LMFDB - Embedded newform 460.2.e.a.91.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(91,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("460.91");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.e (of order $2$, degree $1$, 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:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	16.0.7465802011608416256.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{14} + x^{12} + 8x^{10} - 20x^{8} + 32x^{6} + 16x^{4} - 64x^{2} + 256 $ x^16 - x^14 + x^12 + 8x^10 - 20x^8 + 32x^6 + 16x^4 - 64*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.9
Root			$-0.977642 + 1.02187i$ of defining polynomial
Character	$\chi$	$=$	460.91
Dual form			460.2.e.a.91.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.637910 - 1.26217i) q^{2} -0.348132i q^{3} +(-1.18614 - 1.61030i) q^{4} -1.00000i q^{5} +(-0.439402 - 0.222077i) q^{6} -4.89140 q^{7} +(-2.78912 + 0.469882i) q^{8} +2.87880 q^{9} +O(q^{10})$	\(q+(0.637910 - 1.26217i) q^{2} -0.348132i q^{3} +(-1.18614 - 1.61030i) q^{4} -1.00000i q^{5} +(-0.439402 - 0.222077i) q^{6} -4.89140 q^{7} +(-2.78912 + 0.469882i) q^{8} +2.87880 q^{9} +(-1.26217 - 0.637910i) q^{10} -2.68161 q^{11} +(-0.560598 + 0.412934i) q^{12} -3.09987 q^{13} +(-3.12027 + 6.17377i) q^{14} -0.348132 q^{15} +(-1.18614 + 3.82009i) q^{16} -0.769298i q^{17} +(1.83642 - 3.63354i) q^{18} +4.89140 q^{19} +(-1.61030 + 1.18614i) q^{20} +1.70285i q^{21} +(-1.71063 + 3.38465i) q^{22} +(-2.20979 - 4.25639i) q^{23} +(0.163581 + 0.970984i) q^{24} -1.00000 q^{25} +(-1.97744 + 3.91256i) q^{26} -2.04660i q^{27} +(5.80189 + 7.87663i) q^{28} -1.72418 q^{29} +(-0.222077 + 0.439402i) q^{30} -8.95574i q^{31} +(4.06494 + 3.93398i) q^{32} +0.933557i q^{33} +(-0.970984 - 0.490743i) q^{34} +4.89140i q^{35} +(-3.41467 - 4.63574i) q^{36} -2.12461i q^{37} +(3.12027 - 6.17377i) q^{38} +1.07917i q^{39} +(0.469882 + 2.78912i) q^{40} -5.04512 q^{41} +(2.14929 + 1.08627i) q^{42} +0.739645 q^{43} +(3.18077 + 4.31821i) q^{44} -2.87880i q^{45} +(-6.78193 + 0.0739292i) q^{46} +9.51433i q^{47} +(1.32990 + 0.412934i) q^{48} +16.9258 q^{49} +(-0.637910 + 1.26217i) q^{50} -0.267818 q^{51} +(3.67688 + 4.99173i) q^{52} -11.1565i q^{53} +(-2.58316 - 1.30555i) q^{54} +2.68161i q^{55} +(13.6427 - 2.29838i) q^{56} -1.70285i q^{57} +(-1.09987 + 2.17621i) q^{58} -1.87953i q^{59} +(0.412934 + 0.560598i) q^{60} -8.05040i q^{61} +(-11.3037 - 5.71296i) q^{62} -14.0814 q^{63} +(7.55842 - 2.62112i) q^{64} +3.09987i q^{65} +(1.17831 + 0.595525i) q^{66} +5.76872 q^{67} +(-1.23880 + 0.912496i) q^{68} +(-1.48179 + 0.769298i) q^{69} +(6.17377 + 3.12027i) q^{70} +0.619304i q^{71} +(-8.02934 + 1.35270i) q^{72} -12.6534 q^{73} +(-2.68161 - 1.35531i) q^{74} +0.348132i q^{75} +(-5.80189 - 7.87663i) q^{76} +13.1168 q^{77} +(1.36209 + 0.688411i) q^{78} -6.71238 q^{79} +(3.82009 + 1.18614i) q^{80} +7.92392 q^{81} +(-3.21833 + 6.36779i) q^{82} +4.75372 q^{83} +(2.74211 - 2.01983i) q^{84} -0.769298 q^{85} +(0.471827 - 0.933557i) q^{86} +0.600243i q^{87} +(7.47935 - 1.26004i) q^{88} -9.87539i q^{89} +(-3.63354 - 1.83642i) q^{90} +15.1627 q^{91} +(-4.23295 + 8.60710i) q^{92} -3.11778 q^{93} +(12.0087 + 6.06929i) q^{94} -4.89140i q^{95} +(1.36955 - 1.41514i) q^{96} +15.8012i q^{97} +(10.7971 - 21.3632i) q^{98} -7.71984 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 14 q^{6} + 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 + 14 * q^6 + 4 * q^9	$ 16 q + 4 q^{4} + 14 q^{6} + 4 q^{9} - 30 q^{12} + 4 q^{13} + 4 q^{16} + 30 q^{18} + 2 q^{24} - 16 q^{25} - 54 q^{26} - 48 q^{29} + 34 q^{36} - 36 q^{41} - 40 q^{46} + 18 q^{48} + 68 q^{49} + 34 q^{52} - 40 q^{54} + 36 q^{58} + 6 q^{62} + 52 q^{64} + 40 q^{69} + 42 q^{70} - 78 q^{72} + 8 q^{73} + 72 q^{77} + 32 q^{78} + 40 q^{81} - 42 q^{82} + 12 q^{85} - 120 q^{93} + 20 q^{94} - 22 q^{96} - 18 q^{98}+O(q^{100}) $ 16 * q + 4 * q^4 + 14 * q^6 + 4 * q^9 - 30 * q^12 + 4 * q^13 + 4 * q^16 + 30 * q^18 + 2 * q^24 - 16 * q^25 - 54 * q^26 - 48 * q^29 + 34 * q^36 - 36 * q^41 - 40 * q^46 + 18 * q^48 + 68 * q^49 + 34 * q^52 - 40 * q^54 + 36 * q^58 + 6 * q^62 + 52 * q^64 + 40 * q^69 + 42 * q^70 - 78 * q^72 + 8 * q^73 + 72 * q^77 + 32 * q^78 + 40 * q^81 - 42 * q^82 + 12 * q^85 - 120 * q^93 + 20 * q^94 - 22 * q^96 - 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	0.637910	−	1.26217i	0.451071	−	0.892488i
$2$	0.637910	−	1.26217i	0.451071	−	0.892488i
$3$		−	0.348132i		−	0.200994i	−0.994937	−	0.100497i	$-0.967957\pi$
$3$		−	0.348132i		−	0.200994i	0.994937	−	0.100497i	$-0.0320433\pi$
$4$	−1.18614	−	1.61030i	−0.593070	−	0.805151i
$5$		−	1.00000i		−	0.447214i
$5$		−	1.00000i		−	0.447214i
$6$	−0.439402	−	0.222077i	−0.179385	−	0.0906627i
$7$	−4.89140			−1.84878			−0.924388	−	0.381454i	$-0.875423\pi$
$7$	−4.89140			−1.84878			−0.924388	+	0.381454i	$0.875423\pi$
$8$	−2.78912	+	0.469882i	−0.986104	+	0.166128i
$9$	2.87880			0.959601
$10$	−1.26217	−	0.637910i	−0.399133	−	0.201725i
$11$	−2.68161			−0.808537			−0.404268	−	0.914640i	$-0.632474\pi$
$11$	−2.68161			−0.808537			−0.404268	+	0.914640i	$0.632474\pi$
$12$	−0.560598	+	0.412934i	−0.161831	+	0.119204i
$13$	−3.09987			−0.859750			−0.429875	−	0.902888i	$-0.641442\pi$
$13$	−3.09987			−0.859750			−0.429875	+	0.902888i	$0.641442\pi$
$14$	−3.12027	+	6.17377i	−0.833929	+	1.65001i
$15$	−0.348132			−0.0898874
$16$	−1.18614	+	3.82009i	−0.296535	+	0.955022i
$17$		−	0.769298i		−	0.186582i	−0.995639	−	0.0932911i	$-0.970261\pi$
$17$		−	0.769298i		−	0.186582i	0.995639	−	0.0932911i	$-0.0297387\pi$
$18$	1.83642	−	3.63354i	0.432848	−	0.856433i
$19$	4.89140			1.12216			0.561082	−	0.827760i	$-0.310385\pi$
$19$	4.89140			1.12216			0.561082	+	0.827760i	$0.310385\pi$
$20$	−1.61030	+	1.18614i	−0.360074	+	0.265229i
$21$			1.70285i			0.371593i
$22$	−1.71063	+	3.38465i	−0.364707	+	0.721610i
$23$	−2.20979	−	4.25639i	−0.460772	−	0.887518i
$23$	−2.20979	−	4.25639i	−0.460772	−	0.887518i
$24$	0.163581	+	0.970984i	0.0333909	+	0.198201i
$25$	−1.00000			−0.200000
$26$	−1.97744	+	3.91256i	−0.387808	+	0.767317i
$27$		−	2.04660i		−	0.393869i
$28$	5.80189	+	7.87663i	1.09645	+	1.48854i
$29$	−1.72418			−0.320172			−0.160086	−	0.987103i	$-0.551177\pi$
$29$	−1.72418			−0.320172			−0.160086	+	0.987103i	$0.551177\pi$
$30$	−0.222077	+	0.439402i	−0.0405456	+	0.0802234i
$31$		−	8.95574i		−	1.60850i	−0.594292	−	0.804250i	$-0.702568\pi$
$31$		−	8.95574i		−	1.60850i	0.594292	−	0.804250i	$-0.297432\pi$
$32$	4.06494	+	3.93398i	0.718587	+	0.695437i
$33$			0.933557i			0.162511i
$34$	−0.970984	−	0.490743i	−0.166522	−	0.0841618i
$35$			4.89140i			0.826797i
$36$	−3.41467	−	4.63574i	−0.569111	−	0.772624i
$37$		−	2.12461i		−	0.349283i	−0.984632	−	0.174642i	$-0.944123\pi$
$37$		−	2.12461i		−	0.349283i	0.984632	−	0.174642i	$-0.0558767\pi$
$38$	3.12027	−	6.17377i	0.506175	−	1.00152i
$39$			1.07917i			0.172805i
$40$	0.469882	+	2.78912i	0.0742949	+	0.440999i
$41$	−5.04512			−0.787915			−0.393958	−	0.919129i	$-0.628894\pi$
$41$	−5.04512			−0.787915			−0.393958	+	0.919129i	$0.628894\pi$
$42$	2.14929	+	1.08627i	0.331643	+	0.167615i
$43$	0.739645			0.112795			0.0563974	−	0.998408i	$-0.482039\pi$
$43$	0.739645			0.112795			0.0563974	+	0.998408i	$0.482039\pi$
$44$	3.18077	+	4.31821i	0.479519	+	0.650994i
$45$		−	2.87880i		−	0.429147i
$46$	−6.78193	+	0.0739292i	−0.999941	+	0.0109003i
$47$			9.51433i			1.38781i	0.720068	+	0.693904i	$0.244111\pi$
$47$			9.51433i			1.38781i	−0.720068	+	0.693904i	$0.755889\pi$
$48$	1.32990	+	0.412934i	0.191954	+	0.0596019i
$49$	16.9258			2.41797
$50$	−0.637910	+	1.26217i	−0.0902142	+	0.178498i
$51$	−0.267818			−0.0375020
$52$	3.67688	+	4.99173i	0.509892	+	0.692228i
$53$		−	11.1565i		−	1.53246i	−0.642565	−	0.766231i	$-0.722130\pi$
$53$		−	11.1565i		−	1.53246i	0.642565	−	0.766231i	$-0.277870\pi$
$54$	−2.58316	−	1.30555i	−0.351523	−	0.177663i
$55$			2.68161i			0.361589i
$56$	13.6427	−	2.29838i	1.82309	−	0.307134i
$57$		−	1.70285i		−	0.225549i
$58$	−1.09987	+	2.17621i	−0.144420	+	0.285750i
$59$		−	1.87953i		−	0.244694i	−0.992487	−	0.122347i	$-0.960958\pi$
