LMFDB - Embedded newform 279.2.i.d.190.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [279,2,Mod(64,279)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(279, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8]))

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

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

chi := DirichletCharacter("279.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 279 = 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	279.i (of order $5$, degree $4$, 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:	$2.22782621639$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			190.6
Character	$\chi$	$=$	279.190
Dual form			279.2.i.d.163.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.833573 + 2.56547i) q^{2} +(-4.26878 + 3.10145i) q^{4} -3.42101 q^{5} +(1.97584 - 1.43553i) q^{7} +(-7.15039 - 5.19506i) q^{8} +O(q^{10})$	\(q+(0.833573 + 2.56547i) q^{2} +(-4.26878 + 3.10145i) q^{4} -3.42101 q^{5} +(1.97584 - 1.43553i) q^{7} +(-7.15039 - 5.19506i) q^{8} +(-2.85166 - 8.77652i) q^{10} +(-3.56034 + 2.58674i) q^{11} +(-1.31674 + 4.05251i) q^{13} +(5.32982 + 3.87234i) q^{14} +(4.10637 - 12.6381i) q^{16} +(3.00472 + 2.18306i) q^{17} +(0.445686 + 1.37168i) q^{19} +(14.6036 - 10.6101i) q^{20} +(-9.60401 - 6.97772i) q^{22} +(1.84983 + 1.34398i) q^{23} +6.70333 q^{25} -11.4942 q^{26} +(-3.98219 + 12.2559i) q^{28} +(0.696715 + 2.14427i) q^{29} +(-4.47226 + 3.31646i) q^{31} +18.1689 q^{32} +(-3.09592 + 9.52827i) q^{34} +(-6.75937 + 4.91097i) q^{35} +2.58589 q^{37} +(-3.14750 + 2.28679i) q^{38} +(24.4616 + 17.7724i) q^{40} +(-1.47558 - 4.54136i) q^{41} +(-1.68675 - 5.19129i) q^{43} +(7.17566 - 22.0844i) q^{44} +(-1.90598 + 5.86600i) q^{46} +(-0.0697791 + 0.214758i) q^{47} +(-0.319930 + 0.984642i) q^{49} +(5.58772 + 17.1972i) q^{50} +(-6.94778 - 21.3831i) q^{52} +(8.96191 + 6.51121i) q^{53} +(12.1800 - 8.84926i) q^{55} -21.5857 q^{56} +(-4.92031 + 3.57481i) q^{58} +(-1.10051 + 3.38703i) q^{59} -9.41939 q^{61} +(-12.2362 - 8.70896i) q^{62} +(6.93241 + 21.3358i) q^{64} +(4.50458 - 13.8637i) q^{65} +8.78757 q^{67} -19.5971 q^{68} +(-18.2334 - 13.2473i) q^{70} +(-1.85082 - 1.34470i) q^{71} +(4.92762 - 3.58012i) q^{73} +(2.15553 + 6.63402i) q^{74} +(-6.15674 - 4.47313i) q^{76} +(-3.32131 + 10.2219i) q^{77} +(13.6289 + 9.90196i) q^{79} +(-14.0479 + 43.2351i) q^{80} +(10.4207 - 7.57112i) q^{82} +(-2.26010 - 6.95586i) q^{83} +(-10.2792 - 7.46826i) q^{85} +(11.9121 - 8.65464i) q^{86} +38.8961 q^{88} +(11.5297 - 8.37680i) q^{89} +(3.21583 + 9.89732i) q^{91} -12.0648 q^{92} -0.609122 q^{94} +(-1.52470 - 4.69254i) q^{95} +(-12.8734 + 9.35306i) q^{97} -2.79276 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} + 2 q^{7}+O(q^{10}) $ 24 * q - 12 * q^4 + 2 * q^7	$ 24 q - 12 q^{4} + 2 q^{7} - 2 q^{10} - 10 q^{13} + 12 q^{16} + 4 q^{19} - 20 q^{22} + 28 q^{25} + 12 q^{28} - 16 q^{31} + 8 q^{34} - 28 q^{37} + 86 q^{40} + 32 q^{43} + 14 q^{46} - 36 q^{49} - 116 q^{52} + 8 q^{55} - 2 q^{58} - 44 q^{61} - 6 q^{64} - 76 q^{67} - 126 q^{70} - 22 q^{73} + 72 q^{79} + 18 q^{82} - 44 q^{85} + 120 q^{88} + 34 q^{91} + 172 q^{94} - 24 q^{97}+O(q^{100}) $ 24 * q - 12 * q^4 + 2 * q^7 - 2 * q^10 - 10 * q^13 + 12 * q^16 + 4 * q^19 - 20 * q^22 + 28 * q^25 + 12 * q^28 - 16 * q^31 + 8 * q^34 - 28 * q^37 + 86 * q^40 + 32 * q^43 + 14 * q^46 - 36 * q^49 - 116 * q^52 + 8 * q^55 - 2 * q^58 - 44 * q^61 - 6 * q^64 - 76 * q^67 - 126 * q^70 - 22 * q^73 + 72 * q^79 + 18 * q^82 - 44 * q^85 + 120 * q^88 + 34 * q^91 + 172 * q^94 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/279\mathbb{Z}\right)^\times$.

$n$	$127$	$218$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$1$

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 $

$2$	0.833573	+	2.56547i	0.589425	+	1.81406i	0.580721	+	0.814102i	$0.302771\pi$
$2$	0.833573	+	2.56547i	0.589425	+	1.81406i	0.00870381	+	0.999962i	$0.497229\pi$
$3$		0			0
$3$		0			0
$4$	−4.26878	+	3.10145i	−2.13439	+	1.55073i
$5$	−3.42101			−1.52992			−0.764962	−	0.644076i	$-0.777242\pi$
$5$	−3.42101			−1.52992			−0.764962	+	0.644076i	$0.777242\pi$
$6$		0			0
$7$	1.97584	−	1.43553i	0.746797	−	0.542580i	−0.148036	−	0.988982i	$-0.547295\pi$
$7$	1.97584	−	1.43553i	0.746797	−	0.542580i	0.894832	+	0.446402i	$0.147295\pi$
$8$	−7.15039	−	5.19506i	−2.52804	−	1.83673i
$9$		0			0
$10$	−2.85166	−	8.77652i	−0.901776	−	2.77538i
$11$	−3.56034	+	2.58674i	−1.07348	+	0.779930i	−0.976535	−	0.215359i	$-0.930908\pi$
$11$	−3.56034	+	2.58674i	−1.07348	+	0.779930i	−0.0969471	+	0.995290i	$0.530908\pi$
$12$		0			0
$13$	−1.31674	+	4.05251i	−0.365198	+	1.12396i	0.584659	+	0.811279i	$0.301228\pi$
$13$	−1.31674	+	4.05251i	−0.365198	+	1.12396i	−0.949857	+	0.312684i	$0.898772\pi$
$14$	5.32982	+	3.87234i	1.42446	+	1.03493i
$15$		0			0
$16$	4.10637	−	12.6381i	1.02659	−	3.15953i
$17$	3.00472	+	2.18306i	0.728751	+	0.529469i	0.889168	−	0.457581i	$-0.151284\pi$
$17$	3.00472	+	2.18306i	0.728751	+	0.529469i	−0.160417	+	0.987049i	$0.551284\pi$
$18$		0			0
$19$	0.445686	+	1.37168i	0.102247	+	0.314685i	0.989075	−	0.147416i	$-0.0470956\pi$
$19$	0.445686	+	1.37168i	0.102247	+	0.314685i	−0.886827	+	0.462101i	$0.847096\pi$
$20$	14.6036	−	10.6101i	3.26545	−	2.37249i
$21$		0			0
$22$	−9.60401	−	6.97772i	−2.04758	−	1.48765i
$23$	1.84983	+	1.34398i	0.385716	+	0.280239i	0.763698	−	0.645574i	$-0.223382\pi$
$23$	1.84983	+	1.34398i	0.385716	+	0.280239i	−0.377982	+	0.925813i	$0.623382\pi$
$24$		0			0
$25$	6.70333			1.34067
$26$	−11.4942			−2.25420
$27$		0			0
$28$	−3.98219	+	12.2559i	−0.752564	+	2.31615i
$29$	0.696715	+	2.14427i	0.129377	+	0.398181i	0.994673	−	0.103080i	$-0.0328697\pi$
$29$	0.696715	+	2.14427i	0.129377	+	0.398181i	−0.865296	+	0.501261i	$0.832870\pi$
$30$		0			0
$31$	−4.47226	+	3.31646i	−0.803242	+	0.595653i
$31$	−4.47226	+	3.31646i	−0.803242	+	0.595653i
$32$	18.1689			3.21185
$33$		0			0
$34$	−3.09592	+	9.52827i	−0.530946	+	1.63408i
$35$	−6.75937	+	4.91097i	−1.14254	+	0.830105i
$36$		0			0
$37$	2.58589			0.425117			0.212558	−	0.977148i	$-0.431820\pi$
$37$	2.58589			0.425117			0.212558	+	0.977148i	$0.431820\pi$
$38$	−3.14750	+	2.28679i	−0.510592	+	0.370967i
$39$		0			0
$40$	24.4616	+	17.7724i	3.86771	+	2.81006i
$41$	−1.47558	−	4.54136i	−0.230447	−	0.709242i	−0.997693	−	0.0678891i	$-0.978374\pi$
$41$	−1.47558	−	4.54136i	−0.230447	−	0.709242i	0.767246	−	0.641353i	$-0.221626\pi$
$42$		0			0
$43$	−1.68675	−	5.19129i	−0.257227	−	0.791664i	−0.993383	−	0.114852i	$-0.963361\pi$
$43$	−1.68675	−	5.19129i	−0.257227	−	0.791664i	0.736155	−	0.676813i	$-0.236639\pi$
$44$	7.17566	−	22.0844i	1.08177	−	3.32935i
$45$		0			0
$46$	−1.90598	+	5.86600i	−0.281021	+	0.864894i
$47$	−0.0697791	+	0.214758i	−0.0101783	+	0.0313257i	−0.956017	−	0.293312i	$-0.905242\pi$
