LMFDB - Embedded newform 690.2.w.a.493.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			493.3
Character	$\chi$	$=$	690.493
Dual form			690.2.w.a.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.997452 - 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(-0.721297 - 2.11654i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-0.913900 - 1.67368i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +O(q^{10})$	\(q+(-0.997452 - 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(-0.721297 - 2.11654i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-0.913900 - 1.67368i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +(0.568467 + 2.16260i) q^{10} +(-3.05647 - 2.64845i) q^{11} +(0.0713392 + 0.997452i) q^{12} +(1.02708 + 0.560830i) q^{13} +(0.792172 + 1.73462i) q^{14} +(1.91485 - 1.15472i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-4.06133 + 5.42530i) q^{17} +(0.936950 - 0.349464i) q^{18} +(-0.975805 + 6.78687i) q^{19} +(-0.412740 - 2.19765i) q^{20} +(1.44117 - 1.24878i) q^{21} +(2.85974 + 2.85974i) q^{22} +(-1.45623 + 4.56940i) q^{23} -1.00000i q^{24} +(-3.95946 + 3.05330i) q^{25} +(-0.984458 - 0.632673i) q^{26} +(-0.599278 - 0.800541i) q^{27} +(-0.666408 - 1.78671i) q^{28} +(0.845493 - 0.121564i) q^{29} +(-1.99234 + 1.01517i) q^{30} +(0.124229 - 0.0798373i) q^{31} +(-0.936950 - 0.349464i) q^{32} +(1.93822 - 3.54959i) q^{33} +(4.43801 - 5.12174i) q^{34} +(-2.88322 + 3.14153i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-2.62292 + 7.03232i) q^{37} +(1.45749 - 6.69997i) q^{38} +(-0.329691 + 1.12282i) q^{39} +(0.254910 + 2.22149i) q^{40} +(2.18094 - 4.77558i) q^{41} +(-1.52659 + 1.14279i) q^{42} +(0.868206 - 0.188867i) q^{43} +(-2.64845 - 3.05647i) q^{44} +(1.53536 + 1.62563i) q^{45} +(1.77850 - 4.45387i) q^{46} +(-3.33505 + 3.33505i) q^{47} +(-0.0713392 + 0.997452i) q^{48} +(1.81848 - 2.82962i) q^{49} +(4.16719 - 2.76306i) q^{50} +(-6.16461 - 2.81528i) q^{51} +(0.936815 + 0.701291i) q^{52} +(-4.12748 + 2.25377i) q^{53} +(0.540641 + 0.841254i) q^{54} +(-3.40091 + 8.37944i) q^{55} +(0.537248 + 1.82970i) q^{56} +(-6.83920 + 0.489149i) q^{57} +(-0.852011 + 0.0609371i) q^{58} +(-3.50938 - 11.9519i) q^{59} +(2.05969 - 0.870451i) q^{60} +(1.84045 + 2.86379i) q^{61} +(-0.129608 + 0.0707715i) q^{62} +(1.52659 + 1.14279i) q^{63} +(0.909632 + 0.415415i) q^{64} +(0.446186 - 2.57839i) q^{65} +(-2.18651 + 3.40227i) q^{66} +(0.414577 - 5.79654i) q^{67} +(-4.79209 + 4.79209i) q^{68} +(-4.77452 - 0.451655i) q^{69} +(3.09999 - 2.92783i) q^{70} +(-5.30872 - 6.12659i) q^{71} +(0.977147 - 0.212565i) q^{72} +(-0.919382 + 0.688240i) q^{73} +(3.11792 - 6.82728i) q^{74} +(-3.82517 - 3.21995i) q^{75} +(-1.93175 + 6.57892i) q^{76} +(-1.63935 + 7.53597i) q^{77} +(0.408953 - 1.09644i) q^{78} +(-8.18185 + 2.40241i) q^{79} +(-0.0957814 - 2.23402i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-2.51607 + 4.60783i) q^{82} +(-9.55624 - 3.56429i) q^{83} +(1.60422 - 1.03097i) q^{84} +(14.4123 + 4.68270i) q^{85} +(-0.879468 + 0.126448i) q^{86} +(0.298508 + 0.800331i) q^{87} +(2.42365 + 3.23762i) q^{88} +(1.85819 + 1.19419i) q^{89} +(-1.41547 - 1.73102i) q^{90} -2.23156i q^{91} +(-2.09170 + 4.31564i) q^{92} +(0.104420 + 0.104420i) q^{93} +(3.56448 - 3.08864i) q^{94} +(15.0685 - 2.83002i) q^{95} +(0.142315 - 0.989821i) q^{96} +(-4.95347 + 1.84755i) q^{97} +(-2.01571 + 2.69268i) q^{98} +(3.88047 + 1.13941i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 24 q^{6}+O(q^{10}) $ 240 * q - 24 * q^6	$ 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) $ 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{3}{22}\right)$

Coefficient data

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

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

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

$2$	−0.997452	−	0.0713392i	−0.705305	−	0.0504444i
$2$	−0.997452	−	0.0713392i	−0.705305	−	0.0504444i
$3$	0.212565	+	0.977147i	0.122725	+	0.564156i
$3$	0.212565	+	0.977147i	0.122725	+	0.564156i
$4$	0.989821	+	0.142315i	0.494911	+	0.0711574i
$5$	−0.721297	−	2.11654i	−0.322574	−	0.946544i
$5$	−0.721297	−	2.11654i	−0.322574	−	0.946544i
$6$	−0.142315	−	0.989821i	−0.0580998	−	0.404093i
$7$	−0.913900	−	1.67368i	−0.345422	−	0.632593i	0.645994	−	0.763343i	$-0.276443\pi$
$7$	−0.913900	−	1.67368i	−0.345422	−	0.632593i	−0.991415	+	0.130750i	$0.958261\pi$
$8$	−0.977147	−	0.212565i	−0.345474	−	0.0751532i
$9$	−0.909632	+	0.415415i	−0.303211	+	0.138472i
$10$	0.568467	+	2.16260i	0.179765	+	0.683875i
$11$	−3.05647	−	2.64845i	−0.921560	−	0.798536i	0.0582842	−	0.998300i	$-0.481437\pi$
$11$	−3.05647	−	2.64845i	−0.921560	−	0.798536i	−0.979844	+	0.199764i	$0.935983\pi$
$12$	0.0713392	+	0.997452i	0.0205938	+	0.287940i
$13$	1.02708	+	0.560830i	0.284862	+	0.155546i	0.615327	−	0.788272i	$-0.289024\pi$
$13$	1.02708	+	0.560830i	0.284862	+	0.155546i	−0.330465	+	0.943818i	$0.607206\pi$
$14$	0.792172	+	1.73462i	0.211717	+	0.463595i
$15$	1.91485	−	1.15472i	0.494411	−	0.298146i
$16$	0.959493	+	0.281733i	0.239873	+	0.0704331i
$17$	−4.06133	+	5.42530i	−0.985016	+	1.31583i	−0.0364205	+	0.999337i	$0.511596\pi$
$17$	−4.06133	+	5.42530i	−0.985016	+	1.31583i	−0.948596	+	0.316491i	$0.897495\pi$
$18$	0.936950	−	0.349464i	0.220841	−	0.0823695i
$19$	−0.975805	+	6.78687i	−0.223865	+	1.55702i	0.499355	+	0.866398i	$0.333571\pi$
$19$	−0.975805	+	6.78687i	−0.223865	+	1.55702i	−0.723220	+	0.690618i	$0.757339\pi$
$20$	−0.412740	−	2.19765i	−0.0922915	−	0.491408i
$21$	1.44117	−	1.24878i	0.314489	−	0.272506i
$22$	2.85974	+	2.85974i	0.609699	+	0.609699i
$23$	−1.45623	+	4.56940i	−0.303645	+	0.952785i
$23$	−1.45623	+	4.56940i	−0.303645	+	0.952785i
$24$		−	1.00000i		−	0.204124i
$25$	−3.95946	+	3.05330i	−0.791893	+	0.610660i
$26$	−0.984458	−	0.632673i	−0.193068	−	0.124077i
$27$	−0.599278	−	0.800541i	−0.115331	−	0.154064i
$28$	−0.666408	−	1.78671i	−0.125939	−	0.337656i
$29$	0.845493	−	0.121564i	0.157004	−	0.0225738i	−0.0633645	−	0.997990i	$-0.520183\pi$
$29$	0.845493	−	0.121564i	0.157004	−	0.0225738i	0.220369	+	0.975417i	$0.429274\pi$
$30$	−1.99234	+	1.01517i	−0.363750	+	0.185344i
$31$	0.124229	−	0.0798373i	0.0223122	−	0.0143392i	−0.529437	−	0.848349i	$-0.677597\pi$
$31$	0.124229	−	0.0798373i	0.0223122	−	0.0143392i	0.551749	+	0.834010i	$0.313960\pi$
$32$	−0.936950	−	0.349464i	−0.165631	−	0.0617771i
$33$	1.93822	−	3.54959i	0.337401	−	0.617904i
$34$	4.43801	−	5.12174i	0.761113	−	0.878371i
$35$	−2.88322	+	3.14153i	−0.487353	+	0.531015i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	−2.62292	+	7.03232i	−0.431205	+	1.15611i	0.521778	+	0.853082i	$0.325269\pi$
$37$	−2.62292	+	7.03232i	−0.431205	+	1.15611i	−0.952983	+	0.303024i	$0.902004\pi$
$38$	1.45749	−	6.69997i	0.236436	−	1.08688i
$39$	−0.329691	+	1.12282i	−0.0527928	+	0.179796i
$40$	0.254910	+	2.22149i	0.0403048	+	0.351249i
$41$	2.18094	−	4.77558i	0.340605	−	0.745821i	−0.659377	−	0.751812i	$-0.729180\pi$
$41$	2.18094	−	4.77558i	0.340605	−	0.745821i	0.999982	+	0.00599156i	$0.00190718\pi$
$42$	−1.52659	+	1.14279i	−0.235557	+	0.176336i
$43$	0.868206	−	0.188867i	0.132400	−	0.0288019i	−0.145877	−	0.989303i	$-0.546600\pi$
$43$	0.868206	−	0.188867i	0.132400	−	0.0288019i	0.278277	+	0.960501i	$0.410237\pi$
$44$	−2.64845	−	3.05647i	−0.399268	−	0.460780i
$45$	1.53536	+	1.62563i	0.228877	+	0.242335i
$46$	1.77850	−	4.45387i	0.262225	−	0.656687i
$47$	−3.33505	+	3.33505i	−0.486468	+	0.486468i	−0.907190	−	0.420722i	$-0.861777\pi$
$47$	−3.33505	+	3.33505i	−0.486468	+	0.486468i	0.420722	+	0.907190i	$0.361777\pi$
$48$	−0.0713392	+	0.997452i	−0.0102969	+	0.143970i
$49$	1.81848	−	2.82962i	0.259784	−	0.404231i
$50$	4.16719	−	2.76306i	0.589330	−	0.390755i
$51$	−6.16461	−	2.81528i	−0.863218	−	0.394218i
$52$	0.936815	+	0.701291i	0.129913	+	0.0972516i
$53$	−4.12748	+	2.25377i	−0.566953	+	0.309580i	−0.737040	−	0.675849i	$-0.763777\pi$
$53$	−4.12748	+	2.25377i	−0.566953	+	0.309580i	0.170087	+	0.985429i	$0.445595\pi$
$54$	0.540641	+	0.841254i	0.0735719	+	0.114480i
$55$	−3.40091	+	8.37944i	−0.458579	+	1.12988i
$56$	0.537248	+	1.82970i	0.0717927	+	0.244504i
$57$	−6.83920	+	0.489149i	−0.905874	+	0.0647894i
$58$	−0.852011	+	0.0609371i	−0.111875	+	0.00800143i
$59$	−3.50938	−	11.9519i	−0.456882	−	1.55600i	−0.789996	−	0.613112i	$-0.789918\pi$
$59$	−3.50938	−	11.9519i	−0.456882	−	1.55600i	0.333114	−	0.942887i	$-0.391901\pi$
$60$	2.05969	−	0.870451i	0.265905	−	0.112375i
$61$	1.84045	+	2.86379i	0.235645	+	0.366671i	0.938856	−	0.344311i	$-0.111887\pi$
$61$	1.84045	+	2.86379i	0.235645	+	0.366671i	−0.703211	+	0.710981i	$0.748251\pi$
$62$	−0.129608	+	0.0707715i	−0.0164603	+	0.00898799i
$63$	1.52659	+	1.14279i	0.192332	+	0.143978i
$64$	0.909632	+	0.415415i	0.113704	+	0.0519269i
$65$	0.446186	−	2.57839i	0.0553426	−	0.319810i
$66$	−2.18651	+	3.40227i	−0.269140	+	0.418791i
$67$	0.414577	−	5.79654i	0.0506486	−	0.708160i	−0.907166	−	0.420773i	$-0.861759\pi$
$67$	0.414577	−	5.79654i	0.0506486	−	0.708160i	0.957815	−	0.287387i	$-0.0927866\pi$
$68$	−4.79209	+	4.79209i	−0.581126	+	0.581126i
$69$	−4.77452	−	0.451655i	−0.574784	−	0.0543729i
$70$	3.09999	−	2.92783i	0.370519	−	0.349943i
$71$	−5.30872	−	6.12659i	−0.630029	−	0.727092i	0.347550	−	0.937662i	$-0.387014\pi$
$71$	−5.30872	−	6.12659i	−0.630029	−	0.727092i	−0.977579	+	0.210569i	$0.932468\pi$
$72$	0.977147	−	0.212565i	0.115158	−	0.0250511i
$73$	−0.919382	+	0.688240i	−0.107605	+	0.0805524i	−0.651725	−	0.758455i	$-0.725955\pi$
$73$	−0.919382	+	0.688240i	−0.107605	+	0.0805524i	0.544120	+	0.839007i	$0.316864\pi$
$74$	3.11792	−	6.82728i	0.362450	−	0.793655i
