LMFDB - Embedded newform 363.2.f.i.215.2

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			215.2
Character	$\chi$	$=$	363.215
Dual form			363.2.f.i.233.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.739839 - 2.27699i) q^{2} +(0.698961 - 1.58476i) q^{3} +(-3.01929 + 2.19364i) q^{4} +(1.17866 + 0.382969i) q^{5} +(-4.12560 - 0.419062i) q^{6} +(-1.66251 - 2.28825i) q^{7} +(3.35485 + 2.43744i) q^{8} +(-2.02291 - 2.21537i) q^{9} +O(q^{10})$	\(q+(-0.739839 - 2.27699i) q^{2} +(0.698961 - 1.58476i) q^{3} +(-3.01929 + 2.19364i) q^{4} +(1.17866 + 0.382969i) q^{5} +(-4.12560 - 0.419062i) q^{6} +(-1.66251 - 2.28825i) q^{7} +(3.35485 + 2.43744i) q^{8} +(-2.02291 - 2.21537i) q^{9} -2.96713i q^{10} +(1.36603 + 6.31812i) q^{12} +(-3.18230 + 1.03399i) q^{13} +(-3.98033 + 5.47845i) q^{14} +(1.43075 - 1.60020i) q^{15} +(0.761449 - 2.34350i) q^{16} +(1.28144 - 3.94386i) q^{17} +(-3.54774 + 6.24516i) q^{18} +(-1.43977 + 1.98168i) q^{19} +(-4.39881 + 1.42926i) q^{20} +(-4.78834 + 1.03528i) q^{21} +(6.20766 - 3.61295i) q^{24} +(-2.80252 - 2.03615i) q^{25} +(4.70878 + 6.48108i) q^{26} +(-4.92475 + 1.65736i) q^{27} +(10.0392 + 3.26193i) q^{28} +(4.39285 - 3.19159i) q^{29} +(-4.70218 - 2.07391i) q^{30} +(0.0606144 + 0.186552i) q^{31} +2.39417 q^{32} -9.92820 q^{34} +(-1.08320 - 3.33375i) q^{35} +(10.9675 + 2.25130i) q^{36} +(8.46564 - 6.15064i) q^{37} +(5.57747 + 1.81223i) q^{38} +(-0.585677 + 5.76589i) q^{39} +(3.02076 + 4.15771i) q^{40} +(5.81077 + 4.22177i) q^{41} +(5.89992 + 10.1371i) q^{42} +4.24264i q^{43} +(-1.53590 - 3.38587i) q^{45} +(1.99016 - 2.73922i) q^{47} +(-3.18165 - 2.84473i) q^{48} +(-0.309017 + 0.951057i) q^{49} +(-2.56288 + 7.88773i) q^{50} +(-5.35439 - 4.78738i) q^{51} +(7.34008 - 10.1027i) q^{52} +(6.75612 - 2.19520i) q^{53} +(7.41732 + 9.98743i) q^{54} -11.7290i q^{56} +(2.13413 + 3.66681i) q^{57} +(-10.5172 - 7.64121i) q^{58} +(-7.42739 - 10.2229i) q^{59} +(-0.809566 + 7.97004i) q^{60} +(-4.29882 - 1.39677i) q^{61} +(0.379932 - 0.276037i) q^{62} +(-1.70620 + 8.31197i) 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} +(-1.38673 - 12.3629i) q^{72} +(4.76479 + 6.55817i) q^{73} +(-20.2682 - 14.7257i) q^{74} +(-5.18565 + 3.01812i) q^{75} -9.14162i q^{76} +(13.5622 - 2.93225i) q^{78} +(-6.98881 + 2.27080i) q^{79} +(1.79498 - 2.47057i) q^{80} +(-0.815691 + 8.96296i) q^{81} +(5.31390 - 16.3545i) q^{82} +(4.58416 - 14.1086i) q^{83} +(12.1864 - 13.6297i) q^{84} +(3.02076 - 4.15771i) q^{85} +(9.66046 - 3.13887i) q^{86} +(-1.98747 - 9.19239i) q^{87} +9.58244i q^{89} +(-6.57327 + 6.00223i) q^{90} +(7.65662 + 5.56286i) q^{91} +(0.338007 + 0.0343334i) q^{93} +(-7.70959 - 2.50500i) q^{94} +(-2.45592 + 1.78433i) q^{95} +(1.67343 - 3.79418i) 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	$-0.778725\pi$
$2$	−0.739839	−	2.27699i	−0.523145	−	1.61008i	0.244809	−	0.969571i	$-0.421275\pi$
$3$	0.698961	−	1.58476i	0.403545	−	0.914960i
$3$	0.698961	−	1.58476i	0.403545	−	0.914960i
$4$	−3.01929	+	2.19364i	−1.50965	+	1.09682i
$5$	1.17866	+	0.382969i	0.527112	+	0.171269i	0.560470	−	0.828175i	$-0.310620\pi$
$5$	1.17866	+	0.382969i	0.527112	+	0.171269i	−0.0333587	+	0.999443i	$0.510620\pi$
$6$	−4.12560	−	0.419062i	−1.68427	−	0.171082i
$7$	−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
$9$	−2.02291	−	2.21537i	−0.674302	−	0.738455i
$10$		−	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
$15$	1.43075	−	1.60020i	0.369418	−	0.413171i
$16$	0.761449	−	2.34350i	0.190362	−	0.585875i
$17$	1.28144	−	3.94386i	0.310795	−	0.956528i	−0.666656	−	0.745365i	$-0.732275\pi$
$17$	1.28144	−	3.94386i	0.310795	−	0.956528i	0.977451	−	0.211162i	$-0.0677249\pi$
$18$	−3.54774	+	6.24516i	−0.836211	+	1.47200i
$19$	−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			$\pi$
$24$	6.20766	−	3.61295i	1.26713	−	0.737490i
$25$	−2.80252	−	2.03615i	−0.560503	−	0.407230i
$26$	4.70878	+	6.48108i	0.923467	+	1.27104i
$27$	−4.92475	+	1.65736i	−0.947768	+	0.318960i
$28$	10.0392	+	3.26193i	1.89723	+	0.616447i
$29$	4.39285	−	3.19159i	0.815731	−	0.592663i	−0.0997555	−	0.995012i	$-0.531806\pi$
$29$	4.39285	−	3.19159i	0.815731	−	0.592663i	0.915486	+	0.402349i	$0.131806\pi$
$30$	−4.70218	−	2.07391i	−0.858496	−	0.378642i
$31$	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
$36$	10.9675	+	2.25130i	1.82791	+	0.375216i
$37$	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
$39$	−0.585677	+	5.76589i	−0.0937834	+	0.923281i
$40$	3.02076	+	4.15771i	0.477623	+	0.657392i
$41$	5.81077	+	4.22177i	0.907490	+	0.659330i	0.940379	−	0.340129i	$-0.110471\pi$
$41$	5.81077	+	4.22177i	0.907490	+	0.659330i	−0.0328886	+	0.999459i	$0.510471\pi$
$42$	5.89992	+	10.1371i	0.910377	+	1.56418i
$43$			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	−0.638815	−	0.769361i	$-0.720575\pi$
$47$	1.99016	−	2.73922i	0.290295	−	0.399557i	0.929110	+	0.369804i	$0.120575\pi$
$48$	−3.18165	−	2.84473i	−0.459232	−	0.410601i
$49$	−0.309017	+	0.951057i	−0.0441453	+	0.135865i
$50$	−2.56288	+	7.88773i	−0.362446	+	1.11549i
$51$	−5.35439	−	4.78738i	−0.749765	−	0.670367i
$52$	7.34008	−	10.1027i	1.01789	−	1.40100i
$53$	6.75612	−	2.19520i	0.928025	−	0.301534i	0.194270	−	0.980948i	$-0.437766\pi$
$53$	6.75612	−	2.19520i	0.928025	−	0.301534i	0.733755	+	0.679414i	$0.237766\pi$
$54$	7.41732	+	9.98743i	1.00937	+	1.35912i
$55$		0			0
$56$		−	11.7290i		−	1.56735i
$57$	2.13413	+	3.66681i	0.282673	+	0.485680i
$58$	−10.5172	−	7.64121i	−1.38098	−	1.00334i
$59$	−7.42739	−	10.2229i	−0.966964	−	1.33091i	−0.943566	−	0.331185i	$-0.892551\pi$
$59$	−7.42739	−	10.2229i	−0.966964	−	1.33091i	−0.0233981	−	0.999726i	$-0.507449\pi$
$60$	−0.809566	+	7.97004i	−0.104515	+	1.02893i
