LMFDB - Embedded newform 276.2.i.a.133.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(13,276)]

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, 0, 14]))

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

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

chi := DirichletCharacter("276.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.i (of order $11$, 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:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} + 43 x^{18} - 165 x^{17} + 538 x^{16} - 1433 x^{15} + 3444 x^{14} - 7370 x^{13} + \cdots + 529 $ x^20 - 8x^19 + 43x^18 - 165x^17 + 538x^16 - 1433x^15 + 3444x^14 - 7370x^13 + 15500x^12 - 28190x^11 + 41920x^10 - 33520x^9 - 13837x^8 + 78980x^7 - 92652x^6 - 52852x^5 + 177374x^4 + 151360x^3 + 115323x^2 + 12834*x + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			133.2
Root			$1.02355 + 2.24127i$ of defining polynomial
Character	$\chi$	$=$	276.133
Dual form			276.2.i.a.193.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.654861 + 0.755750i) q^{3} +(0.217172 - 1.51046i) q^{5} +(-1.55685 - 3.40903i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})$	\(q+(-0.654861 + 0.755750i) q^{3} +(0.217172 - 1.51046i) q^{5} +(-1.55685 - 3.40903i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(1.04445 - 0.306679i) q^{11} +(1.25796 - 2.75455i) q^{13} +(0.999315 + 1.15327i) q^{15} +(2.61063 - 1.67775i) q^{17} +(-3.49220 - 2.24430i) q^{19} +(3.59589 + 1.05585i) q^{21} +(2.35317 + 4.17883i) q^{23} +(2.56313 + 0.752602i) q^{25} +(0.841254 + 0.540641i) q^{27} +(2.24106 - 1.44024i) q^{29} +(-4.45761 - 5.14435i) q^{31} +(-0.452198 + 0.990176i) q^{33} +(-5.48731 + 1.61122i) q^{35} +(-0.973540 - 6.77112i) q^{37} +(1.25796 + 2.75455i) q^{39} +(-1.41678 + 9.85394i) q^{41} +(-2.62449 + 3.02882i) q^{43} -1.52600 q^{45} -1.56940 q^{47} +(-4.61365 + 5.32444i) q^{49} +(-0.441641 + 3.07168i) q^{51} +(-1.19196 - 2.61003i) q^{53} +(-0.236402 - 1.64421i) q^{55} +(3.98303 - 1.16952i) q^{57} +(-6.11707 + 13.3945i) q^{59} +(3.42833 + 3.95650i) q^{61} +(-3.15276 + 2.02616i) q^{63} +(-3.88745 - 2.49831i) q^{65} +(4.44565 + 1.30536i) q^{67} +(-4.69914 - 0.958148i) q^{69} +(14.6278 + 4.29512i) q^{71} +(2.70682 + 1.73957i) q^{73} +(-2.24727 + 1.44423i) q^{75} +(-2.67153 - 3.08311i) q^{77} +(-1.28701 + 2.81816i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(-0.773779 - 5.38175i) q^{83} +(-1.96723 - 4.30763i) q^{85} +(-0.379120 + 2.63684i) q^{87} +(9.86433 - 11.3840i) q^{89} -11.3488 q^{91} +6.80696 q^{93} +(-4.14834 + 4.78744i) q^{95} +(0.546130 - 3.79842i) q^{97} +(-0.452198 - 0.990176i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9	$ 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9} - 22 q^{13} + 7 q^{15} + 7 q^{17} + 19 q^{19} + 20 q^{23} + 20 q^{25} - 2 q^{27} + 32 q^{29} - 3 q^{31} + 11 q^{33} - 26 q^{35} - 10 q^{37} - 22 q^{39} - 40 q^{41} + 8 q^{43} - 4 q^{45} - 18 q^{47} - 34 q^{49} - 26 q^{51} - 34 q^{53} - 17 q^{55} - 3 q^{57} - 32 q^{59} + 32 q^{61} + 49 q^{65} + 35 q^{67} - 2 q^{69} + 33 q^{71} - q^{73} - 2 q^{75} - 50 q^{77} + 22 q^{79} - 2 q^{81} - 14 q^{83} - 9 q^{85} - 12 q^{87} + 10 q^{89} - 72 q^{91} + 30 q^{93} - 51 q^{95} - 4 q^{97} + 11 q^{99}+O(q^{100}) $ 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9 - 22 * q^13 + 7 * q^15 + 7 * q^17 + 19 * q^19 + 20 * q^23 + 20 * q^25 - 2 * q^27 + 32 * q^29 - 3 * q^31 + 11 * q^33 - 26 * q^35 - 10 * q^37 - 22 * q^39 - 40 * q^41 + 8 * q^43 - 4 * q^45 - 18 * q^47 - 34 * q^49 - 26 * q^51 - 34 * q^53 - 17 * q^55 - 3 * q^57 - 32 * q^59 + 32 * q^61 + 49 * q^65 + 35 * q^67 - 2 * q^69 + 33 * q^71 - q^73 - 2 * q^75 - 50 * q^77 + 22 * q^79 - 2 * q^81 - 14 * q^83 - 9 * q^85 - 12 * q^87 + 10 * q^89 - 72 * q^91 + 30 * q^93 - 51 * q^95 - 4 * q^97 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{6}{11}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$3$	−0.654861	+	0.755750i	−0.378084	+	0.436332i
$4$		0			0
$5$	0.217172	−	1.51046i	0.0971222	−	0.675500i	−0.881854	−	0.471523i	$-0.843704\pi$
$5$	0.217172	−	1.51046i	0.0971222	−	0.675500i	0.978976	−	0.203977i	$-0.0653866\pi$
$6$		0			0
$7$	−1.55685	−	3.40903i	−0.588434	−	1.28849i	−0.936384	−	0.350977i	$-0.885849\pi$
$7$	−1.55685	−	3.40903i	−0.588434	−	1.28849i	0.347950	−	0.937513i	$-0.386878\pi$
$8$		0			0
$9$	−0.142315	−	0.989821i	−0.0474383	−	0.329940i
$10$		0			0
$11$	1.04445	−	0.306679i	0.314914	−	0.0924671i	−0.120456	−	0.992719i	$-0.538436\pi$
$11$	1.04445	−	0.306679i	0.314914	−	0.0924671i	0.435370	+	0.900252i	$0.356617\pi$
$12$		0			0
$13$	1.25796	−	2.75455i	0.348895	−	0.763974i	−0.651092	−	0.758999i	$-0.725689\pi$
$13$	1.25796	−	2.75455i	0.348895	−	0.763974i	0.999988	−	0.00497557i	$-0.00158378\pi$
$14$		0			0
$15$	0.999315	+	1.15327i	0.258022	+	0.297773i
$16$		0			0
$17$	2.61063	−	1.67775i	0.633171	−	0.406915i	−0.184311	−	0.982868i	$-0.559005\pi$
$17$	2.61063	−	1.67775i	0.633171	−	0.406915i	0.817483	+	0.575953i	$0.195369\pi$
$18$		0			0
$19$	−3.49220	−	2.24430i	−0.801166	−	0.514878i	0.0748303	−	0.997196i	$-0.476158\pi$
$19$	−3.49220	−	2.24430i	−0.801166	−	0.514878i	−0.875996	+	0.482318i	$0.839795\pi$
$20$		0			0
$21$	3.59589	+	1.05585i	0.784687	+	0.230405i
$22$		0			0
$23$	2.35317	+	4.17883i	0.490669	+	0.871346i
$23$	2.35317	+	4.17883i	0.490669	+	0.871346i
$24$		0			0
$25$	2.56313	+	0.752602i	0.512626	+	0.150520i
$26$		0			0
$27$	0.841254	+	0.540641i	0.161899	+	0.104046i
$28$		0			0
$29$	2.24106	−	1.44024i	0.416154	−	0.267446i	−0.315765	−	0.948837i	$-0.602261\pi$
$29$	2.24106	−	1.44024i	0.416154	−	0.267446i	0.731919	+	0.681391i	$0.238625\pi$
$30$		0			0
$31$	−4.45761	−	5.14435i	−0.800610	−	0.923953i	0.197804	−	0.980241i	$-0.436619\pi$
$31$	−4.45761	−	5.14435i	−0.800610	−	0.923953i	−0.998415	+	0.0562882i	$0.982073\pi$
$32$		0			0
$33$	−0.452198	+	0.990176i	−0.0787176	+	0.172368i
$34$		0			0
$35$	−5.48731	+	1.61122i	−0.927525	+	0.272346i
$36$		0			0
$37$	−0.973540	−	6.77112i	−0.160049	−	1.11317i	−0.898537	−	0.438898i	$-0.855369\pi$
$37$	−0.973540	−	6.77112i	−0.160049	−	1.11317i	0.738488	−	0.674267i	$-0.235540\pi$
$38$		0			0
$39$	1.25796	+	2.75455i	0.201435	+	0.441081i
$40$		0			0
$41$	−1.41678	+	9.85394i	−0.221264	+	1.53893i	0.512001	+	0.858985i	$0.328904\pi$
$41$	−1.41678	+	9.85394i	−0.221264	+	1.53893i	−0.733265	+	0.679943i	$0.762005\pi$
$42$		0			0
$43$	−2.62449	+	3.02882i	−0.400231	+	0.461891i	−0.919714	−	0.392590i	$-0.871579\pi$
$43$	−2.62449	+	3.02882i	−0.400231	+	0.461891i	0.519483	+	0.854481i	$0.326125\pi$
$44$		0			0
$45$	−1.52600			−0.227482
$46$		0			0
$47$	−1.56940			−0.228921			−0.114461	−	0.993428i	$-0.536514\pi$
$47$	−1.56940			−0.228921			−0.114461	+	0.993428i	$0.536514\pi$
$48$		0			0
$49$	−4.61365	+	5.32444i	−0.659093	+	0.760634i
$50$		0			0
$51$	−0.441641	+	3.07168i	−0.0618421	+	0.430121i
$52$		0			0
$53$	−1.19196	−	2.61003i	−0.163728	−	0.358515i	0.809930	−	0.586526i	$-0.199505\pi$
$53$	−1.19196	−	2.61003i	−0.163728	−	0.358515i	−0.973658	+	0.228011i	$0.926778\pi$
$54$		0			0
$55$	−0.236402	−	1.64421i	−0.0318764	−	0.221705i
$56$		0			0