$75$	−3.82517	−	3.21995i	−0.441692	−	0.371808i
$76$	−1.93175	+	6.57892i	−0.221586	+	0.754654i
$77$	−1.63935	+	7.53597i	−0.186821	+	0.858804i
$78$	0.408953	−	1.09644i	0.0463048	−	0.124148i
$79$	−8.18185	+	2.40241i	−0.920530	+	0.270292i	−0.707467	−	0.706746i	$-0.750162\pi$
$79$	−8.18185	+	2.40241i	−0.920530	+	0.270292i	−0.213063	+	0.977038i	$0.568344\pi$
$80$	−0.0957814	−	2.23402i	−0.0107087	−	0.249771i
$81$	0.654861	−	0.755750i	0.0727623	−	0.0839722i
$82$	−2.51607	+	4.60783i	−0.277853	+	0.508850i
$83$	−9.55624	−	3.56429i	−1.04893	−	0.391232i	−0.234882	−	0.972024i	$-0.575470\pi$
$83$	−9.55624	−	3.56429i	−1.04893	−	0.391232i	−0.814052	+	0.580792i	$0.802743\pi$
$84$	1.60422	−	1.03097i	0.175035	−	0.112488i
$85$	14.4123	+	4.68270i	1.56323	+	0.507910i
$86$	−0.879468	+	0.126448i	−0.0948354	+	0.0136353i
$87$	0.298508	+	0.800331i	0.0320034	+	0.0858045i
$88$	2.42365	+	3.23762i	0.258362	+	0.345131i
$89$	1.85819	+	1.19419i	0.196968	+	0.126584i	0.635407	−	0.772177i	$-0.280832\pi$
$89$	1.85819	+	1.19419i	0.196968	+	0.126584i	−0.438439	+	0.898761i	$0.644469\pi$
$90$	−1.41547	−	1.73102i	−0.149204	−	0.182466i
$91$		−	2.23156i		−	0.233931i
$92$	−2.09170	+	4.31564i	−0.218075	+	0.449937i
$93$	0.104420	+	0.104420i	0.0108278	+	0.0108278i
$94$	3.56448	−	3.08864i	0.367648	−	0.318568i
$95$	15.0685	−	2.83002i	1.54600	−	0.290354i
$96$	0.142315	−	0.989821i	0.0145249	−	0.101023i
$97$	−4.95347	+	1.84755i	−0.502949	+	0.187590i	−0.588116	−	0.808776i	$-0.700130\pi$
$97$	−4.95347	+	1.84755i	−0.502949	+	0.187590i	0.0851674	+	0.996367i	$0.472857\pi$
$98$	−2.01571	+	2.69268i	−0.203618	+	0.272002i
$99$	3.88047	+	1.13941i	0.390001	+	0.114515i
$100$	−4.35369	+	2.45873i	−0.435369	+	0.245873i
$101$	5.44360	+	11.9198i	0.541658	+	1.18607i	0.960570	+	0.278039i	$0.0896846\pi$
$101$	5.44360	+	11.9198i	0.541658	+	1.18607i	−0.418911	+	0.908027i	$0.637588\pi$
$102$	5.94806	+	3.24789i	0.588946	+	0.321589i
$103$	1.02665	+	14.3545i	0.101159	+	1.41439i	0.753991	+	0.656885i	$0.228126\pi$
$103$	1.02665	+	14.3545i	0.101159	+	1.41439i	−0.652832	+	0.757503i	$0.726419\pi$
$104$	−0.884399	−	0.766336i	−0.0867224	−	0.0751454i
$105$	−3.68260	−	2.14955i	−0.359385	−	0.209775i
$106$	4.27774	−	1.95358i	0.415491	−	0.189749i
$107$	−16.6049	−	3.61218i	−1.60526	−	0.349203i	−0.681393	−	0.731918i	$-0.738625\pi$
$107$	−16.6049	−	3.61218i	−1.60526	−	0.349203i	−0.923866	+	0.382715i	$0.874989\pi$
$108$	−0.479249	−	0.877679i	−0.0461158	−	0.0844547i
$109$	−1.22784	−	8.53983i	−0.117606	−	0.817968i	−0.960179	−	0.279386i	$-0.909869\pi$
$109$	−1.22784	−	8.53983i	−0.117606	−	0.817968i	0.842573	−	0.538582i	$-0.181040\pi$
$110$	3.99003	−	8.11548i	0.380435	−	0.773780i
$111$	−7.42915	−	1.06815i	−0.705144	−	0.101384i
$112$	−0.405350	−	1.86336i	−0.0383019	−	0.176071i
$113$	11.0726	+	0.791930i	1.04163	+	0.0744985i	0.581655	−	0.813436i	$-0.302405\pi$
$113$	11.0726	+	0.791930i	1.04163	+	0.0744985i	0.459970	+	0.887934i	$0.347860\pi$
$114$	6.85667			0.642186
$115$	10.7217	−	0.213726i	0.999801	−	0.0199300i
$116$	0.854188			0.0793093
$117$	−1.16725	−	0.0834831i	−0.107912	−	0.00771801i
$118$	2.64780	+	12.1718i	0.243750	+	1.12050i
$119$	12.7919	+	1.83919i	1.17263	+	0.168599i
$120$	−2.11654	+	0.721297i	−0.193213	+	0.0658451i
$121$	0.762275	+	5.30174i	0.0692978	+	0.481977i
$122$	−1.63146	−	2.98779i	−0.147705	−	0.270502i
$123$	5.13004	+	1.11597i	0.462560	+	0.100624i
$124$	0.134327	−	0.0613450i	0.0120629	−	0.00550895i
$125$	9.31838	+	6.17802i	0.833461	+	0.552578i
$126$	−1.44117	−	1.24878i	−0.128390	−	0.111250i
$127$	−0.454230	−	6.35097i	−0.0403064	−	0.563557i	−0.976977	−	0.213345i	$-0.931564\pi$
$127$	−0.454230	−	6.35097i	−0.0403064	−	0.563557i	0.936670	−	0.350212i	$-0.113890\pi$
$128$	−0.877679	−	0.479249i	−0.0775766	−	0.0423600i
$129$	0.369101	+	0.808219i	0.0324975	+	0.0711597i
$130$	−0.628989	+	2.53999i	−0.0551660	+	0.222772i
$131$	3.72133	+	1.09268i	0.325135	+	0.0954681i	0.440227	−	0.897887i	$-0.354898\pi$
$131$	3.72133	+	1.09268i	0.325135	+	0.0954681i	−0.115092	+	0.993355i	$0.536716\pi$
$132$	2.42365	−	3.23762i	0.210952	−	0.281799i
$133$	12.2509	−	4.56934i	1.06228	−	0.396212i
$134$	−0.827041	+	5.75220i	−0.0714454	+	0.496914i
$135$	−1.26212	+	1.84582i	−0.108626	+	0.158863i
$136$	5.12174	−	4.43801i	0.439186	−	0.380557i
$137$	−2.06556	−	2.06556i	−0.176473	−	0.176473i	0.613343	−	0.789816i	$-0.289824\pi$
$137$	−2.06556	−	2.06556i	−0.176473	−	0.176473i	−0.789816	+	0.613343i	$0.789824\pi$
$138$	4.73013	+	0.791114i	0.402655	+	0.0673441i
$139$		−	16.4508i		−	1.39534i	−0.716419	−	0.697670i	$-0.754220\pi$
$139$		−	16.4508i		−	1.39534i	0.716419	−	0.697670i	$-0.245780\pi$
$140$	−3.30096	+	2.69922i	−0.278982	+	0.228126i
$141$	−3.96775	−	2.54992i	−0.334145	−	0.214742i
$142$	4.85813	+	6.48970i	0.407685	+	0.544603i
$143$	−1.65392	−	4.43434i	−0.138308	−	0.370818i
$144$	−0.989821	+	0.142315i	−0.0824851	+	0.0118596i
$145$	−0.867145	−	1.70183i	−0.0720125	−	0.141330i
$146$	0.966138	−	0.620899i	0.0799581	−	0.0513860i
$147$	3.15150	+	1.17545i	0.259931	+	0.0969493i
$148$	−3.59702	+	6.58746i	−0.295674	+	0.541486i
$149$	−3.49745	+	4.03628i	−0.286523	+	0.330665i	−0.880705	−	0.473666i	$-0.842930\pi$
$149$	−3.49745	+	4.03628i	−0.286523	+	0.330665i	0.594182	+	0.804331i	$0.297476\pi$
$150$	3.58571	+	3.48463i	0.292772	+	0.284519i
$151$	−3.75228	+	1.10177i	−0.305356	+	0.0896606i	−0.430821	−	0.902437i	$-0.641776\pi$
$151$	−3.75228	+	1.10177i	−0.305356	+	0.0896606i	0.125465	+	0.992098i	$0.459958\pi$
$152$	2.39616	−	6.42435i	0.194354	−	0.521084i
$153$	1.44056	−	6.62216i	0.116463	−	0.535370i
$154$	2.17278	−	7.39982i	0.175088	−	0.596295i
$155$	−0.258585	−	0.205350i	−0.0207700	−	0.0164941i
$156$	−0.486130	+	1.06448i	−0.0389216	+	0.0852263i
$157$	−5.95690	+	4.45928i	−0.475412	+	0.355889i	−0.809956	−	0.586491i	$-0.800509\pi$
$157$	−5.95690	+	4.45928i	−0.475412	+	0.355889i	0.334543	+	0.942380i	$0.391418\pi$
$158$	8.33239	−	1.81260i	0.662889	−	0.144203i
$159$	−3.07963	−	3.55408i	−0.244230	−	0.281857i
$160$	−0.0638355	+	2.23516i	−0.00504664	+	0.176705i
$161$	8.97857	−	1.73871i	0.707610	−	0.137029i
$162$	−0.707107	+	0.707107i	−0.0555556	+	0.0555556i
$163$	0.939863	−	13.1410i	0.0736158	−	1.02928i	−0.817625	−	0.575752i	$-0.804710\pi$
$163$	0.939863	−	13.1410i	0.0736158	−	1.02928i	0.891240	−	0.453531i	$-0.149836\pi$
$164$	2.83837	−	4.41660i	0.221640	−	0.344878i
$165$	−8.91086	−	1.54201i	−0.693710	−	0.120046i
$166$	9.27762	+	4.23695i	0.720083	+	0.328851i
$167$	−10.1259	−	7.58015i	−0.783565	−	0.586570i	0.130824	−	0.991406i	$-0.458238\pi$
$167$	−10.1259	−	7.58015i	−0.783565	−	0.586570i	−0.914389	+	0.404836i	$0.867329\pi$
$168$	−1.67368	+	0.913900i	−0.129127	+	0.0705089i
$169$	−6.28796	−	9.78426i	−0.483689	−	0.752635i
$170$	−14.0415	−	5.69893i	−1.07693	−	0.437088i
$171$	−1.93175	−	6.57892i	−0.147724	−	0.503103i
$172$	0.886248	−	0.0633857i	0.0675758	−	0.00483311i
$173$	17.2791	−	1.23583i	1.31371	−	0.0939581i	0.603166	−	0.797615i	$-0.293905\pi$
$173$	17.2791	−	1.23583i	1.31371	−	0.0939581i	0.710540	+	0.703657i	$0.248451\pi$
$174$	−0.240652	−	0.819587i	−0.0182438	−	0.0621327i
$175$	8.72881	+	3.83647i	0.659836	+	0.290010i
$176$	−2.18651	−	3.40227i	−0.164814	−	0.256456i
$177$	10.9327	−	5.96973i	0.821755	−	0.448712i
$178$	−1.76827	−	1.32371i	−0.132537	−	0.0992161i
$179$	7.05558	+	3.22217i	0.527359	+	0.240837i	0.661258	−	0.750158i	$-0.270023\pi$
$179$	7.05558	+	3.22217i	0.527359	+	0.240837i	−0.133900	+	0.990995i	$0.542750\pi$
$180$	1.28838	+	1.82759i	0.0960299	+	0.136221i
$181$	12.4479	−	19.3693i	0.925245	−	1.43971i	0.0272872	−	0.999628i	$-0.491313\pi$
$181$	12.4479	−	19.3693i	0.925245	−	1.43971i	0.897958	−	0.440082i	$-0.145050\pi$
$182$	−0.159197	+	2.22587i	−0.0118005	+	0.164992i
$183$	−2.40713	+	2.40713i	−0.177940	+	0.177940i
$184$	2.39425	−	4.15543i	0.176506	−	0.306342i
$185$	16.7761	+	0.479120i	1.23340	+	0.0352256i
$186$	−0.0967044	−	0.111603i	−0.00709071	−	0.00818311i
$187$	26.7819	−	5.82605i	1.95849	−	0.426043i
$188$	−3.77574	+	2.82648i	−0.275374	+	0.206142i
$189$	−0.792172	+	1.73462i	−0.0576221	+	0.126175i
$190$	−15.2320	+	1.74783i	−1.10505	+	0.126801i
$191$	−2.90787	+	9.90330i	−0.210406	+	0.716578i	0.784885	+	0.619642i	$0.212722\pi$
$191$	−2.90787	+	9.90330i	−0.210406	+	0.716578i	−0.995291	+	0.0969355i	$0.969096\pi$
$192$	−0.212565	+	0.977147i	−0.0153406	+	0.0705195i
$193$	−4.94646	+	13.2620i	−0.356054	+	0.954618i	0.628230	+	0.778028i	$0.283780\pi$
$193$	−4.94646	+	13.2620i	−0.356054	+	0.954618i	−0.984284	+	0.176591i	$0.943493\pi$
$194$	5.07265	−	1.48947i	0.364195	−	0.106937i
$195$	2.61431	−	0.112086i	0.187214	−	0.00802665i
$196$	2.20267	−	2.54202i	0.157334	−	0.181573i
$197$	9.66444	−	17.6991i	0.688563	−	1.26101i	−0.266279	−	0.963896i	$-0.585794\pi$
$197$	9.66444	−	17.6991i	0.688563	−	1.26101i	0.954842	−	0.297113i	$-0.0960238\pi$
$198$	−3.78929	−	1.41333i	−0.269293	−	0.100441i
$199$	−10.2938	+	6.61543i	−0.729708	+	0.468955i	−0.852002	−	0.523539i	$-0.824612\pi$
$199$	−10.2938	+	6.61543i	−0.729708	+	0.468955i	0.122293	+	0.992494i	$0.460975\pi$
$200$	4.51800	−	2.14188i	0.319471	−	0.151454i
$201$	5.75220	−	0.827041i	0.405729	−	0.0583350i
$202$	−4.57938	−	12.2778i	−0.322204	−	0.863863i
$203$	−0.976155	−	1.30399i	−0.0685127	−	0.0915222i
$204$	−5.70120	−	3.66394i	−0.399164	−	0.256527i
$205$	−11.6808	−	1.17142i	−0.815823	−	0.0818156i
$206$		−	14.3911i		−	1.00268i
$207$	−0.573563	−	4.76141i	−0.0398654	−	0.330941i
$208$	0.827476	+	0.827476i	0.0573751	+	0.0573751i
$209$	20.9572	−	18.1595i	1.44964	−	1.25612i
$210$	3.51987	+	2.40679i	0.242894	+	0.166084i
