LMFDB - Embedded newform 276.2.k.a.17.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(5,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 11, 1]))

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

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

chi := DirichletCharacter("276.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.k (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$8$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			17.2
Character	$\chi$	$=$	276.17
Dual form			276.2.k.a.65.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38704 - 1.03737i) q^{3} +(-1.67238 + 1.07478i) q^{5} +(-0.700880 - 0.100771i) q^{7} +(0.847741 + 2.87773i) q^{9} +O(q^{10})$	\(q+(-1.38704 - 1.03737i) q^{3} +(-1.67238 + 1.07478i) q^{5} +(-0.700880 - 0.100771i) q^{7} +(0.847741 + 2.87773i) q^{9} +(1.80810 + 3.95918i) q^{11} +(0.322105 + 2.24029i) q^{13} +(3.43460 + 0.244122i) q^{15} +(-5.08450 + 5.86783i) q^{17} +(5.10697 - 4.42521i) q^{19} +(0.867609 + 0.866843i) q^{21} +(-4.52706 + 1.58294i) q^{23} +(-0.435348 + 0.953280i) q^{25} +(1.80941 - 4.87094i) q^{27} +(2.92008 + 2.53026i) q^{29} +(-2.86518 + 0.841292i) q^{31} +(1.59922 - 7.36719i) q^{33} +(1.28045 - 0.584761i) q^{35} +(-1.08314 + 1.68540i) q^{37} +(1.87723 - 3.44151i) q^{39} +(-1.35426 - 2.10727i) q^{41} +(-1.89740 + 6.46196i) q^{43} +(-4.51067 - 3.90154i) q^{45} -9.03992i q^{47} +(-6.23537 - 1.83087i) q^{49} +(13.1395 - 2.86440i) q^{51} +(-0.162969 + 1.13348i) q^{53} +(-7.27907 - 4.67797i) q^{55} +(-11.6741 + 0.840134i) q^{57} +(5.03861 - 0.724443i) q^{59} +(-1.95164 - 6.64666i) q^{61} +(-0.304172 - 2.10237i) q^{63} +(-2.94650 - 3.40044i) q^{65} +(2.73935 + 1.25102i) q^{67} +(7.92129 + 2.50064i) q^{69} +(-8.19088 - 3.74065i) q^{71} +(6.50050 + 7.50197i) q^{73} +(1.59274 - 0.870618i) q^{75} +(-0.868287 - 2.95711i) q^{77} +(12.2706 - 1.76424i) q^{79} +(-7.56267 + 4.87914i) q^{81} +(5.58848 + 3.59150i) q^{83} +(2.19664 - 15.2780i) q^{85} +(-1.42544 - 6.53875i) q^{87} +(11.1914 + 3.28610i) q^{89} -1.60263i q^{91} +(4.84683 + 1.80534i) q^{93} +(-3.78470 + 12.8895i) q^{95} +(5.60068 + 8.71483i) q^{97} +(-9.86066 + 8.55957i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 2 q^{3} + 6 q^{9}+O(q^{10}) $ 80 * q - 2 * q^3 + 6 * q^9	$ 80 q - 2 q^{3} + 6 q^{9} - 4 q^{13} + 11 q^{15} + 33 q^{21} + 25 q^{27} + 20 q^{31} + 11 q^{33} - 44 q^{37} - 18 q^{39} - 44 q^{43} - 100 q^{49} - 98 q^{55} - 33 q^{57} - 44 q^{61} - 55 q^{63} - 22 q^{67} - 41 q^{69} - 26 q^{73} - 65 q^{75} - 44 q^{79} - 42 q^{81} + 2 q^{85} - 64 q^{87} - 46 q^{93} + 66 q^{97} - 66 q^{99}+O(q^{100}) $ 80 * q - 2 * q^3 + 6 * q^9 - 4 * q^13 + 11 * q^15 + 33 * q^21 + 25 * q^27 + 20 * q^31 + 11 * q^33 - 44 * q^37 - 18 * q^39 - 44 * q^43 - 100 * q^49 - 98 * q^55 - 33 * q^57 - 44 * q^61 - 55 * q^63 - 22 * q^67 - 41 * q^69 - 26 * q^73 - 65 * q^75 - 44 * q^79 - 42 * q^81 + 2 * q^85 - 64 * q^87 - 46 * q^93 + 66 * q^97 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{7}{22}\right)$	$1$	$-1$

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
$3$	−1.38704	−	1.03737i	−0.800806	−	0.598924i
$3$	−1.38704	−	1.03737i	−0.800806	−	0.598924i
$4$		0			0
$5$	−1.67238	+	1.07478i	−0.747913	+	0.480655i	−0.858245	−	0.513240i	$-0.828445\pi$
$5$	−1.67238	+	1.07478i	−0.747913	+	0.480655i	0.110332	+	0.993895i	$0.464809\pi$
$6$		0			0
$7$	−0.700880	−	0.100771i	−0.264908	−	0.0380880i	0.00858102	−	0.999963i	$-0.497269\pi$
$7$	−0.700880	−	0.100771i	−0.264908	−	0.0380880i	−0.273489	+	0.961875i	$0.588178\pi$
$8$		0			0
$9$	0.847741	+	2.87773i	0.282580	+	0.959244i
$10$		0			0
$11$	1.80810	+	3.95918i	0.545162	+	1.19374i	0.959005	+	0.283389i	$0.0914589\pi$
$11$	1.80810	+	3.95918i	0.545162	+	1.19374i	−0.413843	+	0.910348i	$0.635814\pi$
$12$		0			0
$13$	0.322105	+	2.24029i	0.0893359	+	0.621345i	0.984471	+	0.175549i	$0.0561701\pi$
$13$	0.322105	+	2.24029i	0.0893359	+	0.621345i	−0.895135	+	0.445796i	$0.852921\pi$
$14$		0			0
$15$	3.43460	+	0.244122i	0.886809	+	0.0630320i
$16$		0			0
$17$	−5.08450	+	5.86783i	−1.23317	+	1.42316i	−0.362001	+	0.932178i	$0.617906\pi$
$17$	−5.08450	+	5.86783i	−1.23317	+	1.42316i	−0.871172	+	0.490979i	$0.836639\pi$
$18$		0			0
$19$	5.10697	−	4.42521i	1.17162	−	1.01521i	0.172073	−	0.985084i	$-0.444954\pi$
$19$	5.10697	−	4.42521i	1.17162	−	1.01521i	0.999546	−	0.0301293i	$-0.00959190\pi$
$20$		0			0
$21$	0.867609	+	0.866843i	0.189328	+	0.189161i
$22$		0			0
$23$	−4.52706	+	1.58294i	−0.943958	+	0.330065i
$23$	−4.52706	+	1.58294i	−0.943958	+	0.330065i
$24$		0			0
$25$	−0.435348	+	0.953280i	−0.0870697	+	0.190656i
$26$		0			0
$27$	1.80941	−	4.87094i	0.348222	−	0.937412i
$28$		0			0
$29$	2.92008	+	2.53026i	0.542245	+	0.469858i	0.882392	−	0.470514i	$-0.155932\pi$
$29$	2.92008	+	2.53026i	0.542245	+	0.469858i	−0.340148	+	0.940372i	$0.610477\pi$
$30$		0			0
$31$	−2.86518	+	0.841292i	−0.514601	+	0.151100i	−0.528714	−	0.848800i	$-0.677326\pi$
$31$	−2.86518	+	0.841292i	−0.514601	+	0.151100i	0.0141132	+	0.999900i	$0.495507\pi$
$32$		0			0
$33$	1.59922	−	7.36719i	0.278389	−	1.28246i
$34$		0			0
$35$	1.28045	−	0.584761i	0.216435	−	0.0988426i
$36$		0			0
$37$	−1.08314	+	1.68540i	−0.178068	+	0.277079i	−0.918802	−	0.394720i	$-0.870842\pi$
$37$	−1.08314	+	1.68540i	−0.178068	+	0.277079i	0.740734	+	0.671799i	$0.234478\pi$
$38$		0			0
$39$	1.87723	−	3.44151i	0.300598	−	0.551082i
$40$		0			0
$41$	−1.35426	−	2.10727i	−0.211500	−	0.329101i	0.719253	−	0.694748i	$-0.244484\pi$
$41$	−1.35426	−	2.10727i	−0.211500	−	0.329101i	−0.930754	+	0.365647i	$0.880848\pi$
$42$		0			0
$43$	−1.89740	+	6.46196i	−0.289351	+	0.985440i	0.678643	+	0.734468i	$0.262568\pi$
$43$	−1.89740	+	6.46196i	−0.289351	+	0.985440i	−0.967994	+	0.250972i	$0.919250\pi$
$44$		0			0
$45$	−4.51067	−	3.90154i	−0.672410	−	0.581608i
$46$		0			0
$47$		−	9.03992i		−	1.31861i	−0.751877	−	0.659304i	$-0.770851\pi$
$47$		−	9.03992i		−	1.31861i	0.751877	−	0.659304i	$-0.229149\pi$
$48$		0			0
$49$	−6.23537	−	1.83087i	−0.890768	−	0.261553i
$50$		0			0
$51$	13.1395	−	2.86440i	1.83989	−	0.401096i
$52$		0			0
$53$	−0.162969	+	1.13348i	−0.0223855	+	0.155695i	−0.997948	−	0.0640266i	$-0.979606\pi$
$53$	−0.162969	+	1.13348i	−0.0223855	+	0.155695i	0.975563	+	0.219721i	$0.0705148\pi$
$54$		0			0
$55$	−7.27907	−	4.67797i	−0.981509	−	0.630778i
$56$		0			0
$57$	−11.6741	+	0.840134i	−1.54627	+	0.111278i
$58$		0			0
$59$	5.03861	−	0.724443i	0.655971	−	0.0943144i	0.193711	−	0.981059i	$-0.437948\pi$
$59$	5.03861	−	0.724443i	0.655971	−	0.0943144i	0.462260	+	0.886744i	$0.347039\pi$
$60$		0			0
$61$	−1.95164	−	6.64666i	−0.249881	−	0.851018i	−0.984923	−	0.172996i	$-0.944655\pi$
$61$	−1.95164	−	6.64666i	−0.249881	−	0.851018i	0.735041	−	0.678022i	$-0.237163\pi$
$62$		0			0
$63$	−0.304172	−	2.10237i	−0.0383220	−	0.264874i
$64$		0			0
$65$	−2.94650	−	3.40044i	−0.365468	−	0.421772i
$66$		0			0
$67$	2.73935	+	1.25102i	0.334665	+	0.152836i	0.575658	−	0.817690i	$-0.304746\pi$
$67$	2.73935	+	1.25102i	0.334665	+	0.152836i	−0.240993	+	0.970527i	$0.577473\pi$
