LMFDB - Embedded newform 245.2.x.a.108.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [245,2,Mod(3,245)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(245, base_ring=CyclotomicField(84)) chi = DirichletCharacter(H, H._module([63, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("245.3"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	245.x (of order $84$, degree $24$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.95633484952$
Analytic rank:	$0$
Dimension:	$624$
Relative dimension:	$26$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			108.18
Character	$\chi$	$=$	245.108
Dual form			245.2.x.a.152.18

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.856802 - 0.632349i) q^{2} +(-0.121336 + 0.641277i) q^{3} +(-0.255265 + 0.827550i) q^{4} +(-0.0691167 - 2.23500i) q^{5} +(0.301550 + 0.626175i) q^{6} +(2.52921 - 0.776602i) q^{7} +(1.00801 + 2.88071i) q^{8} +(2.39611 + 0.940403i) q^{9} +(-1.47252 - 1.87125i) q^{10} +(-0.470582 - 1.19902i) q^{11} +(-0.499716 - 0.264108i) q^{12} +(0.159711 + 1.41748i) q^{13} +(1.67595 - 2.26474i) q^{14} +(1.44164 + 0.226863i) q^{15} +(1.25419 + 0.855092i) q^{16} +(-0.0531727 - 1.42107i) q^{17} +(2.64765 - 0.709436i) q^{18} +(-0.606735 - 1.05090i) q^{19} +(1.86722 + 0.513320i) q^{20} +(0.191133 + 1.71615i) q^{21} +(-1.16140 - 0.729753i) q^{22} +(2.15720 + 0.0807169i) q^{23} +(-1.96964 + 0.296876i) q^{24} +(-4.99045 + 0.308952i) q^{25} +(1.03318 + 1.11350i) q^{26} +(-1.93549 + 3.08032i) q^{27} +(-0.00294233 + 2.29128i) q^{28} +(-2.45930 - 0.561319i) q^{29} +(1.37866 - 0.717243i) q^{30} +(-5.39985 - 3.11760i) q^{31} +(-4.48438 + 0.167794i) q^{32} +(0.826005 - 0.156289i) q^{33} +(-0.944171 - 1.18395i) q^{34} +(-1.91051 - 5.59910i) q^{35} +(-1.38987 + 1.74285i) q^{36} +(-5.58761 + 10.5723i) q^{37} +(-1.18438 - 0.516742i) q^{38} +(-0.928375 - 0.0695721i) q^{39} +(6.36872 - 2.45200i) q^{40} +(1.62483 - 3.37399i) q^{41} +(1.24897 + 1.34954i) q^{42} +(-4.34287 - 1.51963i) q^{43} +(1.11237 - 0.0833609i) q^{44} +(1.93619 - 5.42030i) q^{45} +(1.89934 - 1.29495i) q^{46} +(-6.45967 - 8.75254i) q^{47} +(-0.700530 + 0.700530i) q^{48} +(5.79378 - 3.92837i) q^{49} +(-4.08046 + 3.42041i) q^{50} +(0.917753 + 0.138329i) q^{51} +(-1.21380 - 0.229664i) q^{52} +(1.48412 + 2.80809i) q^{53} +(0.289502 + 3.86313i) q^{54} +(-2.64729 + 1.13462i) q^{55} +(4.78662 + 6.50310i) q^{56} +(0.747535 - 0.261574i) q^{57} +(-2.46208 + 1.07420i) q^{58} +(-0.0385687 + 0.514663i) q^{59} +(-0.555742 + 1.13512i) q^{60} +(0.350079 + 1.13493i) q^{61} +(-6.59802 + 0.743418i) q^{62} +(6.79057 + 0.517653i) q^{63} +(-6.10969 + 4.87231i) q^{64} +(3.15702 - 0.454926i) q^{65} +(0.608894 - 0.656231i) q^{66} +(1.61913 + 6.04266i) q^{67} +(1.18958 + 0.318747i) q^{68} +(-0.313509 + 1.37357i) q^{69} +(-5.17752 - 3.58921i) q^{70} +(-1.52615 - 6.68652i) q^{71} +(-0.293742 + 7.85043i) q^{72} +(-8.20379 + 11.1157i) q^{73} +(1.89789 + 12.5917i) q^{74} +(0.407398 - 3.23775i) q^{75} +(1.02455 - 0.233846i) q^{76} +(-2.12136 - 2.66712i) q^{77} +(-0.839428 + 0.527448i) q^{78} +(7.23199 - 4.17539i) q^{79} +(1.82445 - 2.86222i) q^{80} +(3.92022 + 3.63743i) q^{81} +(-0.741382 - 3.91830i) q^{82} +(8.58811 + 0.967647i) q^{83} +(-1.46899 - 0.279903i) q^{84} +(-3.17242 + 0.217061i) q^{85} +(-4.68192 + 1.44418i) q^{86} +(0.658363 - 1.50898i) q^{87} +(2.97969 - 2.56423i) q^{88} +(6.50501 - 16.5745i) q^{89} +(-1.76859 - 5.86847i) q^{90} +(1.50476 + 3.46106i) q^{91} +(-0.617457 + 1.76459i) q^{92} +(2.65445 - 3.08452i) q^{93} +(-11.0693 - 3.41443i) q^{94} +(-2.30682 + 1.42869i) q^{95} +(0.436516 - 2.89609i) q^{96} +(3.80844 + 3.80844i) q^{97} +(2.48002 - 7.02953i) q^{98} -3.31552i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 624 q - 26 q^{2} - 22 q^{3} - 28 q^{5} - 28 q^{6} - 18 q^{7} - 24 q^{8} - 34 q^{10} - 56 q^{11} - 34 q^{12} - 28 q^{13} + 12 q^{15} - 100 q^{16} - 26 q^{17} - 10 q^{18} - 28 q^{20} - 76 q^{21} - 48 q^{22}+ \cdots + 304 q^{98}+O(q^{100}) $ 624 * q - 26 * q^2 - 22 * q^3 - 28 * q^5 - 28 * q^6 - 18 * q^7 - 24 * q^8 - 34 * q^10 - 56 * q^11 - 34 * q^12 - 28 * q^13 + 12 * q^15 - 100 * q^16 - 26 * q^17 - 10 * q^18 - 28 * q^20 - 76 * q^21 - 48 * q^22 - 34 * q^23 - 24 * q^25 - 60 * q^26 - 28 * q^27 - 46 * q^28 - 10 * q^30 - 60 * q^31 + 54 * q^32 - 28 * q^33 - 20 * q^35 + 116 * q^36 - 20 * q^37 + 12 * q^38 - 46 * q^40 - 114 * q^42 - 24 * q^43 + 60 * q^45 + 108 * q^46 - 94 * q^47 - 296 * q^50 + 52 * q^51 - 52 * q^52 - 106 * q^53 + 14 * q^55 + 96 * q^56 + 72 * q^57 - 142 * q^58 - 26 * q^60 + 80 * q^61 - 56 * q^62 - 24 * q^63 - 20 * q^65 - 240 * q^66 - 8 * q^67 - 30 * q^68 + 180 * q^70 + 48 * q^71 + 138 * q^72 - 4 * q^73 - 106 * q^75 + 56 * q^76 - 8 * q^77 - 204 * q^78 - 18 * q^80 - 284 * q^81 - 162 * q^82 + 182 * q^83 - 36 * q^85 - 76 * q^86 - 74 * q^87 + 288 * q^88 - 112 * q^90 + 44 * q^91 - 8 * q^92 + 368 * q^93 + 26 * q^95 + 136 * q^96 + 304 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{13}{42}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.856802	−	0.632349i	0.605851	−	0.447138i	−0.247201	−	0.968964i	$-0.579511\pi$
$2$	0.856802	−	0.632349i	0.605851	−	0.447138i	0.853052	+	0.521826i	$0.174749\pi$
$3$	−0.121336	+	0.641277i	−0.0700535	+	0.370242i	0.929943	+	0.367703i	$0.119856\pi$
$3$	−0.121336	+	0.641277i	−0.0700535	+	0.370242i	−0.999997	+	0.00253867i	$0.999192\pi$
$4$	−0.255265	+	0.827550i	−0.127633	+	0.413775i
$5$	−0.0691167	−	2.23500i	−0.0309099	−	0.999522i
$5$	−0.0691167	−	2.23500i	−0.0309099	−	0.999522i
$6$	0.301550	+	0.626175i	0.123107	+	0.255635i
$7$	2.52921	−	0.776602i	0.955951	−	0.293528i
$7$	2.52921	−	0.776602i	0.955951	−	0.293528i
$8$	1.00801	+	2.88071i	0.356384	+	1.01849i
$9$	2.39611	+	0.940403i	0.798702	+	0.313468i
$10$	−1.47252	−	1.87125i	−0.465651	−	0.591740i
$11$	−0.470582	−	1.19902i	−0.141886	−	0.361519i	0.842212	−	0.539146i	$-0.181253\pi$
$11$	−0.470582	−	1.19902i	−0.141886	−	0.361519i	−0.984098	+	0.177627i	$0.943158\pi$
$12$	−0.499716	−	0.264108i	−0.144256	−	0.0762413i
$13$	0.159711	+	1.41748i	0.0442960	+	0.393138i	0.996224	+	0.0868168i	$0.0276695\pi$
$13$	0.159711	+	1.41748i	0.0442960	+	0.393138i	−0.951928	+	0.306321i	$0.900902\pi$
$14$	1.67595	−	2.26474i	0.447916	−	0.605276i
$15$	1.44164	+	0.226863i	0.372230	+	0.0585759i
$16$	1.25419	+	0.855092i	0.313548	+	0.213773i
$17$	−0.0531727	−	1.42107i	−0.0128963	−	0.344660i	−0.990777	−	0.135499i	$-0.956736\pi$
$17$	−0.0531727	−	1.42107i	−0.0128963	−	0.344660i	0.977881	−	0.209161i	$-0.0670733\pi$
$18$	2.64765	−	0.709436i	0.624058	−	0.167216i
$19$	−0.606735	−	1.05090i	−0.139195	−	0.241092i	0.787997	−	0.615679i	$-0.211118\pi$
$19$	−0.606735	−	1.05090i	−0.139195	−	0.241092i	−0.927192	+	0.374586i	$0.877785\pi$
$20$	1.86722	+	0.513320i	0.417522	+	0.114782i
$21$	0.191133	+	1.71615i	0.0417086	+	0.374495i
$22$	−1.16140	−	0.729753i	−0.247610	−	0.155584i
$23$	2.15720	+	0.0807169i	0.449808	+	0.0168306i	0.261336	−	0.965248i	$-0.415837\pi$
$23$	2.15720	+	0.0807169i	0.449808	+	0.0168306i	0.188472	+	0.982079i	$0.439646\pi$
$24$	−1.96964	+	0.296876i	−0.402052	+	0.0605996i
$25$	−4.99045	+	0.308952i	−0.998089	+	0.0617903i
$26$	1.03318	+	1.11350i	0.202624	+	0.218376i
$27$	−1.93549	+	3.08032i	−0.372486	+	0.592808i
$28$	−0.00294233	+	2.29128i	−0.000556047	+	0.433012i
$29$	−2.45930	−	0.561319i	−0.456680	−	0.104234i	−0.0120085	−	0.999928i	$-0.503823\pi$
$29$	−2.45930	−	0.561319i	−0.456680	−	0.104234i	−0.444672	+	0.895694i	$0.646680\pi$
$30$	1.37866	−	0.717243i	0.251707	−	0.130950i
$31$	−5.39985	−	3.11760i	−0.969842	−	0.559938i	−0.0706537	−	0.997501i	$-0.522509\pi$
$31$	−5.39985	−	3.11760i	−0.969842	−	0.559938i	−0.899188	+	0.437563i	$0.855842\pi$
$32$	−4.48438	+	0.167794i	−0.792734	+	0.0296620i
$33$	0.826005	−	0.156289i	0.143789	−	0.0272063i
$34$	−0.944171	−	1.18395i	−0.161924	−	0.203046i
$35$	−1.91051	−	5.59910i	−0.322936	−	0.946421i
$36$	−1.38987	+	1.74285i	−0.231646	+	0.290474i
$37$	−5.58761	+	10.5723i	−0.918597	+	1.73807i	−0.296701	+	0.954970i	$0.595886\pi$
$37$	−5.58761	+	10.5723i	−0.918597	+	1.73807i	−0.621896	+	0.783100i	$0.713637\pi$
$38$	−1.18438	−	0.516742i	−0.192133	−	0.0838266i
$39$	−0.928375	−	0.0695721i	−0.148659	−	0.0111405i
$40$	6.36872	−	2.45200i	1.00698	−	0.387695i
$41$	1.62483	−	3.37399i	0.253755	−	0.526928i	−0.734709	−	0.678382i	$-0.762681\pi$
$41$	1.62483	−	3.37399i	0.253755	−	0.526928i	0.988464	+	0.151454i	$0.0483956\pi$
$42$	1.24897	+	1.34954i	0.192720	+	0.208239i
$43$	−4.34287	−	1.51963i	−0.662281	−	0.231742i	−0.0218539	−	0.999761i	$-0.506957\pi$
$43$	−4.34287	−	1.51963i	−0.662281	−	0.231742i	−0.640427	+	0.768019i	$0.721243\pi$
$44$	1.11237	−	0.0833609i	0.167697	−	0.0125671i
$45$	1.93619	−	5.42030i	0.288630	−	0.808010i
$46$	1.89934	−	1.29495i	0.280042	−	0.190930i
$47$	−6.45967	−	8.75254i	−0.942239	−	1.27669i	−0.960909	−	0.276863i	$-0.910705\pi$
$47$	−6.45967	−	8.75254i	−0.942239	−	1.27669i	0.0186702	−	0.999826i	$-0.494057\pi$
$48$	−0.700530	+	0.700530i	−0.101113	+	0.101113i
$49$	5.79378	−	3.92837i	0.827683	−	0.561196i
$50$	−4.08046	+	3.42041i	−0.577064	+	0.483719i
$51$	0.917753	+	0.138329i	0.128511	+	0.0193699i
$52$	−1.21380	−	0.229664i	−0.168324	−	0.0318486i
$53$	1.48412	+	2.80809i	0.203860	+	0.385721i	0.964754	−	0.263155i	$-0.0847631\pi$
$53$	1.48412	+	2.80809i	0.203860	+	0.385721i	−0.760894	+	0.648876i	$0.775239\pi$
$54$	0.289502	+	3.86313i	0.0393962	+	0.525706i
$55$	−2.64729	+	1.13462i	−0.356960	+	0.152992i
$56$	4.78662	+	6.50310i	0.639639	+	0.869014i
$57$	0.747535	−	0.261574i	0.0990134	−	0.0346463i
$58$	−2.46208	+	1.07420i	−0.323287	+	0.141049i
$59$	−0.0385687	+	0.514663i	−0.00502121	+	0.0670035i	−0.999151	−	0.0411862i	$-0.986886\pi$
$59$	−0.0385687	+	0.514663i	−0.00502121	+	0.0670035i	0.994130	+	0.108190i	$0.0345054\pi$
