LMFDB - Embedded newform 666.2.bj.c.289.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [666,2,Mod(289,666)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(666, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("666.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.bj (of order $18$, degree $6$, 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:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$2$ over $\Q(\zeta_{18})$
Coefficient field:	$\Q(\zeta_{36})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{6} + 1 $ x^12 - x^6 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			289.1
Root			$-0.342020 - 0.939693i$ of defining polynomial
Character	$\chi$	$=$	666.289
Dual form			666.2.bj.c.613.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.342020 - 0.939693i) q^{2} +(-0.766044 + 0.642788i) q^{4} +(-0.839712 + 0.148064i) q^{5} +(0.240460 + 1.36372i) q^{7} +(0.866025 + 0.500000i) q^{8} +O(q^{10})$	\(q+(-0.342020 - 0.939693i) q^{2} +(-0.766044 + 0.642788i) q^{4} +(-0.839712 + 0.148064i) q^{5} +(0.240460 + 1.36372i) q^{7} +(0.866025 + 0.500000i) q^{8} +(0.426333 + 0.738430i) q^{10} +(-0.466006 + 0.807147i) q^{11} +(-2.34092 - 2.78980i) q^{13} +(1.19923 - 0.692377i) q^{14} +(0.173648 - 0.984808i) q^{16} +(-2.84539 + 3.39101i) q^{17} +(-1.30826 + 3.59443i) q^{19} +(0.548083 - 0.653180i) q^{20} +(0.917853 + 0.161842i) q^{22} +(-0.920780 + 0.531613i) q^{23} +(-4.01527 + 1.46144i) q^{25} +(-1.82091 + 3.15391i) q^{26} +(-1.06078 - 0.890103i) q^{28} +(-0.873775 - 0.504474i) q^{29} +7.33920i q^{31} +(-0.984808 + 0.173648i) q^{32} +(4.15968 + 1.51400i) q^{34} +(-0.403834 - 1.10953i) q^{35} +(1.15600 + 5.97191i) q^{37} +3.82511 q^{38} +(-0.801244 - 0.291629i) q^{40} +(0.186251 - 0.156283i) q^{41} +5.13740i q^{43} +(-0.161842 - 0.917853i) q^{44} +(0.814478 + 0.683428i) q^{46} +(-3.89795 - 6.75145i) q^{47} +(4.77595 - 1.73830i) q^{49} +(2.74661 + 3.27328i) q^{50} +(3.58649 + 0.632396i) q^{52} +(-2.25380 + 12.7819i) q^{53} +(0.271802 - 0.746769i) q^{55} +(-0.473614 + 1.30124i) q^{56} +(-0.175202 + 0.993621i) q^{58} +(9.61896 + 1.69608i) q^{59} +(0.255191 + 0.304124i) q^{61} +(6.89659 - 2.51015i) q^{62} +(0.500000 + 0.866025i) q^{64} +(2.37876 + 1.99602i) q^{65} +(-2.47277 - 14.0238i) q^{67} -4.42664i q^{68} +(-0.904494 + 0.758960i) q^{70} +(-12.8449 - 4.67517i) q^{71} -13.1543 q^{73} +(5.21638 - 3.12879i) q^{74} +(-1.30826 - 3.59443i) q^{76} +(-1.21278 - 0.441414i) q^{77} +(3.43258 - 0.605257i) q^{79} +0.852666i q^{80} +(-0.210560 - 0.121567i) q^{82} +(12.8078 + 10.7470i) q^{83} +(1.88722 - 3.26877i) q^{85} +(4.82758 - 1.75710i) q^{86} +(-0.807147 + 0.466006i) q^{88} +(-6.19352 - 1.09209i) q^{89} +(3.24160 - 3.86318i) q^{91} +(0.363645 - 0.999105i) q^{92} +(-5.01111 + 5.97200i) q^{94} +(0.566360 - 3.21199i) q^{95} +(6.47160 - 3.73638i) q^{97} +(-3.26694 - 3.89339i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{7}+O(q^{10}) $ 12 * q - 12 * q^7	$ 12 q - 12 q^{7} + 6 q^{10} + 6 q^{11} + 6 q^{13} + 18 q^{14} - 18 q^{19} - 18 q^{25} - 12 q^{26} - 6 q^{28} - 18 q^{29} + 12 q^{34} - 18 q^{35} + 30 q^{37} + 24 q^{38} + 12 q^{40} - 24 q^{41} - 6 q^{44} + 30 q^{46} - 6 q^{47} + 12 q^{49} + 36 q^{50} - 12 q^{52} + 12 q^{53} - 18 q^{55} + 6 q^{58} - 36 q^{61} + 6 q^{64} - 36 q^{65} - 30 q^{67} - 12 q^{70} - 12 q^{71} + 48 q^{74} - 18 q^{76} - 12 q^{77} + 6 q^{79} + 48 q^{83} + 18 q^{85} + 36 q^{86} - 36 q^{88} + 18 q^{89} - 6 q^{91} - 18 q^{92} + 36 q^{97} - 36 q^{98}+O(q^{100}) $ 12 * q - 12 * q^7 + 6 * q^10 + 6 * q^11 + 6 * q^13 + 18 * q^14 - 18 * q^19 - 18 * q^25 - 12 * q^26 - 6 * q^28 - 18 * q^29 + 12 * q^34 - 18 * q^35 + 30 * q^37 + 24 * q^38 + 12 * q^40 - 24 * q^41 - 6 * q^44 + 30 * q^46 - 6 * q^47 + 12 * q^49 + 36 * q^50 - 12 * q^52 + 12 * q^53 - 18 * q^55 + 6 * q^58 - 36 * q^61 + 6 * q^64 - 36 * q^65 - 30 * q^67 - 12 * q^70 - 12 * q^71 + 48 * q^74 - 18 * q^76 - 12 * q^77 + 6 * q^79 + 48 * q^83 + 18 * q^85 + 36 * q^86 - 36 * q^88 + 18 * q^89 - 6 * q^91 - 18 * q^92 + 36 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$1$	$e\left(\frac{7}{18}\right)$

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 $

$2$	−0.342020	−	0.939693i	−0.241845	−	0.664463i
$2$	−0.342020	−	0.939693i	−0.241845	−	0.664463i
$3$		0			0
$3$		0			0
$4$	−0.766044	+	0.642788i	−0.383022	+	0.321394i
$5$	−0.839712	+	0.148064i	−0.375530	+	0.0662162i	−0.358228	−	0.933634i	$-0.616619\pi$
$5$	−0.839712	+	0.148064i	−0.375530	+	0.0662162i	−0.0173025	+	0.999850i	$0.505508\pi$
$6$		0			0
$7$	0.240460	+	1.36372i	0.0908854	+	0.515437i	0.995931	+	0.0901216i	$0.0287256\pi$
$7$	0.240460	+	1.36372i	0.0908854	+	0.515437i	−0.905045	+	0.425315i	$0.860163\pi$
$8$	0.866025	+	0.500000i	0.306186	+	0.176777i
$9$		0			0
$10$	0.426333	+	0.738430i	0.134818	+	0.233512i
$11$	−0.466006	+	0.807147i	−0.140506	+	0.243364i	−0.927687	−	0.373358i	$-0.878206\pi$
$11$	−0.466006	+	0.807147i	−0.140506	+	0.243364i	0.787181	+	0.616722i	$0.211540\pi$
$12$		0			0
$13$	−2.34092	−	2.78980i	−0.649254	−	0.773750i	0.336548	−	0.941666i	$-0.390741\pi$
$13$	−2.34092	−	2.78980i	−0.649254	−	0.773750i	−0.985801	+	0.167916i	$0.946296\pi$
$14$	1.19923	−	0.692377i	0.320508	−	0.185046i
$15$		0			0
$16$	0.173648	−	0.984808i	0.0434120	−	0.246202i
$17$	−2.84539	+	3.39101i	−0.690109	+	0.822440i	−0.991369	−	0.131102i	$-0.958148\pi$
$17$	−2.84539	+	3.39101i	−0.690109	+	0.822440i	0.301260	+	0.953542i	$0.402593\pi$
$18$		0			0
$19$	−1.30826	+	3.59443i	−0.300136	+	0.824618i	0.694339	+	0.719648i	$0.255697\pi$
$19$	−1.30826	+	3.59443i	−0.300136	+	0.824618i	−0.994475	+	0.104970i	$0.966525\pi$
$20$	0.548083	−	0.653180i	0.122555	−	0.146055i
$21$		0			0
$22$	0.917853	+	0.161842i	0.195687	+	0.0345049i
$23$	−0.920780	+	0.531613i	−0.191996	+	0.110849i	−0.592917	−	0.805264i	$-0.702024\pi$
$23$	−0.920780	+	0.531613i	−0.191996	+	0.110849i	0.400921	+	0.916113i	$0.368690\pi$
$24$		0			0
$25$	−4.01527	+	1.46144i	−0.803054	+	0.292288i
$26$	−1.82091	+	3.15391i	−0.357110	+	0.618532i
$27$		0			0
$28$	−1.06078	−	0.890103i	−0.200469	−	0.168214i
$29$	−0.873775	−	0.504474i	−0.162256	−	0.0936786i	0.416673	−	0.909056i	$-0.363196\pi$
$29$	−0.873775	−	0.504474i	−0.162256	−	0.0936786i	−0.578929	+	0.815378i	$0.696529\pi$
$30$		0			0
$31$			7.33920i			1.31816i	0.752073	+	0.659080i	$0.229054\pi$
$31$			7.33920i			1.31816i	−0.752073	+	0.659080i	$0.770946\pi$
$32$	−0.984808	+	0.173648i	−0.174091	+	0.0306970i
$33$		0			0
$34$	4.15968	+	1.51400i	0.713380	+	0.259649i
$35$	−0.403834	−	1.10953i	−0.0682605	−	0.187544i
$36$		0			0
$37$	1.15600	+	5.97191i	0.190045	+	0.981775i
$37$	1.15600	+	5.97191i	0.190045	+	0.981775i
$38$	3.82511			0.620515
$39$		0			0
$40$	−0.801244	−	0.291629i	−0.126688	−	0.0461106i
$41$	0.186251	−	0.156283i	0.0290876	−	0.0244074i	−0.628128	−	0.778110i	$-0.716179\pi$
$41$	0.186251	−	0.156283i	0.0290876	−	0.0244074i	0.657216	+	0.753703i	$0.271734\pi$
$42$		0			0
$43$			5.13740i			0.783447i	0.920083	+	0.391723i	$0.128121\pi$
$43$			5.13740i			0.783447i	−0.920083	+	0.391723i	$0.871879\pi$
$44$	−0.161842	−	0.917853i	−0.0243986	−	0.138372i
$45$		0			0
$46$	0.814478	+	0.683428i	0.120088	+	0.100766i
$47$	−3.89795	−	6.75145i	−0.568574	−	0.984800i	−0.996707	−	0.0810838i	$-0.974162\pi$
$47$	−3.89795	−	6.75145i	−0.568574	−	0.984800i	0.428133	−	0.903716i	$-0.359171\pi$
$48$		0			0
$49$	4.77595	−	1.73830i	0.682278	−	0.248329i
$50$	2.74661	+	3.27328i	0.388429	+	0.462911i
$51$		0			0
$52$	3.58649	+	0.632396i	0.497357	+	0.0876975i
$53$	−2.25380	+	12.7819i	−0.309583	+	1.75573i	0.291522	+	0.956564i	$0.405838\pi$
$53$	−2.25380	+	12.7819i	−0.309583	+	1.75573i	−0.601106	+	0.799170i	$0.705273\pi$
$54$		0			0
$55$	0.271802	−	0.746769i	0.0366497	−	0.100694i
$56$	−0.473614	+	1.30124i	−0.0632893	+	0.173886i
$57$		0			0
$58$	−0.175202	+	0.993621i	−0.0230052	+	0.130469i
$59$	9.61896	+	1.69608i	1.25228	+	0.220811i	0.760172	−	0.649722i	$-0.225115\pi$
