LMFDB - Embedded newform 207.2.i.c.100.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [207,2,Mod(55,207)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(207, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 10])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("207.55"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$N$	$=$	$207 = 3^{2} \cdot 23$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	207.i (of order $11$ , degree $10$ , minimal)

Newform invariants

comment:select newform

sage:traces = [10,7] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.65290332184$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\Q(\zeta_{22})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{10} - x^{9} + x^{8} - x^{7} + x^{6} - x^{5} + x^{4} - x^{3} + x^{2} - x + 1$ x^10 - x^9 + x^8 - x^7 + x^6 - x^5 + x^4 - x^3 + x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 23)
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			100.1
Root			$-0.415415 + 0.909632i$ of defining polynomial
Character	$\chi$	$=$	207.100
Dual form			207.2.i.c.118.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.313607 - 2.18119i) q^{2} +(-2.74024 - 0.804606i) q^{4} +(-0.809721 - 0.934468i) q^{5} +(-1.99611 - 1.28282i) q^{7} +(-0.783524 + 1.71568i) q^{8} +(-2.29218 + 1.47310i) q^{10} +(-0.272084 - 1.89238i) q^{11} +(0.165284 - 0.106222i) q^{13} +(-3.42408 + 3.95159i) q^{14} +(-1.30862 - 0.840996i) q^{16} +(-1.49672 + 0.439476i) q^{17} +(7.66103 + 2.24948i) q^{19} +(1.46695 + 3.21217i) q^{20} -4.21297 q^{22} +(4.66752 + 1.10192i) q^{23} +(0.493992 - 3.43579i) q^{25} +(-0.179855 - 0.393828i) q^{26} +(4.43766 + 5.12133i) q^{28} +(4.77570 - 1.40227i) q^{29} +(0.740552 - 1.62158i) q^{31} +(-4.71506 + 5.44146i) q^{32} +(0.489198 + 3.40244i) q^{34} +(0.417537 + 2.90404i) q^{35} +(-2.54297 + 2.93475i) q^{37} +(7.30909 - 16.0047i) q^{38} +(2.23768 - 0.657043i) q^{40} +(0.279295 + 0.322324i) q^{41} +(1.84991 + 4.05075i) q^{43} +(-0.777050 + 5.40450i) q^{44} +(3.86725 - 9.83517i) q^{46} +2.58842 q^{47} +(-0.569072 - 1.24609i) q^{49} +(-7.33918 - 2.15498i) q^{50} +(-0.538385 + 0.158084i) q^{52} +(-8.26060 - 5.30876i) q^{53} +(-1.54806 + 1.78656i) q^{55} +(3.76492 - 2.41956i) q^{56} +(-1.56092 - 10.8565i) q^{58} +(6.07293 - 3.90283i) q^{59} +(3.08639 - 6.75826i) q^{61} +(-3.30473 - 2.12382i) q^{62} +(8.35283 + 9.63968i) q^{64} +(-0.233095 - 0.0684429i) q^{65} +(-1.03413 + 7.19254i) q^{67} +4.45497 q^{68} +6.46519 q^{70} +(-0.103930 + 0.722850i) q^{71} +(6.18330 + 1.81558i) q^{73} +(5.60373 + 6.46705i) q^{74} +(-19.1831 - 12.3282i) q^{76} +(-1.88449 + 4.12645i) q^{77} +(-4.77671 + 3.06980i) q^{79} +(0.273730 + 1.90383i) q^{80} +(0.790638 - 0.508112i) q^{82} +(-8.44098 + 9.74141i) q^{83} +(1.62260 + 1.04278i) q^{85} +(9.41558 - 2.76466i) q^{86} +(3.45991 + 1.01592i) q^{88} +(5.77436 + 12.6441i) q^{89} -0.466190 q^{91} +(-11.9035 - 6.77503i) q^{92} +(0.811746 - 5.64582i) q^{94} +(-4.10123 - 8.98044i) q^{95} +(-2.83147 - 3.26769i) q^{97} +(-2.89643 + 0.850468i) q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$10 q + 7 q^{2} - 3 q^{4} + 3 q^{5} - 5 q^{7} - 4 q^{8} + q^{10} - 7 q^{11} - 3 q^{13} - 9 q^{14} + q^{16} + 10 q^{17} + 2 q^{19} + 9 q^{20} - 6 q^{22} + 12 q^{23} - 4 q^{25} - 12 q^{26} + 7 q^{28} - 14 q^{29}+ \cdots - 17 q^{98}+O(q^{100})$ 10 * q + 7 * q^2 - 3 * q^4 + 3 * q^5 - 5 * q^7 - 4 * q^8 + q^10 - 7 * q^11 - 3 * q^13 - 9 * q^14 + q^16 + 10 * q^17 + 2 * q^19 + 9 * q^20 - 6 * q^22 + 12 * q^23 - 4 * q^25 - 12 * q^26 + 7 * q^28 - 14 * q^29 + 10 * q^31 - 21 * q^32 + 29 * q^34 - 7 * q^35 - 19 * q^37 + 8 * q^38 + q^40 - 7 * q^41 - 11 * q^43 + 34 * q^44 - 29 * q^46 + 18 * q^47 - 18 * q^49 - 16 * q^50 - 20 * q^52 - 29 * q^53 - q^55 + 2 * q^56 - 23 * q^58 + 21 * q^59 + 3 * q^61 - 4 * q^62 + 24 * q^64 - 2 * q^65 + 45 * q^67 + 30 * q^68 + 38 * q^70 + 14 * q^71 + 19 * q^73 - 10 * q^74 - 16 * q^76 - 2 * q^77 - 15 * q^79 + 52 * q^80 + 16 * q^82 - 18 * q^83 - 19 * q^85 + 11 * q^86 + 27 * q^88 - 25 * q^89 - 4 * q^91 - 52 * q^92 + 17 * q^94 - 6 * q^95 - 34 * q^97 - 17 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/207\mathbb{Z}\right)^\times$ .

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{3}{11}\right)$	$1$

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

)

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

$2$	0.313607	−	2.18119i	0.221754	−	1.54233i	−0.509647	−	0.860384i	$-0.670224\pi$
$2$	0.313607	−	2.18119i	0.221754	−	1.54233i	0.731401	−	0.681948i	$-0.238867\pi$
$3$		0			0
$3$		0			0
$4$	−2.74024	−	0.804606i	−1.37012	−	0.402303i
$5$	−0.809721	−	0.934468i	−0.362118	−	0.417907i	0.545230	−	0.838287i	$-0.316442\pi$
$5$	−0.809721	−	0.934468i	−0.362118	−	0.417907i	−0.907348	+	0.420380i	$0.861897\pi$
$6$		0			0
$7$	−1.99611	−	1.28282i	−0.754460	−	0.484862i	0.106009	−	0.994365i	$-0.466193\pi$
$7$	−1.99611	−	1.28282i	−0.754460	−	0.484862i	−0.860469	+	0.509503i	$0.829829\pi$
$8$	−0.783524	+	1.71568i	−0.277017	+	0.606584i
$9$		0			0
$10$	−2.29218	+	1.47310i	−0.724852	+	0.465834i
$11$	−0.272084	−	1.89238i	−0.0820363	−	0.570575i	−0.988835	−	0.149012i	$-0.952391\pi$
$11$	−0.272084	−	1.89238i	−0.0820363	−	0.570575i	0.906799	−	0.421563i	$-0.138518\pi$
$12$		0			0
$13$	0.165284	−	0.106222i	0.0458416	−	0.0294606i	−0.517519	−	0.855672i	$-0.673144\pi$
$13$	0.165284	−	0.106222i	0.0458416	−	0.0294606i	0.563361	+	0.826211i	$0.309508\pi$
$14$	−3.42408	+	3.95159i	−0.915123	+	1.05611i
$15$		0			0
$16$	−1.30862	−	0.840996i	−0.327154	−	0.210249i
$17$	−1.49672	+	0.439476i	−0.363008	+	0.106589i	−0.458150	−	0.888875i	$-0.651488\pi$
$17$	−1.49672	+	0.439476i	−0.363008	+	0.106589i	0.0951421	+	0.995464i	$0.469669\pi$
$18$		0			0
$19$	7.66103	+	2.24948i	1.75756	+	0.516066i	0.991883	−	0.127157i	$-0.0405853\pi$
$19$	7.66103	+	2.24948i	1.75756	+	0.516066i	0.765678	+	0.643224i	$0.222403\pi$
$20$	1.46695	+	3.21217i	0.328020	+	0.718263i
$21$		0			0
$22$	−4.21297			−0.898208
$23$	4.66752	+	1.10192i	0.973246	+	0.229765i
$23$	4.66752	+	1.10192i	0.973246	+	0.229765i
$24$		0			0
$25$	0.493992	−	3.43579i	0.0987984	−	0.687158i
$26$	−0.179855	−	0.393828i	−0.0352725	−	0.0772359i
$27$		0			0
$28$	4.43766	+	5.12133i	0.838638	+	0.967840i
$29$	4.77570	−	1.40227i	0.886825	−	0.260395i	0.193569	−	0.981087i	$-0.437994\pi$
$29$	4.77570	−	1.40227i	0.886825	−	0.260395i	0.693256	+	0.720691i	$0.256175\pi$
$30$		0			0
$31$	0.740552	−	1.62158i	0.133007	−	0.291245i	−0.831397	−	0.555680i	$-0.812458\pi$
$31$	0.740552	−	1.62158i	0.133007	−	0.291245i	0.964404	+	0.264435i	$0.0851854\pi$
$32$	−4.71506	+	5.44146i	−0.833512	+	0.961924i
$33$		0			0
$34$	0.489198	+	3.40244i	0.0838967	+	0.583514i
$35$	0.417537	+	2.90404i	0.0705767	+	0.490872i
$36$		0			0
$37$	−2.54297	+	2.93475i	−0.418062	+	0.482469i	−0.925246	−	0.379369i	$-0.876141\pi$
$37$	−2.54297	+	2.93475i	−0.418062	+	0.482469i	0.507184	+	0.861838i	$0.330687\pi$
$38$	7.30909	−	16.0047i	1.18569	−	2.59630i
$39$		0			0
$40$	2.23768	−	0.657043i	0.353809	−	0.103888i
$41$	0.279295	+	0.322324i	0.0436186	+	0.0503386i	0.777140	−	0.629328i	$-0.216670\pi$
$41$	0.279295	+	0.322324i	0.0436186	+	0.0503386i	−0.733521	+	0.679667i	$0.762124\pi$
$42$		0			0
$43$	1.84991	+	4.05075i	0.282109	+	0.617733i	0.996643	−	0.0818677i	$-0.0260885\pi$
$43$	1.84991	+	4.05075i	0.282109	+	0.617733i	−0.714534	+	0.699601i	$0.753361\pi$
$44$	−0.777050	+	5.40450i	−0.117145	+	0.814759i
$45$		0			0
$46$	3.86725	−	9.83517i	0.570195	−	1.45012i
$47$	2.58842			0.377559			0.188780	−	0.982019i	$-0.439547\pi$
$47$	2.58842			0.377559			0.188780	+	0.982019i	$0.439547\pi$
$48$		0			0
$49$	−0.569072	−	1.24609i	−0.0812960	−	0.178013i
$50$	−7.33918	−	2.15498i	−1.03792	−	0.304760i
$51$		0			0
$52$	−0.538385	+	0.158084i	−0.0746605	+	0.0219223i