$61$	−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
$63$	−1.70620	+	8.31197i	−0.214961	+	1.04721i
$64$	−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	−0.202353	−	0.979313i	$-0.564859\pi$
$71$	−7.93478	−	2.57817i	−0.941685	−	0.305972i	−0.739332	+	0.673341i	$0.764859\pi$
$72$	−1.38673	−	12.3629i	−0.163427	−	1.45699i
$73$	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
$75$	−5.18565	+	3.01812i	−0.598787	+	0.348502i
$76$		−	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
$81$	−0.815691	+	8.96296i	−0.0906323	+	0.995884i
$82$	5.31390	−	16.3545i	0.586822	−	1.80605i
$83$	4.58416	−	14.1086i	0.503177	−	1.54862i	−0.300638	−	0.953738i	$-0.597200\pi$
$83$	4.58416	−	14.1086i	0.503177	−	1.54862i	0.803815	−	0.594880i	$-0.202800\pi$
$84$	12.1864	−	13.6297i	1.32964	−	1.48712i
$85$	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	$0.169566\pi$
$89$			9.58244i			1.01574i	−0.861435	+	0.507868i	$0.830434\pi$
$90$	−6.57327	+	6.00223i	−0.692884	+	0.632690i
$91$	7.65662	+	5.56286i	0.802632	+	0.583146i
$92$		0			0
$93$	0.338007	+	0.0343334i	0.0350497	+	0.00356021i
$94$	−7.70959	−	2.50500i	−0.795184	−	0.258371i
$95$	−2.45592	+	1.78433i	−0.251972	+	0.183069i
$96$	1.67343	−	3.79418i	0.170794	−	0.387242i
$97$	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	0.958017	−	0.286712i	$-0.0925621\pi$
$101$	0.145121	+	0.446637i	0.0144401	+	0.0444421i	−0.943577	+	0.331154i	$0.892562\pi$
$102$	−6.93943	+	15.7338i	−0.687105	+	1.55788i
$103$	−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
$105$	−6.04029	−	0.613550i	−0.589472	−	0.0598763i
$106$	−9.99689	−	13.7595i	−0.970984	−	1.33644i
$107$	−2.83585	−	2.06037i	−0.274152	−	0.199183i	0.442210	−	0.896911i	$-0.354194\pi$
$107$	−2.83585	−	2.06037i	−0.274152	−	0.199183i	−0.716363	+	0.697728i	$0.754194\pi$
$108$	11.2336	−	15.8072i	1.08095	−	1.52105i
$109$		−	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	$-0.591178\pi$
$113$	7.62258	−	10.4916i	0.717072	−	0.986965i	0.999616	−	0.0277104i	$-0.00882162\pi$
$114$	6.77037	−	7.57225i	0.634103	−	0.709206i
$115$		0			0
$116$	−6.26207	+	19.2727i	−0.581419	+	1.78942i
$117$	8.72816	+	4.95828i	0.806919	+	0.458394i
$118$	−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
$123$	10.7520	−	6.25781i	0.969474	−	0.564247i
$124$	−0.592242	−	0.430289i	−0.0531849	−	0.0386411i
$125$	−6.16568	−	8.48633i	−0.551475	−	0.759040i
$126$	20.1886	−	2.26452i	1.79854	−	0.201739i
$127$	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
$129$	6.72355	+	2.96544i	0.591976	+	0.261092i
$130$	3.06798	+	9.44228i	0.269080	+	0.828143i
$131$	13.5516			1.18401			0.592005	−	0.805934i	$-0.298337\pi$
$131$	13.5516			1.18401			0.592005	+	0.805934i	$0.298337\pi$
$132$		0			0
$133$	6.92820			0.600751
$134$	−1.47968	−	4.55398i	−0.127825	−	0.393404i
$135$	−6.43931	+	0.0674361i	−0.554208	+	0.00580398i
$136$	13.9120	−	10.1076i	1.19294	−	0.866723i
$137$	16.9636	+	5.51181i	1.44930	+	0.470905i	0.924783	−	0.380496i	$-0.124247\pi$
$137$	16.9636	+	5.51181i	1.44930	+	0.470905i	0.524515	+	0.851401i	$0.324247\pi$
$138$		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
$141$	−2.94996	−	5.06854i	−0.248431	−	0.426848i
$142$			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
$147$	1.29120	+	1.15447i	0.106497	+	0.0952189i
$148$	−12.0679	+	37.1412i	−0.991976	+	3.05299i
$149$	−2.90624	+	8.94448i	−0.238088	+	0.732761i	0.758608	+	0.651547i	$0.225880\pi$
$149$	−2.90624	+	8.94448i	−0.238088	+	0.732761i	−0.996697	+	0.0812137i	$0.974120\pi$
$150$	10.7088	+	9.57475i	0.874368	+	0.781775i
$151$	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
$156$	−10.8800	−	18.6937i	−0.871095	−	1.49669i
$157$	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
$159$	1.24341	−	12.2412i	0.0986090	−	0.970788i
$160$	2.82191	+	0.916893i	0.223091	+	0.0724868i
$161$		0			0
$162$	21.0121	−	4.77383i	1.65086	−	0.375067i
$163$	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	0.868303	−	0.496035i	$-0.165211\pi$
$167$	−1.62480	−	5.00062i	−0.125731	−	0.386960i	−0.994034	+	0.109075i	$0.965211\pi$
$168$	−18.5876	−	8.19811i	−1.43406	−	0.632498i
$169$	−1.45934	+	1.06028i	−0.112257	+	0.0815596i
$170$	−11.7019	−	3.80219i	−0.897499	−	0.291615i
$171$	7.30267	−	0.819127i	0.558449	−	0.0626402i
$172$	−9.30685	−	12.8098i	−0.709640	−	0.976736i
$173$	−9.16562	−	6.65922i	−0.696850	−	0.506291i	0.182055	−	0.983288i	$-0.441725\pi$
$173$	−9.16562	−	6.65922i	−0.696850	−	0.506291i	−0.878905	+	0.476998i	$0.841725\pi$
$174$	−19.4606	+	11.3263i	−1.47530	+	0.858647i
$175$			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	$0.524517\pi$
$179$	−13.3979	+	18.4406i	−1.00140	+	1.37832i	−0.924460	+	0.381280i	$0.875483\pi$
$180$	12.0647	+	6.85371i	0.899251	+	0.510845i
$181$	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
$183$	−5.21824	+	5.83629i	−0.385744	+	0.431431i
$184$		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
$189$	11.9799	+	8.51366i	0.871408	+	0.619277i
$190$	5.87989	+	4.27199i	0.426572	+	0.309923i
$191$	1.45690	+	2.00525i	0.105418	+	0.145095i	0.858466	−	0.512870i	$-0.171418\pi$
$191$	1.45690	+	2.00525i	0.105418	+	0.145095i	−0.753049	+	0.657965i	$0.771418\pi$
$192$	−18.3696	−	1.86591i	−1.32571	−	0.134661i
$193$	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
$195$	−2.89847	+	6.57171i	−0.207564	+	0.470610i
$196$	−1.15327	−	3.54939i	−0.0823762	−	0.253528i
$197$	−10.6878			−0.761476			−0.380738	−	0.924683i	$-0.624330\pi$
$197$	−10.6878			−0.761476			−0.380738	+	0.924683i	$0.624330\pi$
$198$		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
$201$	1.39792	−	3.16951i	0.0986018	−	0.223560i
$202$	0.909623	−	0.660880i	0.0640008	−	0.0464993i
$203$	−14.6063	−	4.74587i	−1.02516	−	0.333095i
