.470694	+	0.882296i	$0.344003\pi$
$90$		0			0
$91$	−2.00751	−	1.22494i	−0.210444	−	0.128409i
$92$	1.29195	+	0.204625i	0.134695	+	0.0213336i
$93$	0.546535	+	0.146444i	0.0566731	+	0.0151855i
$94$	1.11767	+	10.6339i	0.115279	+	1.09680i
$95$		0			0
$96$	0.343922	+	0.0361476i	0.0351013	+	0.00368930i
$97$	−14.9519	+	2.36815i	−1.51813	+	0.240449i	−0.859156	−	0.511714i	$-0.829011\pi$
$97$	−14.9519	+	2.36815i	−1.51813	+	0.240449i	−0.658978	+	0.752163i	$0.729011\pi$
$98$	−8.23033	−	7.35396i	−0.831389	−	0.742862i
$99$		−	10.6719i		−	1.07257i
$100$		0			0
$101$	−16.4574	−	9.50169i	−1.63757	−	0.945453i	−0.981665	−	0.190612i	$-0.938953\pi$
$101$	−16.4574	−	9.50169i	−1.63757	−	0.945453i	−0.655908	−	0.754841i	$-0.727714\pi$
$102$	0.0698225	−	1.33229i	0.00691346	−	0.131917i
$103$	−7.69124	+	6.22825i	−0.757841	+	0.613687i	−0.928367	−	0.371666i	$-0.878787\pi$
$103$	−7.69124	+	6.22825i	−0.757841	+	0.613687i	0.170526	+	0.985353i	$0.445453\pi$
$104$	−1.71652	−	1.24713i	−0.168319	−	0.122291i
$105$		0			0
$106$	10.4815	−	7.61526i	1.01805	−	0.739660i
$107$	2.95772	−	11.0384i	0.285933	−	1.06712i	−0.662221	−	0.749309i	$-0.730386\pi$
$107$	2.95772	−	11.0384i	0.285933	−	1.06712i	0.948155	−	0.317810i	$-0.102947\pi$
$108$	0.235031	−	0.290239i	0.0226158	−	0.0279282i
$109$	0.940403	−	4.42425i	0.0900743	−	0.423766i	−0.909886	−	0.414858i	$-0.863831\pi$
$109$	0.940403	−	4.42425i	0.0900743	−	0.423766i	0.999960	−	0.00890792i	$-0.00283552\pi$
$110$		0			0
$111$	1.27334	+	0.413733i	0.120860	+	0.0392698i
$112$	−8.64243	−	9.07250i	−0.816633	−	0.857271i
$113$	5.01371	+	2.55462i	0.471651	+	0.240318i	0.673626	−	0.739073i	$-0.264736\pi$
$113$	5.01371	+	2.55462i	0.471651	+	0.240318i	−0.201975	+	0.979391i	$0.564736\pi$
$114$	−0.0432983	−	0.203702i	−0.00405525	−	0.0190785i
$115$		0			0
$116$	−0.196323	−	0.0417297i	−0.0182281	−	0.00387450i
$117$	−2.47580	+	0.950370i	−0.228888	+	0.0878617i
$118$	6.38607	+	6.38607i	0.587885	+	0.587885i
$119$	−11.9772	+	12.6696i	−1.09794	+	1.16142i
$120$		0			0
$121$	−0.187589	+	1.78479i	−0.0170535	+	0.162253i
$122$	−3.03715	+	7.91206i	−0.274971	+	0.716324i
$123$	0.119186	+	0.00624626i	0.0107466	+	0.000563207i
$124$	1.07103	+	1.85509i	0.0961818	+	0.166592i
$125$		0			0
$126$	−12.2334	+	2.29148i	−1.08984	+	0.204141i
$127$	8.63797	−	4.40126i	0.766495	−	0.390549i	−0.0266001	−	0.999646i	$-0.508468\pi$
$127$	8.63797	−	4.40126i	0.766495	−	0.390549i	0.793096	+	0.609097i	$0.208468\pi$
$128$	−8.57473	−	10.5889i	−0.757906	−	0.935936i
$129$	−0.563357	+	0.250823i	−0.0496008	+	0.0220837i
$130$		0			0
$131$	7.38721	−	16.5919i	0.645423	−	1.44964i	−0.233344	−	0.972394i	$-0.574967\pi$
$131$	7.38721	−	16.5919i	0.645423	−	1.44964i	0.878767	−	0.477250i	$-0.158366\pi$
$132$	−0.157868	+	0.157868i	−0.0137407	+	0.0137407i
$133$	−1.29404	+	2.39420i	−0.112207	+	0.207603i
$134$	−16.3470	+	5.31147i	−1.41217	+	0.458841i
$135$		0			0
$136$	−11.6895	+	10.5253i	−1.00237	+	0.902537i
$137$	6.68277	+	10.2906i	0.570948	+	0.879182i	0.999706	−	0.0242369i	$-0.00771559\pi$
$137$	6.68277	+	10.2906i	0.570948	+	0.879182i	−0.428759	+	0.903419i	$0.641049\pi$
$138$	0.544039	−	0.0285119i	0.0463117	−	0.00242709i
$139$	−1.49559	+	4.60294i	−0.126854	+	0.390417i	−0.994234	−	0.107229i	$-0.965802\pi$
$139$	−1.49559	+	4.60294i	−0.126854	+	0.390417i	0.867380	+	0.497646i	$0.165802\pi$
$140$		0			0
$141$	0.269073	+	0.828120i	0.0226600	+	0.0697403i
$142$	3.65725	+	9.52747i	0.306910	+	0.799527i
$143$	3.07109	−	0.822897i	0.256818	−	0.0688141i
$144$	−14.0522	+	1.47695i	−1.17102	+	0.123079i
$145$		0			0
$146$	−10.6357	+	14.6388i	−0.880218	+	1.21152i
$147$	−0.780099	−	0.446431i	−0.0643415	−	0.0368210i
$148$	2.30114	+	4.51624i	0.189153	+	0.371233i
$149$	8.82683	−	5.09617i	0.723122	−	0.417495i	−0.0927785	−	0.995687i	$-0.529575\pi$
$149$	8.82683	−	5.09617i	0.723122	−	0.417495i	0.815901	+	0.578192i	$0.196242\pi$
$150$		0			0
$151$	−0.622057	+	1.07743i	−0.0506223	+	0.0876804i	−0.890226	−	0.455519i	$-0.849454\pi$
$151$	−0.622057	+	1.07743i	−0.0506223	+	0.0876804i	0.839604	+	0.543199i	$0.182787\pi$
$152$	−1.33730	+	2.05926i	−0.108469	+	0.167028i
$153$	3.07559	+	19.4185i	0.248646	+	1.56989i
$154$	14.8736	−	1.19913i	1.19855	−	0.0966283i
$155$		0			0
$156$	0.0506830	+	0.0225655i	0.00405788	+	0.00180669i
$157$	−2.47670	−	9.24318i	−0.197662	−	0.737686i	−0.991562	−	0.129637i	$-0.958619\pi$
$157$	−2.47670	−	9.24318i	−0.197662	−	0.737686i	0.793899	−	0.608050i	$-0.208048\pi$
$158$	16.3696	+	13.2558i	1.30229	+	1.05458i
$159$	0.705970	−	0.784059i	0.0559871	−	0.0621799i
$160$		0			0
$161$	−5.65650	−	4.32326i	−0.445794	−	0.340721i
$162$	−6.33640	+	12.4359i	−0.497834	+	0.977055i
$163$	−0.359496	−	6.85959i	−0.0281579	−	0.537285i	−0.975896	−	0.218236i	$-0.929970\pi$
$163$	−0.359496	−	6.85959i	−0.0281579	−	0.537285i	0.947738	−	0.319049i	$-0.103364\pi$
$164$	0.302336	+	0.335778i	0.0236085	+	0.0262199i
$165$		0			0
$166$	−12.5616	−	11.3105i	−0.974966	−	0.877864i
$167$	−0.493915	+	3.11846i	−0.0382203	+	0.241313i	−0.999401	−	0.0346062i	$-0.988982\pi$
$167$	−0.493915	+	3.11846i	−0.0382203	+	0.241313i	0.961181	+	0.275919i	$0.0889823\pi$
$168$	−0.669168	−	0.458030i	−0.0516275	−	0.0353378i
$169$	7.17681	+	9.87803i	0.552062	+	0.759849i
$170$		0			0
$171$	1.24826	+	2.80364i	0.0954568	+	0.214399i
$172$	−2.17954	−	0.836646i	−0.166188	−	0.0637937i
$173$	3.25418	+	2.11329i	0.247410	+	0.160670i	0.662387	−	0.749162i	$-0.269544\pi$
$173$	3.25418	+	2.11329i	0.247410	+	0.160670i	−0.414976	+	0.909832i	$0.636210\pi$
$174$	−0.0835923			−0.00633712
$175$		0			0
$176$	16.9401			1.27691
$177$	0.616807	+	0.400559i	0.0463620	+	0.0301078i
$178$	7.69250	+	2.95287i	0.576577	+	0.221327i
$179$	7.43942	+	16.7092i	0.556049	+	1.24891i	0.944826	+	0.327574i	$0.106231\pi$
$179$	7.43942	+	16.7092i	0.556049	+	1.24891i	−0.388777	+	0.921332i	$0.627102\pi$
$180$		0			0
$181$	11.0244	+	15.1738i	0.819436	+	1.12786i	0.989798	+	0.142475i	$0.0455062\pi$
$181$	11.0244	+	15.1738i	0.819436	+	1.12786i	−0.170362	+	0.985381i	$0.554494\pi$
$182$	−1.60273	−	3.34377i	−0.118802	−	0.247857i
$183$	−0.107964	+	0.681658i	−0.00798093	+	0.0503896i
$184$	−4.77339	−	4.29798i	−0.351899	−	0.316851i
$185$		0			0
$186$	0.596959	+	0.662991i	0.0437712	+	0.0486128i
$187$	−1.23362	−	23.5389i	−0.0902112	−	1.72133i
$188$	−1.49656	+	2.93716i	−0.109148	+	0.214214i
$189$	−1.87649	+	0.781462i	−0.136494	+	0.0568430i
$190$		0			0
$191$	5.14365	−	5.71260i	0.372182	−	0.413349i	−0.527737	−	0.849408i	$-0.676959\pi$
$191$	5.14365	−	5.71260i	0.372182	−	0.413349i	0.899918	+	0.436058i	$0.143626\pi$
$192$	−0.521411	−	0.422230i	−0.0376296	−	0.0304718i
$193$	3.71761	+	13.8743i	0.267599	+	0.998695i	0.960640	+	0.277796i	$0.0896040\pi$
$193$	3.71761	+	13.8743i	0.267599	+	0.998695i	−0.693041	+	0.720899i	$0.743729\pi$
$194$	−21.8055	−	9.70842i	−1.56554	−	0.697024i
$195$		0			0
$196$	−0.893220	−	3.28339i	−0.0638015	−	0.234528i
$197$	−0.320426	−	2.02309i	−0.0228294	−	0.144139i	0.973641	−	0.228087i	$-0.0732471\pi$
$197$	−0.320426	−	2.02309i	−0.0228294	−	0.144139i	−0.996470	+	0.0839479i	$0.973247\pi$
$198$	9.16452	−	14.1121i	0.651294	−	1.00291i
$199$	−2.93779	+	5.08840i	−0.208254	+	0.360707i	−0.951165	−	0.308684i	$-0.900111\pi$
$199$	−2.93779	+	5.08840i	−0.208254	+	0.360707i	0.742910	+	0.669391i	$0.233445\pi$
$200$		0			0
$201$	−1.21219	+	0.699861i	−0.0855016	+	0.0493644i
$202$	−13.6031	−	26.6975i	−0.957109	−	1.87843i
$203$	0.832030	+	0.707880i	0.0583970	+	0.0496835i
$204$	0.241759	−	0.332753i	0.0169265	−	0.0232973i
$205$		0			0
$206$	−15.5191	+	1.63113i	−1.08127	+	0.113646i