$53$	−8.26060	−	5.30876i	−1.13468	−	0.729215i	−0.168149	−	0.985762i	$-0.553779\pi$
$53$	−8.26060	−	5.30876i	−1.13468	−	0.729215i	−0.966532	+	0.256547i	$0.917415\pi$
$54$		0			0
$55$	−1.54806	+	1.78656i	−0.208741	+	0.240899i
$56$	3.76492	−	2.41956i	0.503108	−	0.323328i
$57$		0			0
$58$	−1.56092	−	10.8565i	−0.204959	−	1.42552i
$59$	6.07293	−	3.90283i	0.790628	−	0.508106i	−0.0819173	−	0.996639i	$-0.526104\pi$
$59$	6.07293	−	3.90283i	0.790628	−	0.508106i	0.872545	+	0.488533i	$0.162468\pi$
$60$		0			0
$61$	3.08639	−	6.75826i	0.395172	−	0.865306i	−0.602565	−	0.798070i	$-0.705855\pi$
$61$	3.08639	−	6.75826i	0.395172	−	0.865306i	0.997737	−	0.0672363i	$-0.0214181\pi$
$62$	−3.30473	−	2.12382i	−0.419701	−	0.269726i
$63$		0			0
$64$	8.35283	+	9.63968i	1.04410	+	1.20496i
$65$	−0.233095	−	0.0684429i	−0.0289119	−	0.00848929i
$66$		0			0
$67$	−1.03413	+	7.19254i	−0.126339	+	0.878708i	0.823800	+	0.566881i	$0.191850\pi$
$67$	−1.03413	+	7.19254i	−0.126339	+	0.878708i	−0.950139	+	0.311827i	$0.899059\pi$
$68$	4.45497			0.540244
$69$		0			0
$70$	6.46519			0.772738
$71$	−0.103930	+	0.722850i	−0.0123342	+	0.0857866i	−0.995059	−	0.0992879i	$-0.968344\pi$
$71$	−0.103930	+	0.722850i	−0.0123342	+	0.0857866i	0.982725	+	0.185074i	$0.0592526\pi$
$72$		0			0
$73$	6.18330	+	1.81558i	0.723700	+	0.212498i	0.622780	−	0.782397i	$-0.286003\pi$
$73$	6.18330	+	1.81558i	0.723700	+	0.212498i	0.100920	+	0.994895i	$0.467821\pi$
$74$	5.60373	+	6.46705i	0.651421	+	0.751780i
$75$		0			0
$76$	−19.1831	−	12.3282i	−2.20045	−	1.41414i
$77$	−1.88449	+	4.12645i	−0.214757	+	0.470253i
$78$		0			0
$79$	−4.77671	+	3.06980i	−0.537422	+	0.345380i	−0.781030	−	0.624494i	$-0.785305\pi$
$79$	−4.77671	+	3.06980i	−0.537422	+	0.345380i	0.243608	+	0.969874i	$0.421669\pi$
$80$	0.273730	+	1.90383i	0.0306039	+	0.212855i
$81$		0			0
$82$	0.790638	−	0.508112i	0.0873113	−	0.0561116i
$83$	−8.44098	+	9.74141i	−0.926518	+	1.06926i	0.0709025	+	0.997483i	$0.477412\pi$
$83$	−8.44098	+	9.74141i	−0.926518	+	1.06926i	−0.997421	+	0.0717758i	$0.977133\pi$
$84$		0			0
$85$	1.62260	+	1.04278i	0.175996	+	0.113106i
$86$	9.41558	−	2.76466i	1.01531	−	0.298121i
$87$		0			0
$88$	3.45991	+	1.01592i	0.368827	+	0.108297i
$89$	5.77436	+	12.6441i	0.612081	+	1.34027i	0.921141	+	0.389228i	$0.127258\pi$
$89$	5.77436	+	12.6441i	0.612081	+	1.34027i	−0.309060	+	0.951043i	$0.600014\pi$
$90$		0			0
$91$	−0.466190			−0.0488700
$92$	−11.9035	−	6.77503i	−1.24103	−	0.706346i
$93$		0			0
$94$	0.811746	−	5.64582i	0.0837252	−	0.582322i
$95$	−4.10123	−	8.98044i	−0.420777	−	0.921374i
$96$		0			0
$97$	−2.83147	−	3.26769i	−0.287492	−	0.331783i	0.593572	−	0.804781i	$-0.297717\pi$
$97$	−2.83147	−	3.26769i	−0.287492	−	0.331783i	−0.881064	+	0.472998i	$0.843172\pi$
$98$	−2.89643	+	0.850468i	−0.292583	+	0.0859103i
$99$		0			0
$100$	−4.11811	+	9.01741i	−0.411811	+	0.901741i
$101$	−1.19203	+	1.37567i	−0.118611	+	0.136885i	−0.811950	−	0.583727i	$-0.801594\pi$
$101$	−1.19203	+	1.37567i	−0.118611	+	0.136885i	0.693338	+	0.720612i	$0.256139\pi$
$102$		0			0
$103$	2.17930	+	15.1574i	0.214733	+	1.49350i	0.757067	+	0.653337i	$0.226631\pi$
$103$	2.17930	+	15.1574i	0.214733	+	1.49350i	−0.542335	+	0.840163i	$0.682459\pi$
$104$	0.0527381	+	0.366802i	0.00517140	+	0.0359679i
$105$		0			0
$106$	−14.1700	+	16.3530i	−1.37631	+	1.58835i
$107$	−0.825981	+	1.80865i	−0.0798506	+	0.174848i	−0.945346	−	0.326068i	$-0.894276\pi$
$107$	−0.825981	+	1.80865i	−0.0798506	+	0.174848i	0.865496	+	0.500916i	$0.167004\pi$
$108$		0			0
$109$	−14.9631	+	4.39356i	−1.43320	+	0.420826i	−0.903950	−	0.427638i	$-0.859346\pi$
$109$	−14.9631	+	4.39356i	−1.43320	+	0.420826i	−0.529253	+	0.848464i	$0.677528\pi$
$110$	3.41133	+	3.93689i	0.325258	+	0.375367i
$111$		0			0
$112$	1.53330	+	3.35745i	0.144883	+	0.317249i
$113$	−0.211799	+	1.47310i	−0.0199244	+	0.138577i	−0.997356	−	0.0726771i	$-0.976846\pi$
$113$	−0.211799	+	1.47310i	−0.0199244	+	0.138577i	0.977431	+	0.211254i	$0.0677548\pi$
$114$		0			0
$115$	−2.74969	−	5.25390i	−0.256410	−	0.489929i
$116$	−14.2148			−1.31981
$117$		0			0
$118$	−6.60829	−	14.4701i	−0.608343	−	1.33208i
$119$	3.55139	+	1.04278i	0.325556	+	0.0955917i
$120$		0			0
$121$	7.04733	−	2.06928i	0.640667	−	0.188117i
$122$	−13.7731	−	8.85143i	−1.24696	−	0.801371i
$123$		0			0
$124$	−3.33402	+	3.84767i	−0.299404	+	0.345531i
$125$	−8.81159	+	5.66287i	−0.788133	+	0.506502i
$126$		0			0
$127$	−0.853087	−	5.93335i	−0.0756993	−	0.526500i	−0.992023	−	0.126061i	$-0.959767\pi$
$127$	−0.853087	−	5.93335i	−0.0756993	−	0.526500i	0.916323	−	0.400439i	$-0.131142\pi$
$128$	11.5312	−	7.41067i	1.01923	−	0.655017i
$129$		0			0
$130$	−0.222387	+	0.486959i	−0.0195046	+	0.0427092i
$131$	10.7418	+	6.90335i	0.938517	+	0.603148i	0.917974	−	0.396641i	$-0.129824\pi$
$131$	10.7418	+	6.90335i	0.938517	+	0.603148i	0.0205431	+	0.999789i	$0.493460\pi$
$132$		0			0
$133$	−12.4066	−	14.3180i	−1.07579	−	1.24153i
$134$	15.3640	+	4.51126i	1.32724	+	0.389714i
$135$		0			0
$136$	0.418715	−	2.91223i	0.0359045	−	0.249721i
$137$	−0.697560			−0.0595966			−0.0297983	−	0.999556i	$-0.509486\pi$
$137$	−0.697560			−0.0595966			−0.0297983	+	0.999556i	$0.509486\pi$
$138$		0			0
$139$	13.9559			1.18372			0.591862	−	0.806039i	$-0.298393\pi$
$139$	13.9559			1.18372			0.591862	+	0.806039i	$0.298393\pi$
$140$	1.19245	−	8.29370i	0.100781	−	0.700946i
$141$		0			0
$142$	1.54408	+	0.453382i	0.129576	+	0.0380470i
$143$	−0.245983	−	0.283880i	−0.0205702	−	0.0237392i
$144$		0			0
$145$	−5.17736	−	3.32729i	−0.429957	−	0.276316i
$146$	5.89924	−	12.9175i	0.488225	−	1.06906i
$147$		0			0
$148$	9.32966	−	5.99581i	0.766893	−	0.492852i
$149$	−2.36798	−	16.4697i	−0.193993	−	1.34925i	−0.821309	−	0.570483i	$-0.806756\pi$
$149$	−2.36798	−	16.4697i	−0.193993	−	1.34925i	0.627317	−	0.778764i	$-0.284153\pi$
$150$		0			0
$151$	11.0961	−	7.13103i	0.902988	−	0.580315i	−0.00468679	−	0.999989i	$-0.501492\pi$
$151$	11.0961	−	7.13103i	0.902988	−	0.580315i	0.907675	+	0.419674i	$0.137855\pi$
$152$	−9.86198	+	11.3813i	−0.799913	+	0.923148i
$153$		0			0
$154$	8.40957	+	5.40450i	0.677662	+	0.435507i
$155$	−2.11496	+	0.621008i	−0.169877	+	0.0498805i
$156$		0			0
$157$	−3.96143	−	1.16318i	−0.316157	−	0.0928320i	0.119804	−	0.992798i	$-0.461773\pi$
$157$	−3.96143	−	1.16318i	−0.316157	−	0.0928320i	−0.435961	+	0.899965i	$0.643591\pi$
$158$	5.19780	+	11.3816i	0.413515	+	0.905471i
$159$		0			0
$160$	8.90276			0.703825
$161$	−7.90335	−	8.18717i	−0.622871	−	0.645239i
$162$		0			0
$163$	2.10474	−	14.6388i	0.164856	−	1.14660i	−0.724464	−	0.689312i	$-0.757913\pi$
$163$	2.10474	−	14.6388i	0.164856	−	1.14660i	0.889320	−	0.457285i	$-0.151178\pi$
$164$	−0.505992	−	1.10797i	−0.0395113	−	0.0865177i
$165$		0			0
$166$	18.6007	+	21.4663i	1.44369	+	1.66611i
$167$	1.27588	−	0.374632i	0.0987306	−	0.0289899i	−0.231994	−	0.972717i	$-0.574525\pi$
$167$	1.27588	−	0.374632i	0.0987306	−	0.0289899i	0.330725	+	0.943727i	$0.392707\pi$
$168$		0			0
$169$	−5.38436	+	11.7901i	−0.414181	+	0.906931i
$170$	2.78336	−	3.21217i	0.213474	−	0.246362i
$171$		0			0
$172$	−1.80995	−	12.5885i	−0.138007	−	0.959861i
$173$	−2.41025	−	16.7637i	−0.183248	−	1.27452i	−0.849019	−	0.528362i	$-0.822806\pi$
$173$	−2.41025	−	16.7637i	−0.183248	−	1.27452i	0.665771	−	0.746156i	$-0.268103\pi$
$174$		0			0
$175$	−5.39358	+	6.22452i	−0.407716	+	0.470530i
$176$	−1.23543	+	2.70522i	−0.0931244	+	0.203914i
$177$		0			0
$178$	29.3900	−	8.62968i	2.20287	−	0.646822i
$179$	−0.937335	−	1.08174i	−0.0700597	−	0.0808532i	0.719638	−	0.694350i	$-0.244308\pi$
$179$	−0.937335	−	1.08174i	−0.0700597	−	0.0808532i	−0.789697	+	0.613497i	$0.789762\pi$
$180$		0			0
$181$	−6.70121	−	14.6736i	−0.498097	−	1.09068i	−0.977083	−	0.212858i	$-0.931723\pi$
$181$	−6.70121	−	14.6736i	−0.498097	−	1.09068i	0.478986	−	0.877822i	$-0.341004\pi$
$182$	−0.146201	+	1.01685i	−0.0108371	+	0.0753737i
