LMFDB - Embedded newform 592.2.bq.b.465.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [592,2,Mod(65,592)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(592, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 0, 17]))

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

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

chi := DirichletCharacter("592.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 592 = 2^{4} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	592.bq (of order $18$, degree $6$, not 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:	$4.72714379966$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 74)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			465.1
Root			$-0.342020 - 0.939693i$ of defining polynomial
Character	$\chi$	$=$	592.465
Dual form			592.2.bq.b.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.326352 + 0.118782i) q^{3} +(0.839712 + 0.148064i) q^{5} +(-0.240460 + 1.36372i) q^{7} +(-2.20574 + 1.85083i) q^{9} +O(q^{10})$	\(q+(-0.326352 + 0.118782i) q^{3} +(0.839712 + 0.148064i) q^{5} +(-0.240460 + 1.36372i) q^{7} +(-2.20574 + 1.85083i) q^{9} +(-0.466006 - 0.807147i) q^{11} +(-2.34092 + 2.78980i) q^{13} +(-0.291629 + 0.0514220i) q^{15} +(2.84539 + 3.39101i) q^{17} +(1.30826 + 3.59443i) q^{19} +(-0.0835109 - 0.473614i) q^{21} +(-0.920780 - 0.531613i) q^{23} +(-4.01527 - 1.46144i) q^{25} +(1.02094 - 1.76833i) q^{27} +(0.873775 - 0.504474i) q^{29} +7.33920i q^{31} +(0.247957 + 0.208060i) q^{33} +(-0.403834 + 1.10953i) q^{35} +(1.15600 - 5.97191i) q^{37} +(0.432584 - 1.18851i) q^{39} +(-0.186251 - 0.156283i) q^{41} +5.13740i q^{43} +(-2.12622 + 1.22758i) q^{45} +(-3.89795 + 6.75145i) q^{47} +(4.77595 + 1.73830i) q^{49} +(-1.33139 - 0.768679i) q^{51} +(2.25380 + 12.7819i) q^{53} +(-0.271802 - 0.746769i) q^{55} +(-0.853909 - 1.01765i) q^{57} +(9.61896 - 1.69608i) q^{59} +(0.255191 - 0.304124i) q^{61} +(-1.99362 - 3.45305i) q^{63} +(-2.37876 + 1.99602i) q^{65} +(2.47277 - 14.0238i) q^{67} +(0.363645 + 0.0641204i) q^{69} +(-12.8449 + 4.67517i) q^{71} -13.1543 q^{73} +1.48398 q^{75} +(1.21278 - 0.441414i) q^{77} +(-3.43258 - 0.605257i) q^{79} +(1.37686 - 7.80856i) q^{81} +(12.8078 - 10.7470i) q^{83} +(1.88722 + 3.26877i) q^{85} +(-0.225236 + 0.268425i) q^{87} +(6.19352 - 1.09209i) q^{89} +(-3.24160 - 3.86318i) q^{91} +(-0.871767 - 2.39516i) q^{93} +(0.566360 + 3.21199i) q^{95} +(6.47160 + 3.73638i) q^{97} +(2.52178 + 0.917853i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 12 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 + 12 * q^7 - 6 * q^9	$ 12 q - 6 q^{3} + 12 q^{7} - 6 q^{9} + 6 q^{11} + 6 q^{13} + 18 q^{19} - 6 q^{21} - 18 q^{25} + 6 q^{27} + 18 q^{29} - 6 q^{33} - 18 q^{35} + 30 q^{37} - 30 q^{39} + 24 q^{41} - 18 q^{45} - 6 q^{47} + 12 q^{49} - 12 q^{53} + 18 q^{55} - 36 q^{57} - 36 q^{61} + 6 q^{63} + 36 q^{65} + 30 q^{67} - 18 q^{69} - 12 q^{71} + 36 q^{75} + 12 q^{77} - 6 q^{79} + 24 q^{81} + 48 q^{83} + 18 q^{85} - 36 q^{87} - 18 q^{89} + 6 q^{91} - 12 q^{93} + 36 q^{97} - 30 q^{99}+O(q^{100}) $ 12 * q - 6 * q^3 + 12 * q^7 - 6 * q^9 + 6 * q^11 + 6 * q^13 + 18 * q^19 - 6 * q^21 - 18 * q^25 + 6 * q^27 + 18 * q^29 - 6 * q^33 - 18 * q^35 + 30 * q^37 - 30 * q^39 + 24 * q^41 - 18 * q^45 - 6 * q^47 + 12 * q^49 - 12 * q^53 + 18 * q^55 - 36 * q^57 - 36 * q^61 + 6 * q^63 + 36 * q^65 + 30 * q^67 - 18 * q^69 - 12 * q^71 + 36 * q^75 + 12 * q^77 - 6 * q^79 + 24 * q^81 + 48 * q^83 + 18 * q^85 - 36 * q^87 - 18 * q^89 + 6 * q^91 - 12 * q^93 + 36 * q^97 - 30 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/592\mathbb{Z}\right)^\times$.

$n$	$113$	$149$	$223$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.326352	+	0.118782i	−0.188419	+	0.0685790i	−0.434507	−	0.900669i	$-0.643077\pi$
$3$	−0.326352	+	0.118782i	−0.188419	+	0.0685790i	0.246087	+	0.969248i	$0.420855\pi$
$4$		0			0
$5$	0.839712	+	0.148064i	0.375530	+	0.0662162i	0.358228	−	0.933634i	$-0.383381\pi$
$5$	0.839712	+	0.148064i	0.375530	+	0.0662162i	0.0173025	+	0.999850i	$0.494492\pi$
$6$		0			0
$7$	−0.240460	+	1.36372i	−0.0908854	+	0.515437i	0.905045	+	0.425315i	$0.139837\pi$
$7$	−0.240460	+	1.36372i	−0.0908854	+	0.515437i	−0.995931	+	0.0901216i	$0.971274\pi$
$8$		0			0
$9$	−2.20574	+	1.85083i	−0.735246	+	0.616944i
$10$		0			0
$11$	−0.466006	−	0.807147i	−0.140506	−	0.243364i	0.787181	−	0.616722i	$-0.211540\pi$
$11$	−0.466006	−	0.807147i	−0.140506	−	0.243364i	−0.927687	+	0.373358i	$0.878206\pi$
$12$		0			0
$13$	−2.34092	+	2.78980i	−0.649254	+	0.773750i	−0.985801	−	0.167916i	$-0.946296\pi$
$13$	−2.34092	+	2.78980i	−0.649254	+	0.773750i	0.336548	+	0.941666i	$0.390741\pi$
$14$		0			0
$15$	−0.291629	+	0.0514220i	−0.0752982	+	0.0132771i
$16$		0			0
$17$	2.84539	+	3.39101i	0.690109	+	0.822440i	0.991369	−	0.131102i	$-0.0418517\pi$
$17$	2.84539	+	3.39101i	0.690109	+	0.822440i	−0.301260	+	0.953542i	$0.597407\pi$
$18$		0			0
$19$	1.30826	+	3.59443i	0.300136	+	0.824618i	0.994475	+	0.104970i	$0.0334746\pi$
$19$	1.30826	+	3.59443i	0.300136	+	0.824618i	−0.694339	+	0.719648i	$0.744303\pi$
$20$		0			0
$21$	−0.0835109	−	0.473614i	−0.0182236	−	0.103351i
$22$		0			0
$23$	−0.920780	−	0.531613i	−0.191996	−	0.110849i	0.400921	−	0.916113i	$-0.368690\pi$
$23$	−0.920780	−	0.531613i	−0.191996	−	0.110849i	−0.592917	+	0.805264i	$0.702024\pi$
$24$		0			0
$25$	−4.01527	−	1.46144i	−0.803054	−	0.292288i
$26$		0			0
$27$	1.02094	−	1.76833i	0.196481	−	0.340315i
$28$		0			0
$29$	0.873775	−	0.504474i	0.162256	−	0.0936786i	−0.416673	−	0.909056i	$-0.636804\pi$
$29$	0.873775	−	0.504474i	0.162256	−	0.0936786i	0.578929	+	0.815378i	$0.303471\pi$
$30$		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			0
$33$	0.247957	+	0.208060i	0.0431637	+	0.0362187i
$34$		0			0
$35$	−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
$38$		0			0
$39$	0.432584	−	1.18851i	0.0692689	−	0.190315i
$40$		0			0
$41$	−0.186251	−	0.156283i	−0.0290876	−	0.0244074i	0.628128	−	0.778110i	$-0.283821\pi$
$41$	−0.186251	−	0.156283i	−0.0290876	−	0.0244074i	−0.657216	+	0.753703i	$0.728266\pi$
$42$		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			0
$45$	−2.12622	+	1.22758i	−0.316959	+	0.182996i
$46$		0			0
$47$	−3.89795	+	6.75145i	−0.568574	+	0.984800i	0.428133	+	0.903716i	$0.359171\pi$
$47$	−3.89795	+	6.75145i	−0.568574	+	0.984800i	−0.996707	+	0.0810838i	$0.974162\pi$
$48$		0			0
$49$	4.77595	+	1.73830i	0.682278	+	0.248329i
$50$		0			0
$51$	−1.33139	−	0.768679i	−0.186432	−	0.107637i
$52$		0			0
$53$	2.25380	+	12.7819i	0.309583	+	1.75573i	0.601106	+	0.799170i	$0.294727\pi$
$53$	2.25380	+	12.7819i	0.309583	+	1.75573i	−0.291522	+	0.956564i	$0.594162\pi$
$54$		0			0
$55$	−0.271802	−	0.746769i	−0.0366497	−	0.100694i
$56$		0			0
$57$	−0.853909	−	1.01765i	−0.113103	−	0.134791i
$58$		0			0
$59$	9.61896	−	1.69608i	1.25228	−	0.220811i	0.492110	−	0.870533i	$-0.336226\pi$
$59$	9.61896	−	1.69608i	1.25228	−	0.220811i	0.760172	+	0.649722i	$0.225115\pi$
$60$		0			0