$60$	−0.555742	+	1.13512i	−0.0717460	+	0.146543i
$61$	0.350079	+	1.13493i	0.0448230	+	0.145313i	0.975218	−	0.221246i	$-0.0710122\pi$
$61$	0.350079	+	1.13493i	0.0448230	+	0.145313i	−0.930395	+	0.366558i	$0.880536\pi$
$62$	−6.59802	+	0.743418i	−0.837949	+	0.0944142i
$63$	6.79057	+	0.517653i	0.855531	+	0.0652181i
$64$	−6.10969	+	4.87231i	−0.763711	+	0.609039i
$65$	3.15702	−	0.454926i	0.391581	−	0.0564267i
$66$	0.608894	−	0.656231i	0.0749497	−	0.0807765i
$67$	1.61913	+	6.04266i	0.197808	+	0.738229i	0.991522	+	0.129938i	$0.0414778\pi$
$67$	1.61913	+	6.04266i	0.197808	+	0.738229i	−0.793714	+	0.608291i	$0.791855\pi$
$68$	1.18958	+	0.318747i	0.144258	+	0.0386538i
$69$	−0.313509	+	1.37357i	−0.0377420	+	0.165359i
$70$	−5.17752	−	3.58921i	−0.618832	−	0.428993i
$71$	−1.52615	−	6.68652i	−0.181121	−	0.793544i	−0.981098	−	0.193513i	$-0.938012\pi$
$71$	−1.52615	−	6.68652i	−0.181121	−	0.793544i	0.799977	−	0.600031i	$-0.204845\pi$
$72$	−0.293742	+	7.85043i	−0.0346179	+	0.925182i
$73$	−8.20379	+	11.1157i	−0.960181	+	1.30100i	−0.00656291	+	0.999978i	$0.502089\pi$
$73$	−8.20379	+	11.1157i	−0.960181	+	1.30100i	−0.953618	+	0.301020i	$0.902673\pi$
$74$	1.89789	+	12.5917i	0.220625	+	1.46375i
$75$	0.407398	−	3.23775i	0.0470423	−	0.373863i
$76$	1.02455	−	0.233846i	0.117524	−	0.0268240i
$77$	−2.12136	−	2.66712i	−0.241752	−	0.303947i
$78$	−0.839428	+	0.527448i	−0.0950465	+	0.0597217i
$79$	7.23199	−	4.17539i	0.813662	−	0.469768i	−0.0345637	−	0.999402i	$-0.511004\pi$
$79$	7.23199	−	4.17539i	0.813662	−	0.469768i	0.848226	+	0.529634i	$0.177671\pi$
$80$	1.82445	−	2.86222i	0.203979	−	0.320005i
$81$	3.92022	+	3.63743i	0.435580	+	0.404159i
$82$	−0.741382	−	3.91830i	−0.0818719	−	0.432704i
$83$	8.58811	+	0.967647i	0.942667	+	0.106213i	0.569902	−	0.821713i	$-0.306981\pi$
$83$	8.58811	+	0.967647i	0.942667	+	0.106213i	0.372765	+	0.927926i	$0.378410\pi$
$84$	−1.46899	−	0.279903i	−0.160280	−	0.0305399i
$85$	−3.17242	+	0.217061i	−0.344097	+	0.0235435i
$86$	−4.68192	+	1.44418i	−0.504864	+	0.155730i
$87$	0.658363	−	1.50898i	0.0705839	−	0.161780i
$88$	2.97969	−	2.56423i	0.317636	−	0.273348i
$89$	6.50501	−	16.5745i	0.689529	−	1.75689i	0.0367736	−	0.999324i	$-0.488292\pi$
$89$	6.50501	−	16.5745i	0.689529	−	1.75689i	0.652756	−	0.757568i	$-0.273613\pi$
$90$	−1.76859	−	5.86847i	−0.186425	−	0.618591i
$91$	1.50476	+	3.46106i	0.157742	+	0.362818i
$92$	−0.617457	+	1.76459i	−0.0643743	+	0.183971i
$93$	2.65445	−	3.08452i	0.275253	−	0.319850i
$94$	−11.0693	−	3.41443i	−1.14171	−	0.352172i
$95$	−2.30682	+	1.42869i	−0.236674	+	0.146580i
$96$	0.436516	−	2.89609i	0.0445517	−	0.295581i
$97$	3.80844	+	3.80844i	0.386689	+	0.386689i	0.873505	−	0.486816i	$-0.161842\pi$
$97$	3.80844	+	3.80844i	0.386689	+	0.386689i	−0.486816	+	0.873505i	$0.661842\pi$
$98$	2.48002	−	7.02953i	0.250520	−	0.710090i
$99$		−	3.31552i		−	0.333223i
$100$	1.01821	−	4.20871i	0.101821	−	0.420871i
$101$	6.75389	+	9.90614i	0.672037	+	0.985697i	0.999171	+	0.0407192i	$0.0129649\pi$
$101$	6.75389	+	9.90614i	0.672037	+	0.985697i	−0.327134	+	0.944978i	$0.606083\pi$
$102$	0.873805	−	0.461819i	0.0865195	−	0.0457269i
$103$	−6.56150	−	5.64663i	−0.646524	−	0.556379i	0.266729	−	0.963772i	$-0.414057\pi$
$103$	−6.56150	−	5.64663i	−0.646524	−	0.556379i	−0.913253	+	0.407393i	$0.866438\pi$
$104$	−3.92236	+	1.88891i	−0.384619	+	0.185223i
$105$	3.82239	−	0.545796i	0.373027	−	0.0532643i
$106$	3.04729	+	1.46750i	0.295979	+	0.142536i
$107$	1.17939	+	2.70318i	0.114015	+	0.261326i	0.964209	−	0.265145i	$-0.0854197\pi$
$107$	1.17939	+	2.70318i	0.114015	+	0.261326i	−0.850193	+	0.526471i	$0.823515\pi$
$108$	−2.05506	−	2.38802i	−0.197748	−	0.229787i
$109$	1.26419	−	0.496156i	0.121087	−	0.0475232i	−0.304024	−	0.952664i	$-0.598330\pi$
$109$	1.26419	−	0.496156i	0.121087	−	0.0475232i	0.425111	+	0.905141i	$0.360235\pi$
$110$	−1.55073	+	2.64616i	−0.147856	+	0.252301i
$111$	−6.10178	−	4.86601i	−0.579155	−	0.461861i
$112$	3.83617	+	1.18870i	0.362484	+	0.112322i
$113$	−0.625505	+	5.55151i	−0.0588425	+	0.522242i	0.929370	+	0.369151i	$0.120351\pi$
$113$	−0.625505	+	5.55151i	−0.0588425	+	0.522242i	−0.988212	+	0.153091i	$0.951077\pi$
$114$	0.475084	−	0.696820i	0.0444957	−	0.0652632i
$115$	0.0313033	−	4.82693i	0.00291905	−	0.450113i
$116$	1.09229	−	1.89191i	0.101417	−	0.175659i
$117$	−0.950314	+	3.54662i	−0.0878566	+	0.327885i
$118$	0.292401	+	0.465354i	0.0269177	+	0.0428393i
$119$	−1.23809	−	3.55289i	−0.113496	−	0.325693i
$120$	0.799653	+	4.38163i	0.0729980	+	0.399987i
$121$	6.84736	−	6.35342i	0.622488	−	0.577584i
$122$	1.01762	+	0.751037i	0.0921309	+	0.0679957i
$123$	1.96651	+	1.45135i	0.177314	+	0.130864i
$124$	3.95837	−	3.67283i	0.355472	−	0.329830i
$125$	1.03543	+	11.1323i	0.0926117	+	0.995702i
$126$	6.14551	−	3.85048i	0.547486	−	0.343028i
$127$	−10.0997	−	16.0735i	−0.896201	−	1.42630i	−0.904567	−	0.426331i	$-0.859806\pi$
$127$	−10.0997	−	16.0735i	−0.896201	−	1.42630i	0.00836551	−	0.999965i	$-0.497337\pi$
$128$	0.169119	−	0.631160i	0.0149481	−	0.0557872i
$129$	1.50145	−	2.60060i	0.132196	−	0.228970i
$130$	2.41727	−	2.38612i	0.212009	−	0.209277i
$131$	−7.73784	+	11.3493i	−0.676058	+	0.991595i	0.322921	+	0.946426i	$0.395335\pi$
$131$	−7.73784	+	11.3493i	−0.676058	+	0.991595i	−0.998979	+	0.0451691i	$0.985617\pi$
$132$	−0.0815138	+	0.723455i	−0.00709487	+	0.0629687i
$133$	−2.35069	−	2.18674i	−0.203830	−	0.189615i
$134$	5.20834	+	4.15351i	0.449932	+	0.358809i
$135$	7.01829	+	4.11293i	0.604039	+	0.353984i
$136$	4.04010	−	1.58562i	0.346436	−	0.135966i
$137$	7.52602	+	8.74540i	0.642991	+	0.747170i	0.981007	−	0.193971i	$-0.0621367\pi$
$137$	7.52602	+	8.74540i	0.642991	+	0.747170i	−0.338016	+	0.941140i	$0.609756\pi$
$138$	0.599962	+	1.37513i	0.0510721	+	0.117059i
$139$	−9.67332	−	4.65843i	−0.820481	−	0.395123i	−0.0239442	−	0.999713i	$-0.507622\pi$
$139$	−9.67332	−	4.65843i	−0.820481	−	0.395123i	−0.796536	+	0.604591i	$0.793337\pi$
$140$	5.12122	−	0.151790i	0.432822	−	0.0128286i
$141$	6.39660	−	3.08044i	0.538691	−	0.259420i
$142$	−5.53583	−	4.76396i	−0.464556	−	0.399783i
$143$	1.62443	−	0.858537i	0.135842	−	0.0717944i
$144$	2.20104	+	3.22834i	0.183420	+	0.269028i
$145$	−1.08457	+	5.53533i	−0.0900685	+	0.459684i
$146$			14.7116i			1.21754i
$147$	1.81618	+	4.19207i	0.149796	+	0.345756i
$148$	−7.32276	−	7.32276i	−0.601927	−	0.601927i
$149$	3.35314	−	22.2466i	0.274700	−	1.82251i	−0.246574	−	0.969124i	$-0.579305\pi$
$149$	3.35314	−	22.2466i	0.274700	−	1.82251i	0.521274	−	0.853389i	$-0.325457\pi$
$150$	−1.69833	−	3.03173i	−0.138668	−	0.247539i
$151$	3.67843	+	1.13464i	0.299346	+	0.0923360i	0.440790	−	0.897610i	$-0.354698\pi$
$151$	3.67843	+	1.13464i	0.299346	+	0.0923360i	−0.141444	+	0.989946i	$0.545175\pi$
$152$	2.41574	−	2.80714i	0.195942	−	0.227689i
$153$	1.20897	−	3.45504i	0.0977396	−	0.279324i
$154$	−3.50414	−	0.943756i	−0.282372	−	0.0760500i
$155$	−6.59463	+	12.2841i	−0.529693	+	0.986686i
$156$	0.294556	−	0.750518i	0.0235834	−	0.0600895i
$157$	6.44004	−	5.54210i	0.513971	−	0.442308i	−0.356667	−	0.934231i	$-0.616087\pi$
$157$	6.44004	−	5.54210i	0.513971	−	0.442308i	0.870638	+	0.491924i	$0.163706\pi$
$158$	3.55608	−	8.15062i	0.282907	−	0.648429i
$159$	−1.98084	+	0.611009i	−0.157091	+	0.0484562i
$160$	0.684965	+	10.0110i	0.0541512	+	0.791439i
$161$	5.51870	−	1.47114i	0.434935	−	0.115942i
$162$	5.65898	+	0.637614i	0.444612	+	0.0500957i
$163$	4.23307	+	22.3723i	0.331559	+	1.75233i	0.610491	+	0.792023i	$0.290972\pi$
$163$	4.23307	+	22.3723i	0.331559	+	1.75233i	−0.278932	+	0.960311i	$0.589980\pi$
$164$	2.37738	+	2.20589i	0.185642	+	0.172251i
$165$	−0.406396	−	1.83532i	−0.0316378	−	0.142879i
$166$	7.97020	−	4.60160i	0.618608	−	0.357153i
$167$	−3.40237	+	2.13785i	−0.263283	+	0.165432i	−0.657204	−	0.753712i	$-0.728261\pi$
$167$	−3.40237	+	2.13785i	−0.263283	+	0.165432i	0.393921	+	0.919144i	$0.371118\pi$
$168$	−4.75108	+	2.28049i	−0.366554	+	0.175944i
$169$	10.6903	−	2.44000i	0.822333	−	0.187692i
$170$	−2.58088	+	2.19205i	−0.197944	+	0.168123i
$171$	−0.465537	−	3.08863i	−0.0356005	−	0.236194i
$172$	2.36616	−	3.20603i	0.180418	−	0.244457i
$173$	−0.266631	+	7.12586i	−0.0202716	+	0.541769i	0.951750	+	0.306876i	$0.0992836\pi$
$173$	−0.266631	+	7.12586i	−0.0202716	+	0.541769i	−0.972021	+	0.234893i	$0.924526\pi$
$174$	−0.390118	−	1.70922i	−0.0295747	−	0.129575i
$175$	−12.3819	+	4.65699i	−0.935987	+	0.352035i
$176$	0.435076	−	1.90619i	0.0327951	−	0.143685i
$177$	−0.325362	−	0.0871805i	−0.0244557	−	0.00655289i
$178$	−4.90735	−	18.3145i	−0.367822	−	1.37273i
$179$	−8.88298	+	9.57357i	−0.663945	+	0.715562i	−0.971783	−	0.235876i	$-0.924204\pi$
$179$	−8.88298	+	9.57357i	−0.663945	+	0.715562i	0.307838	+	0.951439i	$0.400394\pi$
$180$	3.99132	+	2.98591i	0.297496	+	0.222556i
$181$	−13.3525	+	10.6483i	−0.992482	+	0.791478i	−0.978040	−	0.208417i	$-0.933169\pi$
$181$	−13.3525	+	10.6483i	−0.992482	+	0.791478i	−0.0144424	+	0.999896i	$0.504597\pi$
$182$	3.47788	+	2.01391i	0.257798	+	0.149281i
$183$	−0.770281	+	0.0867898i	−0.0569408	+	0.00641569i
$184$	1.94195	+	6.29565i	0.143163	+	0.464121i
$185$	24.0152	+	11.7576i	1.76563	+	0.864434i
$186$	0.323841	−	4.32136i	0.0237452	−	0.316858i
$187$	−1.67887	+	0.732485i	−0.122771	+	0.0535646i
$188$	8.89209	−	3.11148i	0.648522	−	0.226928i
$189$	−2.50308	+	9.29388i	−0.182073	+	0.676030i
$190$	−1.07306	+	2.68282i	−0.0778477	+	0.194632i
$191$	−1.10866	−	14.7940i	−0.0802195	−	1.07045i	−0.881506	−	0.472173i	$-0.843470\pi$
$191$	−1.10866	−	14.7940i	−0.0802195	−	1.07045i	0.801286	−	0.598281i	$-0.204149\pi$
$192$	−2.38318	−	4.50919i	−0.171991	−	0.325423i
$193$	−14.9055	−	2.82027i	−1.07292	−	0.203008i	−0.380704	−	0.924697i	$-0.624318\pi$
$193$	−14.9055	−	2.82027i	−1.07292	−	0.203008i	−0.692217	+	0.721689i	$0.743366\pi$
$194$	5.67135	+	0.854818i	0.407179	+	0.0613723i