$211$	−3.54927	+	24.6857i	−0.244342	+	1.69943i	0.385499	+	0.922708i	$0.374029\pi$
$211$	−3.54927	+	24.6857i	−0.244342	+	1.69943i	−0.629841	+	0.776724i	$0.716880\pi$
$212$	−4.40621	+	1.64343i	−0.302620	+	0.112871i
$213$	4.85813	−	6.48970i	0.332873	−	0.444667i
$214$	16.3049	+	4.78756i	1.11458	+	0.327271i
$215$	−1.02598	−	1.70136i	−0.0699711	−	0.116032i
$216$	0.415415	+	0.909632i	0.0282654	+	0.0618926i
$217$	−0.247156	−	0.134957i	−0.0167780	−	0.00916149i
$218$	0.615490	+	8.60567i	0.0416862	+	0.582849i
$219$	−0.867941	−	0.752075i	−0.0586500	−	0.0508205i
$220$	−4.55882	+	7.81015i	−0.307355	+	0.526560i
$221$	−7.21399	+	3.29452i	−0.485266	+	0.221613i
$222$	7.33402	+	1.59542i	0.492227	+	0.107077i
$223$	−10.4897	−	19.2105i	−0.702445	−	1.28643i	−0.948377	−	0.317145i	$-0.897276\pi$
$223$	−10.4897	−	19.2105i	−0.702445	−	1.28643i	0.245932	−	0.969287i	$-0.420906\pi$
$224$	0.271386	+	1.88753i	0.0181327	+	0.126116i
$225$	2.33327	−	4.42220i	0.155551	−	0.294813i
$226$	−10.9879	−	1.57982i	−0.730906	−	0.105088i
$227$	5.66486	+	26.0410i	0.375990	+	1.72840i	0.644038	+	0.764994i	$0.277258\pi$
$227$	5.66486	+	26.0410i	0.375990	+	1.72840i	−0.268047	+	0.963406i	$0.586378\pi$
$228$	−6.83920	−	0.489149i	−0.452937	−	0.0323947i
$229$	−7.42891			−0.490916			−0.245458	−	0.969407i	$-0.578938\pi$
$229$	−7.42891			−0.490916			−0.245458	+	0.969407i	$0.578938\pi$
$230$	−10.7096	−	0.551694i	−0.706170	−	0.0363777i
$231$	−7.71222			−0.507427
$232$	−0.852011	−	0.0609371i	−0.0559373	−	0.00400071i
$233$	5.88731	+	27.0635i	0.385691	+	1.77299i	0.603870	+	0.797083i	$0.293624\pi$
$233$	5.88731	+	27.0635i	0.385691	+	1.77299i	−0.218180	+	0.975909i	$0.570012\pi$
$234$	1.15832	+	0.166541i	0.0757215	+	0.0108871i
$235$	9.46433	+	4.65320i	0.617385	+	0.303542i
$236$	−1.77273	−	12.3296i	−0.115395	−	0.802591i
$237$	−4.08668	−	7.48420i	−0.265459	−	0.486151i
$238$	−12.6281	−	2.74707i	−0.818556	−	0.178066i
$239$	−1.47592	+	0.674032i	−0.0954696	+	0.0435995i	−0.462577	−	0.886579i	$-0.653075\pi$
$239$	−1.47592	+	0.674032i	−0.0954696	+	0.0435995i	0.367108	+	0.930178i	$0.380348\pi$
$240$	2.16260	−	0.568467i	0.139595	−	0.0366944i
$241$	0.569493	+	0.493469i	0.0366843	+	0.0317871i	0.673010	−	0.739633i	$-0.265001\pi$
$241$	0.569493	+	0.493469i	0.0366843	+	0.0317871i	−0.636326	+	0.771421i	$0.719547\pi$
$242$	−0.382111	−	5.34261i	−0.0245630	−	0.343436i
$243$	0.877679	+	0.479249i	0.0563031	+	0.0307438i
$244$	1.41415	+	3.09656i	0.0905319	+	0.198237i
$245$	−7.30066	−	1.80790i	−0.466422	−	0.115502i
$246$	−5.03735	−	1.47910i	−0.321170	−	0.0943040i
$247$	−4.80852	+	6.42343i	−0.305959	+	0.408713i
$248$	−0.138361	+	0.0516060i	−0.00878593	+	0.00327698i
$249$	1.45151	−	10.0955i	0.0919859	−	0.639776i
$250$	−8.85390	−	6.82704i	−0.559970	−	0.431780i
$251$	−23.3058	+	20.1946i	−1.47105	+	1.27467i	−0.585043	+	0.811002i	$0.698923\pi$
$251$	−23.3058	+	20.1946i	−1.47105	+	1.27467i	−0.886007	+	0.463671i	$0.846532\pi$
$252$	1.34841	+	1.34841i	0.0849419	+	0.0849419i
$253$	16.5527	−	10.1095i	1.04066	−	0.635577i
$254$			6.36719i			0.399513i
$255$	−1.51214	+	15.0783i	−0.0946939	+	0.944238i
$256$	0.841254	+	0.540641i	0.0525783	+	0.0337901i
$257$	−12.9220	−	17.2617i	−0.806051	−	1.07676i	−0.995490	−	0.0948656i	$-0.969758\pi$
$257$	−12.9220	−	17.2617i	−0.806051	−	1.07676i	0.189439	−	0.981892i	$-0.439333\pi$
$258$	−0.310503	−	0.832491i	−0.0193311	−	0.0518286i
$259$	14.1670	−	2.03690i	0.880292	−	0.126567i
$260$	0.808587	−	2.48864i	0.0501465	−	0.154339i
$261$	−0.718588	+	0.461809i	−0.0444795	+	0.0285852i
$262$	−3.63390	−	1.35538i	−0.224503	−	0.0837354i
$263$	−13.4043	+	24.5481i	−0.826543	+	1.51370i	0.0311367	+	0.999515i	$0.490087\pi$
$263$	−13.4043	+	24.5481i	−0.826543	+	1.51370i	−0.857679	+	0.514185i	$0.828095\pi$
$264$	−2.64845	+	3.05647i	−0.163001	+	0.188113i
$265$	7.74733	+	7.11032i	0.475915	+	0.436784i
$266$	−12.5456	+	3.68373i	−0.769222	+	0.225864i
$267$	−0.771910	+	2.06957i	−0.0472401	+	0.126656i
$268$	1.23529	−	5.67854i	0.0754574	−	0.346872i
$269$	−1.38178	+	4.70591i	−0.0842487	+	0.286925i	−0.990832	−	0.135103i	$-0.956863\pi$
$269$	−1.38178	+	4.70591i	−0.0842487	+	0.286925i	0.906583	+	0.422028i	$0.138682\pi$
$270$	1.39058	−	1.75108i	0.0846281	−	0.106567i
$271$	7.49644	−	16.4149i	0.455376	−	0.997135i	−0.533141	−	0.846027i	$-0.678988\pi$
$271$	7.49644	−	16.4149i	0.455376	−	0.997135i	0.988517	−	0.151109i	$-0.0482844\pi$
$272$	−5.42530	+	4.06133i	−0.328957	+	0.246254i
$273$	2.18056	−	0.474351i	0.131973	−	0.0287090i
$274$	1.91295	+	2.20766i	0.115565	+	0.133369i
$275$	20.1885	+	1.15410i	1.21741	+	0.0695947i
$276$	−4.66164	−	1.12654i	−0.280598	−	0.0678099i
$277$	−6.98324	+	6.98324i	−0.419582	+	0.419582i	−0.885060	−	0.465477i	$-0.845883\pi$
$277$	−6.98324	+	6.98324i	−0.419582	+	0.419582i	0.465477	+	0.885060i	$0.345883\pi$
$278$	−1.17359	+	16.4089i	−0.0703871	+	0.984141i
$279$	−0.0798373	+	0.124229i	−0.00477974	+	0.00743741i
$280$	3.48511	−	2.45686i	0.208275	−	0.146825i
$281$	−8.63414	−	3.94308i	−0.515070	−	0.235224i	0.140883	−	0.990026i	$-0.455006\pi$
$281$	−8.63414	−	3.94308i	−0.515070	−	0.235224i	−0.655953	+	0.754802i	$0.727733\pi$
$282$	3.77574	+	2.82648i	0.224842	+	0.168314i
$283$	24.3205	−	13.2800i	1.44570	−	0.789414i	0.451032	−	0.892508i	$-0.351056\pi$
$283$	24.3205	−	13.2800i	1.44570	−	0.789414i	0.994672	+	0.103094i	$0.0328741\pi$
$284$	−4.38278	−	6.81974i	−0.260070	−	0.404677i
$285$	5.96839	+	14.1226i	0.353537	+	0.836550i
$286$	1.33337	+	4.54103i	0.0788436	+	0.268517i
$287$	−9.98597	+	0.714211i	−0.589453	+	0.0421585i
$288$	0.997452	−	0.0713392i	0.0587754	−	0.00420370i
$289$	−8.15001	−	27.7564i	−0.479413	−	1.63273i
$290$	0.743528	+	1.75936i	0.0436615	+	0.103313i
$291$	−2.85826	−	4.44754i	−0.167554	−	0.260720i
$292$	−1.00797	+	0.550393i	−0.0589870	+	0.0322093i
$293$	23.6889	+	17.7333i	1.38392	+	1.03599i	0.993315	+	0.115432i	$0.0368254\pi$
$293$	23.6889	+	17.7333i	1.38392	+	1.03599i	0.390606	+	0.920558i	$0.372266\pi$
$294$	−3.05961	−	1.39728i	−0.178440	−	0.0814909i
$295$	−22.7652	+	16.0486i	−1.32544	+	0.934383i
$296$	4.05780	−	6.31407i	0.235855	−	0.366998i
$297$	−0.288516	+	4.03398i	−0.0167414	+	0.234075i
$298$	3.77649	−	3.77649i	0.218766	−	0.218766i
$299$	−4.05833	+	3.87646i	−0.234699	+	0.224181i
$300$	−3.32799	−	3.73155i	−0.192141	−	0.215441i
$301$	−1.10956	−	1.28050i	−0.0639538	−	0.0738066i
$302$	3.82132	−	0.831277i	0.219892	−	0.0478346i
$303$	−10.4903	+	7.85294i	−0.602652	+	0.451139i
$304$	−2.84836	+	6.23704i	−0.163365	+	0.357719i
$305$	4.73381	−	5.96102i	0.271057	−	0.341327i
$306$	−1.90931	+	6.50252i	−0.109148	+	0.371724i
$307$	−7.00839	+	32.2170i	−0.399990	+	1.83872i	0.131050	+	0.991376i	$0.458165\pi$
$307$	−7.00839	+	32.2170i	−0.399990	+	1.83872i	−0.531039	+	0.847347i	$0.678198\pi$
$308$	−2.69515	+	7.22596i	−0.153570	+	0.411737i
$309$	−13.8082	+	4.05445i	−0.785521	+	0.230650i
$310$	0.243277	+	0.223274i	0.0138172	+	0.0126811i
$311$	−11.1534	+	12.8717i	−0.632449	+	0.729885i	−0.978021	−	0.208507i	$-0.933140\pi$
$311$	−11.1534	+	12.8717i	−0.632449	+	0.729885i	0.345572	+	0.938392i	$0.387685\pi$
$312$	0.560830	−	1.02708i	0.0317508	−	0.0581472i
$313$	7.68445	+	2.86615i	0.434351	+	0.162004i	0.557122	−	0.830431i	$-0.311905\pi$
$313$	7.68445	+	2.86615i	0.434351	+	0.162004i	−0.122771	+	0.992435i	$0.539178\pi$
$314$	6.25984	−	4.02295i	0.353263	−	0.227028i
$315$	1.31763	−	4.05536i	0.0742402	−	0.228494i
$316$	−8.44047	+	1.21356i	−0.474813	+	0.0682679i
$317$	−1.63676	−	4.38833i	−0.0919297	−	0.246473i	0.882845	−	0.469665i	$-0.155625\pi$
$317$	−1.63676	−	4.38833i	−0.0919297	−	0.246473i	−0.974775	+	0.223192i	$0.928352\pi$
$318$	2.81823	+	3.76472i	0.158039	+	0.211115i
$319$	−2.90618	−	1.86769i	−0.162715	−	0.104570i
$320$	0.223127	−	2.22491i	0.0124732	−	0.124376i
$321$		−	16.9933i		−	0.948472i
$322$	−9.07973	+	1.09375i	−0.505994	+	0.0609524i
$323$	−32.8577	−	32.8577i	−1.82825	−	1.82825i
$324$	0.755750	−	0.654861i	0.0419861	−	0.0363812i
$325$	−5.77909	+	0.915411i	−0.320566	+	0.0507779i
$326$	−1.87494	+	13.0405i	−0.103843	+	0.722245i
$327$	8.08368	−	3.01506i	0.447028	−	0.166733i
$328$	−3.14622	+	4.20286i	−0.173721	+	0.232064i
$329$	8.62973	+	2.53392i	0.475772	+	0.139699i
$330$	8.77815	+	2.17378i	0.483221	+	0.119663i
$331$	2.87836	+	6.30272i	0.158209	+	0.346429i	0.972092	−	0.234599i	$-0.0753778\pi$
$331$	2.87836	+	6.30272i	0.158209	+	0.346429i	−0.813883	+	0.581028i	$0.802651\pi$
$332$	−8.95172	−	4.88801i	−0.491289	−	0.268264i
$333$	−0.535439	−	7.48642i	−0.0293419	−	0.410253i
$334$	9.55934	+	8.28321i	0.523064	+	0.453237i
$335$	−12.5676	+	3.30356i	−0.686643	+	0.180493i
$336$	1.73462	−	0.792172i	0.0946310	−	0.0432165i
$337$	−3.46390	−	0.753524i	−0.188690	−	0.0410471i	0.117227	−	0.993105i	$-0.462599\pi$
$337$	−3.46390	−	0.753524i	−0.188690	−	0.0410471i	−0.305917	+	0.952058i	$0.598963\pi$
$338$	5.57394	+	10.2079i	0.303182	+	0.555237i
$339$	1.57982	+	10.9879i	0.0858043	+	0.596782i
$340$	13.5991	+	6.68612i	0.737517	+	0.362606i
$341$	−0.591148	−	0.0849942i	−0.0320124	−	0.00460269i
$342$	1.45749	+	6.69997i	0.0788120	+	0.362293i
$343$	−19.7124	−	1.40986i	−1.06437	−	0.0761251i
$344$	−0.888512			−0.0479053
$345$	2.48790	+	10.4312i	0.133944	+	0.561598i
$346$	−17.3232			−0.931303
$347$	8.95823	+	0.640705i	0.480903	+	0.0343949i	0.309687	−	0.950839i	$-0.399776\pi$
$347$	8.95823	+	0.640705i	0.480903	+	0.0343949i	0.171216	+	0.985233i	$0.445230\pi$
$348$	0.181571	+	0.834667i	0.00973321	+	0.0447428i
$349$	4.93667	+	0.709787i	0.264254	+	0.0379940i	0.273168	−	0.961966i	$-0.411928\pi$
$349$	4.93667	+	0.709787i	0.264254	+	0.0379940i	−0.00891418	+	0.999960i	$0.502838\pi$
$350$	−8.43288	−	4.44940i	−0.450756	−	0.237831i
