LMFDB - Embedded newform 280.2.l.a.29.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [280,2,Mod(29,280)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(280, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("280.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 280 = 2^{3} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	280.l (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:	$2.23581125660$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.9
Character	$\chi$	$=$	280.29
Dual form			280.2.l.a.29.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12571 - 0.856025i) q^{2} +1.65329 q^{3} +(0.534444 + 1.92727i) q^{4} +(2.21195 + 0.327549i) q^{5} +(-1.86112 - 1.41526i) q^{6} -1.00000i q^{7} +(1.04816 - 2.62704i) q^{8} -0.266637 q^{9} +O(q^{10})$	\(q+(-1.12571 - 0.856025i) q^{2} +1.65329 q^{3} +(0.534444 + 1.92727i) q^{4} +(2.21195 + 0.327549i) q^{5} +(-1.86112 - 1.41526i) q^{6} -1.00000i q^{7} +(1.04816 - 2.62704i) q^{8} -0.266637 q^{9} +(-2.20962 - 2.26221i) q^{10} +0.550169i q^{11} +(0.883590 + 3.18633i) q^{12} +3.69124 q^{13} +(-0.856025 + 1.12571i) q^{14} +(3.65699 + 0.541533i) q^{15} +(-3.42874 + 2.06004i) q^{16} +2.20317i q^{17} +(0.300156 + 0.228248i) q^{18} +4.02822i q^{19} +(0.550887 + 4.43808i) q^{20} -1.65329i q^{21} +(0.470959 - 0.619331i) q^{22} -7.96482i q^{23} +(1.73291 - 4.34326i) q^{24} +(4.78542 + 1.44904i) q^{25} +(-4.15526 - 3.15979i) q^{26} -5.40069 q^{27} +(1.92727 - 0.534444i) q^{28} -2.33857i q^{29} +(-3.65314 - 3.74008i) q^{30} +1.60339 q^{31} +(5.62321 + 0.616083i) q^{32} +0.909589i q^{33} +(1.88597 - 2.48013i) q^{34} +(0.327549 - 2.21195i) q^{35} +(-0.142503 - 0.513882i) q^{36} -7.31341 q^{37} +(3.44826 - 4.53461i) q^{38} +6.10268 q^{39} +(3.17896 - 5.46756i) q^{40} -0.475409 q^{41} +(-1.41526 + 1.86112i) q^{42} -6.94385 q^{43} +(-1.06033 + 0.294035i) q^{44} +(-0.589788 - 0.0873368i) q^{45} +(-6.81808 + 8.96607i) q^{46} -4.81556i q^{47} +(-5.66869 + 3.40583i) q^{48} -1.00000 q^{49} +(-4.14658 - 5.72764i) q^{50} +3.64248i q^{51} +(1.97276 + 7.11401i) q^{52} +9.39345 q^{53} +(6.07961 + 4.62313i) q^{54} +(-0.180207 + 1.21695i) q^{55} +(-2.62704 - 1.04816i) q^{56} +6.65981i q^{57} +(-2.00187 + 2.63255i) q^{58} -1.71937i q^{59} +(0.910775 + 7.33742i) q^{60} +13.9978i q^{61} +(-1.80495 - 1.37254i) q^{62} +0.266637i q^{63} +(-5.80271 - 5.50713i) q^{64} +(8.16482 + 1.20906i) q^{65} +(0.778630 - 1.02393i) q^{66} -8.80942 q^{67} +(-4.24611 + 1.17747i) q^{68} -13.1681i q^{69} +(-2.26221 + 2.20962i) q^{70} -11.7667 q^{71} +(-0.279479 + 0.700468i) q^{72} +14.2999i q^{73} +(8.23277 + 6.26046i) q^{74} +(7.91169 + 2.39568i) q^{75} +(-7.76347 + 2.15286i) q^{76} +0.550169 q^{77} +(-6.86984 - 5.22404i) q^{78} -7.79860 q^{79} +(-8.25895 + 3.43361i) q^{80} -8.12899 q^{81} +(0.535172 + 0.406962i) q^{82} -4.75889 q^{83} +(3.18633 - 0.883590i) q^{84} +(-0.721646 + 4.87330i) q^{85} +(7.81676 + 5.94411i) q^{86} -3.86633i q^{87} +(1.44532 + 0.576666i) q^{88} -4.88971 q^{89} +(0.589167 + 0.603189i) q^{90} -3.69124i q^{91} +(15.3504 - 4.25675i) q^{92} +2.65087 q^{93} +(-4.12224 + 5.42093i) q^{94} +(-1.31944 + 8.91022i) q^{95} +(9.29678 + 1.01856i) q^{96} -18.8491i q^{97} +(1.12571 + 0.856025i) q^{98} -0.146696i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9}+O(q^{10}) $ 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9	$ 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9} - 8 q^{10} + 20 q^{16} - 24 q^{20} - 48 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{30} - 16 q^{31} + 12 q^{34} - 20 q^{36} - 32 q^{39} + 16 q^{40} - 8 q^{41} + 56 q^{44} - 36 q^{49} - 12 q^{50} - 52 q^{54} - 32 q^{55} + 12 q^{56} - 20 q^{60} - 20 q^{64} - 24 q^{65} - 28 q^{66} - 12 q^{70} + 56 q^{71} - 24 q^{74} + 48 q^{76} + 24 q^{79} + 64 q^{80} + 36 q^{81} + 24 q^{86} - 40 q^{89} - 52 q^{90} - 92 q^{94} + 40 q^{95} + 48 q^{96}+O(q^{100}) $ 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9 - 8 * q^10 + 20 * q^16 - 24 * q^20 - 48 * q^24 + 4 * q^25 - 4 * q^26 + 4 * q^30 - 16 * q^31 + 12 * q^34 - 20 * q^36 - 32 * q^39 + 16 * q^40 - 8 * q^41 + 56 * q^44 - 36 * q^49 - 12 * q^50 - 52 * q^54 - 32 * q^55 + 12 * q^56 - 20 * q^60 - 20 * q^64 - 24 * q^65 - 28 * q^66 - 12 * q^70 + 56 * q^71 - 24 * q^74 + 48 * q^76 + 24 * q^79 + 64 * q^80 + 36 * q^81 + 24 * q^86 - 40 * q^89 - 52 * q^90 - 92 * q^94 + 40 * q^95 + 48 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/280\mathbb{Z}\right)^\times$.

$n$	$57$	$71$	$141$	$241$
$\chi(n)$	$-1$	$1$	$-1$	$1$

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 $

$2$	−1.12571	−	0.856025i	−0.795997	−	0.605301i
$2$	−1.12571	−	0.856025i	−0.795997	−	0.605301i
$3$	1.65329			0.954527			0.477263	−	0.878760i	$-0.341629\pi$
$3$	1.65329			0.954527			0.477263	+	0.878760i	$0.341629\pi$
$4$	0.534444	+	1.92727i	0.267222	+	0.963635i
$5$	2.21195	+	0.327549i	0.989213	+	0.146484i
$5$	2.21195	+	0.327549i	0.989213	+	0.146484i
$6$	−1.86112	−	1.41526i	−0.759800	−	0.577776i
$7$		−	1.00000i		−	0.377964i
$7$		−	1.00000i		−	0.377964i
$8$	1.04816	−	2.62704i	0.370581	−	0.928800i
$9$	−0.266637			−0.0888791
$10$	−2.20962	−	2.26221i	−0.698743	−	0.715372i
$11$			0.550169i			0.165882i	0.996554	+	0.0829412i	$0.0264314\pi$
$11$			0.550169i			0.165882i	−0.996554	+	0.0829412i	$0.973569\pi$
$12$	0.883590	+	3.18633i	0.255071	+	0.919815i
$13$	3.69124			1.02376			0.511882	−	0.859056i	$-0.328948\pi$
$13$	3.69124			1.02376			0.511882	+	0.859056i	$0.328948\pi$
$14$	−0.856025	+	1.12571i	−0.228782	+	0.300859i
$15$	3.65699	+	0.541533i	0.944230	+	0.139823i
$16$	−3.42874	+	2.06004i	−0.857185	+	0.515009i
$17$			2.20317i			0.534347i	0.963648	+	0.267174i	$0.0860898\pi$
$17$			2.20317i			0.534347i	−0.963648	+	0.267174i	$0.913910\pi$
$18$	0.300156	+	0.228248i	0.0707475	+	0.0537986i
$19$			4.02822i			0.924138i	0.886844	+	0.462069i	$0.152893\pi$
$19$			4.02822i			0.924138i	−0.886844	+	0.462069i	$0.847107\pi$
$20$	0.550887	+	4.43808i	0.123182	+	0.992384i
$21$		−	1.65329i		−	0.360777i
$22$	0.470959	−	0.619331i	0.100409	−	0.132042i
$23$		−	7.96482i		−	1.66078i	−0.557183	−	0.830390i	$-0.688118\pi$
$23$		−	7.96482i		−	1.66078i	0.557183	−	0.830390i	$-0.311882\pi$
$24$	1.73291	−	4.34326i	0.353729	−	0.886564i
$25$	4.78542	+	1.44904i	0.957085	+	0.289808i
$26$	−4.15526	−	3.15979i	−0.814913	−	0.619686i
$27$	−5.40069			−1.03936
$28$	1.92727	−	0.534444i	0.364220	−	0.101000i
$29$		−	2.33857i		−	0.434262i	−0.976143	−	0.217131i	$-0.930330\pi$
$29$		−	2.33857i		−	0.434262i	0.976143	−	0.217131i	$-0.0696698\pi$
$30$	−3.65314	−	3.74008i	−0.666969	−	0.682842i
$31$	1.60339			0.287978			0.143989	−	0.989579i	$-0.454007\pi$
$31$	1.60339			0.287978			0.143989	+	0.989579i	$0.454007\pi$
$32$	5.62321	+	0.616083i	0.994052	+	0.108909i
$33$			0.909589i			0.158339i
$34$	1.88597	−	2.48013i	0.323441	−	0.425339i
$35$	0.327549	−	2.21195i	0.0553659	−	0.373887i
$36$	−0.142503	−	0.513882i	−0.0237505	−	0.0856470i
$37$	−7.31341			−1.20232			−0.601158	−	0.799130i	$-0.705294\pi$
$37$	−7.31341			−1.20232			−0.601158	+	0.799130i	$0.705294\pi$
$38$	3.44826	−	4.53461i	0.559381	−	0.735611i
$39$	6.10268			0.977211
$40$	3.17896	−	5.46756i	0.502638	−	0.864497i
$41$	−0.475409			−0.0742464			−0.0371232	−	0.999311i	$-0.511819\pi$
$41$	−0.475409			−0.0742464			−0.0371232	+	0.999311i	$0.511819\pi$
$42$	−1.41526	+	1.86112i	−0.218379	+	0.287177i
$43$	−6.94385			−1.05893			−0.529464	−	0.848333i	$-0.677607\pi$
$43$	−6.94385			−1.05893			−0.529464	+	0.848333i	$0.677607\pi$
$44$	−1.06033	+	0.294035i	−0.159850	+	0.0443274i
$45$	−0.589788	−	0.0873368i	−0.0879204	−	0.0130194i
$46$	−6.81808	+	8.96607i	−1.00527	+	1.32197i
$47$		−	4.81556i		−	0.702422i	−0.936296	−	0.351211i	$-0.885770\pi$
$47$		−	4.81556i		−	0.702422i	0.936296	−	0.351211i	$-0.114230\pi$
$48$	−5.66869	+	3.40583i	−0.818206	+	0.491590i
$49$	−1.00000			−0.142857
$50$	−4.14658	−	5.72764i	−0.586415	−	0.810011i
$51$			3.64248i			0.510049i
$52$	1.97276	+	7.11401i	0.273572	+	0.986535i
$53$	9.39345			1.29029			0.645145	−	0.764060i	$-0.276797\pi$
$53$	9.39345			1.29029			0.645145	+	0.764060i	$0.276797\pi$
$54$	6.07961	+	4.62313i	0.827330	+	0.629128i
$55$	−0.180207	+	1.21695i	−0.0242992	+	0.164093i
$56$	−2.62704	−	1.04816i	−0.351053	−	0.140066i
$57$			6.65981i			0.882114i
$58$	−2.00187	+	2.63255i	−0.262859	+	0.345671i
$59$		−	1.71937i		−	0.223842i	−0.993717	−	0.111921i	$-0.964300\pi$