$57$	3.98303	−	1.16952i	0.527566	−	0.154907i
$58$		0			0
$59$	−6.11707	+	13.3945i	−0.796374	+	1.74382i	−0.138946	+	0.990300i	$0.544371\pi$
$59$	−6.11707	+	13.3945i	−0.796374	+	1.74382i	−0.657429	+	0.753517i	$0.728356\pi$
$60$		0			0
$61$	3.42833	+	3.95650i	0.438952	+	0.506578i	0.931517	−	0.363698i	$-0.118486\pi$
$61$	3.42833	+	3.95650i	0.438952	+	0.506578i	−0.492565	+	0.870276i	$0.663940\pi$
$62$		0			0
$63$	−3.15276	+	2.02616i	−0.397211	+	0.255272i
$64$		0			0
$65$	−3.88745	−	2.49831i	−0.482179	−	0.309878i
$66$		0			0
$67$	4.44565	+	1.30536i	0.543123	+	0.159475i	0.541775	−	0.840524i	$-0.317753\pi$
$67$	4.44565	+	1.30536i	0.543123	+	0.159475i	0.00134834	+	0.999999i	$0.499571\pi$
$68$		0			0
$69$	−4.69914	−	0.958148i	−0.565710	−	0.115347i
$70$		0			0
$71$	14.6278	+	4.29512i	1.73600	+	0.509736i	0.988066	−	0.154033i	$-0.0492263\pi$
$71$	14.6278	+	4.29512i	1.73600	+	0.509736i	0.747937	+	0.663770i	$0.231044\pi$
$72$		0			0
$73$	2.70682	+	1.73957i	0.316809	+	0.203601i	0.689375	−	0.724405i	$-0.257885\pi$
$73$	2.70682	+	1.73957i	0.316809	+	0.203601i	−0.372566	+	0.928006i	$0.621522\pi$
$74$		0			0
$75$	−2.24727	+	1.44423i	−0.259492	+	0.166766i
$76$		0			0
$77$	−2.67153	−	3.08311i	−0.304449	−	0.351353i
$78$		0			0
$79$	−1.28701	+	2.81816i	−0.144800	+	0.317068i	−0.968111	−	0.250523i	$-0.919397\pi$
$79$	−1.28701	+	2.81816i	−0.144800	+	0.317068i	0.823311	+	0.567591i	$0.192125\pi$
$80$		0			0
$81$	−0.959493	+	0.281733i	−0.106610	+	0.0313036i
$82$		0			0
$83$	−0.773779	−	5.38175i	−0.0849333	−	0.590724i	−0.987193	−	0.159531i	$-0.949002\pi$
$83$	−0.773779	−	5.38175i	−0.0849333	−	0.590724i	0.902260	−	0.431193i	$-0.141907\pi$
$84$		0			0
$85$	−1.96723	−	4.30763i	−0.213376	−	0.467228i
$86$		0			0
$87$	−0.379120	+	2.63684i	−0.0406459	+	0.282699i
$88$		0			0
$89$	9.86433	−	11.3840i	1.04562	−	1.20671i	0.0677018	−	0.997706i	$-0.478433\pi$
$89$	9.86433	−	11.3840i	1.04562	−	1.20671i	0.977915	−	0.209001i	$-0.0670212\pi$
$90$		0			0
$91$	−11.3488			−1.18968
$92$		0			0
$93$	6.80696			0.705848
$94$		0			0
$95$	−4.14834	+	4.78744i	−0.425611	+	0.491181i
$96$		0			0
$97$	0.546130	−	3.79842i	0.0554511	−	0.385671i	−0.943130	−	0.332423i	$-0.892134\pi$
$97$	0.546130	−	3.79842i	0.0554511	−	0.385671i	0.998581	−	0.0532474i	$-0.0169572\pi$
$98$		0			0
$99$	−0.452198	−	0.990176i	−0.0454476	−	0.0995164i
$100$		0			0
$101$	1.05517	+	7.33887i	0.104993	+	0.730245i	0.972514	+	0.232844i	$0.0748031\pi$
$101$	1.05517	+	7.33887i	0.104993	+	0.730245i	−0.867521	+	0.497401i	$0.834288\pi$
$102$		0			0
$103$	12.7260	−	3.73670i	1.25393	−	0.368188i	0.413700	−	0.910413i	$-0.364236\pi$
$103$	12.7260	−	3.73670i	1.25393	−	0.368188i	0.840233	+	0.542225i	$0.182418\pi$
$104$		0			0
$105$	2.37575	−	5.20216i	0.231849	−	0.507679i
$106$		0			0
$107$	0.152798	+	0.176338i	0.0147716	+	0.0170473i	0.763087	−	0.646295i	$-0.223683\pi$
$107$	0.152798	+	0.176338i	0.0147716	+	0.0170473i	−0.748316	+	0.663343i	$0.769137\pi$
$108$		0			0
$109$	−9.97148	+	6.40828i	−0.955095	+	0.613802i	−0.922636	−	0.385671i	$-0.873970\pi$
$109$	−9.97148	+	6.40828i	−0.955095	+	0.613802i	−0.0324583	+	0.999473i	$0.510334\pi$
$110$		0			0
$111$	5.75481	+	3.69839i	0.546222	+	0.351036i
$112$		0			0
$113$	7.65402	+	2.24742i	0.720030	+	0.211420i	0.621164	−	0.783681i	$-0.286660\pi$
$113$	7.65402	+	2.24742i	0.720030	+	0.211420i	0.0988662	+	0.995101i	$0.468478\pi$
$114$		0			0
$115$	6.82301	−	2.64685i	0.636249	−	0.246820i
$116$		0			0
$117$	−2.90554	−	0.853143i	−0.268617	−	0.0788731i
$118$		0			0
$119$	−9.78386	−	6.28771i	−0.896885	−	0.576393i
$120$		0			0
$121$	−8.25696	+	5.30643i	−0.750633	+	0.482402i
$122$		0			0
$123$	−6.51932	−	7.52369i	−0.587827	−	0.678389i
$124$		0			0
$125$	4.86303	−	10.6485i	0.434962	−	0.952435i
$126$		0			0
$127$	9.85281	−	2.89305i	0.874296	−	0.256716i	0.186354	−	0.982483i	$-0.440333\pi$
$127$	9.85281	−	2.89305i	0.874296	−	0.256716i	0.687941	+	0.725766i	$0.258515\pi$
$128$		0			0
$129$	−0.570356	−	3.96691i	−0.0502170	−	0.349267i
$130$		0			0
$131$	−8.47190	−	18.5509i	−0.740193	−	1.62080i	−0.783237	−	0.621724i	$-0.786433\pi$
$131$	−8.47190	−	18.5509i	−0.740193	−	1.62080i	0.0430434	−	0.999073i	$-0.486295\pi$
$132$		0			0
$133$	−2.21405	+	15.3990i	−0.191982	+	1.33527i
$134$		0			0
$135$	0.999315	−	1.15327i	0.0860073	−	0.0992578i
$136$		0			0
$137$	9.77788			0.835380			0.417690	−	0.908590i	$-0.362840\pi$
$137$	9.77788			0.835380			0.417690	+	0.908590i	$0.362840\pi$
$138$		0			0
$139$	−3.43414			−0.291280			−0.145640	−	0.989338i	$-0.546524\pi$
$139$	−3.43414			−0.291280			−0.145640	+	0.989338i	$0.546524\pi$
$140$		0			0
$141$	1.02774	−	1.18608i	0.0865515	−	0.0998857i
$142$		0			0
$143$	0.469117	−	3.26278i	0.0392296	−	0.272848i
$144$		0			0
$145$	−1.68874	−	3.69782i	−0.140242	−	0.307087i
$146$		0			0
$147$	−1.00264	−	6.97353i	−0.0826965	−	0.575167i
$148$		0			0
$149$	−19.5536	+	5.74146i	−1.60189	+	0.470359i	−0.956073	−	0.293130i	$-0.905303\pi$
$149$	−19.5536	+	5.74146i	−1.60189	+	0.470359i	−0.645822	+	0.763488i	$0.723485\pi$
$150$		0			0
$151$	5.81632	−	12.7360i	0.473325	−	1.03644i	−0.510920	−	0.859629i	$-0.670695\pi$
$151$	5.81632	−	12.7360i	0.473325	−	1.03644i	0.984245	−	0.176810i	$-0.0565777\pi$
$152$		0			0
$153$	−2.03221	−	2.34529i	−0.164294	−	0.189606i
$154$		0			0
$155$	−8.73843	+	5.61585i	−0.701887	+	0.451076i
$156$		0			0
$157$	15.1481	+	9.73511i	1.20895	+	0.776946i	0.980483	−	0.196605i	$-0.0629916\pi$
$157$	15.1481	+	9.73511i	1.20895	+	0.776946i	0.228469	+	0.973551i	$0.426628\pi$
$158$		0			0
$159$	2.75310	+	0.808382i	0.218335	+	0.0641089i
$160$		0			0
$161$	10.5822	−	14.5278i	0.833995	−	1.14495i
$162$		0			0
$163$	10.8066	+	3.17311i	0.846439	+	0.248537i	0.676065	−	0.736842i	$-0.263684\pi$
$163$	10.8066	+	3.17311i	0.846439	+	0.248537i	0.170375	+	0.985379i	$0.445502\pi$
$164$		0			0
$165$	1.39742	+	0.898068i	0.108789	+	0.0699145i
$166$		0			0
$167$	15.6618	−	10.0652i	1.21194	−	0.778870i	0.230962	−	0.972963i	$-0.425813\pi$
$167$	15.6618	−	10.0652i	1.21194	−	0.778870i	0.980983	+	0.194093i	$0.0621764\pi$
$168$		0			0
$169$	2.50812	+	2.89452i	0.192932	+	0.222656i
$170$		0			0
$171$	−1.72447	+	3.77605i	−0.131873	+	0.288762i
$172$		0			0
$173$	−11.1330	+	3.26895i	−0.846427	+	0.248533i	−0.676059	−	0.736847i	$-0.736314\pi$
$173$	−11.1330	+	3.26895i	−0.846427	+	0.248533i	−0.170368	+	0.985381i	$0.554496\pi$
$174$		0			0
$175$	−1.42476	−	9.90946i	−0.107702	−	0.749085i
$176$		0			0
$177$	−6.11707	−	13.3945i	−0.459787	−	1.00679i
$178$		0			0
$179$	−1.66482	+	11.5791i	−0.124434	+	0.865461i	0.828002	+	0.560725i	$0.189477\pi$
$179$	−1.66482	+	11.5791i	−0.124434	+	0.865461i	−0.952437	+	0.304736i	$0.901432\pi$
$180$		0			0
$181$	9.76420	−	11.2685i	0.725767	−	0.837580i	−0.266221	−	0.963912i	$-0.585775\pi$
$181$	9.76420	−	11.2685i	0.725767	−	0.837580i	0.991988	+	0.126332i	$0.0403205\pi$
$182$		0			0
$183$	−5.23520			−0.386997
$184$		0			0
$185$	−10.4390			−0.767487
$186$		0			0
$187$	2.21215	−	2.55296i	0.161768	−	0.186691i
$188$		0			0
$189$	0.533353	−	3.70955i	0.0387957	−	0.269830i
$190$		0			0
$191$	3.72672	+	8.16038i	0.269656	+	0.590465i	0.995217	−	0.0976939i	$-0.0311466\pi$
