LMFDB - Embedded newform 875.2.bb.a.332.14

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,-2] 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			332.14
Character	$\chi$	$=$	875.332
Dual form			875.2.bb.a.593.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.23083 - 0.996709i) q^{2} +(-0.510519 - 0.786131i) q^{3} +(0.105698 - 0.497271i) q^{4} +(-1.41191 - 0.458757i) q^{6} +(2.64502 + 0.0623449i) q^{7} +(1.07251 + 2.10492i) q^{8} +(0.862838 - 1.93797i) q^{9} +(-2.58948 + 1.15291i) q^{11} +(-0.444881 + 0.170774i) q^{12} +(4.35361 + 0.689545i) q^{13} +(3.31771 - 2.55958i) q^{14} +(4.34693 + 1.93538i) q^{16} +(-3.89051 - 0.203893i) q^{17} +(-0.869579 - 3.24531i) q^{18} +(4.84954 - 1.03080i) q^{19} +(-1.30132 - 2.11116i) q^{21} +(-2.03810 + 4.00000i) q^{22} +(0.626170 + 0.773256i) q^{23} +(1.10721 - 1.91774i) q^{24} +(6.04585 - 3.49057i) q^{26} +(-4.74143 + 0.750969i) q^{27} +(0.310576 - 1.30870i) q^{28} +(4.01849 - 1.30569i) q^{29} +(4.25980 - 3.83554i) q^{31} +(2.71554 - 0.727626i) q^{32} +(2.22832 + 1.44709i) q^{33} +(-4.99179 + 3.62674i) q^{34} +(-0.872494 - 0.633904i) q^{36} +(0.0624587 + 0.162710i) q^{37} +(4.94157 - 6.10233i) q^{38} +(-1.68053 - 3.77454i) q^{39} +(-4.52386 - 6.22657i) q^{41} +(-3.70592 - 1.30144i) q^{42} +(2.45065 - 2.45065i) q^{43} +(0.299606 + 1.40953i) q^{44} +(1.54142 + 0.327640i) q^{46} +(-0.199164 - 3.80028i) q^{47} +(-0.697732 - 4.40531i) q^{48} +(6.99223 + 0.329807i) q^{49} +(1.82589 + 3.16254i) q^{51} +(0.803060 - 2.09204i) q^{52} +(-11.7548 + 7.63368i) q^{53} +(-5.08741 + 5.65015i) q^{54} +(2.70558 + 5.63442i) q^{56} +(-3.28613 - 3.28613i) q^{57} +(3.64471 - 5.61236i) q^{58} +(-1.04652 - 9.95696i) q^{59} +(-9.83200 - 1.03338i) q^{61} +(1.42018 - 8.96669i) q^{62} +(2.40304 - 5.07216i) q^{63} +(-2.97658 + 4.09692i) q^{64} +(4.18501 - 0.439863i) q^{66} +(-0.572651 + 10.9268i) q^{67} +(-0.512609 + 1.91308i) q^{68} +(0.288208 - 0.887014i) q^{69} +(2.13171 + 6.56074i) q^{71} +(5.00467 - 0.262283i) q^{72} +(4.95641 + 1.90259i) q^{73} +(0.239051 + 0.138016i) q^{74} -2.52049i q^{76} +(-6.92109 + 2.88803i) q^{77} +(-5.83057 - 2.97082i) q^{78} +(3.18486 + 2.86766i) q^{79} +(-1.24746 - 1.38545i) q^{81} +(-11.7742 - 3.15489i) q^{82} +(-1.82179 + 0.928247i) q^{83} +(-1.18736 + 0.423964i) q^{84} +(0.573756 - 5.45892i) q^{86} +(-3.07796 - 2.49248i) q^{87} +(-5.20403 - 4.21414i) q^{88} +(0.768774 - 7.31439i) q^{89} +(11.4724 + 2.09528i) q^{91} +(0.450703 - 0.229645i) q^{92} +(-5.18994 - 1.39064i) q^{93} +(-4.03292 - 4.47901i) q^{94} +(-1.95835 - 1.76330i) q^{96} +(7.31730 + 3.72835i) q^{97} +(8.93499 - 6.56328i) q^{98} +6.01310i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) $ 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Character values

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

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{9}{20}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	1.23083	−	0.996709i	0.870331	−	0.704780i	−0.0862419	−	0.996274i	$-0.527486\pi$
$2$	1.23083	−	0.996709i	0.870331	−	0.704780i	0.956573	+	0.291494i	$0.0941525\pi$
$3$	−0.510519	−	0.786131i	−0.294749	−	0.453873i	0.660009	−	0.751257i	$-0.270552\pi$
$3$	−0.510519	−	0.786131i	−0.294749	−	0.453873i	−0.954758	+	0.297385i	$0.903886\pi$
$4$	0.105698	−	0.497271i	0.0528491	−	0.248635i
$5$		0			0
$5$		0			0
$6$	−1.41191	−	0.458757i	−0.576409	−	0.187287i
$7$	2.64502	+	0.0623449i	0.999722	+	0.0235642i
$7$	2.64502	+	0.0623449i	0.999722	+	0.0235642i
$8$	1.07251	+	2.10492i	0.379190	+	0.744202i
$9$	0.862838	−	1.93797i	0.287613	−	0.645989i
$10$		0			0
$11$	−2.58948	+	1.15291i	−0.780757	+	0.347616i	−0.758109	−	0.652128i	$-0.773877\pi$
$11$	−2.58948	+	1.15291i	−0.780757	+	0.347616i	−0.0226485	+	0.999743i	$0.507210\pi$
$12$	−0.444881	+	0.170774i	−0.128426	+	0.0492982i
$13$	4.35361	+	0.689545i	1.20748	+	0.191245i	0.727544	−	0.686061i	$-0.240662\pi$
$13$	4.35361	+	0.689545i	1.20748	+	0.191245i	0.479931	+	0.877306i	$0.340662\pi$
$14$	3.31771	−	2.55958i	0.886697	−	0.684076i
$15$		0			0
$16$	4.34693	+	1.93538i	1.08673	+	0.483845i
$17$	−3.89051	−	0.203893i	−0.943586	−	0.0494513i	−0.425666	−	0.904880i	$-0.639960\pi$
$17$	−3.89051	−	0.203893i	−0.943586	−	0.0494513i	−0.517920	+	0.855429i	$0.673294\pi$
$18$	−0.869579	−	3.24531i	−0.204962	−	0.764927i
$19$	4.84954	−	1.03080i	1.11256	−	0.236482i	0.385265	−	0.922806i	$-0.374110\pi$
$19$	4.84954	−	1.03080i	1.11256	−	0.236482i	0.727296	+	0.686324i	$0.240777\pi$
$20$		0			0
$21$	−1.30132	−	2.11116i	−0.283972	−	0.460692i
$22$	−2.03810	+	4.00000i	−0.434525	+	0.852803i
$23$	0.626170	+	0.773256i	0.130566	+	0.161235i	0.838236	−	0.545308i	$-0.183587\pi$
$23$	0.626170	+	0.773256i	0.130566	+	0.161235i	−0.707670	+	0.706543i	$0.750254\pi$
$24$	1.10721	−	1.91774i	0.226007	−	0.391456i
$25$		0			0
$26$	6.04585	−	3.49057i	1.18569	−	0.684558i
$27$	−4.74143	+	0.750969i	−0.912489	+	0.144524i
$28$	0.310576	−	1.30870i	0.0586933	−	0.247321i
$29$	4.01849	−	1.30569i	0.746216	−	0.242460i	0.0888637	−	0.996044i	$-0.471676\pi$
$29$	4.01849	−	1.30569i	0.746216	−	0.242460i	0.657352	+	0.753584i	$0.271676\pi$
$30$		0			0
$31$	4.25980	−	3.83554i	0.765082	−	0.688883i	−0.191128	−	0.981565i	$-0.561215\pi$
$31$	4.25980	−	3.83554i	0.765082	−	0.688883i	0.956210	+	0.292682i	$0.0945478\pi$
$32$	2.71554	−	0.727626i	0.480044	−	0.128627i
$33$	2.22832	+	1.44709i	0.387900	+	0.251906i
$34$	−4.99179	+	3.62674i	−0.856084	+	0.621982i
$35$		0			0
$36$	−0.872494	−	0.633904i	−0.145416	−	0.105651i
$37$	0.0624587	+	0.162710i	0.0102681	+	0.0267494i	0.938619	−	0.344956i	$-0.112106\pi$
$37$	0.0624587	+	0.162710i	0.0102681	+	0.0267494i	−0.928351	+	0.371706i	$0.878773\pi$
$38$	4.94157	−	6.10233i	0.801628	−	0.989928i
$39$	−1.68053	−	3.77454i	−0.269101	−	0.604410i
$40$		0			0
$41$	−4.52386	−	6.22657i	−0.706509	−	0.972426i	−0.999865	−	0.0164229i	$-0.994772\pi$
$41$	−4.52386	−	6.22657i	−0.706509	−	0.972426i	0.293356	−	0.956003i	$-0.405228\pi$
$42$	−3.70592	−	1.30144i	−0.571836	−	0.200817i
$43$	2.45065	−	2.45065i	0.373720	−	0.373720i	−0.495110	−	0.868830i	$-0.664872\pi$
$43$	2.45065	−	2.45065i	0.373720	−	0.373720i	0.868830	+	0.495110i	$0.164872\pi$
$44$	0.299606	+	1.40953i	0.0451672	+	0.212495i
$45$		0			0
$46$	1.54142	+	0.327640i	0.227270	+	0.0483078i
$47$	−0.199164	−	3.80028i	−0.0290511	−	0.554328i	−0.973922	−	0.226884i	$-0.927146\pi$
$47$	−0.199164	−	3.80028i	−0.0290511	−	0.554328i	0.944871	−	0.327444i	$-0.106187\pi$
$48$	−0.697732	−	4.40531i	−0.100709	−	0.635851i
$49$	6.99223	+	0.329807i	0.998889	+	0.0471153i
$50$		0			0
$51$	1.82589	+	3.16254i	0.255676	+	0.442844i
$52$	0.803060	−	2.09204i	0.111364	−	0.290114i
$53$	−11.7548	+	7.63368i	−1.61465	+	1.04857i	−0.659816	+	0.751428i	$0.729366\pi$
$53$	−11.7548	+	7.63368i	−1.61465	+	1.04857i	−0.954834	+	0.297138i	$0.903968\pi$
$54$	−5.08741	+	5.65015i	−0.692309	+	0.768887i
$55$		0			0
$56$	2.70558	+	5.63442i	0.361548	+	0.752930i
$57$	−3.28613	−	3.28613i	−0.435259	−	0.435259i
$58$	3.64471	−	5.61236i	0.478573	−	0.736938i
$59$	−1.04652	−	9.95696i	−0.136245	−	1.29629i	−0.822433	−	0.568862i	$-0.807384\pi$
$59$	−1.04652	−	9.95696i	−0.136245	−	1.29629i	0.686188	−	0.727424i	$-0.259283\pi$
$60$		0			0
$61$	−9.83200	−	1.03338i	−1.25886	−	0.132311i	−0.548499	−	0.836151i	$-0.684801\pi$
$61$	−9.83200	−	1.03338i	−1.25886	−	0.132311i	−0.710359	+	0.703840i	$0.751467\pi$
$62$	1.42018	−	8.96669i	0.180363	−	1.13877i
$63$	2.40304	−	5.07216i	0.302755	−	0.639032i
$64$	−2.97658	+	4.09692i	−0.372073	+	0.512115i
$65$		0			0
$66$	4.18501	−	0.439863i	0.515140	−	0.0541434i
$67$	−0.572651	+	10.9268i	−0.0699604	+	1.33492i	0.707822	+	0.706391i	$0.249678\pi$
$67$	−0.572651	+	10.9268i	−0.0699604	+	1.33492i	−0.777783	+	0.628533i	$0.783656\pi$
$68$	−0.512609	+	1.91308i	−0.0621630	+	0.231995i
$69$	0.288208	−	0.887014i	0.0346962	−	0.106784i
$70$		0			0
$71$	2.13171	+	6.56074i	0.252988	+	0.778617i	0.994219	+	0.107367i	$0.0342420\pi$
$71$	2.13171	+	6.56074i	0.252988	+	0.778617i	−0.741232	+	0.671249i	$0.765758\pi$
$72$	5.00467	−	0.262283i	0.589806	−	0.0309104i
$73$	4.95641	+	1.90259i	0.580103	+	0.222681i	0.630685	−	0.776039i	$-0.282774\pi$
$73$	4.95641	+	1.90259i	0.580103	+	0.222681i	−0.0505814	+	0.998720i	$0.516107\pi$
$74$	0.239051	+	0.138016i	0.0277892	+	0.0160441i
$75$		0			0
$76$		−	2.52049i		−	0.289120i
$77$	−6.92109	+	2.88803i	−0.788732	+	0.329121i
$78$	−5.83057	−	2.97082i	−0.660182	−	0.336380i
$79$	3.18486	+	2.86766i	0.358325	+	0.322637i	0.828556	−	0.559906i	$-0.189163\pi$
$79$	3.18486	+	2.86766i	0.358325	+	0.322637i	−0.470231	+	0.882543i	$0.655830\pi$
$80$		0			0