$59$		−	1.87953i		−	0.244694i	0.992487	−	0.122347i	$-0.0390420\pi$
$60$	0.412934	+	0.560598i	0.0533096	+	0.0723729i
$61$		−	8.05040i		−	1.03075i	−0.856965	−	0.515374i	$-0.827653\pi$
$61$		−	8.05040i		−	1.03075i	0.856965	−	0.515374i	$-0.172347\pi$
$62$	−11.3037	−	5.71296i	−1.43557	−	0.725547i
$63$	−14.0814			−1.77409
$64$	7.55842	−	2.62112i	0.944803	−	0.327640i
$65$			3.09987i			0.384492i
$66$	1.17831	+	0.595525i	0.145039	+	0.0733041i
$67$	5.76872			0.704762			0.352381	−	0.935857i	$-0.385372\pi$
$67$	5.76872			0.704762			0.352381	+	0.935857i	$0.385372\pi$
$68$	−1.23880	+	0.912496i	−0.150227	+	0.110656i
$69$	−1.48179	+	0.769298i	−0.178386	+	0.0926126i
$70$	6.17377	+	3.12027i	0.737907	+	0.372944i
$71$			0.619304i			0.0734978i	0.999325	+	0.0367489i	$0.0117002\pi$
$71$			0.619304i			0.0734978i	−0.999325	+	0.0367489i	$0.988300\pi$
$72$	−8.02934	+	1.35270i	−0.946267	+	0.159417i
$73$	−12.6534			−1.48097			−0.740483	−	0.672075i	$-0.765403\pi$
$73$	−12.6534			−1.48097			−0.740483	+	0.672075i	$0.765403\pi$
$74$	−2.68161	−	1.35531i	−0.311731	−	0.157551i
$75$			0.348132i			0.0401989i
$76$	−5.80189	−	7.87663i	−0.665522	−	0.903511i
$77$	13.1168			1.49480
$78$	1.36209	+	0.688411i	0.154226	+	0.0779472i
$79$	−6.71238			−0.755201			−0.377601	−	0.925969i	$-0.623251\pi$
$79$	−6.71238			−0.755201			−0.377601	+	0.925969i	$0.623251\pi$
$80$	3.82009	+	1.18614i	0.427099	+	0.132615i
$81$	7.92392			0.880436
$82$	−3.21833	+	6.36779i	−0.355406	+	0.703205i
$83$	4.75372			0.521789			0.260894	−	0.965367i	$-0.415983\pi$
$83$	4.75372			0.521789			0.260894	+	0.965367i	$0.415983\pi$
$84$	2.74211	−	2.01983i	0.299189	−	0.220381i
$85$	−0.769298			−0.0834421
$86$	0.471827	−	0.933557i	0.0508784	−	0.100668i
$87$			0.600243i			0.0643528i
$88$	7.47935	−	1.26004i	0.797302	−	0.134321i
$89$		−	9.87539i		−	1.04679i	−0.852090	−	0.523395i	$-0.824665\pi$
$89$		−	9.87539i		−	1.04679i	0.852090	−	0.523395i	$-0.175335\pi$
$90$	−3.63354	−	1.83642i	−0.383008	−	0.193576i
$91$	15.1627			1.58948
$92$	−4.23295	+	8.60710i	−0.441316	+	0.897352i
$93$	−3.11778			−0.323299
$94$	12.0087	+	6.06929i	1.23860	+	0.626000i
$95$		−	4.89140i		−	0.501847i
$96$	1.36955	−	1.41514i	0.139779	−	0.144432i
$97$			15.8012i			1.60437i	0.597077	+	0.802184i	$0.296329\pi$
$97$			15.8012i			1.60437i	−0.597077	+	0.802184i	$0.703671\pi$
$98$	10.7971	−	21.3632i	1.09068	−	2.15801i
$99$	−7.71984			−0.775873
$100$	1.18614	+	1.61030i	0.118614	+	0.161030i
$101$	12.6951			1.26321			0.631604	−	0.775291i	$-0.282397\pi$
$101$	12.6951			1.26321			0.631604	+	0.775291i	$0.282397\pi$
$102$	−0.170844	+	0.338031i	−0.0169160	+	0.0334701i
$103$	15.2929			1.50685			0.753425	−	0.657534i	$-0.228400\pi$
$103$	15.2929			1.50685			0.753425	+	0.657534i	$0.228400\pi$
$104$	8.64593	−	1.45657i	0.847803	−	0.142829i
$105$	1.70285			0.166182
$106$	−14.0814	−	7.11684i	−1.36770	−	0.691249i
$107$	−0.739645			−0.0715042			−0.0357521	−	0.999361i	$-0.511383\pi$
$107$	−0.739645			−0.0715042			−0.0357521	+	0.999361i	$0.511383\pi$
$108$	−3.29565	+	2.42756i	−0.317124	+	0.233592i
$109$			14.4722i			1.38618i	0.720851	+	0.693090i	$0.243751\pi$
$109$			14.4722i			1.38618i	−0.720851	+	0.693090i	$0.756249\pi$
$110$	3.38465	+	1.71063i	0.322714	+	0.163102i
$111$	−0.739645			−0.0702040
$112$	5.80189	−	18.6856i	0.548227	−	1.76562i
$113$		−	14.8197i		−	1.39412i	−0.717013	−	0.697060i	$-0.754491\pi$
$113$		−	14.8197i		−	1.39412i	0.717013	−	0.697060i	$-0.245509\pi$
$114$	−2.14929	−	1.08627i	−0.201299	−	0.101738i
$115$	−4.25639	+	2.20979i	−0.396910	+	0.206064i
$116$	2.04512	+	2.77645i	0.189885	+	0.257787i
$117$	−8.92392			−0.825017
$118$	−2.37228	−	1.19897i	−0.218386	−	0.110374i
$119$			3.76295i			0.344949i
$120$	0.970984	−	0.163581i	0.0886383	−	0.0149328i
$121$	−3.80895			−0.346268
$122$	−10.1610	−	5.13543i	−0.919931	−	0.464940i
$123$			1.75637i			0.158367i
$124$	−14.4214	+	10.6228i	−1.29508	+	0.953953i
$125$			1.00000i			0.0894427i
$126$	−8.98266	+	17.7731i	−0.800239	+	1.58335i
$127$		−	7.80725i		−	0.692781i	−0.938090	−	0.346391i	$-0.887407\pi$
$127$		−	7.80725i		−	0.692781i	0.938090	−	0.346391i	$-0.112593\pi$
$128$	1.51330	−	11.2120i	0.133758	−	0.991014i
$129$		−	0.257494i		−	0.0226711i
$130$	3.91256	+	1.97744i	0.343154	+	0.173433i
$131$		−	13.1943i		−	1.15279i	−0.817172	−	0.576394i	$-0.804459\pi$
$131$		−	13.1943i		−	1.15279i	0.817172	−	0.576394i	$-0.195541\pi$
$132$	1.50331	−	1.10733i	0.130846	−	0.0963807i
$133$	−23.9258			−2.07463
$134$	3.67993	−	7.28110i	0.317897	−	0.628991i
$135$	−2.04660			−0.176143
$136$	0.361479	+	2.14567i	0.0309966	+	0.183990i
$137$		−	10.8089i		−	0.923471i	−0.887018	−	0.461735i	$-0.847227\pi$
$137$		−	10.8089i		−	0.923471i	0.887018	−	0.461735i	$-0.152773\pi$
$138$	0.0257371	+	2.36101i	0.00219089	+	0.200982i
$139$			2.31388i			0.196261i	0.995174	+	0.0981305i	$0.0312863\pi$
$139$			2.31388i			0.196261i	−0.995174	+	0.0981305i	$0.968714\pi$
$140$	7.87663	−	5.80189i	0.665697	−	0.490349i
$141$	3.31225			0.278942
$142$	0.781666	+	0.395060i	0.0655960	+	0.0331527i
$143$	8.31266			0.695139
$144$	−3.41467	+	10.9973i	−0.284556	+	0.916440i
$145$			1.72418i			0.143185i
$146$	−8.07172	+	15.9707i	−0.668021	+	1.32175i
$147$		−	5.89242i		−	0.485998i
$148$	−3.42126	+	2.52008i	−0.281226	+	0.207150i
$149$			4.69262i			0.384434i	0.981352	+	0.192217i	$0.0615678\pi$
$149$			4.69262i			0.384434i	−0.981352	+	0.192217i	$0.938432\pi$
$150$	0.439402	+	0.222077i	0.0358770	+	0.0181325i
$151$			4.65716i			0.378995i	0.981881	+	0.189497i	$0.0606858\pi$
$151$			4.65716i			0.378995i	−0.981881	+	0.189497i	$0.939314\pi$
$152$	−13.6427	+	2.29838i	−1.10657	+	0.186423i
$153$		−	2.21466i		−	0.179045i
$154$	8.36737	−	16.5557i	0.674262	−	1.33409i
$155$	−8.95574			−0.719343
$156$	1.73778	−	1.28004i	0.139134	−	0.102485i
$157$		−	16.5705i		−	1.32247i	−0.750179	−	0.661234i	$-0.770033\pi$
$157$		−	16.5705i		−	1.32247i	0.750179	−	0.661234i	$-0.229967\pi$
$158$	−4.28189	+	8.47215i	−0.340649	+	0.674008i
$159$	−3.88394			−0.308016
$160$	3.93398	−	4.06494i	0.311009	−	0.321362i
$161$	10.8089	+	20.8197i	0.851865	+	1.64082i
$162$	5.05475	−	10.0013i	0.397139	−	0.785779i
$163$			14.7245i			1.15331i	0.816988	+	0.576655i	$0.195642\pi$
$163$			14.7245i			1.15331i	−0.816988	+	0.576655i	$0.804358\pi$
$164$	5.98422	+	8.12416i	0.467289	+	0.634390i
$165$	0.933557			0.0726773
$166$	3.03245	−	6.00000i	0.235364	−	0.465690i
$167$			1.87953i			0.145442i	0.997352	+	0.0727211i	$0.0231683\pi$
$167$			1.87953i			0.145442i	−0.997352	+	0.0727211i	$0.976832\pi$
$168$	−0.800141	−	4.74947i	−0.0617322	−	0.366430i
$169$	−3.39079			−0.260830
$170$	−0.490743	+	0.970984i	−0.0376383	+	0.0744711i
$171$	14.0814			1.07683
$172$	−0.877323	−	1.19105i	−0.0668952	−	0.0908168i
$173$	0.769298			0.0584887			0.0292443	−	0.999572i	$-0.490690\pi$
$173$	0.769298			0.0584887			0.0292443	+	0.999572i	$0.490690\pi$
$174$	0.757608	+	0.382901i	0.0574341	+	0.0290277i
$175$	4.89140			0.369755
$176$	3.18077	−	10.2440i	0.239760	−	0.772170i
$177$	−0.654324			−0.0491820
$178$	−12.4644	−	6.29962i	−0.934247	−	0.472176i
$179$			13.1943i			0.986185i	0.869977	+	0.493093i	$0.164134\pi$
$179$			13.1943i			0.986185i	−0.869977	+	0.493093i	$0.835866\pi$
$180$	−4.63574	+	3.41467i	−0.345528	+	0.254514i
$181$			11.8779i			0.882875i	0.897292	+	0.441437i	$0.145531\pi$
$181$			11.8779i			0.882875i	−0.897292	+	0.441437i	$0.854469\pi$
$182$	9.67245	−	19.1379i	0.716970	−	1.41860i
$183$	−2.80261			−0.207175
$184$	8.16337	+	10.8333i	0.601811	+	0.798638i
$185$	−2.12461			−0.156204
$186$	−1.98887	+	3.93517i	−0.145831	+	0.288541i
$187$			2.06296i			0.150859i
$188$	15.3209	−	11.2853i	1.11739	−	0.823068i
$189$			10.0107i			0.728175i
$190$	−6.17377	−	3.12027i	−0.447893	−	0.226369i
$191$	−4.75372			−0.343967			−0.171984	−	0.985100i	$-0.555018\pi$
$191$	−4.75372			−0.343967			−0.171984	+	0.985100i	$0.555018\pi$
$192$	−0.912496	−	2.63133i	−0.0658537	−	0.189900i
$193$	−6.85313			−0.493299			−0.246649	−	0.969105i	$-0.579330\pi$
$193$	−6.85313			−0.493299			−0.246649	+	0.969105i	$0.579330\pi$