$183$		0			0
$184$	−5.54765	+	7.14459i	−0.408978	+	0.526706i
$185$	4.80153			0.353015
$186$		0			0
$187$	1.23889	+	2.71279i	0.0905967	+	0.198379i
$188$	−7.09288	−	2.08266i	−0.517301	−	0.151893i
$189$		0			0
$190$	−20.8742	+	6.12922i	−1.51437	+	0.444660i
$191$	17.4514	+	11.2153i	1.26274	+	0.811512i	0.988656	−	0.150195i	$-0.0479900\pi$
$191$	17.4514	+	11.2153i	1.26274	+	0.811512i	0.274081	+	0.961707i	$0.411626\pi$
$192$		0			0
$193$	−9.59519	+	11.0734i	−0.690677	+	0.797083i	−0.987461	−	0.157861i	$-0.949540\pi$
$193$	−9.59519	+	11.0734i	−0.690677	+	0.797083i	0.296785	+	0.954944i	$0.404086\pi$
$194$	−8.01540	+	5.15119i	−0.575472	+	0.369834i
$195$		0			0
$196$	0.556778	+	3.87247i	0.0397698	+	0.276605i
$197$	−9.82407	+	6.31355i	−0.699936	+	0.449822i	−0.841606	−	0.540092i	$-0.818389\pi$
$197$	−9.82407	+	6.31355i	−0.699936	+	0.449822i	0.141669	+	0.989914i	$0.454753\pi$
$198$		0			0
$199$	−2.37759	+	5.20620i	−0.168543	+	0.369057i	−0.974990	−	0.222249i	$-0.928660\pi$
$199$	−2.37759	+	5.20620i	−0.168543	+	0.369057i	0.806447	+	0.591306i	$0.201388\pi$
$200$	5.50765	+	3.53955i	0.389450	+	0.250284i
$201$		0			0
$202$	2.62677	+	3.03146i	0.184819	+	0.213293i
$203$	−11.3317	−	3.32729i	−0.795330	−	0.233530i
$204$		0			0
$205$	0.0750502	−	0.521985i	0.00524173	−	0.0364570i
$206$	33.7445			2.35109
$207$		0			0
$208$	−0.305626			−0.0211913
$209$	2.17244	−	15.1097i	0.150271	−	1.04516i
$210$		0			0
$211$	13.4979	+	3.96334i	0.929234	+	0.272848i	0.711116	−	0.703075i	$-0.248190\pi$
$211$	13.4979	+	3.96334i	0.929234	+	0.272848i	0.218118	+	0.975922i	$0.430008\pi$
$212$	18.3645	+	21.1938i	1.26128	+	1.45560i
$213$		0			0
$214$	3.68596	+	2.36882i	0.251967	+	0.161929i
$215$	2.28738	−	5.00866i	0.155998	−	0.341588i
$216$		0			0
$217$	−3.55843	+	2.28687i	−0.241562	+	0.155243i
$218$	4.89064	+	34.0151i	0.331236	+	2.30379i
$219$		0			0
$220$	5.67953	−	3.65001i	0.382914	−	0.246084i
$221$	−0.200702	+	0.231623i	−0.0135007	+	0.0155806i
$222$		0			0
$223$	−3.53628	−	2.27263i	−0.236807	−	0.152187i	0.416856	−	0.908973i	$-0.363132\pi$
$223$	−3.53628	−	2.27263i	−0.236807	−	0.152187i	−0.653663	+	0.756786i	$0.726768\pi$
$224$	16.3922	−	4.81319i	1.09525	−	0.321595i
$225$		0			0
$226$	3.14668	+	0.923948i	0.209314	+	0.0614601i
$227$	−7.65642	−	16.7652i	−0.508174	−	1.11275i	−0.973725	−	0.227726i	$-0.926871\pi$
$227$	−7.65642	−	16.7652i	−0.508174	−	1.11275i	0.465551	−	0.885021i	$-0.345856\pi$
$228$		0			0
$229$	10.9247			0.721923			0.360961	−	0.932581i	$-0.382449\pi$
$229$	10.9247			0.721923			0.360961	+	0.932581i	$0.382449\pi$
$230$	−12.3221	+	4.34992i	−0.812492	+	0.286825i
$231$		0			0
$232$	−1.33603	+	9.29227i	−0.0877145	+	0.610068i
$233$	−1.73013	−	3.78846i	−0.113345	−	0.248190i	0.844455	−	0.535626i	$-0.179924\pi$
$233$	−1.73013	−	3.78846i	−0.113345	−	0.248190i	−0.957800	+	0.287436i	$0.907197\pi$
$234$		0			0
$235$	−2.09590	−	2.41879i	−0.136721	−	0.157785i
$236$	−19.7815	+	5.80837i	−1.28767	+	0.378093i
$237$		0			0
$238$	3.38825	−	7.41922i	0.219627	−	0.480917i
$239$	−14.7456	+	17.0173i	−0.953813	+	1.10076i	0.0410120	+	0.999159i	$0.486942\pi$
$239$	−14.7456	+	17.0173i	−0.953813	+	1.10076i	−0.994825	+	0.101601i	$0.967604\pi$
$240$		0			0
$241$	−0.843804	−	5.86878i	−0.0543542	−	0.378042i	−0.998783	−	0.0493250i	$-0.984293\pi$
$241$	−0.843804	−	5.86878i	−0.0543542	−	0.378042i	0.944429	−	0.328717i	$-0.106616\pi$
$242$	−2.30340	−	16.0205i	−0.148068	−	1.02984i
$243$		0			0
$244$	−13.8952	+	16.0359i	−0.889548	+	1.02659i
$245$	−0.703646	+	1.54077i	−0.0449543	+	0.0984361i
$246$		0			0
$247$	1.50519	−	0.441964i	0.0957730	−	0.0281215i
$248$	2.20187	+	2.54110i	0.139819	+	0.161360i
$249$		0			0
$250$	9.58839	+	20.9956i	0.606423	+	1.32788i
$251$	−0.220675	+	1.53483i	−0.0139289	+	0.0968775i	−0.995600	−	0.0937056i	$-0.970129\pi$
$251$	−0.220675	+	1.53483i	−0.0139289	+	0.0968775i	0.981671	+	0.190583i	$0.0610379\pi$
$252$		0			0
$253$	0.815292	−	9.13256i	0.0512570	−	0.574159i
$254$	−13.2093			−0.828824
$255$		0			0
$256$	−1.95044	−	4.27088i	−0.121903	−	0.266930i
$257$	26.3456	+	7.73578i	1.64340	+	0.482545i	0.967166	−	0.254145i	$-0.0817942\pi$
$257$	26.3456	+	7.73578i	1.64340	+	0.482545i	0.676230	+	0.736690i	$0.263612\pi$
$258$		0			0
$259$	8.84083	−	2.59590i	0.549342	−	0.161301i
$260$	0.583666	+	0.375099i	0.0361974	+	0.0232627i
$261$		0			0
$262$	18.4262	−	21.2650i	1.13837	−	1.31375i
$263$	10.8864	−	6.99627i	0.671285	−	0.431408i	−0.160104	−	0.987100i	$-0.551183\pi$
$263$	10.8864	−	6.99627i	0.671285	−	0.431408i	0.831388	+	0.555692i	$0.187547\pi$
$264$		0			0
$265$	1.72791	+	12.0179i	0.106145	+	0.738253i
$266$	−35.1210	+	22.5709i	−2.15341	+	1.38391i
$267$		0			0
$268$	8.62092	−	18.8772i	0.526607	−	1.15311i
$269$	8.41057	+	5.40514i	0.512801	+	0.329557i	0.771319	−	0.636449i	$-0.219598\pi$
$269$	8.41057	+	5.40514i	0.512801	+	0.329557i	−0.258517	+	0.966007i	$0.583234\pi$
$270$		0			0
$271$	−2.88885	−	3.33391i	−0.175485	−	0.202520i	0.661193	−	0.750216i	$-0.270051\pi$
$271$	−2.88885	−	3.33391i	−0.175485	−	0.202520i	−0.836678	+	0.547696i	$0.815505\pi$
$272$	2.32823	+	0.683629i	0.141169	+	0.0414511i
$273$		0			0
$274$	−0.218760	+	1.52151i	−0.0132158	+	0.0919177i
$275$	−6.63624			−0.400180
$276$		0			0
$277$	−30.8042			−1.85085			−0.925423	−	0.378935i	$-0.876290\pi$
$277$	−30.8042			−1.85085			−0.925423	+	0.378935i	$0.876290\pi$
$278$	4.37667	−	30.4404i	0.262495	−	1.82570i
$279$		0			0
$280$	−5.30954	−	1.55902i	−0.317306	−	0.0931694i
$281$	−2.34395	−	2.70506i	−0.139828	−	0.161370i	0.681516	−	0.731803i	$-0.261321\pi$
$281$	−2.34395	−	2.70506i	−0.139828	−	0.161370i	−0.821344	+	0.570433i	$0.806775\pi$
$282$		0			0
$283$	12.4341	+	7.99089i	0.739129	+	0.475009i	0.855243	−	0.518227i	$-0.173408\pi$
$283$	12.4341	+	7.99089i	0.739129	+	0.475009i	−0.116115	+	0.993236i	$0.537044\pi$
$284$	0.866403	−	1.89716i	0.0514116	−	0.112576i
$285$		0			0
$286$	−0.696337	+	0.447509i	−0.0411753	+	0.0264618i
$287$	−0.144020	−	1.00168i	−0.00850125	−	0.0591275i
$288$		0			0
$289$	−12.2543	+	7.87535i	−0.720840	+	0.463256i
$290$	−8.88110	+	10.2493i	−0.521516	+	0.601862i
$291$		0			0
$292$	−15.4829	−	9.95024i	−0.906067	−	0.582294i
$293$	20.6420	−	6.06104i	1.20592	−	0.354090i	0.383806	−	0.923414i	$-0.374613\pi$
$293$	20.6420	−	6.06104i	1.20592	−	0.354090i	0.822113	+	0.569324i	$0.192795\pi$
$294$		0			0
$295$	−8.56445	−	2.51475i	−0.498642	−	0.146414i
$296$	−3.04260	−	6.66236i	−0.176847	−	0.387242i
$297$		0			0
$298$	−36.6660			−2.12401
$299$	0.888516	−	0.313663i	0.0513842	−	0.0181396i
$300$		0			0
$301$	1.50376	−	10.4589i	0.0866752	−	0.602839i
$302$	−12.0743	−	26.4390i	−0.694797	−	1.52139i
$303$		0			0
$304$	−8.13354	−	9.38660i	−0.466490	−	0.538359i
$305$	−8.81450	+	2.58817i	−0.504717	+	0.148198i
$306$		0			0
$307$	5.87602	−	12.8667i	0.335362	−	0.734341i	−0.664555	−	0.747240i	$-0.731379\pi$
$307$	5.87602	−	12.8667i	0.335362	−	0.734341i	0.999917	+	0.0128989i	$0.00410596\pi$
$308$	8.48411	−	9.79118i	0.483427	−	0.557904i
$309$		0			0
$310$	0.691267	+	4.80787i	0.0392613	+	0.273069i
$311$	0.0811393	+	0.564336i	0.00460099	+	0.0320006i	0.991993	−	0.126296i	$-0.0403089\pi$
$311$	0.0811393	+	0.564336i	0.00460099	+	0.0320006i	−0.987392	+	0.158297i	$0.949400\pi$
$312$		0			0
$313$	13.8390	−	15.9711i	0.782227	−	0.902738i	−0.215041	−	0.976605i	$-0.568989\pi$
$313$	13.8390	−	15.9711i	0.782227	−	0.902738i	0.997268	+	0.0738672i	$0.0235341\pi$
$314$	−3.77945	+	8.27584i	−0.213287	+	0.467033i
$315$		0			0
$316$	15.5593	−	4.56862i	0.875279	−	0.257005i
$317$	−5.77072	−	6.65977i	−0.324116	−	0.374050i	0.570185	−	0.821517i	$-0.306872\pi$
$317$	−5.77072	−	6.65977i	−0.324116	−	0.374050i	−0.894301	+	0.447467i	$0.852326\pi$
$318$		0			0
$319$	−3.95303	−	8.65592i	−0.221327	−	0.484639i
$320$	2.24451	−	15.6109i	0.125472	−	0.872676i
$321$		0			0