$207$	−7.75477	+	2.07789i	−0.538994	+	0.144423i
$208$	−1.50858	−	3.92998i	−0.104601	−	0.272495i
$209$	−1.13700	−	3.49932i	−0.0786478	−	0.242053i
$210$		0			0
$211$	5.78925	−	17.8175i	0.398549	−	1.22661i	−0.527615	−	0.849484i	$-0.676914\pi$
$211$	5.78925	−	17.8175i	0.398549	−	1.22661i	0.926163	−	0.377123i	$-0.123086\pi$
$212$	3.98877	−	0.209043i	0.273950	−	0.0143571i
$213$	0.452630	+	0.696989i	0.0310137	+	0.0477569i
$214$	13.3904	−	12.0568i	0.915349	−	0.824184i
$215$		0			0
$216$	−1.74416	+	0.566713i	−0.118675	+	0.0385599i
$217$	−0.327423	−	11.6542i	−0.0222269	−	0.791140i
$218$	5.04289	−	5.04289i	0.341548	−	0.341548i
$219$	−0.599336	+	1.34613i	−0.0404993	+	0.0909630i
$220$		0			0
$221$	−5.35098	+	2.38241i	−0.359946	+	0.160258i
$222$	1.32852	+	1.64059i	0.0891645	+	0.110109i
$223$	−9.90574	+	5.04723i	−0.663338	+	0.337987i	−0.753034	−	0.657982i	$-0.771410\pi$
$223$	−9.90574	+	5.04723i	−0.663338	+	0.337987i	0.0896962	+	0.995969i	$0.471410\pi$
$224$	−1.31191	−	7.00386i	−0.0876558	−	0.467965i
$225$		0			0
$226$	4.43617	+	7.68367i	0.295090	+	0.511110i
$227$	−19.2637	−	1.00957i	−1.27858	−	0.0670074i	−0.599082	−	0.800688i	$-0.704468\pi$
$227$	−19.2637	−	1.00957i	−1.27858	−	0.0670074i	−0.679495	+	0.733680i	$0.737801\pi$
$228$	0.0230085	−	0.0599393i	0.00152378	−	0.00396958i
$229$	−2.84107	+	27.0310i	−0.187743	+	1.78626i	0.343617	+	0.939110i	$0.388348\pi$
$229$	−2.84107	+	27.0310i	−0.187743	+	1.78626i	−0.531360	+	0.847146i	$0.678319\pi$
$230$		0			0
$231$	1.16445	−	0.347344i	0.0766154	−	0.0228536i
$232$	0.696914	+	0.696914i	0.0457546	+	0.0457546i
$233$	20.7289	−	7.95709i	1.35800	−	0.521286i	0.433046	−	0.901372i	$-0.357439\pi$
$233$	20.7289	−	7.95709i	1.35800	−	0.521286i	0.924951	+	0.380085i	$0.124105\pi$
$234$	−4.09004	−	0.869364i	−0.267374	−	0.0568321i
$235$		0			0
$236$	0.578890	+	2.72346i	0.0376825	+	0.177282i
$237$	1.52836	+	0.778736i	0.0992774	+	0.0505843i
$238$	−26.7182	+	6.46841i	−1.73189	+	0.419284i
$239$	−27.7649	−	9.02136i	−1.79596	−	0.583543i	−0.796192	−	0.605044i	$-0.793156\pi$
$239$	−27.7649	−	9.02136i	−1.79596	−	0.583543i	−0.999769	+	0.0215007i	$0.993156\pi$
$240$		0			0
$241$	−0.390608	+	1.83766i	−0.0251612	+	0.118374i	−0.988936	−	0.148344i	$-0.952606\pi$
$241$	−0.390608	+	1.83766i	−0.0251612	+	0.118374i	0.963775	+	0.266718i	$0.0859392\pi$
$242$	−1.78075	+	2.19905i	−0.114471	+	0.141360i
$243$	−0.890715	+	3.32420i	−0.0571394	+	0.213247i
$244$	−2.11380	+	1.53577i	−0.135322	+	0.0983173i
$245$		0			0
$246$	0.152243	+	0.110611i	0.00970666	+	0.00705230i
$247$	−0.710561	+	0.575401i	−0.0452119	+	0.0366119i
$248$	0.550506	−	10.5043i	0.0349572	−	0.667022i
$249$	−1.19209	−	0.688255i	−0.0755458	−	0.0436164i
$250$		0			0
$251$			16.4158i			1.03616i	0.855333	+	0.518078i	$0.173352\pi$
$251$			16.4158i			1.03616i	−0.855333	+	0.518078i	$0.826648\pi$
$252$	−3.54783	−	1.46164i	−0.223492	−	0.0920744i
$253$	9.50673	−	1.50572i	0.597683	−	0.0946636i
$254$	15.2021	+	1.59781i	0.953866	+	0.100255i
$255$		0			0
$256$	−1.15327	−	10.9727i	−0.0720796	−	0.685792i
$257$	6.19747	+	1.66061i	0.386587	+	0.103586i	0.446878	−	0.894595i	$-0.352536\pi$
$257$	6.19747	+	1.66061i	0.386587	+	0.103586i	−0.0602903	+	0.998181i	$0.519203\pi$
$258$	−0.960357	−	0.152106i	−0.0597892	−	0.00946969i
$259$	0.669560	−	27.5797i	0.0416044	−	1.71372i
$260$		0			0
$261$	1.20495	−	0.256121i	0.0745848	−	0.0158535i
$262$	24.0170	−	15.5968i	1.48377	−	0.963573i
$263$	4.57419	−	2.97051i	0.282056	−	0.183170i	−0.395855	−	0.918313i	$-0.629552\pi$
$263$	4.57419	−	2.97051i	0.282056	−	0.183170i	0.677912	+	0.735143i	$0.262885\pi$
$264$	1.07236	−	0.227938i	0.0659995	−	0.0140286i
$265$		0			0
$266$	−3.76721	+	2.05474i	−0.230982	+	0.125984i
$267$	0.662742	+	0.104968i	0.0405592	+	0.00642394i
$268$	−5.11852	−	1.37150i	−0.312664	−	0.0837780i
$269$	1.26767	+	12.0610i	0.0772910	+	0.735375i	0.962702	+	0.270565i	$0.0872106\pi$
$269$	1.26767	+	12.0610i	0.0772910	+	0.735375i	−0.885411	+	0.464810i	$0.846123\pi$
$270$		0			0
$271$	14.1276	+	1.48487i	0.858191	+	0.0901995i	0.523394	−	0.852091i	$-0.324666\pi$
$271$	14.1276	+	1.48487i	0.858191	+	0.0901995i	0.334797	+	0.942290i	$0.391332\pi$
$272$	−30.8241	+	4.88206i	−1.86899	+	0.296018i
$273$	−0.184280	−	0.239212i	−0.0111531	−	0.0144778i
$274$			19.3467i			1.16878i
$275$		0			0
$276$	0.145454	+	0.0839777i	0.00875528	+	0.00505486i
$277$	−0.492974	+	9.40651i	−0.0296199	+	0.565182i	0.943002	+	0.332788i	$0.107989\pi$
$277$	−0.492974	+	9.40651i	−0.0296199	+	0.565182i	−0.972622	+	0.232394i	$0.925344\pi$
$278$	−5.93050	+	4.80243i	−0.355688	+	0.288030i
$279$	−10.6363	−	7.72774i	−0.636780	−	0.462648i
$280$		0			0
$281$	−0.976989	+	0.709824i	−0.0582823	+	0.0423446i	−0.616545	−	0.787320i	$-0.711468\pi$
$281$	−0.976989	+	0.709824i	−0.0582823	+	0.0423446i	0.558263	+	0.829664i	$0.311468\pi$
$282$	−0.355339	+	1.32614i	−0.0211601	+	0.0789707i
$283$	3.31396	−	4.09240i	0.196994	−	0.243268i	−0.669071	−	0.743198i	$-0.733308\pi$
$283$	3.31396	−	4.09240i	0.196994	−	0.243268i	0.866065	+	0.499931i	$0.166641\pi$
$284$	−0.654143	+	3.07750i	−0.0388163	+	0.182616i
$285$		0			0
$286$	4.76777	+	1.54914i	0.281924	+	0.0916026i
$287$	−0.578658	−	2.39019i	−0.0341571	−	0.141088i
$288$	−7.15954	−	3.64797i	−0.421880	−	0.214959i
$289$	5.49396	+	25.8471i	0.323174	+	1.52042i
$290$		0			0
$291$	−1.90129	−	0.404132i	−0.111456	−	0.0236906i
$292$	−5.20796	+	1.99915i	−0.304773	+	0.116991i
$293$	−15.0009	−	15.0009i	−0.876365	−	0.876365i	0.116792	−	0.993156i	$-0.462739\pi$
$293$	−15.0009	−	15.0009i	−0.876365	−	0.876365i	−0.993156	+	0.116792i	$0.962739\pi$
$294$	−0.648200	−	1.26026i	−0.0378038	−	0.0734996i
$295$		0			0
$296$	2.60171	−	24.7536i	0.151221	−	1.43878i
$297$	0.984844	−	2.56561i	0.0571465	−	0.148872i
$298$	16.0486	+	0.841073i	0.929673	+	0.0487221i
$299$	−1.19592	−	2.07140i	−0.0691619	−	0.119792i
$300$		0			0
$301$	8.27078	+	9.64652i	0.476720	+	0.556016i
$302$	−1.74784	+	0.890567i	−0.100577	+	0.0512464i
$303$	−1.53558	−	1.89628i	−0.0882165	−	0.108938i
$304$	−4.45038	+	1.98144i	−0.255247	+	0.113643i
$305$		0			0
$306$	−12.6086	+	28.3195i	−0.720788	+	1.61892i
$307$	9.86884	−	9.86884i	0.563245	−	0.563245i	−0.366983	−	0.930228i	$-0.619609\pi$
$307$	9.86884	−	9.86884i	0.563245	−	0.563245i	0.930228	+	0.366983i	$0.119609\pi$
$308$	4.04704	+	2.18738i	0.230602	+	0.124638i
$309$	−1.20856	+	0.392686i	−0.0687527	+	0.0223391i
$310$		0			0
$311$	18.4706	−	16.6310i	1.04737	−	0.943058i	0.0489271	−	0.998802i	$-0.484420\pi$
$311$	18.4706	−	16.6310i	1.04737	−	0.943058i	0.998445	+	0.0557442i	$0.0177531\pi$
$312$	−0.148378	−	0.228482i	−0.00840024	−	0.0129352i
$313$	28.2118	−	1.47852i	1.59463	−	0.0835709i	0.765801	−	0.643077i	$-0.222343\pi$
$313$	28.2118	−	1.47852i	1.59463	−	0.0835709i	0.828826	+	0.559506i	$0.189009\pi$
$314$	4.66251	−	14.3497i	0.263121	−	0.809802i
$315$		0			0
$316$	2.00671	+	6.17603i	0.112886	+	0.347429i
$317$	−0.00445631	−	0.0116091i	−0.000250291	−	0.000652031i	0.933455	−	0.358694i	$-0.116778\pi$
$317$	−0.00445631	−	0.0116091i	−0.000250291	−	0.000652031i	−0.933706	+	0.358042i	$0.883444\pi$
$318$	1.60686	−	0.430557i	0.0901084	−	0.0241445i
$319$	−1.46881	+	0.154378i	−0.0822377	+	0.00864353i
$320$		0			0
$321$	0.862478	−	1.18710i	0.0481388	−	0.0662574i
$322$	−3.76733	−	10.5745i	−0.209945	−	0.589292i
$323$	3.07736	+	6.03965i	0.171229	+	0.336055i
$324$	−3.72644	+	2.15146i	−0.207025	+	0.119526i
$325$		0			0
$326$	5.41531	−	9.37960i	0.299926	−	0.519488i
$327$	0.316310	−	0.487074i	0.0174920	−	0.0269353i
$328$	−0.347088	−	2.19143i	−0.0191647	−	0.121001i