$47$	−0.0697791	+	0.214758i	−0.0101783	+	0.0313257i	0.945838	+	0.324638i	$0.105242\pi$
$48$		0			0
$49$	−0.319930	+	0.984642i	−0.0457042	+	0.140663i
$50$	5.58772	+	17.1972i	0.790222	+	2.43205i
$51$		0			0
$52$	−6.94778	−	21.3831i	−0.963484	−	2.96530i
$53$	8.96191	+	6.51121i	1.23101	+	0.894383i	0.996966	−	0.0778418i	$-0.0248029\pi$
$53$	8.96191	+	6.51121i	1.23101	+	0.894383i	0.234047	+	0.972225i	$0.424803\pi$
$54$		0			0
$55$	12.1800	−	8.84926i	1.64235	−	1.19323i
$56$	−21.5857			−2.88451
$57$		0			0
$58$	−4.92031	+	3.57481i	−0.646068	+	0.469396i
$59$	−1.10051	+	3.38703i	−0.143274	+	0.440953i	−0.996785	−	0.0801222i	$-0.974469\pi$
$59$	−1.10051	+	3.38703i	−0.143274	+	0.440953i	0.853511	+	0.521075i	$0.174469\pi$
$60$		0			0
$61$	−9.41939			−1.20603			−0.603015	−	0.797730i	$-0.706034\pi$
$61$	−9.41939			−1.20603			−0.603015	+	0.797730i	$0.706034\pi$
$62$	−12.2362	−	8.70896i	−1.55400	−	1.10604i
$63$		0			0
$64$	6.93241	+	21.3358i	0.866552	+	2.66697i
$65$	4.50458	−	13.8637i	0.558725	−	1.71958i
$66$		0			0
$67$	8.78757			1.07357			0.536786	−	0.843718i	$-0.319638\pi$
$67$	8.78757			1.07357			0.536786	+	0.843718i	$0.319638\pi$
$68$	−19.5971			−2.37650
$69$		0			0
$70$	−18.2334	−	13.2473i	−2.17931	−	1.58336i
$71$	−1.85082	−	1.34470i	−0.219652	−	0.159587i	0.472518	−	0.881321i	$-0.343345\pi$
$71$	−1.85082	−	1.34470i	−0.219652	−	0.159587i	−0.692170	+	0.721734i	$0.743345\pi$
$72$		0			0
$73$	4.92762	−	3.58012i	0.576734	−	0.419022i	−0.260811	−	0.965390i	$-0.583990\pi$
$73$	4.92762	−	3.58012i	0.576734	−	0.419022i	0.837545	+	0.546368i	$0.183990\pi$
$74$	2.15553	+	6.63402i	0.250575	+	0.771190i
$75$		0			0
$76$	−6.15674	−	4.47313i	−0.706226	−	0.513103i
$77$	−3.32131	+	10.2219i	−0.378499	+	1.16490i
$78$		0			0
$79$	13.6289	+	9.90196i	1.53337	+	1.11406i	0.954329	+	0.298757i	$0.0965721\pi$
$79$	13.6289	+	9.90196i	1.53337	+	1.11406i	0.579039	+	0.815300i	$0.303428\pi$
$80$	−14.0479	+	43.2351i	−1.57061	+	4.83383i
$81$		0			0
$82$	10.4207	−	7.57112i	1.15078	−	0.836090i
$83$	−2.26010	−	6.95586i	−0.248078	−	0.763505i	−0.995115	−	0.0987229i	$-0.968524\pi$
$83$	−2.26010	−	6.95586i	−0.248078	−	0.763505i	0.747037	−	0.664782i	$-0.231476\pi$
$84$		0			0
$85$	−10.2792	−	7.46826i	−1.11493	−	0.810047i
$86$	11.9121	−	8.65464i	1.28451	−	0.933254i
$87$		0			0
$88$	38.8961			4.14633
$89$	11.5297	−	8.37680i	1.22214	−	0.887939i	0.225867	−	0.974158i	$-0.427479\pi$
$89$	11.5297	−	8.37680i	1.22214	−	0.887939i	0.996276	+	0.0862195i	$0.0274786\pi$
$90$		0			0
$91$	3.21583	+	9.89732i	0.337111	+	1.03752i
$92$	−12.0648			−1.25784
$93$		0			0
$94$	−0.609122			−0.0628261
$95$	−1.52470	−	4.69254i	−0.156431	−	0.481444i
$96$		0			0
$97$	−12.8734	+	9.35306i	−1.30709	+	0.949659i	−0.999998	−	0.00201961i	$-0.999357\pi$
$97$	−12.8734	+	9.35306i	−1.30709	+	0.949659i	−0.307096	+	0.951679i	$0.599357\pi$
$98$	−2.79276			−0.282111
$99$		0			0
$100$	−28.6150	+	20.7900i	−2.86150	+	2.07900i
$101$	−1.14513	−	0.831989i	−0.113945	−	0.0827860i	0.529353	−	0.848401i	$-0.322435\pi$
$101$	−1.14513	−	0.831989i	−0.113945	−	0.0827860i	−0.643299	+	0.765615i	$0.722435\pi$
$102$		0			0
$103$	0.840536	+	2.58690i	0.0828205	+	0.254895i	0.983889	−	0.178782i	$-0.0572157\pi$
$103$	0.840536	+	2.58690i	0.0828205	+	0.254895i	−0.901068	+	0.433677i	$0.857216\pi$
$104$	30.4682	−	22.1365i	2.98766	−	2.17066i
$105$		0			0
$106$	−9.23393	+	28.4191i	−0.896879	+	2.76031i
$107$	−3.31094	−	2.40554i	−0.320081	−	0.232553i	0.416129	−	0.909306i	$-0.363386\pi$
$107$	−3.31094	−	2.40554i	−0.320081	−	0.232553i	−0.736210	+	0.676753i	$0.763386\pi$
$108$		0			0
$109$	−6.10846	+	18.7999i	−0.585085	+	1.80071i	0.0138455	+	0.999904i	$0.495593\pi$
$109$	−6.10846	+	18.7999i	−0.585085	+	1.80071i	−0.598930	+	0.800801i	$0.704407\pi$
$110$	32.8554	+	23.8709i	3.13264	+	2.27600i
$111$		0			0
$112$	−10.0289	−	30.8657i	−0.947638	−	2.91653i
$113$	0.164716	−	0.119673i	0.0154952	−	0.0112579i	−0.580011	−	0.814609i	$-0.696952\pi$
$113$	0.164716	−	0.119673i	0.0154952	−	0.0112579i	0.595506	+	0.803351i	$0.296952\pi$
$114$		0			0
$115$	−6.32829	−	4.59777i	−0.590116	−	0.428745i
$116$	−9.62447	−	6.99259i	−0.893610	−	0.649246i
$117$		0			0
$118$	−9.60668			−0.884367
$119$	9.07068			0.831508
$120$		0			0
$121$	2.58561	−	7.95768i	0.235055	−	0.723426i
$122$	−7.85175	−	24.1652i	−0.710864	−	2.18781i
$123$		0			0
$124$	8.80527	−	28.0277i	0.790736	−	2.51696i
$125$	−5.82711			−0.521193
$126$		0			0
$127$	3.20567	−	9.86605i	0.284458	−	0.875471i	−0.702103	−	0.712075i	$-0.747755\pi$
$127$	3.20567	−	9.86605i	0.284458	−	0.875471i	0.986561	−	0.163395i	$-0.0522446\pi$
$128$	−19.5597	+	14.2110i	−1.72885	+	1.25608i
$129$		0			0
$130$	39.3218			3.44875
$131$	5.64165	−	4.09890i	0.492913	−	0.358122i	−0.313391	−	0.949624i	$-0.601465\pi$
$131$	5.64165	−	4.09890i	0.492913	−	0.358122i	0.806303	+	0.591502i	$0.201465\pi$
$132$		0			0
$133$	2.84969	+	2.07042i	0.247100	+	0.179529i
$134$	7.32508	+	22.5443i	0.632791	+	1.94753i
$135$		0			0
$136$	−10.1438	−	31.2194i	−0.869823	−	2.67704i
$137$	0.683838	−	2.10464i	0.0584242	−	0.179811i	−0.917585	−	0.397539i	$-0.869864\pi$
$137$	0.683838	−	2.10464i	0.0584242	−	0.179811i	0.976010	+	0.217728i	$0.0698644\pi$
$138$		0			0
$139$	0.500753	−	1.54116i	0.0424733	−	0.130719i	−0.927571	−	0.373646i	$-0.878107\pi$
$139$	0.500753	−	1.54116i	0.0424733	−	0.130719i	0.970045	+	0.242927i	$0.0781075\pi$
$140$	13.6231	−	41.9277i	1.15137	−	3.54354i
$141$		0			0
$142$	1.90700	−	5.86915i	0.160032	−	0.492528i
$143$	−5.79473	−	17.8344i	−0.484580	−	1.49138i
$144$		0			0
$145$	−2.38347	−	7.33557i	−0.197937	−	0.609186i
$146$	13.2922	+	9.65738i	1.10007	+	0.799250i
$147$		0			0
$148$	−11.0386	+	8.02000i	−0.907366	+	0.659240i
$149$	−18.3673			−1.50471			−0.752353	−	0.658760i	$-0.771081\pi$
$149$	−18.3673			−1.50471			−0.752353	+	0.658760i	$0.771081\pi$
$150$		0			0
$151$	13.1446	−	9.55010i	1.06969	−	0.777176i	0.0938343	−	0.995588i	$-0.470088\pi$
$151$	13.1446	−	9.55010i	1.06969	−	0.777176i	0.975857	+	0.218412i	$0.0700876\pi$
$152$	3.93914	−	12.1234i	0.319506	−	0.983339i
$153$		0			0
$154$	−28.9927			−2.33630
$155$	15.2997	−	11.3456i	1.22890	−	0.911304i
$156$		0			0
$157$	−1.60288	−	4.93314i	−0.127923	−	0.393708i	0.866499	−	0.499179i	$-0.166365\pi$
$157$	−1.60288	−	4.93314i	−0.127923	−	0.393708i	−0.994422	+	0.105471i	$0.966365\pi$
$158$	−14.0426	+	43.2185i	−1.11717	+	3.43828i
$159$		0			0
$160$	−62.1562			−4.91388
$161$	5.58429			0.440104
$162$		0			0
$163$	0.536492	+	0.389785i	0.0420213	+	0.0305303i	0.608598	−	0.793479i	$-0.291732\pi$
$163$	0.536492	+	0.389785i	0.0420213	+	0.0305303i	−0.566576	+	0.824009i	$0.691732\pi$
$164$	20.3837	+	14.8096i	1.59170	+	1.15644i
$165$		0			0
$166$	15.9611	−	11.5964i	1.23882	−	0.900059i
$167$	4.91940	+	15.1403i	0.380674	+	1.17159i	0.939570	+	0.342357i	$0.111225\pi$
