LMFDB - Embedded newform 363.2.f.i.215.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [363,2,Mod(161,363)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(363, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("363.161");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 363 = 3 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	363.f (of order $10$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.89856959337$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			215.7
Character	$\chi$	$=$	363.215
Dual form			363.2.f.i.233.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.739839 + 2.27699i) q^{2} +(-1.29120 + 1.15447i) q^{3} +(-3.01929 + 2.19364i) q^{4} +(-1.17866 - 0.382969i) q^{5} +(-3.58400 - 2.08594i) q^{6} +(-1.66251 - 2.28825i) q^{7} +(-3.35485 - 2.43744i) q^{8} +(0.334407 - 2.98130i) q^{9} +O(q^{10})$	\(q+(0.739839 + 2.27699i) q^{2} +(-1.29120 + 1.15447i) q^{3} +(-3.01929 + 2.19364i) q^{4} +(-1.17866 - 0.382969i) q^{5} +(-3.58400 - 2.08594i) q^{6} +(-1.66251 - 2.28825i) q^{7} +(-3.35485 - 2.43744i) q^{8} +(0.334407 - 2.98130i) q^{9} -2.96713i q^{10} +(1.36603 - 6.31812i) q^{12} +(-3.18230 + 1.03399i) q^{13} +(3.98033 - 5.47845i) q^{14} +(1.96401 - 0.866232i) q^{15} +(0.761449 - 2.34350i) q^{16} +(-1.28144 + 3.94386i) q^{17} +(7.03581 - 1.44424i) q^{18} +(-1.43977 + 1.98168i) q^{19} +(4.39881 - 1.42926i) q^{20} +(4.78834 + 1.03528i) q^{21} +(7.14574 - 0.725837i) q^{24} +(-2.80252 - 2.03615i) q^{25} +(-4.70878 - 6.48108i) q^{26} +(3.01003 + 4.23553i) q^{27} +(10.0392 + 3.26193i) q^{28} +(-4.39285 + 3.19159i) q^{29} +(3.42545 + 3.83116i) q^{30} +(0.0606144 + 0.186552i) q^{31} -2.39417 q^{32} -9.92820 q^{34} +(1.08320 + 3.33375i) q^{35} +(5.53025 + 9.73500i) q^{36} +(8.46564 - 6.15064i) q^{37} +(-5.57747 - 1.81223i) q^{38} +(2.91528 - 5.00895i) q^{39} +(3.02076 + 4.15771i) q^{40} +(-5.81077 - 4.22177i) q^{41} +(1.18529 + 11.6689i) q^{42} +4.24264i q^{43} +(-1.53590 + 3.38587i) q^{45} +(-1.99016 + 2.73922i) q^{47} +(1.72231 + 3.90500i) q^{48} +(-0.309017 + 0.951057i) q^{49} +(2.56288 - 7.88773i) q^{50} +(-2.89847 - 6.57171i) q^{51} +(7.34008 - 10.1027i) q^{52} +(-6.75612 + 2.19520i) q^{53} +(-7.41732 + 9.98743i) q^{54} +11.7290i q^{56} +(-0.428745 - 4.22092i) q^{57} +(-10.5172 - 7.64121i) q^{58} +(7.42739 + 10.2229i) q^{59} +(-4.02972 + 6.92375i) q^{60} +(-4.29882 - 1.39677i) q^{61} +(-0.379932 + 0.276037i) q^{62} +(-7.37791 + 4.19123i) q^{63} +(-3.29420 - 10.1385i) q^{64} +4.14682 q^{65} +2.00000 q^{67} +(-4.78240 - 14.7187i) q^{68} +(-6.78952 + 4.93287i) q^{70} +(7.93478 + 2.57817i) q^{71} +(-8.38864 + 9.18673i) q^{72} +(4.76479 + 6.55817i) q^{73} +(20.2682 + 14.7257i) q^{74} +(5.96928 - 0.606337i) q^{75} -9.14162i q^{76} +(13.5622 + 2.93225i) q^{78} +(-6.98881 + 2.27080i) q^{79} +(-1.79498 + 2.47057i) q^{80} +(-8.77634 - 1.99394i) q^{81} +(5.31390 - 16.3545i) q^{82} +(-4.58416 + 14.1086i) q^{83} +(-16.7284 + 7.37811i) q^{84} +(3.02076 - 4.15771i) q^{85} +(-9.66046 + 3.13887i) q^{86} +(1.98747 - 9.19239i) q^{87} -9.58244i q^{89} +(-8.84591 - 0.992229i) q^{90} +(7.65662 + 5.56286i) q^{91} +(-0.293634 - 0.170899i) q^{93} +(-7.70959 - 2.50500i) q^{94} +(2.45592 - 1.78433i) q^{95} +(3.09136 - 2.76399i) q^{96} +(0.700835 + 2.15695i) q^{97} -2.39417 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 4 q^{3} - 16 q^{4} + 8 q^{9}+O(q^{10}) $ 32 * q + 4 * q^3 - 16 * q^4 + 8 * q^9	$ 32 q + 4 q^{3} - 16 q^{4} + 8 q^{9} + 16 q^{12} - 4 q^{15} + 8 q^{16} + 4 q^{27} + 40 q^{31} - 96 q^{34} + 40 q^{36} + 56 q^{37} - 64 q^{42} - 160 q^{45} - 28 q^{48} + 8 q^{49} - 104 q^{58} + 28 q^{60} + 16 q^{64} + 64 q^{67} + 16 q^{70} - 24 q^{75} + 240 q^{78} + 8 q^{81} - 96 q^{82} + 48 q^{91} - 56 q^{93} - 32 q^{97}+O(q^{100}) $ 32 * q + 4 * q^3 - 16 * q^4 + 8 * q^9 + 16 * q^12 - 4 * q^15 + 8 * q^16 + 4 * q^27 + 40 * q^31 - 96 * q^34 + 40 * q^36 + 56 * q^37 - 64 * q^42 - 160 * q^45 - 28 * q^48 + 8 * q^49 - 104 * q^58 + 28 * q^60 + 16 * q^64 + 64 * q^67 + 16 * q^70 - 24 * q^75 + 240 * q^78 + 8 * q^81 - 96 * q^82 + 48 * q^91 - 56 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/363\mathbb{Z}\right)^\times$.

$n$	$122$	$244$
$\chi(n)$	$-1$	$e\left(\frac{9}{10}\right)$

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 $

$2$	0.739839	+	2.27699i	0.523145	+	1.61008i	0.767954	+	0.640505i	$0.221275\pi$
$2$	0.739839	+	2.27699i	0.523145	+	1.61008i	−0.244809	+	0.969571i	$0.578725\pi$
$3$	−1.29120	+	1.15447i	−0.745476	+	0.666532i
$3$	−1.29120	+	1.15447i	−0.745476	+	0.666532i
$4$	−3.01929	+	2.19364i	−1.50965	+	1.09682i
$5$	−1.17866	−	0.382969i	−0.527112	−	0.171269i	0.0333587	−	0.999443i	$-0.489380\pi$
$5$	−1.17866	−	0.382969i	−0.527112	−	0.171269i	−0.560470	+	0.828175i	$0.689380\pi$
$6$	−3.58400	−	2.08594i	−1.46316	−	0.851580i
$7$	−1.66251	−	2.28825i	−0.628369	−	0.864876i	0.369560	−	0.929207i	$-0.379509\pi$
$7$	−1.66251	−	2.28825i	−0.628369	−	0.864876i	−0.997929	+	0.0643314i	$0.979509\pi$
$8$	−3.35485	−	2.43744i	−1.18612	−	0.861766i
$9$	0.334407	−	2.98130i	0.111469	−	0.993768i
$10$		−	2.96713i		−	0.938288i
$11$		0			0
$11$		0			0
$12$	1.36603	−	6.31812i	0.394338	−	1.82388i
$13$	−3.18230	+	1.03399i	−0.882610	+	0.286778i	−0.715041	−	0.699083i	$-0.753592\pi$
$13$	−3.18230	+	1.03399i	−0.882610	+	0.286778i	−0.167570	+	0.985860i	$0.553592\pi$
$14$	3.98033	−	5.47845i	1.06379	−	1.46418i
$15$	1.96401	−	0.866232i	0.507105	−	0.223660i
$16$	0.761449	−	2.34350i	0.190362	−	0.585875i
$17$	−1.28144	+	3.94386i	−0.310795	+	0.956528i	0.666656	+	0.745365i	$0.267725\pi$
$17$	−1.28144	+	3.94386i	−0.310795	+	0.956528i	−0.977451	+	0.211162i	$0.932275\pi$
$18$	7.03581	−	1.44424i	1.65836	−	0.340411i
$19$	−1.43977	+	1.98168i	−0.330307	+	0.454628i	−0.941579	−	0.336792i	$-0.890658\pi$
$19$	−1.43977	+	1.98168i	−0.330307	+	0.454628i	0.611272	+	0.791420i	$0.290658\pi$
$20$	4.39881	−	1.42926i	0.983604	−	0.319592i
$21$	4.78834	+	1.03528i	1.04490	+	0.225916i
$22$		0			0
$23$		0			0		1.00000			$0$
$23$		0			0		−1.00000			$\pi$
$24$	7.14574	−	0.725837i	1.45862	−	0.148161i
$25$	−2.80252	−	2.03615i	−0.560503	−	0.407230i
$26$	−4.70878	−	6.48108i	−0.923467	−	1.27104i
$27$	3.01003	+	4.23553i	0.579281	+	0.815128i
$28$	10.0392	+	3.26193i	1.89723	+	0.616447i
$29$	−4.39285	+	3.19159i	−0.815731	+	0.592663i	−0.915486	−	0.402349i	$-0.868194\pi$
$29$	−4.39285	+	3.19159i	−0.815731	+	0.592663i	0.0997555	+	0.995012i	$0.468194\pi$
$30$	3.42545	+	3.83116i	0.625400	+	0.699471i
$31$	0.0606144	+	0.186552i	0.0108867	+	0.0335057i	0.956352	−	0.292216i	$-0.0943927\pi$
$31$	0.0606144	+	0.186552i	0.0108867	+	0.0335057i	−0.945466	+	0.325722i	$0.894393\pi$
$32$	−2.39417			−0.423233
$33$		0			0
$34$	−9.92820			−1.70267
$35$	1.08320	+	3.33375i	0.183094	+	0.563506i
$36$	5.53025	+	9.73500i	0.921708	+	1.62250i
$37$	8.46564	−	6.15064i	1.39174	−	1.01116i	0.396070	−	0.918220i	$-0.370374\pi$
$37$	8.46564	−	6.15064i	1.39174	−	1.01116i	0.995672	−	0.0929395i	$-0.0296263\pi$
$38$	−5.57747	−	1.81223i	−0.904785	−	0.293982i
$39$	2.91528	−	5.00895i	0.466818	−	0.802074i
$40$	3.02076	+	4.15771i	0.477623	+	0.657392i
$41$	−5.81077	−	4.22177i	−0.907490	−	0.659330i	0.0328886	−	0.999459i	$-0.489529\pi$
$41$	−5.81077	−	4.22177i	−0.907490	−	0.659330i	−0.940379	+	0.340129i	$0.889529\pi$
$42$	1.18529	+	11.6689i	0.182894	+	1.80056i
$43$			4.24264i			0.646997i	0.946229	+	0.323498i	$0.104859\pi$
$43$			4.24264i			0.646997i	−0.946229	+	0.323498i	$0.895141\pi$
$44$		0			0
$45$	−1.53590	+	3.38587i	−0.228958	+	0.504735i
$46$		0			0
$47$	−1.99016	+	2.73922i	−0.290295	+	0.399557i	−0.929110	−	0.369804i	$-0.879425\pi$
$47$	−1.99016	+	2.73922i	−0.290295	+	0.399557i	0.638815	+	0.769361i	$0.279425\pi$
$48$	1.72231	+	3.90500i	0.248594	+	0.563638i
$49$	−0.309017	+	0.951057i	−0.0441453	+	0.135865i
$50$	2.56288	−	7.88773i	0.362446	−	1.11549i
$51$	−2.89847	−	6.57171i	−0.405867	−	0.920223i
$52$	7.34008	−	10.1027i	1.01789	−	1.40100i
$53$	−6.75612	+	2.19520i	−0.928025	+	0.301534i	−0.733755	−	0.679414i	$-0.762234\pi$
$53$	−6.75612	+	2.19520i	−0.928025	+	0.301534i	−0.194270	+	0.980948i	$0.562234\pi$
$54$	−7.41732	+	9.98743i	−1.00937	+	1.35912i
$55$		0			0
$56$			11.7290i			1.56735i
$57$	−0.428745	−	4.22092i	−0.0567887	−	0.559075i
$58$	−10.5172	−	7.64121i	−1.38098	−	1.00334i
$59$	7.42739	+	10.2229i	0.966964	+	1.33091i	0.943566	+	0.331185i	$0.107449\pi$
$59$	7.42739	+	10.2229i	0.966964	+	1.33091i	0.0233981	+	0.999726i	$0.492551\pi$
$60$	−4.02972	+	6.92375i	−0.520234	+	0.893852i
$61$	−4.29882	−	1.39677i	−0.550407	−	0.178838i	0.0205933	−	0.999788i	$-0.493444\pi$
$61$	−4.29882	−	1.39677i	−0.550407	−	0.178838i	−0.571000	+	0.820950i	$0.693444\pi$
$62$	−0.379932	+	0.276037i	−0.0482515	+	0.0350567i
$63$	−7.37791	+	4.19123i	−0.929529	+	0.528046i
$64$	−3.29420	−	10.1385i	−0.411775	−	1.26731i