$59$	9.61896	+	1.69608i	1.25228	+	0.220811i	0.492110	+	0.870533i	$0.336226\pi$
$60$		0			0
$61$	0.255191	+	0.304124i	0.0326738	+	0.0389391i	0.782134	−	0.623110i	$-0.214131\pi$
$61$	0.255191	+	0.304124i	0.0326738	+	0.0389391i	−0.749460	+	0.662050i	$0.769687\pi$
$62$	6.89659	−	2.51015i	0.875868	−	0.318790i
$63$		0			0
$64$	0.500000	+	0.866025i	0.0625000	+	0.108253i
$65$	2.37876	+	1.99602i	0.295049	+	0.247576i
$66$		0			0
$67$	−2.47277	−	14.0238i	−0.302097	−	1.71328i	−0.636862	−	0.770978i	$-0.719768\pi$
$67$	−2.47277	−	14.0238i	−0.302097	−	1.71328i	0.334765	−	0.942302i	$-0.391343\pi$
$68$		−	4.42664i		−	0.536809i
$69$		0			0
$70$	−0.904494	+	0.758960i	−0.108108	+	0.0907131i
$71$	−12.8449	−	4.67517i	−1.52441	−	0.554840i	−0.562166	−	0.827024i	$-0.690032\pi$
$71$	−12.8449	−	4.67517i	−1.52441	−	0.554840i	−0.962245	+	0.272184i	$0.912254\pi$
$72$		0			0
$73$	−13.1543			−1.53959			−0.769794	−	0.638292i	$-0.779641\pi$
$73$	−13.1543			−1.53959			−0.769794	+	0.638292i	$0.779641\pi$
$74$	5.21638	−	3.12879i	0.606392	−	0.363715i
$75$		0			0
$76$	−1.30826	−	3.59443i	−0.150068	−	0.412309i
$77$	−1.21278	−	0.441414i	−0.138209	−	0.0503038i
$78$		0			0
$79$	3.43258	−	0.605257i	0.386196	−	0.0680968i	0.0228205	−	0.999740i	$-0.492735\pi$
$79$	3.43258	−	0.605257i	0.386196	−	0.0680968i	0.363375	+	0.931643i	$0.381624\pi$
$80$			0.852666i			0.0953309i
$81$		0			0
$82$	−0.210560	−	0.121567i	−0.0232525	−	0.0134248i
$83$	12.8078	+	10.7470i	1.40584	+	1.17964i	0.958438	+	0.285302i	$0.0920939\pi$
$83$	12.8078	+	10.7470i	1.40584	+	1.17964i	0.447399	+	0.894335i	$0.352351\pi$
$84$		0			0
$85$	1.88722	−	3.26877i	0.204698	−	0.354548i
$86$	4.82758	−	1.75710i	0.520571	−	0.189472i
$87$		0			0
$88$	−0.807147	+	0.466006i	−0.0860421	+	0.0496764i
$89$	−6.19352	−	1.09209i	−0.656512	−	0.115761i	−0.164538	−	0.986371i	$-0.552613\pi$
$89$	−6.19352	−	1.09209i	−0.656512	−	0.115761i	−0.491974	+	0.870610i	$0.663725\pi$
$90$		0			0
$91$	3.24160	−	3.86318i	0.339812	−	0.404972i
$92$	0.363645	−	0.999105i	0.0379126	−	0.104164i
$93$		0			0
$94$	−5.01111	+	5.97200i	−0.516856	+	0.615965i
$95$	0.566360	−	3.21199i	0.0581073	−	0.329543i
$96$		0			0
$97$	6.47160	−	3.73638i	0.657092	−	0.379372i	−0.134076	−	0.990971i	$-0.542807\pi$
$97$	6.47160	−	3.73638i	0.657092	−	0.379372i	0.791168	+	0.611599i	$0.209473\pi$
$98$	−3.26694	−	3.89339i	−0.330011	−	0.393291i
$99$		0			0
$100$	2.13648	−	3.70049i	0.213648	−	0.370049i
$101$	−2.01440	−	3.48904i	−0.200440	−	0.347173i	0.748230	−	0.663439i	$-0.230904\pi$
$101$	−2.01440	−	3.48904i	−0.200440	−	0.347173i	−0.948670	+	0.316267i	$0.897571\pi$
$102$		0			0
$103$	0.201874	+	0.116552i	0.0198912	+	0.0114842i	0.509913	−	0.860226i	$-0.329678\pi$
$103$	0.201874	+	0.116552i	0.0198912	+	0.0114842i	−0.490021	+	0.871710i	$0.663011\pi$
$104$	−0.632396	−	3.58649i	−0.0620115	−	0.351685i
$105$		0			0
$106$	12.7819	−	2.25380i	1.24149	−	0.218908i
$107$	−4.94031	+	4.14542i	−0.477598	+	0.400753i	−0.849557	−	0.527497i	$-0.823131\pi$
$107$	−4.94031	+	4.14542i	−0.477598	+	0.400753i	0.371959	+	0.928249i	$0.378686\pi$
$108$		0			0
$109$	4.71183	+	12.9456i	0.451311	+	1.23997i	0.931802	+	0.362967i	$0.118236\pi$
$109$	4.71183	+	12.9456i	0.451311	+	1.23997i	−0.480491	+	0.877000i	$0.659542\pi$
$110$	−0.794695			−0.0757712
$111$		0			0
$112$	1.38475			0.130847
$113$	−1.45712	−	4.00340i	−0.137074	−	0.376608i	0.852095	−	0.523387i	$-0.175332\pi$
$113$	−1.45712	−	4.00340i	−0.137074	−	0.376608i	−0.989169	+	0.146779i	$0.953110\pi$
$114$		0			0
$115$	0.694477	−	0.582736i	0.0647604	−	0.0543404i
$116$	0.993621	−	0.175202i	0.0922554	−	0.0162671i
$117$		0			0
$118$	−1.69608	−	9.61896i	−0.156137	−	0.885497i
$119$	−5.30857	−	3.06491i	−0.486636	−	0.280960i
$120$		0			0
$121$	5.06568	+	8.77401i	0.460516	+	0.797637i
$122$	0.198503	−	0.343818i	0.0179716	−	0.0311278i
$123$		0			0
$124$	−4.71755	−	5.62215i	−0.423648	−	0.504884i
$125$	6.84743	−	3.95337i	0.612453	−	0.353600i
$126$		0			0
$127$	2.00201	−	11.3540i	0.177649	−	1.00750i	−0.757392	−	0.652961i	$-0.773527\pi$
$127$	2.00201	−	11.3540i	0.177649	−	1.00750i	0.935041	−	0.354539i	$-0.115362\pi$
$128$	0.642788	−	0.766044i	0.0568149	−	0.0677094i
$129$		0			0
$130$	1.06206	−	2.91799i	0.0931488	−	0.255924i
$131$	6.71929	−	8.00774i	0.587067	−	0.699640i	−0.387972	−	0.921671i	$-0.626824\pi$
$131$	6.71929	−	8.00774i	0.587067	−	0.699640i	0.975039	+	0.222032i	$0.0712688\pi$
$132$		0			0
$133$	−5.21637	−	0.919786i	−0.452316	−	0.0797556i
$134$	−12.3323	+	7.12007i	−1.06535	+	0.615080i
$135$		0			0
$136$	−4.15968	+	1.51400i	−0.356690	+	0.129825i
$137$	−3.38948	+	5.87074i	−0.289582	+	0.501572i	−0.973710	−	0.227791i	$-0.926850\pi$
$137$	−3.38948	+	5.87074i	−0.289582	+	0.501572i	0.684128	+	0.729362i	$0.260183\pi$
$138$		0			0
$139$	−14.6691	−	12.3088i	−1.24421	−	1.04402i	−0.997183	−	0.0750129i	$-0.976100\pi$
$139$	−14.6691	−	12.3088i	−1.24421	−	1.04402i	−0.247032	−	0.969007i	$-0.579455\pi$
$140$	1.02254	+	0.590366i	0.0864208	+	0.0498951i
$141$		0			0
$142$			13.6693i			1.14710i
$143$	3.34266	−	0.589401i	0.279527	−	0.0492882i
$144$		0			0
$145$	0.808414	+	0.294239i	0.0671351	+	0.0244352i
$146$	4.49902	+	12.3610i	0.372341	+	1.02300i
$147$		0			0
$148$	−4.72421	−	3.83169i	−0.388328	−	0.314963i
$149$	−4.47583			−0.366674			−0.183337	−	0.983050i	$-0.558690\pi$
$149$	−4.47583			−0.366674			−0.183337	+	0.983050i	$0.558690\pi$
$150$		0			0
$151$	−8.30906	−	3.02425i	−0.676181	−	0.246110i	−0.0189744	−	0.999820i	$-0.506040\pi$
$151$	−8.30906	−	3.02425i	−0.676181	−	0.246110i	−0.657207	+	0.753710i	$0.728262\pi$
$152$	−2.93020	+	2.45873i	−0.237671	+	0.199430i
$153$		0			0
$154$			1.29061i			0.104000i
$155$	−1.08667	−	6.16281i	−0.0872834	−	0.495009i
$156$		0			0
$157$	−14.1119	−	11.8413i	−1.12626	−	0.945041i	−0.127352	−	0.991858i	$-0.540648\pi$
$157$	−14.1119	−	11.8413i	−1.12626	−	0.945041i	−0.998903	+	0.0468171i	$0.985092\pi$
$158$	−1.74277	−	3.01856i	−0.138647	−	0.240144i
$159$		0			0
$160$	0.801244	−	0.291629i	0.0633439	−	0.0230553i
$161$	−0.946380	−	1.12785i	−0.0745852	−	0.0888872i
$162$		0			0
$163$	9.09259	+	1.60327i	0.712186	+	0.125578i	0.517992	−	0.855385i	$-0.326680\pi$
$163$	9.09259	+	1.60327i	0.712186	+	0.125578i	0.194194	+	0.980963i	$0.437791\pi$
$164$	−0.0422197	+	0.239440i	−0.00329681	+	0.0186971i
$165$		0			0
$166$	5.71836	−	15.7111i	0.443831	−	1.21942i
$167$	5.57821	−	15.3260i	0.431655	−	1.18596i	−0.513142	−	0.858304i	$-0.671518\pi$
$167$	5.57821	−	15.3260i	0.431655	−	1.18596i	0.944796	−	0.327658i	$-0.106259\pi$
$168$		0			0
$169$	−0.0456446	+	0.258863i	−0.00351112	+	0.0199126i
$170$	−3.71710	−	0.655426i	−0.285089	−	0.0502689i
$171$		0			0
$172$	−3.30226	−	3.93548i	−0.251795	−	0.300077i
$173$	1.80631	−	0.657444i	0.137331	−	0.0499846i	−0.272440	−	0.962173i	$-0.587831\pi$
$173$	1.80631	−	0.657444i	0.137331	−	0.0499846i	0.409772	+	0.912188i	$0.365608\pi$
$174$		0			0
$175$	−2.95850	−	5.12427i	−0.223642	−	0.387359i
$176$	0.713963	+	0.599086i	0.0538170	+	0.0451578i
$177$		0			0
$178$	1.09209	+	6.19352i	0.0818553	+	0.464224i
$179$			18.8954i			1.41231i	0.708059	+	0.706154i	$0.249571\pi$
$179$			18.8954i			1.41231i	−0.708059	+	0.706154i	$0.750429\pi$
$180$		0			0
$181$	5.25019	−	4.40543i	0.390243	−	0.327453i	−0.426465	−	0.904504i	$-0.640241\pi$
$181$	5.25019	−	4.40543i	0.390243	−	0.327453i	0.816708	+	0.577051i	$0.195797\pi$
$182$	−4.73890	−	1.72482i	−0.351270	−	0.127852i
$183$		0			0
$184$	−1.06323			−0.0783820
$185$	−1.85493	−	4.84352i	−0.136377	−	0.356103i
$186$		0			0
$187$	−1.41107	−	3.87688i	−0.103188	−	0.283505i
$188$	7.32575	+	2.66635i	0.534285	+	0.194464i
$189$		0			0
$190$	−3.21199	+	0.566360i	−0.233022	+	0.0410881i
$191$		−	21.1777i		−	1.53236i	−0.642625	−	0.766181i	$-0.722155\pi$
$191$		−	21.1777i		−	1.53236i	0.642625	−	0.766181i	$-0.277845\pi$
$192$		0			0
$193$	6.64750	+	3.83793i	0.478497	+	0.276261i	0.719790	−	0.694192i	$-0.244238\pi$
$193$	6.64750	+	3.83793i	0.478497	+	0.276261i	−0.241293	+	0.970452i	$0.577571\pi$