$322$	−20.3363	+	14.6711i	−1.13330	+	0.817589i
$323$	−12.4550			−0.693015
$324$		0			0
$325$	−0.283306	−	0.620354i	−0.0157150	−	0.0344111i
$326$	−31.2698	−	9.18165i	−1.73188	−	0.508525i
$327$		0			0
$328$	−0.771839	+	0.226632i	−0.0426177	+	0.0125137i
$329$	−5.16678	−	3.32049i	−0.284854	−	0.183064i
$330$		0			0
$331$	−19.7686	+	22.8142i	−1.08658	+	1.25398i	−0.121342	+	0.992611i	$0.538720\pi$
$331$	−19.7686	+	22.8142i	−1.08658	+	1.25398i	−0.965239	+	0.261371i	$0.915826\pi$
$332$	30.9683	−	19.9021i	1.69961	−	1.09227i
$333$		0			0
$334$	−0.417017	−	2.90042i	−0.0228182	−	0.158704i
$335$	7.55856	−	4.85759i	0.412968	−	0.265398i
$336$		0			0
$337$	−2.05870	+	4.50792i	−0.112145	+	0.245562i	−0.957380	−	0.288832i	$-0.906733\pi$
$337$	−2.05870	+	4.50792i	−0.112145	+	0.245562i	0.845235	+	0.534394i	$0.179460\pi$
$338$	24.0278	+	15.4418i	1.30694	+	0.839920i
$339$		0			0
$340$	−3.60728	−	4.16303i	−0.195632	−	0.225772i
$341$	−3.27015	−	0.960202i	−0.177088	−	0.0519979i
$342$		0			0
$343$	−2.82637	+	19.6578i	−0.152609	+	1.06142i
$344$	−8.39923			−0.452856
$345$		0			0
$346$	−37.3205			−2.00636
$347$	−0.963038	+	6.69808i	−0.0516986	+	0.359572i	0.947508	+	0.319733i	$0.103593\pi$
$347$	−0.963038	+	6.69808i	−0.0516986	+	0.359572i	−0.999206	+	0.0398383i	$0.987316\pi$
$348$		0			0
$349$	−9.68306	−	2.84320i	−0.518322	−	0.152193i	0.0121000	−	0.999927i	$-0.496148\pi$
$349$	−9.68306	−	2.84320i	−0.518322	−	0.152193i	−0.530422	+	0.847734i	$0.677967\pi$
$350$	11.8854	+	13.7165i	0.635300	+	0.733175i
$351$		0			0
$352$	11.5802	+	7.44216i	0.617228	+	0.396669i
$353$	−10.1649	+	22.2580i	−0.541023	+	1.18468i	0.419827	+	0.907604i	$0.362091\pi$
$353$	−10.1649	+	22.2580i	−0.541023	+	1.18468i	−0.960850	+	0.277071i	$0.910636\pi$
$354$		0			0
$355$	0.759635	−	0.488188i	0.0403173	−	0.0259103i
$356$	−5.64961	−	39.2939i	−0.299429	−	2.08257i
$357$		0			0
$358$	−2.65343	+	1.70526i	−0.140238	+	0.0901257i
$359$	0.274264	−	0.316518i	0.0144751	−	0.0167052i	−0.748466	−	0.663173i	$-0.769209\pi$
$359$	0.274264	−	0.316518i	0.0144751	−	0.0167052i	0.762941	+	0.646468i	$0.223755\pi$
$360$		0			0
$361$	37.6474	+	24.1945i	1.98144	+	1.27340i
$362$	−34.1074	+	10.0148i	−1.79265	+	0.526368i
$363$		0			0
$364$	1.27747	+	0.375099i	0.0669577	+	0.0196606i
$365$	−3.31015	−	7.24821i	−0.173261	−	0.379389i
$366$		0			0
$367$	28.5682			1.49125			0.745624	−	0.666367i	$-0.232151\pi$
$367$	28.5682			1.49125			0.745624	+	0.666367i	$0.232151\pi$
$368$	−5.18129	−	5.36735i	−0.270093	−	0.279793i
$369$		0			0
$370$	1.50579	−	10.4730i	0.0782825	−	0.544466i
$371$	9.67888	+	21.1938i	0.502503	+	1.10033i
$372$		0			0
$373$	−9.43508	−	10.8887i	−0.488530	−	0.563794i	0.456942	−	0.889496i	$-0.348945\pi$
$373$	−9.43508	−	10.8887i	−0.488530	−	0.563794i	−0.945472	+	0.325703i	$0.894399\pi$
$374$	6.30563	−	1.85150i	0.326056	−	0.0957388i
$375$		0			0
$376$	−2.02809	+	4.44089i	−0.104591	+	0.229021i
$377$	0.640396	−	0.739056i	0.0329821	−	0.0380633i
$378$		0			0
$379$	0.800823	+	5.56985i	0.0411355	+	0.286104i	0.999998	+	0.00223119i	$0.000710211\pi$
$379$	0.800823	+	5.56985i	0.0411355	+	0.286104i	−0.958862	+	0.283873i	$0.908381\pi$
$380$	4.01263	+	27.9084i	0.205843	+	1.43167i
$381$		0			0
$382$	29.9356	−	34.5475i	1.53164	−	1.76760i
$383$	−0.0962350	+	0.210725i	−0.00491738	+	0.0107676i	−0.912075	−	0.410024i	$-0.865520\pi$
$383$	−0.0962350	+	0.210725i	−0.00491738	+	0.0107676i	0.907157	+	0.420792i	$0.138248\pi$
$384$		0			0
$385$	5.38195	−	1.58028i	0.274289	−	0.0805386i
$386$	21.1441	+	24.4016i	1.07621	+	1.24201i
$387$		0			0
$388$	5.12969	+	11.2325i	0.260421	+	0.570241i
$389$	−4.29361	+	29.8627i	−0.217695	+	1.51410i	0.528821	+	0.848733i	$0.322634\pi$
$389$	−4.29361	+	29.8627i	−0.217695	+	1.51410i	−0.746516	+	0.665367i	$0.768275\pi$
$390$		0			0
$391$	−7.47023	+	0.402007i	−0.377786	+	0.0203304i
$392$	2.58378			0.130500
$393$		0			0
$394$	10.6901	+	23.4081i	0.538561	+	1.17928i
$395$	6.73644	+	1.97800i	0.338947	+	0.0995238i
$396$		0			0
$397$	12.5168	−	3.67528i	0.628202	−	0.184457i	0.0478924	−	0.998853i	$-0.484750\pi$
$397$	12.5168	−	3.67528i	0.628202	−	0.184457i	0.580310	+	0.814396i	$0.302931\pi$
$398$	10.6101	+	6.81867i	0.531834	+	0.341789i
$399$		0			0
$400$	−3.53593	+	4.08068i	−0.176797	+	0.204034i
$401$	17.9404	−	11.5296i	0.895899	−	0.575759i	−0.00967246	−	0.999953i	$-0.503079\pi$
$401$	17.9404	−	11.5296i	0.895899	−	0.575759i	0.905571	+	0.424194i	$0.139443\pi$
$402$		0			0
$403$	−0.0498457	−	0.346685i	−0.00248299	−	0.0172696i
$404$	4.37332	−	2.81056i	0.217581	−	0.139831i
$405$		0			0
$406$	−10.8111	+	23.6731i	−0.536548	+	1.17488i
$407$	6.24557	+	4.01378i	0.309581	+	0.198956i
$408$		0			0
$409$	5.99134	+	6.91437i	0.296253	+	0.341894i	0.884288	−	0.466941i	$-0.154644\pi$
$409$	5.99134	+	6.91437i	0.296253	+	0.341894i	−0.588036	+	0.808835i	$0.700099\pi$
$410$	−1.11501	−	0.327397i	−0.0550665	−	0.0161690i
$411$		0			0
$412$	6.22391	−	43.2882i	0.306630	−	2.13266i
$413$	−17.1289			−0.842859
$414$		0			0
$415$	15.9379			0.782360
$416$	−0.201323	+	1.40023i	−0.00987065	+	0.0686519i
$417$		0			0
$418$	−32.2757	−	9.47700i	−1.57866	−	0.463535i
$419$	−5.87685	−	6.78225i	−0.287103	−	0.331334i	0.593817	−	0.804600i	$-0.297620\pi$
$419$	−5.87685	−	6.78225i	−0.287103	−	0.331334i	−0.880920	+	0.473266i	$0.843075\pi$
$420$		0			0
$421$	26.4762	+	17.0152i	1.29037	+	0.829270i	0.992129	−	0.125221i	$-0.0399638\pi$
$421$	26.4762	+	17.0152i	1.29037	+	0.829270i	0.298241	+	0.954491i	$0.403600\pi$
$422$	12.8778	−	28.1985i	0.626882	−	1.37268i
$423$		0			0
$424$	15.5805	−	10.0130i	0.756656	−	0.486273i
$425$	0.770581	+	5.35951i	0.0373787	+	0.259974i
$426$		0			0
$427$	−14.8305	+	9.53095i	−0.717696	+	0.461235i
$428$	3.71863	−	4.29153i	0.179747	−	0.207439i
$429$		0			0
$430$	−10.2075	−	6.55995i	−0.492249	−	0.316349i
$431$	−21.2071	+	6.22697i	−1.02151	+	0.299942i	−0.749254	−	0.662283i	$-0.769588\pi$
$431$	−21.2071	+	6.22697i	−1.02151	+	0.299942i	−0.272256	+	0.962225i	$0.587770\pi$
$432$		0			0
$433$	−12.1810	−	3.57666i	−0.585382	−	0.171884i	−0.0243864	−	0.999703i	$-0.507763\pi$
$433$	−12.1810	−	3.57666i	−0.585382	−	0.171884i	−0.560995	+	0.827819i	$0.689581\pi$
$434$	3.87213	+	8.47878i	0.185868	+	0.406994i
$435$		0			0
$436$	44.5375			2.13296
$437$	33.2793	+	18.9413i	1.59196	+	0.906086i
$438$		0			0
$439$	−2.62158	+	18.2335i	−0.125121	+	0.870238i	0.826494	+	0.562946i	$0.190332\pi$
$439$	−2.62158	+	18.2335i	−0.125121	+	0.870238i	−0.951615	+	0.307292i	$0.900577\pi$
$440$	−1.85221	−	4.05578i	−0.0883009	−	0.193352i
$441$		0			0
$442$	0.442270	+	0.510407i	0.0210366	+	0.0242776i
$443$	−13.3492	+	3.91968i	−0.634240	+	0.186230i	−0.583020	−	0.812458i	$-0.698129\pi$
$443$	−13.3492	+	3.91968i	−0.634240	+	0.186230i	−0.0512201	+	0.998687i	$0.516311\pi$
$444$		0			0
$445$	7.13988	−	15.6342i	0.338463	−	0.741130i
$446$	−6.06603	+	7.00057i	−0.287235	+	0.331487i
$447$		0			0
$448$	−4.30718	−	29.9571i	−0.203495	−	1.41534i
$449$	4.28260	+	29.7862i	0.202109	+	1.40570i	0.798013	+	0.602641i	$0.205885\pi$
$449$	4.28260	+	29.7862i	0.202109	+	1.40570i	−0.595904	+	0.803056i	$0.703206\pi$
$450$		0			0
$451$	0.533969	−	0.616233i	0.0251436	−	0.0290173i
$452$	1.76564	−	3.86622i	0.0830489	−	0.181852i
$453$		0			0
$454$	−38.9692	+	11.4424i	−1.82891	+	0.537017i
$455$	0.377484	+	0.435640i	0.0176967	+	0.0204231i
$456$		0			0
$457$	15.8055	+	34.6093i	0.739351	+	1.61895i	0.784619	+	0.619978i	$0.212859\pi$
$457$	15.8055	+	34.6093i	0.739351	+	1.61895i	−0.0452680	+	0.998975i	$0.514414\pi$
$458$	3.42606	−	23.8287i	0.160089	−	1.11344i
$459$		0			0
$460$	3.30748	+	16.6093i	0.154212	+	0.774415i
$461$	−8.76016			−0.408001			−0.204001	−	0.978971i	$-0.565394\pi$
$461$	−8.76016			−0.408001			−0.204001	+	0.978971i	$0.565394\pi$
$462$		0			0
$463$	−11.5638	−	25.3212i	−0.537415	−	1.17677i	−0.962416	−	0.271581i	$-0.912453\pi$