$65$	4.14682			0.514350
$66$		0			0
$67$	2.00000			0.244339			0.122169	−	0.992509i	$-0.461015\pi$
$67$	2.00000			0.244339			0.122169	+	0.992509i	$0.461015\pi$
$68$	−4.78240	−	14.7187i	−0.579951	−	1.78490i
$69$		0			0
$70$	−6.78952	+	4.93287i	−0.811503	+	0.589591i
$71$	7.93478	+	2.57817i	0.941685	+	0.305972i	0.739332	−	0.673341i	$-0.235141\pi$
$71$	7.93478	+	2.57817i	0.941685	+	0.305972i	0.202353	+	0.979313i	$0.435141\pi$
$72$	−8.38864	+	9.18673i	−0.988611	+	1.08267i
$73$	4.76479	+	6.55817i	0.557676	+	0.767576i	0.991029	−	0.133649i	$-0.0426694\pi$
$73$	4.76479	+	6.55817i	0.557676	+	0.767576i	−0.433352	+	0.901225i	$0.642669\pi$
$74$	20.2682	+	14.7257i	2.35613	+	1.71183i
$75$	5.96928	−	0.606337i	0.689274	−	0.0700138i
$76$		−	9.14162i		−	1.04862i
$77$		0			0
$78$	13.5622	+	2.93225i	1.53561	+	0.332012i
$79$	−6.98881	+	2.27080i	−0.786303	+	0.255485i	−0.674529	−	0.738249i	$-0.735653\pi$
$79$	−6.98881	+	2.27080i	−0.786303	+	0.255485i	−0.111774	+	0.993734i	$0.535653\pi$
$80$	−1.79498	+	2.47057i	−0.200684	+	0.276218i
$81$	−8.77634	−	1.99394i	−0.975149	−	0.221549i
$82$	5.31390	−	16.3545i	0.586822	−	1.80605i
$83$	−4.58416	+	14.1086i	−0.503177	+	1.54862i	0.300638	+	0.953738i	$0.402800\pi$
$83$	−4.58416	+	14.1086i	−0.503177	+	1.54862i	−0.803815	+	0.594880i	$0.797200\pi$
$84$	−16.7284	+	7.37811i	−1.82522	+	0.805018i
$85$	3.02076	−	4.15771i	0.327647	−	0.450967i
$86$	−9.66046	+	3.13887i	−1.04171	+	0.338473i
$87$	1.98747	−	9.19239i	0.213079	−	0.985527i
$88$		0			0
$89$		−	9.58244i		−	1.01574i	−0.861435	−	0.507868i	$-0.830434\pi$
$89$		−	9.58244i		−	1.01574i	0.861435	−	0.507868i	$-0.169566\pi$
$90$	−8.84591	−	0.992229i	−0.932441	−	0.104590i
$91$	7.65662	+	5.56286i	0.802632	+	0.583146i
$92$		0			0
$93$	−0.293634	−	0.170899i	−0.0304484	−	0.0177214i
$94$	−7.70959	−	2.50500i	−0.795184	−	0.258371i
$95$	2.45592	−	1.78433i	0.251972	−	0.183069i
$96$	3.09136	−	2.76399i	0.315510	−	0.282099i
$97$	0.700835	+	2.15695i	0.0711590	+	0.219005i	0.980311	−	0.197459i	$-0.0632691\pi$
$97$	0.700835	+	2.15695i	0.0711590	+	0.219005i	−0.909152	+	0.416464i	$0.863269\pi$
$98$	−2.39417			−0.241848
$99$		0			0
$100$	12.9282			1.29282
$101$	−0.145121	−	0.446637i	−0.0144401	−	0.0444421i	0.943577	−	0.331154i	$-0.107438\pi$
$101$	−0.145121	−	0.446637i	−0.0144401	−	0.0444421i	−0.958017	+	0.286712i	$0.907438\pi$
$102$	12.8193	−	11.4618i	1.26930	−	1.13489i
$103$	−10.3004	+	7.48371i	−1.01493	+	0.737392i	−0.965238	−	0.261372i	$-0.915825\pi$
$103$	−10.3004	+	7.48371i	−1.01493	+	0.737392i	−0.0496950	+	0.998764i	$0.515825\pi$
$104$	13.1964	+	4.28778i	1.29402	+	0.420451i
$105$	−5.24733	−	3.05402i	−0.512087	−	0.298042i
$106$	−9.99689	−	13.7595i	−0.970984	−	1.33644i
$107$	2.83585	+	2.06037i	0.274152	+	0.199183i	0.716363	−	0.697728i	$-0.245806\pi$
$107$	2.83585	+	2.06037i	0.274152	+	0.199183i	−0.442210	+	0.896911i	$0.645806\pi$
$108$	−18.3794	−	6.18536i	−1.76856	−	0.595187i
$109$		−	10.6945i		−	1.02435i	−0.858881	−	0.512175i	$-0.828840\pi$
$109$		−	10.6945i		−	1.02435i	0.858881	−	0.512175i	$-0.171160\pi$
$110$		0			0
$111$	−3.83013	+	17.7150i	−0.363540	+	1.68144i
$112$	−6.62842	+	2.15370i	−0.626327	+	0.203506i
$113$	−7.62258	+	10.4916i	−0.717072	+	0.986965i	0.282544	+	0.959254i	$0.408822\pi$
$113$	−7.62258	+	10.4916i	−0.717072	+	0.986965i	−0.999616	+	0.0277104i	$0.991178\pi$
$114$	9.29380	−	4.09905i	0.870444	−	0.383911i
$115$		0			0
$116$	6.26207	−	19.2727i	0.581419	−	1.78942i
$117$	2.01846	+	9.83317i	0.186607	+	0.909077i
$118$	−17.7824	+	24.4754i	−1.63701	+	2.25315i
$119$	11.1549	−	3.62446i	1.02257	−	0.332253i
$120$	−8.70035	−	1.88108i	−0.794230	−	0.171719i
$121$		0			0
$122$		−	10.8217i		−	0.979755i
$123$	12.3768	−	1.25719i	1.11598	−	0.113357i
$124$	−0.592242	−	0.430289i	−0.0531849	−	0.0386411i
$125$	6.16568	+	8.48633i	0.551475	+	0.759040i
$126$	−15.0019	−	13.6986i	−1.33647	−	1.22037i
$127$	13.7138	+	4.45588i	1.21690	+	0.395396i	0.845953	−	0.533257i	$-0.179032\pi$
$127$	13.7138	+	4.45588i	1.21690	+	0.395396i	0.370949	+	0.928653i	$0.379032\pi$
$128$	16.7743	−	12.1872i	1.48265	−	1.07721i
$129$	−4.89799	−	5.47811i	−0.431244	−	0.482320i
$130$	3.06798	+	9.44228i	0.269080	+	0.828143i
$131$	−13.5516			−1.18401			−0.592005	−	0.805934i	$-0.701663\pi$
$131$	−13.5516			−1.18401			−0.592005	+	0.805934i	$0.701663\pi$
$132$		0			0
$133$	6.92820			0.600751
$134$	1.47968	+	4.55398i	0.127825	+	0.393404i
$135$	−1.92572	−	6.14499i	−0.165740	−	0.528876i
$136$	13.9120	−	10.1076i	1.19294	−	0.866723i
$137$	−16.9636	−	5.51181i	−1.44930	−	0.470905i	−0.524515	−	0.851401i	$-0.675753\pi$
$137$	−16.9636	−	5.51181i	−1.44930	−	0.470905i	−0.924783	+	0.380496i	$0.875753\pi$
$138$		0			0
$139$	3.04260	+	4.18778i	0.258070	+	0.355203i	0.918317	−	0.395846i	$-0.129548\pi$
$139$	3.04260	+	4.18778i	0.258070	+	0.355203i	−0.660247	+	0.751048i	$0.729548\pi$
$140$	−10.5836	−	7.68940i	−0.894473	−	0.649873i
$141$	−0.592644	−	5.83447i	−0.0499096	−	0.491351i
$142$			19.9749i			1.67625i
$143$		0			0
$144$	−6.73205	−	3.05379i	−0.561004	−	0.254483i
$145$	6.39994	−	2.07947i	0.531486	−	0.172690i
$146$	−11.4077	+	15.7014i	−0.944109	+	1.29946i
$147$	−0.698961	−	1.58476i	−0.0576493	−	0.130709i
$148$	−12.0679	+	37.1412i	−0.991976	+	3.05299i
$149$	2.90624	−	8.94448i	0.238088	−	0.732761i	−0.758608	−	0.651547i	$-0.774120\pi$
$149$	2.90624	−	8.94448i	0.238088	−	0.732761i	0.996697	−	0.0812137i	$-0.0258796\pi$
$150$	5.79694	+	13.1434i	0.473318	+	1.07316i
$151$	9.69263	−	13.3408i	0.788775	−	1.08566i	−0.205484	−	0.978660i	$-0.565877\pi$
$151$	9.69263	−	13.3408i	0.788775	−	1.08566i	0.994260	−	0.106995i	$-0.0341230\pi$
$152$	9.66046	−	3.13887i	0.783566	−	0.254596i
$153$	11.3293	+	5.13922i	0.915922	+	0.415481i
$154$		0			0
$155$		−	0.243094i		−	0.0195258i
$156$	2.18578	+	21.5186i	0.175002	+	1.72287i
$157$	9.27465	+	6.73843i	0.740198	+	0.537785i	0.892773	−	0.450507i	$-0.148757\pi$
$157$	9.27465	+	6.73843i	0.740198	+	0.537785i	−0.152575	+	0.988292i	$0.548757\pi$
$158$	−10.3412	−	14.2334i	−0.822701	−	1.13235i
$159$	6.18924	−	10.6342i	0.490838	−	0.843345i
$160$	2.82191	+	0.916893i	0.223091	+	0.0724868i
$161$		0			0
$162$	−1.95290	−	21.4589i	−0.153434	−	1.68597i
$163$	3.82943	+	11.7858i	0.299944	+	0.923134i	0.981516	+	0.191382i	$0.0612969\pi$
$163$	3.82943	+	11.7858i	0.299944	+	0.923134i	−0.681571	+	0.731752i	$0.738703\pi$
$164$	26.8055			2.09316
$165$		0			0
$166$	−35.5167			−2.75663
$167$	1.62480	+	5.00062i	0.125731	+	0.386960i	0.994034	−	0.109075i	$-0.0347889\pi$
$167$	1.62480	+	5.00062i	0.125731	+	0.386960i	−0.868303	+	0.496035i	$0.834789\pi$
$168$	−13.5407	−	15.1445i	−1.04469	−	1.16842i
$169$	−1.45934	+	1.06028i	−0.112257	+	0.0815596i
$170$	11.7019	+	3.80219i	0.897499	+	0.291615i
$171$	5.42652	+	4.95509i	0.414976	+	0.378925i
$172$	−9.30685	−	12.8098i	−0.709640	−	0.976736i
$173$	9.16562	+	6.65922i	0.696850	+	0.506291i	0.878905	−	0.476998i	$-0.158275\pi$
$173$	9.16562	+	6.65922i	0.696850	+	0.506291i	−0.182055	+	0.983288i	$0.558275\pi$
$174$	22.4014	−	2.27545i	1.69825	−	0.172501i
$175$			9.79796i			0.740656i
$176$		0			0
$177$	−21.3923	−	4.62518i	−1.60794	−	0.347650i
$178$	21.8191	−	7.08946i	1.63541	−	0.531378i
$179$	13.3979	−	18.4406i	1.00140	−	1.37832i	0.0769449	−	0.997035i	$-0.475483\pi$
$179$	13.3979	−	18.4406i	1.00140	−	1.37832i	0.924460	−	0.381280i	$-0.124517\pi$
$180$	−2.79006	−	13.5921i	−0.207959	−	1.01310i
$181$	3.97285	−	12.2272i	0.295299	−	0.908838i	−0.687821	−	0.725880i	$-0.741433\pi$
$181$	3.97285	−	12.2272i	0.295299	−	0.908838i	0.983121	−	0.182958i	$-0.0585673\pi$
$182$	−7.00191	+	21.5497i	−0.519016	+	1.59737i
$183$	7.16317	−	3.15933i	0.529517	−	0.233545i
$184$		0			0
$185$	−12.3336	+	4.00743i	−0.906784	+	0.294632i
$186$	0.171894	−	0.795040i	0.0126039	−	0.0582951i
$187$		0			0
$188$		−	12.6362i		−	0.921592i
$189$	4.68773	−	13.9293i	0.340982	−	1.01321i
$190$	5.87989	+	4.27199i	0.426572	+	0.309923i
$191$	−1.45690	−	2.00525i	−0.105418	−	0.145095i	0.753049	−	0.657965i	$-0.228582\pi$
$191$	−1.45690	−	2.00525i	−0.105418	−	0.145095i	−0.858466	+	0.512870i	$0.828582\pi$
$192$	15.9581	+	9.28781i	1.15167	+	0.670290i
$193$	2.72534	+	0.885517i	0.196174	+	0.0637409i	0.405456	−	0.914114i	$-0.367113\pi$
$193$	2.72534	+	0.885517i	0.196174	+	0.0637409i	−0.209282	+	0.977855i	$0.567113\pi$
$194$	−4.39285	+	3.19159i	−0.315388	+	0.229143i
$195$	−5.35439	+	4.78738i	−0.383436	+	0.342831i
$196$	−1.15327	−	3.54939i	−0.0823762	−	0.253528i
$197$	10.6878			0.761476			0.380738	−	0.924683i	$-0.375670\pi$
$197$	10.6878			0.761476			0.380738	+	0.924683i	$0.375670\pi$
$198$		0			0
$199$	7.66025			0.543021			0.271511	−	0.962435i	$-0.412477\pi$
$199$	7.66025			0.543021			0.271511	+	0.962435i	$0.412477\pi$
$200$	4.43904	+	13.6619i	0.313887	+	0.966046i
$201$	−2.58240	+	2.30894i	−0.182149	+	0.162860i