$194$	−5.72447	−	4.80340i	−0.410993	−	0.344864i
$195$		0			0
$196$	−2.54123	+	4.40154i	−0.181516	+	0.314395i
$197$	−10.6770	+	3.88610i	−0.760703	+	0.276873i	−0.693102	−	0.720839i	$-0.743757\pi$
$197$	−10.6770	+	3.88610i	−0.760703	+	0.276873i	−0.0676007	+	0.997712i	$0.521534\pi$
$198$		0			0
$199$	21.5452	−	12.4391i	1.52730	−	0.881788i	0.527828	−	0.849352i	$-0.323007\pi$
$199$	21.5452	−	12.4391i	1.52730	−	0.881788i	0.999474	−	0.0324362i	$-0.0103266\pi$
$200$	−4.20805	−	0.741992i	−0.297554	−	0.0524668i
$201$		0			0
$202$	−2.58966	+	3.08624i	−0.182208	+	0.217147i
$203$	0.477852	−	1.31289i	0.0335387	−	0.0921467i
$204$		0			0
$205$	−0.133257	+	0.158810i	−0.00930711	+	0.0110918i
$206$	0.0404781	−	0.229563i	0.00282024	−	0.0159944i
$207$		0			0
$208$	−3.15391	+	1.82091i	−0.218684	+	0.126257i
$209$	−2.29157	−	2.73099i	−0.158511	−	0.188906i
$210$		0			0
$211$	−6.56480	+	11.3706i	−0.451939	+	0.782782i	−0.998506	−	0.0546333i	$-0.982601\pi$
$211$	−6.56480	+	11.3706i	−0.451939	+	0.782782i	0.546567	+	0.837415i	$0.315934\pi$
$212$	−6.48956	−	11.2402i	−0.445705	−	0.771983i
$213$		0			0
$214$	5.58510	+	3.22456i	0.381790	+	0.220426i
$215$	−0.760664	−	4.31394i	−0.0518768	−	0.294208i
$216$		0			0
$217$	−10.0086	+	1.76478i	−0.679427	+	0.119801i
$218$	10.5534	−	8.85533i	0.714765	−	0.599759i
$219$		0			0
$220$	0.271802	+	0.746769i	0.0183249	+	0.0503472i
$221$	16.1210			1.08442
$222$		0			0
$223$	1.40208			0.0938902			0.0469451	−	0.998897i	$-0.485051\pi$
$223$	1.40208			0.0938902			0.0469451	+	0.998897i	$0.485051\pi$
$224$	−0.473614	−	1.30124i	−0.0316447	−	0.0869430i
$225$		0			0
$226$	−3.26360	+	2.73849i	−0.217092	+	0.182161i
$227$	−2.96048	+	0.522013i	−0.196494	+	0.0346472i	−0.271029	−	0.962571i	$-0.587364\pi$
$227$	−2.96048	+	0.522013i	−0.196494	+	0.0346472i	0.0745348	+	0.997218i	$0.476253\pi$
$228$		0			0
$229$	1.61197	+	9.14196i	0.106522	+	0.604118i	0.990601	+	0.136780i	$0.0436755\pi$
$229$	1.61197	+	9.14196i	0.106522	+	0.604118i	−0.884079	+	0.467337i	$0.845213\pi$
$230$	−0.785118	−	0.453288i	−0.0517691	−	0.0298889i
$231$		0			0
$232$	−0.504474	−	0.873775i	−0.0331204	−	0.0573662i
$233$	−13.7108	+	23.7478i	−0.898225	+	1.55577i	−0.0684634	+	0.997654i	$0.521810\pi$
$233$	−13.7108	+	23.7478i	−0.898225	+	1.55577i	−0.829762	+	0.558118i	$0.811524\pi$
$234$		0			0
$235$	4.27280	+	5.09212i	0.278727	+	0.332173i
$236$	−8.45877	+	4.88367i	−0.550619	+	0.317900i
$237$		0			0
$238$	−1.06443	+	6.03669i	−0.0689968	+	0.391300i
$239$	−0.475493	+	0.566671i	−0.0307571	+	0.0366549i	−0.781204	−	0.624276i	$-0.785394\pi$
$239$	−0.475493	+	0.566671i	−0.0307571	+	0.0366549i	0.750447	+	0.660931i	$0.229838\pi$
$240$		0			0
$241$	−0.315775	+	0.867585i	−0.0203409	+	0.0558861i	−0.949448	−	0.313926i	$-0.898356\pi$
$241$	−0.315775	+	0.867585i	−0.0203409	+	0.0558861i	0.929107	+	0.369812i	$0.120578\pi$
$242$	6.51231	−	7.76107i	0.418627	−	0.498900i
$243$		0			0
$244$	−0.390975	−	0.0689394i	−0.0250296	−	0.00441339i
$245$	−3.75304	+	2.16682i	−0.239773	+	0.138433i
$246$		0			0
$247$	13.0903	−	4.76446i	0.832913	−	0.303156i
$248$	−3.66960	+	6.35593i	−0.233020	+	0.403602i
$249$		0			0
$250$	−6.05691	−	5.08235i	−0.383073	−	0.321436i
$251$	8.51425	+	4.91571i	0.537415	+	0.310277i	0.744031	−	0.668146i	$-0.232912\pi$
$251$	8.51425	+	4.91571i	0.537415	+	0.310277i	−0.206616	+	0.978422i	$0.566245\pi$
$252$		0			0
$253$		−	0.990940i		−	0.0622999i
$254$	−11.3540	+	2.00201i	−0.712410	+	0.125617i
$255$		0			0
$256$	−0.939693	−	0.342020i	−0.0587308	−	0.0213763i
$257$	−1.76857	−	4.85911i	−0.110320	−	0.303103i	0.872231	−	0.489094i	$-0.162673\pi$
$257$	−1.76857	−	4.85911i	−0.110320	−	0.303103i	−0.982551	+	0.185991i	$0.940450\pi$
$258$		0			0
$259$	−7.86602	+	3.01246i	−0.488771	+	0.187185i
$260$	−3.10525			−0.192580
$261$		0			0
$262$	−9.82295	−	3.57526i	−0.606864	−	0.220880i
$263$	15.7224	−	13.1926i	0.969483	−	0.813493i	−0.0129864	−	0.999916i	$-0.504134\pi$
$263$	15.7224	−	13.1926i	0.969483	−	0.813493i	0.982470	+	0.186423i	$0.0596894\pi$
$264$		0			0
$265$		−	11.0668i		−	0.679831i
$266$	0.919786	+	5.21637i	0.0563957	+	0.319836i
$267$		0			0
$268$	10.9086	+	9.15338i	0.666347	+	0.559132i
$269$	8.25822	+	14.3037i	0.503512	+	0.872109i	0.999992	+	0.00406062i	$0.00129254\pi$
$269$	8.25822	+	14.3037i	0.503512	+	0.872109i	−0.496479	+	0.868049i	$0.665374\pi$
$270$		0			0
$271$	9.99255	−	3.63699i	0.607004	−	0.220932i	−0.0201876	−	0.999796i	$-0.506426\pi$
$271$	9.99255	−	3.63699i	0.607004	−	0.220932i	0.627192	+	0.778865i	$0.284204\pi$
$272$	2.84539	+	3.39101i	0.172527	+	0.205610i
$273$		0			0
$274$	6.67596	+	1.17715i	0.403310	+	0.0711144i
$275$	0.691546	−	3.92195i	0.0417018	−	0.236503i
$276$		0			0
$277$	2.24164	−	6.15886i	0.134687	−	0.370050i	−0.853953	−	0.520350i	$-0.825802\pi$
$277$	2.24164	−	6.15886i	0.134687	−	0.370050i	0.988641	+	0.150299i	$0.0480238\pi$
$278$	−6.54938	+	17.9943i	−0.392806	+	1.07923i
$279$		0			0
$280$	0.205032	−	1.16279i	0.0122530	−	0.0694903i
$281$	24.3511	+	4.29375i	1.45266	+	0.256144i	0.843598	−	0.536976i	$-0.180433\pi$
$281$	24.3511	+	4.29375i	1.45266	+	0.256144i	0.609066	+	0.793119i	$0.291544\pi$
$282$		0			0
$283$	12.6719	+	15.1018i	0.753267	+	0.897709i	0.997402	−	0.0720321i	$-0.0229484\pi$
$283$	12.6719	+	15.1018i	0.753267	+	0.897709i	−0.244135	+	0.969741i	$0.578504\pi$
$284$	12.8449	−	4.67517i	0.762206	−	0.277420i
$285$		0			0
$286$	−1.69711	−	2.93948i	−0.100352	−	0.173815i
$287$	0.257912	+	0.216414i	0.0152241	+	0.0127745i
$288$		0			0
$289$	−0.450647	−	2.55575i	−0.0265086	−	0.150338i
$290$		−	0.860296i		−	0.0505183i
$291$		0			0
$292$	10.0767	−	8.45539i	0.589697	−	0.494814i
$293$	1.10192	+	0.401067i	0.0643751	+	0.0234306i	0.374007	−	0.927426i	$-0.377984\pi$
$293$	1.10192	+	0.401067i	0.0643751	+	0.0234306i	−0.309632	+	0.950856i	$0.600206\pi$
$294$		0			0
$295$	−8.32828			−0.484891
$296$	−1.98483	+	5.74982i	−0.115366	+	0.334202i
$297$		0			0
$298$	1.53082	+	4.20590i	0.0886782	+	0.243641i
$299$	3.63856	+	1.32433i	0.210423	+	0.0765879i
$300$		0			0
$301$	−7.00596	+	1.23534i	−0.403817	+	0.0712038i
$302$			8.84231i			0.508818i
$303$		0			0
$304$	3.31264	+	1.91255i	0.189993	+	0.109693i
$305$	−0.259316	−	0.217592i	−0.0148484	−	0.0124593i
$306$		0			0
$307$	−9.36820	+	16.2262i	−0.534671	+	0.926078i	0.464508	+	0.885569i	$0.346231\pi$
$307$	−9.36820	+	16.2262i	−0.534671	+	0.926078i	−0.999179	+	0.0405091i	$0.987102\pi$
$308$	1.21278	−	0.441414i	0.0691043	−	0.0251519i
$309$		0			0
$310$	−5.41949	+	3.12894i	−0.307806	+	0.177712i
$311$	32.3417	+	5.70271i	1.83393	+	0.323371i	0.980301	−	0.197511i	$-0.0632859\pi$
$311$	32.3417	+	5.70271i	1.83393	+	0.323371i	0.853628	+	0.520882i	$0.174397\pi$
$312$		0			0
$313$	−13.8536	+	16.5101i	−0.783052	+	0.933206i	−0.999067	−	0.0431845i	$-0.986250\pi$
$313$	−13.8536	+	16.5101i	−0.783052	+	0.933206i	0.216015	+	0.976390i	$0.430694\pi$
$314$	−6.30064	+	17.3109i	−0.355565	+	0.976908i
$315$		0			0
$316$	−2.24046	+	2.67008i	−0.126036	+	0.150204i
$317$	−3.06019	+	17.3552i	−0.171877	+	0.974764i	0.769810	+	0.638273i	$0.220351\pi$
$317$	−3.06019	+	17.3552i	−0.171877	+	0.974764i	−0.941687	+	0.336490i	$0.890760\pi$
$318$		0			0
$319$	0.814370	−	0.470177i	0.0455960	−	0.0263248i
$320$	−0.548083	−	0.653180i	−0.0306388	−	0.0365139i
$321$		0			0
$322$	−0.736153	+	1.27505i	−0.0410242	+	0.0710560i
$323$	−8.46620	−	14.6639i	−0.471072	−	0.815920i
$324$		0			0
$325$	13.4765	+	7.78068i	0.747543	+	0.431594i
$326$	−1.60327	−	9.09259i	−0.0887968	−	0.503592i
$327$		0			0
$328$	0.239440	−	0.0422197i	0.0132209	−	0.00233120i
$329$	8.26976	−	6.93915i	0.455927	−	0.382568i
$330$		0			0
$331$	2.42916	+	6.67405i	0.133518	+	0.366839i	0.988377	−	0.152022i	$-0.0485784\pi$
$331$	2.42916	+	6.67405i	0.133518	+	0.366839i	−0.854859	+	0.518861i	$0.826356\pi$
$332$	−16.7194			−0.917594
$333$		0			0
$334$	−16.3096			−0.892421
$335$	4.15283	+	11.4098i	0.226894	+	0.623385i
$336$		0			0
$337$	−0.781329	+	0.655612i	−0.0425617	+	0.0357135i	−0.663820	−	0.747892i	$-0.731066\pi$