$463$	−11.5638	−	25.3212i	−0.537415	−	1.17677i	0.425001	−	0.905193i	$-0.360274\pi$
$464$	−7.42886	−	2.18131i	−0.344876	−	0.101265i
$465$		0			0
$466$	−8.80592	+	2.58565i	−0.407926	+	0.119778i
$467$	14.6095	+	9.38895i	0.676047	+	0.434469i	0.833101	−	0.553121i	$-0.186563\pi$
$467$	14.6095	+	9.38895i	0.676047	+	0.434469i	−0.157054	+	0.987590i	$0.550200\pi$
$468$		0			0
$469$	11.2910	−	13.0305i	0.521370	−	0.601693i
$470$	−5.93313	+	3.81299i	−0.273675	+	0.175880i
$471$		0			0
$472$	1.93772	+	13.4771i	0.0891909	+	0.620336i
$473$	7.16224	−	4.60289i	0.329320	−	0.211641i
$474$		0			0
$475$	11.5132	−	25.2105i	0.528263	−	1.15674i
$476$	−8.89263	−	5.71494i	−0.407593	−	0.261944i
$477$		0			0
$478$	32.4936	+	37.4996i	1.48622	+	1.71519i
$479$	−24.4458	−	7.17792i	−1.11695	−	0.327968i	−0.329387	−	0.944195i	$-0.606842\pi$
$479$	−24.4458	−	7.17792i	−1.11695	−	0.327968i	−0.787568	+	0.616228i	$0.788660\pi$
$480$		0			0
$481$	−0.108579	+	0.755186i	−0.00495079	+	0.0344335i
$482$	−13.0655			−0.595119
$483$		0			0
$484$	−20.9763			−0.953469
$485$	−0.760851	+	5.29183i	−0.0345485	+	0.240290i
$486$		0			0
$487$	5.91151	+	1.73577i	0.267876	+	0.0786555i	0.412912	−	0.910771i	$-0.364512\pi$
$487$	5.91151	+	1.73577i	0.267876	+	0.0786555i	−0.145036	+	0.989426i	$0.546330\pi$
$488$	9.17673	+	10.5905i	0.415411	+	0.479410i
$489$		0			0
$490$	3.14004	+	2.01798i	0.141852	+	0.0911630i
$491$	13.5623	−	29.6973i	0.612058	−	1.34022i	−0.309099	−	0.951030i	$-0.600027\pi$
$491$	13.5623	−	29.6973i	0.612058	−	1.34022i	0.921157	−	0.389191i	$-0.127245\pi$
$492$		0			0
$493$	−6.53161	+	4.19761i	−0.294169	+	0.189051i
$494$	−0.491967	−	3.42171i	−0.0221346	−	0.153950i
$495$		0			0
$496$	−2.33284	+	1.49923i	−0.104748	+	0.0673172i
$497$	1.13475	−	1.30957i	0.0509004	−	0.0587421i
$498$		0			0
$499$	−7.21265	−	4.63529i	−0.322882	−	0.207504i	0.369151	−	0.929369i	$-0.379649\pi$
$499$	−7.21265	−	4.63529i	−0.322882	−	0.207504i	−0.692033	+	0.721866i	$0.743285\pi$
$500$	28.7022	−	8.42774i	1.28360	−	0.376900i
$501$		0			0
$502$	3.27854	+	0.962667i	0.146329	+	0.0429659i
$503$	−2.80635	−	6.14505i	−0.125129	−	0.273994i	0.836692	−	0.547674i	$-0.184487\pi$
$503$	−2.80635	−	6.14505i	−0.125129	−	0.273994i	−0.961821	+	0.273679i	$0.911759\pi$
$504$		0			0
$505$	2.25073			0.100156
$506$	−19.6641	−	4.64234i	−0.874177	−	0.206377i
$507$		0			0
$508$	−2.43635	+	16.9452i	−0.108096	+	0.751821i
$509$	−17.0206	−	37.2699i	−0.754425	−	1.65196i	−0.758246	−	0.651968i	$-0.773943\pi$
$509$	−17.0206	−	37.2699i	−0.754425	−	1.65196i	0.00382066	−	0.999993i	$-0.498784\pi$
$510$		0			0
$511$	−10.0135	−	11.5562i	−0.442971	−	0.511216i
$512$	16.3767	−	4.80863i	0.723754	−	0.212513i
$513$		0			0
$514$	25.1354	−	55.0388i	1.10867	−	2.42766i
$515$	12.3995	−	14.3097i	0.546385	−	0.630562i
$516$		0			0
$517$	−0.704266	−	4.89828i	−0.0309736	−	0.215426i
$518$	−2.88960	−	20.0976i	−0.126962	−	0.883037i
$519$		0			0
$520$	0.300061	−	0.346289i	0.0131586	−	0.0151858i
$521$	7.77941	−	17.0345i	0.340822	−	0.746297i	−0.659162	−	0.752001i	$-0.729089\pi$
$521$	7.77941	−	17.0345i	0.340822	−	0.746297i	0.999984	+	0.00570487i	$0.00181593\pi$
$522$		0			0
$523$	−22.6095	+	6.63875i	−0.988644	+	0.290292i	−0.735788	−	0.677212i	$-0.763188\pi$
$523$	−22.6095	+	6.63875i	−0.988644	+	0.290292i	−0.252856	+	0.967504i	$0.581370\pi$
$524$	−23.8807	−	27.5597i	−1.04323	−	1.20395i
$525$		0			0
$526$	−11.8461	−	25.9394i	−0.516515	−	1.13101i
$527$	−0.395751	+	2.75251i	−0.0172392	+	0.119901i
$528$		0			0
$529$	20.5716	+	10.2864i	0.894416	+	0.447237i
$530$	26.7551			1.16217
$531$		0			0
$532$	22.4767	+	49.2171i	0.974488	+	2.13383i
$533$	0.0804009	+	0.0236078i	0.00348255	+	0.00102257i
$534$		0			0
$535$	2.35894	−	0.692647i	0.101986	−	0.0299457i
$536$	−11.5298	−	7.40976i	−0.498012	−	0.320053i
$537$		0			0
$538$	14.4272	−	16.6499i	0.622002	−	0.717829i
$539$	−2.20325	+	1.41595i	−0.0949009	+	0.0609891i
$540$		0			0
$541$	−0.135667	−	0.943585i	−0.00583278	−	0.0405679i	0.986697	−	0.162569i	$-0.0519780\pi$
$541$	−0.135667	−	0.943585i	−0.00583278	−	0.0405679i	−0.992530	+	0.122001i	$0.961069\pi$
$542$	−8.17784	+	5.25558i	−0.351268	+	0.225746i
$543$		0			0
$544$	4.66572	−	10.2165i	0.200041	−	0.438029i
$545$	16.2216	+	10.4250i	0.694856	+	0.446557i
$546$		0			0
$547$	−19.5057	−	22.5108i	−0.834003	−	0.962491i	0.165717	−	0.986173i	$-0.447006\pi$
$547$	−19.5057	−	22.5108i	−0.834003	−	0.962491i	−0.999720	+	0.0236827i	$0.992461\pi$
$548$	1.91148	+	0.561261i	0.0816544	+	0.0239759i
$549$		0			0
$550$	−2.08117	+	14.4749i	−0.0887415	+	0.617211i
$551$	39.7412			1.69303
$552$		0			0
$553$	13.4729			0.572925
$554$	−9.66043	+	67.1897i	−0.410432	+	2.85462i
$555$		0			0
$556$	−38.2425	−	11.2290i	−1.62184	−	0.476216i
$557$	−3.93487	−	4.54108i	−0.166726	−	0.192412i	0.666238	−	0.745739i	$-0.267903\pi$
$557$	−3.93487	−	4.54108i	−0.166726	−	0.192412i	−0.832964	+	0.553327i	$0.813358\pi$
$558$		0			0
$559$	0.736039	+	0.473023i	0.0311311	+	0.0200068i
$560$	1.89589	−	4.15141i	0.0801159	−	0.175429i
$561$		0			0
$562$	−6.63532	+	4.26426i	−0.279894	+	0.179877i
$563$	0.0126931	+	0.0882822i	0.000534949	+	0.00372065i	0.990087	−	0.140454i	$-0.0448563\pi$
$563$	0.0126931	+	0.0882822i	0.000534949	+	0.00372065i	−0.989552	+	0.144175i	$0.953947\pi$
$564$		0			0
$565$	1.54806	−	0.994879i	0.0651274	−	0.0418549i
$566$	21.3290	−	24.6150i	0.896526	−	1.03465i
$567$		0			0
$568$	−1.15875	−	0.744681i	−0.0486199	−	0.0312461i
$569$	−39.6842	+	11.6523i	−1.66365	+	0.488491i	−0.972243	−	0.233975i	$-0.924827\pi$
$569$	−39.6842	+	11.6523i	−1.66365	+	0.488491i	−0.691406	+	0.722466i	$0.743009\pi$
$570$		0			0
$571$	−24.7458	−	7.26602i	−1.03558	−	0.304073i	−0.280602	−	0.959824i	$-0.590534\pi$
$571$	−24.7458	−	7.26602i	−1.03558	−	0.304073i	−0.754977	+	0.655751i	$0.772352\pi$
$572$	0.445641	+	0.975819i	0.0186332	+	0.0408010i
$573$		0			0
$574$	−2.23002			−0.0930793
$575$	6.09167	−	15.4923i	0.254040	−	0.646073i
$576$		0			0
$577$	−3.86302	+	26.8679i	−0.160820	+	1.11853i	0.736273	+	0.676684i	$0.236584\pi$
$577$	−3.86302	+	26.8679i	−0.160820	+	1.11853i	−0.897093	+	0.441842i	$0.854325\pi$
$578$	13.3346	+	29.1986i	0.554645	+	1.21450i
$579$		0			0
$580$	11.5100	+	13.2833i	0.477929	+	0.551559i
$581$	29.3457	−	8.61667i	1.21746	−	0.357480i
$582$		0			0
$583$	−7.79865	+	17.0767i	−0.322987	+	0.707243i
$584$	−7.95971	+	9.18600i	−0.329375	+	0.380119i
$585$		0			0
$586$	−6.74678	−	46.9249i	−0.278707	−	1.93845i
$587$	4.50210	+	31.3128i	0.185822	+	1.29242i	0.842685	+	0.538407i	$0.180974\pi$
$587$	4.50210	+	31.3128i	0.185822	+	1.29242i	−0.656863	+	0.754010i	$0.728117\pi$
$588$		0			0
$589$	9.32111	−	10.7571i	0.384070	−	0.443240i
$590$	−8.17101	+	17.8920i	−0.336395	+	0.736603i
$591$		0			0
$592$	5.79588	−	1.70182i	0.238209	−	0.0699446i
$593$	−16.8600	−	19.4575i	−0.692358	−	0.799024i	0.295341	−	0.955392i	$-0.404567\pi$
$593$	−16.8600	−	19.4575i	−0.692358	−	0.799024i	−0.987699	+	0.156368i	$0.950021\pi$
$594$		0			0
$595$	−1.90119	−	4.16303i	−0.0779412	−	0.170667i
$596$	−6.76277	+	47.0361i	−0.277014	+	1.92667i
$597$		0			0
$598$	−0.405513	−	2.03638i	−0.0165826	−	0.0832740i
$599$	−16.9434			−0.692289			−0.346144	−	0.938181i	$-0.612509\pi$
$599$	−16.9434			−0.692289			−0.346144	+	0.938181i	$0.612509\pi$
$600$		0			0
$601$	−4.01081	−	8.78246i	−0.163605	−	0.358244i	0.810019	−	0.586403i	$-0.199457\pi$
$601$	−4.01081	−	8.78246i	−0.163605	−	0.358244i	−0.973624	+	0.228159i	$0.926729\pi$
$602$	−22.3411	−	6.55995i	−0.910557	−	0.267364i
$603$		0			0
$604$	−36.1436	+	10.6127i	−1.47066	+	0.431826i
$605$	−7.64006	−	4.90997i	−0.310613	−	0.199619i
$606$		0			0
$607$	−2.12520	+	2.45261i	−0.0862592	+	0.0995484i	−0.797238	−	0.603665i	$-0.793707\pi$
$607$	−2.12520	+	2.45261i	−0.0862592	+	0.0995484i	0.710979	+	0.703213i	$0.248252\pi$
$608$	−48.3627	+	31.0808i	−1.96136	+	1.26049i
