LMFDB - Embedded newform 245.2.x.a.103.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,2,Mod(3,245)]

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

lf = mfeigenbasis(mf)

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")

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

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			103.18
Character	$\chi$	$=$	245.103
Dual form			245.2.x.a.157.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.632349 - 0.856802i) q^{2} +(0.641277 - 0.121336i) q^{3} +(0.255265 + 0.827550i) q^{4} +(0.264765 - 2.22034i) q^{5} +(0.301550 - 0.626175i) q^{6} +(0.776602 - 2.52921i) q^{7} +(2.88071 + 1.00801i) q^{8} +(-2.39611 + 0.940403i) q^{9} +(-1.73497 - 1.63088i) q^{10} +(-0.470582 + 1.19902i) q^{11} +(0.264108 + 0.499716i) q^{12} +(1.41748 + 0.159711i) q^{13} +(-1.67595 - 2.26474i) q^{14} +(-0.0996198 - 1.45598i) q^{15} +(1.25419 - 0.855092i) q^{16} +(1.42107 + 0.0531727i) q^{17} +(-0.709436 + 2.64765i) q^{18} +(0.606735 - 1.05090i) q^{19} +(1.90503 - 0.347669i) q^{20} +(0.191133 - 1.71615i) q^{21} +(0.729753 + 1.16140i) q^{22} +(0.0807169 + 2.15720i) q^{23} +(1.96964 + 0.296876i) q^{24} +(-4.85980 - 1.17573i) q^{25} +(1.03318 - 1.11350i) q^{26} +(-3.08032 + 1.93549i) q^{27} +(2.29128 - 0.00294233i) q^{28} +(2.45930 - 0.561319i) q^{29} +(-1.31048 - 0.835332i) q^{30} +(-5.39985 + 3.11760i) q^{31} +(-0.167794 + 4.48438i) q^{32} +(-0.156289 + 0.826005i) q^{33} +(0.944171 - 1.18395i) q^{34} +(-5.41008 - 2.39396i) q^{35} +(-1.38987 - 1.74285i) q^{36} +(-10.5723 + 5.58761i) q^{37} +(-0.516742 - 1.18438i) q^{38} +(0.928375 - 0.0695721i) q^{39} +(3.00082 - 6.12927i) q^{40} +(1.62483 + 3.37399i) q^{41} +(-1.34954 - 1.24897i) q^{42} +(-1.51963 - 4.34287i) q^{43} +(-1.11237 - 0.0833609i) q^{44} +(1.45361 + 5.56915i) q^{45} +(1.89934 + 1.29495i) q^{46} +(8.75254 + 6.45967i) 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} +(0.229664 + 1.21380i) q^{52} +(2.80809 + 1.48412i) q^{53} +(-0.289502 + 3.86313i) q^{54} +(2.53764 + 1.36231i) q^{55} +(4.78662 - 6.50310i) q^{56} +(0.261574 - 0.747535i) q^{57} +(1.07420 - 2.46208i) q^{58} +(0.0385687 + 0.514663i) q^{59} +(1.17946 - 0.454101i) q^{60} +(0.350079 - 1.13493i) q^{61} +(-0.743418 + 6.59802i) q^{62} +(0.517653 + 6.79057i) q^{63} +(6.10969 + 4.87231i) q^{64} +(0.729911 - 3.10499i) q^{65} +(0.608894 + 0.656231i) q^{66} +(-6.04266 - 1.61913i) q^{67} +(0.318747 + 1.18958i) q^{68} +(0.313509 + 1.37357i) q^{69} +(-5.47221 + 3.12155i) q^{70} +(-1.52615 + 6.68652i) q^{71} +(-7.85043 + 0.293742i) q^{72} +(11.1157 - 8.20379i) q^{73} +(-1.89789 + 12.5917i) q^{74} +(-3.25914 - 0.164302i) q^{75} +(1.02455 + 0.233846i) q^{76} +(2.66712 + 2.12136i) q^{77} +(0.527448 - 0.839428i) q^{78} +(-7.23199 - 4.17539i) q^{79} +(-1.56653 - 3.01112i) q^{80} +(3.92022 - 3.63743i) q^{81} +(3.91830 + 0.741382i) q^{82} +(0.967647 + 8.58811i) q^{83} +(1.46899 - 0.279903i) q^{84} +(0.494311 - 3.14118i) q^{85} +(-4.68192 - 1.44418i) q^{86} +(1.50898 - 0.658363i) q^{87} +(-2.56423 + 2.97969i) q^{88} +(-6.50501 - 16.5745i) q^{89} +(5.69085 + 2.27619i) q^{90} +(1.50476 - 3.46106i) q^{91} +(-1.76459 + 0.617457i) q^{92} +(-3.08452 + 2.65445i) q^{93} +(11.0693 - 3.41443i) q^{94} +(-2.17270 - 1.62540i) q^{95} +(0.436516 + 2.89609i) q^{96} +(-3.80844 - 3.80844i) q^{97} +(-7.02953 + 2.48002i) 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 $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{29}{42}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.632349	−	0.856802i	0.447138	−	0.605851i	−0.521826	−	0.853052i	$-0.674749\pi$
$2$	0.632349	−	0.856802i	0.447138	−	0.605851i	0.968964	+	0.247201i	$0.0795109\pi$
$3$	0.641277	−	0.121336i	0.370242	−	0.0700535i	0.00253867	−	0.999997i	$-0.499192\pi$
$3$	0.641277	−	0.121336i	0.370242	−	0.0700535i	0.367703	+	0.929943i	$0.380144\pi$
$4$	0.255265	+	0.827550i	0.127633	+	0.413775i
$5$	0.264765	−	2.22034i	0.118406	−	0.992965i
$5$	0.264765	−	2.22034i	0.118406	−	0.992965i
$6$	0.301550	−	0.626175i	0.123107	−	0.255635i
$7$	0.776602	−	2.52921i	0.293528	−	0.955951i
$7$	0.776602	−	2.52921i	0.293528	−	0.955951i
$8$	2.88071	+	1.00801i	1.01849	+	0.356384i
$9$	−2.39611	+	0.940403i	−0.798702	+	0.313468i
$10$	−1.73497	−	1.63088i	−0.548645	−	0.515729i
$11$	−0.470582	+	1.19902i	−0.141886	+	0.361519i	−0.984098	−	0.177627i	$-0.943158\pi$
$11$	−0.470582	+	1.19902i	−0.141886	+	0.361519i	0.842212	+	0.539146i	$0.181253\pi$
$12$	0.264108	+	0.499716i	0.0762413	+	0.144256i
$13$	1.41748	+	0.159711i	0.393138	+	0.0442960i	0.306321	−	0.951928i	$-0.400902\pi$
$13$	1.41748	+	0.159711i	0.393138	+	0.0442960i	0.0868168	+	0.996224i	$0.472331\pi$
$14$	−1.67595	−	2.26474i	−0.447916	−	0.605276i
$15$	−0.0996198	−	1.45598i	−0.0257217	−	0.375932i
$16$	1.25419	−	0.855092i	0.313548	−	0.213773i
$17$	1.42107	+	0.0531727i	0.344660	+	0.0128963i	0.209161	−	0.977881i	$-0.432927\pi$
$17$	1.42107	+	0.0531727i	0.344660	+	0.0128963i	0.135499	+	0.990777i	$0.456736\pi$
$18$	−0.709436	+	2.64765i	−0.167216	+	0.624058i
$19$	0.606735	−	1.05090i	0.139195	−	0.241092i	−0.787997	−	0.615679i	$-0.788882\pi$
$19$	0.606735	−	1.05090i	0.139195	−	0.241092i	0.927192	+	0.374586i	$0.122215\pi$
$20$	1.90503	−	0.347669i	0.425977	−	0.0777412i
$21$	0.191133	−	1.71615i	0.0417086	−	0.374495i
$22$	0.729753	+	1.16140i	0.155584	+	0.247610i
$23$	0.0807169	+	2.15720i	0.0168306	+	0.449808i	0.982079	+	0.188472i	$0.0603535\pi$
$23$	0.0807169	+	2.15720i	0.0168306	+	0.449808i	−0.965248	+	0.261336i	$0.915837\pi$
$24$	1.96964	+	0.296876i	0.402052	+	0.0605996i
$25$	−4.85980	−	1.17573i	−0.971960	−	0.235147i
$26$	1.03318	−	1.11350i	0.202624	−	0.218376i
$27$	−3.08032	+	1.93549i	−0.592808	+	0.372486i
$28$	2.29128	−	0.00294233i	0.433012	−	0.000556047i
$29$	2.45930	−	0.561319i	0.456680	−	0.104234i	0.0120085	−	0.999928i	$-0.496177\pi$
$29$	2.45930	−	0.561319i	0.456680	−	0.104234i	0.444672	+	0.895694i	$0.353320\pi$
$30$	−1.31048	−	0.835332i	−0.239260	−	0.152510i
$31$	−5.39985	+	3.11760i	−0.969842	+	0.559938i	−0.899188	−	0.437563i	$-0.855842\pi$
$31$	−5.39985	+	3.11760i	−0.969842	+	0.559938i	−0.0706537	+	0.997501i	$0.522509\pi$
$32$	−0.167794	+	4.48438i	−0.0296620	+	0.792734i
$33$	−0.156289	+	0.826005i	−0.0272063	+	0.143789i
$34$	0.944171	−	1.18395i	0.161924	−	0.203046i
$35$	−5.41008	−	2.39396i	−0.914470	−	0.404654i
$36$	−1.38987	−	1.74285i	−0.231646	−	0.290474i
$37$	−10.5723	+	5.58761i	−1.73807	+	0.918597i	−0.783100	+	0.621896i	$0.786363\pi$
$37$	−10.5723	+	5.58761i	−1.73807	+	0.918597i	−0.954970	+	0.296701i	$0.904114\pi$
$38$	−0.516742	−	1.18438i	−0.0838266	−	0.192133i
$39$	0.928375	−	0.0695721i	0.148659	−	0.0111405i
$40$	3.00082	−	6.12927i	0.474472	−	0.969123i
$41$	1.62483	+	3.37399i	0.253755	+	0.526928i	0.988464	−	0.151454i	$-0.0483956\pi$
$41$	1.62483	+	3.37399i	0.253755	+	0.526928i	−0.734709	+	0.678382i	$0.762681\pi$
$42$	−1.34954	−	1.24897i	−0.208239	−	0.192720i
$43$	−1.51963	−	4.34287i	−0.231742	−	0.662281i	−0.999761	−	0.0218539i	$-0.993043\pi$
$43$	−1.51963	−	4.34287i	−0.231742	−	0.662281i	0.768019	−	0.640427i	$-0.221243\pi$
$44$	−1.11237	−	0.0833609i	−0.167697	−	0.0125671i
$45$	1.45361	+	5.56915i	0.216691	+	0.830200i
$46$	1.89934	+	1.29495i	0.280042	+	0.190930i
$47$	8.75254	+	6.45967i	1.27669	+	0.942239i	0.999826	−	0.0186702i	$-0.00594325\pi$
$47$	8.75254	+	6.45967i	1.27669	+	0.942239i	0.276863	+	0.960909i	$0.410705\pi$
$48$	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
$52$	0.229664	+	1.21380i	0.0318486	+	0.168324i
$53$	2.80809	+	1.48412i	0.385721	+	0.203860i	0.648876	−	0.760894i	$-0.275239\pi$
$53$	2.80809	+	1.48412i	0.385721	+	0.203860i	−0.263155	+	0.964754i	$0.584763\pi$
$54$	−0.289502	+	3.86313i	−0.0393962	+	0.525706i
$55$	2.53764	+	1.36231i	0.342176	+	0.183694i
$56$	4.78662	−	6.50310i	0.639639	−	0.869014i
$57$	0.261574	−	0.747535i	0.0346463	−	0.0990134i
$58$	1.07420	−	2.46208i	0.141049	−	0.323287i
$59$	0.0385687	+	0.514663i	0.00502121	+	0.0670035i	0.999151	−	0.0411862i	$-0.0131137\pi$
$59$	0.0385687	+	0.514663i	0.00502121	+	0.0670035i	−0.994130	+	0.108190i	$0.965495\pi$
$60$	1.17946	−	0.454101i	0.152268	−	0.0586242i
$61$	0.350079	−	1.13493i	0.0448230	−	0.145313i	−0.930395	−	0.366558i	$-0.880536\pi$
$61$	0.350079	−	1.13493i	0.0448230	−	0.145313i	0.975218	+	0.221246i	$0.0710122\pi$
$62$	−0.743418	+	6.59802i	−0.0944142	+	0.837949i
$63$	0.517653	+	6.79057i	0.0652181	+	0.855531i
$64$	6.10969	+	4.87231i	0.763711	+	0.609039i
$65$	0.729911	−	3.10499i	0.0905344	−	0.385127i
$66$	0.608894	+	0.656231i	0.0749497	+	0.0807765i
$67$	−6.04266	−	1.61913i	−0.738229	−	0.197808i	−0.129938	−	0.991522i	$-0.541478\pi$
$67$	−6.04266	−	1.61913i	−0.738229	−	0.197808i	−0.608291	+	0.793714i	$0.708145\pi$
$68$	0.318747	+	1.18958i	0.0386538	+	0.144258i
$69$	0.313509	+	1.37357i	0.0377420	+	0.165359i
$70$	−5.47221	+	3.12155i	−0.654054	+	0.373096i
$71$	−1.52615	+	6.68652i	−0.181121	+	0.793544i	0.799977	+	0.600031i	$0.204845\pi$
$71$	−1.52615	+	6.68652i	−0.181121	+	0.793544i	−0.981098	+	0.193513i	$0.938012\pi$
$72$	−7.85043	+	0.293742i	−0.925182	+	0.0346179i
$73$	11.1157	−	8.20379i	1.30100	−	0.960181i	0.301020	−	0.953618i	$-0.402673\pi$
$73$	11.1157	−	8.20379i	1.30100	−	0.960181i	0.999978	−	0.00656291i	$-0.00208905\pi$
$74$	−1.89789	+	12.5917i	−0.220625	+	1.46375i
