LMFDB - Embedded newform 276.2.i.a.13.2

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			13.2
Root			$-0.962045 - 0.282482i$ of defining polynomial
Character	$\chi$	$=$	276.13
Dual form			276.2.i.a.85.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.841254 + 0.540641i) q^{3} +(1.11647 - 2.44474i) q^{5} +(0.161591 + 0.0474474i) q^{7} +(0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(0.841254 + 0.540641i) q^{3} +(1.11647 - 2.44474i) q^{5} +(0.161591 + 0.0474474i) q^{7} +(0.415415 + 0.909632i) q^{9} +(3.48648 - 4.02361i) q^{11} +(-3.68628 + 1.08239i) q^{13} +(2.26096 - 1.45303i) q^{15} +(0.947403 + 6.58933i) q^{17} +(0.980961 - 6.82274i) q^{19} +(0.110287 + 0.127278i) q^{21} +(2.24153 + 4.23976i) q^{23} +(-1.45592 - 1.68022i) q^{25} +(-0.142315 + 0.989821i) q^{27} +(0.0811036 + 0.564088i) q^{29} +(-5.85469 + 3.76258i) q^{31} +(5.10834 - 1.49994i) q^{33} +(0.296409 - 0.342074i) q^{35} +(3.67937 + 8.05671i) q^{37} +(-3.68628 - 1.08239i) q^{39} +(2.02205 - 4.42768i) q^{41} +(-5.68465 - 3.65331i) q^{43} +2.68761 q^{45} -2.26730 q^{47} +(-5.86491 - 3.76915i) q^{49} +(-2.76546 + 6.05550i) q^{51} +(-4.67826 - 1.37366i) q^{53} +(-5.94411 - 13.0158i) q^{55} +(4.51389 - 5.20930i) q^{57} +(-2.18859 + 0.642628i) q^{59} +(-11.7447 + 7.54785i) q^{61} +(0.0239677 + 0.166699i) q^{63} +(-1.46948 + 10.2205i) q^{65} +(1.05513 + 1.21768i) q^{67} +(-0.406487 + 4.77857i) q^{69} +(6.21899 + 7.17709i) q^{71} +(-0.545240 + 3.79223i) q^{73} +(-0.316402 - 2.20063i) q^{75} +(0.754293 - 0.484755i) q^{77} +(-2.51952 + 0.739797i) q^{79} +(-0.654861 + 0.755750i) q^{81} +(-3.72608 - 8.15898i) q^{83} +(17.1669 + 5.04067i) q^{85} +(-0.236740 + 0.518389i) q^{87} +(5.28849 + 3.39870i) q^{89} -0.647026 q^{91} -6.95948 q^{93} +(-15.5846 - 10.0156i) q^{95} +(-5.51602 + 12.0784i) q^{97} +(5.10834 + 1.49994i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{7}{11}\right)$	$1$	$1$

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
$3$	0.841254	+	0.540641i	0.485698	+	0.312139i
$3$	0.841254	+	0.540641i	0.485698	+	0.312139i
$4$		0			0
$5$	1.11647	−	2.44474i	0.499302	−	1.09332i	−0.477393	−	0.878690i	$-0.658418\pi$
$5$	1.11647	−	2.44474i	0.499302	−	1.09332i	0.976695	−	0.214630i	$-0.0688545\pi$
$6$		0			0
$7$	0.161591	+	0.0474474i	0.0610756	+	0.0179334i	0.312128	−	0.950040i	$-0.398958\pi$
$7$	0.161591	+	0.0474474i	0.0610756	+	0.0179334i	−0.251052	+	0.967974i	$0.580777\pi$
$8$		0			0
$9$	0.415415	+	0.909632i	0.138472	+	0.303211i
$10$		0			0
$11$	3.48648	−	4.02361i	1.05121	−	1.21316i	0.0748118	−	0.997198i	$-0.476164\pi$
$11$	3.48648	−	4.02361i	1.05121	−	1.21316i	0.976401	−	0.215966i	$-0.0692901\pi$
$12$		0			0
$13$	−3.68628	+	1.08239i	−1.02239	+	0.300201i	−0.749613	−	0.661876i	$-0.769760\pi$
$13$	−3.68628	+	1.08239i	−1.02239	+	0.300201i	−0.272777	+	0.962077i	$0.587942\pi$
$14$		0			0
$15$	2.26096	−	1.45303i	0.583778	−	0.375171i
$16$		0			0
$17$	0.947403	+	6.58933i	0.229779	+	1.59815i	0.699036	+	0.715086i	$0.253613\pi$
$17$	0.947403	+	6.58933i	0.229779	+	1.59815i	−0.469258	+	0.883061i	$0.655478\pi$
$18$		0			0
$19$	0.980961	−	6.82274i	0.225048	−	1.56524i	−0.493488	−	0.869753i	$-0.664278\pi$
$19$	0.980961	−	6.82274i	0.225048	−	1.56524i	0.718536	−	0.695490i	$-0.244813\pi$
$20$		0			0
$21$	0.110287	+	0.127278i	0.0240666	+	0.0277743i
$22$		0			0
$23$	2.24153	+	4.23976i	0.467392	+	0.884050i
$23$	2.24153	+	4.23976i	0.467392	+	0.884050i
$24$		0			0
$25$	−1.45592	−	1.68022i	−0.291185	−	0.336045i
$26$		0			0
$27$	−0.142315	+	0.989821i	−0.0273885	+	0.190491i
$28$		0			0
$29$	0.0811036	+	0.564088i	0.0150606	+	0.104748i	0.995965	−	0.0897412i	$-0.0286040\pi$
$29$	0.0811036	+	0.564088i	0.0150606	+	0.104748i	−0.980905	+	0.194490i	$0.937695\pi$
$30$		0			0
$31$	−5.85469	+	3.76258i	−1.05153	+	0.675779i	−0.947813	−	0.318827i	$-0.896711\pi$
$31$	−5.85469	+	3.76258i	−1.05153	+	0.675779i	−0.103720	+	0.994607i	$0.533075\pi$
$32$		0			0
$33$	5.10834	−	1.49994i	0.889248	−	0.261107i
$34$		0			0
$35$	0.296409	−	0.342074i	0.0501022	−	0.0578210i
$36$		0			0
$37$	3.67937	+	8.05671i	0.604885	+	1.32451i	0.926018	+	0.377480i	$0.123209\pi$
$37$	3.67937	+	8.05671i	0.604885	+	1.32451i	−0.321132	+	0.947034i	$0.604063\pi$
$38$		0			0
$39$	−3.68628	−	1.08239i	−0.590277	−	0.173321i
$40$		0			0
$41$	2.02205	−	4.42768i	0.315792	−	0.691487i	−0.683467	−	0.729981i	$-0.739529\pi$
$41$	2.02205	−	4.42768i	0.315792	−	0.691487i	0.999259	+	0.0384940i	$0.0122561\pi$
$42$		0			0
$43$	−5.68465	−	3.65331i	−0.866902	−	0.557124i	0.0299019	−	0.999553i	$-0.490480\pi$
$43$	−5.68465	−	3.65331i	−0.866902	−	0.557124i	−0.896804	+	0.442429i	$0.854117\pi$
$44$		0			0
$45$	2.68761			0.400645
$46$		0			0
$47$	−2.26730			−0.330720			−0.165360	−	0.986233i	$-0.552879\pi$
$47$	−2.26730			−0.330720			−0.165360	+	0.986233i	$0.552879\pi$
$48$		0			0
$49$	−5.86491	−	3.76915i	−0.837845	−	0.538450i
$50$		0			0
$51$	−2.76546	+	6.05550i	−0.387241	+	0.847940i
$52$		0			0
$53$	−4.67826	−	1.37366i	−0.642608	−	0.188687i	−0.0558372	−	0.998440i	$-0.517783\pi$
$53$	−4.67826	−	1.37366i	−0.642608	−	0.188687i	−0.586771	+	0.809753i	$0.699601\pi$
$54$		0			0
$55$	−5.94411	−	13.0158i	−0.801503	−	1.75505i
$56$		0			0
$57$	4.51389	−	5.20930i	0.597879	−	0.689989i
$58$		0			0
$59$	−2.18859	+	0.642628i	−0.284930	+	0.0836631i	−0.421075	−	0.907026i	$-0.638347\pi$
$59$	−2.18859	+	0.642628i	−0.284930	+	0.0836631i	0.136145	+	0.990689i	$0.456529\pi$
$60$		0			0
$61$	−11.7447	+	7.54785i	−1.50375	+	0.966404i	−0.509372	+	0.860547i	$0.670122\pi$
$61$	−11.7447	+	7.54785i	−1.50375	+	0.966404i	−0.994381	+	0.105857i	$0.966241\pi$
$62$		0			0
$63$	0.0239677	+	0.166699i	0.00301964	+	0.0210021i
$64$		0			0
$65$	−1.46948	+	10.2205i	−0.182266	+	1.26769i
$66$		0			0
$67$	1.05513	+	1.21768i	0.128904	+	0.148763i	0.816532	−	0.577300i	$-0.195894\pi$
$67$	1.05513	+	1.21768i	0.128904	+	0.148763i	−0.687628	+	0.726063i	$0.741348\pi$
$68$		0			0
$69$	−0.406487	+	4.77857i	−0.0489353	+	0.575273i
$70$		0			0
$71$	6.21899	+	7.17709i	0.738058	+	0.851764i	0.993354	−	0.115099i	$-0.0367184\pi$
$71$	6.21899	+	7.17709i	0.738058	+	0.851764i	−0.255296	+	0.966863i	$0.582173\pi$
$72$		0			0
$73$	−0.545240	+	3.79223i	−0.0638156	+	0.443847i	0.932715	+	0.360615i	$0.117433\pi$
$73$	−0.545240	+	3.79223i	−0.0638156	+	0.443847i	−0.996530	+	0.0832317i	$0.973476\pi$
$74$		0			0
$75$	−0.316402	−	2.20063i	−0.0365350	−	0.254106i
$76$		0			0
$77$	0.754293	−	0.484755i	0.0859597	−	0.0552429i
$78$		0			0
$79$	−2.51952	+	0.739797i	−0.283468	+	0.0832336i	−0.420376	−	0.907350i	$-0.638102\pi$
$79$	−2.51952	+	0.739797i	−0.283468	+	0.0832336i	0.136908	+	0.990584i	$0.456284\pi$
$80$		0			0
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$		0			0