$61$	0.255191	−	0.304124i	0.0326738	−	0.0389391i	−0.749460	−	0.662050i	$-0.769687\pi$
$61$	0.255191	−	0.304124i	0.0326738	−	0.0389391i	0.782134	+	0.623110i	$0.214131\pi$
$62$		0			0
$63$	−1.99362	−	3.45305i	−0.251173	−	0.435044i
$64$		0			0
$65$	−2.37876	+	1.99602i	−0.295049	+	0.247576i
$66$		0			0
$67$	2.47277	−	14.0238i	0.302097	−	1.71328i	−0.334765	−	0.942302i	$-0.608657\pi$
$67$	2.47277	−	14.0238i	0.302097	−	1.71328i	0.636862	−	0.770978i	$-0.280232\pi$
$68$		0			0
$69$	0.363645	+	0.0641204i	0.0437777	+	0.00771918i
$70$		0			0
$71$	−12.8449	+	4.67517i	−1.52441	+	0.554840i	−0.962245	−	0.272184i	$-0.912254\pi$
$71$	−12.8449	+	4.67517i	−1.52441	+	0.554840i	−0.562166	+	0.827024i	$0.690032\pi$
$72$		0			0
$73$	−13.1543			−1.53959			−0.769794	−	0.638292i	$-0.779641\pi$
$73$	−13.1543			−1.53959			−0.769794	+	0.638292i	$0.779641\pi$
$74$		0			0
$75$	1.48398			0.171356
$76$		0			0
$77$	1.21278	−	0.441414i	0.138209	−	0.0503038i
$78$		0			0
$79$	−3.43258	−	0.605257i	−0.386196	−	0.0680968i	−0.0228205	−	0.999740i	$-0.507265\pi$
$79$	−3.43258	−	0.605257i	−0.386196	−	0.0680968i	−0.363375	+	0.931643i	$0.618376\pi$
$80$		0			0
$81$	1.37686	−	7.80856i	0.152984	−	0.867617i
$82$		0			0
$83$	12.8078	−	10.7470i	1.40584	−	1.17964i	0.447399	−	0.894335i	$-0.352351\pi$
$83$	12.8078	−	10.7470i	1.40584	−	1.17964i	0.958438	−	0.285302i	$-0.0920939\pi$
$84$		0			0
$85$	1.88722	+	3.26877i	0.204698	+	0.354548i
$86$		0			0
$87$	−0.225236	+	0.268425i	−0.0241478	+	0.0287782i
$88$		0			0
$89$	6.19352	−	1.09209i	0.656512	−	0.115761i	0.164538	−	0.986371i	$-0.447387\pi$
$89$	6.19352	−	1.09209i	0.656512	−	0.115761i	0.491974	+	0.870610i	$0.336275\pi$
$90$		0			0
$91$	−3.24160	−	3.86318i	−0.339812	−	0.404972i
$92$		0			0
$93$	−0.871767	−	2.39516i	−0.0903981	−	0.248367i
$94$		0			0
$95$	0.566360	+	3.21199i	0.0581073	+	0.329543i
$96$		0			0
$97$	6.47160	+	3.73638i	0.657092	+	0.379372i	0.791168	−	0.611599i	$-0.209473\pi$
$97$	6.47160	+	3.73638i	0.657092	+	0.379372i	−0.134076	+	0.990971i	$0.542807\pi$
$98$		0			0
$99$	2.52178	+	0.917853i	0.253449	+	0.0922477i
$100$		0			0
$101$	2.01440	−	3.48904i	0.200440	−	0.347173i	−0.748230	−	0.663439i	$-0.769096\pi$
$101$	2.01440	−	3.48904i	0.200440	−	0.347173i	0.948670	+	0.316267i	$0.102429\pi$
$102$		0			0
$103$	−0.201874	+	0.116552i	−0.0198912	+	0.0114842i	−0.509913	−	0.860226i	$-0.670322\pi$
$103$	−0.201874	+	0.116552i	−0.0198912	+	0.0114842i	0.490021	+	0.871710i	$0.336989\pi$
$104$		0			0
$105$		−	0.410064i		−	0.0400182i
$106$		0			0
$107$	−4.94031	−	4.14542i	−0.477598	−	0.400753i	0.371959	−	0.928249i	$-0.378686\pi$
$107$	−4.94031	−	4.14542i	−0.477598	−	0.400753i	−0.849557	+	0.527497i	$0.823131\pi$
$108$		0			0
$109$	4.71183	−	12.9456i	0.451311	−	1.23997i	−0.480491	−	0.877000i	$-0.659542\pi$
$109$	4.71183	−	12.9456i	0.451311	−	1.23997i	0.931802	−	0.362967i	$-0.118236\pi$
$110$		0			0
$111$	0.332095	+	2.08625i	0.0315211	+	0.198019i
$112$		0			0
$113$	1.45712	−	4.00340i	0.137074	−	0.376608i	−0.852095	−	0.523387i	$-0.824668\pi$
$113$	1.45712	−	4.00340i	0.137074	−	0.376608i	0.989169	+	0.146779i	$0.0468905\pi$
$114$		0			0
$115$	−0.694477	−	0.582736i	−0.0647604	−	0.0543404i
$116$		0			0
$117$		−	10.4862i		−	0.969450i
$118$		0			0
$119$	−5.30857	+	3.06491i	−0.486636	+	0.280960i
$120$		0			0
$121$	5.06568	−	8.77401i	0.460516	−	0.797637i
$122$		0			0
$123$	0.0793472	+	0.0288800i	0.00715449	+	0.00260402i
$124$		0			0
$125$	−6.84743	−	3.95337i	−0.612453	−	0.353600i
$126$		0			0
$127$	−2.00201	−	11.3540i	−0.177649	−	1.00750i	−0.935041	−	0.354539i	$-0.884638\pi$
$127$	−2.00201	−	11.3540i	−0.177649	−	1.00750i	0.757392	−	0.652961i	$-0.226473\pi$
$128$		0			0
$129$	−0.610233	−	1.67660i	−0.0537280	−	0.147616i
$130$		0			0
$131$	6.71929	+	8.00774i	0.587067	+	0.699640i	0.975039	−	0.222032i	$-0.0712688\pi$
$131$	6.71929	+	8.00774i	0.587067	+	0.699640i	−0.387972	+	0.921671i	$0.626824\pi$
$132$		0			0
$133$	−5.21637	+	0.919786i	−0.452316	+	0.0797556i
$134$		0			0
$135$	1.11912	−	1.33372i	0.0963189	−	0.114788i
$136$		0			0
$137$	3.38948	+	5.87074i	0.289582	+	0.501572i	0.973710	−	0.227791i	$-0.0731502\pi$
$137$	3.38948	+	5.87074i	0.289582	+	0.501572i	−0.684128	+	0.729362i	$0.739817\pi$
$138$		0			0
$139$	14.6691	−	12.3088i	1.24421	−	1.04402i	0.247032	−	0.969007i	$-0.420545\pi$
$139$	14.6691	−	12.3088i	1.24421	−	1.04402i	0.997183	−	0.0750129i	$-0.0238998\pi$
$140$		0			0
$141$	0.470150	−	2.66635i	0.0395938	−	0.224548i
$142$		0			0
$143$	3.34266	+	0.589401i	0.279527	+	0.0492882i
$144$		0			0
$145$	0.808414	−	0.294239i	0.0671351	−	0.0244352i
$146$		0			0
$147$	−1.76512			−0.145584
$148$		0			0
$149$	4.47583			0.366674			0.183337	−	0.983050i	$-0.441310\pi$
$149$	4.47583			0.366674			0.183337	+	0.983050i	$0.441310\pi$
$150$		0			0
$151$	8.30906	−	3.02425i	0.676181	−	0.246110i	0.0189744	−	0.999820i	$-0.493960\pi$
$151$	8.30906	−	3.02425i	0.676181	−	0.246110i	0.657207	+	0.753710i	$0.271738\pi$
$152$		0			0
$153$	−12.5524	−	2.21332i	−1.01480	−	0.178936i
$154$		0			0
$155$	−1.08667	+	6.16281i	−0.0872834	+	0.495009i
$156$		0			0
$157$	−14.1119	+	11.8413i	−1.12626	+	0.945041i	−0.998903	−	0.0468171i	$-0.985092\pi$
$157$	−14.1119	+	11.8413i	−1.12626	+	0.945041i	−0.127352	+	0.991858i	$0.540648\pi$
$158$		0			0
$159$	−2.25380	−	3.90370i	−0.178738	−	0.309583i
$160$		0			0
$161$	0.946380	−	1.12785i	0.0745852	−	0.0888872i
$162$		0			0
$163$	−9.09259	+	1.60327i	−0.712186	+	0.125578i	−0.517992	−	0.855385i	$-0.673320\pi$
$163$	−9.09259	+	1.60327i	−0.712186	+	0.125578i	−0.194194	+	0.980963i	$0.562209\pi$
$164$		0			0
$165$	0.177406	+	0.211424i	0.0138110	+	0.0164594i
$166$		0			0
$167$	5.57821	+	15.3260i	0.431655	+	1.18596i	0.944796	+	0.327658i	$0.106259\pi$
$167$	5.57821	+	15.3260i	0.431655	+	1.18596i	−0.513142	+	0.858304i	$0.671518\pi$
$168$		0			0
$169$	−0.0456446	−	0.258863i	−0.00351112	−	0.0199126i
$170$		0			0
$171$	−9.53837	−	5.50698i	−0.729417	−	0.421129i
$172$		0			0
$173$	−1.80631	−	0.657444i	−0.137331	−	0.0499846i	0.272440	−	0.962173i	$-0.412169\pi$
$173$	−1.80631	−	0.657444i	−0.137331	−	0.0499846i	−0.409772	+	0.912188i	$0.634392\pi$
$174$		0			0
$175$	2.95850	−	5.12427i	0.223642	−	0.387359i
$176$		0			0
$177$	−2.93770	+	1.69608i	−0.220811	+	0.127485i
$178$		0			0
$179$		−	18.8954i		−	1.41231i	−0.708059	−	0.706154i	$-0.750429\pi$
$179$		−	18.8954i		−	1.41231i	0.708059	−	0.706154i	$-0.249571\pi$
$180$		0			0
$181$	5.25019	+	4.40543i	0.390243	+	0.327453i	0.816708	−	0.577051i	$-0.195797\pi$
$181$	5.25019	+	4.40543i	0.390243	+	0.327453i	−0.426465	+	0.904504i	$0.640241\pi$
$182$		0			0
$183$	−0.0471573	+	0.129564i	−0.00348597	+	0.00957763i
$184$		0			0
$185$	1.85493	−	4.84352i	0.136377	−	0.356103i
$186$		0			0
$187$	1.41107	−	3.87688i	0.103188	−	0.283505i
$188$		0			0
$189$	2.16600	+	1.81749i	0.157553	+	0.132203i
$190$		0			0
$191$			21.1777i			1.53236i	0.642625	+	0.766181i	$0.277845\pi$
$191$			21.1777i			1.53236i	−0.642625	+	0.766181i	$0.722155\pi$
$192$		0			0
$193$	6.64750	−	3.83793i	0.478497	−	0.276261i	−0.241293	−	0.970452i	$-0.577571\pi$