$202$	0.909623	−	0.660880i	0.0640008	−	0.0464993i
$203$	14.6063	+	4.74587i	1.02516	+	0.333095i
$204$	23.1673	+	13.4837i	1.62204	+	0.944048i
$205$	5.23210	+	7.20137i	0.365426	+	0.502966i
$206$	−24.6610	−	17.9173i	−1.71821	−	1.24836i
$207$		0			0
$208$			8.24504i			0.571691i
$209$		0			0
$210$	3.07180	−	14.2076i	0.211974	−	0.980419i
$211$	1.80195	−	0.585490i	0.124052	−	0.0403068i	−0.246333	−	0.969185i	$-0.579226\pi$
$211$	1.80195	−	0.585490i	0.124052	−	0.0403068i	0.370385	+	0.928878i	$0.379226\pi$
$212$	15.5832	−	21.4485i	1.07026	−	1.47309i
$213$	−13.2218	+	5.83152i	−0.905944	+	0.399569i
$214$	−2.59336	+	7.98156i	−0.177279	+	0.545608i
$215$	1.62480	−	5.00062i	0.110810	−	0.341039i
$216$	0.225646	−	21.5464i	0.0153532	−	1.46604i
$217$	0.326105	−	0.448845i	0.0221374	−	0.0304696i
$218$	24.3514	−	7.91224i	1.64928	−	0.535884i
$219$	−13.7235	−	2.96713i	−0.927349	−	0.200500i
$220$		0			0
$221$		−	13.8755i		−	0.933370i
$222$	−43.1707	+	4.38511i	−2.89742	+	0.294309i
$223$	−10.4591	−	7.59901i	−0.700396	−	0.508867i	0.179665	−	0.983728i	$-0.442498\pi$
$223$	−10.4591	−	7.59901i	−0.700396	−	0.508867i	−0.880061	+	0.474861i	$0.842498\pi$
$224$	3.98033	+	5.47845i	0.265947	+	0.366044i
$225$	−7.00756	+	7.67425i	−0.467170	+	0.511617i
$226$	−29.5287	−	9.59446i	−1.96422	−	0.638214i
$227$	4.25378	−	3.09055i	0.282333	−	0.205127i	−0.437601	−	0.899169i	$-0.644172\pi$
$227$	4.25378	−	3.09055i	0.282333	−	0.205127i	0.719935	+	0.694042i	$0.244172\pi$
$228$	10.5537	+	11.8037i	0.698936	+	0.781718i
$229$	1.71069	+	5.26495i	0.113045	+	0.347918i	0.991534	−	0.129845i	$-0.0414479\pi$
$229$	1.71069	+	5.26495i	0.113045	+	0.347918i	−0.878489	+	0.477763i	$0.841448\pi$
$230$		0			0
$231$		0			0
$232$	22.5167			1.47829
$233$	−1.67792	−	5.16410i	−0.109924	−	0.338311i	0.880931	−	0.473246i	$-0.156918\pi$
$233$	−1.67792	−	5.16410i	−0.109924	−	0.338311i	−0.990855	+	0.134934i	$0.956918\pi$
$234$	−20.8967	+	11.8710i	−1.36606	+	0.776030i
$235$	3.39476	−	2.46644i	0.221450	−	0.160893i
$236$	−44.8509	−	14.5729i	−2.91955	−	0.948618i
$237$	6.40240	−	11.0004i	0.415881	−	0.714554i
$238$	16.5057	+	22.7182i	1.06991	+	1.47260i
$239$	−8.12763	−	5.90507i	−0.525733	−	0.381967i	0.293026	−	0.956104i	$-0.405338\pi$
$239$	−8.12763	−	5.90507i	−0.525733	−	0.381967i	−0.818759	+	0.574137i	$0.805338\pi$
$240$	−0.534520	−	5.26225i	−0.0345031	−	0.339677i
$241$		−	3.76217i		−	0.242343i	−0.992632	−	0.121171i	$-0.961335\pi$
$241$		−	3.76217i		−	0.242343i	0.992632	−	0.121171i	$-0.0386650\pi$
$242$		0			0
$243$	13.6340	−	7.55743i	0.874620	−	0.484809i
$244$	16.0434	−	5.21282i	1.02707	−	0.333716i
$245$	0.728450	−	1.00263i	0.0465390	−	0.0640554i
$246$	12.0194	+	27.2517i	0.766331	+	1.73751i
$247$	2.53275	−	7.79500i	0.161155	−	0.495984i
$248$	0.251357	−	0.773599i	0.0159612	−	0.0491236i
$249$	−10.3688	−	23.5093i	−0.657098	−	1.48984i
$250$	−14.7617	+	20.3177i	−0.933611	+	1.28500i
$251$	−8.16598	+	2.65329i	−0.515432	+	0.167474i	−0.555171	−	0.831736i	$-0.687347\pi$
$251$	−8.16598	+	2.65329i	−0.515432	+	0.167474i	0.0397393	+	0.999210i	$0.487347\pi$
$252$	13.0820	−	28.8391i	0.824088	−	1.81669i
$253$		0			0
$254$			34.5228i			2.16615i
$255$	0.899540	+	8.85581i	0.0563314	+	0.554573i
$256$	22.9118	+	16.6464i	1.43199	+	1.04040i
$257$	−13.5931	−	18.7093i	−0.847912	−	1.16705i	−0.984319	−	0.176398i	$-0.943555\pi$
$257$	−13.5931	−	18.7093i	−0.847912	−	1.16705i	0.136407	−	0.990653i	$-0.456445\pi$
$258$	8.84988	−	15.2056i	0.550969	−	0.946660i
$259$	−28.1484	−	9.14596i	−1.74905	−	0.568302i
$260$	−12.5205	+	9.09666i	−0.776487	+	0.564151i
$261$	8.04610	+	14.1637i	0.498041	+	0.876711i
$262$	−10.0260	−	30.8569i	−0.619409	−	1.90635i
$263$	−23.4721			−1.44735			−0.723675	−	0.690141i	$-0.757549\pi$
$263$	−23.4721			−1.44735			−0.723675	+	0.690141i	$0.757549\pi$
$264$		0			0
$265$	8.80385			0.540816
$266$	5.12576	+	15.7755i	0.314280	+	0.967255i
$267$	11.0626	+	12.3729i	0.677021	+	0.757207i
$268$	−6.03859	+	4.38729i	−0.368865	+	0.267996i
$269$	−15.5537	−	5.05372i	−0.948328	−	0.308131i	−0.206292	−	0.978490i	$-0.566140\pi$
$269$	−15.5537	−	5.05372i	−0.948328	−	0.308131i	−0.742036	+	0.670360i	$0.766140\pi$
$270$	12.5674	−	8.93115i	0.764825	−	0.543533i
$271$	−5.37331	−	7.39573i	−0.326405	−	0.449258i	0.614004	−	0.789303i	$-0.289558\pi$
$271$	−5.37331	−	7.39573i	−0.326405	−	0.449258i	−0.940409	+	0.340045i	$0.889558\pi$
$272$	8.26669	+	6.00611i	0.501242	+	0.364174i
$273$	−16.3084	+	1.65654i	−0.987029	+	0.100259i
$274$		−	42.7038i		−	2.57983i
$275$		0			0
$276$		0			0
$277$	−5.96886	+	1.93940i	−0.358634	+	0.116527i	−0.482792	−	0.875735i	$-0.660377\pi$
$277$	−5.96886	+	1.93940i	−0.358634	+	0.116527i	0.124158	+	0.992262i	$0.460377\pi$
$278$	−7.28450	+	10.0263i	−0.436895	+	0.601335i
$279$	0.576438	−	0.118326i	0.0345105	−	0.00708397i
$280$	4.49184	−	13.8245i	0.268439	−	0.826170i
$281$	0.251357	−	0.773599i	0.0149947	−	0.0461490i	−0.943279	−	0.332001i	$-0.892276\pi$
$281$	0.251357	−	0.773599i	0.0149947	−	0.0461490i	0.958274	+	0.285852i	$0.0922764\pi$
$282$	12.8466	−	5.66602i	0.765003	−	0.337406i
$283$	3.99322	−	5.49619i	0.237372	−	0.326715i	−0.673667	−	0.739035i	$-0.735282\pi$
$283$	3.99322	−	5.49619i	0.237372	−	0.326715i	0.911039	+	0.412321i	$0.135282\pi$
$284$	−29.6130	+	9.62185i	−1.75721	+	0.570952i
$285$	−1.11114	+	5.13922i	−0.0658181	+	0.304421i
$286$		0			0
$287$			20.3152i			1.19917i
$288$	−0.800628	+	7.13775i	−0.0471774	+	0.420596i
$289$	−0.158691	−	0.115296i	−0.00933474	−	0.00678209i
$290$	9.46985	+	13.0341i	0.556089	+	0.765391i
$291$	−3.39505	−	1.97596i	−0.199021	−	0.115833i
$292$	−28.7726	−	9.34878i	−1.68379	−	0.547096i
$293$	−26.3198	+	19.1225i	−1.53762	+	1.11715i	−0.585814	+	0.810446i	$0.699225\pi$
$293$	−26.3198	+	19.1225i	−1.53762	+	1.11715i	−0.951806	+	0.306701i	$0.900775\pi$
$294$	3.09136	−	2.76399i	0.180292	−	0.161199i
$295$	−4.83928	−	14.8938i	−0.281754	−	0.867150i
$296$	−43.3928			−2.52215
$297$		0			0
$298$	22.5167			1.30436
$299$		0			0
$300$	−16.6929	+	14.9252i	−0.963767	+	0.861707i
$301$	9.70820	−	7.05342i	0.559572	−	0.406553i
$302$	37.5478	+	12.2000i	2.16063	+	0.702032i
$303$	0.703009	+	0.409161i	0.0403868	+	0.0235057i
$304$	3.54775	+	4.88306i	0.203477	+	0.280063i
$305$	4.53191	+	3.29263i	0.259496	+	0.188535i
$306$	−3.32006	+	29.5990i	−0.189795	+	1.69206i
$307$			31.1870i			1.77994i	0.456021	+	0.889969i	$0.349274\pi$
$307$			31.1870i			1.77994i	−0.456021	+	0.889969i	$0.650726\pi$
$308$		0			0
$309$	4.66025	−	21.5545i	0.265113	−	1.22619i
$310$	0.553524	−	0.179851i	0.0314380	−	0.0102148i
$311$	0.390375	−	0.537306i	0.0221362	−	0.0304678i	−0.797805	−	0.602915i	$-0.794006\pi$
$311$	0.390375	−	0.537306i	0.0221362	−	0.0304678i	0.819942	+	0.572447i	$0.194006\pi$
$312$	−21.9894	+	9.69846i	−1.24490	+	0.549067i
$313$	−2.28435	+	7.03050i	−0.129119	+	0.397387i	−0.994629	−	0.103504i	$-0.966994\pi$
$313$	−2.28435	+	7.03050i	−0.129119	+	0.397387i	0.865510	+	0.500892i	$0.166994\pi$
$314$	−8.48159	+	26.1037i	−0.478644	+	1.47311i
$315$	10.3011	−	2.11452i	0.580404	−	0.119140i
$316$	16.1199	−	22.1872i	0.906817	−	1.24813i
$317$	23.4039	−	7.60439i	1.31449	−	0.427105i	0.433893	−	0.900964i	$-0.357139\pi$
$317$	23.4039	−	7.60439i	1.31449	−	0.427105i	0.880601	+	0.473859i	$0.157139\pi$
$318$	28.7930	+	6.22526i	1.61463	+	0.349095i
$319$		0			0
$320$			13.2114i			0.738540i
$321$	−6.04029	+	0.613550i	−0.337136	+	0.0342450i
$322$		0			0
$323$	−5.97049	−	8.21767i	−0.332207	−	0.457244i
$324$	30.8723	−	13.2319i	1.71513	−	0.735105i
$325$	11.0238	+	3.58185i	0.611490	+	0.198685i
$326$	−24.0030	+	17.4392i	−1.32940	+	0.965866i
$327$	12.3465	+	13.8088i	0.682763	+	0.763629i
$328$	9.20395	+	28.3268i	0.508203	+	1.56409i
$329$	9.57668			0.527979
$330$		0			0
$331$	−0.392305			−0.0215630			−0.0107815	−	0.999942i	$-0.503432\pi$
$331$	−0.392305			−0.0215630			−0.0107815	+	0.999942i	$0.503432\pi$
$332$	−17.1083	−	52.6540i	−0.938940	−	2.88976i
$333$	−15.5060	−	27.2955i	−0.849722	−	1.49578i
$334$	−10.1843	+	7.39931i	−0.557259	+	0.404872i
$335$	−2.35731	−	0.765938i	−0.128794	−	0.0418477i
$336$	6.07225	−	10.4332i	0.331268	−	0.569176i
$337$	−5.00937	−	6.89480i	−0.272878	−	0.375584i	0.650481	−	0.759523i	$-0.274567\pi$
$337$	−5.00937	−	6.89480i	−0.272878	−	0.375584i	−0.923359	+	0.383939i	$0.874567\pi$
$338$	−3.49392	−	2.53848i	−0.190044	−	0.138075i
$339$	−2.26990	−	22.3468i	−0.123284	−	1.21371i
$340$			19.1798i			1.04017i
$341$		0			0
$342$	−7.26795	+	16.0221i	−0.393006	+	0.866376i
$343$	−16.1400	+	5.24419i	−0.871476	+	0.283160i
$344$	10.3412	−	14.2334i	0.557560	−	0.767415i
$345$		0			0
$346$	−8.38189	+	25.7968i	−0.450613	+	1.38684i
$347$	−0.396479	+	1.22024i	−0.0212841	+	0.0655057i	−0.961134	−	0.276081i	$-0.910964\pi$
$347$	−0.396479	+	1.22024i	−0.0212841	+	0.0655057i	0.939850	+	0.341587i	$0.110964\pi$