$68$		0			0
$69$	7.92129	+	2.50064i	0.953611	+	0.301041i
$70$		0			0
$71$	−8.19088	−	3.74065i	−0.972079	−	0.443934i	−0.134898	−	0.990860i	$-0.543071\pi$
$71$	−8.19088	−	3.74065i	−0.972079	−	0.443934i	−0.837181	+	0.546926i	$0.815798\pi$
$72$		0			0
$73$	6.50050	+	7.50197i	0.760825	+	0.878039i	0.995571	−	0.0940176i	$-0.0299710\pi$
$73$	6.50050	+	7.50197i	0.760825	+	0.878039i	−0.234745	+	0.972057i	$0.575426\pi$
$74$		0			0
$75$	1.59274	−	0.870618i	0.183914	−	0.100530i
$76$		0			0
$77$	−0.868287	−	2.95711i	−0.0989505	−	0.336994i
$78$		0			0
$79$	12.2706	−	1.76424i	1.38055	−	0.198492i	0.588274	−	0.808662i	$-0.299808\pi$
$79$	12.2706	−	1.76424i	1.38055	−	0.198492i	0.792271	+	0.610169i	$0.208899\pi$
$80$		0			0
$81$	−7.56267	+	4.87914i	−0.840297	+	0.542127i
$82$		0			0
$83$	5.58848	+	3.59150i	0.613415	+	0.394218i	0.810136	−	0.586242i	$-0.199393\pi$
$83$	5.58848	+	3.59150i	0.613415	+	0.394218i	−0.196721	+	0.980459i	$0.563029\pi$
$84$		0			0
$85$	2.19664	−	15.2780i	0.238259	−	1.65713i
$86$		0			0
$87$	−1.42544	−	6.53875i	−0.152824	−	0.701028i
$88$		0			0
$89$	11.1914	+	3.28610i	1.18629	+	0.348325i	0.814595	−	0.580030i	$-0.196959\pi$
$89$	11.1914	+	3.28610i	1.18629	+	0.348325i	0.371693	+	0.928356i	$0.378777\pi$
$90$		0			0
$91$		−	1.60263i		−	0.168002i
$92$		0			0
$93$	4.84683	+	1.80534i	0.502593	+	0.187205i
$94$		0			0
$95$	−3.78470	+	12.8895i	−0.388302	+	1.32244i
$96$		0			0
$97$	5.60068	+	8.71483i	0.568663	+	0.884856i	0.999848	−	0.0174067i	$-0.00554101\pi$
$97$	5.60068	+	8.71483i	0.568663	+	0.884856i	−0.431186	+	0.902263i	$0.641905\pi$
$98$		0			0
$99$	−9.86066	+	8.55957i	−0.991033	+	0.860269i
$100$		0			0
$101$	3.05187	−	4.74880i	0.303672	−	0.472523i	−0.655560	−	0.755143i	$-0.727567\pi$
$101$	3.05187	−	4.74880i	0.303672	−	0.472523i	0.959232	+	0.282620i	$0.0912036\pi$
$102$		0			0
$103$	−14.2046	+	6.48701i	−1.39962	+	0.639185i	−0.965197	−	0.261525i	$-0.915775\pi$
$103$	−14.2046	+	6.48701i	−1.39962	+	0.639185i	−0.434422	+	0.900709i	$0.643047\pi$
$104$		0			0
$105$	−2.38264	−	0.517209i	−0.232522	−	0.0504744i
$106$		0			0
$107$	−5.38279	+	1.58053i	−0.520374	+	0.152796i	−0.531363	−	0.847144i	$-0.678320\pi$
$107$	−5.38279	+	1.58053i	−0.520374	+	0.152796i	0.0109894	+	0.999940i	$0.496502\pi$
$108$		0			0
$109$	1.79145	+	1.55230i	0.171590	+	0.148684i	0.736422	−	0.676522i	$-0.236514\pi$
$109$	1.79145	+	1.55230i	0.171590	+	0.148684i	−0.564832	+	0.825206i	$0.691059\pi$
$110$		0			0
$111$	3.25074	−	1.21410i	0.308547	−	0.115237i
$112$		0			0
$113$	−2.26800	+	4.96623i	−0.213356	+	0.467184i	−0.985805	−	0.167892i	$-0.946304\pi$
$113$	−2.26800	+	4.96623i	−0.213356	+	0.467184i	0.772450	+	0.635076i	$0.219031\pi$
$114$		0			0
$115$	5.86969	−	7.51286i	0.547352	−	0.700578i
$116$		0			0
$117$	−6.17389	+	2.82612i	−0.570777	+	0.261275i
$118$		0			0
$119$	4.15493	−	3.60027i	0.380882	−	0.330036i
$120$		0			0
$121$	−5.20242	+	6.00391i	−0.472947	+	0.545810i
$122$		0			0
$123$	−0.307604	+	4.32773i	−0.0277357	+	0.390218i
$124$		0			0
$125$	−1.71108	−	11.9008i	−0.153044	−	1.06444i
$126$		0			0
$127$	4.59279	+	10.0568i	0.407544	+	0.892398i	0.996449	+	0.0841953i	$0.0268320\pi$
$127$	4.59279	+	10.0568i	0.407544	+	0.892398i	−0.588905	+	0.808202i	$0.700441\pi$
$128$		0			0
$129$	9.33519	−	6.99467i	0.821918	−	0.615847i
$130$		0			0
$131$	−5.58173	−	0.802531i	−0.487678	−	0.0701175i	−0.105910	−	0.994376i	$-0.533776\pi$
$131$	−5.58173	−	0.802531i	−0.487678	−	0.0701175i	−0.381768	+	0.924258i	$0.624685\pi$
$132$		0			0
$133$	−4.02531	+	2.58691i	−0.349038	+	0.224313i
$134$		0			0
$135$	2.20913	+	10.0908i	0.190132	+	0.868477i
$136$		0			0
$137$	4.61126			0.393967			0.196983	−	0.980407i	$-0.436885\pi$
$137$	4.61126			0.393967			0.196983	+	0.980407i	$0.436885\pi$
$138$		0			0
$139$	−6.30418			−0.534714			−0.267357	−	0.963598i	$-0.586150\pi$
$139$	−6.30418			−0.534714			−0.267357	+	0.963598i	$0.586150\pi$
$140$		0			0
$141$	−9.37771	+	12.5387i	−0.789746	+	1.05595i
$142$		0			0
$143$	−8.28732	+	5.32594i	−0.693020	+	0.445377i
$144$		0			0
$145$	−7.60296	−	1.09314i	−0.631391	−	0.0907803i
$146$		0			0
$147$	6.74941	+	9.00785i	0.556682	+	0.742955i
$148$		0			0
$149$	6.70786	+	14.6882i	0.549529	+	1.20330i	0.957001	+	0.290083i	$0.0936829\pi$
$149$	6.70786	+	14.6882i	0.549529	+	1.20330i	−0.407473	+	0.913217i	$0.633590\pi$
$150$		0			0
$151$	0.503304	+	3.50056i	0.0409583	+	0.284871i	0.999999	+	0.00160199i	$0.000509931\pi$
$151$	0.503304	+	3.50056i	0.0409583	+	0.284871i	−0.959040	+	0.283269i	$0.908581\pi$
$152$		0			0
$153$	−21.1964	−	9.65743i	−1.71362	−	0.780757i
$154$		0			0
$155$	3.88748	−	4.48639i	0.312250	−	0.360355i
$156$		0			0
$157$	12.6345	−	10.9479i	1.00835	−	0.873736i	0.0163318	−	0.999867i	$-0.494801\pi$
$157$	12.6345	−	10.9479i	1.00835	−	0.873736i	0.992014	+	0.126130i	$0.0402557\pi$
$158$		0			0
$159$	1.40187	−	1.40311i	0.111176	−	0.111274i
$160$		0			0
$161$	3.33244	−	0.653250i	0.262633	−	0.0514833i
$162$		0			0
$163$	8.47853	−	18.5654i	0.664090	−	1.45415i	−0.214572	−	0.976708i	$-0.568836\pi$
$163$	8.47853	−	18.5654i	0.664090	−	1.45415i	0.878662	−	0.477445i	$-0.158437\pi$
$164$		0			0
$165$	5.24356	+	14.0396i	0.408211	+	1.09298i
$166$		0			0
$167$	−17.5540	−	15.2106i	−1.35837	−	1.17703i	−0.966396	−	0.257057i	$-0.917247\pi$
$167$	−17.5540	−	15.2106i	−1.35837	−	1.17703i	−0.391973	−	0.919977i	$-0.628208\pi$
$168$		0			0
$169$	7.55826	−	2.21930i	0.581404	−	0.170716i
$170$		0			0
$171$	17.0640	+	10.9450i	1.30491	+	0.836989i
$172$		0			0
$173$	23.2655	−	10.6250i	1.76884	−	0.807804i	0.787300	−	0.616570i	$-0.211478\pi$
$173$	23.2655	−	10.6250i	1.76884	−	0.807804i	0.981544	−	0.191234i	$-0.0612491\pi$
$174$		0			0
$175$	0.401190	−	0.624264i	0.0303271	−	0.0471899i
$176$		0			0
$177$	−7.74025	−	4.22206i	−0.581793	−	0.317349i
$178$		0			0
$179$	9.54336	+	14.8498i	0.713304	+	1.10992i	0.988890	+	0.148646i	$0.0474916\pi$
$179$	9.54336	+	14.8498i	0.713304	+	1.10992i	−0.275586	+	0.961276i	$0.588872\pi$
$180$		0			0
$181$	−6.37631	+	21.7157i	−0.473948	+	1.61412i	0.281951	+	0.959429i	$0.409018\pi$
$181$	−6.37631	+	21.7157i	−0.473948	+	1.61412i	−0.755899	+	0.654689i	$0.772800\pi$
$182$		0			0
$183$	−4.18804	+	11.2437i	−0.309589	+	0.831160i
$184$		0			0
$185$		−	3.98278i		−	0.292820i
$186$		0			0
$187$	−32.4250	−	9.52085i	−2.37115	−	0.696233i
$188$		0			0
$189$	−1.75903	+	3.23160i	−0.127951	+	0.235065i
$190$		0			0
$191$	0.369500	−	2.56993i	0.0267361	−	0.185954i	−0.972077	−	0.234662i	$-0.924602\pi$
$191$	0.369500	−	2.56993i	0.0267361	−	0.185954i	0.998813	+	0.0487088i	$0.0155106\pi$
$192$		0			0
$193$	9.34500	+	6.00566i	0.672667	+	0.432297i	0.831886	−	0.554946i	$-0.187261\pi$
$193$	9.34500	+	6.00566i	0.672667	+	0.432297i	−0.159219	+	0.987243i	$0.550898\pi$
$194$		0			0
$195$	0.559397	+	7.77313i	0.0400593	+	0.556645i
$196$		0			0
$197$	−10.9504	+	1.57444i	−0.780187	+	0.112174i	−0.520890	−	0.853624i	$-0.674400\pi$
$197$	−10.9504	+	1.57444i	−0.780187	+	0.112174i	−0.259297	+	0.965798i	$0.583491\pi$