$83$	−3.72608	−	8.15898i	−0.408991	−	0.895565i	−0.996279	−	0.0861869i	$-0.972532\pi$
$83$	−3.72608	−	8.15898i	−0.408991	−	0.895565i	0.587288	−	0.809378i	$-0.300195\pi$
$84$		0			0
$85$	17.1669	+	5.04067i	1.86202	+	0.546737i
$86$		0			0
$87$	−0.236740	+	0.518389i	−0.0253812	+	0.0555771i
$88$		0			0
$89$	5.28849	+	3.39870i	0.560578	+	0.360262i	0.790039	−	0.613056i	$-0.210060\pi$
$89$	5.28849	+	3.39870i	0.560578	+	0.360262i	−0.229461	+	0.973318i	$0.573696\pi$
$90$		0			0
$91$	−0.647026			−0.0678268
$92$		0			0
$93$	−6.95948			−0.721665
$94$		0			0
$95$	−15.5846	−	10.0156i	−1.59894	−	1.02758i
$96$		0			0
$97$	−5.51602	+	12.0784i	−0.560067	+	1.22638i	0.391853	+	0.920028i	$0.371834\pi$
$97$	−5.51602	+	12.0784i	−0.560067	+	1.22638i	−0.951920	+	0.306348i	$0.900893\pi$
$98$		0			0
$99$	5.10834	+	1.49994i	0.513407	+	0.150750i
$100$		0			0
$101$	−3.01867	−	6.60995i	−0.300368	−	0.657715i	0.697921	−	0.716174i	$-0.254108\pi$
$101$	−3.01867	−	6.60995i	−0.300368	−	0.657715i	−0.998290	+	0.0584593i	$0.981381\pi$
$102$		0			0
$103$	2.80445	−	3.23651i	0.276331	−	0.318903i	−0.600572	−	0.799571i	$-0.705060\pi$
$103$	2.80445	−	3.23651i	0.276331	−	0.318903i	0.876903	+	0.480668i	$0.159606\pi$
$104$		0			0
$105$	0.434294	−	0.127520i	0.0423827	−	0.0124447i
$106$		0			0
$107$	8.16992	−	5.25049i	0.789816	−	0.507584i	−0.0824617	−	0.996594i	$-0.526278\pi$
$107$	8.16992	−	5.25049i	0.789816	−	0.507584i	0.872278	+	0.489010i	$0.162642\pi$
$108$		0			0
$109$	1.25949	+	8.75997i	0.120638	+	0.839053i	0.956836	+	0.290627i	$0.0938638\pi$
$109$	1.25949	+	8.75997i	0.120638	+	0.839053i	−0.836199	+	0.548426i	$0.815227\pi$
$110$		0			0
$111$	−1.26050	+	8.76695i	−0.119641	+	0.832122i
$112$		0			0
$113$	−5.59605	−	6.45819i	−0.526432	−	0.607535i	0.428797	−	0.903401i	$-0.358937\pi$
$113$	−5.59605	−	6.45819i	−0.526432	−	0.607535i	−0.955230	+	0.295865i	$0.904392\pi$
$114$		0			0
$115$	12.8677	−	0.746382i	1.19992	−	0.0696005i
$116$		0			0
$117$	−2.51591	−	2.90352i	−0.232596	−	0.268430i
$118$		0			0
$119$	−0.159555	+	1.10973i	−0.0146264	+	0.101729i
$120$		0			0
$121$	−2.46845	−	17.1684i	−0.224404	−	1.56077i
$122$		0			0
$123$	4.09484	−	2.63160i	0.369220	−	0.237283i
$124$		0			0
$125$	7.16051	−	2.10252i	0.640456	−	0.188055i
$126$		0			0
$127$	9.93153	−	11.4616i	0.881281	−	1.01705i	−0.118429	−	0.992963i	$-0.537786\pi$
$127$	9.93153	−	11.4616i	0.881281	−	1.01705i	0.999710	−	0.0240899i	$-0.00766880\pi$
$128$		0			0
$129$	−2.80711	−	6.14671i	−0.247152	−	0.541188i
$130$		0			0
$131$	1.68835	+	0.495744i	0.147512	+	0.0433133i	0.354655	−	0.934997i	$-0.384598\pi$
$131$	1.68835	+	0.495744i	0.147512	+	0.0433133i	−0.207143	+	0.978311i	$0.566417\pi$
$132$		0			0
$133$	0.482235	−	1.05595i	0.0418151	−	0.0915623i
$134$		0			0
$135$	2.26096	+	1.45303i	0.194593	+	0.125057i
$136$		0			0
$137$	14.6865			1.25475			0.627375	−	0.778717i	$-0.284129\pi$
$137$	14.6865			1.25475			0.627375	+	0.778717i	$0.284129\pi$
$138$		0			0
$139$	22.3528			1.89594			0.947972	−	0.318355i	$-0.103130\pi$
$139$	22.3528			1.89594			0.947972	+	0.318355i	$0.103130\pi$
$140$		0			0
$141$	−1.90737	−	1.22580i	−0.160630	−	0.103231i
$142$		0			0
$143$	−8.49702	+	18.6059i	−0.710557	+	1.55590i
$144$		0			0
$145$	1.46960	+	0.431512i	0.122043	+	0.0358352i
$146$		0			0
$147$	−2.89612	−	6.34162i	−0.238868	−	0.523048i
$148$		0			0
$149$	4.49440	−	5.18681i	0.368195	−	0.424920i	−0.541173	−	0.840911i	$-0.682020\pi$
$149$	4.49440	−	5.18681i	0.368195	−	0.424920i	0.909369	+	0.415991i	$0.136565\pi$
$150$		0			0
$151$	1.45687	−	0.427777i	0.118559	−	0.0348120i	−0.221915	−	0.975066i	$-0.571231\pi$
$151$	1.45687	−	0.427777i	0.118559	−	0.0348120i	0.340474	+	0.940254i	$0.389413\pi$
$152$		0			0
$153$	−5.60030	+	3.59909i	−0.452757	+	0.290970i
$154$		0			0
$155$	2.66191	+	18.5140i	0.213810	+	1.48708i
$156$		0			0
$157$	0.937916	−	6.52335i	0.0748538	−	0.520620i	−0.917552	−	0.397615i	$-0.869838\pi$
$157$	0.937916	−	6.52335i	0.0748538	−	0.520620i	0.992406	−	0.123005i	$-0.0392530\pi$
$158$		0			0
$159$	−3.19294	−	3.68485i	−0.253217	−	0.292228i
$160$		0			0
$161$	0.161046	+	0.791461i	0.0126922	+	0.0623759i
$162$		0			0
$163$	−1.60484	−	1.85208i	−0.125701	−	0.145066i	0.689411	−	0.724371i	$-0.257870\pi$
$163$	−1.60484	−	1.85208i	−0.125701	−	0.145066i	−0.815111	+	0.579305i	$0.803324\pi$
$164$		0			0
$165$	2.03636	−	14.1632i	0.158530	−	1.10260i
$166$		0			0
$167$	−1.46665	−	10.2008i	−0.113493	−	0.789362i	−0.964476	−	0.264169i	$-0.914902\pi$
$167$	−1.46665	−	10.2008i	−0.113493	−	0.789362i	0.850983	−	0.525193i	$-0.176007\pi$
$168$		0			0
$169$	1.48081	−	0.951657i	0.113908	−	0.0732044i
$170$		0			0
$171$	6.61368	−	1.94195i	0.505761	−	0.148505i
$172$		0			0
$173$	1.97409	−	2.27822i	0.150088	−	0.173210i	−0.675727	−	0.737152i	$-0.736170\pi$
$173$	1.97409	−	2.27822i	0.150088	−	0.173210i	0.825815	+	0.563942i	$0.190716\pi$
$174$		0			0
$175$	−0.155542	−	0.340589i	−0.0117578	−	0.0257461i
$176$		0			0
$177$	−2.18859	−	0.642628i	−0.164505	−	0.0483029i
$178$		0			0
$179$	−5.61315	+	12.2911i	−0.419547	+	0.918679i	0.575362	+	0.817899i	$0.304861\pi$
$179$	−5.61315	+	12.2911i	−0.419547	+	0.918679i	−0.994909	+	0.100780i	$0.967866\pi$
$180$		0			0
$181$	11.6931	+	7.51470i	0.869141	+	0.558563i	0.897490	−	0.441035i	$-0.145389\pi$
$181$	11.6931	+	7.51470i	0.869141	+	0.558563i	−0.0283489	+	0.999598i	$0.509025\pi$
$182$		0			0
$183$	−13.9609			−1.03202
$184$		0			0
$185$	23.8045			1.75014
$186$		0			0
$187$	29.8160	+	19.1616i	2.18036	+	1.40123i
$188$		0			0
$189$	−0.0699612	+	0.153194i	−0.00508893	+	0.0111432i
$190$		0			0
$191$	−12.2796	−	3.60563i	−0.888524	−	0.260894i	−0.194549	−	0.980893i	$-0.562324\pi$
$191$	−12.2796	−	3.60563i	−0.888524	−	0.260894i	−0.693975	+	0.719999i	$0.744142\pi$
$192$		0			0
$193$	6.70400	+	14.6797i	0.482564	+	1.05667i	0.981750	+	0.190174i	$0.0609052\pi$
$193$	6.70400	+	14.6797i	0.482564	+	1.05667i	−0.499186	+	0.866495i	$0.666368\pi$
$194$		0			0
$195$	−6.76180	+	7.80353i	−0.484222	+	0.558822i
$196$		0			0
$197$	−12.6411	+	3.71175i	−0.900639	+	0.264451i	−0.699095	−	0.715028i	$-0.746414\pi$
$197$	−12.6411	+	3.71175i	−0.900639	+	0.264451i	−0.201543	+	0.979480i	$0.564596\pi$
$198$		0			0
$199$	−7.78674	+	5.00423i	−0.551987	+	0.354741i	−0.786711	−	0.617321i	$-0.788218\pi$
$199$	−7.78674	+	5.00423i	−0.551987	+	0.354741i	0.234724	+	0.972062i	$0.424581\pi$
$200$		0			0
$201$	0.229301	+	1.59482i	0.0161736	+	0.112490i
$202$		0			0
$203$	−0.0136589	+	0.0949996i	−0.000958666	+	0.00666767i
$204$		0			0
$205$	−8.56694	−	9.88678i	−0.598341	−	0.690522i
$206$		0			0
$207$	−2.92545	+	3.80023i	−0.203333	+	0.264134i
$208$		0			0
$209$	−24.0319	−	27.7343i	−1.66232	−	1.91842i
$210$		0			0
$211$	2.10427	−	14.6355i	0.144864	−	1.00755i	−0.779599	−	0.626279i	$-0.784577\pi$