$348$	14.1641	+	32.1143i	0.759275	+	1.72151i
$349$	−11.9418	+	16.4365i	−0.639231	+	0.879826i	−0.998574	−	0.0533798i	$-0.983001\pi$
$349$	−11.9418	+	16.4365i	−0.639231	+	0.879826i	0.359344	+	0.933205i	$0.383001\pi$
$350$	−22.3099	+	7.24891i	−1.19251	+	0.387471i
$351$	−13.9583	−	10.3664i	−0.745040	−	0.553316i
$352$		0			0
$353$			9.58244i			0.510022i	0.966938	+	0.255011i	$0.0820790\pi$
$353$			9.58244i			0.510022i	−0.966938	+	0.255011i	$0.917921\pi$
$354$	−5.29537	−	52.1320i	−0.281446	−	2.77078i
$355$	−8.36503	−	6.07755i	−0.443970	−	0.322563i
$356$	21.0205	+	28.9322i	1.11408	+	1.53340i
$357$	−10.2190	+	17.5579i	−0.540844	+	0.929264i
$358$	51.9014	+	16.8638i	2.74307	+	0.891278i
$359$	27.8768	−	20.2537i	1.47128	−	1.06895i	0.491042	−	0.871136i	$-0.336616\pi$
$359$	27.8768	−	20.2537i	1.47128	−	1.06895i	0.980240	−	0.197813i	$-0.0633837\pi$
$360$	13.4056	−	7.61542i	0.706535	−	0.401368i
$361$	4.01722	+	12.3637i	0.211433	+	0.650723i
$362$	30.7804			1.61778
$363$		0			0
$364$	−35.3205			−1.85130
$365$	−3.10448	−	9.55460i	−0.162496	−	0.500111i
$366$	12.4934	+	13.9731i	0.653039	+	0.730384i
$367$	19.3002	−	14.0224i	1.00746	−	0.731966i	0.0437885	−	0.999041i	$-0.486057\pi$
$367$	19.3002	−	14.0224i	1.00746	−	0.731966i	0.963676	+	0.267075i	$0.0860572\pi$
$368$		0			0
$369$	−14.5296	+	15.9119i	−0.756378	+	0.828340i
$370$	−18.2497	−	25.1186i	−0.948759	−	1.30586i
$371$	16.2553	+	11.8101i	0.843931	+	0.613152i
$372$	1.26146	−	0.128134i	0.0654036	−	0.00664345i
$373$		−	9.62209i		−	0.498213i	−0.968476	−	0.249107i	$-0.919863\pi$
$373$		−	9.62209i		−	0.498213i	0.968476	−	0.249107i	$-0.0801369\pi$
$374$		0			0
$375$	−17.7583	−	3.83949i	−0.917036	−	0.198270i
$376$	13.3534	−	4.33878i	0.688649	−	0.223756i
$377$	10.6793	−	14.6987i	0.550010	−	0.757024i
$378$	35.1850	+	0.368478i	1.80972	+	0.0189525i
$379$	−9.45235	+	29.0914i	−0.485535	+	1.49432i	0.345670	+	0.938356i	$0.387652\pi$
$379$	−9.45235	+	29.0914i	−0.485535	+	1.49432i	−0.831205	+	0.555966i	$0.812348\pi$
$380$	−3.50096	+	10.7748i	−0.179595	+	0.552738i
$381$	−22.8515	+	10.0787i	−1.17072	+	0.516347i
$382$	3.48807	−	4.80091i	0.178465	−	0.245636i
$383$	9.02881	−	2.93364i	0.461351	−	0.149902i	−0.0691142	−	0.997609i	$-0.522017\pi$
$383$	9.02881	−	2.93364i	0.461351	−	0.149902i	0.530465	+	0.847707i	$0.322017\pi$
$384$	−7.58922	+	35.1015i	−0.387286	+	1.79127i
$385$		0			0
$386$			6.86071i			0.349201i
$387$	12.6486	+	1.41877i	0.642964	+	0.0721201i
$388$	−6.84760	−	4.97507i	−0.347634	−	0.252571i
$389$	−11.2125	−	15.4327i	−0.568498	−	0.782470i	0.423878	−	0.905719i	$-0.360669\pi$
$389$	−11.2125	−	15.4327i	−0.568498	−	0.782470i	−0.992376	+	0.123249i	$0.960669\pi$
$390$	−14.8622	−	8.65001i	−0.752577	−	0.438010i
$391$		0			0
$392$	3.35485	−	2.43744i	0.169446	−	0.123109i
$393$	17.4979	−	15.6449i	0.882651	−	0.789181i
$394$	7.90727	+	24.3361i	0.398362	+	1.22603i
$395$	9.10706			0.458226
$396$		0			0
$397$	−21.1962			−1.06380			−0.531902	−	0.846806i	$-0.678523\pi$
$397$	−21.1962			−1.06380			−0.531902	+	0.846806i	$0.678523\pi$
$398$	5.66736	+	17.4423i	0.284079	+	0.874305i
$399$	−8.94571	+	7.99839i	−0.447846	+	0.400420i
$400$	−6.90569	+	5.01728i	−0.345284	+	0.250864i
$401$	−1.17866	−	0.382969i	−0.0588593	−	0.0191246i	0.279439	−	0.960163i	$-0.409851\pi$
$401$	−1.17866	−	0.382969i	−0.0588593	−	0.0191246i	−0.338299	+	0.941039i	$0.609851\pi$
$402$	−7.16799	−	4.17187i	−0.357507	−	0.208074i
$403$	−0.385786	−	0.530989i	−0.0192174	−	0.0264505i
$404$	1.41793	+	1.03018i	0.0705445	+	0.0512536i
$405$	9.58069	+	5.71124i	0.476068	+	0.283794i
$406$			36.7696i			1.82484i
$407$		0			0
$408$	−6.29423	+	29.1120i	−0.311611	+	1.44126i
$409$	−31.5945	+	10.2657i	−1.56225	+	0.507605i	−0.957407	−	0.288742i	$-0.906763\pi$
$409$	−31.5945	+	10.2657i	−1.56225	+	0.507605i	−0.604840	+	0.796347i	$0.706763\pi$
$410$	−12.5265	+	17.2413i	−0.618642	+	0.851487i
$411$	28.2666	−	12.4671i	1.39429	−	0.614955i
$412$	14.6835	−	45.1910i	0.723402	−	2.22640i
$413$	11.0445	−	33.9914i	0.543463	−	1.67261i
$414$		0			0
$415$	10.8063	−	14.8736i	0.530460	−	0.730116i
$416$	7.61896	−	2.47555i	0.373550	−	0.121374i
$417$	−8.76327	−	1.89469i	−0.429139	−	0.0927832i
$418$		0			0
$419$			11.0648i			0.540553i	0.962783	+	0.270277i	$0.0871151\pi$
$419$			11.0648i			0.540553i	−0.962783	+	0.270277i	$0.912885\pi$
$420$	22.5427	−	2.28980i	1.09997	−	0.111731i
$421$	15.5300	+	11.2832i	0.756887	+	0.549910i	0.897954	−	0.440090i	$-0.145053\pi$
$421$	15.5300	+	11.2832i	0.756887	+	0.549910i	−0.141067	+	0.990000i	$0.545053\pi$
$422$	2.66631	+	3.66987i	0.129794	+	0.178646i
$423$	7.50094	+	6.84930i	0.364708	+	0.333024i
$424$	28.0165	+	9.10310i	1.36060	+	0.442086i
$425$	11.6215	−	8.44355i	0.563728	−	0.409572i
$426$	−23.0603	−	25.7916i	−1.11728	−	1.24961i
$427$	3.95066	+	12.1589i	0.191186	+	0.588410i
$428$	−13.0820			−0.632342
$429$		0			0
$430$	12.5885			0.607069
$431$	6.46031	+	19.8828i	0.311182	+	0.957721i	0.977297	+	0.211872i	$0.0679560\pi$
$431$	6.46031	+	19.8828i	0.311182	+	0.957721i	−0.666115	+	0.745849i	$0.732044\pi$
$432$	12.2179	−	3.82887i	0.587836	−	0.184217i
$433$	−10.5597	+	7.67210i	−0.507469	+	0.368698i	−0.811863	−	0.583849i	$-0.801546\pi$
$433$	−10.5597	+	7.67210i	−0.507469	+	0.368698i	0.304394	+	0.952546i	$0.401546\pi$
$434$	1.26328	+	0.410465i	0.0606394	+	0.0197029i
$435$	−5.86294	+	10.0735i	−0.281106	+	0.482989i
$436$	23.4600	+	32.2899i	1.12353	+	1.54641i
$437$		0			0
$438$	−3.39706	−	33.4435i	−0.162318	−	1.59799i
$439$		−	8.38375i		−	0.400134i	−0.979782	−	0.200067i	$-0.935884\pi$
$439$		−	8.38375i		−	0.400134i	0.979782	−	0.200067i	$-0.0641160\pi$
$440$		0			0
$441$	2.73205	+	1.23931i	0.130098	+	0.0590149i
$442$	31.5945	−	10.2657i	1.50280	−	0.488288i
$443$	−14.9977	+	20.6425i	−0.712561	+	0.980756i	0.287178	+	0.957877i	$0.407283\pi$
$443$	−14.9977	+	20.6425i	−0.712561	+	0.980756i	−0.999738	+	0.0228783i	$0.992717\pi$
$444$	−27.2962	−	61.8888i	−1.29542	−	2.93711i
$445$	−3.66978	+	11.2944i	−0.173964	+	0.535406i
$446$	9.56479	−	29.4374i	0.452906	−	1.39390i
$447$	6.57358	+	14.9043i	0.310920	+	0.704949i
$448$	−17.7228	+	24.3933i	−0.837321	+	1.15247i
$449$	−38.3260	+	12.4529i	−1.80872	+	0.587687i	−1.00000		0.000512011i	$-0.999837\pi$
$449$	−38.3260	+	12.4529i	−1.80872	+	0.587687i	−0.808716	+	0.588199i	$0.799837\pi$
$450$	−22.6587	−	10.2784i	−1.06814	−	0.484530i
$451$		0			0
$452$		−	48.3984i		−	2.27647i
$453$	2.88633	+	28.4155i	0.135612	+	1.33507i
$454$	10.1843	+	7.39931i	0.477972	+	0.347267i
$455$	−6.89413	−	9.48895i	−0.323202	−	0.444849i
$456$	−8.84988	+	15.2056i	−0.414433	+	0.712068i
$457$	17.5203	+	5.69269i	0.819565	+	0.266293i	0.688644	−	0.725100i	$-0.258206\pi$
$457$	17.5203	+	5.69269i	0.819565	+	0.266293i	0.130922	+	0.991393i	$0.458206\pi$
$458$	−10.7226	+	7.79044i	−0.501035	+	0.364023i
$459$	−20.5615	+	6.44359i	−0.959730	+	0.300761i
$460$		0			0
$461$	−2.86379			−0.133380			−0.0666901	−	0.997774i	$-0.521244\pi$
$461$	−2.86379			−0.133380			−0.0666901	+	0.997774i	$0.521244\pi$
$462$		0			0
$463$	−1.26795			−0.0589266			−0.0294633	−	0.999566i	$-0.509380\pi$
$463$	−1.26795			−0.0589266			−0.0294633	+	0.999566i	$0.509380\pi$
$464$	4.13456	+	12.7249i	0.191942	+	0.590737i
$465$	0.280645	+	0.313884i	0.0130146	+	0.0145560i
$466$	10.5172	−	7.64121i	0.487201	−	0.353972i
$467$	18.4581	+	5.99739i	0.854138	+	0.277526i	0.703178	−	0.711014i	$-0.251764\pi$
$467$	18.4581	+	5.99739i	0.854138	+	0.277526i	0.150960	+	0.988540i	$0.451764\pi$
$468$	−27.6648	−	25.2614i	−1.27881	−	1.16771i
$469$	−3.32502	−	4.57649i	−0.153535	−	0.211323i
$470$	8.12763	+	5.90507i	0.374900	+	0.272381i
$471$	−19.7548	+	2.00661i	−0.910251	+	0.0924599i
$472$		−	52.4002i		−	2.41192i
$473$		0			0
$474$	29.7846	+	6.43966i	1.36805	+	0.295784i
$475$	8.06998	−	2.62210i	0.370276	−	0.120310i
$476$	−25.7292	+	35.4133i	−1.17930	+	1.62316i
$477$	4.28525	+	20.8761i	0.196208	+	0.955853i
$478$	7.43265	−	22.8753i	0.339961	−	1.04629i
$479$	2.02128	−	6.22086i	0.0923546	−	0.284238i	−0.894201	−	0.447666i	$-0.852255\pi$
$479$	2.02128	−	6.22086i	0.0923546	−	0.284238i	0.986555	+	0.163428i	$0.0522552\pi$
$480$	−4.70218	+	2.07391i	−0.214624	+	0.0946604i
$481$	−20.5805	+	28.3266i	−0.938388	+	1.29158i
$482$	8.56642	−	2.78340i	0.390190	−	0.126780i
$483$		0			0
$484$		0			0
$485$		−	2.81070i		−	0.127627i
$486$	27.2951	+	25.4532i	1.23813	+	1.15458i
$487$	−26.8407	−	19.5009i	−1.21627	−	0.883670i	−0.220483	−	0.975391i	$-0.570763\pi$
$487$	−26.8407	−	19.5009i	−1.21627	−	0.883670i	−0.995785	+	0.0917207i	$0.970763\pi$
$488$	11.0173	+	15.1641i	0.498732	+	0.686445i
$489$	−18.5509	−	10.7969i	−0.838900	−	0.488251i
$490$	2.82191	+	0.916893i	0.127481	+	0.0414210i
$491$	16.9133	−	12.2882i	0.763288	−	0.554561i	−0.136629	−	0.990622i	$-0.543627\pi$
$491$	16.9133	−	12.2882i	0.763288	−	0.554561i	0.899917	+	0.436061i	$0.143627\pi$