$59$		−	1.71937i		−	0.223842i	0.993717	−	0.111921i	$-0.0357004\pi$
$60$	0.910775	+	7.33742i	0.117581	+	0.947257i
$61$			13.9978i			1.79224i	0.443813	+	0.896119i	$0.353625\pi$
$61$			13.9978i			1.79224i	−0.443813	+	0.896119i	$0.646375\pi$
$62$	−1.80495	−	1.37254i	−0.229229	−	0.174313i
$63$			0.266637i			0.0335931i
$64$	−5.80271	−	5.50713i	−0.725339	−	0.688392i
$65$	8.16482	+	1.20906i	1.01272	+	0.149965i
$66$	0.778630	−	1.02393i	0.0958428	−	0.126037i
$67$	−8.80942			−1.07624			−0.538121	−	0.842868i	$-0.680866\pi$
$67$	−8.80942			−1.07624			−0.538121	+	0.842868i	$0.680866\pi$
$68$	−4.24611	+	1.17747i	−0.514916	+	0.142789i
$69$		−	13.1681i		−	1.58526i
$70$	−2.26221	+	2.20962i	−0.270385	+	0.264100i
$71$	−11.7667			−1.39645			−0.698224	−	0.715880i	$-0.746026\pi$
$71$	−11.7667			−1.39645			−0.698224	+	0.715880i	$0.746026\pi$
$72$	−0.279479	+	0.700468i	−0.0329369	+	0.0825509i
$73$			14.2999i			1.67368i	0.547446	+	0.836841i	$0.315600\pi$
$73$			14.2999i			1.67368i	−0.547446	+	0.836841i	$0.684400\pi$
$74$	8.23277	+	6.26046i	0.957040	+	0.727763i
$75$	7.91169	+	2.39568i	0.913563	+	0.276630i
$76$	−7.76347	+	2.15286i	−0.890531	+	0.246950i
$77$	0.550169			0.0626976
$78$	−6.86984	−	5.22404i	−0.777857	−	0.591506i
$79$	−7.79860			−0.877411			−0.438706	−	0.898631i	$-0.644563\pi$
$79$	−7.79860			−0.877411			−0.438706	+	0.898631i	$0.644563\pi$
$80$	−8.25895	+	3.43361i	−0.923379	+	0.383889i
$81$	−8.12899			−0.903221
$82$	0.535172	+	0.406962i	0.0590999	+	0.0449414i
$83$	−4.75889			−0.522356			−0.261178	−	0.965291i	$-0.584111\pi$
$83$	−4.75889			−0.522356			−0.261178	+	0.965291i	$0.584111\pi$
$84$	3.18633	−	0.883590i	0.347657	−	0.0964076i
$85$	−0.721646	+	4.87330i	−0.0782735	+	0.528583i
$86$	7.81676	+	5.94411i	0.842903	+	0.640969i
$87$		−	3.86633i		−	0.414514i
$88$	1.44532	+	0.576666i	0.154072	+	0.0614729i
$89$	−4.88971			−0.518309			−0.259154	−	0.965836i	$-0.583444\pi$
$89$	−4.88971			−0.518309			−0.259154	+	0.965836i	$0.583444\pi$
$90$	0.589167	+	0.603189i	0.0621037	+	0.0635817i
$91$		−	3.69124i		−	0.386947i
$92$	15.3504	−	4.25675i	1.60038	−	0.443797i
$93$	2.65087			0.274882
$94$	−4.12224	+	5.42093i	−0.425177	+	0.559126i
$95$	−1.31944	+	8.91022i	−0.135372	+	0.914169i
$96$	9.29678	+	1.01856i	0.948849	+	0.103957i
$97$		−	18.8491i		−	1.91384i	−0.290355	−	0.956919i	$-0.593773\pi$
$97$		−	18.8491i		−	1.91384i	0.290355	−	0.956919i	$-0.406227\pi$
$98$	1.12571	+	0.856025i	0.113714	+	0.0864715i
$99$		−	0.146696i		−	0.0147435i
$100$	−0.235154	+	9.99723i	−0.0235154	+	0.999723i
$101$		−	1.08462i		−	0.107924i	−0.998543	−	0.0539618i	$-0.982815\pi$
$101$		−	1.08462i		−	0.107924i	0.998543	−	0.0539618i	$-0.0171849\pi$
$102$	3.11805	−	4.10037i	0.308733	−	0.405997i
$103$		−	12.2447i		−	1.20651i	−0.797550	−	0.603253i	$-0.793871\pi$
$103$		−	12.2447i		−	1.20651i	0.797550	−	0.603253i	$-0.206129\pi$
$104$	3.86901	−	9.69704i	0.379388	−	0.950873i
$105$	0.541533	−	3.65699i	0.0528482	−	0.356885i
$106$	−10.5743	−	8.04103i	−1.02707	−	0.781014i
$107$	3.40130			0.328816			0.164408	−	0.986392i	$-0.447429\pi$
$107$	3.40130			0.328816			0.164408	+	0.986392i	$0.447429\pi$
$108$	−2.88637	−	10.4086i	−0.277741	−	1.00157i
$109$			9.56316i			0.915984i	0.888956	+	0.457992i	$0.151431\pi$
$109$			9.56316i			0.915984i	−0.888956	+	0.457992i	$0.848569\pi$
$110$	1.24460	−	1.21567i	0.118668	−	0.115909i
$111$	−12.0912			−1.14764
$112$	2.06004	+	3.42874i	0.194655	+	0.323985i
$113$			10.3841i			0.976853i	0.872605	+	0.488427i	$0.162429\pi$
$113$			10.3841i			0.976853i	−0.872605	+	0.488427i	$0.837571\pi$
$114$	5.70096	−	7.49702i	0.533944	−	0.702160i
$115$	2.60887	−	17.6178i	0.243278	−	1.64286i
$116$	4.50706	−	1.24983i	0.418470	−	0.116044i
$117$	−0.984221			−0.0909913
$118$	−1.47182	+	1.93551i	−0.135492	+	0.178178i
$119$	2.20317			0.201964
$120$	5.25574	−	9.03945i	0.479782	−	0.825185i
$121$	10.6973			0.972483
$122$	11.9825	−	15.7575i	1.08484	−	1.42662i
$123$	−0.785988			−0.0708702
$124$	0.856923	+	3.09017i	0.0769540	+	0.277505i
$125$	10.1105	+	4.77266i	0.904308	+	0.426880i
$126$	0.228248	−	0.300156i	0.0203340	−	0.0267400i
$127$			17.8598i			1.58480i	0.610001	+	0.792401i	$0.291169\pi$
$127$			17.8598i			1.58480i	−0.610001	+	0.792401i	$0.708831\pi$
$128$	1.81793	+	11.1667i	0.160684	+	0.987006i
$129$	−11.4802			−1.01077
$130$	−8.15623	−	8.35034i	−0.715349	−	0.732373i
$131$		−	10.5809i		−	0.924460i	−0.886760	−	0.462230i	$-0.847050\pi$
$131$		−	10.5809i		−	0.924460i	0.886760	−	0.462230i	$-0.152950\pi$
$132$	−1.75302	+	0.486124i	−0.152581	+	0.0423117i
$133$	4.02822			0.349291
$134$	9.91685	+	7.54108i	0.856685	+	0.651450i
$135$	−11.9461	−	1.76899i	−1.02815	−	0.152251i
$136$	5.78783	+	2.30928i	0.496302	+	0.198019i
$137$		−	0.0372832i		−	0.00318532i	−0.999999	−	0.00159266i	$-0.999493\pi$
$137$		−	0.0372832i		−	0.00318532i	0.999999	−	0.00159266i	$-0.000506960\pi$
$138$	−11.2722	+	14.8235i	−0.959558	+	1.26186i
$139$			4.11189i			0.348766i	0.984678	+	0.174383i	$0.0557931\pi$
$139$			4.11189i			0.348766i	−0.984678	+	0.174383i	$0.944207\pi$
$140$	4.43808	−	0.550887i	0.375086	−	0.0465585i
$141$		−	7.96151i		−	0.670480i
$142$	13.2459	+	10.0726i	1.11157	+	0.845270i
$143$			2.03081i			0.169824i
$144$	0.914230	−	0.549282i	0.0761858	−	0.0457735i
$145$	0.765996	−	5.17279i	0.0636125	−	0.429577i
$146$	12.2411	−	16.0976i	1.01308	−	1.33225i
$147$	−1.65329			−0.136361
$148$	−3.90861	−	14.0949i	−0.321286	−	1.15859i
$149$		−	20.6192i		−	1.68919i	−0.535407	−	0.844594i	$-0.679842\pi$
$149$		−	20.6192i		−	1.68919i	0.535407	−	0.844594i	$-0.320158\pi$
$150$	−6.85550	−	9.46944i	−0.559749	−	0.773177i
$151$	7.49786			0.610167			0.305084	−	0.952326i	$-0.401316\pi$
$151$	7.49786			0.610167			0.305084	+	0.952326i	$0.401316\pi$
$152$	10.5823	+	4.22223i	0.858339	+	0.342468i
$153$		−	0.587448i		−	0.0474923i
$154$	−0.619331	−	0.470959i	−0.0499071	−	0.0379509i
$155$	3.54662	+	0.525189i	0.284871	+	0.0421842i
$156$	3.26154	+	11.7615i	0.261132	+	0.941674i
$157$	−11.9810			−0.956185			−0.478092	−	0.878310i	$-0.658672\pi$
$157$	−11.9810			−0.956185			−0.478092	+	0.878310i	$0.658672\pi$
$158$	8.77896	+	6.67579i	0.698416	+	0.531098i
$159$	15.5301			1.23162
$160$	12.2364	+	3.20462i	0.967375	+	0.253347i
$161$	−7.96482			−0.627715
$162$	9.15088	+	6.95862i	0.718961	+	0.546721i
$163$	16.5049			1.29276			0.646382	−	0.763014i	$-0.276281\pi$
$163$	16.5049			1.29276			0.646382	+	0.763014i	$0.276281\pi$
$164$	−0.254080	−	0.916241i	−0.0198403	−	0.0715464i
$165$	−0.297935	+	2.01196i	−0.0231942	+	0.156631i
$166$	5.35713	+	4.07373i	0.415794	+	0.316183i
$167$		−	18.9917i		−	1.46962i	−0.678273	−	0.734810i	$-0.737271\pi$
$167$		−	18.9917i		−	1.46962i	0.678273	−	0.734810i	$-0.262729\pi$
$168$	−4.34326	−	1.73291i	−0.335090	−	0.133697i
$169$	0.625224			0.0480942
$170$	4.98403	−	4.86817i	0.382257	−	0.373372i
$171$		−	1.07407i		−	0.0821365i
$172$	−3.71110	−	13.3827i	−0.282969	−	1.02042i
$173$	−4.58728			−0.348764			−0.174382	−	0.984678i	$-0.555793\pi$
$173$	−4.58728			−0.348764			−0.174382	+	0.984678i	$0.555793\pi$
$174$	−3.30967	+	4.35237i	−0.250906	+	0.329952i
$175$	1.44904	−	4.78542i	0.109537	−	0.361744i
$176$	−1.13337	−	1.88639i	−0.0854309	−	0.142192i
$177$		−	2.84261i		−	0.213663i
$178$	5.50440	+	4.18571i	0.412572	+	0.313733i
$179$			23.3279i			1.74361i	0.489853	+	0.871805i	$0.337050\pi$
$179$			23.3279i			1.74361i	−0.489853	+	0.871805i	$0.662950\pi$
$180$	−0.146887	−	1.18336i	−0.0109483	−	0.0882022i
$181$		−	3.44282i		−	0.255903i	−0.991780	−	0.127952i	$-0.959160\pi$
$181$		−	3.44282i		−	0.255903i	0.991780	−	0.127952i	$-0.0408402\pi$
$182$	−3.15979	+	4.15526i	−0.234219	+	0.308008i
$183$			23.1425i			1.71074i
$184$	−20.9239	−	8.34841i	−1.54253	−	0.615453i
$185$	−16.1769	−	2.39550i	−1.18935	−	0.176121i
$186$	−2.98411	−	2.26921i	−0.218805	−	0.166386i
$187$	−1.21212			−0.0886388
$188$	9.28089	−	2.57365i	0.676878	−	0.187703i
$189$			5.40069i			0.392843i
$190$	9.11267	−	8.90084i	0.661103	−	0.645735i
$191$	−3.46757			−0.250905			−0.125452	−	0.992100i	$-0.540038\pi$
$191$	−3.46757			−0.250905			−0.125452	+	0.992100i	$0.540038\pi$
$192$	−9.59356	−	9.10488i	−0.692356	−	0.657088i
$193$		−	15.8570i		−	1.14141i	−0.821155	−	0.570705i	$-0.806670\pi$
$193$		−	15.8570i		−	1.14141i	0.821155	−	0.570705i	$-0.193330\pi$
$194$	−16.1353	+	21.2186i	−1.15845	+	1.52341i