$211$	2.10427	−	14.6355i	0.144864	−	1.00755i	0.924463	−	0.381271i	$-0.124514\pi$
$212$		0			0
$213$	1.35152	+	9.39999i	0.0926043	+	0.644077i
$214$		0			0
$215$	−15.2781	+	9.81866i	−1.04196	+	0.669627i
$216$		0			0
$217$	−1.12459	+	0.330209i	−0.0763421	+	0.0224161i
$218$		0			0
$219$	−2.50892	+	2.89545i	−0.169537	+	0.195656i
$220$		0			0
$221$	−10.6246	−	23.2647i	−0.714689	−	1.56495i
$222$		0			0
$223$	−14.3582	−	4.21594i	−0.961495	−	0.282320i	−0.236930	−	0.971527i	$-0.576141\pi$
$223$	−14.3582	−	4.21594i	−0.961495	−	0.282320i	−0.724565	+	0.689206i	$0.757959\pi$
$224$		0			0
$225$	0.923574	−	2.02234i	0.0615716	−	0.134823i
$226$		0			0
$227$	16.2385	+	10.4358i	1.07779	+	0.692651i	0.954045	−	0.299664i	$-0.0968744\pi$
$227$	16.2385	+	10.4358i	1.07779	+	0.692651i	0.123741	+	0.992315i	$0.460511\pi$
$228$		0			0
$229$	−26.6442			−1.76070			−0.880349	−	0.474326i	$-0.842692\pi$
$229$	−26.6442			−1.76070			−0.880349	+	0.474326i	$0.842692\pi$
$230$		0			0
$231$	0.896630			0.0589939
$232$		0			0
$233$	−12.1545	−	7.81123i	−0.796269	−	0.511731i	0.0781274	−	0.996943i	$-0.475106\pi$
$233$	−12.1545	−	7.81123i	−0.796269	−	0.511731i	−0.874396	+	0.485212i	$0.838742\pi$
$234$		0			0
$235$	−2.53138	+	5.54295i	−0.165129	+	0.361582i
$236$		0			0
$237$	−2.51952	−	0.739797i	−0.163660	−	0.0480550i
$238$		0			0
$239$	−10.0163	−	21.9326i	−0.647901	−	1.41870i	−0.893380	−	0.449303i	$-0.851672\pi$
$239$	−10.0163	−	21.9326i	−0.647901	−	1.41870i	0.245479	−	0.969402i	$-0.421055\pi$
$240$		0			0
$241$	7.34261	−	8.47382i	0.472979	−	0.545847i	−0.468259	−	0.883591i	$-0.655119\pi$
$241$	7.34261	−	8.47382i	0.472979	−	0.545847i	0.941238	+	0.337745i	$0.109664\pi$
$242$		0			0
$243$	−0.959493	+	0.281733i	−0.0615515	+	0.0180732i
$244$		0			0
$245$	−15.7626	+	10.1300i	−1.00704	+	0.647183i
$246$		0			0
$247$	3.76876	+	26.2123i	0.239801	+	1.66785i
$248$		0			0
$249$	1.27650	−	8.87825i	0.0808948	−	0.562636i
$250$		0			0
$251$	18.7772	+	21.6700i	1.18520	+	1.36780i	0.914221	+	0.405215i	$0.132803\pi$
$251$	18.7772	+	21.6700i	1.18520	+	1.36780i	0.270983	+	0.962584i	$0.412651\pi$
$252$		0			0
$253$	24.8742	+	5.76276i	1.56383	+	0.362302i
$254$		0			0
$255$	11.7166	+	13.5216i	0.733719	+	0.846757i
$256$		0			0
$257$	−2.64973	+	18.4293i	−0.165286	+	1.14959i	0.723185	+	0.690655i	$0.242678\pi$
$257$	−2.64973	+	18.4293i	−0.165286	+	1.14959i	−0.888471	+	0.458934i	$0.848232\pi$
$258$		0			0
$259$	0.212284	+	1.47647i	0.0131907	+	0.0917432i
$260$		0			0
$261$	−0.479421	+	0.308105i	−0.0296754	+	0.0190712i
$262$		0			0
$263$	13.7309	−	4.03175i	0.846683	−	0.248608i	0.170514	−	0.985355i	$-0.445457\pi$
$263$	13.7309	−	4.03175i	0.846683	−	0.248608i	0.676169	+	0.736747i	$0.263639\pi$
$264$		0			0
$265$	−8.58139	+	9.90345i	−0.527151	+	0.608364i
$266$		0			0
$267$	2.61148	+	5.71834i	0.159820	+	0.349957i
$268$		0			0
$269$	6.73185	+	1.97665i	0.410448	+	0.120518i	0.480437	−	0.877029i	$-0.340478\pi$
$269$	6.73185	+	1.97665i	0.410448	+	0.120518i	−0.0699888	+	0.997548i	$0.522296\pi$
$270$		0			0
$271$	4.44140	−	9.72532i	0.269796	−	0.590771i	−0.725438	−	0.688288i	$-0.758363\pi$
$271$	4.44140	−	9.72532i	0.269796	−	0.590771i	0.995234	+	0.0975167i	$0.0310899\pi$
$272$		0			0
$273$	−0.544313	−	0.349809i	−0.0329433	−	0.0211714i
$274$		0			0
$275$	−11.8366			−0.713774
$276$		0			0
$277$	22.1540			1.33111			0.665553	−	0.746351i	$-0.268196\pi$
$277$	22.1540			1.33111			0.665553	+	0.746351i	$0.268196\pi$
$278$		0			0
$279$	−5.85469	−	3.76258i	−0.350511	−	0.225260i
$280$		0			0
$281$	2.93397	−	6.42449i	0.175026	−	0.383253i	−0.801706	−	0.597719i	$-0.796074\pi$
$281$	2.93397	−	6.42449i	0.175026	−	0.383253i	0.976731	+	0.214466i	$0.0688012\pi$
$282$		0			0
$283$	−25.8425	−	7.58804i	−1.53618	−	0.451062i	−0.599243	−	0.800567i	$-0.704532\pi$
$283$	−25.8425	−	7.58804i	−1.53618	−	0.451062i	−0.936934	+	0.349505i	$0.886350\pi$
$284$		0			0
$285$	−7.69574	−	16.8513i	−0.455856	−	0.998186i
$286$		0			0
$287$	0.536827	−	0.619532i	0.0316879	−	0.0365698i
$288$		0			0
$289$	−26.2103	+	7.69605i	−1.54178	+	0.452709i
$290$		0			0
$291$	−11.1704	+	7.17881i	−0.654823	+	0.420829i
$292$		0			0
$293$	−4.06035	−	28.2404i	−0.237208	−	1.64982i	−0.665659	−	0.746256i	$-0.731850\pi$
$293$	−4.06035	−	28.2404i	−0.237208	−	1.64982i	0.428451	−	0.903565i	$-0.359059\pi$
$294$		0			0
$295$	−0.872448	+	6.06801i	−0.0507959	+	0.353293i
$296$		0			0
$297$	3.48648	+	4.02361i	0.202306	+	0.233474i
$298$		0			0
$299$	−12.8520	−	13.2027i	−0.743250	−	0.763533i
$300$		0			0
$301$	−0.745249	−	0.860063i	−0.0429554	−	0.0495732i
$302$		0			0
$303$	1.03415	−	7.19266i	0.0594103	−	0.413208i
$304$		0			0
$305$	5.33988	+	37.1397i	0.305760	+	2.12661i
$306$		0			0
$307$	−9.78399	+	6.28779i	−0.558402	+	0.358863i	−0.789198	−	0.614139i	$-0.789503\pi$
$307$	−9.78399	+	6.28779i	−0.558402	+	0.358863i	0.230796	+	0.973002i	$0.425867\pi$
$308$		0			0
$309$	4.10904	−	1.20652i	0.233755	−	0.0686367i
$310$		0			0
$311$	−17.1917	+	19.8402i	−0.974850	+	1.12504i	0.0172830	+	0.999851i	$0.494498\pi$
$311$	−17.1917	+	19.8402i	−0.974850	+	1.12504i	−0.992133	+	0.125186i	$0.960047\pi$
$312$		0			0
$313$	−10.6415	−	23.3016i	−0.601491	−	1.31708i	−0.928244	−	0.371972i	$-0.878682\pi$
$313$	−10.6415	−	23.3016i	−0.601491	−	1.31708i	0.326753	−	0.945110i	$-0.394046\pi$
$314$		0			0
$315$	0.434294	+	0.127520i	0.0244697	+	0.00718495i
$316$		0			0
$317$	8.38985	−	18.3712i	0.471221	−	1.03183i	−0.513564	−	0.858051i	$-0.671675\pi$
$317$	8.38985	−	18.3712i	0.471221	−	1.03183i	0.984785	−	0.173778i	$-0.0555976\pi$
$318$		0			0
$319$	2.55243	+	1.64035i	0.142909	+	0.0918420i
$320$		0			0
$321$	9.71161			0.542049
$322$		0			0
$323$	45.8866			2.55320
$324$		0			0
$325$	7.18560	+	4.61790i	0.398585	+	0.256155i
$326$		0			0
$327$	−3.67644	+	8.05029i	−0.203308	+	0.445182i
$328$		0			0
$329$	−0.366375	−	0.107577i	−0.0201989	−	0.00593094i
$330$		0			0
$331$	−8.94888	−	19.5953i	−0.491875	−	1.07706i	−0.979025	−	0.203738i	$-0.934691\pi$
$331$	−8.94888	−	19.5953i	−0.491875	−	1.07706i	0.487150	−	0.873318i	$-0.338036\pi$
$332$		0			0
$333$	−5.80017	+	6.69375i	−0.317847	+	0.366815i
$334$		0			0
$335$	4.15493	−	1.22000i	0.227008	−	0.0666556i
$336$		0			0
$337$	1.64816	−	1.05921i	0.0897811	−	0.0576988i	−0.494980	−	0.868904i	$-0.664825\pi$
$337$	1.64816	−	1.05921i	0.0897811	−	0.0576988i	0.584761	+	0.811206i	$0.301188\pi$
$338$		0			0
$339$	−1.21614	−	8.45843i	−0.0660516	−	0.459399i
$340$		0			0
$341$	−5.27309	+	36.6751i	−0.285554	+	1.98607i
$342$		0			0
$343$	−1.54089	−	1.77828i	−0.0832002	−	0.0960182i
$344$		0			0
$345$	11.2285	+	6.32891i	0.604523	+	0.340737i
$346$		0			0
$347$	−6.39079	−	7.37537i	−0.343076	−	0.395931i	0.557823	−	0.829960i	$-0.311637\pi$
$347$	−6.39079	−	7.37537i	−0.343076	−	0.395931i	−0.900899	+	0.434029i	$0.857091\pi$
