LMFDB - Embedded newform 276.2.k.a.17.1

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			17.1
Character	$\chi$	$=$	276.17
Dual form			276.2.k.a.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.72769 + 0.122800i) q^{3} +(1.67238 - 1.07478i) q^{5} +(-0.700880 - 0.100771i) q^{7} +(2.96984 - 0.424320i) q^{9} +O(q^{10})$	\(q+(-1.72769 + 0.122800i) q^{3} +(1.67238 - 1.07478i) q^{5} +(-0.700880 - 0.100771i) q^{7} +(2.96984 - 0.424320i) q^{9} +(-1.80810 - 3.95918i) q^{11} +(0.322105 + 2.24029i) q^{13} +(-2.75738 + 2.06225i) q^{15} +(5.08450 - 5.86783i) q^{17} +(5.10697 - 4.42521i) q^{19} +(1.22328 + 0.0880339i) q^{21} +(4.52706 - 1.58294i) q^{23} +(-0.435348 + 0.953280i) q^{25} +(-5.07886 + 1.09779i) q^{27} +(-2.92008 - 2.53026i) q^{29} +(-2.86518 + 0.841292i) q^{31} +(3.61002 + 6.61821i) q^{33} +(-1.28045 + 0.584761i) q^{35} +(-1.08314 + 1.68540i) q^{37} +(-0.831606 - 3.83098i) q^{39} +(1.35426 + 2.10727i) q^{41} +(-1.89740 + 6.46196i) q^{43} +(4.51067 - 3.90154i) q^{45} +9.03992i q^{47} +(-6.23537 - 1.83087i) q^{49} +(-8.06388 + 10.7622i) q^{51} +(0.162969 - 1.13348i) q^{53} +(-7.27907 - 4.67797i) q^{55} +(-8.27985 + 8.27254i) q^{57} +(-5.03861 + 0.724443i) q^{59} +(-1.95164 - 6.64666i) q^{61} +(-2.12426 - 0.00187702i) q^{63} +(2.94650 + 3.40044i) q^{65} +(2.73935 + 1.25102i) q^{67} +(-7.62699 + 3.29075i) q^{69} +(8.19088 + 3.74065i) q^{71} +(6.50050 + 7.50197i) q^{73} +(0.635085 - 1.70043i) q^{75} +(0.868287 + 2.95711i) q^{77} +(12.2706 - 1.76424i) q^{79} +(8.63990 - 2.52033i) q^{81} +(-5.58848 - 3.59150i) q^{83} +(2.19664 - 15.2780i) q^{85} +(5.35571 + 4.01293i) q^{87} +(-11.1914 - 3.28610i) q^{89} -1.60263i q^{91} +(4.84683 - 1.80534i) q^{93} +(3.78470 - 12.8895i) q^{95} +(5.60068 + 8.71483i) q^{97} +(-7.04972 - 10.9909i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.72769	+	0.122800i	−0.997484	+	0.0708985i
$3$	−1.72769	+	0.122800i	−0.997484	+	0.0708985i
$4$		0			0
$5$	1.67238	−	1.07478i	0.747913	−	0.480655i	−0.110332	−	0.993895i	$-0.535191\pi$
$5$	1.67238	−	1.07478i	0.747913	−	0.480655i	0.858245	+	0.513240i	$0.171555\pi$
$6$		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
$9$	2.96984	−	0.424320i	0.989947	−	0.141440i
$10$		0			0
$11$	−1.80810	−	3.95918i	−0.545162	−	1.19374i	−0.959005	−	0.283389i	$-0.908541\pi$
$11$	−1.80810	−	3.95918i	−0.545162	−	1.19374i	0.413843	−	0.910348i	$-0.364186\pi$
$12$		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
$15$	−2.75738	+	2.06225i	−0.711953	+	0.532471i
$16$		0			0
$17$	5.08450	−	5.86783i	1.23317	−	1.42316i	0.362001	−	0.932178i	$-0.382094\pi$
$17$	5.08450	−	5.86783i	1.23317	−	1.42316i	0.871172	−	0.490979i	$-0.163361\pi$
$18$		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
$21$	1.22328	+	0.0880339i	0.266941	+	0.0192106i
$22$		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
$27$	−5.07886	+	1.09779i	−0.977428	+	0.211270i
$28$		0			0
$29$	−2.92008	−	2.53026i	−0.542245	−	0.469858i	0.340148	−	0.940372i	$-0.389523\pi$
$29$	−2.92008	−	2.53026i	−0.542245	−	0.469858i	−0.882392	+	0.470514i	$0.844068\pi$
$30$		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
$33$	3.61002	+	6.61821i	0.628424	+	1.15208i
$34$		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
$39$	−0.831606	−	3.83098i	−0.133164	−	0.613448i
$40$		0			0
$41$	1.35426	+	2.10727i	0.211500	+	0.329101i	0.930754	−	0.365647i	$-0.119152\pi$
$41$	1.35426	+	2.10727i	0.211500	+	0.329101i	−0.719253	+	0.694748i	$0.755516\pi$
$42$		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	$0.229149\pi$
$47$			9.03992i			1.31861i	−0.751877	+	0.659304i	$0.770851\pi$
$48$		0			0
$49$	−6.23537	−	1.83087i	−0.890768	−	0.261553i
$50$		0			0
$51$	−8.06388	+	10.7622i	−1.12917	+	1.50701i
$52$		0			0
$53$	0.162969	−	1.13348i	0.0223855	−	0.155695i	−0.975563	−	0.219721i	$-0.929485\pi$
$53$	0.162969	−	1.13348i	0.0223855	−	0.155695i	0.997948	+	0.0640266i	$0.0203943\pi$
$54$		0			0
$55$	−7.27907	−	4.67797i	−0.981509	−	0.630778i
$56$		0			0
$57$	−8.27985	+	8.27254i	−1.09669	+	1.09572i
$58$		0			0
$59$	−5.03861	+	0.724443i	−0.655971	+	0.0943144i	−0.462260	−	0.886744i	$-0.652961\pi$
$59$	−5.03861	+	0.724443i	−0.655971	+	0.0943144i	−0.193711	+	0.981059i	$0.562052\pi$
$60$		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
$63$	−2.12426	−	0.00187702i	−0.267632	−	0.000236483i
$64$		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
$69$	−7.62699	+	3.29075i	−0.918182	+	0.396160i
$70$		0			0
$71$	8.19088	+	3.74065i	0.972079	+	0.443934i	0.837181	−	0.546926i	$-0.184202\pi$