$492$	−34.6113	+	30.9461i	−1.56040	+	1.39516i
$493$	−6.95803	−	21.4146i	−0.313374	−	0.964466i
$494$	19.6230			0.882880
$495$		0			0
$496$	0.483340			0.0217026
$497$	−7.29216	−	22.4430i	−0.327098	−	1.00670i
$498$	45.8592	−	41.0028i	2.05500	−	1.83738i
$499$	−20.8758	+	15.1671i	−0.934527	+	0.678974i	−0.947097	−	0.320947i	$-0.895999\pi$
$499$	−20.8758	+	15.1671i	−0.934527	+	0.678974i	0.0125700	+	0.999921i	$0.495999\pi$
$500$	−37.2320	−	12.0974i	−1.66506	−	0.541012i
$501$	−7.87100	−	4.58103i	−0.351650	−	0.204665i
$502$	−12.0830	−	16.6309i	−0.539292	−	0.742271i
$503$	2.83585	+	2.06037i	0.126444	+	0.0918673i	0.649210	−	0.760609i	$-0.275100\pi$
$503$	2.83585	+	2.06037i	0.126444	+	0.0918673i	−0.522765	+	0.852477i	$0.675100\pi$
$504$	34.9677	+	3.92226i	1.55758	+	0.174711i
$505$			0.582009i			0.0258991i
$506$		0			0
$507$	0.660254	−	3.05379i	0.0293229	−	0.135624i
$508$	−51.1806	+	16.6296i	−2.27077	+	0.737818i
$509$	6.89413	−	9.48895i	0.305577	−	0.420590i	−0.628419	−	0.777875i	$-0.716297\pi$
$509$	6.89413	−	9.48895i	0.305577	−	0.420590i	0.933995	+	0.357285i	$0.116297\pi$
$510$	−19.4991	+	8.60012i	−0.863435	+	0.380820i
$511$	7.08520	−	21.8060i	0.313431	−	0.964641i
$512$	−8.13823	+	25.0469i	−0.359662	+	1.10693i
$513$	−12.7272	−	0.133287i	−0.561921	−	0.00588475i
$514$	32.5441	−	44.7931i	1.43546	−	1.97574i
$515$	15.0067	−	4.87598i	0.661275	−	0.214861i
$516$	26.8055	+	5.79555i	1.18005	+	0.255135i
$517$		0			0
$518$		−	70.8601i		−	3.11342i
$519$	−19.5225	+	1.98302i	−0.856944	+	0.0870451i
$520$	−13.9120	−	10.1076i	−0.610081	−	0.443250i
$521$	−1.45690	−	2.00525i	−0.0638280	−	0.0878517i	0.775910	−	0.630844i	$-0.217291\pi$
$521$	−1.45690	−	2.00525i	−0.0638280	−	0.0878517i	−0.839738	+	0.542992i	$0.817291\pi$
$522$	−26.2978	+	28.7998i	−1.15102	+	1.26053i
$523$	−34.3198	−	11.1512i	−1.50070	−	0.487607i	−0.560479	−	0.828169i	$-0.689383\pi$
$523$	−34.3198	−	11.1512i	−1.50070	−	0.487607i	−0.940222	+	0.340561i	$0.889383\pi$
$524$	40.9163	−	29.7274i	1.78744	−	1.29865i
$525$	−11.3114	−	12.6511i	−0.493671	−	0.552141i
$526$	−17.3656	−	53.4457i	−0.757175	−	2.33034i
$527$	−0.813410			−0.0354327
$528$		0			0
$529$	23.0000			1.00000
$530$	6.51343	+	20.0463i	0.282925	+	0.870755i
$531$	32.9614	−	18.7247i	1.43040	−	0.812582i
$532$	−20.9183	+	15.1980i	−0.906922	+	0.658917i
$533$	22.8569	+	7.42665i	0.990041	+	0.321684i
$534$	−19.9883	+	34.3434i	−0.864980	+	1.48618i
$535$	−2.55344	−	3.51451i	−0.110395	−	0.151946i
$536$	−6.70970	−	4.87488i	−0.289815	−	0.210563i
$537$	3.98971	+	39.2780i	0.172169	+	1.69497i
$538$		−	39.1547i		−	1.68808i
$539$		0			0
$540$	19.2942	+	14.3292i	0.830291	+	0.616629i
$541$	5.01960	−	1.63097i	0.215809	−	0.0701207i	−0.199117	−	0.979976i	$-0.563807\pi$
$541$	5.01960	−	1.63097i	0.215809	−	0.0701207i	0.414926	+	0.909855i	$0.363807\pi$
$542$	12.8646	−	17.7066i	0.552583	−	0.760565i
$543$	8.98612	+	20.3743i	0.385632	+	0.874344i
$544$	3.06798	−	9.44228i	0.131539	−	0.404835i
$545$	−4.09568	+	12.6052i	−0.175439	+	0.539947i
$546$	−15.8375	−	35.9085i	−0.677783	−	1.53674i
$547$	12.4091	−	17.0797i	0.530576	−	0.730275i	−0.456642	−	0.889650i	$-0.650948\pi$
$547$	12.4091	−	17.0797i	0.530576	−	0.730275i	0.987218	+	0.159375i	$0.0509480\pi$
$548$	63.3090	−	20.5703i	2.70443	−	0.878721i
$549$	−5.60175	+	12.3490i	−0.239077	+	0.527042i
$550$		0			0
$551$		−	13.3004i		−	0.566615i
$552$		0			0
$553$	16.8151	+	12.2169i	0.715051	+	0.519515i
$554$	−8.83199	−	12.1562i	−0.375235	−	0.516467i
$555$	11.2987	−	19.4131i	0.479604	−	0.824042i
$556$	−18.3730	−	5.96975i	−0.779189	−	0.253174i
$557$	−8.40576	+	6.10714i	−0.356163	+	0.258768i	−0.751450	−	0.659790i	$-0.770645\pi$
$557$	−8.40576	+	6.10714i	−0.356163	+	0.258768i	0.395287	+	0.918558i	$0.370645\pi$
$558$	0.695898	+	1.22500i	0.0294597	+	0.0518585i
$559$	−4.38685	−	13.5013i	−0.185544	−	0.571046i
$560$	8.63744			0.364998
$561$		0			0
$562$	1.94744			0.0821478
$563$	−10.9382	−	33.6644i	−0.460992	−	1.41879i	−0.863954	−	0.503570i	$-0.832020\pi$
$563$	−10.9382	−	33.6644i	−0.460992	−	1.41879i	0.402963	−	0.915216i	$-0.367980\pi$
$564$	14.5881	+	16.3159i	0.614271	+	0.687025i
$565$	13.0024	−	9.44677i	0.547013	−	0.397428i
$566$	15.4691	+	5.02622i	0.650216	+	0.211268i
$567$	10.0281	+	23.3974i	0.421141	+	0.982597i
$568$	−20.3359	−	27.9899i	−0.853275	−	1.17443i
$569$	−25.4209	−	18.4694i	−1.06570	−	0.774276i	−0.0905647	−	0.995891i	$-0.528867\pi$
$569$	−25.4209	−	18.4694i	−1.06570	−	0.774276i	−0.975134	+	0.221615i	$0.928867\pi$
$570$	−12.5240	+	1.27214i	−0.524573	+	0.0532842i
$571$		−	27.3233i		−	1.14345i	−0.820447	−	0.571723i	$-0.806275\pi$
$571$		−	27.3233i		−	1.14345i	0.820447	−	0.571723i	$-0.193725\pi$
$572$		0			0
$573$	4.19615	+	0.907241i	0.175297	+	0.0379005i
$574$	−46.2575	+	15.0300i	−1.93075	+	0.627340i
$575$		0			0
$576$	−31.3276	+	6.43062i	−1.30532	+	0.267943i
$577$	1.48447	−	4.56873i	0.0617993	−	0.190199i	−0.915390	−	0.402568i	$-0.868118\pi$
$577$	1.48447	−	4.56873i	0.0617993	−	0.190199i	0.977190	+	0.212369i	$0.0681178\pi$
$578$	0.145121	−	0.446637i	0.00603625	−	0.0185777i
$579$	−4.54127	+	2.00294i	−0.188729	+	0.0832392i
$580$	−14.7617	+	20.3177i	−0.612945	+	0.843647i
$581$	39.9051	−	12.9660i	1.65554	−	0.537918i
$582$	1.98747	−	9.19239i	0.0823831	−	0.381037i
$583$		0			0
$584$		−	33.6156i		−	1.39102i
$585$	1.38673	−	12.3629i	0.0573341	−	0.511145i
$586$	−63.0141	−	45.7824i	−2.60309	−	1.89125i
$587$	−3.83744	−	5.28178i	−0.158388	−	0.218002i	0.722446	−	0.691427i	$-0.243018\pi$
$587$	−3.83744	−	5.28178i	−0.158388	−	0.218002i	−0.880834	+	0.473425i	$0.843018\pi$
$588$	5.58676	+	3.25157i	0.230394	+	0.134093i
$589$	−0.456957	−	0.148474i	−0.0188286	−	0.00611778i
$590$	30.3327	−	22.0380i	1.24878	−	0.907291i
$591$	−13.8001	+	12.3387i	−0.567662	+	0.507548i
$592$	−7.96788	−	24.5226i	−0.327478	−	1.00787i
$593$	26.3359			1.08148			0.540742	−	0.841188i	$-0.318143\pi$
$593$	26.3359			1.08148			0.540742	+	0.841188i	$0.318143\pi$
$594$		0			0
$595$	−14.5359			−0.595914
$596$	10.8462	+	33.3813i	0.444279	+	1.36735i
$597$	−9.89094	+	8.84352i	−0.404809	+	0.361941i
$598$		0			0
$599$	−2.58851	−	0.841058i	−0.105764	−	0.0343647i	0.255657	−	0.966768i	$-0.417708\pi$
$599$	−2.58851	−	0.841058i	−0.105764	−	0.0343647i	−0.361421	+	0.932403i	$0.617708\pi$
$600$	−21.5040	−	12.5156i	−0.877896	−	0.510948i
$601$	24.4106	+	33.5983i	0.995730	+	1.37050i	0.927909	+	0.372807i	$0.121605\pi$
$601$	24.4106	+	33.5983i	0.995730	+	1.37050i	0.0678213	+	0.997697i	$0.478395\pi$
$602$	23.2431	+	16.8871i	0.947318	+	0.688267i
$603$	0.668814	−	5.96261i	0.0272362	−	0.242816i
$604$			61.5419i			2.50410i
$605$		0			0
$606$	−0.411543	+	1.90346i	−0.0167178	+	0.0773228i
$607$	42.2226	−	13.7189i	1.71376	−	0.556835i	0.722808	−	0.691049i	$-0.242851\pi$
$607$	42.2226	−	13.7189i	1.71376	−	0.556835i	0.990952	+	0.134214i	$0.0428509\pi$
$608$	3.44706	−	4.74448i	0.139797	−	0.192414i
$609$	−24.3386	+	10.7346i	−0.986251	+	0.434988i
$610$	−4.14439	+	12.7551i	−0.167802	+	0.516440i
$611$	3.50096	−	10.7748i	0.141634	−	0.435903i
$612$	−45.4802	+	9.33574i	−1.83843	+	0.377375i
$613$	9.06227	−	12.4731i	0.366021	−	0.503785i	−0.585793	−	0.810461i	$-0.699217\pi$
$613$	9.06227	−	12.4731i	0.366021	−	0.503785i	0.951814	+	0.306676i	$0.0992167\pi$
$614$	−71.0126	+	23.0734i	−2.86583	+	0.931166i
$615$	−15.0695	−	3.25813i	−0.607659	−	0.131381i
$616$		0			0
$617$			13.6325i			0.548822i	0.961613	+	0.274411i	$0.0884828\pi$
$617$			13.6325i			0.548822i	−0.961613	+	0.274411i	$0.911517\pi$
$618$	52.5273	−	5.33552i	2.11296	−	0.214626i
$619$	0.116170	+	0.0844022i	0.00466925	+	0.00339241i	0.590117	−	0.807317i	$-0.299081\pi$
$619$	0.116170	+	0.0844022i	0.00466925	+	0.00339241i	−0.585448	+	0.810710i	$0.699081\pi$
$620$	0.533263	+	0.733973i	0.0214163	+	0.0294771i
$621$		0			0
$622$	1.51226	+	0.491361i	0.0606359	+	0.0197018i
$623$	−21.9270	+	15.9309i	−0.878485	+	0.638257i
$624$	−9.51864	−	10.6460i	−0.381051	−	0.426182i
$625$	1.33511	+	4.10905i	0.0534044	+	0.164362i
$626$	−17.6984			−0.707372
$627$		0			0
$628$	−42.7846			−1.70729
$629$	13.4091	+	41.2690i	0.534656	+	1.64550i
$630$	12.4359	+	21.8912i	0.495459	+	0.872166i
$631$	−22.1028	+	16.0586i	−0.879897	+	0.639282i	−0.933224	−	0.359295i	$-0.883017\pi$
$631$	−22.1028	+	16.0586i	−0.879897	+	0.639282i	0.0533274	+	0.998577i	$0.483017\pi$
$632$	28.9814	+	9.41662i	1.15282	+	0.374573i
$633$	−1.65076	+	2.83629i	−0.0656117	+	0.112732i
$634$	34.6302	+	47.6644i	1.37534	+	1.89300i
$635$	−14.4574	−	10.5039i	−0.573724	−	0.416835i
$636$	4.64048	+	45.6847i	0.184007	+	1.81151i
$637$		−	3.34607i		−	0.132576i
$638$		0			0
$639$	10.3397	−	22.7938i	0.409034	−	0.901710i
$640$	−24.4384	+	7.94053i	−0.966014	+	0.313877i
$641$	−27.7717	+	38.2245i	−1.09692	+	1.50978i	−0.257506	+	0.966277i	$0.582901\pi$