$194$	19.9438	+	10.0797i	1.43188	+	0.723683i
$195$	1.07917			0.0772807
$196$	−20.0764	−	27.2556i	−1.43403	−	1.94683i
$197$	10.6181			0.756507			0.378254	−	0.925702i	$-0.376525\pi$
$197$	10.6181			0.756507			0.378254	+	0.925702i	$0.376525\pi$
$198$	−4.92457	+	9.74374i	−0.349974	+	0.692458i
$199$	1.01500			0.0719515			0.0359757	−	0.999353i	$-0.488546\pi$
$199$	1.01500			0.0719515			0.0359757	+	0.999353i	$0.488546\pi$
$200$	2.78912	−	0.469882i	0.197221	−	0.0332257i
$201$		−	2.00828i		−	0.141653i
$202$	8.09833	−	16.0233i	0.569797	−	1.12740i
$203$	8.43365			0.591926
$204$	0.317669	+	0.431267i	0.0222413	+	0.0301947i
$205$			5.04512i			0.352366i
$206$	9.75547	−	19.3022i	0.679696	−	1.34485i
$207$	−6.36154	−	12.2533i	−0.442158	−	0.851664i
$208$	3.67688	−	11.8418i	0.254946	−	0.821080i
$209$	−13.1168			−0.907311
$210$	1.08627	−	2.14929i	0.0749597	−	0.148315i
$211$			10.9279i			0.752310i	0.926557	+	0.376155i	$0.122754\pi$
$211$			10.9279i			0.752310i	−0.926557	+	0.376155i	$0.877246\pi$
$212$	−17.9653	+	13.2332i	−1.23386	+	0.908858i
$213$	0.215600			0.0147727
$214$	−0.471827	+	0.933557i	−0.0322534	+	0.0638166i
$215$		−	0.739645i		−	0.0504434i
$216$	0.961661	+	5.70823i	0.0654328	+	0.388396i
$217$			43.8061i			2.97375i
$218$	18.2663	+	9.23194i	1.23715	+	0.625266i
$219$			4.40505i			0.297666i
$220$	4.31821	−	3.18077i	0.291133	−	0.214448i
$221$			2.38473i			0.160414i
$222$	−0.471827	+	0.933557i	−0.0316670	+	0.0626562i
$223$			22.2639i			1.49090i	0.666561	+	0.745450i	$0.267766\pi$
$223$			22.2639i			1.49090i	−0.666561	+	0.745450i	$0.732234\pi$
$224$	−19.8833	−	19.2427i	−1.32851	−	1.28571i
$225$	−2.87880			−0.191920
$226$	−18.7050	−	9.45364i	−1.24424	−	0.628847i
$227$	28.9763			1.92322			0.961611	−	0.274415i	$-0.0884840\pi$
$227$	28.9763			1.92322			0.961611	+	0.274415i	$0.0884840\pi$
$228$	−2.74211	+	2.01983i	−0.181601	+	0.133766i
$229$			26.8197i			1.77230i	0.463403	+	0.886148i	$0.346628\pi$
$229$			26.8197i			1.77230i	−0.463403	+	0.886148i	$0.653372\pi$
$230$	0.0739292	+	6.78193i	0.00487475	+	0.447187i
$231$		−	4.56640i		−	0.300447i
$232$	4.80895	−	0.810161i	0.315723	−	0.0531897i
$233$	−23.4406			−1.53564			−0.767822	−	0.640663i	$-0.778660\pi$
$233$	−23.4406			−1.53564			−0.767822	+	0.640663i	$0.778660\pi$
$234$	−5.69266	+	11.2635i	−0.372141	+	0.736318i
$235$	9.51433			0.620647
$236$	−3.02661	+	2.22938i	−0.197015	+	0.145121i
$237$			2.33680i			0.151791i
$238$	4.74947	+	2.40042i	0.307863	+	0.155596i
$239$		−	7.29540i		−	0.471900i	−0.971765	−	0.235950i	$-0.924180\pi$
$239$		−	7.29540i		−	0.471900i	0.971765	−	0.235950i	$-0.0758202\pi$
$240$	0.412934	−	1.32990i	0.0266548	−	0.0858444i
$241$			14.4459i			0.930541i	0.885169	+	0.465270i	$0.154043\pi$
$241$			14.4459i			0.930541i	−0.885169	+	0.465270i	$0.845957\pi$
$242$	−2.42977	+	4.80754i	−0.156191	+	0.309040i
$243$		−	8.89838i		−	0.570831i
$244$	−12.9636	+	9.54891i	−0.829908	+	0.611306i
$245$		−	16.9258i		−	1.08135i
$246$	2.21683	+	1.12041i	0.141340	+	0.0714345i
$247$	−15.1627			−0.964780
$248$	4.20814	+	24.9787i	0.267217	+	1.58615i
$249$		−	1.65492i		−	0.104877i
$250$	1.26217	+	0.637910i	0.0798266	+	0.0403450i
$251$	−16.3575			−1.03248			−0.516238	−	0.856445i	$-0.672668\pi$
$251$	−16.3575			−1.03248			−0.516238	+	0.856445i	$0.672668\pi$
$252$	16.7025	+	22.6753i	1.05216	+	1.42841i
$253$	5.92579	+	11.4140i	0.372551	+	0.717591i
$254$	−9.85407	−	4.98033i	−0.618299	−	0.312493i
$255$			0.267818i			0.0167714i
$256$	−13.1861	−	9.06232i	−0.824134	−	0.566395i
$257$	−13.2545			−0.826793			−0.413396	−	0.910551i	$-0.635658\pi$
$257$	−13.2545			−0.826793			−0.413396	+	0.910551i	$0.635658\pi$
$258$	−0.325001	−	0.164258i	−0.0202337	−	0.0102263i
$259$			10.3923i			0.645746i
$260$	4.99173	−	3.67688i	0.309574	−	0.228031i
$261$	−4.96357			−0.307237
$262$	−16.6534	−	8.41676i	−1.02885	−	0.519989i
$263$	−23.4662			−1.44699			−0.723495	−	0.690330i	$-0.757465\pi$
$263$	−23.4662			−1.44699			−0.723495	+	0.690330i	$0.757465\pi$
$264$	−0.438661	−	2.60380i	−0.0269977	−	0.160253i
$265$	−11.1565			−0.685338
$266$	−15.2625	+	30.1984i	−0.935805	+	1.85158i
$267$	−3.43794			−0.210399
$268$	−6.84252	−	9.28938i	−0.417973	−	0.567439i
$269$	11.8144			0.720338			0.360169	−	0.932887i	$-0.382719\pi$
$269$	11.8144			0.720338			0.360169	+	0.932887i	$0.382719\pi$
$270$	−1.30555	+	2.58316i	−0.0794532	+	0.157206i
$271$		−	15.4138i		−	0.936324i	−0.883643	−	0.468162i	$-0.844916\pi$
$271$		−	15.4138i		−	0.936324i	0.883643	−	0.468162i	$-0.155084\pi$
$272$	2.93879	+	0.912496i	0.178190	+	0.0553282i
$273$		−	5.27863i		−	0.319477i
$274$	−13.6427	−	6.89514i	−0.824187	−	0.416551i
$275$	2.68161			0.161707
$276$	2.99641	+	1.47363i	0.180363	+	0.0887019i
$277$	−9.94277			−0.597403			−0.298701	−	0.954347i	$-0.596553\pi$
$277$	−9.94277			−0.597403			−0.298701	+	0.954347i	$0.596553\pi$
$278$	2.92051	+	1.47605i	0.175161	+	0.0885276i
$279$		−	25.7818i		−	1.54352i
$280$	−2.29838	−	13.6427i	−0.137354	−	0.815308i
$281$		−	26.9360i		−	1.60687i	−0.595393	−	0.803434i	$-0.703004\pi$
$281$		−	26.9360i		−	1.60687i	0.595393	−	0.803434i	$-0.296996\pi$
$282$	2.11292	−	4.18062i	0.125822	−	0.248952i
$283$	−2.08879			−0.124166			−0.0620830	−	0.998071i	$-0.519774\pi$
$283$	−2.08879			−0.124166			−0.0620830	+	0.998071i	$0.519774\pi$
$284$	0.997266	−	0.734582i	0.0591768	−	0.0435894i
$285$	−1.70285			−0.100868
$286$	5.30273	−	10.4920i	0.313557	−	0.620404i
$287$	24.6777			1.45668
$288$	11.7022	+	11.3252i	0.689557	+	0.667342i
$289$	16.4082			0.965187
$290$	2.17621	+	1.09987i	0.127791	+	0.0645867i
$291$	5.50090			0.322469
$292$	15.0087	+	20.3758i	0.878317	+	1.19240i
$293$			6.11633i			0.357320i	0.983911	+	0.178660i	$0.0571762\pi$
$293$			6.11633i			0.357320i	−0.983911	+	0.178660i	$0.942824\pi$
$294$	−7.43723	−	3.75883i	−0.433748	−	0.219220i
$295$	−1.87953			−0.109430
$296$	0.998315	+	5.92579i	0.0580259	+	0.344430i
$297$			5.48820i			0.318457i
$298$	5.92288	+	2.99347i	0.343103	+	0.173407i
$299$	6.85005	+	13.1943i	0.396149	+	0.763044i
$300$	0.560598	−	0.412934i	0.0323661	−	0.0238408i
$301$	−3.61790			−0.208532
$302$	5.87813	+	2.97085i	0.338248	+	0.170953i
$303$		−	4.41957i		−	0.253898i
$304$	−5.80189	+	18.6856i	−0.332761	+	1.07169i
$305$	−8.05040			−0.460965
$306$	−2.79527	−	1.41275i	−0.159795	−	0.0807618i
$307$		−	9.32012i		−	0.531927i	−0.963983	−	0.265964i	$-0.914310\pi$
$307$		−	9.32012i		−	0.531927i	0.963983	−	0.265964i	$-0.0856901\pi$
$308$	−15.5584	−	21.1221i	−0.886523	−	1.20354i
$309$		−	5.32394i		−	0.302868i
$310$	−5.71296	+	11.3037i	−0.324474	+	0.642005i
$311$		−	9.31162i		−	0.528014i	−0.964521	−	0.264007i	$-0.914956\pi$
$311$		−	9.31162i		−	0.528014i	0.964521	−	0.264007i	$-0.0850442\pi$
$312$	−0.507081	−	3.00993i	−0.0287078	−	0.170404i
$313$			10.8089i			0.610958i	0.952199	+	0.305479i	$0.0988166\pi$
$313$			10.8089i			0.610958i	−0.952199	+	0.305479i	$0.901183\pi$
$314$	−20.9147	−	10.5705i	−1.18029	−	0.596527i
$315$			14.0814i			0.793396i
$316$	7.96182	+	10.8089i	0.447888	+	0.608051i
$317$	31.0426			1.74353			0.871764	−	0.489926i	$-0.162976\pi$
$317$	31.0426			1.74353			0.871764	+	0.489926i	$0.162976\pi$
$318$	−2.47760	+	4.90219i	−0.138937	+	0.274901i
$319$	4.62358			0.258871
$320$	−2.62112	−	7.55842i	−0.146525	−	0.422529i
$321$			0.257494i			0.0143719i
$322$	33.1731	−	0.361617i	1.84867	−	0.0201521i
$323$		−	3.76295i		−	0.209376i
$324$	−9.39889	−	12.7599i	−0.522160	−	0.708884i
$325$	3.09987			0.171950
$326$	18.5848	+	9.39289i	1.02931	+	0.520224i
$327$	5.03823			0.278615
$328$	14.0715	−	2.37061i	0.776966	−	0.130895i
$329$		−	46.5384i		−	2.56574i
$330$	0.595525	−	1.17831i	0.0327826	−	0.0648636i
$331$		−	24.6366i		−	1.35415i	−0.735915	−	0.677074i	$-0.763248\pi$
$331$		−	24.6366i		−	1.35415i	0.735915	−	0.677074i	$-0.236752\pi$
$332$	−5.63858	−	7.65492i	−0.309457	−	0.420119i
$333$		−	6.11633i		−	0.335173i
$334$	2.37228	+	1.19897i	0.129805	+	0.0656047i
$335$		−	5.76872i		−	0.315179i
$336$	−6.50506	−	2.01983i	−0.354880	−	0.110191i
$337$		−	10.4351i		−	0.568438i	−0.958759	−	0.284219i	$-0.908266\pi$