$609$		0			0
$610$	2.88099	+	20.0377i	0.116648	+	0.811304i
$611$	0.427825	−	0.274946i	0.0173079	−	0.0111231i
$612$		0			0
$613$	−13.6731	+	29.9399i	−0.552251	+	1.20926i	0.403471	+	0.914992i	$0.367803\pi$
$613$	−13.6731	+	29.9399i	−0.552251	+	1.20926i	−0.955723	+	0.294269i	$0.904924\pi$
$614$	−26.2219	−	16.8518i	−1.05823	−	0.680083i
$615$		0			0
$616$	−5.60312	−	6.46634i	−0.225756	−	0.260536i
$617$	2.90191	+	0.852079i	0.116827	+	0.0343034i	0.339623	−	0.940562i	$-0.389700\pi$
$617$	2.90191	+	0.852079i	0.116827	+	0.0343034i	−0.222797	+	0.974865i	$0.571519\pi$
$618$		0			0
$619$	−1.48326	+	10.3163i	−0.0596172	+	0.414647i	0.938057	+	0.346482i	$0.112624\pi$
$619$	−1.48326	+	10.3163i	−0.0596172	+	0.414647i	−0.997674	+	0.0681655i	$0.978285\pi$
$620$	6.29515			0.252819
$621$		0			0
$622$	1.25637			0.0503758
$623$	4.69386	−	32.6465i	0.188056	−	1.30796i
$624$		0			0
$625$	−4.22587	−	1.24083i	−0.169035	−	0.0496331i
$626$	−30.4958	−	35.1941i	−1.21886	−	1.40664i
$627$		0			0
$628$	9.91937	+	6.37479i	0.395826	+	0.254382i
$629$	2.51636	−	5.51006i	0.100334	−	0.219701i
$630$		0			0
$631$	28.6878	−	18.4366i	1.14205	−	0.733948i	0.174005	−	0.984745i	$-0.444329\pi$
$631$	28.6878	−	18.4366i	1.14205	−	0.733948i	0.968040	+	0.250797i	$0.0806926\pi$
$632$	−1.52413	−	10.6006i	−0.0606266	−	0.421667i
$633$		0			0
$634$	−16.3359	+	10.4985i	−0.648783	+	0.416947i
$635$	−4.85377	+	5.60155i	−0.192616	+	0.222291i
$636$		0			0
$637$	−0.226421	−	0.145512i	−0.00897113	−	0.00576539i
$638$	−20.1199	+	5.90773i	−0.796553	+	0.233889i
$639$		0			0
$640$	−16.2621	−	4.77499i	−0.642817	−	0.188748i
$641$	3.74109	+	8.19184i	0.147764	+	0.323558i	0.969012	−	0.247013i	$-0.0794491\pi$
$641$	3.74109	+	8.19184i	0.147764	+	0.323558i	−0.821248	+	0.570571i	$0.806722\pi$
$642$		0			0
$643$	−22.9522			−0.905146			−0.452573	−	0.891727i	$-0.649494\pi$
$643$	−22.9522			−0.905146			−0.452573	+	0.891727i	$0.649494\pi$
$644$	15.0696	+	28.7939i	0.593825	+	1.13464i
$645$		0			0
$646$	−3.90598	+	27.1667i	−0.153679	+	1.06886i
$647$	18.6747	+	40.8919i	0.734178	+	1.60763i	0.792900	+	0.609352i	$0.208570\pi$
$647$	18.6747	+	40.8919i	0.734178	+	1.60763i	−0.0587216	+	0.998274i	$0.518702\pi$
$648$		0			0
$649$	−9.03801	−	10.4304i	−0.354773	−	0.409430i
$650$	−1.44196	+	0.423396i	−0.0565581	+	0.0166070i
$651$		0			0
$652$	−17.5459	+	38.4202i	−0.687152	+	1.50465i
$653$	−19.2289	+	22.1914i	−0.752486	+	0.868415i	−0.994807	−	0.101781i	$-0.967546\pi$
$653$	−19.2289	+	22.1914i	−0.752486	+	0.868415i	0.242321	+	0.970196i	$0.422091\pi$
$654$		0			0
$655$	−2.24692	−	15.6277i	−0.0877945	−	0.610624i
$656$	−0.0944170	−	0.656685i	−0.00368636	−	0.0256392i
$657$		0			0
$658$	−8.86294	+	10.2284i	−0.345513	+	0.398744i
$659$	16.6805	−	36.5251i	0.649778	−	1.42282i	−0.241970	−	0.970284i	$-0.577794\pi$
$659$	16.6805	−	36.5251i	0.649778	−	1.42282i	0.891748	−	0.452532i	$-0.149479\pi$
$660$		0			0
$661$	−9.56288	+	2.80792i	−0.371953	+	0.109215i	−0.462366	−	0.886689i	$-0.652999\pi$
$661$	−9.56288	+	2.80792i	−0.371953	+	0.109215i	0.0904132	+	0.995904i	$0.471181\pi$
$662$	43.5624	+	50.2737i	1.69310	+	1.95394i
$663$		0			0
$664$	−10.0994	−	22.1146i	−0.391933	−	0.858214i
$665$	−3.33381	+	23.1872i	−0.129280	+	0.899159i
$666$		0			0
$667$	23.8359	−	1.28272i	0.922929	−	0.0496669i
$668$	−3.79764			−0.146935
$669$		0			0
$670$	−8.22489	−	18.0100i	−0.317755	−	0.695787i
$671$	−13.6290	−	4.00183i	−0.526141	−	0.154489i
$672$		0			0
$673$	32.6772	−	9.59489i	1.25961	−	0.369856i	0.417263	−	0.908786i	$-0.362989\pi$
$673$	32.6772	−	9.59489i	1.25961	−	0.369856i	0.842351	+	0.538930i	$0.181171\pi$
$674$	9.18700	+	5.90412i	0.353870	+	0.227418i
$675$		0			0
$676$	24.2408	−	27.9754i	0.932339	−	1.07598i
$677$	21.0239	−	13.5112i	0.808012	−	0.519278i	−0.0702091	−	0.997532i	$-0.522367\pi$
$677$	21.0239	−	13.5112i	0.808012	−	0.519278i	0.878221	+	0.478254i	$0.158730\pi$
$678$		0			0
$679$	1.46006	+	10.1550i	0.0560320	+	0.389711i
$680$	−3.06043	+	1.96682i	−0.117362	+	0.0754240i
$681$		0			0
$682$	−3.11992	+	6.83168i	−0.119468	+	0.261598i
$683$	−29.0032	−	18.6392i	−1.10978	−	0.713210i	−0.148532	−	0.988908i	$-0.547455\pi$
$683$	−29.0032	−	18.6392i	−1.10978	−	0.713210i	−0.961244	+	0.275698i	$0.911091\pi$
$684$		0			0
$685$	0.564829	+	0.651848i	0.0215810	+	0.0249058i
$686$	41.9910	+	12.3297i	1.60322	+	0.470749i
$687$		0			0
$688$	0.985836	−	6.85664i	0.0375846	−	0.261407i
$689$	−1.92925			−0.0734987
$690$		0			0
$691$	−21.2259			−0.807470			−0.403735	−	0.914876i	$-0.632288\pi$
$691$	−21.2259			−0.807470			−0.403735	+	0.914876i	$0.632288\pi$
$692$	−6.88349	+	47.8757i	−0.261671	+	1.81996i
$693$		0			0
$694$	14.3077	+	4.20113i	0.543114	+	0.159473i
$695$	−11.3004	−	13.0414i	−0.428649	−	0.494687i
$696$		0			0
$697$	−0.559680	−	0.359685i	−0.0211994	−	0.0136240i
$698$	−9.23823	+	20.2289i	−0.349672	+	0.765675i
$699$		0			0
$700$	19.7880	−	12.7170i	0.747915	−	0.480656i
$701$	−3.43351	−	23.8806i	−0.129682	−	0.901957i	−0.945957	−	0.324293i	$-0.894874\pi$
$701$	−3.43351	−	23.8806i	−0.129682	−	0.901957i	0.816275	−	0.577664i	$-0.196035\pi$
$702$		0			0
$703$	−26.0834	+	16.7628i	−0.983756	+	0.632221i
$704$	15.9693	−	18.4296i	0.601866	−	0.694590i
$705$		0			0
$706$	45.3611	+	29.1518i	1.70719	+	1.09714i
$707$	4.14417	−	1.21684i	0.155858	−	0.0457639i
$708$		0			0
$709$	−6.75188	−	1.98253i	−0.253572	−	0.0744556i	0.152476	−	0.988307i	$-0.451275\pi$
$709$	−6.75188	−	1.98253i	−0.253572	−	0.0744556i	−0.406048	+	0.913852i	$0.633094\pi$
$710$	−0.826602	−	1.81001i	−0.0310218	−	0.0679283i
$711$		0			0
$712$	−26.2175			−0.982544
$713$	5.24339	−	6.75275i	0.196367	−	0.252892i
$714$		0			0
$715$	−0.0660988	+	0.459728i	−0.00247196	+	0.0171928i
$716$	1.69814	+	3.71841i	0.0634626	+	0.138964i
$717$		0			0
$718$	−0.604373	−	0.697483i	−0.0225550	−	0.0260298i
$719$	25.4920	−	7.48514i	0.950693	−	0.279149i	0.230618	−	0.973044i	$-0.425925\pi$
$719$	25.4920	−	7.48514i	0.950693	−	0.279149i	0.720075	+	0.693896i	$0.244107\pi$
$720$		0			0
$721$	15.0941	−	33.0515i	0.562134	−	1.23090i
$722$	64.5792	−	74.5284i	2.40339	−	2.77366i
$723$		0			0
$724$	6.55643	+	45.6010i	0.243668	+	1.69475i
$725$	−2.45875	−	17.1010i	−0.0913158	−	0.635115i
$726$		0			0
$727$	3.42332	−	3.95072i	0.126964	−	0.146524i	−0.688708	−	0.725039i	$-0.741822\pi$
$727$	3.42332	−	3.95072i	0.126964	−	0.146524i	0.815672	+	0.578514i	$0.196367\pi$
$728$	0.365271	−	0.799832i	0.0135378	−	0.0296437i
$729$		0			0
$730$	−16.8478	+	4.94696i	−0.623564	+	0.183095i
$731$	−4.54901	−	5.24983i	−0.168251	−	0.194172i
$732$		0			0
$733$	−11.0870	−	24.2771i	−0.409506	−	0.896694i	−0.996217	−	0.0868973i	$-0.972305\pi$
$733$	−11.0870	−	24.2771i	−0.409506	−	0.896694i	0.586711	−	0.809796i	$-0.300422\pi$
$734$	8.95920	−	62.3126i	0.330690	−	2.30000i
$735$		0			0
$736$	−28.0037	+	20.2026i	−1.03223	+	0.744677i
$737$	13.8924			0.511734
$738$		0			0
$739$	−0.930342	−	2.03716i	−0.0342232	−	0.0749383i	0.891748	−	0.452532i	$-0.149479\pi$
$739$	−0.930342	−	2.03716i	−0.0342232	−	0.0749383i	−0.925972	+	0.377593i	$0.876752\pi$
$740$	−13.1573	−	3.86334i	−0.483673	−	0.142019i
$741$		0			0
$742$	49.2630	−	14.4649i	1.80850	−	0.531024i
$743$	−15.2605	−	9.80730i	−0.559852	−	0.359795i	0.229907	−	0.973213i	$-0.426158\pi$
$743$	−15.2605	−	9.80730i	−0.559852	−	0.359795i	−0.789759	+	0.613418i	$0.789794\pi$
$744$		0			0
$745$	−13.4730	+	15.5486i	−0.493612	+	0.569658i
$746$	−26.7091	+	17.1649i	−0.977890	+	0.628452i
$747$		0			0
$748$	−1.21212	−	8.43051i	−0.0443197	−	0.308250i
$749$	3.96893	−	2.55068i	0.145022	−	0.0931997i
$750$		0			0
$751$	11.7258	−	25.6759i	0.427880	−	0.936927i	−0.565786	−	0.824552i	$-0.691427\pi$
$751$	11.7258	−	25.6759i	0.427880	−	0.936927i	0.993666	−	0.112375i	$-0.0358457\pi$
$752$	−3.38724	−	2.17685i	−0.123520	−	0.0793815i
$753$		0			0
$754$	−1.41119	−	1.62860i	−0.0513924	−	0.0593100i