$71$	8.19088	+	3.74065i	0.972079	+	0.443934i	0.134898	+	0.990860i	$0.456929\pi$
$72$		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
$75$	0.635085	−	1.70043i	0.0733333	−	0.196349i
$76$		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
$81$	8.63990	−	2.52033i	0.959989	−	0.280036i
$82$		0			0
$83$	−5.58848	−	3.59150i	−0.613415	−	0.394218i	0.196721	−	0.980459i	$-0.436971\pi$
$83$	−5.58848	−	3.59150i	−0.613415	−	0.394218i	−0.810136	+	0.586242i	$0.800607\pi$
$84$		0			0
$85$	2.19664	−	15.2780i	0.238259	−	1.65713i
$86$		0			0
$87$	5.35571	+	4.01293i	0.574192	+	0.430231i
$88$		0			0
$89$	−11.1914	−	3.28610i	−1.18629	−	0.348325i	−0.371693	−	0.928356i	$-0.621223\pi$
$89$	−11.1914	−	3.28610i	−1.18629	−	0.348325i	−0.814595	+	0.580030i	$0.803041\pi$
$90$		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
$99$	−7.04972	−	10.9909i	−0.708523	−	1.10463i
$100$		0			0
$101$	−3.05187	+	4.74880i	−0.303672	+	0.472523i	−0.959232	−	0.282620i	$-0.908796\pi$
$101$	−3.05187	+	4.74880i	−0.303672	+	0.472523i	0.655560	+	0.755143i	$0.272433\pi$
$102$		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
$105$	2.14041	−	1.16753i	0.208883	−	0.113939i
$106$		0			0
$107$	5.38279	−	1.58053i	0.520374	−	0.152796i	−0.0109894	−	0.999940i	$-0.503498\pi$
$107$	5.38279	−	1.58053i	0.520374	−	0.152796i	0.531363	+	0.847144i	$0.321680\pi$
$108$		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
$111$	1.66437	−	3.04487i	0.157975	−	0.289006i
$112$		0			0
$113$	2.26800	−	4.96623i	0.213356	−	0.467184i	−0.772450	−	0.635076i	$-0.780969\pi$
$113$	2.26800	−	4.96623i	0.213356	−	0.467184i	0.985805	+	0.167892i	$0.0536961\pi$
$114$		0			0
$115$	5.86969	−	7.51286i	0.547352	−	0.700578i
$116$		0			0
$117$	1.90720	+	6.51663i	0.176321	+	0.602463i
$118$		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
$123$	−2.59852	−	3.47442i	−0.234301	−	0.313278i
$124$		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
$129$	2.48460	−	11.3973i	0.218757	−	1.00347i
$130$		0			0
$131$	5.58173	+	0.802531i	0.487678	+	0.0701175i	0.381768	−	0.924258i	$-0.375315\pi$
$131$	5.58173	+	0.802531i	0.487678	+	0.0701175i	0.105910	+	0.994376i	$0.466224\pi$
$132$		0			0
$133$	−4.02531	+	2.58691i	−0.349038	+	0.224313i
$134$		0			0
$135$	−7.31393	+	7.29457i	−0.629483	+	0.627817i
$136$		0			0
$137$	−4.61126			−0.393967			−0.196983	−	0.980407i	$-0.563115\pi$
$137$	−4.61126			−0.393967			−0.196983	+	0.980407i	$0.563115\pi$
$138$		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
$141$	−1.11010	−	15.6182i	−0.0934873	−	1.31529i
$142$		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
$147$	10.9976	+	2.39748i	0.907070	+	0.197741i
$148$		0			0
$149$	−6.70786	−	14.6882i	−0.549529	−	1.20330i	−0.957001	−	0.290083i	$-0.906317\pi$
$149$	−6.70786	−	14.6882i	−0.549529	−	1.20330i	0.407473	−	0.913217i	$-0.366410\pi$
$150$		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
$153$	12.6103	−	19.5840i	1.01948	−	1.58327i
$154$		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
$159$	−0.142370	+	1.97831i	−0.0112907	+	0.156890i
$160$		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
$165$	13.1504	+	7.18823i	1.02376	+	0.559603i
$166$		0			0
$167$	17.5540	+	15.2106i	1.35837	+	1.17703i	0.966396	+	0.257057i	$0.0827530\pi$
$167$	17.5540	+	15.2106i	1.35837	+	1.17703i	0.391973	+	0.919977i	$0.371792\pi$
$168$		0			0
$169$	7.55826	−	2.21930i	0.581404	−	0.170716i
$170$		0			0
$171$	13.2892	−	15.3092i	1.01625	−	1.17072i
$172$		0			0
$173$	−23.2655	+	10.6250i	−1.76884	+	0.807804i	−0.787300	+	0.616570i	$0.788522\pi$
$173$	−23.2655	+	10.6250i	−1.76884	+	0.807804i	−0.981544	+	0.191234i	$0.938751\pi$
$174$		0			0
$175$	0.401190	−	0.624264i	0.0303271	−	0.0471899i
$176$		0			0
$177$	8.61621	−	1.87035i	0.647634	−	0.140584i
$178$		0			0
$179$	−9.54336	−	14.8498i	−0.713304	−	1.10992i	−0.988890	−	0.148646i	$-0.952508\pi$
$179$	−9.54336	−	14.8498i	−0.713304	−	1.10992i	0.275586	−	0.961276i	$-0.411128\pi$
$180$		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
$189$	3.67030	−	0.257616i	0.266975	−	0.0187388i
$190$		0			0
$191$	−0.369500	+	2.56993i	−0.0267361	+	0.185954i	−0.998813	−	0.0487088i	$-0.984489\pi$
$191$	−0.369500	+	2.56993i	−0.0267361	+	0.185954i	0.972077	+	0.234662i	$0.0753985\pi$
$192$		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
$195$	−5.50821	−	5.51308i	−0.394451	−	0.394800i
$196$		0			0
$197$	10.9504	−	1.57444i	0.780187	−	0.112174i	0.259297	−	0.965798i	$-0.416509\pi$
$197$	10.9504	−	1.57444i	0.780187	−	0.112174i	0.520890	+	0.853624i	$0.325600\pi$
