LMFDB - Embedded newform 276.2.i.b.193.2

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} - 4 x^{19} + 18 x^{18} - 58 x^{17} + 169 x^{16} - 363 x^{15} + 800 x^{14} - 1682 x^{13} + \cdots + 529 $ x^20 - 4x^19 + 18x^18 - 58x^17 + 169x^16 - 363x^15 + 800x^14 - 1682x^13 + 2817x^12 - 3731x^11 + 5829x^10 - 8312x^9 + 7737x^8 + 4348x^7 - 12995x^6 - 2574x^5 + 24401x^4 + 22582x^3 + 9558x^2 + 2829*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			193.2
Root			$-0.908456 + 1.98924i$ of defining polynomial
Character	$\chi$	$=$	276.193
Dual form			276.2.i.b.133.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.654861 + 0.755750i) q^{3} +(0.355980 + 2.47589i) q^{5} +(-0.671250 + 1.46983i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})$	\(q+(0.654861 + 0.755750i) q^{3} +(0.355980 + 2.47589i) q^{5} +(-0.671250 + 1.46983i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-2.90865 - 0.854058i) q^{11} +(0.814407 + 1.78330i) q^{13} +(-1.63804 + 1.89040i) q^{15} +(-0.513691 - 0.330129i) q^{17} +(4.77936 - 3.07151i) q^{19} +(-1.55040 + 0.455239i) q^{21} +(-1.13430 + 4.65976i) q^{23} +(-1.20586 + 0.354071i) q^{25} +(-0.841254 + 0.540641i) q^{27} +(5.08975 + 3.27098i) q^{29} +(6.59855 - 7.61514i) q^{31} +(-1.25931 - 2.75750i) q^{33} +(-3.87810 - 1.13871i) q^{35} +(0.255743 - 1.77873i) q^{37} +(-0.814407 + 1.78330i) q^{39} +(0.781353 + 5.43443i) q^{41} +(-6.13145 - 7.07607i) q^{43} -2.50135 q^{45} -1.60979 q^{47} +(2.87420 + 3.31700i) q^{49} +(-0.0869011 - 0.604411i) q^{51} +(3.13986 - 6.87534i) q^{53} +(1.07913 - 7.50554i) q^{55} +(5.45110 + 1.60059i) q^{57} +(-3.62648 - 7.94087i) q^{59} +(1.65940 - 1.91505i) q^{61} +(-1.35934 - 0.873596i) q^{63} +(-4.12535 + 2.65120i) q^{65} +(0.507772 - 0.149095i) q^{67} +(-4.26442 + 2.19425i) q^{69} +(-0.986827 + 0.289758i) q^{71} +(2.40469 - 1.54540i) q^{73} +(-1.05726 - 0.679458i) q^{75} +(3.20775 - 3.70195i) q^{77} +(-1.69594 - 3.71359i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(1.25332 - 8.71701i) q^{83} +(0.634501 - 1.38936i) q^{85} +(0.861033 + 5.98861i) q^{87} +(-9.26229 - 10.6892i) q^{89} -3.16782 q^{91} +10.0763 q^{93} +(9.30607 + 10.7398i) q^{95} +(2.48478 + 17.2820i) q^{97} +(1.25931 - 2.75750i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9}+O(q^{10}) $ 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9	$ 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9} + 14 q^{13} - 11 q^{15} + 3 q^{17} + 7 q^{19} + 4 q^{21} + 24 q^{23} + 12 q^{25} + 2 q^{27} - 26 q^{29} + 33 q^{31} - 11 q^{33} - 2 q^{35} - 18 q^{37} - 14 q^{39} + 4 q^{41} - 40 q^{43} - 54 q^{47} + 30 q^{49} - 14 q^{51} - 14 q^{53} + 11 q^{55} - 29 q^{57} + 4 q^{59} + 12 q^{61} - 4 q^{63} - 33 q^{65} + 15 q^{67} - 2 q^{69} - 33 q^{71} + 15 q^{73} + 10 q^{75} + 66 q^{77} - 42 q^{79} - 2 q^{81} - 14 q^{83} - 13 q^{85} + 4 q^{87} - 66 q^{89} - 16 q^{91} - 22 q^{93} - 31 q^{95} - 24 q^{97} + 11 q^{99}+O(q^{100}) $ 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9 + 14 * q^13 - 11 * q^15 + 3 * q^17 + 7 * q^19 + 4 * q^21 + 24 * q^23 + 12 * q^25 + 2 * q^27 - 26 * q^29 + 33 * q^31 - 11 * q^33 - 2 * q^35 - 18 * q^37 - 14 * q^39 + 4 * q^41 - 40 * q^43 - 54 * q^47 + 30 * q^49 - 14 * q^51 - 14 * q^53 + 11 * q^55 - 29 * q^57 + 4 * q^59 + 12 * q^61 - 4 * q^63 - 33 * q^65 + 15 * q^67 - 2 * q^69 - 33 * q^71 + 15 * q^73 + 10 * q^75 + 66 * q^77 - 42 * q^79 - 2 * q^81 - 14 * q^83 - 13 * q^85 + 4 * q^87 - 66 * q^89 - 16 * q^91 - 22 * q^93 - 31 * q^95 - 24 * q^97 + 11 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{5}{11}\right)$	$1$	$1$

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
$5$	0.355980	+	2.47589i	0.159199	+	1.10725i	0.900114	+	0.435654i	$0.143483\pi$
$5$	0.355980	+	2.47589i	0.159199	+	1.10725i	−0.740915	+	0.671599i	$0.765608\pi$
$6$		0			0
$7$	−0.671250	+	1.46983i	−0.253709	+	0.555544i	−0.993037	−	0.117800i	$-0.962416\pi$
$7$	−0.671250	+	1.46983i	−0.253709	+	0.555544i	0.739329	+	0.673345i	$0.235143\pi$
$8$		0			0
$9$	−0.142315	+	0.989821i	−0.0474383	+	0.329940i
$10$		0			0
$11$	−2.90865	−	0.854058i	−0.876992	−	0.257508i	−0.187905	−	0.982187i	$-0.560170\pi$
$11$	−2.90865	−	0.854058i	−0.876992	−	0.257508i	−0.689087	+	0.724679i	$0.741988\pi$
$12$		0			0
$13$	0.814407	+	1.78330i	0.225876	+	0.494599i	0.988308	−	0.152469i	$-0.0487223\pi$
$13$	0.814407	+	1.78330i	0.225876	+	0.494599i	−0.762432	+	0.647068i	$0.775995\pi$
$14$		0			0
$15$	−1.63804	+	1.89040i	−0.422939	+	0.488098i
$16$		0			0
$17$	−0.513691	−	0.330129i	−0.124588	−	0.0800681i	0.476862	−	0.878978i	$-0.341774\pi$
$17$	−0.513691	−	0.330129i	−0.124588	−	0.0800681i	−0.601451	+	0.798910i	$0.705410\pi$
$18$		0			0
$19$	4.77936	−	3.07151i	1.09646	−	0.704652i	0.138158	−	0.990410i	$-0.455882\pi$
$19$	4.77936	−	3.07151i	1.09646	−	0.704652i	0.958302	+	0.285758i	$0.0922455\pi$
$20$		0			0
$21$	−1.55040	+	0.455239i	−0.338325	+	0.0993412i
$22$		0			0
$23$	−1.13430	+	4.65976i	−0.236518	+	0.971627i
$23$	−1.13430	+	4.65976i	−0.236518	+	0.971627i
$24$		0			0
$25$	−1.20586	+	0.354071i	−0.241171	+	0.0708143i
$26$		0			0
$27$	−0.841254	+	0.540641i	−0.161899	+	0.104046i
$28$		0			0
$29$	5.08975	+	3.27098i	0.945143	+	0.607406i	0.919849	−	0.392274i	$-0.128311\pi$
$29$	5.08975	+	3.27098i	0.945143	+	0.607406i	0.0252942	+	0.999680i	$0.491948\pi$
$30$		0			0
$31$	6.59855	−	7.61514i	1.18514	−	1.36772i	0.270864	−	0.962618i	$-0.412691\pi$
$31$	6.59855	−	7.61514i	1.18514	−	1.36772i	0.914272	−	0.405101i	$-0.132764\pi$
$32$		0			0
$33$	−1.25931	−	2.75750i	−0.219218	−	0.480019i
$34$		0			0
$35$	−3.87810	−	1.13871i	−0.655518	−	0.192477i
$36$		0			0
$37$	0.255743	−	1.77873i	0.0420439	−	0.292422i	−0.957941	−	0.286964i	$-0.907354\pi$
$37$	0.255743	−	1.77873i	0.0420439	−	0.292422i	0.999985	−	0.00545711i	$-0.00173706\pi$
$38$		0			0
$39$	−0.814407	+	1.78330i	−0.130409	+	0.285557i
$40$		0			0
$41$	0.781353	+	5.43443i	0.122027	+	0.848716i	0.955254	+	0.295785i	$0.0955813\pi$
$41$	0.781353	+	5.43443i	0.122027	+	0.848716i	−0.833228	+	0.552930i	$0.813510\pi$
$42$		0			0
$43$	−6.13145	−	7.07607i	−0.935037	−	1.07909i	−0.996715	−	0.0809942i	$-0.974190\pi$
$43$	−6.13145	−	7.07607i	−0.935037	−	1.07909i	0.0616774	−	0.998096i	$-0.480355\pi$
$44$		0			0
$45$	−2.50135			−0.372880
$46$		0			0
$47$	−1.60979			−0.234812			−0.117406	−	0.993084i	$-0.537458\pi$
$47$	−1.60979			−0.234812			−0.117406	+	0.993084i	$0.537458\pi$
$48$		0			0
$49$	2.87420	+	3.31700i	0.410599	+	0.473857i
$50$		0			0
$51$	−0.0869011	−	0.604411i	−0.0121686	−	0.0846344i
$52$		0			0
$53$	3.13986	−	6.87534i	0.431293	−	0.944400i	−0.561822	−	0.827258i	$-0.689899\pi$
$53$	3.13986	−	6.87534i	0.431293	−	0.944400i	0.993115	−	0.117142i	$-0.0373733\pi$
$54$		0			0
$55$	1.07913	−	7.50554i	0.145510	−	1.01205i
$56$		0			0
$57$	5.45110	+	1.60059i	0.722016	+	0.212003i
$58$		0			0
$59$	−3.62648	−	7.94087i	−0.472127	−	1.03381i	−0.984554	−	0.175083i	$-0.943981\pi$
$59$	−3.62648	−	7.94087i	−0.472127	−	1.03381i	0.512427	−	0.858731i	$-0.328747\pi$
$60$		0			0
$61$	1.65940	−	1.91505i	0.212465	−	0.245197i	−0.639507	−	0.768785i	$-0.720861\pi$