$755$	−15.6485	−	4.59481i	−0.569507	−	0.167222i
$756$		0			0
$757$	−0.0173643	+	0.120772i	−0.000631118	+	0.00438952i	−0.990135	−	0.140120i	$-0.955251\pi$
$757$	−0.0173643	+	0.120772i	−0.000631118	+	0.00438952i	0.989503	+	0.144509i	$0.0461603\pi$
$758$	12.4000			0.450389
$759$		0			0
$760$	18.6210			0.675453
$761$	−3.80057	+	26.4336i	−0.137771	+	0.958216i	0.797257	+	0.603640i	$0.206284\pi$
$761$	−3.80057	+	26.4336i	−0.137771	+	0.958216i	−0.935027	+	0.354576i	$0.884625\pi$
$762$		0			0
$763$	35.5042	+	10.4250i	1.28534	+	0.377409i
$764$	−38.7970	−	44.7741i	−1.40363	−	1.61987i
$765$		0			0
$766$	0.429451	+	0.275992i	0.0155167	+	0.00997198i
$767$	0.589194	−	1.29015i	0.0212745	−	0.0465848i
$768$		0			0
$769$	−6.60471	+	4.24459i	−0.238172	+	0.153064i	−0.654283	−	0.756250i	$-0.727029\pi$
$769$	−6.60471	+	4.24459i	−0.238172	+	0.153064i	0.416111	+	0.909314i	$0.363393\pi$
$770$	−1.75907	−	12.2346i	−0.0633926	−	0.440905i
$771$		0			0
$772$	35.2028	−	22.6235i	1.26698	−	0.814237i
$773$	−22.4497	+	25.9084i	−0.807460	+	0.931859i	−0.998766	−	0.0496716i	$-0.984183\pi$
$773$	−22.4497	+	25.9084i	−0.807460	+	0.931859i	0.191305	+	0.981531i	$0.438728\pi$
$774$		0			0
$775$	−5.20559	−	3.34543i	−0.186990	−	0.120171i
$776$	7.82482	−	2.29757i	0.280895	−	0.0824781i
$777$		0			0
$778$	63.7897	+	18.7303i	2.28697	+	0.671515i
$779$	1.41463	+	3.09760i	0.0506843	+	0.110983i
$780$		0			0
$781$	1.39619			0.0499596
$782$	−1.46587	+	16.4200i	−0.0524193	+	0.587180i
$783$		0			0
$784$	−0.303264	+	2.10925i	−0.0108308	+	0.0753302i
$785$	2.12070	+	4.64369i	0.0756911	+	0.165740i
$786$		0			0
$787$	−10.4860	−	12.1015i	−0.373785	−	0.431370i	0.537426	−	0.843311i	$-0.319397\pi$
$787$	−10.4860	−	12.1015i	−0.373785	−	0.431370i	−0.911211	+	0.411940i	$0.864851\pi$
$788$	32.0002	−	9.39611i	1.13996	−	0.334723i
$789$		0			0
$790$	6.42697	−	14.0731i	0.228661	−	0.500699i
$791$	2.31250	−	2.66877i	0.0822231	−	0.0948905i
$792$		0			0
$793$	−0.207742	−	1.44488i	−0.00737712	−	0.0513090i
$794$	−4.09109	−	28.4542i	−0.145187	−	1.00980i
$795$		0			0
$796$	10.7041	−	12.3532i	0.379397	−	0.437847i
$797$	−8.94128	+	19.5787i	−0.316716	+	0.693512i	−0.999304	−	0.0372914i	$-0.988127\pi$
$797$	−8.94128	+	19.5787i	−0.316716	+	0.693512i	0.682588	+	0.730803i	$0.260854\pi$
$798$		0			0
$799$	−3.87413	+	1.13755i	−0.137057	+	0.0402435i
$800$	16.3665	+	18.8880i	0.578644	+	0.667791i
$801$		0			0
$802$	−19.5219	−	42.7470i	−0.689343	−	1.50945i
$803$	1.75340	−	12.1952i	0.0618761	−	0.430358i
$804$		0			0
$805$	−1.25114	+	14.0148i	−0.0440969	+	0.493955i
$806$	−0.771816			−0.0271860
$807$		0			0
$808$	−1.42623	−	3.12301i	−0.0501746	−	0.109867i
$809$	23.1479	+	6.79683i	0.813836	+	0.238964i	0.662060	−	0.749451i	$-0.269682\pi$
$809$	23.1479	+	6.79683i	0.813836	+	0.238964i	0.151776	+	0.988415i	$0.451501\pi$
$810$		0			0
$811$	−13.7575	+	4.03956i	−0.483091	+	0.141848i	−0.514205	−	0.857668i	$-0.671913\pi$
$811$	−13.7575	+	4.03956i	−0.483091	+	0.141848i	0.0311137	+	0.999516i	$0.490095\pi$
$812$	28.3744	+	18.2351i	0.995747	+	0.639927i
$813$		0			0
$814$	10.7135	−	12.3640i	0.375507	−	0.433358i
$815$	−15.3837	+	9.88652i	−0.538868	+	0.346310i
$816$		0			0
$817$	5.06017	+	35.1942i	0.177033	+	1.23129i
$818$	16.9605	−	10.8998i	0.593008	−	0.381103i
$819$		0			0
$820$	−0.625648	+	1.36998i	−0.0218486	+	0.0478417i
$821$	−11.9529	−	7.68167i	−0.417160	−	0.268092i	0.315180	−	0.949032i	$-0.397935\pi$
$821$	−11.9529	−	7.68167i	−0.417160	−	0.268092i	−0.732339	+	0.680940i	$0.761572\pi$
$822$		0			0
$823$	−10.4929	−	12.1095i	−0.365760	−	0.422109i	0.542802	−	0.839861i	$-0.317364\pi$
$823$	−10.4929	−	12.1095i	−0.365760	−	0.422109i	−0.908561	+	0.417752i	$0.862818\pi$
$824$	−27.7127	−	8.13718i	−0.965417	−	0.283472i
$825$		0			0
$826$	−5.37175	+	37.3613i	−0.186907	+	1.29997i
$827$	−35.1240			−1.22138			−0.610690	−	0.791870i	$-0.709108\pi$
$827$	−35.1240			−1.22138			−0.610690	+	0.791870i	$0.709108\pi$
$828$		0			0
$829$	−2.29604			−0.0797447			−0.0398723	−	0.999205i	$-0.512695\pi$
$829$	−2.29604			−0.0797447			−0.0398723	+	0.999205i	$0.512695\pi$
$830$	4.99824	−	34.7635i	0.173491	−	1.20666i
$831$		0			0
$832$	2.40453	+	0.706035i	0.0833622	+	0.0244774i
$833$	1.39937	+	1.61496i	0.0484853	+	0.0559550i
$834$		0			0
$835$	−1.38319	−	0.888922i	−0.0478672	−	0.0307624i
$836$	−18.1103	+	39.6561i	−0.626359	+	1.37153i
$837$		0			0
$838$	−16.6364	+	10.6915i	−0.574694	+	0.369333i
$839$	5.49501	+	38.2187i	0.189709	+	1.31945i	0.832761	+	0.553632i	$0.186759\pi$
$839$	5.49501	+	38.2187i	0.189709	+	1.31945i	−0.643052	+	0.765822i	$0.722332\pi$
$840$		0			0
$841$	−3.55542	+	2.28493i	−0.122601	+	0.0787906i
$842$	45.4164	−	52.4134i	1.56515	−	1.80628i
$843$		0			0
$844$	−33.7985	−	21.7210i	−1.16339	−	0.747667i
$845$	15.3773	−	4.51519i	0.528996	−	0.155327i
$846$		0			0
$847$	−16.7218	−	4.90997i	−0.574568	−	0.168708i
$848$	6.34530	+	13.8943i	0.217898	+	0.477131i
$849$		0			0
$850$	11.9317			0.409255
$851$	−15.1032	+	10.8959i	−0.517732	+	0.373505i
$852$		0			0
$853$	5.46907	−	38.0382i	0.187257	−	1.30240i	−0.651812	−	0.758380i	$-0.725991\pi$
$853$	5.46907	−	38.0382i	0.187257	−	1.30240i	0.839070	−	0.544024i	$-0.183100\pi$
$854$	16.1378	+	35.3369i	0.552226	+	1.20921i
$855$		0			0
$856$	−2.45588	−	2.83423i	−0.0839402	−	0.0968721i
$857$	−48.8281	+	14.3372i	−1.66794	+	0.489750i	−0.973286	−	0.229598i	$-0.926259\pi$
$857$	−48.8281	+	14.3372i	−1.66794	+	0.489750i	−0.694650	+	0.719348i	$0.744441\pi$
$858$		0			0
$859$	3.79985	−	8.32050i	0.129649	−	0.283892i	−0.833664	−	0.552272i	$-0.813761\pi$
$859$	3.79985	−	8.32050i	0.129649	−	0.283892i	0.963313	+	0.268380i	$0.0864883\pi$
$860$	−10.2980	+	11.8845i	−0.351158	+	0.405257i
$861$		0			0
$862$	6.93147	+	48.2094i	0.236087	+	1.64202i
$863$	1.75600	+	12.2133i	0.0597750	+	0.415744i	0.997635	+	0.0687310i	$0.0218950\pi$
$863$	1.75600	+	12.2133i	0.0597750	+	0.415744i	−0.937860	+	0.347013i	$0.887196\pi$
$864$		0			0
$865$	−13.7135	+	15.8262i	−0.466272	+	0.538107i
$866$	−11.6214	+	25.4474i	−0.394912	+	0.864737i
$867$		0			0
$868$	11.5910	−	3.40342i	0.393423	−	0.115519i
$869$	7.10891	+	8.20412i	0.241153	+	0.278306i
$870$		0			0
$871$	0.593078	+	1.29866i	0.0200957	+	0.0440034i
$872$	4.18600	−	29.1143i	0.141756	−	0.985934i
$873$		0			0
$874$	51.7512	−	66.6482i	1.75051	−	2.25441i
$875$	24.8534			0.840199
$876$		0			0
$877$	0.958445	+	2.09870i	0.0323644	+	0.0708681i	0.925124	−	0.379666i	$-0.123961\pi$
$877$	0.958445	+	2.09870i	0.0323644	+	0.0708681i	−0.892759	+	0.450534i	$0.851234\pi$
$878$	38.9485	+	11.4363i	1.31445	+	0.385957i
$879$		0			0
$880$	3.52831	−	1.03600i	0.118939	−	0.0349237i
$881$	29.9489	+	19.2470i	1.00901	+	0.648448i	0.937135	−	0.348966i	$-0.113467\pi$
$881$	29.9489	+	19.2470i	1.00901	+	0.648448i	0.0718697	+	0.997414i	$0.477103\pi$
$882$		0			0
$883$	−19.9566	+	23.0311i	−0.671592	+	0.775059i	−0.984625	−	0.174684i	$-0.944110\pi$
$883$	−19.9566	+	23.0311i	−0.671592	+	0.775059i	0.313032	+	0.949742i	$0.398655\pi$
$884$	0.736336	−	0.473214i	0.0247657	−	0.0159159i
$885$		0			0
$886$	4.36315	+	30.3464i	0.146583	+	1.01951i
$887$	−17.4906	+	11.2405i	−0.587278	+	0.377421i	−0.800276	−	0.599632i	$-0.795314\pi$
$887$	−17.4906	+	11.2405i	−0.587278	+	0.377421i	0.212998	+	0.977053i	$0.431677\pi$
$888$		0			0
$889$	−5.90859	+	12.9380i	−0.198168	+	0.433927i
$890$	−31.8619	−	20.4764i	−1.06801	−	0.686370i
$891$		0			0
$892$	7.86168	+	9.07286i	0.263228	+	0.303782i
$893$	19.8299	+	5.82260i	0.663584	+	0.194846i
$894$		0			0
$895$	−0.251874	+	1.75182i	−0.00841920	+	0.0585569i
$896$	−32.5243			−1.08656
$897$		0			0
$898$	66.3122			2.21287
$899$	1.26275	−	8.78264i	0.0421152	−	0.292918i
$900$		0			0
$901$	14.6969	+	4.31539i	0.489624	+	0.143766i
$902$	−1.17666	−	1.35794i	−0.0391786	−	0.0452145i
$903$		0			0
$904$	−2.36141	−	1.51759i	−0.0785393	−	0.0504742i