$198$		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
$201$	−4.88638	−	1.82498i	−0.344659	−	0.128724i
$202$		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
$207$	12.7730	−	6.62199i	0.887784	−	0.460260i
$208$		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
$213$	−14.6107	−	5.45685i	−1.00111	−	0.373897i
$214$		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
$219$	−12.1521	−	12.1628i	−0.821163	−	0.821888i
$220$		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
$225$	−0.888419	+	3.01582i	−0.0592279	+	0.201054i
$226$		0			0
$227$	−1.02611	−	0.301292i	−0.0681050	−	0.0199974i	0.247503	−	0.968887i	$-0.420390\pi$
$227$	−1.02611	−	0.301292i	−0.0681050	−	0.0199974i	−0.315608	+	0.948890i	$0.602208\pi$
$228$		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	$0.279381\pi$
$233$	−4.80023	+	16.3481i	−0.314473	+	1.07100i	−0.953395	+	0.301726i	$0.902437\pi$
$234$		0			0
$235$	9.71589	+	15.1182i	0.633795	+	0.986204i
$236$		0			0
$237$	−20.9831	+	4.55488i	−1.36300	+	0.295872i
$238$		0			0
$239$	7.21763	−	11.2309i	0.466870	−	0.726463i	−0.525360	−	0.850880i	$-0.676070\pi$
$239$	7.21763	−	11.2309i	0.466870	−	0.726463i	0.992230	+	0.124416i	$0.0397059\pi$
$240$		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
$243$	−14.6176	+	5.41533i	−0.937719	+	0.347394i
$244$		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
$249$	10.0962	+	5.51874i	0.639821	+	0.349736i
$250$		0			0
$251$	−8.22119	+	18.0019i	−0.518917	+	1.13627i	0.450931	+	0.892559i	$0.351092\pi$
$251$	−8.22119	+	18.0019i	−0.518917	+	1.13627i	−0.969848	+	0.243710i	$0.921635\pi$
$252$		0			0
$253$	−14.4525	−	15.0614i	−0.908621	−	0.946899i
$254$		0			0
$255$	−1.91899	+	26.6654i	−0.120172	+	1.66985i
$256$		0			0
$257$	−12.3814	+	10.7286i	−0.772332	+	0.669229i	−0.949083	−	0.315026i	$-0.897987\pi$
$257$	−12.3814	+	10.7286i	−0.772332	+	0.669229i	0.176751	+	0.984256i	$0.443441\pi$
$258$		0			0
$259$	0.928994	−	1.07212i	0.0577249	−	0.0666181i
$260$		0			0
$261$	−9.74580	−	6.27542i	−0.603250	−	0.388439i
$262$		0			0
$263$	2.83561	+	19.7221i	0.174851	+	1.21612i	0.868458	+	0.495762i	$0.165111\pi$
$263$	2.83561	+	19.7221i	0.174851	+	1.21612i	−0.693607	+	0.720353i	$0.743980\pi$
$264$		0			0
$265$	−0.945686	−	2.07076i	−0.0580930	−	0.127206i
$266$		0			0
$267$	19.7389	+	4.30306i	1.20800	+	0.263343i
$268$		0			0
$269$	20.2794	+	2.91573i	1.23645	+	0.177775i	0.729369	−	0.684120i	$-0.239814\pi$
$269$	20.2794	+	2.91573i	1.23645	+	0.177775i	0.507086	+	0.861896i	$0.330723\pi$
$270$		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
$273$	0.196803	+	2.76886i	0.0119111	+	0.167579i
$274$		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
$279$	−8.15214	+	3.71426i	−0.488056	+	0.222367i
$280$		0			0
$281$	−22.8406	+	14.6788i	−1.36256	+	0.875663i	−0.998448	−	0.0556929i	$-0.982263\pi$
$281$	−22.8406	+	14.6788i	−1.36256	+	0.875663i	−0.364110	+	0.931356i	$0.618627\pi$
$282$		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
$285$	−4.95597	+	22.7339i	−0.293566	+	1.34664i
$286$		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
$291$	−10.7464	−	14.3688i	−0.629967	−	0.842312i
$292$		0			0
$293$	−6.42217	+	7.41158i	−0.375187	+	0.432989i	−0.911671	−	0.410922i	$-0.865207\pi$
$293$	−6.42217	+	7.41158i	−0.375187	+	0.432989i	0.536483	+	0.843911i	$0.319752\pi$
$294$		0			0
$295$	−7.64788	+	6.62693i	−0.445277	+	0.385835i
$296$		0			0
$297$	13.5294	+	18.1232i	0.785057	+	1.05162i
$298$		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
$303$	4.68953	−	8.57923i	0.269407	−	0.492864i
$304$		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
$309$	23.7445	−	12.9519i	1.35078	−	0.736807i
$310$		0			0
$311$	28.0072	−	12.7905i	1.58814	−	0.725280i	0.591434	−	0.806353i	$-0.298562\pi$
$311$	28.0072	−	12.7905i	1.58814	−	0.725280i	0.996708	+	0.0810730i	$0.0258347\pi$
$312$		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
$315$	−3.55460	+	2.27997i	−0.200279	+	0.128462i
$316$		0			0
$317$	4.33423	+	6.74419i	0.243435	+	0.378792i	0.941374	−	0.337365i	$-0.109536\pi$
$317$	4.33423	+	6.74419i	0.243435	+	0.378792i	−0.697939	+	0.716157i	$0.745899\pi$
$318$		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
$327$	−3.28570	−	2.46191i	−0.181700	−	0.136144i
$328$		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
$333$	−2.50161	+	5.46498i	−0.137088	+	0.299479i
$334$		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
$339$	−3.30856	+	8.85863i	−0.179696	+	0.481135i
$340$		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
$345$	−9.21844	+	13.7007i	−0.496304	+	0.737621i