$81$	−1.24746	−	1.38545i	−0.138607	−	0.153939i
$82$	−11.7742	−	3.15489i	−1.30024	−	0.348399i
$83$	−1.82179	+	0.928247i	−0.199967	+	0.101888i	−0.551107	−	0.834435i	$-0.685794\pi$
$83$	−1.82179	+	0.928247i	−0.199967	+	0.101888i	0.351140	+	0.936323i	$0.385794\pi$
$84$	−1.18736	+	0.423964i	−0.129552	+	0.0462582i
$85$		0			0
$86$	0.573756	−	5.45892i	0.0618697	−	0.588651i
$87$	−3.07796	−	2.49248i	−0.329992	−	0.267222i
$88$	−5.20403	−	4.21414i	−0.554751	−	0.449229i
$89$	0.768774	−	7.31439i	0.0814898	−	0.775324i	−0.875111	−	0.483922i	$-0.839212\pi$
$89$	0.768774	−	7.31439i	0.0814898	−	0.775324i	0.956601	−	0.291402i	$-0.0941216\pi$
$90$		0			0
$91$	11.4724	+	2.09528i	1.20263	+	0.219645i
$92$	0.450703	−	0.229645i	0.0469890	−	0.0239421i
$93$	−5.18994	−	1.39064i	−0.538172	−	0.144203i
$94$	−4.03292	−	4.47901i	−0.415964	−	0.461974i
$95$		0			0
$96$	−1.95835	−	1.76330i	−0.199873	−	0.179966i
$97$	7.31730	+	3.72835i	0.742959	+	0.378556i	0.784131	−	0.620596i	$-0.213109\pi$
$97$	7.31730	+	3.72835i	0.742959	+	0.378556i	−0.0411720	+	0.999152i	$0.513109\pi$
$98$	8.93499	−	6.56328i	0.902570	−	0.662991i
$99$			6.01310i			0.604339i
$100$		0			0
$101$	10.1754	+	5.87479i	1.01249	+	0.584563i	0.911921	−	0.410367i	$-0.134599\pi$
$101$	10.1754	+	5.87479i	1.01249	+	0.584563i	0.100572	+	0.994930i	$0.467933\pi$
$102$	5.39950	+	2.07267i	0.534630	+	0.205225i
$103$	−10.9468	+	0.573699i	−1.07862	+	0.0565283i	−0.583359	−	0.812214i	$-0.698262\pi$
$103$	−10.9468	+	0.573699i	−1.07862	+	0.0565283i	−0.495264	+	0.868742i	$0.664929\pi$
$104$	3.21786	+	9.90356i	0.315537	+	0.971124i
$105$		0			0
$106$	−6.85968	+	21.1119i	−0.666271	+	2.05057i
$107$	−1.85148	+	6.90983i	−0.178990	+	0.667999i	0.816848	+	0.576853i	$0.195720\pi$
$107$	−1.85148	+	6.90983i	−0.178990	+	0.667999i	−0.995838	+	0.0911455i	$0.970947\pi$
$108$	−0.127726	+	2.43715i	−0.0122904	+	0.234515i
$109$	−14.1671	+	1.48902i	−1.35696	+	0.142622i	−0.754906	−	0.655833i	$-0.772317\pi$
$109$	−14.1671	+	1.48902i	−1.35696	+	0.142622i	−0.602054	+	0.798455i	$0.705651\pi$
$110$		0			0
$111$	0.0960254	−	0.132168i	0.00911433	−	0.0125448i
$112$	11.3770	+	5.39012i	1.07503	+	0.509318i
$113$	−2.84433	+	17.9584i	−0.267572	+	1.68938i	0.378096	+	0.925766i	$0.376579\pi$
$113$	−2.84433	+	17.9584i	−0.267572	+	1.68938i	−0.645668	+	0.763618i	$0.723421\pi$
$114$	−7.31999	−	0.769362i	−0.685580	−	0.0720574i
$115$		0			0
$116$	−0.224533	−	2.13629i	−0.0208474	−	0.198349i
$117$	5.09278	−	7.84219i	0.470828	−	0.725011i
$118$	−11.2123	−	11.2123i	−1.03217	−	1.03217i
$119$	−10.2777	−	0.781853i	−0.942159	−	0.0716724i
$120$		0			0
$121$	−1.98424	+	2.20372i	−0.180385	+	0.200338i
$122$	−13.1315	+	8.52772i	−1.18887	+	0.772063i
$123$	−2.58538	+	6.73513i	−0.233115	+	0.607286i
$124$	−1.45705	−	2.52368i	−0.130847	−	0.226633i
$125$		0			0
$126$	−2.09772	−	8.63812i	−0.186880	−	0.769545i
$127$	−2.82772	−	17.8535i	−0.250919	−	1.58424i	−0.715436	−	0.698678i	$-0.753772\pi$
$127$	−2.82772	−	17.8535i	−0.250919	−	1.58424i	0.464517	−	0.885564i	$-0.346228\pi$
$128$	0.714023	+	13.6244i	0.0631113	+	1.20424i
$129$	−3.17763	−	0.675427i	−0.279775	−	0.0594680i
$130$		0			0
$131$	3.07880	+	14.4846i	0.268996	+	1.26553i	0.880409	+	0.474215i	$0.157268\pi$
$131$	3.07880	+	14.4846i	0.268996	+	1.26553i	−0.611413	+	0.791312i	$0.709399\pi$
$132$	0.955123	−	0.955123i	0.0831328	−	0.0831328i
$133$	12.8914	−	2.42414i	1.11782	−	0.210200i
$134$	10.1860	+	14.0199i	0.879939	+	1.21113i
$135$		0			0
$136$	−3.74343	−	8.40788i	−0.320997	−	0.720970i
$137$	−9.30881	+	11.4954i	−0.795305	+	0.982120i	0.204689	+	0.978827i	$0.434382\pi$
$137$	−9.30881	+	11.4954i	−0.795305	+	0.982120i	−0.999995	+	0.00329306i	$0.998952\pi$
$138$	−0.529359	−	1.37903i	−0.0450620	−	0.117391i
$139$	−0.341041	−	0.247781i	−0.0289267	−	0.0210165i	0.573228	−	0.819396i	$-0.305691\pi$
$139$	−0.341041	−	0.247781i	−0.0289267	−	0.0210165i	−0.602155	+	0.798379i	$0.705691\pi$
$140$		0			0
$141$	−2.88584	+	2.09669i	−0.243032	+	0.176573i
$142$	9.16293	+	5.95048i	0.768936	+	0.499353i
$143$	−12.0686	+	3.23377i	−1.00923	+	0.270421i
$144$	7.50140	−	6.75429i	0.625116	−	0.562857i
$145$		0			0
$146$	7.99683	−	2.59833i	0.661823	−	0.215039i
$147$	−3.31040	−	5.66518i	−0.273037	−	0.467256i
$148$	0.0875130	−	0.0138607i	0.00719352	−	0.00113934i
$149$	5.68925	−	3.28469i	0.466081	−	0.269092i	−0.248517	−	0.968628i	$-0.579943\pi$
$149$	5.68925	−	3.28469i	0.466081	−	0.269092i	0.714598	+	0.699536i	$0.246610\pi$
$150$		0			0
$151$	2.85500	−	4.94500i	0.232336	−	0.402419i	−0.726159	−	0.687527i	$-0.758696\pi$
$151$	2.85500	−	4.94500i	0.232336	−	0.402419i	0.958495	+	0.285108i	$0.0920296\pi$
$152$	7.37094	+	9.10235i	0.597862	+	0.738298i
$153$	−3.75201	+	7.36374i	−0.303332	+	0.595323i
$154$	−5.64019	+	10.4530i	−0.454500	+	0.842327i
$155$		0			0
$156$	−2.05460	+	0.436718i	−0.164499	+	0.0349654i
$157$	2.23488	+	8.34069i	0.178363	+	0.665660i	0.995954	+	0.0898608i	$0.0286422\pi$
$157$	2.23488	+	8.34069i	0.178363	+	0.665660i	−0.817591	+	0.575799i	$0.804691\pi$
$158$	6.77825	+	0.355233i	0.539249	+	0.0282608i
$159$	12.0021	+	5.34370i	0.951832	+	0.423783i
$160$		0			0
$161$	1.60802	+	2.08431i	0.126730	+	0.164267i
$162$	−2.91631	−	0.461898i	−0.229127	−	0.0362901i
$163$	10.6907	−	4.10379i	0.837363	−	0.321434i	0.0983730	−	0.995150i	$-0.468636\pi$
$163$	10.6907	−	4.10379i	0.837363	−	0.321434i	0.738990	+	0.673716i	$0.235303\pi$
$164$	−3.57445	+	1.59145i	−0.279118	+	0.124271i
$165$		0			0
$166$	−1.31712	+	2.95831i	−0.102229	+	0.229609i
$167$	−4.34514	−	8.52782i	−0.336237	−	0.659903i	0.659544	−	0.751666i	$-0.270750\pi$
$167$	−4.34514	−	8.52782i	−0.336237	−	0.659903i	−0.995781	+	0.0917636i	$0.970750\pi$
$168$	3.04814	−	5.00342i	0.235169	−	0.386022i
$169$	6.11475	+	1.98680i	0.470366	+	0.152831i
$170$		0			0
$171$	2.18671	−	10.2877i	0.167222	−	0.786717i
$172$	−0.959607	−	1.47767i	−0.0731693	−	0.112671i
$173$	6.86731	−	5.56104i	0.522112	−	0.422798i	−0.331696	−	0.943386i	$-0.607621\pi$
$173$	6.86731	−	5.56104i	0.522112	−	0.422798i	0.853808	+	0.520588i	$0.174287\pi$
$174$	−6.27274			−0.475535
$175$		0			0
$176$	−13.4876			−1.01667
$177$	−7.29321	+	5.90592i	−0.548191	+	0.443916i
$178$	−6.34409	−	9.76904i	−0.475510	−	0.732221i
$179$	2.62382	−	12.3441i	0.196114	−	0.922643i	−0.764471	−	0.644658i	$-0.777000\pi$
$179$	2.62382	−	12.3441i	0.196114	−	0.922643i	0.960585	−	0.277986i	$-0.0896667\pi$
$180$		0			0
$181$	−20.9424	−	6.80460i	−1.55664	−	0.505782i	−0.600730	−	0.799452i	$-0.705123\pi$
$181$	−20.9424	−	6.80460i	−1.55664	−	0.505782i	−0.955907	+	0.293670i	$0.905123\pi$
$182$	16.2090	−	8.85570i	1.20149	−	0.656428i
$183$	4.20705	+	8.25680i	0.310994	+	0.610360i
$184$	−0.956068	+	2.14736i	−0.0704823	+	0.158306i
$185$		0			0
$186$	−7.77402	+	3.46122i	−0.570019	+	0.253789i
$187$	10.3095	−	3.95743i	0.753902	−	0.289396i
$188$	−1.91082	−	0.302644i	−0.139361	−	0.0220726i
$189$	−12.5880	+	1.69072i	−0.915641	+	0.122982i
$190$		0			0
$191$	−12.6852	−	5.64783i	−0.917871	−	0.408663i	−0.107249	−	0.994232i	$-0.534204\pi$
$191$	−12.6852	−	5.64783i	−0.917871	−	0.408663i	−0.810622	+	0.585570i	$0.800871\pi$
$192$	4.74032	+	0.248430i	0.342103	+	0.0179289i
$193$	4.04325	+	15.0896i	0.291040	+	1.08618i	0.944312	+	0.329052i	$0.106729\pi$
$193$	4.04325	+	15.0896i	0.291040	+	1.08618i	−0.653272	+	0.757123i	$0.726604\pi$
$194$	12.7225	−	2.70424i	0.913419	−	0.194153i
$195$		0			0
$196$	0.903069	−	3.44217i	0.0645049	−	0.245869i
$197$	3.76513	−	7.38948i	0.268254	−	0.526479i	−0.717106	−	0.696964i	$-0.754534\pi$
$197$	3.76513	−	7.38948i	0.268254	−	0.526479i	0.985360	+	0.170486i	$0.0545336\pi$
$198$	5.99331	+	7.40112i	0.425926	+	0.525975i
$199$	−3.90101	+	6.75675i	−0.276535	+	0.478973i	−0.970521	−	0.241015i	$-0.922520\pi$
$199$	−3.90101	+	6.75675i	−0.276535	+	0.478973i	0.693986	+	0.719989i	$0.255853\pi$
$200$		0			0
$201$	8.88227	−	5.12818i	0.626507	−	0.361714i
$202$	18.3797	−	2.91106i	1.29319	−	0.204822i
$203$	10.7104	−	3.20303i	0.751722	−	0.224809i
$204$	1.76563	−	0.573688i	0.123619	−	0.0401662i
$205$		0			0
$206$	−12.9019	+	11.6169i	−0.898919	+	0.809390i
$207$	2.03883	−	0.546302i	0.141708	−	0.0379706i
$208$	17.5903	+	11.4233i	1.21967	+	0.792063i
$209$	−11.3694	+	8.26033i	−0.786435	+	0.571379i
$210$		0			0
$211$	−22.7260	−	16.5114i	−1.56452	−	1.13669i	−0.932176	−	0.362006i	$-0.882092\pi$
$211$	−22.7260	−	16.5114i	−1.56452	−	1.13669i	−0.632347	−	0.774686i	$-0.717908\pi$
$212$	2.55354	+	6.65220i	0.175378	+	0.456875i
$213$	4.06932	−	5.02519i	0.278825	−	0.344320i
$214$	4.60822	+	10.3502i	0.315012	+	0.707528i
$215$		0			0
$216$	−6.66597	−	9.17491i	−0.453561	−	0.624274i
$217$	11.5064	−	9.87948i	0.781102	−	0.670663i