$193$	6.64750	−	3.83793i	0.478497	−	0.276261i	0.719790	+	0.694192i	$0.244238\pi$
$194$		0			0
$195$	0.539222	−	0.933960i	0.0386145	−	0.0668822i
$196$		0			0
$197$	10.6770	+	3.88610i	0.760703	+	0.276873i	0.693102	−	0.720839i	$-0.256243\pi$
$197$	10.6770	+	3.88610i	0.760703	+	0.276873i	0.0676007	+	0.997712i	$0.478466\pi$
$198$		0			0
$199$	−21.5452	−	12.4391i	−1.52730	−	0.881788i	−0.999474	−	0.0324362i	$-0.989673\pi$
$199$	−21.5452	−	12.4391i	−1.52730	−	0.881788i	−0.527828	−	0.849352i	$-0.676993\pi$
$200$		0			0
$201$	0.858785	+	4.87041i	0.0605740	+	0.343532i
$202$		0			0
$203$	0.477852	+	1.31289i	0.0335387	+	0.0921467i
$204$		0			0
$205$	−0.133257	−	0.158810i	−0.00930711	−	0.0110918i
$206$		0			0
$207$	3.01493	−	0.531613i	0.209552	−	0.0369496i
$208$		0			0
$209$	2.29157	−	2.73099i	0.158511	−	0.188906i
$210$		0			0
$211$	6.56480	+	11.3706i	0.451939	+	0.782782i	0.998506	−	0.0546333i	$-0.0173990\pi$
$211$	6.56480	+	11.3706i	0.451939	+	0.782782i	−0.546567	+	0.837415i	$0.684066\pi$
$212$		0			0
$213$	3.63664	−	3.05150i	0.249178	−	0.209085i
$214$		0			0
$215$	−0.760664	+	4.31394i	−0.0518768	+	0.294208i
$216$		0			0
$217$	−10.0086	−	1.76478i	−0.679427	−	0.119801i
$218$		0			0
$219$	4.29291	−	1.56249i	0.290088	−	0.105583i
$220$		0			0
$221$	−16.1210			−1.08442
$222$		0			0
$223$	−1.40208			−0.0938902			−0.0469451	−	0.998897i	$-0.514949\pi$
$223$	−1.40208			−0.0938902			−0.0469451	+	0.998897i	$0.514949\pi$
$224$		0			0
$225$	11.5615	−	4.20805i	0.770767	−	0.280536i
$226$		0			0
$227$	−2.96048	−	0.522013i	−0.196494	−	0.0346472i	0.0745348	−	0.997218i	$-0.476253\pi$
$227$	−2.96048	−	0.522013i	−0.196494	−	0.0346472i	−0.271029	+	0.962571i	$0.587364\pi$
$228$		0			0
$229$	1.61197	−	9.14196i	0.106522	−	0.604118i	−0.884079	−	0.467337i	$-0.845213\pi$
$229$	1.61197	−	9.14196i	0.106522	−	0.604118i	0.990601	−	0.136780i	$-0.0436755\pi$
$230$		0			0
$231$	−0.343359	+	0.288113i	−0.0225914	+	0.0189564i
$232$		0			0
$233$	13.7108	+	23.7478i	0.898225	+	1.55577i	0.829762	+	0.558118i	$0.188476\pi$
$233$	13.7108	+	23.7478i	0.898225	+	1.55577i	0.0684634	+	0.997654i	$0.478190\pi$
$234$		0			0
$235$	−4.27280	+	5.09212i	−0.278727	+	0.332173i
$236$		0			0
$237$	1.19212	−	0.210204i	0.0774368	−	0.0136542i
$238$		0			0
$239$	−0.475493	−	0.566671i	−0.0307571	−	0.0366549i	0.750447	−	0.660931i	$-0.229838\pi$
$239$	−0.475493	−	0.566671i	−0.0307571	−	0.0366549i	−0.781204	+	0.624276i	$0.785394\pi$
$240$		0			0
$241$	−0.315775	−	0.867585i	−0.0203409	−	0.0558861i	0.929107	−	0.369812i	$-0.120578\pi$
$241$	−0.315775	−	0.867585i	−0.0203409	−	0.0558861i	−0.949448	+	0.313926i	$0.898356\pi$
$242$		0			0
$243$	1.54189	+	8.74449i	0.0989122	+	0.560959i
$244$		0			0
$245$	3.75304	+	2.16682i	0.239773	+	0.138433i
$246$		0			0
$247$	−13.0903	−	4.76446i	−0.832913	−	0.303156i
$248$		0			0
$249$	−2.90329	+	5.02864i	−0.183988	+	0.318677i
$250$		0			0
$251$	8.51425	−	4.91571i	0.537415	−	0.310277i	−0.206616	−	0.978422i	$-0.566245\pi$
$251$	8.51425	−	4.91571i	0.537415	−	0.310277i	0.744031	+	0.668146i	$0.232912\pi$
$252$		0			0
$253$			0.990940i			0.0622999i
$254$		0			0
$255$	−1.00417	−	0.842599i	−0.0628836	−	0.0527656i
$256$		0			0
$257$	1.76857	−	4.85911i	0.110320	−	0.303103i	−0.872231	−	0.489094i	$-0.837327\pi$
$257$	1.76857	−	4.85911i	0.110320	−	0.303103i	0.982551	+	0.185991i	$0.0595496\pi$
$258$		0			0
$259$	7.86602	+	3.01246i	0.488771	+	0.187185i
$260$		0			0
$261$	−0.993621	+	2.72995i	−0.0615036	+	0.168980i
$262$		0			0
$263$	15.7224	+	13.1926i	0.969483	+	0.813493i	0.982470	−	0.186423i	$-0.0596894\pi$
$263$	15.7224	+	13.1926i	0.969483	+	0.813493i	−0.0129864	+	0.999916i	$0.504134\pi$
$264$		0			0
$265$			11.0668i			0.679831i
$266$		0			0
$267$	−1.89155	+	1.09209i	−0.115761	+	0.0668345i
$268$		0			0
$269$	−8.25822	+	14.3037i	−0.503512	+	0.872109i	0.496479	+	0.868049i	$0.334626\pi$
$269$	−8.25822	+	14.3037i	−0.503512	+	0.872109i	−0.999992	+	0.00406062i	$0.998707\pi$
$270$		0			0
$271$	−9.99255	−	3.63699i	−0.607004	−	0.220932i	0.0201876	−	0.999796i	$-0.493574\pi$
$271$	−9.99255	−	3.63699i	−0.607004	−	0.220932i	−0.627192	+	0.778865i	$0.715796\pi$
$272$		0			0
$273$	1.51678	+	0.875712i	0.0917996	+	0.0530005i
$274$		0			0
$275$	0.691546	+	3.92195i	0.0417018	+	0.236503i
$276$		0			0
$277$	2.24164	+	6.15886i	0.134687	+	0.370050i	0.988641	−	0.150299i	$-0.0480238\pi$
$277$	2.24164	+	6.15886i	0.134687	+	0.370050i	−0.853953	+	0.520350i	$0.825802\pi$
$278$		0			0
$279$	−13.5836	−	16.1883i	−0.813231	−	0.969171i
$280$		0			0
$281$	−24.3511	+	4.29375i	−1.45266	+	0.256144i	−0.843598	−	0.536976i	$-0.819567\pi$
$281$	−24.3511	+	4.29375i	−1.45266	+	0.256144i	−0.609066	+	0.793119i	$0.708456\pi$
$282$		0			0
$283$	−12.6719	+	15.1018i	−0.753267	+	0.897709i	−0.997402	−	0.0720321i	$-0.977052\pi$
$283$	−12.6719	+	15.1018i	−0.753267	+	0.897709i	0.244135	+	0.969741i	$0.421496\pi$
$284$		0			0
$285$	−0.566360	−	0.980965i	−0.0335483	−	0.0581073i
$286$		0			0
$287$	0.257912	−	0.216414i	0.0152241	−	0.0127745i
$288$		0			0
$289$	−0.450647	+	2.55575i	−0.0265086	+	0.150338i
$290$		0			0
$291$	−2.55584	−	0.450663i	−0.149826	−	0.0264183i
$292$		0			0
$293$	−1.10192	+	0.401067i	−0.0643751	+	0.0234306i	−0.374007	−	0.927426i	$-0.622016\pi$
$293$	−1.10192	+	0.401067i	−0.0643751	+	0.0234306i	0.309632	+	0.950856i	$0.399794\pi$
$294$		0			0
$295$	8.32828			0.484891
$296$		0			0
$297$	−1.90307			−0.110427
$298$		0			0
$299$	3.63856	−	1.32433i	0.210423	−	0.0765879i
$300$		0			0
$301$	−7.00596	−	1.23534i	−0.403817	−	0.0712038i
$302$		0			0
$303$	−0.242966	+	1.37793i	−0.0139581	+	0.0791601i
$304$		0			0
$305$	0.259316	−	0.217592i	0.0148484	−	0.0124593i
$306$		0			0
$307$	9.36820	+	16.2262i	0.534671	+	0.926078i	0.999179	+	0.0405091i	$0.0128980\pi$
$307$	9.36820	+	16.2262i	0.534671	+	0.926078i	−0.464508	+	0.885569i	$0.653769\pi$
$308$		0			0
$309$	0.0520376	−	0.0620160i	0.00296032	−	0.00352797i
$310$		0			0
$311$	32.3417	−	5.70271i	1.83393	−	0.323371i	0.853628	−	0.520882i	$-0.174397\pi$
$311$	32.3417	−	5.70271i	1.83393	−	0.323371i	0.980301	+	0.197511i	$0.0632859\pi$
$312$		0			0
$313$	−13.8536	−	16.5101i	−0.783052	−	0.933206i	0.216015	−	0.976390i	$-0.430694\pi$
$313$	−13.8536	−	16.5101i	−0.783052	−	0.933206i	−0.999067	+	0.0431845i	$0.986250\pi$
$314$		0			0
$315$	−1.16279	−	3.19475i	−0.0655160	−	0.180004i
$316$		0			0
$317$	3.06019	+	17.3552i	0.171877	+	0.974764i	0.941687	+	0.336490i	$0.109240\pi$
$317$	3.06019	+	17.3552i	0.171877	+	0.974764i	−0.769810	+	0.638273i	$0.779649\pi$
$318$		0			0
$319$	−0.814370	−	0.470177i	−0.0455960	−	0.0263248i
$320$		0			0
$321$	2.10468	+	0.766042i	0.117472	+	0.0427563i
$322$		0			0
$323$	−8.46620	+	14.6639i	−0.471072	+	0.815920i
$324$		0			0
$325$	13.4765	−	7.78068i	0.747543	−	0.431594i
$326$		0			0
$327$			4.78451i			0.264584i
$328$		0			0
$329$	−8.26976	−	6.93915i	−0.455927	−	0.382568i
$330$		0			0
$331$	−2.42916	+	6.67405i	−0.133518	+	0.366839i	−0.988377	−	0.152022i	$-0.951422\pi$