$346$		0			0
$347$	−7.55571	−	3.45058i	−0.405612	−	0.185237i	0.202153	−	0.979354i	$-0.435206\pi$
$347$	−7.55571	−	3.45058i	−0.405612	−	0.185237i	−0.607764	+	0.794117i	$0.707934\pi$
$348$		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
$351$	−4.09530	−	11.0245i	−0.218591	−	0.588446i
$352$		0			0
$353$	−9.66476	−	32.9151i	−0.514403	−	1.75190i	−0.648791	−	0.760967i	$-0.724725\pi$
$353$	−9.66476	−	32.9151i	−0.514403	−	1.75190i	0.134388	−	0.990929i	$-0.457093\pi$
$354$		0			0
$355$	17.7187	−	2.54756i	0.940409	−	0.135210i
$356$		0			0
$357$	6.73633	−	6.73038i	0.356524	−	0.356210i
$358$		0			0
$359$	−8.13675	−	5.22917i	−0.429441	−	0.275985i	0.308013	−	0.951382i	$-0.400336\pi$
$359$	−8.13675	−	5.22917i	−0.429441	−	0.275985i	−0.737454	+	0.675397i	$0.763972\pi$
$360$		0			0
$361$	3.79463	−	26.3922i	0.199717	−	1.38907i
$362$		0			0
$363$	8.25090	−	11.0118i	0.433060	−	0.577968i
$364$		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
$375$	−4.41764	−	20.3508i	−0.228126	−	1.05091i
$376$		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
$381$	−9.16990	−	16.8111i	−0.469788	−	0.861258i
$382$		0			0
$383$	5.86770	−	1.72291i	0.299825	−	0.0880367i	−0.128360	−	0.991728i	$-0.540971\pi$
$383$	5.86770	−	1.72291i	0.299825	−	0.0880367i	0.428185	+	0.903691i	$0.359153\pi$
$384$		0			0
$385$	4.63035	+	4.01222i	0.235984	+	0.204482i
$386$		0			0
$387$	−2.89304	+	19.9961i	−0.147062	+	1.01646i
$388$		0			0
$389$	5.18968	−	11.3638i	0.263127	−	0.576169i	−0.731244	−	0.682116i	$-0.761060\pi$
$389$	5.18968	−	11.3638i	0.263127	−	0.576169i	0.994372	+	0.105947i	$0.0337874\pi$
$390$		0			0
$391$	13.7295	−	34.6125i	0.694329	−	1.75043i
$392$		0			0
$393$	−9.74206	−	0.701092i	−0.491422	−	0.0353654i
$394$		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
$399$	6.63682	−	4.96369i	0.332257	−	0.248495i
$400$		0			0
$401$	−4.88560	−	33.9801i	−0.243975	−	1.69689i	−0.631783	−	0.775145i	$-0.717677\pi$
$401$	−4.88560	−	33.9801i	−0.243975	−	1.69689i	0.387808	−	0.921740i	$-0.373233\pi$
$402$		0			0
$403$	−2.80763	−	6.14785i	−0.139858	−	0.306246i
$404$		0			0
$405$	11.7405	−	13.5009i	0.583388	−	0.670866i
$406$		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
$411$	7.96685	−	0.566262i	0.392976	−	0.0279317i
$412$		0			0
$413$	3.60446			0.177364
$414$		0			0
$415$	−13.2061			−0.648264
$416$		0			0
$417$	10.8917	−	0.774152i	0.533368	−	0.0379104i
$418$		0			0
$419$	−2.50929	+	1.61263i	−0.122587	+	0.0787819i	−0.600497	−	0.799627i	$-0.705031\pi$
$419$	−2.50929	+	1.61263i	−0.122587	+	0.0787819i	0.477910	+	0.878409i	$0.341394\pi$
$420$		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
$423$	3.83582	+	26.8471i	0.186504	+	1.30535i
$424$		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
$429$	−13.6639	+	10.2193i	−0.659700	+	0.493390i
$430$		0			0
$431$	−1.32252	+	1.52626i	−0.0637033	+	0.0735176i	−0.786707	−	0.617327i	$-0.788216\pi$
$431$	−1.32252	+	1.52626i	−0.0637033	+	0.0735176i	0.723003	+	0.690844i	$0.242761\pi$
$432$		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
$435$	13.2698	+	0.954968i	0.636238	+	0.0457872i
$436$		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
$441$	−19.2949	−	2.79160i	−0.918807	−	0.132933i
$442$		0			0
$443$	−5.42068	−	4.69705i	−0.257544	−	0.223164i	0.516512	−	0.856280i	$-0.327230\pi$
$443$	−5.42068	−	4.69705i	−0.257544	−	0.223164i	−0.774057	+	0.633116i	$0.781776\pi$
$444$		0			0
$445$	−22.2482	+	6.53265i	−1.05466	+	0.309677i
$446$		0			0
$447$	13.3928	+	24.5529i	0.633458	+	1.16131i
$448$		0			0
$449$	17.0929	−	7.80607i	0.806664	−	0.368391i	0.0309859	−	0.999520i	$-0.490135\pi$
$449$	17.0929	−	7.80607i	0.806664	−	0.368391i	0.775678	+	0.631129i	$0.217408\pi$
$450$		0			0
$451$	5.89444	−	9.17192i	0.277558	−	0.431889i
$452$		0			0
$453$	−1.29942	−	5.98608i	−0.0610522	−	0.281251i
$454$		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	$0.126201\pi$
$461$			16.5827i			0.772331i	−0.922430	+	0.386166i	$0.873799\pi$
$462$		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
$465$	6.16544	−	8.22848i	0.285915	−	0.381587i
$466$		0			0
$467$	−1.67750	+	11.6673i	−0.0776255	+	0.539897i	0.913487	+	0.406869i	$0.133379\pi$
$467$	−1.67750	+	11.6673i	−0.0776255	+	0.539897i	−0.991112	+	0.133029i	$0.957530\pi$
$468$		0			0
$469$	−1.79389	−	1.15286i	−0.0828341	−	0.0532342i
$470$		0			0
$471$	−20.4842	+	20.4661i	−0.943861	+	0.943028i
$472$		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
$477$	0.00303555	−	3.43539i	0.000138988	−	0.157296i
$478$		0			0