$218$	−15.9532	+	15.9532i	−1.08049	+	1.08049i
$219$	−1.03466	−	4.86769i	−0.0699158	−	0.328928i
$220$		0			0
$221$	−16.7972	−	3.57035i	−1.12990	−	0.240168i
$222$	−0.0135414	−	0.258386i	−0.000908841	−	0.0173417i
$223$	−1.96762	−	12.4231i	−0.131762	−	0.831912i	−0.961710	−	0.274070i	$-0.911630\pi$
$223$	−1.96762	−	12.4231i	−0.131762	−	0.831912i	0.829948	−	0.557841i	$-0.188370\pi$
$224$	7.22801	−	1.75528i	0.482942	−	0.117280i
$225$		0			0
$226$	14.3984	+	24.9388i	0.957768	+	1.65890i
$227$	−3.90645	+	10.1766i	−0.259280	+	0.675447i	0.740714	+	0.671821i	$0.234488\pi$
$227$	−3.90645	+	10.1766i	−0.259280	+	0.675447i	−0.999993	+	0.00362623i	$0.998846\pi$
$228$	−1.98143	+	1.28676i	−0.131224	+	0.0852177i
$229$	−1.85586	+	2.06114i	−0.122639	+	0.136204i	−0.801337	−	0.598213i	$-0.795878\pi$
$229$	−1.85586	+	2.06114i	−0.122639	+	0.136204i	0.678698	+	0.734417i	$0.262544\pi$
$230$		0			0
$231$	5.80372	+	3.96649i	0.381857	+	0.260976i
$232$	7.05825	+	7.05825i	0.463397	+	0.463397i
$233$	−15.4308	+	23.7613i	−1.01090	+	1.55666i	−0.193083	+	0.981182i	$0.561849\pi$
$233$	−15.4308	+	23.7613i	−1.01090	+	1.55666i	−0.817821	+	0.575473i	$0.804818\pi$
$234$	−1.54802	−	14.7284i	−0.101197	−	0.962829i
$235$		0			0
$236$	−5.06192	−	0.532029i	−0.329503	−	0.0346322i
$237$	0.628424	−	3.96771i	0.0408205	−	0.257731i
$238$	−13.4295	+	9.28159i	−0.870503	+	0.601636i
$239$	7.39994	−	10.1851i	0.478662	−	0.658822i	−0.499585	−	0.866265i	$-0.666514\pi$
$239$	7.39994	−	10.1851i	0.478662	−	0.658822i	0.978247	+	0.207443i	$0.0665140\pi$
$240$		0			0
$241$	6.96570	−	0.732124i	0.448700	−	0.0471603i	0.122516	−	0.992467i	$-0.460904\pi$
$241$	6.96570	−	0.732124i	0.448700	−	0.0471603i	0.326184	+	0.945306i	$0.394237\pi$
$242$	−0.245798	+	4.69011i	−0.0158005	+	0.301492i
$243$	−4.17970	+	15.5988i	−0.268128	+	1.00067i
$244$	−1.55310	+	4.77994i	−0.0994268	+	0.306004i
$245$		0			0
$246$	3.53080	+	10.8667i	0.225116	+	0.692835i
$247$	21.8238	−	1.14374i	1.38862	−	0.0727743i
$248$	12.6422	+	4.85288i	0.802779	+	0.308158i
$249$	1.65978	+	0.958275i	0.105184	+	0.0607282i
$250$		0			0
$251$			3.04599i			0.192261i	0.995369	+	0.0961305i	$0.0306466\pi$
$251$			3.04599i			0.192261i	−0.995369	+	0.0961305i	$0.969353\pi$
$252$	−2.26824	−	1.73108i	−0.142886	−	0.109048i
$253$	−2.51295	−	1.28041i	−0.157988	−	0.0804988i
$254$	−21.2752	−	19.1563i	−1.33492	−	1.20197i
$255$		0			0
$256$	7.68133	+	8.53099i	0.480083	+	0.533187i
$257$	−5.50579	−	1.47527i	−0.343442	−	0.0920249i	0.0829753	−	0.996552i	$-0.473558\pi$
$257$	−5.50579	−	1.47527i	−0.343442	−	0.0920249i	−0.426417	+	0.904527i	$0.640224\pi$
$258$	−4.58434	+	2.33584i	−0.285409	+	0.145423i
$259$	0.155060	+	0.434266i	0.00963497	+	0.0269840i
$260$		0			0
$261$	0.936931	−	8.91430i	0.0579946	−	0.551782i
$262$	18.2264	+	14.7595i	1.12603	+	0.911843i
$263$	−3.10902	−	2.51764i	−0.191710	−	0.155244i	0.528660	−	0.848834i	$-0.322695\pi$
$263$	−3.10902	−	2.51764i	−0.191710	−	0.155244i	−0.720370	+	0.693590i	$0.756028\pi$
$264$	−0.656108	+	6.24245i	−0.0403806	+	0.384196i
$265$		0			0
$266$	13.4510	−	15.8327i	0.824732	−	0.970764i
$267$	−6.14255	+	3.12978i	−0.375918	+	0.191540i
$268$	5.37306	+	1.43971i	0.328212	+	0.0879442i
$269$	3.15201	+	3.50066i	0.192182	+	0.213439i	0.831533	−	0.555475i	$-0.187464\pi$
$269$	3.15201	+	3.50066i	0.192182	+	0.213439i	−0.639351	+	0.768915i	$0.720797\pi$
$270$		0			0
$271$	−1.63260	−	1.47000i	−0.0991733	−	0.0892960i	0.618053	−	0.786137i	$-0.287922\pi$
$271$	−1.63260	−	1.47000i	−0.0991733	−	0.0892960i	−0.717226	+	0.696841i	$0.754588\pi$
$272$	−16.5172	−	8.41591i	−1.00150	−	0.510290i
$273$	−4.20971	−	10.0885i	−0.254783	−	0.610583i
$274$			23.4271i			1.41528i
$275$		0			0
$276$	−0.410623	−	0.237073i	−0.0247166	−	0.0142701i
$277$	−6.38913	−	2.45256i	−0.383886	−	0.147360i	0.158769	−	0.987316i	$-0.449247\pi$
$277$	−6.38913	−	2.45256i	−0.383886	−	0.147360i	−0.542655	+	0.839956i	$0.682581\pi$
$278$	−0.666730	+	0.0349418i	−0.0399878	+	0.00209567i
$279$	−3.75763	−	11.5648i	−0.224963	−	0.692366i
$280$		0			0
$281$	−0.775793	+	2.38765i	−0.0462799	+	0.142435i	−0.971526	−	0.236932i	$-0.923858\pi$
$281$	−0.775793	+	2.38765i	−0.0462799	+	0.142435i	0.925246	+	0.379367i	$0.123858\pi$
$282$	−1.46220	+	5.45702i	−0.0870730	+	0.324961i
$283$	0.391263	−	7.46574i	0.0232582	−	0.443792i	−0.962036	−	0.272924i	$-0.912009\pi$
$283$	0.391263	−	7.46574i	0.0232582	−	0.443792i	0.985294	−	0.170869i	$-0.0546574\pi$
$284$	3.48778	−	0.366581i	0.206962	−	0.0217526i
$285$		0			0
$286$	−11.6313	+	16.0091i	−0.687772	+	0.946637i
$287$	−11.5775	−	16.7514i	−0.683398	−	0.988804i
$288$	0.932955	−	5.89045i	0.0549749	−	0.347098i
$289$	−1.81241	−	0.190492i	−0.106612	−	0.0112054i
$290$		0			0
$291$	−0.804651	−	7.65575i	−0.0471695	−	0.448788i
$292$	1.46998	−	2.26358i	0.0860243	−	0.132466i
$293$	−9.76381	−	9.76381i	−0.570408	−	0.570408i	0.361835	−	0.932242i	$-0.382151\pi$
$293$	−9.76381	−	9.76381i	−0.570408	−	0.570408i	−0.932242	+	0.361835i	$0.882151\pi$
$294$	−9.72108	−	3.67339i	−0.566945	−	0.214236i
$295$		0			0
$296$	−0.275505	+	0.305979i	−0.0160134	+	0.0177847i
$297$	11.4120	−	7.41106i	0.662194	−	0.430034i
$298$	3.72864	−	9.71343i	0.215994	−	0.562684i
$299$	2.19291	+	3.79823i	0.126819	+	0.219657i
$300$		0			0
$301$	6.63479	−	6.32922i	0.382423	−	0.364810i
$302$	−1.41470	−	8.93208i	−0.0814070	−	0.513983i
$303$	−0.576402	−	10.9984i	−0.0331135	−	0.631842i
$304$	23.0756	+	4.90487i	1.32348	+	0.281314i
$305$		0			0
$306$	2.72141	+	12.8032i	0.155572	+	0.731910i
$307$	1.41797	−	1.41797i	0.0809280	−	0.0809280i	−0.665484	−	0.746412i	$-0.731775\pi$
$307$	1.41797	−	1.41797i	0.0809280	−	0.0809280i	0.746412	+	0.665484i	$0.231775\pi$
$308$	0.704584	+	3.74692i	0.0401474	+	0.213500i
$309$	6.03957	+	8.31276i	0.343579	+	0.472896i
$310$		0			0
$311$	−4.07937	−	9.16242i	−0.231320	−	0.519553i	0.760172	−	0.649722i	$-0.225115\pi$
$311$	−4.07937	−	9.16242i	−0.231320	−	0.519553i	−0.991492	+	0.130169i	$0.958448\pi$
$312$	6.14271	−	7.58562i	0.347763	−	0.429451i
$313$	−6.48894	−	16.9043i	−0.366776	−	0.955485i	−0.985470	−	0.169852i	$-0.945671\pi$
$313$	−6.48894	−	16.9043i	−0.366776	−	0.955485i	0.618693	−	0.785633i	$-0.287662\pi$
$314$	11.0640	+	8.03848i	0.624378	+	0.453637i
$315$		0			0
$316$	1.76264	−	1.28063i	0.0991561	−	0.0720411i
$317$	12.2633	+	7.96390i	0.688777	+	0.447297i	0.840990	−	0.541051i	$-0.181973\pi$
$317$	12.2633	+	7.96390i	0.688777	+	0.447297i	−0.152213	+	0.988348i	$0.548640\pi$
$318$	20.0987	−	5.38544i	1.12708	−	0.302001i
$319$	−8.90047	+	8.01402i	−0.498331	+	0.448699i
$320$		0			0
$321$	6.37725	−	2.07209i	0.355943	−	0.115653i
$322$	4.05666	+	0.962712i	0.226069	+	0.0536498i
$323$	−19.0773	+	3.02155i	−1.06149	+	0.168124i
$324$	−0.820798	+	0.473888i	−0.0455999	+	0.0263271i
$325$		0			0
$326$	9.06823	−	15.7066i	0.502243	−	0.869910i
$327$	8.40313	+	10.3770i	0.464694	+	0.573850i
$328$	8.25453	−	16.2004i	0.455780	−	0.894519i
$329$	−0.289865	−	10.0642i	−0.0159808	−	0.554859i
$330$		0			0
$331$	31.2229	−	6.63663i	1.71617	−	0.364782i	0.758280	−	0.651929i	$-0.226040\pi$
$331$	31.2229	−	6.63663i	1.71617	−	0.364782i	0.957887	+	0.287147i	$0.0927068\pi$
$332$	0.269030	+	1.00404i	0.0147650	+	0.0551036i
$333$	0.369219	+	0.0193500i	0.0202331	+	0.00106037i
$334$	−13.8479	−	6.16548i	−0.757724	−	0.337360i
$335$		0			0
$336$	−1.57086	−	11.6956i	−0.0856977	−	0.638048i
$337$	−22.8944	−	3.62612i	−1.24714	−	0.197527i	−0.502254	−	0.864720i	$-0.667496\pi$
$337$	−22.8944	−	3.62612i	−1.24714	−	0.197527i	−0.744885	+	0.667193i	$0.767496\pi$
$338$	9.50651	−	3.64921i	0.517086	−	0.198491i
$339$	15.5697	−	6.93210i	0.845632	−	0.376500i
$340$		0			0
$341$	−6.60862	+	14.8432i	−0.357877	+	0.803805i
$342$	−7.56233	−	14.8419i	−0.408924	−	0.802558i
$343$	18.4740	+	1.30827i	0.997502	+	0.0706402i
$344$	7.78677	+	2.53007i	0.419834	+	0.136412i
$345$		0			0
$346$	2.90978	−	13.6894i	0.156431	−	0.735948i
$347$	−2.56079	−	3.94327i	−0.137470	−	0.211686i	0.763230	−	0.646127i	$-0.223612\pi$
$347$	−2.56079	−	3.94327i	−0.137470	−	0.211686i	−0.900700	+	0.434441i	$0.856946\pi$
$348$	−1.56477	+	1.26713i	−0.0838807	+	0.0679253i
$349$	−18.4434			−0.987251			−0.493625	−	0.869675i	$-0.664329\pi$
$349$	−18.4434			−0.987251			−0.493625	+	0.869675i	$0.664329\pi$
$350$		0			0
$351$	−21.1602			−1.12945
$352$	−6.19294	+	5.01495i	−0.330085	+	0.267298i
$353$	−2.81747	−	4.33853i	−0.149959	−	0.230916i	0.755706	−	0.654911i	$-0.227294\pi$
$353$	−2.81747	−	4.33853i	−0.149959	−	0.230916i	−0.905665	+	0.423995i	$0.860627\pi$
$354$	−3.09024	+	14.5384i	−0.164244	+	0.772708i
$355$		0			0
$356$	−3.55598	−	1.15541i	−0.188466	−	0.0612364i