$329$	14.7669	−	10.1906i	0.814128	−	0.561824i
$330$		0			0
$331$	−19.8914	−	8.85621i	−1.09333	−	0.486781i	−0.220788	−	0.975322i	$-0.570863\pi$
$331$	−19.8914	−	8.85621i	−1.09333	−	0.486781i	−0.872541	+	0.488541i	$0.837529\pi$
$332$	−1.34876	−	5.03364i	−0.0740228	−	0.276257i
$333$	−24.1768	−	19.5780i	−1.32488	−	1.07287i
$334$	−3.33112	+	3.69958i	−0.182271	+	0.202432i
$335$		0			0
$336$	−0.618522	−	1.48523i	−0.0337431	−	0.0810257i
$337$	−10.8166	+	21.2288i	−0.589219	+	1.15641i	0.383309	+	0.923620i	$0.374784\pi$
$337$	−10.8166	+	21.2288i	−0.589219	+	1.15641i	−0.972528	+	0.232787i	$0.925216\pi$
$338$	1.00756	+	19.2255i	0.0548042	+	1.04573i
$339$	0.483457	+	0.536934i	0.0262578	+	0.0291622i
$340$		0			0
$341$	11.7137	+	10.5470i	0.634331	+	0.571154i
$342$	−0.756978	+	4.77937i	−0.0409327	+	0.258439i
$343$	−4.22035	+	18.0330i	−0.227877	+	0.973690i
$344$	6.73844	+	9.27467i	0.363312	+	0.500057i
$345$		0			0
$346$	2.48841	+	5.58907i	0.133778	+	0.300470i
$347$	21.1545	+	8.12046i	1.13563	+	0.435929i	0.852280	−	0.523086i	$-0.175219\pi$
$347$	21.1545	+	8.12046i	1.13563	+	0.435929i	0.283355	+	0.959015i	$0.408553\pi$
$348$	−0.0216135	−	0.0140360i	−0.00115861	−	0.000752409i
$349$	10.6290			0.568958			0.284479	−	0.958682i	$-0.408179\pi$
$349$	10.6290			0.568958			0.284479	+	0.958682i	$0.408179\pi$
$350$		0			0
$351$	−0.682905			−0.0364508
$352$	8.07945	+	5.24685i	0.430636	+	0.279658i
$353$	4.31622	+	1.65684i	0.229729	+	0.0881849i	0.470510	−	0.882395i	$-0.344070\pi$
$353$	4.31622	+	1.65684i	0.229729	+	0.0881849i	−0.240780	+	0.970580i	$0.577403\pi$
$354$	0.471661	+	1.05937i	0.0250685	+	0.0563048i
$355$		0			0
$356$	1.49315	+	2.05514i	0.0791366	+	0.108922i
$357$	−2.01872	+	0.967613i	−0.106842	+	0.0512115i
$358$	−4.51147	+	28.4843i	−0.238438	+	1.50544i
$359$	2.16199	+	1.94666i	0.114105	+	0.102741i	0.724209	−	0.689581i	$-0.242205\pi$
$359$	2.16199	+	1.94666i	0.114105	+	0.102741i	−0.610103	+	0.792322i	$0.708872\pi$
$360$		0			0
$361$	−12.0055	−	13.3334i	−0.631867	−	0.701759i
$362$	1.54773	+	29.5325i	0.0813469	+	1.55219i
$363$	−0.104613	+	0.205315i	−0.00549078	+	0.0107763i
$364$	0.147052	−	1.13368i	0.00770762	−	0.0594208i
$365$		0			0
$366$	−0.728144	+	0.808686i	−0.0380607	+	0.0422707i
$367$	23.7437	+	19.2273i	1.23941	+	1.00365i	0.999460	+	0.0328696i	$0.0104646\pi$
$367$	23.7437	+	19.2273i	1.23941	+	1.00365i	0.239951	+	0.970785i	$0.422869\pi$
$368$	−3.29835	−	12.3096i	−0.171938	−	0.641683i
$369$	−2.53343	−	1.12796i	−0.131885	−	0.0587191i
$370$		0			0
$371$	−19.6399	−	9.32179i	−1.01965	−	0.483963i
$372$	0.0430264	+	0.271658i	0.00223081	+	0.0140848i
$373$	−7.76641	+	11.9592i	−0.402129	+	0.619225i	−0.980493	−	0.196554i	$-0.937025\pi$
$373$	−7.76641	+	11.9592i	−0.402129	+	0.619225i	0.578364	+	0.815779i	$0.303692\pi$
$374$	18.5828	−	32.1863i	0.960892	−	1.66431i
$375$		0			0
$376$	14.0186	−	8.09365i	0.722955	−	0.417398i
$377$	0.166617	+	0.327005i	0.00858123	+	0.0168416i
$378$	−3.15248	−	0.578060i	−0.162146	−	0.0297322i
$379$	17.6898	−	24.3480i	0.908666	−	1.25067i	−0.0589546	−	0.998261i	$-0.518777\pi$
$379$	17.6898	−	24.3480i	0.908666	−	1.25067i	0.967620	−	0.252410i	$-0.0812233\pi$
$380$		0			0
$381$	1.23798	−	0.130117i	0.0634236	−	0.00666609i
$382$	11.7075	−	3.13701i	0.599007	−	0.160504i
$383$	−7.27458	−	18.9509i	−0.371714	−	0.968347i	−0.984073	−	0.177767i	$-0.943113\pi$
$383$	−7.27458	−	18.9509i	−0.371714	−	0.968347i	0.612359	−	0.790580i	$-0.290221\pi$
$384$	−0.540629	−	1.66389i	−0.0275889	−	0.0849098i
$385$		0			0
$386$	−6.99857	+	21.5394i	−0.356218	+	1.09633i
$387$	14.3093	−	0.749917i	0.727381	−	0.0381204i
$388$	−4.00786	−	6.17156i	−0.203468	−	0.313314i
$389$	−1.97080	+	1.77452i	−0.0999237	+	0.0899717i	−0.717579	−	0.696478i	$-0.754750\pi$
$389$	−1.97080	+	1.77452i	−0.0999237	+	0.0899717i	0.617655	+	0.786449i	$0.288083\pi$
$390$		0			0
$391$	−16.8644	+	5.47958i	−0.852870	+	0.277114i
$392$	−5.10275	+	15.9109i	−0.257728	+	0.803623i
$393$	1.64900	−	1.64900i	0.0831810	−	0.0831810i
$394$	1.31361	−	2.95042i	0.0661789	−	0.148640i
$395$		0			0
$396$	4.73914	−	2.11000i	0.238151	−	0.106032i
$397$	−7.59556	−	9.37974i	−0.381210	−	0.470756i	0.550039	−	0.835139i	$-0.314613\pi$
$397$	−7.59556	−	9.37974i	−0.381210	−	0.470756i	−0.931249	+	0.364384i	$0.881280\pi$
$398$	−8.25450	+	4.20588i	−0.413761	+	0.210822i
$399$	−0.265288	+	0.227454i	−0.0132810	+	0.0113869i
$400$		0			0
$401$	−13.8545	−	23.9967i	−0.691861	−	1.19834i	−0.971227	−	0.238154i	$-0.923458\pi$
$401$	−13.8545	−	23.9967i	−0.691861	−	1.19834i	0.279366	−	0.960185i	$-0.409876\pi$
$402$	−2.20397	−	0.115505i	−0.109924	−	0.00576087i
$403$	1.40369	−	3.65673i	0.0699226	−	0.182155i
$404$	0.965591	−	9.18699i	0.0480400	−	0.457070i
$405$		0			0
$406$	0.492352	+	1.65058i	0.0244350	+	0.0819171i
$407$	26.3735	+	26.3735i	1.30728	+	1.30728i
$408$	−1.88557	+	0.723804i	−0.0933498	+	0.0358336i
$409$	−3.38271	−	0.719016i	−0.167264	−	0.0355531i	0.123518	−	0.992342i	$-0.460582\pi$
$409$	−3.38271	−	0.719016i	−0.167264	−	0.0355531i	−0.290782	+	0.956789i	$0.593916\pi$
$410$		0			0
$411$	0.327563	+	1.54106i	0.0161575	+	0.0760151i
$412$	−4.28650	−	2.18408i	−0.211181	−	0.107602i
$413$	4.27635	−	14.5385i	0.210425	−	0.715393i
$414$	−12.0390	−	3.91172i	−0.591686	−	0.192250i
$415$		0			0
$416$	0.497727	−	2.34162i	0.0244031	−	0.114807i
$417$	−0.391084	+	0.482948i	−0.0191515	+	0.0236501i
$418$	1.50153	−	5.60377i	0.0734420	−	0.274089i
$419$	2.09086	−	1.51910i	0.102145	−	0.0742128i	−0.535540	−	0.844510i	$-0.679892\pi$
$419$	2.09086	−	1.51910i	0.102145	−	0.0742128i	0.637685	+	0.770297i	$0.279892\pi$
$420$		0			0
$421$	2.23083	+	1.62080i	0.108724	+	0.0789928i	0.640819	−	0.767692i	$-0.278595\pi$
$421$	2.23083	+	1.62080i	0.108724	+	0.0789928i	−0.532095	+	0.846685i	$0.678595\pi$
$422$	22.9563	−	18.5897i	1.11750	−	0.904930i
$423$	1.05888	−	20.2046i	0.0514845	−	0.982383i
$424$	−16.9861	−	9.80692i	−0.824917	−	0.476266i
$425$		0			0
$426$			1.31037i			0.0634877i
$427$	14.0957	−	1.88309i	0.682138	−	0.0911292i
$428$	5.48667	−	0.869002i	0.265208	−	0.0420048i
$429$	0.406006	+	0.0426729i	0.0196021	+	0.00206027i
$430$		0			0
$431$	−1.09731	−	10.4402i	−0.0528556	−	0.502887i	−0.988639	−	0.150311i	$-0.951972\pi$
$431$	−1.09731	−	10.4402i	−0.0528556	−	0.502887i	0.935783	−	0.352576i	$-0.114694\pi$
$432$	−3.51457	−	0.941726i	−0.169095	−	0.0453088i
$433$	−0.117809	−	0.0186591i	−0.00566154	−	0.000896700i	0.153603	−	0.988133i	$-0.450912\pi$
$433$	−0.117809	−	0.0186591i	−0.00566154	−	0.000896700i	−0.159265	+	0.987236i	$0.550912\pi$
$434$	9.57513	−	15.6923i	0.459621	−	0.753255i
$435$		0			0
$436$	2.15064	−	0.457132i	0.102997	−	0.0218927i
$437$	−2.32141	+	1.50754i	−0.111048	+	0.0721155i
$438$	−1.94853	+	1.26539i	−0.0931045	+	0.0604628i
$439$	33.1898	−	7.05471i	1.58406	−	0.336703i	0.670027	−	0.742337i	$-0.266282\pi$
$439$	33.1898	−	7.05471i	1.58406	−	0.336703i	0.914036	+	0.405634i	$0.132949\pi$
$440$		0			0
$441$	13.2049	+	16.1801i	0.628806	+	0.770482i
$442$	−9.12184	−	1.44476i	−0.433881	−	0.0687201i
$443$	−13.7414	−	3.68199i	−0.652872	−	0.174937i	−0.0828450	−	0.996562i	$-0.526401\pi$
$443$	−13.7414	−	3.68199i	−0.652872	−	0.174937i	−0.570027	+	0.821626i	$0.693067\pi$
$444$	0.0680299	+	0.647261i	0.00322856	+	0.0307177i
$445$		0			0
$446$	−17.4333	−	1.83232i	−0.825492	−	0.0867627i
$447$	1.29260	−	0.204727i	0.0611377	−	0.00968326i
$448$	−5.26614	+	12.7825i	−0.248802	+	0.603916i
$449$			34.5384i			1.62997i	0.579485	+	0.814983i	$0.303254\pi$
$449$			34.5384i			1.62997i	−0.579485	+	0.814983i	$0.696746\pi$
$450$		0			0