$195$	−0.0913274	+	2.07973i	−0.00654009	+	0.148932i
$196$	1.77197	+	5.79742i	0.126570	+	0.414101i
$197$	12.3800	−	12.3800i	0.882040	−	0.882040i	−0.111702	−	0.993742i	$-0.535630\pi$
$197$	12.3800	−	12.3800i	0.882040	−	0.882040i	0.993742	+	0.111702i	$0.0356302\pi$
$198$	−2.09657	−	2.84075i	−0.148997	−	0.201883i
$199$	−2.90054	+	1.97755i	−0.205614	+	0.140185i	−0.661749	−	0.749725i	$-0.730186\pi$
$199$	−2.90054	+	1.97755i	−0.205614	+	0.140185i	0.456136	+	0.889910i	$0.349233\pi$
$200$	−5.92040	−	14.0646i	−0.418635	−	0.994519i
$201$	−4.07148	+	0.305115i	−0.287180	+	0.0215212i
$202$	12.0509	+	4.21679i	0.847897	+	0.296692i
$203$	−6.65600	+	0.490204i	−0.467159	+	0.0344056i
$204$	−0.348745	+	0.724175i	−0.0244170	+	0.0507024i
$205$	−7.65316	−	3.39829i	−0.534520	−	0.237347i
$206$	−9.19255	−	0.688886i	−0.640475	−	0.0479970i
$207$	5.09299	+	2.22205i	0.353987	+	0.154443i
$208$	−1.01177	+	1.91435i	−0.0701534	+	0.132737i
$209$	−0.974530	+	1.22202i	−0.0674096	+	0.0845290i
$210$	2.92990	−	2.88472i	0.202182	−	0.199065i
$211$	−13.9526	−	17.4960i	−0.960535	−	1.20447i	−0.978837	−	0.204641i	$-0.934397\pi$
$211$	−13.9526	−	17.4960i	−0.960535	−	1.20447i	0.0183017	−	0.999833i	$-0.494174\pi$
$212$	−2.70268	+	0.511375i	−0.185621	+	0.0351214i
$213$	4.47309	−	0.167371i	0.306491	−	0.0114681i
$214$	2.71985	+	1.57031i	0.185925	+	0.107344i
$215$	−3.09622	+	9.81134i	−0.211160	+	0.669128i
$216$	−10.8245	−	2.47062i	−0.736515	−	0.168105i
$217$	−16.0785	−	3.69154i	−1.09148	−	0.250598i
$218$	0.769413	−	1.22451i	0.0521112	−	0.0829346i
$219$	−6.13285	−	6.60965i	−0.414420	−	0.446638i
$220$	−0.263195	−	2.48039i	−0.0177446	−	0.167228i
$221$	2.00584	−	0.302332i	0.134928	−	0.0203371i
$222$	−8.30503	−	0.310752i	−0.557397	−	0.0208563i
$223$	−6.50319	−	4.08622i	−0.435486	−	0.273634i	0.296396	−	0.955065i	$-0.404215\pi$
$223$	−6.50319	−	4.08622i	−0.435486	−	0.273634i	−0.731882	+	0.681431i	$0.761358\pi$
$224$	−11.2116	+	3.90696i	−0.749108	+	0.261045i
$225$	−12.2482	−	3.95275i	−0.816545	−	0.263516i
$226$	2.97456	+	5.15208i	0.197865	+	0.342711i
$227$	9.30311	−	2.49276i	0.617469	−	0.165450i	0.0634923	−	0.997982i	$-0.479776\pi$
$227$	9.30311	−	2.49276i	0.617469	−	0.165450i	0.553977	+	0.832532i	$0.313110\pi$
$228$	0.0256456	+	0.685393i	0.00169842	+	0.0453913i
$229$	20.2014	+	13.7731i	1.33494	+	0.910150i	0.999491	−	0.0319073i	$-0.0101581\pi$
$229$	20.2014	+	13.7731i	1.33494	+	0.910150i	0.335453	+	0.942057i	$0.391110\pi$
$230$	−3.02548	−	4.15552i	−0.199494	−	0.274007i
$231$	1.96776	−	1.03676i	0.129469	−	0.0682140i
$232$	−0.861987	−	7.65035i	−0.0565922	−	0.502270i
$233$	14.2444	+	7.52837i	0.933179	+	0.493200i	0.863488	−	0.504369i	$-0.168275\pi$
$233$	14.2444	+	7.52837i	0.933179	+	0.493200i	0.0696911	+	0.997569i	$0.477799\pi$
$234$	1.42847	+	3.63968i	0.0933820	+	0.237934i
$235$	−19.1154	+	15.0423i	−1.24695	+	0.981251i
$236$	−0.416064	−	0.163293i	−0.0270835	−	0.0106295i
$237$	1.80008	+	5.14434i	0.116928	+	0.334161i
$238$	−3.30746	−	2.26122i	−0.214391	−	0.146573i
$239$	11.1967	+	23.2501i	0.724252	+	1.50392i	0.858410	+	0.512964i	$0.171453\pi$
$239$	11.1967	+	23.2501i	0.724252	+	1.50392i	−0.134158	+	0.990960i	$0.542833\pi$
$240$	1.61410	+	1.51727i	0.104190	+	0.0979391i
$241$	−8.26435	+	26.7924i	−0.532354	+	1.72585i	0.144287	+	0.989536i	$0.453911\pi$
$241$	−8.26435	+	26.7924i	−0.532354	+	1.72585i	−0.676641	+	0.736313i	$0.736565\pi$
$242$	1.84926	−	9.77355i	0.118875	−	0.628268i
$243$	−11.5895	+	8.55342i	−0.743465	+	0.548702i
$244$	−1.02857			−0.0658476
$245$	−9.18036	−	12.6776i	−0.586512	−	0.809941i
$246$	2.60267			0.165940
$247$	1.39272	−	1.02787i	0.0886166	−	0.0654020i
$248$	3.53785	−	18.6980i	0.224654	−	1.18732i
$249$	−1.66258	+	5.38995i	−0.105362	+	0.341574i
$250$	7.92665	+	8.88342i	0.501325	+	0.561837i
$251$	−7.06773	−	14.6763i	−0.446111	−	0.926359i	−0.995849	−	0.0910219i	$-0.970987\pi$
$251$	−7.06773	−	14.6763i	−0.446111	−	0.926359i	0.549738	−	0.835337i	$-0.314728\pi$
$252$	−2.16178	+	5.48740i	−0.136179	+	0.345673i
$253$	−0.918359	−	2.62452i	−0.0577368	−	0.165002i
$254$	−18.8175	−	7.38533i	−1.18072	−	0.463397i
$255$	0.245733	−	2.06074i	0.0153884	−	0.129048i
$256$	−5.96419	−	15.1965i	−0.372762	−	0.949782i
$257$	−6.46882	−	3.41887i	−0.403514	−	0.213263i	0.253182	−	0.967419i	$-0.418523\pi$
$257$	−6.46882	−	3.41887i	−0.403514	−	0.213263i	−0.656696	+	0.754155i	$0.728047\pi$
$258$	−0.358034	−	3.17764i	−0.0222902	−	0.197831i
$259$	−5.92178	+	31.0788i	−0.367961	+	1.93114i
$260$	−0.429404	+	2.72872i	−0.0266305	+	0.169228i
$261$	−5.36488	−	3.65771i	−0.332078	−	0.226407i
$262$	0.546935	+	14.6171i	0.0337897	+	0.903050i
$263$	8.83724	−	2.36793i	0.544928	−	0.146013i	0.0241548	−	0.999708i	$-0.492311\pi$
$263$	8.83724	−	2.36793i	0.544928	−	0.146013i	0.520773	+	0.853695i	$0.325644\pi$
$264$	1.28284	+	2.22194i	0.0789533	+	0.136751i
$265$	6.17351	−	3.51109i	0.379236	−	0.215685i
$266$	−3.39686	−	0.387152i	−0.208275	−	0.0237378i
$267$	9.83955	+	6.18260i	0.602171	+	0.378369i
$268$	−5.41391	−	0.202574i	−0.330707	−	0.0123742i
$269$	−21.8291	+	3.29021i	−1.33094	+	0.200607i	−0.775711	−	0.631088i	$-0.782609\pi$
$269$	−21.8291	+	3.29021i	−1.33094	+	0.200607i	−0.555232	+	0.831695i	$0.687371\pi$
$270$	8.61409	−	0.914044i	0.524237	−	0.0556269i
$271$	−9.74349	−	10.5010i	−0.591875	−	0.637889i	0.364093	−	0.931363i	$-0.381379\pi$
$271$	−9.74349	−	10.5010i	−0.591875	−	0.637889i	−0.955967	+	0.293474i	$0.905189\pi$
$272$	1.14846	−	1.82776i	0.0696355	−	0.110824i
$273$	−2.40208	+	0.545016i	−0.145381	+	0.0329858i
$274$	11.9785	+	2.73400i	0.723645	+	0.165167i
$275$	2.71885	+	5.83827i	0.163953	+	0.352061i
$276$	−1.05667	−	0.610070i	−0.0636042	−	0.0367219i
$277$	5.53508	−	0.207108i	0.332571	−	0.0124439i	0.129415	−	0.991590i	$-0.458690\pi$
$277$	5.53508	−	0.207108i	0.332571	−	0.0124439i	0.203155	+	0.979147i	$0.434880\pi$
$278$	−11.2339	+	2.12556i	−0.673763	+	0.127483i
$279$	−10.0068	−	12.5481i	−0.599092	−	0.751238i
$280$	14.2036	−	11.1476i	0.848827	−	0.666195i
$281$	−0.609489	+	0.764275i	−0.0363591	+	0.0455928i	−0.799679	−	0.600428i	$-0.794997\pi$
$281$	−0.609489	+	0.764275i	−0.0363591	+	0.0455928i	0.763320	+	0.646021i	$0.223568\pi$
$282$	3.53271	−	6.68421i	0.210370	−	0.398039i
$283$	10.3576	+	4.51896i	0.615693	+	0.268624i	0.684508	−	0.729005i	$-0.260017\pi$
$283$	10.3576	+	4.51896i	0.615693	+	0.268624i	−0.0688151	+	0.997629i	$0.521922\pi$
$284$	5.92300	+	0.443868i	0.351466	+	0.0263387i
$285$	−0.636284	−	1.65266i	−0.0376902	−	0.0978952i
$286$	0.848921	−	1.76280i	0.0501978	−	0.104237i
$287$	1.48928	−	9.79536i	0.0879094	−	0.578202i
$288$	−10.9029	−	3.81507i	−0.642457	−	0.224805i
$289$	14.9358	−	1.11929i	0.878579	−	0.0658404i
$290$	2.57100	+	5.42851i	0.150974	+	0.318773i
$291$	−2.90437	+	1.98017i	−0.170257	+	0.116079i
$292$	−7.10468	−	9.62651i	−0.415770	−	0.563349i
$293$	15.9481	−	15.9481i	0.931697	−	0.931697i	−0.0661153	−	0.997812i	$-0.521061\pi$
$293$	15.9481	−	15.9481i	0.931697	−	0.931697i	0.997812	+	0.0661153i	$0.0210605\pi$
$294$	4.20696	+	2.44332i	0.245355	+	0.142497i
$295$	1.15294	+	0.0506292i	0.0671266	+	0.00294774i
$296$	−36.0880	−	5.43939i	−2.09757	−	0.316158i
$297$	4.60418	+	0.871159i	0.267162	+	0.0505498i
$298$	−11.1946	−	21.1813i	−0.648488	−	1.22700i
$299$	0.230116	+	3.07068i	0.0133079	+	0.177582i
$300$	2.57540	+	1.16363i	0.148691	+	0.0671820i
$301$	−12.1642	−	0.470794i	−0.701131	−	0.0271361i
$302$	3.86917	−	1.35388i	0.222646	−	0.0779072i
$303$	−7.17207	+	3.12914i	−0.412025	+	0.179765i
$304$	0.137652	−	1.83684i	0.00789488	−	0.105350i
$305$	2.51237	−	0.860869i	0.143858	−	0.0492932i
$306$	−1.14894	−	3.72478i	−0.0656807	−	0.212931i
$307$	15.2736	−	1.72093i	0.871713	−	0.0982184i	0.335237	−	0.942134i	$-0.391184\pi$
$307$	15.2736	−	1.72093i	0.871713	−	0.0982184i	0.536476	+	0.843916i	$0.319755\pi$
$308$	2.74869	−	1.07471i	0.156621	−	0.0612372i
$309$	4.41720	−	3.52260i	0.251286	−	0.200394i
$310$	2.11757	+	14.6952i	0.120270	+	0.834630i
$311$	−10.1040	+	10.8895i	−0.572945	+	0.617488i	−0.951335	−	0.308158i	$-0.900287\pi$
$311$	−10.1040	+	10.8895i	−0.572945	+	0.617488i	0.378390	+	0.925646i	$0.376478\pi$
$312$	−0.735390	−	2.74451i	−0.0416333	−	0.155377i
$313$	18.0964	+	4.84891i	1.02287	+	0.274077i	0.730997	−	0.682381i	$-0.239055\pi$
$313$	18.0964	+	4.84891i	1.02287	+	0.274077i	0.291871	+	0.956458i	$0.405722\pi$
$314$	2.01330	−	8.82084i	0.113617	−	0.497789i
$315$	0.687612	−	15.2127i	0.0387425	−	0.857138i
$316$	1.60927	+	7.05066i	0.0905284	+	0.396631i
$317$	−0.122021	+	3.26109i	−0.00685340	+	0.183161i	0.991669	+	0.128814i	$0.0411171\pi$
$317$	−0.122021	+	3.26109i	−0.00685340	+	0.183161i	−0.998522	+	0.0543466i	$0.982692\pi$
$318$	−1.31082	+	1.77610i	−0.0735071	+	0.0995986i
$319$	0.484267	+	3.21290i	0.0271137	+	0.179888i
$320$	11.3119	+	13.3184i	0.632355	+	0.744521i
$321$	−1.87659	+	0.428319i	−0.104741	+	0.0239065i
$322$	3.79816	−	4.75022i	0.211663	−	0.264719i
$323$	−1.46114	+	0.918093i	−0.0812998	+	0.0510840i
$324$	−4.01085	+	2.31567i	−0.222825	+	0.128648i
$325$	−1.23496	−	7.02450i	−0.0685034	−	0.389649i
$326$	17.7740	+	16.4919i	0.984411	+	0.913400i
$327$	0.164782	+	0.870895i	0.00911248	+	0.0481606i
$328$	11.3573	+	1.27966i	0.627103	+	0.0706576i
$329$	−23.1351	−	17.1204i	−1.27548	−	0.943878i
$330$	−1.50876	−	1.31552i	−0.0830546	−	0.0724170i
$331$	20.5877	−	6.35045i	1.13160	−	0.349052i	0.328268	−	0.944584i	$-0.393535\pi$
$331$	20.5877	−	6.35045i	1.13160	−	0.349052i	0.803332	+	0.595532i	$0.203059\pi$
$332$	−2.99302	+	6.86008i	−0.164263	+	0.376496i
$333$	−23.3307	+	20.0777i	−1.27851	+	1.10025i
$334$	−1.56329	+	3.98320i	−0.0855394	+	0.217951i
$335$	13.3934	−	4.03640i	0.731762	−	0.220532i
$336$	−1.22775	+	2.31582i	−0.0669794	+	0.126338i
$337$	1.03326	−	2.95290i	0.0562855	−	0.160855i	−0.912308	−	0.409505i	$-0.865701\pi$