$195$	13.4988	+	1.99893i	0.966669	+	0.143146i
$196$	−0.534444	−	1.92727i	−0.0381746	−	0.137662i
$197$	−3.36343			−0.239634			−0.119817	−	0.992796i	$-0.538231\pi$
$197$	−3.36343			−0.239634			−0.119817	+	0.992796i	$0.538231\pi$
$198$	−0.125575	+	0.165137i	−0.00892424	+	0.0117358i
$199$	15.2545			1.08137			0.540683	−	0.841227i	$-0.318166\pi$
$199$	15.2545			1.08137			0.540683	+	0.841227i	$0.318166\pi$
$200$	8.82259	−	11.0527i	0.623852	−	0.781543i
$201$	−14.5645			−1.02730
$202$	−0.928460	+	1.22096i	−0.0653262	+	0.0859068i
$203$	−2.33857			−0.164135
$204$	−7.02004	+	1.94670i	−0.491501	+	0.136296i
$205$	−1.05158	−	0.155720i	−0.0734455	−	0.0108759i
$206$	−10.4818	+	13.7840i	−0.730299	+	0.960374i
$207$			2.12372i			0.147609i
$208$	−12.6563	+	7.60408i	−0.877556	+	0.527248i
$209$	−2.21621			−0.153298
$210$	−3.74008	+	3.65314i	−0.258090	+	0.252091i
$211$			9.60962i			0.661554i	0.943709	+	0.330777i	$0.107311\pi$
$211$			9.60962i			0.661554i	−0.943709	+	0.330777i	$0.892689\pi$
$212$	5.02028	+	18.1037i	0.344794	+	1.24337i
$213$	−19.4537			−1.33295
$214$	−3.82888	−	2.91160i	−0.261737	−	0.199033i
$215$	−15.3594	−	2.27445i	−1.04750	−	0.155116i
$216$	−5.66080	+	14.1879i	−0.385169	+	0.965361i
$217$		−	1.60339i		−	0.108845i
$218$	8.18630	−	10.7653i	0.554446	−	0.729121i
$219$			23.6419i			1.59757i
$220$	−2.44169	+	0.303081i	−0.164619	+	0.0204337i
$221$			8.13242i			0.547046i
$222$	13.6111	+	10.3503i	0.913520	+	0.694669i
$223$			18.3933i			1.23171i	0.787861	+	0.615854i	$0.211189\pi$
$223$			18.3933i			1.23171i	−0.787861	+	0.615854i	$0.788811\pi$
$224$	0.616083	−	5.62321i	0.0411638	−	0.375716i
$225$	−1.27597	−	0.386369i	−0.0850648	−	0.0257579i
$226$	8.88904	−	11.6895i	0.591290	−	0.777572i
$227$	−10.7478			−0.713358			−0.356679	−	0.934227i	$-0.616091\pi$
$227$	−10.7478			−0.713358			−0.356679	+	0.934227i	$0.616091\pi$
$228$	−12.8353	+	3.55930i	−0.850036	+	0.235720i
$229$		−	19.5459i		−	1.29163i	−0.763494	−	0.645815i	$-0.776518\pi$
$229$		−	19.5459i		−	1.29163i	0.763494	−	0.645815i	$-0.223482\pi$
$230$	−18.0181	+	17.5992i	−1.18808	+	1.16046i
$231$	0.909589			0.0598465
$232$	−6.14353	−	2.45120i	−0.403342	−	0.160929i
$233$		−	6.58938i		−	0.431685i	−0.976428	−	0.215842i	$-0.930750\pi$
$233$		−	6.58938i		−	0.431685i	0.976428	−	0.215842i	$-0.0692498\pi$
$234$	1.10795	+	0.842518i	0.0724288	+	0.0550771i
$235$	1.57733	−	10.6518i	0.102894	−	0.694845i
$236$	3.31368	−	0.918905i	0.215702	−	0.0598156i
$237$	−12.8933			−0.837512
$238$	−2.48013	−	1.88597i	−0.160763	−	0.122249i
$239$	19.9963			1.29345			0.646726	−	0.762722i	$-0.276138\pi$
$239$	19.9963			1.29345			0.646726	+	0.762722i	$0.276138\pi$
$240$	−13.6544	+	5.67675i	−0.881390	+	0.366433i
$241$	23.7573			1.53034			0.765170	−	0.643828i	$-0.222655\pi$
$241$	23.7573			1.53034			0.765170	+	0.643828i	$0.222655\pi$
$242$	−12.0421	−	9.15716i	−0.774093	−	0.588645i
$243$	2.76251			0.177215
$244$	−26.9776	+	7.48106i	−1.72706	+	0.478926i
$245$	−2.21195	−	0.327549i	−0.141316	−	0.0209263i
$246$	0.884794	+	0.672825i	0.0564124	+	0.0428978i
$247$			14.8691i			0.946100i
$248$	1.68061	−	4.21218i	0.106719	−	0.267474i
$249$	−7.86782			−0.498603
$250$	−7.29594	−	14.0274i	−0.461436	−	0.887174i
$251$		−	2.41879i		−	0.152672i	−0.997082	−	0.0763362i	$-0.975678\pi$
$251$		−	2.41879i		−	0.152672i	0.997082	−	0.0763362i	$-0.0243222\pi$
$252$	−0.513882	+	0.142503i	−0.0323715	+	0.00897683i
$253$	4.38200			0.275494
$254$	15.2884	−	20.1050i	0.959281	−	1.26150i
$255$	−1.19309	+	8.05697i	−0.0747141	+	0.504547i
$256$	7.51250	−	14.1267i	0.469532	−	0.882916i
$257$		−	4.68842i		−	0.292455i	−0.989251	−	0.146228i	$-0.953287\pi$
$257$		−	4.68842i		−	0.292455i	0.989251	−	0.146228i	$-0.0467132\pi$
$258$	12.9234	+	9.82732i	0.804573	+	0.611822i
$259$			7.31341i			0.454433i
$260$	2.03345	+	16.3820i	0.126109	+	1.01597i
$261$			0.623550i			0.0385968i
$262$	−9.05753	+	11.9110i	−0.559576	+	0.735867i
$263$		−	4.01452i		−	0.247546i	−0.992311	−	0.123773i	$-0.960501\pi$
$263$		−	4.01452i		−	0.247546i	0.992311	−	0.123773i	$-0.0394995\pi$
$264$	2.38953	+	0.953396i	0.147065	+	0.0586775i
$265$	20.7778	+	3.07682i	1.27637	+	0.189007i
$266$	−4.53461	−	3.44826i	−0.278035	−	0.211426i
$267$	−8.08411			−0.494739
$268$	−4.70814	−	16.9781i	−0.287596	−	1.03710i
$269$			18.9516i			1.15550i	0.816213	+	0.577751i	$0.196069\pi$
$269$			18.9516i			1.15550i	−0.816213	+	0.577751i	$0.803931\pi$
$270$	11.9335	+	12.2175i	0.726249	+	0.743532i
$271$	26.3199			1.59882			0.799411	−	0.600784i	$-0.205145\pi$
$271$	26.3199			1.59882			0.799411	+	0.600784i	$0.205145\pi$
$272$	−4.53861	−	7.55410i	−0.275194	−	0.458034i
$273$		−	6.10268i		−	0.369351i
$274$	−0.0319154	+	0.0419701i	−0.00192808	+	0.00253551i
$275$	−0.797219	+	2.63279i	−0.0480741	+	0.158763i
$276$	25.3786	−	7.03763i	1.52761	−	0.423616i
$277$	−18.1985			−1.09344			−0.546720	−	0.837316i	$-0.684124\pi$
$277$	−18.1985			−1.09344			−0.546720	+	0.837316i	$0.684124\pi$
$278$	3.51988	−	4.62879i	0.211108	−	0.277617i
$279$	−0.427524			−0.0255952
$280$	−5.46756	−	3.17896i	−0.326749	−	0.189979i
$281$	25.8034			1.53930			0.769650	−	0.638466i	$-0.220431\pi$
$281$	25.8034			1.53930			0.769650	+	0.638466i	$0.220431\pi$
$282$	−6.81525	+	8.96235i	−0.405842	+	0.533700i
$283$	22.4823			1.33643			0.668217	−	0.743966i	$-0.267058\pi$
$283$	22.4823			1.33643			0.668217	+	0.743966i	$0.267058\pi$
$284$	−6.28863	−	22.6776i	−0.373161	−	1.34567i
$285$	−2.18141	+	14.7312i	−0.129216	+	0.872599i
$286$	1.73842	−	2.28610i	0.102795	−	0.135180i
$287$			0.475409i			0.0280625i
$288$	−1.49936	−	0.164271i	−0.0883504	−	0.00967974i
$289$	12.1460			0.714473
$290$	−5.29033	+	5.16735i	−0.310659	+	0.303437i
$291$		−	31.1630i		−	1.82681i
$292$	−27.5599	+	7.64252i	−1.61282	+	0.447245i
$293$	−0.882752			−0.0515709			−0.0257855	−	0.999667i	$-0.508209\pi$
$293$	−0.882752			−0.0515709			−0.0257855	+	0.999667i	$0.508209\pi$
$294$	1.86112	+	1.41526i	0.108543	+	0.0825394i
$295$	0.563176	−	3.80315i	0.0327894	−	0.221428i
$296$	−7.66563	+	19.2126i	−0.445556	+	1.11671i
$297$		−	2.97130i		−	0.172412i
$298$	−17.6505	+	23.2112i	−1.02247	+	1.34459i
$299$		−	29.4000i		−	1.70025i
$300$	−0.388777	+	16.5283i	−0.0224460	+	0.954263i
$301$			6.94385i			0.400237i
$302$	−8.44042	−	6.41835i	−0.485691	−	0.369335i
$303$		−	1.79319i		−	0.103016i
$304$	−8.29828	−	13.8117i	−0.475939	−	0.792157i
$305$	−4.58497	+	30.9625i	−0.262535	+	1.77291i
$306$	−0.502870	+	0.661295i	−0.0287471	+	0.0378037i
$307$	10.8688			0.620316			0.310158	−	0.950685i	$-0.399618\pi$
$307$	10.8688			0.620316			0.310158	+	0.950685i	$0.399618\pi$
$308$	0.294035	+	1.06033i	0.0167542	+	0.0604176i
$309$		−	20.2440i		−	1.15164i
$310$	−3.54289	−	3.62720i	−0.201222	−	0.206011i
$311$	16.7567			0.950186			0.475093	−	0.879936i	$-0.342414\pi$
$311$	16.7567			0.950186			0.475093	+	0.879936i	$0.342414\pi$
$312$	6.39659	−	16.0320i	0.362136	−	0.907633i
$313$		−	33.2957i		−	1.88198i	−0.338430	−	0.940992i	$-0.609896\pi$
$313$		−	33.2957i		−	1.88198i	0.338430	−	0.940992i	$-0.390104\pi$
$314$	13.4871	+	10.2560i	0.761120	+	0.578779i
$315$	−0.0873368	+	0.589788i	−0.00492087	+	0.0332308i
$316$	−4.16792	−	15.0300i	−0.234464	−	0.845504i
$317$	19.2384			1.08054			0.540269	−	0.841492i	$-0.318322\pi$
$317$	19.2384			1.08054			0.540269	+	0.841492i	$0.318322\pi$
$318$	−17.4824	−	13.2941i	−0.980363	−	0.745498i
$319$	1.28661			0.0720363
$320$	−11.0314	−	14.0822i	−0.616677	−	0.787217i
$321$	5.62333			0.313864
$322$	8.96607	+	6.81808i	0.499660	+	0.379957i
$323$	−8.87486			−0.493811
$324$	−4.34449	−	15.6668i	−0.241361	−	0.870376i
$325$	17.6641	+	5.34876i	0.979830	+	0.296696i
$326$	−18.5797	−	14.1286i	−1.02904	−	0.782511i
$327$			15.8107i			0.874331i
$328$	−0.498305	+	1.24892i	−0.0275143	+	0.0689601i
$329$	−4.81556			−0.265491
$330$	2.05768	−	2.00985i	0.113271	−	0.110638i
$331$			5.08151i			0.279305i	0.990201	+	0.139652i	$0.0445985\pi$
$331$			5.08151i			0.279305i	−0.990201	+	0.139652i	$0.955401\pi$
$332$	−2.54336	−	9.17167i	−0.139585	−	0.503361i
$333$	1.95003			0.106861
$334$	−16.2573	+	21.3791i	−0.889562	+	1.16981i
$335$	−19.4860	−	2.88552i	−1.06463	−	0.157653i
$336$	3.40583	+	5.66869i	0.185803	+	0.309253i
$337$			7.96789i			0.434038i	0.976167	+	0.217019i	$0.0696334\pi$
$337$			7.96789i			0.434038i	−0.976167	+	0.217019i	$0.930367\pi$
$338$	−0.703821	−	0.535207i	−0.0382828	−	0.0291114i
$339$			17.1679i			0.932432i