$348$		0			0
$349$	2.32886	−	16.1975i	0.124661	−	0.867035i	−0.827506	−	0.561457i	$-0.810241\pi$
$349$	2.32886	−	16.1975i	0.124661	−	0.867035i	0.952167	−	0.305578i	$-0.0988497\pi$
$350$		0			0
$351$	−0.546760	−	3.80280i	−0.0291839	−	0.202978i
$352$		0			0
$353$	−15.8365	+	10.1775i	−0.842894	+	0.541695i	−0.889351	−	0.457225i	$-0.848843\pi$
$353$	−15.8365	+	10.1775i	−0.842894	+	0.541695i	0.0464568	+	0.998920i	$0.485207\pi$
$354$		0			0
$355$	24.4894	−	7.19075i	1.29976	−	0.381645i
$356$		0			0
$357$	−0.734190	+	0.847301i	−0.0388575	+	0.0448439i
$358$		0			0
$359$	−5.47158	−	11.9811i	−0.288779	−	0.632338i	0.708527	−	0.705683i	$-0.249360\pi$
$359$	−5.47158	−	11.9811i	−0.288779	−	0.632338i	−0.997307	+	0.0733451i	$0.976633\pi$
$360$		0			0
$361$	−27.3571	−	8.03276i	−1.43985	−	0.422777i
$362$		0			0
$363$	7.20536	−	15.7775i	0.378183	−	0.828106i
$364$		0			0
$365$	8.66226	+	5.56690i	0.453403	+	0.291385i
$366$		0			0
$367$	12.2223			0.638000			0.319000	−	0.947755i	$-0.396653\pi$
$367$	12.2223			0.638000			0.319000	+	0.947755i	$0.396653\pi$
$368$		0			0
$369$	4.86755			0.253394
$370$		0			0
$371$	−0.690787	−	0.443942i	−0.0358639	−	0.0230483i
$372$		0			0
$373$	−10.6821	+	23.3904i	−0.553096	+	1.21111i	0.402225	+	0.915541i	$0.368237\pi$
$373$	−10.6821	+	23.3904i	−0.553096	+	1.21111i	−0.955321	+	0.295571i	$0.904490\pi$
$374$		0			0
$375$	7.16051	+	2.10252i	0.369767	+	0.108573i
$376$		0			0
$377$	−0.909533	−	1.99160i	−0.0468434	−	0.102573i
$378$		0			0
$379$	−12.6498	+	14.5987i	−0.649779	+	0.749884i	−0.981072	−	0.193643i	$-0.937970\pi$
$379$	−12.6498	+	14.5987i	−0.649779	+	0.749884i	0.331293	+	0.943528i	$0.392515\pi$
$380$		0			0
$381$	14.5515	−	4.27272i	0.745498	−	0.218898i
$382$		0			0
$383$	22.4745	−	14.4435i	1.14839	−	0.738027i	0.179074	−	0.983836i	$-0.442690\pi$
$383$	22.4745	−	14.4435i	1.14839	−	0.738027i	0.969318	+	0.245808i	$0.0790534\pi$
$384$		0			0
$385$	−0.342949	−	2.38526i	−0.0174783	−	0.121564i
$386$		0			0
$387$	0.961673	−	6.68858i	0.0488846	−	0.340000i
$388$		0			0
$389$	3.70667	+	4.27773i	0.187936	+	0.216889i	0.841896	−	0.539639i	$-0.181439\pi$
$389$	3.70667	+	4.27773i	0.187936	+	0.216889i	−0.653961	+	0.756528i	$0.726894\pi$
$390$		0			0
$391$	−25.8135	+	18.7870i	−1.30545	+	0.950097i
$392$		0			0
$393$	1.15231	+	1.32984i	0.0581263	+	0.0670813i
$394$		0			0
$395$	−1.00437	+	6.98552i	−0.0505351	+	0.351480i
$396$		0			0
$397$	−1.11388	−	7.74722i	−0.0559041	−	0.388822i	−0.998494	−	0.0548680i	$-0.982526\pi$
$397$	−1.11388	−	7.74722i	−0.0559041	−	0.388822i	0.942590	−	0.333954i	$-0.108383\pi$
$398$		0			0
$399$	0.976571	−	0.627604i	0.0488897	−	0.0314195i
$400$		0			0
$401$	8.50273	−	2.49663i	0.424606	−	0.124676i	−0.0624463	−	0.998048i	$-0.519890\pi$
$401$	8.50273	−	2.49663i	0.424606	−	0.124676i	0.487053	+	0.873373i	$0.338072\pi$
$402$		0			0
$403$	17.5094	−	20.2070i	0.872208	−	1.00658i
$404$		0			0
$405$	1.11647	+	2.44474i	0.0554780	+	0.121480i
$406$		0			0
$407$	45.2451	+	13.2852i	2.24272	+	0.658521i
$408$		0			0
$409$	5.62678	−	12.3209i	0.278226	−	0.609231i	−0.717998	−	0.696045i	$-0.754941\pi$
$409$	5.62678	−	12.3209i	0.278226	−	0.609231i	0.996225	+	0.0868141i	$0.0276686\pi$
$410$		0			0
$411$	12.3550	+	7.94011i	0.609429	+	0.391657i
$412$		0			0
$413$	−0.384147			−0.0189027
$414$		0			0
$415$	−24.1066			−1.18335
$416$		0			0
$417$	18.8044	+	12.0849i	0.920856	+	0.591798i
$418$		0			0
$419$	3.92505	−	8.59466i	0.191751	−	0.419877i	−0.789199	−	0.614138i	$-0.789504\pi$
$419$	3.92505	−	8.59466i	0.191751	−	0.419877i	0.980950	+	0.194261i	$0.0622310\pi$
$420$		0			0
$421$	29.8747	+	8.77200i	1.45600	+	0.427521i	0.911522	−	0.411252i	$-0.134908\pi$
$421$	29.8747	+	8.77200i	1.45600	+	0.427521i	0.544481	+	0.838773i	$0.316727\pi$
$422$		0			0
$423$	−0.941871	−	2.06241i	−0.0457953	−	0.100278i
$424$		0			0
$425$	9.69221	−	11.1854i	0.470141	−	0.542572i
$426$		0			0
$427$	−2.25596	+	0.662410i	−0.109174	+	0.0320563i
$428$		0			0
$429$	−17.2073	+	11.0584i	−0.830774	+	0.533906i
$430$		0			0
$431$	3.07047	+	21.3556i	0.147900	+	1.02866i	0.919650	+	0.392739i	$0.128472\pi$
$431$	3.07047	+	21.3556i	0.147900	+	1.02866i	−0.771751	+	0.635925i	$0.780619\pi$
$432$		0			0
$433$	0.0751560	−	0.522721i	0.00361176	−	0.0251204i	−0.987936	−	0.154864i	$-0.950506\pi$
$433$	0.0751560	−	0.522721i	0.00361176	−	0.0251204i	0.991548	+	0.129743i	$0.0414153\pi$
$434$		0			0
$435$	1.00301	+	1.15754i	0.0480906	+	0.0554996i
$436$		0			0
$437$	31.1256	−	11.1344i	1.48894	−	0.532628i
$438$		0			0
$439$	−14.1594	−	16.3408i	−0.675790	−	0.779903i	0.309481	−	0.950906i	$-0.399845\pi$
$439$	−14.1594	−	16.3408i	−0.675790	−	0.779903i	−0.985271	+	0.171003i	$0.945299\pi$
$440$		0			0
$441$	0.992167	−	6.90068i	0.0472461	−	0.328604i
$442$		0			0
$443$	−3.16475	−	22.0113i	−0.150362	−	1.04579i	−0.915614	−	0.402059i	$-0.868295\pi$
$443$	−3.16475	−	22.0113i	−0.150362	−	1.04579i	0.765252	−	0.643731i	$-0.222615\pi$
$444$		0			0
$445$	14.2134	−	9.13439i	0.673779	−	0.433012i
$446$		0			0
$447$	6.58513	−	1.93357i	0.311466	−	0.0914547i
$448$		0			0
$449$	27.3177	−	31.5263i	1.28920	−	1.48782i	0.511343	−	0.859377i	$-0.329148\pi$
$449$	27.3177	−	31.5263i	1.28920	−	1.48782i	0.777858	−	0.628440i	$-0.216306\pi$
$450$		0			0
$451$	−10.7654	−	23.5730i	−0.506923	−	1.11001i
$452$		0			0
$453$	1.45687	+	0.427777i	0.0684500	+	0.0200987i
$454$		0			0
$455$	−0.722388	+	1.58181i	−0.0338661	+	0.0741564i
$456$		0			0
$457$	16.5228	+	10.6185i	0.772903	+	0.496714i	0.866671	−	0.498880i	$-0.166255\pi$
$457$	16.5228	+	10.6185i	0.772903	+	0.496714i	−0.0937686	+	0.995594i	$0.529891\pi$
$458$		0			0
$459$	−6.65709			−0.310726
$460$		0			0
$461$	−14.8017			−0.689383			−0.344692	−	0.938716i	$-0.612017\pi$
$461$	−14.8017			−0.689383			−0.344692	+	0.938716i	$0.612017\pi$
$462$		0			0
$463$	12.8377	+	8.25026i	0.596617	+	0.383422i	0.803817	−	0.594876i	$-0.202799\pi$
$463$	12.8377	+	8.25026i	0.596617	+	0.383422i	−0.207201	+	0.978298i	$0.566435\pi$
$464$		0			0
$465$	−7.77008	+	17.0141i	−0.360329	+	0.789010i
$466$		0			0
$467$	−14.8229	−	4.35240i	−0.685923	−	0.201405i	−0.0798415	−	0.996808i	$-0.525441\pi$
$467$	−14.8229	−	4.35240i	−0.685923	−	0.201405i	−0.606082	+	0.795402i	$0.707260\pi$
$468$		0			0
$469$	0.112723	+	0.246829i	0.00520507	+	0.0113975i
$470$		0			0
$471$	4.31581	−	4.98071i	0.198862	−	0.229499i
$472$		0			0
$473$	−34.5189	+	10.1357i	−1.58718	+	0.466038i
$474$		0			0
$475$	−12.8919	+	8.28514i	−0.591522	+	0.380148i
$476$		0			0
$477$	−0.693893	−	4.82613i	−0.0317712	−	0.220973i
$478$		0			0
$479$	−2.68993	+	18.7089i	−0.122906	+	0.854832i	0.831330	+	0.555779i	$0.187580\pi$
$479$	−2.68993	+	18.7089i	−0.122906	+	0.854832i	−0.954237	+	0.299053i	$0.903329\pi$
$480$		0			0