$337$	1.03326	−	2.95290i	0.0562855	−	0.160855i	0.968593	+	0.248651i	$0.0799871\pi$
$338$	7.61657	−	8.85061i	0.414287	−	0.481410i
$339$	−3.48416	−	1.07472i	−0.189234	−	0.0583708i
$340$	0.630180	−	2.68074i	0.0341763	−	0.145384i
$341$	−1.19701	+	7.94163i	−0.0648216	+	0.430063i
$342$	−2.35197	−	2.35197i	−0.127180	−	0.127180i
$343$	11.6029	−	14.4351i	0.626497	−	0.779424i
$344$		−	14.0424i		−	0.757113i
$345$	3.09160	+	0.605756i	0.166446	+	0.0326128i
$346$	4.27758	+	6.27405i	0.229964	+	0.337295i
$347$	24.3101	−	12.8483i	1.30504	−	0.689731i	0.337228	−	0.941423i	$-0.390511\pi$
$347$	24.3101	−	12.8483i	1.30504	−	0.689731i	0.967807	+	0.251692i	$0.0809870\pi$
$348$	1.08070	+	0.930020i	0.0579317	+	0.0498543i
$349$	4.23769	−	2.04077i	0.226839	−	0.109240i	−0.317013	−	0.948421i	$-0.602680\pi$
$349$	4.23769	−	2.04077i	0.226839	−	0.109240i	0.543851	+	0.839182i	$0.316966\pi$
$350$	−7.66403	+	11.8198i	−0.409660	+	0.631796i
$351$	−4.67541	−	2.25156i	−0.249555	−	0.120179i
$352$	2.31146	+	5.29792i	0.123201	+	0.282380i
$353$	14.4578	+	16.8002i	0.769510	+	0.894187i	0.996824	−	0.0796346i	$-0.0253753\pi$
$353$	14.4578	+	16.8002i	0.769510	+	0.894187i	−0.227314	+	0.973822i	$0.572994\pi$
$354$	−0.333900	+	0.131046i	−0.0177466	+	0.00696501i
$355$	−14.8389	+	3.87311i	−0.787566	+	0.205563i
$356$	12.0557	+	9.61411i	0.638951	+	0.509547i
$357$	2.42861	−	0.362866i	0.128536	−	0.0192049i
$358$	−1.55712	+	13.8198i	−0.0822962	+	0.730399i
$359$	−6.53131	+	9.57967i	−0.344709	+	0.505596i	−0.958970	−	0.283507i	$-0.908502\pi$
$359$	−6.53131	+	9.57967i	−0.344709	+	0.505596i	0.614261	+	0.789103i	$0.289454\pi$
$360$	17.5660	+	0.113918i	0.925810	+	0.00600401i
$361$	8.76374	−	15.1793i	0.461250	−	0.798908i
$362$	−4.70703	+	17.5669i	−0.247396	+	0.923294i
$363$	3.24347	+	5.16196i	0.170238	+	0.270933i
$364$	−3.24832	+	0.361774i	−0.170258	+	0.0189621i
$365$	25.4107	+	17.5672i	1.33006	+	0.919508i
$366$	−0.605097	+	0.561448i	−0.0316289	+	0.0293474i
$367$	17.6261	+	13.0086i	0.920074	+	0.679046i	0.947220	−	0.320586i	$-0.103880\pi$
$367$	17.6261	+	13.0086i	0.920074	+	0.679046i	−0.0271451	+	0.999632i	$0.508642\pi$
$368$	2.63652	+	1.94584i	0.137438	+	0.101434i
$369$	7.06617	−	6.55644i	0.367850	−	0.341315i
$370$	28.0112	−	5.11207i	1.45623	−	0.265764i
$371$	5.93442	+	5.94968i	0.308100	+	0.308892i
$372$	1.87501	+	2.98406i	0.0972147	+	0.154716i
$373$	−3.41097	+	12.7299i	−0.176614	+	0.659131i	0.819658	+	0.572854i	$0.194164\pi$
$373$	−3.41097	+	12.7299i	−0.176614	+	0.659131i	−0.996271	+	0.0862770i	$0.972503\pi$
$374$	−0.975277	+	1.68923i	−0.0504304	+	0.0873480i
$375$	−7.26452	−	0.686752i	−0.375138	−	0.0354637i
$376$	18.7022	−	27.4310i	0.964491	−	1.41465i
$377$	0.402879	−	3.57565i	0.0207493	−	0.184155i
$378$	3.73233	+	9.54584i	0.191970	+	0.490985i
$379$	22.6737	+	18.0816i	1.16467	+	0.928791i	0.998358	−	0.0572824i	$-0.0182435\pi$
$379$	22.6737	+	18.0816i	1.16467	+	0.928791i	0.166309	+	0.986074i	$0.446815\pi$
$380$	−0.593460	−	2.27370i	−0.0304438	−	0.116638i
$381$	11.5331	−	4.52639i	0.590856	−	0.231894i
$382$	−10.3049	−	11.9745i	−0.527242	−	0.612667i
$383$	3.94532	+	9.04278i	0.201597	+	0.462064i	0.987765	−	0.155948i	$-0.0498431\pi$
$383$	3.94532	+	9.04278i	0.201597	+	0.462064i	−0.786169	+	0.618012i	$0.787938\pi$
$384$	0.384228	+	0.185035i	0.0196076	+	0.00944251i
$385$	−5.81440	+	4.92558i	−0.296329	+	0.251031i
$386$	−14.5545	+	7.00906i	−0.740802	+	0.356752i
$387$	−8.97690	−	7.72525i	−0.456322	−	0.392697i
$388$	−4.12384	+	2.17951i	−0.209356	+	0.110648i
$389$	−13.9772	−	20.5009i	−0.708674	−	1.03943i	−0.996649	−	0.0817964i	$-0.973934\pi$
$389$	−13.9772	−	20.5009i	−0.708674	−	1.03943i	0.287975	−	0.957638i	$-0.407018\pi$
$390$	1.23686	+	1.83967i	0.0626310	+	0.0931551i
$391$		−	3.06983i		−	0.155248i
$392$	17.1567	+	12.7304i	0.866543	+	0.642982i
$393$	−6.33918	−	6.33918i	−0.319770	−	0.319770i
$394$	2.77874	−	18.4357i	0.139991	−	0.928778i
$395$	−9.83185	−	15.8749i	−0.494694	−	0.798753i
$396$	2.74376	+	0.846338i	0.137879	+	0.0425301i
$397$	14.1940	−	16.4937i	0.712375	−	0.827795i	−0.278801	−	0.960349i	$-0.589937\pi$
$397$	14.1940	−	16.4937i	0.712375	−	0.827795i	0.991176	+	0.132554i	$0.0423179\pi$
$398$	−1.23468	+	3.52852i	−0.0618891	+	0.176869i
$399$	1.68753	−	1.24211i	0.0844823	−	0.0621833i
$400$	−6.52315	−	3.87981i	−0.326157	−	0.193990i
$401$	−10.3157	+	26.2840i	−0.515142	+	1.31256i	0.402598	+	0.915377i	$0.368107\pi$
$401$	−10.3157	+	26.2840i	−0.515142	+	1.31256i	−0.917740	+	0.397182i	$0.869988\pi$
$402$	−3.29552	+	2.83602i	−0.164365	+	0.141448i
$403$	3.55672	−	8.15209i	0.177173	−	0.406084i
$404$	−9.92185	+	3.06049i	−0.493631	+	0.152265i
$405$	7.85871	−	9.01310i	0.390502	−	0.447864i
$406$	−5.39289	+	4.62892i	−0.267645	+	0.229729i
$407$	15.3058	+	1.72455i	0.758681	+	0.0854828i
$408$	0.526613	+	2.78322i	0.0260712	+	0.137790i
$409$	13.1635	+	12.2140i	0.650894	+	0.603942i	0.934913	−	0.354877i	$-0.115477\pi$
$409$	13.1635	+	12.2140i	0.650894	+	0.603942i	−0.284019	+	0.958819i	$0.591668\pi$
$410$	−8.70615	+	1.92781i	−0.429966	+	0.0952077i
$411$	−6.52140	+	3.76513i	−0.321677	+	0.185720i
$412$	6.34779	−	3.98858i	0.312733	−	0.196503i
$413$	0.302140	+	1.33164i	0.0148673	+	0.0655259i
$414$	5.76879	−	1.31669i	0.283521	−	0.0647117i
$415$	1.56911	−	19.2613i	0.0770246	−	0.945500i
$416$	−0.954051	−	6.32971i	−0.0467762	−	0.310340i
$417$	4.16107	−	5.63805i	0.203768	−	0.276096i
$418$	−0.0622353	+	1.66327i	−0.00304403	+	0.0813534i
$419$	−7.52942	−	32.9886i	−0.367836	−	1.61160i	−0.732711	−	0.680540i	$-0.761745\pi$
$419$	−7.52942	−	32.9886i	−0.367836	−	1.61160i	0.364875	−	0.931057i	$-0.381112\pi$
$420$	−0.524050	+	3.30254i	−0.0255710	+	0.161148i
$421$	1.73093	−	7.58369i	0.0843603	−	0.369607i	−0.915072	−	0.403290i	$-0.867867\pi$
$421$	1.73093	−	7.58369i	0.0843603	−	0.369607i	0.999433	+	0.0336833i	$0.0107238\pi$
$422$	−23.0182	−	6.16770i	−1.12051	−	0.300239i
$423$	−7.24714	−	27.0467i	−0.352368	−	1.31506i
$424$	−6.59331	+	7.10590i	−0.320199	+	0.345093i
$425$	0.704398	+	7.07535i	0.0341683	+	0.343205i
$426$	3.72672	−	2.97196i	0.180560	−	0.143992i
$427$	1.76681	+	2.59860i	0.0855019	+	0.125755i
$428$	−2.53807	+	0.285972i	−0.122682	+	0.0138230i
$429$	0.353458	+	1.14588i	0.0170651	+	0.0553237i
$430$	3.55134	+	10.3643i	0.171261	+	0.499809i
$431$	0.772412	−	10.3071i	0.0372058	−	0.496476i	−0.947209	−	0.320616i	$-0.896110\pi$
$431$	0.772412	−	10.3071i	0.0372058	−	0.496476i	0.984415	−	0.175861i	$-0.0562708\pi$
$432$	−5.06144	+	2.20828i	−0.243519	+	0.106246i
$433$	−25.3835	+	8.88207i	−1.21985	+	0.426845i	−0.861988	−	0.506928i	$-0.830781\pi$
$433$	−25.3835	+	8.88207i	−1.21985	+	0.426845i	−0.357865	+	0.933773i	$0.616495\pi$
$434$	−16.1104	+	7.00429i	−0.773325	+	0.336217i
$435$	−3.41808	−	1.36715i	−0.163885	−	0.0655496i
$436$	0.0878913	+	1.17283i	0.00420923	+	0.0561683i
$437$	−1.22403	−	2.31597i	−0.0585531	−	0.110788i
$438$	−9.43425	−	1.78506i	−0.450786	−	0.0852933i
$439$	22.0698	+	3.32648i	1.05333	+	0.158764i	0.652810	−	0.757522i	$-0.273590\pi$
$439$	22.0698	+	3.32648i	1.05333	+	0.158764i	0.400524	+	0.916286i	$0.368828\pi$
$440$	−5.93700	−	6.48238i	−0.283036	−	0.309035i
$441$	17.5768	−	3.96432i	0.836989	−	0.188777i
$442$	1.52743	−	1.52743i	0.0726526	−	0.0726526i
$443$	−23.6085	−	31.9883i	−1.12167	−	1.51981i	−0.825262	−	0.564751i	$-0.808972\pi$
$443$	−23.6085	−	31.9883i	−1.12167	−	1.51981i	−0.296410	−	0.955061i	$-0.595790\pi$
$444$	5.58443	−	3.80740i	0.265026	−	0.180691i
$445$	−37.4936	−	13.3931i	−1.77737	−	0.634894i
$446$	−8.15587	+	0.611198i	−0.386191	+	0.0289410i
$447$	13.8594	+	4.84961i	0.655527	+	0.229379i
$448$	−11.6688	+	17.0679i	−0.551300	+	0.806382i
$449$	−0.540769	+	1.12292i	−0.0255205	+	0.0529938i	−0.913339	−	0.407199i	$-0.866505\pi$
$449$	−0.540769	+	1.12292i	−0.0255205	+	0.0529938i	0.887819	+	0.460193i	$0.152220\pi$
$450$	−12.9938	+	4.35840i	−0.612533	+	0.205457i
$451$	−4.81010	−	0.360467i	−0.226499	−	0.0169737i
$452$	−4.43448	−	1.93474i	−0.208580	−	0.0910027i
$453$	−1.17395	+	2.22122i	−0.0551569	+	0.104362i
$454$	6.39463	−	8.01862i	0.300115	−	0.376332i
$455$	7.63147	−	3.60235i	0.357769	−	0.168881i
$456$	1.50704	+	1.88977i	0.0705735	+	0.0884964i
$457$	−29.3278	+	5.54912i	−1.37190	+	0.259577i	−0.819057	−	0.573712i	$-0.805503\pi$
$457$	−29.3278	+	5.54912i	−1.37190	+	0.259577i	−0.552839	+	0.833288i	$0.686455\pi$
$458$	26.0180	−	0.973523i	1.21574	−	0.0454898i
$459$	4.48027	+	2.58669i	0.209121	+	0.120736i
$460$	3.98653	+	1.25805i	0.185873	+	0.0586570i
$461$	−10.6182	−	2.42354i	−0.494539	−	0.112875i	−0.0320248	−	0.999487i	$-0.510196\pi$
$461$	−10.6182	−	2.42354i	−0.494539	−	0.112875i	−0.462515	+	0.886612i	$0.653053\pi$
$462$	1.03039	−	2.13261i	0.0479380	−	0.0992182i
$463$	16.6518	−	26.5012i	0.773876	−	1.23162i	−0.194201	−	0.980962i	$-0.562211\pi$
$463$	16.6518	−	26.5012i	0.773876	−	1.23162i	0.968077	−	0.250655i	$-0.0806459\pi$
$464$	−2.60445	−	2.80693i	−0.120908	−	0.130308i
$465$	−7.07738	−	5.71950i	−0.328205	−	0.265235i
$466$	16.9652	−	2.55709i	0.785896	−	0.118455i
$467$	−27.7375	−	1.03786i	−1.28354	−	0.0480266i	−0.613108	−	0.789999i	$-0.710081\pi$
$467$	−27.7375	−	1.03786i	−1.28354	−	0.0480266i	−0.670430	+	0.741972i	$0.733890\pi$
$468$	−2.69242	−	1.69176i	−0.124457	−	0.0782017i
$469$	8.78785	+	14.0257i	0.405785	+	0.647648i
$470$	−6.86618	+	24.9759i	−0.316713	+	1.15205i
$471$	2.77261	+	4.80231i	0.127755	+	0.221279i
$472$	−1.52147	+	0.407678i	−0.0700316	+	0.0187649i
$473$	0.221597	+	5.92231i	0.0101890	+	0.272308i
$474$	4.79533	+	3.26940i	0.220257	+	0.150169i
$475$	3.35255	+	5.05699i	0.153826	+	0.232031i
$476$	3.25623	−	0.117653i	0.149249	−	0.00539260i
$477$	0.915373	+	8.12416i	0.0419120	+	0.371980i
$478$	24.2955	+	12.8405i	1.11125	+	0.587313i
$479$	5.87752	+	14.9757i	0.268551	+	0.684256i	0.999997	+	0.00235715i	$0.000750306\pi$