$204$	26.6683	+	2.70886i	1.86715	+	0.189658i
$205$	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
$213$	−9.63187	+	10.7727i	−0.659965	+	0.738130i
$214$	−2.59336	+	7.98156i	−0.177279	+	0.545608i
$215$	−1.62480	+	5.00062i	−0.110810	+	0.341039i
$216$	−20.5615	−	6.44359i	−1.39903	−	0.438431i
$217$	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
$222$	−37.5033	+	21.8274i	−2.51706	+	1.46496i
$223$	−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
$225$	1.15842	+	10.3275i	0.0772280	+	0.688503i
$226$	−29.5287	−	9.59446i	−1.96422	−	0.638214i
$227$	−4.25378	+	3.09055i	−0.282333	+	0.205127i	−0.719935	−	0.694042i	$-0.755828\pi$
$227$	−4.25378	+	3.09055i	−0.282333	+	0.205127i	0.437601	+	0.899169i	$0.355828\pi$
$228$	−14.4872	−	6.38963i	−0.959441	−	0.423164i
$229$	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	0.990855	−	0.134934i	$-0.0430823\pi$
$233$	1.67792	+	5.16410i	0.109924	+	0.338311i	−0.880931	+	0.473246i	$0.843082\pi$
$234$	4.83253	−	23.5423i	0.315913	−	1.53901i
$235$	3.39476	−	2.46644i	0.221450	−	0.160893i
$236$	44.8509	+	14.5729i	2.91955	+	0.948618i
$237$	−1.28624	+	12.6628i	−0.0835500	+	0.822535i
$238$	16.5057	+	22.7182i	1.06991	+	1.47260i
$239$	8.12763	+	5.90507i	0.525733	+	0.381967i	0.818759	−	0.574137i	$-0.194662\pi$
$239$	8.12763	+	5.90507i	0.525733	+	0.381967i	−0.293026	+	0.956104i	$0.594662\pi$
$240$	−2.66064	−	4.57143i	−0.171743	−	0.295085i
$241$		−	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
$246$	−22.2037	−	19.8524i	−1.41566	−	1.26574i
$247$	2.53275	−	7.79500i	0.161155	−	0.495984i
$248$	−0.251357	+	0.773599i	−0.0159612	+	0.0491236i
$249$	−19.1545	−	17.1261i	−1.21387	−	1.08532i
$250$	−14.7617	+	20.3177i	−0.933611	+	1.28500i
$251$	8.16598	−	2.65329i	0.515432	−	0.167474i	−0.0397393	−	0.999210i	$-0.512653\pi$
$251$	8.16598	−	2.65329i	0.515432	−	0.167474i	0.555171	+	0.831736i	$0.312653\pi$
$252$	−13.0820	−	28.8391i	−0.824088	−	1.81669i
$253$		0			0
$254$		−	34.5228i		−	2.16615i
$255$	−4.47757	−	7.69324i	−0.280397	−	0.481769i
$256$	22.9118	+	16.6464i	1.43199	+	1.04040i
$257$	13.5931	+	18.7093i	0.847912	+	1.16705i	0.984319	+	0.176398i	$0.0564446\pi$
$257$	13.5931	+	18.7093i	0.847912	+	1.16705i	−0.136407	+	0.990653i	$0.543555\pi$
$258$	1.77793	−	17.5034i	0.110689	−	1.08972i
$259$	−28.1484	−	9.14596i	−1.74905	−	0.568302i
$260$	12.5205	−	9.09666i	0.776487	−	0.564151i
$261$	−15.9569	−	3.27547i	−0.987705	−	0.202747i
$262$	−10.0260	−	30.8569i	−0.619409	−	1.90635i
$263$	23.4721			1.44735			0.723675	−	0.690141i	$-0.242451\pi$
$263$	23.4721			1.44735			0.723675	+	0.690141i	$0.242451\pi$
$264$		0			0
$265$	8.80385			0.540816
$266$	−5.12576	−	15.7755i	−0.314280	−	0.967255i
$267$	15.1858	+	6.69775i	0.929358	+	0.409896i
$268$	−6.03859	+	4.38729i	−0.368865	+	0.267996i
$269$	15.5537	+	5.05372i	0.948328	+	0.308131i	0.742036	−	0.670360i	$-0.233860\pi$
$269$	15.5537	+	5.05372i	0.948328	+	0.308131i	0.206292	+	0.978490i	$0.433860\pi$
$270$	4.91761	+	14.6124i	0.299276	+	0.889280i
$271$	−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
$273$	14.1675	−	8.24566i	0.857453	−	0.499050i
$274$		−	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
$279$	0.290664	−	0.511661i	0.0174016	−	0.0306323i
$280$	4.49184	−	13.8245i	0.268439	−	0.826170i
$281$	−0.251357	+	0.773599i	−0.0149947	+	0.0461490i	−0.958274	−	0.285852i	$-0.907724\pi$
$281$	−0.251357	+	0.773599i	−0.0149947	+	0.0461490i	0.943279	+	0.332001i	$0.107724\pi$
$282$	−9.35851	+	10.4669i	−0.557291	+	0.623297i
$283$	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
$288$	−4.84318	−	5.30396i	−0.285387	−	0.312539i
$289$	−0.158691	−	0.115296i	−0.00933474	−	0.00678209i
$290$	−9.46985	−	13.0341i	−0.556089	−	0.765391i
$291$	3.90809	+	0.396969i	0.229097	+	0.0232708i
$292$	−28.7726	−	9.34878i	−1.68379	−	0.547096i
$293$	26.3198	−	19.1225i	1.53762	−	1.11715i	0.585814	−	0.810446i	$-0.300775\pi$
$293$	26.3198	−	19.1225i	1.53762	−	1.11715i	0.951806	−	0.306701i	$-0.0992251\pi$
$294$	1.67343	−	3.79418i	0.0975965	−	0.221281i
$295$	−4.83928	−	14.8938i	−0.281754	−	0.867150i
$296$	43.3928			2.52215
$297$		0			0
$298$	22.5167			1.30436
$299$		0			0
$300$	9.03631	−	20.4881i	0.521711	−	1.18288i
$301$	9.70820	−	7.05342i	0.559572	−	0.406553i
$302$	−37.5478	−	12.2000i	−2.16063	−	0.702032i
$303$	0.809246	+	0.0822001i	0.0464899	+	0.00472227i
$304$	3.54775	+	4.88306i	0.203477	+	0.280063i
$305$	−4.53191	−	3.29263i	−0.259496	−	0.188535i
$306$	20.0838	+	21.9946i	1.14812	+	1.25735i
$307$			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	−0.819942	−	0.572447i	$-0.805994\pi$
$311$	−0.390375	+	0.537306i	−0.0221362	+	0.0304678i	0.797805	+	0.602915i	$0.205994\pi$
$312$	−16.0189	+	17.9161i	−0.906890	+	1.01430i
$313$	−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
$315$	−5.19425	+	9.14354i	−0.292663	+	0.515180i
$316$	16.1199	−	22.1872i	0.906817	−	1.24813i
$317$	−23.4039	+	7.60439i	−1.31449	+	0.427105i	−0.880601	−	0.473859i	$-0.842861\pi$
$317$	−23.4039	+	7.60439i	−1.31449	+	0.427105i	−0.433893	+	0.900964i	$0.642861\pi$
$318$	−28.7930	+	6.22526i	−1.61463	+	0.349095i
$319$		0			0
$320$		−	13.2114i		−	0.738540i
$321$	−5.24733	+	3.05402i	−0.292878	+	0.170459i
$322$		0			0
$323$	5.97049	+	8.21767i	0.332207	+	0.457244i
$324$	−17.1987	−	28.8511i	−0.955485	−	1.60284i
$325$	11.0238	+	3.58185i	0.611490	+	0.198685i
$326$	24.0030	−	17.4392i	1.32940	−	0.965866i
$327$	−16.9482	−	7.47506i	−0.937240	−	0.413372i
$328$	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
$333$	−30.7511	−	6.31230i	−1.68515	−	0.345912i
$334$	−10.1843	+	7.39931i	−0.557259	+	0.404872i
$335$	2.35731	+	0.765938i	0.128794	+	0.0418477i
$336$	−1.21991	+	12.0098i	−0.0665515	+	0.655188i