$167$	4.91940	+	15.1403i	0.380674	+	1.17159i	−0.558896	+	0.829238i	$0.688775\pi$
$168$		0			0
$169$	−4.17179	−	3.03099i	−0.320907	−	0.233153i
$170$	10.5912	−	32.5963i	0.812307	−	2.50002i
$171$		0			0
$172$	23.3009	+	16.9291i	1.77668	+	1.29083i
$173$	1.26701	−	3.89946i	0.0963291	−	0.296471i	−0.891269	−	0.453476i	$-0.850184\pi$
$173$	1.26701	−	3.89946i	0.0963291	−	0.296471i	0.987598	+	0.157005i	$0.0501839\pi$
$174$		0			0
$175$	13.2447	−	9.62284i	1.00120	−	0.727418i
$176$	18.0714	+	55.6180i	1.36218	+	4.19236i
$177$		0			0
$178$	31.1013	+	22.5964i	2.33114	+	1.69367i
$179$	2.46602	−	1.79167i	0.184319	−	0.133916i	−0.491799	−	0.870708i	$-0.663661\pi$
$179$	2.46602	−	1.79167i	0.184319	−	0.133916i	0.676119	+	0.736793i	$0.263661\pi$
$180$		0			0
$181$	−21.1703			−1.57357			−0.786787	−	0.617225i	$-0.788257\pi$
$181$	−21.1703			−1.57357			−0.786787	+	0.617225i	$0.788257\pi$
$182$	−22.7107	+	16.5003i	−1.68343	+	1.22308i
$183$		0			0
$184$	−6.24495	−	19.2200i	−0.460384	−	1.41691i
$185$	−8.84635			−0.650396
$186$		0			0
$187$	−16.3448			−1.19525
$188$	−0.368190	−	1.13317i	−0.0268530	−	0.0826450i
$189$		0			0
$190$	10.7676	−	7.82315i	0.781167	−	0.567551i
$191$	26.4740			1.91559			0.957796	−	0.287450i	$-0.0928075\pi$
$191$	26.4740			1.91559			0.957796	+	0.287450i	$0.0928075\pi$
$192$		0			0
$193$	−11.0345	+	8.01701i	−0.794279	+	0.577077i	−0.909230	−	0.416294i	$-0.863329\pi$
$193$	−11.0345	+	8.01701i	−0.794279	+	0.577077i	0.114951	+	0.993371i	$0.463329\pi$
$194$	−34.7259	−	25.2299i	−2.49318	−	1.81140i
$195$		0			0
$196$	−1.68811	−	5.19547i	−0.120579	−	0.371105i
$197$	−2.83782	+	2.06179i	−0.202186	+	0.146897i	−0.684271	−	0.729228i	$-0.739880\pi$
$197$	−2.83782	+	2.06179i	−0.202186	+	0.146897i	0.482085	+	0.876124i	$0.339880\pi$
$198$		0			0
$199$	−1.63949	+	5.04582i	−0.116220	+	0.357689i	−0.992200	−	0.124660i	$-0.960216\pi$
$199$	−1.63949	+	5.04582i	−0.116220	+	0.357689i	0.875979	+	0.482348i	$0.160216\pi$
$200$	−47.9314	−	34.8242i	−3.38926	−	2.46244i
$201$		0			0
$202$	1.17989	−	3.63134i	0.0830170	−	0.255500i
$203$	4.45476	+	3.23657i	0.312663	+	0.227163i
$204$		0			0
$205$	5.04797	+	15.5361i	0.352566	+	1.08509i
$206$	−5.93599	+	4.31275i	−0.413580	+	0.300483i
$207$		0			0
$208$	45.8090	+	33.2822i	3.17628	+	2.30770i
$209$	−5.13497	−	3.73077i	−0.355193	−	0.258063i
$210$		0			0
$211$	17.3644			1.19542			0.597709	−	0.801713i	$-0.296078\pi$
$211$	17.3644			1.19542			0.597709	+	0.801713i	$0.296078\pi$
$212$	−58.4506			−4.01441
$213$		0			0
$214$	3.41144	−	10.4993i	0.233201	−	0.717720i
$215$	5.77040	+	17.7595i	0.393538	+	1.21119i
$216$		0			0
$217$	−4.07559	+	12.9729i	−0.276669	+	0.880655i
$218$	−53.3226			−3.61146
$219$		0			0
$220$	−24.5480	+	75.5511i	−1.65503	+	5.09365i
$221$	−12.8033	+	9.30213i	−0.861242	+	0.625729i
$222$		0			0
$223$	−16.1458			−1.08120			−0.540601	−	0.841279i	$-0.681803\pi$
$223$	−16.1458			−1.08120			−0.540601	+	0.841279i	$0.681803\pi$
$224$	35.8989	−	26.0821i	2.39860	−	1.74268i
$225$		0			0
$226$	0.444321	+	0.322818i	0.0295558	+	0.0214735i
$227$	6.74408	+	20.7561i	0.447620	+	1.37763i	0.879585	+	0.475743i	$0.157821\pi$
$227$	6.74408	+	20.7561i	0.447620	+	1.37763i	−0.431964	+	0.901891i	$0.642179\pi$
$228$		0			0
$229$	−2.14965	−	6.61593i	−0.142053	−	0.437193i	0.854568	−	0.519340i	$-0.173822\pi$
$229$	−2.14965	−	6.61593i	−0.142053	−	0.437193i	−0.996620	+	0.0821473i	$0.973822\pi$
$230$	6.52038	−	20.0677i	0.429941	−	1.32322i
$231$		0			0
$232$	6.15783	−	18.9518i	0.404281	−	1.24425i
$233$	−8.50025	+	26.1611i	−0.556870	+	1.71387i	0.134083	+	0.990970i	$0.457191\pi$
$233$	−8.50025	+	26.1611i	−0.556870	+	1.71387i	−0.690953	+	0.722900i	$0.742809\pi$
$234$		0			0
$235$	0.238715	−	0.734690i	0.0155721	−	0.0479259i
$236$	−5.80685	−	17.8717i	−0.377994	−	1.16335i
$237$		0			0
$238$	7.56108	+	23.2706i	0.490112	+	1.50841i
$239$	−15.5327	−	11.2852i	−1.00473	−	0.729978i	−0.0416315	−	0.999133i	$-0.513256\pi$
$239$	−15.5327	−	11.2852i	−1.00473	−	0.729978i	−0.963097	+	0.269155i	$0.913256\pi$
$240$		0			0
$241$	1.81304	−	1.31725i	0.116788	−	0.0848513i	−0.527858	−	0.849333i	$-0.677005\pi$
$241$	1.81304	−	1.31725i	0.116788	−	0.0848513i	0.644646	+	0.764481i	$0.277005\pi$
$242$	22.5705			1.45089
$243$		0			0
$244$	40.2093	−	29.2138i	2.57414	−	1.87022i
$245$	1.09448	−	3.36847i	0.0699240	−	0.215204i
$246$		0			0
$247$	−6.14560			−0.391035
$248$	49.2076	−	0.480299i	3.12469	−	0.0304990i
$249$		0			0
$250$	−4.85732	−	14.9493i	−0.307204	−	0.945477i
$251$	6.49446	−	19.9879i	0.409927	−	1.26162i	−0.506784	−	0.862073i	$-0.669166\pi$
$251$	6.49446	−	19.9879i	0.409927	−	1.26162i	0.916711	−	0.399552i	$-0.130834\pi$
$252$		0			0
$253$	−10.0625			−0.632627
$254$	27.9833			1.75583
$255$		0			0
$256$	−16.4638	−	11.9616i	−1.02899	−	0.747602i
$257$	−7.69610	−	5.59155i	−0.480070	−	0.348791i	0.321283	−	0.946983i	$-0.395886\pi$
$257$	−7.69610	−	5.59155i	−0.480070	−	0.348791i	−0.801353	+	0.598192i	$0.795886\pi$
$258$		0			0
$259$	5.10929	−	3.71212i	0.317476	−	0.230660i
$260$	23.7685	+	73.1518i	1.47406	+	4.53668i
$261$		0			0
$262$	15.2183	+	11.0568i	0.940192	+	0.683089i
$263$	−1.71112	+	5.26628i	−0.105512	+	0.324733i	−0.989850	−	0.142114i	$-0.954610\pi$
$263$	−1.71112	+	5.26628i	−0.105512	+	0.324733i	0.884338	+	0.466847i	$0.154610\pi$
$264$		0			0
$265$	−30.6588	−	22.2749i	−1.88336	−	1.36834i
$266$	−2.93619	+	9.03667i	−0.180029	+	0.554074i
$267$		0			0
$268$	−37.5122	+	27.2542i	−2.29142	+	1.66482i
$269$	6.37952	+	19.6342i	0.388966	+	1.19712i	0.933562	+	0.358416i	$0.116683\pi$
$269$	6.37952	+	19.6342i	0.388966	+	1.19712i	−0.544595	+	0.838699i	$0.683317\pi$
$270$		0			0
$271$	−2.82483	−	2.05236i	−0.171596	−	0.124672i	0.498672	−	0.866790i	$-0.333821\pi$
$271$	−2.82483	−	2.05236i	−0.171596	−	0.124672i	−0.670268	+	0.742119i	$0.733821\pi$
$272$	39.9282	−	29.0095i	2.42100	−	1.75896i
$273$		0			0
$274$	5.96942			0.360626
$275$	−23.8661	+	17.3397i	−1.43918	+	1.04563i
$276$		0			0
$277$	5.76053	+	17.7291i	0.346117	+	1.06524i	0.960983	+	0.276607i	$0.0892099\pi$
$277$	5.76053	+	17.7291i	0.346117	+	1.06524i	−0.614867	+	0.788631i	$0.710790\pi$
$278$	4.37122			0.262168
$279$		0			0
$280$	73.8449			4.41308
$281$	−3.66847	−	11.2904i	−0.218842	−	0.673528i	−0.998858	−	0.0477682i	$-0.984789\pi$
$281$	−3.66847	−	11.2904i	−0.218842	−	0.673528i	0.780016	−	0.625760i	$-0.215211\pi$
$282$		0			0
$283$	7.68760	−	5.58537i	0.456981	−	0.332016i	−0.335365	−	0.942088i	$-0.608860\pi$
$283$	7.68760	−	5.58537i	0.456981	−	0.332016i	0.792346	+	0.610072i	$0.208860\pi$
$284$	12.0713			0.716299
$285$		0			0
$286$	40.9232	−	29.7325i	2.41984	−	1.75812i
$287$	−9.43477	−	6.85476i	−0.556917	−	0.404624i
$288$		0			0
$289$	−0.990689	−	3.04903i	−0.0582758	−	0.179354i
$290$	16.8324	−	12.2295i	0.988434	−	0.718140i
$291$		0			0
$292$	−9.93134	+	30.5655i	−0.581188	+	1.78871i