$479$	5.87752	+	14.9757i	0.268551	+	0.684256i	−0.731447	+	0.681899i	$0.761154\pi$
$480$	−6.50294	−	0.775444i	−0.296817	−	0.0353940i
$481$	−15.8784	−	6.23180i	−0.723991	−	0.284146i
$482$	9.86121	+	28.1817i	0.449166	+	1.28364i
$483$	0.273790	+	3.71752i	0.0124579	+	0.169153i
$484$	3.50988	+	7.28834i	0.159540	+	0.331288i
$485$	8.24864	−	8.77509i	0.374551	−	0.398456i
$486$	−4.52114	+	14.6572i	−0.205083	+	0.664863i
$487$	−0.877370	+	4.63701i	−0.0397574	+	0.210123i	−0.996812	−	0.0797843i	$-0.974577\pi$
$487$	−0.877370	+	4.63701i	−0.0397574	+	0.210123i	0.957055	+	0.289907i	$0.0936245\pi$
$488$	−2.91652	+	2.15249i	−0.132025	+	0.0974387i
$489$	−14.8605			−0.672014
$490$	−15.8824	−	5.05699i	−0.717494	−	0.228451i
$491$	20.3270			0.917345			0.458673	−	0.888605i	$-0.348325\pi$
$491$	20.3270			0.917345			0.458673	+	0.888605i	$0.348325\pi$
$492$	−1.70305	+	1.25691i	−0.0767793	+	0.0566657i
$493$	−0.666906	+	3.52469i	−0.0300360	+	0.158744i
$494$	0.543310	−	1.76137i	0.0244447	−	0.0792477i
$495$	−7.41019	+	0.229158i	−0.333063	+	0.0102999i
$496$	−4.10660	−	8.52744i	−0.184392	−	0.382893i
$497$	−9.05273	−	15.7264i	−0.406070	−	0.705425i
$498$	1.98383	+	5.66945i	0.0888974	+	0.254054i
$499$	−9.87920	−	3.87730i	−0.442254	−	0.173572i	0.133757	−	0.991014i	$-0.457296\pi$
$499$	−9.87920	−	3.87730i	−0.442254	−	0.173572i	−0.576010	+	0.817442i	$0.695391\pi$
$500$	−9.47683	−	1.98482i	−0.423817	−	0.0887637i
$501$	−0.958124	−	2.44126i	−0.0428058	−	0.109067i
$502$	−15.3362	−	8.10541i	−0.684487	−	0.361762i
$503$	−2.11807	−	18.7984i	−0.0944400	−	0.838178i	−0.948235	−	0.317569i	$-0.897134\pi$
$503$	−2.11807	−	18.7984i	−0.0944400	−	0.838178i	0.853795	−	0.520609i	$-0.174295\pi$
$504$	5.35372	+	20.0835i	0.238474	+	0.894589i
$505$	21.6734	−	15.7796i	0.964454	−	0.702184i
$506$	−2.44646	−	1.66797i	−0.108759	−	0.0741504i
$507$	0.267591	+	7.15153i	0.0118841	+	0.317610i
$508$	15.8798	−	4.25497i	0.704550	−	0.188784i
$509$	−2.75212	−	4.76681i	−0.121986	−	0.211285i	0.798565	−	0.601909i	$-0.205593\pi$
$509$	−2.75212	−	4.76681i	−0.121986	−	0.211285i	−0.920551	+	0.390623i	$0.872259\pi$
$510$	−1.09256	−	1.92103i	−0.0483794	−	0.0850648i
$511$	−12.1166	+	34.4851i	−0.536006	+	1.52553i
$512$	−13.6131	−	8.55367i	−0.601619	−	0.378022i
$513$	4.41143	+	0.165064i	0.194769	+	0.00728776i
$514$	−7.70442	+	1.16125i	−0.339827	+	0.0512207i
$515$	−12.1667	+	15.0552i	−0.536129	+	0.663413i
$516$	1.76885	+	1.90637i	0.0778694	+	0.0839233i
$517$	−7.45469	+	11.8641i	−0.327857	+	0.521781i
$518$	14.5789	+	30.3730i	0.640558	+	1.33451i
$519$	−4.53730	−	1.03561i	−0.199165	−	0.0454582i
$520$	4.49281	+	8.63591i	0.197023	+	0.378710i
$521$	−22.2256	−	12.8320i	−0.973723	−	0.562179i	−0.0733540	−	0.997306i	$-0.523370\pi$
$521$	−22.2256	−	12.8320i	−0.973723	−	0.562179i	−0.900369	+	0.435127i	$0.856704\pi$
$522$	−6.90959	+	0.258539i	−0.302424	+	0.0113159i
$523$	2.02162	−	0.382512i	0.0883995	−	0.0167261i	−0.141524	−	0.989935i	$-0.545200\pi$
$523$	2.02162	−	0.382512i	0.0883995	−	0.0167261i	0.229923	+	0.973209i	$0.426153\pi$
$524$	−7.41693	−	9.30053i	−0.324010	−	0.406296i
$525$	−1.48405	−	8.50532i	−0.0647691	−	0.371203i
$526$	6.07441	−	7.61707i	0.264857	−	0.332120i
$527$	−4.14321	+	7.83934i	−0.180481	+	0.341487i
$528$	1.16961	+	0.510295i	0.0509007	+	0.0222077i
$529$	−18.2887	−	1.37055i	−0.795160	−	0.0595890i
$530$	3.06924	−	6.91212i	0.133319	−	0.300243i
$531$	−0.576405	+	1.19692i	−0.0250139	+	0.0519418i
$532$	2.40969	−	1.38711i	0.104473	−	0.0601389i
$533$	5.04206	+	1.76429i	0.218396	+	0.0764200i
$534$	12.3401	−	0.924763i	0.534009	−	0.0400184i
$535$	5.96009	−	2.82276i	0.257677	−	0.122039i
$536$	−15.7751	+	10.7553i	−0.681380	+	0.464557i
$537$	−5.06149	−	6.85807i	−0.218419	−	0.295948i
$538$	−16.6227	+	16.6227i	−0.716654	+	0.716654i
$539$	−7.43666	−	5.09825i	−0.320319	−	0.219597i
$540$	−5.19518	+	4.75810i	−0.223565	+	0.204756i
$541$	16.2874	+	2.45493i	0.700250	+	0.105546i	0.489512	−	0.871997i	$-0.337175\pi$
$541$	16.2874	+	2.45493i	0.700250	+	0.105546i	0.210738	+	0.977543i	$0.432413\pi$
$542$	−14.9885	−	2.83598i	−0.643812	−	0.121816i
$543$	−5.20834	−	9.85467i	−0.223511	−	0.422904i
$544$	0.476894	+	6.36370i	0.0204466	+	0.272842i
$545$	−1.19629	−	2.79116i	−0.0512432	−	0.119560i
$546$	−1.71347	+	1.98593i	−0.0733298	+	0.0849898i
$547$	−8.57550	+	3.00070i	−0.366662	+	0.128301i	−0.507320	−	0.861758i	$-0.669364\pi$
$547$	−8.57550	+	3.00070i	−0.366662	+	0.128301i	0.140658	+	0.990058i	$0.455078\pi$
$548$	−9.15838	+	3.99576i	−0.391227	+	0.170690i
$549$	−0.228463	+	3.04862i	−0.00975056	+	0.130112i
$550$	6.02134	+	3.28298i	0.256751	+	0.139987i
$551$	0.902255	+	2.92504i	0.0384374	+	0.124611i
$552$	−4.27289	+	0.481439i	−0.181866	+	0.0204914i
$553$	15.0486	−	16.1768i	0.639931	−	0.687908i
$554$	4.61150	−	3.67755i	0.195924	−	0.156244i
$555$	−10.4538	+	13.9738i	−0.443738	+	0.593155i
$556$	6.32434	−	6.81602i	0.268212	−	0.289064i
$557$	−4.55758	−	17.0091i	−0.193111	−	0.720700i	−0.992748	−	0.120216i	$-0.961641\pi$
$557$	−4.55758	−	17.0091i	−0.193111	−	0.720700i	0.799637	−	0.600484i	$-0.205025\pi$
$558$	−16.5087	−	4.42348i	−0.698868	−	0.187261i
$559$	1.46044	−	6.39862i	0.0617702	−	0.270633i
$560$	2.39160	−	8.65600i	0.101064	−	0.365783i
$561$	−0.266018	−	1.16550i	−0.0112313	−	0.0492075i
$562$	−0.0389231	+	1.04024i	−0.00164187	+	0.0438800i
$563$	−23.2550	+	31.5094i	−0.980082	+	1.32796i	−0.0356121	+	0.999366i	$0.511338\pi$
$563$	−23.2550	+	31.5094i	−0.980082	+	1.32796i	−0.944470	+	0.328598i	$0.893424\pi$
$564$	0.916387	+	6.07983i	0.0385869	+	0.256007i
$565$	12.4509	+	1.01430i	0.523811	+	0.0426720i
$566$	11.7319	−	2.67774i	0.493130	−	0.112554i
$567$	12.7399	+	6.15537i	0.535025	+	0.258501i
$568$	17.7236	−	11.1365i	0.743665	−	0.467276i
$569$	15.2569	−	8.80859i	0.639604	−	0.369275i	−0.144858	−	0.989452i	$-0.546273\pi$
$569$	15.2569	−	8.80859i	0.639604	−	0.369275i	0.784462	+	0.620177i	$0.212939\pi$
$570$	−1.59023	−	1.01365i	−0.0666073	−	0.0424571i
$571$	−2.81671	−	2.61352i	−0.117875	−	0.109372i	0.619033	−	0.785365i	$-0.287525\pi$
$571$	−2.81671	−	2.61352i	−0.117875	−	0.109372i	−0.736909	+	0.675992i	$0.763715\pi$
$572$	0.295821	+	1.56345i	0.0123689	+	0.0653712i
$573$	9.62157	+	1.08409i	0.401947	+	0.0452885i
$574$	−4.91807	−	9.33443i	−0.205276	−	0.389612i
$575$	−10.7903	+	0.263659i	−0.449989	+	0.0109953i
$576$	−19.2214	+	5.92902i	−0.800892	+	0.247042i
$577$	−15.3668	+	35.2211i	−0.639728	+	1.46627i	0.230225	+	0.973138i	$0.426054\pi$
$577$	−15.3668	+	35.2211i	−0.639728	+	1.46627i	−0.869953	+	0.493135i	$0.835851\pi$
$578$	12.0893	−	10.4037i	0.502848	−	0.432736i
$579$	3.61715	−	9.21636i	0.150324	−	0.383019i
$580$	−4.30391	−	2.31051i	−0.178710	−	0.0959388i
$581$	22.4726	−	4.22216i	0.932320	−	0.175165i
$582$	−1.23631	+	3.53319i	−0.0512469	+	0.146455i
$583$	2.66857	−	3.10093i	0.110521	−	0.128427i
$584$	−40.2907	−	12.4280i	−1.66724	−	0.514276i
$585$	7.99238	+	1.87882i	0.330444	+	0.0776797i
$586$	3.57960	−	23.7491i	0.147872	−	0.981066i
$587$	−19.4958	−	19.4958i	−0.804677	−	0.804677i	0.179145	−	0.983823i	$-0.442667\pi$
$587$	−19.4958	−	19.4958i	−0.804677	−	0.804677i	−0.983823	+	0.179145i	$0.942667\pi$
$588$	−3.93276	+	0.432890i	−0.162184	+	0.0178521i
$589$			7.56624i			0.311762i
$590$	1.01986	−	0.685680i	0.0419868	−	0.0282290i
$591$	6.43688	+	9.44117i	0.264778	+	0.388358i
$592$	−16.0482	+	8.48171i	−0.659576	+	0.348596i
$593$	−1.41911	−	1.22125i	−0.0582761	−	0.0501506i	0.622667	−	0.782487i	$-0.286049\pi$
$593$	−1.41911	−	1.22125i	−0.0582761	−	0.0501506i	−0.680943	+	0.732336i	$0.738430\pi$
$594$	4.49575	−	2.16504i	0.184463	−	0.0888327i
$595$	−7.85513	+	3.01270i	−0.322029	+	0.123509i
$596$	17.5542	+	8.45368i	0.719050	+	0.346276i
$597$	−0.916220	−	2.10000i	−0.0374984	−	0.0859472i
$598$	2.13891	+	2.48545i	0.0874663	+	0.101638i
$599$	34.5521	−	13.5607i	1.41176	−	0.554076i	0.467712	−	0.883881i	$-0.345078\pi$
$599$	34.5521	−	13.5607i	1.41176	−	0.554076i	0.944049	+	0.329805i	$0.106983\pi$
$600$	9.73768	−	2.09007i	0.397539	−	0.0853267i
$601$	17.6154	+	14.0478i	0.718547	+	0.573022i	0.913034	−	0.407883i	$-0.133733\pi$
$601$	17.6154	+	14.0478i	0.718547	+	0.573022i	−0.194487	+	0.980905i	$0.562304\pi$
$602$	−10.7200	+	7.28862i	−0.436914	+	0.297062i
$603$	−1.80294	+	16.0015i	−0.0734212	+	0.651631i
$604$	−1.87795	+	2.75445i	−0.0764127	+	0.112077i
$605$	−14.6732	−	14.8647i	−0.596549	−	0.604337i
$606$	−4.16634	+	7.21631i	−0.169246	+	0.293143i
$607$	−6.71568	+	25.0633i	−0.272581	+	1.01729i	0.684864	+	0.728671i	$0.259862\pi$
$607$	−6.71568	+	25.0633i	−0.272581	+	1.01729i	−0.957445	+	0.288616i	$0.906805\pi$
$608$	2.89717	+	4.61081i	0.117496	+	0.186993i
$609$	0.493257	−	4.32782i	0.0199878	−	0.175372i
$610$	1.60823	−	2.32629i	0.0651154	−	0.0941886i
$611$	11.3748	−	10.5543i	0.460177	−	0.426982i
$612$	2.55061	+	1.88244i	0.103102	+	0.0760930i
$613$	−0.645553	−	0.476440i	−0.0260736	−	0.0192432i	0.580705	−	0.814114i	$-0.302777\pi$
$613$	−0.645553	−	0.476440i	−0.0260736	−	0.0192432i	−0.606779	+	0.794871i	$0.707539\pi$
$614$	11.9983	−	11.1328i	0.484211	−	0.449282i
$615$	3.10785	−	4.49547i	0.125321	−	0.181275i
$616$	5.54487	−	8.79951i	0.223409	−	0.354542i
$617$	−8.10485	−	12.8988i	−0.326289	−	0.519286i	0.642788	−	0.766044i	$-0.277778\pi$
$617$	−8.10485	−	12.8988i	−0.326289	−	0.519286i	−0.969077	+	0.246758i	$0.920635\pi$
$618$	1.55716	−	5.81139i	0.0626380	−	0.233768i
$619$	18.2623	−	31.6312i	0.734024	−	1.27137i	−0.221126	−	0.975245i	$-0.570973\pi$
$619$	18.2623	−	31.6312i	0.734024	−	1.27137i	0.955150	−	0.296122i	$-0.0956935\pi$
$620$	−8.48236	−	8.59310i	−0.340660	−	0.345107i
$621$	−4.42389	+	6.48866i	−0.177525	+	0.260381i
$622$	−1.77115	+	15.7194i	−0.0710168	+	0.630291i
$623$	3.58074	−	46.9721i	0.143459	−	1.88190i
$624$	−1.10487	−	0.881103i	−0.0442301	−	0.0352724i
$625$	24.8091	−	3.08361i	0.992364	−	0.123345i