$75$	−3.25914	−	0.164302i	−0.376333	−	0.0189719i
$76$	1.02455	+	0.233846i	0.117524	+	0.0268240i
$77$	2.66712	+	2.12136i	0.303947	+	0.241752i
$78$	0.527448	−	0.839428i	0.0597217	−	0.0950465i
$79$	−7.23199	−	4.17539i	−0.813662	−	0.469768i	0.0345637	−	0.999402i	$-0.488996\pi$
$79$	−7.23199	−	4.17539i	−0.813662	−	0.469768i	−0.848226	+	0.529634i	$0.822329\pi$
$80$	−1.56653	−	3.01112i	−0.175143	−	0.336654i
$81$	3.92022	−	3.63743i	0.435580	−	0.404159i
$82$	3.91830	+	0.741382i	0.432704	+	0.0818719i
$83$	0.967647	+	8.58811i	0.106213	+	0.942667i	0.927926	+	0.372765i	$0.121590\pi$
$83$	0.967647	+	8.58811i	0.106213	+	0.942667i	−0.821713	+	0.569902i	$0.806981\pi$
$84$	1.46899	−	0.279903i	0.160280	−	0.0305399i
$85$	0.494311	−	3.14118i	0.0536155	−	0.340709i
$86$	−4.68192	−	1.44418i	−0.504864	−	0.155730i
$87$	1.50898	−	0.658363i	0.161780	−	0.0705839i
$88$	−2.56423	+	2.97969i	−0.273348	+	0.317636i
$89$	−6.50501	−	16.5745i	−0.689529	−	1.75689i	−0.652756	−	0.757568i	$-0.726387\pi$
$89$	−6.50501	−	16.5745i	−0.689529	−	1.75689i	−0.0367736	−	0.999324i	$-0.511708\pi$
$90$	5.69085	+	2.27619i	0.599868	+	0.239932i
$91$	1.50476	−	3.46106i	0.157742	−	0.362818i
$92$	−1.76459	+	0.617457i	−0.183971	+	0.0643743i
$93$	−3.08452	+	2.65445i	−0.319850	+	0.275253i
$94$	11.0693	−	3.41443i	1.14171	−	0.352172i
$95$	−2.17270	−	1.62540i	−0.222915	−	0.166762i
$96$	0.436516	+	2.89609i	0.0445517	+	0.295581i
$97$	−3.80844	−	3.80844i	−0.386689	−	0.386689i	0.486816	−	0.873505i	$-0.338158\pi$
$97$	−3.80844	−	3.80844i	−0.386689	−	0.386689i	−0.873505	+	0.486816i	$0.838158\pi$
$98$	−7.02953	+	2.48002i	−0.710090	+	0.250520i
$99$		−	3.31552i		−	0.333223i
$100$	−0.267560	−	4.32185i	−0.0267560	−	0.432185i
$101$	6.75389	−	9.90614i	0.672037	−	0.985697i	−0.327134	−	0.944978i	$-0.606083\pi$
$101$	6.75389	−	9.90614i	0.672037	−	0.985697i	0.999171	−	0.0407192i	$-0.0129649\pi$
$102$	0.461819	−	0.873805i	0.0457269	−	0.0865195i
$103$	−5.64663	−	6.56150i	−0.556379	−	0.646524i	0.407393	−	0.913253i	$-0.366438\pi$
$103$	−5.64663	−	6.56150i	−0.556379	−	0.646524i	−0.963772	+	0.266729i	$0.914057\pi$
$104$	3.92236	+	1.88891i	0.384619	+	0.185223i
$105$	−3.75984	−	0.878756i	−0.366922	−	0.0857578i
$106$	3.04729	−	1.46750i	0.295979	−	0.142536i
$107$	−2.70318	−	1.17939i	−0.261326	−	0.114015i	0.265145	−	0.964209i	$-0.414580\pi$
$107$	−2.70318	−	1.17939i	−0.261326	−	0.114015i	−0.526471	+	0.850193i	$0.676485\pi$
$108$	−2.38802	−	2.05506i	−0.229787	−	0.197748i
$109$	−1.26419	−	0.496156i	−0.121087	−	0.0475232i	0.304024	−	0.952664i	$-0.401670\pi$
$109$	−1.26419	−	0.496156i	−0.121087	−	0.0475232i	−0.425111	+	0.905141i	$0.639765\pi$
$110$	2.77190	−	1.31280i	0.264291	−	0.125171i
$111$	−6.10178	+	4.86601i	−0.579155	+	0.461861i
$112$	−1.18870	−	3.83617i	−0.112322	−	0.362484i
$113$	5.55151	−	0.625505i	0.522242	−	0.0588425i	0.153091	−	0.988212i	$-0.451077\pi$
$113$	5.55151	−	0.625505i	0.522242	−	0.0588425i	0.369151	+	0.929370i	$0.379649\pi$
$114$	−0.475084	−	0.696820i	−0.0444957	−	0.0652632i
$115$	4.81109	+	0.391933i	0.448637	+	0.0365479i
$116$	1.09229	+	1.89191i	0.101417	+	0.175659i
$117$	−3.54662	+	0.950314i	−0.327885	+	0.0878566i
$118$	0.465354	+	0.292401i	0.0428393	+	0.0269177i
$119$	1.23809	−	3.55289i	0.113496	−	0.325693i
$120$	1.18066	−	4.29467i	0.107779	−	0.392048i
$121$	6.84736	+	6.35342i	0.622488	+	0.577584i
$122$	−0.751037	−	1.01762i	−0.0679957	−	0.0921309i
$123$	1.45135	+	1.96651i	0.130864	+	0.177314i
$124$	−3.95837	−	3.67283i	−0.355472	−	0.329830i
$125$	−3.89723	+	10.4791i	−0.348579	+	0.937279i
$126$	6.14551	+	3.85048i	0.547486	+	0.343028i
$127$	16.0735	+	10.0997i	1.42630	+	0.896201i	0.999965	−	0.00836551i	$-0.00266286\pi$
$127$	16.0735	+	10.0997i	1.42630	+	0.896201i	0.426331	+	0.904567i	$0.359806\pi$
$128$	−0.631160	+	0.169119i	−0.0557872	+	0.0149481i
$129$	−1.50145	−	2.60060i	−0.132196	−	0.228970i
$130$	−2.19881	−	2.58883i	−0.192848	−	0.227055i
$131$	−7.73784	−	11.3493i	−0.676058	−	0.991595i	−0.998979	−	0.0451691i	$-0.985617\pi$
$131$	−7.73784	−	11.3493i	−0.676058	−	0.991595i	0.322921	−	0.946426i	$-0.395335\pi$
$132$	−0.723455	+	0.0815138i	−0.0629687	+	0.00709487i
$133$	−2.18674	−	2.35069i	−0.189615	−	0.203830i
$134$	−5.20834	+	4.15351i	−0.449932	+	0.358809i
$135$	3.48189	+	7.35181i	0.299673	+	0.632743i
$136$	4.04010	+	1.58562i	0.346436	+	0.135966i
$137$	−8.74540	−	7.52602i	−0.747170	−	0.642991i	0.193971	−	0.981007i	$-0.437863\pi$
$137$	−8.74540	−	7.52602i	−0.747170	−	0.642991i	−0.941140	+	0.338016i	$0.890244\pi$
$138$	1.37513	+	0.599962i	0.117059	+	0.0510721i
$139$	9.67332	−	4.65843i	0.820481	−	0.395123i	0.0239442	−	0.999713i	$-0.492378\pi$
$139$	9.67332	−	4.65843i	0.820481	−	0.395123i	0.796536	+	0.604591i	$0.206663\pi$
$140$	0.600118	−	5.08820i	0.0507192	−	0.430032i
$141$	6.39660	+	3.08044i	0.538691	+	0.259420i
$142$	4.76396	+	5.53583i	0.399783	+	0.464556i
$143$	−0.858537	+	1.62443i	−0.0717944	+	0.135842i
$144$	−2.20104	+	3.22834i	−0.183420	+	0.269028i
$145$	−0.595182	−	5.60909i	−0.0494272	−	0.465810i
$146$		−	14.7116i		−	1.21754i
$147$	−4.19207	−	1.81618i	−0.345756	−	0.149796i
$148$	−7.32276	−	7.32276i	−0.601927	−	0.601927i
$149$	−3.35314	−	22.2466i	−0.274700	−	1.82251i	−0.521274	−	0.853389i	$-0.674543\pi$
$149$	−3.35314	−	22.2466i	−0.274700	−	1.82251i	0.246574	−	0.969124i	$-0.420695\pi$
$150$	−2.20169	+	2.68854i	−0.179767	+	0.219518i
$151$	3.67843	−	1.13464i	0.299346	−	0.0923360i	−0.141444	−	0.989946i	$-0.545175\pi$
$151$	3.67843	−	1.13464i	0.299346	−	0.0923360i	0.440790	+	0.897610i	$0.354698\pi$
$152$	2.80714	−	2.41574i	0.227689	−	0.195942i
$153$	−3.45504	+	1.20897i	−0.279324	+	0.0977396i
$154$	3.50414	−	0.943756i	0.282372	−	0.0760500i
$155$	5.49245	+	12.8149i	0.441164	+	1.02932i
$156$	0.294556	+	0.750518i	0.0235834	+	0.0600895i
$157$	5.54210	−	6.44004i	0.442308	−	0.513971i	−0.491924	−	0.870638i	$-0.663706\pi$
$157$	5.54210	−	6.44004i	0.442308	−	0.513971i	0.934231	+	0.356667i	$0.116087\pi$
$158$	−8.15062	+	3.55608i	−0.648429	+	0.282907i
$159$	1.98084	+	0.611009i	0.157091	+	0.0484562i
$160$	9.91242	+	1.55986i	0.783645	+	0.123318i
$161$	5.51870	+	1.47114i	0.434935	+	0.115942i
$162$	−0.637614	−	5.65898i	−0.0500957	−	0.444612i
$163$	22.3723	+	4.23307i	1.75233	+	0.331559i	0.960311	−	0.278932i	$-0.0899804\pi$
$163$	22.3723	+	4.23307i	1.75233	+	0.331559i	0.792023	+	0.610491i	$0.209028\pi$
$164$	−2.37738	+	2.20589i	−0.185642	+	0.172251i
$165$	1.79263	+	0.565710i	0.139556	+	0.0440405i
$166$	7.97020	+	4.60160i	0.618608	+	0.357153i
$167$	−2.13785	+	3.40237i	−0.165432	+	0.263283i	−0.919144	−	0.393921i	$-0.871118\pi$
$167$	−2.13785	+	3.40237i	−0.165432	+	0.263283i	0.753712	+	0.657204i	$0.228261\pi$
$168$	2.28049	−	4.75108i	0.175944	−	0.366554i
$169$	−10.6903	−	2.44000i	−0.822333	−	0.187692i
$170$	−2.37879	−	2.40985i	−0.182445	−	0.184827i
$171$	−0.465537	+	3.08863i	−0.0356005	+	0.236194i
$172$	3.20603	−	2.36616i	0.244457	−	0.180418i
$173$	7.12586	−	0.266631i	0.541769	−	0.0202716i	0.234893	−	0.972021i	$-0.424526\pi$
$173$	7.12586	−	0.266631i	0.541769	−	0.0202716i	0.306876	+	0.951750i	$0.400716\pi$
$174$	0.390118	−	1.70922i	0.0295747	−	0.129575i
$175$	−6.74780	+	11.3784i	−0.510086	+	0.860123i
$176$	0.435076	+	1.90619i	0.0327951	+	0.143685i
$177$	0.0871805	+	0.325362i	0.00655289	+	0.0244557i
$178$	−18.3145	−	4.90735i	−1.37273	−	0.367822i
$179$	8.88298	+	9.57357i	0.663945	+	0.715562i	0.971783	−	0.235876i	$-0.0757960\pi$
$179$	8.88298	+	9.57357i	0.663945	+	0.715562i	−0.307838	+	0.951439i	$0.599606\pi$
$180$	−4.23770	+	2.62454i	−0.315859	+	0.195622i
$181$	−13.3525	−	10.6483i	−0.992482	−	0.791478i	−0.0144424	−	0.999896i	$-0.504597\pi$
$181$	−13.3525	−	10.6483i	−0.992482	−	0.791478i	−0.978040	+	0.208417i	$0.933169\pi$
$182$	−2.01391	−	3.47788i	−0.149281	−	0.257798i
$183$	0.0867898	−	0.770281i	0.00641569	−	0.0569408i
$184$	−1.94195	+	6.29565i	−0.143163	+	0.464121i
$185$	9.60721	+	24.9534i	0.706336	+	1.83461i
$186$	0.323841	+	4.32136i	0.0237452	+	0.316858i
$187$	−0.732485	+	1.67887i	−0.0535646	+	0.122771i
$188$	−3.11148	+	8.89209i	−0.226928	+	0.648522i
$189$	2.50308	+	9.29388i	0.182073	+	0.676030i
$190$	−2.76655	+	0.833758i	−0.200707	+	0.0604872i
$191$	−1.10866	+	14.7940i	−0.0802195	+	1.07045i	0.801286	+	0.598281i	$0.204149\pi$
$191$	−1.10866	+	14.7940i	−0.0802195	+	1.07045i	−0.881506	+	0.472173i	$0.843470\pi$
$192$	4.50919	+	2.38318i	0.325423	+	0.171991i
$193$	−2.82027	−	14.9055i	−0.203008	−	1.07292i	−0.924697	−	0.380704i	$-0.875682\pi$
$193$	−2.82027	−	14.9055i	−0.203008	−	1.07292i	0.721689	−	0.692217i	$-0.243366\pi$
$194$	−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	$0.0356302\pi$
$198$	−2.84075	−	2.09657i	−0.201883	−	0.148997i
$199$	2.90054	+	1.97755i	0.205614	+	0.140185i	0.661749	−	0.749725i	$-0.269814\pi$
$199$	2.90054	+	1.97755i	0.205614	+	0.140185i	−0.456136	+	0.889910i	$0.650767\pi$
$200$	−12.8145	−	8.28566i	−0.906125	−	0.585884i
$201$	−4.07148	−	0.305115i	−0.287180	−	0.0215212i
$202$	−4.21679	−	12.0509i	−0.296692	−	0.847897i
$203$	0.490204	−	6.65600i	0.0344056	−	0.467159i
$204$	0.348745	+	0.724175i	0.0244170	+	0.0507024i
$205$	7.92159	−	2.71435i	0.553268	−	0.189579i
$206$	−9.19255	+	0.688886i	−0.640475	+	0.0479970i
$207$	−2.22205	−	5.09299i	−0.154443	−	0.353987i
$208$	1.91435	−	1.01177i	0.132737	−	0.0701534i