$293$	−6.86084	−	4.98469i	−0.400815	−	0.291209i	0.369058	−	0.929406i	$-0.379680\pi$
$293$	−6.86084	−	4.98469i	−0.400815	−	0.291209i	−0.769873	+	0.638197i	$0.779680\pi$
$294$		0			0
$295$	3.76486	−	11.5871i	0.219199	−	0.674625i
$296$	−18.4901	−	13.4338i	−1.07471	−	0.780826i
$297$		0			0
$298$	−15.3105	−	47.1208i	−0.886911	−	2.72963i
$299$	−7.88224	+	5.72678i	−0.455841	+	0.331188i
$300$		0			0
$301$	−10.7850	−	7.83577i	−0.621637	−	0.451646i
$302$	35.4575	+	25.7614i	2.04035	+	1.48240i
$303$		0			0
$304$	19.1656			1.09922
$305$	32.2239			1.84513
$306$		0			0
$307$	2.40408	−	7.39899i	0.137208	−	0.422283i	−0.858719	−	0.512447i	$-0.828739\pi$
$307$	2.40408	−	7.39899i	0.137208	−	0.422283i	0.995927	+	0.0901640i	$0.0287391\pi$
$308$	−17.5249	−	53.9361i	−0.998575	−	3.07330i
$309$		0			0
$310$	41.8603	+	29.7935i	2.37751	+	1.69215i
$311$	−0.451108			−0.0255800			−0.0127900	−	0.999918i	$-0.504071\pi$
$311$	−0.451108			−0.0255800			−0.0127900	+	0.999918i	$0.504071\pi$
$312$		0			0
$313$	6.58174	−	20.2565i	0.372022	−	1.14497i	−0.573444	−	0.819245i	$-0.694393\pi$
$313$	6.58174	−	20.2565i	0.372022	−	1.14497i	0.945466	−	0.325721i	$-0.105607\pi$
$314$	11.3197	−	8.22427i	0.638810	−	0.464123i
$315$		0			0
$316$	−88.8891			−5.00040
$317$	−12.7909	+	9.29313i	−0.718408	+	0.521954i	−0.885875	−	0.463924i	$-0.846441\pi$
$317$	−12.7909	+	9.29313i	−0.718408	+	0.521954i	0.167467	+	0.985878i	$0.446441\pi$
$318$		0			0
$319$	−8.02720	−	5.83210i	−0.449437	−	0.326535i
$320$	−23.7159	−	72.9900i	−1.32576	−	4.08026i
$321$		0			0
$322$	4.65492	+	14.3264i	0.259408	+	0.798377i
$323$	−1.65529	+	5.09447i	−0.0921030	+	0.283464i
$324$		0			0
$325$	−8.82654	+	27.1653i	−0.489608	+	1.50686i
$326$	−0.552777	+	1.70127i	−0.0306155	+	0.0942247i
$327$		0			0
$328$	−13.0417	+	40.1382i	−0.720107	+	2.21626i
$329$	0.170419	+	0.524497i	0.00939552	+	0.0289165i
$330$		0			0
$331$	1.85694	+	5.71506i	0.102066	+	0.314128i	0.989031	−	0.147710i	$-0.0471902\pi$
$331$	1.85694	+	5.71506i	0.102066	+	0.314128i	−0.886964	+	0.461838i	$0.847190\pi$
$332$	31.2211	+	22.6835i	1.71348	+	1.24492i
$333$		0			0
$334$	−34.7415	+	25.2412i	−1.90097	+	1.38114i
$335$	−30.0624			−1.64248
$336$		0			0
$337$	0.460745	−	0.334751i	0.0250984	−	0.0182350i	−0.575165	−	0.818037i	$-0.695062\pi$
$337$	0.460745	−	0.334751i	0.0250984	−	0.0182350i	0.600264	+	0.799802i	$0.295062\pi$
$338$	4.29842	−	13.2292i	0.233803	−	0.719573i
$339$		0			0
$340$	67.0420			3.63586
$341$	7.34395	−	23.3763i	0.397697	−	1.26590i
$342$		0			0
$343$	6.06428	+	18.6639i	0.327440	+	1.00776i
$344$	−14.9081	+	45.8825i	−0.803793	+	2.47382i
$345$		0			0
$346$	11.0601			0.594596
$347$	23.5963			1.26671			0.633357	−	0.773859i	$-0.281676\pi$
$347$	23.5963			1.26671			0.633357	+	0.773859i	$0.281676\pi$
$348$		0			0
$349$	9.68006	+	7.03297i	0.518162	+	0.376466i	0.815911	−	0.578178i	$-0.196236\pi$
$349$	9.68006	+	7.03297i	0.518162	+	0.376466i	−0.297749	+	0.954644i	$0.596236\pi$
$350$	35.7276	+	25.9576i	1.90972	+	1.38749i
$351$		0			0
$352$	−64.6876	+	46.9983i	−3.44786	+	2.50502i
$353$	−2.99151	−	9.20694i	−0.159222	−	0.490036i	0.839342	−	0.543604i	$-0.182941\pi$
$353$	−2.99151	−	9.20694i	−0.159222	−	0.490036i	−0.998564	+	0.0535681i	$0.982941\pi$
$354$		0			0
$355$	6.33169	+	4.60024i	0.336051	+	0.244155i
$356$	−23.2374	+	71.5174i	−1.23158	+	3.79042i
$357$		0			0
$358$	6.65209	+	4.83303i	0.351574	+	0.255433i
$359$	−8.03812	+	24.7388i	−0.424236	+	1.30566i	0.479488	+	0.877548i	$0.340822\pi$
$359$	−8.03812	+	24.7388i	−0.424236	+	1.30566i	−0.903724	+	0.428115i	$0.859178\pi$
$360$		0			0
$361$	13.6885	−	9.94524i	0.720445	−	0.523434i
$362$	−17.6470	−	54.3118i	−0.927504	−	2.85456i
$363$		0			0
$364$	−44.4238	−	32.2757i	−2.32844	−	1.69171i
$365$	−16.8574	+	12.2476i	−0.882359	+	0.641071i
$366$		0			0
$367$	−27.2442			−1.42213			−0.711067	−	0.703124i	$-0.751788\pi$
$367$	−27.2442			−1.42213			−0.711067	+	0.703124i	$0.751788\pi$
$368$	24.5814	−	17.8595i	1.28140	−	0.930989i
$369$		0			0
$370$	−7.37408	−	22.6951i	−0.383360	−	1.17986i
$371$	27.0543			1.40459
$372$		0			0
$373$	8.99458			0.465722			0.232861	−	0.972510i	$-0.425191\pi$
$373$	8.99458			0.465722			0.232861	+	0.972510i	$0.425191\pi$
$374$	−13.6246	−	41.9322i	−0.704511	−	2.16826i
$375$		0			0
$376$	1.61463	−	1.17310i	0.0832681	−	0.0604978i
$377$	−9.60706			−0.494789
$378$		0			0
$379$	11.9495	−	8.68183i	0.613805	−	0.445956i	−0.236947	−	0.971523i	$-0.576147\pi$
$379$	11.9495	−	8.68183i	0.613805	−	0.445956i	0.850752	+	0.525567i	$0.176147\pi$
$380$	21.0623	+	15.3026i	1.08047	+	0.785009i
$381$		0			0
$382$	22.0680	+	67.9184i	1.12910	+	3.47501i
$383$	−14.0629	+	10.2173i	−0.718582	+	0.522080i	−0.885931	−	0.463817i	$-0.846479\pi$
$383$	−14.0629	+	10.2173i	−0.718582	+	0.522080i	0.167349	+	0.985898i	$0.446479\pi$
$384$		0			0
$385$	11.3622	−	34.9694i	0.579074	−	1.78221i
$386$	−29.7655	−	21.6259i	−1.51502	−	1.10073i
$387$		0			0
$388$	25.9456	−	79.8523i	1.31719	−	4.05389i
$389$	19.1838	+	13.9378i	0.972657	+	0.706677i	0.956056	−	0.293186i	$-0.0947154\pi$
$389$	19.1838	+	13.9378i	0.972657	+	0.706677i	0.0166013	+	0.999862i	$0.494715\pi$
$390$		0			0
$391$	2.62424	+	8.07657i	0.132713	+	0.408449i
$392$	7.40290	−	5.37852i	0.373903	−	0.271656i
$393$		0			0
$394$	−7.65501	−	5.56169i	−0.385654	−	0.280194i
$395$	−46.6246	−	33.8747i	−2.34594	−	1.70442i
$396$		0			0
$397$	−12.9547			−0.650176			−0.325088	−	0.945684i	$-0.605394\pi$
$397$	−12.9547			−0.650176			−0.325088	+	0.945684i	$0.605394\pi$
$398$	−14.3115			−0.717373
$399$		0			0
$400$	27.5263	−	84.7174i	1.37632	−	4.23587i
$401$	3.44212	+	10.5938i	0.171891	+	0.529027i	0.999478	−	0.0323111i	$-0.0102867\pi$
$401$	3.44212	+	10.5938i	0.171891	+	0.529027i	−0.827587	+	0.561338i	$0.810287\pi$
$402$		0			0
$403$	−7.55117	−	22.4908i	−0.376151	−	1.12035i
$404$	7.46870			0.371582
$405$		0			0
$406$	−4.58998	+	14.1265i	−0.227797	+	0.701086i
$407$	−9.20662	+	6.68900i	−0.456355	+	0.331562i
$408$		0			0
$409$	−1.29793			−0.0641784			−0.0320892	−	0.999485i	$-0.510216\pi$
$409$	−1.29793			−0.0641784			−0.0320892	+	0.999485i	$0.510216\pi$
$410$	−35.6495	+	25.9009i	−1.76060	+	1.27915i
$411$		0			0
$412$	−11.6112	−	8.43605i	−0.572044	−	0.415614i
$413$	2.68775	+	8.27203i	0.132255	+	0.407040i
$414$		0			0
$415$	7.73182	+	23.7961i	0.379540	+	1.16810i
$416$	−23.9238	+	73.6298i	−1.17296	+	3.61000i
$417$		0			0
$418$	5.29083	−	16.2835i	0.258783	−	0.796452i
$419$	0.542898	−	1.67087i	0.0265223	−	0.0816272i	−0.936919	−	0.349546i	$-0.886336\pi$
$419$	0.542898	−	1.67087i	0.0265223	−	0.0816272i	0.963442	+	0.267919i	$0.0863359\pi$
$420$		0			0
$421$	−9.13210	+	28.1057i	−0.445071	+	1.36979i	0.437335	+	0.899299i	$0.355923\pi$
$421$	−9.13210	+	28.1057i	−0.445071	+	1.36979i	−0.882406	+	0.470489i	$0.844077\pi$
$422$	14.4745	+	44.5480i	0.704609	+	2.16856i