$61$	1.65940	−	1.91505i	0.212465	−	0.245197i	0.851972	+	0.523588i	$0.175407\pi$
$62$		0			0
$63$	−1.35934	−	0.873596i	−0.171261	−	0.110063i
$64$		0			0
$65$	−4.12535	+	2.65120i	−0.511687	+	0.328841i
$66$		0			0
$67$	0.507772	−	0.149095i	0.0620343	−	0.0182149i	−0.250568	−	0.968099i	$-0.580617\pi$
$67$	0.507772	−	0.149095i	0.0620343	−	0.0182149i	0.312602	+	0.949884i	$0.398799\pi$
$68$		0			0
$69$	−4.26442	+	2.19425i	−0.513376	+	0.264156i
$70$		0			0
$71$	−0.986827	+	0.289758i	−0.117115	+	0.0343880i	−0.339765	−	0.940510i	$-0.610347\pi$
$71$	−0.986827	+	0.289758i	−0.117115	+	0.0343880i	0.222650	+	0.974898i	$0.428529\pi$
$72$		0			0
$73$	2.40469	−	1.54540i	0.281447	−	0.180875i	−0.392299	−	0.919838i	$-0.628320\pi$
$73$	2.40469	−	1.54540i	0.281447	−	0.180875i	0.673747	+	0.738962i	$0.264684\pi$
$74$		0			0
$75$	−1.05726	−	0.679458i	−0.122082	−	0.0784570i
$76$		0			0
$77$	3.20775	−	3.70195i	0.365557	−	0.421876i
$78$		0			0
$79$	−1.69594	−	3.71359i	−0.190808	−	0.417811i	0.789914	−	0.613217i	$-0.210125\pi$
$79$	−1.69594	−	3.71359i	−0.190808	−	0.417811i	−0.980723	+	0.195406i	$0.937398\pi$
$80$		0			0
$81$	−0.959493	−	0.281733i	−0.106610	−	0.0313036i
$82$		0			0
$83$	1.25332	−	8.71701i	0.137569	−	0.956816i	−0.797744	−	0.602996i	$-0.793974\pi$
$83$	1.25332	−	8.71701i	0.137569	−	0.956816i	0.935314	−	0.353820i	$-0.115117\pi$
$84$		0			0
$85$	0.634501	−	1.38936i	0.0688213	−	0.150698i
$86$		0			0
$87$	0.861033	+	5.98861i	0.0923124	+	0.642047i
$88$		0			0
$89$	−9.26229	−	10.6892i	−0.981800	−	1.13306i	−0.991102	−	0.133101i	$-0.957506\pi$
$89$	−9.26229	−	10.6892i	−0.981800	−	1.13306i	0.00930212	−	0.999957i	$-0.497039\pi$
$90$		0			0
$91$	−3.16782			−0.332078
$92$		0			0
$93$	10.0763			1.04486
$94$		0			0
$95$	9.30607	+	10.7398i	0.954783	+	1.10188i
$96$		0			0
$97$	2.48478	+	17.2820i	0.252291	+	1.75472i	0.584386	+	0.811476i	$0.301336\pi$
$97$	2.48478	+	17.2820i	0.252291	+	1.75472i	−0.332095	+	0.943246i	$0.607755\pi$
$98$		0			0
$99$	1.25931	−	2.75750i	0.126565	−	0.277139i
$100$		0			0
$101$	0.479387	−	3.33421i	0.0477008	−	0.331767i	−0.951972	−	0.306185i	$-0.900947\pi$
$101$	0.479387	−	3.33421i	0.0477008	−	0.331767i	0.999673	−	0.0255812i	$-0.00814365\pi$
$102$		0			0
$103$	−6.21481	−	1.82483i	−0.612363	−	0.179806i	−0.0391785	−	0.999232i	$-0.512474\pi$
$103$	−6.21481	−	1.82483i	−0.612363	−	0.179806i	−0.573185	+	0.819426i	$0.694292\pi$
$104$		0			0
$105$	−1.67903	−	3.67657i	−0.163857	−	0.358796i
$106$		0			0
$107$	−9.07731	+	10.4758i	−0.877537	+	1.01273i	0.122258	+	0.992498i	$0.460986\pi$
$107$	−9.07731	+	10.4758i	−0.877537	+	1.01273i	−0.999795	+	0.0202334i	$0.993559\pi$
$108$		0			0
$109$	7.10123	+	4.56368i	0.680174	+	0.437121i	0.834580	−	0.550886i	$-0.185710\pi$
$109$	7.10123	+	4.56368i	0.680174	+	0.437121i	−0.154406	+	0.988007i	$0.549346\pi$
$110$		0			0
$111$	1.51175	−	0.971543i	0.143489	−	0.0922148i
$112$		0			0
$113$	−3.85561	+	1.13211i	−0.362705	+	0.106500i	−0.458007	−	0.888949i	$-0.651437\pi$
$113$	−3.85561	+	1.13211i	−0.362705	+	0.106500i	0.0953017	+	0.995448i	$0.469618\pi$
$114$		0			0
$115$	−11.9409	−	1.14963i	−1.11349	−	0.107203i
$116$		0			0
$117$	−1.88105	+	0.552327i	−0.173903	+	0.0510626i
$118$		0			0
$119$	0.830050	−	0.533440i	0.0760905	−	0.0489004i
$120$		0			0
$121$	−1.52294	−	0.978735i	−0.138449	−	0.0889759i
$122$		0			0
$123$	−3.59539	+	4.14930i	−0.324186	+	0.374130i
$124$		0			0
$125$	3.88959	+	8.51702i	0.347896	+	0.761786i
$126$		0			0
$127$	15.6937	+	4.60810i	1.39259	+	0.408903i	0.890134	−	0.455698i	$-0.150610\pi$
$127$	15.6937	+	4.60810i	1.39259	+	0.408903i	0.502460	+	0.864601i	$0.332429\pi$
$128$		0			0
$129$	1.33249	−	9.26768i	0.117319	−	0.815974i
$130$		0			0
$131$	−2.48164	+	5.43403i	−0.216822	+	0.474774i	−0.986521	−	0.163633i	$-0.947679\pi$
$131$	−2.48164	+	5.43403i	−0.216822	+	0.474774i	0.769699	+	0.638406i	$0.220406\pi$
$132$		0			0
$133$	1.30646	+	9.08660i	0.113284	+	0.787908i
$134$		0			0
$135$	−1.63804	−	1.89040i	−0.140980	−	0.162699i
$136$		0			0
$137$	9.20400			0.786350			0.393175	−	0.919464i	$-0.371377\pi$
$137$	9.20400			0.786350			0.393175	+	0.919464i	$0.371377\pi$
$138$		0			0
$139$	−7.62219			−0.646506			−0.323253	−	0.946313i	$-0.604776\pi$
$139$	−7.62219			−0.646506			−0.323253	+	0.946313i	$0.604776\pi$
$140$		0			0
$141$	−1.05419	−	1.21660i	−0.0887787	−	0.102456i
$142$		0			0
$143$	−0.845784	−	5.88256i	−0.0707280	−	0.491924i
$144$		0			0
$145$	−6.28676	+	13.7661i	−0.522087	+	1.14321i
$146$		0			0
$147$	−0.624622	+	4.34434i	−0.0515180	+	0.358315i
$148$		0			0
$149$	10.5125	+	3.08675i	0.861219	+	0.252877i	0.682377	−	0.731001i	$-0.260946\pi$
$149$	10.5125	+	3.08675i	0.861219	+	0.252877i	0.178843	+	0.983878i	$0.442765\pi$
$150$		0			0
$151$	7.45242	+	16.3185i	0.606470	+	1.32798i	0.924963	+	0.380058i	$0.124096\pi$
$151$	7.45242	+	16.3185i	0.606470	+	1.32798i	−0.318493	+	0.947925i	$0.603177\pi$
$152$		0			0
$153$	0.399875	−	0.461480i	0.0323280	−	0.0373085i
$154$		0			0
$155$	21.2032	+	13.6265i	1.70308	+	1.09450i
$156$		0			0
$157$	−14.4538	+	9.28890i	−1.15354	+	0.741335i	−0.970341	−	0.241741i	$-0.922282\pi$
$157$	−14.4538	+	9.28890i	−1.15354	+	0.741335i	−0.183199	+	0.983076i	$0.558645\pi$
$158$		0			0
$159$	7.25221	−	2.12944i	0.575137	−	0.168876i
$160$		0			0
$161$	−6.08766	−	4.79510i	−0.479775	−	0.377906i
$162$		0			0
$163$	−16.3595	+	4.80359i	−1.28138	+	0.376246i	−0.850409	−	0.526121i	$-0.823646\pi$
$163$	−16.3595	+	4.80359i	−1.28138	+	0.376246i	−0.430967	+	0.902368i	$0.641828\pi$
$164$		0			0
$165$	6.37899	−	4.09953i	0.496604	−	0.319148i
$166$		0			0
$167$	19.3476	+	12.4339i	1.49716	+	0.962166i	0.995261	+	0.0972393i	$0.0310012\pi$
$167$	19.3476	+	12.4339i	1.49716	+	0.962166i	0.501898	+	0.864927i	$0.332635\pi$
$168$		0			0
$169$	5.99628	−	6.92008i	0.461252	−	0.532314i
$170$		0			0
$171$	2.36007	+	5.16783i	0.180479	+	0.395194i
$172$		0			0
$173$	−6.98436	−	2.05079i	−0.531011	−	0.155919i	0.00522586	−	0.999986i	$-0.498337\pi$
$173$	−6.98436	−	2.05079i	−0.531011	−	0.155919i	−0.536237	+	0.844067i	$0.680155\pi$
$174$		0			0
$175$	0.289005	−	2.01008i	0.0218467	−	0.151947i
$176$		0			0
$177$	3.62648	−	7.94087i	0.272583	−	0.596873i
$178$		0			0
$179$	−1.90103	−	13.2219i	−0.142089	−	0.988253i	−0.928707	−	0.370813i	$-0.879079\pi$
$179$	−1.90103	−	13.2219i	−0.142089	−	0.988253i	0.786618	−	0.617440i	$-0.211830\pi$
$180$		0			0
$181$	−17.1977	−	19.8472i	−1.27829	−	1.47523i	−0.803713	−	0.595017i	$-0.797145\pi$
$181$	−17.1977	−	19.8472i	−1.27829	−	1.47523i	−0.474581	−	0.880212i	$-0.657400\pi$
$182$		0			0
$183$	2.53398			0.187317
$184$		0			0
$185$	4.49498			0.330478
$186$		0			0
$187$	1.21220	+	1.39895i	0.0886448	+	0.102302i
$188$		0			0
$189$	−0.229960	−	1.59941i	−0.0167271	−	0.116340i
$190$		0			0
$191$	−1.12174	+	2.45628i	−0.0811665	+	0.177730i	−0.945864	−	0.324563i	$-0.894783\pi$
$191$	−1.12174	+	2.45628i	−0.0811665	+	0.177730i	0.864698	+	0.502293i	$0.167510\pi$
$192$		0			0
$193$	−2.20061	+	15.3056i	−0.158403	+	1.10172i	0.743173	+	0.669100i	$0.233320\pi$
$193$	−2.20061	+	15.3056i	−0.158403	+	1.10172i	−0.901576	+	0.432621i	$0.857589\pi$