$337$	−0.781329	+	0.655612i	−0.0425617	+	0.0357135i	0.621259	+	0.783606i	$0.286622\pi$
$338$	0.258863	−	0.0456446i	0.0140803	−	0.00248274i
$339$		0			0
$340$	0.655426	+	3.71710i	0.0355455	+	0.201588i
$341$	−5.92381	−	3.42011i	−0.320792	−	0.185210i
$342$		0			0
$343$	8.36562	+	14.4897i	0.451701	+	0.782369i
$344$	−2.56870	+	4.44912i	−0.138495	+	0.239881i
$345$		0			0
$346$	−1.23559	−	1.47252i	−0.0664258	−	0.0791632i
$347$	4.31707	−	2.49246i	0.231752	−	0.133802i	−0.379628	−	0.925139i	$-0.623948\pi$
$347$	4.31707	−	2.49246i	0.231752	−	0.133802i	0.611380	+	0.791337i	$0.290615\pi$
$348$		0			0
$349$	−4.46786	+	25.3385i	−0.239159	+	1.35634i	0.594516	+	0.804084i	$0.297344\pi$
$349$	−4.46786	+	25.3385i	−0.239159	+	1.35634i	−0.833675	+	0.552255i	$0.813767\pi$
$350$	−3.80338	+	4.53269i	−0.203299	+	0.242282i
$351$		0			0
$352$	0.318767	−	0.875805i	0.0169903	−	0.0466806i
$353$	−17.2409	+	20.5469i	−0.917642	+	1.09360i	0.0776786	+	0.996978i	$0.475249\pi$
$353$	−17.2409	+	20.5469i	−0.917642	+	1.09360i	−0.995321	+	0.0966250i	$0.969195\pi$
$354$		0			0
$355$	11.4783	+	2.02393i	0.609202	+	0.107419i
$356$	5.44649	−	3.14453i	0.288664	−	0.166660i
$357$		0			0
$358$	17.7559	−	6.46260i	0.938426	−	0.341559i
$359$	9.96674	−	17.2629i	0.526024	−	0.911101i	−0.473516	−	0.880785i	$-0.657015\pi$
$359$	9.96674	−	17.2629i	0.526024	−	0.911101i	0.999540	−	0.0303155i	$-0.00965121\pi$
$360$		0			0
$361$	3.34650	+	2.80805i	0.176132	+	0.147792i
$362$	−5.93542	−	3.42682i	−0.311959	−	0.180109i
$363$		0			0
$364$			5.04303i			0.264326i
$365$	11.0458	−	1.94767i	0.578162	−	0.101946i
$366$		0			0
$367$	−13.9399	−	5.07371i	−0.727657	−	0.264846i	−0.0484843	−	0.998824i	$-0.515439\pi$
$367$	−13.9399	−	5.07371i	−0.727657	−	0.264846i	−0.679173	+	0.733978i	$0.737661\pi$
$368$	0.363645	+	0.999105i	0.0189563	+	0.0520820i
$369$		0			0
$370$	−3.91700	+	3.39964i	−0.203635	+	0.176739i
$371$	−17.9729			−0.933106
$372$		0			0
$373$	2.54239	+	0.925355i	0.131640	+	0.0479131i	0.407000	−	0.913428i	$-0.366575\pi$
$373$	2.54239	+	0.925355i	0.131640	+	0.0479131i	−0.275360	+	0.961341i	$0.588797\pi$
$374$	−3.16046	+	2.65194i	−0.163424	+	0.137129i
$375$		0			0
$376$		−	7.79590i		−	0.402043i
$377$	0.638055	+	3.61859i	0.0328615	+	0.186367i
$378$		0			0
$379$	15.4191	+	12.9382i	0.792027	+	0.664589i	0.946246	−	0.323447i	$-0.104842\pi$
$379$	15.4191	+	12.9382i	0.792027	+	0.664589i	−0.154220	+	0.988037i	$0.549286\pi$
$380$	1.63077	+	2.82458i	0.0836567	+	0.144898i
$381$		0			0
$382$	−19.9005	+	7.24319i	−1.01820	+	0.370594i
$383$	−17.2995	−	20.6168i	−0.883965	−	1.05347i	−0.998198	−	0.0600143i	$-0.980885\pi$
$383$	−17.2995	−	20.6168i	−0.883965	−	1.05347i	0.114233	−	0.993454i	$-0.463559\pi$
$384$		0			0
$385$	1.08374	+	0.191092i	0.0552325	+	0.00973897i
$386$	1.33290	−	7.55925i	0.0678428	−	0.384756i
$387$		0			0
$388$	−2.55584	+	7.02210i	−0.129753	+	0.356493i
$389$	0.332286	−	0.912949i	0.0168476	−	0.0462883i	−0.930984	−	0.365061i	$-0.881048\pi$
$389$	0.332286	−	0.912949i	0.0168476	−	0.0462883i	0.947831	+	0.318772i	$0.103271\pi$
$390$		0			0
$391$	0.817279	−	4.63502i	0.0413316	−	0.234403i
$392$	5.00524	+	0.882559i	0.252803	+	0.0445760i
$393$		0			0
$394$	7.30348	+	8.70395i	0.367944	+	0.438499i
$395$	−2.79276	+	1.01648i	−0.140519	+	0.0511448i
$396$		0			0
$397$	−11.0940	−	19.2154i	−0.556794	−	0.964395i	−0.997762	−	0.0668724i	$-0.978698\pi$
$397$	−11.0940	−	19.2154i	−0.556794	−	0.964395i	0.440968	−	0.897523i	$-0.354635\pi$
$398$	−19.0579	−	15.9915i	−0.955285	−	0.801579i
$399$		0			0
$400$	0.741992	+	4.20805i	0.0370996	+	0.210402i
$401$			23.0731i			1.15222i	0.817374	+	0.576108i	$0.195429\pi$
$401$			23.0731i			1.15222i	−0.817374	+	0.576108i	$0.804571\pi$
$402$		0			0
$403$	20.4749	−	17.1805i	1.01993	−	0.855820i
$404$	3.78583	+	1.37793i	0.188352	+	0.0685546i
$405$		0			0
$406$	−1.39715			−0.0693392
$407$	−5.35891	−	1.84989i	−0.265631	−	0.0916955i
$408$		0			0
$409$	4.96326	+	13.6365i	0.245418	+	0.674279i	0.999840	+	0.0178901i	$0.00569489\pi$
$409$	4.96326	+	13.6365i	0.245418	+	0.674279i	−0.754422	+	0.656389i	$0.772083\pi$
$410$	0.194809	+	0.0709048i	0.00962095	+	0.00350174i
$411$		0			0
$412$	−0.229563	+	0.0404781i	−0.0113097	+	0.00199421i
$413$			13.5254i			0.665540i
$414$		0			0
$415$	−12.3461	−	7.12801i	−0.606045	−	0.349900i
$416$	2.78980	+	2.34092i	0.136781	+	0.114773i
$417$		0			0
$418$	−1.78252	+	3.08742i	−0.0871861	+	0.151011i
$419$	15.9383	−	5.80108i	0.778639	−	0.283401i	0.0780339	−	0.996951i	$-0.475136\pi$
$419$	15.9383	−	5.80108i	0.778639	−	0.283401i	0.700605	+	0.713549i	$0.252914\pi$
$420$		0			0
$421$	13.6763	−	7.89599i	0.666540	−	0.384827i	−0.128224	−	0.991745i	$-0.540928\pi$
$421$	13.6763	−	7.89599i	0.666540	−	0.384827i	0.794764	+	0.606918i	$0.207594\pi$
$422$	12.9301	+	2.27993i	0.629429	+	0.110985i
$423$		0			0
$424$	−8.34281	+	9.94258i	−0.405163	+	0.482854i
$425$	6.46927	−	17.7742i	0.313806	−	0.862174i
$426$		0			0
$427$	−0.353376	+	0.421138i	−0.0171011	+	0.0203803i
$428$	1.11988	−	6.35115i	0.0541314	−	0.306994i
$429$		0			0
$430$	−3.79361	+	2.19024i	−0.182944	+	0.105623i
$431$	24.0972	+	28.7180i	1.16072	+	1.38330i	0.909675	+	0.415321i	$0.136331\pi$
$431$	24.0972	+	28.7180i	1.16072	+	1.38330i	0.251048	+	0.967975i	$0.419225\pi$
$432$		0			0
$433$	−8.01147	+	13.8763i	−0.385007	+	0.666852i	−0.991770	−	0.128031i	$-0.959134\pi$
$433$	−8.01147	+	13.8763i	−0.385007	+	0.666852i	0.606763	+	0.794883i	$0.292468\pi$
$434$	5.08150	+	8.80141i	0.243920	+	0.422481i
$435$		0			0
$436$	−11.9308	−	6.88823i	−0.571380	−	0.329886i
$437$	−0.706219	−	4.00517i	−0.0337830	−	0.191593i
$438$		0			0
$439$	−29.8670	+	5.26636i	−1.42548	+	0.251350i	−0.832569	−	0.553921i	$-0.813131\pi$
$439$	−29.8670	+	5.26636i	−1.42548	+	0.251350i	−0.592907	+	0.805271i	$0.702020\pi$
$440$	0.608772	−	0.510820i	0.0290221	−	0.0243524i
$441$		0			0
$442$	−5.51372	−	15.1488i	−0.262261	−	0.720556i
$443$	−24.5626			−1.16700			−0.583502	−	0.812112i	$-0.698318\pi$
$443$	−24.5626			−1.16700			−0.583502	+	0.812112i	$0.698318\pi$
$444$		0			0
$445$	5.36247			0.254206
$446$	−0.479539	−	1.31752i	−0.0227069	−	0.0623866i
$447$		0			0
$448$	−1.06078	+	0.890103i	−0.0501173	+	0.0420534i
$449$	−26.1350	+	4.60830i	−1.23339	+	0.217479i	−0.752079	−	0.659073i	$-0.770949\pi$
$449$	−26.1350	+	4.60830i	−1.23339	+	0.217479i	−0.481307	+	0.876552i	$0.659838\pi$
$450$		0			0
$451$	0.0393493	+	0.223161i	0.00185289	+	0.0105082i
$452$	3.68955	+	2.13017i	0.173542	+	0.100195i
$453$		0			0
$454$	1.50308	+	2.60340i	0.0705429	+	0.122184i
$455$	−2.15001	+	3.72392i	−0.100794	+	0.174580i
$456$		0			0
$457$	−15.2270	−	18.1468i	−0.712288	−	0.848872i	0.281569	−	0.959541i	$-0.409145\pi$
$457$	−15.2270	−	18.1468i	−0.712288	−	0.848872i	−0.993857	+	0.110669i	$0.964701\pi$
$458$	8.03930	−	4.64149i	0.375652	−	0.216883i
$459$		0			0
$460$	−0.157425	+	0.892803i	−0.00733999	+	0.0416272i
$461$	11.4935	−	13.6974i	0.535306	−	0.637953i	−0.428823	−	0.903389i	$-0.641071\pi$
$461$	11.4935	−	13.6974i	0.535306	−	0.637953i	0.964128	+	0.265436i	$0.0855159\pi$
$462$		0			0
$463$	−3.97134	+	10.9112i	−0.184564	+	0.507085i	−0.997124	−	0.0757928i	$-0.975851\pi$
$463$	−3.97134	+	10.9112i	−0.184564	+	0.507085i	0.812560	+	0.582878i	$0.198073\pi$
$464$	−0.648540	+	0.772900i	−0.0301077	+	0.0358810i
$465$		0			0
$466$	27.0050	+	4.76171i	1.25098	+	0.220582i
$467$	5.99577	−	3.46166i	0.277451	−	0.160187i	−0.354818	−	0.934935i	$-0.615457\pi$
$467$	5.99577	−	3.46166i	0.277451	−	0.160187i	0.632269	+	0.774749i	$0.282124\pi$
$468$		0			0
$469$	18.5299	−	6.74433i	0.855631	−	0.311424i
$470$	3.32365	−	5.75673i	0.153308	−	0.265538i
$471$		0			0
$472$	7.48222	+	6.27833i	0.344397	+	0.288984i
$473$	−4.14664	−	2.39406i	−0.190663	−	0.110079i
$474$		0			0
$475$		−	16.3445i		−	0.749939i
$476$	6.03669	−	1.06443i	0.276691	−	0.0487881i
$477$		0			0
$478$	0.695124	+	0.253005i	0.0317942	+	0.0115722i