$340$	−9.77784	+	1.21370i	−0.530278	+	0.0658220i
$341$			0.882137i			0.0477704i
$342$	−0.919434	+	1.20910i	−0.0497173	+	0.0653804i
$343$			1.00000i			0.0539949i
$344$	−7.27828	+	18.2418i	−0.392418	+	0.983532i
$345$	4.31321	−	29.1272i	0.232215	−	1.56816i
$346$	5.16394	+	3.92682i	0.277615	+	0.211107i
$347$	12.0115			0.644811			0.322406	−	0.946602i	$-0.395509\pi$
$347$	12.0115			0.644811			0.322406	+	0.946602i	$0.395509\pi$
$348$	7.45146	−	2.06634i	0.399440	−	0.110767i
$349$		−	3.89860i		−	0.208687i	−0.994541	−	0.104344i	$-0.966726\pi$
$349$		−	3.89860i		−	0.208687i	0.994541	−	0.104344i	$-0.0332741\pi$
$350$	−5.72764	+	4.14658i	−0.306155	+	0.221644i
$351$	−19.9352			−1.06406
$352$	−0.338950	+	3.09372i	−0.0180661	+	0.164896i
$353$			13.4826i			0.717605i	0.933413	+	0.358803i	$0.116815\pi$
$353$			13.4826i			0.717605i	−0.933413	+	0.358803i	$0.883185\pi$
$354$	−2.43334	+	3.19995i	−0.129331	+	0.170075i
$355$	−26.0273	−	3.85416i	−1.38138	−	0.204558i
$356$	−2.61328	−	9.42380i	−0.138503	−	0.499460i
$357$	3.64248			0.192780
$358$	19.9693	−	26.2605i	1.05541	−	1.38791i
$359$	−25.8636			−1.36503			−0.682514	−	0.730873i	$-0.739113\pi$
$359$	−25.8636			−1.36503			−0.682514	+	0.730873i	$0.739113\pi$
$360$	−0.847630	+	1.45786i	−0.0446740	+	0.0768357i
$361$	2.77342			0.145969
$362$	−2.94714	+	3.87562i	−0.154898	+	0.203698i
$363$	17.6857			0.928261
$364$	7.11401	−	1.97276i	0.372875	−	0.103401i
$365$	−4.68393	+	31.6307i	−0.245168	+	1.65563i
$366$	19.8105	−	26.0517i	1.03551	−	1.36174i
$367$			1.26740i			0.0661576i	0.999453	+	0.0330788i	$0.0105312\pi$
$367$			1.26740i			0.0661576i	−0.999453	+	0.0330788i	$0.989469\pi$
$368$	16.4078	+	27.3093i	0.855316	+	1.42359i
$369$	0.126762			0.00659895
$370$	16.1599	+	16.5444i	0.840111	+	0.860104i
$371$		−	9.39345i		−	0.487684i
$372$	1.41674	+	5.10894i	0.0734546	+	0.264886i
$373$	−18.8627			−0.976674			−0.488337	−	0.872655i	$-0.662396\pi$
$373$	−18.8627			−0.976674			−0.488337	+	0.872655i	$0.662396\pi$
$374$	1.36449	+	1.03760i	0.0705562	+	0.0536531i
$375$	16.7155	+	7.89059i	0.863186	+	0.407468i
$376$	−12.6507	−	5.04749i	−0.652410	−	0.260304i
$377$		−	8.63222i		−	0.444582i
$378$	4.62313	−	6.07961i	0.237788	−	0.312702i
$379$		−	9.43604i		−	0.484697i	−0.970189	−	0.242348i	$-0.922082\pi$
$379$		−	9.43604i		−	0.484697i	0.970189	−	0.242348i	$-0.0779177\pi$
$380$	−17.8776	+	2.21910i	−0.917100	+	0.113837i
$381$			29.5274i			1.51273i
$382$	3.90348	+	2.96833i	0.199719	+	0.151873i
$383$		−	14.1486i		−	0.722961i	−0.932380	−	0.361480i	$-0.882271\pi$
$383$		−	14.1486i		−	0.722961i	0.932380	−	0.361480i	$-0.117729\pi$
$384$	3.00556	+	18.4618i	0.153377	+	0.942123i
$385$	1.21695	+	0.180207i	0.0620213	+	0.00918422i
$386$	−13.5740	+	17.8504i	−0.690897	+	0.908559i
$387$	1.85149			0.0941165
$388$	36.3273	−	10.0738i	1.84424	−	0.511420i
$389$		−	5.71633i		−	0.289829i	−0.989444	−	0.144915i	$-0.953709\pi$
$389$		−	5.71633i		−	0.289829i	0.989444	−	0.144915i	$-0.0462908\pi$
$390$	−13.4846	−	13.8055i	−0.682819	−	0.699069i
$391$	17.5479			0.887433
$392$	−1.04816	+	2.62704i	−0.0529402	+	0.132686i
$393$		−	17.4933i		−	0.882421i
$394$	3.78624	+	2.87918i	0.190748	+	0.145051i
$395$	−17.2501	−	2.55442i	−0.867946	−	0.128527i
$396$	0.282722	−	0.0784006i	0.0142073	−	0.00393978i
$397$	18.0459			0.905700			0.452850	−	0.891587i	$-0.350407\pi$
$397$	18.0459			0.905700			0.452850	+	0.891587i	$0.350407\pi$
$398$	−17.1722	−	13.0583i	−0.860764	−	0.654551i
$399$	6.65981			0.333408
$400$	−19.3930	+	4.88976i	−0.969652	+	0.244488i
$401$	24.0416			1.20058			0.600291	−	0.799782i	$-0.295052\pi$
$401$	24.0416			1.20058			0.600291	+	0.799782i	$0.295052\pi$
$402$	16.3954	+	12.4676i	0.817729	+	0.621826i
$403$	5.91850			0.294821
$404$	2.09035	−	0.579668i	0.103999	−	0.0288395i
$405$	−17.9809	−	2.66264i	−0.893478	−	0.132308i
$406$	2.63255	+	2.00187i	0.130651	+	0.0993513i
$407$		−	4.02361i		−	0.199443i
$408$	9.56895	+	3.81790i	0.473733	+	0.189014i
$409$	−37.6802			−1.86317			−0.931584	−	0.363526i	$-0.881573\pi$
$409$	−37.6802			−1.86317			−0.931584	+	0.363526i	$0.881573\pi$
$410$	1.05047	+	1.07547i	0.0518792	+	0.0531138i
$411$		−	0.0616399i		−	0.00304047i
$412$	23.5988	−	6.54410i	1.16263	−	0.322405i
$413$	−1.71937			−0.0846045
$414$	1.81795	−	2.39069i	0.0893476	−	0.117496i
$415$	−10.5264	−	1.55877i	−0.516722	−	0.0765170i
$416$	20.7566	+	2.27411i	1.01768	+	0.111497i
$417$			6.79814i			0.332906i
$418$	2.49480	+	1.89713i	0.122025	+	0.0927915i
$419$			15.7055i			0.767262i	0.923486	+	0.383631i	$0.125327\pi$
$419$			15.7055i			0.767262i	−0.923486	+	0.383631i	$0.874673\pi$
$420$	7.33742	−	0.910775i	0.358029	−	0.0444413i
$421$		−	21.9675i		−	1.07063i	−0.844652	−	0.535316i	$-0.820193\pi$
$421$		−	21.9675i		−	1.07063i	0.844652	−	0.535316i	$-0.179807\pi$
$422$	8.22607	−	10.8176i	0.400439	−	0.526595i
$423$			1.28401i			0.0624306i
$424$	9.84586	−	24.6770i	0.478157	−	1.19842i
$425$	−3.19249	+	10.5431i	−0.154858	+	0.511416i
$426$	21.8992	+	16.6528i	1.06102	+	0.806833i
$427$	13.9978			0.677403
$428$	1.81781	+	6.55523i	0.0878670	+	0.316859i
$429$			3.35751i			0.162102i
$430$	15.3433	+	15.7084i	0.739918	+	0.757527i
$431$	−26.3493			−1.26920			−0.634601	−	0.772840i	$-0.718835\pi$
$431$	−26.3493			−1.26920			−0.634601	+	0.772840i	$0.718835\pi$
$432$	18.5176	−	11.1256i	0.890927	−	0.535282i
$433$			20.1807i			0.969824i	0.874563	+	0.484912i	$0.161148\pi$
$433$			20.1807i			0.969824i	−0.874563	+	0.484912i	$0.838852\pi$
$434$	−1.37254	+	1.80495i	−0.0658841	+	0.0866405i
$435$	1.26641	−	8.55212i	0.0607198	−	0.410043i
$436$	−18.4308	+	5.11097i	−0.882674	+	0.244771i
$437$	32.0841			1.53479
$438$	20.2381	−	26.6140i	0.967013	−	1.27166i
$439$	−1.68685			−0.0805090			−0.0402545	−	0.999189i	$-0.512817\pi$
$439$	−1.68685			−0.0805090			−0.0402545	+	0.999189i	$0.512817\pi$
$440$	3.00808	+	1.74897i	0.143405	+	0.0833788i
$441$	0.266637			0.0126970
$442$	6.96155	−	9.15475i	0.331127	−	0.435447i
$443$	−27.9674			−1.32877			−0.664386	−	0.747390i	$-0.731307\pi$
$443$	−27.9674			−1.32877			−0.664386	+	0.747390i	$0.731307\pi$
$444$	−6.46206	−	23.3030i	−0.306676	−	1.10591i
$445$	−10.8158	−	1.60162i	−0.512718	−	0.0759241i
$446$	15.7451	−	20.7055i	0.745553	−	0.980435i
$447$		−	34.0894i		−	1.61237i
$448$	−5.50713	+	5.80271i	−0.260188	+	0.274152i
$449$	−14.2693			−0.673410			−0.336705	−	0.941610i	$-0.609312\pi$
$449$	−14.2693			−0.673410			−0.336705	+	0.941610i	$0.609312\pi$
$450$	1.10563	+	1.52720i	0.0521201	+	0.0719930i
$451$		−	0.261556i		−	0.0123162i
$452$	−20.0129	+	5.54972i	−0.941330	+	0.261037i
$453$	12.3961			0.582421
$454$	12.0989	+	9.20039i	0.567830	+	0.431796i
$455$	1.20906	−	8.16482i	0.0566816	−	0.382773i
$456$	17.4956	+	6.98056i	0.819308	+	0.326895i
$457$			26.1976i			1.22547i	0.790287	+	0.612737i	$0.209931\pi$
$457$			26.1976i			1.22547i	−0.790287	+	0.612737i	$0.790069\pi$
$458$	−16.7318	+	22.0030i	−0.781825	+	1.02813i
$459$		−	11.8987i		−	0.555381i
$460$	35.3485	−	4.38771i	1.64813	−	0.204578i
$461$			13.1335i			0.611686i	0.952082	+	0.305843i	$0.0989383\pi$
$461$			13.1335i			0.611686i	−0.952082	+	0.305843i	$0.901062\pi$
$462$	−1.02393	−	0.778630i	−0.0476377	−	0.0362252i
$463$		−	0.362997i		−	0.0168699i	−0.999964	−	0.00843494i	$-0.997315\pi$
$463$		−	0.362997i		−	0.0168699i	0.999964	−	0.00843494i	$-0.00268496\pi$
$464$	4.81754	+	8.01835i	0.223649	+	0.372242i
$465$	5.86358	+	0.868289i	0.271917	+	0.0402659i
$466$	−5.64067	+	7.41773i	−0.261299	+	0.343620i
$467$	2.98115			0.137951			0.0689757	−	0.997618i	$-0.478027\pi$
$467$	2.98115			0.137951			0.0689757	+	0.997618i	$0.478027\pi$
$468$	−0.526011	−	1.89686i	−0.0243149	−	0.0876824i
$469$			8.80942i			0.406781i
$470$	−10.8938	+	10.6406i	−0.502493	+	0.490813i
$471$	−19.8080			−0.912704
$472$	−4.51685	−	1.80217i	−0.207905	−	0.0829517i
$473$		−	3.82029i		−	0.175657i
$474$	14.5142	+	11.0370i	0.666657	+	0.506947i
$475$	−5.83706	+	19.2768i	−0.267823	+	0.884478i
$476$	1.17747	+	4.24611i	0.0539693	+	0.194620i
$477$	−2.50465			−0.114680
$478$	−22.5100	−	17.1173i	−1.02958	−	0.782927i
$479$	7.35237			0.335938			0.167969	−	0.985792i	$-0.446279\pi$
$479$	7.35237			0.335938			0.167969	+	0.985792i	$0.446279\pi$
$480$	20.2304	+	5.29816i	0.923385	+	0.241827i
$481$	−26.9955			−1.23089
$482$	−26.7438	−	20.3368i	−1.21815	−	0.926316i
$483$	−13.1681			−0.599171
$484$	5.71712	+	20.6166i	0.259869	+	0.937119i