$351$	−0.166541	−	1.15832i	−0.00888929	−	0.0618263i
$352$	1.93822	+	3.54959i	0.103308	+	0.189194i
$353$	16.2981	+	3.54542i	0.867458	+	0.188704i	0.624207	−	0.781259i	$-0.285422\pi$
$353$	16.2981	+	3.54542i	0.867458	+	0.188704i	0.243251	+	0.969963i	$0.421786\pi$
$354$	−11.3308	+	5.17459i	−0.602223	+	0.275026i
$355$	−9.13800	+	15.6552i	−0.484994	+	0.830891i
$356$	1.66933	+	1.44648i	0.0884742	+	0.0766634i
$357$	0.921946	+	12.8905i	0.0487945	+	0.682237i
$358$	−6.80773	−	3.71730i	−0.359800	−	0.196466i
$359$	−0.616819	−	1.35065i	−0.0325545	−	0.0712844i	0.892656	−	0.450738i	$-0.148839\pi$
$359$	−0.616819	−	1.35065i	−0.0325545	−	0.0712844i	−0.925211	+	0.379454i	$0.876112\pi$
$360$	−1.15472	−	1.91485i	−0.0608588	−	0.100921i
$361$	−26.8791	−	7.89242i	−1.41469	−	0.415390i
$362$	−13.7980	+	18.4319i	−0.725205	+	0.968761i
$363$	−5.01855	+	1.87182i	−0.263405	+	0.0982451i
$364$	0.317583	−	2.20884i	0.0166459	−	0.115775i
$365$	2.11983	+	1.44948i	0.110957	+	0.0758693i
$366$	2.57272	−	2.22927i	0.134478	−	0.116526i
$367$	−10.4850	−	10.4850i	−0.547311	−	0.547311i	0.378351	−	0.925662i	$-0.376491\pi$
$367$	−10.4850	−	10.4850i	−0.547311	−	0.547311i	−0.925662	+	0.378351i	$0.876491\pi$
$368$	−2.68459	+	3.97404i	−0.139944	+	0.207161i
$369$			5.25002i			0.273305i
$370$	−16.6991	−	1.67469i	−0.868147	−	0.0870630i
$371$	7.54420	+	4.84837i	0.391676	+	0.251715i
$372$	0.0884963	+	0.118217i	0.00458832	+	0.00612928i
$373$	−12.4638	−	33.4168i	−0.645351	−	1.73025i	−0.682439	−	0.730942i	$-0.739081\pi$
$373$	−12.4638	−	33.4168i	−0.645351	−	1.73025i	0.0370878	−	0.999312i	$-0.488192\pi$
$374$	−27.1293	+	3.90060i	−1.40282	+	0.201695i
$375$	−4.05607	+	10.4187i	−0.209454	+	0.538017i
$376$	3.96775	−	2.54992i	0.204621	−	0.131502i
$377$	0.936569	+	0.349322i	0.0482358	+	0.0179910i
$378$	0.913900	−	1.67368i	0.0470059	−	0.0860850i
$379$	4.82623	−	5.56977i	0.247907	−	0.286100i	−0.618134	−	0.786073i	$-0.712111\pi$
$379$	4.82623	−	5.56977i	0.247907	−	0.286100i	0.866041	+	0.499973i	$0.166657\pi$
$380$	15.3179	−	0.656741i	0.785792	−	0.0336901i
$381$	6.10927	−	1.79384i	0.312988	−	0.0919015i
$382$	3.60696	−	9.67062i	0.184548	−	0.494792i
$383$	3.72729	−	17.1341i	0.190456	−	0.875510i	−0.778378	−	0.627796i	$-0.783957\pi$
$383$	3.72729	−	17.1341i	0.190456	−	0.875510i	0.968833	−	0.247714i	$-0.0796793\pi$
$384$	0.281733	−	0.959493i	0.0143771	−	0.0489639i
$385$	17.1326	−	1.96592i	0.873160	−	0.100193i
$386$	5.87996	−	12.8753i	0.299282	−	0.655336i
$387$	−0.711290	+	0.532465i	−0.0361569	+	0.0270667i
$388$	−5.16598	+	1.12379i	−0.262263	+	0.0570519i
$389$	18.7288	+	21.6142i	0.949588	+	1.09588i	0.995291	+	0.0969275i	$0.0309015\pi$
$389$	18.7288	+	21.6142i	0.949588	+	1.09588i	−0.0457038	+	0.998955i	$0.514553\pi$
$390$	−2.61564	−	0.0747021i	−0.132448	−	0.00378269i
$391$	−18.8761	−	26.4583i	−0.954606	−	1.33805i
$392$	−2.37841	+	2.37841i	−0.120128	+	0.120128i
$393$	−0.276685	+	3.86856i	−0.0139569	+	0.195143i
$394$	−10.9025	+	16.9646i	−0.549258	+	0.854662i
$395$	10.9863	+	15.5843i	0.552782	+	0.784134i
$396$	3.67881	+	1.68006i	0.184867	+	0.0844261i
$397$	5.08819	+	3.80897i	0.255369	+	0.191167i	0.719290	−	0.694710i	$-0.244467\pi$
$397$	5.08819	+	3.80897i	0.255369	+	0.191167i	−0.463921	+	0.885876i	$0.653558\pi$
$398$	10.7395	−	5.86422i	0.538323	−	0.293947i
$399$	7.06902	+	10.9996i	0.353894	+	0.550669i
$400$	−4.65929	+	1.81411i	−0.232965	+	0.0907056i
$401$	9.54088	+	32.4932i	0.476449	+	1.62263i	0.750465	+	0.660910i	$0.229829\pi$
$401$	9.54088	+	32.4932i	0.476449	+	1.62263i	−0.274017	+	0.961725i	$0.588352\pi$
$402$	−5.79654	+	0.414577i	−0.289105	+	0.0206772i
$403$	0.172369	−	0.0123281i	0.00858632	−	0.000614106i
$404$	3.69182	+	12.5732i	0.183675	+	0.625540i
$405$	−2.07192	−	0.840918i	−0.102955	−	0.0417855i
$406$	0.880642	+	1.37031i	0.0437055	+	0.0680072i
$407$	26.6416	−	14.5474i	1.32057	−	0.721088i
$408$	5.42530	+	4.06133i	0.268592	+	0.201066i
$409$	8.13727	+	3.71617i	0.402362	+	0.183753i	0.606309	−	0.795229i	$-0.292650\pi$
$409$	8.13727	+	3.71617i	0.402362	+	0.183753i	−0.203947	+	0.978982i	$0.565377\pi$
$410$	11.5675	+	2.00174i	0.571277	+	0.0988587i
$411$	1.57929	−	2.45743i	0.0779008	−	0.121216i
$412$	−1.02665	+	14.3545i	−0.0505795	+	0.707194i
$413$	−16.7964	+	16.7964i	−0.826496	+	0.826496i
$414$	0.232427	+	4.79020i	0.0114232	+	0.235425i
$415$	−0.651078	+	22.7971i	−0.0319602	+	1.11906i
$416$	−0.766336	−	0.884399i	−0.0375727	−	0.0433612i
$417$	16.0749	−	3.49687i	0.787190	−	0.171243i
$418$	−22.1993	+	16.6182i	−1.08580	+	0.812821i
$419$	12.2219	−	26.7622i	0.597077	−	1.30742i	−0.333992	−	0.942576i	$-0.608396\pi$
$419$	12.2219	−	26.7622i	0.597077	−	1.30742i	0.931070	−	0.364841i	$-0.118877\pi$
$420$	−3.33921	−	2.65176i	−0.162937	−	0.129393i
$421$	−4.64335	+	15.8138i	−0.226303	+	0.770718i	0.765555	+	0.643370i	$0.222464\pi$
$421$	−4.64335	+	15.8138i	−0.226303	+	0.770718i	−0.991858	+	0.127347i	$0.959354\pi$
$422$	5.30128	−	24.3696i	0.258062	−	1.18629i
$423$	1.64824	−	4.41910i	0.0801402	−	0.214864i
$424$	4.51223	−	1.32491i	0.219133	−	0.0643433i
$425$	−0.484401	−	33.8817i	−0.0234969	−	1.64350i
$426$	−5.30872	+	6.12659i	−0.257208	+	0.296834i
$427$	3.11109	−	5.69754i	0.150556	−	0.275723i
$428$	−15.9218	−	5.93854i	−0.769612	−	0.287050i
$429$	3.98143	−	2.55871i	0.192225	−	0.123536i
$430$	0.901990	+	1.77022i	0.0434978	+	0.0853676i
$431$	30.8964	−	4.44223i	1.48823	−	0.213975i	0.650267	−	0.759706i	$-0.274657\pi$
$431$	30.8964	−	4.44223i	1.48823	−	0.213975i	0.837960	+	0.545731i	$0.183748\pi$
$432$	−0.349464	−	0.936950i	−0.0168136	−	0.0450790i
$433$	−23.8096	−	31.8059i	−1.14422	−	1.52850i	−0.810418	−	0.585852i	$-0.800760\pi$
$433$	−23.8096	−	31.8059i	−1.14422	−	1.52850i	−0.333799	−	0.942644i	$-0.608331\pi$
$434$	0.236898	+	0.152245i	0.0113715	+	0.00730800i
$435$	1.47862	−	1.20908i	0.0708943	−	0.0579709i
$436$		−	8.62765i		−	0.413190i
$437$	−29.5909	−	14.3421i	−1.41553	−	0.686075i
$438$	0.812077	+	0.812077i	0.0388025	+	0.0388025i
$439$	−20.4028	+	17.6791i	−0.973773	+	0.843779i	−0.987738	−	0.156123i	$-0.950100\pi$
$439$	−20.4028	+	17.6791i	−0.973773	+	0.843779i	0.0139644	+	0.999902i	$0.495555\pi$
$440$	5.10437	−	7.46503i	0.243341	−	0.355881i
$441$	−0.478686	+	3.32934i	−0.0227946	+	0.158540i
$442$	7.43064	−	2.77149i	0.353440	−	0.131826i
$443$	8.27882	−	11.0592i	0.393339	−	0.525439i	−0.559535	−	0.828807i	$-0.689020\pi$
$443$	8.27882	−	11.0592i	0.393339	−	0.525439i	0.952874	+	0.303368i	$0.0981111\pi$
$444$	−7.20152	−	2.11456i	−0.341769	−	0.100352i
$445$	1.18724	−	4.79430i	0.0562804	−	0.227272i
$446$	9.09255	+	19.9099i	0.430545	+	0.942762i
$447$	−4.68747	−	2.55955i	−0.221710	−	0.121063i
$448$	−0.136040	−	1.90208i	−0.00642727	−	0.0898650i
$449$	−14.9053	−	12.9155i	−0.703426	−	0.609522i	0.227910	−	0.973682i	$-0.426811\pi$
$449$	−14.9053	−	12.9155i	−0.703426	−	0.609522i	−0.931337	+	0.364160i	$0.881356\pi$
$450$	−2.64280	+	4.24448i	−0.124583	+	0.200087i
$451$	−19.3138	+	8.82033i	−0.909453	+	0.415333i
$452$	10.8472	+	2.35967i	0.510210	+	0.110989i
$453$	−1.87419	−	3.43233i	−0.0880573	−	0.161265i
$454$	−3.79269	−	26.3787i	−0.178000	−	1.23802i
$455$	−4.72317	+	1.60961i	−0.221426	+	0.0754598i
$456$	6.78687	+	0.975805i	0.317825	+	0.0456963i
$457$	−2.80305	−	12.8854i	−0.131121	−	0.602755i	−0.995070	−	0.0991749i	$-0.968380\pi$
$457$	−2.80305	−	12.8854i	−0.131121	−	0.602755i	0.863949	−	0.503580i	$-0.167984\pi$
$458$	7.40998	+	0.529972i	0.346246	+	0.0247640i
$459$	6.77703			0.316325
$460$	10.6430	+	1.31430i	0.496231	+	0.0612797i
$461$	1.84467			0.0859148			0.0429574	−	0.999077i	$-0.486322\pi$
$461$	1.84467			0.0859148			0.0429574	+	0.999077i	$0.486322\pi$
$462$	7.69257	+	0.550184i	0.357891	+	0.0255969i
$463$	−1.91391	−	8.79812i	−0.0889471	−	0.408883i	0.911047	−	0.412302i	$-0.135275\pi$
$463$	−1.91391	−	8.79812i	−0.0889471	−	0.408883i	−0.999994	+	0.00341924i	$0.998912\pi$
$464$	0.845493	+	0.121564i	0.0392510	+	0.00564345i
$465$	0.145691	−	0.296326i	0.00675624	−	0.0137418i
$466$	−3.94162	−	27.4146i	−0.182592	−	1.26996i
$467$	−17.4287	−	31.9183i	−0.806505	−	1.47700i	−0.877526	−	0.479530i	$-0.840807\pi$
$467$	−17.4287	−	31.9183i	−0.806505	−	1.47700i	0.0710204	−	0.997475i	$-0.477374\pi$
$468$	−1.14348	−	0.248750i	−0.0528576	−	0.0114985i
$469$	−10.0805	+	4.60359i	−0.465472	+	0.212574i
$470$	−9.10826	−	5.31653i	−0.420133	−	0.245233i
$471$	−5.62360	−	4.87288i	−0.259122	−	0.224530i
$472$	0.888631	+	12.4247i	0.0409026	+	0.571893i
$473$	−3.15385	−	1.72213i	−0.145014	−	0.0791837i
$474$	3.54235	+	7.75667i	0.162706	+	0.356276i
$475$	−16.8587	−	29.8518i	−0.773531	−	1.36969i
$476$	12.3999	+	3.64095i	0.568349	+	0.166882i
$477$	2.81823	−	3.76472i	0.129038	−	0.172375i
$478$	1.52025	−	0.567024i	0.0695346	−	0.0259351i
$479$	−2.59986	+	18.0824i	−0.118791	+	0.826206i	0.840100	+	0.542431i	$0.182496\pi$
$479$	−2.59986	+	18.0824i	−0.118791	+	0.826206i	−0.958891	+	0.283775i	$0.908413\pi$
$480$	−2.19765	+	0.412740i	−0.100308	+	0.0188389i
$481$	−6.63789	+	5.75177i	−0.302662	+	0.262258i
$482$	−0.532838	−	0.532838i	−0.0242701	−	0.0242701i
$483$	3.60750	+	8.40379i	0.164147	+	0.382386i
$484$			5.35626i			0.243466i
$485$	7.48333	+	9.15158i	0.339800	+	0.415552i
$486$	−0.841254	−	0.540641i	−0.0381600	−	0.0245240i
$487$	−5.39094	−	7.20145i	−0.244287	−	0.326329i	0.661594	−	0.749863i	$-0.269880\pi$
$487$	−5.39094	−	7.20145i	−0.244287	−	0.326329i	−0.905880	+	0.423534i	$0.860790\pi$
$488$	−1.18964	−	3.18956i	−0.0538527	−	0.144385i
$489$	13.0405	−	1.87494i	0.589711	−	0.0847876i
$490$	7.15308	+	2.32411i	0.323143	+	0.104993i
$491$	21.7034	−	13.9479i	0.979461	−	0.629461i	0.0501429	−	0.998742i	$-0.484032\pi$