$357$	4.63235	+	8.47880i	0.245170	+	0.448746i
$358$	−9.07401	−	17.8088i	−0.479576	−	0.941222i
$359$	4.74434	−	10.6560i	0.250397	−	0.562400i	−0.743992	−	0.668189i	$-0.767070\pi$
$359$	4.74434	−	10.6560i	0.250397	−	0.562400i	0.994389	+	0.105788i	$0.0337366\pi$
$360$		0			0
$361$	5.09812	−	2.26983i	0.268322	−	0.119465i
$362$	−32.5588	+	12.4982i	−1.71125	+	0.656889i
$363$	2.74540	+	0.434829i	0.144096	+	0.0228226i
$364$	2.25453	−	5.48342i	0.118170	−	0.287409i
$365$		0			0
$366$	13.4078	+	5.96954i	0.700837	+	0.312033i
$367$	−32.9227	−	1.72540i	−1.71855	−	0.0900654i	−0.832608	−	0.553862i	$-0.813154\pi$
$367$	−32.9227	−	1.72540i	−1.71855	−	0.0900654i	−0.885942	+	0.463797i	$0.846487\pi$
$368$	1.22538	+	4.57317i	0.0638772	+	0.238393i
$369$	−15.9702	+	3.39458i	−0.831377	+	0.176715i
$370$		0			0
$371$	−31.5676	+	19.4583i	−1.63891	+	1.01023i
$372$	−1.24009	+	2.43382i	−0.0642958	+	0.126188i
$373$	7.39810	+	9.13589i	0.383059	+	0.473039i	0.931810	−	0.362948i	$-0.118230\pi$
$373$	7.39810	+	9.13589i	0.383059	+	0.473039i	−0.548750	+	0.835986i	$0.684896\pi$
$374$	8.74482	−	15.1465i	0.452184	−	0.783205i
$375$		0			0
$376$	7.78569	−	4.49507i	0.401516	−	0.231816i
$377$	18.3953	−	2.91353i	0.947407	−	0.150054i
$378$	−13.8086	+	14.6276i	−0.710235	+	0.752360i
$379$	4.38145	−	1.42362i	0.225060	−	0.0731264i	−0.194316	−	0.980939i	$-0.562249\pi$
$379$	4.38145	−	1.42362i	0.225060	−	0.0731264i	0.419376	+	0.907813i	$0.362249\pi$
$380$		0			0
$381$	−12.5916	+	11.3375i	−0.645087	+	0.580839i
$382$	−21.2427	+	5.69195i	−1.08687	+	0.291226i
$383$	−7.26031	−	4.71490i	−0.370985	−	0.240920i	0.345658	−	0.938360i	$-0.387656\pi$
$383$	−7.26031	−	4.71490i	−0.370985	−	0.240920i	−0.716643	+	0.697440i	$0.754322\pi$
$384$	10.3460	−	7.51682i	0.527968	−	0.383591i
$385$		0			0
$386$	20.0165	+	14.5429i	1.01882	+	0.740213i
$387$	−2.63476	−	6.86379i	−0.133932	−	0.348906i
$388$	2.62742	−	3.24460i	0.133387	−	0.164720i
$389$	5.07744	+	11.4041i	0.257437	+	0.578212i	0.995311	−	0.0967259i	$-0.0308370\pi$
$389$	5.07744	+	11.4041i	0.257437	+	0.578212i	−0.737874	+	0.674938i	$0.764170\pi$
$390$		0			0
$391$	−2.27846	−	3.13603i	−0.115227	−	0.158596i
$392$	6.80502	+	15.0718i	0.343705	+	0.761241i
$393$	9.81502	−	9.81502i	0.495102	−	0.495102i
$394$	−2.73092	−	12.8480i	−0.137582	−	0.647271i
$395$		0			0
$396$	2.99014	+	0.635574i	0.150260	+	0.0319388i
$397$	1.35850	+	25.9217i	0.0681812	+	1.30097i	0.791802	+	0.610777i	$0.209143\pi$
$397$	1.35850	+	25.9217i	0.0681812	+	1.30097i	−0.723621	+	0.690197i	$0.757524\pi$
$398$	1.93302	+	12.2046i	0.0968935	+	0.611762i
$399$	−8.48699	−	8.89674i	−0.424881	−	0.445394i
$400$		0			0
$401$	−2.67960	−	4.64121i	−0.133813	−	0.231771i	0.791330	−	0.611389i	$-0.209389\pi$
$401$	−2.67960	−	4.64121i	−0.133813	−	0.231771i	−0.925143	+	0.379618i	$0.876055\pi$
$402$	5.82129	−	15.1650i	0.290339	−	0.756360i
$403$	21.1903	−	13.7611i	1.05556	−	0.685491i
$404$	3.99688	−	4.43899i	0.198852	−	0.220848i
$405$		0			0
$406$	9.99021	−	14.6175i	0.495806	−	0.725457i
$407$	−0.349326	−	0.349326i	−0.0173155	−	0.0173155i
$408$	−4.69860	+	7.23521i	−0.232616	+	0.358196i
$409$	0.701543	+	6.67473i	0.0346890	+	0.330044i	0.998080	+	0.0619427i	$0.0197296\pi$
$409$	0.701543	+	6.67473i	0.0346890	+	0.330044i	−0.963391	+	0.268102i	$0.913604\pi$
$410$		0			0
$411$	13.7892	+	1.44931i	0.680173	+	0.0714890i
$412$	−0.871776	+	5.50418i	−0.0429493	+	0.271171i
$413$	−2.14729	−	26.4016i	−0.105661	−	1.29914i
$414$	1.96495	−	2.70453i	0.0965721	−	0.132920i
$415$		0			0
$416$	12.3241	−	1.29532i	0.604241	−	0.0635083i
$417$	−0.0206801	+	0.394600i	−0.00101271	+	0.0193236i
$418$	−5.76065	+	21.4990i	−0.281763	+	1.05155i
$419$	−11.2169	+	34.5222i	−0.547984	+	1.68652i	0.165804	+	0.986159i	$0.446978\pi$
$419$	−11.2169	+	34.5222i	−0.547984	+	1.68652i	−0.713788	+	0.700362i	$0.753022\pi$
$420$		0			0
$421$	10.0786	+	31.0186i	0.491199	+	1.51175i	0.822798	+	0.568334i	$0.192412\pi$
$421$	10.0786	+	31.0186i	0.491199	+	1.51175i	−0.331599	+	0.943421i	$0.607588\pi$
$422$	−44.4290	+	2.32842i	−2.16277	+	0.113346i
$423$	−7.53667	−	2.89306i	−0.366445	−	0.140665i
$424$	−28.6755	−	16.5558i	−1.39260	−	0.804020i
$425$		0			0
$426$		−	10.2411i		−	0.496183i
$427$	−25.9414	−	3.34630i	−1.25539	−	0.161939i
$428$	3.24036	+	1.65105i	0.156629	+	0.0798063i
$429$	8.70341	+	7.83658i	0.420205	+	0.378354i
$430$		0			0
$431$	16.9198	+	18.7913i	0.814998	+	0.905147i	0.996941	−	0.0781619i	$-0.0249051\pi$
$431$	16.9198	+	18.7913i	0.814998	+	0.905147i	−0.181942	+	0.983309i	$0.558238\pi$
$432$	−22.0641	−	5.91206i	−1.06156	−	0.284444i
$433$	−17.1376	+	8.73204i	−0.823581	+	0.419635i	−0.814387	−	0.580322i	$-0.802927\pi$
$433$	−17.1376	+	8.73204i	−0.823581	+	0.419635i	−0.00919384	+	0.999958i	$0.502927\pi$
$434$	4.31544	−	23.6285i	0.207148	−	1.13420i
$435$		0			0
$436$	−0.756988	+	7.20226i	−0.0362531	+	0.344926i
$437$	3.83371	+	3.10448i	0.183391	+	0.148507i
$438$	−6.12517	−	4.96006i	−0.292672	−	0.237001i
$439$	−0.657874	+	6.25925i	−0.0313986	+	0.298738i	0.967542	+	0.252712i	$0.0813224\pi$
$439$	−0.657874	+	6.25925i	−0.0313986	+	0.298738i	−0.998940	+	0.0460261i	$0.985344\pi$
$440$		0			0
$441$	6.67231	−	13.2661i	0.317729	−	0.631720i
$442$	−24.2331	+	12.3474i	−1.15265	+	0.587305i
$443$	23.6811	+	6.34534i	1.12513	+	0.301476i	0.772956	−	0.634460i	$-0.218777\pi$
$443$	23.6811	+	6.34534i	1.12513	+	0.301476i	0.352170	+	0.935936i	$0.385444\pi$
$444$	−0.0555734	−	0.0617205i	−0.00263740	−	0.00292913i
$445$		0			0
$446$	−14.8040	−	13.3296i	−0.700991	−	0.631175i
$447$	−5.48667	−	2.79560i	−0.259510	−	0.132227i
$448$	−8.12854	+	10.6508i	−0.384037	+	0.503205i
$449$		−	29.0905i		−	1.37286i	−0.727194	−	0.686432i	$-0.759176\pi$
$449$		−	29.0905i		−	1.37286i	0.727194	−	0.686432i	$-0.240824\pi$
$450$		0			0
$451$	18.8931	+	10.9080i	0.889643	+	0.513635i
$452$	8.62955	+	3.31257i	0.405900	+	0.155810i
$453$	−5.34495	+	0.280117i	−0.251128	+	0.0131610i
$454$	5.33497	+	16.4193i	0.250382	+	0.770598i
$455$		0			0
$456$	3.39263	−	10.4415i	0.158875	−	0.488966i
$457$	7.75345	−	28.9363i	0.362691	−	1.35358i	−0.507833	−	0.861456i	$-0.669553\pi$
$457$	7.75345	−	28.9363i	0.362691	−	1.35358i	0.870524	−	0.492126i	$-0.163780\pi$
$458$	−0.229896	+	4.38668i	−0.0107423	+	0.204976i
$459$	18.5997	−	1.95491i	0.868159	−	0.0912472i
$460$		0			0
$461$	7.92746	−	10.9112i	0.369218	−	0.508186i	−0.583470	−	0.812135i	$-0.698305\pi$
$461$	7.92746	−	10.9112i	0.369218	−	0.508186i	0.952688	+	0.303949i	$0.0983053\pi$
$462$	11.0969	−	0.902530i	0.516272	−	0.0419895i
$463$	0.129975	−	0.820628i	0.00604043	−	0.0381378i	−0.984484	−	0.175474i	$-0.943854\pi$
$463$	0.129975	−	0.820628i	0.00604043	−	0.0381378i	0.990524	+	0.137336i	$0.0438541\pi$
$464$	19.9951	+	2.10157i	0.928250	+	0.0975631i
$465$		0			0
$466$	4.69041	+	44.6262i	0.217279	+	2.06727i
$467$	15.5397	−	23.9291i	0.719093	−	1.10731i	−0.270403	−	0.962747i	$-0.587157\pi$
$467$	15.5397	−	23.9291i	0.719093	−	1.10731i	0.989496	−	0.144559i	$-0.0461765\pi$
$468$	−3.36140	−	3.36140i	−0.155381	−	0.155381i
$469$	−2.19590	+	28.8659i	−0.101397	+	1.33290i
$470$		0			0
$471$	5.41593	−	6.01500i	0.249553	−	0.277156i
$472$	19.8362	−	12.8818i	0.913036	−	0.592932i
$473$	−3.52053	+	9.17128i	−0.161874	+	0.421696i
$474$	−3.18117	−	5.50995i	−0.146116	−	0.253080i
$475$		0			0
$476$	−1.47513	+	5.02818i	−0.0676125	+	0.230466i
$477$	4.65129	+	29.3671i	0.212968	+	1.34463i
$478$	−1.04353	−	19.9118i	−0.0477301	−	0.910745i
$479$	−28.6904	−	6.09834i	−1.31090	−	0.278640i	−0.501122	−	0.865377i	$-0.667079\pi$
$479$	−28.6904	−	6.09834i	−1.31090	−	0.278640i	−0.809778	+	0.586736i	$0.800412\pi$
$480$		0			0
$481$	0.159725	+	0.751447i	0.00728283	+	0.0342630i
$482$	7.84390	−	7.84390i	0.357280	−	0.357280i
$483$	0.817617	−	2.32820i	0.0372029	−	0.105937i
$484$	0.886114	+	1.21963i	0.0402779	+	0.0554378i
$485$		0			0
$486$	10.4030	+	23.3655i	0.471890	+	1.05988i
$487$	−2.20185	+	2.71906i	−0.0997754	+	0.123212i	−0.824588	−	0.565734i	$-0.808593\pi$
$487$	−2.20185	+	2.71906i	−0.0997754	+	0.123212i	0.724813	+	0.688946i	$0.241926\pi$
$488$	−8.36973	−	21.8039i	−0.378880	−	0.987016i
$489$	−8.68395	−	6.30926i	−0.392702	−	0.285315i
$490$		0			0
$491$	31.7981	−	23.1026i	1.43503	−	1.04261i	0.445973	−	0.895046i	$-0.352858\pi$
$491$	31.7981	−	23.1026i	1.43503	−	1.04261i	0.989053	−	0.147561i	$-0.0471424\pi$
$492$	3.07592	+	1.99752i	0.138673	+	0.0900553i
$493$	−15.9002	+	4.26044i	−0.716109	+	0.191881i
$494$	25.7215	−	23.1597i	1.15727	−	1.04201i
$495$		0			0
$496$	25.9403	−	8.42850i	1.16475	−	0.378451i
$497$	5.22939	+	17.4862i	0.234570	+	0.784362i
$498$	2.99804	−	0.474842i	0.134345	−	0.0212782i