$337$	−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
$339$	−11.2987	−	19.4131i	−0.613662	−	1.05438i
$340$			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	−0.939850	−	0.341587i	$-0.889036\pi$
$347$	0.396479	−	1.22024i	0.0212841	−	0.0655057i	0.961134	+	0.276081i	$0.0890358\pi$
$348$	26.1656	+	23.3947i	1.40262	+	1.25409i
$349$	−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	$-0.917921\pi$
$353$		−	9.58244i		−	0.510022i	0.966938	−	0.255011i	$-0.0820790\pi$
$354$	26.3584	+	45.2882i	1.40093	+	2.40704i
$355$	−8.36503	−	6.07755i	−0.443970	−	0.322563i
$356$	−21.0205	−	28.9322i	−1.11408	−	1.53340i
$357$	−2.05298	+	20.2112i	−0.108655	+	1.06969i
$358$	51.9014	+	16.8638i	2.74307	+	0.891278i
$359$	−27.8768	+	20.2537i	−1.47128	+	1.06895i	−0.491042	+	0.871136i	$0.663384\pi$
$359$	−27.8768	+	20.2537i	−1.47128	+	1.06895i	−0.980240	+	0.197813i	$0.936616\pi$
$360$	3.10015	−	15.1027i	0.163392	−	0.795985i
$361$	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
$366$	17.1498	+	7.56398i	0.896437	+	0.395376i
$367$	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
$369$	−2.40188	−	21.4132i	−0.125037	−	1.11473i
$370$	−18.2497	−	25.1186i	−0.948759	−	1.30586i
$371$	−16.2553	−	11.8101i	−0.843931	−	0.613152i
$372$	−1.09586	+	0.637804i	−0.0568175	+	0.0330686i
$373$		−	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
$378$	10.5223	−	33.5768i	0.541210	−	1.72701i
$379$	−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
$381$	16.6469	−	18.6185i	0.852846	−	0.953857i
$382$	3.48807	−	4.80091i	0.178465	−	0.245636i
$383$	−9.02881	+	2.93364i	−0.461351	+	0.149902i	−0.530465	−	0.847707i	$-0.677983\pi$
$383$	−9.02881	+	2.93364i	−0.461351	+	0.149902i	0.0691142	+	0.997609i	$0.477983\pi$
$384$	7.58922	+	35.1015i	0.387286	+	1.79127i
$385$		0			0
$386$		−	6.86071i		−	0.349201i
$387$	9.39900	−	8.58247i	0.477778	−	0.436271i
$388$	−6.84760	−	4.97507i	−0.347634	−	0.252571i
$389$	11.2125	+	15.4327i	0.568498	+	0.782470i	0.992376	−	0.123249i	$-0.0393315\pi$
$389$	11.2125	+	15.4327i	0.568498	+	0.782470i	−0.423878	+	0.905719i	$0.639331\pi$
$390$	17.1081	+	1.73778i	0.866303	+	0.0879958i
$391$		0			0
$392$	−3.35485	+	2.43744i	−0.169446	+	0.123109i
$393$	9.47205	−	21.4760i	0.477802	−	1.08332i
$394$	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
$399$	4.84254	−	10.9795i	0.242430	−	0.549663i
$400$	−6.90569	+	5.01728i	−0.345284	+	0.250864i
$401$	1.17866	+	0.382969i	0.0588593	+	0.0191246i	0.338299	−	0.941039i	$-0.390149\pi$
$401$	1.17866	+	0.382969i	0.0588593	+	0.0191246i	−0.279439	+	0.960163i	$0.590149\pi$
$402$	−8.25119	−	0.838125i	−0.411532	−	0.0418019i
$403$	−0.385786	−	0.530989i	−0.0192174	−	0.0264505i
$404$	−1.41793	−	1.03018i	−0.0705445	−	0.0512536i
$405$	−4.39396	+	10.2519i	−0.218337	+	0.509420i
$406$			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
$411$	20.5918	−	23.0306i	1.01572	−	1.13602i
$412$	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	$-0.912885\pi$
$419$		−	11.0648i		−	0.540553i	0.962783	−	0.270277i	$-0.0871151\pi$
$420$	19.5833	−	11.3978i	0.955568	−	0.556154i
$421$	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
$423$	−10.0943	+	1.13226i	−0.490802	+	0.0550523i
$424$	28.0165	+	9.10310i	1.36060	+	0.442086i
$425$	−11.6215	+	8.44355i	−0.563728	+	0.409572i
$426$	31.6553	+	13.9616i	1.53370	+	0.676444i
$427$	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	$-0.932044\pi$
$431$	−6.46031	−	19.8828i	−0.311182	−	0.957721i	0.666115	−	0.745849i	$-0.267956\pi$
$432$	0.134082	+	12.8031i	0.00645102	+	0.615992i
$433$	−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
$435$	1.17786	−	11.5958i	0.0564740	−	0.555977i
$436$	23.4600	+	32.2899i	1.12353	+	1.54641i
$437$		0			0
$438$	−16.9093	−	29.0531i	−0.807958	−	1.38821i
$439$		−	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	$-0.592717\pi$
$443$	14.9977	−	20.6425i	0.712561	−	0.980756i	0.999738	−	0.0228783i	$-0.00728303\pi$
$444$	50.4248	+	45.0849i	2.39305	+	2.13964i
$445$	−3.66978	+	11.2944i	−0.173964	+	0.535406i
$446$	−9.56479	+	29.4374i	−0.452906	+	1.39390i
$447$	12.1435	+	10.8575i	0.574367	+	0.513543i
$448$	−17.7228	+	24.3933i	−0.837321	+	1.15247i
$449$	38.3260	−	12.4529i	1.80872	−	0.587687i	0.808716	−	0.588199i	$-0.200163\pi$
$449$	38.3260	−	12.4529i	1.80872	−	0.587687i	1.00000		0.000512011i	$0.000162978\pi$
$450$	22.6587	−	10.2784i	1.06814	−	0.484530i
$451$		0			0
$452$			48.3984i			2.27647i
$453$	−14.3671	−	24.6851i	−0.675025	−	1.15981i
$454$	10.1843	+	7.39931i	0.477972	+	0.347267i
$455$	6.89413	+	9.48895i	0.323202	+	0.444849i
$456$	−1.77793	+	17.5034i	−0.0832593	+	0.819673i
$457$	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
$459$	0.225646	+	21.5464i	0.0105322	+	1.00570i
$460$		0			0
$461$	2.86379			0.133380			0.0666901	−	0.997774i	$-0.478756\pi$
$461$	2.86379			0.133380			0.0666901	+	0.997774i	$0.478756\pi$
$462$		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
$465$	0.385245	+	0.169913i	0.0178653	+	0.00787955i
$466$	10.5172	−	7.64121i	0.487201	−	0.353972i
$467$	−18.4581	−	5.99739i	−0.854138	−	0.277526i	−0.150960	−	0.988540i	$-0.548236\pi$
$467$	−18.4581	−	5.99739i	−0.854138	−	0.277526i	−0.703178	+	0.711014i	$0.748236\pi$
$468$	−37.2296	+	4.17597i	−1.72094	+	0.193034i
$469$	−3.32502	−	4.57649i	−0.153535	−	0.211323i
$470$	−8.12763	−	5.90507i	−0.374900	−	0.272381i
$471$	17.1614	−	9.98817i	0.790755	−	0.460231i
$472$		−	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
$477$	−18.5302	−	10.5266i	−0.848439	−	0.481980i
$478$	7.43265	−	22.8753i	0.339961	−	1.04629i
$479$	−2.02128	+	6.22086i	−0.0923546	+	0.284238i	−0.986555	−	0.163428i	$-0.947745\pi$
$479$	−2.02128	+	6.22086i	−0.0923546	+	0.284238i	0.894201	+	0.447666i	$0.147745\pi$