$209$	0.974530	+	1.22202i	0.0674096	+	0.0845290i
$210$	−3.13045	+	2.66576i	−0.216021	+	0.183955i
$211$	−13.9526	+	17.4960i	−0.960535	+	1.20447i	0.0183017	+	0.999833i	$0.494174\pi$
$211$	−13.9526	+	17.4960i	−0.960535	+	1.20447i	−0.978837	+	0.204641i	$0.934397\pi$
$212$	−0.511375	+	2.70268i	−0.0351214	+	0.185621i
$213$	−0.167371	+	4.47309i	−0.0114681	+	0.306491i
$214$	−2.71985	+	1.57031i	−0.185925	+	0.107344i
$215$	−10.0450	+	2.22426i	−0.685062	+	0.151694i
$216$	−10.8245	+	2.47062i	−0.736515	+	0.168105i
$217$	3.69154	+	16.0785i	0.250598	+	1.09148i
$218$	−1.22451	+	0.769413i	−0.0829346	+	0.0521112i
$219$	6.13285	−	6.60965i	0.414420	−	0.446638i
$220$	−0.479607	+	2.44778i	−0.0323351	+	0.165029i
$221$	2.00584	+	0.302332i	0.134928	+	0.0203371i
$222$	0.310752	+	8.30503i	0.0208563	+	0.557397i
$223$	−4.08622	−	6.50319i	−0.273634	−	0.435486i	0.681431	−	0.731882i	$-0.261358\pi$
$223$	−4.08622	−	6.50319i	−0.273634	−	0.435486i	−0.955065	+	0.296396i	$0.904215\pi$
$224$	11.2116	+	3.90696i	0.749108	+	0.261045i
$225$	12.7503	−	1.75298i	0.850018	−	0.116866i
$226$	2.97456	−	5.15208i	0.197865	−	0.342711i
$227$	2.49276	−	9.30311i	0.165450	−	0.617469i	−0.832532	−	0.553977i	$-0.813110\pi$
$227$	2.49276	−	9.30311i	0.165450	−	0.617469i	0.997982	−	0.0634923i	$-0.0202238\pi$
$228$	0.685393	+	0.0256456i	0.0453913	+	0.00169842i
$229$	−20.2014	+	13.7731i	−1.33494	+	0.910150i	−0.999491	−	0.0319073i	$-0.989842\pi$
$229$	−20.2014	+	13.7731i	−1.33494	+	0.910150i	−0.335453	+	0.942057i	$0.608890\pi$
$230$	3.37810	−	3.87432i	0.222745	−	0.255465i
$231$	1.96776	+	1.03676i	0.129469	+	0.0682140i
$232$	7.65035	+	0.861987i	0.502270	+	0.0565922i
$233$	7.52837	+	14.2444i	0.493200	+	0.933179i	0.997569	+	0.0696911i	$0.0222014\pi$
$233$	7.52837	+	14.2444i	0.493200	+	0.933179i	−0.504369	+	0.863488i	$0.668275\pi$
$234$	−1.42847	+	3.63968i	−0.0933820	+	0.237934i
$235$	16.6600	−	17.7233i	1.08678	−	1.15614i
$236$	−0.416064	+	0.163293i	−0.0270835	+	0.0106295i
$237$	−5.14434	−	1.80008i	−0.334161	−	0.116928i
$238$	−2.26122	−	3.30746i	−0.146573	−	0.214391i
$239$	−11.1967	+	23.2501i	−0.724252	+	1.50392i	0.134158	+	0.990960i	$0.457167\pi$
$239$	−11.1967	+	23.2501i	−0.724252	+	1.50392i	−0.858410	+	0.512964i	$0.828547\pi$
$240$	−1.36994	−	1.74089i	−0.0884291	−	0.112374i
$241$	−8.26435	−	26.7924i	−0.532354	−	1.72585i	−0.676641	−	0.736313i	$-0.736565\pi$
$241$	−8.26435	−	26.7924i	−0.532354	−	1.72585i	0.144287	−	0.989536i	$-0.453911\pi$
$242$	9.77355	−	1.84926i	0.628268	−	0.118875i
$243$	8.55342	−	11.5895i	0.548702	−	0.743465i
$244$	1.02857			0.0658476
$245$	−10.2563	+	11.8241i	−0.655251	+	0.755411i
$246$	2.60267			0.165940
$247$	1.02787	−	1.39272i	0.0654020	−	0.0886166i
$248$	−18.6980	+	3.53785i	−1.18732	+	0.224654i
$249$	1.66258	+	5.38995i	0.105362	+	0.341574i
$250$	6.51411	+	9.96560i	0.411989	+	0.630280i
$251$	−7.06773	+	14.6763i	−0.446111	+	0.926359i	0.549738	+	0.835337i	$0.314728\pi$
$251$	−7.06773	+	14.6763i	−0.446111	+	0.926359i	−0.995849	+	0.0910219i	$0.970987\pi$
$252$	−5.48740	+	2.16178i	−0.345673	+	0.136179i
$253$	−2.62452	−	0.918359i	−0.165002	−	0.0577368i
$254$	18.8175	−	7.38533i	1.18072	−	0.463397i
$255$	−0.0641485	−	2.07435i	−0.00401714	−	0.129901i
$256$	−5.96419	+	15.1965i	−0.372762	+	0.949782i
$257$	3.41887	+	6.46882i	0.213263	+	0.403514i	0.967419	−	0.253182i	$-0.0814773\pi$
$257$	3.41887	+	6.46882i	0.213263	+	0.403514i	−0.754155	+	0.656696i	$0.771953\pi$
$258$	−3.17764	−	0.358034i	−0.197831	−	0.0222902i
$259$	5.92178	+	31.0788i	0.367961	+	1.93114i
$260$	2.75586	−	0.188559i	0.170911	−	0.0116939i
$261$	−5.36488	+	3.65771i	−0.332078	+	0.226407i
$262$	−14.6171	−	0.546935i	−0.903050	−	0.0337897i
$263$	−2.36793	+	8.83724i	−0.146013	+	0.544928i	0.853695	+	0.520773i	$0.174356\pi$
$263$	−2.36793	+	8.83724i	−0.146013	+	0.544928i	−0.999708	+	0.0241548i	$0.992311\pi$
$264$	−1.28284	+	2.22194i	−0.0789533	+	0.136751i
$265$	4.03873	−	5.84197i	0.248097	−	0.358869i
$266$	−3.39686	+	0.387152i	−0.208275	+	0.0237378i
$267$	−6.18260	−	9.83955i	−0.378369	−	0.602171i
$268$	−0.202574	−	5.41391i	−0.0123742	−	0.330707i
$269$	21.8291	+	3.29021i	1.33094	+	0.200607i	0.775711	−	0.631088i	$-0.217391\pi$
$269$	21.8291	+	3.29021i	1.33094	+	0.200607i	0.555232	+	0.831695i	$0.312629\pi$
$270$	8.50081	+	1.66561i	0.517343	+	0.101366i
$271$	−9.74349	+	10.5010i	−0.591875	+	0.637889i	−0.955967	−	0.293474i	$-0.905189\pi$
$271$	−9.74349	+	10.5010i	−0.591875	+	0.637889i	0.364093	+	0.931363i	$0.381379\pi$
$272$	1.82776	−	1.14846i	0.110824	−	0.0696355i
$273$	0.545016	−	2.40208i	0.0329858	−	0.145381i
$274$	−11.9785	+	2.73400i	−0.723645	+	0.165167i
$275$	3.69666	−	5.27373i	0.222917	−	0.318018i
$276$	−1.05667	+	0.610070i	−0.0636042	+	0.0367219i
$277$	0.207108	−	5.53508i	0.0124439	−	0.332571i	−0.979147	−	0.203155i	$-0.934880\pi$
$277$	0.207108	−	5.53508i	0.0124439	−	0.332571i	0.991590	−	0.129415i	$-0.0413101\pi$
$278$	2.12556	−	11.2339i	0.127483	−	0.673763i
$279$	10.0068	−	12.5481i	0.599092	−	0.751238i
$280$	−13.1718	−	12.3497i	−0.787163	−	0.738036i
$281$	−0.609489	−	0.764275i	−0.0363591	−	0.0455928i	0.763320	−	0.646021i	$-0.223568\pi$
$281$	−0.609489	−	0.764275i	−0.0363591	−	0.0455928i	−0.799679	+	0.600428i	$0.794997\pi$
$282$	6.68421	−	3.53271i	0.398039	−	0.210370i
$283$	4.51896	+	10.3576i	0.268624	+	0.615693i	0.997629	−	0.0688151i	$-0.0219218\pi$
$283$	4.51896	+	10.3576i	0.268624	+	0.615693i	−0.729005	+	0.684508i	$0.760017\pi$
$284$	−5.92300	+	0.443868i	−0.351466	+	0.0263387i
$285$	−1.59052	−	0.778703i	−0.0942145	−	0.0461264i
$286$	0.848921	+	1.76280i	0.0501978	+	0.104237i
$287$	9.79536	−	1.48928i	0.578202	−	0.0879094i
$288$	−3.81507	−	10.9029i	−0.224805	−	0.642457i
$289$	−14.9358	−	1.11929i	−0.878579	−	0.0658404i
$290$	−5.18224	−	3.03695i	−0.304312	−	0.178336i
$291$	−2.90437	−	1.98017i	−0.170257	−	0.116079i
$292$	9.62651	+	7.10468i	0.563349	+	0.415770i
$293$	−15.9481	+	15.9481i	−0.931697	+	0.931697i	−0.997812	−	0.0661153i	$-0.978939\pi$
$293$	−15.9481	+	15.9481i	−0.931697	+	0.931697i	0.0661153	+	0.997812i	$0.478939\pi$
$294$	−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
$297$	−0.871159	−	4.60418i	−0.0505498	−	0.267162i
$298$	−21.1813	−	11.1946i	−1.22700	−	0.648488i
$299$	−0.230116	+	3.07068i	−0.0133079	+	0.177582i
$300$	−0.695977	−	2.73904i	−0.0401823	−	0.158139i
$301$	−12.1642	+	0.470794i	−0.701131	+	0.0271361i
$302$	1.35388	−	3.86917i	0.0779072	−	0.222646i
$303$	3.12914	−	7.17207i	0.179765	−	0.412025i
$304$	−0.137652	−	1.83684i	−0.00789488	−	0.105350i
$305$	−2.42724	−	1.07778i	−0.138983	−	0.0617136i
$306$	−1.14894	+	3.72478i	−0.0656807	+	0.212931i
$307$	1.72093	−	15.2736i	0.0982184	−	0.871713i	−0.843916	−	0.536476i	$-0.819755\pi$
$307$	1.72093	−	15.2736i	0.0982184	−	0.871713i	0.942134	−	0.335237i	$-0.108816\pi$
$308$	−1.07471	+	2.74869i	−0.0612372	+	0.156621i
$309$	−4.41720	−	3.52260i	−0.251286	−	0.200394i
$310$	14.4530	+	3.39756i	0.820875	+	0.192968i
$311$	−10.1040	−	10.8895i	−0.572945	−	0.617488i	0.378390	−	0.925646i	$-0.376478\pi$
$311$	−10.1040	−	10.8895i	−0.572945	−	0.617488i	−0.951335	+	0.308158i	$0.900287\pi$
$312$	2.74451	+	0.735390i	0.155377	+	0.0416333i
$313$	4.84891	+	18.0964i	0.274077	+	1.02287i	0.956458	+	0.291871i	$0.0942779\pi$
$313$	4.84891	+	18.0964i	0.274077	+	1.02287i	−0.682381	+	0.730997i	$0.739055\pi$
$314$	−2.01330	−	8.82084i	−0.113617	−	0.497789i
$315$	15.2144	+	0.648539i	0.857235	+	0.0365410i
$316$	1.60927	−	7.05066i	0.0905284	−	0.396631i
$317$	−3.26109	+	0.122021i	−0.183161	+	0.00685340i	−0.128814	−	0.991669i	$-0.541117\pi$
$317$	−3.26109	+	0.122021i	−0.183161	+	0.00685340i	−0.0543466	+	0.998522i	$0.517308\pi$
$318$	1.77610	−	1.31082i	0.0995986	−	0.0735071i
$319$	−0.484267	+	3.21290i	−0.0271137	+	0.179888i
$320$	12.4358	−	12.2756i	0.695183	−	0.686224i
$321$	−1.87659	−	0.428319i	−0.104741	−	0.0239065i
$322$	4.75022	−	3.79816i	0.264719	−	0.211663i
$323$	0.918093	−	1.46114i	0.0510840	−	0.0812998i
$324$	4.01085	+	2.31567i	0.222825	+	0.128648i
$325$	−6.70088	−	2.44274i	−0.371698	−	0.135499i
$326$	17.7740	−	16.4919i	0.984411	−	0.913400i
$327$	−0.870895	−	0.164782i	−0.0481606	−	0.00911248i
$328$	1.27966	+	11.3573i	0.0706576	+	0.627103i
$329$	23.1351	−	17.1204i	1.27548	−	0.943878i
$330$	1.61827	−	1.17820i	0.0890828	−	0.0648579i
$331$	20.5877	+	6.35045i	1.13160	+	0.349052i	0.803332	−	0.595532i	$-0.203059\pi$
$331$	20.5877	+	6.35045i	1.13160	+	0.349052i	0.328268	+	0.944584i	$0.393535\pi$
$332$	−6.86008	+	2.99302i	−0.376496	+	0.164263i
$333$	20.0777	−	23.3307i	1.10025	−	1.27851i
$334$	1.56329	+	3.98320i	0.0855394	+	0.217951i
$335$	−5.19489	+	12.9881i	−0.283827	+	0.709614i
$336$	−1.22775	−	2.31582i	−0.0669794	−	0.126338i
$337$	2.95290	−	1.03326i	0.160855	−	0.0562855i	−0.248651	−	0.968593i	$-0.579987\pi$
$337$	2.95290	−	1.03326i	0.160855	−	0.0562855i	0.409505	+	0.912308i	$0.365701\pi$
$338$	−8.85061	+	7.61657i	−0.481410	+	0.414287i
$339$	3.48416	−	1.07472i	0.189234	−	0.0583708i
$340$	2.72566	−	0.392767i	0.147820	−	0.0213008i
$341$	−1.19701	−	7.94163i	−0.0648216	−	0.430063i
$342$	2.35197	+	2.35197i	0.127180	+	0.127180i
$343$	−14.4351	+	11.6029i	−0.779424	+	0.626497i
$344$		−	14.0424i		−	0.757113i
$345$	3.13280	−	0.332422i	0.168664	−	0.0178970i
$346$	4.27758	−	6.27405i	0.229964	−	0.337295i