$331$	−2.42916	+	6.67405i	−0.133518	+	0.366839i	0.854859	+	0.518861i	$0.173644\pi$
$332$		0			0
$333$	8.50318	+	15.3120i	0.465971	+	0.839093i
$334$		0			0
$335$	4.15283	−	11.4098i	0.226894	−	0.623385i
$336$		0			0
$337$	−0.781329	−	0.655612i	−0.0425617	−	0.0357135i	0.621259	−	0.783606i	$-0.286622\pi$
$337$	−0.781329	−	0.655612i	−0.0425617	−	0.0357135i	−0.663820	+	0.747892i	$0.731066\pi$
$338$		0			0
$339$			1.47960i			0.0803607i
$340$		0			0
$341$	5.92381	−	3.42011i	0.320792	−	0.185210i
$342$		0			0
$343$	−8.36562	+	14.4897i	−0.451701	+	0.782369i
$344$		0			0
$345$	0.295863	+	0.107685i	0.0159287	+	0.00579758i
$346$		0			0
$347$	4.31707	+	2.49246i	0.231752	+	0.133802i	0.611380	−	0.791337i	$-0.290615\pi$
$347$	4.31707	+	2.49246i	0.231752	+	0.133802i	−0.379628	+	0.925139i	$0.623948\pi$
$348$		0			0
$349$	−4.46786	−	25.3385i	−0.239159	−	1.35634i	−0.833675	−	0.552255i	$-0.813767\pi$
$349$	−4.46786	−	25.3385i	−0.239159	−	1.35634i	0.594516	−	0.804084i	$-0.297344\pi$
$350$		0			0
$351$	2.54333	+	6.98774i	0.135753	+	0.372978i
$352$		0			0
$353$	17.2409	+	20.5469i	0.917642	+	1.09360i	0.995321	+	0.0966250i	$0.0308048\pi$
$353$	17.2409	+	20.5469i	0.917642	+	1.09360i	−0.0776786	+	0.996978i	$0.524751\pi$
$354$		0			0
$355$	−11.4783	+	2.02393i	−0.609202	+	0.107419i
$356$		0			0
$357$	1.36841	−	1.63080i	0.0724237	−	0.0863112i
$358$		0			0
$359$	9.96674	+	17.2629i	0.526024	+	0.911101i	0.999540	+	0.0303155i	$0.00965121\pi$
$359$	9.96674	+	17.2629i	0.526024	+	0.911101i	−0.473516	+	0.880785i	$0.657015\pi$
$360$		0			0
$361$	3.34650	−	2.80805i	0.176132	−	0.147792i
$362$		0			0
$363$	−0.610995	+	3.46513i	−0.0320689	+	0.181872i
$364$		0			0
$365$	−11.0458	−	1.94767i	−0.578162	−	0.101946i
$366$		0			0
$367$	13.9399	−	5.07371i	0.727657	−	0.264846i	0.0484843	−	0.998824i	$-0.484561\pi$
$367$	13.9399	−	5.07371i	0.727657	−	0.264846i	0.679173	+	0.733978i	$0.262339\pi$
$368$		0			0
$369$	0.700076			0.0364445
$370$		0			0
$371$	−17.9729			−0.933106
$372$		0			0
$373$	2.54239	−	0.925355i	0.131640	−	0.0479131i	−0.275360	−	0.961341i	$-0.588797\pi$
$373$	2.54239	−	0.925355i	0.131640	−	0.0479131i	0.407000	+	0.913428i	$0.366575\pi$
$374$		0			0
$375$	2.70426	+	0.476834i	0.139648	+	0.0246236i
$376$		0			0
$377$	−0.638055	+	3.61859i	−0.0328615	+	0.186367i
$378$		0			0
$379$	−15.4191	+	12.9382i	−0.792027	+	0.664589i	−0.946246	−	0.323447i	$-0.895158\pi$
$379$	−15.4191	+	12.9382i	−0.792027	+	0.664589i	0.154220	+	0.988037i	$0.450714\pi$
$380$		0			0
$381$	2.00201	+	3.46758i	0.102566	+	0.177649i
$382$		0			0
$383$	−17.2995	+	20.6168i	−0.883965	+	1.05347i	0.114233	+	0.993454i	$0.463559\pi$
$383$	−17.2995	+	20.6168i	−0.883965	+	1.05347i	−0.998198	+	0.0600143i	$0.980885\pi$
$384$		0			0
$385$	1.08374	−	0.191092i	0.0552325	−	0.00973897i
$386$		0			0
$387$	−9.50848	−	11.3318i	−0.483343	−	0.576026i
$388$		0			0
$389$	−0.332286	−	0.912949i	−0.0168476	−	0.0462883i	0.930984	−	0.365061i	$-0.118952\pi$
$389$	−0.332286	−	0.912949i	−0.0168476	−	0.0462883i	−0.947831	+	0.318772i	$0.896729\pi$
$390$		0			0
$391$	−0.817279	−	4.63502i	−0.0413316	−	0.234403i
$392$		0			0
$393$	−3.14403	−	1.81521i	−0.158595	−	0.0915651i
$394$		0			0
$395$	−2.79276	−	1.01648i	−0.140519	−	0.0511448i
$396$		0			0
$397$	−11.0940	+	19.2154i	−0.556794	+	0.964395i	0.440968	+	0.897523i	$0.354635\pi$
$397$	−11.0940	+	19.2154i	−0.556794	+	0.964395i	−0.997762	+	0.0668724i	$0.978698\pi$
$398$		0			0
$399$	1.59312	−	0.919786i	0.0797556	−	0.0460469i
$400$		0			0
$401$			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
$404$		0			0
$405$	2.31233	−	6.35307i	0.114901	−	0.315687i
$406$		0			0
$407$	−5.35891	+	1.84989i	−0.265631	+	0.0916955i
$408$		0			0
$409$	4.96326	−	13.6365i	0.245418	−	0.674279i	−0.754422	−	0.656389i	$-0.772083\pi$
$409$	4.96326	−	13.6365i	0.245418	−	0.674279i	0.999840	−	0.0178901i	$-0.00569489\pi$
$410$		0			0
$411$	−1.80350	−	1.51332i	−0.0889602	−	0.0746465i
$412$		0			0
$413$			13.5254i			0.665540i
$414$		0			0
$415$	12.3461	−	7.12801i	0.606045	−	0.349900i
$416$		0			0
$417$	−3.32521	+	5.75943i	−0.162836	+	0.282041i
$418$		0			0
$419$	15.9383	+	5.80108i	0.778639	+	0.283401i	0.700605	−	0.713549i	$-0.252914\pi$
$419$	15.9383	+	5.80108i	0.778639	+	0.283401i	0.0780339	+	0.996951i	$0.475136\pi$
$420$		0			0
$421$	13.6763	+	7.89599i	0.666540	+	0.384827i	0.794764	−	0.606918i	$-0.207594\pi$
$421$	13.6763	+	7.89599i	0.666540	+	0.384827i	−0.128224	+	0.991745i	$0.540928\pi$
$422$		0			0
$423$	−3.89795	−	22.1064i	−0.189525	−	1.07485i
$424$		0			0
$425$	−6.46927	−	17.7742i	−0.313806	−	0.862174i
$426$		0			0
$427$	0.353376	+	0.421138i	0.0171011	+	0.0203803i
$428$		0			0
$429$	−1.16089	+	0.204697i	−0.0560484	+	0.00988285i
$430$		0			0
$431$	24.0972	−	28.7180i	1.16072	−	1.38330i	0.251048	−	0.967975i	$-0.419225\pi$
$431$	24.0972	−	28.7180i	1.16072	−	1.38330i	0.909675	−	0.415321i	$-0.136331\pi$
$432$		0			0
$433$	−8.01147	−	13.8763i	−0.385007	−	0.666852i	0.606763	−	0.794883i	$-0.292468\pi$
$433$	−8.01147	−	13.8763i	−0.385007	−	0.666852i	−0.991770	+	0.128031i	$0.959134\pi$
$434$		0			0
$435$	−0.228877	+	0.192051i	−0.0109738	+	0.00920812i
$436$		0			0
$437$	0.706219	−	4.00517i	0.0337830	−	0.191593i
$438$		0			0
$439$	29.8670	+	5.26636i	1.42548	+	0.251350i	0.832569	−	0.553921i	$-0.186869\pi$
$439$	29.8670	+	5.26636i	1.42548	+	0.251350i	0.592907	+	0.805271i	$0.297980\pi$
$440$		0			0
$441$	−13.7518	+	5.00524i	−0.654847	+	0.238345i
$442$		0			0
$443$	−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			0
$447$	−1.46069	+	0.531649i	−0.0690885	+	0.0251462i
$448$		0			0
$449$	26.1350	+	4.60830i	1.23339	+	0.217479i	0.752079	−	0.659073i	$-0.229051\pi$
$449$	26.1350	+	4.60830i	1.23339	+	0.217479i	0.481307	+	0.876552i	$0.340162\pi$
$450$		0			0
$451$	−0.0393493	+	0.223161i	−0.00185289	+	0.0105082i
$452$		0			0
$453$	−2.35245	+	1.97394i	−0.110528	+	0.0927437i
$454$		0			0
$455$	−2.15001	−	3.72392i	−0.100794	−	0.174580i
$456$		0			0
$457$	−15.2270	+	18.1468i	−0.712288	+	0.848872i	−0.993857	−	0.110669i	$-0.964701\pi$
$457$	−15.2270	+	18.1468i	−0.712288	+	0.848872i	0.281569	+	0.959541i	$0.409145\pi$
$458$		0			0
$459$	8.90140	−	1.56956i	0.415482	−	0.0732606i
$460$		0			0
$461$	−11.4935	−	13.6974i	−0.535306	−	0.637953i	0.428823	−	0.903389i	$-0.358929\pi$
$461$	−11.4935	−	13.6974i	−0.535306	−	0.637953i	−0.964128	+	0.265436i	$0.914484\pi$
$462$		0			0
$463$	3.97134	+	10.9112i	0.184564	+	0.507085i	0.997124	−	0.0757928i	$-0.0241487\pi$
$463$	3.97134	+	10.9112i	0.184564	+	0.507085i	−0.812560	+	0.582878i	$0.801927\pi$
$464$		0			0
$465$	−0.377397	−	2.14032i	−0.0175013	−	0.0992551i
$466$		0			0
$467$	5.99577	+	3.46166i	0.277451	+	0.160187i	0.632269	−	0.774749i	$-0.282124\pi$
$467$	5.99577	+	3.46166i	0.277451	+	0.160187i	−0.354818	+	0.934935i	$0.615457\pi$
$468$		0			0
$469$	18.5299	+	6.74433i	0.855631	+	0.311424i
$470$		0			0
$471$	3.19892	−	5.54069i	0.147398	−	0.255301i
$472$		0			0
$473$	4.14664	−	2.39406i	0.190663	−	0.110079i
$474$		0			0
$475$		−	16.3445i		−	0.749939i