$485$	6.17401	−	41.6933i	0.280347	−	1.89319i
$486$	−3.10979	−	2.36478i	−0.141063	−	0.107268i
$487$		−	21.7509i		−	0.985626i	−0.870135	−	0.492813i	$-0.835969\pi$
$487$		−	21.7509i		−	0.985626i	0.870135	−	0.492813i	$-0.164031\pi$
$488$	36.7729	+	14.6720i	1.66463	+	0.664170i
$489$	27.2874			1.23398
$490$	2.20962	+	2.26221i	0.0998205	+	0.102196i
$491$			29.5530i			1.33371i	0.745189	+	0.666853i	$0.232359\pi$
$491$			29.5530i			1.33371i	−0.745189	+	0.666853i	$0.767641\pi$
$492$	−0.420067	−	1.51481i	−0.0189381	−	0.0682930i
$493$	5.15227			0.232047
$494$	12.7283	−	16.7383i	0.572675	−	0.753092i
$495$	0.0480500	−	0.324483i	0.00215969	−	0.0145844i
$496$	−5.49761	+	3.30304i	−0.246850	+	0.148311i
$497$			11.7667i			0.527807i
$498$	8.85688	+	6.73505i	0.396886	+	0.301805i
$499$			39.1370i			1.75201i	0.482301	+	0.876006i	$0.339801\pi$
$499$			39.1370i			1.75201i	−0.482301	+	0.876006i	$0.660199\pi$
$500$	−3.79473	+	22.0363i	−0.169706	+	0.985495i
$501$		−	31.3987i		−	1.40279i
$502$	−2.07054	+	2.72285i	−0.0924128	+	0.121527i
$503$			11.0632i			0.493285i	0.969106	+	0.246643i	$0.0793274\pi$
$503$			11.0632i			0.493285i	−0.969106	+	0.246643i	$0.920673\pi$
$504$	0.700468	+	0.279479i	0.0312013	+	0.0124490i
$505$	0.355265	−	2.39912i	0.0158091	−	0.106759i
$506$	−4.93286	−	3.75110i	−0.219292	−	0.166757i
$507$	1.03368			0.0459071
$508$	−34.4207	+	9.54507i	−1.52717	+	0.423494i
$509$		−	33.7020i		−	1.49382i	−0.664927	−	0.746908i	$-0.731537\pi$
$509$		−	33.7020i		−	1.49382i	0.664927	−	0.746908i	$-0.268463\pi$
$510$	8.24003	−	8.04849i	0.364875	−	0.356393i
$511$	14.2999			0.632592
$512$	−20.5497	+	9.47162i	−0.908175	+	0.418590i
$513$		−	21.7552i		−	0.960515i
$514$	−4.01340	+	5.27780i	−0.177023	+	0.232794i
$515$	4.01073	−	27.0846i	0.176734	−	1.19349i
$516$	−6.13552	−	22.1254i	−0.270101	−	0.974017i
$517$	2.64938			0.116519
$518$	6.26046	−	8.23277i	0.275069	−	0.361727i
$519$	−7.58409			−0.332905
$520$	11.7343	−	20.1820i	0.514583	−	0.885041i
$521$	−25.1217			−1.10060			−0.550302	−	0.834966i	$-0.685487\pi$
$521$	−25.1217			−1.10060			−0.550302	+	0.834966i	$0.685487\pi$
$522$	0.533774	−	0.701936i	0.0233627	−	0.0307229i
$523$	14.0217			0.613126			0.306563	−	0.951850i	$-0.400821\pi$
$523$	14.0217			0.613126			0.306563	+	0.951850i	$0.400821\pi$
$524$	20.3923	−	5.65491i	0.890842	−	0.247036i
$525$	2.39568	−	7.91169i	0.104556	−	0.345294i
$526$	−3.43653	+	4.51918i	−0.149840	+	0.197046i
$527$			3.53255i			0.153880i
$528$	−1.87379	−	3.11874i	−0.0815460	−	0.135726i
$529$	−40.4383			−1.75819
$530$	−20.7560	−	21.2499i	−0.901582	−	0.923038i
$531$			0.458447i			0.0198949i
$532$	2.15286	+	7.76347i	0.0933383	+	0.336589i
$533$	−1.75485			−0.0760109
$534$	9.10036	+	6.92019i	0.393811	+	0.299466i
$535$	7.52350	+	1.11409i	0.325269	+	0.0481664i
$536$	−9.23369	+	23.1427i	−0.398835	+	0.999614i
$537$			38.5678i			1.66432i
$538$	16.2231	−	21.3340i	0.699426	−	0.919776i
$539$		−	0.550169i		−	0.0236975i
$540$	−2.97517	−	23.9687i	−0.128031	−	1.03145i
$541$		−	25.9463i		−	1.11552i	−0.830003	−	0.557759i	$-0.811661\pi$
$541$		−	25.9463i		−	1.11552i	0.830003	−	0.557759i	$-0.188339\pi$
$542$	−29.6286	−	22.5305i	−1.27266	−	0.967769i
$543$		−	5.69198i		−	0.244266i
$544$	−1.35734	+	12.3889i	−0.0581953	+	0.531169i
$545$	−3.13240	+	21.1532i	−0.134177	+	0.906103i
$546$	−5.22404	+	6.86984i	−0.223568	+	0.294002i
$547$	36.2809			1.55126			0.775629	−	0.631189i	$-0.217433\pi$
$547$	36.2809			1.55126			0.775629	+	0.631189i	$0.217433\pi$
$548$	0.0718548	−	0.0199258i	0.00306949	−	0.000851188i
$549$		−	3.73234i		−	0.159293i
$550$	3.15117	−	2.28132i	0.134366	−	0.0972759i
$551$	9.42028			0.401318
$552$	−34.5933	−	13.8023i	−1.47239	−	0.587466i
$553$			7.79860i			0.331630i
$554$	20.4862	+	15.5783i	0.870374	+	0.661860i
$555$	−26.7450	−	3.96045i	−1.13526	−	0.168112i
$556$	−7.92472	+	2.19757i	−0.336083	+	0.0931979i
$557$	13.7294			0.581732			0.290866	−	0.956764i	$-0.406057\pi$
$557$	13.7294			0.581732			0.290866	+	0.956764i	$0.406057\pi$
$558$	0.481268	+	0.365971i	0.0203737	+	0.0154928i
$559$	−25.6314			−1.08409
$560$	3.43361	+	8.25895i	0.145097	+	0.349004i
$561$	−2.00398			−0.0846081
$562$	−29.0471	−	22.0883i	−1.22528	−	0.931739i
$563$	−21.5815			−0.909553			−0.454777	−	0.890606i	$-0.650281\pi$
$563$	−21.5815			−0.909553			−0.454777	+	0.890606i	$0.650281\pi$
$564$	15.3440	−	4.25498i	0.646098	−	0.179167i
$565$	−3.40130	+	22.9691i	−0.143094	+	0.966316i
$566$	−25.3086	−	19.2454i	−1.06380	−	0.808945i
$567$			8.12899i			0.341386i
$568$	−12.3334	+	30.9116i	−0.517497	+	1.29702i
$569$	−3.01571			−0.126425			−0.0632127	−	0.998000i	$-0.520135\pi$
$569$	−3.01571			−0.126425			−0.0632127	+	0.998000i	$0.520135\pi$
$570$	15.0659	−	14.7157i	0.631040	−	0.616371i
$571$			4.82021i			0.201720i	0.994901	+	0.100860i	$0.0321593\pi$
$571$			4.82021i			0.201720i	−0.994901	+	0.100860i	$0.967841\pi$
$572$	−3.91391	+	1.08535i	−0.163649	+	0.0453808i
$573$	−5.73290			−0.239495
$574$	0.406962	−	0.535172i	0.0169863	−	0.0223377i
$575$	11.5414	−	38.1150i	0.481308	−	1.58951i
$576$	1.54722	+	1.46841i	0.0644675	+	0.0611836i
$577$		−	40.7032i		−	1.69450i	−0.531197	−	0.847248i	$-0.678258\pi$
$577$		−	40.7032i		−	1.69450i	0.531197	−	0.847248i	$-0.321742\pi$
$578$	−13.6729	−	10.3973i	−0.568718	−	0.432471i
$579$		−	26.2162i		−	1.08951i
$580$	10.3788	−	1.28829i	0.430954	−	0.0534933i
$581$			4.75889i			0.197432i
$582$	−26.6763	+	35.0805i	−1.10577	+	1.45413i
$583$			5.16799i			0.214036i
$584$	37.5666	+	14.9887i	1.55452	+	0.620235i
$585$	−2.17705	−	0.322381i	−0.0900098	−	0.0133288i
$586$	0.993723	+	0.755658i	0.0410503	+	0.0312159i
$587$	−17.5616			−0.724844			−0.362422	−	0.932014i	$-0.618050\pi$
$587$	−17.5616			−0.724844			−0.362422	+	0.932014i	$0.618050\pi$
$588$	−0.883590	−	3.18633i	−0.0364386	−	0.131402i
$589$			6.45882i			0.266131i
$590$	−3.88956	+	3.79915i	−0.160131	+	0.156408i
$591$	−5.56072			−0.228737
$592$	25.0758	−	15.0659i	1.03061	−	0.619204i
$593$			46.7165i			1.91842i	0.282699	+	0.959209i	$0.408770\pi$
$593$			46.7165i			1.91842i	−0.282699	+	0.959209i	$0.591230\pi$
$594$	−2.54350	+	3.34482i	−0.104361	+	0.137240i
$595$	4.87330	+	0.721646i	0.199786	+	0.0295846i
$596$	39.7387	−	11.0198i	1.62776	−	0.451388i
$597$	25.2202			1.03219
$598$	−25.1671	+	33.0959i	−1.02916	+	1.35339i
$599$	10.6823			0.436465			0.218233	−	0.975897i	$-0.429971\pi$
$599$	10.6823			0.436465			0.218233	+	0.975897i	$0.429971\pi$
$600$	14.5863	−	18.2733i	0.595483	−	0.746003i
$601$	−15.0541			−0.614070			−0.307035	−	0.951698i	$-0.599337\pi$
$601$	−15.0541			−0.614070			−0.307035	+	0.951698i	$0.599337\pi$
$602$	5.94411	−	7.81676i	0.242264	−	0.318587i
$603$	2.34892			0.0956554
$604$	4.00719	+	14.4504i	0.163050	+	0.587979i
$605$	23.6619	+	3.50389i	0.961993	+	0.142454i
$606$	−1.53501	+	2.01861i	−0.0623556	+	0.0820003i
$607$			14.3664i			0.583114i	0.956553	+	0.291557i	$0.0941734\pi$
$607$			14.3664i			0.583114i	−0.956553	+	0.291557i	$0.905827\pi$
$608$	−2.48172	+	22.6515i	−0.100647	+	0.918641i
$609$	−3.86633			−0.156672
$610$	31.6660	−	30.9299i	1.28212	−	1.25231i
$611$		−	17.7754i		−	0.719115i
$612$	1.13217	−	0.313958i	0.0457653	−	0.0126910i
$613$	3.00757			0.121474			0.0607372	−	0.998154i	$-0.480655\pi$
$613$	3.00757			0.121474			0.0607372	+	0.998154i	$0.480655\pi$
$614$	−12.2351	−	9.30398i	−0.493770	−	0.375478i
$615$	−1.73856	−	0.257450i	−0.0701057	−	0.0103814i
$616$	0.576666	−	1.44532i	0.0232346	−	0.0582336i
$617$			32.6161i			1.31307i	0.754294	+	0.656537i	$0.227979\pi$
$617$			32.6161i			1.31307i	−0.754294	+	0.656537i	$0.772021\pi$
$618$	−17.3294	+	22.7889i	−0.697089	+	0.916703i
$619$		−	13.6950i		−	0.550448i	−0.961380	−	0.275224i	$-0.911248\pi$
$619$		−	13.6950i		−	0.550448i	0.961380	−	0.275224i	$-0.0887520\pi$
$620$	0.883288	+	7.11597i	0.0354737	+	0.285784i
$621$			43.0155i			1.72615i
$622$	−18.8632	−	14.3442i	−0.756345	−	0.575148i
$623$			4.88971i			0.195902i
$624$	−20.9245	+	12.5717i	−0.837650	+	0.503272i
$625$	20.8006	+	13.8686i	0.832022	+	0.554742i
$626$	−28.5019	+	37.4813i	−1.13917	+	1.49805i
$627$	−3.66403			−0.146327
$628$	−6.40315	−	23.0906i	−0.255514	−	0.921413i
$629$		−	16.1127i		−	0.642455i
$630$	0.603189	−	0.589167i	0.0240316	−	0.0234730i
$631$	−28.1184			−1.11937			−0.559687	−	0.828704i	$-0.689079\pi$
$631$	−28.1184			−1.11937			−0.559687	+	0.828704i	$0.689079\pi$