$626$	18.5712	−	7.28867i	0.742256	−	0.291314i
$627$	−0.665409	−	0.773219i	−0.0265739	−	0.0308794i
$628$	2.94245	+	6.74416i	0.117416	+	0.269121i
$629$	15.3211	+	7.37823i	0.610890	+	0.294189i
$630$	−9.03058	−	13.4691i	−0.359787	−	0.536621i
$631$	29.3543	−	14.1363i	1.16858	−	0.562757i	0.254014	−	0.967200i	$-0.418249\pi$
$631$	29.3543	−	14.1363i	1.16858	−	0.562757i	0.914563	+	0.404443i	$0.132535\pi$
$632$	19.3180	+	16.6245i	0.768428	+	0.661286i
$633$	12.9127	−	6.82458i	0.513235	−	0.271253i
$634$	1.95760	+	2.87127i	0.0777461	+	0.114033i
$635$	−35.2263	+	23.6837i	−1.39791	+	0.939860i
$636$		−	1.79522i		−	0.0711850i
$637$	6.49372	+	7.58515i	0.257290	+	0.300535i
$638$	2.44660	+	2.44660i	0.0968616	+	0.0968616i
$639$	2.63119	−	17.4568i	0.104088	−	0.690581i
$640$	−1.42233	−	0.334357i	−0.0562226	−	0.0132166i
$641$	31.1194	+	9.59906i	1.22914	+	0.379140i	0.840278	−	0.542155i	$-0.182391\pi$
$641$	31.1194	+	9.59906i	1.22914	+	0.379140i	0.388864	+	0.921295i	$0.372868\pi$
$642$	−1.33702	+	1.55364i	−0.0527679	+	0.0613175i
$643$	−13.6764	+	39.0849i	−0.539345	+	1.54136i	0.275276	+	0.961365i	$0.411231\pi$
$643$	−13.6764	+	39.0849i	−0.539345	+	1.54136i	−0.814621	+	0.579994i	$0.803055\pi$
$644$	−0.191293	+	4.94253i	−0.00753798	+	0.194763i
$645$	−5.91611	−	3.17601i	−0.232946	−	0.125055i
$646$	−0.671350	+	1.71057i	−0.0264139	+	0.0673015i
$647$	25.4480	−	21.8998i	1.00046	−	0.860969i	0.0101686	−	0.999948i	$-0.496763\pi$
$647$	25.4480	−	21.8998i	1.00046	−	0.860969i	0.990295	+	0.138979i	$0.0443822\pi$
$648$	−6.52680	+	14.9596i	−0.256397	+	0.587668i
$649$	0.635243	−	0.195946i	0.0249355	−	0.00769157i
$650$	−5.50006	−	5.23768i	−0.215730	−	0.205439i
$651$	4.31820	−	9.86285i	0.169244	−	0.386555i
$652$	−19.5947	−	2.20780i	−0.767390	−	0.0864640i
$653$	3.03688	+	16.0503i	0.118842	+	0.628096i	0.990448	+	0.137888i	$0.0440314\pi$
$653$	3.03688	+	16.0503i	0.118842	+	0.628096i	−0.871606	+	0.490208i	$0.836921\pi$
$654$	0.691896	+	0.641985i	0.0270553	+	0.0251036i
$655$	25.9005	+	16.5096i	1.01202	+	0.645085i
$656$	4.92291	−	2.84225i	0.192207	−	0.110971i
$657$	−30.1104	+	18.9196i	−1.17472	+	0.738125i
$658$	−30.6482	−	0.0393566i	−1.19479	−	0.00153428i
$659$	−36.8755	+	8.41660i	−1.43647	+	0.327864i	−0.868706	−	0.495329i	$-0.835048\pi$
$659$	−36.8755	+	8.41660i	−1.43647	+	0.327864i	−0.567762	+	0.823193i	$0.692191\pi$
$660$	1.62256	+	0.132181i	0.0631579	+	0.00514512i
$661$	3.28164	+	21.7723i	0.127641	+	0.846844i	0.957409	+	0.288735i	$0.0932347\pi$
$661$	3.28164	+	21.7723i	0.127641	+	0.846844i	−0.829768	+	0.558109i	$0.811527\pi$
$662$	13.6239	−	18.4597i	0.529506	−	0.717455i
$663$	−0.0495027	+	1.32299i	−0.00192252	+	0.0513805i
$664$	5.86934	+	25.7153i	0.227775	+	0.997946i
$665$	−4.72490	+	5.40492i	−0.183224	+	0.209594i
$666$	−7.29369	+	31.9557i	−0.282625	+	1.23826i
$667$	−5.25990	−	1.40939i	−0.203664	−	0.0545717i
$668$	−0.900670	−	3.36135i	−0.0348480	−	0.130054i
$669$	3.40948	−	3.67454i	0.131818	−	0.142066i
$670$	8.92312	−	11.9277i	0.344730	−	0.460808i
$671$	1.19606	−	0.953829i	0.0461735	−	0.0368222i
$672$	−1.14507	−	7.66382i	−0.0441721	−	0.295638i
$673$	−22.4883	+	2.53382i	−0.866861	+	0.0976717i	−0.534183	−	0.845369i	$-0.679381\pi$
$673$	−22.4883	+	2.53382i	−0.866861	+	0.0976717i	−0.332678	+	0.943041i	$0.607952\pi$
$674$	−0.981959	−	3.18343i	−0.0378236	−	0.122621i
$675$	8.70731	−	15.9702i	0.335145	−	0.614692i
$676$	−0.709650	+	9.46963i	−0.0272942	+	0.364216i
$677$	−8.66089	+	3.77871i	−0.332865	+	0.145228i	−0.559677	−	0.828711i	$-0.689075\pi$
$677$	−8.66089	+	3.77871i	−0.332865	+	0.145228i	0.226812	+	0.973939i	$0.427170\pi$
$678$	−3.66484	+	1.28238i	−0.140747	+	0.0492496i
$679$	12.5900	+	6.67470i	0.483159	+	0.256151i
$680$	−3.82310	−	8.92003i	−0.146609	−	0.342067i
$681$	0.469747	+	6.26834i	0.0180007	+	0.240203i
$682$	3.99628	+	7.56133i	0.153026	+	0.289538i
$683$	−1.47189	−	0.278497i	−0.0563204	−	0.0106564i	0.157675	−	0.987491i	$-0.449600\pi$
$683$	−1.47189	−	0.278497i	−0.0563204	−	0.0106564i	−0.213995	+	0.976835i	$0.568648\pi$
$684$	2.67483	+	0.403166i	0.102275	+	0.0154155i
$685$	19.0258	−	17.4251i	0.726938	−	0.665779i
$686$	0.813344	−	19.7051i	0.0310536	−	0.752345i
$687$	−11.2835	+	11.2835i	−0.430493	+	0.430493i
$688$	−4.14735	−	5.61946i	−0.158116	−	0.214240i
$689$	−3.74338	+	2.55219i	−0.142611	+	0.0972308i
$690$	3.03194	−	1.43596i	0.115424	−	0.0546660i
$691$	38.9494	−	2.91885i	1.48170	−	0.111038i	0.690830	−	0.723017i	$-0.257245\pi$
$691$	38.9494	−	2.91885i	1.48170	−	0.111038i	0.790874	+	0.611979i	$0.209626\pi$
$692$	−5.82894	−	2.03963i	−0.221583	−	0.0775353i
$693$	−2.57484	−	8.38564i	−0.0978101	−	0.318544i
$694$	12.7044	−	26.3809i	0.482251	−	1.00141i
$695$	−9.74299	+	21.9418i	−0.369573	+	0.832302i
$696$	5.01059	+	0.375491i	0.189926	+	0.0142330i
$697$	−4.88107	−	2.12959i	−0.184884	−	0.0806640i
$698$	2.34039	−	4.42823i	0.0885851	−	0.167611i
$699$	−6.55613	+	8.22113i	−0.247976	+	0.310952i
$700$	−0.693213	−	11.4354i	−0.0262010	−	0.432219i
$701$	−9.28885	−	11.6478i	−0.350835	−	0.439933i	0.574833	−	0.818271i	$-0.305067\pi$
$701$	−9.28885	−	11.6478i	−0.350835	−	0.439933i	−0.925668	+	0.378338i	$0.876496\pi$
$702$	−5.42967	+	1.02735i	−0.204930	+	0.0387748i
$703$	14.5006	−	0.542572i	0.546899	−	0.0204635i
$704$	8.71712	+	5.03283i	0.328539	+	0.189682i
$705$	−7.32689	−	14.0835i	−0.275947	−	0.530415i
$706$	23.0111	+	5.25213i	0.866033	+	0.197666i
$707$	24.7751	+	19.8096i	0.931764	+	0.745016i
$708$	0.155200	−	0.246999i	0.00583277	−	0.00928280i
$709$	3.58006	+	3.85839i	0.134452	+	0.144905i	0.796689	−	0.604390i	$-0.206583\pi$
$709$	3.58006	+	3.85839i	0.134452	+	0.144905i	−0.662237	+	0.749295i	$0.730393\pi$
$710$	−10.2648	+	12.7018i	−0.385233	+	0.476692i
$711$	21.2552	−	3.20370i	0.797131	−	0.120148i
$712$	54.3034	+	2.03189i	2.03511	+	0.0761483i
$713$	−11.3969	−	7.16117i	−0.426819	−	0.268188i
$714$	1.85138	−	1.84663i	0.0692863	−	0.0691086i
$715$	−2.03110	−	3.57126i	−0.0759590	−	0.133558i
$716$	−5.65509	−	9.79491i	−0.211341	−	0.366053i
$717$	−16.2683	+	4.35909i	−0.607552	+	0.162793i
$718$	0.461654	+	12.3380i	0.0172288	+	0.460448i
$719$	−37.0151	−	25.2365i	−1.38043	−	0.941162i	−0.999865	−	0.0164089i	$-0.994777\pi$
$719$	−37.0151	−	25.2365i	−1.38043	−	0.941162i	−0.380566	−	0.924754i	$-0.624271\pi$
$720$	7.06320	−	5.14246i	0.263230	−	0.191648i
$721$	−20.9806	−	9.18582i	−0.781358	−	0.342098i
$722$	−2.08979	−	18.5474i	−0.0777738	−	0.690261i
$723$	−16.1786	−	8.55063i	−0.601688	−	0.318001i
$724$	−5.40353	−	13.7680i	−0.200821	−	0.511683i
$725$	12.4464	+	2.04143i	0.462248	+	0.0758167i
$726$	6.04318	+	2.37177i	0.224283	+	0.0880247i
$727$	2.54438	+	7.27142i	0.0943658	+	0.269682i	0.981385	−	0.192050i	$-0.0615137\pi$
$727$	2.54438	+	7.27142i	0.0943658	+	0.269682i	−0.887019	+	0.461732i	$0.847228\pi$
$728$	−8.45353	+	7.82355i	−0.313309	+	0.289960i
$729$	2.88209	+	5.98472i	0.106744	+	0.221656i
$730$	32.8805	−	1.01682i	1.21696	−	0.0376342i
$731$	−1.92859	+	6.25233i	−0.0713314	+	0.231251i
$732$	0.124803	−	0.659600i	0.00461286	−	0.0243795i
$733$	13.0255	−	9.61327i	0.481109	−	0.355074i	−0.326105	−	0.945333i	$-0.605736\pi$
$733$	13.0255	−	9.61327i	0.481109	−	0.355074i	0.807214	+	0.590259i	$0.200974\pi$
$734$	23.3281			0.861055
$735$	9.24376	−	4.34891i	0.340961	−	0.160412i
$736$	−9.68727			−0.357078
$737$	6.48336	−	4.78494i	0.238818	−	0.176255i
$738$	1.90835	−	10.0859i	0.0702472	−	0.371266i
$739$	−4.14777	+	13.4467i	−0.152578	+	0.494646i	−0.999301	−	0.0373883i	$-0.988096\pi$
$739$	−4.14777	+	13.4467i	−0.152578	+	0.494646i	0.846723	+	0.532035i	$0.178572\pi$
$740$	−15.8602	+	16.8725i	−0.583034	+	0.620245i
$741$	0.490165	+	1.01784i	0.0180067	+	0.0373912i
$742$	8.84689	+	1.34508i	0.324780	+	0.0493793i
$743$	5.50123	+	15.7216i	0.201821	+	0.576770i	0.999659	−	0.0261009i	$-0.00830912\pi$
$743$	5.50123	+	15.7216i	0.201821	+	0.576770i	−0.797839	+	0.602871i	$0.794023\pi$
$744$	11.5613	+	4.53749i	0.423859	+	0.166352i
$745$	−49.9529	−	5.95665i	−1.83013	−	0.218235i
$746$	5.12722	+	13.0640i	0.187721	+	0.478305i
$747$	19.6680	+	10.3949i	0.719616	+	0.380328i
$748$	−0.177610	−	1.57633i	−0.00649406	−	0.0576363i
$749$	5.08220	+	5.92099i	0.185700	+	0.216348i
$750$	−6.65853	+	4.00530i	−0.243135	+	0.146253i
$751$	4.67784	+	3.18930i	0.170697	+	0.116379i	0.645655	−	0.763629i	$-0.276584\pi$
$751$	4.67784	+	3.18930i	0.170697	+	0.116379i	−0.474958	+	0.880008i	$0.657537\pi$
$752$	−0.617422	−	16.5010i	−0.0225151	−	0.601728i
$753$	10.2691	−	2.75161i	0.374228	−	0.100274i
$754$	−1.91587	−	3.31839i	−0.0697719	−	0.120848i
$755$	2.28169	−	8.29970i	0.0830391	−	0.302057i
$756$	−7.05220	−	4.44383i	−0.256486	−	0.161621i
$757$	−33.8639	−	21.2781i	−1.23080	−	0.773366i	−0.249979	−	0.968251i	$-0.580424\pi$
$757$	−33.8639	−	21.2781i	−1.23080	−	0.773366i	−0.980826	+	0.194886i	$0.937566\pi$
$758$	30.8607	+	1.15473i	1.12091	+	0.0419416i
$759$	1.79448	−	0.270474i	0.0651354	−	0.00981758i
$760$	−6.44092	−	5.20515i	−0.233637	−	0.188811i
$761$	1.09648	+	1.18172i	0.0397474	+	0.0428375i	0.752613	−	0.658464i	$-0.228793\pi$
$761$	1.09648	+	1.18172i	0.0397474	+	0.0428375i	−0.712865	+	0.701301i	$0.752603\pi$
$762$	7.01929	−	11.1711i	0.254282	−	0.404688i
$763$	2.81207	−	2.23665i	0.101804	−	0.0809722i
$764$	12.5258	+	2.85892i	0.453166	+	0.103432i
$765$	−7.80558	−	2.46325i	−0.282211	−	0.0890590i
$766$	9.09855	+	5.25305i	0.328744	+	0.189800i
$767$	−0.735684	+	0.0275273i	−0.0265640	+	0.000993955i
$768$	10.4688	−	1.98081i	0.377762	−	0.0714764i
$769$	−2.87676	−	3.60734i	−0.103739	−	0.130084i	0.727252	−	0.686371i	$-0.240797\pi$
$769$	−2.87676	−	3.60734i	−0.103739	−	0.130084i	−0.830991	+	0.556287i	$0.812226\pi$
$770$	−1.86710	+	7.89698i	−0.0672856	+	0.284587i
$771$	2.97735	−	3.73347i	0.107227	−	0.134458i
$772$	6.13877	−	11.6151i	0.220939	−	0.418037i