$451$	2.87936	+	1.66240i	0.135584	+	0.0782793i
$452$	−0.143155	+	2.73156i	−0.00673345	+	0.128482i
$453$	−0.124146	+	0.100531i	−0.00583287	+	0.00472336i
$454$	−24.6067	−	17.8778i	−1.15485	−	0.839046i
$455$		0			0
$456$	−0.255062	+	0.185313i	−0.0119444	+	0.00867809i
$457$	−3.21108	+	11.9839i	−0.150208	+	0.560584i	0.849260	+	0.527975i	$0.177048\pi$
$457$	−3.21108	+	11.9839i	−0.150208	+	0.560584i	−0.999468	+	0.0326096i	$0.989618\pi$
$458$	−26.9698	+	33.3050i	−1.26022	+	1.55624i
$459$	−1.05262	+	4.95218i	−0.0491320	+	0.231148i
$460$		0			0
$461$	5.98374	+	1.94423i	0.278691	+	0.0905520i	0.445027	−	0.895517i	$-0.353194\pi$
$461$	5.98374	+	1.94423i	0.278691	+	0.0905520i	−0.166337	+	0.986069i	$0.553194\pi$
$462$	1.83811	+	0.540662i	0.0855168	+	0.0251539i
$463$	9.49520	+	4.83804i	0.441279	+	0.224843i	0.660490	−	0.750834i	$-0.270348\pi$
$463$	9.49520	+	4.83804i	0.441279	+	0.224843i	−0.219211	+	0.975677i	$0.570348\pi$
$464$	0.406556	+	1.91270i	0.0188739	+	0.0887947i
$465$		0			0
$466$	34.2444	+	7.27886i	1.58634	+	0.337187i
$467$	34.2308	−	13.1400i	1.58401	−	0.608045i	0.602275	−	0.798289i	$-0.294261\pi$
$467$	34.2308	−	13.1400i	1.58401	−	0.608045i	0.981737	+	0.190244i	$0.0609278\pi$
$468$	−0.911541	−	0.911541i	−0.0421360	−	0.0421360i
$469$	20.9589	+	19.8134i	0.967793	+	0.914899i
$470$		0			0
$471$	0.128434	−	1.22197i	0.00591794	−	0.0563054i
$472$	4.89975	−	12.7643i	0.225529	−	0.587524i
$473$	−17.1555	−	0.899081i	−0.788810	−	0.0413398i
$474$	1.35230	+	2.34225i	0.0621132	+	0.107583i
$475$		0			0
$476$	−7.99435	−	2.81380i	−0.366421	−	0.128970i
$477$	−21.8432	+	11.1296i	−1.00013	+	0.509592i
$478$	−28.9682	−	35.7727i	−1.32497	−	1.63620i
$479$	−17.6666	+	7.86567i	−0.807207	+	0.359392i	−0.768493	−	0.639859i	$-0.778993\pi$
$479$	−17.6666	+	7.86567i	−0.807207	+	0.359392i	−0.0387145	+	0.999250i	$0.512326\pi$
$480$		0			0
$481$	3.76979	−	8.46709i	0.171888	−	0.386066i
$482$	−2.09462	+	2.09462i	−0.0954076	+	0.0954076i
$483$	−0.479125	−	0.778524i	−0.0218010	−	0.0354241i
$484$	−0.829672	+	0.269577i	−0.0377124	+	0.0122535i
$485$		0			0
$486$	−4.03251	+	3.63089i	−0.182918	+	0.164701i
$487$	0.239206	+	0.368346i	0.0108395	+	0.0166913i	0.844049	−	0.536266i	$-0.180166\pi$
$487$	0.239206	+	0.368346i	0.0108395	+	0.0166913i	−0.833209	+	0.552958i	$0.813499\pi$
$488$	12.8126	−	0.671482i	0.580001	−	0.0303966i
$489$	0.272549	−	0.838820i	0.0123251	−	0.0379328i
$490$		0			0
$491$	7.42044	+	22.8378i	0.334880	+	1.03065i	0.966781	+	0.255605i	$0.0822747\pi$
$491$	7.42044	+	22.8378i	0.334880	+	1.03065i	−0.631902	+	0.775049i	$0.717725\pi$
$492$	0.0207911	+	0.0541626i	0.000937334	+	0.00244184i
$493$	2.62814	−	0.704209i	0.118366	−	0.0317160i
$494$	−1.43375	+	0.150693i	−0.0645074	+	0.00678000i
$495$		0			0
$496$	12.2667	−	16.8837i	0.550791	−	0.758099i
$497$	11.0965	−	13.0427i	0.497748	−	0.585044i
$498$	−0.985339	−	1.93384i	−0.0441541	−	0.0866573i
$499$	−4.58467	+	2.64696i	−0.205238	+	0.118494i	−0.599096	−	0.800677i	$-0.704473\pi$
$499$	−4.58467	+	2.64696i	−0.205238	+	0.118494i	0.393858	+	0.919171i	$0.371140\pi$
$500$		0			0
$501$	−0.202702	+	0.351090i	−0.00905606	+	0.0156856i
$502$	−14.0971	+	21.7077i	−0.629185	+	0.968860i
$503$	0.292858	+	1.84903i	0.0130579	+	0.0824444i	0.993357	−	0.115076i	$-0.0367111\pi$
$503$	0.292858	+	1.84903i	0.0130579	+	0.0824444i	−0.980299	+	0.197520i	$0.936711\pi$
$504$	10.7020	+	15.5080i	0.476704	+	0.690782i
$505$		0			0
$506$	13.8644	+	6.17282i	0.616347	+	0.274415i
$507$	0.405768	+	1.51435i	0.0180208	+	0.0672545i
$508$	3.66236	+	2.96572i	0.162491	+	0.131583i
$509$	3.35972	−	3.73135i	0.148917	−	0.165389i	−0.664071	−	0.747670i	$-0.731173\pi$
$509$	3.35972	−	3.73135i	0.148917	−	0.165389i	0.812988	+	0.582280i	$0.197839\pi$
$510$		0			0
$511$	30.1102	+	3.90567i	1.33200	+	0.172777i
$512$	−4.47382	+	8.78037i	−0.197717	+	0.388041i
$513$	0.0413608	+	0.789210i	0.00182612	+	0.0348445i
$514$	6.76925	+	7.51802i	0.298579	+	0.331606i
$515$		0			0
$516$	−0.222769	−	0.200582i	−0.00980686	−	0.00883014i
$517$	−3.79459	+	23.9581i	−0.166886	+	1.05368i
$518$	24.5696	−	35.8954i	1.07952	−	1.57715i
$519$	0.292844	+	0.403066i	0.0128544	+	0.0176926i
$520$		0			0
$521$	−7.65571	−	17.1950i	−0.335403	−	0.753327i	−0.999981	−	0.00610832i	$-0.998056\pi$
$521$	−7.65571	−	17.1950i	−0.335403	−	0.753327i	0.664579	−	0.747218i	$-0.268611\pi$
$522$	1.81333	+	0.696073i	0.0793674	+	0.0304663i
$523$	−1.45606	−	0.945577i	−0.0636691	−	0.0413472i	0.512412	−	0.858740i	$-0.328752\pi$
$523$	−1.45606	−	0.945577i	−0.0636691	−	0.0413472i	−0.576081	+	0.817393i	$0.695419\pi$
$524$	8.82866			0.385682
$525$		0			0
$526$	8.59967			0.374964
$527$	−24.3537	−	15.8155i	−1.06086	−	0.688932i
$528$	2.03066	+	0.779498i	0.0883732	+	0.0339233i
$529$	6.40979	+	14.3966i	0.278686	+	0.625940i
$530$		0			0
$531$	−10.0447	−	13.8253i	−0.435902	−	0.599967i
$532$	−1.31906	−	0.101281i	−0.0571884	−	0.00439108i
$533$	0.129247	−	0.816031i	0.00559830	−	0.0353462i
$534$	0.786244	+	0.707938i	0.0340241	+	0.0306355i
$535$		0			0
$536$	17.4117	+	19.3376i	0.752069	+	0.835257i
$537$	0.122912	+	2.34530i	0.00530405	+	0.101207i
$538$	−8.68114	+	17.0377i	−0.374271	+	0.734547i
$539$	−13.7171	−	20.9470i	−0.590836	−	0.902253i
$540$		0			0
$541$	−8.81443	+	9.78942i	−0.378962	+	0.420880i	−0.902208	−	0.431302i	$-0.858054\pi$
$541$	−8.81443	+	9.78942i	−0.378962	+	0.420880i	0.523246	+	0.852182i	$0.324721\pi$
$542$	17.4067	+	14.0957i	0.747682	+	0.605461i
$543$	0.623305	+	2.32621i	0.0267486	+	0.0998270i
$544$	−16.2134	−	7.21867i	−0.695144	−	0.309498i
$545$		0			0
$546$	−0.0382609	−	0.474576i	−0.00163742	−	0.0203100i
$547$	−4.06079	−	25.6388i	−0.173627	−	1.09624i	−0.908455	−	0.417983i	$-0.862737\pi$
$547$	−4.06079	−	25.6388i	−0.173627	−	1.09624i	0.734828	−	0.678253i	$-0.237263\pi$
$548$	−3.24851	+	5.00227i	−0.138770	+	0.213686i
$549$	8.01819	−	13.8879i	0.342208	−	0.592722i
$550$		0			0
$551$	0.367817	−	0.212359i	0.0156695	−	0.00904682i
$552$	−0.374428	−	0.734857i	−0.0159367	−	0.0312776i
$553$	6.37475	−	34.7650i	0.271082	−	1.47836i
$554$	−8.72976	+	12.0155i	−0.370892	+	0.510489i
$555$		0			0
$556$	−2.33976	+	0.245919i	−0.0992280	+	0.0104293i
$557$	−13.9053	+	3.72592i	−0.589188	+	0.157872i	−0.541082	−	0.840970i	$-0.681985\pi$
$557$	−13.9053	+	3.72592i	−0.589188	+	0.157872i	−0.0481059	+	0.998842i	$0.515318\pi$
$558$	−7.42886	−	19.3529i	−0.314489	−	0.819272i
$559$	1.31918	+	4.06001i	0.0557952	+	0.171720i
$560$		0			0
$561$	0.935259	−	2.87843i	0.0394867	−	0.121527i
$562$	−1.90150	+	0.0996534i	−0.0802099	+	0.00420362i
$563$	−22.6282	−	34.8443i	−0.953663	−	1.46851i	−0.882092	−	0.471077i	$-0.843865\pi$
$563$	−22.6282	−	34.8443i	−0.953663	−	1.46851i	−0.0715712	−	0.997435i	$-0.522801\pi$
$564$	−0.314549	+	0.283221i	−0.0132449	+	0.0119258i
$565$		0			0
$566$	7.89661	−	2.56577i	0.331919	−	0.107847i
$567$	23.4107	−	0.657717i	0.983155	−	0.0276215i
$568$	10.9246	−	10.9246i	0.458388	−	0.458388i
$569$	9.42580	−	21.1707i	0.395150	−	0.887522i	−0.600950	−	0.799287i	$-0.705211\pi$
$569$	9.42580	−	21.1707i	0.395150	−	0.887522i	0.996100	−	0.0882349i	$-0.0281226\pi$
$570$		0			0
$571$	7.98064	−	3.55321i	0.333979	−	0.148697i	−0.232894	−	0.972502i	$-0.574820\pi$
$571$	7.98064	−	3.55321i	0.333979	−	0.148697i	0.566873	+	0.823805i	$0.308153\pi$
$572$	0.972632	+	1.20110i	0.0406678	+	0.0502206i
$573$	0.879448	−	0.448101i	0.0367395	−	0.0187197i
$574$	1.28739	−	3.65762i	0.0537345	−	0.152666i
$575$		0			0
$576$	7.79483	+	13.5010i	0.324785	+	0.562544i
$577$	−13.3903	−	0.701754i	−0.557444	−	0.0292144i	−0.228466	−	0.973552i	$-0.573371\pi$