$347$	12.8483	−	24.3101i	0.689731	−	1.30504i	−0.251692	−	0.967807i	$-0.580987\pi$
$347$	12.8483	−	24.3101i	0.689731	−	1.30504i	0.941423	−	0.337228i	$-0.109489\pi$
$348$	0.930020	+	1.08070i	0.0498543	+	0.0579317i
$349$	−4.23769	−	2.04077i	−0.226839	−	0.109240i	0.317013	−	0.948421i	$-0.397320\pi$
$349$	−4.23769	−	2.04077i	−0.226839	−	0.109240i	−0.543851	+	0.839182i	$0.683034\pi$
$350$	5.48204	+	12.9766i	0.293027	+	0.693630i
$351$	−4.67541	+	2.25156i	−0.249555	+	0.120179i
$352$	−5.29792	−	2.31146i	−0.282380	−	0.123201i
$353$	16.8002	+	14.4578i	0.894187	+	0.769510i	0.973822	−	0.227314i	$-0.0729944\pi$
$353$	16.8002	+	14.4578i	0.894187	+	0.769510i	−0.0796346	+	0.996824i	$0.525375\pi$
$354$	0.333900	+	0.131046i	0.0177466	+	0.00696501i
$355$	14.4423	+	5.15893i	0.766516	+	0.273808i
$356$	12.0557	−	9.61411i	0.638951	−	0.509547i
$357$	0.362866	−	2.42861i	0.0192049	−	0.128536i
$358$	13.8198	−	1.55712i	0.730399	−	0.0822962i
$359$	6.53131	+	9.57967i	0.344709	+	0.505596i	0.958970	−	0.283507i	$-0.0914980\pi$
$359$	6.53131	+	9.57967i	0.344709	+	0.505596i	−0.614261	+	0.789103i	$0.710546\pi$
$360$	−1.42631	+	17.5084i	−0.0751731	+	0.922772i
$361$	8.76374	+	15.1793i	0.461250	+	0.798908i
$362$	−17.5669	+	4.70703i	−0.923294	+	0.247396i
$363$	5.16196	+	3.24347i	0.270933	+	0.170238i
$364$	3.24832	+	0.361774i	0.170258	+	0.0189621i
$365$	−15.2721	−	26.8528i	−0.799380	−	1.40554i
$366$	−0.605097	−	0.561448i	−0.0316289	−	0.0293474i
$367$	−13.0086	−	17.6261i	−0.679046	−	0.920074i	0.320586	−	0.947220i	$-0.396120\pi$
$367$	−13.0086	−	17.6261i	−0.679046	−	0.920074i	−0.999632	+	0.0271451i	$0.991358\pi$
$368$	1.94584	+	2.63652i	0.101434	+	0.137438i
$369$	−7.06617	−	6.55644i	−0.367850	−	0.341315i
$370$	27.4552	+	7.54778i	1.42733	+	0.392390i
$371$	5.93442	−	5.94968i	0.308100	−	0.308892i
$372$	−2.98406	−	1.87501i	−0.154716	−	0.0972147i
$373$	12.7299	−	3.41097i	0.659131	−	0.176614i	0.0862770	−	0.996271i	$-0.472503\pi$
$373$	12.7299	−	3.41097i	0.659131	−	0.176614i	0.572854	+	0.819658i	$0.305836\pi$
$374$	0.975277	+	1.68923i	0.0504304	+	0.0873480i
$375$	−1.22771	+	7.19289i	−0.0633987	+	0.371439i
$376$	18.7022	+	27.4310i	0.964491	+	1.41465i
$377$	3.57565	−	0.402879i	0.184155	−	0.0207493i
$378$	9.54584	+	3.73233i	0.490985	+	0.191970i
$379$	−22.6737	+	18.0816i	−1.16467	+	0.928791i	−0.998358	−	0.0572824i	$-0.981756\pi$
$379$	−22.6737	+	18.0816i	−1.16467	+	0.928791i	−0.166309	+	0.986074i	$0.553185\pi$
$380$	0.790482	−	2.21293i	0.0405508	−	0.113521i
$381$	11.5331	+	4.52639i	0.590856	+	0.231894i
$382$	11.9745	+	10.3049i	0.612667	+	0.527242i
$383$	9.04278	+	3.94532i	0.462064	+	0.201597i	0.618012	−	0.786169i	$-0.287938\pi$
$383$	9.04278	+	3.94532i	0.462064	+	0.201597i	−0.155948	+	0.987765i	$0.549843\pi$
$384$	−0.384228	+	0.185035i	−0.0196076	+	0.00944251i
$385$	5.41630	−	5.36025i	0.276040	−	0.273184i
$386$	−14.5545	−	7.00906i	−0.740802	−	0.356752i
$387$	7.72525	+	8.97690i	0.392697	+	0.456322i
$388$	2.17951	−	4.12384i	0.110648	−	0.209356i
$389$	13.9772	−	20.5009i	0.708674	−	1.03943i	−0.287975	−	0.957638i	$-0.592982\pi$
$389$	13.9772	−	20.5009i	0.708674	−	1.03943i	0.996649	−	0.0817964i	$-0.0260657\pi$
$390$	−1.72416	−	1.39336i	−0.0873064	−	0.0705557i
$391$			3.06983i			0.155248i
$392$	−12.7304	−	17.1567i	−0.642982	−	0.866543i
$393$	−6.33918	−	6.33918i	−0.319770	−	0.319770i
$394$	−2.77874	−	18.4357i	−0.139991	−	0.928778i
$395$	−11.1856	+	14.9520i	−0.562806	+	0.752315i
$396$	2.74376	−	0.846338i	0.137879	−	0.0425301i
$397$	16.4937	−	14.1940i	0.827795	−	0.712375i	−0.132554	−	0.991176i	$-0.542318\pi$
$397$	16.4937	−	14.1940i	0.827795	−	0.712375i	0.960349	+	0.278801i	$0.0899369\pi$
$398$	3.52852	−	1.23468i	0.176869	−	0.0618891i
$399$	−1.68753	−	1.24211i	−0.0844823	−	0.0621833i
$400$	−7.10047	+	2.68098i	−0.355024	+	0.134049i
$401$	−10.3157	−	26.2840i	−0.515142	−	1.31256i	−0.917740	−	0.397182i	$-0.869988\pi$
$401$	−10.3157	−	26.2840i	−0.515142	−	1.31256i	0.402598	−	0.915377i	$-0.368107\pi$
$402$	−2.83602	+	3.29552i	−0.141448	+	0.164365i
$403$	−8.15209	+	3.55672i	−0.406084	+	0.177173i
$404$	9.92185	+	3.06049i	0.493631	+	0.152265i
$405$	−7.03839	−	9.66728i	−0.349741	−	0.480371i
$406$	−5.39289	−	4.62892i	−0.267645	−	0.229729i
$407$	−1.72455	−	15.3058i	−0.0854828	−	0.758681i
$408$	2.78322	+	0.526613i	0.137790	+	0.0260712i
$409$	−13.1635	+	12.2140i	−0.650894	+	0.603942i	−0.934913	−	0.354877i	$-0.884523\pi$
$409$	−13.1635	+	12.2140i	−0.650894	+	0.603942i	0.284019	+	0.958819i	$0.408332\pi$
$410$	2.68355	−	8.50365i	0.132531	−	0.419965i
$411$	−6.52140	−	3.76513i	−0.321677	−	0.185720i
$412$	3.98858	−	6.34779i	0.196503	−	0.312733i
$413$	1.33164	+	0.302140i	0.0655259	+	0.0148673i
$414$	−5.76879	−	1.31669i	−0.283521	−	0.0647117i
$415$	19.3247	+	0.125324i	0.948612	+	0.00615189i
$416$	−0.954051	+	6.32971i	−0.0467762	+	0.310340i
$417$	5.63805	−	4.16107i	0.276096	−	0.203768i
$418$	1.66327	−	0.0622353i	0.0813534	−	0.00304403i
$419$	7.52942	−	32.9886i	0.367836	−	1.61160i	−0.364875	−	0.931057i	$-0.618888\pi$
$419$	7.52942	−	32.9886i	0.367836	−	1.61160i	0.732711	−	0.680540i	$-0.238255\pi$
$420$	−0.232541	−	3.33577i	−0.0113469	−	0.162769i
$421$	1.73093	+	7.58369i	0.0843603	+	0.369607i	0.999433	−	0.0336833i	$-0.0107238\pi$
$421$	1.73093	+	7.58369i	0.0843603	+	0.369607i	−0.915072	+	0.403290i	$0.867867\pi$
$422$	6.16770	+	23.0182i	0.300239	+	1.12051i
$423$	−27.0467	−	7.24714i	−1.31506	−	0.352368i
$424$	6.59331	+	7.10590i	0.320199	+	0.345093i
$425$	−6.84360	−	1.92921i	−0.331964	−	0.0935804i
$426$	3.72672	+	2.97196i	0.180560	+	0.143992i
$427$	−2.59860	−	1.76681i	−0.125755	−	0.0855019i
$428$	0.285972	−	2.53807i	0.0138230	−	0.122682i
$429$	−0.353458	+	1.14588i	−0.0170651	+	0.0553237i
$430$	−4.44617	+	10.0131i	−0.214414	+	0.482873i
$431$	0.772412	+	10.3071i	0.0372058	+	0.496476i	0.984415	+	0.175861i	$0.0562708\pi$
$431$	0.772412	+	10.3071i	0.0372058	+	0.496476i	−0.947209	+	0.320616i	$0.896110\pi$
$432$	−2.20828	+	5.06144i	−0.106246	+	0.243519i
$433$	8.88207	−	25.3835i	0.426845	−	1.21985i	−0.506928	−	0.861988i	$-0.669219\pi$
$433$	8.88207	−	25.3835i	0.426845	−	1.21985i	0.933773	−	0.357865i	$-0.116495\pi$
$434$	16.1104	+	7.00429i	0.773325	+	0.336217i
$435$	−1.06226	−	3.52477i	−0.0509316	−	0.169000i
$436$	0.0878913	−	1.17283i	0.00420923	−	0.0561683i
$437$	2.31597	+	1.22403i	0.110788	+	0.0585531i
$438$	−1.78506	−	9.43425i	−0.0852933	−	0.450786i
$439$	−22.0698	+	3.32648i	−1.05333	+	0.158764i	−0.652810	−	0.757522i	$-0.726410\pi$
$439$	−22.0698	+	3.32648i	−1.05333	+	0.158764i	−0.400524	+	0.916286i	$0.631172\pi$
$440$	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
$443$	−31.9883	−	23.6085i	−1.51981	−	1.12167i	−0.955061	−	0.296410i	$-0.904210\pi$
$443$	−31.9883	−	23.6085i	−1.51981	−	1.12167i	−0.564751	−	0.825262i	$-0.691028\pi$
$444$	−5.58443	−	3.80740i	−0.265026	−	0.180691i
$445$	−38.5233	+	10.0550i	−1.82618	+	0.476651i
$446$	−8.15587	−	0.611198i	−0.386191	−	0.0289410i
$447$	−4.84961	−	13.8594i	−0.229379	−	0.655527i
$448$	17.0679	−	11.6688i	0.806382	−	0.551300i
$449$	0.540769	+	1.12292i	0.0255205	+	0.0529938i	0.913339	−	0.407199i	$-0.133495\pi$
$449$	0.540769	+	1.12292i	0.0255205	+	0.0529938i	−0.887819	+	0.460193i	$0.847780\pi$
$450$	6.56065	−	12.0330i	0.309272	−	0.567239i
$451$	−4.81010	+	0.360467i	−0.226499	+	0.0169737i
$452$	1.93474	+	4.43448i	0.0910027	+	0.208580i
$453$	2.22122	−	1.17395i	0.104362	−	0.0551569i
$454$	−6.39463	−	8.01862i	−0.300115	−	0.376332i
$455$	−7.28632	−	4.25744i	−0.341588	−	0.199592i
$456$	1.50704	−	1.88977i	0.0705735	−	0.0884964i
$457$	−5.54912	+	29.3278i	−0.259577	+	1.37190i	0.573712	+	0.819057i	$0.305503\pi$
$457$	−5.54912	+	29.3278i	−0.259577	+	1.37190i	−0.833288	+	0.552839i	$0.813545\pi$
$458$	−0.973523	+	26.0180i	−0.0454898	+	1.21574i
$459$	−4.48027	+	2.58669i	−0.209121	+	0.120736i
$460$	0.903761	+	4.08147i	0.0421381	+	0.190299i
$461$	−10.6182	+	2.42354i	−0.494539	+	0.112875i	−0.462515	−	0.886612i	$-0.653053\pi$
$461$	−10.6182	+	2.42354i	−0.494539	+	0.112875i	−0.0320248	+	0.999487i	$0.510196\pi$
$462$	2.13261	−	1.03039i	0.0992182	−	0.0479380i
$463$	−26.5012	+	16.6518i	−1.23162	+	0.773876i	−0.980962	−	0.194201i	$-0.937789\pi$
$463$	−26.5012	+	16.6518i	−1.23162	+	0.773876i	−0.250655	+	0.968077i	$0.580646\pi$
$464$	2.60445	−	2.80693i	0.120908	−	0.130308i
$465$	5.07710	+	7.55149i	0.235445	+	0.350192i
$466$	16.9652	+	2.55709i	0.785896	+	0.118455i
$467$	1.03786	+	27.7375i	0.0480266	+	1.28354i	0.789999	+	0.613108i	$0.210081\pi$
$467$	1.03786	+	27.7375i	0.0480266	+	1.28354i	−0.741972	+	0.670430i	$0.766110\pi$
$468$	−1.69176	−	2.69242i	−0.0782017	−	0.124457i
$469$	−8.78785	+	14.0257i	−0.405785	+	0.647648i
$470$	−4.65043	−	25.4816i	−0.214508	−	1.17538i
$471$	2.77261	−	4.80231i	0.127755	−	0.221279i
$472$	−0.407678	+	1.52147i	−0.0187649	+	0.0700316i
$473$	5.92231	+	0.221597i	0.272308	+	0.0101890i
$474$	−4.79533	+	3.26940i	−0.220257	+	0.150169i
$475$	−4.18419	+	4.39378i	−0.191984	+	0.201601i
$476$	3.25623	+	0.117653i	0.149249	+	0.00539260i
$477$	−8.12416	−	0.915373i	−0.371980	−	0.0419120i
$478$	12.8405	+	24.2955i	0.587313	+	1.11125i
$479$	−5.87752	+	14.9757i	−0.268551	+	0.684256i	0.731447	+	0.681899i	$0.238846\pi$
$479$	−5.87752	+	14.9757i	−0.268551	+	0.684256i	−0.999997	+	0.00235715i	$0.999250\pi$