$479$	−25.3051	−	29.2036i	−1.15622	−	1.33435i	−0.933125	−	0.359551i	$-0.882930\pi$
$479$	−25.3051	−	29.2036i	−1.15622	−	1.33435i	−0.223094	−	0.974797i	$-0.571616\pi$
$480$		0			0
$481$	−4.12468	−	1.88368i	−0.188069	−	0.0858884i
$482$		0			0
$483$	5.67722	−	1.53784i	0.258322	−	0.0699741i
$484$		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
$489$	−12.3685	+	33.1164i	−0.559321	+	1.49758i
$490$		0			0
$491$	−2.84974	−	9.70534i	−0.128607	−	0.437996i	0.869863	−	0.493294i	$-0.164207\pi$
$491$	−2.84974	−	9.70534i	−0.128607	−	0.437996i	−0.998470	+	0.0552981i	$0.982389\pi$
$492$		0			0
$493$	−29.6943	+	4.26939i	−1.33736	+	0.192284i
$494$		0			0
$495$	−23.6026	−	10.8042i	−1.06086	−	0.485611i
$496$		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
$501$	−32.1958	−	24.1237i	−1.43840	−	1.07777i
$502$		0			0
$503$	−33.5865	−	9.86188i	−1.49755	−	0.439720i	−0.572606	−	0.819830i	$-0.694068\pi$
$503$	−33.5865	−	9.86188i	−1.49755	−	0.439720i	−0.924941	+	0.380111i	$0.875886\pi$
$504$		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	$-0.817613\pi$
$509$	3.60329	−	12.2717i	0.159713	−	0.543932i	0.999998	−	0.00178803i	$-0.000569147\pi$
$510$		0			0
$511$	−3.80008	−	5.91305i	−0.168106	−	0.261578i
$512$		0			0
$513$	−21.0796	+	28.0814i	−0.930689	+	1.23983i
$514$		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
$519$	38.8909	−	21.2137i	1.70712	−	0.931180i
$520$		0			0
$521$	31.1068	−	9.13379i	1.36282	−	0.400159i	0.483061	−	0.875587i	$-0.339525\pi$
$521$	31.1068	−	9.13379i	1.36282	−	0.400159i	0.879755	+	0.475428i	$0.157707\pi$
$522$		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
$525$	−0.616474	+	1.12780i	−0.0269051	+	0.0492213i
$526$		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
$531$	−14.6565	+	4.28947i	−0.636037	+	0.186147i
$532$		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
$537$	18.3115	+	24.4839i	0.790201	+	1.05656i
$538$		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
$543$	8.34962	−	38.3011i	0.358316	−	1.64366i
$544$		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
$549$	−8.61636	−	18.9114i	−0.367737	−	0.807119i
$550$		0			0
$551$	−26.1097			−1.11231
$552$		0			0
$553$	−8.77797			−0.373277
$554$		0			0
$555$	−0.489085	−	6.88102i	−0.0207605	−	0.292083i
$556$		0			0
$557$	28.9068	−	18.5773i	1.22482	−	0.787144i	0.241743	−	0.970340i	$-0.422281\pi$
$557$	28.9068	−	18.5773i	1.22482	−	0.787144i	0.983076	+	0.183196i	$0.0586444\pi$
$558$		0			0
$559$	−15.0878	−	2.16930i	−0.638148	−	0.0917518i
$560$		0			0
$561$	57.1896	+	12.4673i	2.41455	+	0.526370i
$562$		0			0
$563$	1.03633	+	2.26926i	0.0436763	+	0.0956377i	0.930212	−	0.367022i	$-0.119623\pi$
$563$	1.03633	+	2.26926i	0.0436763	+	0.0956377i	−0.886536	+	0.462659i	$0.846895\pi$
$564$		0			0
$565$	−1.54462	−	10.7430i	−0.0649825	−	0.451963i
$566$		0			0
$567$	−6.30951	+	0.895793i	−0.264975	+	0.0376198i
$568$		0			0
$569$	−6.01806	+	6.94521i	−0.252290	+	0.291158i	−0.867741	−	0.497017i	$-0.834429\pi$
$569$	−6.01806	+	6.94521i	−0.252290	+	0.291158i	0.615451	+	0.788175i	$0.288974\pi$
$570$		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
$573$	0.322796	−	4.48542i	0.0134850	−	0.187381i
$574$		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
$579$	−16.8828	−	9.22838i	−0.701624	−	0.383518i
$580$		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
$585$	10.1935	+	8.84850i	0.421449	+	0.365840i
$586$		0			0
$587$	−18.6700	+	8.52630i	−0.770593	+	0.351918i	−0.761605	−	0.648041i	$-0.775588\pi$
$587$	−18.6700	+	8.52630i	−0.770593	+	0.351918i	−0.00898833	+	0.999960i	$0.502861\pi$
$588$		0			0
$589$	−10.9095	+	16.9755i	−0.449517	+	0.699462i
$590$		0			0
$591$	−18.7256	+	4.06485i	−0.770270	+	0.167206i
$592$		0			0
$593$	5.02730	+	7.82263i	0.206446	+	0.321237i	0.929001	−	0.370077i	$-0.120669\pi$
$593$	5.02730	+	7.82263i	0.206446	+	0.321237i	−0.722555	+	0.691314i	$0.757032\pi$
$594$		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	$0.185699\pi$
$599$			26.9638i			1.10171i	−0.834600	+	0.550856i	$0.814301\pi$
$600$		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
$603$	8.66626	+	2.55296i	0.352918	+	0.103965i
$604$		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
$609$	−3.34932	−	3.35228i	−0.135721	−	0.135841i
$610$		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
$615$	−8.07995	−	3.01773i	−0.325815	−	0.121687i
$616$		0			0
$617$	−12.7759	−	14.7442i	−0.514339	−	0.593579i	0.437865	−	0.899041i	$-0.355735\pi$
$617$	−12.7759	−	14.7442i	−0.514339	−	0.593579i	−0.952204	+	0.305462i	$0.901189\pi$
$618$		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