$481$	−22.2837	−	25.7168i	−1.01605	−	1.17258i
$482$		0			0
$483$	−0.292416	+	0.752888i	−0.0133054	+	0.0342576i
$484$		0			0
$485$	23.3700	+	26.9704i	1.06118	+	1.22466i
$486$		0			0
$487$	−1.46822	+	10.2117i	−0.0665313	+	0.462735i	0.929135	+	0.369740i	$0.120553\pi$
$487$	−1.46822	+	10.2117i	−0.0665313	+	0.462735i	−0.995667	+	0.0929953i	$0.970356\pi$
$488$		0			0
$489$	−0.348765	−	2.42571i	−0.0157717	−	0.109694i
$490$		0			0
$491$	5.85642	−	3.76369i	0.264296	−	0.169853i	−0.401781	−	0.915736i	$-0.631609\pi$
$491$	5.85642	−	3.76369i	0.264296	−	0.169853i	0.666077	+	0.745883i	$0.267972\pi$
$492$		0			0
$493$	−3.64012	+	1.06884i	−0.163943	+	0.0481380i
$494$		0			0
$495$	9.37030	−	10.8139i	0.421164	−	0.486049i
$496$		0			0
$497$	0.664398	+	1.45483i	0.0298023	+	0.0652580i
$498$		0			0
$499$	0.979391	+	0.287575i	0.0438435	+	0.0128736i	0.303581	−	0.952806i	$-0.401818\pi$
$499$	0.979391	+	0.287575i	0.0438435	+	0.0128736i	−0.259737	+	0.965679i	$0.583636\pi$
$500$		0			0
$501$	4.28114	−	9.37440i	0.191267	−	0.418817i
$502$		0			0
$503$	−12.1305	−	7.79581i	−0.540873	−	0.347598i	0.241507	−	0.970399i	$-0.422358\pi$
$503$	−12.1305	−	7.79581i	−0.540873	−	0.347598i	−0.782380	+	0.622801i	$0.785995\pi$
$504$		0			0
$505$	−19.5299			−0.869068
$506$		0			0
$507$	1.76024			0.0781750
$508$		0			0
$509$	−21.0513	−	13.5289i	−0.933084	−	0.599657i	−0.0166583	−	0.999861i	$-0.505303\pi$
$509$	−21.0513	−	13.5289i	−0.933084	−	0.599657i	−0.916426	+	0.400204i	$0.868939\pi$
$510$		0			0
$511$	−0.268037	+	0.586920i	−0.0118573	+	0.0259638i
$512$		0			0
$513$	6.61368	+	1.94195i	0.292001	+	0.0857393i
$514$		0			0
$515$	−4.78132	−	10.4696i	−0.210690	−	0.461347i
$516$		0			0
$517$	−7.90489	+	9.12273i	−0.347657	+	0.401217i
$518$		0			0
$519$	2.89241	−	0.849289i	0.126963	−	0.0372797i
$520$		0			0
$521$	29.0057	−	18.6408i	1.27076	−	0.816670i	0.281045	−	0.959695i	$-0.409319\pi$
$521$	29.0057	−	18.6408i	1.27076	−	0.816670i	0.989719	+	0.143024i	$0.0456827\pi$
$522$		0			0
$523$	1.78837	+	12.4384i	0.0781998	+	0.543892i	0.990831	+	0.135108i	$0.0431380\pi$
$523$	1.78837	+	12.4384i	0.0781998	+	0.543892i	−0.912631	+	0.408784i	$0.865953\pi$
$524$		0			0
$525$	0.0532862	−	0.370614i	0.00232560	−	0.0161749i
$526$		0			0
$527$	−30.3396	−	35.0138i	−1.32161	−	1.52522i
$528$		0			0
$529$	−12.9511	+	19.0071i	−0.563090	+	0.826396i
$530$		0			0
$531$	−1.49373	−	1.72385i	−0.0648223	−	0.0748089i
$532$		0			0
$533$	−2.66138	+	18.5103i	−0.115277	+	0.801771i
$534$		0			0
$535$	−3.71456	−	25.8354i	−0.160595	−	1.11696i
$536$		0			0
$537$	−11.3672	+	7.30523i	−0.490529	+	0.315244i
$538$		0			0
$539$	−35.6135	+	10.4571i	−1.53398	+	0.450418i
$540$		0			0
$541$	8.60529	−	9.93103i	0.369970	−	0.426969i	−0.539985	−	0.841675i	$-0.681570\pi$
$541$	8.60529	−	9.93103i	0.369970	−	0.426969i	0.909955	+	0.414706i	$0.136116\pi$
$542$		0			0
$543$	5.77411	+	12.6435i	0.247791	+	0.542586i
$544$		0			0
$545$	22.8220	+	6.70115i	0.977588	+	0.287046i
$546$		0			0
$547$	−14.5743	+	31.9134i	−0.623154	+	1.36452i	0.290049	+	0.957012i	$0.406328\pi$
$547$	−14.5743	+	31.9134i	−0.623154	+	1.36452i	−0.913203	+	0.407505i	$0.866399\pi$
$548$		0			0
$549$	−11.7447	−	7.54785i	−0.501251	−	0.322135i
$550$		0			0
$551$	3.92818			0.167346
$552$		0			0
$553$	−0.442233			−0.0188056
$554$		0			0
$555$	20.0256	+	12.8697i	0.850039	+	0.546287i
$556$		0			0
$557$	−0.267339	+	0.585391i	−0.0113275	+	0.0248038i	−0.915211	−	0.402974i	$-0.867976\pi$
$557$	−0.267339	+	0.585391i	−0.0113275	+	0.0248038i	0.903884	+	0.427778i	$0.140704\pi$
$558$		0			0
$559$	24.9095	+	7.31410i	1.05356	+	0.309353i
$560$		0			0
$561$	14.7233	+	32.2395i	0.621617	+	1.36115i
$562$		0			0
$563$	7.62376	−	8.79829i	0.321303	−	0.370804i	−0.572004	−	0.820251i	$-0.693834\pi$
$563$	7.62376	−	8.79829i	0.321303	−	0.370804i	0.893307	+	0.449447i	$0.148379\pi$
$564$		0			0
$565$	−22.0364	+	6.47048i	−0.927079	+	0.272215i
$566$		0			0
$567$	−0.141678	+	0.0910509i	−0.00594991	+	0.00382378i
$568$		0			0
$569$	5.06376	+	35.2193i	0.212284	+	1.47647i	0.765503	+	0.643432i	$0.222490\pi$
$569$	5.06376	+	35.2193i	0.212284	+	1.47647i	−0.553219	+	0.833036i	$0.686601\pi$
$570$		0			0
$571$	−0.588588	+	4.09372i	−0.0246316	+	0.171317i	−0.998424	−	0.0561226i	$-0.982126\pi$
$571$	−0.588588	+	4.09372i	−0.0246316	+	0.171317i	0.973792	+	0.227439i	$0.0730353\pi$
$572$		0			0
$573$	−8.38095	−	9.67213i	−0.350119	−	0.404059i
$574$		0			0
$575$	3.86024	−	9.93904i	0.160983	−	0.414486i
$576$		0			0
$577$	2.18302	+	2.51934i	0.0908803	+	0.104881i	0.799368	−	0.600842i	$-0.205168\pi$
$577$	2.18302	+	2.51934i	0.0908803	+	0.104881i	−0.708488	+	0.705723i	$0.750622\pi$
$578$		0			0
$579$	−2.29669	+	15.9738i	−0.0954471	+	0.663849i
$580$		0			0
$581$	−0.214979	−	1.49521i	−0.00891883	−	0.0620318i
$582$		0			0
$583$	−21.8377	+	14.0342i	−0.904425	+	0.581239i
$584$		0			0
$585$	−9.90729	+	2.90904i	−0.409616	+	0.120274i
$586$		0			0
$587$	−9.03818	+	10.4306i	−0.373045	+	0.430517i	−0.910968	−	0.412477i	$-0.864664\pi$
$587$	−9.03818	+	10.4306i	−0.373045	+	0.430517i	0.537923	+	0.842994i	$0.319209\pi$
$588$		0			0
$589$	19.9279	+	43.6359i	0.821113	+	1.79799i
$590$		0			0
$591$	−12.6411	−	3.71175i	−0.519984	−	0.152681i
$592$		0			0
$593$	−15.0251	+	32.9004i	−0.617006	+	1.35106i	0.300670	+	0.953728i	$0.402790\pi$
$593$	−15.0251	+	32.9004i	−0.617006	+	1.35106i	−0.917677	+	0.397328i	$0.869938\pi$
$594$		0			0
$595$	2.53485	+	1.62905i	0.103919	+	0.0667846i
$596$		0			0
$597$	−9.25611			−0.378828
$598$		0			0
$599$	18.8219			0.769041			0.384520	−	0.923117i	$-0.374367\pi$
$599$	18.8219			0.769041			0.384520	+	0.923117i	$0.374367\pi$
$600$		0			0
$601$	−37.3898	−	24.0289i	−1.52516	−	0.980161i	−0.990864	−	0.134864i	$-0.956940\pi$
$601$	−37.3898	−	24.0289i	−1.52516	−	0.980161i	−0.534296	−	0.845297i	$-0.679423\pi$
$602$		0			0
$603$	−0.669326	+	1.46562i	−0.0272571	+	0.0596846i
$604$		0			0
$605$	−44.7282	−	13.1334i	−1.81846	−	0.533948i
$606$		0			0
$607$	−10.1913	−	22.3159i	−0.413654	−	0.905775i	−0.995701	−	0.0926204i	$-0.970476\pi$
$607$	−10.1913	−	22.3159i	−0.413654	−	0.905775i	0.582048	−	0.813154i	$-0.302252\pi$
$608$		0			0
$609$	−0.0628513	+	0.0725342i	−0.00254686	+	0.00293924i
$610$		0			0
$611$	8.35791	−	2.45410i	0.338125	−	0.0992824i
$612$		0			0
$613$	−1.91550	+	1.23102i	−0.0773665	+	0.0497204i	−0.578752	−	0.815503i	$-0.696460\pi$
$613$	−1.91550	+	1.23102i	−0.0773665	+	0.0497204i	0.501386	+	0.865224i	$0.332824\pi$
$614$		0			0
$615$	−1.86177	−	12.9489i	−0.0750740	−	0.522151i
$616$		0			0
$617$	1.75141	−	12.1813i	0.0705091	−	0.490402i	−0.923715	−	0.383080i	$-0.874863\pi$
$617$	1.75141	−	12.1813i	0.0705091	−	0.490402i	0.994224	−	0.107322i	$-0.0342275\pi$
$618$		0			0
$619$	−5.84291	−	6.74307i	−0.234846	−	0.271027i	0.626078	−	0.779761i	$-0.284659\pi$