$337$		−	10.4351i		−	0.568438i	0.958759	−	0.284219i	$-0.0917342\pi$
$338$	−2.16302	+	4.27976i	−0.117653	+	0.232788i
$339$	−5.15922			−0.280210
$340$	0.912496	+	1.23880i	0.0494870	+	0.0671835i
$341$			24.0158i			1.30053i
$342$	8.98266	−	17.7731i	0.485727	−	0.961058i
$343$	−48.5510			−2.62151
$344$	−2.06296	+	0.347546i	−0.111227	+	0.0187384i
$345$	0.769298	+	1.48179i	0.0414176	+	0.0797767i
$346$	0.490743	−	0.970984i	0.0263825	−	0.0522004i
$347$		−	32.9279i		−	1.76766i	−0.467805	−	0.883831i	$-0.654955\pi$
$347$		−	32.9279i		−	1.76766i	0.467805	−	0.883831i	$-0.345045\pi$
$348$	0.966572	−	0.711972i	0.0518137	−	0.0381657i
$349$	1.02721			0.0549851			0.0274925	−	0.999622i	$-0.491248\pi$
$349$	1.02721			0.0549851			0.0274925	+	0.999622i	$0.491248\pi$
$350$	3.12027	−	6.17377i	0.166786	−	0.330002i
$351$			6.34420i			0.338629i
$352$	−10.9006	−	10.5494i	−0.581004	−	0.562286i
$353$	10.0183			0.533222			0.266611	−	0.963804i	$-0.414096\pi$
$353$	10.0183			0.533222			0.266611	+	0.963804i	$0.414096\pi$
$354$	−0.417400	+	0.825868i	−0.0221846	+	0.0438944i
$355$	0.619304			0.0328692
$356$	−15.9024	+	11.7136i	−0.842823	+	0.620820i
$357$	1.31000			0.0693327
$358$	16.6534	+	8.41676i	0.880159	+	0.444839i
$359$	−15.3095			−0.808007			−0.404003	−	0.914758i	$-0.632382\pi$
$359$	−15.3095			−0.808007			−0.404003	+	0.914758i	$0.632382\pi$
$360$	1.35270	+	8.02934i	0.0712934	+	0.423183i
$361$	4.92579			0.259252
$362$	14.9919	+	7.57701i	0.787955	+	0.398239i
$363$			1.32602i			0.0695979i
$364$	−17.9851	−	24.4165i	−0.942676	−	1.27977i
$365$			12.6534i			0.662308i
$366$	−1.78781	+	3.53736i	−0.0934504	+	0.184901i
$367$	−25.2963			−1.32046			−0.660229	−	0.751064i	$-0.729541\pi$
$367$	−25.2963			−1.32046			−0.660229	+	0.751064i	$0.729541\pi$
$368$	18.8809	−	3.39290i	0.984235	−	0.176867i
$369$	−14.5239			−0.756084
$370$	−1.35531	+	2.68161i	−0.0704592	+	0.139410i
$371$			54.5709i			2.83318i
$372$	3.69813	+	5.02057i	0.191739	+	0.260305i
$373$		−	8.71062i		−	0.451019i	−0.974241	−	0.225509i	$-0.927595\pi$
$373$		−	8.71062i		−	0.451019i	0.974241	−	0.225509i	$-0.0724046\pi$
$374$	2.60380	+	1.31598i	0.134640	+	0.0680479i
$375$	0.348132			0.0179775
$376$	−4.47061	−	26.5366i	−0.230554	−	1.36852i
$377$	5.34473			0.275268
$378$	12.6353	+	6.38596i	0.649887	+	0.328458i
$379$	26.6288			1.36783			0.683915	−	0.729562i	$-0.260276\pi$
$379$	26.6288			1.36783			0.683915	+	0.729562i	$0.260276\pi$
$380$	−7.87663	+	5.80189i	−0.404062	+	0.297631i
$381$	−2.71796			−0.139245
$382$	−3.03245	+	6.00000i	−0.155154	+	0.306987i
$383$	6.10287			0.311842			0.155921	−	0.987770i	$-0.450165\pi$
$383$	6.10287			0.311842			0.155921	+	0.987770i	$0.450165\pi$
$384$	−3.90328	−	0.526830i	−0.199188	−	0.0268847i
$385$		−	13.1168i		−	0.668496i
$386$	−4.37168	+	8.64980i	−0.222513	+	0.440263i
$387$	2.12929			0.108238
$388$	25.4447	−	18.7424i	1.29176	−	0.951503i
$389$		−	22.9660i		−	1.16442i	−0.813038	−	0.582210i	$-0.802188\pi$
$389$		−	22.9660i		−	1.16442i	0.813038	−	0.582210i	$-0.197812\pi$
$390$	0.688411	−	1.36209i	0.0348591	−	0.0689721i
$391$	−3.27443	+	1.69998i	−0.165595	+	0.0859719i
$392$	−47.2081	+	7.95312i	−2.38437	+	0.401693i
$393$	−4.59335			−0.231704
$394$	6.77339	−	13.4018i	0.341238	−	0.675174i
$395$			6.71238i			0.337736i
$396$	9.15682	+	12.4313i	0.460147	+	0.624695i
$397$	13.8346			0.694339			0.347170	−	0.937802i	$-0.387143\pi$
$397$	13.8346			0.694339			0.347170	+	0.937802i	$0.387143\pi$
$398$	0.647479	−	1.28110i	0.0324552	−	0.0642159i
$399$			8.32934i			0.416989i
$400$	1.18614	−	3.82009i	0.0593070	−	0.191004i
$401$			0.116328i			0.00580915i	0.999996	+	0.00290457i	$0.000924556\pi$
$401$			0.116328i			0.00580915i	−0.999996	+	0.00290457i	$0.999075\pi$
$402$	−2.53479	−	1.28110i	−0.126424	−	0.0638956i
$403$			27.7617i			1.38291i
$404$	−15.0582	−	20.4429i	−0.749172	−	1.01707i
$405$		−	7.92392i		−	0.393743i
$406$	5.37991	−	10.6447i	0.267001	−	0.528287i
$407$			5.69738i			0.282408i
$408$	0.746977	−	0.125843i	0.0369809	−	0.00623014i
$409$	9.27395			0.458567			0.229284	−	0.973360i	$-0.426362\pi$
$409$	9.27395			0.458567			0.229284	+	0.973360i	$0.426362\pi$
$410$	6.36779	+	3.21833i	0.314483	+	0.158942i
$411$	−3.76295			−0.185612
$412$	−18.1395	−	24.6261i	−0.893668	−	1.21324i
$413$			9.19352i			0.452384i
$414$	−19.5238	+	0.212828i	−0.959544	+	0.0104599i
$415$		−	4.75372i		−	0.233351i
$416$	−12.6008	−	12.1948i	−0.617805	−	0.597901i
$417$	0.805538			0.0394474
$418$	−8.36737	+	16.5557i	−0.409261	+	0.809764i
$419$	34.5998			1.69031			0.845155	−	0.534521i	$-0.179508\pi$
$419$	34.5998			1.69031			0.845155	+	0.534521i	$0.179508\pi$
$420$	−2.01983	−	2.74211i	−0.0985574	−	0.133801i
$421$		−	24.5730i		−	1.19761i	−0.800894	−	0.598806i	$-0.795642\pi$
$421$		−	24.5730i		−	1.19761i	0.800894	−	0.598806i	$-0.204358\pi$
$422$	13.7929	+	6.97105i	0.671428	+	0.339345i
$423$			27.3899i			1.33174i
$424$	5.24224	+	31.1168i	0.254585	+	1.51117i
$425$			0.769298i			0.0373164i
$426$	0.137533	−	0.272123i	0.00666351	−	0.0131844i
$427$			39.3777i			1.90562i
$428$	0.877323	+	1.19105i	0.0424070	+	0.0575716i
$429$		−	2.89391i		−	0.139719i
$430$	−0.933557	−	0.471827i	−0.0450201	−	0.0227535i
$431$	−35.8188			−1.72533			−0.862665	−	0.505775i	$-0.831206\pi$
$431$	−35.8188			−1.72533			−0.862665	+	0.505775i	$0.831206\pi$
$432$	7.81820	+	2.42756i	0.376153	+	0.116796i
$433$		−	27.5411i		−	1.32354i	−0.749707	−	0.661770i	$-0.769806\pi$
$433$		−	27.5411i		−	1.32354i	0.749707	−	0.661770i	$-0.230194\pi$
$434$	55.2907	+	27.9444i	2.65404	+	1.34137i
$435$	0.600243			0.0287794
$436$	23.3045	−	17.1660i	1.11608	−	0.822103i
$437$	−10.8089	−	20.8197i	−0.517062	−	0.995941i
$438$	5.55992	+	2.81003i	0.265663	+	0.134268i
$439$		−	17.7949i		−	0.849304i	−0.905357	−	0.424652i	$-0.860396\pi$
$439$		−	17.7949i		−	0.849304i	0.905357	−	0.424652i	$-0.139604\pi$
$440$	−1.26004	−	7.47935i	−0.0600701	−	0.356564i
$441$	48.7260			2.32029
$442$	3.00993	+	1.52124i	0.143168	+	0.0723581i
$443$		−	22.1711i		−	1.05338i	−0.850057	−	0.526690i	$-0.823433\pi$
$443$		−	22.1711i		−	1.05338i	0.850057	−	0.526690i	$-0.176567\pi$
$444$	0.877323	+	1.19105i	0.0416359	+	0.0565248i
$445$	−9.87539			−0.468139
$446$	28.1008	+	14.2024i	1.33061	+	0.672502i
$447$	1.63365			0.0772692
$448$	−36.9713	+	12.8209i	−1.74673	+	0.605732i
$449$	−0.495960			−0.0234058			−0.0117029	−	0.999932i	$-0.503725\pi$
$449$	−0.495960			−0.0234058			−0.0117029	+	0.999932i	$0.503725\pi$
$450$	−1.83642	+	3.63354i	−0.0865696	+	0.171287i
$451$	13.5291			0.637059
$452$	−23.8642	+	17.5782i	−1.12248	+	0.826811i
$453$	1.62131			0.0761758
$454$	18.4843	−	36.5730i	0.867510	−	1.71645i
$455$		−	15.1627i		−	0.710839i
$456$	0.800141	+	4.74947i	0.0374700	+	0.222414i
$457$			16.8280i			0.787180i	0.919286	+	0.393590i	$0.128767\pi$
$457$			16.8280i			0.787180i	−0.919286	+	0.393590i	$0.871233\pi$
$458$	33.8510	+	17.1086i	1.58175	+	0.799431i
$459$	−1.57445			−0.0734889
$460$	8.60710	+	4.23295i	0.401308	+	0.197362i
$461$	33.3266			1.55217			0.776086	−	0.630627i	$-0.217202\pi$
$461$	33.3266			1.55217			0.776086	+	0.630627i	$0.217202\pi$
$462$	−5.76357	−	2.91295i	−0.268145	−	0.135523i
$463$		−	29.8840i		−	1.38883i	−0.719575	−	0.694414i	$-0.755663\pi$
$463$		−	29.8840i		−	1.38883i	0.719575	−	0.694414i	$-0.244337\pi$
$464$	2.04512	−	6.58652i	0.0949423	−	0.305771i
$465$			3.11778i			0.144584i
$466$	−14.9530	+	29.5860i	−0.692684	+	1.37054i
$467$	6.17422			0.285709			0.142854	−	0.989744i	$-0.454372\pi$
$467$	6.17422			0.285709			0.142854	+	0.989744i	$0.454372\pi$
$468$	10.5850	+	14.3702i	0.489293	+	0.664263i
$469$	−28.2171			−1.30295
$470$	6.06929	−	12.0087i	0.279956	−	0.553920i
$471$	−5.76872			−0.265809
$472$	0.883156	+	5.24224i	0.0406506	+	0.241293i
$473$	−1.98344			−0.0911987
$474$	2.94943	+	1.49067i	0.135472	+	0.0684686i
$475$	−4.89140			−0.224433
$476$	6.05948	−	4.46338i	0.277736	−	0.204579i
$477$		−	32.1174i		−	1.47055i
$478$	−9.20802	−	4.65381i	−0.421165	−	0.212860i
$479$	24.0773			1.10012			0.550061	−	0.835125i	$-0.314605\pi$
$479$	24.0773			1.10012			0.550061	+	0.835125i	$0.314605\pi$