$773$	8.12731	+	3.54591i	0.292319	+	0.127537i	0.540934	−	0.841065i	$-0.318071\pi$
$773$	8.12731	+	3.54591i	0.292319	+	0.127537i	−0.248615	+	0.968602i	$0.579976\pi$
$774$	−12.5765	−	0.942477i	−0.452052	−	0.0338766i
$775$	27.9108	+	13.8899i	1.00259	+	0.498942i
$776$	−7.13210	+	14.8100i	−0.256027	+	0.531647i
$777$	−19.2116	−	7.56849i	−0.689213	−	0.271518i
$778$	−24.9394	−	8.72668i	−0.894122	−	0.312867i
$779$	−4.53155	+	0.339593i	−0.162360	+	0.0121672i
$780$	−1.69777	−	0.606460i	−0.0607897	−	0.0217148i
$781$	−7.29911	+	4.97645i	−0.261183	+	0.178071i
$782$	−1.94120	−	2.63024i	−0.0694173	−	0.0940572i
$783$	6.48900	−	6.48900i	0.231898	−	0.231898i
$784$	10.6256	+	0.0272896i	0.379487	+	0.000974628i
$785$	−12.8317	−	14.0104i	−0.457983	−	0.500054i
$786$	−9.44000	−	1.42285i	−0.336714	−	0.0507514i
$787$	33.2762	+	6.29620i	1.18617	+	0.224435i	0.741309	−	0.671164i	$-0.234205\pi$
$787$	33.2762	+	6.29620i	1.18617	+	0.224435i	0.444861	+	0.895600i	$0.353253\pi$
$788$	7.08489	+	13.4053i	0.252389	+	0.477543i
$789$	0.446223	+	5.95444i	0.0158860	+	0.211984i
$790$	−18.4624	−	7.38449i	−0.656864	−	0.262729i
$791$	2.72928	+	14.5267i	0.0970420	+	0.516509i
$792$	9.55107	−	3.34206i	0.339383	−	0.118755i
$793$	−1.55282	+	0.677490i	−0.0551424	+	0.0240584i
$794$	1.73166	−	23.1074i	0.0614542	−	0.820050i
$795$	1.50252	+	4.38495i	0.0532887	+	0.155518i
$796$	−0.896117	−	2.90514i	−0.0317620	−	0.102970i
$797$	−41.9414	+	4.72566i	−1.48564	+	0.167392i	−0.817192	−	0.576366i	$-0.804470\pi$
$797$	−41.9414	+	4.72566i	−1.48564	+	0.167392i	−0.668450	+	0.743757i	$0.733042\pi$
$798$	0.660434	−	2.13135i	0.0233791	−	0.0754491i
$799$	−12.0945	+	9.64504i	−0.427873	+	0.341217i
$800$	22.3272	−	2.22282i	0.789387	−	0.0785887i
$801$	31.1734	−	33.5969i	1.10146	−	1.18709i
$802$	7.78213	+	29.0433i	0.274796	+	1.02555i
$803$	17.1886	+	4.60566i	0.606572	+	0.162530i
$804$	0.786810	−	3.44724i	0.0277486	−	0.121575i
$805$	−3.66943	−	12.2326i	−0.129330	−	0.431143i
$806$	−2.10756	−	9.23381i	−0.0742355	−	0.325247i
$807$	0.538725	−	14.3977i	0.0189640	−	0.506824i
$808$	−21.7288	+	29.4415i	−0.764416	+	1.03575i
$809$	5.81835	+	38.6022i	0.204562	+	1.35718i	0.821518	+	0.570183i	$0.193128\pi$
$809$	5.81835	+	38.6022i	0.204562	+	1.35718i	−0.616956	+	0.786998i	$0.711634\pi$
$810$	1.03394	−	12.6919i	0.0363288	−	0.445948i
$811$	−40.1579	+	9.16578i	−1.41013	+	0.321854i	−0.858749	−	0.512397i	$-0.828758\pi$
$811$	−40.1579	+	9.16578i	−1.41013	+	0.321854i	−0.551386	+	0.834251i	$0.685901\pi$
$812$	1.29338	−	5.63330i	0.0453886	−	0.197690i
$813$	7.91628	−	4.97413i	0.277636	−	0.174450i
$814$	14.2046	−	8.20101i	0.497870	−	0.287445i
$815$	49.7095	−	11.0072i	1.74125	−	0.385566i
$816$	1.03275	+	0.958254i	0.0361536	+	0.0335456i
$817$	1.03799	+	5.48592i	0.0363147	+	0.191928i
$818$	19.0020	+	2.14101i	0.664390	+	0.0748588i
$819$	0.350770	+	9.70816i	0.0122569	+	0.339230i
$820$	4.76584	−	5.46591i	0.166430	−	0.190878i
$821$	−17.0102	+	5.24696i	−0.593661	+	0.183120i	−0.577004	−	0.816741i	$-0.695778\pi$
$821$	−17.0102	+	5.24696i	−0.593661	+	0.183120i	−0.0166564	+	0.999861i	$0.505302\pi$
$822$	−3.20668	+	7.34978i	−0.111846	+	0.256353i
$823$	−12.2212	+	10.5172i	−0.426006	+	0.366607i	−0.839005	−	0.544124i	$-0.816862\pi$
$823$	−12.2212	+	10.5172i	−0.426006	+	0.366607i	0.412999	+	0.910731i	$0.364481\pi$
$824$	9.65229	−	24.5936i	0.336254	−	0.856760i
$825$	−4.07385	+	1.03514i	−0.141833	+	0.0360391i
$826$	1.10094	+	0.949896i	0.0383065	+	0.0330511i
$827$	−5.10475	+	14.5885i	−0.177510	+	0.507293i	−0.997919	−	0.0644836i	$-0.979460\pi$
$827$	−5.10475	+	14.5885i	−0.177510	+	0.507293i	0.820409	+	0.571777i	$0.193746\pi$
$828$	−3.13892	+	3.64749i	−0.109085	+	0.126759i
$829$	−42.4857	−	13.1051i	−1.47559	−	0.455160i	−0.550477	−	0.834850i	$-0.685554\pi$
$829$	−42.4857	−	13.1051i	−1.47559	−	0.455160i	−0.925114	+	0.379690i	$0.876031\pi$
$830$	−10.8354	−	17.4953i	−0.376104	−	0.607272i
$831$	−0.538792	+	3.57465i	−0.0186905	+	0.124003i
$832$	−7.88218	−	7.88218i	−0.273266	−	0.273266i
$833$	−5.89057	−	8.02449i	−0.204096	−	0.278032i
$834$		−	7.46194i		−	0.258386i
$835$	5.01325	+	7.45653i	0.173491	+	0.258044i
$836$	−0.762520	−	1.11841i	−0.0263723	−	0.0386811i
$837$	20.0546	−	10.5992i	0.693189	−	0.366361i
$838$	−27.3115	−	23.5034i	−0.943460	−	0.811913i
$839$	−13.7442	+	6.61884i	−0.474501	+	0.228508i	−0.655821	−	0.754916i	$-0.727677\pi$
$839$	−13.7442	+	6.61884i	−0.474501	+	0.228508i	0.181320	+	0.983424i	$0.441963\pi$
$840$	5.42527	+	10.4610i	0.187190	+	0.360941i
$841$	−20.3950	−	9.82173i	−0.703277	−	0.338680i
$842$	−3.31248	−	7.59228i	−0.114155	−	0.261647i
$843$	−0.416159	−	0.483586i	−0.0143333	−	0.0166556i
$844$	18.0404	−	7.08034i	0.620977	−	0.243715i
$845$	−6.19227	−	23.7242i	−0.213021	−	0.816138i
$846$	−23.3123	−	18.5910i	−0.801494	−	0.639170i
$847$	12.3843	−	21.3868i	0.425530	−	0.734859i
$848$	−0.539809	+	4.79094i	−0.0185371	+	0.164522i
$849$	−4.15465	+	6.09375i	−0.142587	+	0.209137i
$850$	5.07762	+	5.61675i	0.174161	+	0.192653i
$851$	−12.9070	+	22.3555i	−0.442445	+	0.766338i
$852$	−1.00332	+	3.74443i	−0.0343731	+	0.128282i
$853$	19.1924	+	30.5445i	0.657134	+	1.04582i	0.994529	+	0.104459i	$0.0333111\pi$
$853$	19.1924	+	30.5445i	0.657134	+	1.04582i	−0.337396	+	0.941363i	$0.609546\pi$
$854$	3.15703	+	1.10924i	0.108031	+	0.0379575i
$855$	−6.87092	+	1.25395i	−0.234981	+	0.0428842i
$856$	−6.59826	+	6.12229i	−0.225524	+	0.209256i
$857$	−13.1629	−	9.71464i	−0.449635	−	0.331846i	0.345351	−	0.938474i	$-0.387760\pi$
$857$	−13.1629	−	9.71464i	−0.449635	−	0.331846i	−0.794986	+	0.606628i	$0.792522\pi$
$858$	1.02744	+	0.758286i	0.0350763	+	0.0258875i
$859$	−20.4284	+	18.9548i	−0.697009	+	0.646730i	−0.946894	−	0.321546i	$-0.895798\pi$
$859$	−20.4284	+	18.9548i	−0.697009	+	0.646730i	0.249885	+	0.968276i	$0.419607\pi$
$860$	−7.32901	−	5.06677i	−0.249917	−	0.172775i
$861$	6.10084	+	2.14357i	0.207916	+	0.0730528i
$862$	−5.85589	−	9.31959i	−0.199452	−	0.317427i
$863$	−1.72891	+	6.45238i	−0.0588528	+	0.219642i	−0.989089	−	0.147320i	$-0.952935\pi$
$863$	−1.72891	+	6.45238i	−0.0588528	+	0.219642i	0.930236	+	0.366962i	$0.119602\pi$
$864$	8.16264	−	14.1381i	0.277699	−	0.480988i
$865$	15.9447	+	0.103404i	0.542137	+	0.00351584i
$866$	−16.1321	+	23.6614i	−0.548190	+	0.804047i
$867$	−1.09449	+	9.71383i	−0.0371707	+	0.329899i
$868$	7.15921	−	12.3634i	0.242999	−	0.419642i
$869$	−8.40963	−	6.70646i	−0.285277	−	0.227501i
$870$	−3.79313	+	0.990048i	−0.128599	+	0.0335658i
$871$	−8.30675	+	3.26016i	−0.281463	+	0.110466i
$872$	2.70359	+	3.14163i	0.0915551	+	0.106389i
$873$	5.54397	+	12.7069i	0.187635	+	0.430064i
$874$	−2.51325	−	1.21032i	−0.0850120	−	0.0409396i
$875$	11.2642	+	27.3518i	0.380799	+	0.924658i
$876$	7.03532	−	3.38803i	0.237701	−	0.114471i
$877$	5.56619	+	4.79010i	0.187957	+	0.161750i	0.741233	−	0.671248i	$-0.234241\pi$
$877$	5.56619	+	4.79010i	0.187957	+	0.161750i	−0.553276	+	0.832998i	$0.686622\pi$
$878$	21.0129	−	11.1057i	0.709152	−	0.374798i
$879$	8.29206	+	12.1622i	0.279684	+	0.410222i
$880$	−4.29041	−	0.840645i	−0.144630	−	0.0283381i
$881$			3.97077i			0.133779i	0.997760	+	0.0668893i	$0.0213074\pi$
$881$			3.97077i			0.133779i	−0.997760	+	0.0668893i	$0.978693\pi$
$882$	12.5530	−	14.5113i	0.422681	−	0.488620i
$883$	23.3560	+	23.3560i	0.785991	+	0.785991i	0.980834	−	0.194843i	$-0.0624198\pi$
$883$	23.3560	+	23.3560i	0.785991	+	0.785991i	−0.194843	+	0.980834i	$0.562420\pi$
$884$	−0.261827	+	1.73711i	−0.00880621	+	0.0584254i
$885$	−0.172360	+	0.733210i	−0.00579383	+	0.0246466i
$886$	−40.4556	−	12.4789i	−1.35913	−	0.419236i
$887$	15.4371	−	17.9383i	0.518328	−	0.602308i	−0.436413	−	0.899746i	$-0.643751\pi$
$887$	15.4371	−	17.9383i	0.518328	−	0.602308i	0.954741	+	0.297439i	$0.0961324\pi$
$888$	7.86694	−	22.4824i	0.263997	−	0.754461i
$889$	−38.0269	−	32.8099i	−1.27538	−	1.10041i
$890$	−40.5937	+	12.2338i	−1.36070	+	0.410077i
$891$	2.51658	−	6.41214i	0.0843086	−	0.214815i
$892$	5.04159	−	4.33864i	0.168805	−	0.145268i
$893$	−5.27870	+	12.0989i	−0.176645	+	0.404875i
$894$	14.9414	−	4.60881i	0.499715	−	0.154142i
$895$	22.0109	+	19.1918i	0.735743	+	0.641510i
$896$	−0.0624234	−	1.72767i	−0.00208542	−	0.0577175i
$897$	−1.99708	−	0.225017i	−0.0666805	−	0.00751309i
$898$	0.246744	+	1.30407i	0.00823396	+	0.0435175i
$899$	11.5299	+	10.6982i	0.384543	+	0.356804i
$900$	6.39763	−	9.12698i	0.213254	−	0.304233i
$901$	3.91158	−	2.25835i	0.130314	−	0.0752367i
$902$	−4.34925	+	2.73281i	−0.144814	+	0.0909927i
$903$	1.77786	−	7.74348i	0.0591636	−	0.257687i
$904$	−16.6228	+	3.79405i	−0.552867	+	0.126188i
$905$	24.7217	+	29.1068i	0.821778	+	0.967544i
$906$	0.398743	+	2.64549i	0.0132474	+	0.0878905i
$907$	−11.5958	+	15.7118i	−0.385033	+	0.521701i	−0.953657	−	0.300896i	$-0.902714\pi$
$907$	−11.5958	+	15.7118i	−0.385033	+	0.521701i	0.568624	+	0.822598i	$0.307476\pi$
$908$	−0.311878	+	8.33511i	−0.0103500	+	0.276610i
$909$	6.86728	+	30.0875i	0.227773	+	0.997941i
$910$	4.26072	−	7.91226i	0.141241	−	0.262289i
$911$	−1.95694	+	8.57391i	−0.0648363	+	0.284066i	−0.996944	−	0.0781137i	$-0.975110\pi$
$911$	−1.95694	+	8.57391i	−0.0648363	+	0.284066i	0.932108	+	0.362180i	$0.117967\pi$
$912$	1.16122	+	0.311148i	0.0384519	+	0.0103031i
$913$	−2.88118	−	10.7527i	−0.0953530	−	0.355862i
$914$	−21.6191	+	23.2999i	−0.715097	+	0.770692i
$915$	0.247215	+	1.71558i	0.00817266	+	0.0567153i
$916$	−16.5546	+	13.2019i	−0.546980	+	0.436202i
$917$	−10.7567	+	34.7140i	−0.355217	+	1.14636i
$918$	5.47440	−	0.616816i	0.180682	−	0.0203580i
$919$	7.76013	+	25.1577i	0.255983	+	0.829877i	0.988773	+	0.149423i	$0.0477415\pi$
$919$	7.76013	+	25.1577i	0.255983	+	0.829877i	−0.732790	+	0.680455i	$0.761782\pi$
$920$	13.9366	−	4.77539i	0.459475	−	0.157440i
$921$	−0.749655	+	10.0035i	−0.0247020	+	0.329625i
$922$	−10.6302	+	4.63792i	−0.350088	+	0.152742i