$491$	21.7034	−	13.9479i	0.979461	−	0.629461i	0.929318	+	0.369281i	$0.120396\pi$
$492$	4.91900	+	1.83469i	0.221766	+	0.0827143i
$493$	−2.77430	+	5.08076i	−0.124948	+	0.228826i
$494$	5.25451	−	6.06403i	0.236412	−	0.272833i
$495$	−0.387367	−	9.03500i	−0.0174109	−	0.406093i
$496$	0.141690	−	0.0416039i	0.00636207	−	0.00186807i
$497$	−5.40233	+	14.4842i	−0.242328	+	0.649705i
$498$	−2.16802	+	9.96622i	−0.0971513	+	0.446597i
$499$	−10.1088	+	34.4274i	−0.452532	+	1.54118i	0.345412	+	0.938451i	$0.387739\pi$
$499$	−10.1088	+	34.4274i	−0.452532	+	1.54118i	−0.797944	+	0.602731i	$0.794079\pi$
$500$	8.34430	+	7.44128i	0.373169	+	0.332784i
$501$	5.25451	−	11.5058i	0.234754	−	0.514040i
$502$	24.6871	−	18.4805i	1.10184	−	0.824827i
$503$	−24.4617	+	5.32132i	−1.09069	+	0.237266i	−0.721728	−	0.692177i	$-0.756652\pi$
$503$	−24.4617	+	5.32132i	−1.09069	+	0.237266i	−0.368966	+	0.929443i	$0.620288\pi$
$504$	−1.24878	−	1.44117i	−0.0556251	−	0.0641948i
$505$	21.3023	−	20.1193i	0.947940	−	0.895298i
$506$	−17.2317	+	8.90286i	−0.766045	+	0.395780i
$507$	8.22405	−	8.22405i	0.365243	−	0.365243i
$508$	0.454230	−	6.35097i	0.0201532	−	0.281779i
$509$	−20.5096	+	31.9135i	−0.909070	+	1.41454i	0.000960889		1.00000i	$0.499694\pi$
$509$	−20.5096	+	31.9135i	−0.909070	+	1.41454i	−0.910031	+	0.414541i	$0.863942\pi$
$510$	2.58396	−	14.9320i	0.114420	−	0.661199i
$511$	1.99212	+	0.909770i	0.0881262	+	0.0402459i
$512$	−0.800541	−	0.599278i	−0.0353793	−	0.0264846i
$513$	6.01795	−	3.28605i	0.265699	−	0.145083i
$514$	11.6576	+	18.1396i	0.514195	+	0.800104i
$515$	29.6413	−	12.5268i	1.30615	−	0.551996i
$516$	0.250323	+	0.852521i	0.0110198	+	0.0375301i
$517$	19.0262	−	1.36078i	0.836771	−	0.0598470i
$518$	−14.2762	+	1.02105i	−0.627259	+	0.0448624i
$519$	4.88052	+	16.6215i	0.214231	+	0.729604i
$520$	−0.984065	+	2.42462i	−0.0431541	+	0.106327i
$521$	12.7594	+	19.8540i	0.558999	+	0.869819i	0.999611	−	0.0278782i	$-0.00887505\pi$
$521$	12.7594	+	19.8540i	0.558999	+	0.869819i	−0.440612	+	0.897697i	$0.645239\pi$
$522$	0.749703	−	0.409369i	0.0328136	−	0.0179176i
$523$	−1.17200	−	0.877351i	−0.0512481	−	0.0383639i	0.573347	−	0.819313i	$-0.305645\pi$
$523$	−1.17200	−	0.877351i	−0.0512481	−	0.0383639i	−0.624595	+	0.780949i	$0.714736\pi$
$524$	3.52795	+	1.61116i	0.154119	+	0.0703839i
$525$	−1.89335	+	9.34483i	−0.0826327	+	0.407842i
$526$	15.1214	−	23.5293i	0.659323	−	1.02593i
$527$	−0.0713945	+	0.998226i	−0.00310999	+	0.0434834i
$528$	2.85974	−	2.85974i	0.124454	−	0.124454i
$529$	−18.7588	−	13.3082i	−0.815600	−	0.578617i
$530$	−7.22035	−	7.64490i	−0.313632	−	0.332073i
$531$	8.15722	+	9.41394i	0.353993	+	0.408530i
$532$	12.7765	−	2.77935i	0.553929	−	0.120500i
$533$	4.91830	−	3.68179i	0.213035	−	0.159476i
$534$	0.917585	−	2.00923i	0.0397078	−	0.0869479i
$535$	4.33176	+	37.7504i	0.187278	+	1.63209i
$536$	−1.63725	+	5.57595i	−0.0707182	+	0.240844i
$537$	−1.64877	+	7.57926i	−0.0711495	+	0.327069i
$538$	1.71398	−	4.59535i	0.0738948	−	0.198120i
$539$	−13.0522	+	3.83248i	−0.562199	+	0.165077i
$540$	−1.51196	+	1.64742i	−0.0650644	+	0.0708935i
$541$	15.4540	−	17.8348i	0.664418	−	0.766780i	−0.319074	−	0.947730i	$-0.603372\pi$
$541$	15.4540	−	17.8348i	0.664418	−	0.766780i	0.983492	+	0.180950i	$0.0579173\pi$
$542$	−8.64837	+	15.8383i	−0.371479	+	0.680313i
$543$	21.5726	+	8.04618i	0.925771	+	0.345295i
$544$	5.70120	−	3.66394i	0.244437	−	0.157090i
$545$	−17.1892	+	8.75853i	−0.736306	+	0.375174i
$546$	−2.20884	+	0.317583i	−0.0945297	+	0.0135913i
$547$	−4.16990	−	11.1799i	−0.178292	−	0.478019i	0.816806	−	0.576912i	$-0.195743\pi$
$547$	−4.16990	−	11.1799i	−0.178292	−	0.478019i	−0.995098	+	0.0988932i	$0.968470\pi$
$548$	−1.75058	−	2.33850i	−0.0747811	−	0.0998958i
$549$	−2.86379	−	1.84045i	−0.122224	−	0.0785484i
$550$	−20.0547	−	2.59139i	−0.855136	−	0.110497i
$551$			5.85688i			0.249511i
$552$	4.56940	+	1.45623i	0.194486	+	0.0619813i
$553$	11.4983	+	11.4983i	0.488956	+	0.488956i
$554$	7.46363	−	6.46727i	0.317099	−	0.274768i
$555$	3.09784	+	16.4945i	0.131496	+	0.700154i
$556$	2.34120	−	16.2834i	0.0992888	−	0.690569i
$557$	−4.08705	+	1.52439i	−0.173174	+	0.0645905i	−0.434556	−	0.900645i	$-0.643095\pi$
$557$	−4.08705	+	1.52439i	−0.173174	+	0.0645905i	0.261382	+	0.965235i	$0.415822\pi$
$558$	0.0884963	−	0.118217i	0.00374635	−	0.00500454i
$559$	0.997643	+	0.292934i	0.0421958	+	0.0123898i
$560$	−3.65150	+	2.20197i	−0.154304	+	0.0930504i
$561$	11.3858	+	24.9314i	0.480709	+	1.05261i
$562$	8.33085	+	4.54899i	0.351416	+	0.191887i
$563$	−1.12949	−	15.7924i	−0.0476024	−	0.665569i	−0.964102	−	0.265533i	$-0.914452\pi$
$563$	−1.12949	−	15.7924i	−0.0476024	−	0.665569i	0.916499	−	0.400036i	$-0.131002\pi$
$564$	−3.56448	−	3.08864i	−0.150092	−	0.130055i
$565$	−6.31050	−	24.0068i	−0.265485	−	1.00998i
$566$	−25.2059	+	11.5112i	−1.05948	+	0.483850i
$567$	−1.86336	−	0.405350i	−0.0782539	−	0.0170231i
$568$	3.88510	+	7.11503i	0.163015	+	0.298540i
$569$	1.79708	+	12.4990i	0.0753376	+	0.523985i	0.992188	+	0.124753i	$0.0398139\pi$
$569$	1.79708	+	12.4990i	0.0753376	+	0.523985i	−0.916850	+	0.399231i	$0.869277\pi$
$570$	−4.94569	−	14.5124i	−0.207152	−	0.607857i
$571$	21.8148	+	3.13650i	0.912923	+	0.131259i	0.582740	−	0.812659i	$-0.301981\pi$
$571$	21.8148	+	3.13650i	0.912923	+	0.131259i	0.330183	+	0.943917i	$0.392890\pi$
$572$	−1.00602	−	4.62458i	−0.0420636	−	0.193363i
$573$	−10.2951	−	0.736319i	−0.430084	−	0.0307602i
$574$	10.0115			0.417871
$575$	−8.18587	−	22.5387i	−0.341374	−	0.939927i
$576$	−1.00000			−0.0416667
$577$	2.51039	+	0.179547i	0.104509	+	0.00747462i	0.123496	−	0.992345i	$-0.460589\pi$
$577$	2.51039	+	0.179547i	0.104509	+	0.00747462i	−0.0189868	+	0.999820i	$0.506044\pi$
$578$	6.14913	+	28.2671i	0.255770	+	1.17576i
$579$	−14.0104	−	2.01438i	−0.582250	−	0.0837150i
$580$	−0.616123	−	1.80792i	−0.0255831	−	0.0750698i
$581$	2.76795	+	19.2515i	0.114834	+	0.798688i
$582$	2.53370	+	4.64012i	0.105025	+	0.192339i
$583$	18.5845	+	4.04281i	0.769691	+	0.167436i
$584$	1.04467	−	0.477083i	0.0432286	−	0.0197418i
$585$	0.665235	+	2.53074i	0.0275041	+	0.104633i
$586$	−22.3635	−	19.3781i	−0.923827	−	0.800501i
$587$	−0.777326	−	10.8684i	−0.0320837	−	0.448588i	−0.987949	−	0.154782i	$-0.950532\pi$
$587$	−0.777326	−	10.8684i	−0.0320837	−	0.448588i	0.955865	−	0.293806i	$-0.0949221\pi$
$588$	2.95214	+	1.61199i	0.121744	+	0.0664773i
$589$	0.420622	+	0.921034i	0.0173314	+	0.0379506i
$590$	23.8521	−	14.3836i	0.981976	−	0.592164i
$591$	19.3489	+	5.68136i	0.795909	+	0.233700i
$592$	−4.49790	+	6.00850i	−0.184863	+	0.246948i
$593$	25.6852	−	9.58007i	1.05476	−	0.393407i	0.238534	−	0.971134i	$-0.423333\pi$
$593$	25.6852	−	9.58007i	1.05476	−	0.393407i	0.816230	+	0.577728i	$0.196060\pi$
$594$	0.575562	−	4.00312i	0.0236156	−	0.164250i
$595$	−5.33401	−	28.4011i	−0.218673	−	1.16433i
$596$	−4.03628	+	3.49745i	−0.165332	+	0.143261i
$597$	−8.65235	−	8.65235i	−0.354117	−	0.354117i
$598$	4.32453	−	3.57706i	0.176843	−	0.146277i
$599$		−	16.2672i		−	0.664662i	−0.943163	−	0.332331i	$-0.892165\pi$
$599$		−	16.2672i		−	0.664662i	0.943163	−	0.332331i	$-0.107835\pi$
$600$	3.05330	+	3.95946i	0.124651	+	0.161644i
$601$	−1.86381	−	1.19780i	−0.0760264	−	0.0488592i	0.502075	−	0.864824i	$-0.332570\pi$
$601$	−1.86381	−	1.19780i	−0.0760264	−	0.0488592i	−0.578102	+	0.815965i	$0.696206\pi$
$602$	1.01538	+	1.35639i	0.0413838	+	0.0552823i
$603$	2.03086	+	5.44494i	0.0827029	+	0.221735i
$604$	−3.87088	+	0.556549i	−0.157504	+	0.0226457i
$605$	10.6715	−	5.43751i	0.433859	−	0.221066i
$606$	11.0238	−	7.08456i	0.447811	−	0.287791i
$607$	16.8021	+	6.26687i	0.681977	+	0.254364i	0.666488	−	0.745516i	$-0.267797\pi$
$607$	16.8021	+	6.26687i	0.681977	+	0.254364i	0.0154893	+	0.999880i	$0.495069\pi$
$608$	3.28605	−	6.01795i	0.133267	−	0.244060i
$609$	1.06669	−	1.23103i	0.0432246	−	0.0498839i
$610$	−5.14701	+	5.60812i	−0.208396	+	0.227066i
$611$	−5.29578	+	1.55498i	−0.214244	+	0.0629078i
$612$	2.36833	−	6.34974i	0.0957341	−	0.256673i
$613$	−1.24723	+	5.73343i	−0.0503752	+	0.231571i	−0.995450	−	0.0952822i	$-0.969625\pi$
$613$	−1.24723	+	5.73343i	−0.0503752	+	0.231571i	0.945075	+	0.326853i	$0.105988\pi$
$614$	9.28887	−	31.6350i	0.374868	−	1.27668i
$615$	−1.33828	−	11.6629i	−0.0539648	−	0.470292i
$616$	3.20377	−	7.01528i	0.129084	−	0.282654i
$617$	−12.1261	+	9.07749i	−0.488179	+	0.365446i	−0.814831	−	0.579699i	$-0.803170\pi$
$617$	−12.1261	+	9.07749i	−0.488179	+	0.365446i	0.326652	+	0.945145i	$0.394079\pi$
$618$	14.0623	−	3.05906i	0.565667	−	0.123053i
$619$	−1.45069	−	1.67419i	−0.0583082	−	0.0672913i	0.725846	−	0.687857i	$-0.241448\pi$
$619$	−1.45069	−	1.67419i	−0.0583082	−	0.0672913i	−0.784154	+	0.620566i	$0.786903\pi$
$620$	−0.226729	−	0.240060i	−0.00910564	−	0.00964104i
$621$	4.53068	−	1.57257i	0.181810	−	0.0631049i
$622$	12.0432	−	12.0432i	0.482888	−	0.482888i
$623$	0.300490	−	4.20139i	0.0120389	−	0.168325i
$624$	−0.632673	+	0.984458i	−0.0253272	+	0.0394099i
$625$	6.35469	−	24.1789i	0.254188	−	0.967155i
$626$	−7.46040	−	3.40705i	−0.298178	−	0.136173i
$627$	22.1993	+	16.6182i	0.886553	+	0.663666i
$628$	−6.53089	+	3.56613i	−0.260611	+	0.142304i
$629$	−27.4999	−	42.7906i	−1.09649	−	1.70617i
$630$	−1.60358	+	3.95103i	−0.0638882	+	0.157413i
$631$	8.85751	+	30.1659i	0.352612	+	1.20089i	0.924701	+	0.380694i	$0.124315\pi$
$631$	8.85751	+	30.1659i	0.352612	+	1.20089i	−0.572089	+	0.820191i	$0.693867\pi$
$632$	8.50554	−	0.608328i	0.338332	−	0.0241980i
$633$	−24.8760	+	1.77917i	−0.988732	+	0.0707155i
$634$	1.31953	+	4.49391i	0.0524053	+	0.178476i
$635$	−13.1144	+	5.54233i	−0.520430	+	0.219940i