$194$		0			0
$195$	−4.70518	−	1.38156i	−0.336945	−	0.0989359i
$196$		0			0
$197$	−9.28776	−	20.3374i	−0.661725	−	1.44898i	−0.880906	−	0.473292i	$-0.843066\pi$
$197$	−9.28776	−	20.3374i	−0.661725	−	1.44898i	0.219180	−	0.975684i	$-0.429662\pi$
$198$		0			0
$199$	−3.29918	+	3.80746i	−0.233873	+	0.269904i	−0.860539	−	0.509384i	$-0.829873\pi$
$199$	−3.29918	+	3.80746i	−0.233873	+	0.269904i	0.626667	+	0.779287i	$0.284419\pi$
$200$		0			0
$201$	0.445199	+	0.286112i	0.0314019	+	0.0201808i
$202$		0			0
$203$	−8.22429	+	5.28543i	−0.577232	+	0.370964i
$204$		0			0
$205$	−13.1769	+	3.86909i	−0.920316	+	0.270229i
$206$		0			0
$207$	−4.45090	−	1.78591i	−0.309359	−	0.124129i
$208$		0			0
$209$	−16.5247	+	4.85210i	−1.14304	+	0.335627i
$210$		0			0
$211$	18.4314	−	11.8451i	1.26887	−	0.815453i	0.279398	−	0.960175i	$-0.409865\pi$
$211$	18.4314	−	11.8451i	1.26887	−	0.815453i	0.989472	+	0.144722i	$0.0462288\pi$
$212$		0			0
$213$	−0.865219	−	0.556042i	−0.0592838	−	0.0380994i
$214$		0			0
$215$	15.3369	−	17.6997i	1.04597	−	1.20711i
$216$		0			0
$217$	6.76369	+	14.8104i	0.459149	+	1.00540i
$218$		0			0
$219$	2.74267	+	0.805320i	0.185332	+	0.0544185i
$220$		0			0
$221$	0.170367	−	1.18493i	0.0114601	−	0.0797067i
$222$		0			0
$223$	6.42932	−	14.0782i	0.430539	−	0.942749i	−0.562700	−	0.826661i	$-0.690237\pi$
$223$	6.42932	−	14.0782i	0.430539	−	0.942749i	0.993239	−	0.116088i	$-0.0370354\pi$
$224$		0			0
$225$	−0.178856	−	1.24397i	−0.0119237	−	0.0829315i
$226$		0			0
$227$	5.89546	+	6.80372i	0.391295	+	0.451579i	0.916880	−	0.399162i	$-0.130699\pi$
$227$	5.89546	+	6.80372i	0.391295	+	0.451579i	−0.525585	+	0.850741i	$0.676154\pi$
$228$		0			0
$229$	−28.7181			−1.89775			−0.948874	−	0.315656i	$-0.897775\pi$
$229$	−28.7181			−1.89775			−0.948874	+	0.315656i	$0.897775\pi$
$230$		0			0
$231$	4.89838			0.322289
$232$		0			0
$233$	−13.8636	−	15.9995i	−0.908236	−	1.04816i	−0.998634	−	0.0522548i	$-0.983359\pi$
$233$	−13.8636	−	15.9995i	−0.908236	−	1.04816i	0.0903974	−	0.995906i	$-0.471186\pi$
$234$		0			0
$235$	−0.573053	−	3.98567i	−0.0373818	−	0.259996i
$236$		0			0
$237$	1.69594	−	3.71359i	0.110163	−	0.241224i
$238$		0			0
$239$	1.05689	−	7.35085i	0.0683647	−	0.475487i	−0.926663	−	0.375892i	$-0.877336\pi$
$239$	1.05689	−	7.35085i	0.0683647	−	0.475487i	0.995028	−	0.0995946i	$-0.0317546\pi$
$240$		0			0
$241$	−7.31515	−	2.14792i	−0.471210	−	0.138360i	0.0375017	−	0.999297i	$-0.488060\pi$
$241$	−7.31515	−	2.14792i	−0.471210	−	0.138360i	−0.508712	+	0.860937i	$0.669878\pi$
$242$		0			0
$243$	−0.415415	−	0.909632i	−0.0266489	−	0.0583529i
$244$		0			0
$245$	−7.18938	+	8.29698i	−0.459312	+	0.530075i
$246$		0			0
$247$	9.36976	+	6.02158i	0.596184	+	0.383144i
$248$		0			0
$249$	7.40862	−	4.76123i	0.469502	−	0.301731i
$250$		0			0
$251$	−20.0357	+	5.88303i	−1.26465	+	0.371333i	−0.844221	−	0.535994i	$-0.819937\pi$
$251$	−20.0357	+	5.88303i	−1.26465	+	0.371333i	−0.420424	+	0.907328i	$0.638119\pi$
$252$		0			0
$253$	7.27899	−	12.5849i	0.457626	−	0.791204i
$254$		0			0
$255$	1.46552	−	0.430316i	0.0917744	−	0.0269474i
$256$		0			0
$257$	17.2321	−	11.0744i	1.07491	−	0.690803i	0.121534	−	0.992587i	$-0.461219\pi$
$257$	17.2321	−	11.0744i	1.07491	−	0.690803i	0.953376	+	0.301785i	$0.0975824\pi$
$258$		0			0
$259$	2.44277	+	1.56987i	0.151786	+	0.0975471i
$260$		0			0
$261$	−3.96204	+	4.57243i	−0.245244	+	0.283027i
$262$		0			0
$263$	−1.76803	−	3.87144i	−0.109021	−	0.238723i	0.847256	−	0.531185i	$-0.178253\pi$
$263$	−1.76803	−	3.87144i	−0.109021	−	0.238723i	−0.956277	+	0.292461i	$0.905526\pi$
$264$		0			0
$265$	18.1403	+	5.32648i	1.11435	+	0.327203i
$266$		0			0
$267$	2.01289	−	13.9999i	0.123187	−	0.856782i
$268$		0			0
$269$	11.4807	−	25.1393i	0.699993	−	1.53277i	−0.139987	−	0.990153i	$-0.544706\pi$
$269$	11.4807	−	25.1393i	0.699993	−	1.53277i	0.839980	−	0.542617i	$-0.182567\pi$
$270$		0			0
$271$	2.72634	+	18.9621i	0.165613	+	1.15187i	0.887820	+	0.460190i	$0.152219\pi$
$271$	2.72634	+	18.9621i	0.165613	+	1.15187i	−0.722207	+	0.691677i	$0.756872\pi$
$272$		0			0
$273$	−2.07448	−	2.39408i	−0.125553	−	0.144896i
$274$		0			0
$275$	3.80981			0.229740
$276$		0			0
$277$	−0.797542			−0.0479197			−0.0239598	−	0.999713i	$-0.507627\pi$
$277$	−0.797542			−0.0479197			−0.0239598	+	0.999713i	$0.507627\pi$
$278$		0			0
$279$	6.59855	+	7.61514i	0.395045	+	0.455906i
$280$		0			0
$281$	−3.52989	−	24.5509i	−0.210576	−	1.46459i	−0.771241	−	0.636544i	$-0.780363\pi$
$281$	−3.52989	−	24.5509i	−0.210576	−	1.46459i	0.560665	−	0.828043i	$-0.310546\pi$
$282$		0			0
$283$	2.38329	−	5.21867i	0.141672	−	0.310218i	−0.825474	−	0.564440i	$-0.809092\pi$
$283$	2.38329	−	5.21867i	0.141672	−	0.310218i	0.967146	+	0.254222i	$0.0818195\pi$
$284$		0			0
$285$	−2.02240	+	14.0661i	−0.119797	+	0.833205i
$286$		0			0
$287$	−8.51218	−	2.49940i	−0.502458	−	0.147535i
$288$		0			0
$289$	−6.90716	−	15.1246i	−0.406304	−	0.889681i
$290$		0			0
$291$	−11.4337	+	13.1952i	−0.670255	+	0.773515i
$292$		0			0
$293$	16.6240	+	10.6836i	0.971182	+	0.624141i	0.927071	−	0.374886i	$-0.122318\pi$
$293$	16.6240	+	10.6836i	0.971182	+	0.624141i	0.0441110	+	0.999027i	$0.485954\pi$
$294$		0			0
$295$	18.3698	−	11.8055i	1.06953	−	0.687346i
$296$		0			0
$297$	2.90865	−	0.854058i	0.168777	−	0.0495574i
$298$		0			0
$299$	−9.23354	+	1.77214i	−0.533990	+	0.102485i
$300$		0			0
$301$	14.5164	−	4.26239i	0.836709	−	0.245680i
$302$		0			0
$303$	2.83376	−	1.82115i	0.162795	−	0.104622i
$304$		0			0
$305$	5.33217	+	3.42678i	0.305319	+	0.196217i
$306$		0			0
$307$	−20.7426	+	23.9382i	−1.18384	+	1.36623i	−0.268636	+	0.963242i	$0.586573\pi$
$307$	−20.7426	+	23.9382i	−1.18384	+	1.36623i	−0.915207	+	0.402985i	$0.867973\pi$
$308$		0			0
$309$	−2.69072	−	5.89185i	−0.153070	−	0.335176i
$310$		0			0
$311$	13.7275	+	4.03076i	0.778415	+	0.228563i	0.646721	−	0.762727i	$-0.276140\pi$
$311$	13.7275	+	4.03076i	0.778415	+	0.228563i	0.131695	+	0.991290i	$0.457958\pi$
$312$		0			0
$313$	3.07729	−	21.4031i	0.173939	−	1.20977i	−0.696522	−	0.717535i	$-0.745270\pi$
$313$	3.07729	−	21.4031i	0.173939	−	1.20977i	0.870461	−	0.492237i	$-0.163821\pi$
$314$		0			0
$315$	1.67903	−	3.67657i	0.0946027	−	0.207151i
$316$		0			0
$317$	3.98125	+	27.6902i	0.223609	+	1.55524i	0.724223	+	0.689566i	$0.242199\pi$
$317$	3.98125	+	27.6902i	0.223609	+	1.55524i	−0.500614	+	0.865671i	$0.666892\pi$
$318$		0			0
$319$	−12.0107	−	13.8611i	−0.672470	−	0.776072i
$320$		0			0
$321$	−13.8614			−0.773670
$322$		0			0
$323$	−3.46911			−0.193026
$324$		0			0
$325$	−1.61347	−	1.86205i	−0.0894994	−	0.103288i
$326$		0			0
$327$	1.20131	+	8.35532i	0.0664328	+	0.462050i
$328$		0			0
$329$	1.08057	−	2.36612i	0.0595739	−	0.130449i
$330$		0			0
$331$	3.08444	−	21.4527i	0.169536	−	1.17915i	−0.710309	−	0.703890i	$-0.751445\pi$
$331$	3.08444	−	21.4527i	0.169536	−	1.17915i	0.879846	−	0.475260i	$-0.157646\pi$
$332$		0			0
$333$	1.72423	+	0.506280i	0.0944872	+	0.0277439i
$334$		0			0
$335$	0.549901	+	1.20411i	0.0300443	+	0.0657878i
$336$		0			0
$337$	−10.9749	+	12.6657i	−0.597841	+	0.689945i	−0.971342	−	0.237684i	$-0.923612\pi$