$480$	6.54588	−	0.202429i	0.298777	−	0.00923959i
$481$	−15.8784	+	6.23180i	−0.723991	+	0.284146i
$482$	−28.1817	−	9.86121i	−1.28364	−	0.449166i
$483$	3.71752	+	0.273790i	0.169153	+	0.0124579i
$484$	−3.50988	+	7.28834i	−0.159540	+	0.331288i
$485$	−9.46437	+	7.44769i	−0.429755	+	0.338182i
$486$	−4.52114	−	14.6572i	−0.205083	−	0.664863i
$487$	−4.63701	+	0.877370i	−0.210123	+	0.0397574i	−0.289907	−	0.957055i	$-0.593624\pi$
$487$	−4.63701	+	0.877370i	−0.210123	+	0.0397574i	0.0797843	+	0.996812i	$0.474577\pi$
$488$	2.15249	−	2.91652i	0.0974387	−	0.132025i
$489$	14.8605			0.672014
$490$	3.64531	+	16.2646i	0.164678	+	0.734757i
$491$	20.3270			0.917345			0.458673	−	0.888605i	$-0.348325\pi$
$491$	20.3270			0.917345			0.458673	+	0.888605i	$0.348325\pi$
$492$	−1.25691	+	1.70305i	−0.0566657	+	0.0767793i
$493$	3.52469	−	0.666906i	0.158744	−	0.0300360i
$494$	−0.543310	−	1.76137i	−0.0244447	−	0.0792477i
$495$	−7.36158	−	0.877833i	−0.330878	−	0.0394557i
$496$	−4.10660	+	8.52744i	−0.184392	+	0.382893i
$497$	15.7264	+	9.05273i	0.705425	+	0.406070i
$498$	5.66945	+	1.98383i	0.254054	+	0.0888974i
$499$	9.87920	−	3.87730i	0.442254	−	0.173572i	−0.133757	−	0.991014i	$-0.542704\pi$
$499$	9.87920	−	3.87730i	0.442254	−	0.173572i	0.576010	+	0.817442i	$0.304609\pi$
$500$	−9.66681	−	0.550200i	−0.432313	−	0.0246057i
$501$	−0.958124	+	2.44126i	−0.0428058	+	0.109067i
$502$	8.10541	+	15.3362i	0.361762	+	0.684487i
$503$	−18.7984	−	2.11807i	−0.838178	−	0.0944400i	−0.317569	−	0.948235i	$-0.602866\pi$
$503$	−18.7984	−	2.11807i	−0.838178	−	0.0944400i	−0.520609	+	0.853795i	$0.674295\pi$
$504$	−5.35372	+	20.0835i	−0.238474	+	0.894589i
$505$	−20.2068	−	17.6187i	−0.899190	−	0.784022i
$506$	−2.44646	+	1.66797i	−0.108759	+	0.0741504i
$507$	−7.15153	−	0.267591i	−0.317610	−	0.0118841i
$508$	−4.25497	+	15.8798i	−0.188784	+	0.704550i
$509$	2.75212	−	4.76681i	0.121986	−	0.211285i	−0.798565	−	0.601909i	$-0.794407\pi$
$509$	2.75212	−	4.76681i	0.121986	−	0.211285i	0.920551	+	0.390623i	$0.127741\pi$
$510$	−1.81787	−	1.25675i	−0.0804965	−	0.0556497i
$511$	−12.1166	−	34.4851i	−0.536006	−	1.52553i
$512$	8.55367	+	13.6131i	0.378022	+	0.601619i
$513$	0.165064	+	4.41143i	0.00728776	+	0.194769i
$514$	7.70442	+	1.16125i	0.339827	+	0.0512207i
$515$	−16.0638	+	10.8002i	−0.707855	+	0.475912i
$516$	1.76885	−	1.90637i	0.0778694	−	0.0839233i
$517$	−11.8641	+	7.45469i	−0.521781	+	0.327857i
$518$	30.3730	+	14.5789i	1.33451	+	0.640558i
$519$	4.53730	−	1.03561i	0.199165	−	0.0454582i
$520$	5.23252	−	8.20884i	0.229461	−	0.359982i
$521$	−22.2256	+	12.8320i	−0.973723	+	0.562179i	−0.900369	−	0.435127i	$-0.856704\pi$
$521$	−22.2256	+	12.8320i	−0.973723	+	0.562179i	−0.0733540	+	0.997306i	$0.523370\pi$
$522$	−0.258539	+	6.90959i	−0.0113159	+	0.302424i
$523$	−0.382512	+	2.02162i	−0.0167261	+	0.0883995i	−0.989935	−	0.141524i	$-0.954800\pi$
$523$	−0.382512	+	2.02162i	−0.0167261	+	0.0883995i	0.973209	+	0.229923i	$0.0738475\pi$
$524$	7.41693	−	9.30053i	0.324010	−	0.406296i
$525$	−2.94661	+	8.11544i	−0.128600	+	0.354187i
$526$	6.07441	+	7.61707i	0.264857	+	0.332120i
$527$	−7.83934	+	4.14321i	−0.341487	+	0.180481i
$528$	0.510295	+	1.16961i	0.0222077	+	0.0509007i
$529$	18.2887	−	1.37055i	0.795160	−	0.0595890i
$530$	−2.45153	−	7.15456i	−0.106487	−	0.310774i
$531$	−0.576405	−	1.19692i	−0.0250139	−	0.0519418i
$532$	1.38711	−	2.40969i	0.0601389	−	0.104473i
$533$	1.76429	+	5.04206i	0.0764200	+	0.218396i
$534$	−12.3401	−	0.924763i	−0.534009	−	0.0400184i
$535$	−3.33434	+	5.68971i	−0.144156	+	0.245988i
$536$	−15.7751	−	10.7553i	−0.681380	−	0.464557i
$537$	6.85807	+	5.06149i	0.295948	+	0.218419i
$538$	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	0.210738	−	0.977543i	$-0.432413\pi$
$541$	16.2874	−	2.45493i	0.700250	−	0.105546i	0.489512	+	0.871997i	$0.337175\pi$
$542$	2.83598	+	14.9885i	0.121816	+	0.643812i
$543$	−9.85467	−	5.20834i	−0.422904	−	0.223511i
$544$	−0.476894	+	6.36370i	−0.0204466	+	0.272842i
$545$	−1.43635	+	2.67555i	−0.0615263	+	0.114608i
$546$	−1.71347	−	1.98593i	−0.0733298	−	0.0849898i
$547$	−3.00070	+	8.57550i	−0.128301	+	0.366662i	−0.990058	−	0.140658i	$-0.955078\pi$
$547$	−3.00070	+	8.57550i	−0.128301	+	0.366662i	0.861758	+	0.507320i	$0.169364\pi$
$548$	3.99576	−	9.15838i	0.170690	−	0.391227i
$549$	0.228463	+	3.04862i	0.00975056	+	0.130112i
$550$	−2.18096	−	6.50215i	−0.0929966	−	0.277252i
$551$	0.902255	−	2.92504i	0.0384374	−	0.124611i
$552$	−0.481439	+	4.27289i	−0.0204914	+	0.181866i
$553$	−16.1768	+	15.0486i	−0.687908	+	0.639931i
$554$	−4.61150	−	3.67755i	−0.195924	−	0.156244i
$555$	9.18864	+	14.8364i	0.390036	+	0.629768i
$556$	6.32434	+	6.81602i	0.268212	+	0.289064i
$557$	17.0091	+	4.55758i	0.720700	+	0.193111i	0.600484	−	0.799637i	$-0.294975\pi$
$557$	17.0091	+	4.55758i	0.720700	+	0.193111i	0.120216	+	0.992748i	$0.461641\pi$
$558$	−4.42348	−	16.5087i	−0.187261	−	0.698868i
$559$	−1.46044	−	6.39862i	−0.0617702	−	0.270633i
$560$	−8.83232	+	1.62363i	−0.373234	+	0.0686110i
$561$	−0.266018	+	1.16550i	−0.0112313	+	0.0492075i
$562$	−1.04024	+	0.0389231i	−0.0438800	+	0.00164187i
$563$	31.5094	−	23.2550i	1.32796	−	0.980082i	0.328598	−	0.944470i	$-0.393424\pi$
$563$	31.5094	−	23.2550i	1.32796	−	0.980082i	0.999366	−	0.0356121i	$-0.0113381\pi$
$564$	−0.916387	+	6.07983i	−0.0385869	+	0.256007i
$565$	0.0810114	−	12.4918i	0.00340817	−	0.525535i
$566$	11.7319	+	2.67774i	0.493130	+	0.112554i
$567$	−6.15537	−	12.7399i	−0.258501	−	0.535025i
$568$	−11.1365	+	17.7236i	−0.467276	+	0.743665i
$569$	−15.2569	−	8.80859i	−0.639604	−	0.369275i	0.144858	−	0.989452i	$-0.453727\pi$
$569$	−15.2569	−	8.80859i	−0.639604	−	0.369275i	−0.784462	+	0.620177i	$0.787061\pi$
$570$	−1.67296	+	0.870353i	−0.0700726	+	0.0364551i
$571$	−2.81671	+	2.61352i	−0.117875	+	0.109372i	−0.736909	−	0.675992i	$-0.763715\pi$
$571$	−2.81671	+	2.61352i	−0.117875	+	0.109372i	0.619033	+	0.785365i	$0.287525\pi$
$572$	−1.56345	−	0.295821i	−0.0653712	−	0.0123689i
$573$	1.08409	+	9.62157i	0.0452885	+	0.401947i
$574$	4.91807	−	9.33443i	0.205276	−	0.389612i
$575$	2.14403	−	10.5785i	0.0894122	−	0.441153i
$576$	−19.2214	−	5.92902i	−0.800892	−	0.247042i
$577$	−35.2211	+	15.3668i	−1.46627	+	0.639728i	−0.973138	−	0.230225i	$-0.926054\pi$
$577$	−35.2211	+	15.3668i	−1.46627	+	0.639728i	−0.493135	+	0.869953i	$0.664149\pi$
$578$	−10.4037	+	12.0893i	−0.432736	+	0.502848i
$579$	−3.61715	−	9.21636i	−0.150324	−	0.383019i
$580$	4.48987	−	1.92435i	0.186432	−	0.0799043i
$581$	22.4726	+	4.22216i	0.932320	+	0.175165i
$582$	−3.53319	+	1.23631i	−0.146455	+	0.0512469i
$583$	−3.10093	+	2.66857i	−0.128427	+	0.110521i
$584$	40.2907	−	12.4280i	1.66724	−	0.514276i
$585$	1.17100	+	8.12631i	0.0484148	+	0.335981i
$586$	3.57960	+	23.7491i	0.147872	+	0.981066i
$587$	19.4958	+	19.4958i	0.804677	+	0.804677i	0.983823	−	0.179145i	$-0.0573333\pi$
$587$	19.4958	+	19.4958i	0.804677	+	0.804677i	−0.179145	+	0.983823i	$0.557333\pi$
$588$	0.432890	−	3.93276i	0.0178521	−	0.162184i
$589$			7.56624i			0.311762i
$590$	0.772438	−	0.955824i	0.0318008	−	0.0393507i
$591$	6.43688	−	9.44117i	0.264778	−	0.388358i
$592$	−8.48171	+	16.0482i	−0.348596	+	0.659576i
$593$	−1.22125	−	1.41911i	−0.0501506	−	0.0582761i	0.732336	−	0.680943i	$-0.238430\pi$
$593$	−1.22125	−	1.41911i	−0.0501506	−	0.0582761i	−0.782487	+	0.622667i	$0.786049\pi$
$594$	−4.49575	−	2.16504i	−0.184463	−	0.0888327i
$595$	−7.56081	−	3.68966i	−0.309963	−	0.151261i
$596$	17.5542	−	8.45368i	0.719050	−	0.346276i
$597$	2.10000	+	0.916220i	0.0859472	+	0.0374984i
$598$	2.48545	+	2.13891i	0.101638	+	0.0874663i
$599$	−34.5521	−	13.5607i	−1.41176	−	0.554076i	−0.467712	−	0.883881i	$-0.654922\pi$
$599$	−34.5521	−	13.5607i	−1.41176	−	0.554076i	−0.944049	+	0.329805i	$0.893017\pi$
$600$	−9.22303	−	3.75854i	−0.376529	−	0.153442i
$601$	17.6154	−	14.0478i	0.718547	−	0.573022i	−0.194487	−	0.980905i	$-0.562304\pi$
$601$	17.6154	−	14.0478i	0.718547	−	0.573022i	0.913034	+	0.407883i	$0.133733\pi$
$602$	−7.28862	+	10.7200i	−0.297062	+	0.436914i
$603$	16.0015	−	1.80294i	0.651631	−	0.0734212i
$604$	1.87795	+	2.75445i	0.0764127	+	0.112077i
$605$	15.9197	−	13.5213i	0.647227	−	0.549719i
$606$	−4.16634	−	7.21631i	−0.169246	−	0.293143i
$607$	−25.0633	+	6.71568i	−1.01729	+	0.272581i	−0.728671	−	0.684864i	$-0.759862\pi$
$607$	−25.0633	+	6.71568i	−1.01729	+	0.272581i	−0.288616	+	0.957445i	$0.593195\pi$
$608$	4.61081	+	2.89717i	0.186993	+	0.117496i
$609$	−0.493257	−	4.32782i	−0.0199878	−	0.175372i
$610$	−2.45831	+	1.39813i	−0.0995339	+	0.0566085i
$611$	11.3748	+	10.5543i	0.460177	+	0.426982i
$612$	−1.88244	−	2.55061i	−0.0760930	−	0.103102i
$613$	−0.476440	−	0.645553i	−0.0192432	−	0.0260736i	0.794871	−	0.606779i	$-0.207539\pi$
$613$	−0.476440	−	0.645553i	−0.0192432	−	0.0260736i	−0.814114	+	0.580705i	$0.802777\pi$
$614$	−11.9983	−	11.1328i	−0.484211	−	0.449282i
$615$	4.75059	−	2.70183i	0.191562	−	0.108948i
$616$	5.54487	+	8.79951i	0.223409	+	0.354542i
$617$	12.8988	+	8.10485i	0.519286	+	0.326289i	0.766044	−	0.642788i	$-0.222222\pi$
$617$	12.8988	+	8.10485i	0.519286	+	0.326289i	−0.246758	+	0.969077i	$0.579365\pi$
$618$	−5.81139	+	1.55716i	−0.233768	+	0.0626380i
$619$	−18.2623	−	31.6312i	−0.734024	−	1.27137i	−0.955150	−	0.296122i	$-0.904307\pi$
$619$	−18.2623	−	31.6312i	−0.734024	−	1.27137i	0.221126	−	0.975245i	$-0.429027\pi$
