LMFDB - Embedded newform 280.2.l.a.29.10

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

$q$-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	$-0.973569\pi$
$11$		−	0.550169i		−	0.165882i	0.996554	−	0.0829412i	$-0.0264314\pi$
$12$	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	$-0.913910\pi$
$17$		−	2.20317i		−	0.534347i	0.963648	−	0.267174i	$-0.0860898\pi$
$18$	0.300156	−	0.228248i	0.0707475	−	0.0537986i
$19$		−	4.02822i		−	0.924138i	−0.886844	−	0.462069i	$-0.847107\pi$
$19$		−	4.02822i		−	0.924138i	0.886844	−	0.462069i	$-0.152893\pi$
$20$	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	$0.311882\pi$
$23$			7.96482i			1.66078i	−0.557183	+	0.830390i	$0.688118\pi$
$24$	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	$0.0696698\pi$
$29$			2.33857i			0.434262i	−0.976143	+	0.217131i	$0.930330\pi$
$30$	−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	$0.114230\pi$
$47$			4.81556i			0.702422i	−0.936296	+	0.351211i	$0.885770\pi$
$48$	−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	$0.0357004\pi$
$59$			1.71937i			0.223842i	−0.993717	+	0.111921i	$0.964300\pi$
$60$	0.910775	−	7.33742i	0.117581	−	0.947257i
$61$		−	13.9978i		−	1.79224i	−0.443813	−	0.896119i	$-0.646375\pi$
$61$		−	13.9978i		−	1.79224i	0.443813	−	0.896119i	$-0.353625\pi$
$62$	−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	$-0.684400\pi$
$73$		−	14.2999i		−	1.67368i	0.547446	−	0.836841i	$-0.315600\pi$
$74$	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	$0.406227\pi$
$97$			18.8491i			1.91384i	−0.290355	+	0.956919i	$0.593773\pi$
$98$	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	$0.0171849\pi$
$101$			1.08462i			0.107924i	−0.998543	+	0.0539618i	$0.982815\pi$
$102$	3.11805	+	4.10037i	0.308733	+	0.405997i
$103$			12.2447i			1.20651i	0.797550	+	0.603253i	$0.206129\pi$
$103$			12.2447i			1.20651i	−0.797550	+	0.603253i	$0.793871\pi$
$104$	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	$-0.848569\pi$
$109$		−	9.56316i		−	0.915984i	0.888956	−	0.457992i	$-0.151431\pi$
$110$	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	$-0.837571\pi$
$113$		−	10.3841i		−	0.976853i	0.872605	−	0.488427i	$-0.162429\pi$
$114$	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	$-0.708831\pi$
$127$		−	17.8598i		−	1.58480i	0.610001	−	0.792401i	$-0.291169\pi$
$128$	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	$0.152950\pi$
$131$			10.5809i			0.924460i	−0.886760	+	0.462230i	$0.847050\pi$
$132$	−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	$0.000506960\pi$
$137$			0.0372832i			0.00318532i	−0.999999	+	0.00159266i	$0.999493\pi$
$138$	−11.2722	−	14.8235i	−0.959558	−	1.26186i
$139$		−	4.11189i		−	0.348766i	−0.984678	−	0.174383i	$-0.944207\pi$
$139$		−	4.11189i		−	0.348766i	0.984678	−	0.174383i	$-0.0557931\pi$
$140$	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	$0.320158\pi$
$149$			20.6192i			1.68919i	−0.535407	+	0.844594i	$0.679842\pi$
$150$	−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	$0.262729\pi$
$167$			18.9917i			1.46962i	−0.678273	+	0.734810i	$0.737271\pi$
$168$	−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	$-0.662950\pi$
$179$		−	23.3279i		−	1.74361i	0.489853	−	0.871805i	$-0.337050\pi$
$180$	−0.146887	+	1.18336i	−0.0109483	+	0.0882022i
$181$			3.44282i			0.255903i	0.991780	+	0.127952i	$0.0408402\pi$
$181$			3.44282i			0.255903i	−0.991780	+	0.127952i	$0.959160\pi$
$182$	−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	$0.193330\pi$
$193$			15.8570i			1.14141i	−0.821155	+	0.570705i	$0.806670\pi$
$194$	−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	$-0.892689\pi$
$211$		−	9.60962i		−	0.661554i	0.943709	−	0.330777i	$-0.107311\pi$
$212$	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	$-0.788811\pi$
$223$		−	18.3933i		−	1.23171i	0.787861	−	0.615854i	$-0.211189\pi$
$224$	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	$0.223482\pi$
$229$			19.5459i			1.29163i	−0.763494	+	0.645815i	$0.776518\pi$
$230$	−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	$0.0692498\pi$
$233$			6.58938i			0.431685i	−0.976428	+	0.215842i	$0.930750\pi$
$234$	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	$0.0243222\pi$
$251$			2.41879i			0.152672i	−0.997082	+	0.0763362i	$0.975678\pi$