$480$	3.42545	−	3.83116i	0.156350	−	0.174868i
$481$	−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
$486$	7.12125	−	36.6357i	0.323026	−	1.66183i
$487$	−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
$489$	21.3542	+	2.16908i	0.965671	+	0.0980892i
$490$	2.82191	+	0.916893i	0.127481	+	0.0414210i
$491$	−16.9133	+	12.2882i	−0.763288	+	0.554561i	−0.899917	−	0.436061i	$-0.856373\pi$
$491$	−16.9133	+	12.2882i	−0.763288	+	0.554561i	0.136629	+	0.990622i	$0.456373\pi$
$492$	−18.7360	+	42.4802i	−0.844684	+	1.91515i
$493$	−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
$498$	−24.8248	+	56.2853i	−1.11242	+	2.52220i
$499$	−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
$501$	−9.06044	−	0.920325i	−0.404790	−	0.0411171i
$502$	−12.0830	−	16.6309i	−0.539292	−	0.742271i
$503$	−2.83585	−	2.06037i	−0.126444	−	0.0918673i	0.522765	−	0.852477i	$-0.324900\pi$
$503$	−2.83585	−	2.06037i	−0.126444	−	0.0918673i	−0.649210	+	0.760609i	$0.724900\pi$
$504$	−25.9840	+	23.7267i	−1.15742	+	1.05687i
$505$			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	−0.933995	−	0.357285i	$-0.883703\pi$
$509$	−6.89413	+	9.48895i	−0.305577	+	0.420590i	0.628419	+	0.777875i	$0.283703\pi$
$510$	−14.2048	+	15.8872i	−0.628997	+	0.703495i
$511$	7.08520	−	21.8060i	0.313431	−	0.964641i
$512$	8.13823	−	25.0469i	0.359662	−	1.10693i
$513$	3.80617	−	12.1455i	0.168046	−	0.536237i
$514$	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
$519$	−16.9596	+	9.87075i	−0.744446	+	0.433278i
$520$	−13.9120	−	10.1076i	−0.610081	−	0.443250i
$521$	1.45690	+	2.00525i	0.0638280	+	0.0878517i	0.839738	−	0.542992i	$-0.182709\pi$
$521$	1.45690	+	2.00525i	0.0638280	+	0.0878517i	−0.775910	+	0.630844i	$0.782709\pi$
$522$	4.34729	+	38.7569i	0.190276	+	1.69635i
$523$	−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
$525$	15.5274	+	6.84839i	0.677670	+	0.298888i
$526$	−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
$531$	−7.62260	+	37.1344i	−0.330792	+	1.61150i
$532$	−20.9183	+	15.1980i	−0.906922	+	0.658917i
$533$	−22.8569	−	7.42665i	−0.990041	−	0.321684i
$534$	4.01564	−	39.5333i	0.173774	−	1.71077i
$535$	−2.55344	−	3.51451i	−0.110395	−	0.151946i
$536$	6.70970	+	4.87488i	0.289815	+	0.210563i
$537$	19.8593	+	34.1216i	0.856991	+	1.47246i
$538$		−	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
$543$	−16.6002	−	14.8423i	−0.712384	−	0.636944i
$544$	3.06798	−	9.44228i	0.131539	−	0.404835i
$545$	4.09568	−	12.6052i	0.175439	−	0.539947i
$546$	−29.2569	−	26.1587i	−1.25208	−	1.11949i
$547$	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
$555$	2.26990	−	22.3468i	0.0963519	−	0.948568i
$556$	−18.3730	−	5.96975i	−0.779189	−	0.253174i
$557$	8.40576	−	6.10714i	0.356163	−	0.258768i	−0.395287	−	0.918558i	$-0.629355\pi$
$557$	8.40576	−	6.10714i	0.356163	−	0.258768i	0.751450	+	0.659790i	$0.229355\pi$
$558$	−1.38009	−	0.283292i	−0.0584239	−	0.0119927i
$559$	−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	$0.167980\pi$
$563$	10.9382	+	33.6644i	0.460992	+	1.41879i	−0.402963	+	0.915216i	$0.632020\pi$
$564$	20.0254	+	8.83223i	0.843219	+	0.371904i
$565$	13.0024	−	9.44677i	0.547013	−	0.397428i
$566$	−15.4691	−	5.02622i	−0.650216	−	0.211268i
$567$	21.8655	−	13.0345i	0.918267	−	0.547397i
$568$	−20.3359	−	27.9899i	−0.853275	−	1.17443i
$569$	25.4209	+	18.4694i	1.06570	+	0.774276i	0.975134	−	0.221615i	$-0.0711328\pi$
$569$	25.4209	+	18.4694i	1.06570	+	0.774276i	0.0905647	+	0.995891i	$0.471133\pi$
$570$	10.8799	−	6.33225i	0.455708	−	0.265229i
$571$		−	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
$576$	−15.7966	+	27.8071i	−0.658193	+	1.15863i
$577$	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
$579$	3.30823	−	3.70006i	0.137486	−	0.153769i
$580$	−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
$585$	8.38864	+	9.18673i	0.346828	+	0.379825i
$586$	−63.0141	−	45.7824i	−2.60309	−	1.89125i
$587$	3.83744	+	5.28178i	0.158388	+	0.218002i	0.880834	−	0.473425i	$-0.156982\pi$
$587$	3.83744	+	5.28178i	0.158388	+	0.218002i	−0.722446	+	0.691427i	$0.756982\pi$
$588$	−6.43101	−	0.653238i	−0.265210	−	0.0269391i
$589$	−0.456957	−	0.148474i	−0.0188286	−	0.00611778i
$590$	−30.3327	+	22.0380i	−1.24878	+	0.907291i
$591$	−7.47037	+	16.9376i	−0.307290	+	0.696719i
$592$	−7.96788	−	24.5226i	−0.327478	−	1.00787i
$593$	−26.3359			−1.08148			−0.540742	−	0.841188i	$-0.681857\pi$
$593$	−26.3359			−1.08148			−0.540742	+	0.841188i	$0.681857\pi$
$594$		0			0
$595$	−14.5359			−0.595914
$596$	−10.8462	−	33.3813i	−0.444279	−	1.36735i
$597$	5.35422	−	12.1396i	0.219134	−	0.496842i
$598$		0			0
$599$	2.58851	+	0.841058i	0.105764	+	0.0343647i	0.361421	−	0.932403i	$-0.382292\pi$
$599$	2.58851	+	0.841058i	0.105764	+	0.0343647i	−0.255657	+	0.966768i	$0.582292\pi$
$600$	−24.7536	−	2.51437i	−1.01056	−	0.102649i
$601$	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
$603$	−4.04581	−	4.43073i	−0.164758	−	0.180433i
$604$			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
$609$	−17.7303	+	19.8302i	−0.718467	+	0.803561i
$610$	−4.14439	+	12.7551i	−0.167802	+	0.516440i
$611$	−3.50096	+	10.7748i	−0.141634	+	0.435903i
$612$	22.9330	−	40.3693i	0.927010	−	1.63183i
$613$	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	$-0.911517\pi$
$617$		−	13.6325i		−	0.548822i	0.961613	−	0.274411i	$-0.0884828\pi$
$618$	45.6316	−	26.5582i	1.83557	−	1.06833i
$619$	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
$624$	13.0664	+	5.76296i	0.523074	+	0.230703i
$625$	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
$630$	24.6627	+	5.06252i	0.982585	+	0.201696i
$631$	−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
$633$	0.331636	−	3.26489i	0.0131813	−	0.129768i