$499$	25.9919	−	15.0064i	1.16356	−	0.671780i	0.211403	−	0.977399i	$-0.432197\pi$
$499$	25.9919	−	15.0064i	1.16356	−	0.671780i	0.952154	+	0.305619i	$0.0988634\pi$
$500$		0			0
$501$	−4.48571	+	7.76947i	−0.200407	+	0.347114i
$502$	3.03596	+	3.74910i	0.135502	+	0.167331i
$503$	19.0522	−	37.3921i	0.849497	−	1.66723i	0.110142	−	0.993916i	$-0.464869\pi$
$503$	19.0522	−	37.3921i	0.849497	−	1.66723i	0.739355	−	0.673316i	$-0.235131\pi$
$504$	13.2538	−	0.381729i	0.590370	−	0.0170035i
$505$		0			0
$506$	−4.36922	+	0.928707i	−0.194236	+	0.0412861i
$507$	−1.55981	−	5.82130i	−0.0692737	−	0.258533i
$508$	−9.17691	−	0.480941i	−0.407160	−	0.0213383i
$509$	2.64690	+	1.17848i	0.117322	+	0.0522350i	0.464558	−	0.885543i	$-0.346213\pi$
$509$	2.64690	+	1.17848i	0.117322	+	0.0522350i	−0.347236	+	0.937778i	$0.612880\pi$
$510$		0			0
$511$	12.9912	+	5.34138i	0.574695	+	0.236289i
$512$	−8.99285	−	1.42433i	−0.397431	−	0.0629470i
$513$	−22.2197	+	8.52933i	−0.981022	+	0.376579i
$514$	−8.24713	+	3.67186i	−0.363765	+	0.161959i
$515$		0			0
$516$	−0.671740	+	1.50875i	−0.0295717	+	0.0664192i
$517$	4.89712	+	9.61114i	0.215375	+	0.422697i
$518$	0.623690	+	0.379959i	0.0274034	+	0.0166944i
$519$	−7.87760	−	2.55959i	−0.345788	−	0.112353i
$520$		0			0
$521$	5.02801	−	23.6549i	0.220281	−	1.03634i	−0.719481	−	0.694512i	$-0.755620\pi$
$521$	5.02801	−	23.6549i	0.220281	−	1.03634i	0.939762	−	0.341829i	$-0.111046\pi$
$522$	−7.73176	−	11.9059i	−0.338410	−	0.521106i
$523$	29.8282	−	24.1544i	1.30430	−	1.05620i	0.309870	−	0.950779i	$-0.399715\pi$
$523$	29.8282	−	24.1544i	1.30430	−	1.05620i	0.994428	−	0.105420i	$-0.0336188\pi$
$524$	7.52820			0.328871
$525$		0			0
$526$	−6.33604			−0.276264
$527$	−17.3548	+	14.0536i	−0.755987	+	0.612186i
$528$	6.88569	+	10.6030i	0.299661	+	0.461438i
$529$	4.57613	−	21.5290i	0.198962	−	0.936044i
$530$		0			0
$531$	−20.1992	−	6.56313i	−0.876572	−	0.284815i
$532$	0.157140	−	6.66673i	0.00681287	−	0.289040i
$533$	−15.4017	−	30.2275i	−0.667120	−	1.30930i
$534$	−4.44097	+	9.97457i	−0.192179	+	0.431642i
$535$		0			0
$536$	−23.6143	+	10.5138i	−1.01998	+	0.454125i
$537$	−11.0436	+	4.23925i	−0.476567	+	0.182937i
$538$	7.36875	+	1.16709i	0.317689	+	0.0503170i
$539$	−18.4865	+	7.20738i	−0.796268	+	0.310444i
$540$		0			0
$541$	−23.2155	−	10.3362i	−0.998114	−	0.444389i	−0.158375	−	0.987379i	$-0.550625\pi$
$541$	−23.2155	−	10.3362i	−0.998114	−	0.444389i	−0.839739	+	0.542990i	$0.817292\pi$
$542$	−3.47462	−	0.182097i	−0.149248	−	0.00782173i
$543$	5.34220	+	19.9374i	0.229256	+	0.855594i
$544$	−10.7132	+	2.27716i	−0.459324	+	0.0976323i
$545$		0			0
$546$	−15.2367	−	8.22139i	−0.652072	−	0.351843i
$547$	−6.68428	+	13.1186i	−0.285799	+	0.560912i	−0.988616	−	0.150458i	$-0.951925\pi$
$547$	−6.68428	+	13.1186i	−0.285799	+	0.560912i	0.702817	+	0.711370i	$0.251925\pi$
$548$	4.73241	+	5.84404i	0.202159	+	0.249645i
$549$	−10.4861	+	18.1624i	−0.447535	+	0.775154i
$550$		0			0
$551$	18.1419	−	10.4743i	0.772873	−	0.446218i
$552$	2.17620	−	0.344676i	0.0926253	−	0.0146704i
$553$	8.24522	+	7.78357i	0.350622	+	0.330991i
$554$	−10.3084	+	3.34942i	−0.437964	+	0.142303i
$555$		0			0
$556$	−0.159261	+	0.143400i	−0.00675419	+	0.00608150i
$557$	−12.2713	+	3.28809i	−0.519952	+	0.139321i	−0.509245	−	0.860622i	$-0.670075\pi$
$557$	−12.2713	+	3.28809i	−0.519952	+	0.139321i	−0.0107078	+	0.999943i	$0.503408\pi$
$558$	−16.1517	−	10.4891i	−0.683758	−	0.444037i
$559$	12.3590	−	8.97935i	0.522730	−	0.379786i
$560$		0			0
$561$	−8.37424	−	6.08424i	−0.353560	−	0.256877i
$562$	1.42492	+	3.71204i	0.0601065	+	0.156583i
$563$	−12.5170	+	15.4572i	−0.527528	+	0.651443i	−0.969357	−	0.245656i	$-0.920997\pi$
$563$	−12.5170	+	15.4572i	−0.527528	+	0.651443i	0.441829	+	0.897099i	$0.354330\pi$
$564$	0.737593	+	1.65666i	0.0310583	+	0.0697581i
$565$		0			0
$566$	−6.95960	−	9.57906i	−0.292534	−	0.402638i
$567$	−3.21319	−	3.74231i	−0.134941	−	0.157162i
$568$	−11.5236	+	11.5236i	−0.483517	+	0.483517i
$569$	−0.271241	−	1.27609i	−0.0113710	−	0.0534965i	0.972096	−	0.234582i	$-0.0753722\pi$
$569$	−0.271241	−	1.27609i	−0.0113710	−	0.0534965i	−0.983467	+	0.181086i	$0.942039\pi$
$570$		0			0
$571$	20.3922	+	4.33450i	0.853389	+	0.181393i	0.613781	−	0.789476i	$-0.289648\pi$
$571$	20.3922	+	4.33450i	0.853389	+	0.181393i	0.239608	+	0.970870i	$0.422981\pi$
$572$	0.332431	+	6.34316i	0.0138996	+	0.265221i
$573$	2.03612	+	12.8556i	0.0850603	+	0.537050i
$574$	−30.9463	−	9.07879i	−1.29167	−	0.378941i
$575$		0			0
$576$	5.37138	+	9.30350i	0.223807	+	0.387646i
$577$	11.3894	−	29.6705i	0.474149	−	1.23520i	−0.463028	−	0.886344i	$-0.653237\pi$
$577$	11.3894	−	29.6705i	0.474149	−	1.23520i	0.937176	−	0.348856i	$-0.113430\pi$
$578$	−2.42064	+	1.57198i	−0.100685	+	0.0653859i
$579$	9.79827	−	10.8821i	0.407202	−	0.452244i
$580$		0			0
$581$	−4.87653	+	2.34165i	−0.202312	+	0.0971480i
$582$	−8.62095	−	8.62095i	−0.357350	−	0.357350i
$583$	21.6379	−	33.3195i	0.896152	−	1.37995i
$584$	1.31101	+	12.4734i	0.0542498	+	0.516152i
$585$		0			0
$586$	−21.7493	−	2.28594i	−0.898455	−	0.0944315i
$587$	0.789333	−	4.98365i	0.0325793	−	0.205697i	−0.966029	−	0.258433i	$-0.916794\pi$
$587$	0.789333	−	4.98365i	0.0325793	−	0.205697i	0.998609	+	0.0527353i	$0.0167940\pi$
$588$	−3.16703	+	1.04736i	−0.130606	+	0.0431926i
$589$	16.7044	−	22.9916i	0.688292	−	0.947352i
$590$		0			0
$591$	−7.73127	+	0.812589i	−0.318022	+	0.0334255i
$592$	−0.0434027	+	0.828173i	−0.00178384	+	0.0340377i
$593$	2.62542	−	9.79820i	0.107813	−	0.402364i	−0.890836	−	0.454325i	$-0.849880\pi$
$593$	2.62542	−	9.79820i	0.107813	−	0.402364i	0.998649	+	0.0519610i	$0.0165472\pi$
$594$	6.65964	−	20.4963i	0.273248	−	0.840972i
$595$		0			0
$596$	−1.03204	−	3.17628i	−0.0422739	−	0.130106i
$597$	7.30323	−	0.382746i	0.298901	−	0.0156648i
$598$	6.48484	+	2.48930i	0.265185	+	0.101795i
$599$	35.8204	+	20.6809i	1.46358	+	0.844999i	0.999175	−	0.0406237i	$-0.0129345\pi$
$599$	35.8204	+	20.6809i	1.46358	+	0.844999i	0.464406	+	0.885622i	$0.346268\pi$
$600$		0			0
$601$			42.8734i			1.74884i	0.485169	+	0.874420i	$0.338758\pi$
$601$			42.8734i			1.74884i	−0.485169	+	0.874420i	$0.661242\pi$
$602$	1.85793	−	14.4032i	0.0757236	−	0.587030i
$603$	20.6817	+	10.5379i	0.842224	+	0.429135i
$604$	−2.15724	−	1.94239i	−0.0877767	−	0.0790345i
$605$		0			0
$606$	−11.6717	−	12.9627i	−0.474129	−	0.526574i
$607$	18.5840	+	4.97957i	0.754302	+	0.202115i	0.615425	−	0.788195i	$-0.288984\pi$
$607$	18.5840	+	4.97957i	0.754302	+	0.202115i	0.138876	+	0.990310i	$0.455651\pi$
$608$	12.4191	−	6.32784i	0.503660	−	0.256628i
$609$	−7.98587	−	6.78456i	−0.323604	−	0.274924i
$610$		0			0
$611$	1.75338	−	16.6823i	0.0709342	−	0.674894i
$612$	3.26519	+	2.64410i	0.131988	+	0.106881i
$613$	9.68283	+	7.84100i	0.391086	+	0.316695i	0.804616	−	0.593795i	$-0.202371\pi$
$613$	9.68283	+	7.84100i	0.391086	+	0.316695i	−0.413530	+	0.910490i	$0.635704\pi$
$614$	0.331982	−	3.15860i	0.0133977	−	0.127471i
$615$		0			0
$616$	−13.5020	−	11.4709i	−0.544012	−	0.462176i
$617$	16.0963	−	8.20148i	0.648013	−	0.330179i	−0.0989034	−	0.995097i	$-0.531533\pi$
$617$	16.0963	−	8.20148i	0.648013	−	0.330179i	0.746916	+	0.664918i	$0.231533\pi$
$618$	15.7191	+	4.21192i	0.632316	+	0.169428i
$619$	5.97986	+	6.64131i	0.240351	+	0.266937i	0.851237	−	0.524782i	$-0.175853\pi$
$619$	5.97986	+	6.64131i	0.240351	+	0.266937i	−0.610886	+	0.791719i	$0.709187\pi$
$620$		0			0
$621$	−3.54963	−	3.19611i	−0.142442	−	0.128255i
$622$	−14.1533	−	7.21147i	−0.567496	−	0.289154i
$623$	2.48943	−	19.2988i	0.0997371	−	0.773189i
$624$		−	19.6601i		−	0.787035i
$625$		0			0
$626$	−24.8354	−	14.3387i	−0.992624	−	0.573091i
$627$	12.2980	+	4.72075i	0.491134	+	0.188529i
$628$	4.38381	−	0.229746i	0.174933	−	0.00916785i
$629$	−0.209820	−	0.645761i	−0.00836609	−	0.0257482i
$630$		0			0
$631$	14.0918	−	43.3700i	0.560984	−	1.72653i	−0.118608	−	0.992941i	$-0.537843\pi$
$631$	14.0918	−	43.3700i	0.560984	−	1.72653i	0.679592	−	0.733590i	$-0.262157\pi$
$632$	−2.62040	+	9.77947i	−0.104234	+	0.389006i
$633$	−1.37806	+	26.2950i	−0.0547731	+	1.04513i
$634$	23.0318	−	2.42074i	0.914710	−	0.0961399i
$635$		0			0
$636$	3.92587	−	5.40349i	0.155671	−	0.214263i
$637$	30.2140	+	6.25730i	1.19712	+	0.247923i
$638$	−2.96735	+	18.7351i	−0.117478	+	0.741730i
$639$	14.5538	+	1.52967i	0.575740	+	0.0605127i
$640$		0			0
$641$	0.223909	+	2.13035i	0.00884387	+	0.0841438i	0.998054	−	0.0623630i	$-0.0198636\pi$
$641$	0.223909	+	2.13035i	0.00884387	+	0.0841438i	−0.989210	+	0.146507i	$0.953197\pi$
$642$	5.78406	−	8.90667i	0.228279	−	0.351518i
$643$	6.86315	+	6.86315i	0.270656	+	0.270656i	0.829364	−	0.558708i	$-0.188703\pi$