$636$	−2.54248	−	3.95618i	−0.100816	−	0.156873i
$637$	3.45467	−	1.88639i	0.136879	−	0.0747416i
$638$	2.76553	+	2.07025i	0.109489	+	0.0819621i
$639$	7.37406	+	3.36762i	0.291713	+	0.133221i
$640$	−0.381282	+	2.20332i	−0.0150715	+	0.0870939i
$641$	18.7627	−	29.1953i	0.741081	−	1.15314i	−0.242054	−	0.970263i	$-0.577821\pi$
$641$	18.7627	−	29.1953i	0.741081	−	1.15314i	0.983135	−	0.182882i	$-0.0585425\pi$
$642$	−1.21229	+	16.9500i	−0.0478451	+	0.668962i
$643$	32.2500	−	32.2500i	1.27182	−	1.27182i	0.326682	−	0.945134i	$-0.394069\pi$
$643$	32.2500	−	32.2500i	1.27182	−	1.27182i	0.945134	−	0.326682i	$-0.105931\pi$
$644$	9.13463	−	0.443224i	0.359955	−	0.0174655i
$645$	1.44439	−	1.36418i	0.0568729	−	0.0537146i
$646$	30.4300	+	35.1181i	1.19725	+	1.38170i
$647$	−5.55695	+	1.20884i	−0.218466	+	0.0475244i	−0.320466	−	0.947260i	$-0.603840\pi$
$647$	−5.55695	+	1.20884i	−0.218466	+	0.0475244i	0.102000	+	0.994784i	$0.467476\pi$
$648$	−0.800541	+	0.599278i	−0.0314482	+	0.0235419i
$649$	−20.9275	+	45.8249i	−0.821477	+	1.79878i
$650$	5.82967	−	0.500804i	0.228658	−	0.0196431i
$651$	0.0793363	−	0.270194i	0.00310943	−	0.0105898i
$652$	2.80046	−	12.8735i	0.109674	−	0.504165i
$653$	−8.32708	+	22.3258i	−0.325864	+	0.873675i	0.665952	+	0.745995i	$0.268026\pi$
$653$	−8.32708	+	22.3258i	−0.325864	+	0.873675i	−0.991815	+	0.127680i	$0.959247\pi$
$654$	−8.27817	+	2.43069i	−0.323702	+	0.0950475i
$655$	−0.371482	−	8.66449i	−0.0145150	−	0.338550i
$656$	3.43803	−	3.96770i	0.134233	−	0.154913i
$657$	0.550393	−	1.00797i	0.0214729	−	0.0393247i
$658$	−8.42697	−	3.14310i	−0.328518	−	0.122531i
$659$	5.58121	−	3.58683i	0.217413	−	0.139723i	−0.427402	−	0.904062i	$-0.640571\pi$
$659$	5.58121	−	3.58683i	0.217413	−	0.139723i	0.644815	+	0.764339i	$0.276935\pi$
$660$	−8.60071	−	2.79447i	−0.334782	−	0.108774i
$661$	25.8332	−	3.71426i	1.00480	−	0.144468i	0.379777	−	0.925078i	$-0.376001\pi$
$661$	25.8332	−	3.71426i	1.00480	−	0.144468i	0.625018	+	0.780610i	$0.285091\pi$
$662$	−2.42139	−	6.49200i	−0.0941100	−	0.252319i
$663$	−4.75267	−	6.34883i	−0.184579	−	0.246568i
$664$	8.58020	+	5.51416i	0.332977	+	0.213991i
$665$	−18.5077	−	22.6336i	−0.717697	−	0.877692i
$666$			7.50554i			0.290834i
$667$	−0.675760	+	4.04042i	−0.0261655	+	0.156446i
$668$	−8.94406	−	8.94406i	−0.346056	−	0.346056i
$669$	16.5418	−	14.3335i	0.639541	−	0.554166i
$670$	12.7713	−	2.39858i	0.493398	−	0.0926650i
$671$	1.95933	−	13.6274i	0.0756389	−	0.526080i
$672$	−1.78671	+	0.666408i	−0.0689238	+	0.0257072i
$673$	−6.41624	+	8.57109i	−0.247328	+	0.330391i	−0.906975	−	0.421184i	$-0.861615\pi$
$673$	−6.41624	+	8.57109i	−0.247328	+	0.330391i	0.659647	+	0.751575i	$0.270706\pi$
$674$	3.40131	+	0.998716i	0.131014	+	0.0384691i
$675$	4.81711	+	1.33994i	0.185411	+	0.0515742i
$676$	−4.83151	−	10.5795i	−0.185827	−	0.406905i
$677$	17.1728	+	9.37706i	0.660004	+	0.360390i	0.774085	−	0.633082i	$-0.218210\pi$
$677$	17.1728	+	9.37706i	0.660004	+	0.360390i	−0.114081	+	0.993471i	$0.536392\pi$
$678$	−0.791930	−	11.0726i	−0.0304139	−	0.425242i
$679$	7.61919	+	6.60206i	0.292398	+	0.253364i
$680$	−13.0875	−	7.63923i	−0.501883	−	0.292951i
$681$	−24.2417	+	11.0708i	−0.928944	+	0.424234i
$682$	0.583578	+	0.126950i	0.0223464	+	0.00486115i
$683$	8.49215	+	15.5522i	0.324943	+	0.595089i	0.988176	−	0.153324i	$-0.0489979\pi$
$683$	8.49215	+	15.5522i	0.324943	+	0.595089i	−0.663233	+	0.748413i	$0.730816\pi$
$684$	−0.975805	−	6.78687i	−0.0373108	−	0.259503i
$685$	−2.88196	+	5.86173i	−0.110114	+	0.223965i
$686$	19.5616	+	2.81253i	0.746864	+	0.107383i
$687$	−1.57913	−	7.25913i	−0.0602475	−	0.276953i
$688$	0.886248	+	0.0633857i	0.0337879	+	0.00241656i
$689$	−5.50325			−0.209657
$690$	−1.73740	−	10.5821i	−0.0661418	−	0.402855i
$691$	−17.0102			−0.647100			−0.323550	−	0.946211i	$-0.604876\pi$
$691$	−17.0102			−0.647100			−0.323550	+	0.946211i	$0.604876\pi$
$692$	17.2791	+	1.23583i	0.656853	+	0.0469791i
$693$	−1.63935	−	7.53597i	−0.0622738	−	0.286268i
$694$	−8.88970	−	1.27815i	−0.337448	−	0.0485177i
$695$	−34.8188	+	11.8659i	−1.32075	+	0.450100i
$696$	−0.121564	−	0.845493i	−0.00460786	−	0.0320483i
$697$	17.0515	+	31.2274i	0.645870	+	1.18282i
$698$	−4.87346	−	1.06016i	−0.184463	−	0.0401275i
$699$	−25.1936	+	11.5055i	−0.952910	+	0.435179i
$700$	8.09398	+	5.03966i	0.305924	+	0.190481i
$701$	37.7075	+	32.6738i	1.42419	+	1.23407i	0.931436	+	0.363904i	$0.118556\pi$
$701$	37.7075	+	32.6738i	1.42419	+	1.23407i	0.492757	+	0.870167i	$0.335989\pi$
$702$	0.0834831	+	1.16725i	0.00315087	+	0.0440549i
$703$	−45.1680	−	24.6636i	−1.70354	−	0.930205i
$704$	−1.68006	−	3.67881i	−0.0633196	−	0.138650i
$705$	−2.53508	+	10.2371i	−0.0954765	+	0.385553i
$706$	−16.0036	−	4.69908i	−0.602303	−	0.176852i
$707$	14.9751	−	20.0044i	0.563196	−	0.752342i
$708$	11.6710	−	4.35307i	0.438625	−	0.163599i
$709$	1.16913	−	8.13145i	0.0439075	−	0.305383i	−0.956020	−	0.293303i	$-0.905246\pi$
$709$	1.16913	−	8.13145i	0.0439075	−	0.305383i	0.999927	−	0.0120802i	$-0.00384534\pi$
$710$	10.2315	−	14.9634i	0.383983	−	0.561567i
$711$	6.44448	−	5.58417i	0.241687	−	0.209423i
$712$	−1.56188	−	1.56188i	−0.0585341	−	0.0585341i
$713$	0.183902	+	0.683915i	0.00688719	+	0.0256128i
$714$		−	12.9234i		−	0.483646i
$715$	−8.19247	+	6.69906i	−0.306381	+	0.250531i
$716$	6.52520	+	4.19349i	0.243858	+	0.156718i
$717$	−0.972359	−	1.29892i	−0.0363134	−	0.0485090i
$718$	0.518894	+	1.39121i	0.0193649	+	0.0519194i
$719$	−22.5243	+	3.23850i	−0.840014	+	0.120776i	−0.548875	−	0.835905i	$-0.684944\pi$
$719$	−22.5243	+	3.23850i	−0.840014	+	0.120776i	−0.291140	+	0.956681i	$0.594034\pi$
$720$	1.01517	+	1.99234i	0.0378331	+	0.0742502i
$721$	23.0866	−	14.8368i	0.859789	−	0.552553i
$722$	26.2476	+	9.78984i	0.976834	+	0.364340i
$723$	−0.361137	+	0.661373i	−0.0134308	+	0.0245967i
$724$	15.0777	−	17.4006i	0.560360	−	0.646689i
$725$	−2.97653	+	3.06287i	−0.110546	+	0.113752i
$726$	5.13929	−	1.50903i	0.190737	−	0.0560055i
$727$	2.31363	−	6.20308i	0.0858078	−	0.230060i	−0.886958	−	0.461850i	$-0.847186\pi$
$727$	2.31363	−	6.20308i	0.0858078	−	0.230060i	0.972766	+	0.231791i	$0.0744584\pi$
$728$	−0.474351	+	2.18056i	−0.0175806	+	0.0808168i
$729$	−0.281733	+	0.959493i	−0.0104345	+	0.0355368i
$730$	−2.01103	−	1.59701i	−0.0744315	−	0.0591082i
$731$	−2.50141	+	5.47732i	−0.0925180	+	0.202586i
$732$	−2.72520	+	2.04006i	−0.100726	+	0.0754027i
$733$	39.5554	−	8.60475i	1.46101	−	0.317824i	0.589328	−	0.807894i	$-0.299393\pi$
$733$	39.5554	−	8.60475i	1.46101	−	0.317824i	0.871683	+	0.490070i	$0.163029\pi$
$734$	9.71026	+	11.2062i	0.358412	+	0.413630i
$735$	0.214715	−	7.51811i	0.00791990	−	0.277310i
$736$	2.96125	−	3.77240i	0.109153	−	0.139052i
$737$	−16.6190	+	16.6190i	−0.612167	+	0.612167i
$738$	0.374532	−	5.23664i	0.0137867	−	0.192763i
$739$	−13.1124	+	20.4033i	−0.482348	+	0.750548i	−0.994086	−	0.108593i	$-0.965365\pi$
$739$	−13.1124	+	20.4033i	−0.482348	+	0.750548i	0.511738	+	0.859141i	$0.329002\pi$
$740$	16.5371	+	2.86173i	0.607917	+	0.105199i
$741$	−7.29876	−	3.33323i	−0.268127	−	0.122449i
$742$	−7.17910	−	5.37421i	−0.263553	−	0.197293i
$743$	−12.5162	+	6.83439i	−0.459176	+	0.250729i	−0.692150	−	0.721754i	$-0.743336\pi$
$743$	−12.5162	+	6.83439i	−0.459176	+	0.250729i	0.232973	+	0.972483i	$0.425154\pi$
$744$	−0.0798373	−	0.124229i	−0.00292698	−	0.00455447i
$745$	11.0656	+	4.49114i	0.405413	+	0.164543i
$746$	10.0481	+	34.2208i	0.367888	+	1.25291i
$747$	10.1733	−	0.727610i	0.372222	−	0.0266219i
$748$	27.3384	−	1.95528i	0.999592	−	0.0714923i
$749$	9.12960	+	31.0926i	0.333588	+	1.13610i
$750$	4.78899	−	10.1028i	0.174869	−	0.368900i
$751$	−4.59675	−	7.15268i	−0.167738	−	0.261005i	0.747201	−	0.664598i	$-0.231397\pi$
$751$	−4.59675	−	7.15268i	−0.167738	−	0.261005i	−0.914938	+	0.403594i	$0.867761\pi$
$752$	−4.13955	+	2.26037i	−0.150954	+	0.0824271i
$753$	−24.6871	−	18.4805i	−0.899649	−	0.673468i
$754$	−0.909263	−	0.415246i	−0.0331134	−	0.0151224i
$755$	5.03844	+	7.14714i	0.183368	+	0.260111i
$756$	−1.03097	+	1.60422i	−0.0374960	+	0.0583450i
$757$	−3.60672	+	50.4285i	−0.131088	+	1.83285i	0.328247	+	0.944592i	$0.393542\pi$
$757$	−3.60672	+	50.4285i	−0.131088	+	1.83285i	−0.459335	+	0.888263i	$0.651912\pi$
$758$	−5.21128	+	5.21128i	−0.189282	+	0.189282i
$759$	13.3970	+	14.0255i	0.486279	+	0.509094i
$760$	−15.3257	−	0.437699i	−0.555922	−	0.0158770i
$761$	−33.9845	−	39.2203i	−1.23194	−	1.42173i	−0.872535	−	0.488551i	$-0.837526\pi$
$761$	−33.9845	−	39.2203i	−1.23194	−	1.42173i	−0.359403	−	0.933182i	$-0.617020\pi$
$762$	−6.22168	+	1.35344i	−0.225388	+	0.0490301i
$763$	−13.1708	+	9.85957i	−0.476817	+	0.356941i
$764$	−4.28766	+	9.38866i	−0.155122	+	0.339670i
$765$	−15.0551	+	1.72754i	−0.544319	+	0.0624592i
$766$	−4.94012	+	16.8245i	−0.178494	+	0.607894i
$767$	3.09853	−	14.2437i	0.111881	−	0.514311i
$768$	−0.349464	+	0.936950i	−0.0126102	+	0.0338093i
$769$	20.0302	−	5.88139i	0.722306	−	0.212088i	0.100140	−	0.994973i	$-0.468071\pi$
$769$	20.0302	−	5.88139i	0.722306	−	0.212088i	0.622166	+	0.782885i	$0.286253\pi$
$770$	−17.2292	+	0.738687i	−0.620898	+	0.0266204i
$771$	14.1205	−	16.2959i	0.508537	−	0.586883i
$772$	−6.78349	+	12.4230i	−0.244143	+	0.447115i
$773$	−20.4496	−	7.62730i	−0.735521	−	0.274335i	−0.0463412	−	0.998926i	$-0.514756\pi$
$773$	−20.4496	−	7.62730i	−0.735521	−	0.274335i	−0.689180	+	0.724591i	$0.742029\pi$
$774$	0.747463	−	0.480366i	0.0268670	−	0.0172664i
$775$	−0.248114	+	0.695423i	−0.00891251	+	0.0249803i
$776$	5.23299	−	0.752391i	0.187853	−	0.0270093i
$777$	5.00175	+	13.4102i	0.179437	+	0.481089i
$778$	−17.1391	−	22.8952i	−0.614468	−	0.820833i
$779$	30.2831	+	19.4618i	1.08501	+	0.697291i