$480$	−1.41514	−	1.36955i	−0.0645920	−	0.0625110i
$481$			6.58601i			0.300296i
$482$	18.2331	+	9.21517i	0.830497	+	0.419740i
$483$	7.24801	−	3.76295i	0.329796	−	0.171220i
$484$	4.51795	+	6.13356i	0.205361	+	0.278798i
$485$	15.8012			0.717495
$486$	−11.2313	−	5.67637i	−0.509460	−	0.257485i
$487$		−	19.4857i		−	0.882983i	−0.897266	−	0.441491i	$-0.854450\pi$
$487$		−	19.4857i		−	0.882983i	0.897266	−	0.441491i	$-0.145550\pi$
$488$	3.78274	+	22.4536i	0.171236	+	1.01643i
$489$	5.12606			0.231809
$490$	−21.3632	−	10.7971i	−0.965091	−	0.487765i
$491$		−	8.73549i		−	0.394227i	−0.980381	−	0.197114i	$-0.936843\pi$
$491$		−	8.73549i		−	0.394227i	0.980381	−	0.197114i	$-0.0631568\pi$
$492$	2.82828	−	2.08330i	0.127509	−	0.0939225i
$493$			1.32641i			0.0597384i
$494$	−9.67245	+	19.1379i	−0.435184	+	0.861055i
$495$			7.71984i			0.346981i
$496$	34.2117	+	10.6228i	1.53615	+	0.476977i
$497$		−	3.02926i		−	0.135881i
$498$	−2.08879	−	1.05569i	−0.0936011	−	0.0473068i
$499$		−	25.9227i		−	1.16046i	−0.814452	−	0.580231i	$-0.802962\pi$
$499$		−	25.9227i		−	1.16046i	0.814452	−	0.580231i	$-0.197038\pi$
$500$	1.61030	−	1.18614i	0.0720149	−	0.0530458i
$501$	0.654324			0.0292331
$502$	−10.4346	+	20.6459i	−0.465720	+	0.921473i
$503$	9.84913			0.439151			0.219576	−	0.975596i	$-0.429533\pi$
$503$	9.84913			0.439151			0.219576	+	0.975596i	$0.429533\pi$
$504$	39.2747	−	6.61659i	1.74943	−	0.294726i
$505$		−	12.6951i		−	0.564924i
$506$	18.1865	−	0.198249i	0.808489	−	0.00881326i
$507$			1.18045i			0.0524254i
$508$	−12.5720	+	9.26050i	−0.557793	+	0.410868i
$509$	−41.5701			−1.84256			−0.921282	−	0.388895i	$-0.872857\pi$
$509$	−41.5701			−1.84256			−0.921282	+	0.388895i	$0.872857\pi$
$510$	0.338031	+	0.170844i	0.0149683	+	0.00756509i
$511$	61.8928			2.73797
$512$	−19.8498	+	10.8622i	−0.877244	+	0.480045i
$513$		−	10.0107i		−	0.441985i
$514$	−8.45518	+	16.7294i	−0.372942	+	0.737903i
$515$		−	15.2929i		−	0.673884i
$516$	−0.414643	+	0.305424i	−0.0182537	+	0.0134456i
$517$		−	25.5138i		−	1.12209i
$518$	13.1168	+	6.62936i	0.576321	+	0.291277i
$519$		−	0.267818i		−	0.0117559i
$520$	−1.45657	−	8.64593i	−0.0638750	−	0.379149i
$521$		−	17.2728i		−	0.756736i	−0.925655	−	0.378368i	$-0.876485\pi$
$521$		−	17.2728i		−	0.756736i	0.925655	−	0.378368i	$-0.123515\pi$
$522$	−3.16632	+	6.26487i	−0.138586	+	0.274206i
$523$	9.24464			0.404240			0.202120	−	0.979361i	$-0.435217\pi$
$523$	9.24464			0.404240			0.202120	+	0.979361i	$0.435217\pi$
$524$	−21.2467	+	15.6502i	−0.928168	+	0.683684i
$525$		−	1.70285i		−	0.0743187i
$526$	−14.9693	+	29.6183i	−0.652695	+	1.29142i
$527$	−6.88964			−0.300117
$528$	−3.56627	−	1.10733i	−0.155202	−	0.0481903i
$529$	−13.2337	+	18.8114i	−0.575378	+	0.817888i
$530$	−7.11684	+	14.0814i	−0.309136	+	0.611656i
$531$		−	5.41079i		−	0.234808i
$532$	28.3794	+	38.5277i	1.23040	+	1.67039i
$533$	15.6392			0.677410
$534$	−2.19310	+	4.33927i	−0.0949047	+	0.187778i
$535$			0.739645i			0.0319776i
$536$	−16.0897	+	2.71062i	−0.694968	+	0.117081i
$537$	4.59335			0.198218
$538$	7.53654	−	14.9118i	0.324923	−	0.642893i
$539$	−45.3884			−1.95502
$540$	2.42756	+	3.29565i	0.104465	+	0.141822i
$541$	−15.7687			−0.677949			−0.338974	−	0.940796i	$-0.610080\pi$
$541$	−15.7687			−0.677949			−0.338974	+	0.940796i	$0.610080\pi$
$542$	−19.4549	−	9.83265i	−0.835658	−	0.422349i
$543$	4.13507			0.177453
$544$	3.02641	−	3.12715i	0.129756	−	0.134076i
$545$	14.4722			0.619919
$546$	−6.66252	−	3.36729i	−0.285130	−	0.144107i
$547$			12.5618i			0.537104i	0.963265	+	0.268552i	$0.0865451\pi$
$547$			12.5618i			0.537104i	−0.963265	+	0.268552i	$0.913455\pi$
$548$	−17.4057	+	12.8209i	−0.743533	+	0.547683i
$549$		−	23.1755i		−	0.989107i
$550$	1.71063	−	3.38465i	0.0729415	−	0.144322i
$551$	−8.43365			−0.359286
$552$	3.77141	−	2.84193i	0.160522	−	0.120961i
$553$	32.8329			1.39620
$554$	−6.34259	+	12.5494i	−0.269471	+	0.533175i
$555$			0.739645i			0.0313962i
$556$	3.72605	−	2.74459i	0.158020	−	0.116397i
$557$			29.2656i			1.24002i	0.784593	+	0.620011i	$0.212872\pi$
$557$			29.2656i			1.24002i	−0.784593	+	0.620011i	$0.787128\pi$
$558$	−32.5410	−	16.4465i	−1.37757	−	0.696236i
$559$	−2.29280			−0.0969753
$560$	−18.6856	−	5.80189i	−0.789610	−	0.245175i
$561$	0.718183			0.0303217
$562$	−33.9978	−	17.1828i	−1.43411	−	0.724811i
$563$	−1.47929			−0.0623446			−0.0311723	−	0.999514i	$-0.509924\pi$
$563$	−1.47929			−0.0623446			−0.0311723	+	0.999514i	$0.509924\pi$
$564$	−3.92879	−	5.33372i	−0.165432	−	0.224590i
$565$	−14.8197			−0.623469
$566$	−1.33246	+	2.63641i	−0.0560076	+	0.110817i
$567$	−38.7591			−1.62773
$568$	−0.291000	−	1.72732i	−0.0122101	−	0.0724765i
$569$			30.9277i			1.29656i	0.761403	+	0.648279i	$0.224511\pi$
$569$			30.9277i			1.29656i	−0.761403	+	0.648279i	$0.775489\pi$
$570$	−1.08627	+	2.14929i	−0.0454988	+	0.0900239i
$571$	0.388810			0.0162712			0.00813559	−	0.999967i	$-0.497410\pi$
$571$	0.388810			0.0162712			0.00813559	+	0.999967i	$0.497410\pi$
$572$	−9.85998	−	13.3859i	−0.412267	−	0.559692i
$573$			1.65492i			0.0691355i
$574$	15.7422	−	31.1474i	0.657065	−	1.30007i
$575$	2.20979	+	4.25639i	0.0921545	+	0.177504i
$576$	21.7592	−	7.54568i	0.906634	−	0.314403i
$577$	32.8871			1.36911			0.684553	−	0.728963i	$-0.259997\pi$
$577$	32.8871			1.36911			0.684553	+	0.728963i	$0.259997\pi$
$578$	10.4669	−	20.7099i	0.435368	−	0.861418i
$579$			2.38580i			0.0991503i
$580$	2.77645	−	2.04512i	0.115286	−	0.0849189i
$581$	−23.2524			−0.964670
$582$	3.50908	−	6.94307i	0.145456	−	0.287800i
$583$			29.9174i			1.23905i
$584$	35.2919	−	5.94560i	1.46039	−	0.246031i
$585$			8.92392i			0.368959i
$586$	7.71984	+	3.90167i	0.318904	+	0.161176i
$587$			24.5665i			1.01397i	0.861955	+	0.506984i	$0.169240\pi$
$587$			24.5665i			1.01397i	−0.861955	+	0.506984i	$0.830760\pi$
$588$	−9.48857	+	6.98924i	−0.391302	+	0.288231i
$589$		−	43.8061i		−	1.80500i
$590$	−1.19897	+	2.37228i	−0.0493608	+	0.0976653i
$591$		−	3.69650i		−	0.152054i
$592$	8.11619	+	2.52008i	0.333573	+	0.103575i
$593$	35.8516			1.47225			0.736124	−	0.676847i	$-0.236654\pi$
$593$	35.8516			1.47225			0.736124	+	0.676847i	$0.236654\pi$
$594$	6.92703	+	3.50098i	0.284219	+	0.143647i
$595$	3.76295			0.154266
$596$	7.55653	−	5.56611i	0.309528	−	0.227997i
$597$		−	0.353355i		−	0.0144618i
$598$	21.0231	−	0.229171i	0.859699	−	0.00937150i
$599$		−	33.8638i		−	1.38364i	−0.722072	−	0.691818i	$-0.756810\pi$
$599$		−	33.8638i		−	1.38364i	0.722072	−	0.691818i	$-0.243190\pi$
$600$	−0.163581	−	0.970984i	−0.00667817	−	0.0396403i
$601$	12.5633			0.512469			0.256235	−	0.966615i	$-0.417518\pi$
$601$	12.5633			0.512469			0.256235	+	0.966615i	$0.417518\pi$
$602$	−2.30789	+	4.56640i	−0.0940628	+	0.186113i
$603$	16.6070			0.676290
$604$	7.49944	−	5.52405i	0.305148	−	0.224770i
$605$			3.80895i			0.154856i
$606$	−5.57825	−	2.81929i	−0.226601	−	0.114526i
$607$			19.8410i			0.805320i	0.915350	+	0.402660i	$0.131914\pi$
$607$			19.8410i			0.805320i	−0.915350	+	0.402660i	$0.868086\pi$
$608$	19.8833	+	19.2427i	0.806373	+	0.780394i
$609$		−	2.93603i		−	0.118974i
$610$	−5.13543	+	10.1610i	−0.207928	+	0.411405i
$611$		−	29.4932i		−	1.19317i
$612$	−3.56627	+	2.62690i	−0.144158	+	0.106186i
$613$			31.7187i			1.28111i	0.767914	+	0.640553i	$0.221295\pi$
$613$			31.7187i			1.28111i	−0.767914	+	0.640553i	$0.778705\pi$
$614$	−11.7636	−	5.94540i	−0.474739	−	0.239937i
$615$	1.75637			0.0708237
$616$	−36.5845	+	6.16337i	−1.47403	+	0.248329i
$617$		−	31.1431i		−	1.25377i	−0.779110	−	0.626887i	$-0.784329\pi$
$617$		−	31.1431i		−	1.25377i	0.779110	−	0.626887i	$-0.215671\pi$
$618$	−6.71971	−	3.39620i	−0.270306	−	0.136615i
$619$	−43.2425			−1.73806			−0.869031	−	0.494758i	$-0.835257\pi$
$619$	−43.2425			−1.73806			−0.869031	+	0.494758i	$0.835257\pi$
$620$	10.6228	+	14.4214i	0.426621	+	0.579179i
$621$	−8.71113	+	4.52255i	−0.349566	+	0.181484i
$622$	−11.7528	−	5.93998i	−0.471246	−	0.238172i
$623$			48.3045i			1.93528i
$624$	−4.12251	−	1.28004i	−0.165032	−	0.0512427i
$625$	1.00000			0.0400000
$626$	13.6427	+	6.89514i	0.545273	+	0.275585i
$627$			4.56640i			0.182364i