$634$	34.6302	+	47.6644i	1.37534	+	1.89300i
$635$	14.4574	+	10.5039i	0.573724	+	0.416835i
$636$	23.0985	+	39.6873i	0.915917	+	1.57370i
$637$		−	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	$-0.417099\pi$
$641$	27.7717	−	38.2245i	1.09692	−	1.50978i	0.839410	−	0.543499i	$-0.182901\pi$
$642$	10.8362	+	9.68865i	0.427669	+	0.382380i
$643$	−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
$645$	6.78909	+	6.07015i	0.267320	+	0.239012i
$646$	14.2944	−	19.6745i	0.562404	−	0.774083i
$647$	15.8696	−	5.15633i	0.623897	−	0.202716i	0.0200272	−	0.999799i	$-0.493625\pi$
$647$	15.8696	−	5.15633i	0.623897	−	0.202716i	0.603870	+	0.797083i	$0.293625\pi$
$648$	−24.5832	+	28.0812i	−0.965720	+	1.10313i
$649$		0			0
$650$		−	27.7511i		−	1.08849i
$651$	−0.483375	−	0.830522i	−0.0189450	−	0.0325507i
$652$	−37.4160	−	27.1843i	−1.46532	−	1.06462i
$653$	−22.8154	−	31.4028i	−0.892837	−	1.22888i	−0.972697	−	0.232079i	$-0.925447\pi$
$653$	−22.8154	−	31.4028i	−0.892837	−	1.22888i	0.0798602	−	0.996806i	$-0.474553\pi$
$654$	−4.48168	+	44.1213i	−0.175247	+	1.72528i
$655$	15.9727	+	5.18985i	0.624105	+	0.202784i
$656$	14.3183	−	10.4029i	0.559037	−	0.406164i
$657$	4.89002	−	23.8223i	0.190778	−	0.929397i
$658$	7.08520	+	21.8060i	0.276210	+	0.850087i
$659$	−13.5516			−0.527896			−0.263948	−	0.964537i	$-0.585025\pi$
$659$	−13.5516			−0.527896			−0.263948	+	0.964537i	$0.585025\pi$
$660$		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
$663$	21.9894	+	9.69846i	0.853996	+	0.376657i
$664$	49.7680	−	36.1586i	1.93137	−	1.40323i
$665$	8.16598	+	2.65329i	0.316663	+	0.102890i
$666$	8.37785	+	74.6901i	0.324635	+	2.89418i
$667$		0			0
$668$	15.8753	+	11.5341i	0.614235	+	0.446268i
$669$	−19.3531	+	11.2638i	−0.748234	+	0.435483i
$670$		−	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
$675$	17.1763	+	5.38273i	0.661117	+	0.207181i
$676$	2.08032	−	6.40256i	0.0800122	−	0.246252i
$677$	−3.55408	+	10.9383i	−0.136594	+	0.420394i	−0.995835	−	0.0911783i	$-0.970937\pi$
$677$	−3.55408	+	10.9383i	−0.136594	+	0.420394i	0.859240	+	0.511572i	$0.170937\pi$
$678$	−35.8443	+	40.0897i	−1.37659	+	1.53963i
$679$	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	$-0.710056\pi$
$683$		−	41.2946i		−	1.58009i	0.613047	−	0.790046i	$-0.289944\pi$
$684$	−20.2520	+	18.4927i	−0.774356	+	0.707084i
$685$	17.8834	+	12.9931i	0.683290	+	0.496439i
$686$	23.8820	+	32.8707i	0.911817	+	1.25501i
$687$	9.53937	+	0.968973i	0.363950	+	0.0369686i
$688$	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
$696$	15.7383	−	35.6834i	0.596557	−	1.35258i
$697$	24.0963	−	17.5070i	0.912711	−	0.663123i
$698$	46.2608	+	15.0310i	1.75100	+	0.568933i
$699$	9.35664	+	0.950412i	0.353901	+	0.0359479i
$700$	−21.4932	−	29.5829i	−0.812368	−	1.11813i
$701$	−16.1162	−	11.7091i	−0.608700	−	0.442247i	0.240256	−	0.970710i	$-0.422769\pi$
$701$	−16.1162	−	11.7091i	−0.608700	−	0.442247i	−0.848956	+	0.528463i	$0.822769\pi$
$702$	−33.9310	−	24.1135i	−1.28064	−	0.910106i
$703$			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
$708$	54.4436	−	60.8919i	2.04612	−	2.28846i
$709$	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
$711$	19.1684	+	10.8891i	0.718870	+	0.408375i
$712$	−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
$717$	15.0390	−	8.75290i	0.561641	−	0.326883i
$718$	66.7418	+	48.4908i	2.49078	+	1.80966i
$719$	−21.0728	−	29.0042i	−0.785881	−	1.08167i	−0.994609	−	0.103699i	$-0.966932\pi$
$719$	−21.0728	−	29.0042i	−0.785881	−	1.08167i	0.208727	−	0.977974i	$-0.433068\pi$
$720$	−9.10429	+	1.02121i	−0.339297	+	0.0380583i
$721$	34.2491	+	11.1282i	1.27550	+	0.414437i
$722$	25.1800	−	18.2944i	0.937103	−	0.680845i
$723$	−5.96212	−	2.62961i	−0.221734	−	0.0977962i
$724$	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
$729$	21.5063	−	16.3242i	0.796530	−	0.604599i
$730$	19.4589	−	14.1377i	0.720207	−	0.523261i
$731$	16.7324	+	5.43669i	0.618870	+	0.201083i
$732$	2.95266	−	29.0684i	0.109134	−	1.07440i
$733$	−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
$735$	1.07976	+	1.85521i	0.0398275	+	0.0684306i
$736$		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
$741$	−10.5829	−	9.46220i	−0.388772	−	0.347602i
$742$	−14.8653	+	45.7507i	−0.545722	+	1.67956i
$743$	8.77184	−	26.9969i	0.321807	−	0.990421i	−0.651054	−	0.759032i	$-0.725673\pi$
$743$	8.77184	−	26.9969i	0.321807	−	0.990421i	0.972861	−	0.231390i	$-0.0743273\pi$
$744$	1.05028	+	0.939055i	0.0385050	+	0.0344274i
$745$	−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
$750$	21.8808	+	37.5950i	0.798974	+	1.37277i
$751$	−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
$753$	1.50288	−	14.7956i	0.0547682	−	0.539183i
$754$	41.3699	+	13.4419i	1.50660	+	0.489525i
$755$	16.5334	−	12.0122i	0.601712	−	0.437169i
$756$	−54.8467	+	0.574386i	−1.99476	+	0.0208902i
$757$	−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	$0.0755037\pi$
$761$	8.93119	+	27.4874i	0.323755	+	0.996417i	−0.648244	+	0.761433i	$0.724496\pi$
$762$	−54.7103	−	24.1301i	−1.98194	−	0.874141i
$763$	−24.4717	+	17.7797i	−0.885936	+	0.643670i
$764$	−8.79762	−	2.85852i	−0.318287	−	0.103418i
$765$	−15.3216	+	1.71859i	−0.553952	+	0.0621358i
$766$	13.3597	+	18.3881i	0.482707	+	0.664389i
$767$	34.2066	+	24.8525i	1.23513	+	0.897373i
$768$	42.3949	−	24.6744i	1.52979	−	0.890361i
$769$		−	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	−0.999230	−	0.0392390i	$-0.987507\pi$
$773$	−18.1590	+	24.9937i	−0.653132	+	0.898959i	0.346098	+	0.938199i	$0.387507\pi$
$774$	−26.4960	−	15.0518i	−0.952378	−	0.541026i
$775$	0.209975	−	0.646235i	0.00754251	−	0.0232135i
$776$	−2.90624	+	8.94448i	−0.104328	+	0.321088i
$777$	−34.1687	+	38.2157i	−1.22580	+	1.37098i