$337$	−10.9749	+	12.6657i	−0.597841	+	0.689945i	0.373501	+	0.927630i	$0.378157\pi$
$338$		0			0
$339$	−3.38048	−	2.17250i	−0.183602	−	0.117994i
$340$		0			0
$341$	−25.6967	+	16.5142i	−1.39155	+	0.894297i
$342$		0			0
$343$	−17.6575	+	5.18472i	−0.953417	+	0.279949i
$344$		0			0
$345$	−6.95076	−	9.77714i	−0.374216	−	0.526384i
$346$		0			0
$347$	−28.8306	+	8.46543i	−1.54771	+	0.454448i	−0.940415	−	0.340029i	$-0.889563\pi$
$347$	−28.8306	+	8.46543i	−1.54771	+	0.454448i	−0.607294	+	0.794478i	$0.707745\pi$
$348$		0			0
$349$	4.71136	−	3.02781i	0.252193	−	0.162075i	−0.408436	−	0.912787i	$-0.633926\pi$
$349$	4.71136	−	3.02781i	0.252193	−	0.162075i	0.660630	+	0.750712i	$0.270289\pi$
$350$		0			0
$351$	−1.64925	−	1.05991i	−0.0880304	−	0.0565737i
$352$		0			0
$353$	13.9623	−	16.1134i	0.743140	−	0.857629i	−0.250745	−	0.968053i	$-0.580675\pi$
$353$	13.9623	−	16.1134i	0.743140	−	0.857629i	0.993885	+	0.110424i	$0.0352209\pi$
$354$		0			0
$355$	−1.06870	−	2.34013i	−0.0567207	−	0.124201i
$356$		0			0
$357$	0.946714	+	0.277980i	0.0501054	+	0.0147123i
$358$		0			0
$359$	−2.62462	+	18.2546i	−0.138522	+	0.963444i	0.795430	+	0.606046i	$0.207245\pi$
$359$	−2.62462	+	18.2546i	−0.138522	+	0.963444i	−0.933952	+	0.357398i	$0.883664\pi$
$360$		0			0
$361$	5.51521	−	12.0766i	0.290274	−	0.635612i
$362$		0			0
$363$	−0.257636	−	1.79190i	−0.0135224	−	0.0940502i
$364$		0			0
$365$	4.68226	+	5.40361i	0.245080	+	0.282838i
$366$		0			0
$367$	7.46516			0.389678			0.194839	−	0.980835i	$-0.437582\pi$
$367$	7.46516			0.389678			0.194839	+	0.980835i	$0.437582\pi$
$368$		0			0
$369$	−5.49032			−0.285814
$370$		0			0
$371$	7.99796	+	9.23014i	0.415233	+	0.479205i
$372$		0			0
$373$	−0.661732	−	4.60245i	−0.0342632	−	0.238306i	0.965492	−	0.260433i	$-0.0838653\pi$
$373$	−0.661732	−	4.60245i	−0.0342632	−	0.238306i	−0.999755	+	0.0221271i	$0.992956\pi$
$374$		0			0
$375$	−3.88959	+	8.51702i	−0.200858	+	0.439817i
$376$		0			0
$377$	−1.68803	+	11.7405i	−0.0869377	+	0.604665i
$378$		0			0
$379$	3.92080	+	1.15125i	0.201398	+	0.0591358i	0.380876	−	0.924626i	$-0.375623\pi$
$379$	3.92080	+	1.15125i	0.201398	+	0.0591358i	−0.179478	+	0.983762i	$0.557441\pi$
$380$		0			0
$381$	6.79465	+	14.8782i	0.348100	+	0.762233i
$382$		0			0
$383$	−17.3199	+	19.9883i	−0.885008	+	1.02135i	0.114602	+	0.993412i	$0.463441\pi$
$383$	−17.3199	+	19.9883i	−0.885008	+	1.02135i	−0.999610	+	0.0279421i	$0.991105\pi$
$384$		0			0
$385$	10.3075	+	6.62424i	0.525319	+	0.337602i
$386$		0			0
$387$	7.87664	−	5.06201i	0.400392	−	0.257316i
$388$		0			0
$389$	8.71837	−	2.55994i	0.442039	−	0.129794i	−0.0531368	−	0.998587i	$-0.516922\pi$
$389$	8.71837	−	2.55994i	0.442039	−	0.129794i	0.495176	+	0.868793i	$0.335104\pi$
$390$		0			0
$391$	2.12100	−	2.01921i	0.107264	−	0.102116i
$392$		0			0
$393$	−5.73190	+	1.68304i	−0.289136	+	0.0848979i
$394$		0			0
$395$	8.59073	−	5.52093i	0.432246	−	0.277788i
$396$		0			0
$397$	−1.35151	−	0.868564i	−0.0678305	−	0.0435920i	0.506286	−	0.862366i	$-0.331018\pi$
$397$	−1.35151	−	0.868564i	−0.0678305	−	0.0435920i	−0.574117	+	0.818774i	$0.694654\pi$
$398$		0			0
$399$	−6.01165	+	6.93781i	−0.300959	+	0.347325i
$400$		0			0
$401$	13.6987	+	29.9960i	0.684081	+	1.49793i	0.858260	+	0.513215i	$0.171546\pi$
$401$	13.6987	+	29.9960i	0.684081	+	1.49793i	−0.174178	+	0.984714i	$0.555727\pi$
$402$		0			0
$403$	18.9540	+	5.56540i	0.944166	+	0.277232i
$404$		0			0
$405$	0.355980	−	2.47589i	0.0176888	−	0.123028i
$406$		0			0
$407$	−2.26301	+	4.95529i	−0.112173	+	0.245625i
$408$		0			0
$409$	3.77104	+	26.2281i	0.186466	+	1.29690i	0.841070	+	0.540926i	$0.181926\pi$
$409$	3.77104	+	26.2281i	0.186466	+	1.29690i	−0.654604	+	0.755972i	$0.727165\pi$
$410$		0			0
$411$	6.02734	+	6.95592i	0.297307	+	0.343110i
$412$		0			0
$413$	14.1060			0.694112
$414$		0			0
$415$	22.0285			1.08134
$416$		0			0
$417$	−4.99147	−	5.76047i	−0.244434	−	0.282091i
$418$		0			0
$419$	−3.26435	−	22.7040i	−0.159474	−	1.10916i	−0.899606	−	0.436703i	$-0.856146\pi$
$419$	−3.26435	−	22.7040i	−0.159474	−	1.10916i	0.740132	−	0.672461i	$-0.234763\pi$
$420$		0			0
$421$	6.15716	−	13.4823i	0.300082	−	0.657087i	−0.698186	−	0.715916i	$-0.746009\pi$
$421$	6.15716	−	13.4823i	0.300082	−	0.657087i	0.998268	+	0.0588288i	$0.0187366\pi$
$422$		0			0
$423$	0.229097	−	1.59341i	0.0111391	−	0.0774740i
$424$		0			0
$425$	0.736327	+	0.216205i	0.0357171	+	0.0104875i
$426$		0			0
$427$	1.70093	+	3.72452i	0.0823138	+	0.180242i
$428$		0			0
$429$	3.89187	−	4.49146i	0.187901	−	0.216850i
$430$		0			0
$431$	1.05600	+	0.678649i	0.0508657	+	0.0326894i	0.565827	−	0.824524i	$-0.308557\pi$
$431$	1.05600	+	0.678649i	0.0508657	+	0.0326894i	−0.514961	+	0.857214i	$0.672194\pi$
$432$		0			0
$433$	0.294500	−	0.189264i	0.0141528	−	0.00909544i	−0.533545	−	0.845771i	$-0.679141\pi$
$433$	0.294500	−	0.189264i	0.0141528	−	0.00909544i	0.547698	+	0.836676i	$0.315504\pi$
$434$		0			0
$435$	−14.5207	+	4.26365i	−0.696212	+	0.204426i
$436$		0			0
$437$	8.89125	+	25.7547i	0.425326	+	1.23201i
$438$		0			0
$439$	−17.2354	+	5.06076i	−0.822600	+	0.241537i	−0.665835	−	0.746099i	$-0.731925\pi$
$439$	−17.2354	+	5.06076i	−0.822600	+	0.241537i	−0.156765	+	0.987636i	$0.550106\pi$
$440$		0			0
$441$	−3.69228	+	2.37288i	−0.175823	+	0.112994i
$442$		0			0
$443$	13.7884	+	8.86127i	0.655107	+	0.421011i	0.825529	−	0.564360i	$-0.190877\pi$
$443$	13.7884	+	8.86127i	0.655107	+	0.421011i	−0.170422	+	0.985371i	$0.554513\pi$
$444$		0			0
$445$	23.1682	−	26.7376i	1.09828	−	1.26748i
$446$		0			0
$447$	4.55142	+	9.96623i	0.215275	+	0.471386i
$448$		0			0
$449$	−30.2638	−	8.88625i	−1.42824	−	0.419368i	−0.525954	−	0.850513i	$-0.676292\pi$
$449$	−30.2638	−	8.88625i	−1.42824	−	0.419368i	−0.902283	+	0.431145i	$0.858110\pi$
$450$		0			0
$451$	2.36863	−	16.4742i	0.111535	−	0.775740i
$452$		0			0
$453$	−7.45242	+	16.3185i	−0.350145	+	0.766712i
$454$		0			0
$455$	−1.12768	−	7.84319i	−0.0528665	−	0.367695i
$456$		0			0
$457$	15.9113	+	18.3627i	0.744301	+	0.858969i	0.994003	−	0.109354i	$-0.0348781\pi$
$457$	15.9113	+	18.3627i	0.744301	+	0.858969i	−0.249702	+	0.968323i	$0.580333\pi$
$458$		0			0
$459$	0.610626			0.0285016
$460$		0			0
$461$	−40.1961			−1.87212			−0.936060	−	0.351840i	$-0.885556\pi$
$461$	−40.1961			−1.87212			−0.936060	+	0.351840i	$0.885556\pi$
$462$		0			0
$463$	14.7810	+	17.0582i	0.686933	+	0.792763i	0.986925	−	0.161178i	$-0.0515295\pi$
$463$	14.7810	+	17.0582i	0.686933	+	0.792763i	−0.299992	+	0.953942i	$0.596984\pi$
$464$		0			0
$465$	3.58695	+	24.9478i	0.166341	+	1.15692i
$466$		0			0
$467$	8.65531	−	18.9525i	0.400520	−	0.877016i	−0.596697	−	0.802466i	$-0.703521\pi$
$467$	8.65531	−	18.9525i	0.400520	−	0.877016i	0.997217	−	0.0745500i	$-0.0237520\pi$
$468$		0			0
$469$	−0.121697	+	0.846420i	−0.00561944	+	0.0390840i
$470$		0			0
$471$	−16.4853	−	4.84053i	−0.759603	−	0.223040i
$472$		0			0
$473$	11.7909	+	25.8184i	0.542146	+	1.18713i
$474$		0			0
$475$	−4.67568	+	5.39603i	−0.214535	+	0.247587i
$476$		0			0
$477$	6.35851	+	4.08637i	0.291136	+	0.187102i
$478$		0			0