$632$	−8.17419	+	20.4873i	−0.325152	+	0.814939i
$633$			15.8875i			0.631470i
$634$	−21.6569	−	16.4686i	−0.860105	−	0.654050i
$635$	−5.84996	+	39.5050i	−0.232149	+	1.56771i
$636$	8.29996	+	29.9307i	0.329115	+	1.18683i
$637$	−3.69124			−0.146252
$638$	−1.44835	−	1.10137i	−0.0573407	−	0.0436036i
$639$	3.13743			0.124115
$640$	0.363529	+	25.2956i	0.0143697	+	0.999897i
$641$	20.4015			0.805812			0.402906	−	0.915241i	$-0.368000\pi$
$641$	20.4015			0.805812			0.402906	+	0.915241i	$0.368000\pi$
$642$	−6.33024	−	4.81371i	−0.249835	−	0.189982i
$643$	−25.4312			−1.00291			−0.501454	−	0.865184i	$-0.667201\pi$
$643$	−25.4312			−1.00291			−0.501454	+	0.865184i	$0.667201\pi$
$644$	−4.25675	−	15.3504i	−0.167739	−	0.604889i
$645$	−25.3936	−	3.76032i	−0.999871	−	0.148063i
$646$	9.99052	+	7.59710i	0.393072	+	0.298904i
$647$			12.1998i			0.479625i	0.970819	+	0.239813i	$0.0770860\pi$
$647$			12.1998i			0.479625i	−0.970819	+	0.239813i	$0.922914\pi$
$648$	−8.52050	+	21.3552i	−0.334717	+	0.838912i
$649$	0.945942			0.0371315
$650$	−15.3060	−	21.1421i	−0.600351	−	0.829260i
$651$		−	2.65087i		−	0.103896i
$652$	8.82095	+	31.8094i	0.345455	+	1.24575i
$653$	−29.7908			−1.16581			−0.582903	−	0.812542i	$-0.698083\pi$
$653$	−29.7908			−1.16581			−0.582903	+	0.812542i	$0.698083\pi$
$654$	13.5343	−	17.7982i	0.529233	−	0.695965i
$655$	3.46577	−	23.4044i	0.135419	−	0.914487i
$656$	1.63005	−	0.979360i	0.0636429	−	0.0382376i
$657$		−	3.81290i		−	0.148755i
$658$	5.42093	+	4.12224i	0.211330	+	0.160702i
$659$			12.5844i			0.490219i	0.969495	+	0.245109i	$0.0788239\pi$
$659$			12.5844i			0.490219i	−0.969495	+	0.245109i	$0.921176\pi$
$660$	−4.03682	+	0.501081i	−0.157133	+	0.0195045i
$661$		−	36.0309i		−	1.40144i	−0.713436	−	0.700720i	$-0.752862\pi$
$661$		−	36.0309i		−	1.40144i	0.713436	−	0.700720i	$-0.247138\pi$
$662$	4.34990	−	5.72030i	0.169064	−	0.222326i
$663$			13.4452i			0.522170i
$664$	−4.98809	+	12.5018i	−0.193575	+	0.485165i
$665$	8.91022	+	1.31944i	0.345523	+	0.0511657i
$666$	−2.19516	−	1.66927i	−0.0850609	−	0.0646830i
$667$	−18.6263			−0.721213
$668$	36.6021	−	10.1500i	1.41618	−	0.392715i
$669$			30.4094i			1.17570i
$670$	19.4655	+	19.9287i	0.752017	+	0.769914i
$671$	−7.70118			−0.297301
$672$	1.01856	−	9.29678i	0.0392919	−	0.358631i
$673$		−	14.7199i		−	0.567411i	−0.958911	−	0.283706i	$-0.908436\pi$
$673$		−	14.7199i		−	0.567411i	0.958911	−	0.283706i	$-0.0915639\pi$
$674$	6.82071	−	8.96953i	0.262724	−	0.345493i
$675$	−25.8446	−	7.82583i	−0.994759	−	0.301216i
$676$	0.334147	+	1.20498i	0.0128518	+	0.0463452i
$677$	−8.03421			−0.308780			−0.154390	−	0.988010i	$-0.549341\pi$
$677$	−8.03421			−0.308780			−0.154390	+	0.988010i	$0.549341\pi$
$678$	14.6961	−	19.3261i	0.564402	−	0.742213i
$679$	−18.8491			−0.723363
$680$	12.0460	+	7.00380i	0.461942	+	0.268583i
$681$	−17.7692			−0.680919
$682$	0.755131	−	0.993030i	0.0289155	−	0.0380251i
$683$	−44.8772			−1.71718			−0.858589	−	0.512665i	$-0.828658\pi$
$683$	−44.8772			−1.71718			−0.858589	+	0.512665i	$0.828658\pi$
$684$	2.07003	−	0.574033i	0.0791496	−	0.0219487i
$685$	0.0122121	−	0.0824685i	0.000466600	−	0.00315096i
$686$	0.856025	−	1.12571i	0.0326832	−	0.0429798i
$687$		−	32.3150i		−	1.23290i
$688$	23.8087	−	14.3046i	0.907696	−	0.545357i
$689$	34.6735			1.32095
$690$	−29.7890	+	29.0966i	−1.13405	+	1.10769i
$691$			19.6063i			0.745858i	0.927860	+	0.372929i	$0.121647\pi$
$691$			19.6063i			0.745858i	−0.927860	+	0.372929i	$0.878353\pi$
$692$	−2.45164	−	8.84092i	−0.0931975	−	0.336082i
$693$	−0.146696			−0.00557251
$694$	−13.5215	−	10.2821i	−0.513268	−	0.390305i
$695$	−1.34684	+	9.09528i	−0.0510887	+	0.345004i
$696$	−10.1570	−	4.05254i	−0.385001	−	0.153611i
$697$		−	1.04741i		−	0.0396734i
$698$	−3.33729	+	4.38869i	−0.126318	+	0.166114i
$699$		−	10.8942i		−	0.412055i
$700$	9.99723	+	0.235154i	0.377860	+	0.00888798i
$701$			29.8316i			1.12672i	0.826210	+	0.563362i	$0.190492\pi$
$701$			29.8316i			1.12672i	−0.826210	+	0.563362i	$0.809508\pi$
$702$	22.4413	+	17.0651i	0.846992	+	0.644079i
$703$		−	29.4600i		−	1.11111i
$704$	3.02986	−	3.19248i	0.114192	−	0.120321i
$705$	2.60779	−	17.6105i	0.0982149	−	0.663248i
$706$	11.5414	−	15.1775i	0.434367	−	0.571212i
$707$	−1.08462			−0.0407913
$708$	5.47847	−	1.51921i	0.205894	−	0.0570956i
$709$			30.6524i			1.15118i	0.817740	+	0.575588i	$0.195227\pi$
$709$			30.6524i			1.15118i	−0.817740	+	0.575588i	$0.804773\pi$
$710$	25.9999	+	26.6186i	0.975758	+	0.998980i
$711$	2.07940			0.0779835
$712$	−5.12521	+	12.8455i	−0.192075	+	0.481405i
$713$		−	12.7707i		−	0.478267i
$714$	−4.10037	−	3.11805i	−0.153453	−	0.116690i
$715$	−0.665188	+	4.49203i	−0.0248766	+	0.167993i
$716$	−44.9592	+	12.4675i	−1.68020	+	0.465931i
$717$	33.0596			1.23463
$718$	29.1149	+	22.1399i	1.08656	+	0.826252i
$719$	0.461162			0.0171984			0.00859922	−	0.999963i	$-0.497263\pi$
$719$	0.461162			0.0171984			0.00859922	+	0.999963i	$0.497263\pi$
$720$	2.20215	−	0.915529i	0.0820691	−	0.0341198i
$721$	−12.2447			−0.456016
$722$	−3.12206	−	2.37411i	−0.116191	−	0.0883554i
$723$	39.2776			1.46075
$724$	6.63525	−	1.84000i	0.246597	−	0.0683829i
$725$	3.38869	−	11.1910i	0.125853	−	0.415625i
$726$	−19.9090	−	15.1394i	−0.738893	−	0.561877i
$727$			15.3149i			0.567999i	0.958824	+	0.283999i	$0.0916614\pi$
$727$			15.3149i			0.567999i	−0.958824	+	0.283999i	$0.908339\pi$
$728$	−9.69704	−	3.86901i	−0.359396	−	0.143395i
$729$	28.9542			1.07238
$730$	32.3494	−	31.5975i	1.19731	−	1.16947i
$731$		−	15.2985i		−	0.565835i
$732$	−44.6018	+	12.3683i	−1.64853	+	0.457147i
$733$	−8.36691			−0.309039			−0.154520	−	0.987990i	$-0.549383\pi$
$733$	−8.36691			−0.309039			−0.154520	+	0.987990i	$0.549383\pi$
$734$	1.08492	−	1.42672i	0.0400453	−	0.0526613i
$735$	−3.65699	−	0.541533i	−0.134890	−	0.0199747i
$736$	4.90699	−	44.7878i	0.180874	−	1.65090i
$737$		−	4.84667i		−	0.178529i
$738$	−0.142697	−	0.108511i	−0.00525275	−	0.00399435i
$739$		−	9.03974i		−	0.332532i	−0.986081	−	0.166266i	$-0.946829\pi$
$739$		−	9.03974i		−	0.332532i	0.986081	−	0.166266i	$-0.0531711\pi$
$740$	−4.02886	−	32.4575i	−0.148104	−	1.19316i
$741$			24.5829i			0.903077i
$742$	−8.04103	+	10.5743i	−0.295195	+	0.388195i
$743$		−	34.5685i		−	1.26820i	−0.773253	−	0.634098i	$-0.781372\pi$
$743$		−	34.5685i		−	1.26820i	0.773253	−	0.634098i	$-0.218628\pi$
$744$	2.77854	−	6.96395i	0.101866	−	0.255311i
$745$	6.75378	−	45.6085i	0.247440	−	1.67097i
$746$	21.2339	+	16.1469i	0.777430	+	0.591182i
$747$	1.26890			0.0464266
$748$	−0.647809	−	2.33608i	−0.0236862	−	0.0854154i
$749$		−	3.40130i		−	0.124281i
$750$	−12.0623	−	23.1914i	−0.440453	−	0.846831i
$751$	19.2651			0.702993			0.351496	−	0.936189i	$-0.385673\pi$
$751$	19.2651			0.702993			0.351496	+	0.936189i	$0.385673\pi$
$752$	9.92023	+	16.5113i	0.361754	+	0.602105i
$753$		−	3.99895i		−	0.145730i
$754$	−7.38939	+	9.71737i	−0.269106	+	0.353886i
$755$	16.5849	+	2.45592i	0.603586	+	0.0893800i
$756$	−10.4086	+	2.88637i	−0.378557	+	0.104976i
$757$	23.8714			0.867621			0.433810	−	0.901004i	$-0.357169\pi$
$757$	23.8714			0.867621			0.433810	+	0.901004i	$0.357169\pi$
$758$	−8.07748	+	10.6222i	−0.293387	+	0.385817i
$759$	7.24471			0.262966
$760$	22.0245	+	12.8056i	0.798914	+	0.464507i
$761$	2.39911			0.0869677			0.0434839	−	0.999054i	$-0.486154\pi$
$761$	2.39911			0.0869677			0.0434839	+	0.999054i	$0.486154\pi$
$762$	25.2762	−	33.2393i	0.915660	−	1.20413i
$763$	9.56316			0.346209
$764$	−1.85322	−	6.68295i	−0.0670472	−	0.241781i
$765$	0.192418	−	1.29940i	0.00695688	−	0.0469800i
$766$	−12.1116	+	15.9272i	−0.437609	+	0.575474i
$767$		−	6.34658i		−	0.229162i
$768$	12.4203	−	23.3554i	0.448180	−	0.842766i
$769$	16.4385			0.592786			0.296393	−	0.955066i	$-0.404216\pi$
$769$	16.4385			0.592786			0.296393	+	0.955066i	$0.404216\pi$
$770$	−1.21567	−	1.24460i	−0.0438096	−	0.0448522i
$771$		−	7.75131i		−	0.279156i
$772$	30.5607	−	8.47467i	1.09990	−	0.305010i
$773$	−42.0326			−1.51181			−0.755904	−	0.654683i	$-0.772802\pi$
$773$	−42.0326			−1.51181			−0.755904	+	0.654683i	$0.772802\pi$
$774$	−2.08424	−	1.58492i	−0.0749164	−	0.0569688i
$775$	7.67291	+	2.32338i	0.275619	+	0.0834583i
$776$	−49.5175	−	19.7569i	−1.77757	−	0.709232i
$777$			12.0912i			0.433768i
$778$	−4.89332	+	6.43493i	−0.175434	+	0.230703i
$779$		−	1.91505i		−	0.0686139i
$780$	3.36189	+	27.0842i	0.120375	+	0.969768i
$781$		−	6.47366i		−	0.231646i