$778$	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
$783$	−16.3440	+	22.9983i	−0.584088	+	0.821893i
$784$	1.99350	+	1.44836i	0.0711964	+	0.0517272i
$785$	8.35103	+	11.4942i	0.298061	+	0.410246i
$786$	−55.9085	−	5.67897i	−1.99419	−	0.202562i
$787$	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
$789$	16.4061	−	37.1975i	0.584071	−	1.32427i
$790$	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
$795$	6.15354	−	13.9520i	0.218244	−	0.494825i
$796$	−23.1285	+	16.8039i	−0.819770	+	0.595598i
$797$	−14.6063	−	4.74587i	−0.517381	−	0.168107i	0.0386754	−	0.999252i	$-0.487686\pi$
$797$	−14.6063	−	4.74587i	−0.517381	−	0.168107i	−0.556056	+	0.831145i	$0.687686\pi$
$798$	−28.5830	−	2.90335i	−1.01183	−	0.102777i
$799$	−8.25286	−	11.3591i	−0.291965	−	0.401855i
$800$	−6.70970	−	4.87488i	−0.237224	−	0.172353i
$801$	21.2286	−	19.3844i	0.750076	−	0.684913i
$802$		−	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
$807$	18.8804	−	21.1165i	0.664620	−	0.743338i
$808$	−0.601792	+	1.85213i	−0.0211710	+	0.0651576i
$809$	16.0251	−	49.3202i	0.563413	−	1.73401i	−0.109208	−	0.994019i	$-0.534832\pi$
$809$	16.0251	−	49.3202i	0.563413	−	1.73401i	0.672621	−	0.739987i	$-0.265168\pi$
$810$	26.5942	+	2.42026i	0.934427	+	0.0850392i
$811$	−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
$816$	−15.2963	+	8.90267i	−0.535478	+	0.311656i
$817$	−8.40755	−	6.10844i	−0.294143	−	0.213707i
$818$	46.7497	+	64.3454i	1.63456	+	2.24979i
$819$	−3.16486	−	28.2154i	−0.110589	−	0.985925i
$820$	−31.5945	−	10.2657i	−1.10333	−	0.358493i
$821$	17.6732	−	12.8403i	0.616798	−	0.448130i	−0.235003	−	0.971995i	$-0.575510\pi$
$821$	17.6732	−	12.8403i	0.616798	−	0.448130i	0.851802	+	0.523864i	$0.175510\pi$
$822$	−67.6751	−	29.8483i	−2.36044	−	1.04108i
$823$	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	$-0.993950\pi$
$827$	−5.81248	−	17.8890i	−0.202120	−	0.622060i	0.797700	−	0.603055i	$-0.206050\pi$
$828$		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
$831$	−1.09852	+	10.8148i	−0.0381073	+	0.375160i
$832$	20.9662	+	28.8576i	0.726874	+	1.00046i
$833$	3.35485	+	2.43744i	0.116239	+	0.0844524i
$834$	−10.7976	−	18.5521i	−0.373890	−	0.642408i
$835$		−	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	−0.955680	−	0.294407i	$-0.904878\pi$
$839$	−11.0173	+	15.1641i	−0.380361	+	0.523522i	0.575319	+	0.817929i	$0.304878\pi$
$840$	−18.7688	−	16.7812i	−0.647585	−	0.579007i
$841$	0.149360	−	0.459683i	0.00515035	−	0.0158511i
$842$	14.2021	−	43.7095i	0.489436	−	1.50633i
$843$	1.05028	+	0.939055i	0.0361734	+	0.0323428i
$844$	−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
$849$	−5.91902	−	10.1699i	−0.203140	−	0.349030i
$850$	27.8240	+	20.2153i	0.954354	+	0.693379i
$851$		0			0
$852$	5.45004	−	53.6547i	0.186715	−	1.83818i
$853$	−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
$855$	8.92105	+	1.83123i	0.305093	+	0.0626266i
$856$	−4.49184	−	13.8245i	−0.153528	−	0.472510i
$857$	56.3029			1.92327			0.961635	−	0.274332i	$-0.0884568\pi$
$857$	56.3029			1.92327			0.961635	+	0.274332i	$0.0884568\pi$
$858$		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
$861$	−32.1947	−	14.1995i	−1.09719	−	0.483919i
$862$	−40.4934	+	29.4202i	−1.37921	+	1.00205i
$863$	27.4869	+	8.93103i	0.935665	+	0.304016i	0.736877	−	0.676027i	$-0.236300\pi$
$863$	27.4869	+	8.93103i	0.935665	+	0.304016i	0.198787	+	0.980043i	$0.436300\pi$
$864$	−11.7907	+	3.96801i	−0.401127	+	0.134994i
$865$	−8.25286	−	11.3591i	−0.280606	−	0.386220i
$866$	25.2818	+	18.3683i	0.859111	+	0.624181i
$867$	−0.293634	+	0.170899i	−0.00997233	+	0.00580403i
$868$			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
$873$	3.36070	−	5.91591i	0.113743	−	0.200223i
$874$		0			0
$875$	−9.16831	+	28.2172i	−0.309946	+	0.953914i
$876$	−34.9265	+	39.0631i	−1.18006	+	1.31982i
$877$	−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	$-0.926244\pi$
$881$		−	13.6325i		−	0.459289i	0.973275	−	0.229644i	$-0.0737563\pi$
$882$	−4.84318	−	5.30396i	−0.163079	−	0.178594i
$883$	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
$885$	−26.9855	−	2.74109i	−0.907108	−	0.0921406i
$886$	−58.0987	−	18.8774i	−1.95186	−	0.634199i
$887$	36.6625	−	26.6369i	1.23101	−	0.894378i	0.234041	−	0.972227i	$-0.424805\pi$
$887$	36.6625	−	26.6369i	1.23101	−	0.894378i	0.996965	+	0.0778484i	$0.0248050\pi$
$888$	30.3299	−	68.7670i	1.01780	−	2.30767i
$889$	−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
$894$	15.7383	−	35.6834i	0.526366	−	1.19343i
$895$	−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
$900$	−26.1526	−	28.6407i	−0.871752	−	0.954690i
$901$		−	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
$906$	−45.5785	+	50.9768i	−1.51424	+	1.69359i
$907$	−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
$909$	0.695898	−	1.22500i	0.0230815	−	0.0406308i
$910$	16.5057	−	22.7182i	0.547159	−	0.753100i
$911$	30.2446	−	9.82708i	1.00205	−	0.325586i	0.238365	−	0.971176i	$-0.423388\pi$
$911$	30.2446	−	9.82708i	1.00205	−	0.325586i	0.763684	+	0.645590i	$0.223388\pi$
$912$	10.2182	−	2.20925i	0.338358	−	0.0731557i
$913$		0			0
$914$		−	44.1053i		−	1.45887i
$915$	−8.38564	+	4.88056i	−0.277221	+	0.161346i
$916$	−16.7145	−	12.1438i	−0.552263	−	0.401242i
$917$	−22.5297	−	31.0094i	−0.743995	−	1.02402i
$918$	48.8939	−	16.4546i	1.61374	−	0.543084i
$919$	−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
$921$	49.4239	+	21.7985i	1.62857	+	0.718285i
$922$	−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
$927$	37.4160	+	7.68040i	1.22890	+	0.252257i
$928$	10.5172	−	7.64121i	0.345245	−	0.250835i
$929$	−30.3912	−	9.87471i	−0.997104	−	0.323979i	−0.235396	−	0.971900i	$-0.575639\pi$