$620$	−9.20296	+	7.81648i	−0.369600	+	0.313917i
$621$	−4.42389	−	6.48866i	−0.177525	−	0.260381i
$622$	−15.7194	+	1.77115i	−0.630291	+	0.0710168i
$623$	−46.9721	+	3.58074i	−1.88190	+	0.143459i
$624$	1.10487	−	0.881103i	0.0442301	−	0.0352724i
$625$	22.2353	+	11.4277i	0.889412	+	0.457106i
$626$	18.5712	+	7.28867i	0.742256	+	0.291314i
$627$	0.773219	+	0.665409i	0.0308794	+	0.0265739i
$628$	6.74416	+	2.94245i	0.269121	+	0.117416i
$629$	−15.3211	+	7.37823i	−0.610890	+	0.294189i
$630$	10.1765	−	12.6256i	0.405441	−	0.503018i
$631$	29.3543	+	14.1363i	1.16858	+	0.562757i	0.914563	−	0.404443i	$-0.132535\pi$
$631$	29.3543	+	14.1363i	1.16858	+	0.562757i	0.254014	+	0.967200i	$0.418249\pi$
$632$	−16.6245	−	19.3180i	−0.661286	−	0.768428i
$633$	−6.82458	+	12.9127i	−0.271253	+	0.513235i
$634$	−1.95760	+	2.87127i	−0.0777461	+	0.114033i
$635$	26.6804	−	33.0147i	1.05878	−	1.31015i
$636$			1.79522i			0.0711850i
$637$	−7.58515	−	6.49372i	−0.300535	−	0.257290i
$638$	2.44660	+	2.44660i	0.0968616	+	0.0968616i
$639$	−2.63119	−	17.4568i	−0.104088	−	0.690581i
$640$	0.208392	+	1.44617i	0.00823742	+	0.0571647i
$641$	31.1194	−	9.59906i	1.22914	−	0.379140i	0.388864	−	0.921295i	$-0.372868\pi$
$641$	31.1194	−	9.59906i	1.22914	−	0.379140i	0.840278	+	0.542155i	$0.182391\pi$
$642$	−1.55364	+	1.33702i	−0.0613175	+	0.0527679i
$643$	39.0849	−	13.6764i	1.54136	−	0.539345i	0.579994	−	0.814621i	$-0.303055\pi$
$643$	39.0849	−	13.6764i	1.54136	−	0.539345i	0.961365	+	0.275276i	$0.0887692\pi$
$644$	0.191293	+	4.94253i	0.00753798	+	0.194763i
$645$	−6.17173	+	2.64519i	−0.243012	+	0.104154i
$646$	−0.671350	−	1.71057i	−0.0264139	−	0.0673015i
$647$	21.8998	−	25.4480i	0.860969	−	1.00046i	−0.138979	−	0.990295i	$-0.544382\pi$
$647$	21.8998	−	25.4480i	0.860969	−	1.00046i	0.999948	−	0.0101686i	$-0.00323683\pi$
$648$	14.9596	−	6.52680i	0.587668	−	0.256397i
$649$	−0.635243	−	0.195946i	−0.0249355	−	0.00769157i
$650$	−6.33024	+	4.19666i	−0.248292	+	0.164607i
$651$	4.31820	+	9.86285i	0.169244	+	0.386555i
$652$	2.20780	+	19.5947i	0.0864640	+	0.767390i
$653$	16.0503	+	3.03688i	0.628096	+	0.118842i	0.490208	−	0.871606i	$-0.336921\pi$
$653$	16.0503	+	3.03688i	0.628096	+	0.118842i	0.137888	+	0.990448i	$0.455969\pi$
$654$	−0.691896	+	0.641985i	−0.0270553	+	0.0251036i
$655$	−27.2480	+	14.1757i	−1.06467	+	0.553891i
$656$	4.92291	+	2.84225i	0.192207	+	0.110971i
$657$	−18.9196	+	30.1104i	−0.738125	+	1.17472i
$658$	−0.0393566	−	30.6482i	−0.00153428	−	1.19479i
$659$	36.8755	+	8.41660i	1.43647	+	0.327864i	0.868706	−	0.495329i	$-0.164952\pi$
$659$	36.8755	+	8.41660i	1.43647	+	0.327864i	0.567762	+	0.823193i	$0.307809\pi$
$660$	−0.0105572	+	1.62790i	−0.000410937	+	0.0633658i
$661$	3.28164	−	21.7723i	0.127641	−	0.846844i	−0.829768	−	0.558109i	$-0.811527\pi$
$661$	3.28164	−	21.7723i	0.127641	−	0.846844i	0.957409	−	0.288735i	$-0.0932347\pi$
$662$	18.4597	−	13.6239i	0.717455	−	0.529506i
$663$	1.32299	−	0.0495027i	0.0513805	−	0.00192252i
$664$	−5.86934	+	25.7153i	−0.227775	+	0.997946i
$665$	−5.79829	+	4.23293i	−0.224848	+	0.164146i
$666$	−7.29369	−	31.9557i	−0.282625	−	1.23826i
$667$	1.40939	+	5.25990i	0.0545717	+	0.203664i
$668$	−3.36135	−	0.900670i	−0.130054	−	0.0348480i
$669$	−3.40948	−	3.67454i	−0.131818	−	0.142066i
$670$	7.84322	+	12.6640i	0.303010	+	0.489252i
$671$	1.19606	+	0.953829i	0.0461735	+	0.0368222i
$672$	7.66382	+	1.14507i	0.295638	+	0.0441721i
$673$	2.53382	−	22.4883i	0.0976717	−	0.866861i	−0.845369	−	0.534183i	$-0.820619\pi$
$673$	2.53382	−	22.4883i	0.0976717	−	0.866861i	0.943041	−	0.332678i	$-0.107952\pi$
$674$	0.981959	−	3.18343i	0.0378236	−	0.122621i
$675$	17.2454	−	5.78448i	0.663775	−	0.222645i
$676$	−0.709650	−	9.46963i	−0.0272942	−	0.364216i
$677$	−3.77871	+	8.66089i	−0.145228	+	0.332865i	−0.973939	−	0.226812i	$-0.927170\pi$
$677$	−3.77871	+	8.66089i	−0.145228	+	0.332865i	0.828711	+	0.559677i	$0.189075\pi$
$678$	1.28238	−	3.66484i	0.0492496	−	0.140747i
$679$	−12.5900	+	6.67470i	−0.483159	+	0.256151i
$680$	4.59029	−	8.55057i	0.176030	−	0.327899i
$681$	0.469747	−	6.26834i	0.0180007	−	0.240203i
$682$	−7.56133	−	3.99628i	−0.289538	−	0.153026i
$683$	−0.278497	−	1.47189i	−0.0106564	−	0.0563204i	0.976835	−	0.213995i	$-0.0686478\pi$
$683$	−0.278497	−	1.47189i	−0.0106564	−	0.0563204i	−0.987491	+	0.157675i	$0.949600\pi$
$684$	−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
$688$	−5.61946	−	4.14735i	−0.214240	−	0.158116i
$689$	3.74338	+	2.55219i	0.142611	+	0.0972308i
$690$	1.69620	−	2.89440i	0.0645733	−	0.110188i
$691$	38.9494	+	2.91885i	1.48170	+	0.111038i	0.790874	−	0.611979i	$-0.209626\pi$
$691$	38.9494	+	2.91885i	1.48170	+	0.111038i	0.690830	+	0.723017i	$0.257245\pi$
$692$	2.03963	+	5.82894i	0.0775353	+	0.221583i
$693$	−8.38564	−	2.57484i	−0.318544	−	0.0978101i
$694$	−12.7044	−	26.3809i	−0.482251	−	1.00141i
$695$	−7.78213	−	22.7114i	−0.295193	−	0.861494i
$696$	5.01059	−	0.375491i	0.189926	−	0.0142330i
$697$	2.12959	+	4.88107i	0.0806640	+	0.184884i
$698$	−4.42823	+	2.34039i	−0.167611	+	0.0885851i
$699$	6.55613	+	8.22113i	0.247976	+	0.310952i
$700$	−11.1386	−	2.67964i	−0.421001	−	0.101281i
$701$	−9.28885	+	11.6478i	−0.350835	+	0.439933i	−0.925668	−	0.378338i	$-0.876496\pi$
$701$	−9.28885	+	11.6478i	−0.350835	+	0.439933i	0.574833	+	0.818271i	$0.305067\pi$
$702$	−1.02735	+	5.42967i	−0.0387748	+	0.204930i
$703$	−0.542572	+	14.5006i	−0.0204635	+	0.546899i
$704$	−8.71712	+	5.03283i	−0.328539	+	0.189682i
$705$	8.53321	−	13.3870i	0.321379	−	0.504184i
$706$	23.0111	−	5.25213i	0.866033	−	0.197666i
$707$	−19.8096	−	24.7751i	−0.745016	−	0.931764i
$708$	−0.246999	+	0.155200i	−0.00928280	+	0.00583277i
$709$	−3.58006	+	3.85839i	−0.134452	+	0.144905i	−0.796689	−	0.604390i	$-0.793417\pi$
$709$	−3.58006	+	3.85839i	−0.134452	+	0.144905i	0.662237	+	0.749295i	$0.269607\pi$
$710$	13.5527	−	9.11192i	0.508625	−	0.341964i
$711$	21.2552	+	3.20370i	0.797131	+	0.120148i
$712$	−2.03189	−	54.3034i	−0.0761483	−	2.03511i
$713$	−7.16117	−	11.3969i	−0.268188	−	0.426819i
$714$	−1.85138	−	1.84663i	−0.0692863	−	0.0691086i
$715$	3.37947	+	2.33633i	0.126385	+	0.0873739i
$716$	−5.65509	+	9.79491i	−0.211341	+	0.366053i
$717$	−4.35909	+	16.2683i	−0.162793	+	0.607552i
$718$	12.3380	+	0.461654i	0.460448	+	0.0172288i
$719$	37.0151	−	25.2365i	1.38043	−	0.941162i	0.380566	−	0.924754i	$-0.375729\pi$
$719$	37.0151	−	25.2365i	1.38043	−	0.941162i	0.999865	−	0.0164089i	$-0.00522334\pi$
$720$	6.58524	+	5.74181i	0.245417	+	0.213985i
$721$	−20.9806	+	9.18582i	−0.781358	+	0.342098i
$722$	18.5474	+	2.08979i	0.690261	+	0.0777738i
$723$	−8.55063	−	16.1786i	−0.318001	−	0.601688i
$724$	5.40353	−	13.7680i	0.200821	−	0.511683i
$725$	−12.6117	−	0.163584i	−0.468385	−	0.00607535i
$726$	6.04318	−	2.37177i	0.224283	−	0.0880247i
$727$	−7.27142	−	2.54438i	−0.269682	−	0.0943658i	0.192050	−	0.981385i	$-0.438486\pi$
$727$	−7.27142	−	2.54438i	−0.269682	−	0.0943658i	−0.461732	+	0.887019i	$0.652772\pi$
$728$	7.82355	−	8.45353i	0.289960	−	0.313309i
$729$	−2.88209	+	5.98472i	−0.106744	+	0.221656i
$730$	−32.6648	−	3.89512i	−1.20898	−	0.144165i
$731$	−1.92859	−	6.25233i	−0.0713314	−	0.231251i
$732$	0.659600	−	0.124803i	0.0243795	−	0.00461286i
$733$	−9.61327	+	13.0255i	−0.355074	+	0.481109i	−0.945333	−	0.326105i	$-0.894264\pi$
$733$	−9.61327	+	13.0255i	−0.355074	+	0.481109i	0.590259	+	0.807214i	$0.299026\pi$
$734$	−23.3281			−0.861055
$735$	−5.14245	+	8.82696i	−0.189682	+	0.325587i
$736$	−9.68727			−0.357078
$737$	4.78494	−	6.48336i	0.176255	−	0.238818i
$738$	−10.0859	+	1.90835i	−0.371266	+	0.0702472i
$739$	4.14777	+	13.4467i	0.152578	+	0.494646i	0.999301	−	0.0373883i	$-0.0119038\pi$
$739$	4.14777	+	13.4467i	0.152578	+	0.494646i	−0.846723	+	0.532035i	$0.821428\pi$
$740$	−18.1978	+	14.3202i	−0.668964	+	0.526421i
$741$	0.490165	−	1.01784i	0.0180067	−	0.0373912i
$742$	−1.34508	−	8.84689i	−0.0493793	−	0.324780i
$743$	15.7216	+	5.50123i	0.576770	+	0.201821i	0.602871	−	0.797839i	$-0.294023\pi$
$743$	15.7216	+	5.50123i	0.576770	+	0.201821i	−0.0261009	+	0.999659i	$0.508309\pi$
$744$	−11.5613	+	4.53749i	−0.423859	+	0.166352i
$745$	−50.2828	+	1.55498i	−1.84222	+	0.0569701i
$746$	5.12722	−	13.0640i	0.187721	−	0.478305i
$747$	−10.3949	−	19.6680i	−0.380328	−	0.719616i
$748$	−1.57633	−	0.177610i	−0.0576363	−	0.00649406i
$749$	−5.08220	+	5.92099i	−0.185700	+	0.216348i
$750$	5.38654	+	5.60032i	0.196689	+	0.204495i
$751$	4.67784	−	3.18930i	0.170697	−	0.116379i	−0.474958	−	0.880008i	$-0.657537\pi$
$751$	4.67784	−	3.18930i	0.170697	−	0.116379i	0.645655	+	0.763629i	$0.276584\pi$
$752$	16.5010	+	0.617422i	0.601728	+	0.0225151i
$753$	−2.75161	+	10.2691i	−0.100274	+	0.374228i
$754$	1.91587	−	3.31839i	0.0697719	−	0.120848i
$755$	−1.54538	−	8.46776i	−0.0562420	−	0.308173i
$756$	−7.05220	+	4.44383i	−0.256486	+	0.161621i
$757$	21.2781	+	33.8639i	0.773366	+	1.23080i	0.968251	+	0.249979i	$0.0804236\pi$
$757$	21.2781	+	33.8639i	0.773366	+	1.23080i	−0.194886	+	0.980826i	$0.562434\pi$
$758$	1.15473	+	30.8607i	0.0419416	+	1.12091i
$759$	−1.79448	−	0.270474i	−0.0651354	−	0.00981758i
$760$	−4.62052	−	6.87240i	−0.167604	−	0.249288i
$761$	1.09648	−	1.18172i	0.0397474	−	0.0428375i	−0.712865	−	0.701301i	$-0.752603\pi$
$761$	1.09648	−	1.18172i	0.0397474	−	0.0428375i	0.752613	+	0.658464i	$0.228793\pi$