$577$	−13.3903	−	0.701754i	−0.557444	−	0.0292144i	−0.328978	+	0.944337i	$0.606704\pi$
$578$	−14.9312	+	38.8972i	−0.621057	+	1.61791i
$579$	−0.192784	+	1.83422i	−0.00801183	+	0.0762274i
$580$		0			0
$581$	−6.56871	+	27.5924i	−0.272516	+	1.14473i
$582$	−2.16715	−	2.16715i	−0.0898313	−	0.0898313i
$583$	27.4392	−	10.5329i	1.13642	−	0.436230i
$584$	26.7947	+	5.69539i	1.10877	+	0.235677i
$585$		0			0
$586$	−6.95460	−	32.7188i	−0.287292	−	1.35160i
$587$	−6.86391	−	3.49734i	−0.283304	−	0.144350i	0.306565	−	0.951850i	$-0.400820\pi$
$587$	−6.86391	−	3.49734i	−0.283304	−	0.144350i	−0.589868	+	0.807499i	$0.700820\pi$
$588$	0.0440118	−	0.434690i	0.00181502	−	0.0179263i
$589$	−4.31098	−	1.40072i	−0.177631	−	0.0577157i
$590$		0			0
$591$	0.0546817	−	0.257257i	0.00224931	−	0.0105822i
$592$	31.0773	−	38.3773i	1.27727	−	1.57730i
$593$	−10.6395	+	39.7071i	−0.436911	+	1.63057i	0.299540	+	0.954084i	$0.403167\pi$
$593$	−10.6395	+	39.7071i	−0.436911	+	1.63057i	−0.736451	+	0.676491i	$0.763500\pi$
$594$	3.50555	−	2.54693i	0.143834	−	0.104502i
$595$		0			0
$596$	4.00830	+	2.91220i	0.164186	+	0.119288i
$597$	−0.586302	+	0.474778i	−0.0239958	+	0.0194314i
$598$	0.197375	−	3.76614i	0.00807127	−	0.154009i
$599$	−22.8775	−	13.2083i	−0.934750	−	0.539678i	−0.0464390	−	0.998921i	$-0.514787\pi$
$599$	−22.8775	−	13.2083i	−0.934750	−	0.539678i	−0.888311	+	0.459243i	$0.848121\pi$
$600$		0			0
$601$		−	9.66655i		−	0.394307i	−0.980373	−	0.197153i	$-0.936830\pi$
$601$		−	9.66655i		−	0.394307i	0.980373	−	0.197153i	$-0.0631697\pi$
$602$	2.65300	+	19.8588i	0.108128	+	0.809383i
$603$	32.1234	−	5.08784i	1.30816	−	0.207193i
$604$	−0.601454	−	0.0632154i	−0.0244728	−	0.00257220i
$605$		0			0
$606$	−0.402155	−	3.82625i	−0.0163364	−	0.155431i
$607$	−27.2330	−	7.29707i	−1.10535	−	0.296179i	−0.340412	−	0.940277i	$-0.610566\pi$
$607$	−27.2330	−	7.29707i	−1.10535	−	0.296179i	−0.764943	+	0.644098i	$0.777233\pi$
$608$	−2.73628	−	0.433384i	−0.110971	−	0.0175760i
$609$	0.0671647	+	0.123141i	0.00272165	+	0.00498993i
$610$		0			0
$611$	5.89601	−	1.25324i	0.238527	−	0.0507005i
$612$	−8.01520	+	5.20513i	−0.323995	+	0.210405i
$613$	2.98129	−	1.93607i	0.120413	−	0.0781973i	−0.483027	−	0.875605i	$-0.660463\pi$
$613$	2.98129	−	1.93607i	0.120413	−	0.0781973i	0.603440	+	0.797408i	$0.293796\pi$
$614$	21.5251	−	4.57530i	0.868682	−	0.184644i
$615$		0			0
$616$	−10.8169	−	19.8320i	−0.435826	−	0.799054i
$617$	−30.7567	−	4.87138i	−1.23822	−	0.196114i	−0.497222	−	0.867623i	$-0.665646\pi$
$617$	−30.7567	−	4.87138i	−1.23822	−	0.196114i	−0.740996	+	0.671509i	$0.765646\pi$
$618$	−1.93538	−	0.518583i	−0.0778523	−	0.0208605i
$619$	−5.00868	−	47.6544i	−0.201316	−	1.91539i	−0.368786	−	0.929514i	$-0.620226\pi$
$619$	−5.00868	−	47.6544i	−0.201316	−	1.91539i	0.167470	−	0.985877i	$-0.446440\pi$
$620$		0			0
$621$	−2.05606	−	0.216101i	−0.0825070	−	0.00867183i
$622$	38.7068	−	6.13055i	1.55200	−	0.245813i
$623$	−1.83083	−	13.7045i	−0.0733508	−	0.549060i
$624$		−	0.540515i		−	0.0216379i
$625$		0			0
$626$	38.5760	+	22.2719i	1.54181	+	0.890163i
$627$	0.0247255	−	0.471792i	0.000987443	−	0.0188415i
$628$	3.61500	−	2.92737i	0.144254	−	0.116815i
$629$	−55.5896	−	40.3882i	−2.21650	−	1.61038i
$630$		0			0
$631$	−9.95692	+	7.23413i	−0.396379	+	0.287986i	−0.768064	−	0.640373i	$-0.778780\pi$
$631$	−9.95692	+	7.23413i	−0.396379	+	0.287986i	0.371686	+	0.928359i	$0.378780\pi$
$632$	8.25329	−	30.8017i	0.328298	−	1.22523i
$633$	1.51384	−	1.86944i	0.0601698	−	0.0743035i
$634$	0.00407648	−	0.0191783i	0.000161898	−	0.000761668i
$635$		0			0
$636$	0.487764	+	0.158484i	0.0193411	+	0.00628430i
$637$	−3.63800	+	5.04766i	−0.144143	+	0.199996i
$638$	−2.07488	−	1.05720i	−0.0821451	−	0.0418550i
$639$	−4.01488	−	18.8885i	−0.158826	−	0.747219i
$640$		0			0
$641$	−29.5923	−	6.29003i	−1.16882	−	0.248441i	−0.417689	−	0.908590i	$-0.637160\pi$
$641$	−29.5923	−	6.29003i	−1.16882	−	0.248441i	−0.751135	+	0.660149i	$0.770493\pi$
$642$	2.15993	−	0.829121i	0.0852458	−	0.0327228i
$643$	30.5033	+	30.5033i	1.20293	+	1.20293i	0.973270	+	0.229664i	$0.0737627\pi$
$643$	30.5033	+	30.5033i	1.20293	+	1.20293i	0.229664	+	0.973270i	$0.426237\pi$
$644$	0.801483	−	3.36670i	0.0315829	−	0.132666i
$645$		0			0
$646$	−1.11718	+	10.6293i	−0.0439550	+	0.418204i
$647$	2.09634	−	5.46115i	0.0824156	−	0.214700i	−0.886180	−	0.463341i	$-0.846651\pi$
$647$	2.09634	−	5.46115i	0.0824156	−	0.214700i	0.968596	+	0.248641i	$0.0799839\pi$
$648$	21.1007	+	1.10584i	0.828913	+	0.0434415i
$649$	10.2441	+	17.7433i	0.402115	+	0.696484i
$650$		0			0
$651$	0.497018	−	1.41209i	0.0194797	−	0.0553442i
$652$	2.97511	−	1.51589i	0.116514	−	0.0593670i
$653$	19.8767	+	24.5456i	0.777834	+	0.960544i	0.999895	−	0.0144882i	$-0.00461191\pi$
$653$	19.8767	+	24.5456i	0.777834	+	0.960544i	−0.222061	+	0.975033i	$0.571279\pi$
$654$	0.836553	−	0.372457i	0.0327118	−	0.0145642i
$655$		0			0
$656$	1.79047	−	4.02147i	0.0699063	−	0.157012i
$657$	24.2104	−	24.2104i	0.944536	−	0.944536i
$658$	28.2785	−	0.794477i	1.10241	−	0.0309719i
$659$	−15.9469	+	5.18146i	−0.621202	+	0.201841i	−0.602674	−	0.797988i	$-0.705898\pi$
$659$	−15.9469	+	5.18146i	−0.621202	+	0.201841i	−0.0185282	+	0.999828i	$0.505898\pi$
$660$		0			0
$661$	10.7955	−	9.72033i	0.419897	−	0.378077i	−0.431924	−	0.901910i	$-0.642165\pi$
$661$	10.7955	−	9.72033i	0.419897	−	0.378077i	0.851821	+	0.523833i	$0.175498\pi$
$662$	−18.6983	−	28.7929i	−0.726731	−	1.11907i
$663$	−0.751062	+	0.0393615i	−0.0291688	+	0.00152867i
$664$	−7.90768	+	24.3373i	−0.306878	+	0.944472i
$665$		0			0
$666$	−15.1579	−	46.6512i	−0.587356	−	1.80770i
$667$	0.398166	+	1.03726i	0.0154171	+	0.0401628i
$668$	−1.48249	+	0.397232i	−0.0573592	+	0.0153693i
$669$	−1.41968	+	0.149214i	−0.0548878	+	0.00576894i
$670$		0			0
$671$	−11.3008	+	15.5543i	−0.436264	+	0.600466i
$672$	0.165019	−	0.899939i	0.00636574	−	0.0347159i
$673$	13.3101	+	26.1226i	0.513068	+	1.00695i	0.991656	+	0.128912i	$0.0411486\pi$
$673$	13.3101	+	26.1226i	0.513068	+	1.00695i	−0.478588	+	0.878039i	$0.658851\pi$
$674$	−32.5338	+	18.7834i	−1.25316	+	0.723510i
$675$		0			0
$676$	−2.96764	+	5.14010i	−0.114140	+	0.197696i
$677$	−11.6189	+	17.8915i	−0.446549	+	0.687626i	−0.988233	−	0.152957i	$-0.951120\pi$
$677$	−11.6189	+	17.8915i	−0.446549	+	0.687626i	0.541683	+	0.840583i	$0.317787\pi$
$678$	0.178213	+	1.12519i	0.00684423	+	0.0432128i
$679$	3.21860	+	39.9225i	0.123519	+	1.53209i
$680$		0			0
$681$	−2.26274	−	1.00744i	−0.0867083	−	0.0386050i
$682$	6.43243	+	24.0062i	0.246311	+	0.919244i
$683$	−22.7339	−	18.4095i	−0.869888	−	0.704421i	0.0865846	−	0.996245i	$-0.472405\pi$
$683$	−22.7339	−	18.4095i	−0.869888	−	0.704421i	−0.956472	+	0.291823i	$0.905738\pi$
$684$	−0.998229	+	1.10865i	−0.0381682	+	0.0423901i
$685$		0			0
$686$	−21.0667	+	20.2219i	−0.804331	+	0.772077i
$687$	−1.58439	+	3.10954i	−0.0604483	+	0.118636i
$688$	1.19039	+	22.7139i	0.0453831	+	0.865961i
$689$	−4.88712	−	5.42770i	−0.186184	−	0.206779i
$690$		0			0
$691$	12.8377	+	11.5591i	0.488369	+	0.439729i	0.876162	−	0.482017i	$-0.160096\pi$
$691$	12.8377	+	11.5591i	0.488369	+	0.439729i	−0.387793	+	0.921747i	$0.626762\pi$
$692$	−0.295060	+	1.86293i	−0.0112165	+	0.0708181i
$693$	−28.1523	−	2.16161i	−1.06942	−	0.0821129i
$694$	21.0005	+	28.9047i	0.797168	+	1.09721i
$695$		0			0
$696$	0.0514726	+	0.115609i	0.00195106	+	0.00438216i
$697$	−5.71835	−	2.19507i	−0.216598	−	0.0831442i
$698$	14.0554	+	9.12769i	0.532005	+	0.345488i
$699$	2.85098			0.107834
$700$		0			0
$701$	−16.6238			−0.627872			−0.313936	−	0.949444i	$-0.601648\pi$