$198$		0			0
$199$	3.13560	+	10.6789i	0.222277	+	0.757005i	0.992820	+	0.119617i	$0.0381668\pi$
$199$	3.13560	+	10.6789i	0.222277	+	0.757005i	−0.770543	+	0.637388i	$0.780015\pi$
$200$		0			0
$201$	−2.50181	−	4.57692i	−0.176464	−	0.322831i
$202$		0			0
$203$	−1.79165	−	2.06767i	−0.125749	−	0.145122i
$204$		0			0
$205$	4.52970	+	2.06864i	0.316368	+	0.144480i
$206$		0			0
$207$	−8.39304	−	11.6858i	−0.583357	−	0.812216i
$208$		0			0
$209$	26.7541	+	12.2182i	1.85062	+	0.845150i
$210$		0			0
$211$	6.23463	+	7.19514i	0.429209	+	0.495334i	0.928620	−	0.371031i	$-0.120996\pi$
$211$	6.23463	+	7.19514i	0.429209	+	0.495334i	−0.499411	+	0.866365i	$0.666450\pi$
$212$		0			0
$213$	7.48063	+	13.6854i	0.512564	+	0.937706i
$214$		0			0
$215$	−3.77198	−	12.8462i	−0.257247	−	0.876102i
$216$		0			0
$217$	2.09292	−	0.300917i	0.142077	−	0.0204276i
$218$		0			0
$219$	−1.23413	−	17.1489i	−0.0833947	−	1.15882i
$220$		0			0
$221$	−14.7834	−	9.50070i	−0.994438	−	0.639086i
$222$		0			0
$223$	3.20994	−	22.3256i	0.214953	−	1.49503i	−0.541341	−	0.840803i	$-0.682083\pi$
$223$	3.20994	−	22.3256i	0.214953	−	1.49503i	0.756295	−	0.654231i	$-0.227008\pi$
$224$		0			0
$225$	−3.11235	−	0.444681i	−0.207490	−	0.0296454i
$226$		0			0
$227$	1.02611	+	0.301292i	0.0681050	+	0.0199974i	0.315608	−	0.948890i	$-0.397792\pi$
$227$	1.02611	+	0.301292i	0.0681050	+	0.0199974i	−0.247503	+	0.968887i	$0.579610\pi$
$228$		0			0
$229$		−	8.68447i		−	0.573886i	−0.957948	−	0.286943i	$-0.907361\pi$
$229$		−	8.68447i		−	0.573886i	0.957948	−	0.286943i	$-0.0926390\pi$
$230$		0			0
$231$	−1.86327	+	5.00236i	−0.122594	+	0.329131i
$232$		0			0
$233$	4.80023	−	16.3481i	0.314473	−	1.07100i	−0.638921	−	0.769272i	$-0.720619\pi$
$233$	4.80023	−	16.3481i	0.314473	−	1.07100i	0.953395	−	0.301726i	$-0.0975628\pi$
$234$		0			0
$235$	9.71589	+	15.1182i	0.633795	+	0.986204i
$236$		0			0
$237$	−18.8499	−	10.2820i	−1.22443	−	0.667888i
$238$		0			0
$239$	−7.21763	+	11.2309i	−0.466870	+	0.726463i	−0.992230	−	0.124416i	$-0.960294\pi$
$239$	−7.21763	+	11.2309i	−0.466870	+	0.726463i	0.525360	+	0.850880i	$0.323930\pi$
$240$		0			0
$241$	−5.10623	+	2.33194i	−0.328921	+	0.150213i	−0.573029	−	0.819535i	$-0.694232\pi$
$241$	−5.10623	+	2.33194i	−0.328921	+	0.150213i	0.244109	+	0.969748i	$0.421505\pi$
$242$		0			0
$243$	15.5512	+	1.07772i	0.997607	+	0.0691356i
$244$		0			0
$245$	12.3957	−	3.63971i	0.791934	−	0.232533i
$246$		0			0
$247$	11.5587	+	10.0157i	0.735466	+	0.637284i
$248$		0			0
$249$	−4.02572	−	10.7788i	−0.255120	−	0.683081i
$250$		0			0
$251$	8.22119	−	18.0019i	0.518917	−	1.13627i	−0.450931	−	0.892559i	$-0.648908\pi$
$251$	8.22119	−	18.0019i	0.518917	−	1.13627i	0.969848	−	0.243710i	$-0.0783646\pi$
$252$		0			0
$253$	−14.4525	−	15.0614i	−0.908621	−	0.946899i
$254$		0			0
$255$	−18.8957	+	18.9124i	−1.18329	+	1.18434i
$256$		0			0
$257$	12.3814	−	10.7286i	0.772332	−	0.669229i	−0.176751	−	0.984256i	$-0.556559\pi$
$257$	12.3814	−	10.7286i	0.772332	−	0.669229i	0.949083	+	0.315026i	$0.102013\pi$
$258$		0			0
$259$	0.928994	−	1.07212i	0.0577249	−	0.0666181i
$260$		0			0
$261$	−4.80594	+	10.5482i	−0.297480	+	0.652917i
$262$		0			0
$263$	−2.83561	−	19.7221i	−0.174851	−	1.21612i	−0.868458	−	0.495762i	$-0.834889\pi$
$263$	−2.83561	−	19.7221i	−0.174851	−	1.21612i	0.693607	−	0.720353i	$-0.256020\pi$
$264$		0			0
$265$	−0.945686	−	2.07076i	−0.0580930	−	0.127206i
$266$		0			0
$267$	−12.1140	−	16.1675i	−0.741366	−	0.989437i
$268$		0			0
$269$	−20.2794	−	2.91573i	−1.23645	−	0.177775i	−0.507086	−	0.861896i	$-0.669277\pi$
$269$	−20.2794	−	2.91573i	−1.23645	−	0.177775i	−0.729369	+	0.684120i	$0.760186\pi$
$270$		0			0
$271$	−0.673998	+	0.433152i	−0.0409425	+	0.0263121i	−0.560952	−	0.827848i	$-0.689565\pi$
$271$	−0.673998	+	0.433152i	−0.0409425	+	0.0263121i	0.520009	+	0.854160i	$0.325928\pi$
$272$		0			0
$273$	−1.66252	+	2.22291i	−0.100620	+	0.134537i
$274$		0			0
$275$	−4.56136			−0.275060
$276$		0			0
$277$	−19.0562			−1.14498			−0.572488	−	0.819913i	$-0.694022\pi$
$277$	−19.0562			−1.14498			−0.572488	+	0.819913i	$0.694022\pi$
$278$		0			0
$279$	−4.84994	−	7.53201i	−0.290358	−	0.450930i
$280$		0			0
$281$	22.8406	−	14.6788i	1.36256	−	0.875663i	0.364110	−	0.931356i	$-0.381373\pi$
$281$	22.8406	−	14.6788i	1.36256	−	0.875663i	0.998448	+	0.0556929i	$0.0177368\pi$
$282$		0			0
$283$	15.5165	+	2.23093i	0.922359	+	0.132615i	0.587103	−	0.809512i	$-0.300268\pi$
$283$	15.5165	+	2.23093i	0.922359	+	0.132615i	0.335256	+	0.942127i	$0.391177\pi$
$284$		0			0
$285$	18.6207	−	13.9521i	1.10299	−	0.826451i
$286$		0			0
$287$	0.736823	+	1.61342i	0.0434933	+	0.0952370i
$288$		0			0
$289$	−6.15988	−	42.8429i	−0.362346	−	2.52017i
$290$		0			0
$291$	1.27212	−	17.8977i	0.0745732	−	1.04918i
$292$		0			0
$293$	6.42217	−	7.41158i	0.375187	−	0.432989i	−0.536483	−	0.843911i	$-0.680248\pi$
$293$	6.42217	−	7.41158i	0.375187	−	0.432989i	0.911671	+	0.410922i	$0.134793\pi$
$294$		0			0
$295$	−7.64788	+	6.62693i	−0.445277	+	0.385835i
$296$		0			0
$297$	22.5565	−	1.64333i	1.30886	−	0.0953554i
$298$		0			0
$299$	−5.00443	−	9.63207i	−0.289414	−	0.557037i
$300$		0			0
$301$	1.98103	−	4.33786i	0.114185	−	0.250030i
$302$		0			0
$303$	−9.15929	+	3.42085i	−0.526188	+	0.196523i
$304$		0			0
$305$	10.4076	+	9.01821i	0.595935	+	0.516381i
$306$		0			0
$307$	−27.4210	+	8.05153i	−1.56500	+	0.459525i	−0.945541	−	0.325504i	$-0.894466\pi$
$307$	−27.4210	+	8.05153i	−1.56500	+	0.459525i	−0.619459	+	0.785029i	$0.712648\pi$
$308$		0			0
$309$	26.4317	+	5.73763i	1.50365	+	0.326403i
$310$		0			0
$311$	−28.0072	+	12.7905i	−1.58814	+	0.725280i	−0.996708	−	0.0810730i	$-0.974165\pi$
$311$	−28.0072	+	12.7905i	−1.58814	+	0.725280i	−0.591434	+	0.806353i	$0.701438\pi$
$312$		0			0
$313$	−4.52001	+	7.03327i	−0.255486	+	0.397544i	−0.945176	−	0.326560i	$-0.894110\pi$
$313$	−4.52001	+	7.03327i	−0.255486	+	0.397544i	0.689690	+	0.724105i	$0.257747\pi$
$314$		0			0
$315$	2.76827	+	3.18906i	0.155974	+	0.179683i
$316$		0			0
$317$	−4.33423	−	6.74419i	−0.243435	−	0.378792i	0.697939	−	0.716157i	$-0.254101\pi$
$317$	−4.33423	−	6.74419i	−0.243435	−	0.378792i	−0.941374	+	0.337365i	$0.890464\pi$
$318$		0			0
$319$	−4.73798	+	16.1361i	−0.265276	+	0.903446i
$320$		0			0
$321$	9.10572	+	3.39167i	0.508231	+	0.189305i
$322$		0			0
$323$			52.4668i			2.91933i
$324$		0			0
$325$	−2.27585	−	0.668251i	−0.126242	−	0.0370679i
$326$		0			0
$327$	−0.874504	−	4.01150i	−0.0483602	−	0.221836i
$328$		0			0
$329$	−0.910964	+	6.33590i	−0.0502231	+	0.349309i
$330$		0			0
$331$	2.30515	+	1.48143i	0.126703	+	0.0814268i	0.602457	−	0.798151i	$-0.294189\pi$
$331$	2.30515	+	1.48143i	0.126703	+	0.0814268i	−0.475754	+	0.879578i	$0.657825\pi$
$332$		0			0
$333$	−5.76837	−	1.68821i	−0.316105	−	0.0925133i
$334$		0			0
$335$	−5.92581	+	0.852003i	−0.323762	+	0.0465499i
$336$		0			0
$337$	0.510679	+	1.73921i	0.0278185	+	0.0947409i	0.972232	−	0.234019i	$-0.0751876\pi$
$337$	0.510679	+	1.73921i	0.0278185	+	0.0947409i	−0.944414	+	0.328759i	$0.893369\pi$