$641$	−27.7717	+	38.2245i	−1.09692	+	1.50978i	−0.839410	+	0.543499i	$0.817099\pi$
$642$	−5.86589	−	13.2998i	−0.231508	−	0.524900i
$643$	−1.17545	+	3.61767i	−0.0463554	+	0.142667i	−0.971555	−	0.236813i	$-0.923897\pi$
$643$	−1.17545	+	3.61767i	−0.0463554	+	0.142667i	0.925200	+	0.379480i	$0.123897\pi$
$644$		0			0
$645$	3.67511	+	8.33259i	0.144707	+	0.328095i
$646$	14.2944	−	19.6745i	0.562404	−	0.774083i
$647$	−15.8696	+	5.15633i	−0.623897	+	0.202716i	−0.603870	−	0.797083i	$-0.706375\pi$
$647$	−15.8696	+	5.15633i	−0.623897	+	0.202716i	−0.0200272	+	0.999799i	$0.506375\pi$
$648$	24.5832	+	28.0812i	0.965720	+	1.10313i
$649$		0			0
$650$			27.7511i			1.08849i
$651$	0.0971096	+	0.956027i	0.00380603	+	0.0374697i
$652$	−37.4160	−	27.1843i	−1.46532	−	1.06462i
$653$	22.8154	+	31.4028i	0.892837	+	1.22888i	0.972697	+	0.232079i	$0.0745526\pi$
$653$	22.8154	+	31.4028i	0.892837	+	1.22888i	−0.0798602	+	0.996806i	$0.525447\pi$
$654$	−22.3081	+	38.3292i	−0.872316	+	1.49879i
$655$	15.9727	+	5.18985i	0.624105	+	0.202784i
$656$	−14.3183	+	10.4029i	−0.559037	+	0.406164i
$657$	21.1453	−	12.0122i	0.824956	−	0.468640i
$658$	7.08520	+	21.8060i	0.276210	+	0.850087i
$659$	13.5516			0.527896			0.263948	−	0.964537i	$-0.414975\pi$
$659$	13.5516			0.527896			0.263948	+	0.964537i	$0.414975\pi$
$660$		0			0
$661$	3.19615			0.124316			0.0621580	−	0.998066i	$-0.480202\pi$
$661$	3.19615			0.124316			0.0621580	+	0.998066i	$0.480202\pi$
$662$	−0.290243	−	0.893275i	−0.0112806	−	0.0347181i
$663$	16.0189	+	17.9161i	0.622121	+	0.695805i
$664$	49.7680	−	36.1586i	1.93137	−	1.40323i
$665$	−8.16598	−	2.65329i	−0.316663	−	0.102890i
$666$	50.6796	−	55.5012i	1.96379	−	2.15063i
$667$		0			0
$668$	−15.8753	−	11.5341i	−0.614235	−	0.446268i
$669$	22.2777	−	2.26288i	0.861305	−	0.0874881i
$670$		−	5.93426i		−	0.229260i
$671$		0			0
$672$	−11.4641	−	2.47863i	−0.442237	−	0.0956151i
$673$	34.6095	−	11.2453i	1.33410	−	0.433475i	0.446785	−	0.894641i	$-0.352569\pi$
$673$	34.6095	−	11.2453i	1.33410	−	0.433475i	0.887314	+	0.461166i	$0.152569\pi$
$674$	11.9933	−	16.5073i	0.461964	−	0.635839i
$675$	0.188496	−	17.9990i	0.00725521	−	0.692782i
$676$	2.08032	−	6.40256i	0.0800122	−	0.246252i
$677$	3.55408	−	10.9383i	0.136594	−	0.420394i	−0.859240	−	0.511572i	$-0.829063\pi$
$677$	3.55408	−	10.9383i	0.136594	−	0.420394i	0.995835	+	0.0911783i	$0.0290633\pi$
$678$	49.2040	−	21.7016i	1.88967	−	0.833444i
$679$	3.77048	−	5.18962i	0.144698	−	0.199160i
$680$	−20.2684	+	6.58559i	−0.777257	+	0.252546i
$681$	−1.92455	+	8.90138i	−0.0737488	+	0.341102i
$682$		0			0
$683$			41.2946i			1.58009i	0.613047	+	0.790046i	$0.289944\pi$
$683$			41.2946i			1.58009i	−0.613047	+	0.790046i	$0.710056\pi$
$684$	−27.2539	−	3.05702i	−1.04208	−	0.116888i
$685$	17.8834	+	12.9931i	0.683290	+	0.496439i
$686$	−23.8820	−	32.8707i	−0.911817	−	1.25501i
$687$	−8.28706	−	4.82319i	−0.316171	−	0.184016i
$688$	9.94263	+	3.23056i	0.379059	+	0.123164i
$689$	19.2302	−	13.9715i	0.732611	−	0.532273i
$690$		0			0
$691$	0.799877	+	2.46177i	0.0304288	+	0.0936501i	0.965117	−	0.261817i	$-0.0843217\pi$
$691$	0.799877	+	2.46177i	0.0304288	+	0.0936501i	−0.934689	+	0.355467i	$0.884322\pi$
$692$	−42.2817			−1.60731
$693$		0			0
$694$	−3.07180			−0.116604
$695$	−1.98239	−	6.10118i	−0.0751965	−	0.231431i
$696$	−29.0736	+	25.9948i	−1.10203	+	0.985329i
$697$	24.0963	−	17.5070i	0.912711	−	0.663123i
$698$	−46.2608	−	15.0310i	−1.75100	−	0.568933i
$699$	8.12832	+	4.73080i	0.307441	+	0.178935i
$700$	−21.4932	−	29.5829i	−0.812368	−	1.11813i
$701$	16.1162	+	11.7091i	0.608700	+	0.442247i	0.848956	−	0.528463i	$-0.177231\pi$
$701$	16.1162	+	11.7091i	0.608700	+	0.442247i	−0.240256	+	0.970710i	$0.577231\pi$
$702$	13.2772	−	39.4524i	0.501116	−	1.48904i
$703$			25.6317i			0.966718i
$704$		0			0
$705$	−1.53590	+	7.10381i	−0.0578453	+	0.267545i
$706$	−21.8191	+	7.08946i	−0.821174	+	0.266815i
$707$	−0.780751	+	1.07461i	−0.0293632	+	0.0404149i
$708$	74.7356	−	32.9623i	2.80874	−	1.23880i
$709$	12.1507	−	37.3960i	0.456329	−	1.40444i	−0.413238	−	0.910623i	$-0.635602\pi$
$709$	12.1507	−	37.3960i	0.456329	−	1.40444i	0.869567	−	0.493814i	$-0.164398\pi$
$710$	7.64975	−	23.5435i	0.287090	−	0.883572i
$711$	4.43284	+	21.5951i	0.166245	+	0.809881i
$712$	−23.3566	+	32.1476i	−0.875327	+	1.20478i
$713$		0			0
$714$	−47.5396	−	10.2784i	−1.77913	−	0.384661i
$715$		0			0
$716$			85.0677i			3.17913i
$717$	17.3116	−	1.75845i	0.646515	−	0.0656705i
$718$	66.7418	+	48.4908i	2.49078	+	1.80966i
$719$	21.0728	+	29.0042i	0.785881	+	1.08167i	0.994609	+	0.103699i	$0.0330678\pi$
$719$	21.0728	+	29.0042i	0.785881	+	1.08167i	−0.208727	+	0.977974i	$0.566932\pi$
$720$	6.76527	+	6.17754i	0.252127	+	0.230223i
$721$	34.2491	+	11.1282i	1.27550	+	0.414437i
$722$	−25.1800	+	18.2944i	−0.937103	+	0.680845i
$723$	4.34330	+	4.85772i	0.161529	+	0.180661i
$724$	14.8269	+	45.6324i	0.551036	+	1.69592i
$725$	18.8096			0.698570
$726$		0			0
$727$	−28.9282			−1.07289			−0.536444	−	0.843936i	$-0.680233\pi$
$727$	−28.9282			−1.07289			−0.536444	+	0.843936i	$0.680233\pi$
$728$	−12.1277	−	37.3251i	−0.449481	−	1.38336i
$729$	−8.87941	+	25.4982i	−0.328867	+	0.944376i
$730$	19.4589	−	14.1377i	0.720207	−	0.523261i
$731$	−16.7324	−	5.43669i	−0.618870	−	0.201083i
$732$	−14.6972	+	25.2524i	−0.543226	+	0.933355i
$733$	−16.8697	−	23.2191i	−0.623095	−	0.857617i	0.374479	−	0.927236i	$-0.377822\pi$
$733$	−16.8697	−	23.2191i	−0.623095	−	0.857617i	−0.997574	+	0.0696189i	$0.977822\pi$
$734$	46.2081	+	33.5721i	1.70557	+	1.23917i
$735$	0.216923	+	2.13557i	0.00800131	+	0.0787715i
$736$		0			0
$737$		0			0
$738$	−46.9808	−	21.3114i	−1.72939	−	0.784484i
$739$	21.4234	−	6.96088i	0.788072	−	0.256060i	0.112789	−	0.993619i	$-0.464022\pi$
$739$	21.4234	−	6.96088i	0.788072	−	0.256060i	0.675283	+	0.737559i	$0.264022\pi$
$740$	28.4478	−	39.1551i	1.04576	−	1.43937i
$741$	5.72879	+	12.9889i	0.210452	+	0.477159i
$742$	−14.8653	+	45.7507i	−0.545722	+	1.67956i
$743$	−8.77184	+	26.9969i	−0.321807	+	0.990421i	0.651054	+	0.759032i	$0.274327\pi$
$743$	−8.77184	+	26.9969i	−0.321807	+	0.990421i	−0.972861	+	0.231390i	$0.925673\pi$
$744$	0.568541	+	1.28906i	0.0208437	+	0.0472591i
$745$	−6.85092	+	9.42948i	−0.250998	+	0.345470i
$746$	21.9094	−	7.11880i	0.802161	−	0.260638i
$747$	40.5290	+	18.3848i	1.48288	+	0.672664i
$748$		0			0
$749$		−	9.91451i		−	0.362268i
$750$	−4.39583	−	43.2762i	−0.160513	−	1.58022i
$751$	−3.94448	−	2.86583i	−0.143936	−	0.104576i	0.513487	−	0.858097i	$-0.328353\pi$
$751$	−3.94448	−	2.86583i	−0.143936	−	0.104576i	−0.657423	+	0.753522i	$0.728353\pi$
$752$	4.90396	+	6.74973i	0.178829	+	0.246137i
$753$	7.48079	−	12.8533i	0.272615	−	0.468400i
$754$	41.3699	+	13.4419i	1.50660	+	0.489525i
$755$	−16.5334	+	12.0122i	−0.601712	+	0.437169i
$756$	16.4023	+	52.3398i	0.596546	+	1.90358i
$757$	−2.05813	−	6.33428i	−0.0748041	−	0.230223i	0.906662	−	0.421857i	$-0.138621\pi$
$757$	−2.05813	−	6.33428i	−0.0748041	−	0.230223i	−0.981467	+	0.191634i	$0.938621\pi$
$758$	−73.2340			−2.65998
$759$		0			0
$760$	−12.5885			−0.456631
$761$	−8.93119	−	27.4874i	−0.323755	−	0.996417i	−0.971999	−	0.234984i	$-0.924496\pi$
$761$	−8.93119	−	27.4874i	−0.323755	−	0.996417i	0.648244	−	0.761433i	$-0.275504\pi$
$762$	−39.8555	−	44.5760i	−1.44381	−	1.61482i
$763$	−24.4717	+	17.7797i	−0.885936	+	0.643670i
$764$	8.79762	+	2.85852i	0.318287	+	0.103418i
$765$	−11.3852	−	10.3962i	−0.411634	−	0.375874i
$766$	13.3597	+	18.3881i	0.482707	+	0.664389i
$767$	−34.2066	−	24.8525i	−1.23513	−	0.897373i
$768$	−48.8014	+	4.95707i	−1.76097	+	0.178873i
$769$		−	11.9329i		−	0.430311i	−0.976580	−	0.215155i	$-0.930974\pi$
$769$		−	11.9329i		−	0.430311i	0.976580	−	0.215155i	$-0.0690258\pi$
$770$		0			0
$771$	39.1506	+	8.46467i	1.40998	+	0.304848i
$772$	−10.1711	+	3.30479i	−0.366066	+	0.118942i
$773$	18.1590	−	24.9937i	0.653132	−	0.898959i	−0.346098	−	0.938199i	$-0.612493\pi$
$773$	18.1590	−	24.9937i	0.653132	−	0.898959i	0.999230	+	0.0392390i	$0.0124934\pi$
$774$	6.12741	+	29.8504i	0.220245	+	1.07295i
$775$	0.209975	−	0.646235i	0.00754251	−	0.0232135i
$776$	2.90624	−	8.94448i	0.104328	−	0.321088i
$777$	46.9040	−	20.6871i	1.68267	−	0.742146i
$778$	26.8447	−	36.9486i	0.962429	−	1.32467i
$779$	16.7324	−	5.43669i	0.599500	−	0.194789i
$780$	5.66467	−	26.2001i	0.202828	−	0.938115i
$781$		0			0
$782$		0			0
$783$	−26.7407	−	8.99924i	−0.955634	−	0.321607i
$784$	1.99350	+	1.44836i	0.0711964	+	0.0517272i
$785$	−8.35103	−	11.4942i	−0.298061	−	0.410246i
$786$	48.5689	+	28.2678i	1.73240	+	1.00828i
$787$	43.3037	+	14.0702i	1.54361	+	0.501550i	0.952370	−	0.304945i	$-0.0986381\pi$
$787$	43.3037	+	14.0702i	1.54361	+	0.501550i	0.591241	+	0.806495i	$0.298638\pi$
$788$	−32.2697	+	23.4453i	−1.14956	+	0.835203i
$789$	30.3072	−	27.0978i	1.07897	−	0.964706i