$479$	−10.2916	+	6.61398i	−0.470233	+	0.302200i	−0.754213	−	0.656630i	$-0.771981\pi$
$479$	−10.2916	+	6.61398i	−0.470233	+	0.302200i	0.283980	+	0.958830i	$0.408345\pi$
$480$		0			0
$481$	3.38029	−	0.992544i	0.154128	−	0.0452561i
$482$		0			0
$483$	−0.362681	−	7.74087i	−0.0165025	−	0.352222i
$484$		0			0
$485$	−41.9039	+	12.3041i	−1.90276	+	0.558700i
$486$		0			0
$487$	−3.00238	+	1.92951i	−0.136051	+	0.0874345i	−0.606896	−	0.794781i	$-0.707585\pi$
$487$	−3.00238	+	1.92951i	−0.136051	+	0.0874345i	0.470845	+	0.882216i	$0.343949\pi$
$488$		0			0
$489$	−14.3435	−	9.21802i	−0.648636	−	0.416853i
$490$		0			0
$491$	14.0655	−	16.2325i	0.634769	−	0.732563i	−0.343672	−	0.939090i	$-0.611671\pi$
$491$	14.0655	−	16.2325i	0.634769	−	0.732563i	0.978441	+	0.206527i	$0.0662162\pi$
$492$		0			0
$493$	−1.53471	−	3.36055i	−0.0691199	−	0.151352i
$494$		0			0
$495$	7.27557	+	2.13630i	0.327012	+	0.0960195i
$496$		0			0
$497$	0.236511	−	1.64497i	0.0106090	−	0.0737870i
$498$		0			0
$499$	3.35323	−	7.34254i	0.150111	−	0.328697i	−0.819606	−	0.572927i	$-0.805808\pi$
$499$	3.35323	−	7.34254i	0.150111	−	0.328697i	0.969717	+	0.244230i	$0.0785351\pi$
$500$		0			0
$501$	3.27303	+	22.7644i	0.146228	+	1.01704i
$502$		0			0
$503$	−22.9232	−	26.4548i	−1.02210	−	1.17956i	−0.983611	−	0.180302i	$-0.942293\pi$
$503$	−22.9232	−	26.4548i	−1.02210	−	1.17956i	−0.0384842	−	0.999259i	$-0.512253\pi$
$504$		0			0
$505$	8.42580			0.374943
$506$		0			0
$507$	9.15657			0.406658
$508$		0			0
$509$	6.65162	+	7.67637i	0.294828	+	0.340249i	0.883766	−	0.467928i	$-0.155000\pi$
$509$	6.65162	+	7.67637i	0.294828	+	0.340249i	−0.588939	+	0.808178i	$0.700454\pi$
$510$		0			0
$511$	0.657330	+	4.57183i	0.0290786	+	0.202246i
$512$		0			0
$513$	−2.36007	+	5.16783i	−0.104200	+	0.228165i
$514$		0			0
$515$	2.30574	−	16.0368i	0.101603	−	0.706666i
$516$		0			0
$517$	4.68232	+	1.37485i	0.205928	+	0.0604660i
$518$		0			0
$519$	−3.02390	−	6.62141i	−0.132734	−	0.290648i
$520$		0			0
$521$	22.0514	−	25.4487i	0.966090	−	1.11493i	−0.0272413	−	0.999629i	$-0.508672\pi$
$521$	22.0514	−	25.4487i	0.966090	−	1.11493i	0.993331	−	0.115298i	$-0.0367823\pi$
$522$		0			0
$523$	−5.36033	−	3.44488i	−0.234391	−	0.150634i	0.418173	−	0.908367i	$-0.362670\pi$
$523$	−5.36033	−	3.44488i	−0.234391	−	0.150634i	−0.652564	+	0.757733i	$0.726307\pi$
$524$		0			0
$525$	1.70837	−	1.09790i	0.0745595	−	0.0479165i
$526$		0			0
$527$	−5.90360	+	1.73345i	−0.257165	+	0.0755104i
$528$		0			0
$529$	−20.4267	−	10.5711i	−0.888118	−	0.459615i
$530$		0			0
$531$	8.37615	−	2.45946i	0.363494	−	0.106731i
$532$		0			0
$533$	−9.05489	+	5.81923i	−0.392211	+	0.252059i
$534$		0			0
$535$	−29.1682	−	18.7453i	−1.26105	−	0.810429i
$536$		0			0
$537$	8.74756	−	10.0952i	0.377485	−	0.435641i
$538$		0			0
$539$	−5.52713	−	12.1027i	−0.238070	−	0.521301i
$540$		0			0
$541$	3.87014	+	1.13638i	0.166390	+	0.0488566i	0.363867	−	0.931451i	$-0.381456\pi$
$541$	3.87014	+	1.13638i	0.166390	+	0.0488566i	−0.197476	+	0.980308i	$0.563275\pi$
$542$		0			0
$543$	3.73741	−	25.9943i	0.160388	−	1.11552i
$544$		0			0
$545$	−8.77129	+	19.2064i	−0.375721	+	0.822714i
$546$		0			0
$547$	−1.33463	−	9.28254i	−0.0570645	−	0.396893i	−0.998257	−	0.0590210i	$-0.981202\pi$
$547$	−1.33463	−	9.28254i	−0.0570645	−	0.396893i	0.941192	−	0.337872i	$-0.109707\pi$
$548$		0			0
$549$	1.65940	+	1.91505i	0.0708215	+	0.0817324i
$550$		0			0
$551$	34.3726			1.46432
$552$		0			0
$553$	6.59675			0.280522
$554$		0			0
$555$	2.94359	+	3.39708i	0.124948	+	0.144198i
$556$		0			0
$557$	−1.40952	−	9.80344i	−0.0597234	−	0.415385i	−0.997648	−	0.0685460i	$-0.978164\pi$
$557$	−1.40952	−	9.80344i	−0.0597234	−	0.415385i	0.937925	−	0.346839i	$-0.112745\pi$
$558$		0			0
$559$	7.62528	−	16.6970i	0.322515	−	0.706209i
$560$		0			0
$561$	−0.263436	+	1.83224i	−0.0111223	+	0.0773572i
$562$		0			0
$563$	−13.7671	−	4.04239i	−0.580215	−	0.170366i	−0.0215613	−	0.999768i	$-0.506864\pi$
$563$	−13.7671	−	4.04239i	−0.580215	−	0.170366i	−0.558654	+	0.829401i	$0.688682\pi$
$564$		0			0
$565$	−4.17550	−	9.14307i	−0.175665	−	0.384652i
$566$		0			0
$567$	1.05816	−	1.22118i	0.0444385	−	0.0512848i
$568$		0			0
$569$	14.6520	+	9.41629i	0.614245	+	0.394751i	0.810447	−	0.585812i	$-0.199224\pi$
$569$	14.6520	+	9.41629i	0.614245	+	0.394751i	−0.196202	+	0.980564i	$0.562861\pi$
$570$		0			0
$571$	10.6294	−	6.83113i	0.444828	−	0.285874i	−0.298989	−	0.954256i	$-0.596650\pi$
$571$	10.6294	−	6.83113i	0.444828	−	0.285874i	0.743818	+	0.668383i	$0.233013\pi$
$572$		0			0
$573$	−2.59091	+	0.760761i	−0.108237	+	0.0317813i
$574$		0			0
$575$	−0.282083	−	6.02062i	−0.0117637	−	0.251077i
$576$		0			0
$577$	13.7269	−	4.03057i	0.571457	−	0.167795i	0.0167776	−	0.999859i	$-0.494659\pi$
$577$	13.7269	−	4.03057i	0.571457	−	0.167795i	0.554679	+	0.832064i	$0.312841\pi$
$578$		0			0
$579$	−13.0083	+	8.35992i	−0.540606	+	0.347426i
$580$		0			0
$581$	11.9712	+	7.69345i	0.496651	+	0.319178i
$582$		0			0
$583$	−15.0047	+	17.3164i	−0.621431	+	0.717170i
$584$		0			0
$585$	−2.03712	−	4.46067i	−0.0842245	−	0.184426i
$586$		0			0
$587$	2.18381	+	0.641224i	0.0901354	+	0.0264661i	0.326489	−	0.945201i	$-0.394134\pi$
$587$	2.18381	+	0.641224i	0.0901354	+	0.0264661i	−0.236354	+	0.971667i	$0.575952\pi$
$588$		0			0
$589$	8.14690	−	56.6630i	0.335687	−	2.33476i
$590$		0			0
$591$	9.28776	−	20.3374i	0.382047	−	0.836567i
$592$		0			0
$593$	−3.01280	−	20.9545i	−0.123721	−	0.860497i	−0.953282	−	0.302082i	$-0.902319\pi$
$593$	−3.01280	−	20.9545i	−0.123721	−	0.860497i	0.829561	−	0.558416i	$-0.188591\pi$
$594$		0			0
$595$	1.61622	+	1.86522i	0.0662586	+	0.0764665i
$596$		0			0
$597$	−5.03799			−0.206191
$598$		0			0
$599$	−26.2579			−1.07287			−0.536434	−	0.843942i	$-0.680229\pi$
$599$	−26.2579			−1.07287			−0.536434	+	0.843942i	$0.680229\pi$
$600$		0			0
$601$	−3.58618	−	4.13868i	−0.146283	−	0.168820i	0.677879	−	0.735173i	$-0.262899\pi$
$601$	−3.58618	−	4.13868i	−0.146283	−	0.168820i	−0.824163	+	0.566353i	$0.808354\pi$
$602$		0			0
$603$	0.0753143	+	0.523822i	0.00306703	+	0.0213317i
$604$		0			0
$605$	1.88111	−	4.11905i	0.0764778	−	0.167463i
$606$		0			0
$607$	−6.16397	+	42.8713i	−0.250188	+	1.74009i	0.346886	+	0.937907i	$0.387239\pi$
$607$	−6.16397	+	42.8713i	−0.250188	+	1.74009i	−0.597074	+	0.802186i	$0.703670\pi$
$608$		0			0
$609$	−9.38022	−	2.75428i	−0.380106	−	0.111609i
$610$		0			0
$611$	−1.31102	−	2.87074i	−0.0530384	−	0.116138i
$612$		0			0
$613$	10.5692	−	12.1975i	0.426885	−	0.492652i	−0.501037	−	0.865426i	$-0.667048\pi$
$613$	10.5692	−	12.1975i	0.426885	−	0.492652i	0.927922	+	0.372774i	$0.121593\pi$
$614$		0			0
$615$	−11.5531	−	7.42474i	−0.465867	−	0.299394i
$616$		0			0
$617$	26.9966	−	17.3497i	1.08684	−	0.698472i	0.130715	−	0.991420i	$-0.458273\pi$
$617$	26.9966	−	17.3497i	1.08684	−	0.698472i	0.956128	+	0.292948i	$0.0946363\pi$
$618$		0			0
$619$	−0.217610	+	0.0638960i	−0.00874648	+	0.00256820i	−0.286103	−	0.958199i	$-0.592360\pi$
$619$	−0.217610	+	0.0638960i	−0.00874648	+	0.00256820i	0.277356	+	0.960767i	$0.410542\pi$
$620$		0			0
$621$	−1.56502	−	4.53329i	−0.0628021	−	0.181915i