$701$	−16.6238			−0.627872			−0.313936	+	0.949444i	$0.601648\pi$
$702$	−0.903049	−	0.586447i	−0.0340834	−	0.0221340i
$703$	−10.0135	−	3.84381i	−0.377665	−	0.144972i
$704$	−7.60214	−	17.0747i	−0.286516	−	0.643526i
$705$		0			0
$706$	4.28480	+	5.89752i	0.161261	+	0.221956i
$707$	−28.3988	+	41.4898i	−1.06805	+	1.56039i
$708$	−0.0559265	+	0.353106i	−0.00210185	+	0.0132705i
$709$	−0.546293	−	0.491885i	−0.0205165	−	0.0184731i	0.658809	−	0.752311i	$-0.271061\pi$
$709$	−0.546293	−	0.491885i	−0.0205165	−	0.0184731i	−0.679325	+	0.733837i	$0.737727\pi$
$710$		0			0
$711$	−26.6694	−	29.6194i	−1.00018	−	1.11081i
$712$	−0.652848	−	12.4571i	−0.0244665	−	0.466849i
$713$	5.38332	−	10.5654i	0.201607	−	0.395676i
$714$	−3.50043	−	0.454049i	−0.131000	−	0.0169924i
$715$		0			0
$716$	−5.94928	+	6.60735i	−0.222335	+	0.246928i
$717$	−2.91314	−	2.35901i	−0.108793	−	0.0880989i
$718$	1.18723	+	4.43081i	0.0443071	+	0.165357i
$719$	−23.3719	−	10.4058i	−0.871624	−	0.388072i	−0.0783421	−	0.996927i	$-0.524963\pi$
$719$	−23.3719	−	10.4058i	−0.871624	−	0.388072i	−0.793282	+	0.608855i	$0.791629\pi$
$720$		0			0
$721$	14.8722	+	21.5509i	0.553868	+	0.802599i
$722$	−4.42548	−	27.9414i	−0.164699	−	1.03987i
$723$	−0.131383	+	0.202312i	−0.00488619	+	0.00752407i
$724$	−4.55862	+	7.89576i	−0.169420	+	0.293444i
$725$		0			0
$726$	−0.314652	+	0.181665i	−0.0116778	+	0.00674221i
$727$	0.931344	+	1.82787i	0.0345416	+	0.0677918i	0.907632	−	0.419766i	$-0.137888\pi$
$727$	0.931344	+	1.82787i	0.0345416	+	0.0677918i	−0.873091	+	0.487558i	$0.837888\pi$
$728$	−3.63758	+	4.27555i	−0.134818	+	0.158462i
$729$	15.3493	−	21.1265i	0.568492	−	0.782463i
$730$		0			0
$731$	31.4751	−	3.30816i	1.16415	−	0.122357i
$732$	−0.324055	+	0.0868302i	−0.0119774	+	0.00320934i
$733$	−3.98909	−	10.3919i	−0.147340	−	0.383834i	0.839971	−	0.542631i	$-0.182572\pi$
$733$	−3.98909	−	10.3919i	−0.147340	−	0.383834i	−0.987311	+	0.158797i	$0.949239\pi$
$734$	14.8863	+	45.8154i	0.549464	+	1.69108i
$735$		0			0
$736$	2.23953	−	6.89255i	0.0825500	−	0.254063i
$737$	−38.9396	+	2.04074i	−1.43436	+	0.0751715i
$738$	−2.38148	−	3.66716i	−0.0876637	−	0.134990i
$739$	−17.3948	+	15.6624i	−0.639879	+	0.576150i	−0.923884	−	0.382673i	$-0.875004\pi$
$739$	−17.3948	+	15.6624i	−0.639879	+	0.576150i	0.284004	+	0.958823i	$0.408337\pi$
$740$		0			0
$741$	−0.111654	+	0.0362785i	−0.00410171	+	0.00133273i
$742$	−17.9659	−	29.1926i	−0.659549	−	1.07169i
$743$	−9.74553	+	9.74553i	−0.357529	+	0.357529i	−0.862901	−	0.505373i	$-0.831355\pi$
$743$	−9.74553	+	9.74553i	−0.357529	+	0.357529i	0.505373	+	0.862901i	$0.331355\pi$
$744$	0.549343	−	1.23384i	0.0201399	−	0.0452349i
$745$		0			0
$746$	−20.5400	+	9.14501i	−0.752024	+	0.334823i
$747$	20.1285	+	24.8566i	0.736462	+	0.909455i
$748$	10.2092	−	5.20182i	0.373284	−	0.190198i
$749$	−28.5199	−	10.0383i	−1.04210	−	0.366790i
$750$		0			0
$751$	−12.3488	−	21.3888i	−0.450616	−	0.780490i	0.547808	−	0.836604i	$-0.315462\pi$
$751$	−12.3488	−	21.3888i	−0.450616	−	0.780490i	−0.998424	+	0.0561142i	$0.982129\pi$
$752$	32.0720	+	1.68082i	1.16955	+	0.0612933i
$753$	−0.755370	+	1.96781i	−0.0275272	+	0.0717109i
$754$	−0.0604878	+	0.575503i	−0.00220284	+	0.0209586i
$755$		0			0
$756$	−0.718040	−	0.678796i	−0.0261149	−	0.0246876i
$757$	4.91711	+	4.91711i	0.178715	+	0.178715i	0.790796	−	0.612080i	$-0.209667\pi$
$757$	4.91711	+	4.91711i	0.178715	+	0.178715i	−0.612080	+	0.790796i	$0.709667\pi$
$758$	44.3013	−	17.0057i	1.60910	−	0.617674i
$759$	1.20888	+	0.256956i	0.0438796	+	0.00932691i
$760$		0			0
$761$	5.59529	+	26.3238i	0.202829	+	0.954235i	0.955306	+	0.295617i	$0.0955253\pi$
$761$	5.59529	+	26.3238i	0.202829	+	0.954235i	−0.752478	+	0.658618i	$0.771141\pi$
$762$	1.74880	+	0.891057i	0.0633523	+	0.0322796i
$763$	−11.4806	−	3.37691i	−0.415627	−	0.122252i
$764$	3.55381	+	1.15470i	0.128573	+	0.0417757i
$765$		0			0
$766$	6.65453	−	31.3071i	0.240438	−	1.13117i
$767$	3.20403	−	3.95664i	0.115691	−	0.142866i
$768$	0.366659	−	1.36839i	0.0132307	−	0.0493776i
$769$	39.8628	−	28.9620i	1.43749	−	1.04440i	0.448929	−	0.893567i	$-0.351806\pi$
$769$	39.8628	−	28.9620i	1.43749	−	1.04440i	0.988560	−	0.150829i	$-0.0481944\pi$
$770$		0			0
$771$	0.666494	+	0.484237i	0.0240032	+	0.0174394i
$772$	−5.42623	+	4.39407i	−0.195294	+	0.158146i
$773$	1.81709	−	34.6722i	0.0653563	−	1.24707i	−0.747363	−	0.664416i	$-0.768680\pi$
$773$	1.81709	−	34.6722i	0.0653563	−	1.24707i	0.812719	−	0.582656i	$-0.197987\pi$
$774$	19.5660	+	11.2965i	0.703287	+	0.406043i
$775$		0			0
$776$			36.1353i			1.29718i
$777$	1.34934	−	3.27525i	0.0484072	−	0.117499i
$778$	−4.12999	+	0.654126i	−0.148067	+	0.0234516i
$779$	−0.950888	−	0.0999424i	−0.0340691	−	0.00358081i
$780$		0			0
$781$	2.41999	+	23.0247i	0.0865942	+	0.823889i
$782$	−27.0065	−	7.23637i	−0.965750	−	0.258772i
$783$	0.313316	+	0.0496244i	0.0111970	+	0.00177343i
$784$	−25.6837	+	20.9610i	−0.917274	+	0.748606i
$785$		0			0
$786$	3.59666	−	0.764494i	0.128289	−	0.0272686i
$787$	−22.4126	+	14.5549i	−0.798922	+	0.518826i	−0.878352	−	0.478014i	$-0.841357\pi$
$787$	−22.4126	+	14.5549i	−0.798922	+	0.518826i	0.0794300	+	0.996840i	$0.474690\pi$
$788$	0.835053	−	0.542290i	0.0297475	−	0.0193183i
$789$	0.685008	−	0.145603i	0.0243869	−	0.00518360i
$790$		0			0
$791$	7.75458	−	12.7087i	0.275721	−	0.451868i
$792$	−25.1604	−	3.98502i	−0.894036	−	0.141601i
$793$	4.61485	+	1.23654i	0.163878	+	0.0439110i
$794$	−1.98922	−	18.9261i	−0.0705947	−	0.671664i
$795$		0			0
$796$	−2.84049	−	0.298547i	−0.100678	−	0.0105817i
$797$	−40.7379	+	6.45225i	−1.44301	+	0.228551i	−0.828337	−	0.560230i	$-0.810713\pi$
$797$	−40.7379	+	6.45225i	−1.44301	+	0.228551i	−0.614675	+	0.788781i	$0.710713\pi$
$798$	−0.546134	+	0.0729600i	−0.0193329	+	0.00258275i
$799$		−	44.6875i		−	1.58093i
$800$		0			0
$801$	−13.5025	−	7.79568i	−0.477088	−	0.275447i
$802$	2.28655	−	43.6300i	0.0807409	−	1.54063i
$803$	−31.9010	+	25.8329i	−1.12576	+	0.911624i
$804$	−0.550462	−	0.399934i	−0.0194133	−	0.0141046i
$805$		0			0
$806$	4.99641	−	3.63011i	0.175991	−	0.127865i
$807$	−0.403028	+	1.50412i	−0.0141873	+	0.0529476i
$808$	−28.5469	+	35.2525i	−1.00428	+	1.24018i
$809$	−1.43539	+	6.75300i	−0.0504658	+	0.237423i	−0.996150	−	0.0876635i	$-0.972060\pi$
$809$	−1.43539	+	6.75300i	−0.0504658	+	0.237423i	0.945684	+	0.325086i	$0.105393\pi$
$810$		0			0
$811$	−22.5964	−	7.34202i	−0.793467	−	0.257813i	−0.115887	−	0.993262i	$-0.536971\pi$
$811$	−22.5964	−	7.34202i	−0.793467	−	0.257813i	−0.677580	+	0.735449i	$0.736971\pi$
$812$	−0.149848	+	0.509444i	−0.00525863	+	0.0178780i
$813$	1.62519	+	0.828075i	0.0569979	+	0.0290419i
$814$	12.2270	+	57.5236i	0.428557	+	2.01620i
$815$		0			0
$816$	−3.91962	−	0.833141i	−0.137214	−	0.0291658i
$817$	4.61211	−	1.77042i	0.161357	−	0.0619393i
$818$	−3.85571	−	3.85571i	−0.134812	−	0.134812i
$819$	2.00558	+	6.72362i	0.0700808	+	0.234942i
$820$		0			0
$821$	−0.723127	+	6.88010i	−0.0252373	+	0.240117i	0.974630	+	0.223822i	$0.0718536\pi$
$821$	−0.723127	+	6.88010i	−0.0252373	+	0.240117i	−0.999867	+	0.0162945i	$0.994813\pi$
$822$	−0.890236	+	2.31914i	−0.0310505	+	0.0808894i
$823$	−21.8561	−	1.14543i	−0.761857	−	0.0399272i	−0.332550	−	0.943086i	$-0.607909\pi$
$823$	−21.8561	−	1.14543i	−0.761857	−	0.0399272i	−0.429307	+	0.903158i	$0.641242\pi$
$824$	11.8119	+	20.4588i	0.411487	+	0.712717i
$825$		0			0
$826$	18.1399	−	15.5529i	0.631167	−	0.541153i
$827$	30.9277	−	15.7585i	1.07546	−	0.547975i	0.175739	−	0.984437i	$-0.443768\pi$
$827$	30.9277	−	15.7585i	1.07546	−	0.547975i	0.899723	+	0.436461i	$0.143768\pi$