$423$		0			0
$424$	−30.2550	−	93.1154i	−1.46931	−	4.52208i
$425$	20.1416	+	14.6337i	0.977012	+	0.709841i
$426$		0			0
$427$	−18.6112	+	13.5218i	−0.900659	+	0.654367i
$428$	21.5944			1.04380
$429$		0			0
$430$	−40.7514	+	29.6076i	−1.96521	+	1.42781i
$431$	11.5400	−	35.5166i	0.555864	−	1.71077i	−0.137786	−	0.990462i	$-0.543999\pi$
$431$	11.5400	−	35.5166i	0.555864	−	1.71077i	0.693650	−	0.720312i	$-0.256001\pi$
$432$		0			0
$433$	31.6910			1.52297			0.761486	−	0.648181i	$-0.224470\pi$
$433$	31.6910			1.52297			0.761486	+	0.648181i	$0.224470\pi$
$434$	−36.6788	+	0.358010i	−1.76064	+	0.0171850i
$435$		0			0
$436$	−32.2313	−	99.1978i	−1.54360	−	4.75071i
$437$	−1.01907	+	3.13637i	−0.0487487	+	0.150033i
$438$		0			0
$439$	5.00816			0.239026			0.119513	−	0.992833i	$-0.461867\pi$
$439$	5.00816			0.239026			0.119513	+	0.992833i	$0.461867\pi$
$440$	−133.064			−6.34357
$441$		0			0
$442$	−34.5368	−	25.0925i	−1.64275	−	1.19353i
$443$	−4.01246	−	2.91522i	−0.190638	−	0.138506i	0.488372	−	0.872635i	$-0.337591\pi$
$443$	−4.01246	−	2.91522i	−0.190638	−	0.138506i	−0.679010	+	0.734129i	$0.737591\pi$
$444$		0			0
$445$	−39.4432	+	28.6571i	−1.86978	+	1.35848i
$446$	−13.4587	−	41.4216i	−0.637288	−	1.96137i
$447$		0			0
$448$	44.3255	+	32.2043i	2.09418	+	1.52151i
$449$	5.44788	−	16.7668i	0.257101	−	0.791276i	−0.736307	−	0.676647i	$-0.763432\pi$
$449$	5.44788	−	16.7668i	0.257101	−	0.791276i	0.993408	−	0.114629i	$-0.0365679\pi$
$450$		0			0
$451$	17.0009	+	12.3518i	0.800539	+	0.581626i
$452$	−0.331976	+	1.02172i	−0.0156148	+	0.0480575i
$453$		0			0
$454$	−47.6277	+	34.6035i	−2.23528	+	1.62402i
$455$	−11.0014	−	33.8589i	−0.515754	−	1.58733i
$456$		0			0
$457$	13.9435	+	10.1305i	0.652250	+	0.473887i	0.864037	−	0.503429i	$-0.167928\pi$
$457$	13.9435	+	10.1305i	0.652250	+	0.473887i	−0.211787	+	0.977316i	$0.567928\pi$
$458$	15.1811	−	11.0297i	0.709367	−	0.515385i
$459$		0			0
$460$	41.2739			1.92440
$461$	27.4264	−	19.9265i	1.27738	−	0.928069i	0.277907	−	0.960608i	$-0.410359\pi$
$461$	27.4264	−	19.9265i	1.27738	−	0.928069i	0.999470	+	0.0325394i	$0.0103594\pi$
$462$		0			0
$463$	−9.23759	−	28.4304i	−0.429307	−	1.32127i	−0.898809	−	0.438340i	$-0.855567\pi$
$463$	−9.23759	−	28.4304i	−0.429307	−	1.32127i	0.469502	−	0.882931i	$-0.344433\pi$
$464$	29.9605			1.39088
$465$		0			0
$466$	−74.2012			−3.43730
$467$	9.21011	+	28.3458i	0.426193	+	1.31169i	0.901847	+	0.432055i	$0.142211\pi$
$467$	9.21011	+	28.3458i	0.426193	+	1.31169i	−0.475654	+	0.879632i	$0.657789\pi$
$468$		0			0
$469$	17.3628	−	12.6148i	0.801740	−	0.582498i
$470$	2.08381			0.0961192
$471$		0			0
$472$	25.4649	−	18.5013i	1.17212	−	0.851593i
$473$	19.4339	+	14.1196i	0.893572	+	0.649218i
$474$		0			0
$475$	2.98758	+	9.19483i	0.137080	+	0.421888i
$476$	−38.7208	+	28.1323i	−1.77476	+	1.28944i
$477$		0			0
$478$	16.0042	−	49.2558i	0.732015	−	2.25291i
$479$	26.4724	+	19.2333i	1.20955	+	0.878792i	0.995190	−	0.0979624i	$-0.0312325\pi$
$479$	26.4724	+	19.2333i	1.20955	+	0.878792i	0.214363	+	0.976754i	$0.431232\pi$
$480$		0			0
$481$	−3.40494	+	10.4793i	−0.155252	+	0.477816i
$482$	4.89066	+	3.55327i	0.222764	+	0.161847i
$483$		0			0
$484$	13.6430	+	41.9887i	0.620135	+	1.90858i
$485$	44.0400	−	31.9969i	1.99975	−	1.45291i
$486$		0			0
$487$	30.0123	+	21.8052i	1.35999	+	0.988090i	0.998446	+	0.0557343i	$0.0177500\pi$
$487$	30.0123	+	21.8052i	1.35999	+	0.988090i	0.361543	+	0.932355i	$0.382250\pi$
$488$	67.3523	+	48.9343i	3.04890	+	2.21515i
$489$		0			0
$490$	9.55406			0.431609
$491$	28.8846			1.30354			0.651772	−	0.758415i	$-0.274026\pi$
$491$	28.8846			1.30354			0.651772	+	0.758415i	$0.274026\pi$
$492$		0			0
$493$	−2.58763	+	7.96389i	−0.116541	+	0.358676i
$494$	−5.12281	−	15.7664i	−0.230486	−	0.709363i
$495$		0			0
$496$	23.5490	+	70.1395i	1.05738	+	3.14935i
$497$	−5.58729			−0.250624
$498$		0			0
$499$	8.26503	−	25.4371i	0.369994	−	1.13872i	−0.576801	−	0.816885i	$-0.695699\pi$
$499$	8.26503	−	25.4371i	0.369994	−	1.13872i	0.946795	−	0.321838i	$-0.104301\pi$
$500$	24.8747	−	18.0725i	1.11243	−	0.808227i
$501$		0			0
$502$	56.6921			2.53029
$503$	−16.8504	+	12.2426i	−0.751324	+	0.545869i	−0.896237	−	0.443576i	$-0.853710\pi$
$503$	−16.8504	+	12.2426i	−0.751324	+	0.545869i	0.144913	+	0.989444i	$0.453710\pi$
$504$		0			0
$505$	3.91752	+	2.84624i	0.174327	+	0.126656i
$506$	−8.38787	−	25.8152i	−0.372886	−	1.14763i
$507$		0			0
$508$	16.9148	+	52.0583i	0.750471	+	2.30971i
$509$	8.79989	−	27.0833i	0.390048	−	1.20044i	−0.542703	−	0.839924i	$-0.682599\pi$
$509$	8.79989	−	27.0833i	0.390048	−	1.20044i	0.932751	−	0.360520i	$-0.117401\pi$
$510$		0			0
$511$	4.59680	−	14.1475i	0.203350	−	0.625848i
$512$	2.02121	−	6.22063i	0.0893255	−	0.274916i
$513$		0			0
$514$	7.92970	−	24.4051i	0.349764	−	1.07646i
$515$	−2.87549	−	8.84983i	−0.126709	−	0.389970i
$516$		0			0
$517$	−0.307085	−	0.945110i	−0.0135056	−	0.0415659i
$518$	13.7823	+	10.0134i	0.605560	+	0.439965i
$519$		0			0
$520$	−104.232	+	75.7291i	−4.57088	+	3.32094i
$521$	−28.2660			−1.23836			−0.619178	−	0.785250i	$-0.712534\pi$
$521$	−28.2660			−1.23836			−0.619178	+	0.785250i	$0.712534\pi$
$522$		0			0
$523$	−13.2651	+	9.63766i	−0.580042	+	0.421425i	−0.838739	−	0.544533i	$-0.816707\pi$
$523$	−13.2651	+	9.63766i	−0.580042	+	0.421425i	0.258697	+	0.965959i	$0.416707\pi$
$524$	−11.3704	+	34.9946i	−0.496719	+	1.52875i
$525$		0			0
$526$	−14.9369			−0.651278
$527$	−20.6779	+	0.201830i	−0.900743	+	0.00879185i
$528$		0			0
$529$	−5.49180	−	16.9020i	−0.238774	−	0.734871i
$530$	31.5894	−	97.2222i	1.37216	−	4.22306i
$531$		0			0
$532$	−18.5860			−0.805807
$533$	20.3469			0.881320
$534$		0			0
$535$	11.3268	+	8.22939i	0.489700	+	0.355788i
$536$	−62.8345	−	45.6520i	−2.71404	−	1.97186i
$537$		0			0
$538$	−45.0531	+	32.7330i	−1.94238	+	1.41122i
$539$	−1.40795	−	4.33323i	−0.0606448	−	0.186645i
$540$		0			0
$541$	25.6223	+	18.6157i	1.10159	+	0.800350i	0.981318	−	0.192392i	$-0.0616244\pi$
$541$	25.6223	+	18.6157i	1.10159	+	0.800350i	0.120269	+	0.992741i	$0.461624\pi$
$542$	2.91057	−	8.95781i	0.125020	−	0.384771i
$543$		0			0
$544$	54.5926	+	39.6638i	2.34064	+	1.70057i
$545$	20.8971	−	64.3148i	0.895135	−	2.75494i
$546$		0			0
$547$	9.68138	−	7.03394i	0.413946	−	0.300749i	−0.361251	−	0.932468i	$-0.617650\pi$
$547$	9.68138	−	7.03394i	0.413946	−	0.300749i	0.775197	+	0.631719i	$0.217650\pi$
$548$	3.60827	+	11.1051i	0.154138	+	0.474387i
$549$		0			0
$550$	−64.3788	−	46.7740i	−2.74512	−	1.99445i
$551$	−2.63074	+	1.91134i	−0.112073	+	0.0814259i
$552$		0			0
$553$	41.1430			1.74958
$554$	−40.6817	+	29.5570i	−1.72840	+	1.25576i
$555$		0			0
$556$	2.64222	+	8.13193i	0.112055	+	0.344871i
$557$	−4.56973			−0.193626			−0.0968129	−	0.995303i	$-0.530865\pi$
$557$	−4.56973			−0.193626			−0.0968129	+	0.995303i	$0.530865\pi$
$558$		0			0