$191$	3.72672	+	8.16038i	0.269656	+	0.590465i	−0.725560	+	0.688159i	$0.758419\pi$
$192$		0			0
$193$	3.17993	+	22.1169i	0.228897	+	1.59201i	0.702769	+	0.711418i	$0.251947\pi$
$193$	3.17993	+	22.1169i	0.228897	+	1.59201i	−0.473873	+	0.880593i	$0.657144\pi$
$194$		0			0
$195$	4.43384	−	1.30189i	0.317514	−	0.0932304i
$196$		0			0
$197$	2.12840	−	4.66054i	0.151642	−	0.332050i	−0.818531	−	0.574462i	$-0.805211\pi$
$197$	2.12840	−	4.66054i	0.151642	−	0.332050i	0.970173	+	0.242412i	$0.0779386\pi$
$198$		0			0
$199$	17.4100	+	20.0922i	1.23416	+	1.42430i	0.870065	+	0.492937i	$0.164077\pi$
$199$	17.4100	+	20.0922i	1.23416	+	1.42430i	0.364097	+	0.931361i	$0.381378\pi$
$200$		0			0
$201$	−3.89781	+	2.50497i	−0.274930	+	0.176687i
$202$		0			0
$203$	−8.39881	−	5.39759i	−0.589481	−	0.378836i
$204$		0			0
$205$	14.5763	+	4.28000i	1.01806	+	0.298928i
$206$		0			0
$207$	3.80140	−	2.92392i	0.264216	−	0.203227i
$208$		0			0
$209$	−4.33572	−	1.27308i	−0.299908	−	0.0880609i
$210$		0			0
$211$	−10.3560	−	6.65540i	−0.712937	−	0.458177i	0.133237	−	0.991084i	$-0.457463\pi$
$211$	−10.3560	−	6.65540i	−0.712937	−	0.458177i	−0.846173	+	0.532908i	$0.821099\pi$
$212$		0			0
$213$	−12.8252	+	8.24227i	−0.878769	+	0.564751i
$214$		0			0
$215$	4.00496	+	4.62197i	0.273136	+	0.315216i
$216$		0			0
$217$	−10.5974	+	23.2051i	−0.719399	+	1.57526i
$218$		0			0
$219$	−3.08726	+	0.906503i	−0.208618	+	0.0612558i
$220$		0			0
$221$	−1.33738	−	9.30166i	−0.0899617	−	0.625697i
$222$		0			0
$223$	−4.00684	−	8.77376i	−0.268318	−	0.587535i	0.726731	−	0.686922i	$-0.241039\pi$
$223$	−4.00684	−	8.77376i	−0.268318	−	0.587535i	−0.995049	+	0.0993879i	$0.968312\pi$
$224$		0			0
$225$	0.380171	−	2.64415i	0.0253447	−	0.176276i
$226$		0			0
$227$	12.1922	−	14.0705i	0.809223	−	0.933893i	−0.189626	−	0.981856i	$-0.560728\pi$
$227$	12.1922	−	14.0705i	0.809223	−	0.933893i	0.998849	+	0.0479634i	$0.0152731\pi$
$228$		0			0
$229$	−6.22102			−0.411097			−0.205548	−	0.978647i	$-0.565898\pi$
$229$	−6.22102			−0.411097			−0.205548	+	0.978647i	$0.565898\pi$
$230$		0			0
$231$	4.07954			0.268414
$232$		0			0
$233$	2.42419	−	2.79767i	0.158814	−	0.183281i	−0.670766	−	0.741669i	$-0.734034\pi$
$233$	2.42419	−	2.79767i	0.158814	−	0.183281i	0.829580	+	0.558388i	$0.188580\pi$
$234$		0			0
$235$	−0.340831	+	2.37053i	−0.0222333	+	0.154636i
$236$		0			0
$237$	−1.28701	−	2.81816i	−0.0836003	−	0.183059i
$238$		0			0
$239$	2.28878	+	15.9188i	0.148049	+	1.02970i	0.919408	+	0.393304i	$0.128668\pi$
$239$	2.28878	+	15.9188i	0.148049	+	1.02970i	−0.771359	+	0.636400i	$0.780423\pi$
$240$		0			0
$241$	−27.6789	+	8.12724i	−1.78295	+	0.523522i	−0.995661	−	0.0930597i	$-0.970335\pi$
$241$	−27.6789	+	8.12724i	−1.78295	+	0.523522i	−0.787291	+	0.616581i	$0.788517\pi$
$242$		0			0
$243$	0.415415	−	0.909632i	0.0266489	−	0.0583529i
$244$		0			0
$245$	7.04041	+	8.12507i	0.449795	+	0.519092i
$246$		0			0
$247$	−10.5751	+	6.79619i	−0.672876	+	0.432431i
$248$		0			0
$249$	4.57398	+	2.93952i	0.289864	+	0.186284i
$250$		0			0
$251$	−0.175438	−	0.0515133i	−0.0110736	−	0.00325149i	0.276191	−	0.961103i	$-0.410928\pi$
$251$	−0.175438	−	0.0515133i	−0.0110736	−	0.00325149i	−0.287265	+	0.957851i	$0.592746\pi$
$252$		0			0
$253$	3.73933	+	3.64292i	0.235089	+	0.229028i
$254$		0			0
$255$	4.54375	+	1.33416i	0.284540	+	0.0835486i
$256$		0			0
$257$	−20.6833	−	13.2923i	−1.29019	−	0.829152i	−0.298078	−	0.954541i	$-0.596346\pi$
$257$	−20.6833	−	13.2923i	−1.29019	−	0.829152i	−0.992108	+	0.125389i	$0.959982\pi$
$258$		0			0
$259$	−21.5673	+	13.8604i	−1.34012	+	0.861246i
$260$		0			0
$261$	−1.74452	−	2.01328i	−0.107983	−	0.124619i
$262$		0			0
$263$	−4.88909	+	10.7056i	−0.301474	+	0.660136i	−0.998372	−	0.0570340i	$-0.981836\pi$
$263$	−4.88909	+	10.7056i	−0.301474	+	0.660136i	0.696898	+	0.717170i	$0.254563\pi$
$264$		0			0
$265$	−4.20122	+	1.23359i	−0.258079	+	0.0757787i
$266$		0			0
$267$	2.14372	+	14.9099i	0.131194	+	0.912473i
$268$		0			0
$269$	1.90568	+	4.17285i	0.116191	+	0.254423i	0.958788	−	0.284121i	$-0.0917018\pi$
$269$	1.90568	+	4.17285i	0.116191	+	0.254423i	−0.842597	+	0.538544i	$0.818975\pi$
$270$		0			0
$271$	1.13617	−	7.90226i	0.0690176	−	0.480028i	−0.925772	−	0.378082i	$-0.876584\pi$
$271$	1.13617	−	7.90226i	0.0690176	−	0.480028i	0.994790	−	0.101946i	$-0.0325070\pi$
$272$		0			0
$273$	7.43187	−	8.57683i	0.449797	−	0.519094i
$274$		0			0
$275$	2.90787			0.175351
$276$		0			0
$277$	5.12957			0.308206			0.154103	−	0.988055i	$-0.450751\pi$
$277$	5.12957			0.308206			0.154103	+	0.988055i	$0.450751\pi$
$278$		0			0
$279$	−4.45761	+	5.14435i	−0.266870	+	0.307984i
$280$		0			0
$281$	−3.79046	+	26.3632i	−0.226120	+	1.57270i	0.488108	+	0.872783i	$0.337687\pi$
$281$	−3.79046	+	26.3632i	−0.226120	+	1.57270i	−0.714228	+	0.699913i	$0.753222\pi$
$282$		0			0
$283$	1.47222	+	3.22371i	0.0875143	+	0.191630i	0.948329	−	0.317289i	$-0.102773\pi$
$283$	1.47222	+	3.22371i	0.0875143	+	0.191630i	−0.860815	+	0.508919i	$0.830045\pi$
$284$		0			0
$285$	−0.901521	−	6.27022i	−0.0534015	−	0.371416i
$286$		0			0
$287$	35.7981	−	10.5113i	2.11309	−	0.620460i
$288$		0			0
$289$	−3.06150	+	6.70376i	−0.180088	+	0.394339i
$290$		0			0
$291$	2.51301	+	2.90017i	0.147315	+	0.170011i
$292$		0			0
$293$	−24.1167	+	15.4989i	−1.40891	+	0.905454i	−0.999975	−	0.00710728i	$-0.997738\pi$
$293$	−24.1167	+	15.4989i	−1.40891	+	0.905454i	−0.408940	+	0.912561i	$0.634101\pi$
$294$		0			0
$295$	18.9035	+	12.1485i	1.10060	+	0.707314i
$296$		0			0
$297$	1.04445	+	0.306679i	0.0606053	+	0.0177953i
$298$		0			0
$299$	14.4710	−	1.22511i	0.836878	−	0.0708497i
$300$		0			0
$301$	14.4113	+	4.23153i	0.830651	+	0.243901i
$302$		0			0
$303$	−6.23734	−	4.00849i	−0.358326	−	0.230282i
$304$		0			0
$305$	6.72069	−	4.31912i	0.384826	−	0.247312i
$306$		0			0
$307$	−14.2345	−	16.4275i	−0.812406	−	0.937566i	0.186587	−	0.982438i	$-0.440257\pi$
$307$	−14.2345	−	16.4275i	−0.812406	−	0.937566i	−0.998993	+	0.0448722i	$0.985712\pi$
$308$		0			0
$309$	−5.50977	+	12.0647i	−0.313440	+	0.686338i
$310$		0			0
$311$	−22.2553	+	6.53475i	−1.26198	+	0.370552i	−0.843232	−	0.537550i	$-0.819350\pi$
$311$	−22.2553	+	6.53475i	−1.26198	+	0.370552i	−0.418751	+	0.908101i	$0.637532\pi$
$312$		0			0
$313$	−1.45243	−	10.1019i	−0.0820964	−	0.570993i	−0.988802	−	0.149230i	$-0.952320\pi$
$313$	−1.45243	−	10.1019i	−0.0820964	−	0.570993i	0.906706	−	0.421763i	$-0.138589\pi$
$314$		0			0
$315$	2.37575	+	5.20216i	0.133858	+	0.293109i
$316$		0			0
$317$	−2.15164	+	14.9650i	−0.120848	+	0.840518i	0.835750	+	0.549109i	$0.185033\pi$
$317$	−2.15164	+	14.9650i	−0.120848	+	0.840518i	−0.956599	+	0.291408i	$0.905876\pi$
$318$		0			0
$319$	1.89899	−	2.19155i	0.106323	−	0.122703i
$320$		0			0
$321$	−0.233329			−0.0130232
$322$		0			0
$323$	−12.8822			−0.716787
$324$		0			0
$325$	5.29739	−	6.11351i	0.293846	−	0.339117i
$326$		0			0
$327$	1.68688	−	11.7325i	0.0932844	−	0.648807i
$328$		0			0
$329$	2.44333	+	5.35014i	0.134705	+	0.294963i
$330$		0			0
$331$	−4.22495	−	29.3852i	−0.232224	−	1.61515i	−0.688446	−	0.725288i	$-0.741707\pi$