$252$	−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	$0.0467132\pi$
$257$			4.68842i			0.292455i	−0.989251	+	0.146228i	$0.953287\pi$
$258$	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	$0.0394995\pi$
$263$			4.01452i			0.247546i	−0.992311	+	0.123773i	$0.960501\pi$
$264$	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	$-0.803931\pi$
$269$		−	18.9516i		−	1.15550i	0.816213	−	0.577751i	$-0.196069\pi$
$270$	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	$0.390104\pi$
$313$			33.2957i			1.88198i	−0.338430	+	0.940992i	$0.609896\pi$
$314$	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	$-0.955401\pi$
$331$		−	5.08151i		−	0.279305i	0.990201	−	0.139652i	$-0.0445985\pi$
$332$	−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	$-0.930367\pi$
$337$		−	7.96789i		−	0.434038i	0.976167	−	0.217019i	$-0.0696334\pi$
$338$	−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	$0.0332741\pi$
$349$			3.89860i			0.208687i	−0.994541	+	0.104344i	$0.966726\pi$
$350$	−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	$-0.883185\pi$
$353$		−	13.4826i		−	0.717605i	0.933413	−	0.358803i	$-0.116815\pi$
$354$	−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	$-0.989469\pi$
$367$		−	1.26740i		−	0.0661576i	0.999453	−	0.0330788i	$-0.0105312\pi$
$368$	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	$0.0779177\pi$
$379$			9.43604i			0.484697i	−0.970189	+	0.242348i	$0.922082\pi$
$380$	−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	$0.117729\pi$
$383$			14.1486i			0.722961i	−0.932380	+	0.361480i	$0.882271\pi$
$384$	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	$0.0462908\pi$
$389$			5.71633i			0.289829i	−0.989444	+	0.144915i	$0.953709\pi$
$390$	−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	$-0.874673\pi$
$419$		−	15.7055i		−	0.767262i	0.923486	−	0.383631i	$-0.125327\pi$
$420$	7.33742	+	0.910775i	0.358029	+	0.0444413i
$421$			21.9675i			1.07063i	0.844652	+	0.535316i	$0.179807\pi$
$421$			21.9675i			1.07063i	−0.844652	+	0.535316i	$0.820193\pi$
$422$	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	$-0.838852\pi$
$433$		−	20.1807i		−	0.969824i	0.874563	−	0.484912i	$-0.161148\pi$
$434$	−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	$-0.790069\pi$
$457$		−	26.1976i		−	1.22547i	0.790287	−	0.612737i	$-0.209931\pi$
$458$	−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	$-0.901062\pi$
$461$		−	13.1335i		−	0.611686i	0.952082	−	0.305843i	$-0.0989383\pi$
$462$	−1.02393	+	0.778630i	−0.0476377	+	0.0362252i
$463$			0.362997i			0.0168699i	0.999964	+	0.00843494i	$0.00268496\pi$
$463$			0.362997i			0.0168699i	−0.999964	+	0.00843494i	$0.997315\pi$
$464$	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	$0.164031\pi$
$487$			21.7509i			0.985626i	−0.870135	+	0.492813i	$0.835969\pi$
$488$	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	$-0.767641\pi$
$491$		−	29.5530i		−	1.33371i	0.745189	−	0.666853i	$-0.232359\pi$
$492$	−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	$-0.660199\pi$
$499$		−	39.1370i		−	1.75201i	0.482301	−	0.876006i	$-0.339801\pi$
$500$	−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	$-0.920673\pi$
$503$		−	11.0632i		−	0.493285i	0.969106	−	0.246643i	$-0.0793274\pi$
$504$	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	$0.268463\pi$
$509$			33.7020i			1.49382i	−0.664927	+	0.746908i	$0.731537\pi$
$510$	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	$0.188339\pi$
$541$			25.9463i			1.11552i	−0.830003	+	0.557759i	$0.811661\pi$
$542$	−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	$-0.967841\pi$
$571$		−	4.82021i		−	0.201720i	0.994901	−	0.100860i	$-0.0321593\pi$
$572$	−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	$0.321742\pi$
$577$			40.7032i			1.69450i	−0.531197	+	0.847248i	$0.678258\pi$
$578$	−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	$-0.591230\pi$
$593$		−	46.7165i		−	1.91842i	0.282699	−	0.959209i	$-0.408770\pi$
$594$	−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	$-0.905827\pi$
$607$		−	14.3664i		−	0.583114i	0.956553	−	0.291557i	$-0.0941734\pi$
$608$	−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	$-0.772021\pi$
$617$		−	32.6161i		−	1.31307i	0.754294	−	0.656537i	$-0.227979\pi$
$618$	−17.3294	−	22.7889i	−0.697089	−	0.916703i