$476$		0			0
$477$	−28.6285	−	24.0222i	−1.31081	−	1.09990i
$478$		0			0
$479$	10.5351	−	28.9450i	0.481361	−	1.32253i	−0.426966	−	0.904268i	$-0.640417\pi$
$479$	10.5351	−	28.9450i	0.481361	−	1.32253i	0.908327	−	0.418261i	$-0.137360\pi$
$480$		0			0
$481$	13.9543	+	17.2047i	0.636262	+	0.784468i
$482$		0			0
$483$	−0.174884	+	0.480490i	−0.00795750	+	0.0218630i
$484$		0			0
$485$	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			0
$489$	2.77694	−	1.60327i	0.125578	−	0.0725023i
$490$		0			0
$491$	4.72126	−	8.17747i	0.213068	−	0.369044i	−0.739605	−	0.673041i	$-0.764988\pi$
$491$	4.72126	−	8.17747i	0.213068	−	0.369044i	0.952673	+	0.303997i	$0.0983212\pi$
$492$		0			0
$493$	4.19691	+	1.52755i	0.189019	+	0.0687974i
$494$		0			0
$495$	1.98167	+	1.14412i	0.0890694	+	0.0514242i
$496$		0			0
$497$	−3.28692	−	18.6410i	−0.147438	−	0.836164i
$498$		0			0
$499$	4.66741	+	12.8236i	0.208942	+	0.574063i	0.999253	−	0.0386425i	$-0.0123034\pi$
$499$	4.66741	+	12.8236i	0.208942	+	0.574063i	−0.790311	+	0.612706i	$0.790081\pi$
$500$		0			0
$501$	−3.64092	−	4.33908i	−0.162664	−	0.193856i
$502$		0			0
$503$	−19.6874	+	3.47142i	−0.877817	+	0.154783i	−0.594357	−	0.804201i	$-0.702593\pi$
$503$	−19.6874	+	3.47142i	−0.877817	+	0.154783i	−0.283460	+	0.958984i	$0.591482\pi$
$504$		0			0
$505$	2.20812	−	2.63153i	0.0982599	−	0.117102i
$506$		0			0
$507$	0.0456446	+	0.0790588i	0.00202715	+	0.00351112i
$508$		0			0
$509$	18.6781	−	15.6728i	0.827894	−	0.694685i	−0.126913	−	0.991914i	$-0.540507\pi$
$509$	18.6781	−	15.6728i	0.827894	−	0.694685i	0.954806	+	0.297229i	$0.0960624\pi$
$510$		0			0
$511$	3.16307	−	17.9387i	0.139926	−	0.793560i
$512$		0			0
$513$	7.69179	+	1.35627i	0.339601	+	0.0598808i
$514$		0			0
$515$	−0.186773	+	0.0679798i	−0.00823020	+	0.00299555i
$516$		0			0
$517$	7.26588			0.319553
$518$		0			0
$519$	0.667587			0.0293038
$520$		0			0
$521$	13.8664	−	5.04695i	0.607497	−	0.221111i	−0.0199104	−	0.999802i	$-0.506338\pi$
$521$	13.8664	−	5.04695i	0.607497	−	0.221111i	0.627408	+	0.778691i	$0.284116\pi$
$522$		0			0
$523$	−9.25252	−	1.63147i	−0.404585	−	0.0713392i	−0.0323471	−	0.999477i	$-0.510298\pi$
$523$	−9.25252	−	1.63147i	−0.404585	−	0.0713392i	−0.372237	+	0.928138i	$0.621409\pi$
$524$		0			0
$525$	−0.356839	+	2.02373i	−0.0155737	+	0.0883230i
$526$		0			0
$527$	−24.8873	+	20.8829i	−1.08411	+	0.909673i
$528$		0			0
$529$	−10.9348	−	18.9396i	−0.475425	−	0.823460i
$530$		0			0
$531$	−18.0777	+	21.5442i	−0.784507	+	0.934939i
$532$		0			0
$533$	0.871998	−	0.153757i	0.0377704	−	0.00665994i
$534$		0			0
$535$	−3.53465	−	4.21244i	−0.152816	−	0.182119i
$536$		0			0
$537$	2.24444	+	6.16654i	0.0968547	+	0.266106i
$538$		0			0
$539$	−0.822556	−	4.66495i	−0.0354300	−	0.200934i
$540$		0			0
$541$	−37.3740	−	21.5779i	−1.60684	−	0.927707i	−0.990072	−	0.140559i	$-0.955110\pi$
$541$	−37.3740	−	21.5779i	−1.60684	−	0.927707i	−0.616763	−	0.787149i	$-0.711556\pi$
$542$		0			0
$543$	−2.23669	−	0.814090i	−0.0959858	−	0.0349360i
$544$		0			0
$545$	5.87335	−	10.1729i	0.251587	−	0.435761i
$546$		0			0
$547$	21.1110	−	12.1884i	0.902641	−	0.521140i	0.0245851	−	0.999698i	$-0.492174\pi$
$547$	21.1110	−	12.1884i	0.902641	−	0.521140i	0.878056	+	0.478558i	$0.158840\pi$
$548$		0			0
$549$			1.14313i			0.0487878i
$550$		0			0
$551$	2.95643	+	2.48074i	0.125948	+	0.105683i
$552$		0			0
$553$	1.65080	−	4.53553i	0.0701991	−	0.192870i
$554$		0			0
$555$	−0.0300345	+	1.80102i	−0.00127489	+	0.0764492i
$556$		0			0
$557$	10.4716	−	28.7704i	0.443695	−	1.21904i	−0.493350	−	0.869831i	$-0.664228\pi$
$557$	10.4716	−	28.7704i	0.443695	−	1.21904i	0.937045	−	0.349210i	$-0.113550\pi$
$558$		0			0
$559$	−14.3323	−	12.0262i	−0.606192	−	0.508656i
$560$		0			0
$561$			1.43284i			0.0604944i
$562$		0			0
$563$	−3.05690	+	1.76490i	−0.128833	+	0.0743819i	−0.563032	−	0.826435i	$-0.690365\pi$
$563$	−3.05690	+	1.76490i	−0.128833	+	0.0743819i	0.434198	+	0.900817i	$0.357032\pi$
$564$		0			0
$565$	1.81632	−	3.14596i	0.0764131	−	0.132351i
$566$		0			0
$567$	10.3176	+	3.75529i	0.433298	+	0.157707i
$568$		0			0
$569$	−31.5781	−	18.2316i	−1.32382	−	0.764310i	−0.339487	−	0.940611i	$-0.610254\pi$
$569$	−31.5781	−	18.2316i	−1.32382	−	0.764310i	−0.984336	+	0.176301i	$0.943587\pi$
$570$		0			0
$571$	6.71527	+	38.0842i	0.281025	+	1.59377i	0.719147	+	0.694858i	$0.244533\pi$
$571$	6.71527	+	38.0842i	0.281025	+	1.59377i	−0.438122	+	0.898915i	$0.644356\pi$
$572$		0			0
$573$	−2.51553	−	6.91137i	−0.105088	−	0.288727i
$574$		0			0
$575$	2.92026	+	3.48023i	0.121783	+	0.145136i
$576$		0			0
$577$	42.7190	−	7.53251i	1.77842	−	0.313583i	0.814574	−	0.580060i	$-0.196971\pi$
$577$	42.7190	−	7.53251i	1.77842	−	0.313583i	0.963841	+	0.266477i	$0.0858596\pi$
$578$		0			0
$579$	−1.71354	+	2.04212i	−0.0712124	+	0.0848677i
$580$		0			0
$581$	11.5761	+	20.0504i	0.480258	+	0.831831i
$582$		0			0
$583$	9.26661	−	7.77561i	0.383784	−	0.322033i
$584$		0			0
$585$	1.55263	−	8.80539i	0.0641932	−	0.364058i
$586$		0			0
$587$	0.0109487	+	0.00193056i	0.000451903	+	7.96826e-5i	0.173874	−	0.984768i	$-0.444371\pi$
$587$	0.0109487	+	0.00193056i	0.000451903	+	7.96826e-5i	−0.173422	+	0.984848i	$0.555483\pi$
$588$		0			0
$589$	−26.3802	+	9.60161i	−1.08698	+	0.395628i
$590$		0			0
$591$	−3.94605			−0.162319
$592$		0			0
$593$	−36.1152			−1.48307			−0.741537	−	0.670912i	$-0.765903\pi$
$593$	−36.1152			−1.48307			−0.741537	+	0.670912i	$0.765903\pi$
$594$		0			0
$595$	−4.91147	+	1.78763i	−0.201351	+	0.0732857i
$596$		0			0
$597$	8.50888	+	1.50034i	0.348245	+	0.0614050i
$598$		0			0
$599$	2.78662	−	15.8037i	0.113858	−	0.645721i	−0.873451	−	0.486912i	$-0.838123\pi$
$599$	2.78662	−	15.8037i	0.113858	−	0.645721i	0.987309	−	0.158809i	$-0.0507655\pi$
$600$		0			0
$601$	−15.1796	+	12.7372i	−0.619189	+	0.519561i	−0.897549	−	0.440916i	$-0.854654\pi$
$601$	−15.1796	+	12.7372i	−0.619189	+	0.519561i	0.278359	+	0.960477i	$0.410209\pi$
$602$		0			0
$603$	20.5014	+	35.5095i	0.834882	+	1.44606i
$604$		0			0
$605$	5.55282	−	6.61759i	0.225754	−	0.269043i
$606$		0			0
$607$	14.4410	−	2.54634i	0.586143	−	0.103353i	0.127291	−	0.991865i	$-0.459372\pi$
$607$	14.4410	−	2.54634i	0.586143	−	0.103353i	0.458852	+	0.888513i	$0.348261\pi$
$608$		0			0
$609$	−0.311896	−	0.371703i	−0.0126387	−	0.0150622i
$610$		0			0
$611$	−9.71038	−	26.6791i	−0.392840	−	1.07932i
$612$		0			0
$613$	−1.23791	−	7.02054i	−0.0499988	−	0.283557i	0.949549	−	0.313618i	$-0.101541\pi$
$613$	−1.23791	−	7.02054i	−0.0499988	−	0.283557i	−0.999548	+	0.0300607i	$0.990430\pi$
$614$		0			0
$615$	0.0623527	+	0.0359993i	0.00251430	+	0.00145163i
$616$		0			0
$617$	−1.54788	−	0.563382i	−0.0623153	−	0.0226809i	0.310674	−	0.950516i	$-0.399445\pi$
$617$	−1.54788	−	0.563382i	−0.0623153	−	0.0226809i	−0.372990	+	0.927835i	$0.621667\pi$
$618$		0			0
$619$	6.28743	−	10.8902i	0.252713	−	0.437712i	−0.711559	−	0.702627i	$-0.752010\pi$
$619$	6.28743	−	10.8902i	0.252713	−	0.437712i	0.964272	+	0.264914i	$0.0853437\pi$
$620$		0			0
$621$	−1.88013	+	1.08549i	−0.0754471	+	0.0435594i