$621$	−21.2546	+	13.0093i	−0.852918	+	0.522045i
$622$		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
$627$	47.7232	+	17.8239i	1.90588	+	0.711817i
$628$		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
$633$	−11.6551	−	11.6654i	−0.463248	−	0.463657i
$634$		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
$639$	25.9128	+	7.63358i	1.02510	+	0.301980i
$640$		0			0
$641$	4.54533	+	1.33463i	0.179530	+	0.0527146i	0.370262	−	0.928927i	$-0.379268\pi$
$641$	4.54533	+	1.33463i	0.179530	+	0.0527146i	−0.190732	+	0.981642i	$0.561086\pi$
$642$		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	−0.963964	−	0.266033i	$-0.914287\pi$
$647$	−0.233954	+	0.796772i	−0.00919766	+	0.0313244i	0.954766	+	0.297357i	$0.0961052\pi$
$648$		0			0
$649$	11.9785	+	18.6389i	0.470197	+	0.731641i
$650$		0			0
$651$	−3.57897	+	0.776902i	−0.140271	+	0.0304492i
$652$		0			0
$653$	−11.9152	+	18.5404i	−0.466277	+	0.725541i	−0.992154	−	0.125019i	$-0.960101\pi$
$653$	−11.9152	+	18.5404i	−0.466277	+	0.725541i	0.525877	+	0.850560i	$0.323737\pi$
$654$		0			0
$655$	10.1973	−	4.65697i	0.398443	−	0.181963i
$656$		0			0
$657$	22.4887	+	19.5214i	0.877367	+	0.761601i
$658$		0			0
$659$	−2.77548	+	0.814955i	−0.108117	+	0.0317461i	−0.335344	−	0.942096i	$-0.608852\pi$
$659$	−2.77548	+	0.814955i	−0.108117	+	0.0317461i	0.227226	+	0.973842i	$0.427034\pi$
$660$		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
$663$	−26.7078	−	14.5989i	−1.03725	−	0.566974i
$664$		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
$669$	−2.80421	+	38.9660i	−0.108417	+	1.50651i
$670$		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
$675$	1.16457	−	5.31950i	0.0448244	−	0.204748i
$676$		0			0
$677$	−1.55771	−	10.8341i	−0.0598677	−	0.416389i	−0.997612	−	0.0690632i	$-0.977999\pi$
$677$	−1.55771	−	10.8341i	−0.0598677	−	0.416389i	0.937745	−	0.347325i	$-0.112910\pi$
$678$		0			0
$679$	−3.04720	−	6.67243i	−0.116941	−	0.256065i
$680$		0			0
$681$	1.80979	+	0.394534i	0.0693514	+	0.0151186i
$682$		0			0
$683$	−39.6246	−	5.69716i	−1.51619	−	0.217996i	−0.666593	−	0.745422i	$-0.732248\pi$
$683$	−39.6246	−	5.69716i	−1.51619	−	0.217996i	−0.849601	+	0.527426i	$0.823157\pi$
$684$		0			0
$685$	−7.71181	+	4.95608i	−0.294653	+	0.189362i
$686$		0			0
$687$	1.06645	+	15.0041i	0.0406876	+	0.572442i
$688$		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
$693$	3.83344	+	8.41372i	0.145620	+	0.319611i
$694$		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
$699$	6.28578	−	28.8339i	0.237750	−	1.09060i
$700$		0			0
$701$	15.2962	+	33.4941i	0.577731	+	1.26506i	0.942578	+	0.333987i	$0.108394\pi$
$701$	15.2962	+	33.4941i	0.577731	+	1.26506i	−0.364846	+	0.931068i	$0.618878\pi$
$702$		0			0
$703$	1.92669	+	13.4005i	0.0726666	+	0.505408i
$704$		0			0
$705$	−18.6426	−	24.9265i	−0.702120	−	0.938787i
$706$		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
$711$	35.6930	−	10.4462i	1.33859	−	0.391762i
$712$		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
$717$	−11.0907	+	20.2898i	−0.414190	+	0.757736i
$718$		0			0
$719$	−31.9012	−	27.6426i	−1.18972	−	1.03089i	−0.998784	−	0.0492908i	$-0.984304\pi$
$719$	−31.9012	−	27.6426i	−1.18972	−	1.03089i	−0.190931	−	0.981603i	$-0.561151\pi$
$720$		0			0
$721$	10.6094	−	3.11520i	0.395115	−	0.116016i
$722$		0			0
$723$	8.53563	−	4.65591i	0.317443	−	0.173155i
$724$		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
$729$	24.5897	−	11.1511i	0.910730	−	0.413002i
$730$		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
$741$	−21.1999	−	15.8847i	−0.778797	−	0.583537i
$742$		0			0
$743$	4.99792	−	34.7613i	0.183356	−	1.27527i	−0.665402	−	0.746485i	$-0.731740\pi$
$743$	4.99792	−	34.7613i	0.183356	−	1.27527i	0.848758	−	0.528782i	$-0.177351\pi$
$744$		0			0
$745$	−27.0046	−	17.3548i	−0.989372	−	0.635831i
$746$		0			0
$747$	−18.1208	−	8.29487i	−0.663007	−	0.303493i
$748$		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
$753$	11.9931	−	32.1113i	0.437051	−	1.17020i
$754$		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
$759$	26.8190	+	24.2466i	0.973468	+	0.880097i
$760$		0			0
$761$	39.3321	+	17.9623i	1.42579	+	0.651135i	0.970915	−	0.239423i	$-0.0769583\pi$
$761$	39.3321	+	17.9623i	1.42579	+	0.651135i	0.454871	+	0.890558i	$0.349686\pi$
$762$		0			0
$763$	−1.09917	−	1.26851i	−0.0397925	−	0.0459230i
$764$		0			0
$765$	0.0409158	−	46.3052i	0.00147931	−	1.67417i
$766$		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
$771$	20.0738	−	20.0561i	0.722941	−	0.722302i
$772$		0			0