$338$		0			0
$339$	8.29760	−	4.53559i	0.450664	−	0.246340i
$340$		0			0
$341$	−8.51134	−	9.82261i	−0.460915	−	0.531924i
$342$		0			0
$343$	8.69444	+	3.97062i	0.469456	+	0.214393i
$344$		0			0
$345$	−15.9351	+	4.33159i	−0.857915	+	0.233205i
$346$		0			0
$347$	7.55571	+	3.45058i	0.405612	+	0.185237i	0.607764	−	0.794117i	$-0.292066\pi$
$347$	7.55571	+	3.45058i	0.405612	+	0.185237i	−0.202153	+	0.979354i	$0.564794\pi$
$348$		0			0
$349$	23.4514	+	27.0644i	1.25533	+	1.44872i	0.843201	+	0.537598i	$0.180668\pi$
$349$	23.4514	+	27.0644i	1.25533	+	1.44872i	0.412126	+	0.911127i	$0.364786\pi$
$350$		0			0
$351$	11.4951	+	2.48466i	0.613565	+	0.132621i
$352$		0			0
$353$	9.66476	+	32.9151i	0.514403	+	1.75190i	0.648791	+	0.760967i	$0.275275\pi$
$353$	9.66476	+	32.9151i	0.514403	+	1.75190i	−0.134388	+	0.990929i	$0.542907\pi$
$354$		0			0
$355$	17.7187	−	2.54756i	0.940409	−	0.135210i
$356$		0			0
$357$	−9.49784	+	0.683517i	−0.502679	+	0.0361755i
$358$		0			0
$359$	8.13675	+	5.22917i	0.429441	+	0.275985i	0.737454	−	0.675397i	$-0.236028\pi$
$359$	8.13675	+	5.22917i	0.429441	+	0.275985i	−0.308013	+	0.951382i	$0.599664\pi$
$360$		0			0
$361$	3.79463	−	26.3922i	0.199717	−	1.38907i
$362$		0			0
$363$	13.4442	−	2.93083i	0.705638	−	0.153829i
$364$		0			0
$365$	−18.9343	−	5.55960i	−0.991065	−	0.291003i
$366$		0			0
$367$			13.6345i			0.711716i	0.934540	+	0.355858i	$0.115811\pi$
$367$			13.6345i			0.711716i	−0.934540	+	0.355858i	$0.884189\pi$
$368$		0			0
$369$	4.91610	−	5.68362i	0.255922	−	0.295878i
$370$		0			0
$371$	0.228444	−	0.778008i	0.0118602	−	0.0403921i
$372$		0			0
$373$	6.69476	+	10.4172i	0.346641	+	0.539385i	0.970173	−	0.242414i	$-0.0779391\pi$
$373$	6.69476	+	10.4172i	0.346641	+	0.539385i	−0.623532	+	0.781798i	$0.714303\pi$
$374$		0			0
$375$	−9.97218	+	18.2819i	−0.514961	+	0.944073i
$376$		0			0
$377$	−4.72795	+	7.35683i	−0.243502	+	0.378896i
$378$		0			0
$379$	−0.552248	+	0.252203i	−0.0283671	+	0.0129548i	−0.429548	−	0.903044i	$-0.641327\pi$
$379$	−0.552248	+	0.252203i	−0.0283671	+	0.0129548i	0.401181	+	0.915999i	$0.368600\pi$
$380$		0			0
$381$	4.06223	−	18.7136i	0.208114	−	0.958725i
$382$		0			0
$383$	−5.86770	+	1.72291i	−0.299825	+	0.0880367i	−0.428185	−	0.903691i	$-0.640847\pi$
$383$	−5.86770	+	1.72291i	−0.299825	+	0.0880367i	0.128360	+	0.991728i	$0.459029\pi$
$384$		0			0
$385$	4.63035	+	4.01222i	0.235984	+	0.204482i
$386$		0			0
$387$	−20.2043	+	0.0178527i	−1.02704	+	0.000907506i
$388$		0			0
$389$	−5.18968	+	11.3638i	−0.263127	+	0.576169i	−0.994372	−	0.105947i	$-0.966213\pi$
$389$	−5.18968	+	11.3638i	−0.263127	+	0.576169i	0.731244	+	0.682116i	$0.238940\pi$
$390$		0			0
$391$	13.7295	−	34.6125i	0.694329	−	1.75043i
$392$		0			0
$393$	6.90954	+	6.90344i	0.348540	+	0.348232i
$394$		0			0
$395$	−18.6249	+	16.1386i	−0.937122	+	0.812021i
$396$		0			0
$397$	−13.3779	+	15.4389i	−0.671418	+	0.774857i	−0.984597	−	0.174837i	$-0.944060\pi$
$397$	−13.3779	+	15.4389i	−0.671418	+	0.774857i	0.313180	+	0.949694i	$0.398606\pi$
$398$		0			0
$399$	8.26682	+	0.587584i	0.413859	+	0.0294160i
$400$		0			0
$401$	4.88560	+	33.9801i	0.243975	+	1.69689i	0.631783	+	0.775145i	$0.282323\pi$
$401$	4.88560	+	33.9801i	0.243975	+	1.69689i	−0.387808	+	0.921740i	$0.626767\pi$
$402$		0			0
$403$	−2.80763	−	6.14785i	−0.139858	−	0.306246i
$404$		0			0
$405$	7.40371	−	16.2880i	0.367893	−	0.809356i
$406$		0			0
$407$	−8.63125	−	1.24099i	−0.427835	−	0.0615134i
$408$		0			0
$409$	−31.4579	+	20.2167i	−1.55549	+	0.999653i	−0.571673	+	0.820482i	$0.693705\pi$
$409$	−31.4579	+	20.2167i	−1.55549	+	0.999653i	−0.983818	+	0.179172i	$0.942658\pi$
$410$		0			0
$411$	−6.39599	−	4.78357i	−0.315491	−	0.235956i
$412$		0			0
$413$	−3.60446			−0.177364
$414$		0			0
$415$	−13.2061			−0.648264
$416$		0			0
$417$	8.74413	+	6.53975i	0.428202	+	0.320253i
$418$		0			0
$419$	2.50929	−	1.61263i	0.122587	−	0.0787819i	−0.477910	−	0.878409i	$-0.658606\pi$
$419$	2.50929	−	1.61263i	0.122587	−	0.0787819i	0.600497	+	0.799627i	$0.294969\pi$
$420$		0			0
$421$	29.8057	+	4.28541i	1.45264	+	0.208858i	0.823005	−	0.568034i	$-0.192296\pi$
$421$	29.8057	+	4.28541i	1.45264	+	0.208858i	0.629634	+	0.776892i	$0.283205\pi$
$422$		0			0
$423$	26.0144	−	7.66351i	1.26487	−	0.372612i
$424$		0			0
$425$	−3.38015	−	7.40150i	−0.163961	−	0.359025i
$426$		0			0
$427$	0.698070	+	4.85518i	0.0337820	+	0.234959i
$428$		0			0
$429$	17.0198	+	1.20972i	0.821722	+	0.0584058i
$430$		0			0
$431$	1.32252	−	1.52626i	0.0637033	−	0.0735176i	−0.723003	−	0.690844i	$-0.757239\pi$
$431$	1.32252	−	1.52626i	0.0637033	−	0.0735176i	0.786707	+	0.617327i	$0.211784\pi$
$432$		0			0
$433$	22.0073	−	19.0694i	1.05760	−	0.916418i	0.0609476	−	0.998141i	$-0.480588\pi$
$433$	22.0073	−	19.0694i	1.05760	−	0.916418i	0.996655	+	0.0817231i	$0.0260423\pi$
$434$		0			0
$435$	9.41159	+	9.40328i	0.451251	+	0.450853i
$436$		0			0
$437$	−16.1147	+	28.1172i	−0.770873	+	1.34503i
$438$		0			0
$439$	5.32466	−	11.6594i	0.254132	−	0.556472i	−0.738968	−	0.673740i	$-0.764687\pi$
$439$	5.32466	−	11.6594i	0.254132	−	0.556472i	0.993100	+	0.117269i	$0.0374139\pi$
$440$		0			0
$441$	−0.0172267	−	19.4958i	−0.000820321	−	0.928373i
$442$		0			0
$443$	5.42068	+	4.69705i	0.257544	+	0.223164i	0.774057	−	0.633116i	$-0.218224\pi$
$443$	5.42068	+	4.69705i	0.257544	+	0.223164i	−0.516512	+	0.856280i	$0.672770\pi$
$444$		0			0
$445$	−22.2482	+	6.53265i	−1.05466	+	0.309677i
$446$		0			0
$447$	5.93296	−	27.3315i	0.280619	−	1.29274i
$448$		0			0
$449$	−17.0929	+	7.80607i	−0.806664	+	0.368391i	−0.775678	−	0.631129i	$-0.782592\pi$
$449$	−17.0929	+	7.80607i	−0.806664	+	0.368391i	−0.0309859	+	0.999520i	$0.509865\pi$
$450$		0			0
$451$	5.89444	−	9.17192i	0.277558	−	0.431889i
$452$		0			0
$453$	2.93326	−	5.37751i	0.137817	−	0.252658i
$454$		0			0
$455$	1.72247	+	2.68022i	0.0807508	+	0.125651i
$456$		0			0
$457$	−0.0922090	+	0.314035i	−0.00431335	+	0.0146899i	−0.961622	−	0.274379i	$-0.911528\pi$
$457$	−0.0922090	+	0.314035i	−0.00431335	+	0.0146899i	0.957308	+	0.289069i	$0.0933458\pi$
$458$		0			0
$459$	19.3818	+	35.3836i	0.904666	+	1.65157i
$460$		0			0
$461$		−	16.5827i		−	0.772331i	−0.922430	−	0.386166i	$-0.873799\pi$
$461$		−	16.5827i		−	0.772331i	0.922430	−	0.386166i	$-0.126201\pi$
$462$		0			0
$463$	−12.7224	−	3.73564i	−0.591261	−	0.173610i	−0.0276041	−	0.999619i	$-0.508788\pi$
$463$	−12.7224	−	3.73564i	−0.591261	−	0.173610i	−0.563657	+	0.826009i	$0.690606\pi$
$464$		0			0
$465$	−10.0461	+	2.19005i	−0.465877	+	0.101561i
$466$		0			0
$467$	1.67750	−	11.6673i	0.0776255	−	0.539897i	−0.913487	−	0.406869i	$-0.866621\pi$
$467$	1.67750	−	11.6673i	0.0776255	−	0.539897i	0.991112	−	0.133029i	$-0.0424702\pi$
$468$		0			0
$469$	−1.79389	−	1.15286i	−0.0828341	−	0.0532342i
$470$		0			0
$471$	−28.8815	+	2.07847i	−1.33079	+	0.0957710i
$472$		0			0
$473$	−29.0148	+	4.17169i	−1.33410	+	0.191815i
$474$		0			0
$475$	1.99516	+	6.79488i	0.0915441	+	0.311770i
$476$		0			0
$477$	−3.39999	+	0.491912i	−0.155675	+	0.0225231i