$628$	−26.6835	+	19.6549i	−1.06479	+	0.784317i
$629$	−1.63446			−0.0651701
$630$	17.7731	+	8.98266i	0.708096	+	0.357878i
$631$	−43.9563			−1.74987			−0.874936	−	0.484239i	$-0.839096\pi$
$631$	−43.9563			−1.74987			−0.874936	+	0.484239i	$0.839096\pi$
$632$	18.7216	−	3.15402i	0.744707	−	0.125460i
$633$	3.80437			0.151210
$634$	19.8024	−	39.1811i	0.786455	−	1.55608i
$635$	−7.80725			−0.309821
$636$	4.60690	+	6.25431i	0.182675	+	0.248000i
$637$	−52.4678			−2.07885
$638$	2.94943	−	5.83574i	0.116769	−	0.231039i
$639$			1.78285i			0.0705286i
$640$	−11.2120	−	1.51330i	−0.443195	−	0.0598185i
$641$			19.7640i			0.780631i	0.920681	+	0.390316i	$0.127634\pi$
$641$			19.7640i			0.780631i	−0.920681	+	0.390316i	$0.872366\pi$
$642$	0.325001	+	0.164258i	0.0128268	+	0.00648276i
$643$	9.44865			0.372618			0.186309	−	0.982491i	$-0.440347\pi$
$643$	9.44865			0.372618			0.186309	+	0.982491i	$0.440347\pi$
$644$	20.7051	−	42.1008i	0.815893	−	1.65900i
$645$	−0.257494			−0.0101388
$646$	−4.74947	−	2.40042i	−0.186866	−	0.0944433i
$647$			0.950541i			0.0373696i	0.999825	+	0.0186848i	$0.00594791\pi$
$647$			0.950541i			0.0373696i	−0.999825	+	0.0186848i	$0.994052\pi$
$648$	−22.1008	+	3.72331i	−0.868201	+	0.146265i
$649$			5.04017i			0.197844i
$650$	1.97744	−	3.91256i	0.0775616	−	0.153463i
$651$	15.2503			0.597708
$652$	23.7108	−	17.4653i	0.928588	−	0.683993i
$653$	−5.83079			−0.228176			−0.114088	−	0.993471i	$-0.536395\pi$
$653$	−5.83079			−0.228176			−0.114088	+	0.993471i	$0.536395\pi$
$654$	3.21394	−	6.35909i	0.125675	−	0.248660i
$655$	−13.1943			−0.515542
$656$	5.98422	−	19.2728i	0.233645	−	0.752476i
$657$	−36.4266			−1.42114
$658$	−58.7393	−	29.6873i	−2.28990	−	1.15733i
$659$	−1.14514			−0.0446083			−0.0223042	−	0.999751i	$-0.507100\pi$
$659$	−1.14514			−0.0446083			−0.0223042	+	0.999751i	$0.507100\pi$
$660$	−1.10733	−	1.50331i	−0.0431027	−	0.0585162i
$661$			17.1348i			0.666468i	0.942844	+	0.333234i	$0.108140\pi$
$661$			17.1348i			0.666468i	−0.942844	+	0.333234i	$0.891860\pi$
$662$	−31.0955	−	15.7159i	−1.20856	−	0.610817i
$663$	0.830200			0.0322423
$664$	−13.2587	+	2.23369i	−0.514538	+	0.0866839i
$665$			23.9258i			0.927802i
$666$	−7.71984	−	3.90167i	−0.299138	−	0.151187i
$667$	3.81007	+	7.33878i	0.147526	+	0.284159i
$668$	3.02661	−	2.22938i	0.117103	−	0.0862575i
$669$	7.75079			0.299663
$670$	−7.28110	−	3.67993i	−0.281294	−	0.142168i
$671$			21.5881i			0.833398i
$672$	−6.69900	+	6.92201i	−0.258420	+	0.267022i
$673$	26.3083			1.01411			0.507055	−	0.861913i	$-0.330734\pi$
$673$	26.3083			1.01411			0.507055	+	0.861913i	$0.330734\pi$
$674$	−13.1709	−	6.65668i	−0.507324	−	0.256406i
$675$			2.04660i			0.0787738i
$676$	4.02196	+	5.46020i	0.154691	+	0.210008i
$677$			37.5386i			1.44273i	0.692557	+	0.721363i	$0.256484\pi$
$677$			37.5386i			1.44273i	−0.692557	+	0.721363i	$0.743516\pi$
$678$	−3.29112	+	6.51180i	−0.126395	+	0.250084i
$679$		−	77.2899i		−	2.96611i
$680$	2.14567	−	0.361479i	0.0822826	−	0.0138621i
$681$		−	10.0876i		−	0.386557i
$682$	30.3121	+	15.3200i	1.16071	+	0.586631i
$683$		−	33.5658i		−	1.28436i	−0.766553	−	0.642180i	$-0.778030\pi$
$683$		−	33.5658i		−	1.28436i	0.766553	−	0.642180i	$-0.221970\pi$
$684$	−16.7025	−	22.6753i	−0.638636	−	0.867010i
$685$	−10.8089			−0.412989
$686$	−30.9712	+	61.2796i	−1.18249	+	2.33967i
$687$	9.33681			0.356221
$688$	−0.877323	+	2.82551i	−0.0334476	+	0.107721i
$689$			34.5837i			1.31753i
$690$	2.36101	−	0.0257371i	0.0898821	−	0.000979796i
$691$			8.91302i			0.339067i	0.985524	+	0.169534i	$0.0542261\pi$
$691$			8.91302i			0.339067i	−0.985524	+	0.169534i	$0.945774\pi$
$692$	−0.912496	−	1.23880i	−0.0346879	−	0.0470922i
$693$	37.7608			1.43441
$694$	−41.5606	−	21.0051i	−1.57762	−	0.797341i
$695$	2.31388			0.0877706
$696$	−0.282043	−	1.67415i	−0.0106908	−	0.0634585i
$697$			3.88120i			0.147011i
$698$	0.655265	−	1.29651i	0.0248022	−	0.0490735i
$699$			8.16043i			0.308656i
$700$	−5.80189	−	7.87663i	−0.219291	−	0.297709i
$701$		−	19.6286i		−	0.741364i	−0.928760	−	0.370682i	$-0.879124\pi$
$701$		−	19.6286i		−	0.741364i	0.928760	−	0.370682i	$-0.120876\pi$
$702$	8.00746	+	4.04703i	0.302222	+	0.152745i
$703$		−	10.3923i		−	0.391953i
$704$	−20.2688	+	7.02882i	−0.763908	+	0.264909i
$705$		−	3.31225i		−	0.124746i
$706$	6.39079	−	12.6448i	0.240521	−	0.475894i
$707$	−62.0968			−2.33539
$708$	0.776121	+	1.05366i	0.0291684	+	0.0395990i
$709$			30.9947i			1.16403i	0.813178	+	0.582015i	$0.197736\pi$
$709$			30.9947i			1.16403i	−0.813178	+	0.582015i	$0.802264\pi$
$710$	0.395060	−	0.781666i	0.0148264	−	0.0293354i
$711$	−19.3236			−0.724692
$712$	4.64027	+	27.5437i	0.173901	+	1.03224i
$713$	−38.1191	+	19.7903i	−1.42757	+	0.741152i
$714$	0.835665	−	1.65345i	0.0312740	−	0.0618786i
$715$		−	8.31266i		−	0.310876i
$716$	21.2467	−	15.6502i	0.794028	−	0.584877i
$717$	−2.53976			−0.0948492
$718$	−9.76611	+	19.3232i	−0.364468	+	0.721136i
$719$		−	6.45760i		−	0.240828i	−0.992724	−	0.120414i	$-0.961578\pi$
$719$		−	6.45760i		−	0.240828i	0.992724	−	0.120414i	$-0.0384222\pi$
$720$	10.9973	+	3.41467i	0.409845	+	0.127257i
$721$	−74.8035			−2.78583
$722$	3.14221	−	6.21718i	0.116941	−	0.231380i
$723$	5.02908			0.187033
$724$	19.1269	−	14.0888i	0.710847	−	0.523607i
$725$	1.72418			0.0640344
$726$	1.67366	+	0.845881i	0.0621153	+	0.0313936i
$727$	16.4785			0.611153			0.305577	−	0.952167i	$-0.401151\pi$
$727$	16.4785			0.611153			0.305577	+	0.952167i	$0.401151\pi$
$728$	−42.2907	+	7.12468i	−1.56740	+	0.264058i
$729$	20.6740			0.765702
$730$	15.9707	+	8.07172i	0.591102	+	0.298748i
$731$		−	0.569007i		−	0.0210455i
$732$	3.32428	+	4.51304i	0.122869	+	0.166807i
$733$			16.1329i			0.595882i	0.954584	+	0.297941i	$0.0962998\pi$
$733$			16.1329i			0.595882i	−0.954584	+	0.297941i	$0.903700\pi$
$734$	−16.1368	+	31.9283i	−0.595620	+	1.17849i
$735$	−5.89242			−0.217345
$736$	7.76190	−	25.9952i	0.286108	−	0.958198i
$737$	−15.4695			−0.569826
$738$	−9.26495	+	18.3316i	−0.341048	+	0.674796i
$739$			33.9931i			1.25045i	0.780443	+	0.625227i	$0.214994\pi$
$739$			33.9931i			1.25045i	−0.780443	+	0.625227i	$0.785006\pi$
$740$	2.52008	+	3.42126i	0.0926401	+	0.125768i
$741$			5.27863i			0.193915i
$742$	68.8777	+	34.8113i	2.52858	+	1.27796i
$743$	−14.8782			−0.545829			−0.272914	−	0.962038i	$-0.587988\pi$
$743$	−14.8782			−0.545829			−0.272914	+	0.962038i	$0.587988\pi$
$744$	8.69589	−	1.46499i	0.318807	−	0.0537092i
$745$	4.69262			0.171924
$746$	−10.9943	−	5.55659i	−0.402529	−	0.203441i
$747$	13.6850			0.500709
$748$	3.32199	−	2.44696i	0.121464	−	0.0894698i
$749$	3.61790			0.132195
$750$	0.222077	−	0.439402i	0.00810912	−	0.0160447i
$751$	1.07379			0.0391833			0.0195916	−	0.999808i	$-0.493763\pi$
$751$	1.07379			0.0391833			0.0195916	+	0.999808i	$0.493763\pi$
$752$	−36.3456	−	11.2853i	−1.32539	−	0.411534i
$753$			5.69458i			0.207522i
$754$	3.40946	−	6.74596i	0.124165	−	0.245673i
$755$	4.65716			0.169492
$756$	16.1203	−	11.8742i	0.586290	−	0.431859i
$757$			49.0368i			1.78227i	0.453735	+	0.891137i	$0.350091\pi$
$757$			49.0368i			1.78227i	−0.453735	+	0.891137i	$0.649909\pi$
$758$	16.9868	−	33.6101i	0.616988	−	1.22077i
$759$	3.97358	−	2.06296i	0.144232	−	0.0748807i
$760$	2.29838	+	13.6427i	0.0833710	+	0.494873i
$761$	15.4133			0.558731			0.279366	−	0.960185i	$-0.409876\pi$
$761$	15.4133			0.558731			0.279366	+	0.960185i	$0.409876\pi$
$762$	−1.73381	+	3.43052i	−0.0628094	+	0.124275i
$763$		−	70.7891i		−	2.56274i
$764$	5.63858	+	7.65492i	0.203997	+	0.276945i
$765$	−2.21466			−0.0800712
$766$	3.89309	−	7.70285i	0.140663	−	0.278315i
$767$			5.82629i			0.210375i
$768$	−3.15489	+	4.59052i	−0.113842	+	0.165646i
$769$		−	31.8146i		−	1.14726i	−0.819114	−	0.573631i	$-0.805534\pi$
$769$		−	31.8146i		−	1.14726i	0.819114	−	0.573631i	$-0.194466\pi$
$770$	−16.5557	−	8.36737i	−0.596625	−	0.301539i
$771$			4.61432i			0.166181i
$772$	8.12877	+	11.0356i	0.292561	+	0.397180i
$773$		−	41.4024i		−	1.48914i	−0.667545	−	0.744570i	$-0.732655\pi$
$773$		−	41.4024i		−	1.48914i	0.667545	−	0.744570i	$-0.267345\pi$
$774$	1.35830	−	2.68753i	0.0488230	−	0.0966011i