$622$		0			0
$623$			8.70882i			0.348911i
$624$		0			0
$625$	11.2019	+	9.39949i	0.448075	+	0.375979i
$626$		0			0
$627$	−0.423465	+	1.16346i	−0.0169116	+	0.0464641i
$628$		0			0
$629$	23.5400	−	13.0724i	0.938603	−	0.521232i
$630$		0			0
$631$	7.72595	−	21.2269i	0.307565	−	0.845028i	−0.685565	−	0.728012i	$-0.740445\pi$
$631$	7.72595	−	21.2269i	0.307565	−	0.845028i	0.993130	−	0.117017i	$-0.0373331\pi$
$632$		0			0
$633$	−3.49306	−	2.93102i	−0.138837	−	0.116498i
$634$		0			0
$635$		−	9.83047i		−	0.390110i
$636$		0			0
$637$	−16.0296	+	9.25469i	−0.635116	+	0.366684i
$638$		0			0
$639$	19.6796	−	34.0860i	0.778511	−	1.34842i
$640$		0			0
$641$	29.1189	+	10.5984i	1.15013	+	0.418613i	0.845562	−	0.533878i	$-0.179266\pi$
$641$	29.1189	+	10.5984i	1.15013	+	0.418613i	0.304568	+	0.952491i	$0.401488\pi$
$642$		0			0
$643$	0.920945	+	0.531708i	0.0363185	+	0.0209685i	0.518049	−	0.855351i	$-0.326658\pi$
$643$	0.920945	+	0.531708i	0.0363185	+	0.0209685i	−0.481731	+	0.876319i	$0.659992\pi$
$644$		0			0
$645$	−0.264176	−	1.49821i	−0.0104019	−	0.0589922i
$646$		0			0
$647$	4.56612	+	12.5453i	0.179513	+	0.493207i	0.996514	−	0.0834293i	$-0.0265873\pi$
$647$	4.56612	+	12.5453i	0.179513	+	0.493207i	−0.817001	+	0.576636i	$0.804365\pi$
$648$		0			0
$649$	−5.85148	−	6.97353i	−0.229691	−	0.273735i
$650$		0			0
$651$	3.47595	−	0.612903i	0.136233	−	0.0240216i
$652$		0			0
$653$	−5.99298	+	7.14215i	−0.234523	+	0.279494i	−0.870451	−	0.492254i	$-0.836173\pi$
$653$	−5.99298	+	7.14215i	−0.234523	+	0.279494i	0.635928	+	0.771748i	$0.280617\pi$
$654$		0			0
$655$	4.45661	+	7.71908i	0.174134	+	0.301609i
$656$		0			0
$657$	29.0148	−	24.3463i	1.13198	−	0.949841i
$658$		0			0
$659$	3.29553	−	18.6899i	0.128376	−	0.728054i	−0.850870	−	0.525376i	$-0.823925\pi$
$659$	3.29553	−	18.6899i	0.128376	−	0.728054i	0.979246	−	0.202677i	$-0.0649643\pi$
$660$		0			0
$661$	21.2508	+	3.74709i	0.826560	+	0.145745i	0.570898	−	0.821021i	$-0.306595\pi$
$661$	21.2508	+	3.74709i	0.826560	+	0.145745i	0.255662	+	0.966766i	$0.417706\pi$
$662$		0			0
$663$	5.26113	−	1.91490i	0.204325	−	0.0743684i
$664$		0			0
$665$	−4.51643			−0.175140
$666$		0			0
$667$	−1.07274			−0.0415367
$668$		0			0
$669$	0.457571	−	0.166542i	0.0176907	−	0.00643890i
$670$		0			0
$671$	−0.364394	−	0.0642524i	−0.0140673	−	0.00248044i
$672$		0			0
$673$	−7.18577	+	40.7525i	−0.276991	+	1.57089i	0.455574	+	0.890198i	$0.349434\pi$
$673$	−7.18577	+	40.7525i	−0.276991	+	1.57089i	−0.732565	+	0.680697i	$0.761677\pi$
$674$		0			0
$675$	−6.68367	+	5.60827i	−0.257255	+	0.215862i
$676$		0			0
$677$	2.29044	+	3.96715i	0.0880287	+	0.152470i	0.906678	−	0.421824i	$-0.138610\pi$
$677$	2.29044	+	3.96715i	0.0880287	+	0.152470i	−0.818649	+	0.574294i	$0.805277\pi$
$678$		0			0
$679$	−6.65153	+	7.92699i	−0.255262	+	0.304210i
$680$		0			0
$681$	1.02816	−	0.181293i	0.0393994	−	0.00694717i
$682$		0			0
$683$	−23.1346	−	27.5707i	−0.885220	−	1.05496i	−0.998116	−	0.0613577i	$-0.980457\pi$
$683$	−23.1346	−	27.5707i	−0.885220	−	1.05496i	0.112895	−	0.993607i	$-0.463987\pi$
$684$		0			0
$685$	1.97694	+	5.43159i	0.0755349	+	0.207530i
$686$		0			0
$687$	0.559833	+	3.17497i	0.0213590	+	0.121133i
$688$		0			0
$689$	−40.9350	−	23.6338i	−1.55950	−	0.900376i
$690$		0			0
$691$	−33.8223	−	12.3103i	−1.28666	−	0.468306i	−0.394031	−	0.919097i	$-0.628920\pi$
$691$	−33.8223	−	12.3103i	−1.28666	−	0.468306i	−0.892629	+	0.450791i	$0.851142\pi$
$692$		0			0
$693$	−1.85808	+	3.21829i	−0.0705826	+	0.122253i
$694$		0			0
$695$	14.1403	−	8.16390i	0.536372	−	0.309674i
$696$		0			0
$697$		−	1.07627i		−	0.0407665i
$698$		0			0
$699$	−7.29537	−	6.12154i	−0.275936	−	0.231538i
$700$		0			0
$701$	−2.16083	+	5.93682i	−0.0816132	+	0.224231i	−0.973787	−	0.227462i	$-0.926957\pi$
$701$	−2.16083	+	5.93682i	−0.0816132	+	0.224231i	0.892174	+	0.451692i	$0.149180\pi$
$702$		0			0
$703$	22.9779	−	3.65769i	0.866629	−	0.137952i
$704$		0			0
$705$	0.789581	−	2.16936i	0.0297373	−	0.0817027i
$706$		0			0
$707$	4.27368	+	3.58605i	0.160728	+	0.134867i
$708$		0			0
$709$			15.4046i			0.578533i	0.957249	+	0.289267i	$0.0934114\pi$
$709$			15.4046i			0.578533i	−0.957249	+	0.289267i	$0.906589\pi$
$710$		0			0
$711$	8.69161	−	5.01810i	0.325961	−	0.188194i
$712$		0			0
$713$	3.90161	−	6.75779i	0.146117	−	0.253081i
$714$		0			0
$715$	2.71960	+	0.989853i	0.101707	+	0.0370184i
$716$		0			0
$717$	0.222489	+	0.128454i	0.00830899	+	0.00479719i
$718$		0			0
$719$	0.517948	+	2.93743i	0.0193162	+	0.109548i	0.992941	−	0.118606i	$-0.0378424\pi$
$719$	0.517948	+	2.93743i	0.0193162	+	0.109548i	−0.973625	+	0.228153i	$0.926731\pi$
$720$		0			0
$721$	−0.110401	−	0.303325i	−0.00411156	−	0.0112964i
$722$		0			0
$723$	0.206108	+	0.245630i	0.00766523	+	0.00913506i
$724$		0			0
$725$	−4.24570	+	0.748632i	−0.157681	+	0.0278035i
$726$		0			0
$727$	11.3263	−	13.4981i	0.420068	−	0.500618i	−0.513961	−	0.857813i	$-0.671823\pi$
$727$	11.3263	−	13.4981i	0.420068	−	0.500618i	0.934030	+	0.357195i	$0.116267\pi$
$728$		0			0
$729$	10.3516	+	17.9296i	0.383394	+	0.664058i
$730$		0			0
$731$	−17.4210	+	14.6179i	−0.644338	+	0.540663i
$732$		0			0
$733$	−3.34139	+	18.9500i	−0.123417	+	0.699933i	0.858818	+	0.512280i	$0.171199\pi$
$733$	−3.34139	+	18.9500i	−0.123417	+	0.699933i	−0.982235	+	0.187653i	$0.939912\pi$
$734$		0			0
$735$	−1.48219	−	0.261350i	−0.0546714	−	0.00964005i
$736$		0			0
$737$	−12.4716	+	4.53929i	−0.459397	+	0.167207i
$738$		0			0
$739$	−33.3412			−1.22648			−0.613238	−	0.789898i	$-0.710133\pi$
$739$	−33.3412			−1.22648			−0.613238	+	0.789898i	$0.710133\pi$
$740$		0			0
$741$	4.83796			0.177727
$742$		0			0
$743$	−34.4286	+	12.5310i	−1.26306	+	0.459717i	−0.884795	−	0.465980i	$-0.845702\pi$
$743$	−34.4286	+	12.5310i	−1.26306	+	0.459717i	−0.378267	+	0.925697i	$0.623480\pi$
$744$		0			0
$745$	3.75840	+	0.662708i	0.137697	+	0.0242797i
$746$		0			0
$747$	−8.35968	+	47.4101i	−0.305865	+	1.73465i
$748$		0			0
$749$	6.84112	−	5.74038i	0.249969	−	0.209749i
$750$		0			0
$751$	9.48212	+	16.4235i	0.346008	+	0.599303i	0.985536	−	0.169465i	$-0.0542038\pi$
$751$	9.48212	+	16.4235i	0.346008	+	0.599303i	−0.639529	+	0.768767i	$0.720870\pi$
$752$		0			0
$753$	−2.19474	+	2.61559i	−0.0799809	+	0.0953175i
$754$		0			0
$755$	7.42499	−	1.30923i	0.270223	−	0.0476476i
$756$		0			0
$757$	−28.2928	−	33.7181i	−1.02832	−	1.22551i	−0.973898	−	0.226987i	$-0.927112\pi$
$757$	−28.2928	−	33.7181i	−1.02832	−	1.22551i	−0.0544232	−	0.998518i	$-0.517332\pi$
$758$		0			0
$759$	−0.117706	−	0.323395i	−0.00427246	−	0.0117385i
$760$		0			0
$761$	1.42559	+	8.08493i	0.0516776	+	0.293078i	0.999683	−	0.0251759i	$-0.00801457\pi$
$761$	1.42559	+	8.08493i	0.0516776	+	0.293078i	−0.948005	+	0.318254i	$0.896903\pi$
$762$		0			0
$763$	16.5212	+	9.53850i	0.598107	+	0.345317i
$764$		0			0
$765$	−10.2127	−	3.71710i	−0.369239	−	0.134392i
$766$		0			0
$767$	−17.7855	+	30.8053i	−0.642196	+	1.11232i
$768$		0			0
$769$	46.6866	−	26.9545i	1.68356	−	0.972006i	0.724303	−	0.689482i	$-0.242162\pi$