$622$		0			0
$623$	21.9287	−	6.43885i	0.878555	−	0.257967i
$624$		0			0
$625$	−24.9889	+	16.0594i	−0.999556	+	0.642376i
$626$		0			0
$627$	−14.4884	−	9.31111i	−0.578610	−	0.371850i
$628$		0			0
$629$	−0.718584	+	0.829290i	−0.0286518	+	0.0330660i
$630$		0			0
$631$	−13.9417	−	30.5281i	−0.555010	−	1.21530i	−0.954402	−	0.298523i	$-0.903506\pi$
$631$	−13.9417	−	30.5281i	−0.555010	−	1.21530i	0.399392	−	0.916780i	$-0.369221\pi$
$632$		0			0
$633$	21.0220	+	6.17261i	0.835548	+	0.245339i
$634$		0			0
$635$	−5.82250	+	40.4964i	−0.231059	+	1.60705i
$636$		0			0
$637$	−3.57445	+	7.82695i	−0.141625	+	0.310115i
$638$		0			0
$639$	−0.146369	−	1.01802i	−0.00579027	−	0.0402722i
$640$		0			0
$641$	−20.4259	−	23.5728i	−0.806775	−	0.931068i	0.191958	−	0.981403i	$-0.438516\pi$
$641$	−20.4259	−	23.5728i	−0.806775	−	0.931068i	−0.998732	+	0.0503354i	$0.983971\pi$
$642$		0			0
$643$	−5.46023			−0.215331			−0.107665	−	0.994187i	$-0.534337\pi$
$643$	−5.46023			−0.215331			−0.107665	+	0.994187i	$0.534337\pi$
$644$		0			0
$645$	23.4201			0.922166
$646$		0			0
$647$	13.6796	+	15.7871i	0.537802	+	0.620657i	0.957997	−	0.286777i	$-0.0925839\pi$
$647$	13.6796	+	15.7871i	0.537802	+	0.620657i	−0.420195	+	0.907434i	$0.638038\pi$
$648$		0			0
$649$	3.76620	+	26.1945i	0.147836	+	1.02822i
$650$		0			0
$651$	−6.76369	+	14.8104i	−0.265090	+	0.580466i
$652$		0			0
$653$	2.13271	−	14.8333i	0.0834594	−	0.580473i	−0.904584	−	0.426296i	$-0.859818\pi$
$653$	2.13271	−	14.8333i	0.0834594	−	0.580473i	0.988043	−	0.154177i	$-0.0492727\pi$
$654$		0			0
$655$	−14.3375	−	4.20987i	−0.560212	−	0.164493i
$656$		0			0
$657$	1.18745	+	2.60014i	0.0463266	+	0.101441i
$658$		0			0
$659$	7.35307	−	8.48590i	0.286435	−	0.330564i	−0.594237	−	0.804290i	$-0.702546\pi$
$659$	7.35307	−	8.48590i	0.286435	−	0.330564i	0.880672	+	0.473726i	$0.157091\pi$
$660$		0			0
$661$	−35.3819	−	22.7386i	−1.37620	−	0.884429i	−0.377070	−	0.926185i	$-0.623068\pi$
$661$	−35.3819	−	22.7386i	−1.37620	−	0.884429i	−0.999128	+	0.0417560i	$0.986705\pi$
$662$		0			0
$663$	1.00707	−	0.647207i	0.0391115	−	0.0251354i
$664$		0			0
$665$	−22.0324	+	6.46929i	−0.854379	+	0.250868i
$666$		0			0
$667$	−21.0153	+	20.0067i	−0.813716	+	0.774664i
$668$		0			0
$669$	14.8499	−	4.36033i	0.574132	−	0.168580i
$670$		0			0
$671$	−6.46219	+	4.15299i	−0.249470	+	0.160325i
$672$		0			0
$673$	12.7664	+	8.20450i	0.492110	+	0.316260i	0.763054	−	0.646335i	$-0.223699\pi$
$673$	12.7664	+	8.20450i	0.492110	+	0.316260i	−0.270943	+	0.962595i	$0.587336\pi$
$674$		0			0
$675$	0.823005	−	0.949799i	0.0316775	−	0.0365578i
$676$		0			0
$677$	−1.26590	−	2.77194i	−0.0486526	−	0.106534i	0.883745	−	0.467969i	$-0.155014\pi$
$677$	−1.26590	−	2.77194i	−0.0486526	−	0.106534i	−0.932397	+	0.361435i	$0.882287\pi$
$678$		0			0
$679$	−27.0696	−	7.94834i	−1.03883	−	0.305029i
$680$		0			0
$681$	−1.28121	+	8.91098i	−0.0490959	+	0.341469i
$682$		0			0
$683$	13.7116	−	30.0241i	0.524658	−	1.14884i	−0.442987	−	0.896528i	$-0.646081\pi$
$683$	13.7116	−	30.0241i	0.524658	−	1.14884i	0.967646	−	0.252313i	$-0.0811913\pi$
$684$		0			0
$685$	3.27643	+	22.7881i	0.125186	+	0.870689i
$686$		0			0
$687$	−18.8064	−	21.7037i	−0.717508	−	0.828048i
$688$		0			0
$689$	14.8179			0.564518
$690$		0			0
$691$	22.9216			0.871980			0.435990	−	0.899952i	$-0.356398\pi$
$691$	22.9216			0.871980			0.435990	+	0.899952i	$0.356398\pi$
$692$		0			0
$693$	3.20775	+	3.70195i	0.121852	+	0.140625i
$694$		0			0
$695$	−2.71334	−	18.8717i	−0.102923	−	0.715845i
$696$		0			0
$697$	1.39269	−	3.04957i	0.0527519	−	0.115511i
$698$		0			0
$699$	3.01285	−	20.9549i	0.113957	−	0.792586i
$700$		0			0
$701$	47.5411	+	13.9593i	1.79560	+	0.527237i	0.997193	−	0.0748762i	$-0.0238562\pi$
$701$	47.5411	+	13.9593i	1.79560	+	0.527237i	0.798411	+	0.602113i	$0.205674\pi$
$702$		0			0
$703$	−4.24110	−	9.28670i	−0.159956	−	0.350255i
$704$		0			0
$705$	2.63690	−	3.04314i	0.0993113	−	0.114611i
$706$		0			0
$707$	4.57894	+	2.94271i	0.172209	+	0.110672i
$708$		0			0
$709$	−0.475138	+	0.305353i	−0.0178442	+	0.0114678i	−0.549532	−	0.835472i	$-0.685194\pi$
$709$	−0.475138	+	0.305353i	−0.0178442	+	0.0114678i	0.531688	+	0.846940i	$0.321558\pi$
$710$		0			0
$711$	3.91715	−	1.15018i	0.146905	−	0.0431351i
$712$		0			0
$713$	28.0000	+	39.3855i	1.04861	+	1.47500i
$714$		0			0
$715$	14.2635	−	4.18814i	0.533425	−	0.156628i
$716$		0			0
$717$	6.24752	−	4.01503i	0.233318	−	0.149944i
$718$		0			0
$719$	2.35123	+	1.51105i	0.0876862	+	0.0563525i	0.583749	−	0.811934i	$-0.301585\pi$
$719$	2.35123	+	1.51105i	0.0876862	+	0.0563525i	−0.496063	+	0.868287i	$0.665222\pi$
$720$		0			0
$721$	6.85389	−	7.90981i	0.255252	−	0.294577i
$722$		0			0
$723$	−3.16712	−	6.93501i	−0.117786	−	0.257916i
$724$		0			0
$725$	−7.29567	−	2.14220i	−0.270954	−	0.0795593i
$726$		0			0
$727$	−4.27336	+	29.7218i	−0.158490	+	1.10232i	0.742928	+	0.669372i	$0.233437\pi$
$727$	−4.27336	+	29.7218i	−0.158490	+	1.10232i	−0.901418	+	0.432950i	$0.857473\pi$
$728$		0			0
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$		0			0
$731$	0.813653	+	5.65908i	0.0300941	+	0.209309i
$732$		0			0
$733$	10.8893	+	12.5669i	0.402204	+	0.464168i	0.920334	−	0.391134i	$-0.127917\pi$
$733$	10.8893	+	12.5669i	0.402204	+	0.464168i	−0.518130	+	0.855302i	$0.673372\pi$
$734$		0			0
$735$	−10.9785			−0.404947
$736$		0			0
$737$	−1.60427			−0.0590940
$738$		0			0
$739$	19.7465	+	22.7886i	0.726386	+	0.838294i	0.992060	−	0.125769i	$-0.0401399\pi$
$739$	19.7465	+	22.7886i	0.726386	+	0.838294i	−0.265674	+	0.964063i	$0.585594\pi$
$740$		0			0
$741$	1.58508	+	11.0245i	0.0582295	+	0.404995i
$742$		0			0
$743$	13.1160	−	28.7201i	0.481180	−	1.05364i	−0.500957	−	0.865472i	$-0.667019\pi$
$743$	13.1160	−	28.7201i	0.481180	−	1.05364i	0.982137	−	0.188165i	$-0.0602541\pi$
$744$		0			0
$745$	−3.90023	+	27.1267i	−0.142893	+	0.993845i
$746$		0			0
$747$	8.44991	+	2.48112i	0.309166	+	0.0907794i
$748$		0			0
$749$	−9.30449	−	20.3740i	−0.339979	−	0.744449i
$750$		0			0
$751$	−18.8275	+	21.7281i	−0.687024	+	0.792868i	−0.986938	−	0.161098i	$-0.948497\pi$
$751$	−18.8275	+	21.7281i	−0.687024	+	0.792868i	0.299914	+	0.953966i	$0.403042\pi$
$752$		0			0
$753$	−17.5667	−	11.2894i	−0.640167	−	0.411410i
$754$		0			0
$755$	−37.7500	+	24.2605i	−1.37386	+	0.882929i
$756$		0			0
$757$	−0.365428	+	0.107299i	−0.0132817	+	0.00389986i	−0.288367	−	0.957520i	$-0.593112\pi$
$757$	−0.365428	+	0.107299i	−0.0132817	+	0.00389986i	0.275085	+	0.961420i	$0.411294\pi$
$758$		0			0
$759$	14.2777	−	2.74024i	0.518249	−	0.0994643i
$760$		0			0
$761$	−37.7681	+	11.0897i	−1.36909	+	0.402002i	−0.881959	−	0.471325i	$-0.843776\pi$
$761$	−37.7681	+	11.0897i	−1.36909	+	0.402002i	−0.487134	+	0.873327i	$0.661958\pi$
$762$		0			0
$763$	−11.4745	+	7.37424i	−0.415406	+	0.266965i
$764$		0			0
$765$	1.28492	+	0.825770i	0.0464565	+	0.0298558i
$766$		0			0
$767$	11.2075	−	12.9342i	0.404681	−	0.467027i
$768$		0			0
$769$	18.1975	+	39.8470i	0.656218	+	1.43692i	0.886004	+	0.463677i	$0.153470\pi$
$769$	18.1975	+	39.8470i	0.656218	+	1.43692i	−0.229786	+	0.973241i	$0.573803\pi$