$775$			8.95574i			0.321700i
$776$	−7.42469	−	44.0715i	−0.266531	−	1.58207i
$777$	3.61790			0.129791
$778$	−28.9869	−	14.6502i	−1.03923	−	0.525236i
$779$	−24.6777			−0.884170
$780$	−1.28004	−	1.73778i	−0.0458329	−	0.0622226i
$781$		−	1.66073i		−	0.0594257i
$782$	0.0568736	+	5.21732i	0.00203380	+	0.186571i
$783$			3.52871i			0.126106i
$784$	−20.0764	+	64.6580i	−0.717013	+	2.30921i
$785$	−16.5705			−0.591426
$786$	−2.93015	+	5.79758i	−0.104515	+	0.206793i
$787$	52.5560			1.87342			0.936709	−	0.350110i	$-0.113856\pi$
$787$	52.5560			1.87342			0.936709	+	0.350110i	$0.113856\pi$
$788$	−12.5945	−	17.0983i	−0.448662	−	0.609102i
$789$			8.16935i			0.290837i
$790$	8.47215	+	4.28189i	0.301426	+	0.152343i
$791$			72.4891i			2.57741i
$792$	21.5316	−	3.62741i	0.765092	−	0.128894i
$793$			24.9552i			0.886185i
$794$	8.82524	−	17.4616i	0.313196	−	0.619690i
$795$			3.88394i			0.137749i
$796$	−1.20393	−	1.63446i	−0.0426723	−	0.0579318i
$797$		−	31.5518i		−	1.11762i	−0.829295	−	0.558811i	$-0.811258\pi$
$797$		−	31.5518i		−	1.11762i	0.829295	−	0.558811i	$-0.188742\pi$
$798$	10.5130	+	5.31338i	0.372158	+	0.188091i
$799$	7.31936			0.258940
$800$	−4.06494	−	3.93398i	−0.143717	−	0.139087i
$801$		−	28.4293i		−	1.00450i
$802$	0.146826	+	0.0742069i	0.00518460	+	0.00262034i
$803$	33.9315			1.19742
$804$	−3.23393	+	2.38210i	−0.114052	+	0.0840103i
$805$	20.8197	−	10.8089i	0.733798	−	0.380965i
$806$	35.0399	+	17.7095i	1.23423	+	0.623789i
$807$		−	4.11298i		−	0.144784i
$808$	−35.4082	+	5.96519i	−1.24566	+	0.209855i
$809$	−44.2553			−1.55593			−0.777967	−	0.628305i	$-0.783749\pi$
$809$	−44.2553			−1.55593			−0.777967	+	0.628305i	$0.783749\pi$
$810$	−10.0013	−	5.05475i	−0.351411	−	0.177606i
$811$		−	20.1920i		−	0.709037i	−0.935049	−	0.354519i	$-0.884645\pi$
$811$		−	20.1920i		−	0.709037i	0.935049	−	0.354519i	$-0.115355\pi$
$812$	−10.0035	−	13.5807i	−0.351054	−	0.476590i
$813$	−5.36606			−0.188196
$814$	7.19105	+	3.63442i	0.252046	+	0.127386i
$815$	14.7245			0.515776
$816$	0.317669	−	1.02309i	0.0111207	−	0.0358152i
$817$	3.61790			0.126574
$818$	5.91595	−	11.7053i	0.206846	−	0.409266i
$819$	43.6505			1.52527
$820$	8.12416	−	5.98422i	0.283708	−	0.208978i
$821$	−23.0606			−0.804822			−0.402411	−	0.915459i	$-0.631828\pi$
$821$	−23.0606			−0.804822			−0.402411	+	0.915459i	$0.631828\pi$
$822$	−2.40042	+	4.74947i	−0.0837243	+	0.165657i
$823$		−	16.1779i		−	0.563927i	−0.959425	−	0.281963i	$-0.909014\pi$
$823$		−	16.1779i		−	0.563927i	0.959425	−	0.281963i	$-0.0909857\pi$
$824$	−42.6537	+	7.18583i	−1.48591	+	0.250330i
$825$		−	0.933557i		−	0.0325023i
$826$	11.6038	+	5.86464i	0.403747	+	0.204057i
$827$	−21.0266			−0.731166			−0.365583	−	0.930779i	$-0.619130\pi$
$827$	−21.0266			−0.731166			−0.365583	+	0.930779i	$0.619130\pi$
$828$	−12.1858	+	24.7781i	−0.423487	+	0.861100i
$829$	6.23369			0.216505			0.108252	−	0.994123i	$-0.465475\pi$
$829$	6.23369			0.216505			0.108252	+	0.994123i	$0.465475\pi$
$830$	−6.00000	−	3.03245i	−0.208263	−	0.105258i
$831$			3.46140i			0.120075i
$832$	−23.4301	+	8.12513i	−0.812294	+	0.281688i
$833$		−	13.0210i		−	0.451150i
$834$	0.513861	−	1.01672i	0.0177935	−	0.0352063i
$835$	1.87953			0.0650437
$836$	15.5584	+	21.1221i	0.538099	+	0.730522i
$837$	−18.3288			−0.633538
$838$	22.0716	−	43.6708i	0.762449	−	1.50858i
$839$	19.3616			0.668436			0.334218	−	0.942496i	$-0.391528\pi$
$839$	19.3616			0.668436			0.334218	+	0.942496i	$0.391528\pi$
$840$	−4.74947	+	0.800141i	−0.163872	+	0.0276075i
$841$	−26.0272			−0.897490
$842$	−31.0152	−	15.6753i	−1.06886	−	0.540208i
$843$	−9.37730			−0.322972
$844$	17.5973	−	12.9621i	0.605723	−	0.446173i
$845$			3.39079i			0.116647i
$846$	34.5707	+	17.4723i	1.18856	+	0.600710i
$847$	18.6311			0.640172
$848$	42.6188	+	13.2332i	1.46354	+	0.454429i
$849$			0.727177i			0.0249567i
$850$	0.970984	+	0.490743i	0.0333045	+	0.0168324i
$851$	−9.04316	+	4.69493i	−0.309995	+	0.160940i
$852$	−0.255732	−	0.347181i	−0.00876122	−	0.0118942i
$853$	39.7903			1.36239			0.681197	−	0.732100i	$-0.261460\pi$
$853$	39.7903			1.36239			0.681197	+	0.732100i	$0.261460\pi$
$854$	49.7013	+	25.1195i	1.70074	+	0.859570i
$855$		−	14.0814i		−	0.481573i
$856$	2.06296	−	0.347546i	0.0705105	−	0.0118789i
$857$	23.1378			0.790372			0.395186	−	0.918601i	$-0.370680\pi$
$857$	23.1378			0.790372			0.395186	+	0.918601i	$0.370680\pi$
$858$	−3.65260	−	1.84605i	−0.124698	−	0.0630232i
$859$			44.7107i			1.52551i	0.646687	+	0.762755i	$0.276154\pi$
$859$			44.7107i			1.52551i	−0.646687	+	0.762755i	$0.723846\pi$
$860$	−1.19105	+	0.877323i	−0.0406145	+	0.0299165i
$861$		−	8.59111i		−	0.292784i
$862$	−22.8492	+	45.2094i	−0.778246	+	1.53984i
$863$		−	3.39308i		−	0.115502i	−0.998331	−	0.0577509i	$-0.981607\pi$
$863$		−	3.39308i		−	0.115502i	0.998331	−	0.0577509i	$-0.0183929\pi$
$864$	8.05130	−	8.31932i	0.273911	−	0.283029i
$865$		−	0.769298i		−	0.0261569i
$866$	−34.7615	−	17.5687i	−1.18124	−	0.597010i
$867$		−	5.71222i		−	0.193997i
$868$	70.5411	−	51.9602i	2.39432	−	1.76365i
$869$	18.0000			0.610608
$870$	0.382901	−	0.757608i	0.0129816	−	0.0256853i
$871$	−17.8823			−0.605919
$872$	−6.80020	−	40.3646i	−0.230284	−	1.36692i
$873$			45.4885i			1.53955i
$874$	−33.1731	+	0.361617i	−1.12210	+	0.0122319i
$875$		−	4.89140i		−	0.165359i
$876$	7.09346	−	5.22501i	0.239666	−	0.176537i
$877$	−1.69211			−0.0571383			−0.0285692	−	0.999592i	$-0.509095\pi$
$877$	−1.69211			−0.0571383			−0.0285692	+	0.999592i	$0.509095\pi$
$878$	−22.4602	−	11.3515i	−0.757994	−	0.383096i
$879$	2.12929			0.0718192
$880$	−10.2440	−	3.18077i	−0.345325	−	0.107224i
$881$			7.53860i			0.253982i	0.991904	+	0.126991i	$0.0405319\pi$
$881$			7.53860i			0.253982i	−0.991904	+	0.126991i	$0.959468\pi$
$882$	31.0828	−	61.5005i	1.04661	−	2.07083i
$883$		−	8.23718i		−	0.277203i	−0.990348	−	0.138602i	$-0.955739\pi$
$883$		−	8.23718i		−	0.277203i	0.990348	−	0.138602i	$-0.0442607\pi$
$884$	3.84013	−	2.82862i	0.129157	−	0.0951368i
$885$			0.654324i			0.0219949i
$886$	−27.9837	−	14.1432i	−0.940129	−	0.475149i
$887$		−	9.60780i		−	0.322598i	−0.986906	−	0.161299i	$-0.948432\pi$
$887$		−	9.60780i		−	0.322598i	0.986906	−	0.161299i	$-0.0515684\pi$
$888$	2.06296	−	0.347546i	0.0692284	−	0.0116629i
$889$			38.1884i			1.28080i
$890$	−6.29962	+	12.4644i	−0.211164	+	0.417808i
$891$	−21.2489			−0.711865
$892$	35.8516	−	26.4081i	1.20040	−	0.884209i
$893$			46.5384i			1.55735i
$894$	1.04212	−	2.06195i	0.0348539	−	0.0689618i
$895$	13.1943			0.441035
$896$	−7.40217	+	54.8426i	−0.247289	+	1.83216i
$897$	4.59335	−	2.38473i	0.153367	−	0.0796237i
$898$	−0.316378	+	0.625985i	−0.0105577	+	0.0208894i
$899$			15.4413i			0.514996i
$900$	3.41467	+	4.63574i	0.113822	+	0.154525i
$901$	−8.58267			−0.285930
$902$	8.63033	−	17.0760i	0.287358	−	0.568567i
$903$			1.25951i			0.0419138i
$904$	6.96351	+	41.3340i	0.231603	+	1.37475i
$905$	11.8779			0.394834
$906$	1.03425	−	2.04637i	0.0343607	−	0.0679860i
$907$	−31.5673			−1.04818			−0.524088	−	0.851664i	$-0.675594\pi$
$907$	−31.5673			−1.04818			−0.524088	+	0.851664i	$0.675594\pi$
$908$	−34.3699	−	46.6605i	−1.14061	−	1.54848i
$909$	36.5467			1.21218
$910$	−19.1379	−	9.67245i	−0.634415	−	0.320639i
$911$	28.9429			0.958921			0.479461	−	0.877563i	$-0.340832\pi$
$911$	28.9429			0.958921			0.479461	+	0.877563i	$0.340832\pi$
$912$	6.50506	+	2.01983i	0.215404	+	0.0668831i
$913$	−12.7476			−0.421885
$914$	21.2398	+	10.7347i	0.702549	+	0.355074i
$915$			2.80261i			0.0926513i
$916$	43.1878	−	31.8119i	1.42696	−	1.05110i
$917$			64.5384i			2.13125i
$918$	−1.00436	+	1.98722i	−0.0331487	+	0.0655880i
$919$	49.9290			1.64701			0.823503	−	0.567312i	$-0.192017\pi$
$919$	49.9290			1.64701			0.823503	+	0.567312i	$0.192017\pi$
$920$	10.8333	−	8.16337i	0.357162	−	0.269138i
$921$	−3.24464			−0.106914
$922$	21.2594	−	42.0637i	0.700139	−	1.38530i
$923$		−	1.91976i		−	0.0631898i
$924$	−7.35328	+	5.41639i	−0.241905	+	0.178186i
$925$			2.12461i			0.0698567i
$926$	−37.7187	−	19.0633i	−1.23951	−	0.626460i
$927$	44.0251			1.44597
$928$	−7.00869	−	6.78289i	−0.230072	−	0.222659i