$769$	46.6866	−	26.9545i	1.68356	−	0.972006i	0.959260	−	0.282524i	$-0.0911717\pi$
$770$		0			0
$771$			1.79585i			0.0646761i
$772$		0			0
$773$	−2.07004	−	1.73697i	−0.0744543	−	0.0624746i	0.604801	−	0.796377i	$-0.293253\pi$
$773$	−2.07004	−	1.73697i	−0.0744543	−	0.0624746i	−0.679255	+	0.733902i	$0.737697\pi$
$774$		0			0
$775$	10.7258	−	29.4689i	0.385282	−	1.05855i
$776$		0			0
$777$	−2.92492	−	0.0487769i	−0.104931	−	0.00174986i
$778$		0			0
$779$	0.318083	−	0.873927i	0.0113965	−	0.0313117i
$780$		0			0
$781$	9.75936	+	8.18908i	0.349217	+	0.293028i
$782$		0			0
$783$		−	2.06016i		−	0.0736242i
$784$		0			0
$785$	−13.6032	+	7.85383i	−0.485520	+	0.280315i
$786$		0			0
$787$	−4.84358	+	8.38932i	−0.172655	+	0.299047i	−0.939347	−	0.342968i	$-0.888568\pi$
$787$	−4.84358	+	8.38932i	−0.172655	+	0.299047i	0.766692	+	0.642015i	$0.221901\pi$
$788$		0			0
$789$	−6.69808	−	2.43790i	−0.238458	−	0.0867916i
$790$		0			0
$791$	5.10913	+	2.94976i	0.181660	+	0.104881i
$792$		0			0
$793$	0.251065	+	1.42386i	0.00891558	+	0.0505628i
$794$		0			0
$795$	−1.31455	−	3.61169i	−0.0466221	−	0.128093i
$796$		0			0
$797$	19.7365	+	23.5210i	0.699102	+	0.833157i	0.992424	−	0.122856i	$-0.0392055\pi$
$797$	19.7365	+	23.5210i	0.699102	+	0.833157i	−0.293323	+	0.956013i	$0.594761\pi$
$798$		0			0
$799$	−33.9854	+	5.99254i	−1.20232	+	0.212001i
$800$		0			0
$801$	−11.6400	+	13.8720i	−0.411280	+	0.490144i
$802$		0			0
$803$	6.12996	+	10.6174i	0.216322	+	0.374680i
$804$		0			0
$805$	0.961681	−	0.806946i	0.0338948	−	0.0284411i
$806$		0			0
$807$	0.996063	−	5.64895i	0.0350631	−	0.198853i
$808$		0			0
$809$	12.8727	+	2.26981i	0.452580	+	0.0798021i	0.395292	−	0.918556i	$-0.370643\pi$
$809$	12.8727	+	2.26981i	0.452580	+	0.0798021i	0.0572885	+	0.998358i	$0.481755\pi$
$810$		0			0
$811$	−42.7071	+	15.5441i	−1.49965	+	0.545828i	−0.955970	−	0.293464i	$-0.905192\pi$
$811$	−42.7071	+	15.5441i	−1.49965	+	0.545828i	−0.543680	+	0.839292i	$0.682970\pi$
$812$		0			0
$813$	3.69310			0.129523
$814$		0			0
$815$	−7.87254			−0.275763
$816$		0			0
$817$	−18.4660	+	6.72108i	−0.646044	+	0.235141i
$818$		0			0
$819$	14.3002	+	2.52151i	0.499690	+	0.0881088i
$820$		0			0
$821$	−4.91748	+	27.8884i	−0.171621	+	0.973312i	0.770351	+	0.637620i	$0.220081\pi$
$821$	−4.91748	+	27.8884i	−0.171621	+	0.973312i	−0.941972	+	0.335692i	$0.891030\pi$
$822$		0			0
$823$	−18.9218	+	15.8772i	−0.659571	+	0.553446i	−0.909958	−	0.414700i	$-0.863887\pi$
$823$	−18.9218	+	15.8772i	−0.659571	+	0.553446i	0.250387	+	0.968146i	$0.419442\pi$
$824$		0			0
$825$	−0.691546	−	1.19779i	−0.0240765	−	0.0417018i
$826$		0			0
$827$	8.00202	−	9.53644i	0.278258	−	0.331614i	−0.608756	−	0.793357i	$-0.708331\pi$
$827$	8.00202	−	9.53644i	0.278258	−	0.331614i	0.887014	+	0.461743i	$0.152776\pi$
$828$		0			0
$829$	10.6721	−	1.88178i	0.370658	−	0.0653570i	0.0147833	−	0.999891i	$-0.495294\pi$
$829$	10.6721	−	1.88178i	0.370658	−	0.0653570i	0.355874	+	0.934534i	$0.384183\pi$
$830$		0			0
$831$	−1.46313	−	1.74369i	−0.0507554	−	0.0604879i
$832$		0			0
$833$	7.69484	+	21.1414i	0.266611	+	0.732506i
$834$		0			0
$835$	2.41486	+	13.6954i	0.0835697	+	0.473947i
$836$		0			0
$837$	12.9781	+	7.49292i	0.448589	+	0.258993i
$838$		0			0
$839$	23.7039	+	8.62752i	0.818350	+	0.297855i	0.717069	−	0.697003i	$-0.245483\pi$
$839$	23.7039	+	8.62752i	0.818350	+	0.297855i	0.101282	+	0.994858i	$0.467706\pi$
$840$		0			0
$841$	−13.9910	+	24.2331i	−0.482449	+	0.835626i
$842$		0			0
$843$	7.43700	−	4.29375i	0.256144	−	0.147885i
$844$		0			0
$845$		−	0.224129i		−	0.00771027i
$846$		0			0
$847$	10.7472	+	9.01795i	0.369277	+	0.309860i
$848$		0			0
$849$	2.34168	−	6.43370i	0.0803661	−	0.220804i
$850$		0			0
$851$	−4.23916	+	4.88427i	−0.145317	+	0.167431i
$852$		0			0
$853$	3.72709	−	10.2401i	0.127613	−	0.350614i	−0.859389	−	0.511323i	$-0.829156\pi$
$853$	3.72709	−	10.2401i	0.127613	−	0.350614i	0.987002	+	0.160709i	$0.0513779\pi$
$854$		0			0
$855$	−7.19410	−	6.03656i	−0.246033	−	0.206446i
$856$		0			0
$857$			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	$-0.435764\pi$
$859$	33.6788	−	19.4444i	1.14910	−	0.663436i	0.948669	+	0.316271i	$0.102431\pi$
$860$		0			0
$861$	−0.0584640	+	0.101263i	−0.00199245	+	0.00345102i
$862$		0			0
$863$	26.5719	+	9.67137i	0.904517	+	0.329217i	0.752061	−	0.659093i	$-0.229060\pi$
$863$	26.5719	+	9.67137i	0.904517	+	0.329217i	0.152455	+	0.988310i	$0.451282\pi$
$864$		0			0
$865$	−1.41944	−	0.819513i	−0.0482624	−	0.0278643i
$866$		0			0
$867$	−0.156508	−	0.887601i	−0.00531529	−	0.0301445i
$868$		0			0
$869$	1.11107	+	3.05265i	0.0376906	+	0.103554i
$870$		0			0
$871$	33.3350	+	39.7271i	1.12951	+	1.34610i
$872$		0			0
$873$	−21.1901	+	3.73638i	−0.717176	+	0.126457i
$874$		0			0
$875$	7.03781	−	8.38733i	0.237921	−	0.283544i
$876$		0			0
$877$	−0.375638	−	0.650624i	−0.0126844	−	0.0219700i	0.859614	−	0.510945i	$-0.170704\pi$
$877$	−0.375638	−	0.650624i	−0.0126844	−	0.0219700i	−0.872298	+	0.488975i	$0.837371\pi$
$878$		0			0
$879$	0.311975	−	0.261778i	0.0105227	−	0.00882956i
$880$		0			0
$881$	9.26268	−	52.5313i	0.312068	−	1.76982i	−0.276143	−	0.961117i	$-0.589056\pi$
$881$	9.26268	−	52.5313i	0.312068	−	1.76982i	0.588211	−	0.808708i	$-0.299833\pi$
$882$		0			0
$883$	23.7723	+	4.19169i	0.800001	+	0.141062i	0.558680	−	0.829384i	$-0.311308\pi$
$883$	23.7723	+	4.19169i	0.800001	+	0.141062i	0.241321	+	0.970445i	$0.422419\pi$
$884$		0			0
$885$	−2.71795	+	0.989253i	−0.0913629	+	0.0332534i
$886$		0			0
$887$	−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
$890$		0			0
$891$	−6.94427	+	2.52751i	−0.232642	+	0.0846747i
$892$		0			0
$893$	−29.3671	−	5.17822i	−0.982733	−	0.173282i
$894$		0			0
$895$	2.79772	−	15.8667i	0.0935176	−	0.530364i
$896$		0			0
$897$	−1.03014	+	0.864394i	−0.0343955	+	0.0288613i
$898$		0			0
$899$	3.70244	+	6.41281i	0.123483	+	0.213879i
$900$		0			0
$901$	−36.9307	+	44.0123i	−1.23034	+	1.46626i
$902$		0			0
$903$	2.43315	−	0.429029i	0.0809700	−	0.0142772i
$904$		0			0
$905$	3.75636	+	4.47665i	0.124866	+	0.148809i
$906$		0			0
$907$	7.33846	+	20.1623i	0.243670	+	0.669477i	0.999885	+	0.0151542i	$0.00482391\pi$
$907$	7.33846	+	20.1623i	0.243670	+	0.669477i	−0.756216	+	0.654323i	$0.772954\pi$
$908$		0			0
$909$	2.01440	+	11.4242i	0.0668134	+	0.378918i
$910$		0			0
$911$	−18.1914	−	10.5028i	−0.602707	−	0.347973i	0.167399	−	0.985889i	$-0.446463\pi$
$911$	−18.1914	−	10.5028i	−0.602707	−	0.347973i	−0.770106	+	0.637916i	$0.779797\pi$
$912$		0			0
$913$	−14.6429	−	5.32958i	−0.484610	−	0.176384i
$914$		0			0
$915$	−0.0587823	+	0.101814i	−0.00194328	+	0.00336586i
$916$		0			0
$917$	−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			0
$921$	−4.98472	−	4.18267i	−0.164252	−	0.137824i
$922$		0			0
$923$	17.0261	−	46.7789i	0.560422	−	1.53975i
$924$		0			0
$925$	−13.3692	+	22.2894i	−0.439577	+	0.732871i
$926$		0			0
$927$	0.229563	−	0.630718i	0.00753982	−	0.0207155i
$928$		0			0
$929$	26.7338	+	22.4324i	0.877109	+	0.735982i	0.965583	−	0.260097i	$-0.0837545\pi$