$773$	−3.11036	−	1.99891i	−0.111872	−	0.0718958i	0.483508	−	0.875340i	$-0.339362\pi$
$773$	−3.11036	−	1.99891i	−0.111872	−	0.0718958i	−0.595380	+	0.803444i	$0.702999\pi$
$774$		0			0
$775$	0.445363	−	3.09757i	0.0159979	−	0.111268i
$776$		0			0
$777$	−1.47336	+	1.96637i	−0.0528565	+	0.0705430i
$778$		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
$789$	−7.32092	−	33.7255i	−0.260632	−	1.20066i
$790$		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
$795$	1.88814	+	3.46151i	0.0669655	+	0.122767i
$796$		0			0
$797$	−12.1312	+	3.56205i	−0.429710	+	0.126174i	−0.489433	−	0.872041i	$-0.662796\pi$
$797$	−12.1312	+	3.56205i	−0.429710	+	0.126174i	0.0597232	+	0.998215i	$0.480978\pi$
$798$		0			0
$799$	53.0447	+	45.9635i	1.87658	+	1.62607i
$800$		0			0
$801$	−34.6311	−	5.01043i	−1.22363	−	0.177035i
$802$		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
$807$	−35.3946	−	2.54719i	−1.24595	−	0.0896652i
$808$		0			0
$809$	−1.61595	+	1.40023i	−0.0568138	+	0.0492294i	−0.682805	−	0.730601i	$-0.739240\pi$
$809$	−1.61595	+	1.40023i	−0.0568138	+	0.0492294i	0.625991	+	0.779830i	$0.284695\pi$
$810$		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
$813$	1.11127	−	0.831120i	0.0389739	−	0.0291487i
$814$		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
$819$	−0.680031	−	4.75957i	−0.0237622	−	0.166313i
$820$		0			0
$821$	−18.1336	−	2.60722i	−0.632868	−	0.0909927i	−0.181587	−	0.983375i	$-0.558124\pi$
$821$	−18.1336	−	2.60722i	−0.632868	−	0.0909927i	−0.451281	+	0.892382i	$0.649033\pi$
$822$		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
$825$	−7.88062	+	0.560134i	−0.274368	+	0.0195014i
$826$		0			0
$827$	7.84516			0.272803			0.136401	−	0.990654i	$-0.456446\pi$
$827$	7.84516			0.272803			0.136401	+	0.990654i	$0.456446\pi$
$828$		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
$831$	32.9233	−	2.34010i	1.14210	−	0.0811771i
$832$		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
$837$	13.6283	−	7.41817i	0.471062	−	0.256410i
$838$		0			0
$839$	5.75380	+	12.5991i	0.198643	+	0.434968i	0.982572	−	0.185883i	$-0.0595145\pi$
$839$	5.75380	+	12.5991i	0.198643	+	0.434968i	−0.783929	+	0.620851i	$0.786787\pi$
$840$		0			0
$841$	−2.00250	−	13.9277i	−0.0690518	−	0.480266i
$842$		0			0
$843$	37.6590	−	28.1652i	1.29705	−	0.970063i
$844$		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
$849$	−27.0817	−	1.94895i	−0.929440	−	0.0668876i
$850$		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
$855$	5.77068	−	39.8857i	0.197353	−	1.36406i
$856$		0			0
$857$	−15.0495	−	13.0404i	−0.514080	−	0.445453i	0.358781	−	0.933422i	$-0.383193\pi$
$857$	−15.0495	−	13.0404i	−0.514080	−	0.445453i	−0.872861	+	0.487969i	$0.837738\pi$
$858$		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
$861$	1.47113	+	2.69701i	0.0501360	+	0.0919137i
$862$		0			0
$863$	7.27482	−	3.32230i	0.247638	−	0.113092i	−0.287730	−	0.957712i	$-0.592900\pi$
$863$	7.27482	−	3.32230i	0.247638	−	0.113092i	0.535367	+	0.844619i	$0.320173\pi$
$864$		0			0
$865$	−27.4894	+	42.7743i	−0.934667	+	1.45437i
$866$		0			0
$867$	15.9035	+	73.2630i	0.540111	+	2.48814i
$868$		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
$879$	10.1854	−	13.5936i	0.343545	−	0.458500i
$880$		0			0
$881$	4.26249	−	29.6462i	0.143607	−	0.998807i	−0.782797	−	0.622277i	$-0.786208\pi$
$881$	4.26249	−	29.6462i	0.143607	−	0.998807i	0.926404	−	0.376530i	$-0.122883\pi$
$882$		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
$885$	12.3994	−	12.3885i	0.416801	−	0.416433i
$886$		0			0
$887$	−53.7947	+	7.73452i	−1.80625	+	0.259700i	−0.961371	−	0.275256i	$-0.911237\pi$
$887$	−53.7947	+	7.73452i	−1.80625	+	0.259700i	−0.844880	+	0.534956i	$0.820328\pi$
$888$		0			0
$889$	−2.20556	−	7.51144i	−0.0739720	−	0.251926i
$890$		0			0
$891$	−25.6002	−	29.6499i	−0.857639	−	0.993310i
$892$		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
$897$	−9.82893	−	16.0267i	−0.328178	−	0.535116i
$898$		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
$903$	−2.88993	+	7.73775i	−0.0961707	+	0.257496i
$904$		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
$909$	−7.04854	+	15.3981i	−0.233785	+	0.510724i
$910$		0			0
$911$	24.3178	+	15.6281i	0.805684	+	0.517781i	0.877466	−	0.479639i	$-0.159232\pi$
$911$	24.3178	+	15.6281i	0.805684	+	0.517781i	−0.0717823	+	0.997420i	$0.522869\pi$
$912$		0			0
$913$	−4.11487	+	28.6196i	−0.136182	+	0.947169i
$914$		0			0
$915$	19.0885	+	14.3026i	0.631046	+	0.472831i
$916$		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
$927$	−39.4328	+	25.2927i	−1.29514	+	0.830721i