$643$	6.86315	+	6.86315i	0.270656	+	0.270656i	−0.558708	+	0.829364i	$0.688703\pi$
$644$	1.20643	−	0.579315i	0.0475401	−	0.0228282i
$645$		0			0
$646$	−20.4694	+	22.7336i	−0.805358	+	0.894441i
$647$	23.4225	−	15.2108i	0.920834	−	0.597997i	0.00518985	−	0.999987i	$-0.498348\pi$
$647$	23.4225	−	15.2108i	0.920834	−	0.597997i	0.915644	+	0.401990i	$0.131681\pi$
$648$	1.57834	−	4.11172i	0.0620031	−	0.161524i
$649$	14.1894	+	24.5768i	0.556984	+	0.964724i
$650$		0			0
$651$	−13.6408	−	4.00184i	−0.534625	−	0.156844i
$652$	−0.910704	−	5.74996i	−0.0356659	−	0.225186i
$653$	0.654232	+	12.4835i	0.0256021	+	0.488517i	0.981098	+	0.193512i	$0.0619878\pi$
$653$	0.654232	+	12.4835i	0.0256021	+	0.488517i	−0.955496	+	0.295005i	$0.904679\pi$
$654$	20.6857	+	4.39688i	0.808875	+	0.171932i
$655$		0			0
$656$	−7.61417	−	35.8218i	−0.297283	−	1.39861i
$657$	7.96372	−	7.96372i	0.310694	−	0.310694i
$658$	−10.3879	−	12.0985i	−0.404962	−	0.471648i
$659$	−4.46660	−	6.14775i	−0.173994	−	0.239482i	0.713109	−	0.701053i	$-0.247286\pi$
$659$	−4.46660	−	6.14775i	−0.173994	−	0.239482i	−0.887104	+	0.461570i	$0.847286\pi$
$660$		0			0
$661$	18.5203	+	41.5973i	0.720357	+	1.61795i	0.784591	+	0.620013i	$0.212873\pi$
$661$	18.5203	+	41.5973i	0.720357	+	1.61795i	−0.0642344	+	0.997935i	$0.520461\pi$
$662$	31.8154	−	39.2888i	1.23654	−	1.52700i
$663$	5.76852	+	15.0275i	0.224031	+	0.583620i
$664$	−3.90777	−	2.83916i	−0.151651	−	0.110181i
$665$		0			0
$666$	0.473734	−	0.344188i	0.0183568	−	0.0133370i
$667$	3.52589	+	2.28974i	0.136523	+	0.0886592i
$668$	−4.69991	+	1.25934i	−0.181845	+	0.0487252i
$669$	−8.76167	+	7.88904i	−0.338746	+	0.305008i
$670$		0			0
$671$	26.6512	−	8.65949i	1.02886	−	0.334296i
$672$	−5.06992	−	4.78606i	−0.195577	−	0.184626i
$673$	−23.7602	+	3.76325i	−0.915888	+	0.145062i	−0.596548	−	0.802578i	$-0.703461\pi$
$673$	−23.7602	+	3.76325i	−0.915888	+	0.145062i	−0.319341	+	0.947640i	$0.603461\pi$
$674$	−31.7934	+	18.3559i	−1.22464	+	0.707044i
$675$		0			0
$676$	1.63430	−	2.83069i	0.0628576	−	0.108873i
$677$	4.94253	+	6.10351i	0.189957	+	0.234577i	0.863223	−	0.504823i	$-0.168442\pi$
$677$	4.94253	+	6.10351i	0.189957	+	0.234577i	−0.673266	+	0.739400i	$0.735109\pi$
$678$	12.2545	−	24.0508i	0.470630	−	0.923664i
$679$	19.1219	+	10.3177i	0.733832	+	0.395958i
$680$		0			0
$681$	9.99449	−	2.12439i	0.382990	−	0.0814070i
$682$	6.66025	+	24.8564i	0.255034	+	0.951800i
$683$	17.3292	+	0.908183i	0.663082	+	0.0347506i	0.380908	−	0.924613i	$-0.375611\pi$
$683$	17.3292	+	0.908183i	0.663082	+	0.0347506i	0.282173	+	0.959363i	$0.408945\pi$
$684$	−4.88462	−	2.17477i	−0.186768	−	0.0831545i
$685$		0			0
$686$	24.0424	−	16.8029i	0.917942	−	0.641539i
$687$	2.56778	+	0.406697i	0.0979670	+	0.0155164i
$688$	15.3957	−	5.90987i	0.586957	−	0.225312i
$689$	−56.4398	+	25.1286i	−2.15018	+	0.957323i
$690$		0			0
$691$	−15.5580	+	34.9439i	−0.591855	+	1.32933i	0.330800	+	0.943701i	$0.392681\pi$
$691$	−15.5580	+	34.9439i	−0.591855	+	1.32933i	−0.922655	+	0.385627i	$0.873985\pi$
$692$	−2.03948	−	4.00271i	−0.0775294	−	0.152160i
$693$	−0.374886	+	15.9047i	−0.0142407	+	0.604171i
$694$	−7.08220	−	2.30115i	−0.268837	−	0.0873503i
$695$		0			0
$696$	1.94533	−	9.15208i	0.0737377	−	0.346909i
$697$	16.3306	+	25.1469i	0.618564	+	0.952506i
$698$	−22.7007	+	18.3827i	−0.859235	+	0.695795i
$699$	26.5572			1.00449
$700$		0			0
$701$	−38.6073			−1.45818			−0.729088	−	0.684420i	$-0.760056\pi$
$701$	−38.6073			−1.45818			−0.729088	+	0.684420i	$0.760056\pi$
$702$	−26.0447	+	21.0906i	−0.982993	+	0.796012i
$703$	0.470618	+	0.724689i	0.0177497	+	0.0273321i
$704$	2.98443	−	14.0406i	0.112480	−	0.529176i
$705$		0			0
$706$	−7.79209	−	2.53180i	−0.293259	−	0.0952856i
$707$	26.5479	+	16.1733i	0.998437	+	0.608259i
$708$	2.16597	+	4.25095i	0.0814020	+	0.159760i
$709$	−0.0239172	+	0.0537188i	−0.000898228	+	0.00201745i	−0.913994	−	0.405728i	$-0.867018\pi$
$709$	−0.0239172	+	0.0537188i	−0.000898228	+	0.00201745i	0.913096	+	0.407745i	$0.133685\pi$
$710$		0			0
$711$	8.30544	−	3.69782i	0.311478	−	0.138679i
$712$	16.2207	−	6.22656i	0.607898	−	0.233350i
$713$	5.63321	+	0.892213i	0.210965	+	0.0334136i
$714$	14.1525	+	5.81889i	0.529646	+	0.217766i
$715$		0			0
$716$	−5.86104	−	2.60950i	−0.219037	−	0.0975217i
$717$	−11.7847	−	0.617609i	−0.440107	−	0.0230650i
$718$	−4.78140	−	17.8444i	−0.178440	−	0.665949i
$719$	−10.4630	+	2.22399i	−0.390206	+	0.0829408i	−0.398837	−	0.917022i	$-0.630586\pi$
$719$	−10.4630	+	2.22399i	−0.390206	+	0.0829408i	0.00863097	+	0.999963i	$0.497253\pi$
$720$		0			0
$721$	−28.9903	+	0.834964i	−1.07966	+	0.0310957i
$722$	4.01258	−	7.87513i	0.149333	−	0.293082i
$723$	−4.13167	−	5.10219i	−0.153658	−	0.189752i
$724$	−5.59730	+	9.69481i	−0.208022	+	0.360305i
$725$		0			0
$726$	3.81253	−	2.20116i	0.141496	−	0.0816929i
$727$	−34.2911	+	5.43117i	−1.27179	+	0.201431i	−0.755593	−	0.655041i	$-0.772651\pi$
$727$	−34.2911	+	5.43117i	−1.27179	+	0.201431i	−0.516193	+	0.856472i	$0.672651\pi$
$728$	7.89386	+	26.3957i	0.292566	+	0.978289i
$729$	9.07738	−	2.94942i	0.336199	−	0.109238i
$730$		0			0
$731$	−10.0339	+	9.03459i	−0.371118	+	0.334156i
$732$	4.55054	−	1.21931i	0.168193	−	0.0450672i
$733$	18.2293	+	11.8382i	0.673314	+	0.437255i	0.835489	−	0.549507i	$-0.185184\pi$
$733$	18.2293	+	11.8382i	0.673314	+	0.437255i	−0.162176	+	0.986762i	$0.551851\pi$
$734$	−42.2421	+	30.6907i	−1.55918	+	1.13281i
$735$		0			0
$736$	2.26303	+	1.64419i	0.0834164	+	0.0606056i
$737$	−11.1148	−	28.9550i	−0.409418	−	1.06657i
$738$	−16.2733	+	20.0958i	−0.599028	+	0.739738i
$739$	13.4960	+	30.3126i	0.496460	+	1.11507i	0.971916	+	0.235328i	$0.0756165\pi$
$739$	13.4960	+	30.3126i	0.496460	+	1.11507i	−0.475456	+	0.879740i	$0.657717\pi$
$740$		0			0
$741$	−12.0406	−	16.5725i	−0.442323	−	0.608805i
$742$	−19.4602	+	55.4137i	−0.714406	+	2.03430i
$743$	28.3572	−	28.3572i	1.04033	−	1.04033i	0.0411733	−	0.999152i	$-0.486890\pi$
$743$	28.3572	−	28.3572i	1.04033	−	1.04033i	0.999152	−	0.0411733i	$-0.0131096\pi$
$744$	−2.63908	−	12.4159i	−0.0967534	−	0.455189i
$745$		0			0
$746$	18.2117	+	3.87101i	0.666776	+	0.141728i
$747$	0.227004	+	4.33149i	0.00830563	+	0.158481i
$748$	−0.878223	−	5.54488i	−0.0321110	−	0.202741i
$749$	−5.32800	+	18.1612i	−0.194681	+	0.663595i
$750$		0			0
$751$	5.40198	+	9.35651i	0.197121	+	0.341424i	0.947594	−	0.319478i	$-0.103507\pi$
$751$	5.40198	+	9.35651i	0.197121	+	0.341424i	−0.750473	+	0.660901i	$0.770174\pi$
$752$	6.48923	−	16.9050i	0.236638	−	0.616463i
$753$	2.39454	−	1.55504i	0.0872620	−	0.0566686i
$754$	19.7376	−	21.9208i	0.718802	−	0.798310i
$755$		0			0
$756$	−0.489781	+	6.43834i	−0.0178131	+	0.234160i
$757$	8.08043	+	8.08043i	0.293688	+	0.293688i	0.838535	−	0.544847i	$-0.183412\pi$
$757$	8.08043	+	8.08043i	0.293688	+	0.293688i	−0.544847	+	0.838535i	$0.683412\pi$
$758$	3.97390	−	6.11927i	0.144338	−	0.222262i
$759$	0.276338	+	2.62918i	0.0100304	+	0.0954333i
$760$		0			0
$761$	−9.22823	−	0.969926i	−0.334523	−	0.0351598i	−0.0642220	−	0.997936i	$-0.520457\pi$
$761$	−9.22823	−	0.969926i	−0.334523	−	0.0351598i	−0.270301	+	0.962776i	$0.587123\pi$
$762$	−4.19794	+	26.5047i	−0.152075	+	0.960166i
$763$	−37.5650	+	3.05524i	−1.35994	+	0.110607i
$764$	−4.14931	+	5.71103i	−0.150117	+	0.206618i
$765$		0			0
$766$	−13.6356	+	1.43316i	−0.492675	+	0.0517822i
$767$	2.30963	−	44.0704i	0.0833960	−	1.59129i
$768$	2.78500	−	10.3938i	0.100495	−	0.375053i
$769$	0.767310	−	2.36154i	0.0276699	−	0.0851592i	−0.936268	−	0.351287i	$-0.885744\pi$
$769$	0.767310	−	2.36154i	0.0276699	−	0.0851592i	0.963938	+	0.266128i	$0.0857442\pi$
$770$		0			0
$771$	1.65106	+	5.08143i	0.0594613	+	0.183003i
$772$	7.93100	−	0.415646i	0.285443	−	0.0149594i
$773$	21.9950	+	8.44309i	0.791105	+	0.303677i	0.720164	−	0.693804i	$-0.244066\pi$
$773$	21.9950	+	8.44309i	0.791105	+	0.303677i	0.0709410	+	0.997481i	$0.477400\pi$
$774$	−10.0842	−	5.82209i	−0.362467	−	0.209271i
$775$		0			0
$776$			19.4010i			0.696456i
$777$	0.262229	−	0.343599i	0.00940740	−	0.0123265i
$778$	17.6161	+	8.97584i	0.631567	+	0.321800i
$779$	−28.3570	−	25.5328i	−1.01600	−	0.914806i
$780$		0			0
$781$	−13.0840	−	14.5312i	−0.468181	−	0.519968i
$782$	−5.93011	−	1.58897i	−0.212060	−	0.0568214i
$783$	−18.0729	+	9.20860i	−0.645872	+	0.329088i
$784$	29.7564	+	14.9663i	1.06273	+	0.534509i
$785$		0			0
$786$	2.29793	−	21.8634i	0.0819645	−	0.779840i
$787$	22.6806	+	18.3664i	0.808478	+	0.654692i	0.941723	−	0.336391i	$-0.109206\pi$
$787$	22.6806	+	18.3664i	0.808478	+	0.654692i	−0.133245	+	0.991083i	$0.542540\pi$
$788$	−3.27661	−	2.65334i	−0.116724	−	0.0945214i