$782$	−19.7538	−	15.0214i	−0.706394	−	0.537164i
$783$			12.6299i			0.451356i
$784$	3.42874	−	2.06004i	0.122455	−	0.0735727i
$785$	−26.5013	−	3.92435i	−0.945871	−	0.140066i
$786$	−14.9747	+	19.6924i	−0.534130	+	0.702405i
$787$	−23.5230			−0.838505			−0.419252	−	0.907870i	$-0.637708\pi$
$787$	−23.5230			−0.838505			−0.419252	+	0.907870i	$0.637708\pi$
$788$	−1.79756	−	6.48224i	−0.0640356	−	0.230920i
$789$		−	6.63716i		−	0.236289i
$790$	17.2319	+	17.6420i	0.613085	+	0.627676i
$791$	10.3841			0.369216
$792$	−0.385376	−	0.153761i	−0.0136937	−	0.00546365i
$793$			51.6693i			1.83483i
$794$	−20.3145	−	15.4478i	−0.720934	−	0.548221i
$795$	34.3517	+	5.08686i	1.21833	+	0.180412i
$796$	8.15270	+	29.3996i	0.288965	+	1.04204i
$797$	4.18337			0.148183			0.0740913	−	0.997251i	$-0.476394\pi$
$797$	4.18337			0.148183			0.0740913	+	0.997251i	$0.476394\pi$
$798$	−7.49702	−	5.70096i	−0.265392	−	0.201812i
$799$	10.6095			0.375337
$800$	26.0167	+	11.0965i	0.919829	+	0.392320i
$801$	1.30378			0.0460668
$802$	−27.0639	−	20.5802i	−0.955659	−	0.726713i
$803$	−7.86739			−0.277634
$804$	−7.78392	−	28.0697i	−0.274518	−	0.989944i
$805$	−17.6178	−	2.60887i	−0.620944	−	0.0919505i
$806$	−6.66251	−	5.06638i	−0.234677	−	0.178456i
$807$			31.3325i			1.10296i
$808$	−2.84934	−	1.13686i	−0.100239	−	0.0399944i
$809$	29.8081			1.04800			0.523999	−	0.851719i	$-0.324440\pi$
$809$	29.8081			1.04800			0.523999	+	0.851719i	$0.324440\pi$
$810$	17.9620	+	18.3895i	0.631120	+	0.646140i
$811$			9.92022i			0.348346i	0.984715	+	0.174173i	$0.0557252\pi$
$811$			9.92022i			0.348346i	−0.984715	+	0.174173i	$0.944275\pi$
$812$	−1.24983	−	4.50706i	−0.0438606	−	0.158167i
$813$	43.5145			1.52612
$814$	−3.44431	+	4.52942i	−0.120723	+	0.158756i
$815$	36.5080	+	5.40616i	1.27882	+	0.189370i
$816$	−7.50363	−	12.4891i	−0.262680	−	0.437206i
$817$		−	27.9714i		−	0.978595i
$818$	42.4170	+	32.2552i	1.48308	+	1.12778i
$819$			0.984221i			0.0343915i
$820$	−0.261897	−	2.10990i	−0.00914583	−	0.0736810i
$821$		−	13.5600i		−	0.473246i	−0.971602	−	0.236623i	$-0.923959\pi$
$821$		−	13.5600i		−	0.473246i	0.971602	−	0.236623i	$-0.0760405\pi$
$822$	−0.0527653	+	0.0693887i	−0.00184040	+	0.00242021i
$823$			20.9059i			0.728734i	0.931255	+	0.364367i	$0.118715\pi$
$823$			20.9059i			0.728734i	−0.931255	+	0.364367i	$0.881285\pi$
$824$	−32.1673	−	12.8344i	−1.12060	−	0.447108i
$825$	−1.31803	+	4.35277i	−0.0458880	+	0.151544i
$826$	1.93551	+	1.47182i	0.0673449	+	0.0512111i
$827$	27.4305			0.953853			0.476926	−	0.878943i	$-0.341751\pi$
$827$	27.4305			0.953853			0.476926	+	0.878943i	$0.341751\pi$
$828$	−4.09298	+	1.13501i	−0.142241	+	0.0394443i
$829$		−	1.30703i		−	0.0453950i	−0.999742	−	0.0226975i	$-0.992775\pi$
$829$		−	1.30703i		−	0.0453950i	0.999742	−	0.0226975i	$-0.00722546\pi$
$830$	10.5153	+	10.7656i	0.364993	+	0.373679i
$831$	−30.0873			−1.04372
$832$	−21.4192	−	20.3281i	−0.742577	−	0.704751i
$833$		−	2.20317i		−	0.0763353i
$834$	5.81937	−	7.65273i	0.201508	−	0.264992i
$835$	6.22070	−	42.0086i	0.215276	−	1.45377i
$836$	−1.18444	−	4.27123i	−0.0409646	−	0.147723i
$837$	−8.65943			−0.299314
$838$	13.4443	−	17.6798i	0.464424	−	0.610738i
$839$	35.7061			1.23271			0.616357	−	0.787467i	$-0.288608\pi$
$839$	35.7061			1.23271			0.616357	+	0.787467i	$0.288608\pi$
$840$	−9.03945	−	5.25574i	−0.311891	−	0.181340i
$841$	23.5311			0.811417
$842$	−18.8047	+	24.7291i	−0.648054	+	0.852220i
$843$	42.6604			1.46930
$844$	−18.5203	+	5.13580i	−0.637496	+	0.176782i
$845$	1.38296	+	0.204791i	0.0475754	+	0.00704504i
$846$	1.09914	−	1.44542i	0.0377893	−	0.0496946i
$847$		−	10.6973i		−	0.367564i
$848$	−32.2077	+	19.3509i	−1.10602	+	0.664511i
$849$	37.1697			1.27566
$850$	12.6190	−	9.13563i	0.432827	−	0.313349i
$851$			58.2500i			1.99678i
$852$	−10.3969	−	37.4925i	−0.356192	−	1.28447i
$853$	46.1892			1.58149			0.790743	−	0.612148i	$-0.209694\pi$
$853$	46.1892			1.58149			0.790743	+	0.612148i	$0.209694\pi$
$854$	−15.7575	−	11.9825i	−0.539210	−	0.410032i
$855$	0.351812	−	2.37580i	0.0120317	−	0.0812505i
$856$	3.56511	−	8.93537i	0.121853	−	0.305405i
$857$			4.16422i			0.142247i	0.997468	+	0.0711235i	$0.0226584\pi$
$857$			4.16422i			0.142247i	−0.997468	+	0.0711235i	$0.977342\pi$
$858$	2.87411	−	3.77958i	0.0981204	−	0.129033i
$859$		−	32.9477i		−	1.12416i	−0.827083	−	0.562080i	$-0.810001\pi$
$859$		−	32.9477i		−	1.12416i	0.827083	−	0.562080i	$-0.189999\pi$
$860$	−3.82528	−	30.8173i	−0.130441	−	1.05086i
$861$			0.785988i			0.0267864i
$862$	29.6617	+	22.5557i	1.01028	+	0.768249i
$863$		−	39.6266i		−	1.34890i	−0.738319	−	0.674452i	$-0.764380\pi$
$863$		−	39.6266i		−	1.34890i	0.738319	−	0.674452i	$-0.235620\pi$
$864$	−30.3692	−	3.32727i	−1.03318	−	0.113196i
$865$	−10.1468	−	1.50256i	−0.345002	−	0.0510885i
$866$	17.2752	−	22.7176i	0.587035	−	0.771977i
$867$	20.0809			0.681983
$868$	3.09017	−	0.856923i	0.104887	−	0.0290859i
$869$		−	4.29055i		−	0.145547i
$870$	−8.74644	+	8.54313i	−0.296532	+	0.289639i
$871$	−32.5176			−1.10182
$872$	25.1228	+	10.0237i	0.850766	+	0.339446i
$873$			5.02588i			0.170100i
$874$	−36.1173	−	27.4647i	−1.22169	−	0.929009i
$875$	4.77266	−	10.1105i	0.161346	−	0.341796i
$876$	−45.5644	+	12.6353i	−1.53948	+	0.426907i
$877$	−21.3872			−0.722194			−0.361097	−	0.932528i	$-0.617598\pi$
$877$	−21.3872			−0.722194			−0.361097	+	0.932528i	$0.617598\pi$
$878$	1.89890	+	1.44399i	0.0640849	+	0.0487322i
$879$	−1.45944			−0.0492258
$880$	−1.88907	−	4.54382i	−0.0636805	−	0.153172i
$881$	−38.5221			−1.29784			−0.648922	−	0.760855i	$-0.724780\pi$
$881$	−38.5221			−1.29784			−0.648922	+	0.760855i	$0.724780\pi$
$882$	−0.300156	−	0.228248i	−0.0101068	−	0.00768551i
$883$	−15.8933			−0.534852			−0.267426	−	0.963578i	$-0.586173\pi$
$883$	−15.8933			−0.534852			−0.267426	+	0.963578i	$0.586173\pi$
$884$	−15.6734	+	4.34633i	−0.527153	+	0.146183i
$885$	0.931093	−	6.28770i	0.0312983	−	0.211359i
$886$	31.4832	+	23.9408i	1.05770	+	0.804306i
$887$			7.62497i			0.256022i	0.991773	+	0.128011i	$0.0408592\pi$
$887$			7.62497i			0.256022i	−0.991773	+	0.128011i	$0.959141\pi$
$888$	−12.6735	+	31.7640i	−0.425295	+	1.06593i
$889$	17.8598			0.598999
$890$	10.8044	+	11.0615i	0.362165	+	0.370784i
$891$		−	4.47232i		−	0.149828i
$892$	−35.4489	+	9.83020i	−1.18692	+	0.329139i
$893$	19.3982			0.649135
$894$	−29.1814	+	38.3748i	−0.975972	+	1.28345i
$895$	−7.64103	+	51.6001i	−0.255411	+	1.72480i
$896$	11.1667	−	1.81793i	0.373053	−	0.0607328i
$897$		−	48.6067i		−	1.62293i
$898$	16.0631	+	12.2149i	0.536032	+	0.407615i
$899$		−	3.74964i		−	0.125058i
$900$	0.0627008	−	2.66564i	0.00209003	−	0.0888545i
$901$			20.6954i			0.689463i
$902$	−0.223898	+	0.294436i	−0.00745499	+	0.00980363i
$903$			11.4802i			0.382037i
$904$	27.2795	+	10.8842i	0.907301	+	0.362003i
$905$	1.12769	−	7.61534i	0.0374858	−	0.253143i
$906$	−13.9544	−	10.6114i	−0.463605	−	0.352540i
$907$	42.4519			1.40959			0.704796	−	0.709410i	$-0.251038\pi$
$907$	42.4519			1.40959			0.704796	+	0.709410i	$0.251038\pi$
$908$	−5.74411	−	20.7139i	−0.190625	−	0.687416i
$909$			0.289200i			0.00959215i
$910$	−8.35034	+	8.15623i	−0.276811	+	0.270376i
$911$	3.08759			0.102296			0.0511481	−	0.998691i	$-0.483712\pi$
$911$	3.08759			0.102296			0.0511481	+	0.998691i	$0.483712\pi$
$912$	−13.7195	−	22.8348i	−0.454297	−	0.756135i
$913$		−	2.61820i		−	0.0866497i
$914$	22.4258	−	29.4909i	0.741780	−	0.975473i
$915$	−7.58028	+	51.1899i	−0.250596	+	1.69229i
$916$	37.6702	−	10.4462i	1.24466	−	0.345152i
$917$	−10.5809			−0.349413
$918$	−10.1855	+	13.3944i	−0.336173	+	0.442082i
$919$	8.34302			0.275211			0.137605	−	0.990487i	$-0.456059\pi$
$919$	8.34302			0.275211			0.137605	+	0.990487i	$0.456059\pi$
$920$	−43.5481	−	25.3199i	−1.43574	−	0.834771i
$921$	17.9693			0.592108
$922$	11.2426	−	14.7845i	0.370254	−	0.486900i
$923$	−43.4336			−1.42963
$924$	0.486124	+	1.75302i	0.0159923	+	0.0576702i
$925$	−34.9978	−	10.5974i	−1.15072	−	0.348441i
$926$	−0.310734	+	0.408629i	−0.0102113	+	0.0134284i
$927$			3.26489i			0.107233i
$928$	1.44075	−	13.1503i	0.0472950	−	0.431678i
$929$	33.3126			1.09295			0.546475	−	0.837475i	$-0.315969\pi$
$929$	33.3126			1.09295			0.546475	+	0.837475i	$0.315969\pi$
$930$	−5.85741	−	5.99681i	−0.192072	−	0.196643i
$931$		−	4.02822i		−	0.132020i
$932$	12.6995	−	3.52166i	0.415987	−	0.115356i
$933$	27.7037			0.906978
$934$	−3.35591	−	2.55194i	−0.109809	−	0.0835020i