$479$	10.5351	+	28.9450i	0.481361	+	1.32253i	0.908327	+	0.418261i	$0.137360\pi$
$479$	10.5351	+	28.9450i	0.481361	+	1.32253i	−0.426966	+	0.904268i	$0.640417\pi$
$480$		0			0
$481$	13.9543	−	17.2047i	0.636262	−	0.784468i
$482$	0.923265			0.0420536
$483$		0			0
$484$	−9.52036	−	3.46513i	−0.432743	−	0.157506i
$485$	−4.88106	+	4.09569i	−0.221637	+	0.185976i
$486$		0			0
$487$		−	26.1340i		−	1.18425i	−0.805848	−	0.592123i	$-0.798290\pi$
$487$		−	26.1340i		−	1.18425i	0.805848	−	0.592123i	$-0.201710\pi$
$488$	0.0689394	+	0.390975i	0.00312074	+	0.0176986i
$489$		0			0
$490$	3.31976	+	2.78561i	0.149971	+	0.125841i
$491$	4.72126	+	8.17747i	0.213068	+	0.369044i	0.952673	−	0.303997i	$-0.0983212\pi$
$491$	4.72126	+	8.17747i	0.213068	+	0.369044i	−0.739605	+	0.673041i	$0.764988\pi$
$492$		0			0
$493$	4.19691	−	1.52755i	0.189019	−	0.0687974i
$494$	−8.95426	−	10.6713i	−0.402871	−	0.480123i
$495$		0			0
$496$	7.22770	+	1.27444i	0.324533	+	0.0572240i
$497$	3.28692	−	18.6410i	0.147438	−	0.836164i
$498$		0			0
$499$	−4.66741	+	12.8236i	−0.208942	+	0.574063i	−0.999253	−	0.0386425i	$-0.987697\pi$
$499$	−4.66741	+	12.8236i	−0.208942	+	0.574063i	0.790311	+	0.612706i	$0.209919\pi$
$500$	−2.70426	+	7.42990i	−0.120938	+	0.332275i
$501$		0			0
$502$	1.70721	−	9.68205i	0.0761964	−	0.432131i
$503$	−19.6874	−	3.47142i	−0.877817	−	0.154783i	−0.283460	−	0.958984i	$-0.591482\pi$
$503$	−19.6874	−	3.47142i	−0.877817	−	0.154783i	−0.594357	+	0.804201i	$0.702593\pi$
$504$		0			0
$505$	2.20812	+	2.63153i	0.0982599	+	0.117102i
$506$	−0.931179	+	0.338921i	−0.0413959	+	0.0150669i
$507$		0			0
$508$	5.76455	+	9.98450i	0.255761	+	0.442990i
$509$	−18.6781	−	15.6728i	−0.827894	−	0.694685i	0.126913	−	0.991914i	$-0.459493\pi$
$509$	−18.6781	−	15.6728i	−0.827894	−	0.694685i	−0.954806	+	0.297229i	$0.903938\pi$
$510$		0			0
$511$	−3.16307	−	17.9387i	−0.139926	−	0.793560i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−3.96118	+	3.32383i	−0.174720	+	0.146608i
$515$	−0.186773	−	0.0679798i	−0.00823020	−	0.00299555i
$516$		0			0
$517$	7.26588			0.319553
$518$	5.52112	+	6.36132i	0.242584	+	0.279500i
$519$		0			0
$520$	1.06206	+	2.91799i	0.0465744	+	0.127962i
$521$	−13.8664	−	5.04695i	−0.607497	−	0.221111i	0.0199104	−	0.999802i	$-0.493662\pi$
$521$	−13.8664	−	5.04695i	−0.607497	−	0.221111i	−0.627408	+	0.778691i	$0.715884\pi$
$522$		0			0
$523$	9.25252	−	1.63147i	0.404585	−	0.0713392i	0.0323471	−	0.999477i	$-0.489702\pi$
$523$	9.25252	−	1.63147i	0.404585	−	0.0713392i	0.372237	+	0.928138i	$0.378591\pi$
$524$			10.4534i			0.456657i
$525$		0			0
$526$	−17.7744	−	10.2621i	−0.775000	−	0.447447i
$527$	−24.8873	−	20.8829i	−1.08411	−	0.909673i
$528$		0			0
$529$	−10.9348	+	18.9396i	−0.475425	+	0.823460i
$530$	−10.3994	+	3.78508i	−0.451722	+	0.164414i
$531$		0			0
$532$	4.58719	−	2.64842i	0.198880	−	0.114823i
$533$	−0.871998	−	0.153757i	−0.0377704	−	0.00665994i
$534$		0			0
$535$	3.53465	−	4.21244i	0.152816	−	0.182119i
$536$	4.87041	−	13.3814i	0.210370	−	0.577986i
$537$		0			0
$538$	10.6166	−	12.6523i	0.457712	−	0.545480i
$539$	−0.822556	+	4.66495i	−0.0354300	+	0.200934i
$540$		0			0
$541$	−37.3740	+	21.5779i	−1.60684	+	0.927707i	−0.616763	+	0.787149i	$0.711556\pi$
$541$	−37.3740	+	21.5779i	−1.60684	+	0.927707i	−0.990072	+	0.140559i	$0.955110\pi$
$542$	−6.83531	−	8.14600i	−0.293602	−	0.349901i
$543$		0			0
$544$	2.21332	−	3.83359i	0.0948954	−	0.164364i
$545$	−5.87335	−	10.1729i	−0.251587	−	0.435761i
$546$		0			0
$547$	−21.1110	−	12.1884i	−0.902641	−	0.521140i	−0.0245851	−	0.999698i	$-0.507826\pi$
$547$	−21.1110	−	12.1884i	−0.902641	−	0.521140i	−0.878056	+	0.478558i	$0.841160\pi$
$548$	−1.17715	−	6.67596i	−0.0502855	−	0.285183i
$549$		0			0
$550$	−3.92195	+	0.691546i	−0.167233	+	0.0294876i
$551$	2.95643	−	2.48074i	0.125948	−	0.105683i
$552$		0			0
$553$	1.65080	+	4.53553i	0.0701991	+	0.192870i
$554$	−6.55413			−0.278458
$555$		0			0
$556$	19.1491			0.812104
$557$	−10.4716	−	28.7704i	−0.443695	−	1.21904i	−0.937045	−	0.349210i	$-0.886450\pi$
$557$	−10.4716	−	28.7704i	−0.443695	−	1.21904i	0.493350	−	0.869831i	$-0.335772\pi$
$558$		0			0
$559$	14.3323	−	12.0262i	0.606192	−	0.508656i
$560$	−1.16279	+	0.205032i	−0.0491370	+	0.00866418i
$561$		0			0
$562$	−4.29375	−	24.3511i	−0.181121	−	1.02719i
$563$	−3.05690	−	1.76490i	−0.128833	−	0.0743819i	0.434198	−	0.900817i	$-0.357032\pi$
$563$	−3.05690	−	1.76490i	−0.128833	−	0.0743819i	−0.563032	+	0.826435i	$0.690365\pi$
$564$		0			0
$565$	1.81632	+	3.14596i	0.0764131	+	0.132351i
$566$	9.85700	−	17.0728i	0.414321	−	0.717625i
$567$		0			0
$568$	−8.78644	−	10.4713i	−0.368671	−	0.439365i
$569$	31.5781	−	18.2316i	1.32382	−	0.764310i	0.339487	−	0.940611i	$-0.389746\pi$
$569$	31.5781	−	18.2316i	1.32382	−	0.764310i	0.984336	+	0.176301i	$0.0564131\pi$
$570$		0			0
$571$	−6.71527	+	38.0842i	−0.281025	+	1.59377i	0.438122	+	0.898915i	$0.355644\pi$
$571$	−6.71527	+	38.0842i	−0.281025	+	1.59377i	−0.719147	+	0.694858i	$0.755467\pi$
$572$	−2.18176	+	2.60013i	−0.0912242	+	0.108717i
$573$		0			0
$574$	0.115152	−	0.316376i	0.00480633	−	0.0132053i
$575$	2.92026	−	3.48023i	0.121783	−	0.145136i
$576$		0			0
$577$	42.7190	+	7.53251i	1.77842	+	0.313583i	0.963841	−	0.266477i	$-0.0858596\pi$
$577$	42.7190	+	7.53251i	1.77842	+	0.313583i	0.814574	+	0.580060i	$0.196971\pi$
$578$	−2.24749	+	1.29759i	−0.0934831	+	0.0539725i
$579$		0			0
$580$	−0.808414	+	0.294239i	−0.0335676	+	0.0122176i
$581$	−11.5761	+	20.0504i	−0.480258	+	0.831831i
$582$		0			0
$583$	−9.26661	−	7.77561i	−0.383784	−	0.322033i
$584$	−11.3919	−	6.57713i	−0.471401	−	0.272163i
$585$		0			0
$586$		−	1.17264i		−	0.0484414i
$587$	0.0109487	−	0.00193056i	0.000451903	−	7.96826e-5i	−0.173422	−	0.984848i	$-0.555483\pi$
$587$	0.0109487	−	0.00193056i	0.000451903	−	7.96826e-5i	0.173874	+	0.984768i	$0.444371\pi$
$588$		0			0
$589$	−26.3802	−	9.60161i	−1.08698	−	0.395628i
$590$	2.84844	+	7.82602i	0.117268	+	0.322192i
$591$		0			0
$592$	6.08192	−	0.101424i	0.249965	−	0.00416850i
$593$	36.1152			1.48307			0.741537	−	0.670912i	$-0.234097\pi$
$593$	36.1152			1.48307			0.741537	+	0.670912i	$0.234097\pi$
$594$		0			0
$595$	4.91147	+	1.78763i	0.201351	+	0.0732857i
$596$	3.42868	−	2.87701i	0.140444	−	0.117847i
$597$		0			0
$598$		−	3.87208i		−	0.158341i
$599$	2.78662	+	15.8037i	0.113858	+	0.645721i	0.987309	+	0.158809i	$0.0507655\pi$
$599$	2.78662	+	15.8037i	0.113858	+	0.645721i	−0.873451	+	0.486912i	$0.838123\pi$
$600$		0			0
$601$	−15.1796	−	12.7372i	−0.619189	−	0.519561i	0.278359	−	0.960477i	$-0.410209\pi$
$601$	−15.1796	−	12.7372i	−0.619189	−	0.519561i	−0.897549	+	0.440916i	$0.854654\pi$
$602$	3.55702	+	6.16094i	0.144973	+	0.251101i
$603$		0			0
$604$	8.30906	−	3.02425i	0.338091	−	0.123055i
$605$	−5.55282	−	6.61759i	−0.225754	−	0.269043i
$606$		0			0
$607$	−14.4410	−	2.54634i	−0.586143	−	0.103353i	−0.127291	−	0.991865i	$-0.540628\pi$
$607$	−14.4410	−	2.54634i	−0.586143	−	0.103353i	−0.458852	+	0.888513i	$0.651739\pi$
$608$	0.664223	−	3.76700i	0.0269378	−	0.152772i
$609$		0			0
$610$	−0.115778	+	0.318099i	−0.00468773	+	0.0128794i
$611$	−9.71038	+	26.6791i	−0.392840	+	1.07932i
$612$		0			0
$613$	−1.23791	+	7.02054i	−0.0499988	+	0.283557i	−0.999548	−	0.0300607i	$-0.990430\pi$
$613$	−1.23791	+	7.02054i	−0.0499988	+	0.283557i	0.949549	+	0.313618i	$0.101541\pi$
$614$	18.4518	+	3.25354i	0.744652	+	0.131302i
$615$		0			0
$616$	−0.829587	−	0.988664i	−0.0334250	−	0.0398344i
$617$	1.54788	−	0.563382i	0.0623153	−	0.0226809i	−0.310674	−	0.950516i	$-0.600555\pi$
$617$	1.54788	−	0.563382i	0.0623153	−	0.0226809i	0.372990	+	0.927835i	$0.378333\pi$
$618$		0			0
$619$	−6.28743	−	10.8902i	−0.252713	−	0.437712i	0.711559	−	0.702627i	$-0.247990\pi$
$619$	−6.28743	−	10.8902i	−0.252713	−	0.437712i	−0.964272	+	0.264914i	$0.914656\pi$
$620$	4.79382	+	4.02249i	0.192524	+	0.161547i
$621$		0			0
$622$	−5.70271	−	32.3417i	−0.228658	−	1.29678i
$623$		−	8.70882i		−	0.348911i
$624$		0			0
$625$	11.2019	−	9.39949i	0.448075	−	0.375979i