$789$	−0.391976	+	3.72940i	−0.0139547	+	0.132770i
$790$		0			0
$791$	−8.64292	+	47.3229i	−0.307307	+	1.68261i
$792$	−12.6571	+	6.44911i	−0.449750	+	0.229159i
$793$	−42.0922	−	11.2786i	−1.49474	−	0.400513i
$794$	27.5085	+	30.5513i	0.976241	+	1.08423i
$795$		0			0
$796$	2.94760	+	2.65404i	0.104475	+	0.0940698i
$797$	27.4174	+	13.9698i	0.971172	+	0.494837i	0.866232	−	0.499641i	$-0.166535\pi$
$797$	27.4174	+	13.9698i	0.971172	+	0.494837i	0.104940	+	0.994479i	$0.466535\pi$
$798$	−19.3135	−	2.49134i	−0.683692	−	0.0881925i
$799$			14.8256i			0.524493i
$800$		0			0
$801$	−13.5117	−	7.80099i	−0.477413	−	0.275635i
$802$	−7.92408	−	3.04177i	−0.279809	−	0.107409i
$803$	−15.0280	+	0.787585i	−0.530327	+	0.0277933i
$804$	−1.61125	−	4.95893i	−0.0568246	−	0.174888i
$805$		0			0
$806$	12.3659	−	38.0582i	0.435569	−	1.34054i
$807$	1.14282	−	4.26505i	0.0402291	−	0.150137i
$808$	−1.45270	+	27.7192i	−0.0511059	+	0.975160i
$809$	−13.6250	+	1.43205i	−0.479030	+	0.0503480i	−0.340967	−	0.940075i	$-0.610754\pi$
$809$	−13.6250	+	1.43205i	−0.479030	+	0.0503480i	−0.138063	+	0.990423i	$0.544088\pi$
$810$		0			0
$811$	−0.902857	+	1.24268i	−0.0317036	+	0.0436363i	−0.824575	−	0.565753i	$-0.808585\pi$
$811$	−0.902857	+	1.24268i	−0.0317036	+	0.0436363i	0.792871	+	0.609390i	$0.208585\pi$
$812$	−0.460707	−	5.66452i	−0.0161676	−	0.198786i
$813$	−0.322138	+	2.03390i	−0.0112979	+	0.0713319i
$814$	−0.778139	−	0.0817857i	−0.0272738	−	0.00286659i
$815$		0			0
$816$	1.81632	+	17.2811i	0.0635839	+	0.604961i
$817$	9.35839	−	14.4107i	0.327408	−	0.504165i
$818$	7.51625	+	7.51625i	0.262799	+	0.262799i
$819$	13.9594	−	20.4252i	0.487781	−	0.713715i
$820$		0			0
$821$	4.06231	−	4.51165i	0.141775	−	0.157458i	−0.668075	−	0.744094i	$-0.732882\pi$
$821$	4.06231	−	4.51165i	0.141775	−	0.157458i	0.809851	+	0.586636i	$0.199548\pi$
$822$	18.4168	−	11.9600i	0.642359	−	0.417153i
$823$	−6.34598	+	16.5318i	−0.221207	+	0.576264i	−0.998608	−	0.0527412i	$-0.983204\pi$
$823$	−6.34598	+	16.5318i	−0.221207	+	0.576264i	0.777401	+	0.629005i	$0.216537\pi$
$824$	−12.9482	−	22.4269i	−0.451071	−	0.781279i
$825$		0			0
$826$	−28.9577	−	30.3557i	−1.00757	−	1.05621i
$827$	−6.34498	−	40.0606i	−0.220637	−	1.39304i	−0.810593	−	0.585609i	$-0.800855\pi$
$827$	−6.34498	−	40.0606i	−0.220637	−	1.39304i	0.589957	−	0.807435i	$-0.299145\pi$
$828$	−0.0561598	−	1.07159i	−0.00195169	−	0.0372404i
$829$	−29.1828	−	6.20301i	−1.01356	−	0.215439i	−0.328950	−	0.944347i	$-0.606695\pi$
$829$	−29.1828	−	6.20301i	−1.01356	−	0.215439i	−0.684612	+	0.728908i	$0.740028\pi$
$830$		0			0
$831$	1.33374	+	6.27477i	0.0462671	+	0.217669i
$832$	−15.7839	+	15.7839i	−0.547209	+	0.547209i
$833$	−27.1360	−	2.70878i	−0.940208	−	0.0938536i
$834$	0.367847	+	0.506298i	0.0127375	+	0.0175317i
$835$		0			0
$836$	2.90590	+	6.52675i	0.100503	+	0.225733i
$837$	−17.3172	+	21.3849i	−0.598569	+	0.739171i
$838$	20.6024	+	53.6711i	0.711699	+	1.85404i
$839$	11.0058	+	7.99616i	0.379961	+	0.276058i	0.761330	−	0.648365i	$-0.224547\pi$
$839$	11.0058	+	7.99616i	0.379961	+	0.276058i	−0.381368	+	0.924423i	$0.624547\pi$
$840$		0			0
$841$	−9.01801	+	6.55197i	−0.310966	+	0.225930i
$842$	43.3216	+	28.1334i	1.49296	+	0.969540i
$843$	2.27306	−	0.609065i	0.0782884	−	0.0209773i
$844$	−10.6127	+	9.55575i	−0.365305	+	0.328923i
$845$		0			0
$846$	−12.1599	+	3.95100i	−0.418067	+	0.135838i
$847$	−5.38573	+	5.70516i	−0.185056	+	0.196032i
$848$	−65.8715	+	10.4330i	−2.26204	+	0.358271i
$849$	−6.06880	+	3.50382i	−0.208281	+	0.120251i
$850$		0			0
$851$	−0.0867071	+	0.150181i	−0.00297228	+	0.00514814i
$852$	−2.06876	−	2.55471i	−0.0708746	−	0.0875228i
$853$	−13.5441	+	26.5819i	−0.463743	+	0.910146i	0.534158	+	0.845384i	$0.320629\pi$
$853$	−13.5441	+	26.5819i	−0.463743	+	0.910146i	−0.997901	+	0.0647614i	$0.979371\pi$
$854$	−35.2648	+	21.7373i	−1.20674	+	0.743834i
$855$		0			0
$856$	−16.5304	+	3.51364i	−0.564997	+	0.120094i
$857$	4.02791	+	15.0324i	0.137591	+	0.513496i	0.999974	+	0.00723941i	$0.00230440\pi$
$857$	4.02791	+	15.0324i	0.137591	+	0.513496i	−0.862383	+	0.506256i	$0.831029\pi$
$858$	18.5232	+	0.970762i	0.632373	+	0.0331413i
$859$	5.86300	+	2.61038i	0.200043	+	0.0890649i	0.504313	−	0.863521i	$-0.331746\pi$
$859$	5.86300	+	2.61038i	0.200043	+	0.0890649i	−0.304270	+	0.952586i	$0.598412\pi$
$860$		0			0
$861$	−7.25826	+	17.6534i	−0.247361	+	0.601625i
$862$	39.5550	+	6.26489i	1.34725	+	0.213383i
$863$	−5.40342	+	2.07418i	−0.183935	+	0.0706059i	−0.448592	−	0.893737i	$-0.648074\pi$
$863$	−5.40342	+	2.07418i	−0.183935	+	0.0706059i	0.264658	+	0.964342i	$0.414741\pi$
$864$	−12.3291	+	5.48928i	−0.419445	+	0.186749i
$865$		0			0
$866$	−12.3902	+	27.8289i	−0.421037	+	0.945665i
$867$	0.775519	+	1.52204i	0.0263380	+	0.0516913i
$868$	−3.69658	−	6.76602i	−0.125470	−	0.229654i
$869$	−11.5533	−	3.75389i	−0.391918	−	0.127342i
$870$		0			0
$871$	−10.0276	+	47.1763i	−0.339773	+	1.59851i
$872$	−18.3286	−	28.2236i	−0.620685	−	0.955771i
$873$	13.5391	−	10.9637i	0.458227	−	0.371065i
$874$	7.81292			0.264276
$875$		0			0
$876$	−2.52992			−0.0854782
$877$	−0.229111	+	0.185530i	−0.00773652	+	0.00626491i	−0.633181	−	0.774004i	$-0.718251\pi$
$877$	−0.229111	+	0.185530i	−0.00773652	+	0.00626491i	0.625444	+	0.780269i	$0.284918\pi$
$878$	5.42892	+	8.35981i	0.183217	+	0.282130i
$879$	−2.69102	+	12.6602i	−0.0907658	+	0.427020i
$880$		0			0
$881$	12.4276	+	4.03797i	0.418696	+	0.136043i	0.510786	−	0.859708i	$-0.329355\pi$
$881$	12.4276	+	4.03797i	0.418696	+	0.136043i	−0.0920894	+	0.995751i	$0.529355\pi$
$882$	−5.00997	−	22.9787i	−0.168694	−	0.773735i
$883$	−2.90787	−	5.70702i	−0.0978577	−	0.192057i	0.836888	−	0.547374i	$-0.184373\pi$
$883$	−2.90787	−	5.70702i	−0.0978577	−	0.192057i	−0.934746	+	0.355318i	$0.884373\pi$
$884$	−3.55086	+	7.97536i	−0.119428	+	0.268240i
$885$		0			0
$886$	35.4720	−	15.7932i	1.19171	−	0.530582i
$887$	−41.8723	+	16.0733i	−1.40594	+	0.539688i	−0.938789	−	0.344492i	$-0.888051\pi$
$887$	−41.8723	+	16.0733i	−1.40594	+	0.539688i	−0.467146	+	0.884180i	$0.654718\pi$
$888$	0.381191	+	0.0603747i	0.0127919	+	0.00202604i
$889$	−6.36628	−	47.3991i	−0.213518	−	1.58971i
$890$		0			0
$891$	4.82758	+	2.14938i	0.161730	+	0.0720068i
$892$	−6.38561	−	0.334656i	−0.213806	−	0.0112051i
$893$	−4.88319	−	18.2243i	−0.163410	−	0.609854i
$894$	−9.53957	+	2.02770i	−0.319051	+	0.0678164i
$895$		0			0
$896$	1.03919	+	36.0812i	0.0347170	+	1.20539i
$897$	1.86638	−	3.66299i	0.0623168	−	0.122304i
$898$	−28.9947	−	35.8055i	−0.967567	−	1.19485i
$899$	12.1100	−	20.9751i	0.403889	−	0.699557i
$900$		0			0
$901$	47.2887	−	27.3021i	1.57541	−	0.909566i
$902$	34.1263	−	5.40508i	1.13628	−	0.179970i
$903$	−8.36279	−	1.98463i	−0.278296	−	0.0660442i
$904$	−40.8516	+	13.2735i	−1.35870	+	0.441470i
$905$		0			0
$906$	−6.29955	+	5.67214i	−0.209289	+	0.188444i
$907$	−3.72103	+	0.997046i	−0.123555	+	0.0331064i	−0.320067	−	0.947395i	$-0.603705\pi$
$907$	−3.72103	+	0.997046i	−0.123555	+	0.0331064i	0.196512	+	0.980501i	$0.437039\pi$
$908$	4.64764	+	3.01821i	0.154237	+	0.100163i
$909$	20.1649	−	14.6506i	0.668827	−	0.485931i
$910$		0			0
$911$	27.1055	+	19.6933i	0.898046	+	0.652469i	0.937963	−	0.346734i	$-0.112709\pi$
$911$	27.1055	+	19.6933i	0.898046	+	0.652469i	−0.0399171	+	0.999203i	$0.512709\pi$
$912$	−7.92468	−	20.6445i	−0.262412	−	0.683607i
$913$	3.64729	−	4.50403i	0.120708	−	0.149062i
$914$	−19.2978	−	43.3437i	−0.638316	−	1.43368i
$915$		0			0
$916$	0.828785	+	1.14072i	0.0273838	+	0.0376906i
$917$	7.24043	+	38.5040i	0.239100	+	1.27151i
$918$	20.9446	−	20.9446i	0.691276	−	0.691276i
$919$	−1.57605	−	7.41472i	−0.0519890	−	0.244589i	0.944478	−	0.328575i	$-0.106568\pi$
$919$	−1.57605	−	7.41472i	−0.0519890	−	0.244589i	−0.996467	+	0.0839857i	$0.973235\pi$
$920$		0			0
$921$	−1.83862	−	0.390810i	−0.0605845	−	0.0128776i
$922$	−1.11792	−	21.3312i	−0.0368168	−	0.702507i
$923$	4.75673	+	30.0328i	0.156570	+	0.988543i
$924$	2.58586	−	2.46677i	0.0850687	−	0.0811508i
$925$		0			0
$926$	−0.657950	−	1.13960i	−0.0216216	−	0.0374497i
$927$	−8.33353	+	21.7096i	−0.273709	+	0.713037i
$928$	9.96233	−	6.46961i	0.327029	−	0.212375i
$929$	−29.5065	+	32.7703i	−0.968077	+	1.07516i	0.0290625	+	0.999578i	$0.490748\pi$
$929$	−29.5065	+	32.7703i	−0.968077	+	1.07516i	−0.997140	+	0.0755811i	$0.975919\pi$
$930$		0			0
$931$	34.2490	−	5.60819i	1.12247	−	0.183801i
$932$	10.1848	+	10.1848i	0.333614	+	0.333614i
$933$	−5.12027	+	7.88452i	−0.167630	+	0.258128i
$934$	−4.72352	−	44.9413i	−0.154558	−	1.47053i
$935$		0			0
$936$	21.9692	+	2.30906i	0.718087	+	0.0754740i
$937$	−0.491029	+	3.10024i	−0.0160412	+	0.101280i	−0.994410	−	0.105589i	$-0.966327\pi$