$619$			13.6950i			0.550448i	0.961380	+	0.275224i	$0.0887520\pi$
$619$			13.6950i			0.550448i	−0.961380	+	0.275224i	$0.911248\pi$
$620$	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	$-0.922914\pi$
$647$		−	12.1998i		−	0.479625i	0.970819	−	0.239813i	$-0.0770860\pi$
$648$	−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	$-0.921176\pi$
$659$		−	12.5844i		−	0.490219i	0.969495	−	0.245109i	$-0.0788239\pi$
$660$	−4.03682	−	0.501081i	−0.157133	−	0.0195045i
$661$			36.0309i			1.40144i	0.713436	+	0.700720i	$0.247138\pi$
$661$			36.0309i			1.40144i	−0.713436	+	0.700720i	$0.752862\pi$
$662$	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	$0.0915639\pi$
$673$			14.7199i			0.567411i	−0.958911	+	0.283706i	$0.908436\pi$
$674$	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	$-0.878353\pi$
$691$		−	19.6063i		−	0.745858i	0.927860	−	0.372929i	$-0.121647\pi$
$692$	−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	$-0.809508\pi$
$701$		−	29.8316i		−	1.12672i	0.826210	−	0.563362i	$-0.190492\pi$
$702$	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	$-0.804773\pi$
$709$		−	30.6524i		−	1.15118i	0.817740	−	0.575588i	$-0.195227\pi$
$710$	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	$-0.908339\pi$
$727$		−	15.3149i		−	0.567999i	0.958824	−	0.283999i	$-0.0916614\pi$
$728$	−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	$0.0531711\pi$
$739$			9.03974i			0.332532i	−0.986081	+	0.166266i	$0.946829\pi$
$740$	−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	$0.218628\pi$
$743$			34.5685i			1.26820i	−0.773253	+	0.634098i	$0.781372\pi$
$744$	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	$-0.944275\pi$
$811$		−	9.92022i		−	0.348346i	0.984715	−	0.174173i	$-0.0557252\pi$
$812$	−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	$0.0760405\pi$
$821$			13.5600i			0.473246i	−0.971602	+	0.236623i	$0.923959\pi$
$822$	−0.0527653	−	0.0693887i	−0.00184040	−	0.00242021i
$823$		−	20.9059i		−	0.728734i	−0.931255	−	0.364367i	$-0.881285\pi$
$823$		−	20.9059i		−	0.728734i	0.931255	−	0.364367i	$-0.118715\pi$
$824$	−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	$0.00722546\pi$
$829$			1.30703i			0.0453950i	−0.999742	+	0.0226975i	$0.992775\pi$
$830$	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	$-0.977342\pi$
$857$		−	4.16422i		−	0.142247i	0.997468	−	0.0711235i	$-0.0226584\pi$
$858$	2.87411	+	3.77958i	0.0981204	+	0.129033i
$859$			32.9477i			1.12416i	0.827083	+	0.562080i	$0.189999\pi$
$859$			32.9477i			1.12416i	−0.827083	+	0.562080i	$0.810001\pi$
$860$	−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	$0.235620\pi$
$863$			39.6266i			1.34890i	−0.738319	+	0.674452i	$0.764380\pi$
$864$	−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	$-0.959141\pi$
$887$		−	7.62497i		−	0.256022i	0.991773	−	0.128011i	$-0.0408592\pi$
$888$	−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	$-0.885425\pi$
$937$		−	21.5635i		−	0.704450i	0.935915	−	0.352225i	$-0.114575\pi$
$938$	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	$0.183303\pi$
$941$			33.4094i			1.08912i	−0.838723	+	0.544558i	$0.816697\pi$
$942$	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	$0.442250\pi$
$953$			60.7280i			1.96717i	−0.180434	+	0.983587i	$0.557750\pi$
$954$	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	$-0.975583\pi$
$967$		−	4.76598i		−	0.153264i	0.997059	−	0.0766318i	$-0.0244166\pi$
$968$	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	$0.0220108\pi$
$971$			4.30605i			0.138188i	−0.997610	+	0.0690939i	$0.977989\pi$
$972$	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	$0.181041\pi$
$977$			33.6691i			1.07717i	−0.842571	+	0.538585i	$0.818959\pi$
$978$	−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	$0.267067\pi$
$983$			46.6521i			1.48797i	−0.668195	+	0.743986i	$0.732933\pi$
$984$	−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.29.10	yes	36
4.3	odd	2		1120.2.l.a.1009.12		36
5.4	even	2	inner	280.2.l.a.29.27	yes	36
8.3	odd	2		1120.2.l.a.1009.25		36
8.5	even	2	inner	280.2.l.a.29.28	yes	36
20.19	odd	2		1120.2.l.a.1009.26		36
40.19	odd	2		1120.2.l.a.1009.11		36
40.29	even	2	inner	280.2.l.a.29.9	✓	36

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

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