$762$	11.1711	−	7.01929i	0.404688	−	0.254282i
$763$	−2.23665	+	2.81207i	−0.0809722	+	0.101804i
$764$	−12.5258	+	2.85892i	−0.453166	+	0.103432i
$765$	1.76955	+	7.99145i	0.0639783	+	0.288932i
$766$	9.09855	−	5.25305i	0.328744	−	0.189800i
$767$	−0.0275273	+	0.735684i	−0.000993955	+	0.0265640i
$768$	−1.98081	+	10.4688i	−0.0714764	+	0.377762i
$769$	2.87676	−	3.60734i	0.103739	−	0.130084i	−0.727252	−	0.686371i	$-0.759203\pi$
$769$	2.87676	−	3.60734i	0.103739	−	0.130084i	0.830991	+	0.556287i	$0.187774\pi$
$770$	−1.16768	−	8.03025i	−0.0420804	−	0.289390i
$771$	2.97735	+	3.73347i	0.107227	+	0.134458i
$772$	11.6151	−	6.13877i	0.418037	−	0.220939i
$773$	3.54591	+	8.12731i	0.127537	+	0.292319i	0.968602	−	0.248615i	$-0.0799755\pi$
$773$	3.54591	+	8.12731i	0.127537	+	0.292319i	−0.841065	+	0.540934i	$0.818071\pi$
$774$	12.5765	−	0.942477i	0.452052	−	0.0338766i
$775$	29.9077	−	8.80215i	1.07431	−	0.316182i
$776$	−7.13210	−	14.8100i	−0.256027	−	0.531647i
$777$	7.56849	+	19.2116i	0.271518	+	0.689213i
$778$	−8.72668	−	24.9394i	−0.312867	−	0.894122i
$779$	4.53155	+	0.339593i	0.162360	+	0.0121672i
$780$	1.74439	−	0.455304i	0.0624592	−	0.0163025i
$781$	−7.29911	−	4.97645i	−0.261183	−	0.178071i
$782$	2.63024	+	1.94120i	0.0940572	+	0.0694173i
$783$	−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
$787$	−6.29620	−	33.2762i	−0.224435	−	1.18617i	−0.895600	−	0.444861i	$-0.853253\pi$
$787$	−6.29620	−	33.2762i	−0.224435	−	1.18617i	0.671164	−	0.741309i	$-0.265795\pi$
$788$	13.4053	+	7.08489i	0.477543	+	0.252389i
$789$	−0.446223	+	5.95444i	−0.0158860	+	0.211984i
$790$	5.73770	+	19.0387i	0.204138	+	0.677365i
$791$	2.72928	−	14.5267i	0.0970420	−	0.516509i
$792$	3.34206	−	9.55107i	0.118755	−	0.339383i
$793$	0.677490	−	1.55282i	0.0240584	−	0.0551424i
$794$	−1.73166	−	23.1074i	−0.0614542	−	0.820050i
$795$	1.88110	−	4.23637i	0.0667159	−	0.150248i
$796$	−0.896117	+	2.90514i	−0.0317620	+	0.102970i
$797$	−4.72566	+	41.9414i	−0.167392	+	1.48564i	0.576366	+	0.817192i	$0.304470\pi$
$797$	−4.72566	+	41.9414i	−0.167392	+	1.48564i	−0.743757	+	0.668450i	$0.766958\pi$
$798$	−2.13135	+	0.660434i	−0.0754491	+	0.0233791i
$799$	12.0945	+	9.64504i	0.427873	+	0.341217i
$800$	6.08788	−	21.5959i	0.215239	−	0.763531i
$801$	31.1734	+	33.5969i	1.10146	+	1.18709i
$802$	−29.0433	−	7.78213i	−1.02555	−	0.274796i
$803$	4.60566	+	17.1886i	0.162530	+	0.606572i
$804$	−0.786810	−	3.44724i	−0.0277486	−	0.121575i
$805$	4.72758	−	11.8639i	0.166625	−	0.418147i
$806$	−2.10756	+	9.23381i	−0.0742355	+	0.325247i
$807$	14.3977	−	0.538725i	0.506824	−	0.0189640i
$808$	29.4415	−	21.7288i	1.03575	−	0.764416i
$809$	−5.81835	+	38.6022i	−0.204562	+	1.35718i	0.616956	+	0.786998i	$0.288366\pi$
$809$	−5.81835	+	38.6022i	−0.204562	+	1.35718i	−0.821518	+	0.570183i	$0.806872\pi$
$810$	−12.7337	−	0.0825797i	−0.447415	−	0.00290155i
$811$	−40.1579	−	9.16578i	−1.41013	−	0.321854i	−0.551386	−	0.834251i	$-0.685901\pi$
$811$	−40.1579	−	9.16578i	−1.41013	−	0.321854i	−0.858749	+	0.512397i	$0.828758\pi$
$812$	5.63330	−	1.29338i	0.197690	−	0.0453886i
$813$	−4.97413	+	7.91628i	−0.174450	+	0.277636i
$814$	−14.2046	−	8.20101i	−0.497870	−	0.287445i
$815$	15.3222	−	48.5533i	0.536714	−	1.70075i
$816$	1.03275	−	0.958254i	0.0361536	−	0.0335456i
$817$	−5.48592	−	1.03799i	−0.191928	−	0.0363147i
$818$	2.14101	+	19.0020i	0.0748588	+	0.664390i
$819$	−0.350770	+	9.70816i	−0.0122569	+	0.339230i
$820$	4.26837	+	5.86263i	0.149058	+	0.204732i
$821$	−17.0102	−	5.24696i	−0.593661	−	0.183120i	−0.0166564	−	0.999861i	$-0.505302\pi$
$821$	−17.0102	−	5.24696i	−0.593661	−	0.183120i	−0.577004	+	0.816741i	$0.695778\pi$
$822$	−7.34978	+	3.20668i	−0.256353	+	0.111846i
$823$	10.5172	−	12.2212i	0.366607	−	0.426006i	−0.544124	−	0.839005i	$-0.683138\pi$
$823$	10.5172	−	12.2212i	0.366607	−	0.426006i	0.910731	+	0.412999i	$0.135519\pi$
$824$	−9.65229	−	24.5936i	−0.336254	−	0.856760i
$825$	1.73069	−	3.83046i	0.0602550	−	0.133360i
$826$	1.10094	−	0.949896i	0.0383065	−	0.0330511i
$827$	−14.5885	+	5.10475i	−0.507293	+	0.177510i	−0.571777	−	0.820409i	$-0.693746\pi$
$827$	−14.5885	+	5.10475i	−0.507293	+	0.177510i	0.0644836	+	0.997919i	$0.479460\pi$
$828$	3.64749	−	3.13892i	0.126759	−	0.109085i
$829$	42.4857	−	13.1051i	1.47559	−	0.455160i	0.550477	−	0.834850i	$-0.314446\pi$
$829$	42.4857	−	13.1051i	1.47559	−	0.455160i	0.925114	+	0.379690i	$0.123969\pi$
$830$	12.3273	−	16.4782i	0.427888	−	0.571967i
$831$	−0.538792	−	3.57465i	−0.0186905	−	0.124003i
$832$	7.88218	+	7.88218i	0.273266	+	0.273266i
$833$	−8.02449	−	5.89057i	−0.278032	−	0.204096i
$834$		−	7.46194i		−	0.258386i
$835$	6.98838	+	5.64757i	0.241843	+	0.195442i
$836$	−0.762520	+	1.11841i	−0.0263723	+	0.0386811i
$837$	10.5992	−	20.0546i	0.366361	−	0.693189i
$838$	−23.5034	−	27.3115i	−0.811913	−	0.943460i
$839$	13.7442	+	6.61884i	0.474501	+	0.228508i	0.655821	−	0.754916i	$-0.272323\pi$
$839$	13.7442	+	6.61884i	0.474501	+	0.228508i	−0.181320	+	0.983424i	$0.558037\pi$
$840$	−9.94522	−	6.32138i	−0.343143	−	0.218108i
$841$	−20.3950	+	9.82173i	−0.703277	+	0.338680i
$842$	7.59228	+	3.31248i	0.261647	+	0.114155i
$843$	−0.483586	−	0.416159i	−0.0166556	−	0.0143333i
$844$	−18.0404	−	7.08034i	−0.620977	−	0.243715i
$845$	−8.24804	+	23.0901i	−0.283741	+	0.794324i
$846$	−23.3123	+	18.5910i	−0.801494	+	0.639170i
$847$	21.3868	−	12.3843i	0.734859	−	0.425530i
$848$	4.79094	−	0.539809i	0.164522	−	0.0185371i
$849$	4.15465	+	6.09375i	0.142587	+	0.209137i
$850$	−5.98050	+	4.64368i	−0.205129	+	0.159277i
$851$	−12.9070	−	22.3555i	−0.442445	−	0.766338i
$852$	−3.74443	+	1.00332i	−0.128282	+	0.0343731i
$853$	30.5445	+	19.1924i	1.04582	+	0.657134i	0.941363	−	0.337396i	$-0.109546\pi$
$853$	30.5445	+	19.1924i	1.04582	+	0.657134i	0.104459	+	0.994529i	$0.466689\pi$
$854$	−3.15703	+	1.10924i	−0.108031	+	0.0379575i
$855$	6.73455	+	1.85141i	0.230317	+	0.0633169i
$856$	−6.59826	−	6.12229i	−0.225524	−	0.209256i
$857$	9.71464	+	13.1629i	0.331846	+	0.449635i	0.938474	−	0.345351i	$-0.112240\pi$
$857$	9.71464	+	13.1629i	0.331846	+	0.449635i	−0.606628	+	0.794986i	$0.707478\pi$
$858$	0.758286	+	1.02744i	0.0258875	+	0.0350763i
$859$	20.4284	+	18.9548i	0.697009	+	0.646730i	0.946894	−	0.321546i	$-0.104202\pi$
$859$	20.4284	+	18.9548i	0.697009	+	0.646730i	−0.249885	+	0.968276i	$0.580393\pi$
$860$	−4.40482	−	7.74494i	−0.150203	−	0.264100i
$861$	6.10084	−	2.14357i	0.207916	−	0.0730528i
$862$	9.31959	+	5.85589i	0.317427	+	0.199452i
$863$	6.45238	−	1.72891i	0.219642	−	0.0588528i	−0.147320	−	0.989089i	$-0.547065\pi$
$863$	6.45238	−	1.72891i	0.219642	−	0.0588528i	0.366962	+	0.930236i	$0.380398\pi$
$864$	−8.16264	−	14.1381i	−0.277699	−	0.480988i
$865$	1.29466	−	15.8924i	0.0440199	−	0.540358i
$866$	−16.1321	−	23.6614i	−0.548190	−	0.804047i
$867$	−9.71383	+	1.09449i	−0.329899	+	0.0371707i
$868$	−12.3634	+	7.15921i	−0.419642	+	0.242999i
$869$	8.40963	−	6.70646i	0.285277	−	0.227501i
$870$	−3.69175	−	1.31873i	−0.125162	−	0.0447092i
$871$	−8.30675	−	3.26016i	−0.281463	−	0.110466i
$872$	−3.14163	−	2.70359i	−0.106389	−	0.0915551i
$873$	12.7069	+	5.54397i	0.430064	+	0.187635i
$874$	2.51325	−	1.21032i	0.0850120	−	0.0409396i
$875$	23.4772	+	17.9950i	0.793675	+	0.608342i
$876$	7.03532	+	3.38803i	0.237701	+	0.114471i
$877$	−4.79010	−	5.56619i	−0.161750	−	0.187957i	0.671248	−	0.741233i	$-0.265759\pi$
$877$	−4.79010	−	5.56619i	−0.161750	−	0.187957i	−0.832998	+	0.553276i	$0.813378\pi$
$878$	−11.1057	+	21.0129i	−0.374798	+	0.709152i
$879$	−8.29206	+	12.1622i	−0.279684	+	0.410222i
$880$	4.34759	−	0.461323i	0.146557	−	0.0155512i
$881$		−	3.97077i		−	0.133779i	−0.997760	−	0.0668893i	$-0.978693\pi$
$881$		−	3.97077i		−	0.133779i	0.997760	−	0.0668893i	$-0.0213074\pi$
$882$	14.5113	−	12.5530i	0.488620	−	0.422681i
$883$	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
$885$	0.745496	−	0.107426i	0.0250596	−	0.00361108i
$886$	−40.4556	+	12.4789i	−1.35913	+	0.419236i
$887$	17.9383	−	15.4371i	0.602308	−	0.518328i	−0.297439	−	0.954741i	$-0.596132\pi$
$887$	17.9383	−	15.4371i	0.602308	−	0.518328i	0.899746	+	0.436413i	$0.143751\pi$
$888$	−22.4824	+	7.86694i	−0.754461	+	0.263997i
$889$	38.0269	−	32.8099i	1.27538	−	1.10041i
$890$	−15.7450	+	39.3651i	−0.527774	+	1.31952i
$891$	2.51658	+	6.41214i	0.0843086	+	0.214815i
$892$	4.33864	−	5.04159i	0.145268	−	0.168805i
$893$	12.0989	−	5.27870i	0.404875	−	0.176645i
$894$	−14.9414	−	4.60881i	−0.499715	−	0.154142i
$895$	23.6085	−	17.1885i	0.789144	−	0.574547i
$896$	−0.0624234	+	1.72767i	−0.00208542	+	0.0577175i
$897$	0.225017	+	1.99708i	0.00751309	+	0.0666805i
$898$	1.30407	+	0.246744i	0.0435175	+	0.00823396i
$899$	−11.5299	+	10.6982i	−0.384543	+	0.356804i
$900$	4.70538	+	10.1040i	0.156846	+	0.336800i
$901$	3.91158	+	2.25835i	0.130314	+	0.0752367i
$902$	−2.73281	+	4.34925i	−0.0909927	+	0.144814i
$903$	−7.74348	+	1.77786i	−0.257687	+	0.0591636i
$904$	16.6228	+	3.79405i	0.552867	+	0.126188i
$905$	−27.1780	+	26.8277i	−0.903427	+	0.891784i
$906$	0.398743	−	2.64549i	0.0132474	−	0.0878905i
$907$	−15.7118	+	11.5958i	−0.521701	+	0.385033i	−0.822598	−	0.568624i	$-0.807476\pi$
$907$	−15.7118	+	11.5958i	−0.521701	+	0.385033i	0.300896	+	0.953657i	$0.402714\pi$
$908$	8.33511	−	0.311878i	0.276610	−	0.0103500i
$909$	−6.86728	+	30.0875i	−0.227773	+	0.997941i
$910$	−8.25528	+	3.55075i	−0.273660	+	0.117706i