$770$		0			0
$771$	19.6541	+	5.77097i	0.707826	+	0.207836i
$772$		0			0
$773$	−6.11390	+	42.5231i	−0.219902	+	1.52945i	0.518493	+	0.855082i	$0.326493\pi$
$773$	−6.11390	+	42.5231i	−0.219902	+	1.52945i	−0.738395	+	0.674369i	$0.764416\pi$
$774$		0			0
$775$	−5.26061	+	11.5191i	−0.188967	+	0.413779i
$776$		0			0
$777$	0.413243	+	2.87417i	0.0148250	+	0.103110i
$778$		0			0
$779$	20.4263	+	23.5732i	0.731847	+	0.844596i
$780$		0			0
$781$	3.11781			0.111564
$782$		0			0
$783$	−6.05020			−0.216216
$784$		0			0
$785$	−28.1436	−	32.4794i	−1.00449	−	1.15924i
$786$		0			0
$787$	1.74077	+	12.1073i	0.0620519	+	0.431580i	0.997039	+	0.0768984i	$0.0245017\pi$
$787$	1.74077	+	12.1073i	0.0620519	+	0.431580i	−0.934987	+	0.354682i	$0.884589\pi$
$788$		0			0
$789$	1.76803	−	3.87144i	0.0629435	−	0.137827i
$790$		0			0
$791$	0.924067	−	6.42703i	0.0328560	−	0.228519i
$792$		0			0
$793$	4.76654	+	1.39958i	0.169265	+	0.0497007i
$794$		0			0
$795$	7.85390	+	17.1976i	0.278549	+	0.609938i
$796$		0			0
$797$	18.9546	−	21.8748i	0.671407	−	0.774845i	−0.313189	−	0.949691i	$-0.601397\pi$
$797$	18.9546	−	21.8748i	0.671407	−	0.774845i	0.984596	+	0.174846i	$0.0559428\pi$
$798$		0			0
$799$	0.826935	+	0.531439i	0.0292549	+	0.0188010i
$800$		0			0
$801$	11.8986	−	7.64677i	0.420417	−	0.270185i
$802$		0			0
$803$	−8.31425	+	2.44129i	−0.293404	+	0.0861511i
$804$		0			0
$805$	9.70506	−	16.7794i	0.342058	−	0.591395i
$806$		0			0
$807$	26.5173	−	7.78618i	0.933453	−	0.274087i
$808$		0			0
$809$	8.98988	−	5.77745i	0.316067	−	0.203124i	−0.372982	−	0.927839i	$-0.621665\pi$
$809$	8.98988	−	5.77745i	0.316067	−	0.203124i	0.689049	+	0.724714i	$0.258028\pi$
$810$		0			0
$811$	7.21110	+	4.63429i	0.253216	+	0.162732i	0.661091	−	0.750306i	$-0.270094\pi$
$811$	7.21110	+	4.63429i	0.253216	+	0.162732i	−0.407875	+	0.913038i	$0.633730\pi$
$812$		0			0
$813$	−12.5452	+	14.4780i	−0.439981	+	0.507765i
$814$		0			0
$815$	−17.7168	−	38.7944i	−0.620593	−	1.35891i
$816$		0			0
$817$	−51.0386	−	14.9863i	−1.78561	−	0.524303i
$818$		0			0
$819$	0.450828	−	3.13558i	0.0157532	−	0.109566i
$820$		0			0
$821$	−15.9219	+	34.8641i	−0.555678	+	1.21677i	0.398401	+	0.917211i	$0.369565\pi$
$821$	−15.9219	+	34.8641i	−0.555678	+	1.21677i	−0.954079	+	0.299554i	$0.903162\pi$
$822$		0			0
$823$	−0.615787	−	4.28289i	−0.0214650	−	0.149292i	0.976270	−	0.216556i	$-0.0694823\pi$
$823$	−0.615787	−	4.28289i	−0.0214650	−	0.149292i	−0.997735	+	0.0672635i	$0.978573\pi$
$824$		0			0
$825$	2.49490	+	2.87927i	0.0868612	+	0.100243i
$826$		0			0
$827$	34.6700			1.20559			0.602797	−	0.797895i	$-0.294053\pi$
$827$	34.6700			1.20559			0.602797	+	0.797895i	$0.294053\pi$
$828$		0			0
$829$	−1.55014			−0.0538385			−0.0269192	−	0.999638i	$-0.508570\pi$
$829$	−1.55014			−0.0538385			−0.0269192	+	0.999638i	$0.508570\pi$
$830$		0			0
$831$	−0.522279	−	0.602742i	−0.0181177	−	0.0209089i
$832$		0			0
$833$	−0.381411	−	2.65277i	−0.0132151	−	0.0919130i
$834$		0			0
$835$	−23.8977	+	52.3287i	−0.827015	+	1.81091i
$836$		0			0
$837$	−1.43400	+	9.97371i	−0.0495664	+	0.344742i
$838$		0			0
$839$	−3.79245	−	1.11356i	−0.130930	−	0.0384445i	0.215611	−	0.976479i	$-0.430826\pi$
$839$	−3.79245	−	1.11356i	−0.130930	−	0.0384445i	−0.346541	+	0.938035i	$0.612644\pi$
$840$		0			0
$841$	3.15918	+	6.91764i	0.108937	+	0.238539i
$842$		0			0
$843$	16.2428	−	18.7452i	0.559431	−	0.645618i
$844$		0			0
$845$	19.2679	+	12.3827i	0.662837	+	0.425979i
$846$		0			0
$847$	2.46085	−	1.58149i	0.0845558	−	0.0543407i
$848$		0			0
$849$	5.50473	−	1.61633i	0.188922	−	0.0554724i
$850$		0			0
$851$	7.99837	+	3.20932i	0.274181	+	0.110014i
$852$		0			0
$853$	−1.97214	+	0.579072i	−0.0675247	+	0.0198270i	−0.315320	−	0.948985i	$-0.602112\pi$
$853$	−1.97214	+	0.579072i	−0.0675247	+	0.0198270i	0.247796	+	0.968812i	$0.420294\pi$
$854$		0			0
$855$	−11.9549	+	7.68292i	−0.408847	+	0.262750i
$856$		0			0
$857$	7.40147	+	4.75664i	0.252829	+	0.162484i	0.660917	−	0.750459i	$-0.270168\pi$
$857$	7.40147	+	4.75664i	0.252829	+	0.162484i	−0.408087	+	0.912943i	$0.633804\pi$
$858$		0			0
$859$	−36.3074	+	41.9010i	−1.23879	+	1.42964i	−0.374064	+	0.927403i	$0.622036\pi$
$859$	−36.3074	+	41.9010i	−1.23879	+	1.42964i	−0.864728	+	0.502240i	$0.832509\pi$
$860$		0			0
$861$	−3.68537	−	8.06984i	−0.125597	−	0.275019i
$862$		0			0
$863$	−41.2359	−	12.1080i	−1.40369	−	0.412159i	−0.509738	−	0.860330i	$-0.670258\pi$
$863$	−41.2359	−	12.1080i	−1.40369	−	0.412159i	−0.893948	+	0.448170i	$0.852076\pi$
$864$		0			0
$865$	2.59125	−	18.0226i	0.0881053	−	0.612786i
$866$		0			0
$867$	6.90716	−	15.1246i	0.234580	−	0.513657i
$868$		0			0
$869$	1.76128	+	12.2500i	0.0597473	+	0.415552i
$870$		0			0
$871$	0.679415	+	0.784087i	0.0230211	+	0.0265678i
$872$		0			0
$873$	−17.4597			−0.590922
$874$		0			0
$875$	−15.1295			−0.511470
$876$		0			0
$877$	−24.2257	−	27.9579i	−0.818042	−	0.944071i	0.181182	−	0.983450i	$-0.442008\pi$
$877$	−24.2257	−	27.9579i	−0.818042	−	0.944071i	−0.999224	+	0.0393786i	$0.987462\pi$
$878$		0			0
$879$	2.81227	+	19.5598i	0.0948557	+	0.659736i
$880$		0			0
$881$	−16.6152	+	36.3823i	−0.559782	+	1.22575i	0.392280	+	0.919846i	$0.371686\pi$
$881$	−16.6152	+	36.3823i	−0.559782	+	1.22575i	−0.952062	+	0.305905i	$0.901041\pi$
$882$		0			0
$883$	−2.53099	+	17.6034i	−0.0851747	+	0.592403i	0.901876	+	0.431995i	$0.142190\pi$
$883$	−2.53099	+	17.6034i	−0.0851747	+	0.592403i	−0.987051	+	0.160408i	$0.948719\pi$
$884$		0			0
$885$	20.9517	+	6.15197i	0.704284	+	0.206796i
$886$		0			0
$887$	−10.6344	−	23.2861i	−0.357068	−	0.781870i	−0.999875	−	0.0158416i	$-0.994957\pi$
$887$	−10.6344	−	23.2861i	−0.357068	−	0.781870i	0.642806	−	0.766029i	$-0.277770\pi$
$888$		0			0
$889$	−17.3075	+	19.9740i	−0.580477	+	0.669906i
$890$		0			0
$891$	2.55022	+	1.63892i	0.0854355	+	0.0549060i
$892$		0			0
$893$	−7.69377	+	4.94448i	−0.257462	+	0.165461i
$894$		0			0
$895$	32.0593	−	9.41347i	1.07163	−	0.314658i
$896$		0			0
$897$	−7.38598	−	5.81774i	−0.246611	−	0.194249i
$898$		0			0
$899$	58.4940	−	17.1754i	1.95088	−	0.572831i
$900$		0			0
$901$	−3.88267	+	2.49524i	−0.129350	+	0.0831285i
$902$		0			0
$903$	12.7275	+	8.17947i	0.423545	+	0.272196i
$904$		0			0
$905$	43.0175	−	49.6448i	1.42995	−	1.65025i
$906$		0			0
$907$	4.35740	+	9.54137i	0.144685	+	0.316816i	0.968075	−	0.250659i	$-0.0806474\pi$
$907$	4.35740	+	9.54137i	0.144685	+	0.316816i	−0.823390	+	0.567476i	$0.807920\pi$
$908$		0			0
$909$	3.23205	+	0.949016i	0.107200	+	0.0314769i
$910$		0			0
$911$	−7.38396	+	51.3566i	−0.244642	+	1.70152i	0.383598	+	0.923500i	$0.374685\pi$
$911$	−7.38396	+	51.3566i	−0.244642	+	1.70152i	−0.628240	+	0.778020i	$0.716224\pi$
$912$		0			0
$913$	−11.0903	+	24.2843i	−0.367035	+	0.803694i
$914$		0			0
$915$	0.902043	+	6.27385i	0.0298206	+	0.207407i
$916$		0			0
$917$	−6.32131	−	7.29518i	−0.208748	−	0.240908i
$918$		0			0
$919$	13.7901			0.454892			0.227446	−	0.973791i	$-0.426962\pi$
$919$	13.7901			0.454892			0.227446	+	0.973791i	$0.426962\pi$
$920$		0			0
$921$	−31.6748			−1.04372
$922$		0			0
$923$	−1.32041	−	1.52383i	−0.0434617	−	0.0501574i
$924$		0			0