$790$	6.73776	+	20.7367i	0.239719	+	0.737778i
$791$	36.6799			1.30419
$792$		0			0
$793$	15.1244			0.537082
$794$	−15.6817	−	48.2635i	−0.556524	−	1.71281i
$795$	−11.3675	+	10.1638i	−0.403165	+	0.360471i
$796$	−23.1285	+	16.8039i	−0.819770	+	0.595598i
$797$	14.6063	+	4.74587i	0.517381	+	0.168107i	0.556056	−	0.831145i	$-0.312314\pi$
$797$	14.6063	+	4.74587i	0.517381	+	0.168107i	−0.0386754	+	0.999252i	$0.512314\pi$
$798$	−24.8307	−	14.4518i	−0.878995	−	0.511588i
$799$	−8.25286	−	11.3591i	−0.291965	−	0.401855i
$800$	6.70970	+	4.87488i	0.237224	+	0.172353i
$801$	−28.5682	−	3.20444i	−1.00941	−	0.113223i
$802$		−	2.96713i		−	0.104773i
$803$		0			0
$804$	2.73205	−	12.6362i	0.0963520	−	0.445646i
$805$		0			0
$806$	0.923638	−	1.27128i	0.0325338	−	0.0447789i
$807$	25.9174	−	11.4309i	0.912335	−	0.402388i
$808$	−0.601792	+	1.85213i	−0.0211710	+	0.0651576i
$809$	−16.0251	+	49.3202i	−0.563413	+	1.73401i	0.109208	+	0.994019i	$0.465168\pi$
$809$	−16.0251	+	49.3202i	−0.563413	+	1.73401i	−0.672621	+	0.739987i	$0.734832\pi$
$810$	−5.91627	+	26.0405i	−0.207877	+	0.914971i
$811$	−15.2887	+	21.0431i	−0.536858	+	0.738922i	−0.988156	−	0.153452i	$-0.950961\pi$
$811$	−15.2887	+	21.0431i	−0.536858	+	0.738922i	0.451298	+	0.892373i	$0.350961\pi$
$812$	−54.5114	+	17.7118i	−1.91297	+	0.621563i
$813$	15.4762	+	3.34607i	0.542773	+	0.117352i
$814$		0			0
$815$		−	15.3580i		−	0.537966i
$816$	−17.6078	+	1.78854i	−0.616397	+	0.0626113i
$817$	−8.40755	−	6.10844i	−0.294143	−	0.213707i
$818$	−46.7497	−	64.3454i	−1.63456	−	2.24979i
$819$	19.1450	−	20.9664i	0.668981	−	0.732627i
$820$	−31.5945	−	10.2657i	−1.10333	−	0.358493i
$821$	−17.6732	+	12.8403i	−0.616798	+	0.448130i	−0.851802	−	0.523864i	$-0.824490\pi$
$821$	−17.6732	+	12.8403i	−0.616798	+	0.448130i	0.235003	+	0.971995i	$0.424490\pi$
$822$	49.3002	+	55.1393i	1.71954	+	1.92320i
$823$	10.1591	+	31.2666i	0.354125	+	1.08989i	0.956515	+	0.291683i	$0.0942152\pi$
$823$	10.1591	+	31.2666i	0.354125	+	1.08989i	−0.602390	+	0.798202i	$0.705785\pi$
$824$	52.7976			1.83929
$825$		0			0
$826$	85.5692			2.97733
$827$	5.81248	+	17.8890i	0.202120	+	0.622060i	0.999819	+	0.0190055i	$0.00605000\pi$
$827$	5.81248	+	17.8890i	0.202120	+	0.622060i	−0.797700	+	0.603055i	$0.793950\pi$
$828$		0			0
$829$	−15.8474	+	11.5138i	−0.550403	+	0.399891i	−0.827934	−	0.560826i	$-0.810484\pi$
$829$	−15.8474	+	11.5138i	−0.550403	+	0.399891i	0.277531	+	0.960717i	$0.410484\pi$
$830$	41.8620	+	13.6018i	1.45305	+	0.472125i
$831$	5.46803	−	9.39501i	0.189684	−	0.325909i
$832$	20.9662	+	28.8576i	0.726874	+	1.00046i
$833$	−3.35485	−	2.43744i	−0.116239	−	0.0844524i
$834$	−2.16923	−	21.3557i	−0.0751142	−	0.739486i
$835$		−	6.51626i		−	0.225505i
$836$		0			0
$837$	−0.607695	+	0.818262i	−0.0210050	+	0.0282833i
$838$	−25.1946	+	8.18621i	−0.870331	+	0.282788i
$839$	11.0173	−	15.1641i	0.380361	−	0.523522i	−0.575319	−	0.817929i	$-0.695122\pi$
$839$	11.0173	−	15.1641i	0.380361	−	0.523522i	0.955680	+	0.294407i	$0.0951222\pi$
$840$	10.1600	+	23.0359i	0.350554	+	0.794813i
$841$	0.149360	−	0.459683i	0.00515035	−	0.0158511i
$842$	−14.2021	+	43.7095i	−0.489436	+	1.50633i
$843$	0.568541	+	1.28906i	0.0195816	+	0.0443975i
$844$	−4.15627	+	5.72061i	−0.143065	+	0.196912i
$845$	2.12612	−	0.690818i	0.0731407	−	0.0237649i
$846$	−10.0463	+	22.1469i	−0.345399	+	0.761428i
$847$		0			0
$848$			17.5045i			0.601107i
$849$	1.18913	+	11.7067i	0.0408107	+	0.401774i
$850$	27.8240	+	20.2153i	0.954354	+	0.693379i
$851$		0			0
$852$	27.1283	−	46.6110i	0.929399	−	1.59687i
$853$	−40.4818	−	13.1533i	−1.38607	−	0.450362i	−0.481411	−	0.876495i	$-0.659875\pi$
$853$	−40.4818	−	13.1533i	−1.38607	−	0.450362i	−0.904660	+	0.426133i	$0.859875\pi$
$854$	−24.7628	+	17.9912i	−0.847366	+	0.615648i
$855$	−4.49836	−	7.91854i	−0.153841	−	0.270808i
$856$	−4.49184	−	13.8245i	−0.153528	−	0.472510i
$857$	−56.3029			−1.92327			−0.961635	−	0.274332i	$-0.911543\pi$
$857$	−56.3029			−1.92327			−0.961635	+	0.274332i	$0.911543\pi$
$858$		0			0
$859$	1.12436			0.0383625			0.0191813	−	0.999816i	$-0.493894\pi$
$859$	1.12436			0.0383625			0.0191813	+	0.999816i	$0.493894\pi$
$860$	6.06384	+	18.6626i	0.206775	+	0.636388i
$861$	−23.4533	−	26.2310i	−0.799285	−	0.893952i
$862$	−40.4934	+	29.4202i	−1.37921	+	1.00205i
$863$	−27.4869	−	8.93103i	−0.935665	−	0.304016i	−0.198787	−	0.980043i	$-0.563700\pi$
$863$	−27.4869	−	8.93103i	−0.935665	−	0.304016i	−0.736877	+	0.676027i	$0.763700\pi$
$864$	−7.20653	−	10.1406i	−0.245171	−	0.344989i
$865$	−8.25286	−	11.3591i	−0.280606	−	0.386220i
$866$	−25.2818	−	18.3683i	−0.859111	−	0.624181i
$867$	0.338007	−	0.0343334i	0.0114793	−	0.00116602i
$868$			2.07055i			0.0702791i
$869$		0			0
$870$	−27.2750	−	5.89706i	−0.924709	−	0.199929i
$871$	−6.36459	+	2.06798i	−0.215656	+	0.0700709i
$872$	−26.0673	+	35.8786i	−0.882750	+	1.21500i
$873$	6.66488	−	1.36810i	0.225572	−	0.0463033i
$874$		0			0
$875$	9.16831	−	28.2172i	0.309946	−	0.953914i
$876$	47.9441	−	21.1459i	1.61988	−	0.714453i
$877$	−16.9133	+	23.2792i	−0.571123	+	0.786084i	−0.992687	−	0.120715i	$-0.961481\pi$
$877$	−16.9133	+	23.2792i	−0.571123	+	0.786084i	0.421564	+	0.906799i	$0.361481\pi$
$878$	19.0897	−	6.20262i	0.644247	−	0.209328i
$879$	11.9079	−	55.0764i	0.401645	−	1.85768i
$880$		0			0
$881$			13.6325i			0.459289i	0.973275	+	0.229644i	$0.0737563\pi$
$881$			13.6325i			0.459289i	−0.973275	+	0.229644i	$0.926244\pi$
$882$	−0.800628	+	7.13775i	−0.0269585	+	0.240340i
$883$	9.27465	+	6.73843i	0.312117	+	0.226766i	0.732804	−	0.680439i	$-0.238211\pi$
$883$	9.27465	+	6.73843i	0.312117	+	0.226766i	−0.420687	+	0.907206i	$0.638211\pi$
$884$	30.4380	+	41.8943i	1.02374	+	1.40906i
$885$	23.4429	+	13.6441i	0.788024	+	0.458641i
$886$	−58.0987	−	18.8774i	−1.95186	−	0.634199i
$887$	−36.6625	+	26.6369i	−1.23101	+	0.894378i	−0.996965	−	0.0778484i	$-0.975195\pi$
$887$	−36.6625	+	26.6369i	−1.23101	+	0.894378i	−0.234041	+	0.972227i	$0.575195\pi$
$888$	56.0289	−	50.0956i	1.88021	−	1.68110i
$889$	−12.6031	−	38.7885i	−0.422696	−	1.30092i
$890$	−28.4323			−0.953053
$891$		0			0
$892$	48.2487			1.61549
$893$	−2.56288	−	7.88773i	−0.0857635	−	0.263953i
$894$	−29.0736	+	25.9948i	−0.972365	+	0.869395i
$895$	−22.8537	+	16.6042i	−0.763915	+	0.555016i
$896$	−55.7747	−	18.1223i	−1.86330	−	0.605423i
$897$		0			0
$898$	−56.7102	−	78.0548i	−1.89244	−	2.60472i
$899$	−0.861667	−	0.626038i	−0.0287382	−	0.0208795i
$900$	4.32328	−	38.5429i	0.144109	−	1.28476i
$901$		−	29.4582i		−	0.981397i
$902$		0			0
$903$	−4.39230	+	20.3152i	−0.146167	+	0.676048i
$904$	51.1452	−	16.6181i	1.70107	−	0.552710i
$905$	−9.36525	+	12.8902i	−0.311312	+	0.428484i
$906$	−62.5663	+	27.5950i	−2.07863	+	0.916783i
$907$	−8.17191	+	25.1506i	−0.271344	+	0.835111i	0.718820	+	0.695196i	$0.244683\pi$
$907$	−8.17191	+	25.1506i	−0.271344	+	0.835111i	−0.990164	+	0.139914i	$0.955317\pi$
$908$	−6.06384	+	18.6626i	−0.201235	+	0.619339i
$909$	−1.38009	+	0.283292i	−0.0457747	+	0.00939620i
$910$	16.5057	−	22.7182i	0.547159	−	0.753100i
$911$	−30.2446	+	9.82708i	−1.00205	+	0.325586i	−0.763684	−	0.645590i	$-0.776612\pi$
$911$	−30.2446	+	9.82708i	−1.00205	+	0.325586i	−0.238365	+	0.971176i	$0.576612\pi$
$912$	−10.2182	−	2.20925i	−0.338358	−	0.0731557i
$913$		0			0
$914$			44.1053i			1.45887i
$915$	−9.65285	+	0.980500i	−0.319113	+	0.0324143i
$916$	−16.7145	−	12.1438i	−0.552263	−	0.401242i
$917$	22.5297	+	31.0094i	0.743995	+	1.02402i
$918$	−29.8842	−	42.0512i	−0.986326	−	1.38790i
$919$	−37.1064	−	12.0566i	−1.22403	−	0.397710i	−0.375480	−	0.926831i	$-0.622522\pi$
$919$	−37.1064	−	12.0566i	−1.22403	−	0.397710i	−0.848547	+	0.529120i	$0.822522\pi$
$920$		0			0
$921$	−36.0044	−	40.2688i	−1.18639	−	1.32690i
$922$	−2.11875	−	6.52083i	−0.0697772	−	0.214752i
$923$	−27.9166			−0.918887
$924$		0			0
$925$	−36.2487			−1.19185
$926$	−0.938079	−	2.88711i	−0.0308272	−	0.0948763i
$927$	18.8667	+	33.2114i	0.619663	+	1.09080i
$928$	10.5172	−	7.64121i	0.345245	−	0.250835i
$929$	30.3912	+	9.87471i	0.997104	+	0.323979i	0.761708	−	0.647921i	$-0.224361\pi$
$929$	30.3912	+	9.87471i	0.997104	+	0.323979i	0.235396	+	0.971900i	$0.424361\pi$
$930$	−0.507079	+	0.871249i	−0.0166278	+	0.0285694i
$931$	−1.43977	−	1.98168i	−0.0471867	−	0.0649469i
$932$	16.3943	+	11.9112i	0.537014	+	0.390163i
$933$	0.116249	+	1.14445i	0.00380581	+	0.0374675i
$934$			46.4660i			1.52041i
$935$		0			0
$936$	17.1962	−	37.9087i	0.562074	−	1.23908i
$937$	−27.1991	+	8.83753i	−0.888556	+	0.288709i	−0.717506	−	0.696553i	$-0.754716\pi$
$937$	−27.1991	+	8.83753i	−0.888556	+	0.288709i	−0.171051	+	0.985262i	$0.554716\pi$
$938$	7.96065	−	10.9569i	0.259925	−	0.357755i
$939$	−5.16693	−	11.7150i	−0.168616	−	0.382305i
$940$	−4.83928	+	14.8938i	−0.157840	+	0.485782i
$941$	−0.633603	+	1.95003i	−0.0206549	+	0.0635692i	−0.960853	−	0.277060i	$-0.910640\pi$