$929$	26.7338	+	22.4324i	0.877109	+	0.735982i	−0.0884738	+	0.996079i	$0.528199\pi$
$930$		0			0
$931$			19.4409i			0.637151i
$932$		0			0
$933$	−9.87739	+	5.70271i	−0.323371	+	0.186698i
$934$		0			0
$935$	1.75892	−	3.04653i	0.0575227	−	0.0996323i
$936$		0			0
$937$	−10.7395	−	3.90885i	−0.350844	−	0.127697i	0.160586	−	0.987022i	$-0.448662\pi$
$937$	−10.7395	−	3.90885i	−0.350844	−	0.127697i	−0.511430	+	0.859325i	$0.670884\pi$
$938$		0			0
$939$	6.48226	+	3.74253i	0.211541	+	0.122133i
$940$		0			0
$941$	−6.15749	−	34.9209i	−0.200729	−	1.13839i	−0.904021	−	0.427488i	$-0.859399\pi$
$941$	−6.15749	−	34.9209i	−0.200729	−	1.13839i	0.703293	−	0.710901i	$-0.251712\pi$
$942$		0			0
$943$	0.0884143	+	0.242916i	0.00287917	+	0.00791044i
$944$		0			0
$945$	1.54971	+	1.84688i	0.0504122	+	0.0600789i
$946$		0			0
$947$	33.4708	−	5.90181i	1.08765	−	0.191783i	0.399057	−	0.916926i	$-0.369338\pi$
$947$	33.4708	−	5.90181i	1.08765	−	0.191783i	0.688598	+	0.725143i	$0.258226\pi$
$948$		0			0
$949$	30.7930	−	36.6977i	0.999583	−	1.19126i
$950$		0			0
$951$	−3.06019	−	5.30040i	−0.0992333	−	0.171877i
$952$		0			0
$953$	−15.3276	+	12.8614i	−0.496509	+	0.416621i	−0.856352	−	0.516392i	$-0.827275\pi$
$953$	−15.3276	+	12.8614i	−0.496509	+	0.416621i	0.359843	+	0.933013i	$0.382830\pi$
$954$		0			0
$955$	−3.13565	+	17.7831i	−0.101467	+	0.575449i
$956$		0			0
$957$	0.321620	+	0.0567102i	0.0103965	+	0.00183318i
$958$		0			0
$959$	−8.82107	+	3.21061i	−0.284847	+	0.103676i
$960$		0			0
$961$	−22.8639			−0.737544
$962$		0			0
$963$	18.5695			0.598394
$964$		0			0
$965$	6.15024	−	2.23850i	0.197983	−	0.0720600i
$966$		0			0
$967$	−21.1585	−	3.73082i	−0.680413	−	0.119975i	−0.177249	−	0.984166i	$-0.556720\pi$
$967$	−21.1585	−	3.73082i	−0.680413	−	0.119975i	−0.503164	+	0.864191i	$0.667831\pi$
$968$		0			0
$969$	1.02115	−	5.79122i	0.0328040	−	0.186041i
$970$		0			0
$971$	−0.671321	+	0.563305i	−0.0215437	+	0.0180773i	−0.653496	−	0.756930i	$-0.726698\pi$
$971$	−0.671321	+	0.563305i	−0.0215437	+	0.0180773i	0.631952	+	0.775007i	$0.282254\pi$
$972$		0			0
$973$	13.2584	+	22.9642i	0.425045	+	0.736200i
$974$		0			0
$975$	−3.47388	+	4.14001i	−0.111253	+	0.132587i
$976$		0			0
$977$	14.3294	−	2.52665i	0.458437	−	0.0808348i	0.0603394	−	0.998178i	$-0.480782\pi$
$977$	14.3294	−	2.52665i	0.458437	−	0.0808348i	0.398097	+	0.917343i	$0.369671\pi$
$978$		0			0
$979$	−3.76770	−	4.49016i	−0.120416	−	0.143506i
$980$		0			0
$981$	13.5672	+	37.2755i	0.433166	+	1.19011i
$982$		0			0
$983$	2.38729	+	13.5390i	0.0761426	+	0.431826i	0.998919	+	0.0464897i	$0.0148035\pi$
$983$	2.38729	+	13.5390i	0.0761426	+	0.431826i	−0.922776	+	0.385336i	$0.874085\pi$
$984$		0			0
$985$	8.39019	+	4.84408i	0.267334	+	0.154345i
$986$		0			0
$987$	3.52310	+	1.28230i	0.112142	+	0.0408162i
$988$		0			0
$989$	2.73111	−	4.73042i	0.0868442	−	0.150419i
$990$		0			0
$991$	−41.1867	+	23.7791i	−1.30834	+	0.755370i	−0.981819	−	0.189821i	$-0.939209\pi$
$991$	−41.1867	+	23.7791i	−1.30834	+	0.755370i	−0.326520	+	0.945190i	$0.605876\pi$
$992$		0			0
$993$		−	2.46663i		−	0.0782761i
$994$		0			0
$995$	−16.2500	−	13.6354i	−0.515160	−	0.432270i
$996$		0			0
$997$	18.4308	−	50.6383i	0.583711	−	1.60373i	−0.198077	−	0.980187i	$-0.563469\pi$
$997$	18.4308	−	50.6383i	0.583711	−	1.60373i	0.781787	−	0.623545i	$-0.214308\pi$
$998$		0			0
$999$	−9.38008	−	8.14117i	−0.296773	−	0.257575i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	592.2.bq.b.465.1		12
4.3	odd	2		74.2.h.a.21.2	✓	12
12.11	even	2		666.2.bj.c.613.1		12
37.30	even	18	inner	592.2.bq.b.289.1		12
148.67	odd	18		74.2.h.a.67.2	yes	12
148.91	even	36		2738.2.a.s.1.3		6
148.131	even	36		2738.2.a.r.1.4		6
444.215	even	18		666.2.bj.c.289.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.2.h.a.21.2	✓	12	4.3	odd	2
74.2.h.a.67.2	yes	12	148.67	odd	18
592.2.bq.b.289.1		12	37.30	even	18	inner
592.2.bq.b.465.1		12	1.1	even	1	trivial
666.2.bj.c.289.1		12	444.215	even	18
666.2.bj.c.613.1		12	12.11	even	2
2738.2.a.r.1.4		6	148.131	even	36
2738.2.a.s.1.3		6	148.91	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:	\( N \)	\(=\)	\( 592 = 2^{4} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	592.bq (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.326352 + 0.118782i) q^{3} +(0.839712 + 0.148064i) q^{5} +(-0.240460 + 1.36372i) q^{7} +(-2.20574 + 1.85083i) q^{9} +O(q^{10})\)	\(q+(-0.326352 + 0.118782i) q^{3} +(0.839712 + 0.148064i) q^{5} +(-0.240460 + 1.36372i) q^{7} +(-2.20574 + 1.85083i) q^{9} +(-0.466006 - 0.807147i) q^{11} +(-2.34092 + 2.78980i) q^{13} +(-0.291629 + 0.0514220i) q^{15} +(2.84539 + 3.39101i) q^{17} +(1.30826 + 3.59443i) q^{19} +(-0.0835109 - 0.473614i) q^{21} +(-0.920780 - 0.531613i) q^{23} +(-4.01527 - 1.46144i) q^{25} +(1.02094 - 1.76833i) q^{27} +(0.873775 - 0.504474i) q^{29} +7.33920i q^{31} +(0.247957 + 0.208060i) q^{33} +(-0.403834 + 1.10953i) q^{35} +(1.15600 - 5.97191i) q^{37} +(0.432584 - 1.18851i) q^{39} +(-0.186251 - 0.156283i) q^{41} +5.13740i q^{43} +(-2.12622 + 1.22758i) q^{45} +(-3.89795 + 6.75145i) q^{47} +(4.77595 + 1.73830i) q^{49} +(-1.33139 - 0.768679i) q^{51} +(2.25380 + 12.7819i) q^{53} +(-0.271802 - 0.746769i) q^{55} +(-0.853909 - 1.01765i) q^{57} +(9.61896 - 1.69608i) q^{59} +(0.255191 - 0.304124i) q^{61} +(-1.99362 - 3.45305i) q^{63} +(-2.37876 + 1.99602i) q^{65} +(2.47277 - 14.0238i) q^{67} +(0.363645 + 0.0641204i) q^{69} +(-12.8449 + 4.67517i) q^{71} -13.1543 q^{73} +1.48398 q^{75} +(1.21278 - 0.441414i) q^{77} +(-3.43258 - 0.605257i) q^{79} +(1.37686 - 7.80856i) q^{81} +(12.8078 - 10.7470i) q^{83} +(1.88722 + 3.26877i) q^{85} +(-0.225236 + 0.268425i) q^{87} +(6.19352 - 1.09209i) q^{89} +(-3.24160 - 3.86318i) q^{91} +(-0.871767 - 2.39516i) q^{93} +(0.566360 + 3.21199i) q^{95} +(6.47160 + 3.73638i) q^{97} +(2.52178 + 0.917853i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 12 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 + 12 * q^7 - 6 * q^9	\( 12 q - 6 q^{3} + 12 q^{7} - 6 q^{9} + 6 q^{11} + 6 q^{13} + 18 q^{19} - 6 q^{21} - 18 q^{25} + 6 q^{27} + 18 q^{29} - 6 q^{33} - 18 q^{35} + 30 q^{37} - 30 q^{39} + 24 q^{41} - 18 q^{45} - 6 q^{47} + 12 q^{49} - 12 q^{53} + 18 q^{55} - 36 q^{57} - 36 q^{61} + 6 q^{63} + 36 q^{65} + 30 q^{67} - 18 q^{69} - 12 q^{71} + 36 q^{75} + 12 q^{77} - 6 q^{79} + 24 q^{81} + 48 q^{83} + 18 q^{85} - 36 q^{87} - 18 q^{89} + 6 q^{91} - 12 q^{93} + 36 q^{97} - 30 q^{99}+O(q^{100}) \) 12 * q - 6 * q^3 + 12 * q^7 - 6 * q^9 + 6 * q^11 + 6 * q^13 + 18 * q^19 - 6 * q^21 - 18 * q^25 + 6 * q^27 + 18 * q^29 - 6 * q^33 - 18 * q^35 + 30 * q^37 - 30 * q^39 + 24 * q^41 - 18 * q^45 - 6 * q^47 + 12 * q^49 - 12 * q^53 + 18 * q^55 - 36 * q^57 - 36 * q^61 + 6 * q^63 + 36 * q^65 + 30 * q^67 - 18 * q^69 - 12 * q^71 + 36 * q^75 + 12 * q^77 - 6 * q^79 + 24 * q^81 + 48 * q^83 + 18 * q^85 - 36 * q^87 - 18 * q^89 + 6 * q^91 - 12 * q^93 + 36 * q^97 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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