$937$	−0.491029	+	3.10024i	−0.0160412	+	0.101280i	0.978369	+	0.206869i	$0.0663273\pi$
$938$	26.0682	+	37.7178i	0.851155	+	1.23153i
$939$	−9.97623	+	13.7311i	−0.325562	+	0.448098i
$940$		0			0
$941$	−39.0114	+	4.10027i	−1.27174	+	0.133665i	−0.716240	−	0.697854i	$-0.754138\pi$
$941$	−39.0114	+	4.10027i	−1.27174	+	0.133665i	−0.555496	+	0.831519i	$0.687472\pi$
$942$	0.670901	−	12.8016i	0.0218592	−	0.417097i
$943$	1.98202	−	7.39700i	0.0645434	−	0.240879i
$944$	14.7213	−	45.3077i	0.479139	−	1.47464i
$945$		0			0
$946$	4.80792	+	14.7973i	0.156319	+	0.481100i
$947$	−24.1283	+	1.26451i	−0.784063	+	0.0410910i	−0.440166	−	0.897916i	$-0.645080\pi$
$947$	−24.1283	+	1.26451i	−0.784063	+	0.0410910i	−0.343897	+	0.939007i	$0.611747\pi$
$948$	−1.90660	−	0.731877i	−0.0619236	−	0.0237703i
$949$	20.2664	+	11.7008i	0.657874	+	0.379824i
$950$		0			0
$951$		−	13.7063i		−	0.444458i
$952$	−9.37725	−	22.4724i	−0.303918	−	0.728334i
$953$	14.2501	+	7.26077i	0.461605	+	0.235199i	0.669297	−	0.742995i	$-0.266595\pi$
$953$	14.2501	+	7.26077i	0.461605	+	0.235199i	−0.207692	+	0.978194i	$0.566595\pi$
$954$	34.9954	+	31.5100i	1.13302	+	1.02017i
$955$		0			0
$956$	−4.28262	−	4.75633i	−0.138510	−	0.153831i
$957$	10.8439	+	2.90562i	0.350535	+	0.0939254i
$958$	−41.3914	+	21.0900i	−1.33730	+	0.681387i
$959$	−25.3386	+	29.8252i	−0.818227	+	0.963107i
$960$		0			0
$961$	0.194131	−	1.84703i	0.00626228	−	0.0595816i
$962$	0.945569	+	0.765707i	0.0304864	+	0.0246874i
$963$	11.7935	+	9.55018i	0.380040	+	0.307750i
$964$	0.372197	−	3.54122i	0.0119877	−	0.114055i
$965$		0			0
$966$	−1.31419	−	3.68055i	−0.0422833	−	0.118420i
$967$	−19.6328	+	10.0034i	−0.631349	+	0.321688i	−0.740217	−	0.672368i	$-0.765277\pi$
$967$	−19.6328	+	10.0034i	−0.631349	+	0.321688i	0.108868	+	0.994056i	$0.465277\pi$
$968$	−6.76676	−	1.81315i	−0.217492	−	0.0582768i
$969$	12.1147	+	13.4547i	0.389180	+	0.432228i
$970$		0			0
$971$	20.2341	+	18.2189i	0.649343	+	0.584671i	0.926565	−	0.376135i	$-0.122747\pi$
$971$	20.2341	+	18.2189i	0.649343	+	0.584671i	−0.277222	+	0.960806i	$0.589414\pi$
$972$	7.31506	+	3.72721i	0.234631	+	0.119550i
$973$	−0.886611	−	0.676646i	−0.0284234	−	0.0216923i
$974$			5.54132i			0.177555i
$975$		0			0
$976$	−40.7390	−	23.5207i	−1.30402	−	0.752879i
$977$	−11.1583	−	4.28328i	−0.356986	−	0.137034i	0.173264	−	0.984875i	$-0.444569\pi$
$977$	−11.1583	−	4.28328i	−0.356986	−	0.137034i	−0.530250	+	0.847841i	$0.677902\pi$
$978$	−16.9770	+	0.889726i	−0.542864	+	0.0284503i
$979$	6.44212	+	19.8268i	0.205891	+	0.633667i
$980$		0			0
$981$	−9.33822	+	28.7401i	−0.298146	+	0.917600i
$982$	16.1115	−	60.1289i	0.514138	−	1.91879i
$983$	1.56076	−	29.7810i	0.0497804	−	0.949866i	−0.853574	−	0.520971i	$-0.825570\pi$
$983$	1.56076	−	29.7810i	0.0497804	−	0.949866i	0.903355	−	0.428895i	$-0.141097\pi$
$984$	−16.9498	+	1.78149i	−0.540339	+	0.0567919i
$985$		0			0
$986$	−15.3241	+	21.0918i	−0.488018	+	0.671699i
$987$	−7.76382	+	5.36586i	−0.247125	+	0.170797i
$988$	1.73799	−	10.9732i	0.0552928	−	0.349105i
$989$	3.42950	+	0.360455i	0.109052	+	0.0114618i
$990$		0			0
$991$	2.20511	+	20.9803i	0.0700477	+	0.666460i	0.972057	+	0.234744i	$0.0754251\pi$
$991$	2.20511	+	20.9803i	0.0700477	+	0.666460i	−0.902010	+	0.431716i	$0.857908\pi$
$992$	8.77680	−	13.5151i	0.278664	−	0.429105i
$993$	−21.1572	−	21.1572i	−0.671402	−	0.671402i
$994$	23.8651	+	16.3104i	0.756956	+	0.517334i
$995$		0			0
$996$	0.651958	−	0.724073i	0.0206581	−	0.0229431i
$997$	−37.7869	+	24.5391i	−1.19672	+	0.777162i	−0.979986	−	0.199068i	$-0.936209\pi$
$997$	−37.7869	+	24.5391i	−1.19672	+	0.777162i	−0.216739	+	0.976230i	$0.569542\pi$
$998$	17.0346	−	44.3768i	0.539222	−	1.40472i
$999$	−0.418334	−	0.724576i	−0.0132355	−	0.0229246i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.a.332.14		288
5.2	odd	4		175.2.x.a.38.14	✓	288
5.3	odd	4		875.2.bb.c.668.5		288
5.4	even	2		875.2.bb.b.332.5		288
7.5	odd	6	inner	875.2.bb.a.82.5		288
25.2	odd	20		875.2.bb.b.843.14		288
25.11	even	5		875.2.bb.c.157.5		288
25.14	even	10		175.2.x.a.52.14	yes	288
25.23	odd	20	inner	875.2.bb.a.843.5		288
35.12	even	12		175.2.x.a.138.14	yes	288
35.19	odd	6		875.2.bb.b.82.14		288
35.33	even	12		875.2.bb.c.418.5		288
175.61	odd	30		875.2.bb.c.782.5		288
175.89	odd	30		175.2.x.a.152.14	yes	288
175.152	even	60		875.2.bb.b.593.5		288
175.173	even	60	inner	875.2.bb.a.593.14		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.38.14	✓	288	5.2	odd	4
175.2.x.a.52.14	yes	288	25.14	even	10
175.2.x.a.138.14	yes	288	35.12	even	12
175.2.x.a.152.14	yes	288	175.89	odd	30
875.2.bb.a.82.5		288	7.5	odd	6	inner
875.2.bb.a.332.14		288	1.1	even	1	trivial
875.2.bb.a.593.14		288	175.173	even	60	inner
875.2.bb.a.843.5		288	25.23	odd	20	inner
875.2.bb.b.82.14		288	35.19	odd	6
875.2.bb.b.332.5		288	5.4	even	2
875.2.bb.b.593.5		288	175.152	even	60
875.2.bb.b.843.14		288	25.2	odd	20
875.2.bb.c.157.5		288	25.11	even	5
875.2.bb.c.418.5		288	35.33	even	12
875.2.bb.c.668.5		288	5.3	odd	4
875.2.bb.c.782.5		288	175.61	odd	30

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+(1.23083 - 0.996709i) q^{2} +(-0.510519 - 0.786131i) q^{3} +(0.105698 - 0.497271i) q^{4} +(-1.41191 - 0.458757i) q^{6} +(2.64502 + 0.0623449i) q^{7} +(1.07251 + 2.10492i) q^{8} +(0.862838 - 1.93797i) q^{9} +(-2.58948 + 1.15291i) q^{11} +(-0.444881 + 0.170774i) q^{12} +(4.35361 + 0.689545i) q^{13} +(3.31771 - 2.55958i) q^{14} +(4.34693 + 1.93538i) q^{16} +(-3.89051 - 0.203893i) q^{17} +(-0.869579 - 3.24531i) q^{18} +(4.84954 - 1.03080i) q^{19} +(-1.30132 - 2.11116i) q^{21} +(-2.03810 + 4.00000i) q^{22} +(0.626170 + 0.773256i) q^{23} +(1.10721 - 1.91774i) q^{24} +(6.04585 - 3.49057i) q^{26} +(-4.74143 + 0.750969i) q^{27} +(0.310576 - 1.30870i) q^{28} +(4.01849 - 1.30569i) q^{29} +(4.25980 - 3.83554i) q^{31} +(2.71554 - 0.727626i) q^{32} +(2.22832 + 1.44709i) q^{33} +(-4.99179 + 3.62674i) q^{34} +(-0.872494 - 0.633904i) q^{36} +(0.0624587 + 0.162710i) q^{37} +(4.94157 - 6.10233i) q^{38} +(-1.68053 - 3.77454i) q^{39} +(-4.52386 - 6.22657i) q^{41} +(-3.70592 - 1.30144i) q^{42} +(2.45065 - 2.45065i) q^{43} +(0.299606 + 1.40953i) q^{44} +(1.54142 + 0.327640i) q^{46} +(-0.199164 - 3.80028i) q^{47} +(-0.697732 - 4.40531i) q^{48} +(6.99223 + 0.329807i) q^{49} +(1.82589 + 3.16254i) q^{51} +(0.803060 - 2.09204i) q^{52} +(-11.7548 + 7.63368i) q^{53} +(-5.08741 + 5.65015i) q^{54} +(2.70558 + 5.63442i) q^{56} +(-3.28613 - 3.28613i) q^{57} +(3.64471 - 5.61236i) q^{58} +(-1.04652 - 9.95696i) q^{59} +(-9.83200 - 1.03338i) q^{61} +(1.42018 - 8.96669i) q^{62} +(2.40304 - 5.07216i) q^{63} +(-2.97658 + 4.09692i) q^{64} +(4.18501 - 0.439863i) q^{66} +(-0.572651 + 10.9268i) q^{67} +(-0.512609 + 1.91308i) q^{68} +(0.288208 - 0.887014i) q^{69} +(2.13171 + 6.56074i) q^{71} +(5.00467 - 0.262283i) q^{72} +(4.95641 + 1.90259i) q^{73} +(0.239051 + 0.138016i) q^{74} -2.52049i q^{76} +(-6.92109 + 2.88803i) q^{77} +(-5.83057 - 2.97082i) q^{78} +(3.18486 + 2.86766i) q^{79} +(-1.24746 - 1.38545i) q^{81} +(-11.7742 - 3.15489i) q^{82} +(-1.82179 + 0.928247i) q^{83} +(-1.18736 + 0.423964i) q^{84} +(0.573756 - 5.45892i) q^{86} +(-3.07796 - 2.49248i) q^{87} +(-5.20403 - 4.21414i) q^{88} +(0.768774 - 7.31439i) q^{89} +(11.4724 + 2.09528i) q^{91} +(0.450703 - 0.229645i) q^{92} +(-5.18994 - 1.39064i) q^{93} +(-4.03292 - 4.47901i) q^{94} +(-1.95835 - 1.76330i) q^{96} +(7.31730 + 3.72835i) q^{97} +(8.93499 - 6.56328i) q^{98} +6.01310i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 2 q^{2} - 6 q^{3} + 10 q^{4} + 10 q^{7} - 64 q^{8} + 10 q^{9} - 6 q^{11} + 6 q^{12} + 20 q^{14} - 30 q^{16} + 12 q^{17} + 14 q^{18} + 30 q^{19} - 12 q^{21} + 8 q^{22} - 30 q^{23} - 48 q^{26} + 58 q^{28}+ \cdots - 62 q^{98}+O(q^{100}) \) 288 * q - 2 * q^2 - 6 * q^3 + 10 * q^4 + 10 * q^7 - 64 * q^8 + 10 * q^9 - 6 * q^11 + 6 * q^12 + 20 * q^14 - 30 * q^16 + 12 * q^17 + 14 * q^18 + 30 * q^19 - 12 * q^21 + 8 * q^22 - 30 * q^23 - 48 * q^26 + 58 * q^28 - 18 * q^31 - 8 * q^32 + 150 * q^33 + 40 * q^36 - 12 * q^38 - 30 * q^39 - 166 * q^42 + 108 * q^43 + 10 * q^44 - 6 * q^46 + 24 * q^47 - 16 * q^51 + 24 * q^52 + 40 * q^53 + 30 * q^54 + 4 * q^56 + 216 * q^57 + 114 * q^58 - 90 * q^59 - 18 * q^61 + 16 * q^63 + 100 * q^64 - 90 * q^66 - 74 * q^67 - 342 * q^68 - 24 * q^71 + 222 * q^72 + 216 * q^73 - 90 * q^77 + 32 * q^78 + 10 * q^79 - 10 * q^81 - 216 * q^82 - 20 * q^84 - 6 * q^86 + 18 * q^87 - 58 * q^88 - 120 * q^89 - 12 * q^91 + 24 * q^92 - 106 * q^93 + 30 * q^94 - 90 * q^96 - 62 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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