$478$		0			0
$479$	25.3051	+	29.2036i	1.15622	+	1.33435i	0.933125	+	0.359551i	$0.117070\pi$
$479$	25.3051	+	29.2036i	1.15622	+	1.33435i	0.223094	+	0.974797i	$0.428384\pi$
$480$		0			0
$481$	−4.12468	−	1.88368i	−0.188069	−	0.0858884i
$482$		0			0
$483$	−5.29988	−	2.55088i	−0.241153	−	0.116069i
$484$		0			0
$485$	−18.7330	−	8.55507i	−0.850621	−	0.388465i
$486$		0			0
$487$	−1.51761	−	1.75142i	−0.0687695	−	0.0793643i	0.720322	−	0.693640i	$-0.243994\pi$
$487$	−1.51761	−	1.75142i	−0.0687695	−	0.0793643i	−0.789092	+	0.614275i	$0.789448\pi$
$488$		0			0
$489$	−31.0191	+	16.9555i	−1.40273	+	0.766755i
$490$		0			0
$491$	2.84974	+	9.70534i	0.128607	+	0.437996i	0.998470	−	0.0552981i	$-0.0176109\pi$
$491$	2.84974	+	9.70534i	0.128607	+	0.437996i	−0.869863	+	0.493294i	$0.835793\pi$
$492$		0			0
$493$	−29.6943	+	4.26939i	−1.33736	+	0.192284i
$494$		0			0
$495$	7.29118	−	24.9129i	0.327714	−	1.11975i
$496$		0			0
$497$	5.36387	+	3.44715i	0.240603	+	0.154626i
$498$		0			0
$499$	0.540094	−	3.75643i	0.0241779	−	0.168161i	−0.974155	−	0.225881i	$-0.927474\pi$
$499$	0.540094	−	3.75643i	0.0241779	−	0.168161i	0.998333	+	0.0577199i	$0.0183830\pi$
$500$		0			0
$501$	8.56904	+	39.3076i	0.382837	+	1.75614i
$502$		0			0
$503$	33.5865	+	9.86188i	1.49755	+	0.439720i	0.924941	−	0.380111i	$-0.124114\pi$
$503$	33.5865	+	9.86188i	1.49755	+	0.439720i	0.572606	+	0.819830i	$0.305932\pi$
$504$		0			0
$505$			11.2219i			0.499368i
$506$		0			0
$507$	−12.7858	−	4.76243i	−0.567838	−	0.211507i
$508$		0			0
$509$	−3.60329	+	12.2717i	−0.159713	+	0.543932i	0.840286	+	0.542144i	$0.182387\pi$
$509$	−3.60329	+	12.2717i	−0.159713	+	0.543932i	−0.999998	+	0.00178803i	$0.999431\pi$
$510$		0			0
$511$	−3.80008	−	5.91305i	−0.168106	−	0.261578i
$512$		0			0
$513$	−12.3143	−	32.8828i	−0.543690	−	1.45181i
$514$		0			0
$515$	16.7834	−	26.1155i	0.739567	−	1.15079i
$516$		0			0
$517$	35.7907	−	16.3450i	1.57407	−	0.718854i
$518$		0			0
$519$	−43.2922	−	9.39760i	−1.90031	−	0.412509i
$520$		0			0
$521$	−31.1068	+	9.13379i	−1.36282	+	0.400159i	−0.879755	−	0.475428i	$-0.842293\pi$
$521$	−31.1068	+	9.13379i	−1.36282	+	0.400159i	−0.483061	+	0.875587i	$0.660475\pi$
$522$		0			0
$523$	20.6415	+	17.8860i	0.902592	+	0.782100i	0.976579	−	0.215159i	$-0.0690270\pi$
$523$	20.6415	+	17.8860i	0.902592	+	0.782100i	−0.0739873	+	0.997259i	$0.523572\pi$
$524$		0			0
$525$	−1.20406	+	0.449696i	−0.0525493	+	0.0196263i
$526$		0			0
$527$	9.63144	−	21.0899i	0.419552	−	0.918691i
$528$		0			0
$529$	17.9886	−	14.3321i	0.782114	−	0.623135i
$530$		0			0
$531$	6.35619	+	13.8856i	0.275835	+	0.602585i
$532$		0			0
$533$	4.28469	−	3.71271i	0.185591	−	0.160815i
$534$		0			0
$535$	7.30338	−	8.42855i	0.315753	−	0.364398i
$536$		0			0
$537$	2.16765	−	30.4971i	0.0935412	−	1.31605i
$538$		0			0
$539$	−4.02541	−	27.9973i	−0.173387	−	1.20593i
$540$		0			0
$541$	14.8335	+	32.4809i	0.637742	+	1.39646i	0.901885	+	0.431977i	$0.142184\pi$
$541$	14.8335	+	32.4809i	0.637742	+	1.39646i	−0.264142	+	0.964484i	$0.585089\pi$
$542$		0			0
$543$	31.3714	−	23.5059i	1.34627	−	1.00874i
$544$		0			0
$545$	−4.66438	−	0.670637i	−0.199800	−	0.0287269i
$546$		0			0
$547$	13.1102	−	8.42538i	0.560550	−	0.360243i	−0.229479	−	0.973314i	$-0.573702\pi$
$547$	13.1102	−	8.42538i	0.560550	−	0.360243i	0.790028	+	0.613070i	$0.210066\pi$
$548$		0			0
$549$	17.4728	−	11.2509i	0.745722	−	0.480178i
$550$		0			0
$551$	26.1097			1.11231
$552$		0			0
$553$	−8.77797			−0.373277
$554$		0			0
$555$	−4.13161	+	5.52427i	−0.175377	+	0.234492i
$556$		0			0
$557$	−28.9068	+	18.5773i	−1.22482	+	0.787144i	−0.983076	−	0.183196i	$-0.941356\pi$
$557$	−28.9068	+	18.5773i	−1.22482	+	0.787144i	−0.241743	+	0.970340i	$0.577719\pi$
$558$		0			0
$559$	−15.0878	−	2.16930i	−0.638148	−	0.0917518i
$560$		0			0
$561$	35.0981	+	46.8424i	1.48184	+	1.97769i
$562$		0			0
$563$	−1.03633	−	2.26926i	−0.0436763	−	0.0956377i	0.886536	−	0.462659i	$-0.153105\pi$
$563$	−1.03633	−	2.26926i	−0.0436763	−	0.0956377i	−0.930212	+	0.367022i	$0.880377\pi$
$564$		0			0
$565$	−1.54462	−	10.7430i	−0.0649825	−	0.451963i
$566$		0			0
$567$	5.79220	−	2.65759i	0.243250	−	0.111608i
$568$		0			0
$569$	6.01806	−	6.94521i	0.252290	−	0.291158i	−0.615451	−	0.788175i	$-0.711026\pi$
$569$	6.01806	−	6.94521i	0.252290	−	0.291158i	0.867741	+	0.497017i	$0.165571\pi$
$570$		0			0
$571$	−3.28631	+	2.84760i	−0.137528	+	0.119169i	−0.720908	−	0.693030i	$-0.756275\pi$
$571$	−3.28631	+	2.84760i	−0.137528	+	0.119169i	0.583380	+	0.812199i	$0.301730\pi$
$572$		0			0
$573$	−3.17847	+	3.18128i	−0.132782	+	0.132900i
$574$		0			0
$575$	0.461869	−	5.00469i	0.0192613	−	0.208710i
$576$		0			0
$577$	−1.42183	+	3.11337i	−0.0591915	+	0.129611i	−0.936916	−	0.349554i	$-0.886333\pi$
$577$	−1.42183	+	3.11337i	−0.0591915	+	0.129611i	0.877725	+	0.479165i	$0.159060\pi$
$578$		0			0
$579$	−6.73177	−	18.0243i	−0.279763	−	0.749063i
$580$		0			0
$581$	−3.55493	−	3.08037i	−0.147483	−	0.127795i
$582$		0			0
$583$	−4.78230	+	1.40421i	−0.198062	+	0.0581564i
$584$		0			0
$585$	7.28768	−	11.3619i	0.301309	−	0.469757i
$586$		0			0
$587$	18.6700	−	8.52630i	0.770593	−	0.351918i	0.00898833	−	0.999960i	$-0.497139\pi$
$587$	18.6700	−	8.52630i	0.770593	−	0.351918i	0.761605	+	0.648041i	$0.224412\pi$
$588$		0			0
$589$	−10.9095	+	16.9755i	−0.449517	+	0.699462i
$590$		0			0
$591$	16.8219	+	9.17582i	0.691962	+	0.377443i
$592$		0			0
$593$	−5.02730	−	7.82263i	−0.206446	−	0.321237i	0.722555	−	0.691314i	$-0.242968\pi$
$593$	−5.02730	−	7.82263i	−0.206446	−	0.321237i	−0.929001	+	0.370077i	$0.879331\pi$
$594$		0			0
$595$	−3.07916	+	10.4867i	−0.126233	+	0.429911i
$596$		0			0
$597$	6.72871	−	18.0648i	0.275388	−	0.739341i
$598$		0			0
$599$		−	26.9638i		−	1.10171i	−0.834600	−	0.550856i	$-0.814301\pi$
$599$		−	26.9638i		−	1.10171i	0.834600	−	0.550856i	$-0.185699\pi$
$600$		0			0
$601$	−4.85376	−	1.42519i	−0.197989	−	0.0581349i	0.181234	−	0.983440i	$-0.441991\pi$
$601$	−4.85376	−	1.42519i	−0.197989	−	0.0581349i	−0.379224	+	0.925305i	$0.623809\pi$
$602$		0			0
$603$	−1.27784	+	8.94365i	−0.0520376	+	0.364214i
$604$		0			0
$605$	2.24758	−	15.6323i	0.0913773	−	0.635543i
$606$		0			0
$607$	−26.5004	−	17.0308i	−1.07562	−	0.691258i	−0.122078	−	0.992521i	$-0.538956\pi$
$607$	−26.5004	−	17.0308i	−1.07562	−	0.691258i	−0.953541	+	0.301262i	$0.902592\pi$
$608$		0			0
$609$	0.340147	+	4.72653i	0.0137834	+	0.191528i
$610$		0			0
$611$	20.2520	−	2.91180i	0.819310	−	0.117799i
$612$		0			0
$613$	−3.57370	−	12.1709i	−0.144340	−	0.491578i	0.855307	−	0.518121i	$-0.173368\pi$
$613$	−3.57370	−	12.1709i	−0.144340	−	0.491578i	−0.999648	+	0.0265428i	$0.991550\pi$
$614$		0			0
$615$	−4.13691	−	7.56824i	−0.166816	−	0.305181i
$616$		0			0
$617$	12.7759	+	14.7442i	0.514339	+	0.593579i	0.952204	−	0.305462i	$-0.0988108\pi$
$617$	12.7759	+	14.7442i	0.514339	+	0.593579i	−0.437865	+	0.899041i	$0.644265\pi$
$618$		0			0
$619$	−34.1995	−	15.6184i	−1.37459	−	0.627756i	−0.415175	−	0.909742i	$-0.636280\pi$