$619$	−5.84291	−	6.74307i	−0.234846	−	0.271027i	−0.860924	+	0.508734i	$0.830114\pi$
$620$		0			0
$621$	−4.51560	+	1.61534i	−0.181205	+	0.0648213i
$622$		0			0
$623$	0.693312	+	0.800125i	0.0277770	+	0.0320563i
$624$		0			0
$625$	4.43644	−	30.8561i	0.177458	−	1.23424i
$626$		0			0
$627$	−5.22264	−	36.3242i	−0.208572	−	1.45065i
$628$		0			0
$629$	−49.6025	+	31.8776i	−1.97778	+	1.27104i
$630$		0			0
$631$	31.7431	−	9.32063i	1.26367	−	0.371048i	0.419814	−	0.907610i	$-0.362095\pi$
$631$	31.7431	−	9.32063i	1.26367	−	0.371048i	0.843861	+	0.536562i	$0.180277\pi$
$632$		0			0
$633$	9.68278	−	11.1745i	0.384856	−	0.444147i
$634$		0			0
$635$	−16.9323	−	37.0766i	−0.671938	−	1.47134i
$636$		0			0
$637$	25.6994	+	7.54603i	1.01825	+	0.298985i
$638$		0			0
$639$	−3.94505	+	8.63846i	−0.156064	+	0.341732i
$640$		0			0
$641$	38.3241	+	24.6294i	1.51371	+	0.972802i	0.992877	+	0.119143i	$0.0380147\pi$
$641$	38.3241	+	24.6294i	1.51371	+	0.972802i	0.520832	+	0.853659i	$0.325622\pi$
$642$		0			0
$643$	−6.72806			−0.265329			−0.132664	−	0.991161i	$-0.542353\pi$
$643$	−6.72806			−0.265329			−0.132664	+	0.991161i	$0.542353\pi$
$644$		0			0
$645$	−18.1612			−0.715095
$646$		0			0
$647$	−4.02439	−	2.58632i	−0.158215	−	0.101679i	0.459138	−	0.888365i	$-0.348158\pi$
$647$	−4.02439	−	2.58632i	−0.158215	−	0.101679i	−0.617353	+	0.786687i	$0.711795\pi$
$648$		0			0
$649$	−5.04479	+	11.0465i	−0.198025	+	0.433615i
$650$		0			0
$651$	−1.12459	−	0.330209i	−0.0440761	−	0.0129419i
$652$		0			0
$653$	13.0075	+	28.4825i	0.509023	+	1.11460i	0.973430	+	0.228983i	$0.0735401\pi$
$653$	13.0075	+	28.4825i	0.509023	+	1.11460i	−0.464407	+	0.885622i	$0.653733\pi$
$654$		0			0
$655$	3.09696	−	3.57408i	0.121008	−	0.139651i
$656$		0			0
$657$	−3.67603	+	1.07938i	−0.143416	+	0.0421107i
$658$		0			0
$659$	−6.56570	+	4.21952i	−0.255763	+	0.164369i	−0.662239	−	0.749292i	$-0.730394\pi$
$659$	−6.56570	+	4.21952i	−0.255763	+	0.164369i	0.406476	+	0.913661i	$0.366757\pi$
$660$		0			0
$661$	−6.64686	−	46.2299i	−0.258533	−	1.79814i	−0.543300	−	0.839539i	$-0.682825\pi$
$661$	−6.64686	−	46.2299i	−0.258533	−	1.79814i	0.284767	−	0.958597i	$-0.408084\pi$
$662$		0			0
$663$	3.63983	−	25.3156i	0.141359	−	0.983176i
$664$		0			0
$665$	−2.04311	−	2.35788i	−0.0792285	−	0.0914346i
$666$		0			0
$667$	−2.20980	+	1.60828i	−0.0855637	+	0.0622729i
$668$		0			0
$669$	−9.79956	−	11.3093i	−0.378873	−	0.437243i
$670$		0			0
$671$	−10.5780	+	73.5715i	−0.408358	+	2.84019i
$672$		0			0
$673$	6.23439	+	43.3611i	0.240318	+	1.67145i	0.650547	+	0.759466i	$0.274540\pi$
$673$	6.23439	+	43.3611i	0.240318	+	1.67145i	−0.410229	+	0.911982i	$0.634551\pi$
$674$		0			0
$675$	1.87032	−	1.20198i	0.0719887	−	0.0462643i
$676$		0			0
$677$	−24.9943	+	7.33900i	−0.960610	+	0.282061i	−0.724198	−	0.689592i	$-0.757790\pi$
$677$	−24.9943	+	7.33900i	−0.960610	+	0.282061i	−0.236412	+	0.971653i	$0.575972\pi$
$678$		0			0
$679$	−1.46443	+	1.69004i	−0.0561996	+	0.0648578i
$680$		0			0
$681$	8.01864	+	17.5584i	0.307275	+	0.672838i
$682$		0			0
$683$	−11.5806	−	3.40037i	−0.443119	−	0.130111i	0.0525591	−	0.998618i	$-0.483262\pi$
$683$	−11.5806	−	3.40037i	−0.443119	−	0.130111i	−0.495678	+	0.868506i	$0.665080\pi$
$684$		0			0
$685$	16.3971	−	35.9046i	0.626500	−	1.37184i
$686$		0			0
$687$	−22.4145	−	14.4049i	−0.855168	−	0.549583i
$688$		0			0
$689$	18.7322			0.713640
$690$		0			0
$691$	−41.2368			−1.56872			−0.784360	−	0.620305i	$-0.787009\pi$
$691$	−41.2368			−1.56872			−0.784360	+	0.620305i	$0.787009\pi$
$692$		0			0
$693$	0.754293	+	0.484755i	0.0286532	+	0.0184143i
$694$		0			0
$695$	24.9564	−	54.6468i	0.946649	−	2.07287i
$696$		0			0
$697$	31.0911	+	9.12918i	1.17766	+	0.345792i
$698$		0			0
$699$	−6.00196	−	13.1425i	−0.227015	−	0.497093i
$700$		0			0
$701$	10.4429	−	12.0517i	0.394422	−	0.455187i	−0.523454	−	0.852054i	$-0.675357\pi$
$701$	10.4429	−	12.0517i	0.394422	−	0.455187i	0.917876	+	0.396867i	$0.129902\pi$
$702$		0			0
$703$	58.5781	−	17.2001i	2.20932	−	0.648713i
$704$		0			0
$705$	−5.12628	+	3.29446i	−0.193067	+	0.124077i
$706$		0			0
$707$	−0.174164	−	1.21134i	−0.00655011	−	0.0455570i
$708$		0			0
$709$	0.774067	−	5.38375i	0.0290707	−	0.202191i	−0.970110	−	0.242666i	$-0.921978\pi$
$709$	0.774067	−	5.38375i	0.0290707	−	0.202191i	0.999181	+	0.0404751i	$0.0128871\pi$
$710$		0			0
$711$	−1.71959	−	1.98451i	−0.0644896	−	0.0744249i
$712$		0			0
$713$	−29.0759	−	16.3885i	−1.08890	−	0.613754i
$714$		0			0
$715$	35.9998	+	41.5460i	1.34632	+	1.55373i
$716$		0			0
$717$	3.43143	−	23.8661i	0.128149	−	0.891297i
$718$		0			0
$719$	0.797299	+	5.54533i	0.0297342	+	0.206806i	0.999273	−	0.0381331i	$-0.0121411\pi$
$719$	0.797299	+	5.54533i	0.0297342	+	0.206806i	−0.969538	+	0.244939i	$0.921232\pi$
$720$		0			0
$721$	0.606738	−	0.389927i	0.0225961	−	0.0145216i
$722$		0			0
$723$	10.7583	−	3.15892i	0.400105	−	0.117481i
$724$		0			0
$725$	0.829713	−	0.957540i	0.0308148	−	0.0355622i
$726$		0			0
$727$	16.3042	+	35.7013i	0.604691	+	1.32409i	0.926147	+	0.377164i	$0.123101\pi$
$727$	16.3042	+	35.7013i	0.604691	+	1.32409i	−0.321456	+	0.946925i	$0.604172\pi$
$728$		0			0
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$		0			0
$731$	18.6872	−	40.9192i	0.691170	−	1.51345i
$732$		0			0
$733$	−25.4156	−	16.3336i	−0.938748	−	0.603297i	−0.0207088	−	0.999786i	$-0.506592\pi$
$733$	−25.4156	−	16.3336i	−0.938748	−	0.603297i	−0.918040	+	0.396489i	$0.870229\pi$
$734$		0			0
$735$	−18.7371			−0.691127
$736$		0			0
$737$	8.57814			0.315980
$738$		0			0
$739$	−11.4468	−	7.35638i	−0.421076	−	0.270609i	0.312898	−	0.949787i	$-0.398700\pi$
$739$	−11.4468	−	7.35638i	−0.421076	−	0.270609i	−0.733974	+	0.679178i	$0.762337\pi$
$740$		0			0
$741$	−11.0010	+	24.0887i	−0.404130	+	0.884922i
$742$		0			0
$743$	3.15632	+	0.926778i	0.115794	+	0.0340002i	0.339116	−	0.940744i	$-0.389872\pi$
$743$	3.15632	+	0.926778i	0.115794	+	0.0340002i	−0.223322	+	0.974745i	$0.571690\pi$
$744$		0			0
$745$	−7.66251	−	16.7786i	−0.280733	−	0.614719i
$746$		0			0
$747$	5.87380	−	6.77873i	0.214911	−	0.248021i
$748$		0			0
$749$	1.56931	−	0.460790i	0.0573413	−	0.0168369i
$750$		0			0
$751$	−17.2369	+	11.0775i	−0.628984	+	0.404223i	−0.815933	−	0.578146i	$-0.803776\pi$
$751$	−17.2369	+	11.0775i	−0.628984	+	0.404223i	0.186949	+	0.982370i	$0.440140\pi$
$752$		0			0
$753$	4.08067	+	28.3817i	0.148708	+	1.03429i
$754$		0			0
$755$	0.580761	−	4.03928i	0.0211360	−	0.147004i
$756$		0			0
$757$	31.2769	+	36.0955i	1.13678	+	1.31191i	0.943727	+	0.330724i	$0.107293\pi$
$757$	31.2769	+	36.0955i	1.13678	+	1.31191i	0.193052	+	0.981189i	$0.438162\pi$
$758$		0			0
$759$	17.8099	+	18.2959i	0.646459	+	0.664100i
$760$		0			0
$761$	−9.27655	−	10.7057i	−0.336275	−	0.388081i	0.562277	−	0.826949i	$-0.309925\pi$