$928$		0			0
$929$	2.16506	−	3.36889i	0.0710332	−	0.110530i	−0.803920	−	0.594738i	$-0.797256\pi$
$929$	2.16506	−	3.36889i	0.0710332	−	0.110530i	0.874953	+	0.484208i	$0.160892\pi$
$930$		0			0
$931$	−39.9458	+	18.2427i	−1.30917	+	0.597879i
$932$		0			0
$933$	−46.8171	+	25.5373i	−1.53272	+	0.836052i
$934$		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
$939$	6.94550	−	12.7064i	0.226658	−	0.414657i
$940$		0			0
$941$	−0.0414774	+	0.0908229i	−0.00135213	+	0.00296074i	−0.910307	−	0.413934i	$-0.864154\pi$
$941$	−0.0414774	+	0.0908229i	−0.00135213	+	0.00296074i	0.908955	+	0.416895i	$0.136882\pi$
$942$		0			0
$943$	9.46651	+	7.39605i	0.308272	+	0.240849i
$944$		0			0
$945$	5.86127	−	4.37558i	0.190667	−	0.142338i
$946$		0			0
$947$	33.8033	−	29.2907i	1.09846	−	0.951820i	0.0993934	−	0.995048i	$-0.468310\pi$
$947$	33.8033	−	29.2907i	1.09846	−	0.951820i	0.999065	+	0.0432285i	$0.0137643\pi$
$948$		0			0
$949$	−14.7128	+	16.9794i	−0.477596	+	0.551176i
$950$		0			0
$951$	−8.31640	−	11.1196i	−0.269678	−	0.360579i
$952$		0			0
$953$	2.66935	+	18.5657i	0.0864688	+	0.601403i	0.986275	+	0.165113i	$0.0527989\pi$
$953$	2.66935	+	18.5657i	0.0864688	+	0.601403i	−0.899806	+	0.436290i	$0.856292\pi$
$954$		0			0
$955$	2.14415	+	4.69504i	0.0693832	+	0.151928i
$956$		0			0
$957$	6.20426	−	28.4600i	0.200555	−	0.919980i
$958$		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
$963$	15.3154	−	6.97795i	0.493531	−	0.224861i
$964$		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
$969$	6.44291	+	90.6465i	0.206976	+	2.91198i
$970$		0			0
$971$	−2.74903	+	1.76669i	−0.0882206	+	0.0566959i	−0.584007	−	0.811748i	$-0.698516\pi$
$971$	−2.74903	+	1.76669i	−0.0882206	+	0.0566959i	0.495787	+	0.868444i	$0.334880\pi$
$972$		0			0
$973$	4.41847	+	0.635281i	0.141650	+	0.0203662i
$974$		0			0
$975$	4.01403	+	0.875057i	0.128552	+	0.0280243i
$976$		0			0
$977$	−6.02689	−	13.1970i	−0.192817	−	0.422211i	0.788388	−	0.615178i	$-0.210916\pi$
$977$	−6.02689	−	13.1970i	−0.192817	−	0.422211i	−0.981205	+	0.192968i	$0.938189\pi$
$978$		0			0
$979$	7.22492	+	50.2504i	0.230909	+	1.60601i
$980$		0			0
$981$	5.97901	+	3.84995i	0.190895	+	0.122919i
$982$		0			0
$983$	20.2767	−	23.4005i	0.646725	−	0.746361i	−0.333824	−	0.942636i	$-0.608339\pi$
$983$	20.2767	−	23.4005i	0.646725	−	0.746361i	0.980549	+	0.196275i	$0.0628845\pi$
$984$		0			0
$985$	16.6212	−	14.4023i	0.529595	−	0.458897i
$986$		0			0
$987$	−0.795819	+	11.0583i	−0.0253312	+	0.351991i
$988$		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
$993$	−4.16451	−	2.27638i	−0.132157	−	0.0722389i
$994$		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
$999$	3.65092	−	9.74901i	0.115510	−	0.308445i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.72769 + 0.122800i) q^{3} +(1.67238 - 1.07478i) q^{5} +(-0.700880 - 0.100771i) q^{7} +(2.96984 - 0.424320i) q^{9} +O(q^{10})\)	\(q+(-1.72769 + 0.122800i) q^{3} +(1.67238 - 1.07478i) q^{5} +(-0.700880 - 0.100771i) q^{7} +(2.96984 - 0.424320i) q^{9} +(-1.80810 - 3.95918i) q^{11} +(0.322105 + 2.24029i) q^{13} +(-2.75738 + 2.06225i) q^{15} +(5.08450 - 5.86783i) q^{17} +(5.10697 - 4.42521i) q^{19} +(1.22328 + 0.0880339i) q^{21} +(4.52706 - 1.58294i) q^{23} +(-0.435348 + 0.953280i) q^{25} +(-5.07886 + 1.09779i) q^{27} +(-2.92008 - 2.53026i) q^{29} +(-2.86518 + 0.841292i) q^{31} +(3.61002 + 6.61821i) q^{33} +(-1.28045 + 0.584761i) q^{35} +(-1.08314 + 1.68540i) q^{37} +(-0.831606 - 3.83098i) q^{39} +(1.35426 + 2.10727i) q^{41} +(-1.89740 + 6.46196i) q^{43} +(4.51067 - 3.90154i) q^{45} +9.03992i q^{47} +(-6.23537 - 1.83087i) q^{49} +(-8.06388 + 10.7622i) q^{51} +(0.162969 - 1.13348i) q^{53} +(-7.27907 - 4.67797i) q^{55} +(-8.27985 + 8.27254i) q^{57} +(-5.03861 + 0.724443i) q^{59} +(-1.95164 - 6.64666i) q^{61} +(-2.12426 - 0.00187702i) q^{63} +(2.94650 + 3.40044i) q^{65} +(2.73935 + 1.25102i) q^{67} +(-7.62699 + 3.29075i) q^{69} +(8.19088 + 3.74065i) q^{71} +(6.50050 + 7.50197i) q^{73} +(0.635085 - 1.70043i) q^{75} +(0.868287 + 2.95711i) q^{77} +(12.2706 - 1.76424i) q^{79} +(8.63990 - 2.52033i) q^{81} +(-5.58848 - 3.59150i) q^{83} +(2.19664 - 15.2780i) q^{85} +(5.35571 + 4.01293i) q^{87} +(-11.1914 - 3.28610i) q^{89} -1.60263i q^{91} +(4.84683 - 1.80534i) q^{93} +(3.78470 - 12.8895i) q^{95} +(5.60068 + 8.71483i) q^{97} +(-7.04972 - 10.9909i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 2 q^{3} + 6 q^{9}+O(q^{10}) \) 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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