$935$	−2.68114	−	0.397028i	−0.0876826	−	0.0129842i
$936$	−1.03162	+	2.58559i	−0.0337197	+	0.0845127i
$937$			21.5635i			0.704450i	0.935915	+	0.352225i	$0.114575\pi$
$937$			21.5635i			0.704450i	−0.935915	+	0.352225i	$0.885425\pi$
$938$	7.54108	−	9.91685i	0.246225	−	0.323797i
$939$		−	55.0474i		−	1.79640i
$940$	21.3718	−	2.65283i	0.697072	−	0.0865258i
$941$		−	33.4094i		−	1.08912i	−0.838723	−	0.544558i	$-0.816697\pi$
$941$		−	33.4094i		−	1.08912i	0.838723	−	0.544558i	$-0.183303\pi$
$942$	22.2980	+	16.9561i	0.726509	+	0.552460i
$943$			3.78655i			0.123307i
$944$	3.54196	+	5.89526i	0.115281	+	0.191874i
$945$	−1.76899	+	11.9461i	−0.0575453	+	0.388605i
$946$	−3.27027	+	4.30054i	−0.106326	+	0.139823i
$947$	50.9748			1.65646			0.828229	−	0.560390i	$-0.189349\pi$
$947$	50.9748			1.65646			0.828229	+	0.560390i	$0.189349\pi$
$948$	−6.89077	−	24.8489i	−0.223802	−	0.807056i
$949$			52.7845i			1.71346i
$950$	23.0722	−	16.7034i	0.748561	−	0.541928i
$951$	31.8067			1.03140
$952$	2.30928	−	5.78783i	0.0748442	−	0.187585i
$953$		−	60.7280i		−	1.96717i	−0.180434	−	0.983587i	$-0.557750\pi$
$953$		−	60.7280i		−	1.96717i	0.180434	−	0.983587i	$-0.442250\pi$
$954$	2.81950	+	2.14404i	0.0912848	+	0.0694158i
$955$	−7.67009	−	1.13580i	−0.248198	−	0.0367536i
$956$	10.6869	+	38.5382i	0.345639	+	1.24642i
$957$	2.12714			0.0687606
$958$	−8.27664	−	6.29381i	−0.267406	−	0.203344i
$959$	−0.0372832			−0.00120394
$960$	−18.2382	−	23.2819i	−0.588634	−	0.751419i
$961$	−28.4291			−0.917069
$962$	30.3891	+	23.1088i	0.979784	+	0.745058i
$963$	−0.906914			−0.0292249
$964$	12.6969	+	45.7867i	0.408941	+	1.47469i
$965$	5.19394	−	35.0748i	0.167199	−	1.12910i
$966$	14.8235	+	11.2722i	0.476938	+	0.362679i
$967$			4.76598i			0.153264i	0.997059	+	0.0766318i	$0.0244166\pi$
$967$			4.76598i			0.153264i	−0.997059	+	0.0766318i	$0.975583\pi$
$968$	11.2125	−	28.1023i	0.360384	−	0.903242i
$969$	−14.6727			−0.471355
$970$	−42.6406	+	41.6494i	−1.36911	+	1.33728i
$971$		−	4.30605i		−	0.138188i	−0.997610	−	0.0690939i	$-0.977989\pi$
$971$		−	4.30605i		−	0.138188i	0.997610	−	0.0690939i	$-0.0220108\pi$
$972$	1.47641	+	5.32411i	0.0473558	+	0.170771i
$973$	4.11189			0.131821
$974$	−18.6193	+	24.4852i	−0.596600	+	0.784555i
$975$	29.2039	+	8.84304i	0.935273	+	0.283204i
$976$	−28.8360	−	47.9949i	−0.923019	−	1.53628i
$977$		−	33.6691i		−	1.07717i	−0.842571	−	0.538585i	$-0.818959\pi$
$977$		−	33.6691i		−	1.07717i	0.842571	−	0.538585i	$-0.181041\pi$
$978$	−30.7176	−	23.3586i	−0.982242	−	0.746927i
$979$		−	2.69017i		−	0.0859782i
$980$	−0.550887	−	4.43808i	−0.0175974	−	0.141769i
$981$		−	2.54989i		−	0.0814119i
$982$	25.2981	−	33.2681i	0.807294	−	1.06163i
$983$		−	46.6521i		−	1.48797i	−0.668195	−	0.743986i	$-0.732933\pi$
$983$		−	46.6521i		−	1.48797i	0.668195	−	0.743986i	$-0.267067\pi$
$984$	−0.823843	+	2.06483i	−0.0262631	+	0.0658242i
$985$	−7.43973	−	1.10169i	−0.237049	−	0.0351027i
$986$	−5.79996	−	4.41047i	−0.184708	−	0.140458i
$987$	−7.96151			−0.253418
$988$	−28.6568	+	7.94671i	−0.911695	+	0.252819i
$989$			55.3065i			1.75864i
$990$	−0.331856	+	0.324142i	−0.0105471	+	0.0103019i
$991$	39.6194			1.25855			0.629276	−	0.777182i	$-0.283351\pi$
$991$	39.6194			1.25855			0.629276	+	0.777182i	$0.283351\pi$
$992$	9.01620	+	0.987822i	0.286265	+	0.0313634i
$993$			8.40120i			0.266604i
$994$	10.0726	−	13.2459i	0.319482	−	0.420133i
$995$	33.7422	+	4.99661i	1.06970	+	0.158403i
$996$	−4.20491	−	15.1634i	−0.133238	−	0.480471i
$997$	−17.1620			−0.543524			−0.271762	−	0.962364i	$-0.587606\pi$
$997$	−17.1620			−0.543524			−0.271762	+	0.962364i	$0.587606\pi$
$998$	33.5022	−	44.0569i	1.06049	−	1.39460i
$999$	39.4975			1.24964

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	280.2.l.a.29.9	✓	36
4.3	odd	2		1120.2.l.a.1009.11		36
5.4	even	2	inner	280.2.l.a.29.28	yes	36
8.3	odd	2		1120.2.l.a.1009.26		36
8.5	even	2	inner	280.2.l.a.29.27	yes	36
20.19	odd	2		1120.2.l.a.1009.25		36
40.19	odd	2		1120.2.l.a.1009.12		36
40.29	even	2	inner	280.2.l.a.29.10	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.l.a.29.9	✓	36	1.1	even	1	trivial
280.2.l.a.29.10	yes	36	40.29	even	2	inner
280.2.l.a.29.27	yes	36	8.5	even	2	inner
280.2.l.a.29.28	yes	36	5.4	even	2	inner
1120.2.l.a.1009.11		36	4.3	odd	2
1120.2.l.a.1009.12		36	40.19	odd	2
1120.2.l.a.1009.25		36	20.19	odd	2
1120.2.l.a.1009.26		36	8.3	odd	2

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:	\( N \)	\(=\)	\( 280 = 2^{3} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	280.l (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.12571 - 0.856025i) q^{2} +1.65329 q^{3} +(0.534444 + 1.92727i) q^{4} +(2.21195 + 0.327549i) q^{5} +(-1.86112 - 1.41526i) q^{6} -1.00000i q^{7} +(1.04816 - 2.62704i) q^{8} -0.266637 q^{9} +O(q^{10})\)	\(q+(-1.12571 - 0.856025i) q^{2} +1.65329 q^{3} +(0.534444 + 1.92727i) q^{4} +(2.21195 + 0.327549i) q^{5} +(-1.86112 - 1.41526i) q^{6} -1.00000i q^{7} +(1.04816 - 2.62704i) q^{8} -0.266637 q^{9} +(-2.20962 - 2.26221i) q^{10} +0.550169i q^{11} +(0.883590 + 3.18633i) q^{12} +3.69124 q^{13} +(-0.856025 + 1.12571i) q^{14} +(3.65699 + 0.541533i) q^{15} +(-3.42874 + 2.06004i) q^{16} +2.20317i q^{17} +(0.300156 + 0.228248i) q^{18} +4.02822i q^{19} +(0.550887 + 4.43808i) q^{20} -1.65329i q^{21} +(0.470959 - 0.619331i) q^{22} -7.96482i q^{23} +(1.73291 - 4.34326i) q^{24} +(4.78542 + 1.44904i) q^{25} +(-4.15526 - 3.15979i) q^{26} -5.40069 q^{27} +(1.92727 - 0.534444i) q^{28} -2.33857i q^{29} +(-3.65314 - 3.74008i) q^{30} +1.60339 q^{31} +(5.62321 + 0.616083i) q^{32} +0.909589i q^{33} +(1.88597 - 2.48013i) q^{34} +(0.327549 - 2.21195i) q^{35} +(-0.142503 - 0.513882i) q^{36} -7.31341 q^{37} +(3.44826 - 4.53461i) q^{38} +6.10268 q^{39} +(3.17896 - 5.46756i) q^{40} -0.475409 q^{41} +(-1.41526 + 1.86112i) q^{42} -6.94385 q^{43} +(-1.06033 + 0.294035i) q^{44} +(-0.589788 - 0.0873368i) q^{45} +(-6.81808 + 8.96607i) q^{46} -4.81556i q^{47} +(-5.66869 + 3.40583i) q^{48} -1.00000 q^{49} +(-4.14658 - 5.72764i) q^{50} +3.64248i q^{51} +(1.97276 + 7.11401i) q^{52} +9.39345 q^{53} +(6.07961 + 4.62313i) q^{54} +(-0.180207 + 1.21695i) q^{55} +(-2.62704 - 1.04816i) q^{56} +6.65981i q^{57} +(-2.00187 + 2.63255i) q^{58} -1.71937i q^{59} +(0.910775 + 7.33742i) q^{60} +13.9978i q^{61} +(-1.80495 - 1.37254i) q^{62} +0.266637i q^{63} +(-5.80271 - 5.50713i) q^{64} +(8.16482 + 1.20906i) q^{65} +(0.778630 - 1.02393i) q^{66} -8.80942 q^{67} +(-4.24611 + 1.17747i) q^{68} -13.1681i q^{69} +(-2.26221 + 2.20962i) q^{70} -11.7667 q^{71} +(-0.279479 + 0.700468i) q^{72} +14.2999i q^{73} +(8.23277 + 6.26046i) q^{74} +(7.91169 + 2.39568i) q^{75} +(-7.76347 + 2.15286i) q^{76} +0.550169 q^{77} +(-6.86984 - 5.22404i) q^{78} -7.79860 q^{79} +(-8.25895 + 3.43361i) q^{80} -8.12899 q^{81} +(0.535172 + 0.406962i) q^{82} -4.75889 q^{83} +(3.18633 - 0.883590i) q^{84} +(-0.721646 + 4.87330i) q^{85} +(7.81676 + 5.94411i) q^{86} -3.86633i q^{87} +(1.44532 + 0.576666i) q^{88} -4.88971 q^{89} +(0.589167 + 0.603189i) q^{90} -3.69124i q^{91} +(15.3504 - 4.25675i) q^{92} +2.65087 q^{93} +(-4.12224 + 5.42093i) q^{94} +(-1.31944 + 8.91022i) q^{95} +(9.29678 + 1.01856i) q^{96} -18.8491i q^{97} +(1.12571 + 0.856025i) q^{98} -0.146696i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9}+O(q^{10}) \) 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9	\( 36 q + 4 q^{4} - 4 q^{6} + 36 q^{9} - 8 q^{10} + 20 q^{16} - 24 q^{20} - 48 q^{24} + 4 q^{25} - 4 q^{26} + 4 q^{30} - 16 q^{31} + 12 q^{34} - 20 q^{36} - 32 q^{39} + 16 q^{40} - 8 q^{41} + 56 q^{44} - 36 q^{49} - 12 q^{50} - 52 q^{54} - 32 q^{55} + 12 q^{56} - 20 q^{60} - 20 q^{64} - 24 q^{65} - 28 q^{66} - 12 q^{70} + 56 q^{71} - 24 q^{74} + 48 q^{76} + 24 q^{79} + 64 q^{80} + 36 q^{81} + 24 q^{86} - 40 q^{89} - 52 q^{90} - 92 q^{94} + 40 q^{95} + 48 q^{96}+O(q^{100}) \) 36 * q + 4 * q^4 - 4 * q^6 + 36 * q^9 - 8 * q^10 + 20 * q^16 - 24 * q^20 - 48 * q^24 + 4 * q^25 - 4 * q^26 + 4 * q^30 - 16 * q^31 + 12 * q^34 - 20 * q^36 - 32 * q^39 + 16 * q^40 - 8 * q^41 + 56 * q^44 - 36 * q^49 - 12 * q^50 - 52 * q^54 - 32 * q^55 + 12 * q^56 - 20 * q^60 - 20 * q^64 - 24 * q^65 - 28 * q^66 - 12 * q^70 + 56 * q^71 - 24 * q^74 + 48 * q^76 + 24 * q^79 + 64 * q^80 + 36 * q^81 + 24 * q^86 - 40 * q^89 - 52 * q^90 - 92 * q^94 + 40 * q^95 + 48 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more