$761$	−9.27655	−	10.7057i	−0.336275	−	0.388081i	−0.898552	+	0.438867i	$0.855380\pi$
$762$		0			0
$763$	−0.212115	+	1.47529i	−0.00767908	+	0.0534092i
$764$		0			0
$765$	2.54625	+	17.7096i	0.0920599	+	0.640291i
$766$		0			0
$767$	7.37219	−	4.73782i	0.266194	−	0.171073i
$768$		0			0
$769$	43.1487	−	12.6696i	1.55598	−	0.456878i	0.613101	−	0.790004i	$-0.289922\pi$
$769$	43.1487	−	12.6696i	1.55598	−	0.456878i	0.942882	+	0.333126i	$0.108104\pi$
$770$		0			0
$771$	−12.1927	+	14.0712i	−0.439110	+	0.506761i
$772$		0			0
$773$	12.9716	+	28.4038i	0.466555	+	1.02161i	0.985944	+	0.167075i	$0.0534322\pi$
$773$	12.9716	+	28.4038i	0.466555	+	1.02161i	−0.519389	+	0.854538i	$0.673841\pi$
$774$		0			0
$775$	14.8460	+	4.35916i	0.533282	+	0.156586i
$776$		0			0
$777$	−0.619654	+	1.35685i	−0.0222300	+	0.0486768i
$778$		0			0
$779$	−28.2253	−	18.1393i	−1.01128	−	0.649908i
$780$		0			0
$781$	50.5602			1.80919
$782$		0			0
$783$	−0.569888			−0.0203661
$784$		0			0
$785$	−14.9007	−	9.57611i	−0.531829	−	0.341786i
$786$		0			0
$787$	−2.90152	+	6.35343i	−0.103428	+	0.226475i	−0.954270	−	0.298946i	$-0.903365\pi$
$787$	−2.90152	+	6.35343i	−0.103428	+	0.226475i	0.850842	+	0.525421i	$0.176092\pi$
$788$		0			0
$789$	13.7309	+	4.03175i	0.488832	+	0.143534i
$790$		0			0
$791$	−0.597847	−	1.30910i	−0.0212570	−	0.0465463i
$792$		0			0
$793$	35.1245	−	40.5358i	1.24731	−	1.43947i
$794$		0			0
$795$	−12.5733	+	3.69186i	−0.445930	+	0.130937i
$796$		0			0
$797$	2.76552	−	1.77729i	0.0979599	−	0.0629550i	−0.490744	−	0.871304i	$-0.663275\pi$
$797$	2.76552	−	1.77729i	0.0979599	−	0.0629550i	0.588704	+	0.808349i	$0.299639\pi$
$798$		0			0
$799$	−2.14805	−	14.9400i	−0.0759924	−	0.528539i
$800$		0			0
$801$	−0.894653	+	6.22245i	−0.0316110	+	0.219859i
$802$		0			0
$803$	13.3575	+	15.4154i	0.471375	+	0.543996i
$804$		0			0
$805$	2.11472	+	0.489930i	0.0745340	+	0.0172678i
$806$		0			0
$807$	4.59453	+	5.30237i	0.161735	+	0.186652i
$808$		0			0
$809$	5.17892	−	36.0202i	0.182081	−	1.26640i	−0.669751	−	0.742586i	$-0.733599\pi$
$809$	5.17892	−	36.0202i	0.182081	−	1.26640i	0.851832	−	0.523816i	$-0.175492\pi$
$810$		0			0
$811$	7.25717	+	50.4747i	0.254834	+	1.77241i	0.568313	+	0.822812i	$0.307596\pi$
$811$	7.25717	+	50.4747i	0.254834	+	1.77241i	−0.313480	+	0.949595i	$0.601495\pi$
$812$		0			0
$813$	8.99425	−	5.78025i	0.315442	−	0.202722i
$814$		0			0
$815$	−6.31961	+	1.85561i	−0.221366	+	0.0649991i
$816$		0			0
$817$	−30.5020	+	35.2011i	−1.06713	+	1.23153i
$818$		0			0
$819$	−0.268784	−	0.588556i	−0.00939209	−	0.0205658i
$820$		0			0
$821$	−15.8760	−	4.66162i	−0.554077	−	0.162692i	−0.00730524	−	0.999973i	$-0.502325\pi$
$821$	−15.8760	−	4.66162i	−0.554077	−	0.162692i	−0.546772	+	0.837282i	$0.684144\pi$
$822$		0			0
$823$	3.41808	−	7.48455i	0.119147	−	0.260895i	−0.840657	−	0.541569i	$-0.817831\pi$
$823$	3.41808	−	7.48455i	0.119147	−	0.260895i	0.959803	+	0.280674i	$0.0905579\pi$
$824$		0			0
$825$	−9.95759	−	6.39935i	−0.346679	−	0.222797i
$826$		0			0
$827$	22.7771			0.792036			0.396018	−	0.918243i	$-0.370392\pi$
$827$	22.7771			0.792036			0.396018	+	0.918243i	$0.370392\pi$
$828$		0			0
$829$	−5.13824			−0.178459			−0.0892293	−	0.996011i	$-0.528440\pi$
$829$	−5.13824			−0.178459			−0.0892293	+	0.996011i	$0.528440\pi$
$830$		0			0
$831$	18.6371	+	11.9774i	0.646515	+	0.415490i
$832$		0			0
$833$	19.2798	−	42.2168i	0.668004	−	1.46272i
$834$		0			0
$835$	−26.5758	−	7.80335i	−0.919693	−	0.270046i
$836$		0			0
$837$	−2.89107	−	6.33057i	−0.0999301	−	0.218816i
$838$		0			0
$839$	6.72753	−	7.76399i	0.232260	−	0.268043i	−0.627641	−	0.778503i	$-0.715979\pi$
$839$	6.72753	−	7.76399i	0.232260	−	0.268043i	0.859901	+	0.510460i	$0.170525\pi$
$840$		0			0
$841$	27.5137	−	8.07875i	0.948748	−	0.278577i
$842$		0			0
$843$	5.94155	−	3.81840i	0.204638	−	0.131513i
$844$		0			0
$845$	−0.673269	−	4.68269i	−0.0231611	−	0.161089i
$846$		0			0
$847$	0.415718	−	2.89138i	0.0142842	−	0.0993491i
$848$		0			0
$849$	−17.6377	−	20.3550i	−0.605324	−	0.698581i
$850$		0			0
$851$	−25.9110	+	33.6590i	−0.888219	+	1.15382i
$852$		0			0
$853$	20.4817	+	23.6372i	0.701281	+	0.809321i	0.988925	−	0.148416i	$-0.0474176\pi$
$853$	20.4817	+	23.6372i	0.701281	+	0.809321i	−0.287644	+	0.957737i	$0.592872\pi$
$854$		0			0
$855$	2.63644	−	18.3369i	0.0901644	−	0.627107i
$856$		0			0
$857$	−2.66246	−	18.5178i	−0.0909478	−	0.632556i	−0.983405	−	0.181424i	$-0.941929\pi$
$857$	−2.66246	−	18.5178i	−0.0909478	−	0.632556i	0.892457	−	0.451132i	$-0.148980\pi$
$858$		0			0
$859$	34.8252	−	22.3808i	1.18822	−	0.763624i	0.211342	−	0.977412i	$-0.432217\pi$
$859$	34.8252	−	22.3808i	1.18822	−	0.763624i	0.976880	+	0.213788i	$0.0685803\pi$
$860$		0			0
$861$	0.786552	−	0.230953i	0.0268056	−	0.00787084i
$862$		0			0
$863$	5.13066	−	5.92110i	0.174650	−	0.201557i	−0.661675	−	0.749791i	$-0.730154\pi$
$863$	5.13066	−	5.92110i	0.174650	−	0.201557i	0.836325	+	0.548234i	$0.184700\pi$
$864$		0			0
$865$	−3.36564	−	7.36972i	−0.114435	−	0.250578i
$866$		0			0
$867$	−26.2103	−	7.69605i	−0.890149	−	0.261371i
$868$		0			0
$869$	−5.80758	+	12.7168i	−0.197009	+	0.431389i
$870$		0			0
$871$	−5.20750	−	3.34665i	−0.176449	−	0.113397i
$872$		0			0
$873$	−13.2783			−0.449404
$874$		0			0
$875$	1.25683			0.0424887
$876$		0			0
$877$	31.9990	+	20.5645i	1.08053	+	0.694413i	0.954679	−	0.297636i	$-0.0961983\pi$
$877$	31.9990	+	20.5645i	1.08053	+	0.694413i	0.125849	+	0.992049i	$0.459835\pi$
$878$		0			0
$879$	11.8521	−	25.9525i	0.399762	−	0.875357i
$880$		0			0
$881$	−12.1649	−	3.57192i	−0.409844	−	0.120341i	0.0703100	−	0.997525i	$-0.477601\pi$
$881$	−12.1649	−	3.57192i	−0.409844	−	0.120341i	−0.480154	+	0.877184i	$0.659419\pi$
$882$		0			0
$883$	1.46666	+	3.21153i	0.0493569	+	0.108077i	0.932704	−	0.360643i	$-0.117443\pi$
$883$	1.46666	+	3.21153i	0.0493569	+	0.108077i	−0.883347	+	0.468720i	$0.844715\pi$
$884$		0			0
$885$	−4.01456	+	4.63305i	−0.134948	+	0.155738i
$886$		0			0
$887$	−38.6103	+	11.3370i	−1.29641	+	0.380660i	−0.855925	−	0.517101i	$-0.827011\pi$
$887$	−38.6103	+	11.3370i	−1.29641	+	0.380660i	−0.440484	+	0.897761i	$0.645193\pi$
$888$		0			0
$889$	2.14867	−	1.38087i	0.0720640	−	0.0463127i
$890$		0			0
$891$	0.757684	+	5.26981i	0.0253834	+	0.176545i
$892$		0			0
$893$	−2.22413	+	15.4692i	−0.0744278	+	0.517657i
$894$		0			0
$895$	23.7816	+	27.4454i	0.794930	+	0.917398i
$896$		0			0
$897$	−3.67385	−	18.0551i	−0.122666	−	0.602844i
$898$		0			0
$899$	−2.59726	−	2.99740i	−0.0866235	−	0.0999689i
$900$		0			0
$901$	4.61931	−	32.1280i	0.153891	−	1.07034i
$902$		0			0
$903$	−0.161958	−	1.12644i	−0.00538963	−	0.0374857i
$904$		0			0
$905$	31.4265	−	20.1966i	1.04465	−	0.671357i
$906$		0			0
$907$	24.7759	−	7.27487i	0.822672	−	0.241558i	0.156806	−	0.987629i	$-0.449880\pi$