$626$	20.2526	+	7.37135i	0.809458	+	0.294619i
$627$		0			0
$628$	18.4218			0.735111
$629$	−23.5400	−	13.0724i	−0.938603	−	0.521232i
$630$		0			0
$631$	−7.72595	−	21.2269i	−0.307565	−	0.845028i	−0.993130	−	0.117017i	$-0.962667\pi$
$631$	−7.72595	−	21.2269i	−0.307565	−	0.845028i	0.685565	−	0.728012i	$-0.259555\pi$
$632$	3.27533	+	1.19212i	0.130286	+	0.0474201i
$633$		0			0
$634$	17.3552	−	3.06019i	0.689262	−	0.121535i
$635$			9.83047i			0.390110i
$636$		0			0
$637$	−16.0296	−	9.25469i	−0.635116	−	0.366684i
$638$	−0.720352	−	0.604447i	−0.0285190	−	0.0239303i
$639$		0			0
$640$	−0.426333	+	0.738430i	−0.0168523	+	0.0291890i
$641$	−29.1189	+	10.5984i	−1.15013	+	0.418613i	−0.845562	−	0.533878i	$-0.820734\pi$
$641$	−29.1189	+	10.5984i	−1.15013	+	0.418613i	−0.304568	+	0.952491i	$0.598512\pi$
$642$		0			0
$643$	−0.920945	+	0.531708i	−0.0363185	+	0.0209685i	−0.518049	−	0.855351i	$-0.673342\pi$
$643$	−0.920945	+	0.531708i	−0.0363185	+	0.0209685i	0.481731	+	0.876319i	$0.340008\pi$
$644$	1.44994	+	0.255663i	0.0571356	+	0.0100745i
$645$		0			0
$646$	−10.8839	+	12.9710i	−0.428223	+	0.510336i
$647$	4.56612	−	12.5453i	0.179513	−	0.493207i	−0.817001	−	0.576636i	$-0.804365\pi$
$647$	4.56612	−	12.5453i	0.179513	−	0.493207i	0.996514	+	0.0834293i	$0.0265873\pi$
$648$		0			0
$649$	−5.85148	+	6.97353i	−0.229691	+	0.273735i
$650$	2.70220	−	15.3249i	0.105989	−	0.601094i
$651$		0			0
$652$	−7.99589	+	4.61643i	−0.313143	+	0.180793i
$653$	5.99298	+	7.14215i	0.234523	+	0.279494i	0.870451	−	0.492254i	$-0.163827\pi$
$653$	5.99298	+	7.14215i	0.234523	+	0.279494i	−0.635928	+	0.771748i	$0.719383\pi$
$654$		0			0
$655$	−4.45661	+	7.71908i	−0.174134	+	0.301609i
$656$	−0.121567	−	0.210560i	−0.00474639	−	0.00822099i
$657$		0			0
$658$	−9.34909	−	5.39770i	−0.364466	−	0.210424i
$659$	3.29553	+	18.6899i	0.128376	+	0.728054i	0.979246	+	0.202677i	$0.0649643\pi$
$659$	3.29553	+	18.6899i	0.128376	+	0.728054i	−0.850870	+	0.525376i	$0.823925\pi$
$660$		0			0
$661$	21.2508	−	3.74709i	0.826560	−	0.145745i	0.255662	−	0.966766i	$-0.417706\pi$
$661$	21.2508	−	3.74709i	0.826560	−	0.145745i	0.570898	+	0.821021i	$0.306595\pi$
$662$	5.44074	−	4.56532i	0.211460	−	0.177436i
$663$		0			0
$664$	5.71836	+	15.7111i	0.221915	+	0.609708i
$665$	4.51643			0.175140
$666$		0			0
$667$	1.07274			0.0415367
$668$	5.57821	+	15.3260i	0.215827	+	0.592981i
$669$		0			0
$670$	9.30137	−	7.80477i	0.359343	−	0.301525i
$671$	−0.364394	+	0.0642524i	−0.0140673	+	0.00248044i
$672$		0			0
$673$	−7.18577	−	40.7525i	−0.276991	−	1.57089i	−0.732565	−	0.680697i	$-0.761677\pi$
$673$	−7.18577	−	40.7525i	−0.276991	−	1.57089i	0.455574	−	0.890198i	$-0.349434\pi$
$674$	0.883304	+	0.509976i	0.0340236	+	0.0196435i
$675$		0			0
$676$	−0.131428	−	0.227641i	−0.00505494	−	0.00875541i
$677$	−2.29044	+	3.96715i	−0.0880287	+	0.152470i	−0.906678	−	0.421824i	$-0.861390\pi$
$677$	−2.29044	+	3.96715i	−0.0880287	+	0.152470i	0.818649	+	0.574294i	$0.194723\pi$
$678$		0			0
$679$	6.65153	+	7.92699i	0.255262	+	0.304210i
$680$	3.26877	−	1.88722i	0.125351	−	0.0723717i
$681$		0			0
$682$	−1.18779	+	6.73631i	−0.0454830	+	0.257947i
$683$	−23.1346	+	27.5707i	−0.885220	+	1.05496i	0.112895	+	0.993607i	$0.463987\pi$
$683$	−23.1346	+	27.5707i	−0.885220	+	1.05496i	−0.998116	+	0.0613577i	$0.980457\pi$
$684$		0			0
$685$	1.97694	−	5.43159i	0.0755349	−	0.207530i
$686$	10.7546	−	12.8169i	0.410614	−	0.489350i
$687$		0			0
$688$	5.05935	+	0.892101i	0.192886	+	0.0340110i
$689$	40.9350	−	23.6338i	1.55950	−	0.900376i
$690$		0			0
$691$	33.8223	−	12.3103i	1.28666	−	0.468306i	0.394031	−	0.919097i	$-0.371080\pi$
$691$	33.8223	−	12.3103i	1.28666	−	0.468306i	0.892629	+	0.450791i	$0.148858\pi$
$692$	−0.961119	+	1.66471i	−0.0365363	+	0.0632827i
$693$		0			0
$694$	−3.81867	−	3.20425i	−0.144955	−	0.121632i
$695$	14.1403	+	8.16390i	0.536372	+	0.309674i
$696$		0			0
$697$			1.07627i			0.0407665i
$698$	25.3385	−	4.46786i	0.959077	−	0.169111i
$699$		0			0
$700$	5.56016	+	2.02373i	0.210154	+	0.0764900i
$701$	2.16083	+	5.93682i	0.0816132	+	0.224231i	0.973787	−	0.227462i	$-0.0730427\pi$
$701$	2.16083	+	5.93682i	0.0816132	+	0.224231i	−0.892174	+	0.451692i	$0.850820\pi$
$702$		0			0
$703$	−22.9779	−	3.65769i	−0.866629	−	0.137952i
$704$	−0.932013			−0.0351266
$705$		0			0
$706$	25.2046	+	9.17371i	0.948586	+	0.345257i
$707$	4.27368	−	3.58605i	0.160728	−	0.134867i
$708$		0			0
$709$		−	15.4046i		−	0.578533i	−0.957249	−	0.289267i	$-0.906589\pi$
$709$		−	15.4046i		−	0.578533i	0.957249	−	0.289267i	$-0.0934114\pi$
$710$	−2.02393	−	11.4783i	−0.0759566	−	0.430771i
$711$		0			0
$712$	−4.81771	−	4.04254i	−0.180551	−	0.151500i
$713$	−3.90161	−	6.75779i	−0.146117	−	0.253081i
$714$		0			0
$715$	−2.71960	+	0.989853i	−0.101707	+	0.0370184i
$716$	−12.1457	−	14.4747i	−0.453907	−	0.540945i
$717$		0			0
$718$	−19.6306	−	3.46141i	−0.732609	−	0.129179i
$719$	0.517948	−	2.93743i	0.0193162	−	0.109548i	−0.973625	−	0.228153i	$-0.926731\pi$
$719$	0.517948	−	2.93743i	0.0193162	−	0.109548i	0.992941	+	0.118606i	$0.0378424\pi$
$720$		0			0
$721$	−0.110401	+	0.303325i	−0.00411156	+	0.0112964i
$722$	1.49413	−	4.10509i	0.0556058	−	0.152776i
$723$		0			0
$724$	−1.19012	+	6.74951i	−0.0442305	+	0.250844i
$725$	4.24570	+	0.748632i	0.157681	+	0.0278035i
$726$		0			0
$727$	−11.3263	−	13.4981i	−0.420068	−	0.500618i	0.513961	−	0.857813i	$-0.328177\pi$
$727$	−11.3263	−	13.4981i	−0.420068	−	0.500618i	−0.934030	+	0.357195i	$0.883733\pi$
$728$	4.73890	−	1.72482i	0.175635	−	0.0639260i
$729$		0			0
$730$	−5.60809	−	9.71349i	−0.207565	−	0.359513i
$731$	−17.4210	−	14.6179i	−0.644338	−	0.540663i
$732$		0			0
$733$	−3.34139	−	18.9500i	−0.123417	−	0.699933i	−0.982235	−	0.187653i	$-0.939912\pi$
$733$	−3.34139	−	18.9500i	−0.123417	−	0.699933i	0.858818	−	0.512280i	$-0.171199\pi$
$734$			14.8345i			0.547553i
$735$		0			0
$736$	0.814478	−	0.683428i	0.0300221	−	0.0251915i
$737$	12.4716	+	4.53929i	0.459397	+	0.167207i
$738$		0			0
$739$	33.3412			1.22648			0.613238	−	0.789898i	$-0.289867\pi$
$739$	33.3412			1.22648			0.613238	+	0.789898i	$0.289867\pi$
$740$	4.53431	+	2.51803i	0.166685	+	0.0925645i
$741$		0			0
$742$	6.14709	+	16.8890i	0.225667	+	0.620014i
$743$	−34.4286	−	12.5310i	−1.26306	−	0.459717i	−0.378267	−	0.925697i	$-0.623480\pi$
$743$	−34.4286	−	12.5310i	−1.26306	−	0.459717i	−0.884795	+	0.465980i	$0.845702\pi$
$744$		0			0
$745$	3.75840	−	0.662708i	0.137697	−	0.0242797i
$746$		−	2.70556i		−	0.0990575i
$747$		0			0
$748$	3.57295	+	2.06284i	0.130640	+	0.0754250i
$749$	−6.84112	−	5.74038i	−0.249969	−	0.209749i
$750$		0			0
$751$	−9.48212	+	16.4235i	−0.346008	+	0.599303i	−0.985536	−	0.169465i	$-0.945796\pi$
$751$	−9.48212	+	16.4235i	−0.346008	+	0.599303i	0.639529	+	0.768767i	$0.279130\pi$
$752$	−7.32575	+	2.66635i	−0.267143	+	0.0972319i
$753$		0			0
$754$	3.18213	−	1.83721i	0.115886	−	0.0669071i
$755$	7.42499	+	1.30923i	0.270223	+	0.0476476i
$756$		0			0
$757$	−28.2928	+	33.7181i	−1.02832	+	1.22551i	−0.0544232	+	0.998518i	$0.517332\pi$
$757$	−28.2928	+	33.7181i	−1.02832	+	1.22551i	−0.973898	+	0.226987i	$0.927112\pi$
$758$	6.88426	−	18.9143i	0.250047	−	0.687000i
$759$		0			0
$760$	2.09648	−	2.49848i	0.0760472	−	0.0906295i
$761$	−1.42559	+	8.08493i	−0.0516776	+	0.293078i	−0.999683	−	0.0251759i	$-0.991985\pi$
$761$	−1.42559	+	8.08493i	−0.0516776	+	0.293078i	0.948005	+	0.318254i	$0.103097\pi$
$762$		0			0
$763$	−16.5212	+	9.53850i	−0.598107	+	0.345317i
$764$	13.6127	+	16.2230i	0.492492	+	0.586929i
$765$		0			0
$766$	−13.4566	+	23.3076i	−0.486208	+	0.842138i
$767$	−17.7855	−	30.8053i	−0.642196	−	1.11232i
$768$		0			0
$769$	46.6866	+	26.9545i	1.68356	+	0.972006i	0.959260	+	0.282524i	$0.0911717\pi$
$769$	46.6866	+	26.9545i	1.68356	+	0.972006i	0.724303	+	0.689482i	$0.242162\pi$
$770$	−0.191092	−	1.08374i	−0.00688649	−	0.0390553i
$771$		0			0
$772$	−7.55925	+	1.33290i	−0.272063	+	0.0479721i
$773$	2.07004	−	1.73697i	0.0744543	−	0.0624746i	−0.604801	−	0.796377i	$-0.706747\pi$