$331$	−4.22495	−	29.3852i	−0.232224	−	1.61515i	0.456222	−	0.889866i	$-0.349202\pi$
$332$		0			0
$333$	−6.56365	+	1.92726i	−0.359686	+	0.105613i
$334$		0			0
$335$	2.93717	−	6.43151i	0.160475	−	0.351391i
$336$		0			0
$337$	5.04882	+	5.82664i	0.275027	+	0.317398i	0.876413	−	0.481561i	$-0.159930\pi$
$337$	5.04882	+	5.82664i	0.275027	+	0.317398i	−0.601386	+	0.798959i	$0.705385\pi$
$338$		0			0
$339$	−6.71081	+	4.31277i	−0.364481	+	0.234238i
$340$		0			0
$341$	−6.23342	−	4.00598i	−0.337559	−	0.216936i
$342$		0			0
$343$	0.162669	+	0.0477638i	0.00878329	+	0.00257901i
$344$		0			0
$345$	−2.46777	+	6.88980i	−0.132860	+	0.370935i
$346$		0			0
$347$	7.73729	+	2.27187i	0.415359	+	0.121961i	0.482734	−	0.875767i	$-0.339644\pi$
$347$	7.73729	+	2.27187i	0.415359	+	0.121961i	−0.0673742	+	0.997728i	$0.521462\pi$
$348$		0			0
$349$	−13.0709	−	8.40018i	−0.699671	−	0.449651i	0.141841	−	0.989889i	$-0.454698\pi$
$349$	−13.0709	−	8.40018i	−0.699671	−	0.449651i	−0.841512	+	0.540238i	$0.818334\pi$
$350$		0			0
$351$	2.54748	−	1.63717i	0.135975	−	0.0873856i
$352$		0			0
$353$	−5.62082	−	6.48678i	−0.299166	−	0.345256i	0.586187	−	0.810176i	$-0.300629\pi$
$353$	−5.62082	−	6.48678i	−0.299166	−	0.345256i	−0.885353	+	0.464920i	$0.846083\pi$
$354$		0			0
$355$	9.66437	−	21.1620i	0.512931	−	1.12316i
$356$		0			0
$357$	11.1590	−	3.27658i	0.590597	−	0.173415i
$358$		0			0
$359$	−4.80972	−	33.4524i	−0.253847	−	1.76555i	−0.574648	−	0.818401i	$-0.694861\pi$
$359$	−4.80972	−	33.4524i	−0.253847	−	1.76555i	0.320800	−	0.947147i	$-0.396048\pi$
$360$		0			0
$361$	−0.734308	−	1.60791i	−0.0386478	−	0.0846268i
$362$		0			0
$363$	1.39683	−	9.71516i	0.0733146	−	0.509914i
$364$		0			0
$365$	3.21540	−	3.71076i	0.168302	−	0.194230i
$366$		0			0
$367$	13.4110			0.700047			0.350023	−	0.936741i	$-0.386174\pi$
$367$	13.4110			0.700047			0.350023	+	0.936741i	$0.386174\pi$
$368$		0			0
$369$	9.95527			0.518251
$370$		0			0
$371$	−7.04195	+	8.12685i	−0.365600	+	0.421925i
$372$		0			0
$373$	4.27644	−	29.7433i	0.221426	−	1.54005i	−0.511227	−	0.859446i	$-0.670809\pi$
$373$	4.27644	−	29.7433i	0.221426	−	1.54005i	0.732652	−	0.680603i	$-0.238282\pi$
$374$		0			0
$375$	4.86303	+	10.6485i	0.251126	+	0.549888i
$376$		0			0
$377$	−1.14805	−	7.98487i	−0.0591276	−	0.411242i
$378$		0			0
$379$	18.1461	−	5.32818i	0.932103	−	0.273690i	0.219786	−	0.975548i	$-0.429464\pi$
$379$	18.1461	−	5.32818i	0.932103	−	0.273690i	0.712317	+	0.701858i	$0.247646\pi$
$380$		0			0
$381$	−4.26580	+	9.34080i	−0.218544	+	0.478544i
$382$		0			0
$383$	5.12902	+	5.91920i	0.262081	+	0.302457i	0.871505	−	0.490387i	$-0.163145\pi$
$383$	5.12902	+	5.91920i	0.262081	+	0.302457i	−0.609424	+	0.792845i	$0.708599\pi$
$384$		0			0
$385$	−5.23711	+	3.36569i	−0.266908	+	0.171531i
$386$		0			0
$387$	3.37149	+	2.16673i	0.171383	+	0.110141i
$388$		0			0
$389$	7.10650	+	2.08666i	0.360314	+	0.105798i	0.456879	−	0.889529i	$-0.348967\pi$
$389$	7.10650	+	2.08666i	0.360314	+	0.105798i	−0.0965649	+	0.995327i	$0.530786\pi$
$390$		0			0
$391$	13.1543	+	6.96136i	0.665241	+	0.352051i
$392$		0			0
$393$	19.5677	+	5.74560i	0.987061	+	0.289827i
$394$		0			0
$395$	3.97723	+	2.55601i	0.200116	+	0.128607i
$396$		0			0
$397$	−1.57016	+	1.00908i	−0.0788042	+	0.0506444i	−0.579450	−	0.815008i	$-0.696732\pi$
$397$	−1.57016	+	1.00908i	−0.0788042	+	0.0506444i	0.500645	+	0.865652i	$0.333096\pi$
$398$		0			0
$399$	−10.1879	−	11.7575i	−0.510034	−	0.588611i
$400$		0			0
$401$	−4.49667	+	9.84632i	−0.224553	+	0.491702i	−0.988055	−	0.154104i	$-0.950751\pi$
$401$	−4.49667	+	9.84632i	−0.224553	+	0.491702i	0.763502	+	0.645806i	$0.223478\pi$
$402$		0			0
$403$	−19.7779	+	5.80730i	−0.985205	+	0.289282i
$404$		0			0
$405$	0.217172	+	1.51046i	0.0107914	+	0.0750555i
$406$		0			0
$407$	−3.09338	−	6.77355i	−0.153333	−	0.335752i
$408$		0			0
$409$	0.974102	−	6.77503i	0.0481663	−	0.335004i	−0.951463	−	0.307764i	$-0.900419\pi$
$409$	0.974102	−	6.77503i	0.0481663	−	0.335004i	0.999629	−	0.0272395i	$-0.00867169\pi$
$410$		0			0
$411$	−6.40315	+	7.38963i	−0.315844	+	0.364503i
$412$		0			0
$413$	55.1856			2.71551
$414$		0			0
$415$	−8.29699			−0.407283
$416$		0			0
$417$	2.24888	−	2.59535i	0.110128	−	0.127095i
$418$		0			0
$419$	−4.08920	+	28.4410i	−0.199771	+	1.38944i	0.605177	+	0.796091i	$0.293102\pi$
$419$	−4.08920	+	28.4410i	−0.199771	+	1.38944i	−0.804948	+	0.593345i	$0.797807\pi$
$420$		0			0
$421$	−11.4884	−	25.1561i	−0.559911	−	1.22603i	−0.951997	−	0.306106i	$-0.900974\pi$
$421$	−11.4884	−	25.1561i	−0.559911	−	1.22603i	0.392086	−	0.919928i	$-0.371753\pi$
$422$		0			0
$423$	0.223350	+	1.55343i	0.0108596	+	0.0755304i
$424$		0			0
$425$	7.95406	−	2.33552i	0.385829	−	0.113290i
$426$		0			0
$427$	8.15042	−	17.8469i	0.394427	−	0.863674i
$428$		0			0
$429$	2.15864	+	2.49120i	0.104220	+	0.120276i
$430$		0			0
$431$	24.0681	−	15.4677i	1.15932	−	0.745050i	0.187848	−	0.982198i	$-0.439849\pi$
$431$	24.0681	−	15.4677i	1.15932	−	0.745050i	0.971474	+	0.237148i	$0.0762125\pi$
$432$		0			0
$433$	−22.9578	−	14.7541i	−1.10328	−	0.709035i	−0.143461	−	0.989656i	$-0.545823\pi$
$433$	−22.9578	−	14.7541i	−1.10328	−	0.709035i	−0.959819	+	0.280621i	$0.909460\pi$
$434$		0			0
$435$	3.90051	+	1.14529i	0.187015	+	0.0549126i
$436$		0			0
$437$	1.16083	−	19.8745i	0.0555298	−	0.950727i
$438$		0			0
$439$	0.908894	+	0.266875i	0.0433791	+	0.0127373i	0.303350	−	0.952879i	$-0.401895\pi$
$439$	0.908894	+	0.266875i	0.0433791	+	0.0127373i	−0.259971	+	0.965616i	$0.583713\pi$
$440$		0			0
$441$	5.92683	+	3.80894i	0.282230	+	0.181378i
$442$		0			0
$443$	−18.3853	+	11.8155i	−0.873510	+	0.561371i	−0.898825	−	0.438309i	$-0.855578\pi$
$443$	−18.3853	+	11.8155i	−0.873510	+	0.561371i	0.0253144	+	0.999680i	$0.491941\pi$
$444$		0			0
$445$	−15.0529	−	17.3720i	−0.713578	−	0.823512i
$446$		0			0
$447$	8.46579	−	18.5375i	0.400418	−	0.876793i
$448$		0			0
$449$	−5.12412	+	1.50458i	−0.241822	+	0.0710054i	−0.400398	−	0.916341i	$-0.631128\pi$
$449$	−5.12412	+	1.50458i	−0.241822	+	0.0710054i	0.158576	+	0.987347i	$0.449310\pi$
$450$		0			0
$451$	1.54223	+	10.7265i	0.0726209	+	0.505090i
$452$		0			0
$453$	5.81632	+	12.7360i	0.273275	+	0.598388i
$454$		0			0
$455$	−2.46464	+	17.1419i	−0.115544	+	0.803626i
$456$		0			0
$457$	19.5938	−	22.6125i	0.916561	−	1.05777i	−0.0815702	−	0.996668i	$-0.525993\pi$
$457$	19.5938	−	22.6125i	0.916561	−	1.05777i	0.998132	−	0.0611006i	$-0.0194611\pi$
$458$		0			0
$459$	3.10326			0.144848
$460$		0			0
$461$	−2.50571			−0.116702			−0.0583512	−	0.998296i	$-0.518584\pi$
$461$	−2.50571			−0.116702			−0.0583512	+	0.998296i	$0.518584\pi$
$462$		0			0
$463$	−27.7850	+	32.0656i	−1.29128	+	1.49021i	−0.519257	+	0.854618i	$0.673791\pi$
$463$	−27.7850	+	32.0656i	−1.29128	+	1.49021i	−0.772021	+	0.635597i	$0.780754\pi$
$464$		0			0
$465$	1.47828	−	10.2817i	0.0685536	−	0.476801i
$466$		0			0
$467$	−5.75868	−	12.6097i	−0.266480	−	0.583509i	0.728334	−	0.685222i	$-0.240295\pi$
$467$	−5.75868	−	12.6097i	−0.266480	−	0.583509i	−0.994814	+	0.101713i	$0.967568\pi$
$468$		0			0
$469$	−2.47120	−	17.1876i	−0.114110	−	0.793649i
$470$		0			0
$471$	−17.2772	+	5.07305i	−0.796092	+	0.233754i