$559$	23.2588			0.983741
$560$	34.3089	+	105.592i	1.44981	+	4.46207i
$561$		0			0
$562$	25.9073	−	18.8227i	1.09283	−	0.793989i
$563$	15.4106			0.649479			0.324740	−	0.945803i	$-0.394723\pi$
$563$	15.4106			0.649479			0.324740	+	0.945803i	$0.394723\pi$
$564$		0			0
$565$	−0.563495	+	0.409403i	−0.0237064	+	0.0172237i
$566$	20.7373	+	15.0665i	0.871654	+	0.633294i
$567$		0			0
$568$	6.24830	+	19.2303i	0.262173	+	0.806884i
$569$	−20.8234	+	15.1291i	−0.872962	+	0.634244i	−0.931380	−	0.364048i	$-0.881394\pi$
$569$	−20.8234	+	15.1291i	−0.872962	+	0.634244i	0.0584178	+	0.998292i	$0.481394\pi$
$570$		0			0
$571$	2.30114	−	7.08218i	0.0962997	−	0.296380i	−0.891291	−	0.453433i	$-0.850199\pi$
$571$	2.30114	−	7.08218i	0.0962997	−	0.296380i	0.987590	+	0.157053i	$0.0501992\pi$
$572$	80.0488	+	58.1589i	3.34701	+	2.43174i
$573$		0			0
$574$	9.72114	−	29.9186i	0.405753	−	1.24878i
$575$	12.4000	+	9.00914i	0.517117	+	0.375707i
$576$		0			0
$577$	−5.64548	−	17.3750i	−0.235025	−	0.723331i	−0.997118	−	0.0758644i	$-0.975828\pi$
$577$	−5.64548	−	17.3750i	−0.235025	−	0.723331i	0.762094	−	0.647467i	$-0.224172\pi$
$578$	6.99639	−	5.08317i	0.291011	−	0.211432i
$579$		0			0
$580$	32.9254	+	23.9217i	1.36715	+	0.993296i
$581$	−14.4509	−	10.4992i	−0.599526	−	0.435581i
$582$		0			0
$583$	−48.7502			−2.01903
$584$	−53.8333			−2.22764
$585$		0			0
$586$	7.06909	−	21.7564i	0.292021	−	0.898750i
$587$	−8.67618	−	26.7025i	−0.358104	−	1.10213i	−0.954188	−	0.299209i	$-0.903277\pi$
$587$	−8.67618	−	26.7025i	−0.358104	−	1.10213i	0.596084	−	0.802922i	$-0.296723\pi$
$588$		0			0
$589$	−6.54235	−	4.65641i	−0.269573	−	0.191864i
$590$	32.8646			1.35301
$591$		0			0
$592$	10.6186	−	32.6807i	0.436422	−	1.34317i
$593$	−9.90569	+	7.19690i	−0.406778	+	0.295541i	−0.772296	−	0.635263i	$-0.780892\pi$
$593$	−9.90569	+	7.19690i	−0.406778	+	0.295541i	0.365518	+	0.930804i	$0.380892\pi$
$594$		0			0
$595$	−31.0309			−1.27214
$596$	78.4059	−	56.9652i	3.21163	−	2.33339i
$597$		0			0
$598$	−21.2623	−	15.4480i	−0.869481	−	0.631715i
$599$	9.96225	+	30.6607i	0.407047	+	1.25276i	0.919174	+	0.393851i	$0.128858\pi$
$599$	9.96225	+	30.6607i	0.407047	+	1.25276i	−0.512127	+	0.858909i	$0.671142\pi$
$600$		0			0
$601$	−2.76289	−	8.50331i	−0.112701	−	0.346857i	0.878760	−	0.477264i	$-0.158372\pi$
$601$	−2.76289	−	8.50331i	−0.112701	−	0.346857i	−0.991461	+	0.130407i	$0.958372\pi$
$602$	11.1124	−	34.2003i	0.452906	−	1.39390i
$603$		0			0
$604$	−26.4922	+	81.5346i	−1.07795	+	3.31759i
$605$	−8.84540	+	27.2233i	−0.359617	+	1.10679i
$606$		0			0
$607$	10.6530	−	32.7866i	0.432392	−	1.33077i	−0.463343	−	0.886179i	$-0.653350\pi$
$607$	10.6530	−	32.7866i	0.432392	−	1.33077i	0.895735	−	0.444588i	$-0.146650\pi$
$608$	8.09765	+	24.9220i	0.328403	+	1.01072i
$609$		0			0
$610$	26.8609	+	82.6695i	1.08757	+	3.34719i
$611$	−0.778427	−	0.565560i	−0.0314918	−	0.0228801i
$612$		0			0
$613$	12.8454	−	9.33274i	0.518822	−	0.376946i	−0.297338	−	0.954772i	$-0.596099\pi$
$613$	12.8454	−	9.33274i	0.518822	−	0.376946i	0.816160	+	0.577826i	$0.196099\pi$
$614$	20.9859			0.846922
$615$		0			0
$616$	76.8523	−	55.8365i	3.09647	−	2.24972i
$617$	2.29259	−	7.05587i	0.0922962	−	0.284059i	−0.894243	−	0.447581i	$-0.852286\pi$
$617$	2.29259	−	7.05587i	0.0922962	−	0.284059i	0.986540	+	0.163522i	$0.0522856\pi$
$618$		0			0
$619$	38.1293			1.53255			0.766273	−	0.642516i	$-0.222109\pi$
$619$	38.1293			1.53255			0.766273	+	0.642516i	$0.222109\pi$
$620$	−30.1229	+	95.8832i	−1.20977	+	3.85076i
$621$		0			0
$622$	−0.376032	−	1.15731i	−0.0150775	−	0.0464038i
$623$	10.7556	−	33.1024i	0.430915	−	1.32622i
$624$		0			0
$625$	−13.5820			−0.543281
$626$	57.4539			2.29632
$627$		0			0
$628$	22.1422	+	16.0873i	0.883571	+	0.641952i
$629$	7.76986	+	5.64513i	0.309805	+	0.225086i
$630$		0			0
$631$	−8.36095	+	6.07458i	−0.332844	+	0.241825i	−0.741636	−	0.670802i	$-0.765950\pi$
$631$	−8.36095	+	6.07458i	−0.332844	+	0.241825i	0.408792	+	0.912627i	$0.365950\pi$
$632$	−46.0105	−	141.606i	−1.83020	−	5.63277i
$633$		0			0
$634$	−34.5034	−	25.0682i	−1.37031	−	0.995586i
$635$	−10.9667	+	33.7519i	−0.435198	+	1.33940i
$636$		0			0
$637$	−3.56901	−	2.59303i	−0.141409	−	0.102740i
$638$	8.27085	−	25.4551i	0.327446	−	1.00778i
$639$		0			0
$640$	66.9141	−	48.6159i	2.64501	−	1.92171i
$641$	8.78897	+	27.0497i	0.347143	+	1.06840i	0.960426	+	0.278534i	$0.0898486\pi$
$641$	8.78897	+	27.0497i	0.347143	+	1.06840i	−0.613283	+	0.789863i	$0.710151\pi$
$642$		0			0
$643$	19.6705	+	14.2914i	0.775728	+	0.563599i	0.903694	−	0.428179i	$-0.140845\pi$
$643$	19.6705	+	14.2914i	0.775728	+	0.563599i	−0.127966	+	0.991779i	$0.540845\pi$
$644$	−23.8381	+	17.3194i	−0.939353	+	0.682480i
$645$		0			0
$646$	−14.4495			−0.568510
$647$	−5.55924	+	4.03903i	−0.218556	+	0.158791i	−0.691677	−	0.722207i	$-0.743128\pi$
$647$	−5.55924	+	4.03903i	−0.218556	+	0.158791i	0.473120	+	0.880998i	$0.343128\pi$
$648$		0			0
$649$	−4.84315	−	14.9057i	−0.190110	−	0.585099i
$650$	−77.0494			−3.02213
$651$		0			0
$652$	−3.49907			−0.137034
$653$	−7.79912	−	24.0032i	−0.305203	−	0.939319i	−0.979601	−	0.200951i	$-0.935597\pi$
$653$	−7.79912	−	24.0032i	−0.305203	−	0.939319i	0.674398	−	0.738368i	$-0.264403\pi$
$654$		0			0
$655$	−19.3001	+	14.0224i	−0.754119	+	0.547900i
$656$	−63.4535			−2.47744
$657$		0			0
$658$	−1.20353	+	0.874413i	−0.0469183	+	0.0340882i
$659$	−2.48445	−	1.80506i	−0.0967806	−	0.0703152i	0.538343	−	0.842726i	$-0.319051\pi$
$659$	−2.48445	−	1.80506i	−0.0967806	−	0.0703152i	−0.635123	+	0.772411i	$0.719051\pi$
$660$		0			0
$661$	−10.8178	−	33.2938i	−0.420764	−	1.29498i	−0.906992	−	0.421147i	$-0.861628\pi$
$661$	−10.8178	−	33.2938i	−0.420764	−	1.29498i	0.486228	−	0.873832i	$-0.338372\pi$
$662$	−13.1139	+	9.52784i	−0.509688	+	0.370310i
$663$		0			0
$664$	−19.9756	+	61.4785i	−0.775202	+	2.38583i
$665$	−9.74884	−	7.08295i	−0.378044	−	0.274665i
$666$		0			0
$667$	−1.59305	+	4.90291i	−0.0616832	+	0.189841i
$668$	−67.9569	−	49.3735i	−2.62933	−	1.91032i
$669$		0			0
$670$	−25.0592	−	77.1243i	−0.968121	−	2.97957i
$671$	33.5362	−	24.3655i	1.29465	−	0.940619i
$672$		0			0
$673$	29.7311	+	21.6009i	1.14605	+	0.832654i	0.987951	−	0.154770i	$-0.0494635\pi$
$673$	29.7311	+	21.6009i	1.14605	+	0.832654i	0.158099	+	0.987423i	$0.449464\pi$
$674$	1.24286	+	0.902991i	0.0478732	+	0.0347819i
$675$		0			0
$676$	27.2089			1.04650
$677$	−21.4827			−0.825648			−0.412824	−	0.910811i	$-0.635458\pi$
$677$	−21.4827			−0.825648			−0.412824	+	0.910811i	$0.635458\pi$
$678$		0			0
$679$	−12.0091	+	36.9603i	−0.460868	+	1.41840i
$680$	34.7021	+	106.802i	1.33076	+	4.09567i
$681$		0			0
$682$	66.0929	−	0.645111i	2.53083	−	0.0247026i
$683$	−2.76928			−0.105963			−0.0529817	−	0.998595i	$-0.516872\pi$
$683$	−2.76928			−0.105963			−0.0529817	+	0.998595i	$0.516872\pi$
$684$		0			0