$619$	−34.1995	−	15.6184i	−1.37459	−	0.627756i	−0.959419	+	0.281986i	$0.909007\pi$
$620$		0			0
$621$	−0.480957	+	24.9152i	−0.0193001	+	0.999814i
$622$		0			0
$623$	−7.51269	−	3.43093i	−0.300990	−	0.137457i
$624$		0			0
$625$	12.2209	+	14.1037i	0.488835	+	0.564146i
$626$		0			0
$627$	−24.4342	−	44.7009i	−0.975807	−	1.78518i
$628$		0			0
$629$	−4.38242	−	14.9251i	−0.174738	−	0.595104i
$630$		0			0
$631$	−13.2863	+	1.91028i	−0.528919	+	0.0760470i	−0.401601	−	0.915815i	$-0.631546\pi$
$631$	−13.2863	+	1.91028i	−0.528919	+	0.0760470i	−0.127318	+	0.991862i	$0.540637\pi$
$632$		0			0
$633$	−1.18365	−	16.4475i	−0.0470460	−	0.653730i
$634$		0			0
$635$	−18.4897	−	11.8826i	−0.733743	−	0.471548i
$636$		0			0
$637$	2.09324	−	14.5588i	0.0829371	−	0.576840i
$638$		0			0
$639$	3.82084	−	26.7423i	0.151150	−	1.05791i
$640$		0			0
$641$	−4.54533	−	1.33463i	−0.179530	−	0.0527146i	0.190732	−	0.981642i	$-0.438914\pi$
$641$	−4.54533	−	1.33463i	−0.179530	−	0.0527146i	−0.370262	+	0.928927i	$0.620732\pi$
$642$		0			0
$643$			6.72549i			0.265227i	0.991168	+	0.132614i	$0.0423370\pi$
$643$			6.72549i			0.265227i	−0.991168	+	0.132614i	$0.957663\pi$
$644$		0			0
$645$	−8.09432	+	21.7310i	−0.318714	+	0.855659i
$646$		0			0
$647$	0.233954	−	0.796772i	0.00919766	−	0.0313244i	−0.954766	−	0.297357i	$-0.903895\pi$
$647$	0.233954	−	0.796772i	0.00919766	−	0.0313244i	0.963964	+	0.266033i	$0.0857130\pi$
$648$		0			0
$649$	11.9785	+	18.6389i	0.470197	+	0.731641i
$650$		0			0
$651$	−3.21512	−	1.75375i	−0.126011	−	0.0687347i
$652$		0			0
$653$	11.9152	−	18.5404i	0.466277	−	0.725541i	−0.525877	−	0.850560i	$-0.676263\pi$
$653$	11.9152	−	18.5404i	0.466277	−	0.725541i	0.992154	+	0.125019i	$0.0398992\pi$
$654$		0			0
$655$	10.1973	−	4.65697i	0.398443	−	0.181963i
$656$		0			0
$657$	−16.0779	+	25.0664i	−0.627259	+	0.977934i
$658$		0			0
$659$	2.77548	−	0.814955i	0.108117	−	0.0317461i	−0.227226	−	0.973842i	$-0.572966\pi$
$659$	2.77548	−	0.814955i	0.108117	−	0.0317461i	0.335344	+	0.942096i	$0.391148\pi$
$660$		0			0
$661$	−6.84058	−	5.92739i	−0.266068	−	0.230549i	0.511601	−	0.859223i	$-0.329052\pi$
$661$	−6.84058	−	5.92739i	−0.266068	−	0.230549i	−0.777669	+	0.628674i	$0.783598\pi$
$662$		0			0
$663$	10.6494	+	28.5136i	0.413588	+	1.10738i
$664$		0			0
$665$	3.95151	−	8.65261i	0.153233	−	0.335534i
$666$		0			0
$667$	−17.2246	−	6.83236i	−0.666940	−	0.264550i
$668$		0			0
$669$	−27.6122	+	27.6366i	−1.06755	+	1.06849i
$670$		0			0
$671$	22.7866	−	19.7447i	0.879666	−	0.762235i
$672$		0			0
$673$	−6.41151	+	7.39928i	−0.247146	+	0.285221i	−0.865745	−	0.500485i	$-0.833155\pi$
$673$	−6.41151	+	7.39928i	−0.247146	+	0.285221i	0.618599	+	0.785707i	$0.287700\pi$
$674$		0			0
$675$	3.85564	+	3.84543i	0.148404	+	0.148011i
$676$		0			0
$677$	1.55771	+	10.8341i	0.0598677	+	0.416389i	0.997612	+	0.0690632i	$0.0220010\pi$
$677$	1.55771	+	10.8341i	0.0598677	+	0.416389i	−0.937745	+	0.347325i	$0.887090\pi$
$678$		0			0
$679$	−3.04720	−	6.67243i	−0.116941	−	0.256065i
$680$		0			0
$681$	−1.11070	−	1.48235i	−0.0425619	−	0.0568038i
$682$		0			0
$683$	39.6246	+	5.69716i	1.51619	+	0.217996i	0.849601	−	0.527426i	$-0.176843\pi$
$683$	39.6246	+	5.69716i	1.51619	+	0.217996i	0.666593	+	0.745422i	$0.267752\pi$
$684$		0			0
$685$	−7.71181	+	4.95608i	−0.294653	+	0.189362i
$686$		0			0
$687$	−9.00898	+	12.0457i	−0.343714	+	0.459571i
$688$		0			0
$689$	−2.59181			−0.0987400
$690$		0			0
$691$	−30.7446			−1.16958			−0.584790	−	0.811185i	$-0.698823\pi$
$691$	−30.7446			−1.16958			−0.584790	+	0.811185i	$0.698823\pi$
$692$		0			0
$693$	7.77370	−	5.00556i	0.295298	−	0.190146i
$694$		0			0
$695$	10.5430	−	6.77559i	0.399919	−	0.257013i
$696$		0			0
$697$	19.2509	+	2.76786i	0.729178	+	0.104840i
$698$		0			0
$699$	−23.6170	+	17.6958i	−0.893279	+	0.669316i
$700$		0			0
$701$	−15.2962	−	33.4941i	−0.577731	−	1.26506i	−0.942578	−	0.333987i	$-0.891606\pi$
$701$	−15.2962	−	33.4941i	−0.577731	−	1.26506i	0.364846	−	0.931068i	$-0.381122\pi$
$702$		0			0
$703$	1.92669	+	13.4005i	0.0726666	+	0.505408i
$704$		0			0
$705$	2.20684	−	31.0485i	0.0831145	−	1.16935i
$706$		0			0
$707$	−2.61753	+	3.02080i	−0.0984425	+	0.113609i
$708$		0			0
$709$	−0.245199	+	0.212466i	−0.00920863	+	0.00797932i	−0.659453	−	0.751746i	$-0.729212\pi$
$709$	−0.245199	+	0.212466i	−0.00920863	+	0.00797932i	0.650244	+	0.759725i	$0.274667\pi$
$710$		0			0
$711$	15.4793	+	33.8157i	0.580518	+	1.26819i
$712$		0			0
$713$	11.6391	−	8.34397i	0.435889	−	0.312484i
$714$		0			0
$715$	8.13539	−	17.8140i	0.304246	−	0.666207i
$716$		0			0
$717$	21.6616	−	8.09027i	0.808968	−	0.302137i
$718$		0			0
$719$	31.9012	+	27.6426i	1.18972	+	1.03089i	0.998784	+	0.0492908i	$0.0156961\pi$
$719$	31.9012	+	27.6426i	1.18972	+	1.03089i	0.190931	+	0.981603i	$0.438849\pi$
$720$		0			0
$721$	10.6094	−	3.11520i	0.395115	−	0.116016i
$722$		0			0
$723$	9.50159	+	2.06255i	0.353368	+	0.0767070i
$724$		0			0
$725$	−3.68330	+	1.68211i	−0.136794	+	0.0624718i
$726$		0			0
$727$	−3.94384	+	6.13674i	−0.146269	+	0.227599i	−0.906655	−	0.421872i	$-0.861373\pi$
$727$	−3.94384	+	6.13674i	−0.146269	+	0.227599i	0.760386	+	0.649471i	$0.225010\pi$
$728$		0			0
$729$	−20.4520	−	17.6271i	−0.757483	−	0.652855i
$730$		0			0
$731$	−28.2703	−	43.9895i	−1.04562	−	1.62701i
$732$		0			0
$733$	6.16846	−	21.0078i	0.227837	−	0.775942i	−0.763638	−	0.645645i	$-0.776589\pi$
$733$	6.16846	−	21.0078i	0.227837	−	0.775942i	0.991475	−	0.130297i	$-0.0415931\pi$
$734$		0			0
$735$	−20.9690	−	7.81049i	−0.773454	−	0.288094i
$736$		0			0
$737$			13.1075i			0.482822i
$738$		0			0
$739$	17.1915	+	5.04787i	0.632399	+	0.185689i	0.582194	−	0.813050i	$-0.302194\pi$
$739$	17.1915	+	5.04787i	0.632399	+	0.185689i	0.0502047	+	0.998739i	$0.484013\pi$
$740$		0			0
$741$	−5.64244	−	25.8828i	−0.207280	−	0.950829i
$742$		0			0
$743$	−4.99792	+	34.7613i	−0.183356	+	1.27527i	0.665402	+	0.746485i	$0.268260\pi$
$743$	−4.99792	+	34.7613i	−0.183356	+	1.27527i	−0.848758	+	0.528782i	$0.822649\pi$
$744$		0			0
$745$	−27.0046	−	17.3548i	−0.989372	−	0.635831i
$746$		0			0
$747$	−5.59778	+	19.1268i	−0.204812	+	0.699813i
$748$		0			0
$749$	3.93196	−	0.565331i	0.143671	−	0.0206567i
$750$		0			0
$751$	13.4490	+	45.8032i	0.490762	+	1.67138i	0.716813	+	0.697266i	$0.245600\pi$
$751$	13.4490	+	45.8032i	0.490762	+	1.67138i	−0.226051	+	0.974115i	$0.572582\pi$
$752$		0			0
$753$	−30.0776	+	16.4409i	−1.09609	+	0.599139i
$754$		0			0
$755$	−4.60403	−	5.31334i	−0.167558	−	0.193372i
$756$		0			0
$757$	36.0983	+	16.4855i	1.31202	+	0.599177i	0.943786	−	0.330557i	$-0.107237\pi$
$757$	36.0983	+	16.4855i	1.31202	+	0.599177i	0.368230	+	0.929735i	$0.379964\pi$
$758$		0			0
$759$	4.42199	+	35.8832i	0.160508	+	1.30248i
$760$		0			0
$761$	−39.3321	−	17.9623i	−1.42579	−	0.651135i	−0.454871	−	0.890558i	$-0.650314\pi$
$761$	−39.3321	−	17.9623i	−1.42579	−	0.651135i	−0.970915	+	0.239423i	$0.923042\pi$
$762$		0			0
$763$	−1.09917	−	1.26851i	−0.0397925	−	0.0459230i
$764$		0			0
$765$	45.8280	−	6.63042i	1.65692	−	0.239723i
$766$		0			0