$828$	−2.45598	−	3.03288i	−0.0853512	−	0.105400i
$829$	−20.3276	+	9.05041i	−0.706005	+	0.314334i	−0.728147	−	0.685421i	$-0.759618\pi$
$829$	−20.3276	+	9.05041i	−0.706005	+	0.314334i	0.0221418	+	0.999755i	$0.492951\pi$
$830$		0			0
$831$	−0.491933	+	1.10490i	−0.0170650	+	0.0383285i
$832$	−3.28420	+	3.28420i	−0.113859	+	0.113859i
$833$	30.9963	+	34.1619i	1.07396	+	1.18364i
$834$	−0.931888	+	0.302789i	−0.0322686	+	0.0104847i
$835$		0			0
$836$	1.32916	−	1.19678i	0.0459701	−	0.0413917i
$837$	−1.84391	−	2.83937i	−0.0637348	−	0.0981430i
$838$	4.06941	−	0.213269i	0.140575	−	0.00736724i
$839$	−15.5792	+	47.9479i	−0.537855	+	1.65535i	0.199544	+	0.979889i	$0.436054\pi$
$839$	−15.5792	+	47.9479i	−0.537855	+	1.65535i	−0.737399	+	0.675457i	$0.763946\pi$
$840$		0			0
$841$	8.90881	+	27.4185i	0.307200	+	0.945466i
$842$	1.55811	+	4.05902i	0.0536960	+	0.139883i
$843$	−0.149777	+	0.0401326i	−0.00515859	+	0.00138224i
$844$	9.05696	−	0.951925i	0.311753	−	0.0327666i
$845$		0			0
$846$	18.7510	−	25.8085i	0.644673	−	0.887316i
$847$	4.67025	+	0.856369i	0.160472	+	0.0294252i
$848$	−17.6668	−	34.6730i	−0.606679	−	1.19067i
$849$	0.585564	−	0.338075i	0.0200965	−	0.0116027i
$850$		0			0
$851$	14.0293	−	24.2995i	0.480918	−	0.832975i
$852$	−0.220025	+	0.338808i	−0.00753792	+	0.0116074i
$853$	−0.136081	−	0.859182i	−0.00465933	−	0.0294178i	0.985249	−	0.171126i	$-0.0547405\pi$
$853$	−0.136081	−	0.859182i	−0.00465933	−	0.0294178i	−0.989908	+	0.141708i	$0.954741\pi$
$854$	20.2567	+	9.61458i	0.693171	+	0.329004i
$855$		0			0
$856$	−24.9199	−	11.0951i	−0.851746	−	0.379222i
$857$	−0.541246	−	2.01996i	−0.0184886	−	0.0690004i	0.956065	−	0.293154i	$-0.0947049\pi$
$857$	−0.541246	−	2.01996i	−0.0184886	−	0.0690004i	−0.974554	+	0.224154i	$0.928038\pi$
$858$	0.500242	+	0.405088i	0.0170780	+	0.0138295i
$859$	−16.9921	+	18.8717i	−0.579764	+	0.643893i	−0.959669	−	0.281132i	$-0.909290\pi$
$859$	−16.9921	+	18.8717i	−0.579764	+	0.643893i	0.379905	+	0.925026i	$0.375957\pi$
$860$		0			0
$861$	0.0406189	−	0.313145i	0.00138429	−	0.0106720i
$862$	7.51452	−	14.7481i	0.255946	−	0.502321i
$863$	2.08987	+	39.8770i	0.0711398	+	1.35743i	0.768105	+	0.640324i	$0.221200\pi$
$863$	2.08987	+	39.8770i	0.0711398	+	1.35743i	−0.696965	+	0.717105i	$0.745467\pi$
$864$	−1.38456	−	1.53771i	−0.0471037	−	0.0523140i
$865$		0			0
$866$	−0.139763	−	0.125843i	−0.00474933	−	0.00427632i
$867$	−0.530772	+	3.35116i	−0.0180260	+	0.113811i
$868$	5.11063	−	2.44962i	0.173466	−	0.0831457i
$869$	28.0871	+	38.6586i	0.952790	+	1.31140i
$870$		0			0
$871$	3.94114	+	8.85194i	0.133540	+	0.299937i
$872$	−10.0796	−	3.86919i	−0.341338	−	0.131027i
$873$	37.8787	+	24.5987i	1.28200	+	0.832541i
$874$	−4.36436			−0.147627
$875$		0			0
$876$	−0.716283			−0.0242010
$877$	25.3160	+	16.4404i	0.854861	+	0.555153i	0.896027	−	0.443999i	$-0.146441\pi$
$877$	25.3160	+	16.4404i	0.854861	+	0.555153i	−0.0411662	+	0.999152i	$0.513107\pi$
$878$	49.9472	+	19.1729i	1.68564	+	0.647056i
$879$	−1.10794	−	2.48847i	−0.0373698	−	0.0839340i
$880$		0			0
$881$	−30.9331	−	42.5757i	−1.04216	−	1.43441i	−0.895412	−	0.445239i	$-0.853119\pi$
$881$	−30.9331	−	42.5757i	−1.04216	−	1.43441i	−0.146750	−	0.989174i	$-0.546881\pi$
$882$	3.56698	+	32.7358i	0.120107	+	1.10227i
$883$	0.132520	−	0.836696i	0.00445964	−	0.0281571i	−0.985358	−	0.170497i	$-0.945463\pi$
$883$	0.132520	−	0.836696i	0.00445964	−	0.0281571i	0.989818	+	0.142340i	$0.0454626\pi$
$884$	−2.11594	−	1.90520i	−0.0711669	−	0.0640790i
$885$		0			0
$886$	−15.0092	−	16.6694i	−0.504243	−	0.560018i
$887$	−1.95547	−	37.3126i	−0.0656582	−	1.25283i	−0.810558	−	0.585658i	$-0.800836\pi$
$887$	−1.95547	−	37.3126i	−0.0656582	−	1.25283i	0.744900	−	0.667176i	$-0.232497\pi$
$888$	1.45091	−	2.84757i	0.0486893	−	0.0955581i
$889$	−9.86084	−	23.6783i	−0.330722	−	0.794145i
$890$		0			0
$891$	−21.1866	+	23.5301i	−0.709777	+	0.788287i
$892$	−4.19988	−	3.40099i	−0.140622	−	0.113874i
$893$	−1.80542	−	6.73792i	−0.0604161	−	0.225476i
$894$	1.88509	+	0.839297i	0.0630469	+	0.0280703i
$895$		0			0
$896$	−29.6702	+	20.4752i	−0.991213	+	0.684029i
$897$	−0.0480434	−	0.303334i	−0.00160412	−	0.0101280i
$898$	−29.6599	+	45.6723i	−0.989764	+	1.52410i
$899$	−0.909733	+	1.57570i	−0.0303413	+	0.0525527i
$900$		0			0
$901$	−46.8927	+	27.0735i	−1.56222	+	0.901949i
$902$	2.37997	+	4.67095i	0.0792443	+	0.155526i
$903$	0.547558	+	1.53693i	0.0182216	+	0.0511459i
$904$	7.89502	−	10.8666i	0.262585	−	0.361417i
$905$		0			0
$906$	−0.250497	+	0.0263283i	−0.00832221	+	0.000874699i
$907$	−8.71004	+	2.33385i	−0.289212	+	0.0774942i	−0.400508	−	0.916293i	$-0.631166\pi$
$907$	−8.71004	+	2.33385i	−0.289212	+	0.0774942i	0.111296	+	0.993787i	$0.464500\pi$
$908$	−3.36041	−	8.75417i	−0.111519	−	0.290517i
$909$	17.5203	+	53.9219i	0.581111	+	1.78848i
$910$		0			0
$911$	−12.2855	+	37.8110i	−0.407038	+	1.25273i	0.512143	+	0.858900i	$0.328852\pi$
$911$	−12.2855	+	37.8110i	−0.407038	+	1.25273i	−0.919181	+	0.393834i	$0.871148\pi$
$912$	−0.624654	+	0.0327368i	−0.0206844	+	0.00108402i
$913$	−20.8849	−	32.1600i	−0.691191	−	1.06434i
$914$	−14.5375	+	13.0896i	−0.480856	+	0.432965i
$915$		0			0
$916$	−12.5655	+	4.08279i	−0.415177	+	0.134899i
$917$	−42.2730	−	22.8481i	−1.39598	−	0.754510i
$918$	−5.64465	+	5.64465i	−0.186301	+	0.186301i
$919$	19.1394	−	42.9877i	0.631350	−	1.41803i	−0.260398	−	0.965501i	$-0.583854\pi$
$919$	19.1394	−	42.9877i	0.631350	−	1.41803i	0.891748	−	0.452533i	$-0.149480\pi$
$920$		0			0
$921$	1.63712	−	0.728892i	0.0539449	−	0.0240178i
$922$	6.24306	+	7.70954i	0.205604	+	0.253900i
$923$	5.12605	−	2.61185i	0.168726	−	0.0859701i
$924$	0.384478	+	0.448431i	0.0126484	+	0.0147523i
$925$		0			0
$926$	8.40142	+	14.5517i	0.276088	+	0.478198i
$927$	29.4867	+	1.54533i	0.968471	+	0.0507554i
$928$	−0.398514	+	1.03816i	−0.0130819	+	0.0340794i
$929$	1.78540	−	16.9869i	0.0585769	−	0.557322i	−0.925396	−	0.379002i	$-0.876267\pi$
$929$	1.78540	−	16.9869i	0.0585769	−	0.557322i	0.983973	−	0.178320i	$-0.0570662\pi$
$930$		0			0
$931$	6.05375	+	3.89860i	0.198404	+	0.127771i
$932$	7.63199	+	7.63199i	0.249994	+	0.249994i
$933$	2.97939	−	1.14368i	0.0975410	−	0.0374425i
$934$	56.5495	+	12.0200i	1.85036	+	0.393306i
$935$		0			0
$936$	1.31613	+	6.19190i	0.0430190	+	0.202389i
$937$	8.78861	+	4.47802i	0.287111	+	0.146290i	0.591615	−	0.806221i	$-0.298491\pi$
$937$	8.78861	+	4.47802i	0.287111	+	0.146290i	−0.304504	+	0.952511i	$0.598491\pi$
$938$	10.7005	+	44.1991i	0.349383	+	1.44315i
$939$	3.44986	+	1.12093i	0.112582	+	0.0365801i
$940$		0			0
$941$	−9.16095	+	43.0989i	−0.298639	+	1.40498i	0.531326	+	0.847167i	$0.321694\pi$
$941$	−9.16095	+	43.0989i	−0.298639	+	1.40498i	−0.829964	+	0.557816i	$0.811639\pi$
$942$	1.21921	−	1.50560i	0.0397239	−	0.0490550i
$943$	0.647359	−	2.41598i	0.0210809	−	0.0786750i
$944$	21.9457	−	15.9445i	0.714273	−	0.518949i
$945$		0			0
$946$	−21.9137	−	15.9212i	−0.712476	−	0.517644i
$947$	−28.4234	+	23.0169i	−0.923638	+	0.747947i	−0.967969	−	0.251070i	$-0.919218\pi$
$947$	−28.4234	+	23.0169i	−0.923638	+	0.747947i	0.0443312	+	0.999017i	$0.485884\pi$
$948$	−0.0436387	+	0.832675i	−0.00141732	+	0.0270440i
$949$	8.83394	+	5.10028i	0.286762	+	0.165562i
$950$		0			0
$951$		−	0.00159667i		−	5.17755e-5i
$952$	25.3979	+	32.9687i	0.823149	+	1.06852i
$953$	−31.9821	+	5.06547i	−1.03600	+	0.164087i	−0.651195	−	0.758910i	$-0.725732\pi$
$953$	−31.9821	+	5.06547i	−1.03600	+	0.164087i	−0.384807	+	0.922997i	$0.625732\pi$
$954$	−38.4422	−	4.04044i	−1.24461	−	0.130814i
$955$		0			0
$956$	−1.48338	−	14.1134i	−0.0479759	−	0.456460i