$905$	−8.28590	+	18.1436i	−0.275433	+	0.603114i
$906$		0			0
$907$	−19.1064	+	12.2789i	−0.634417	+	0.407715i	−0.817943	−	0.575300i	$-0.804885\pi$
$907$	−19.1064	+	12.2789i	−0.634417	+	0.407715i	0.183525	+	0.983015i	$0.441249\pi$
$908$	7.49100	+	52.1011i	0.248598	+	1.72903i
$909$		0			0
$910$	1.06859	−	0.686743i	0.0354235	−	0.0227653i
$911$	0.546182	−	0.630328i	0.0180958	−	0.0208837i	−0.746630	−	0.665240i	$-0.768329\pi$
$911$	0.546182	−	0.630328i	0.0180958	−	0.0208837i	0.764725	+	0.644356i	$0.222875\pi$
$912$		0			0
$913$	20.7312	+	13.3231i	0.686101	+	0.440930i
$914$	80.4460	−	23.6211i	2.66092	−	0.781315i
$915$		0			0
$916$	−29.9362	−	8.79006i	−0.989120	−	0.290432i
$917$	−12.5861	−	27.5597i	−0.415630	−	0.910103i
$918$		0			0
$919$	−45.3320			−1.49537			−0.747683	−	0.664056i	$-0.768834\pi$
$919$	−45.3320			−1.49537			−0.747683	+	0.664056i	$0.768834\pi$
$920$	11.1684	−	0.601024i	0.368213	−	0.0198152i
$921$		0			0
$922$	−2.74725	+	19.1075i	−0.0904758	+	0.629273i
$923$	0.0596044	+	0.130515i	0.00196190	+	0.00429597i
$924$		0			0
$925$	8.82696	+	10.1869i	0.290229	+	0.334942i
$926$	−58.8566	+	17.2819i	−1.93415	+	0.567918i
$927$		0			0
$928$	−14.8873	+	32.5986i	−0.488699	+	1.07010i
$929$	−11.5958	+	13.3822i	−0.380445	+	0.439056i	−0.913385	−	0.407096i	$-0.866541\pi$
$929$	−11.5958	+	13.3822i	−0.380445	+	0.439056i	0.532941	+	0.846153i	$0.321087\pi$
$930$		0			0
$931$	−1.55661	−	10.8265i	−0.0510159	−	0.354824i
$932$	1.69275	+	11.7734i	0.0554480	+	0.385649i
$933$		0			0
$934$	25.0607	−	28.9216i	0.820011	−	0.946343i
$935$	1.53186	−	3.35431i	0.0500972	−	0.109698i
$936$		0			0
$937$	22.3812	−	6.57170i	0.731161	−	0.214688i	0.105099	−	0.994462i	$-0.466484\pi$
$937$	22.3812	−	6.57170i	0.731161	−	0.214688i	0.626062	+	0.779774i	$0.284666\pi$
$938$	−24.8810	−	28.7143i	−0.812395	−	0.937554i
$939$		0			0
$940$	3.79708	+	8.31444i	0.123847	+	0.271187i
$941$	1.65295	−	11.4965i	0.0538847	−	0.374776i	−0.944980	−	0.327130i	$-0.893919\pi$
$941$	1.65295	−	11.4965i	0.0538847	−	0.374776i	0.998864	−	0.0476470i	$-0.0151722\pi$
$942$		0			0
$943$	0.948444	+	1.81222i	0.0308856	+	0.0590139i
$944$	−11.2294			−0.365486
$945$		0			0
$946$	−7.79363	−	17.0657i	−0.253393	−	0.554853i
$947$	5.75498	+	1.68981i	0.187012	+	0.0549116i	0.373897	−	0.927470i	$-0.378021\pi$
$947$	5.75498	+	1.68981i	0.187012	+	0.0549116i	−0.186886	+	0.982382i	$0.559839\pi$
$948$		0			0
$949$	1.21486	−	0.356714i	0.0394359	−	0.0115794i
$950$	−51.3781	−	33.0187i	−1.66692	−	1.07127i
$951$		0			0
$952$	−4.57168	+	5.27600i	−0.148169	+	0.170996i
$953$	15.0640	−	9.68107i	0.487972	−	0.313601i	−0.273417	−	0.961896i	$-0.588154\pi$
$953$	15.0640	−	9.68107i	0.487972	−	0.313601i	0.761389	+	0.648295i	$0.224518\pi$
$954$		0			0
$955$	−3.65039	−	25.3890i	−0.118124	−	0.821570i
$956$	54.0987	−	34.7671i	1.74968	−	1.12445i
$957$		0			0
$958$	−23.3227	+	51.0697i	−0.753524	+	1.64999i
$959$	1.39241	+	0.894847i	0.0449632	+	0.0288961i
$960$		0			0
$961$	18.2196	+	21.0265i	0.587728	+	0.678274i
$962$	1.61315	+	0.473664i	0.0520101	+	0.0152715i
$963$		0			0
$964$	−2.40984	+	16.7608i	−0.0776156	+	0.539829i
$965$	18.1172			0.583213
$966$		0			0
$967$	33.5068			1.07751			0.538753	−	0.842464i	$-0.318896\pi$
$967$	33.5068			1.07751			0.538753	+	0.842464i	$0.318896\pi$
$968$	−1.97153	+	13.7123i	−0.0633673	+	0.440730i
$969$		0			0
$970$	11.3039	+	3.31911i	0.362945	+	0.106570i
$971$	38.8241	+	44.8054i	1.24592	+	1.43787i	0.855960	+	0.517042i	$0.172967\pi$
$971$	38.8241	+	44.8054i	1.24592	+	1.43787i	0.389964	+	0.920830i	$0.372487\pi$
$972$		0			0
$973$	−27.8576	−	17.9030i	−0.893073	−	0.573943i
$974$	5.63994	−	12.3497i	0.180715	−	0.395711i
$975$		0			0
$976$	−9.72257	+	6.24832i	−0.311212	+	0.200004i
$977$	−1.79914	−	12.5133i	−0.0575596	−	0.400336i	−0.998150	−	0.0607934i	$-0.980637\pi$
$977$	−1.79914	−	12.5133i	−0.0575596	−	0.400336i	0.940591	−	0.339542i	$-0.110272\pi$
$978$		0			0
$979$	22.3564	−	14.3676i	0.714513	−	0.459189i
$980$	3.16787	−	3.65592i	0.101194	−	0.116784i
$981$		0			0
$982$	−60.5221	−	38.8952i	−1.93134	−	1.24120i
$983$	−56.0008	+	16.4433i	−1.78615	+	0.524461i	−0.996072	−	0.0885469i	$-0.971778\pi$
$983$	−56.0008	+	16.4433i	−1.78615	+	0.524461i	−0.790077	+	0.613008i	$0.789960\pi$
$984$		0			0
$985$	13.8546	+	4.06807i	0.441444	+	0.129620i
$986$	7.10741	+	15.5631i	0.226346	+	0.495629i
$987$		0			0
$988$	−4.48019			−0.142534
$989$	4.17093	+	20.9454i	0.132628	+	0.666025i
$990$		0			0
$991$	6.51675	−	45.3250i	0.207011	−	1.43980i	−0.575828	−	0.817571i	$-0.695320\pi$
$991$	6.51675	−	45.3250i	0.207011	−	1.43980i	0.782839	−	0.622224i	$-0.213771\pi$
$992$	5.33204	+	11.6755i	0.169292	+	0.370699i
$993$		0			0
$994$	−2.50055	−	2.88578i	−0.0793125	−	0.0915315i
$995$	6.79021	−	1.99379i	0.215264	−	0.0632073i
$996$		0			0
$997$	−16.3475	+	35.7959i	−0.517729	+	1.13367i	0.452563	+	0.891732i	$0.350510\pi$
$997$	−16.3475	+	35.7959i	−0.517729	+	1.13367i	−0.970292	+	0.241936i	$0.922218\pi$
$998$	−12.3724	+	14.2785i	−0.391640	+	0.451977i
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	207.2.i.c.100.1		10
3.2	odd	2		23.2.c.a.8.1	yes	10
12.11	even	2		368.2.m.c.353.1		10
15.2	even	4		575.2.p.b.399.1		20
15.8	even	4		575.2.p.b.399.2		20
15.14	odd	2		575.2.k.b.376.1		10
23.3	even	11	inner	207.2.i.c.118.1		10
23.7	odd	22		4761.2.a.bn.1.1		5
23.16	even	11		4761.2.a.bo.1.1		5
69.2	odd	22		529.2.c.b.170.1		10
69.5	even	22		529.2.c.e.177.1		10
69.8	odd	22		529.2.c.g.466.1		10
69.11	even	22		529.2.c.h.255.1		10
69.14	even	22		529.2.c.f.487.1		10
69.17	even	22		529.2.c.h.334.1		10
69.20	even	22		529.2.c.a.118.1		10
69.26	odd	22		23.2.c.a.3.1	✓	10
69.29	odd	22		529.2.c.i.334.1		10
69.32	odd	22		529.2.c.g.487.1		10
69.35	odd	22		529.2.c.i.255.1		10
69.38	even	22		529.2.c.f.466.1		10
69.41	odd	22		529.2.c.d.177.1		10
69.44	even	22		529.2.c.c.170.1		10
69.50	odd	22		529.2.c.d.266.1		10
69.53	even	22		529.2.a.j.1.5		5
69.56	even	22		529.2.c.c.501.1		10
69.59	odd	22		529.2.c.b.501.1		10
69.62	odd	22		529.2.a.i.1.5		5
69.65	even	22		529.2.c.e.266.1		10
69.68	even	2		529.2.c.a.399.1		10
276.95	even	22		368.2.m.c.49.1		10
276.131	even	22		8464.2.a.bs.1.5		5
276.191	odd	22		8464.2.a.bt.1.5		5
345.164	odd	22		575.2.k.b.26.1		10
345.233	even	44		575.2.p.b.49.1		20
345.302	even	44		575.2.p.b.49.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.2.c.a.3.1	✓	10	69.26	odd	22
23.2.c.a.8.1	yes	10	3.2	odd	2
207.2.i.c.100.1		10	1.1	even	1	trivial
207.2.i.c.118.1		10	23.3	even	11	inner
368.2.m.c.49.1		10	276.95	even	22
368.2.m.c.353.1		10	12.11	even	2
529.2.a.i.1.5		5	69.62	odd	22
529.2.a.j.1.5		5	69.53	even	22
529.2.c.a.118.1		10	69.20	even	22
529.2.c.a.399.1		10	69.68	even	2
529.2.c.b.170.1		10	69.2	odd	22
529.2.c.b.501.1		10	69.59	odd	22
529.2.c.c.170.1		10	69.44	even	22
529.2.c.c.501.1		10	69.56	even	22
529.2.c.d.177.1		10	69.41	odd	22
529.2.c.d.266.1		10	69.50	odd	22
529.2.c.e.177.1		10	69.5	even	22
529.2.c.e.266.1		10	69.65	even	22
529.2.c.f.466.1		10	69.38	even	22
529.2.c.f.487.1		10	69.14	even	22
529.2.c.g.466.1		10	69.8	odd	22
529.2.c.g.487.1		10	69.32	odd	22
529.2.c.h.255.1		10	69.11	even	22
529.2.c.h.334.1		10	69.17	even	22
529.2.c.i.255.1		10	69.35	odd	22
529.2.c.i.334.1		10	69.29	odd	22
575.2.k.b.26.1		10	345.164	odd	22
575.2.k.b.376.1		10	15.14	odd	2
575.2.p.b.49.1		20	345.233	even	44
575.2.p.b.49.2		20	345.302	even	44
575.2.p.b.399.1		20	15.2	even	4
575.2.p.b.399.2		20	15.8	even	4
4761.2.a.bn.1.1		5	23.7	odd	22
4761.2.a.bo.1.1		5	23.16	even	11
8464.2.a.bs.1.5		5	276.131	even	22
8464.2.a.bt.1.5		5	276.191	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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	207.2.i.c.100.1

Level	$207$
Weight	$2$
Character	207.100
Analytic conductor	$1.653$
Analytic rank	$0$
Dimension	$10$
Inner twists	$2$