$780$	2.60365	+	0.261109i	0.0932255	+	0.00934922i
$781$			32.7856i			1.17316i
$782$	16.9405	+	27.7375i	0.605791	+	0.991890i
$783$	−0.604002	−	0.604002i	−0.0215853	−	0.0215853i
$784$	2.54202	−	2.20267i	0.0907864	−	0.0786668i
$785$	13.7349	+	9.39153i	0.490220	+	0.335198i
$786$	0.551959	−	3.83896i	0.0196877	−	0.136931i
$787$	27.7946	−	10.3668i	0.990769	−	0.369538i	0.198761	−	0.980048i	$-0.436308\pi$
$787$	27.7946	−	10.3668i	0.990769	−	0.369538i	0.792008	+	0.610510i	$0.209036\pi$
$788$	12.0849	−	16.1436i	0.430507	−	0.575091i
$789$	−26.8364	−	7.87987i	−0.955400	−	0.280531i
$790$	−9.84656	−	16.3284i	−0.350325	−	0.580938i
$791$	−8.79383	−	19.2558i	−0.312673	−	0.684658i
$792$	−3.54959	−	1.93822i	−0.126129	−	0.0688717i
$793$	0.284193	+	3.97353i	0.0100920	+	0.141104i
$794$	−4.80350	−	4.16225i	−0.170470	−	0.147713i
$795$	−5.30102	+	9.08169i	−0.188008	+	0.322094i
$796$	−11.1305	+	5.08313i	−0.394510	+	0.180167i
$797$	−51.5818	−	11.2209i	−1.82712	−	0.397466i	−0.838134	−	0.545464i	$-0.816354\pi$
$797$	−51.5818	−	11.2209i	−1.82712	−	0.397466i	−0.988988	+	0.147998i	$0.952717\pi$
$798$	−6.26631	−	11.4759i	−0.221825	−	0.406242i
$799$	−4.54891	−	31.6384i	−0.160929	−	1.11929i
$800$	4.77684	−	1.47710i	0.168887	−	0.0522234i
$801$	−2.18636	−	0.314350i	−0.0772511	−	0.0111070i
$802$	−7.19853	−	33.0911i	−0.254189	−	1.16849i
$803$	4.63283	+	0.331346i	0.163489	+	0.0116930i
$804$	5.81135			0.204950
$805$	−10.1562	−	17.7494i	−0.357961	−	0.625583i
$806$	−0.172809			−0.00608695
$807$	−4.89209	−	0.349889i	−0.172210	−	0.0123167i
$808$	−2.78546	−	12.8045i	−0.0979920	−	0.450462i
$809$	−36.3859	−	5.23150i	−1.27926	−	0.183930i	−0.531021	−	0.847359i	$-0.678191\pi$
$809$	−36.3859	−	5.23150i	−1.27926	−	0.183930i	−0.748239	+	0.663429i	$0.769101\pi$
$810$	2.00665	+	0.986584i	0.0705066	+	0.0346650i
$811$	7.15990	+	49.7982i	0.251418	+	1.74865i	0.589715	+	0.807612i	$0.299240\pi$
$811$	7.15990	+	49.7982i	0.251418	+	1.74865i	−0.338297	+	0.941040i	$0.609851\pi$
$812$	−0.780642	−	1.42964i	−0.0273952	−	0.0501705i
$813$	17.6333	+	3.83588i	0.618426	+	0.134530i
$814$	−27.6115	+	12.6097i	−0.967782	+	0.441971i
$815$	−28.4913	+	7.48930i	−0.998008	+	0.262339i
$816$	−5.12174	−	4.43801i	−0.179297	−	0.155362i
$817$	0.434614	+	6.07670i	0.0152052	+	0.212597i
$818$	−7.85143	−	4.28720i	−0.274519	−	0.149899i
$819$	0.927022	+	2.02989i	0.0323928	+	0.0709302i
$820$	−11.3952	−	2.82185i	−0.397938	−	0.0985433i
$821$	46.9527	+	13.7865i	1.63866	+	0.481154i	0.965945	−	0.258749i	$-0.0833102\pi$
$821$	46.9527	+	13.7865i	1.63866	+	0.481154i	0.672714	+	0.739902i	$0.265128\pi$
$822$	−1.75058	+	2.33850i	−0.0610585	+	0.0815646i
$823$	21.6722	−	8.08332i	0.755447	−	0.281767i	0.0579154	−	0.998321i	$-0.481555\pi$
$823$	21.6722	−	8.08332i	0.755447	−	0.281767i	0.697531	+	0.716555i	$0.254282\pi$
$824$	2.04807	−	14.2447i	0.0713480	−	0.496236i
$825$	3.16365	+	19.9724i	0.110144	+	0.695351i
$826$	17.9518	−	15.5553i	0.624624	−	0.541240i
$827$	−16.2620	−	16.2620i	−0.565484	−	0.565484i	0.365376	−	0.930860i	$-0.380940\pi$
$827$	−16.2620	−	16.2620i	−0.565484	−	0.565484i	−0.930860	+	0.365376i	$0.880940\pi$
$828$	0.109894	−	4.79457i	0.00381908	−	0.166623i
$829$			28.1108i			0.976330i	0.872751	+	0.488165i	$0.162334\pi$
$829$			28.1108i			0.976330i	−0.872751	+	0.488165i	$0.837666\pi$
$830$	2.27574	−	22.6925i	0.0789922	−	0.787669i
$831$	−8.30805	−	5.33926i	−0.288203	−	0.185217i
$832$	0.701291	+	0.936815i	0.0243129	+	0.0324782i
$833$	7.96605	+	21.3578i	0.276007	+	0.740004i
$834$	−16.2834	+	2.34120i	−0.563847	+	0.0810690i
$835$	−8.73990	+	26.8994i	−0.302457	+	0.930891i
$836$	23.3282	−	14.9921i	0.806824	−	0.518514i
$837$	−0.138361	−	0.0516060i	−0.00478245	−	0.00178376i
$838$	−14.0999	+	25.8221i	−0.487074	+	0.892009i
$839$	2.17957	−	2.51536i	0.0752471	−	0.0868398i	−0.716878	−	0.697199i	$-0.754429\pi$
$839$	2.17957	−	2.51536i	0.0752471	−	0.0868398i	0.792125	+	0.610359i	$0.208975\pi$
$840$	3.14153	+	2.88322i	0.108393	+	0.0994805i
$841$	−27.1252	+	7.96468i	−0.935352	+	0.274644i
$842$	5.75967	−	15.4423i	0.198491	−	0.532176i
$843$	2.01765	−	9.27499i	0.0694915	−	0.319447i
$844$	−7.02628	+	23.9293i	−0.241854	+	0.823681i
$845$	−16.1733	+	20.3661i	−0.556377	+	0.700614i
$846$	−1.95930	+	4.29026i	−0.0673620	+	0.147502i
$847$	8.17679	−	6.12107i	0.280958	−	0.210322i
$848$	−4.59525	+	0.999635i	−0.157801	+	0.0343276i
$849$	18.1462	+	20.9418i	0.622776	+	0.718722i
$850$	−1.93393	+	33.8299i	−0.0663331	+	1.16036i
$851$	−28.3139	−	22.2258i	−0.970587	−	0.761892i
$852$	5.73226	−	5.73226i	0.196384	−	0.196384i
$853$	−1.61016	+	22.5130i	−0.0551309	+	0.770830i	0.892416	+	0.451214i	$0.149009\pi$
$853$	−1.61016	+	22.5130i	−0.0551309	+	0.770830i	−0.947547	+	0.319617i	$0.896446\pi$
$854$	−3.50962	+	5.46108i	−0.120097	+	0.186874i
$855$	−12.5312	+	8.83397i	−0.428557	+	0.302115i
$856$	15.4576	+	7.05926i	0.528331	+	0.241281i
$857$	34.9611	+	26.1716i	1.19425	+	0.894003i	0.996277	−	0.0862044i	$-0.0274738\pi$
$857$	34.9611	+	26.1716i	1.19425	+	0.894003i	0.197971	+	0.980208i	$0.436565\pi$
$858$	−4.15382	+	2.26816i	−0.141809	+	0.0774337i
$859$	−16.2151	−	25.2312i	−0.553253	−	0.860879i	0.446166	−	0.894950i	$-0.352789\pi$
$859$	−16.2151	−	25.2312i	−0.553253	−	0.860879i	−0.999419	+	0.0340712i	$0.989153\pi$
$860$	−0.773406	−	1.83006i	−0.0263729	−	0.0624044i
$861$	−2.82056	−	9.60594i	−0.0961244	−	0.327370i
$862$	−31.1346	+	2.22679i	−1.06045	+	0.0758447i
$863$	9.97232	−	0.713234i	0.339462	−	0.0242788i	0.0994321	−	0.995044i	$-0.468297\pi$
$863$	9.97232	−	0.713234i	0.339462	−	0.0242788i	0.240030	+	0.970766i	$0.422843\pi$
$864$	0.281733	+	0.959493i	0.00958474	+	0.0326426i
$865$	−15.0790	−	35.6805i	−0.512702	−	1.21317i
$866$	21.4800	+	33.4235i	0.729919	+	1.13578i
$867$	25.3897	−	13.8638i	0.862278	−	0.470840i
$868$	−0.225433	−	0.168757i	−0.00765171	−	0.00572800i
$869$	31.3702	+	14.3263i	1.06416	+	0.485986i
$870$	−1.56111	+	1.10052i	−0.0529264	+	0.0373110i
$871$	3.67668	−	5.72103i	0.124580	−	0.193850i
$872$	−0.615490	+	8.60567i	−0.0208431	+	0.291425i
$873$	3.73834	−	3.73834i	0.126523	−	0.126523i
$874$	28.4924	+	16.4165i	0.963769	+	0.555298i
$875$	1.82397	−	21.2421i	0.0616616	−	0.718114i
$876$	−0.752075	−	0.867941i	−0.0254103	−	0.0293250i
$877$	7.91744	−	1.72233i	0.267353	−	0.0581591i	−0.0768904	−	0.997040i	$-0.524499\pi$
$877$	7.91744	−	1.72233i	0.267353	−	0.0581591i	0.344243	+	0.938880i	$0.388136\pi$
$878$	21.6120	−	16.1786i	0.729371	−	0.546000i
$879$	−12.2926	+	26.9170i	−0.414619	+	0.907889i
$880$	−5.62391	+	7.08187i	−0.189582	+	0.238730i
$881$	15.3112	−	52.1453i	0.515849	−	1.75682i	−0.128109	−	0.991760i	$-0.540891\pi$
$881$	15.3112	−	52.1453i	0.515849	−	1.75682i	0.643958	−	0.765061i	$-0.277291\pi$
$882$	0.714979	−	3.28670i	0.0240746	−	0.110669i
$883$	−3.78805	+	10.1562i	−0.127478	+	0.341782i	−0.984973	−	0.172711i	$-0.944747\pi$
$883$	−3.78805	+	10.1562i	−0.127478	+	0.341782i	0.857494	+	0.514493i	$0.172020\pi$
$884$	−7.60942	+	2.23433i	−0.255933	+	0.0751486i
$885$	−20.5209	−	18.8336i	−0.689803	−	0.633085i
$886$	−9.04669	+	10.4404i	−0.303929	+	0.350753i
$887$	12.5441	−	22.9728i	0.421189	−	0.771350i	−0.577806	−	0.816174i	$-0.696091\pi$
$887$	12.5441	−	22.9728i	0.421189	−	0.771350i	0.998995	+	0.0448243i	$0.0142728\pi$
$888$	7.03232	+	2.62292i	0.235989	+	0.0880194i
$889$	−10.2144	+	6.56439i	−0.342579	+	0.220162i
$890$	−1.52623	+	4.69739i	−0.0511594	+	0.157457i
$891$	−4.00312	+	0.575562i	−0.134110	+	0.0192821i
$892$	−7.64903	−	20.5078i	−0.256108	−	0.686653i
$893$	−19.3802	−	25.8890i	−0.648535	−	0.866341i
$894$	4.49293	+	2.88743i	0.150266	+	0.0965702i
$895$	1.73069	−	17.2575i	0.0578506	−	0.576856i
$896$			1.90694i			0.0637065i
$897$	−4.65053	−	3.14158i	−0.155277	−	0.104894i
$898$	13.9460	+	13.9460i	0.465383	+	0.465383i
$899$	0.0953297	−	0.0826037i	0.00317942	−	0.00275499i
$900$	2.93886	−	4.04513i	0.0979621	−	0.134838i
$901$	4.53564	−	31.5461i	0.151104	−	1.05095i
$902$	19.8939	−	7.42003i	0.662393	−	0.247060i
$903$	1.01538	−	1.35639i	0.0337897	−	0.0451378i
$904$	−10.6512	−	3.12749i	−0.354255	−	0.104019i
$905$	−49.9745	−	12.3754i	−1.66121	−	0.411373i
$906$	1.62456	+	3.55729i	0.0539723	+	0.118183i
$907$	18.8083	+	10.2701i	0.624519	+	0.341013i	0.760151	−	0.649746i	$-0.225125\pi$
$907$	18.8083	+	10.2701i	0.624519	+	0.341013i	−0.135632	+	0.990759i	$0.543307\pi$
$908$	1.90119	+	26.5821i	0.0630932	+	0.882158i
$909$	−9.90335	−	8.58130i	−0.328473	−	0.284624i
$910$	4.82597	−	1.26856i	0.159979	−	0.0420525i
$911$	−32.4489	+	14.8189i	−1.07508	+	0.490973i	−0.872661	−	0.488326i	$-0.837608\pi$
$911$	−32.4489	+	14.8189i	−1.07508	+	0.490973i	−0.202419	+	0.979299i	$0.564880\pi$
$912$	−6.69997	−	1.45749i	−0.221858	−	0.0482623i
$913$	19.7685	+	36.2033i	0.654242	+	1.19816i
$914$	1.87667	+	13.0526i	0.0620749	+	0.431740i
$915$	6.83103	+	3.35853i	0.225827	+	0.111029i
$916$	−7.35329	−	1.05724i	−0.242960	−	0.0349323i
$917$	−1.57212	−	7.22694i	−0.0519161	−	0.238654i
$918$	−6.75977	−	0.483468i	−0.223106	−	0.0159568i
$919$	−26.6803			−0.880102			−0.440051	−	0.897973i	$-0.645040\pi$
$919$	−26.6803			−0.880102			−0.440051	+	0.897973i	$0.645040\pi$
$920$	−10.5221	−	2.07021i	−0.346903	−	0.0682530i
$921$	−32.9705			−1.08642
$922$	−1.83997	−	0.131597i	−0.0605961	−	0.00433392i
$923$	−2.01652	−	9.26981i	−0.0663747	−	0.305120i
$924$	−7.63372	−	1.09756i	−0.251131	−	0.0361072i
$925$	−11.0864	−	35.8528i	−0.364520	−	1.17883i
$926$	1.28139	+	8.91224i	0.0421090	+	0.292874i
$927$	−6.89694	−	12.6308i	−0.226525	−	0.414850i
$928$	−0.834667	−	0.181571i	−0.0273993	−	0.00596035i
$929$	−3.15873	+	1.44254i	−0.103635	+	0.0473283i	−0.466558	−	0.884491i	$-0.654506\pi$