$941$	−0.633603	+	1.95003i	−0.0206549	+	0.0635692i	0.940198	+	0.340629i	$0.110640\pi$
$942$	−19.1844	−	43.4968i	−0.625061	−	1.41720i
$943$		0			0
$944$	29.6130	−	9.62185i	0.963821	−	0.313165i
$945$	−10.8597	+	14.6226i	−0.353266	+	0.475674i
$946$		0			0
$947$		−	30.2297i		−	0.982334i	−0.871065	−	0.491167i	$-0.836571\pi$
$947$		−	30.2297i		−	0.982334i	0.871065	−	0.491167i	$-0.163429\pi$
$948$	4.80030	+	47.2581i	0.155906	+	1.53487i
$949$	−21.9441	−	15.9433i	−0.712334	−	0.517541i
$950$	11.9410	+	16.4353i	0.387417	+	0.533233i
$951$	−21.4401	+	36.8379i	−0.695244	+	1.19455i
$952$	−46.2575	−	15.0300i	−1.49922	−	0.487125i
$953$	44.5493	−	32.3669i	1.44309	−	1.04847i	0.455707	−	0.890130i	$-0.349386\pi$
$953$	44.5493	−	32.3669i	1.44309	−	1.04847i	0.987385	−	0.158338i	$-0.0506136\pi$
$954$	−44.3644	+	25.2025i	−1.43635	+	0.815960i
$955$	0.949237	+	2.92145i	0.0307166	+	0.0945360i
$956$	37.4933			1.21262
$957$		0			0
$958$	15.6603			0.505960
$959$	15.5897	+	47.9803i	0.503419	+	1.54936i
$960$	−15.2521	−	17.0586i	−0.492261	−	0.550564i
$961$	25.0484	−	18.1987i	0.808013	−	0.587056i
$962$	−79.7256	−	25.9044i	−2.57046	−	0.835192i
$963$	7.09091	−	7.76554i	0.228502	−	0.250241i
$964$	8.25286	+	11.3591i	0.265807	+	0.365851i
$965$	−2.87312	−	2.08744i	−0.0924889	−	0.0671971i
$966$		0			0
$967$			45.0518i			1.44877i	0.689397	+	0.724383i	$0.257875\pi$
$967$			45.0518i			1.44877i	−0.689397	+	0.724383i	$0.742125\pi$
$968$		0			0
$969$	17.1962	+	3.71794i	0.552420	+	0.119437i
$970$	6.39994	−	2.07947i	0.205490	−	0.0667676i
$971$	−4.37070	+	6.01575i	−0.140262	+	0.193055i	−0.873369	−	0.487059i	$-0.838070\pi$
$971$	−4.37070	+	6.01575i	−0.140262	+	0.193055i	0.733107	+	0.680114i	$0.238070\pi$
$972$	−24.5866	+	52.7262i	−0.788617	+	1.69119i
$973$	4.52432	−	13.9244i	0.145043	−	0.446397i
$974$	24.5456	−	75.5435i	0.786491	−	2.42057i
$975$	−18.3691	+	8.10173i	−0.588282	+	0.259463i
$976$	−6.54666	+	9.01070i	−0.209553	+	0.288426i
$977$	−10.6079	+	3.44672i	−0.339377	+	0.110270i	−0.473747	−	0.880661i	$-0.657099\pi$
$977$	−10.6079	+	3.44672i	−0.339377	+	0.110270i	0.134370	+	0.990931i	$0.457099\pi$
$978$	10.8597	−	50.2281i	0.347255	−	1.60612i
$979$		0			0
$980$			4.62518i			0.147746i
$981$	−31.8837	−	3.57633i	−1.01797	−	0.114183i
$982$	40.4934	+	29.4202i	1.29220	+	0.938835i
$983$	0.285775	+	0.393335i	0.00911479	+	0.0125454i	0.813550	−	0.581495i	$-0.197532\pi$
$983$	0.285775	+	0.393335i	0.00911479	+	0.0125454i	−0.804435	+	0.594040i	$0.797532\pi$
$984$	−44.5866	−	25.9500i	−1.42137	−	0.827257i
$985$	−12.5973	−	4.09310i	−0.401383	−	0.130417i
$986$	43.6131	−	31.6867i	1.38892	−	1.00911i
$987$	−12.3654	+	11.0560i	−0.393596	+	0.351915i
$988$	9.45235	+	29.0914i	0.300719	+	0.925519i
$989$		0			0
$990$		0			0
$991$	19.8564			0.630760			0.315380	−	0.948966i	$-0.397868\pi$
$991$	19.8564			0.630760			0.315380	+	0.948966i	$0.397868\pi$
$992$	−0.145121	−	0.446637i	−0.00460760	−	0.0141807i
$993$	0.506545	−	0.452903i	0.0160747	−	0.0143725i
$994$	45.7074	−	33.2084i	1.44975	−	1.05330i
$995$	−9.02881	−	2.93364i	−0.286233	−	0.0930026i
$996$	82.8776	+	48.2359i	2.62608	+	1.52841i
$997$	35.5430	+	48.9208i	1.12566	+	1.54934i	0.796062	+	0.605215i	$0.206913\pi$
$997$	35.5430	+	48.9208i	1.12566	+	1.54934i	0.329597	+	0.944122i	$0.393087\pi$
$998$	−49.9801	−	36.3127i	−1.58209	−	1.14946i
$999$	51.5331	+	17.3428i	1.63043	+	0.548702i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	363.2.f.i.215.7		32
3.2	odd	2	inner	363.2.f.i.215.2		32
11.2	odd	10	inner	363.2.f.i.233.2		32
11.3	even	5		363.2.d.e.362.7	yes	8
11.4	even	5	inner	363.2.f.i.239.2		32
11.5	even	5	inner	363.2.f.i.161.1		32
11.6	odd	10	inner	363.2.f.i.161.7		32
11.7	odd	10	inner	363.2.f.i.239.8		32
11.8	odd	10		363.2.d.e.362.1	✓	8
11.9	even	5	inner	363.2.f.i.233.8		32
11.10	odd	2	inner	363.2.f.i.215.1		32
33.2	even	10	inner	363.2.f.i.233.7		32
33.5	odd	10	inner	363.2.f.i.161.8		32
33.8	even	10		363.2.d.e.362.8	yes	8
33.14	odd	10		363.2.d.e.362.2	yes	8
33.17	even	10	inner	363.2.f.i.161.2		32
33.20	odd	10	inner	363.2.f.i.233.1		32
33.26	odd	10	inner	363.2.f.i.239.7		32
33.29	even	10	inner	363.2.f.i.239.1		32
33.32	even	2	inner	363.2.f.i.215.8		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
363.2.d.e.362.1	✓	8	11.8	odd	10
363.2.d.e.362.2	yes	8	33.14	odd	10
363.2.d.e.362.7	yes	8	11.3	even	5
363.2.d.e.362.8	yes	8	33.8	even	10
363.2.f.i.161.1		32	11.5	even	5	inner
363.2.f.i.161.2		32	33.17	even	10	inner
363.2.f.i.161.7		32	11.6	odd	10	inner
363.2.f.i.161.8		32	33.5	odd	10	inner
363.2.f.i.215.1		32	11.10	odd	2	inner
363.2.f.i.215.2		32	3.2	odd	2	inner
363.2.f.i.215.7		32	1.1	even	1	trivial
363.2.f.i.215.8		32	33.32	even	2	inner
363.2.f.i.233.1		32	33.20	odd	10	inner
363.2.f.i.233.2		32	11.2	odd	10	inner
363.2.f.i.233.7		32	33.2	even	10	inner
363.2.f.i.233.8		32	11.9	even	5	inner
363.2.f.i.239.1		32	33.29	even	10	inner
363.2.f.i.239.2		32	11.4	even	5	inner
363.2.f.i.239.7		32	33.26	odd	10	inner
363.2.f.i.239.8		32	11.7	odd	10	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 363 = 3 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	363.f (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.739839 + 2.27699i) q^{2} +(-1.29120 + 1.15447i) q^{3} +(-3.01929 + 2.19364i) q^{4} +(-1.17866 - 0.382969i) q^{5} +(-3.58400 - 2.08594i) q^{6} +(-1.66251 - 2.28825i) q^{7} +(-3.35485 - 2.43744i) q^{8} +(0.334407 - 2.98130i) q^{9} +O(q^{10})\)	\(q+(0.739839 + 2.27699i) q^{2} +(-1.29120 + 1.15447i) q^{3} +(-3.01929 + 2.19364i) q^{4} +(-1.17866 - 0.382969i) q^{5} +(-3.58400 - 2.08594i) q^{6} +(-1.66251 - 2.28825i) q^{7} +(-3.35485 - 2.43744i) q^{8} +(0.334407 - 2.98130i) q^{9} -2.96713i q^{10} +(1.36603 - 6.31812i) q^{12} +(-3.18230 + 1.03399i) q^{13} +(3.98033 - 5.47845i) q^{14} +(1.96401 - 0.866232i) q^{15} +(0.761449 - 2.34350i) q^{16} +(-1.28144 + 3.94386i) q^{17} +(7.03581 - 1.44424i) q^{18} +(-1.43977 + 1.98168i) q^{19} +(4.39881 - 1.42926i) q^{20} +(4.78834 + 1.03528i) q^{21} +(7.14574 - 0.725837i) q^{24} +(-2.80252 - 2.03615i) q^{25} +(-4.70878 - 6.48108i) q^{26} +(3.01003 + 4.23553i) q^{27} +(10.0392 + 3.26193i) q^{28} +(-4.39285 + 3.19159i) q^{29} +(3.42545 + 3.83116i) q^{30} +(0.0606144 + 0.186552i) q^{31} -2.39417 q^{32} -9.92820 q^{34} +(1.08320 + 3.33375i) q^{35} +(5.53025 + 9.73500i) q^{36} +(8.46564 - 6.15064i) q^{37} +(-5.57747 - 1.81223i) q^{38} +(2.91528 - 5.00895i) q^{39} +(3.02076 + 4.15771i) q^{40} +(-5.81077 - 4.22177i) q^{41} +(1.18529 + 11.6689i) q^{42} +4.24264i q^{43} +(-1.53590 + 3.38587i) q^{45} +(-1.99016 + 2.73922i) q^{47} +(1.72231 + 3.90500i) q^{48} +(-0.309017 + 0.951057i) q^{49} +(2.56288 - 7.88773i) q^{50} +(-2.89847 - 6.57171i) q^{51} +(7.34008 - 10.1027i) q^{52} +(-6.75612 + 2.19520i) q^{53} +(-7.41732 + 9.98743i) q^{54} +11.7290i q^{56} +(-0.428745 - 4.22092i) q^{57} +(-10.5172 - 7.64121i) q^{58} +(7.42739 + 10.2229i) q^{59} +(-4.02972 + 6.92375i) q^{60} +(-4.29882 - 1.39677i) q^{61} +(-0.379932 + 0.276037i) q^{62} +(-7.37791 + 4.19123i) q^{63} +(-3.29420 - 10.1385i) q^{64} +4.14682 q^{65} +2.00000 q^{67} +(-4.78240 - 14.7187i) q^{68} +(-6.78952 + 4.93287i) q^{70} +(7.93478 + 2.57817i) q^{71} +(-8.38864 + 9.18673i) q^{72} +(4.76479 + 6.55817i) q^{73} +(20.2682 + 14.7257i) q^{74} +(5.96928 - 0.606337i) q^{75} -9.14162i q^{76} +(13.5622 + 2.93225i) q^{78} +(-6.98881 + 2.27080i) q^{79} +(-1.79498 + 2.47057i) q^{80} +(-8.77634 - 1.99394i) q^{81} +(5.31390 - 16.3545i) q^{82} +(-4.58416 + 14.1086i) q^{83} +(-16.7284 + 7.37811i) q^{84} +(3.02076 - 4.15771i) q^{85} +(-9.66046 + 3.13887i) q^{86} +(1.98747 - 9.19239i) q^{87} -9.58244i q^{89} +(-8.84591 - 0.992229i) q^{90} +(7.65662 + 5.56286i) q^{91} +(-0.293634 - 0.170899i) q^{93} +(-7.70959 - 2.50500i) q^{94} +(2.45592 - 1.78433i) q^{95} +(3.09136 - 2.76399i) q^{96} +(0.700835 + 2.15695i) q^{97} -2.39417 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 4 q^{3} - 16 q^{4} + 8 q^{9}+O(q^{10}) \) 32 * q + 4 * q^3 - 16 * q^4 + 8 * q^9	\( 32 q + 4 q^{3} - 16 q^{4} + 8 q^{9} + 16 q^{12} - 4 q^{15} + 8 q^{16} + 4 q^{27} + 40 q^{31} - 96 q^{34} + 40 q^{36} + 56 q^{37} - 64 q^{42} - 160 q^{45} - 28 q^{48} + 8 q^{49} - 104 q^{58} + 28 q^{60} + 16 q^{64} + 64 q^{67} + 16 q^{70} - 24 q^{75} + 240 q^{78} + 8 q^{81} - 96 q^{82} + 48 q^{91} - 56 q^{93} - 32 q^{97}+O(q^{100}) \) 32 * q + 4 * q^3 - 16 * q^4 + 8 * q^9 + 16 * q^12 - 4 * q^15 + 8 * q^16 + 4 * q^27 + 40 * q^31 - 96 * q^34 + 40 * q^36 + 56 * q^37 - 64 * q^42 - 160 * q^45 - 28 * q^48 + 8 * q^49 - 104 * q^58 + 28 * q^60 + 16 * q^64 + 64 * q^67 + 16 * q^70 - 24 * q^75 + 240 * q^78 + 8 * q^81 - 96 * q^82 + 48 * q^91 - 56 * q^93 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

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