$907$	24.7759	−	7.27487i	0.822672	−	0.241558i	0.665866	+	0.746071i	$0.268062\pi$
$908$		0			0
$909$	4.75863	−	5.49175i	0.157834	−	0.182150i
$910$		0			0
$911$	−6.16725	−	13.5044i	−0.204330	−	0.447421i	0.779529	−	0.626366i	$-0.215459\pi$
$911$	−6.16725	−	13.5044i	−0.204330	−	0.447421i	−0.983859	+	0.178946i	$0.942731\pi$
$912$		0			0
$913$	−45.8195	−	13.4538i	−1.51640	−	0.445256i
$914$		0			0
$915$	−15.5870	+	34.1308i	−0.515291	+	1.12833i
$916$		0			0
$917$	0.249300	+	0.160215i	0.00823261	+	0.00529078i
$918$		0			0
$919$	−25.3485			−0.836171			−0.418085	−	0.908408i	$-0.637299\pi$
$919$	−25.3485			−0.836171			−0.418085	+	0.908408i	$0.637299\pi$
$920$		0			0
$921$	−11.6303			−0.383230
$922$		0			0
$923$	−30.6934	−	19.7254i	−1.01028	−	0.649270i
$924$		0			0
$925$	8.18019	−	17.9121i	0.268963	−	0.588947i
$926$		0			0
$927$	4.10904	+	1.20652i	0.134959	+	0.0396274i
$928$		0			0
$929$	18.7778	+	41.1175i	0.616078	+	1.34902i	0.918338	+	0.395797i	$0.129532\pi$
$929$	18.7778	+	41.1175i	0.616078	+	1.34902i	−0.302260	+	0.953226i	$0.597741\pi$
$930$		0			0
$931$	−31.4692	+	36.3174i	−1.03136	+	1.19025i
$932$		0			0
$933$	−25.1890	+	7.39616i	−0.824651	+	0.242139i
$934$		0			0
$935$	80.1338	−	51.4989i	2.62066	−	1.68419i
$936$		0			0
$937$	−7.51085	−	52.2391i	−0.245369	−	1.70658i	−0.624326	−	0.781164i	$-0.714626\pi$
$937$	−7.51085	−	52.2391i	−0.245369	−	1.70658i	0.378957	−	0.925414i	$-0.376283\pi$
$938$		0			0
$939$	3.64560	−	25.3557i	0.118970	−	0.827453i
$940$		0			0
$941$	23.1175	+	26.6790i	0.753608	+	0.869711i	0.994913	−	0.100739i	$-0.0321207\pi$
$941$	23.1175	+	26.6790i	0.753608	+	0.869711i	−0.241304	+	0.970449i	$0.577575\pi$
$942$		0			0
$943$	23.3048	−	1.35178i	0.758908	−	0.0440199i
$944$		0			0
$945$	0.296409	+	0.342074i	0.00964217	+	0.0111277i
$946$		0			0
$947$	−8.49915	+	59.1129i	−0.276185	+	1.92091i	0.101221	+	0.994864i	$0.467725\pi$
$947$	−8.49915	+	59.1129i	−0.276185	+	1.92091i	−0.377407	+	0.926048i	$0.623184\pi$
$948$		0			0
$949$	−2.09476	−	14.5694i	−0.0679989	−	0.472942i
$950$		0			0
$951$	16.9902	−	10.9189i	0.550945	−	0.354071i
$952$		0			0
$953$	−51.9634	+	15.2578i	−1.68326	+	0.494249i	−0.976917	−	0.213621i	$-0.931474\pi$
$953$	−51.9634	+	15.2578i	−1.68326	+	0.494249i	−0.706342	+	0.707871i	$0.749656\pi$
$954$		0			0
$955$	−22.5247	+	25.9949i	−0.728883	+	0.841176i
$956$		0			0
$957$	1.26040	+	2.75990i	0.0407431	+	0.0892149i
$958$		0			0
$959$	2.37320	+	0.696835i	0.0766347	+	0.0225020i
$960$		0			0
$961$	7.24250	−	15.8589i	0.233629	−	0.511576i
$962$		0			0
$963$	8.16992	+	5.25049i	0.263272	+	0.169195i
$964$		0			0
$965$	43.3729			1.39622
$966$		0			0
$967$	−13.5723			−0.436457			−0.218229	−	0.975898i	$-0.570028\pi$
$967$	−13.5723			−0.436457			−0.218229	+	0.975898i	$0.570028\pi$
$968$		0			0
$969$	38.6023	+	24.8082i	1.24008	+	0.796954i
$970$		0			0
$971$	−1.52893	+	3.34788i	−0.0490655	+	0.107439i	−0.932577	−	0.360971i	$-0.882445\pi$
$971$	−1.52893	+	3.34788i	−0.0490655	+	0.107439i	0.883512	+	0.468409i	$0.155173\pi$
$972$		0			0
$973$	3.61202	+	1.06058i	0.115796	+	0.0340008i
$974$		0			0
$975$	3.54828	+	7.76966i	0.113636	+	0.248828i
$976$		0			0
$977$	−14.4404	+	16.6651i	−0.461989	+	0.533164i	−0.938166	−	0.346186i	$-0.887477\pi$
$977$	−14.4404	+	16.6651i	−0.461989	+	0.533164i	0.476177	+	0.879349i	$0.342022\pi$
$978$		0			0
$979$	32.1132	−	9.42930i	1.02634	−	0.301362i
$980$		0			0
$981$	−7.44514	+	4.78470i	−0.237705	+	0.152764i
$982$		0			0
$983$	3.87249	+	26.9338i	0.123513	+	0.859053i	0.953526	+	0.301310i	$0.0974237\pi$
$983$	3.87249	+	26.9338i	0.123513	+	0.859053i	−0.830013	+	0.557744i	$0.811667\pi$
$984$		0			0
$985$	−5.03916	+	35.0482i	−0.160561	+	1.11673i
$986$		0			0
$987$	−0.250054	−	0.288577i	−0.00795930	−	0.00918552i
$988$		0			0
$989$	2.74678	−	32.2905i	0.0873426	−	1.02678i
$990$		0			0
$991$	−9.50859	−	10.9735i	−0.302050	−	0.348585i	0.584352	−	0.811500i	$-0.301349\pi$
$991$	−9.50859	−	10.9735i	−0.302050	−	0.348585i	−0.886402	+	0.462916i	$0.846803\pi$
$992$		0			0
$993$	3.06575	−	21.3228i	0.0972886	−	0.676657i
$994$		0			0
$995$	3.54034	+	24.6236i	0.112236	+	0.780622i
$996$		0			0
$997$	−4.27394	+	2.74670i	−0.135357	+	0.0869887i	−0.606567	−	0.795032i	$-0.707454\pi$
$997$	−4.27394	+	2.74670i	−0.135357	+	0.0869887i	0.471210	+	0.882021i	$0.343817\pi$
$998$		0			0
$999$	−8.49833	+	2.49533i	−0.268875	+	0.0789489i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.i.a.13.2	✓	20
3.2	odd	2		828.2.q.c.289.1		20
23.4	even	11		6348.2.a.s.1.9		10
23.16	even	11	inner	276.2.i.a.85.2	yes	20
23.19	odd	22		6348.2.a.t.1.2		10
69.62	odd	22		828.2.q.c.361.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.i.a.13.2	✓	20	1.1	even	1	trivial
276.2.i.a.85.2	yes	20	23.16	even	11	inner
828.2.q.c.289.1		20	3.2	odd	2
828.2.q.c.361.1		20	69.62	odd	22
6348.2.a.s.1.9		10	23.4	even	11
6348.2.a.t.1.2		10	23.19	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)

\(f(q)\)	\(=\)	\(q+(0.841254 + 0.540641i) q^{3} +(1.11647 - 2.44474i) q^{5} +(0.161591 + 0.0474474i) q^{7} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(0.841254 + 0.540641i) q^{3} +(1.11647 - 2.44474i) q^{5} +(0.161591 + 0.0474474i) q^{7} +(0.415415 + 0.909632i) q^{9} +(3.48648 - 4.02361i) q^{11} +(-3.68628 + 1.08239i) q^{13} +(2.26096 - 1.45303i) q^{15} +(0.947403 + 6.58933i) q^{17} +(0.980961 - 6.82274i) q^{19} +(0.110287 + 0.127278i) q^{21} +(2.24153 + 4.23976i) q^{23} +(-1.45592 - 1.68022i) q^{25} +(-0.142315 + 0.989821i) q^{27} +(0.0811036 + 0.564088i) q^{29} +(-5.85469 + 3.76258i) q^{31} +(5.10834 - 1.49994i) q^{33} +(0.296409 - 0.342074i) q^{35} +(3.67937 + 8.05671i) q^{37} +(-3.68628 - 1.08239i) q^{39} +(2.02205 - 4.42768i) q^{41} +(-5.68465 - 3.65331i) q^{43} +2.68761 q^{45} -2.26730 q^{47} +(-5.86491 - 3.76915i) q^{49} +(-2.76546 + 6.05550i) q^{51} +(-4.67826 - 1.37366i) q^{53} +(-5.94411 - 13.0158i) q^{55} +(4.51389 - 5.20930i) q^{57} +(-2.18859 + 0.642628i) q^{59} +(-11.7447 + 7.54785i) q^{61} +(0.0239677 + 0.166699i) q^{63} +(-1.46948 + 10.2205i) q^{65} +(1.05513 + 1.21768i) q^{67} +(-0.406487 + 4.77857i) q^{69} +(6.21899 + 7.17709i) q^{71} +(-0.545240 + 3.79223i) q^{73} +(-0.316402 - 2.20063i) q^{75} +(0.754293 - 0.484755i) q^{77} +(-2.51952 + 0.739797i) q^{79} +(-0.654861 + 0.755750i) q^{81} +(-3.72608 - 8.15898i) q^{83} +(17.1669 + 5.04067i) q^{85} +(-0.236740 + 0.518389i) q^{87} +(5.28849 + 3.39870i) q^{89} -0.647026 q^{91} -6.95948 q^{93} +(-15.5846 - 10.0156i) q^{95} +(-5.51602 + 12.0784i) q^{97} +(5.10834 + 1.49994i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{3} - 4 q^{5} - 2 q^{9}+O(q^{10}) \) 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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