$911$	−1.95694	−	8.57391i	−0.0648363	−	0.284066i	0.932108	−	0.362180i	$-0.117967\pi$
$911$	−1.95694	−	8.57391i	−0.0648363	−	0.284066i	−0.996944	+	0.0781137i	$0.975110\pi$
$912$	−0.311148	−	1.16122i	−0.0103031	−	0.0384519i
$913$	−10.7527	−	2.88118i	−0.355862	−	0.0953530i
$914$	21.6191	+	23.2999i	0.715097	+	0.770692i
$915$	−1.68731	−	0.396646i	−0.0557806	−	0.0131127i
$916$	−16.5546	−	13.2019i	−0.546980	−	0.436202i
$917$	−34.7140	+	10.7567i	−1.14636	+	0.355217i
$918$	−0.616816	+	5.47440i	−0.0203580	+	0.180682i
$919$	−7.76013	+	25.1577i	−0.255983	+	0.829877i	0.732790	+	0.680455i	$0.238218\pi$
$919$	−7.76013	+	25.1577i	−0.255983	+	0.829877i	−0.988773	+	0.149423i	$0.952259\pi$
$920$	13.4643	+	5.97865i	0.443905	+	0.197110i
$921$	−0.749655	−	10.0035i	−0.0247020	−	0.329625i
$922$	−4.63792	+	10.6302i	−0.152742	+	0.350088i
$923$	−3.23120	+	9.23425i	−0.106356	+	0.303949i
$924$	−0.355671	+	1.89307i	−0.0117007	+	0.0622775i
$925$	57.9486	−	14.7245i	1.90534	−	0.484138i
$926$	−2.49070	+	33.2361i	−0.0818495	+	1.09221i
$927$	19.7004	+	10.4120i	0.647045	+	0.341974i
$928$	2.10451	+	11.1226i	0.0690840	+	0.365118i
$929$	−52.7987	+	7.95813i	−1.73227	+	0.261098i	−0.938042	−	0.346522i	$-0.887363\pi$
$929$	−52.7987	+	7.95813i	−1.73227	+	0.261098i	−0.794228	+	0.607620i	$0.792124\pi$
$930$	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
$933$	−7.80076	−	5.75722i	−0.255386	−	0.188483i
$934$	24.4218	+	16.6505i	0.799107	+	0.544822i
$935$	3.53373	+	2.07087i	0.115565	+	0.0677247i
$936$	−11.1747	−	0.837430i	−0.365257	−	0.0273722i
$937$	3.13778	+	8.96726i	0.102507	+	0.292947i	0.983702	−	0.179804i	$-0.0575464\pi$
$937$	3.13778	+	8.96726i	0.102507	+	0.292947i	−0.881196	+	0.472752i	$0.843261\pi$
$938$	6.46029	+	16.3986i	0.210936	+	0.535433i
$939$	5.30525	+	11.0165i	0.173130	+	0.359508i
$940$	18.9196	+	9.26284i	0.617090	+	0.302121i
$941$	−12.4295	+	0.931463i	−0.405190	+	0.0303648i	−0.275767	−	0.961225i	$-0.588932\pi$
$941$	−12.4295	+	0.931463i	−0.405190	+	0.0303648i	−0.129424	+	0.991589i	$0.541313\pi$
$942$	−2.36137	−	5.41232i	−0.0769376	−	0.176343i
$943$	−7.14723	+	3.77742i	−0.232746	+	0.123010i
$944$	0.488457	+	0.612506i	0.0158979	+	0.0199354i
$945$	21.2983	−	3.09700i	0.692833	−	0.100745i
$946$	3.93483	−	4.93412i	0.127932	−	0.160422i
$947$	6.21611	−	32.8529i	0.201996	−	1.06758i	−0.723930	−	0.689873i	$-0.757666\pi$
$947$	6.21611	−	32.8529i	0.201996	−	1.06758i	0.925927	−	0.377704i	$-0.123286\pi$
$948$	0.176486	−	4.71669i	0.00573201	−	0.153191i
$949$	17.0666	−	9.85338i	0.554004	−	0.319854i
$950$	1.11874	+	6.36342i	0.0362967	+	0.206457i
$951$	−2.07646	+	0.473938i	−0.0673337	+	0.0153685i
$952$	7.14792	−	8.98685i	0.231665	−	0.291266i
$953$	25.8559	−	16.2463i	0.837553	−	0.526270i	−0.0436280	−	0.999048i	$-0.513892\pi$
$953$	25.8559	−	16.2463i	0.837553	−	0.526270i	0.881182	+	0.472778i	$0.156749\pi$
$954$	−5.92160	+	6.38196i	−0.191719	+	0.206624i
$955$	32.5541	+	6.37851i	1.05343	+	0.206404i
$956$	−22.0987	−	3.33085i	−0.714724	−	0.107727i
$957$	0.0792919	+	2.11912i	0.00256314	+	0.0685014i
$958$	9.11455	+	14.5057i	0.294478	+	0.468659i
$959$	−25.8266	+	16.2742i	−0.833983	+	0.525521i
$960$	6.48534	−	9.38095i	0.209313	−	0.302769i
$961$	3.93892	−	6.82241i	0.127062	−	0.220078i
$962$	−4.70125	+	17.5453i	−0.151574	+	0.565683i
$963$	7.58620	+	0.283856i	0.244462	+	0.00914712i
$964$	20.0624	−	13.6783i	0.646167	−	0.440549i
$965$	−33.8419	+	2.31551i	−1.08941	+	0.0745388i
$966$	2.58535	−	3.01205i	0.0831824	−	0.0969111i
$967$	−31.8154	−	3.58474i	−1.02312	−	0.115277i	−0.415569	−	0.909562i	$-0.636418\pi$
$967$	−31.8154	−	3.58474i	−1.02312	−	0.115277i	−0.607547	+	0.794284i	$0.707846\pi$
$968$	13.3210	+	25.2046i	0.428153	+	0.810106i
$969$	0.411463	−	1.04839i	0.0132181	−	0.0336792i
$970$	0.396412	+	12.8186i	0.0127280	+	0.411581i
$971$	−42.8602	+	16.8214i	−1.37545	+	0.539824i	−0.933939	−	0.357432i	$-0.883652\pi$
$971$	−42.8602	+	16.8214i	−1.37545	+	0.539824i	−0.441510	+	0.897256i	$0.645557\pi$
$972$	11.7743	+	4.11999i	0.377660	+	0.132149i
$973$	−4.26981	−	28.0836i	−0.136884	−	0.900318i
$974$	−2.18048	+	4.52781i	−0.0698670	+	0.145080i
$975$	−4.59352	−	0.753416i	−0.147110	−	0.0241286i
$976$	−0.531403	−	1.72277i	−0.0170098	−	0.0551444i
$977$	−25.3552	+	4.79746i	−0.811185	+	0.153484i	−0.574926	−	0.818206i	$-0.694969\pi$
$977$	−25.3552	+	4.79746i	−0.811185	+	0.153484i	−0.236259	+	0.971690i	$0.575921\pi$
$978$	9.39700	−	12.7325i	0.300483	−	0.407140i
$979$	22.9343			0.732984
$980$	−12.4031	−	5.46933i	−0.396202	−	0.174711i
$981$	3.49571			0.111609
$982$	12.8538	−	17.4162i	0.410180	−	0.555774i
$983$	−36.5784	+	6.92102i	−1.16667	+	0.220746i	−0.732938	−	0.680295i	$-0.761852\pi$
$983$	−36.5784	+	6.92102i	−1.16667	+	0.220746i	−0.433733	+	0.901041i	$0.642804\pi$
$984$	2.19867	+	7.12793i	0.0700912	+	0.227230i
$985$	−24.2100	−	30.7656i	−0.771396	−	0.980274i
$986$	1.65742	−	3.44168i	0.0527831	−	0.109605i
$987$	12.7587	−	13.7860i	0.406113	−	0.438815i
$988$	1.41493	+	0.495104i	0.0450148	+	0.0157513i
$989$	9.24579	−	3.62871i	0.293999	−	0.115386i
$990$	−5.40722	+	5.75232i	−0.171853	+	0.182821i
$991$	−12.9287	+	32.9419i	−0.410695	+	1.04643i	0.564568	+	0.825387i	$0.309043\pi$
$991$	−12.9287	+	32.9419i	−0.410695	+	1.04643i	−0.975263	+	0.221047i	$0.929052\pi$
$992$	−13.0745	−	24.7381i	−0.415115	−	0.785436i
$993$	13.9729	+	1.57437i	0.443418	+	0.0499612i
$994$	17.7010	−	7.74992i	0.561440	−	0.245813i
$995$	5.15880	−	5.91659i	0.163545	−	0.187568i
$996$	−4.03605	+	2.75173i	−0.127887	+	0.0871920i
$997$	27.1718	+	1.01670i	0.860541	+	0.0321992i	0.464018	−	0.885826i	$-0.346407\pi$
$997$	27.1718	+	1.01670i	0.860541	+	0.0321992i	0.396523	+	0.918025i	$0.370217\pi$
$998$	2.92502	−	10.9163i	0.0925899	−	0.345550i
$999$	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.103.18	✓	624
5.2	odd	4	inner	245.2.x.a.152.18	yes	624
49.10	odd	42	inner	245.2.x.a.108.18	yes	624
245.157	even	84	inner	245.2.x.a.157.18	yes	624

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
245.2.x.a.103.18	✓	624	1.1	even	1	trivial
245.2.x.a.108.18	yes	624	49.10	odd	42	inner
245.2.x.a.152.18	yes	624	5.2	odd	4	inner
245.2.x.a.157.18	yes	624	245.157	even	84	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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.632349 - 0.856802i) q^{2} +(0.641277 - 0.121336i) q^{3} +(0.255265 + 0.827550i) q^{4} +(0.264765 - 2.22034i) q^{5} +(0.301550 - 0.626175i) q^{6} +(0.776602 - 2.52921i) q^{7} +(2.88071 + 1.00801i) q^{8} +(-2.39611 + 0.940403i) q^{9} +(-1.73497 - 1.63088i) q^{10} +(-0.470582 + 1.19902i) q^{11} +(0.264108 + 0.499716i) q^{12} +(1.41748 + 0.159711i) q^{13} +(-1.67595 - 2.26474i) q^{14} +(-0.0996198 - 1.45598i) q^{15} +(1.25419 - 0.855092i) q^{16} +(1.42107 + 0.0531727i) q^{17} +(-0.709436 + 2.64765i) q^{18} +(0.606735 - 1.05090i) q^{19} +(1.90503 - 0.347669i) q^{20} +(0.191133 - 1.71615i) q^{21} +(0.729753 + 1.16140i) q^{22} +(0.0807169 + 2.15720i) q^{23} +(1.96964 + 0.296876i) q^{24} +(-4.85980 - 1.17573i) q^{25} +(1.03318 - 1.11350i) q^{26} +(-3.08032 + 1.93549i) q^{27} +(2.29128 - 0.00294233i) q^{28} +(2.45930 - 0.561319i) q^{29} +(-1.31048 - 0.835332i) q^{30} +(-5.39985 + 3.11760i) q^{31} +(-0.167794 + 4.48438i) q^{32} +(-0.156289 + 0.826005i) q^{33} +(0.944171 - 1.18395i) q^{34} +(-5.41008 - 2.39396i) q^{35} +(-1.38987 - 1.74285i) q^{36} +(-10.5723 + 5.58761i) q^{37} +(-0.516742 - 1.18438i) q^{38} +(0.928375 - 0.0695721i) q^{39} +(3.00082 - 6.12927i) q^{40} +(1.62483 + 3.37399i) q^{41} +(-1.34954 - 1.24897i) q^{42} +(-1.51963 - 4.34287i) q^{43} +(-1.11237 - 0.0833609i) q^{44} +(1.45361 + 5.56915i) q^{45} +(1.89934 + 1.29495i) q^{46} +(8.75254 + 6.45967i) 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} +(0.229664 + 1.21380i) q^{52} +(2.80809 + 1.48412i) q^{53} +(-0.289502 + 3.86313i) q^{54} +(2.53764 + 1.36231i) q^{55} +(4.78662 - 6.50310i) q^{56} +(0.261574 - 0.747535i) q^{57} +(1.07420 - 2.46208i) q^{58} +(0.0385687 + 0.514663i) q^{59} +(1.17946 - 0.454101i) q^{60} +(0.350079 - 1.13493i) q^{61} +(-0.743418 + 6.59802i) q^{62} +(0.517653 + 6.79057i) q^{63} +(6.10969 + 4.87231i) q^{64} +(0.729911 - 3.10499i) q^{65} +(0.608894 + 0.656231i) q^{66} +(-6.04266 - 1.61913i) q^{67} +(0.318747 + 1.18958i) q^{68} +(0.313509 + 1.37357i) q^{69} +(-5.47221 + 3.12155i) q^{70} +(-1.52615 + 6.68652i) q^{71} +(-7.85043 + 0.293742i) q^{72} +(11.1157 - 8.20379i) q^{73} +(-1.89789 + 12.5917i) q^{74} +(-3.25914 - 0.164302i) q^{75} +(1.02455 + 0.233846i) q^{76} +(2.66712 + 2.12136i) q^{77} +(0.527448 - 0.839428i) q^{78} +(-7.23199 - 4.17539i) q^{79} +(-1.56653 - 3.01112i) q^{80} +(3.92022 - 3.63743i) q^{81} +(3.91830 + 0.741382i) q^{82} +(0.967647 + 8.58811i) q^{83} +(1.46899 - 0.279903i) q^{84} +(0.494311 - 3.14118i) q^{85} +(-4.68192 - 1.44418i) q^{86} +(1.50898 - 0.658363i) q^{87} +(-2.56423 + 2.97969i) q^{88} +(-6.50501 - 16.5745i) q^{89} +(5.69085 + 2.27619i) q^{90} +(1.50476 - 3.46106i) q^{91} +(-1.76459 + 0.617457i) q^{92} +(-3.08452 + 2.65445i) q^{93} +(11.0693 - 3.41443i) q^{94} +(-2.17270 - 1.62540i) q^{95} +(0.436516 + 2.89609i) q^{96} +(-3.80844 - 3.80844i) q^{97} +(-7.02953 + 2.48002i) 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

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