$767$	3.24593	+	11.0546i	0.117204	+	0.399159i
$768$		0			0
$769$	−31.9249	+	4.59011i	−1.15124	+	0.165523i	−0.691396	−	0.722476i	$-0.743004\pi$
$769$	−31.9249	+	4.59011i	−1.15124	+	0.165523i	−0.459845	+	0.887999i	$0.652095\pi$
$770$		0			0
$771$	−28.3029	+	2.03683i	−1.01931	+	0.0733548i
$772$		0			0
$773$	3.11036	+	1.99891i	0.111872	+	0.0718958i	0.595380	−	0.803444i	$-0.297001\pi$
$773$	3.11036	+	1.99891i	0.111872	+	0.0718958i	−0.483508	+	0.875340i	$0.660638\pi$
$774$		0			0
$775$	0.445363	−	3.09757i	0.0159979	−	0.111268i
$776$		0			0
$777$	−2.40073	+	0.523357i	−0.0861256	+	0.0187753i
$778$		0			0
$779$	−16.2413	−	4.76888i	−0.581905	−	0.170863i
$780$		0			0
$781$		−	39.1926i		−	1.40242i
$782$		0			0
$783$	17.6084	−	9.64521i	0.629272	−	0.344692i
$784$		0			0
$785$	−9.36327	+	31.8884i	−0.334190	+	1.13814i
$786$		0			0
$787$	−11.3265	−	17.6244i	−0.403747	−	0.628243i	0.578533	−	0.815659i	$-0.303625\pi$
$787$	−11.3265	−	17.6244i	−0.403747	−	0.628243i	−0.982281	+	0.187416i	$0.939989\pi$
$788$		0			0
$789$	−16.5259	+	30.2968i	−0.588339	+	1.07860i
$790$		0			0
$791$	2.09005	−	3.25218i	0.0743136	−	0.115634i
$792$		0			0
$793$	14.2618	−	6.51316i	0.506452	−	0.231289i
$794$		0			0
$795$	−0.836440	+	3.85325i	−0.0296655	+	0.136661i
$796$		0			0
$797$	12.1312	−	3.56205i	0.429710	−	0.126174i	−0.0597232	−	0.998215i	$-0.519022\pi$
$797$	12.1312	−	3.56205i	0.429710	−	0.126174i	0.489433	+	0.872041i	$0.337204\pi$
$798$		0			0
$799$	53.0447	+	45.9635i	1.87658	+	1.62607i
$800$		0			0
$801$	0.0309190	+	34.9916i	0.00109247	+	1.23637i
$802$		0			0
$803$	−17.9481	+	39.3009i	−0.633376	+	1.38690i
$804$		0			0
$805$	−4.87103	+	4.67412i	−0.171681	+	0.164741i
$806$		0			0
$807$	25.1035	+	25.0814i	0.883686	+	0.882906i
$808$		0			0
$809$	1.61595	−	1.40023i	0.0568138	−	0.0492294i	−0.625991	−	0.779830i	$-0.715305\pi$
$809$	1.61595	−	1.40023i	0.0568138	−	0.0492294i	0.682805	+	0.730601i	$0.260760\pi$
$810$		0			0
$811$	17.7795	−	20.5187i	0.624324	−	0.720508i	−0.352198	−	0.935925i	$-0.614566\pi$
$811$	17.7795	−	20.5187i	0.624324	−	0.720508i	0.976522	+	0.215417i	$0.0691111\pi$
$812$		0			0
$813$	1.38420	+	0.0983851i	0.0485459	+	0.00345052i
$814$		0			0
$815$	5.77428	+	40.1610i	0.202264	+	1.40678i
$816$		0			0
$817$	18.9056	+	41.3974i	0.661422	+	1.44831i
$818$		0			0
$819$	4.61195	−	1.35862i	0.161155	−	0.0474740i
$820$		0			0
$821$	18.1336	+	2.60722i	0.632868	+	0.0909927i	0.451281	−	0.892382i	$-0.350967\pi$
$821$	18.1336	+	2.60722i	0.632868	+	0.0909927i	0.181587	+	0.983375i	$0.441876\pi$
$822$		0			0
$823$	14.9670	−	9.61873i	0.521718	−	0.335288i	−0.253133	−	0.967431i	$-0.581461\pi$
$823$	14.9670	−	9.61873i	0.521718	−	0.335288i	0.774851	+	0.632144i	$0.217825\pi$
$824$		0			0
$825$	6.32677	+	4.73180i	0.220270	+	0.164740i
$826$		0			0
$827$	−7.84516			−0.272803			−0.136401	−	0.990654i	$-0.543554\pi$
$827$	−7.84516			−0.272803			−0.136401	+	0.990654i	$0.543554\pi$
$828$		0			0
$829$	28.1822			0.978807			0.489404	−	0.872057i	$-0.337215\pi$
$829$	28.1822			0.978807			0.489404	+	0.872057i	$0.337215\pi$
$830$		0			0
$831$	26.4317	+	19.7683i	0.916904	+	0.685754i
$832$		0			0
$833$	42.4470	−	27.2790i	1.47070	−	0.945162i
$834$		0			0
$835$	45.7051	+	6.57140i	1.58169	+	0.227413i
$836$		0			0
$837$	−1.08641	+	15.4783i	−0.0375520	+	0.535010i
$838$		0			0
$839$	−5.75380	−	12.5991i	−0.198643	−	0.434968i	0.783929	−	0.620851i	$-0.213213\pi$
$839$	−5.75380	−	12.5991i	−0.198643	−	0.434968i	−0.982572	+	0.185883i	$0.940486\pi$
$840$		0			0
$841$	−2.00250	−	13.9277i	−0.0690518	−	0.480266i
$842$		0			0
$843$	−46.9081	−	3.33410i	−1.61560	−	0.114833i
$844$		0			0
$845$	−10.2551	+	11.8350i	−0.352785	+	0.407135i
$846$		0			0
$847$	4.25129	−	3.68377i	0.146076	−	0.126576i
$848$		0			0
$849$	−19.2076	−	19.1907i	−0.659204	−	0.658622i
$850$		0			0
$851$	2.23557	−	9.34448i	0.0766345	−	0.320325i
$852$		0			0
$853$	8.80940	−	19.2899i	0.301628	−	0.660474i	−0.696755	−	0.717309i	$-0.745374\pi$
$853$	8.80940	−	19.2899i	0.301628	−	0.660474i	0.998384	+	0.0568351i	$0.0181009\pi$
$854$		0			0
$855$	−40.3010	+	0.0356104i	−1.37826	+	0.00121785i
$856$		0			0
$857$	15.0495	+	13.0404i	0.514080	+	0.445453i	0.872861	−	0.487969i	$-0.162262\pi$
$857$	15.0495	+	13.0404i	0.514080	+	0.445453i	−0.358781	+	0.933422i	$0.616807\pi$
$858$		0			0
$859$	17.4054	−	5.11068i	0.593864	−	0.174374i	0.0290298	−	0.999579i	$-0.490758\pi$
$859$	17.4054	−	5.11068i	0.593864	−	0.174374i	0.564834	+	0.825204i	$0.308940\pi$
$860$		0			0
$861$	0.651705	−	3.00222i	0.0222100	−	0.102315i
$862$		0			0
$863$	−7.27482	+	3.32230i	−0.247638	+	0.113092i	−0.535367	−	0.844619i	$-0.679827\pi$
$863$	−7.27482	+	3.32230i	−0.247638	+	0.113092i	0.287730	+	0.957712i	$0.407100\pi$
$864$		0			0
$865$	−27.4894	+	42.7743i	−0.934667	+	1.45437i
$866$		0			0
$867$	−35.8999	+	65.8148i	−1.21922	+	2.23519i
$868$		0			0
$869$	29.1713	+	45.3914i	0.989568	+	1.53980i
$870$		0			0
$871$	−1.92029	+	6.53990i	−0.0650665	+	0.221596i
$872$		0			0
$873$	−20.3310	+	23.5052i	−0.688100	+	0.795529i
$874$		0			0
$875$			8.51347i			0.287808i
$876$		0			0
$877$	−35.9983	−	10.5700i	−1.21558	−	0.356925i	−0.389787	−	0.920905i	$-0.627451\pi$
$877$	−35.9983	−	10.5700i	−1.21558	−	0.356925i	−0.825789	+	0.563980i	$0.809270\pi$
$878$		0			0
$879$	−16.5963	+	3.61799i	−0.559780	+	0.122032i
$880$		0			0
$881$	−4.26249	+	29.6462i	−0.143607	+	0.998807i	0.782797	+	0.622277i	$0.213792\pi$
$881$	−4.26249	+	29.6462i	−0.143607	+	0.998807i	−0.926404	+	0.376530i	$0.877117\pi$
$882$		0			0
$883$	−12.9255	−	8.30670i	−0.434977	−	0.279543i	0.304772	−	0.952425i	$-0.401420\pi$
$883$	−12.9255	−	8.30670i	−0.434977	−	0.279543i	−0.739749	+	0.672882i	$0.765056\pi$
$884$		0			0
$885$	17.4824	−	1.25813i	0.587666	−	0.0422917i
$886$		0			0
$887$	53.7947	−	7.73452i	1.80625	−	0.259700i	0.844880	−	0.534956i	$-0.179672\pi$
$887$	53.7947	−	7.73452i	1.80625	−	0.259700i	0.961371	+	0.275256i	$0.0887628\pi$
$888$		0			0
$889$	−2.20556	−	7.51144i	−0.0739720	−	0.251926i
$890$		0			0
$891$	−32.9914	−	21.1200i	−1.10525	−	0.707547i
$892$		0			0
$893$	−40.0036	−	46.1666i	−1.33867	−	1.54491i
$894$		0			0
$895$	−31.9203	−	14.5775i	−1.06698	−	0.487273i
$896$		0			0
$897$	−3.05066	+	18.5515i	−0.101859	+	0.619415i
$898$		0			0
$899$	−10.4952	−	4.79301i	−0.350035	−	0.159856i
$900$		0			0
$901$	−5.82242	−	6.71943i	−0.193973	−	0.223857i
$902$		0			0
$903$	−7.24771	+	3.96171i	−0.241189	+	0.131837i
$904$		0			0
$905$	−12.6759	−	43.1702i	−0.421361	−	1.43502i
$906$		0			0
$907$	5.09413	−	0.732425i	0.169148	−	0.0243198i	−0.0572205	−	0.998362i	$-0.518224\pi$
$907$	5.09413	−	0.732425i	0.169148	−	0.0243198i	0.226368	+	0.974042i	$0.427315\pi$
$908$		0			0
$909$	16.2530	+	4.75670i	0.539076	+	0.157770i
$910$		0			0
$911$	−24.3178	−	15.6281i	−0.805684	−	0.517781i	0.0717823	−	0.997420i	$-0.477131\pi$
$911$	−24.3178	−	15.6281i	−0.805684	−	0.517781i	−0.877466	+	0.479639i	$0.840768\pi$
$912$		0			0
$913$	−4.11487	+	28.6196i	−0.136182	+	0.947169i
$914$		0			0
$915$	−5.08049	−	23.3050i	−0.167956	−	0.770441i