$929$	−3.15873	+	1.44254i	−0.103635	+	0.0473283i	0.362923	+	0.931819i	$0.381779\pi$
$930$	−0.166459	+	0.285177i	−0.00545841	+	0.00935133i
$931$	17.4298	+	15.1030i	0.571238	+	0.494980i
$932$	1.97584	+	27.6259i	0.0647209	+	0.904917i
$933$	−14.9483	−	8.16240i	−0.489386	−	0.267225i
$934$	15.1073	+	33.0804i	0.494326	+	1.08242i
$935$	−31.6487	−	52.4826i	−1.03502	−	1.71636i
$936$	1.12282	+	0.329691i	0.0367007	+	0.0107763i
$937$	10.4844	−	14.0056i	0.342512	−	0.457542i	−0.595901	−	0.803058i	$-0.703205\pi$
$937$	10.4844	−	14.0056i	0.342512	−	0.457542i	0.938413	+	0.345515i	$0.112296\pi$
$938$	10.3832	−	3.87273i	0.339023	−	0.126449i
$939$	−1.16720	+	8.11808i	−0.0380903	+	0.264924i
$940$	8.70578	+	5.95276i	0.283951	+	0.194157i
$941$	7.28777	−	6.31489i	0.237575	−	0.205860i	−0.527934	−	0.849286i	$-0.677033\pi$
$941$	7.28777	−	6.31489i	0.237575	−	0.205860i	0.765508	+	0.643426i	$0.222488\pi$
$942$	5.26164	+	5.26164i	0.171434	+	0.171434i
$943$	18.6456	+	16.9199i	0.607184	+	0.550988i
$944$		−	12.4564i		−	0.405422i
$945$	4.24277	+	0.425490i	0.138017	+	0.0138412i
$946$	3.02296	+	1.94274i	0.0982848	+	0.0631638i
$947$	0.763981	+	1.02056i	0.0248261	+	0.0331637i	0.812783	−	0.582567i	$-0.197952\pi$
$947$	0.763981	+	1.02056i	0.0248261	+	0.0331637i	−0.787956	+	0.615731i	$0.788861\pi$
$948$	−2.97997	−	7.98962i	−0.0967850	−	0.259491i
$949$	−1.33027	+	0.191264i	−0.0431823	+	0.00620868i
$950$	14.6862	+	30.9784i	0.476482	+	1.00507i
$951$	3.94012	−	2.53216i	0.127767	−	0.0821110i
$952$	−12.1086	−	4.51627i	−0.392442	−	0.146373i
$953$	−6.43267	+	11.7806i	−0.208375	+	0.381610i	−0.960875	−	0.276982i	$-0.910666\pi$
$953$	−6.43267	+	11.7806i	−0.208375	+	0.381610i	0.752500	+	0.658592i	$0.228848\pi$
$954$	−3.07963	+	3.55408i	−0.0997066	+	0.115068i
$955$	23.0581	−	0.988597i	0.746144	−	0.0319902i
$956$	−1.55683	+	0.457125i	−0.0503514	+	0.0147845i
$957$	1.20725	−	3.23677i	0.0390249	−	0.104630i
$958$	3.88322	−	17.8509i	0.125461	−	0.576735i
$959$	−1.56938	+	5.34482i	−0.0506779	+	0.172593i
$960$	2.22149	−	0.254910i	0.0716983	−	0.00822719i
$961$	−12.8688	+	28.1788i	−0.415123	+	0.908992i
$962$	7.03131	−	5.26357i	0.226698	−	0.169704i
$963$	16.6049	−	3.61218i	0.535086	−	0.116401i
$964$	0.493469	+	0.569493i	0.0158936	+	0.0183421i
$965$	31.6374	+	0.903555i	1.01844	+	0.0290865i
$966$	−2.99879	−	8.63974i	−0.0964846	−	0.277979i
$967$	−23.8463	+	23.8463i	−0.766845	+	0.766845i	−0.977550	−	0.210705i	$-0.932424\pi$
$967$	−23.8463	+	23.8463i	−0.766845	+	0.766845i	0.210705	+	0.977550i	$0.432424\pi$
$968$	0.382111	−	5.34261i	0.0122815	−	0.171718i
$969$	25.1224	−	39.0913i	0.807048	−	1.25579i
$970$	−6.81139	−	9.66211i	−0.218701	−	0.310232i
$971$	5.95763	+	2.72076i	0.191190	+	0.0873134i	0.508709	−	0.860938i	$-0.330123\pi$
$971$	5.95763	+	2.72076i	0.191190	+	0.0873134i	−0.317520	+	0.948252i	$0.602850\pi$
$972$	0.800541	+	0.599278i	0.0256774	+	0.0192218i
$973$	−27.5335	+	15.0344i	−0.882682	+	0.481981i
$974$	4.86346	+	7.56769i	0.155835	+	0.242484i
$975$	−2.12292	−	5.45243i	−0.0679880	−	0.174618i
$976$	0.959073	+	3.26630i	0.0306992	+	0.104552i
$977$	−46.5752	+	3.33112i	−1.49007	+	0.106572i	−0.792469	−	0.609913i	$-0.791205\pi$
$977$	−46.5752	+	3.33112i	−1.49007	+	0.106572i	−0.697603	+	0.716485i	$0.745750\pi$
$978$	−13.1410	+	0.939863i	−0.420203	+	0.0300535i
$979$	−2.51677	−	8.57132i	−0.0804362	−	0.273941i
$980$	−6.96906	−	2.82849i	−0.222618	−	0.0903527i
$981$	4.66446	+	7.25804i	0.148925	+	0.231731i
$982$	−22.6431	+	12.3641i	−0.722571	+	0.394554i
$983$	16.2531	+	12.1669i	0.518392	+	0.388064i	0.826193	−	0.563387i	$-0.190502\pi$
$983$	16.2531	+	12.1669i	0.518392	+	0.388064i	−0.307801	+	0.951451i	$0.599593\pi$
$984$	−4.77558	−	2.18094i	−0.152240	−	0.0695257i
$985$	−44.4317	−	7.68885i	−1.41571	−	0.244987i
$986$	3.12969	−	4.86990i	0.0996697	−	0.155089i
$987$	−0.641628	+	8.97113i	−0.0204232	+	0.285554i
$988$	−5.67372	+	5.67372i	−0.180505	+	0.180505i
$989$	−0.401301	+	4.24221i	−0.0127606	+	0.134895i
$990$	−0.258169	+	9.03962i	−0.00820515	+	0.287298i
$991$	−9.58937	−	11.0667i	−0.304616	−	0.351546i	0.582717	−	0.812675i	$-0.301990\pi$
$991$	−9.58937	−	11.0667i	−0.304616	−	0.351546i	−0.887333	+	0.461130i	$0.847444\pi$
$992$	−0.144297	+	0.0313899i	−0.00458143	+	0.000996629i
$993$	−5.54684	+	4.15232i	−0.176024	+	0.131770i
$994$	6.42186	−	14.0619i	0.203689	−	0.446016i
$995$	21.4267	+	17.0155i	0.679272	+	0.539429i
$996$	2.87348	−	9.78617i	0.0910496	−	0.310087i
$997$	−4.93167	+	22.6705i	−0.156187	+	0.717982i	0.830719	+	0.556691i	$0.187929\pi$
$997$	−4.93167	+	22.6705i	−0.156187	+	0.717982i	−0.986907	+	0.161291i	$0.948434\pi$
$998$	12.5391	−	33.6185i	0.396917	−	1.06418i
$999$	7.20152	−	2.11456i	0.227846	−	0.0669016i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.a.493.3	yes	240
5.2	odd	4	inner	690.2.w.a.217.7	yes	240
23.7	odd	22	inner	690.2.w.a.283.7	yes	240
115.7	even	44	inner	690.2.w.a.7.3	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.a.7.3	✓	240	115.7	even	44	inner
690.2.w.a.217.7	yes	240	5.2	odd	4	inner
690.2.w.a.283.7	yes	240	23.7	odd	22	inner
690.2.w.a.493.3	yes	240	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.997452 - 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(-0.721297 - 2.11654i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-0.913900 - 1.67368i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +O(q^{10})\)	\(q+(-0.997452 - 0.0713392i) q^{2} +(0.212565 + 0.977147i) q^{3} +(0.989821 + 0.142315i) q^{4} +(-0.721297 - 2.11654i) q^{5} +(-0.142315 - 0.989821i) q^{6} +(-0.913900 - 1.67368i) q^{7} +(-0.977147 - 0.212565i) q^{8} +(-0.909632 + 0.415415i) q^{9} +(0.568467 + 2.16260i) q^{10} +(-3.05647 - 2.64845i) q^{11} +(0.0713392 + 0.997452i) q^{12} +(1.02708 + 0.560830i) q^{13} +(0.792172 + 1.73462i) q^{14} +(1.91485 - 1.15472i) q^{15} +(0.959493 + 0.281733i) q^{16} +(-4.06133 + 5.42530i) q^{17} +(0.936950 - 0.349464i) q^{18} +(-0.975805 + 6.78687i) q^{19} +(-0.412740 - 2.19765i) q^{20} +(1.44117 - 1.24878i) q^{21} +(2.85974 + 2.85974i) q^{22} +(-1.45623 + 4.56940i) q^{23} -1.00000i q^{24} +(-3.95946 + 3.05330i) q^{25} +(-0.984458 - 0.632673i) q^{26} +(-0.599278 - 0.800541i) q^{27} +(-0.666408 - 1.78671i) q^{28} +(0.845493 - 0.121564i) q^{29} +(-1.99234 + 1.01517i) q^{30} +(0.124229 - 0.0798373i) q^{31} +(-0.936950 - 0.349464i) q^{32} +(1.93822 - 3.54959i) q^{33} +(4.43801 - 5.12174i) q^{34} +(-2.88322 + 3.14153i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(-2.62292 + 7.03232i) q^{37} +(1.45749 - 6.69997i) q^{38} +(-0.329691 + 1.12282i) q^{39} +(0.254910 + 2.22149i) q^{40} +(2.18094 - 4.77558i) q^{41} +(-1.52659 + 1.14279i) q^{42} +(0.868206 - 0.188867i) q^{43} +(-2.64845 - 3.05647i) q^{44} +(1.53536 + 1.62563i) q^{45} +(1.77850 - 4.45387i) q^{46} +(-3.33505 + 3.33505i) q^{47} +(-0.0713392 + 0.997452i) q^{48} +(1.81848 - 2.82962i) q^{49} +(4.16719 - 2.76306i) q^{50} +(-6.16461 - 2.81528i) q^{51} +(0.936815 + 0.701291i) q^{52} +(-4.12748 + 2.25377i) q^{53} +(0.540641 + 0.841254i) q^{54} +(-3.40091 + 8.37944i) q^{55} +(0.537248 + 1.82970i) q^{56} +(-6.83920 + 0.489149i) q^{57} +(-0.852011 + 0.0609371i) q^{58} +(-3.50938 - 11.9519i) q^{59} +(2.05969 - 0.870451i) q^{60} +(1.84045 + 2.86379i) q^{61} +(-0.129608 + 0.0707715i) q^{62} +(1.52659 + 1.14279i) q^{63} +(0.909632 + 0.415415i) q^{64} +(0.446186 - 2.57839i) q^{65} +(-2.18651 + 3.40227i) q^{66} +(0.414577 - 5.79654i) q^{67} +(-4.79209 + 4.79209i) q^{68} +(-4.77452 - 0.451655i) q^{69} +(3.09999 - 2.92783i) q^{70} +(-5.30872 - 6.12659i) q^{71} +(0.977147 - 0.212565i) q^{72} +(-0.919382 + 0.688240i) q^{73} +(3.11792 - 6.82728i) q^{74} +(-3.82517 - 3.21995i) q^{75} +(-1.93175 + 6.57892i) q^{76} +(-1.63935 + 7.53597i) q^{77} +(0.408953 - 1.09644i) q^{78} +(-8.18185 + 2.40241i) q^{79} +(-0.0957814 - 2.23402i) q^{80} +(0.654861 - 0.755750i) q^{81} +(-2.51607 + 4.60783i) q^{82} +(-9.55624 - 3.56429i) q^{83} +(1.60422 - 1.03097i) q^{84} +(14.4123 + 4.68270i) q^{85} +(-0.879468 + 0.126448i) q^{86} +(0.298508 + 0.800331i) q^{87} +(2.42365 + 3.23762i) q^{88} +(1.85819 + 1.19419i) q^{89} +(-1.41547 - 1.73102i) q^{90} -2.23156i q^{91} +(-2.09170 + 4.31564i) q^{92} +(0.104420 + 0.104420i) q^{93} +(3.56448 - 3.08864i) q^{94} +(15.0685 - 2.83002i) q^{95} +(0.142315 - 0.989821i) q^{96} +(-4.95347 + 1.84755i) q^{97} +(-2.01571 + 2.69268i) q^{98} +(3.88047 + 1.13941i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 24 q^{6}+O(q^{10}) \) 240 * q - 24 * q^6	\( 240 q - 24 q^{6} + 44 q^{10} - 16 q^{13} + 24 q^{16} + 44 q^{21} + 72 q^{23} + 16 q^{25} + 44 q^{28} - 16 q^{31} - 44 q^{33} - 24 q^{36} + 44 q^{37} + 88 q^{43} - 8 q^{46} + 48 q^{47} + 8 q^{50} - 16 q^{52} + 56 q^{55} + 44 q^{57} + 16 q^{58} + 88 q^{61} + 8 q^{62} + 88 q^{65} - 132 q^{67} + 56 q^{70} - 64 q^{71} + 16 q^{73} - 32 q^{75} - 16 q^{77} - 16 q^{78} + 24 q^{81} - 24 q^{82} + 92 q^{85} - 16 q^{87} - 44 q^{88} + 116 q^{92} - 80 q^{93} + 20 q^{95} + 24 q^{96} - 88 q^{98}+O(q^{100}) \) 240 * q - 24 * q^6 + 44 * q^10 - 16 * q^13 + 24 * q^16 + 44 * q^21 + 72 * q^23 + 16 * q^25 + 44 * q^28 - 16 * q^31 - 44 * q^33 - 24 * q^36 + 44 * q^37 + 88 * q^43 - 8 * q^46 + 48 * q^47 + 8 * q^50 - 16 * q^52 + 56 * q^55 + 44 * q^57 + 16 * q^58 + 88 * q^61 + 8 * q^62 + 88 * q^65 - 132 * q^67 + 56 * q^70 - 64 * q^71 + 16 * q^73 - 32 * q^75 - 16 * q^77 - 16 * q^78 + 24 * q^81 - 24 * q^82 + 92 * q^85 - 16 * q^87 - 44 * q^88 + 116 * q^92 - 80 * q^93 + 20 * q^95 + 24 * q^96 - 88 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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