$925$	0.321408	+	2.23544i	0.0105678	+	0.0735010i
$926$		0			0
$927$	2.69072	−	5.89185i	0.0883748	−	0.193514i
$928$		0			0
$929$	0.468124	−	3.25588i	0.0153587	−	0.106822i	−0.980700	−	0.195518i	$-0.937361\pi$
$929$	0.468124	−	3.25588i	0.0153587	−	0.106822i	0.996059	+	0.0886966i	$0.0282701\pi$
$930$		0			0
$931$	23.9250	+	7.02501i	0.784110	+	0.230235i
$932$		0			0
$933$	5.94336	+	13.0141i	0.194577	+	0.426064i
$934$		0			0
$935$	−3.03214	+	3.49927i	−0.0991615	+	0.114439i
$936$		0			0
$937$	−43.2975	−	27.8256i	−1.41447	−	0.909023i	−0.414467	−	0.910064i	$-0.636032\pi$
$937$	−43.2975	−	27.8256i	−1.41447	−	0.909023i	−0.999999	+	0.00104172i	$0.999668\pi$
$938$		0			0
$939$	18.1905	−	11.6904i	0.593626	−	0.381500i
$940$		0			0
$941$	33.5826	−	9.86073i	1.09476	−	0.321451i	0.315992	−	0.948762i	$-0.397663\pi$
$941$	33.5826	−	9.86073i	1.09476	−	0.321451i	0.778769	+	0.627311i	$0.215845\pi$
$942$		0			0
$943$	−26.2094	−	2.52337i	−0.853497	−	0.0821721i
$944$		0			0
$945$	3.87810	−	1.13871i	0.126154	−	0.0370423i
$946$		0			0
$947$	29.4594	−	18.9324i	0.957303	−	0.615221i	0.0340525	−	0.999420i	$-0.489159\pi$
$947$	29.4594	−	18.9324i	0.957303	−	0.615221i	0.923250	+	0.384199i	$0.125522\pi$
$948$		0			0
$949$	4.71430	+	3.02970i	0.153033	+	0.0983482i
$950$		0			0
$951$	−18.3197	+	21.1421i	−0.594057	+	0.685578i
$952$		0			0
$953$	9.44966	+	20.6919i	0.306104	+	0.670275i	0.998696	−	0.0510549i	$-0.0162584\pi$
$953$	9.44966	+	20.6919i	0.306104	+	0.670275i	−0.692591	+	0.721330i	$0.743531\pi$
$954$		0			0
$955$	−6.48079	−	1.90293i	−0.209713	−	0.0615774i
$956$		0			0
$957$	2.61018	−	18.1542i	0.0843750	−	0.586841i
$958$		0			0
$959$	−6.17818	+	13.5283i	−0.199504	+	0.436852i
$960$		0			0
$961$	−10.0376	−	69.8133i	−0.323795	−	2.25204i
$962$		0			0
$963$	−9.07731	−	10.4758i	−0.292512	−	0.337577i
$964$		0			0
$965$	−38.6784			−1.24510
$966$		0			0
$967$	40.0114			1.28668			0.643341	−	0.765580i	$-0.277548\pi$
$967$	40.0114			1.28668			0.643341	+	0.765580i	$0.277548\pi$
$968$		0			0
$969$	−2.27178	−	2.62178i	−0.0729801	−	0.0842236i
$970$		0			0
$971$	4.26227	+	29.6448i	0.136783	+	0.951346i	0.936425	+	0.350868i	$0.114114\pi$
$971$	4.26227	+	29.6448i	0.136783	+	0.951346i	−0.799642	+	0.600477i	$0.794977\pi$
$972$		0			0
$973$	5.11639	−	11.2033i	0.164024	−	0.359163i
$974$		0			0
$975$	0.350641	−	2.43876i	0.0112295	−	0.0781030i
$976$		0			0
$977$	−34.9792	−	10.2708i	−1.11908	−	0.328592i	−0.330675	−	0.943745i	$-0.607276\pi$
$977$	−34.9792	−	10.2708i	−1.11908	−	0.328592i	−0.788408	+	0.615153i	$0.789094\pi$
$978$		0			0
$979$	17.8115	+	39.0018i	0.569259	+	1.24650i
$980$		0			0
$981$	−5.52784	+	6.37947i	−0.176490	+	0.203681i
$982$		0			0
$983$	12.5494	+	8.06499i	0.400263	+	0.257233i	0.725251	−	0.688485i	$-0.241724\pi$
$983$	12.5494	+	8.06499i	0.400263	+	0.257233i	−0.324988	+	0.945718i	$0.605360\pi$
$984$		0			0
$985$	47.0468	−	30.2352i	1.49904	−	0.963373i
$986$		0			0
$987$	2.49582	−	0.732839i	0.0794428	−	0.0233265i
$988$		0			0
$989$	39.9277	−	20.5447i	1.26963	−	0.653283i
$990$		0			0
$991$	26.3163	−	7.72716i	0.835964	−	0.245461i	0.164387	−	0.986396i	$-0.447435\pi$
$991$	26.3163	−	7.72716i	0.835964	−	0.245461i	0.671577	+	0.740935i	$0.265617\pi$
$992$		0			0
$993$	18.2328	−	11.7175i	0.578600	−	0.371843i
$994$		0			0
$995$	−10.6013	−	6.81304i	−0.336084	−	0.215988i
$996$		0			0
$997$	−28.1351	+	32.4696i	−0.891048	+	1.02832i	0.108367	+	0.994111i	$0.465438\pi$
$997$	−28.1351	+	32.4696i	−0.891048	+	1.02832i	−0.999415	+	0.0342127i	$0.989108\pi$
$998$		0			0
$999$	0.746510	+	1.63463i	0.0236185	+	0.0517174i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.i.b.193.2	yes	20
3.2	odd	2		828.2.q.b.469.1		20
23.8	even	11		6348.2.a.r.1.2		10
23.15	odd	22		6348.2.a.q.1.9		10
23.18	even	11	inner	276.2.i.b.133.2	✓	20
69.41	odd	22		828.2.q.b.685.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.i.b.133.2	✓	20	23.18	even	11	inner
276.2.i.b.193.2	yes	20	1.1	even	1	trivial
828.2.q.b.469.1		20	3.2	odd	2
828.2.q.b.685.1		20	69.41	odd	22
6348.2.a.q.1.9		10	23.15	odd	22
6348.2.a.r.1.2		10	23.8	even	11

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)

\(f(q)\)	\(=\)	\(q+(0.654861 + 0.755750i) q^{3} +(0.355980 + 2.47589i) q^{5} +(-0.671250 + 1.46983i) q^{7} +(-0.142315 + 0.989821i) q^{9} +O(q^{10})\)	\(q+(0.654861 + 0.755750i) q^{3} +(0.355980 + 2.47589i) q^{5} +(-0.671250 + 1.46983i) q^{7} +(-0.142315 + 0.989821i) q^{9} +(-2.90865 - 0.854058i) q^{11} +(0.814407 + 1.78330i) q^{13} +(-1.63804 + 1.89040i) q^{15} +(-0.513691 - 0.330129i) q^{17} +(4.77936 - 3.07151i) q^{19} +(-1.55040 + 0.455239i) q^{21} +(-1.13430 + 4.65976i) q^{23} +(-1.20586 + 0.354071i) q^{25} +(-0.841254 + 0.540641i) q^{27} +(5.08975 + 3.27098i) q^{29} +(6.59855 - 7.61514i) q^{31} +(-1.25931 - 2.75750i) q^{33} +(-3.87810 - 1.13871i) q^{35} +(0.255743 - 1.77873i) q^{37} +(-0.814407 + 1.78330i) q^{39} +(0.781353 + 5.43443i) q^{41} +(-6.13145 - 7.07607i) q^{43} -2.50135 q^{45} -1.60979 q^{47} +(2.87420 + 3.31700i) q^{49} +(-0.0869011 - 0.604411i) q^{51} +(3.13986 - 6.87534i) q^{53} +(1.07913 - 7.50554i) q^{55} +(5.45110 + 1.60059i) q^{57} +(-3.62648 - 7.94087i) q^{59} +(1.65940 - 1.91505i) q^{61} +(-1.35934 - 0.873596i) q^{63} +(-4.12535 + 2.65120i) q^{65} +(0.507772 - 0.149095i) q^{67} +(-4.26442 + 2.19425i) q^{69} +(-0.986827 + 0.289758i) q^{71} +(2.40469 - 1.54540i) q^{73} +(-1.05726 - 0.679458i) q^{75} +(3.20775 - 3.70195i) q^{77} +(-1.69594 - 3.71359i) q^{79} +(-0.959493 - 0.281733i) q^{81} +(1.25332 - 8.71701i) q^{83} +(0.634501 - 1.38936i) q^{85} +(0.861033 + 5.98861i) q^{87} +(-9.26229 - 10.6892i) q^{89} -3.16782 q^{91} +10.0763 q^{93} +(9.30607 + 10.7398i) q^{95} +(2.48478 + 17.2820i) q^{97} +(1.25931 - 2.75750i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9}+O(q^{10}) \) 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9	\( 20 q + 2 q^{3} - 4 q^{7} - 2 q^{9} + 14 q^{13} - 11 q^{15} + 3 q^{17} + 7 q^{19} + 4 q^{21} + 24 q^{23} + 12 q^{25} + 2 q^{27} - 26 q^{29} + 33 q^{31} - 11 q^{33} - 2 q^{35} - 18 q^{37} - 14 q^{39} + 4 q^{41} - 40 q^{43} - 54 q^{47} + 30 q^{49} - 14 q^{51} - 14 q^{53} + 11 q^{55} - 29 q^{57} + 4 q^{59} + 12 q^{61} - 4 q^{63} - 33 q^{65} + 15 q^{67} - 2 q^{69} - 33 q^{71} + 15 q^{73} + 10 q^{75} + 66 q^{77} - 42 q^{79} - 2 q^{81} - 14 q^{83} - 13 q^{85} + 4 q^{87} - 66 q^{89} - 16 q^{91} - 22 q^{93} - 31 q^{95} - 24 q^{97} + 11 q^{99}+O(q^{100}) \) 20 * q + 2 * q^3 - 4 * q^7 - 2 * q^9 + 14 * q^13 - 11 * q^15 + 3 * q^17 + 7 * q^19 + 4 * q^21 + 24 * q^23 + 12 * q^25 + 2 * q^27 - 26 * q^29 + 33 * q^31 - 11 * q^33 - 2 * q^35 - 18 * q^37 - 14 * q^39 + 4 * q^41 - 40 * q^43 - 54 * q^47 + 30 * q^49 - 14 * q^51 - 14 * q^53 + 11 * q^55 - 29 * q^57 + 4 * q^59 + 12 * q^61 - 4 * q^63 - 33 * q^65 + 15 * q^67 - 2 * q^69 - 33 * q^71 + 15 * q^73 + 10 * q^75 + 66 * q^77 - 42 * q^79 - 2 * q^81 - 14 * q^83 - 13 * q^85 + 4 * q^87 - 66 * q^89 - 16 * q^91 - 22 * q^93 - 31 * q^95 - 24 * q^97 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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