$916$		0			0
$917$	3.83125	+	1.12496i	0.126519	+	0.0371493i
$918$		0			0
$919$		−	39.5782i		−	1.30556i	−0.757546	−	0.652782i	$-0.773602\pi$
$919$		−	39.5782i		−	1.30556i	0.757546	−	0.652782i	$-0.226398\pi$
$920$		0			0
$921$	46.3863	+	17.2779i	1.52848	+	0.569325i
$922$		0			0
$923$	5.74182	−	19.5548i	0.188994	−	0.643656i
$924$		0			0
$925$	−1.13512	−	1.76628i	−0.0373224	−	0.0580748i
$926$		0			0
$927$	−30.7097	−	35.3777i	−1.00864	−	1.16195i
$928$		0			0
$929$	−2.16506	+	3.36889i	−0.0710332	+	0.110530i	−0.874953	−	0.484208i	$-0.839108\pi$
$929$	−2.16506	+	3.36889i	−0.0710332	+	0.110530i	0.803920	+	0.594738i	$0.202744\pi$
$930$		0			0
$931$	−39.9458	+	18.2427i	−1.30917	+	0.597879i
$932$		0			0
$933$	52.1154	+	11.3129i	1.70618	+	0.370368i
$934$		0			0
$935$	64.4599	−	18.9271i	2.10807	−	0.618984i
$936$		0			0
$937$	−39.4453	−	34.1796i	−1.28862	−	1.11660i	−0.986576	−	0.163306i	$-0.947784\pi$
$937$	−39.4453	−	34.1796i	−1.28862	−	1.11660i	−0.302048	−	0.953293i	$-0.597670\pi$
$938$		0			0
$939$	13.5655	−	5.06650i	0.442694	−	0.165339i
$940$		0			0
$941$	0.0414774	−	0.0908229i	0.00135213	−	0.00296074i	−0.908955	−	0.416895i	$-0.863118\pi$
$941$	0.0414774	−	0.0908229i	0.00135213	−	0.00296074i	0.910307	+	0.413934i	$0.135846\pi$
$942$		0			0
$943$	9.46651	+	7.39605i	0.308272	+	0.240849i
$944$		0			0
$945$	−0.531472	−	7.29505i	−0.0172888	−	0.237308i
$946$		0			0
$947$	−33.8033	+	29.2907i	−1.09846	+	0.951820i	−0.999065	−	0.0432285i	$-0.986236\pi$
$947$	−33.8033	+	29.2907i	−1.09846	+	0.951820i	−0.0993934	+	0.995048i	$0.531690\pi$
$948$		0			0
$949$	−14.7128	+	16.9794i	−0.477596	+	0.551176i
$950$		0			0
$951$	−0.984466	+	13.8506i	−0.0319235	+	0.449137i
$952$		0			0
$953$	−2.66935	−	18.5657i	−0.0864688	−	0.601403i	−0.986275	−	0.165113i	$-0.947201\pi$
$953$	−2.66935	−	18.5657i	−0.0864688	−	0.601403i	0.899806	−	0.436290i	$-0.143708\pi$
$954$		0			0
$955$	2.14415	+	4.69504i	0.0693832	+	0.151928i
$956$		0			0
$957$	23.3108	−	17.4663i	0.753530	−	0.564605i
$958$		0			0
$959$	−3.23194	−	0.464683i	−0.104365	−	0.0150054i
$960$		0			0
$961$	−18.5774	+	11.9390i	−0.599271	+	0.385128i
$962$		0			0
$963$	−9.11155	−	14.1503i	−0.293616	−	0.455988i
$964$		0			0
$965$	−22.0832			−0.710883
$966$		0			0
$967$	20.5129			0.659649			0.329825	−	0.944042i	$-0.393010\pi$
$967$	20.5129			0.659649			0.329825	+	0.944042i	$0.393010\pi$
$968$		0			0
$969$	54.4273	−	72.7734i	1.74846	−	2.33782i
$970$		0			0
$971$	2.74903	−	1.76669i	0.0882206	−	0.0566959i	−0.495787	−	0.868444i	$-0.665120\pi$
$971$	2.74903	−	1.76669i	0.0882206	−	0.0566959i	0.584007	+	0.811748i	$0.301484\pi$
$972$		0			0
$973$	4.41847	+	0.635281i	0.141650	+	0.0203662i
$974$		0			0
$975$	2.46347	+	3.28778i	0.0788942	+	0.105293i
$976$		0			0
$977$	6.02689	+	13.1970i	0.192817	+	0.422211i	0.981205	−	0.192968i	$-0.0618112\pi$
$977$	6.02689	+	13.1970i	0.192817	+	0.422211i	−0.788388	+	0.615178i	$0.789084\pi$
$978$		0			0
$979$	7.22492	+	50.2504i	0.230909	+	1.60601i
$980$		0			0
$981$	−2.94842	+	6.47128i	−0.0941360	+	0.206612i
$982$		0			0
$983$	−20.2767	+	23.4005i	−0.646725	+	0.746361i	−0.980549	−	0.196275i	$-0.937116\pi$
$983$	−20.2767	+	23.4005i	−0.646725	+	0.746361i	0.333824	+	0.942636i	$0.391661\pi$
$984$		0			0
$985$	16.6212	−	14.4023i	0.529595	−	0.458897i
$986$		0			0
$987$	7.83619	−	7.84312i	0.249429	−	0.249649i
$988$		0			0
$989$	−1.63921	−	32.2572i	−0.0521237	−	1.02572i
$990$		0			0
$991$	16.3456	−	35.7918i	0.519234	−	1.13696i	−0.450495	−	0.892779i	$-0.648753\pi$
$991$	16.3456	−	35.7918i	0.519234	−	1.13696i	0.969729	−	0.244184i	$-0.0785201\pi$
$992$		0			0
$993$	−1.66054	−	4.44608i	−0.0526957	−	0.141092i
$994$		0			0
$995$	−16.7213	−	14.4891i	−0.530102	−	0.459336i
$996$		0			0
$997$	27.7317	−	8.14275i	0.878271	−	0.257884i	0.188641	−	0.982046i	$-0.439592\pi$
$997$	27.7317	−	8.14275i	0.878271	−	0.257884i	0.689629	+	0.724163i	$0.257773\pi$
$998$		0			0
$999$	6.24964	+	8.32552i	0.197730	+	0.263408i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.k.a.17.2	yes	80
3.2	odd	2	inner	276.2.k.a.17.1	✓	80
23.19	odd	22	inner	276.2.k.a.65.1	yes	80
69.65	even	22	inner	276.2.k.a.65.2	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.k.a.17.1	✓	80	3.2	odd	2	inner
276.2.k.a.17.2	yes	80	1.1	even	1	trivial
276.2.k.a.65.1	yes	80	23.19	odd	22	inner
276.2.k.a.65.2	yes	80	69.65	even	22	inner

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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.k (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38704 - 1.03737i) q^{3} +(-1.67238 + 1.07478i) q^{5} +(-0.700880 - 0.100771i) q^{7} +(0.847741 + 2.87773i) q^{9} +O(q^{10})\)	\(q+(-1.38704 - 1.03737i) q^{3} +(-1.67238 + 1.07478i) q^{5} +(-0.700880 - 0.100771i) q^{7} +(0.847741 + 2.87773i) q^{9} +(1.80810 + 3.95918i) q^{11} +(0.322105 + 2.24029i) q^{13} +(3.43460 + 0.244122i) q^{15} +(-5.08450 + 5.86783i) q^{17} +(5.10697 - 4.42521i) q^{19} +(0.867609 + 0.866843i) q^{21} +(-4.52706 + 1.58294i) q^{23} +(-0.435348 + 0.953280i) q^{25} +(1.80941 - 4.87094i) q^{27} +(2.92008 + 2.53026i) q^{29} +(-2.86518 + 0.841292i) q^{31} +(1.59922 - 7.36719i) q^{33} +(1.28045 - 0.584761i) q^{35} +(-1.08314 + 1.68540i) q^{37} +(1.87723 - 3.44151i) q^{39} +(-1.35426 - 2.10727i) q^{41} +(-1.89740 + 6.46196i) q^{43} +(-4.51067 - 3.90154i) q^{45} -9.03992i q^{47} +(-6.23537 - 1.83087i) q^{49} +(13.1395 - 2.86440i) q^{51} +(-0.162969 + 1.13348i) q^{53} +(-7.27907 - 4.67797i) q^{55} +(-11.6741 + 0.840134i) q^{57} +(5.03861 - 0.724443i) q^{59} +(-1.95164 - 6.64666i) q^{61} +(-0.304172 - 2.10237i) q^{63} +(-2.94650 - 3.40044i) q^{65} +(2.73935 + 1.25102i) q^{67} +(7.92129 + 2.50064i) q^{69} +(-8.19088 - 3.74065i) q^{71} +(6.50050 + 7.50197i) q^{73} +(1.59274 - 0.870618i) q^{75} +(-0.868287 - 2.95711i) q^{77} +(12.2706 - 1.76424i) q^{79} +(-7.56267 + 4.87914i) q^{81} +(5.58848 + 3.59150i) q^{83} +(2.19664 - 15.2780i) q^{85} +(-1.42544 - 6.53875i) q^{87} +(11.1914 + 3.28610i) q^{89} -1.60263i q^{91} +(4.84683 + 1.80534i) q^{93} +(-3.78470 + 12.8895i) q^{95} +(5.60068 + 8.71483i) q^{97} +(-9.86066 + 8.55957i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 6 q^{9}+O(q^{10}) \) 80 * q - 2 * q^3 + 6 * q^9	\( 80 q - 2 q^{3} + 6 q^{9} - 4 q^{13} + 11 q^{15} + 33 q^{21} + 25 q^{27} + 20 q^{31} + 11 q^{33} - 44 q^{37} - 18 q^{39} - 44 q^{43} - 100 q^{49} - 98 q^{55} - 33 q^{57} - 44 q^{61} - 55 q^{63} - 22 q^{67} - 41 q^{69} - 26 q^{73} - 65 q^{75} - 44 q^{79} - 42 q^{81} + 2 q^{85} - 64 q^{87} - 46 q^{93} + 66 q^{97} - 66 q^{99}+O(q^{100}) \) 80 * q - 2 * q^3 + 6 * q^9 - 4 * q^13 + 11 * q^15 + 33 * q^21 + 25 * q^27 + 20 * q^31 + 11 * q^33 - 44 * q^37 - 18 * q^39 - 44 * q^43 - 100 * q^49 - 98 * q^55 - 33 * q^57 - 44 * q^61 - 55 * q^63 - 22 * q^67 - 41 * q^69 - 26 * q^73 - 65 * q^75 - 44 * q^79 - 42 * q^81 + 2 * q^85 - 64 * q^87 - 46 * q^93 + 66 * q^97 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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