$472$		0			0
$473$	−1.81228	+	3.96833i	−0.0833286	+	0.182464i
$474$		0			0
$475$	−7.26189	−	8.38067i	−0.333198	−	0.384531i
$476$		0			0
$477$	−2.41383	+	1.55127i	−0.110522	+	0.0710280i
$478$		0			0
$479$	−10.6280	−	6.83019i	−0.485605	−	0.312079i	0.274831	−	0.961493i	$-0.411378\pi$
$479$	−10.6280	−	6.83019i	−0.485605	−	0.312079i	−0.760436	+	0.649413i	$0.775015\pi$
$480$		0			0
$481$	−19.8761	−	5.83614i	−0.906270	−	0.266105i
$482$		0			0
$483$	4.04951	+	17.5112i	0.184259	+	0.796787i
$484$		0			0
$485$	−5.61877	−	1.64982i	−0.255135	−	0.0749144i
$486$		0			0
$487$	−13.1238	−	8.43416i	−0.594697	−	0.382188i	0.208394	−	0.978045i	$-0.433176\pi$
$487$	−13.1238	−	8.43416i	−0.594697	−	0.382188i	−0.803091	+	0.595857i	$0.796813\pi$
$488$		0			0
$489$	−9.47490	+	6.08915i	−0.428470	+	0.275361i
$490$		0			0
$491$	28.5515	+	32.9501i	1.28851	+	1.48702i	0.779720	+	0.626129i	$0.215361\pi$
$491$	28.5515	+	32.9501i	1.28851	+	1.48702i	0.508790	+	0.860891i	$0.330093\pi$
$492$		0			0
$493$	3.43421	−	7.51988i	0.154669	−	0.338678i
$494$		0			0
$495$	−1.59383	+	0.467991i	−0.0716373	+	0.0210346i
$496$		0			0
$497$	−8.13116	−	56.5535i	−0.364732	−	2.53677i
$498$		0			0
$499$	4.18252	+	9.15843i	0.187235	+	0.409988i	0.979850	−	0.199735i	$-0.0640081\pi$
$499$	4.18252	+	9.15843i	0.187235	+	0.409988i	−0.792615	+	0.609723i	$0.791281\pi$
$500$		0			0
$501$	−2.64950	+	18.4277i	−0.118371	+	0.823289i
$502$		0			0
$503$	4.51425	−	5.20973i	0.201281	−	0.232290i	−0.646131	−	0.763226i	$-0.723614\pi$
$503$	4.51425	−	5.20973i	0.201281	−	0.232290i	0.847412	+	0.530936i	$0.178160\pi$
$504$		0			0
$505$	11.3143			0.503478
$506$		0			0
$507$	−3.83000			−0.170096
$508$		0			0
$509$	−12.7523	+	14.7170i	−0.565236	+	0.652318i	−0.964364	−	0.264578i	$-0.914767\pi$
$509$	−12.7523	+	14.7170i	−0.565236	+	0.652318i	0.399128	+	0.916895i	$0.369313\pi$
$510$		0			0
$511$	1.71612	−	11.9359i	0.0759165	−	0.528011i
$512$		0			0
$513$	−1.72447	−	3.77605i	−0.0761370	−	0.166717i
$514$		0			0
$515$	−2.88041	−	20.0337i	−0.126926	−	0.882791i
$516$		0			0
$517$	−1.63917	+	0.481303i	−0.0720905	+	0.0211677i
$518$		0			0
$519$	4.82007	−	10.5545i	0.211577	−	0.463290i
$520$		0			0
$521$	21.9203	+	25.2973i	0.960344	+	1.10830i	0.994057	+	0.108865i	$0.0347216\pi$
$521$	21.9203	+	25.2973i	0.960344	+	1.10830i	−0.0337122	+	0.999432i	$0.510733\pi$
$522$		0			0
$523$	−26.8575	+	17.2602i	−1.17439	+	0.754738i	−0.974348	−	0.225049i	$-0.927746\pi$
$523$	−26.8575	+	17.2602i	−1.17439	+	0.754738i	−0.200047	+	0.979786i	$0.564110\pi$
$524$		0			0
$525$	8.42209	+	5.41255i	0.367570	+	0.236223i
$526$		0			0
$527$	−20.2681	−	5.95126i	−0.882893	−	0.259241i
$528$		0			0
$529$	−11.9252	+	19.6670i	−0.518488	+	0.855085i
$530$		0			0
$531$	14.1287	+	4.14857i	0.613134	+	0.180032i
$532$		0			0
$533$	25.3609	+	16.2985i	1.09850	+	0.705965i
$534$		0			0
$535$	0.299536	−	0.192500i	0.0129501	−	0.00832251i
$536$		0			0
$537$	−7.66065	−	8.84087i	−0.330582	−	0.381512i
$538$		0			0
$539$	−3.18584	+	6.97603i	−0.137224	+	0.300479i
$540$		0			0
$541$	30.5324	−	8.96512i	1.31269	−	0.385441i	0.450841	−	0.892604i	$-0.351124\pi$
$541$	30.5324	−	8.96512i	1.31269	−	0.385441i	0.861850	+	0.507163i	$0.169306\pi$
$542$		0			0
$543$	2.12196	+	14.7586i	0.0910622	+	0.633351i
$544$		0			0
$545$	7.51395	+	16.4533i	0.321862	+	0.704780i
$546$		0			0
$547$	−5.24592	+	36.4862i	−0.224299	+	1.56004i	0.497209	+	0.867631i	$0.334358\pi$
$547$	−5.24592	+	36.4862i	−0.224299	+	1.56004i	−0.721508	+	0.692406i	$0.756551\pi$
$548$		0			0
$549$	3.42833	−	3.95650i	0.146317	−	0.168859i
$550$		0			0
$551$	−11.0586			−0.471111
$552$		0			0
$553$	11.6109			0.493744
$554$		0			0
$555$	6.83606	−	7.88924i	0.290175	−	0.334880i
$556$		0			0
$557$	−4.83552	+	33.6318i	−0.204888	+	1.42503i	0.584631	+	0.811299i	$0.301239\pi$
$557$	−4.83552	+	33.6318i	−0.204888	+	1.42503i	−0.789519	+	0.613726i	$0.789670\pi$
$558$		0			0
$559$	5.04153	+	11.0394i	0.213234	+	0.466917i
$560$		0			0
$561$	0.480746	+	3.34366i	0.0202971	+	0.141170i
$562$		0			0
$563$	17.9632	−	5.27448i	0.757059	−	0.222293i	0.119648	−	0.992816i	$-0.461823\pi$
$563$	17.9632	−	5.27448i	0.757059	−	0.222293i	0.637411	+	0.770524i	$0.280005\pi$
$564$		0			0
$565$	5.05689	−	11.0730i	0.212745	−	0.465846i
$566$		0			0
$567$	2.45422	+	2.83232i	0.103068	+	0.118946i
$568$		0			0
$569$	26.3796	−	16.9531i	1.10589	−	0.710712i	0.145495	−	0.989359i	$-0.453522\pi$
$569$	26.3796	−	16.9531i	1.10589	−	0.710712i	0.960394	+	0.278647i	$0.0898860\pi$
$570$		0			0
$571$	6.29897	+	4.04810i	0.263604	+	0.169408i	0.665766	−	0.746161i	$-0.268105\pi$
$571$	6.29897	+	4.04810i	0.263604	+	0.169408i	−0.402162	+	0.915568i	$0.631741\pi$
$572$		0			0
$573$	−8.60769	−	2.52745i	−0.359591	−	0.105586i
$574$		0			0
$575$	2.88647	+	12.4819i	0.120374	+	0.520530i
$576$		0			0
$577$	39.5545	+	11.6142i	1.64668	+	0.483508i	0.968004	−	0.250935i	$-0.0807379\pi$
$577$	39.5545	+	11.6142i	1.64668	+	0.483508i	0.678671	+	0.734442i	$0.262556\pi$
$578$		0			0
$579$	−18.7973	−	12.0803i	−0.781188	−	0.502039i
$580$		0			0
$581$	−17.1419	+	11.0164i	−0.711165	+	0.457038i
$582$		0			0
$583$	−2.04539	−	2.36050i	−0.0847113	−	0.0977620i
$584$		0			0
$585$	−1.91964	+	4.20343i	−0.0793674	+	0.173790i
$586$		0			0
$587$	−13.3002	+	3.90530i	−0.548959	+	0.161189i	−0.544438	−	0.838801i	$-0.683257\pi$
$587$	−13.3002	+	3.90530i	−0.548959	+	0.161189i	−0.00452086	+	0.999990i	$0.501439\pi$
$588$		0			0
$589$	4.02138	+	27.9693i	0.165698	+	1.15246i
$590$		0			0
$591$	2.12840	+	4.66054i	0.0875505	+	0.191709i
$592$		0			0
$593$	2.08436	−	14.4970i	0.0855943	−	0.595321i	−0.901207	−	0.433388i	$-0.857318\pi$
$593$	2.08436	−	14.4970i	0.0855943	−	0.595321i	0.986802	−	0.161933i	$-0.0517729\pi$
$594$		0			0
$595$	−11.6221	+	13.4127i	−0.476461	+	0.549865i
$596$		0			0
$597$	−26.5858			−1.08808
$598$		0			0
$599$	−25.6306			−1.04724			−0.523618	−	0.851953i	$-0.675418\pi$
$599$	−25.6306			−1.04724			−0.523618	+	0.851953i	$0.675418\pi$
$600$		0			0
$601$	10.9786	−	12.6700i	0.447826	−	0.516819i	−0.486286	−	0.873800i	$-0.661649\pi$
$601$	10.9786	−	12.6700i	0.447826	−	0.516819i	0.934112	+	0.356981i	$0.116194\pi$
$602$		0			0
$603$	0.659392	−	4.58617i	0.0268525	−	0.186763i
$604$		0			0
$605$	6.22198	+	13.6242i	0.252960	+	0.553904i
$606$		0			0
$607$	−1.47889	−	10.2859i	−0.0600263	−	0.417492i	−0.997573	−	0.0696320i	$-0.977818\pi$
$607$	−1.47889	−	10.2859i	−0.0600263	−	0.417492i	0.937546	−	0.347860i	$-0.113092\pi$
$608$		0			0
$609$	9.57928	−	2.81273i	0.388172	−	0.113978i
$610$		0			0
$611$	−1.97425	+	4.32300i	−0.0798695	+	0.174890i
$612$		0			0
$613$	−14.6036	−	16.8534i	−0.589833	−	0.680704i	0.379856	−	0.925046i	$-0.375974\pi$
$613$	−14.6036	−	16.8534i	−0.589833	−	0.680704i	−0.969689	+	0.244342i	$0.921428\pi$
$614$		0			0
$615$	−12.7801	+	8.21326i	−0.515343	+	0.331191i
$616$		0			0
$617$	−9.96316	−	6.40294i	−0.401102	−	0.257773i	0.324502	−	0.945885i	$-0.394803\pi$
$617$	−9.96316	−	6.40294i	−0.401102	−	0.257773i	−0.725604	+	0.688112i	$0.758440\pi$
$618$		0			0
$619$	36.4170	+	10.6930i	1.46372	+	0.429788i	0.914054	−	0.405593i	$-0.132935\pi$