$957$	−0.183174	−	0.0490814i	−0.00592118	−	0.00158658i
$958$	−30.1163	−	4.76996i	−0.973015	−	0.154110i
$959$	28.5000	−	15.5447i	0.920312	−	0.501964i
$960$		0			0
$961$	−11.3286	+	2.40797i	−0.365439	+	0.0776764i
$962$	12.2562	−	7.95926i	0.395155	−	0.256617i
$963$	−28.5943	+	18.5694i	−0.921440	+	0.598390i
$964$	−0.893293	+	0.189875i	−0.0287710	+	0.00611547i
$965$		0			0
$966$	0.0349821	−	1.44094i	0.00112553	−	0.0463616i
$967$	−12.7238	−	2.01526i	−0.409171	−	0.0648063i	−0.0515438	−	0.998671i	$-0.516414\pi$
$967$	−12.7238	−	2.01526i	−0.409171	−	0.0648063i	−0.357627	+	0.933864i	$0.616414\pi$
$968$	4.13782	+	1.10873i	0.132995	+	0.0356358i
$969$	0.0909775	+	0.865593i	0.00292262	+	0.0278069i
$970$		0			0
$971$	−7.14289	−	0.750748i	−0.229226	−	0.0240926i	−0.0107811	−	0.999942i	$-0.503432\pi$
$971$	−7.14289	−	0.750748i	−0.229226	−	0.0240926i	−0.218445	+	0.975849i	$0.570098\pi$
$972$	−1.65231	+	0.261700i	−0.0529977	+	0.00839402i
$973$	11.8396	+	4.87767i	0.379559	+	0.156371i
$974$			0.692506i			0.0221893i
$975$		0			0
$976$	22.0451	+	12.7278i	0.705647	+	0.407405i
$977$	−0.282466	+	5.38977i	−0.00903689	+	0.172434i	0.990382	+	0.138358i	$0.0441823\pi$
$977$	−0.282466	+	5.38977i	−0.00903689	+	0.172434i	−0.999419	+	0.0340765i	$0.989151\pi$
$978$	1.08075	−	0.875173i	0.0345585	−	0.0279849i
$979$	15.1226	+	10.9872i	0.483321	+	0.351153i
$980$		0			0
$981$	−10.9174	+	7.93198i	−0.348567	+	0.253249i
$982$	−9.79948	+	36.5721i	−0.312714	+	1.16706i
$983$	1.86936	−	2.30847i	0.0596234	−	0.0736288i	−0.746462	−	0.665428i	$-0.768249\pi$
$983$	1.86936	−	2.30847i	0.0596234	−	0.0736288i	0.806085	+	0.591799i	$0.201582\pi$
$984$	0.0592318	−	0.278664i	0.00188824	−	0.00888348i
$985$		0			0
$986$	4.08011	+	1.32571i	0.129937	+	0.0422191i
$987$	2.23907	−	0.542073i	0.0712704	−	0.0172544i
$988$	−0.396011	−	0.201778i	−0.0125988	−	0.00641941i
$989$	2.68696	+	12.6412i	0.0854404	+	0.401965i
$990$		0			0
$991$	−28.7883	−	6.11913i	−0.914489	−	0.194381i	−0.273448	−	0.961887i	$-0.588164\pi$
$991$	−28.7883	−	6.11913i	−0.914489	−	0.194381i	−0.641041	+	0.767506i	$0.721497\pi$
$992$	11.0799	−	4.25316i	0.351786	−	0.135038i
$993$	−1.97692	−	1.97692i	−0.0627355	−	0.0627355i
$994$	25.8741	−	7.71797i	0.820677	−	0.244799i
$995$		0			0
$996$	0.0699426	−	0.665459i	0.00221622	−	0.0210859i
$997$	−10.7295	+	27.9513i	−0.339806	+	0.885225i	0.652086	+	0.758145i	$0.273894\pi$
$997$	−10.7295	+	27.9513i	−0.339806	+	0.885225i	−0.991892	+	0.127080i	$0.959439\pi$
$998$	−8.33569	−	0.436855i	−0.263862	−	0.0138284i
$999$	−4.00556	−	6.93784i	−0.126730	−	0.219503i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.c.507.14		288
5.2	odd	4		875.2.bb.b.493.5		288
5.3	odd	4		875.2.bb.a.493.14		288
5.4	even	2		175.2.x.a.122.5	yes	288
7.5	odd	6	inner	875.2.bb.c.257.14		288
25.6	even	5		875.2.bb.a.857.5		288
25.8	odd	20	inner	875.2.bb.c.143.14		288
25.17	odd	20		175.2.x.a.108.5	yes	288
25.19	even	10		875.2.bb.b.857.14		288
35.12	even	12		875.2.bb.b.243.14		288
35.19	odd	6		175.2.x.a.47.5	yes	288
35.33	even	12		875.2.bb.a.243.5		288
175.19	odd	30		875.2.bb.b.607.5		288
175.33	even	60	inner	875.2.bb.c.768.14		288
175.117	even	60		175.2.x.a.33.5	✓	288
175.131	odd	30		875.2.bb.a.607.14		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.5	✓	288	175.117	even	60
175.2.x.a.47.5	yes	288	35.19	odd	6
175.2.x.a.108.5	yes	288	25.17	odd	20
175.2.x.a.122.5	yes	288	5.4	even	2
875.2.bb.a.243.5		288	35.33	even	12
875.2.bb.a.493.14		288	5.3	odd	4
875.2.bb.a.607.14		288	175.131	odd	30
875.2.bb.a.857.5		288	25.6	even	5
875.2.bb.b.243.14		288	35.12	even	12
875.2.bb.b.493.5		288	5.2	odd	4
875.2.bb.b.607.5		288	175.19	odd	30
875.2.bb.b.857.14		288	25.19	even	10
875.2.bb.c.143.14		288	25.8	odd	20	inner
875.2.bb.c.257.14		288	7.5	odd	6	inner
875.2.bb.c.507.14		288	1.1	even	1	trivial
875.2.bb.c.768.14		288	175.33	even	60	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:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.32236 + 0.858753i) q^{2} +(0.119873 + 0.0460148i) q^{3} +(0.197716 + 0.444077i) q^{4} +(0.119000 + 0.163789i) q^{6} +(0.202552 - 2.63799i) q^{7} +(0.373412 - 2.35763i) q^{8} +(-2.21718 - 1.99636i) q^{9} +(2.39345 + 2.65820i) q^{11} +(0.00326660 + 0.0623305i) q^{12} +(0.403536 - 0.791984i) q^{13} +(2.53323 - 3.31444i) q^{14} +(3.16894 - 3.51947i) q^{16} +(-5.12118 - 4.14705i) q^{17} +(-1.21754 - 4.54393i) q^{18} +(-0.939710 - 0.418386i) q^{19} +(0.145667 - 0.306902i) q^{21} +(0.882278 + 5.57049i) q^{22} +(1.46557 - 2.25678i) q^{23} +(0.153248 - 0.265433i) q^{24} +(1.21374 - 0.700753i) q^{26} +(-0.348796 - 0.684551i) q^{27} +(1.21152 - 0.431623i) q^{28} +(-0.242693 + 0.334038i) q^{29} +(4.38248 - 0.460617i) q^{31} +(2.60148 - 0.697064i) q^{32} +(0.164593 + 0.428779i) q^{33} +(-3.21077 - 9.88174i) q^{34} +(0.448165 - 1.37931i) q^{36} +(10.4129 - 0.545719i) q^{37} +(-0.883348 - 1.36024i) q^{38} +(0.0848159 - 0.0763686i) q^{39} +(0.884011 - 0.287233i) q^{41} +(0.456178 - 0.280744i) q^{42} +(-3.39602 + 3.39602i) q^{43} +(-0.707220 + 1.58844i) q^{44} +(3.87603 - 1.72572i) q^{46} +(4.26766 + 5.27013i) q^{47} +(0.541817 - 0.276070i) q^{48} +(-6.91795 - 1.06866i) q^{49} +(-0.423064 - 0.732768i) q^{51} +(0.431487 + 0.0226133i) q^{52} +(2.94467 - 7.67112i) q^{53} +(0.126625 - 1.20475i) q^{54} +(-6.14376 - 1.46260i) q^{56} +(-0.0933936 - 0.0933936i) q^{57} +(-0.607784 + 0.233306i) q^{58} +(5.60265 + 1.19088i) q^{59} +(1.11752 + 5.25754i) q^{61} +(6.19079 + 3.15437i) q^{62} +(-5.71547 + 5.44453i) q^{63} +(-4.96953 - 1.61470i) q^{64} +(-0.150564 + 0.708347i) q^{66} +(-6.86033 + 8.47180i) q^{67} +(0.829071 - 3.09413i) q^{68} +(0.279527 - 0.203088i) q^{69} +(5.23629 + 3.80439i) q^{71} +(-5.53460 + 4.48183i) q^{72} +(-0.600604 + 11.4602i) q^{73} +(14.2383 + 8.22050i) q^{74} -0.500025i q^{76} +(7.49709 - 5.77547i) q^{77} +(0.177739 - 0.0281511i) q^{78} +(13.2858 + 1.39640i) q^{79} +(0.925274 + 8.80340i) q^{81} +(1.41565 + 0.379321i) q^{82} +(-10.5884 - 1.67704i) q^{83} +(0.165089 + 0.00400790i) q^{84} +(-7.40711 + 1.57443i) q^{86} +(-0.0444629 + 0.0288746i) q^{87} +(7.16079 - 4.65027i) q^{88} +(5.11164 - 1.08651i) q^{89} +(-2.00751 - 1.22494i) q^{91} +(1.29195 + 0.204625i) q^{92} +(0.546535 + 0.146444i) q^{93} +(1.11767 + 10.6339i) q^{94} +(0.343922 + 0.0361476i) q^{96} +(-14.9519 + 2.36815i) q^{97} +(-8.23033 - 7.35396i) q^{98} -10.6719i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q + 8 q^{2} + 24 q^{3} - 10 q^{4} + 10 q^{7} + 36 q^{8} - 10 q^{9} - 6 q^{11} + 36 q^{12} - 20 q^{14} - 30 q^{16} + 42 q^{17} + 14 q^{18} - 30 q^{19} - 12 q^{21} - 32 q^{22} + 40 q^{23} - 48 q^{26}+ \cdots - 222 q^{98}+O(q^{100}) \) 288 * q + 8 * q^2 + 24 * q^3 - 10 * q^4 + 10 * q^7 + 36 * q^8 - 10 * q^9 - 6 * q^11 + 36 * q^12 - 20 * q^14 - 30 * q^16 + 42 * q^17 + 14 * q^18 - 30 * q^19 - 12 * q^21 - 32 * q^22 + 40 * q^23 - 48 * q^26 - 22 * q^28 - 18 * q^31 - 8 * q^32 + 30 * q^33 + 40 * q^36 + 10 * q^37 - 72 * q^38 + 30 * q^39 - 6 * q^42 + 108 * q^43 - 10 * q^44 - 6 * q^46 + 54 * q^47 - 16 * q^51 - 216 * q^52 - 50 * q^53 - 30 * q^54 + 4 * q^56 + 216 * q^57 + 4 * q^58 + 90 * q^59 - 18 * q^61 + 66 * q^63 - 100 * q^64 - 90 * q^66 - 4 * q^67 - 342 * q^68 - 24 * q^71 - 58 * q^72 + 6 * q^73 + 80 * q^77 + 132 * q^78 - 10 * q^79 - 10 * q^81 - 216 * q^82 + 20 * q^84 - 6 * q^86 + 48 * q^87 + 122 * q^88 + 120 * q^89 - 12 * q^91 + 4 * q^92 - 106 * q^93 - 30 * q^94 - 90 * q^96 - 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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