$929$	−30.3912	−	9.87471i	−0.997104	−	0.323979i	−0.761708	+	0.647921i	$0.775639\pi$
$930$	0.101872	−	1.00291i	0.00334051	−	0.0328867i
$931$	−1.43977	−	1.98168i	−0.0471867	−	0.0649469i
$932$	−16.3943	−	11.9112i	−0.537014	−	0.390163i
$933$	0.578641	+	0.994205i	0.0189439	+	0.0325488i
$934$			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
$939$	9.54496	+	8.53418i	0.311488	+	0.278502i
$940$	−4.83928	+	14.8938i	−0.157840	+	0.485782i
$941$	0.633603	−	1.95003i	0.0206549	−	0.0635692i	−0.940198	−	0.340629i	$-0.889360\pi$
$941$	0.633603	−	1.95003i	0.0206549	−	0.0635692i	0.960853	+	0.277060i	$0.0893600\pi$
$942$	−35.4396	−	31.6867i	−1.15469	−	1.03241i
$943$		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	$0.163429\pi$
$947$			30.2297i			0.982334i	−0.871065	+	0.491167i	$0.836571\pi$
$948$	−23.8941	−	41.0541i	−0.776044	−	1.33338i
$949$	−21.9441	−	15.9433i	−0.712334	−	0.517541i
$950$	−11.9410	−	16.4353i	−0.387417	−	0.533233i
$951$	−4.30730	+	42.4047i	−0.139674	+	1.37507i
$952$	−46.2575	−	15.0300i	−1.49922	−	0.487125i
$953$	−44.5493	+	32.3669i	−1.44309	+	1.04847i	−0.455707	+	0.890130i	$0.650614\pi$
$953$	−44.5493	+	32.3669i	−1.44309	+	1.04847i	−0.987385	+	0.158338i	$0.949386\pi$
$954$	−10.2596	+	49.9810i	−0.332168	+	1.61820i
$955$	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
$960$	−20.9369	−	9.23425i	−0.675734	−	0.298034i
$961$	25.0484	−	18.1987i	0.808013	−	0.587056i
$962$	79.7256	+	25.9044i	2.57046	+	0.835192i
$963$	1.17220	+	10.4504i	0.0377736	+	0.336759i
$964$	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	−0.733107	−	0.680114i	$-0.761930\pi$
$971$	4.37070	−	6.01575i	0.140262	−	0.193055i	0.873369	+	0.487059i	$0.161930\pi$
$972$	−57.7433	+	7.09000i	−1.85212	+	0.227412i
$973$	4.52432	−	13.9244i	0.145043	−	0.446397i
$974$	−24.5456	+	75.5435i	−0.786491	+	2.42057i
$975$	13.3816	−	14.9665i	0.428553	−	0.479311i
$976$	−6.54666	+	9.01070i	−0.209553	+	0.288426i
$977$	10.6079	−	3.44672i	0.339377	−	0.110270i	−0.134370	−	0.990931i	$-0.542901\pi$
$977$	10.6079	−	3.44672i	0.339377	−	0.110270i	0.473747	+	0.880661i	$0.342901\pi$
$978$	−10.8597	−	50.2281i	−0.347255	−	1.60612i
$979$		0			0
$980$		−	4.62518i		−	0.147746i
$981$	−23.6923	+	21.6341i	−0.756437	+	0.690722i
$982$	40.4934	+	29.4202i	1.29220	+	0.938835i
$983$	−0.285775	−	0.393335i	−0.00911479	−	0.0125454i	0.804435	−	0.594040i	$-0.202468\pi$
$983$	−0.285775	−	0.393335i	−0.00911479	−	0.0125454i	−0.813550	+	0.581495i	$0.802468\pi$
$984$	51.3244	+	5.21333i	1.63616	+	0.166195i
$985$	−12.5973	−	4.09310i	−0.401383	−	0.130417i
$986$	−43.6131	+	31.6867i	−1.38892	+	1.00911i
$987$	−6.69372	+	15.1767i	−0.213064	+	0.483080i
$988$	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
$993$	−0.274206	+	0.621708i	−0.00870166	+	0.0197293i
$994$	45.7074	−	33.2084i	1.44975	−	1.05330i
$995$	9.02881	+	2.93364i	0.286233	+	0.0930026i
$996$	95.4017	+	9.69055i	3.02292	+	0.307057i
$997$	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
$999$	−31.4973	+	44.3210i	−0.996530	+	1.40225i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.739839 - 2.27699i) q^{2} +(0.698961 - 1.58476i) q^{3} +(-3.01929 + 2.19364i) q^{4} +(1.17866 + 0.382969i) q^{5} +(-4.12560 - 0.419062i) q^{6} +(-1.66251 - 2.28825i) q^{7} +(3.35485 + 2.43744i) q^{8} +(-2.02291 - 2.21537i) q^{9} +O(q^{10})\)	\(q+(-0.739839 - 2.27699i) q^{2} +(0.698961 - 1.58476i) q^{3} +(-3.01929 + 2.19364i) q^{4} +(1.17866 + 0.382969i) q^{5} +(-4.12560 - 0.419062i) q^{6} +(-1.66251 - 2.28825i) q^{7} +(3.35485 + 2.43744i) q^{8} +(-2.02291 - 2.21537i) q^{9} -2.96713i q^{10} +(1.36603 + 6.31812i) q^{12} +(-3.18230 + 1.03399i) q^{13} +(-3.98033 + 5.47845i) q^{14} +(1.43075 - 1.60020i) q^{15} +(0.761449 - 2.34350i) q^{16} +(1.28144 - 3.94386i) q^{17} +(-3.54774 + 6.24516i) q^{18} +(-1.43977 + 1.98168i) q^{19} +(-4.39881 + 1.42926i) q^{20} +(-4.78834 + 1.03528i) q^{21} +(6.20766 - 3.61295i) q^{24} +(-2.80252 - 2.03615i) q^{25} +(4.70878 + 6.48108i) q^{26} +(-4.92475 + 1.65736i) q^{27} +(10.0392 + 3.26193i) q^{28} +(4.39285 - 3.19159i) q^{29} +(-4.70218 - 2.07391i) q^{30} +(0.0606144 + 0.186552i) q^{31} +2.39417 q^{32} -9.92820 q^{34} +(-1.08320 - 3.33375i) q^{35} +(10.9675 + 2.25130i) q^{36} +(8.46564 - 6.15064i) q^{37} +(5.57747 + 1.81223i) q^{38} +(-0.585677 + 5.76589i) q^{39} +(3.02076 + 4.15771i) q^{40} +(5.81077 + 4.22177i) q^{41} +(5.89992 + 10.1371i) q^{42} +4.24264i q^{43} +(-1.53590 - 3.38587i) q^{45} +(1.99016 - 2.73922i) q^{47} +(-3.18165 - 2.84473i) q^{48} +(-0.309017 + 0.951057i) q^{49} +(-2.56288 + 7.88773i) q^{50} +(-5.35439 - 4.78738i) q^{51} +(7.34008 - 10.1027i) q^{52} +(6.75612 - 2.19520i) q^{53} +(7.41732 + 9.98743i) q^{54} -11.7290i q^{56} +(2.13413 + 3.66681i) q^{57} +(-10.5172 - 7.64121i) q^{58} +(-7.42739 - 10.2229i) q^{59} +(-0.809566 + 7.97004i) q^{60} +(-4.29882 - 1.39677i) q^{61} +(0.379932 - 0.276037i) q^{62} +(-1.70620 + 8.31197i) 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} +(-1.38673 - 12.3629i) q^{72} +(4.76479 + 6.55817i) q^{73} +(-20.2682 - 14.7257i) q^{74} +(-5.18565 + 3.01812i) q^{75} -9.14162i q^{76} +(13.5622 - 2.93225i) q^{78} +(-6.98881 + 2.27080i) q^{79} +(1.79498 - 2.47057i) q^{80} +(-0.815691 + 8.96296i) q^{81} +(5.31390 - 16.3545i) q^{82} +(4.58416 - 14.1086i) q^{83} +(12.1864 - 13.6297i) q^{84} +(3.02076 - 4.15771i) q^{85} +(9.66046 - 3.13887i) q^{86} +(-1.98747 - 9.19239i) q^{87} +9.58244i q^{89} +(-6.57327 + 6.00223i) q^{90} +(7.65662 + 5.56286i) q^{91} +(0.338007 + 0.0343334i) q^{93} +(-7.70959 - 2.50500i) q^{94} +(-2.45592 + 1.78433i) q^{95} +(1.67343 - 3.79418i) 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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