$773$	2.07004	−	1.73697i	0.0744543	−	0.0624746i	0.679255	+	0.733902i	$0.262303\pi$
$774$		0			0
$775$	−10.7258	−	29.4689i	−0.385282	−	1.05855i
$776$	7.47277			0.268257
$777$		0			0
$778$	−0.971540			−0.0348314
$779$	0.318083	+	0.873927i	0.0113965	+	0.0313117i
$780$		0			0
$781$	9.75936	−	8.18908i	0.349217	−	0.293028i
$782$	−4.63502	+	0.817279i	−0.165748	+	0.0292258i
$783$		0			0
$784$	−0.882559	−	5.00524i	−0.0315200	−	0.178759i
$785$	13.6032	+	7.85383i	0.485520	+	0.280315i
$786$		0			0
$787$	4.84358	+	8.38932i	0.172655	+	0.299047i	0.939347	−	0.342968i	$-0.111432\pi$
$787$	4.84358	+	8.38932i	0.172655	+	0.299047i	−0.766692	+	0.642015i	$0.778099\pi$
$788$	5.68110	−	9.83995i	0.202381	−	0.350534i
$789$		0			0
$790$	1.91036	+	2.27668i	0.0679677	+	0.0810007i
$791$	5.10913	−	2.94976i	0.181660	−	0.104881i
$792$		0			0
$793$	0.251065	−	1.42386i	0.00891558	−	0.0505628i
$794$	−14.2622	+	16.9971i	−0.506147	+	0.603203i
$795$		0			0
$796$	−8.50888	+	23.3780i	−0.301589	+	0.828610i
$797$	−19.7365	+	23.5210i	−0.699102	+	0.833157i	−0.992424	−	0.122856i	$-0.960795\pi$
$797$	−19.7365	+	23.5210i	−0.699102	+	0.833157i	0.293323	+	0.956013i	$0.405239\pi$
$798$		0			0
$799$	33.9854	+	5.99254i	1.20232	+	0.212001i
$800$	3.70049	−	2.13648i	0.130832	−	0.0755360i
$801$		0			0
$802$	21.6816	−	7.89146i	0.765604	−	0.278657i
$803$	6.12996	−	10.6174i	0.216322	−	0.374680i
$804$		0			0
$805$	0.961681	+	0.806946i	0.0338948	+	0.0284411i
$806$	−23.1472	−	13.3640i	−0.815324	−	0.470728i
$807$		0			0
$808$		−	4.02880i		−	0.141733i
$809$	−12.8727	+	2.26981i	−0.452580	+	0.0798021i	−0.395292	−	0.918556i	$-0.629357\pi$
$809$	−12.8727	+	2.26981i	−0.452580	+	0.0798021i	−0.0572885	+	0.998358i	$0.518245\pi$
$810$		0			0
$811$	42.7071	+	15.5441i	1.49965	+	0.545828i	0.955970	−	0.293464i	$-0.0948081\pi$
$811$	42.7071	+	15.5441i	1.49965	+	0.545828i	0.543680	+	0.839292i	$0.317030\pi$
$812$	0.477852	+	1.31289i	0.0167693	+	0.0460733i
$813$		0			0
$814$	0.0945286	+	5.66842i	0.00331322	+	0.198678i
$815$	−7.87254			−0.275763
$816$		0			0
$817$	−18.4660	−	6.72108i	−0.646044	−	0.235141i
$818$	11.1165	−	9.32789i	0.388681	−	0.326142i
$819$		0			0
$820$		−	0.207312i		−	0.00723964i
$821$	4.91748	+	27.8884i	0.171621	+	0.973312i	0.941972	+	0.335692i	$0.108970\pi$
$821$	4.91748	+	27.8884i	0.171621	+	0.973312i	−0.770351	+	0.637620i	$0.779919\pi$
$822$		0			0
$823$	18.9218	+	15.8772i	0.659571	+	0.553446i	0.909958	−	0.414700i	$-0.136113\pi$
$823$	18.9218	+	15.8772i	0.659571	+	0.553446i	−0.250387	+	0.968146i	$0.580558\pi$
$824$	0.116552	+	0.201874i	0.00406028	+	0.00703261i
$825$		0			0
$826$	12.7097	−	4.62595i	0.442227	−	0.160957i
$827$	8.00202	+	9.53644i	0.278258	+	0.331614i	0.887014	−	0.461743i	$-0.152776\pi$
$827$	8.00202	+	9.53644i	0.278258	+	0.331614i	−0.608756	+	0.793357i	$0.708331\pi$
$828$		0			0
$829$	10.6721	+	1.88178i	0.370658	+	0.0653570i	0.355874	−	0.934534i	$-0.384183\pi$
$829$	10.6721	+	1.88178i	0.370658	+	0.0653570i	0.0147833	+	0.999891i	$0.495294\pi$
$830$	−2.47553	+	14.0394i	−0.0859270	+	0.487316i
$831$		0			0
$832$	1.24558	−	3.42219i	0.0431826	−	0.118643i
$833$	−7.69484	+	21.1414i	−0.266611	+	0.732506i
$834$		0			0
$835$	−2.41486	+	13.6954i	−0.0835697	+	0.473947i
$836$	3.51089	+	0.619064i	0.121427	+	0.0214108i
$837$		0			0
$838$	−10.9025	−	12.9931i	−0.376620	−	0.448838i
$839$	23.7039	−	8.62752i	0.818350	−	0.297855i	0.101282	−	0.994858i	$-0.467706\pi$
$839$	23.7039	−	8.62752i	0.818350	−	0.297855i	0.717069	+	0.697003i	$0.245483\pi$
$840$		0			0
$841$	−13.9910	−	24.2331i	−0.482449	−	0.835626i
$842$	−12.0974	−	10.1509i	−0.416903	−	0.349823i
$843$		0			0
$844$	−2.27993	−	12.9301i	−0.0784785	−	0.445073i
$845$		−	0.224129i		−	0.00771027i
$846$		0			0
$847$	−10.7472	+	9.01795i	−0.369277	+	0.309860i
$848$	12.1964	+	4.43912i	0.418825	+	0.152440i
$849$		0			0
$850$	−18.9149			−0.648775
$851$	−4.23916	−	4.88427i	−0.145317	−	0.167431i
$852$		0			0
$853$	3.72709	+	10.2401i	0.127613	+	0.350614i	0.987002	−	0.160709i	$-0.0513779\pi$
$853$	3.72709	+	10.2401i	0.127613	+	0.350614i	−0.859389	+	0.511323i	$0.829156\pi$
$854$	0.516602	+	0.188028i	0.0176778	+	0.00643418i
$855$		0			0
$856$	−6.35115	+	1.11988i	−0.217078	+	0.0382767i
$857$			18.7526i			0.640575i	0.947320	+	0.320288i	$0.103780\pi$
$857$			18.7526i			0.640575i	−0.947320	+	0.320288i	$0.896220\pi$
$858$		0			0
$859$	−33.6788	−	19.4444i	−1.14910	−	0.663436i	−0.200436	−	0.979707i	$-0.564236\pi$
$859$	−33.6788	−	19.4444i	−1.14910	−	0.663436i	−0.948669	+	0.316271i	$0.897569\pi$
$860$	3.35565	+	2.81572i	0.114427	+	0.0960154i
$861$		0			0
$862$	18.7443	−	32.4661i	0.638434	−	1.10580i
$863$	26.5719	−	9.67137i	0.904517	−	0.329217i	0.152455	−	0.988310i	$-0.451282\pi$
$863$	26.5719	−	9.67137i	0.904517	−	0.329217i	0.752061	+	0.659093i	$0.229060\pi$
$864$		0			0
$865$	−1.41944	+	0.819513i	−0.0482624	+	0.0278643i
$866$	15.7795	+	2.78236i	0.536210	+	0.0945483i
$867$		0			0
$868$	6.53264	−	7.78530i	0.221732	−	0.264250i
$869$	−1.11107	+	3.05265i	−0.0376906	+	0.103554i
$870$		0			0
$871$	−33.3350	+	39.7271i	−1.12951	+	1.34610i
$872$	−2.39226	+	13.5672i	−0.0810120	+	0.459442i
$873$		0			0
$874$	−3.52209	+	2.03348i	−0.119136	+	0.0687834i
$875$	7.03781	+	8.38733i	0.237921	+	0.283544i
$876$		0			0
$877$	−0.375638	+	0.650624i	−0.0126844	+	0.0219700i	−0.872298	−	0.488975i	$-0.837371\pi$
$877$	−0.375638	+	0.650624i	−0.0126844	+	0.0219700i	0.859614	+	0.510945i	$0.170704\pi$
$878$	15.1639	+	26.2646i	0.511756	+	0.886388i
$879$		0			0
$880$	−0.688226	−	0.397348i	−0.0232001	−	0.0133946i
$881$	−9.26268	−	52.5313i	−0.312068	−	1.76982i	−0.588211	−	0.808708i	$-0.700167\pi$
$881$	−9.26268	−	52.5313i	−0.312068	−	1.76982i	0.276143	−	0.961117i	$-0.410944\pi$
$882$		0			0
$883$	−23.7723	+	4.19169i	−0.800001	+	0.141062i	−0.558680	−	0.829384i	$-0.688692\pi$
$883$	−23.7723	+	4.19169i	−0.800001	+	0.141062i	−0.241321	+	0.970445i	$0.577581\pi$
$884$	−12.3494	+	10.3624i	−0.415356	+	0.348525i
$885$		0			0
$886$	8.40090	+	23.0813i	0.282234	+	0.775431i
$887$	−47.2073			−1.58506			−0.792532	−	0.609830i	$-0.791238\pi$
$887$	−47.2073			−1.58506			−0.792532	+	0.609830i	$0.791238\pi$
$888$		0			0
$889$	15.9650			0.535448
$890$	−1.83407	−	5.03908i	−0.0614783	−	0.168910i
$891$		0			0
$892$	−1.07406	+	0.901239i	−0.0359620	+	0.0301757i
$893$	29.3671	−	5.17822i	0.982733	−	0.173282i
$894$		0			0
$895$	−2.79772	−	15.8667i	−0.0935176	−	0.530364i
$896$	1.19923	+	0.692377i	0.0400635	+	0.0231307i
$897$		0			0
$898$	13.2691	+	22.9827i	0.442795	+	0.766943i
$899$	3.70244	−	6.41281i	0.123483	−	0.213879i
$900$		0			0
$901$	−36.9307	−	44.0123i	−1.23034	−	1.46626i
$902$	0.196245	−	0.113302i	0.00653423	−	0.00377254i
$903$		0			0
$904$	0.739799	−	4.19561i	0.0246053	−	0.139544i
$905$	−3.75636	+	4.47665i	−0.124866	+	0.148809i
$906$		0			0
$907$	−7.33846	+	20.1623i	−0.243670	+	0.669477i	0.756216	+	0.654323i	$0.227046\pi$
$907$	−7.33846	+	20.1623i	−0.243670	+	0.669477i	−0.999885	+	0.0151542i	$0.995176\pi$
$908$	1.93232	−	2.30285i	0.0641262	−	0.0764226i
$909$		0			0
$910$	4.23469	+	0.746690i	0.140379	+	0.0247525i
$911$	−18.1914	+	10.5028i	−0.602707	+	0.347973i	−0.770106	−	0.637916i	$-0.779797\pi$
$911$	−18.1914	+	10.5028i	−0.602707	+	0.347973i	0.167399	+	0.985889i	$0.446463\pi$
$912$		0			0
$913$	−14.6429	+	5.32958i	−0.484610	+	0.176384i
$914$	−11.8445	+	20.5153i	−0.391781	+	0.678584i
$915$		0			0
$916$	−7.11118	−	5.96699i	−0.234960	−	0.197155i
$917$	12.5360	+	7.23767i	0.413976	+	0.239009i
$918$		0			0
$919$			44.9184i			1.48172i	0.671659	+	0.740860i	$0.265582\pi$
$919$			44.9184i			1.48172i	−0.671659	+	0.740860i	$0.734418\pi$
$920$	0.892803	−	0.157425i	0.0294348	−	0.00519016i
$921$		0			0
$922$	−16.8024	−	6.11557i	−0.553357	−	0.201405i
$923$	17.0261	+	46.7789i	0.560422	+	1.53975i
$924$		0			0
$925$	−13.3692	−	22.2894i	−0.439577	−	0.732871i
$926$	11.6114			0.381575
$927$		0			0
$928$	0.948102	+	0.345081i	0.0311230	+	0.0113278i