$619$	36.4170	+	10.6930i	1.46372	+	0.429788i	0.549671	+	0.835381i	$0.314753\pi$
$620$		0			0
$621$	−0.279637	+	4.78767i	−0.0112215	+	0.192123i
$622$		0			0
$623$	−54.1658	−	15.9045i	−2.17011	−	0.637201i
$624$		0			0
$625$	−3.79177	−	2.43682i	−0.151671	−	0.0974729i
$626$		0			0
$627$	3.80142	−	2.44302i	0.151814	−	0.0975650i
$628$		0			0
$629$	−13.9018	−	16.0435i	−0.554302	−	0.639698i
$630$		0			0
$631$	−3.01905	+	6.61079i	−0.120186	+	0.263171i	−0.960157	−	0.279460i	$-0.909845\pi$
$631$	−3.01905	+	6.61079i	−0.120186	+	0.263171i	0.839971	+	0.542631i	$0.182572\pi$
$632$		0			0
$633$	11.8116	−	3.46819i	0.469467	−	0.137848i
$634$		0			0
$635$	−2.23009	−	15.5106i	−0.0884984	−	0.615520i
$636$		0			0
$637$	8.86263	+	19.4064i	0.351150	+	0.768911i
$638$		0			0
$639$	2.16964	−	15.0902i	0.0858297	−	0.596959i
$640$		0			0
$641$	−17.1302	+	19.7693i	−0.676601	+	0.780840i	−0.985394	−	0.170290i	$-0.945530\pi$
$641$	−17.1302	+	19.7693i	−0.676601	+	0.780840i	0.308793	+	0.951129i	$0.400075\pi$
$642$		0			0
$643$	−33.0605			−1.30378			−0.651889	−	0.758314i	$-0.726023\pi$
$643$	−33.0605			−1.30378			−0.651889	+	0.758314i	$0.726023\pi$
$644$		0			0
$645$	−6.11574			−0.240807
$646$		0			0
$647$	−15.6327	+	18.0411i	−0.614586	+	0.709271i	−0.974670	−	0.223650i	$-0.928203\pi$
$647$	−15.6327	+	18.0411i	−0.614586	+	0.709271i	0.360083	+	0.932920i	$0.382748\pi$
$648$		0			0
$649$	−2.28117	+	15.8659i	−0.0895438	+	0.622791i
$650$		0			0
$651$	−10.5974	−	23.2051i	−0.415345	−	0.909479i
$652$		0			0
$653$	5.83034	+	40.5509i	0.228159	+	1.58688i	0.705857	+	0.708354i	$0.250562\pi$
$653$	5.83034	+	40.5509i	0.228159	+	1.58688i	−0.477698	+	0.878524i	$0.658529\pi$
$654$		0			0
$655$	−29.8603	+	8.76777i	−1.16674	+	0.342585i
$656$		0			0
$657$	1.33664	−	2.92683i	0.0521473	−	0.114187i
$658$		0			0
$659$	3.59931	+	4.15383i	0.140209	+	0.161810i	0.821511	−	0.570192i	$-0.193131\pi$
$659$	3.59931	+	4.15383i	0.140209	+	0.161810i	−0.681302	+	0.732003i	$0.738586\pi$
$660$		0			0
$661$	17.4827	−	11.2354i	0.679997	−	0.437007i	−0.154520	−	0.987990i	$-0.549383\pi$
$661$	17.4827	−	11.2354i	0.679997	−	0.437007i	0.834517	+	0.550982i	$0.185747\pi$
$662$		0			0
$663$	7.90552	+	5.08057i	0.307025	+	0.197313i
$664$		0			0
$665$	22.7789	+	6.68848i	0.883326	+	0.259368i
$666$		0			0
$667$	11.2921	+	5.97588i	0.437232	+	0.231387i
$668$		0			0
$669$	9.25469	+	2.71742i	0.357807	+	0.105062i
$670$		0			0
$671$	4.79410	+	3.08098i	0.185074	+	0.118940i
$672$		0			0
$673$	−9.76169	+	6.27346i	−0.376285	+	0.241824i	−0.715089	−	0.699033i	$-0.753614\pi$
$673$	−9.76169	+	6.27346i	−0.376285	+	0.241824i	0.338804	+	0.940857i	$0.389978\pi$
$674$		0			0
$675$	1.74935	+	2.01886i	0.0673326	+	0.0777060i
$676$		0			0
$677$	3.65441	−	8.00205i	0.140450	−	0.307544i	−0.826315	−	0.563208i	$-0.809567\pi$
$677$	3.65441	−	8.00205i	0.140450	−	0.307544i	0.966766	+	0.255664i	$0.0822942\pi$
$678$		0			0
$679$	−13.7991	+	4.05179i	−0.529562	+	0.155494i
$680$		0			0
$681$	2.64961	+	18.4285i	0.101533	+	0.706180i
$682$		0			0
$683$	−11.9782	−	26.2287i	−0.458334	−	1.00361i	−0.987864	−	0.155320i	$-0.950359\pi$
$683$	−11.9782	−	26.2287i	−0.458334	−	1.00361i	0.529530	−	0.848291i	$-0.322368\pi$
$684$		0			0
$685$	2.12348	−	14.7691i	0.0811340	−	0.564299i
$686$		0			0
$687$	4.07390	−	4.70153i	0.155429	−	0.179375i
$688$		0			0
$689$	−8.68889			−0.331020
$690$		0			0
$691$	9.54501			0.363109			0.181555	−	0.983381i	$-0.441887\pi$
$691$	9.54501			0.363109			0.181555	+	0.983381i	$0.441887\pi$
$692$		0			0
$693$	−2.67153	+	3.08311i	−0.101483	+	0.117118i
$694$		0			0
$695$	−0.745798	+	5.18714i	−0.0282897	+	0.196759i
$696$		0			0
$697$	12.8338	+	28.1020i	0.486114	+	1.06444i
$698$		0			0
$699$	0.526828	+	3.66417i	0.0199265	+	0.138592i
$700$		0			0
$701$	−10.3490	+	3.03875i	−0.390878	+	0.114772i	−0.471265	−	0.881992i	$-0.656202\pi$
$701$	−10.3490	+	3.03875i	−0.390878	+	0.114772i	0.0803874	+	0.996764i	$0.474384\pi$
$702$		0			0
$703$	−11.7966	+	25.8310i	−0.444919	+	0.974236i
$704$		0			0
$705$	−1.56833	−	1.80995i	−0.0590667	−	0.0681666i
$706$		0			0
$707$	23.3757	−	15.0226i	0.879132	−	0.564984i
$708$		0			0
$709$	5.71727	+	3.67427i	0.214717	+	0.137990i	0.643579	−	0.765380i	$-0.277449\pi$
$709$	5.71727	+	3.67427i	0.214717	+	0.137990i	−0.428862	+	0.903370i	$0.641085\pi$
$710$		0			0
$711$	2.97264	+	0.872845i	0.111483	+	0.0327342i
$712$		0			0
$713$	11.0079	−	30.7331i	0.412249	−	1.15096i
$714$		0			0
$715$	−4.82644	−	1.41717i	−0.180498	−	0.0529991i
$716$		0			0
$717$	−13.5295	−	8.69488i	−0.505268	−	0.324716i
$718$		0			0
$719$	31.3385	−	20.1400i	1.16873	−	0.751097i	0.195448	−	0.980714i	$-0.437384\pi$
$719$	31.3385	−	20.1400i	1.16873	−	0.751097i	0.973281	+	0.229617i	$0.0737474\pi$
$720$		0			0
$721$	−32.5510	−	37.5659i	−1.21226	−	1.39903i
$722$		0			0
$723$	11.9836	−	26.2405i	0.445676	−	0.975894i
$724$		0			0
$725$	6.82805	−	2.00490i	0.253587	−	0.0744600i
$726$		0			0
$727$	6.56541	+	45.6634i	0.243498	+	1.69356i	0.634299	+	0.773088i	$0.281289\pi$
$727$	6.56541	+	45.6634i	0.243498	+	1.69356i	−0.390801	+	0.920475i	$0.627802\pi$
$728$		0			0
$729$	0.415415	+	0.909632i	0.0153857	+	0.0336901i
$730$		0			0
$731$	−1.76996	+	12.3104i	−0.0654645	+	0.455316i
$732$		0			0
$733$	22.8021	−	26.3150i	0.842214	−	0.971967i	−0.157665	−	0.987493i	$-0.550397\pi$
$733$	22.8021	−	26.3150i	0.842214	−	0.971967i	0.999879	+	0.0155256i	$0.00494217\pi$
$734$		0			0
$735$	−10.7510			−0.396557
$736$		0			0
$737$	5.04360			0.185783
$738$		0			0
$739$	13.8178	−	15.9466i	0.508295	−	0.586604i	−0.442366	−	0.896834i	$-0.645861\pi$
$739$	13.8178	−	15.9466i	0.508295	−	0.586604i	0.950661	+	0.310231i	$0.100406\pi$
$740$		0			0
$741$	1.78899	−	12.4427i	0.0657201	−	0.457093i
$742$		0			0
$743$	11.7483	+	25.7253i	0.431005	+	0.943769i	0.993163	+	0.116739i	$0.0372441\pi$
$743$	11.7483	+	25.7253i	0.431005	+	0.943769i	−0.562158	+	0.827030i	$0.690029\pi$
$744$		0			0
$745$	4.42577	+	30.7819i	0.162148	+	1.12776i
$746$		0			0
$747$	−5.21685	+	1.53181i	−0.190875	+	0.0560459i
$748$		0			0
$749$	0.363258	−	0.795425i	0.0132732	−	0.0290642i
$750$		0			0
$751$	2.79296	+	3.22325i	0.101917	+	0.117618i	0.804416	−	0.594066i	$-0.202478\pi$
$751$	2.79296	+	3.22325i	0.101917	+	0.117618i	−0.702500	+	0.711684i	$0.747933\pi$
$752$		0			0
$753$	0.153819	−	0.0988533i	0.00560547	−	0.00360241i
$754$		0			0
$755$	−17.9741	−	11.5512i	−0.654143	−	0.420392i
$756$		0			0
$757$	−35.9380	−	10.5523i	−1.30619	−	0.383531i	−0.446698	−	0.894685i	$-0.647400\pi$
$757$	−35.9380	−	10.5523i	−1.30619	−	0.383531i	−0.859489	+	0.511154i	$0.829218\pi$
$758$		0			0
$759$	−5.20187	+	0.440389i	−0.188816	+	0.0159851i
$760$		0			0
$761$	−40.8916	−	12.0068i	−1.48232	−	0.435248i	−0.562237	−	0.826976i	$-0.690059\pi$
$761$	−40.8916	−	12.0068i	−1.48232	−	0.435248i	−0.920081	+	0.391728i	$0.871877\pi$
$762$		0			0
$763$	37.3701	+	24.0163i	1.35289	+	0.869449i
$764$		0			0
$765$	−3.98382	+	2.56024i	−0.144035	+	0.0925658i
$766$		0			0
$767$	29.2008	+	33.6995i	1.05438	+	1.21682i
$768$		0			0
$769$	−7.88108	+	17.2572i	−0.284199	+	0.622309i	−0.996859	−	0.0792007i	$-0.974763\pi$