$685$	−2.33942	+	7.19999i	−0.0893845	+	0.275097i
$686$	−42.8268	+	31.1155i	−1.63513	+	1.18800i
$687$		0			0
$688$	−72.5345			−2.76535
$689$	−38.1872	+	27.7446i	−1.45482	+	1.05699i
$690$		0			0
$691$	−15.4232	−	11.2056i	−0.586725	−	0.426280i	0.254418	−	0.967094i	$-0.418116\pi$
$691$	−15.4232	−	11.2056i	−0.586725	−	0.426280i	−0.841142	+	0.540814i	$0.818116\pi$
$692$	6.68539	+	20.5755i	0.254141	+	0.782164i
$693$		0			0
$694$	19.6692	+	60.5357i	0.746634	+	2.29790i
$695$	−1.71308	+	5.27232i	−0.0649809	+	0.199991i
$696$		0			0
$697$	5.48035	−	16.8668i	0.207583	−	0.638875i
$698$	−9.97388	+	30.6964i	−0.377517	+	1.16188i
$699$		0			0
$700$	−26.6940	+	82.1556i	−1.00894	+	3.10519i
$701$	−13.6860	−	42.1211i	−0.516912	−	1.59089i	−0.779777	−	0.626058i	$-0.784667\pi$
$701$	−13.6860	−	42.1211i	−0.516912	−	1.59089i	0.262865	−	0.964833i	$-0.415333\pi$
$702$		0			0
$703$	1.15249	+	3.54701i	0.0434671	+	0.133778i
$704$	−79.8717	−	58.0302i	−3.01028	−	2.18710i
$705$		0			0
$706$	21.1265	−	15.3493i	0.795107	−	0.577679i
$707$	−3.45695			−0.130012
$708$		0			0
$709$	−14.9450	+	10.8582i	−0.561271	+	0.407787i	−0.831924	−	0.554890i	$-0.812760\pi$
$709$	−14.9450	+	10.8582i	−0.561271	+	0.407787i	0.270653	+	0.962677i	$0.412760\pi$
$710$	−6.52387	+	20.0784i	−0.244837	+	0.753530i
$711$		0			0
$712$	−125.960			−4.72054
$713$	−12.7302	+	0.124255i	−0.476749	+	0.00465339i
$714$		0			0
$715$	19.8239	+	61.0115i	0.741370	+	2.28170i
$716$	−4.97013	+	15.2965i	−0.185742	+	0.571657i
$717$		0			0
$718$	−70.1671			−2.61861
$719$	18.7959			0.700970			0.350485	−	0.936568i	$-0.386017\pi$
$719$	18.7959			0.700970			0.350485	+	0.936568i	$0.386017\pi$
$720$		0			0
$721$	5.37435	+	3.90469i	0.200151	+	0.145418i
$722$	36.9246	+	26.8273i	1.37419	+	0.998408i
$723$		0			0
$724$	90.3712	−	65.6585i	3.35862	−	2.44018i
$725$	4.67031	+	14.3737i	0.173451	+	0.533827i
$726$		0			0
$727$	−11.6998	−	8.50038i	−0.433921	−	0.315262i	0.349294	−	0.937013i	$-0.386421\pi$
$727$	−11.6998	−	8.50038i	−0.433921	−	0.315262i	−0.783215	+	0.621751i	$0.786421\pi$
$728$	28.4227	−	87.4762i	1.05342	−	3.24208i
$729$		0			0
$730$	−45.4729	−	33.0380i	−1.68303	−	1.22279i
$731$	6.26466	−	19.2806i	0.231707	−	0.713120i
$732$		0			0
$733$	−33.2166	+	24.1333i	−1.22688	+	0.891384i	−0.996653	−	0.0817522i	$-0.973948\pi$
$733$	−33.2166	+	24.1333i	−1.22688	+	0.891384i	−0.230232	+	0.973136i	$0.573948\pi$
$734$	−22.7100	−	69.8942i	−0.838242	−	2.57984i
$735$		0			0
$736$	33.6095	+	24.4187i	1.23886	+	0.900086i
$737$	−31.2867	+	22.7311i	−1.15246	+	0.837312i
$738$		0			0
$739$	6.32146			0.232539			0.116269	−	0.993218i	$-0.462906\pi$
$739$	6.32146			0.232539			0.116269	+	0.993218i	$0.462906\pi$
$740$	37.7631	−	27.4365i	1.38820	−	1.00859i
$741$		0			0
$742$	22.5518	+	69.4072i	0.827901	+	2.54802i
$743$	18.1307			0.665151			0.332575	−	0.943077i	$-0.392082\pi$
$743$	18.1307			0.665151			0.332575	+	0.943077i	$0.392082\pi$
$744$		0			0
$745$	62.8347			2.30208
$746$	7.49764	+	23.0754i	0.274508	+	0.844849i
$747$		0			0
$748$	69.7724	−	50.6926i	2.55113	−	1.85350i
$749$	−9.99512			−0.365214
$750$		0			0
$751$	−2.07835	+	1.51001i	−0.0758401	+	0.0551010i	−0.625059	−	0.780577i	$-0.714925\pi$
$751$	−2.07835	+	1.51001i	−0.0758401	+	0.0551010i	0.549219	+	0.835678i	$0.314925\pi$
$752$	2.42759	+	1.76375i	0.0885252	+	0.0643173i
$753$		0			0
$754$	−8.00819	−	24.6467i	−0.291641	−	0.897579i
$755$	−44.9678	+	32.6710i	−1.63655	+	1.18902i
$756$		0			0
$757$	3.65117	−	11.2371i	0.132704	−	0.408420i	−0.862522	−	0.506020i	$-0.831116\pi$
$757$	3.65117	−	11.2371i	0.132704	−	0.408420i	0.995226	+	0.0975992i	$0.0311163\pi$
$758$	32.2338	+	23.4192i	1.17078	+	0.850625i
$759$		0			0
$760$	−13.4758	+	41.4744i	−0.488820	+	1.50443i
$761$	15.3445	+	11.1484i	0.556238	+	0.404131i	0.830080	−	0.557644i	$-0.188295\pi$
$761$	15.3445	+	11.1484i	0.556238	+	0.404131i	−0.273842	+	0.961775i	$0.588295\pi$
$762$		0			0
$763$	14.9185	+	45.9145i	0.540087	+	1.66222i
$764$	−113.012	+	82.1078i	−4.08862	+	2.97056i
$765$		0			0
$766$	−37.9347	−	27.5612i	−1.37064	−	0.995827i
$767$	−12.2769	−	8.91966i	−0.443292	−	0.322070i
$768$		0			0
$769$	18.9894			0.684776			0.342388	−	0.939559i	$-0.388764\pi$
$769$	18.9894			0.684776			0.342388	+	0.939559i	$0.388764\pi$
$770$	99.1844			3.57436
$771$		0			0
$772$	22.2394	−	68.4458i	0.800413	−	2.46342i
$773$	5.20754	+	16.0271i	0.187302	+	0.576456i	0.999980	−	0.00625611i	$-0.00199139\pi$
$773$	5.20754	+	16.0271i	0.187302	+	0.576456i	−0.812678	+	0.582712i	$0.801991\pi$
$774$		0			0
$775$	−29.9790	+	22.2313i	−1.07688	+	0.798572i
$776$	140.639			5.04866
$777$		0			0
$778$	−19.7661	+	60.8337i	−0.708648	+	2.18100i
$779$	5.57166	−	4.04804i	0.199625	−	0.145036i
$780$		0			0
$781$	10.0679			0.360259
$782$	−18.5327	+	13.4648i	−0.662729	+	0.481501i
$783$		0			0
$784$	11.1303	+	8.08660i	0.397509	+	0.288807i
$785$	5.48346	+	16.8764i	0.195713	+	0.602343i
$786$		0			0
$787$	−16.7851	−	51.6591i	−0.598323	−	1.84145i	−0.537436	−	0.843305i	$-0.680607\pi$
$787$	−16.7851	−	51.6591i	−0.598323	−	1.84145i	−0.0608872	−	0.998145i	$-0.519393\pi$
$788$	5.71946	−	17.6027i	0.203747	−	0.627070i
$789$		0			0
$790$	48.0398	−	147.851i	1.70918	−	5.26031i
$791$	0.153658	−	0.472910i	0.00546344	−	0.0168147i
$792$		0			0
$793$	12.4029	−	38.1721i	0.440439	−	1.35553i
$794$	−10.7987	−	33.2349i	−0.383230	−	1.17946i
$795$		0			0
$796$	−8.65075	−	26.6243i	−0.306618	−	0.943672i
$797$	37.4942	+	27.2411i	1.32811	+	0.964930i	0.999793	+	0.0203635i	$0.00648234\pi$
$797$	37.4942	+	27.2411i	1.32811	+	0.964930i	0.328320	+	0.944567i	$0.393518\pi$
$798$		0			0
$799$	−0.678495	+	0.492955i	−0.0240034	+	0.0174395i
$800$	121.792			4.30601
$801$		0			0
$802$	−24.3088	+	17.6613i	−0.858372	+	0.623644i
$803$	−8.28314	+	25.4929i	−0.292306	+	0.899624i
$804$		0			0
$805$	−19.1039			−0.673325
$806$	51.4051	−	38.1200i	1.81067	−	1.34272i
$807$		0			0
$808$	3.86592	+	11.8981i	0.136003	+	0.418573i
$809$	−6.15288	+	18.9366i	−0.216324	+	0.665777i	0.782733	+	0.622358i	$0.213825\pi$
$809$	−6.15288	+	18.9366i	−0.216324	+	0.665777i	−0.999057	+	0.0434189i	$0.986175\pi$
$810$		0			0
$811$	0.0153026			0.000537349			0.000268674	−	1.00000i	$-0.499914\pi$
$811$	0.0153026			0.000537349			0.000268674		1.00000i	$0.499914\pi$
$812$	−29.0545			−1.01961
$813$		0			0
$814$	−24.8349	−	18.0436i	−0.870462	−	0.632427i
$815$	−1.83535	−	1.33346i	−0.0642894	−	0.0467090i
$816$		0			0
$817$	6.36903	−	4.62737i	0.222824	−	0.161891i
$818$	−1.08192	−	3.32980i	−0.0378284	−	0.116424i
$819$		0			0
$820$	−69.7330	−	50.6640i	−2.43518	−	1.76926i
$821$	4.61374	−	14.1996i	0.161021	−	0.495570i	−0.837701	−	0.546130i	$-0.816101\pi$
$821$	4.61374	−	14.1996i	0.161021	−	0.495570i	0.998721	+	0.0505597i	$0.0161005\pi$
$822$		0			0
$823$	−10.0360	−	7.29155i	−0.349832	−	0.254168i	0.398967	−	0.916965i	$-0.369369\pi$