$929$	−26.7338	+	22.4324i	−0.877109	+	0.735982i	−0.965583	−	0.260097i	$-0.916245\pi$
$929$	−26.7338	+	22.4324i	−0.877109	+	0.735982i	0.0884738	+	0.996079i	$0.471801\pi$
$930$		0			0
$931$			19.4409i			0.637151i
$932$	−4.76171	−	27.0050i	−0.155975	−	0.884579i
$933$		0			0
$934$	−5.30357	−	4.45022i	−0.173538	−	0.145616i
$935$	1.75892	+	3.04653i	0.0575227	+	0.0996323i
$936$		0			0
$937$	−10.7395	+	3.90885i	−0.350844	+	0.127697i	−0.511430	−	0.859325i	$-0.670884\pi$
$937$	−10.7395	+	3.90885i	−0.350844	+	0.127697i	0.160586	+	0.987022i	$0.448662\pi$
$938$	−12.6752	−	15.1057i	−0.413860	−	0.493219i
$939$		0			0
$940$	−6.54631	−	1.15429i	−0.213517	−	0.0376488i
$941$	6.15749	−	34.9209i	0.200729	−	1.13839i	−0.703293	−	0.710901i	$-0.748288\pi$
$941$	6.15749	−	34.9209i	0.200729	−	1.13839i	0.904021	−	0.427488i	$-0.140601\pi$
$942$		0			0
$943$	−0.0884143	+	0.242916i	−0.00287917	+	0.00791044i
$944$	3.34063	−	9.17831i	0.108728	−	0.298728i
$945$		0			0
$946$	−0.831449	+	4.71538i	−0.0270327	+	0.153310i
$947$	33.4708	+	5.90181i	1.08765	+	0.191783i	0.688598	−	0.725143i	$-0.258226\pi$
$947$	33.4708	+	5.90181i	1.08765	+	0.191783i	0.399057	+	0.916926i	$0.369338\pi$
$948$		0			0
$949$	30.7930	+	36.6977i	0.999583	+	1.19126i
$950$	−15.3588	+	5.59016i	−0.498307	+	0.181369i
$951$		0			0
$952$	−3.06491	−	5.30857i	−0.0993342	−	0.172052i
$953$	15.3276	+	12.8614i	0.496509	+	0.416621i	0.856352	−	0.516392i	$-0.172725\pi$
$953$	15.3276	+	12.8614i	0.496509	+	0.416621i	−0.359843	+	0.933013i	$0.617170\pi$
$954$		0			0
$955$	3.13565	+	17.7831i	0.101467	+	0.575449i
$956$		−	0.739736i		−	0.0239248i
$957$		0			0
$958$	23.5961	−	19.7995i	0.762357	−	0.639693i
$959$	−8.82107	−	3.21061i	−0.284847	−	0.103676i
$960$		0			0
$961$	−22.8639			−0.737544
$962$	−20.9398	−	7.22840i	−0.675127	−	0.233053i
$963$		0			0
$964$	−0.315775	−	0.867585i	−0.0101704	−	0.0279430i
$965$	−6.15024	−	2.23850i	−0.197983	−	0.0720600i
$966$		0			0
$967$	21.1585	−	3.73082i	0.680413	−	0.119975i	0.177249	−	0.984166i	$-0.443280\pi$
$967$	21.1585	−	3.73082i	0.680413	−	0.119975i	0.503164	+	0.864191i	$0.332169\pi$
$968$			10.1314i			0.325634i
$969$		0			0
$970$	5.51811	+	3.18588i	0.177176	+	0.102293i
$971$	−0.671321	−	0.563305i	−0.0215437	−	0.0180773i	0.631952	−	0.775007i	$-0.282254\pi$
$971$	−0.671321	−	0.563305i	−0.0215437	−	0.0180773i	−0.653496	+	0.756930i	$0.726698\pi$
$972$		0			0
$973$	13.2584	−	22.9642i	0.425045	−	0.736200i
$974$	−24.5580	+	8.93836i	−0.786887	+	0.286404i
$975$		0			0
$976$	0.343818	−	0.198503i	0.0110053	−	0.00635393i
$977$	−14.3294	−	2.52665i	−0.458437	−	0.0808348i	−0.0603394	−	0.998178i	$-0.519218\pi$
$977$	−14.3294	−	2.52665i	−0.458437	−	0.0808348i	−0.398097	+	0.917343i	$0.630329\pi$
$978$		0			0
$979$	3.76770	−	4.49016i	0.120416	−	0.143506i
$980$	1.48219	−	4.07228i	0.0473468	−	0.130084i
$981$		0			0
$982$	6.06954	−	7.23339i	0.193687	−	0.230827i
$983$	2.38729	−	13.5390i	0.0761426	−	0.431826i	−0.922776	−	0.385336i	$-0.874085\pi$
$983$	2.38729	−	13.5390i	0.0761426	−	0.431826i	0.998919	−	0.0464897i	$-0.0148035\pi$
$984$		0			0
$985$	8.39019	−	4.84408i	0.267334	−	0.154345i
$986$	−2.87085	−	3.42135i	−0.0914266	−	0.108958i
$987$		0			0
$988$	−6.96518	+	12.0640i	−0.221592	+	0.383808i
$989$	−2.73111	−	4.73042i	−0.0868442	−	0.150419i
$990$		0			0
$991$	41.1867	+	23.7791i	1.30834	+	0.755370i	0.981819	−	0.189821i	$-0.0607907\pi$
$991$	41.1867	+	23.7791i	1.30834	+	0.755370i	0.326520	+	0.945190i	$0.394124\pi$
$992$	−1.27444	−	7.22770i	−0.0404635	−	0.229480i
$993$		0			0
$994$	−18.6410	+	3.28692i	−0.591257	+	0.104255i
$995$	−16.2500	+	13.6354i	−0.515160	+	0.432270i
$996$		0			0
$997$	18.4308	+	50.6383i	0.583711	+	1.60373i	0.781787	+	0.623545i	$0.214308\pi$
$997$	18.4308	+	50.6383i	0.583711	+	1.60373i	−0.198077	+	0.980187i	$0.563469\pi$
$998$	13.6466			0.431975
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.bj.c.289.1		12
3.2	odd	2		74.2.h.a.67.2	yes	12
12.11	even	2		592.2.bq.b.289.1		12
37.21	even	18	inner	666.2.bj.c.613.1		12
111.50	even	36		2738.2.a.r.1.4		6
111.95	odd	18		74.2.h.a.21.2	✓	12
111.98	even	36		2738.2.a.s.1.3		6
444.95	even	18		592.2.bq.b.465.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.h.a.21.2	✓	12	111.95	odd	18
74.2.h.a.67.2	yes	12	3.2	odd	2
592.2.bq.b.289.1		12	12.11	even	2
592.2.bq.b.465.1		12	444.95	even	18
666.2.bj.c.289.1		12	1.1	even	1	trivial
666.2.bj.c.613.1		12	37.21	even	18	inner
2738.2.a.r.1.4		6	111.50	even	36
2738.2.a.s.1.3		6	111.98	even	36

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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.bj (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.342020 - 0.939693i) q^{2} +(-0.766044 + 0.642788i) q^{4} +(-0.839712 + 0.148064i) q^{5} +(0.240460 + 1.36372i) q^{7} +(0.866025 + 0.500000i) q^{8} +O(q^{10})\)	\(q+(-0.342020 - 0.939693i) q^{2} +(-0.766044 + 0.642788i) q^{4} +(-0.839712 + 0.148064i) q^{5} +(0.240460 + 1.36372i) q^{7} +(0.866025 + 0.500000i) q^{8} +(0.426333 + 0.738430i) q^{10} +(-0.466006 + 0.807147i) q^{11} +(-2.34092 - 2.78980i) q^{13} +(1.19923 - 0.692377i) q^{14} +(0.173648 - 0.984808i) q^{16} +(-2.84539 + 3.39101i) q^{17} +(-1.30826 + 3.59443i) q^{19} +(0.548083 - 0.653180i) q^{20} +(0.917853 + 0.161842i) q^{22} +(-0.920780 + 0.531613i) q^{23} +(-4.01527 + 1.46144i) q^{25} +(-1.82091 + 3.15391i) q^{26} +(-1.06078 - 0.890103i) q^{28} +(-0.873775 - 0.504474i) q^{29} +7.33920i q^{31} +(-0.984808 + 0.173648i) q^{32} +(4.15968 + 1.51400i) q^{34} +(-0.403834 - 1.10953i) q^{35} +(1.15600 + 5.97191i) q^{37} +3.82511 q^{38} +(-0.801244 - 0.291629i) q^{40} +(0.186251 - 0.156283i) q^{41} +5.13740i q^{43} +(-0.161842 - 0.917853i) q^{44} +(0.814478 + 0.683428i) q^{46} +(-3.89795 - 6.75145i) q^{47} +(4.77595 - 1.73830i) q^{49} +(2.74661 + 3.27328i) q^{50} +(3.58649 + 0.632396i) q^{52} +(-2.25380 + 12.7819i) q^{53} +(0.271802 - 0.746769i) q^{55} +(-0.473614 + 1.30124i) q^{56} +(-0.175202 + 0.993621i) q^{58} +(9.61896 + 1.69608i) q^{59} +(0.255191 + 0.304124i) q^{61} +(6.89659 - 2.51015i) q^{62} +(0.500000 + 0.866025i) q^{64} +(2.37876 + 1.99602i) q^{65} +(-2.47277 - 14.0238i) q^{67} -4.42664i q^{68} +(-0.904494 + 0.758960i) q^{70} +(-12.8449 - 4.67517i) q^{71} -13.1543 q^{73} +(5.21638 - 3.12879i) q^{74} +(-1.30826 - 3.59443i) q^{76} +(-1.21278 - 0.441414i) q^{77} +(3.43258 - 0.605257i) q^{79} +0.852666i q^{80} +(-0.210560 - 0.121567i) q^{82} +(12.8078 + 10.7470i) q^{83} +(1.88722 - 3.26877i) q^{85} +(4.82758 - 1.75710i) q^{86} +(-0.807147 + 0.466006i) q^{88} +(-6.19352 - 1.09209i) q^{89} +(3.24160 - 3.86318i) q^{91} +(0.363645 - 0.999105i) q^{92} +(-5.01111 + 5.97200i) q^{94} +(0.566360 - 3.21199i) q^{95} +(6.47160 - 3.73638i) q^{97} +(-3.26694 - 3.89339i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{7}+O(q^{10}) \) 12 * q - 12 * q^7	\( 12 q - 12 q^{7} + 6 q^{10} + 6 q^{11} + 6 q^{13} + 18 q^{14} - 18 q^{19} - 18 q^{25} - 12 q^{26} - 6 q^{28} - 18 q^{29} + 12 q^{34} - 18 q^{35} + 30 q^{37} + 24 q^{38} + 12 q^{40} - 24 q^{41} - 6 q^{44} + 30 q^{46} - 6 q^{47} + 12 q^{49} + 36 q^{50} - 12 q^{52} + 12 q^{53} - 18 q^{55} + 6 q^{58} - 36 q^{61} + 6 q^{64} - 36 q^{65} - 30 q^{67} - 12 q^{70} - 12 q^{71} + 48 q^{74} - 18 q^{76} - 12 q^{77} + 6 q^{79} + 48 q^{83} + 18 q^{85} + 36 q^{86} - 36 q^{88} + 18 q^{89} - 6 q^{91} - 18 q^{92} + 36 q^{97} - 36 q^{98}+O(q^{100}) \) 12 * q - 12 * q^7 + 6 * q^10 + 6 * q^11 + 6 * q^13 + 18 * q^14 - 18 * q^19 - 18 * q^25 - 12 * q^26 - 6 * q^28 - 18 * q^29 + 12 * q^34 - 18 * q^35 + 30 * q^37 + 24 * q^38 + 12 * q^40 - 24 * q^41 - 6 * q^44 + 30 * q^46 - 6 * q^47 + 12 * q^49 + 36 * q^50 - 12 * q^52 + 12 * q^53 - 18 * q^55 + 6 * q^58 - 36 * q^61 + 6 * q^64 - 36 * q^65 - 30 * q^67 - 12 * q^70 - 12 * q^71 + 48 * q^74 - 18 * q^76 - 12 * q^77 + 6 * q^79 + 48 * q^83 + 18 * q^85 + 36 * q^86 - 36 * q^88 + 18 * q^89 - 6 * q^91 - 18 * q^92 + 36 * q^97 - 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more