$769$	−7.88108	+	17.2572i	−0.284199	+	0.622309i	0.712660	+	0.701510i	$0.247490\pi$
$770$		0			0
$771$	23.5903	−	6.92674i	0.849584	−	0.249461i
$772$		0			0
$773$	−7.52233	−	52.3190i	−0.270559	−	1.88178i	−0.442640	−	0.896699i	$-0.645958\pi$
$773$	−7.52233	−	52.3190i	−0.270559	−	1.88178i	0.172081	−	0.985083i	$-0.444951\pi$
$774$		0			0
$775$	−7.55377	−	16.5404i	−0.271339	−	0.594150i
$776$		0			0
$777$	3.64853	−	25.3761i	0.130890	−	0.910363i
$778$		0			0
$779$	27.0629	−	31.2323i	0.969629	−	1.11901i
$780$		0			0
$781$	16.5953			0.593826
$782$		0			0
$783$	2.66395			0.0952019
$784$		0			0
$785$	17.9943	−	20.7665i	0.642243	−	0.741188i
$786$		0			0
$787$	−3.90826	+	27.1825i	−0.139314	+	0.968952i	0.793494	+	0.608578i	$0.208260\pi$
$787$	−3.90826	+	27.1825i	−0.139314	+	0.968952i	−0.932808	+	0.360374i	$0.882649\pi$
$788$		0			0
$789$	−4.88909	−	10.7056i	−0.174056	−	0.381130i
$790$		0			0
$791$	−4.25464	−	29.5917i	−0.151278	−	1.05216i
$792$		0			0
$793$	15.2111	−	4.46637i	0.540161	−	0.158606i
$794$		0			0
$795$	1.81893	−	3.98290i	0.0645107	−	0.141259i
$796$		0			0
$797$	−25.1457	−	29.0197i	−0.890706	−	1.02793i	−0.999427	−	0.0338575i	$-0.989221\pi$
$797$	−25.1457	−	29.0197i	−0.890706	−	1.02793i	0.108720	−	0.994072i	$-0.465325\pi$
$798$		0			0
$799$	−4.09714	+	2.63307i	−0.144946	+	0.0931514i
$800$		0			0
$801$	−12.6720	−	8.14381i	−0.447744	−	0.287747i
$802$		0			0
$803$	3.36063	+	0.986770i	0.118594	+	0.0348223i
$804$		0			0
$805$	−19.6456	−	19.1391i	−0.692415	−	0.674564i
$806$		0			0
$807$	−4.40158	−	1.29242i	−0.154943	−	0.0454954i
$808$		0			0
$809$	10.5055	+	6.75147i	0.369354	+	0.237369i	0.712130	−	0.702048i	$-0.247731\pi$
$809$	10.5055	+	6.75147i	0.369354	+	0.237369i	−0.342776	+	0.939417i	$0.611367\pi$
$810$		0			0
$811$	14.8611	−	9.55067i	0.521845	−	0.335369i	−0.253057	−	0.967451i	$-0.581436\pi$
$811$	14.8611	−	9.55067i	0.521845	−	0.335369i	0.774901	+	0.632082i	$0.217800\pi$
$812$		0			0
$813$	5.22809	+	6.03354i	0.183357	+	0.211606i
$814$		0			0
$815$	7.13976	−	15.6339i	0.250095	−	0.547631i
$816$		0			0
$817$	15.9628	−	4.68711i	0.558468	−	0.163981i
$818$		0			0
$819$	1.61510	+	11.2333i	0.0564361	+	0.392522i
$820$		0			0
$821$	−5.49865	−	12.0404i	−0.191904	−	0.420211i	0.789082	−	0.614287i	$-0.210556\pi$
$821$	−5.49865	−	12.0404i	−0.191904	−	0.420211i	−0.980987	+	0.194076i	$0.937829\pi$
$822$		0			0
$823$	5.67981	−	39.5039i	0.197986	−	1.37702i	−0.612133	−	0.790755i	$-0.709688\pi$
$823$	5.67981	−	39.5039i	0.197986	−	1.37702i	0.810119	−	0.586266i	$-0.199402\pi$
$824$		0			0
$825$	−1.90425	+	2.19762i	−0.0662975	+	0.0765114i
$826$		0			0
$827$	−0.108053			−0.00375736			−0.00187868	−	0.999998i	$-0.500598\pi$
$827$	−0.108053			−0.00375736			−0.00187868	+	0.999998i	$0.500598\pi$
$828$		0			0
$829$	50.3641			1.74922			0.874608	−	0.484830i	$-0.161119\pi$
$829$	50.3641			1.74922			0.874608	+	0.484830i	$0.161119\pi$
$830$		0			0
$831$	−3.35916	+	3.87667i	−0.116528	+	0.134480i
$832$		0			0
$833$	−3.11146	+	21.6407i	−0.107806	+	0.749806i
$834$		0			0
$835$	−11.8018	−	25.8424i	−0.408420	−	0.894314i
$836$		0			0
$837$	−0.968731	−	6.73767i	−0.0334842	−	0.232888i
$838$		0			0
$839$	−3.69755	+	1.08570i	−0.127653	+	0.0374824i	−0.344935	−	0.938626i	$-0.612099\pi$
$839$	−3.69755	+	1.08570i	−0.127653	+	0.0374824i	0.217282	+	0.976109i	$0.430281\pi$
$840$		0			0
$841$	−9.09898	+	19.9240i	−0.313758	+	0.687034i
$842$		0			0
$843$	−17.4418	−	20.1289i	−0.600726	−	0.693275i
$844$		0			0
$845$	4.91677	−	3.15981i	0.169142	−	0.108701i
$846$		0			0
$847$	30.9446	+	19.8869i	1.06327	+	0.683321i
$848$		0			0
$849$	−3.40041	−	0.998452i	−0.116702	−	0.0342668i
$850$		0			0
$851$	26.0045	−	20.0018i	0.891421	−	0.685654i
$852$		0			0
$853$	0.492793	+	0.144697i	0.0168729	+	0.00495433i	0.290158	−	0.956979i	$-0.406292\pi$
$853$	0.492793	+	0.144697i	0.0168729	+	0.00495433i	−0.273285	+	0.961933i	$0.588110\pi$
$854$		0			0
$855$	5.32908	+	3.42479i	0.182251	+	0.117126i
$856$		0			0
$857$	32.7260	−	21.0317i	1.11790	−	0.718431i	0.154899	−	0.987930i	$-0.450495\pi$
$857$	32.7260	−	21.0317i	1.11790	−	0.718431i	0.963001	+	0.269500i	$0.0868583\pi$
$858$		0			0
$859$	31.2989	+	36.1208i	1.06790	+	1.23243i	0.971489	+	0.237085i	$0.0761921\pi$
$859$	31.2989	+	36.1208i	1.06790	+	1.23243i	0.0964148	+	0.995341i	$0.469262\pi$
$860$		0			0
$861$	−15.4989	+	33.9378i	−0.528200	+	1.15660i
$862$		0			0
$863$	−7.32726	+	2.15148i	−0.249423	+	0.0732371i	−0.404054	−	0.914735i	$-0.632399\pi$
$863$	−7.32726	+	2.15148i	−0.249423	+	0.0732371i	0.154631	+	0.987972i	$0.450581\pi$
$864$		0			0
$865$	2.51985	+	17.5259i	0.0856774	+	0.595900i
$866$		0			0
$867$	−3.06150	−	6.70376i	−0.103974	−	0.227672i
$868$		0			0
$869$	−0.479951	+	3.33813i	−0.0162812	+	0.113238i
$870$		0			0
$871$	9.18813	−	10.6037i	0.311328	−	0.359292i
$872$		0			0
$873$	−3.83748			−0.129879
$874$		0			0
$875$	−43.8722			−1.48315
$876$		0			0
$877$	1.60997	−	1.85800i	0.0543648	−	0.0627403i	−0.727916	−	0.685667i	$-0.759511\pi$
$877$	1.60997	−	1.85800i	0.0543648	−	0.0627403i	0.782281	+	0.622926i	$0.214056\pi$
$878$		0			0
$879$	4.07983	−	28.3758i	0.137609	−	0.957092i
$880$		0			0
$881$	2.71552	+	5.94616i	0.0914881	+	0.200331i	0.949844	−	0.312723i	$-0.101241\pi$
$881$	2.71552	+	5.94616i	0.0914881	+	0.200331i	−0.858356	+	0.513054i	$0.828514\pi$
$882$		0			0
$883$	4.62567	+	32.1722i	0.155666	+	1.08268i	0.906505	+	0.422196i	$0.138741\pi$
$883$	4.62567	+	32.1722i	0.155666	+	1.08268i	−0.750839	+	0.660486i	$0.770350\pi$
$884$		0			0
$885$	−21.5604	+	6.33070i	−0.724744	+	0.212804i
$886$		0			0
$887$	5.92245	−	12.9684i	0.198856	−	0.435435i	−0.783765	−	0.621058i	$-0.786703\pi$
$887$	5.92245	−	12.9684i	0.198856	−	0.435435i	0.982621	+	0.185623i	$0.0594304\pi$
$888$		0			0
$889$	−25.2018	−	29.0845i	−0.845242	−	0.975461i
$890$		0			0
$891$	−0.915743	+	0.588512i	−0.0306785	+	0.0197159i
$892$		0			0
$893$	5.48068	+	3.52222i	0.183404	+	0.117866i
$894$		0			0
$895$	17.1282	+	5.02930i	0.572533	+	0.168111i
$896$		0			0
$897$	−8.55060	+	11.7387i	−0.285496	+	0.391944i
$898$		0			0
$899$	−17.3989	−	5.10877i	−0.580285	−	0.170387i
$900$		0			0
$901$	−7.49075	−	4.81401i	−0.249553	−	0.160378i
$902$		0			0
$903$	−12.6353	+	8.12024i	−0.420478	+	0.270225i
$904$		0			0
$905$	−14.9001	−	17.1957i	−0.495297	−	0.571603i
$906$		0			0
$907$	11.5242	−	25.2345i	0.382655	−	0.837897i	−0.616084	−	0.787681i	$-0.711282\pi$
$907$	11.5242	−	25.2345i	0.382655	−	0.837897i	0.998738	−	0.0502161i	$-0.0159910\pi$
$908$		0			0
$909$	7.11400	−	2.08886i	0.235957	−	0.0692831i
$910$		0			0
$911$	2.42768	+	16.8849i	0.0804325	+	0.559421i	0.989694	+	0.143196i	$0.0457379\pi$
$911$	2.42768	+	16.8849i	0.0804325	+	0.559421i	−0.909262	+	0.416225i	$0.863353\pi$
$912$		0			0
$913$	−2.45865	−	5.38368i	−0.0813693	−	0.178174i
$914$		0			0
$915$	−1.13694	+	7.90758i	−0.0375860	+	0.261417i
$916$		0			0
$917$	−50.0509	+	57.7618i	−1.65283	+	1.90746i
$918$		0			0
$919$	−32.9304			−1.08627			−0.543137	−	0.839644i	$-0.682764\pi$
$919$	−32.9304			−1.08627			−0.543137	+	0.839644i	$0.682764\pi$
$920$		0			0
$921$	21.7367			0.716248