$929$	−10.8751			−0.356799			−0.178399	−	0.983958i	$-0.557092\pi$
$929$	−10.8751			−0.356799			−0.178399	+	0.983958i	$0.557092\pi$
$930$	3.93517	+	1.98887i	0.129039	+	0.0652175i
$931$	82.7908			2.71336
$932$	27.8038	+	37.7464i	0.910745	+	1.23643i
$933$	−3.24168			−0.106128
$934$	3.93860	−	7.79291i	0.128875	−	0.254992i
$935$	2.06296			0.0674660
$936$	24.8899	−	4.19319i	0.813553	−	0.137059i
$937$		−	48.0375i		−	1.56932i	−0.619928	−	0.784658i	$-0.712838\pi$
$937$		−	48.0375i		−	1.56932i	0.619928	−	0.784658i	$-0.287162\pi$
$938$	−18.0000	+	35.6148i	−0.587721	+	1.16286i
$939$	3.76295			0.122799
$940$	−11.2853	−	15.3209i	−0.368087	−	0.499714i
$941$		−	29.2945i		−	0.954973i	−0.878639	−	0.477486i	$-0.841548\pi$
$941$		−	29.2945i		−	0.954973i	0.878639	−	0.477486i	$-0.158452\pi$
$942$	−3.67993	+	7.28110i	−0.119899	+	0.237231i
$943$	11.1486	+	21.4740i	0.363050	+	0.699289i
$944$	7.17996	+	2.22938i	0.233688	+	0.0725603i
$945$	10.0107			0.325650
$946$	−1.26526	+	2.50344i	−0.0411371	+	0.0813938i
$947$			4.93626i			0.160407i	0.996779	+	0.0802035i	$0.0255570\pi$
$947$			4.93626i			0.160407i	−0.996779	+	0.0802035i	$0.974443\pi$
$948$	3.76295	−	2.77177i	0.122215	−	0.0900229i
$949$	39.2239			1.27326
$950$	−3.12027	+	6.17377i	−0.101235	+	0.200304i
$951$		−	10.8069i		−	0.350439i
$952$	−1.76814	−	10.4953i	−0.0573057	−	0.340155i
$953$			20.8691i			0.676015i	0.941143	+	0.338008i	$0.109753\pi$
$953$			20.8691i			0.676015i	−0.941143	+	0.338008i	$0.890247\pi$
$954$	−40.5375	−	20.4880i	−1.31245	−	0.663323i
$955$			4.75372i			0.153827i
$956$	−11.7478	+	8.65337i	−0.379951	+	0.279870i
$957$		−	1.60962i		−	0.0520316i
$958$	15.3592	−	30.3897i	0.496233	−	0.981846i
$959$			52.8709i			1.70729i
$960$	−2.63133	+	0.912496i	−0.0849259	+	0.0294507i
$961$	−49.2054			−1.58727
$962$	8.31266	+	4.20128i	0.268011	+	0.135455i
$963$	−2.12929			−0.0686155
$964$	23.2622	−	17.1348i	0.749225	−	0.551876i
$965$			6.85313i			0.220610i
$966$	−0.125891	−	11.5486i	−0.00405047	−	0.371571i
$967$			58.1918i			1.87132i	0.352902	+	0.935660i	$0.385195\pi$
$967$			58.1918i			1.87132i	−0.352902	+	0.935660i	$0.614805\pi$
$968$	10.6236	−	1.78976i	0.341456	−	0.0575249i
$969$	−1.31000			−0.0420834
$970$	10.0797	−	19.9438i	0.323641	−	0.640356i
$971$	−14.4231			−0.462858			−0.231429	−	0.972852i	$-0.574340\pi$
$971$	−14.4231			−0.462858			−0.231429	+	0.972852i	$0.574340\pi$
$972$	−14.3291	+	10.5547i	−0.459605	+	0.338543i
$973$		−	11.3181i		−	0.362843i
$974$	−24.5943	−	12.4301i	−0.788052	−	0.398288i
$975$		−	1.07917i		−	0.0345610i
$976$	30.7532	+	9.54891i	0.984387	+	0.305653i
$977$		−	11.4330i		−	0.365775i	−0.983134	−	0.182887i	$-0.941456\pi$
$977$		−	11.4330i		−	0.365775i	0.983134	−	0.182887i	$-0.0585444\pi$
$978$	3.26997	−	6.46996i	0.104562	−	0.206886i
$979$			26.4820i			0.846368i
$980$	−27.2556	+	20.0764i	−0.870649	+	0.641316i
$981$			41.6625i			1.33018i
$982$	−11.0257	−	5.57246i	−0.351843	−	0.177824i
$983$	−30.0714			−0.959127			−0.479564	−	0.877507i	$-0.659205\pi$
$983$	−30.0714			−0.959127			−0.479564	+	0.877507i	$0.659205\pi$
$984$	−0.825286	−	4.89873i	−0.0263092	−	0.156166i
$985$		−	10.6181i		−	0.338320i
$986$	1.67415	+	0.846130i	0.0533158	+	0.0269463i
$987$	−16.2015			−0.515700
$988$	17.9851	+	24.4165i	0.572183	+	0.776794i
$989$	−1.63446	−	3.14822i	−0.0519727	−	0.100107i
$990$	9.74374	+	4.92457i	0.309676	+	0.156513i
$991$			17.2895i			0.549218i	0.961556	+	0.274609i	$0.0885485\pi$
$991$			17.2895i			0.549218i	−0.961556	+	0.274609i	$0.911452\pi$
$992$	35.2318	−	36.4046i	1.11861	−	1.15585i
$993$	−8.57679			−0.272176
$994$	−3.82344	−	1.93240i	−0.121272	−	0.0612920i
$995$		−	1.01500i		−	0.0321777i
$996$	−2.66493	+	1.96297i	−0.0844415	+	0.0621992i
$997$	33.7032			1.06739			0.533695	−	0.845677i	$-0.320803\pi$
$997$	33.7032			1.06739			0.533695	+	0.845677i	$0.320803\pi$
$998$	−32.7189	−	16.5364i	−1.03570	−	0.523450i
$999$	−4.34823			−0.137572

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.e.a.91.9	✓	16
4.3	odd	2	inner	460.2.e.a.91.11	yes	16
23.22	odd	2	inner	460.2.e.a.91.10	yes	16
92.91	even	2	inner	460.2.e.a.91.12	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.e.a.91.9	✓	16	1.1	even	1	trivial
460.2.e.a.91.10	yes	16	23.22	odd	2	inner
460.2.e.a.91.11	yes	16	4.3	odd	2	inner
460.2.e.a.91.12	yes	16	92.91	even	2	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.637910 - 1.26217i) q^{2} -0.348132i q^{3} +(-1.18614 - 1.61030i) q^{4} -1.00000i q^{5} +(-0.439402 - 0.222077i) q^{6} -4.89140 q^{7} +(-2.78912 + 0.469882i) q^{8} +2.87880 q^{9} +O(q^{10})\)	\(q+(0.637910 - 1.26217i) q^{2} -0.348132i q^{3} +(-1.18614 - 1.61030i) q^{4} -1.00000i q^{5} +(-0.439402 - 0.222077i) q^{6} -4.89140 q^{7} +(-2.78912 + 0.469882i) q^{8} +2.87880 q^{9} +(-1.26217 - 0.637910i) q^{10} -2.68161 q^{11} +(-0.560598 + 0.412934i) q^{12} -3.09987 q^{13} +(-3.12027 + 6.17377i) q^{14} -0.348132 q^{15} +(-1.18614 + 3.82009i) q^{16} -0.769298i q^{17} +(1.83642 - 3.63354i) q^{18} +4.89140 q^{19} +(-1.61030 + 1.18614i) q^{20} +1.70285i q^{21} +(-1.71063 + 3.38465i) q^{22} +(-2.20979 - 4.25639i) q^{23} +(0.163581 + 0.970984i) q^{24} -1.00000 q^{25} +(-1.97744 + 3.91256i) q^{26} -2.04660i q^{27} +(5.80189 + 7.87663i) q^{28} -1.72418 q^{29} +(-0.222077 + 0.439402i) q^{30} -8.95574i q^{31} +(4.06494 + 3.93398i) q^{32} +0.933557i q^{33} +(-0.970984 - 0.490743i) q^{34} +4.89140i q^{35} +(-3.41467 - 4.63574i) q^{36} -2.12461i q^{37} +(3.12027 - 6.17377i) q^{38} +1.07917i q^{39} +(0.469882 + 2.78912i) q^{40} -5.04512 q^{41} +(2.14929 + 1.08627i) q^{42} +0.739645 q^{43} +(3.18077 + 4.31821i) q^{44} -2.87880i q^{45} +(-6.78193 + 0.0739292i) q^{46} +9.51433i q^{47} +(1.32990 + 0.412934i) q^{48} +16.9258 q^{49} +(-0.637910 + 1.26217i) q^{50} -0.267818 q^{51} +(3.67688 + 4.99173i) q^{52} -11.1565i q^{53} +(-2.58316 - 1.30555i) q^{54} +2.68161i q^{55} +(13.6427 - 2.29838i) q^{56} -1.70285i q^{57} +(-1.09987 + 2.17621i) q^{58} -1.87953i q^{59} +(0.412934 + 0.560598i) q^{60} -8.05040i q^{61} +(-11.3037 - 5.71296i) q^{62} -14.0814 q^{63} +(7.55842 - 2.62112i) q^{64} +3.09987i q^{65} +(1.17831 + 0.595525i) q^{66} +5.76872 q^{67} +(-1.23880 + 0.912496i) q^{68} +(-1.48179 + 0.769298i) q^{69} +(6.17377 + 3.12027i) q^{70} +0.619304i q^{71} +(-8.02934 + 1.35270i) q^{72} -12.6534 q^{73} +(-2.68161 - 1.35531i) q^{74} +0.348132i q^{75} +(-5.80189 - 7.87663i) q^{76} +13.1168 q^{77} +(1.36209 + 0.688411i) q^{78} -6.71238 q^{79} +(3.82009 + 1.18614i) q^{80} +7.92392 q^{81} +(-3.21833 + 6.36779i) q^{82} +4.75372 q^{83} +(2.74211 - 2.01983i) q^{84} -0.769298 q^{85} +(0.471827 - 0.933557i) q^{86} +0.600243i q^{87} +(7.47935 - 1.26004i) q^{88} -9.87539i q^{89} +(-3.63354 - 1.83642i) q^{90} +15.1627 q^{91} +(-4.23295 + 8.60710i) q^{92} -3.11778 q^{93} +(12.0087 + 6.06929i) q^{94} -4.89140i q^{95} +(1.36955 - 1.41514i) q^{96} +15.8012i q^{97} +(10.7971 - 21.3632i) q^{98} -7.71984 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 14 q^{6} + 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 + 14 * q^6 + 4 * q^9	\( 16 q + 4 q^{4} + 14 q^{6} + 4 q^{9} - 30 q^{12} + 4 q^{13} + 4 q^{16} + 30 q^{18} + 2 q^{24} - 16 q^{25} - 54 q^{26} - 48 q^{29} + 34 q^{36} - 36 q^{41} - 40 q^{46} + 18 q^{48} + 68 q^{49} + 34 q^{52} - 40 q^{54} + 36 q^{58} + 6 q^{62} + 52 q^{64} + 40 q^{69} + 42 q^{70} - 78 q^{72} + 8 q^{73} + 72 q^{77} + 32 q^{78} + 40 q^{81} - 42 q^{82} + 12 q^{85} - 120 q^{93} + 20 q^{94} - 22 q^{96} - 18 q^{98}+O(q^{100}) \) 16 * q + 4 * q^4 + 14 * q^6 + 4 * q^9 - 30 * q^12 + 4 * q^13 + 4 * q^16 + 30 * q^18 + 2 * q^24 - 16 * q^25 - 54 * q^26 - 48 * q^29 + 34 * q^36 - 36 * q^41 - 40 * q^46 + 18 * q^48 + 68 * q^49 + 34 * q^52 - 40 * q^54 + 36 * q^58 + 6 * q^62 + 52 * q^64 + 40 * q^69 + 42 * q^70 - 78 * q^72 + 8 * q^73 + 72 * q^77 + 32 * q^78 + 40 * q^81 - 42 * q^82 + 12 * q^85 - 120 * q^93 + 20 * q^94 - 22 * q^96 - 18 * q^98

Introduction

L-functions

Modular forms

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Database

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