$923$	9.23425	−	3.23120i	0.303949	−	0.106356i
$924$	0.355671	+	1.89307i	0.0117007	+	0.0622775i
$925$	24.6183	−	54.4866i	0.809446	−	1.79151i
$926$	−2.49070	−	33.2361i	−0.0818495	−	1.09221i
$927$	−10.4120	−	19.7004i	−0.341974	−	0.647045i
$928$	11.1226	+	2.10451i	0.365118	+	0.0690840i
$929$	52.7987	+	7.95813i	1.73227	+	0.261098i	0.938042	−	0.346522i	$-0.112637\pi$
$929$	52.7987	+	7.95813i	1.73227	+	0.261098i	0.794228	+	0.607620i	$0.207876\pi$
$930$	−9.68063	−	0.425107i	−0.317440	−	0.0139398i
$931$	−7.64360	−	3.70518i	−0.250509	−	0.121432i
$932$	−9.86619	+	9.86619i	−0.323178	+	0.323178i
$933$	−5.75722	−	7.80076i	−0.188483	−	0.255386i
$934$	−24.4218	+	16.6505i	−0.799107	+	0.544822i
$935$	1.75314	+	3.70166i	0.0573339	+	0.121057i
$936$	−11.1747	+	0.837430i	−0.365257	+	0.0273722i
$937$	−8.96726	−	3.13778i	−0.292947	−	0.102507i	0.179804	−	0.983702i	$-0.442454\pi$
$937$	−8.96726	−	3.13778i	−0.292947	−	0.102507i	−0.472752	+	0.881196i	$0.656739\pi$
$938$	16.3986	+	6.46029i	0.535433	+	0.210936i
$939$	−5.30525	+	11.0165i	−0.173130	+	0.359508i
$940$	−7.56874	−	19.6588i	−0.246865	−	0.641198i
$941$	−12.4295	−	0.931463i	−0.405190	−	0.0303648i	−0.129424	−	0.991589i	$-0.541313\pi$
$941$	−12.4295	−	0.931463i	−0.405190	−	0.0303648i	−0.275767	+	0.961225i	$0.588932\pi$
$942$	5.41232	+	2.36137i	0.176343	+	0.0769376i
$943$	3.77742	−	7.14723i	0.123010	−	0.232746i
$944$	−0.488457	+	0.612506i	−0.0158979	+	0.0199354i
$945$	20.9448	+	4.95203i	0.681335	+	0.161090i
$946$	3.93483	+	4.93412i	0.127932	+	0.160422i
$947$	32.8529	−	6.21611i	1.06758	−	0.201996i	0.377704	−	0.925927i	$-0.376714\pi$
$947$	32.8529	−	6.21611i	1.06758	−	0.201996i	0.689873	+	0.723930i	$0.257666\pi$
$948$	−4.71669	+	0.176486i	−0.153191	+	0.00573201i
$949$	−17.0666	−	9.85338i	−0.554004	−	0.319854i
$950$	6.07026	+	2.21285i	0.196945	+	0.0717945i
$951$	−2.07646	−	0.473938i	−0.0673337	−	0.0153685i
$952$	8.98685	−	7.14792i	0.291266	−	0.231665i
$953$	−16.2463	+	25.8559i	−0.526270	+	0.837553i	−0.999048	−	0.0436280i	$-0.986108\pi$
$953$	−16.2463	+	25.8559i	−0.526270	+	0.837553i	0.472778	+	0.881182i	$0.343251\pi$
$954$	5.92160	+	6.38196i	0.191719	+	0.206624i
$955$	−32.9879	+	3.50036i	−1.06746	+	0.113269i
$956$	−22.0987	+	3.33085i	−0.714724	+	0.107727i
$957$	−2.11912	−	0.0792919i	−0.0685014	−	0.00256314i
$958$	14.5057	+	9.11455i	0.468659	+	0.294478i
$959$	25.8266	+	16.2742i	0.833983	+	0.525521i
$960$	−9.91333	+	5.63806i	−0.319951	+	0.181968i
$961$	3.93892	+	6.82241i	0.127062	+	0.220078i
$962$	−17.5453	+	4.70125i	−0.565683	+	0.151574i
$963$	0.283856	+	7.58620i	0.00914712	+	0.244462i
$964$	−20.0624	−	13.6783i	−0.646167	−	0.440549i
$965$	−5.27309	+	33.5087i	−0.169747	+	1.07868i
$966$	2.58535	+	3.01205i	0.0831824	+	0.0969111i
$967$	3.58474	+	31.8154i	0.115277	+	1.02312i	0.909562	+	0.415569i	$0.136418\pi$
$967$	3.58474	+	31.8154i	0.115277	+	1.02312i	−0.794284	+	0.607547i	$0.792154\pi$
$968$	25.2046	+	13.3210i	0.810106	+	0.428153i
$969$	−0.411463	−	1.04839i	−0.0132181	−	0.0336792i
$970$	1.51853	−	12.7345i	0.0487571	−	0.408881i
$971$	−42.8602	−	16.8214i	−1.37545	−	0.539824i	−0.441510	−	0.897256i	$-0.645557\pi$
$971$	−42.8602	−	16.8214i	−1.37545	−	0.539824i	−0.933939	+	0.357432i	$0.883652\pi$
$972$	−4.11999	−	11.7743i	−0.132149	−	0.377660i
$973$	−28.0836	−	4.26981i	−0.900318	−	0.136884i
$974$	2.18048	+	4.52781i	0.0698670	+	0.145080i
$975$	4.65450	+	0.0603728i	0.149063	+	0.00193348i
$976$	−0.531403	+	1.72277i	−0.0170098	+	0.0551444i
$977$	−4.79746	+	25.3552i	−0.153484	+	0.811185i	0.818206	+	0.574926i	$0.194969\pi$
$977$	−4.79746	+	25.3552i	−0.153484	+	0.811185i	−0.971690	+	0.236259i	$0.924079\pi$
$978$	−12.7325	+	9.39700i	−0.407140	+	0.300483i
$979$	−22.9343			−0.732984
$980$	12.8348	−	4.36106i	0.409991	−	0.139309i
$981$	3.49571			0.111609
$982$	17.4162	−	12.8538i	0.555774	−	0.410180i
$983$	6.92102	−	36.5784i	0.220746	−	1.16667i	−0.680295	−	0.732938i	$-0.738148\pi$
$983$	6.92102	−	36.5784i	0.220746	−	1.16667i	0.901041	−	0.433733i	$-0.142804\pi$
$984$	−2.19867	+	7.12793i	−0.0700912	+	0.227230i
$985$	−28.5250	−	26.8137i	−0.908882	−	0.854354i
$986$	1.65742	+	3.44168i	0.0527831	+	0.109605i
$987$	13.7860	−	12.7587i	0.438815	−	0.406113i
$988$	0.495104	+	1.41493i	0.0157513	+	0.0450148i
$989$	−9.24579	−	3.62871i	−0.293999	−	0.115386i
$990$	−6.20416	+	4.88217i	−0.197181	+	0.155166i
$991$	−12.9287	−	32.9419i	−0.410695	−	1.04643i	−0.975263	−	0.221047i	$-0.929052\pi$
$991$	−12.9287	−	32.9419i	−0.410695	−	1.04643i	0.564568	−	0.825387i	$-0.309043\pi$
$992$	24.7381	+	13.0745i	0.785436	+	0.415115i
$993$	1.57437	+	13.9729i	0.0499612	+	0.443418i
$994$	−17.7010	−	7.74992i	−0.561440	−	0.245813i
$995$	4.62031	+	6.34602i	0.146474	+	0.201182i
$996$	−4.03605	−	2.75173i	−0.127887	−	0.0871920i
$997$	−1.01670	−	27.1718i	−0.0321992	−	0.860541i	−0.918025	−	0.396523i	$-0.870217\pi$
$997$	−1.01670	−	27.1718i	−0.0321992	−	0.860541i	0.885826	−	0.464018i	$-0.153593\pi$
$998$	−10.9163	+	2.92502i	−0.345550	+	0.0925899i
$999$	−21.7512	−	37.6742i	−0.688178	−	1.19196i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.2.x.a.108.18	yes	624
5.2	odd	4	inner	245.2.x.a.157.18	yes	624
49.5	odd	42	inner	245.2.x.a.103.18	✓	624
245.152	even	84	inner	245.2.x.a.152.18	yes	624

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.2.x.a.103.18	✓	624	49.5	odd	42	inner
245.2.x.a.108.18	yes	624	1.1	even	1	trivial
245.2.x.a.152.18	yes	624	245.152	even	84	inner
245.2.x.a.157.18	yes	624	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.856802 - 0.632349i) q^{2} +(-0.121336 + 0.641277i) q^{3} +(-0.255265 + 0.827550i) q^{4} +(-0.0691167 - 2.23500i) q^{5} +(0.301550 + 0.626175i) q^{6} +(2.52921 - 0.776602i) q^{7} +(1.00801 + 2.88071i) q^{8} +(2.39611 + 0.940403i) q^{9} +(-1.47252 - 1.87125i) q^{10} +(-0.470582 - 1.19902i) q^{11} +(-0.499716 - 0.264108i) q^{12} +(0.159711 + 1.41748i) q^{13} +(1.67595 - 2.26474i) q^{14} +(1.44164 + 0.226863i) q^{15} +(1.25419 + 0.855092i) q^{16} +(-0.0531727 - 1.42107i) q^{17} +(2.64765 - 0.709436i) q^{18} +(-0.606735 - 1.05090i) q^{19} +(1.86722 + 0.513320i) q^{20} +(0.191133 + 1.71615i) q^{21} +(-1.16140 - 0.729753i) q^{22} +(2.15720 + 0.0807169i) q^{23} +(-1.96964 + 0.296876i) q^{24} +(-4.99045 + 0.308952i) q^{25} +(1.03318 + 1.11350i) q^{26} +(-1.93549 + 3.08032i) q^{27} +(-0.00294233 + 2.29128i) q^{28} +(-2.45930 - 0.561319i) q^{29} +(1.37866 - 0.717243i) q^{30} +(-5.39985 - 3.11760i) q^{31} +(-4.48438 + 0.167794i) q^{32} +(0.826005 - 0.156289i) q^{33} +(-0.944171 - 1.18395i) q^{34} +(-1.91051 - 5.59910i) q^{35} +(-1.38987 + 1.74285i) q^{36} +(-5.58761 + 10.5723i) q^{37} +(-1.18438 - 0.516742i) q^{38} +(-0.928375 - 0.0695721i) q^{39} +(6.36872 - 2.45200i) q^{40} +(1.62483 - 3.37399i) q^{41} +(1.24897 + 1.34954i) q^{42} +(-4.34287 - 1.51963i) q^{43} +(1.11237 - 0.0833609i) q^{44} +(1.93619 - 5.42030i) q^{45} +(1.89934 - 1.29495i) q^{46} +(-6.45967 - 8.75254i) q^{47} +(-0.700530 + 0.700530i) q^{48} +(5.79378 - 3.92837i) q^{49} +(-4.08046 + 3.42041i) q^{50} +(0.917753 + 0.138329i) q^{51} +(-1.21380 - 0.229664i) q^{52} +(1.48412 + 2.80809i) q^{53} +(0.289502 + 3.86313i) q^{54} +(-2.64729 + 1.13462i) q^{55} +(4.78662 + 6.50310i) q^{56} +(0.747535 - 0.261574i) q^{57} +(-2.46208 + 1.07420i) q^{58} +(-0.0385687 + 0.514663i) q^{59} +(-0.555742 + 1.13512i) q^{60} +(0.350079 + 1.13493i) q^{61} +(-6.59802 + 0.743418i) q^{62} +(6.79057 + 0.517653i) q^{63} +(-6.10969 + 4.87231i) q^{64} +(3.15702 - 0.454926i) q^{65} +(0.608894 - 0.656231i) q^{66} +(1.61913 + 6.04266i) q^{67} +(1.18958 + 0.318747i) q^{68} +(-0.313509 + 1.37357i) q^{69} +(-5.17752 - 3.58921i) q^{70} +(-1.52615 - 6.68652i) q^{71} +(-0.293742 + 7.85043i) q^{72} +(-8.20379 + 11.1157i) q^{73} +(1.89789 + 12.5917i) q^{74} +(0.407398 - 3.23775i) q^{75} +(1.02455 - 0.233846i) q^{76} +(-2.12136 - 2.66712i) q^{77} +(-0.839428 + 0.527448i) q^{78} +(7.23199 - 4.17539i) q^{79} +(1.82445 - 2.86222i) q^{80} +(3.92022 + 3.63743i) q^{81} +(-0.741382 - 3.91830i) q^{82} +(8.58811 + 0.967647i) q^{83} +(-1.46899 - 0.279903i) q^{84} +(-3.17242 + 0.217061i) q^{85} +(-4.68192 + 1.44418i) q^{86} +(0.658363 - 1.50898i) q^{87} +(2.97969 - 2.56423i) q^{88} +(6.50501 - 16.5745i) q^{89} +(-1.76859 - 5.86847i) q^{90} +(1.50476 + 3.46106i) q^{91} +(-0.617457 + 1.76459i) q^{92} +(2.65445 - 3.08452i) q^{93} +(-11.0693 - 3.41443i) q^{94} +(-2.30682 + 1.42869i) q^{95} +(0.436516 - 2.89609i) q^{96} +(3.80844 + 3.80844i) q^{97} +(2.48002 - 7.02953i) q^{98} -3.31552i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 624 q - 26 q^{2} - 22 q^{3} - 28 q^{5} - 28 q^{6} - 18 q^{7} - 24 q^{8} - 34 q^{10} - 56 q^{11} - 34 q^{12} - 28 q^{13} + 12 q^{15} - 100 q^{16} - 26 q^{17} - 10 q^{18} - 28 q^{20} - 76 q^{21} - 48 q^{22}+ \cdots + 304 q^{98}+O(q^{100}) \) 624 * q - 26 * q^2 - 22 * q^3 - 28 * q^5 - 28 * q^6 - 18 * q^7 - 24 * q^8 - 34 * q^10 - 56 * q^11 - 34 * q^12 - 28 * q^13 + 12 * q^15 - 100 * q^16 - 26 * q^17 - 10 * q^18 - 28 * q^20 - 76 * q^21 - 48 * q^22 - 34 * q^23 - 24 * q^25 - 60 * q^26 - 28 * q^27 - 46 * q^28 - 10 * q^30 - 60 * q^31 + 54 * q^32 - 28 * q^33 - 20 * q^35 + 116 * q^36 - 20 * q^37 + 12 * q^38 - 46 * q^40 - 114 * q^42 - 24 * q^43 + 60 * q^45 + 108 * q^46 - 94 * q^47 - 296 * q^50 + 52 * q^51 - 52 * q^52 - 106 * q^53 + 14 * q^55 + 96 * q^56 + 72 * q^57 - 142 * q^58 - 26 * q^60 + 80 * q^61 - 56 * q^62 - 24 * q^63 - 20 * q^65 - 240 * q^66 - 8 * q^67 - 30 * q^68 + 180 * q^70 + 48 * q^71 + 138 * q^72 - 4 * q^73 - 106 * q^75 + 56 * q^76 - 8 * q^77 - 204 * q^78 - 18 * q^80 - 284 * q^81 - 162 * q^82 + 182 * q^83 - 36 * q^85 - 76 * q^86 - 74 * q^87 + 288 * q^88 - 112 * q^90 + 44 * q^91 - 8 * q^92 + 368 * q^93 + 26 * q^95 + 136 * q^96 + 304 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more