$922$		0			0
$923$	30.2323	−	34.8899i	0.995109	−	1.14842i
$924$		0			0
$925$	2.60065	−	18.0879i	0.0855089	−	0.594728i
$926$		0			0
$927$	−5.50977	−	12.0647i	−0.180965	−	0.396257i
$928$		0			0
$929$	7.97550	+	55.4708i	0.261668	+	1.81994i	0.520323	+	0.853970i	$0.325812\pi$
$929$	7.97550	+	55.4708i	0.261668	+	1.81994i	−0.258655	+	0.965970i	$0.583279\pi$
$930$		0			0
$931$	28.0614	−	8.23958i	0.919676	−	0.270041i
$932$		0			0
$933$	9.63550	−	21.0988i	0.315452	−	0.690743i
$934$		0			0
$935$	−3.37573	−	3.89580i	−0.110398	−	0.127406i
$936$		0			0
$937$	−14.4897	+	9.31194i	−0.473357	+	0.304208i	−0.755482	−	0.655170i	$-0.772597\pi$
$937$	−14.4897	+	9.31194i	−0.473357	+	0.304208i	0.282125	+	0.959378i	$0.408961\pi$
$938$		0			0
$939$	8.58565	+	5.51766i	0.280182	+	0.180062i
$940$		0			0
$941$	−16.9149	−	4.96666i	−0.551410	−	0.161909i	−0.00585385	−	0.999983i	$-0.501863\pi$
$941$	−16.9149	−	4.96666i	−0.551410	−	0.161909i	−0.545556	+	0.838074i	$0.683682\pi$
$942$		0			0
$943$	−44.5119	+	17.2675i	−1.44951	+	0.562306i
$944$		0			0
$945$	−5.48731	−	1.61122i	−0.178502	−	0.0524130i
$946$		0			0
$947$	17.4410	+	11.2087i	0.566758	+	0.364233i	0.792423	−	0.609972i	$-0.208819\pi$
$947$	17.4410	+	11.2087i	0.566758	+	0.364233i	−0.225665	+	0.974205i	$0.572456\pi$
$948$		0			0
$949$	8.19678	−	5.26775i	0.266079	−	0.170999i
$950$		0			0
$951$	−9.90076	−	11.4261i	−0.321054	−	0.370516i
$952$		0			0
$953$	−5.80162	+	12.7038i	−0.187933	+	0.411515i	−0.980022	−	0.198890i	$-0.936266\pi$
$953$	−5.80162	+	12.7038i	−0.187933	+	0.411515i	0.792089	+	0.610406i	$0.208994\pi$
$954$		0			0
$955$	13.1353	−	3.85687i	0.425048	−	0.124805i
$956$		0			0
$957$	0.412689	+	2.87032i	0.0133404	+	0.0927842i
$958$		0			0
$959$	−15.2227	−	33.3330i	−0.491566	−	1.07638i
$960$		0			0
$961$	−2.18235	+	15.1786i	−0.0703983	+	0.489631i
$962$		0			0
$963$	0.152798	−	0.176338i	0.00492385	−	0.00568243i
$964$		0			0
$965$	34.0974			1.09763
$966$		0			0
$967$	18.2603			0.587212			0.293606	−	0.955926i	$-0.405145\pi$
$967$	18.2603			0.587212			0.293606	+	0.955926i	$0.405145\pi$
$968$		0			0
$969$	8.43607	−	9.73574i	0.271006	−	0.312757i
$970$		0			0
$971$	1.49342	−	10.3869i	0.0479260	−	0.333332i	−0.951726	−	0.306949i	$-0.900692\pi$
$971$	1.49342	−	10.3869i	0.0479260	−	0.333332i	0.999652	−	0.0263833i	$-0.00839905\pi$
$972$		0			0
$973$	5.34644	+	11.7071i	0.171399	+	0.375311i
$974$		0			0
$975$	1.15123	+	8.00700i	0.0368690	+	0.256429i
$976$		0			0
$977$	−28.2385	+	8.29157i	−0.903429	+	0.265271i	−0.700273	−	0.713875i	$-0.746938\pi$
$977$	−28.2385	+	8.29157i	−0.903429	+	0.265271i	−0.203157	+	0.979146i	$0.565120\pi$
$978$		0			0
$979$	6.81158	−	14.9153i	0.217699	−	0.476694i
$980$		0			0
$981$	7.76214	+	8.95799i	0.247826	+	0.286007i
$982$		0			0
$983$	−16.1940	+	10.4073i	−0.516509	+	0.331940i	−0.772789	−	0.634662i	$-0.781139\pi$
$983$	−16.1940	+	10.4073i	−0.516509	+	0.331940i	0.256281	+	0.966602i	$0.417503\pi$
$984$		0			0
$985$	−6.57735	−	4.22700i	−0.209572	−	0.134684i
$986$		0			0
$987$	−5.64341	−	1.65705i	−0.179632	−	0.0527446i
$988$		0			0
$989$	−18.8328	−	3.83997i	−0.598847	−	0.122104i
$990$		0			0
$991$	−48.0664	−	14.1136i	−1.52688	−	0.448332i	−0.592786	−	0.805360i	$-0.701972\pi$
$991$	−48.0664	−	14.1136i	−1.52688	−	0.448332i	−0.934094	+	0.357027i	$0.883790\pi$
$992$		0			0
$993$	24.9746	+	16.0502i	0.792544	+	0.509337i
$994$		0			0
$995$	34.1295	−	21.9337i	1.08198	−	0.695345i
$996$		0			0
$997$	23.8904	+	27.5710i	0.756618	+	0.873184i	0.995192	−	0.0979406i	$-0.0312255\pi$
$997$	23.8904	+	27.5710i	0.756618	+	0.873184i	−0.238574	+	0.971124i	$0.576680\pi$
$998$		0			0
$999$	2.84175	−	6.22257i	0.0899090	−	0.196873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.i.a.133.2	✓	20
3.2	odd	2		828.2.q.c.685.1		20
23.3	even	11		6348.2.a.s.1.4		10
23.9	even	11	inner	276.2.i.a.193.2	yes	20
23.20	odd	22		6348.2.a.t.1.7		10
69.32	odd	22		828.2.q.c.469.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.i.a.133.2	✓	20	1.1	even	1	trivial
276.2.i.a.193.2	yes	20	23.9	even	11	inner
828.2.q.c.469.1		20	69.32	odd	22
828.2.q.c.685.1		20	3.2	odd	2
6348.2.a.s.1.4		10	23.3	even	11
6348.2.a.t.1.7		10	23.20	odd	22

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.i (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.654861 + 0.755750i) q^{3} +(0.217172 - 1.51046i) q^{5} +(-1.55685 - 3.40903i) q^{7} +(-0.142315 - 0.989821i) q^{9} +O(q^{10})\)	\(q+(-0.654861 + 0.755750i) q^{3} +(0.217172 - 1.51046i) q^{5} +(-1.55685 - 3.40903i) q^{7} +(-0.142315 - 0.989821i) q^{9} +(1.04445 - 0.306679i) q^{11} +(1.25796 - 2.75455i) q^{13} +(0.999315 + 1.15327i) q^{15} +(2.61063 - 1.67775i) q^{17} +(-3.49220 - 2.24430i) q^{19} +(3.59589 + 1.05585i) q^{21} +(2.35317 + 4.17883i) q^{23} +(2.56313 + 0.752602i) q^{25} +(0.841254 + 0.540641i) q^{27} +(2.24106 - 1.44024i) q^{29} +(-4.45761 - 5.14435i) q^{31} +(-0.452198 + 0.990176i) q^{33} +(-5.48731 + 1.61122i) q^{35} +(-0.973540 - 6.77112i) q^{37} +(1.25796 + 2.75455i) q^{39} +(-1.41678 + 9.85394i) q^{41} +(-2.62449 + 3.02882i) q^{43} -1.52600 q^{45} -1.56940 q^{47} +(-4.61365 + 5.32444i) q^{49} +(-0.441641 + 3.07168i) q^{51} +(-1.19196 - 2.61003i) q^{53} +(-0.236402 - 1.64421i) q^{55} +(3.98303 - 1.16952i) q^{57} +(-6.11707 + 13.3945i) q^{59} +(3.42833 + 3.95650i) q^{61} +(-3.15276 + 2.02616i) q^{63} +(-3.88745 - 2.49831i) q^{65} +(4.44565 + 1.30536i) q^{67} +(-4.69914 - 0.958148i) q^{69} +(14.6278 + 4.29512i) q^{71} +(2.70682 + 1.73957i) q^{73} +(-2.24727 + 1.44423i) q^{75} +(-2.67153 - 3.08311i) q^{77} +(-1.28701 + 2.81816i) q^{79} +(-0.959493 + 0.281733i) q^{81} +(-0.773779 - 5.38175i) q^{83} +(-1.96723 - 4.30763i) q^{85} +(-0.379120 + 2.63684i) q^{87} +(9.86433 - 11.3840i) q^{89} -11.3488 q^{91} +6.80696 q^{93} +(-4.14834 + 4.78744i) q^{95} +(0.546130 - 3.79842i) q^{97} +(-0.452198 - 0.990176i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9	\( 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9} - 22 q^{13} + 7 q^{15} + 7 q^{17} + 19 q^{19} + 20 q^{23} + 20 q^{25} - 2 q^{27} + 32 q^{29} - 3 q^{31} + 11 q^{33} - 26 q^{35} - 10 q^{37} - 22 q^{39} - 40 q^{41} + 8 q^{43} - 4 q^{45} - 18 q^{47} - 34 q^{49} - 26 q^{51} - 34 q^{53} - 17 q^{55} - 3 q^{57} - 32 q^{59} + 32 q^{61} + 49 q^{65} + 35 q^{67} - 2 q^{69} + 33 q^{71} - q^{73} - 2 q^{75} - 50 q^{77} + 22 q^{79} - 2 q^{81} - 14 q^{83} - 9 q^{85} - 12 q^{87} + 10 q^{89} - 72 q^{91} + 30 q^{93} - 51 q^{95} - 4 q^{97} + 11 q^{99}+O(q^{100}) \) 20 * q - 2 * q^3 - 4 * q^5 - 2 * q^9 - 22 * q^13 + 7 * q^15 + 7 * q^17 + 19 * q^19 + 20 * q^23 + 20 * q^25 - 2 * q^27 + 32 * q^29 - 3 * q^31 + 11 * q^33 - 26 * q^35 - 10 * q^37 - 22 * q^39 - 40 * q^41 + 8 * q^43 - 4 * q^45 - 18 * q^47 - 34 * q^49 - 26 * q^51 - 34 * q^53 - 17 * q^55 - 3 * q^57 - 32 * q^59 + 32 * q^61 + 49 * q^65 + 35 * q^67 - 2 * q^69 + 33 * q^71 - q^73 - 2 * q^75 - 50 * q^77 + 22 * q^79 - 2 * q^81 - 14 * q^83 - 9 * q^85 - 12 * q^87 + 10 * q^89 - 72 * q^91 + 30 * q^93 - 51 * q^95 - 4 * q^97 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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