$823$	−10.0360	−	7.29155i	−0.349832	−	0.254168i	−0.748798	+	0.662798i	$0.769369\pi$
$824$	7.42897	−	22.8640i	0.258800	−	0.796506i
$825$		0			0
$826$	−18.9813	+	13.7907i	−0.660442	+	0.479839i
$827$	−11.6803	−	35.9483i	−0.406164	−	1.25004i	−0.919919	−	0.392108i	$-0.871746\pi$
$827$	−11.6803	−	35.9483i	−0.406164	−	1.25004i	0.513755	−	0.857937i	$-0.328254\pi$
$828$		0			0
$829$	31.7057	+	23.0356i	1.10119	+	0.800058i	0.981253	−	0.192724i	$-0.0617322\pi$
$829$	31.7057	+	23.0356i	1.10119	+	0.800058i	0.119932	+	0.992782i	$0.461732\pi$
$830$	−54.6032	+	39.6716i	−1.89531	+	1.37702i
$831$		0			0
$832$	−95.5916			−3.31404
$833$	−3.11083	+	2.26015i	−0.107784	+	0.0783095i
$834$		0			0
$835$	−16.8293	−	51.7953i	−0.582402	−	1.79245i
$836$	33.4909			1.15831
$837$		0			0
$838$	4.73911			0.163710
$839$	−5.68498	−	17.4966i	−0.196267	−	0.604049i	−0.999959	−	0.00900364i	$-0.997134\pi$
$839$	−5.68498	−	17.4966i	−0.196267	−	0.604049i	0.803692	−	0.595046i	$-0.202866\pi$
$840$		0			0
$841$	19.3490	−	14.0579i	0.667207	−	0.484755i
$842$	−79.7167			−2.74722
$843$		0			0
$844$	−74.1250	+	53.8550i	−2.55149	+	1.85376i
$845$	14.2718	+	10.3690i	0.490964	+	0.356706i
$846$		0			0
$847$	−6.31475	−	19.4348i	−0.216978	−	0.667788i
$848$	119.090	−	86.5241i	4.08957	−	2.97125i
$849$		0			0
$850$	−20.7530	+	63.8711i	−0.711821	+	2.19076i
$851$	4.78345	+	3.47538i	0.163975	+	0.119134i
$852$		0			0
$853$	5.37348	−	16.5379i	0.183984	−	0.566246i	−0.815945	−	0.578130i	$-0.803783\pi$
$853$	5.37348	−	16.5379i	0.183984	−	0.566246i	0.999929	+	0.0118837i	$0.00378279\pi$
$854$	−50.2037	−	36.4751i	−1.71793	−	1.24815i
$855$		0			0
$856$	11.1776	+	34.4011i	0.382043	+	1.17581i
$857$	−38.6055	+	28.0485i	−1.31874	+	0.958119i	−0.318791	+	0.947825i	$0.603277\pi$
$857$	−38.6055	+	28.0485i	−1.31874	+	0.958119i	−0.999947	+	0.0102939i	$0.996723\pi$
$858$		0			0
$859$	17.2981	+	12.5678i	0.590205	+	0.428809i	0.842389	−	0.538870i	$-0.181149\pi$
$859$	17.2981	+	12.5678i	0.590205	+	0.428809i	−0.252184	+	0.967679i	$0.581149\pi$
$860$	−79.7127	−	57.9147i	−2.71818	−	1.97487i
$861$		0			0
$862$	100.736			3.43109
$863$	41.3756			1.40844			0.704221	−	0.709981i	$-0.251297\pi$
$863$	41.3756			1.40844			0.704221	+	0.709981i	$0.251297\pi$
$864$		0			0
$865$	−4.33446	+	13.3401i	−0.147376	+	0.453577i
$866$	26.4168	+	81.3024i	0.897678	+	2.76277i
$867$		0			0
$868$	−22.8369	−	68.0185i	−0.775134	−	2.30870i
$869$	−74.1371			−2.51493
$870$		0			0
$871$	−11.5709	+	35.6117i	−0.392066	+	1.20666i
$872$	141.345	−	102.693i	4.78653	−	3.47762i
$873$		0			0
$874$	−8.89575			−0.300903
$875$	−11.5134	+	8.36500i	−0.389225	+	0.282789i
$876$		0			0
$877$	−29.2994	−	21.2873i	−0.989371	−	0.718820i	−0.0295880	−	0.999562i	$-0.509420\pi$
$877$	−29.2994	−	21.2873i	−0.989371	−	0.718820i	−0.959783	+	0.280742i	$0.909420\pi$
$878$	4.17467	+	12.8483i	0.140888	+	0.433609i
$879$		0			0
$880$	−61.8224	−	190.270i	−2.08403	−	6.41400i
$881$	−12.4104	+	38.1952i	−0.418116	+	1.28683i	0.491318	+	0.870980i	$0.336515\pi$
$881$	−12.4104	+	38.1952i	−0.418116	+	1.28683i	−0.909434	+	0.415848i	$0.863485\pi$
$882$		0			0
$883$	5.59881	−	17.2314i	0.188415	−	0.579881i	−0.811576	−	0.584247i	$-0.801390\pi$
$883$	5.59881	−	17.2314i	0.188415	−	0.579881i	0.999990	+	0.00436603i	$0.00138976\pi$
$884$	25.8043	−	79.4175i	0.867893	−	2.67110i
$885$		0			0
$886$	4.13425	−	12.7239i	0.138893	−	0.427469i
$887$	14.2467	+	43.8469i	0.478358	+	1.47223i	0.841375	+	0.540452i	$0.181747\pi$
$887$	14.2467	+	43.8469i	0.478358	+	1.47223i	−0.363017	+	0.931782i	$0.618253\pi$
$888$		0			0
$889$	−7.82913	−	24.0956i	−0.262580	−	0.808139i
$890$	−106.398	−	77.3026i	−3.56647	−	2.59119i
$891$		0			0
$892$	68.9229	−	50.0754i	2.30771	−	1.67665i
$893$	−0.325679			−0.0108984
$894$		0			0
$895$	−8.43629	+	6.12932i	−0.281994	+	0.204881i
$896$	−18.2466	+	56.1572i	−0.609575	+	1.87608i
$897$		0			0
$898$	47.5561			1.58697
$899$	−10.2273	−	7.27910i	−0.341099	−	0.242772i
$900$		0			0
$901$	12.7137	+	39.1287i	0.423554	+	1.30357i
$902$	−17.5169	+	53.9114i	−0.583249	+	1.79505i
$903$		0			0
$904$	−1.79949			−0.0598502
$905$	72.4237			2.40745
$906$		0			0
$907$	−35.3250	−	25.6651i	−1.17295	−	0.852195i	−0.181588	−	0.983375i	$-0.558124\pi$
$907$	−35.3250	−	25.6651i	−1.17295	−	0.852195i	−0.991359	+	0.131179i	$0.958124\pi$
$908$	−93.1631	−	67.6870i	−3.09173	−	2.24627i
$909$		0			0
$910$	77.6936	−	56.4477i	2.57552	−	1.87122i
$911$	7.29263	+	22.4444i	0.241616	+	0.743616i	0.996175	+	0.0873842i	$0.0278508\pi$
$911$	7.29263	+	22.4444i	0.241616	+	0.743616i	−0.754559	+	0.656232i	$0.772149\pi$
$912$		0			0
$913$	26.0397	+	18.9189i	0.861788	+	0.626126i
$914$	−14.3667	+	44.2163i	−0.475209	+	1.46254i
$915$		0			0
$916$	29.6953	+	21.5749i	0.981162	+	0.712856i
$917$	5.26289	−	16.1975i	0.173796	−	0.534889i
$918$		0			0
$919$	8.70504	−	6.32458i	0.287153	−	0.208629i	−0.434878	−	0.900489i	$-0.643209\pi$
$919$	8.70504	−	6.32458i	0.287153	−	0.208629i	0.722031	+	0.691860i	$0.243209\pi$
$920$	21.3640	+	65.7518i	0.704352	+	2.16777i
$921$		0			0
$922$	73.9828	+	53.7517i	2.43649	+	1.77022i
$923$	7.88646	−	5.72985i	0.259586	−	0.188600i
$924$		0			0
$925$	17.3340			0.569940
$926$	65.2372	−	47.3976i	2.14383	−	1.55758i
$927$		0			0
$928$	12.6586	+	38.9591i	0.415538	+	1.27890i
$929$	−19.4549			−0.638294			−0.319147	−	0.947705i	$-0.603396\pi$
$929$	−19.4549			−0.638294			−0.319147	+	0.947705i	$0.603396\pi$
$930$		0			0
$931$	−1.49320			−0.0489377
$932$	−44.8516	−	138.039i	−1.46916	−	4.52162i
$933$		0			0
$934$	−65.0431	+	47.2566i	−2.12828	+	1.54628i
$935$	55.9158			1.82864
$936$		0			0
$937$	−9.76632	+	7.09565i	−0.319052	+	0.231805i	−0.735771	−	0.677231i	$-0.763180\pi$
$937$	−9.76632	+	7.09565i	−0.319052	+	0.231805i	0.416719	+	0.909035i	$0.363180\pi$
$938$	46.8362	+	34.0285i	1.52926	+	1.11107i
$939$		0			0
$940$	1.25958	+	3.87659i	0.0410830	+	0.126440i
$941$	30.8606	−	22.4215i	1.00603	−	0.730921i	0.0426543	−	0.999090i	$-0.486419\pi$
$941$	30.8606	−	22.4215i	1.00603	−	0.730921i	0.963372	+	0.268169i	$0.0864186\pi$
$942$		0			0
$943$	3.37393	−	10.3839i	0.109870	−	0.338146i
$944$	38.2865	+	27.8167i	1.24612	+	0.905358i
$945$		0			0
$946$	−20.0238	+	61.6269i	−0.651029	+	2.00366i
$947$	26.9043	+	19.5471i	0.874273	+	0.635197i	0.931730	−	0.363151i	$-0.118299\pi$
$947$	26.9043	+	19.5471i	0.874273	+	0.635197i	−0.0574569	+	0.998348i	$0.518299\pi$
$948$		0			0
$949$	8.02009	+	24.6833i	0.260343	+	0.801254i
$950$	−21.0987	+	15.3291i	−0.684533	+	0.497343i
$951$		0			0
$952$	−64.8589	−	47.1228i	−2.10209	−	1.52726i
$953$	2.82149	+	2.04993i	0.0913970	+	0.0664038i	0.632545	−	0.774523i	$-0.282010\pi$
$953$	2.82149	+	2.04993i	0.0913970	+	0.0664038i	−0.541148	+	0.840927i	$0.682010\pi$
$954$		0			0
$955$	−90.5679			−2.93071
$956$	101.306			3.27648
$957$		0			0
$958$	−27.2759	+	83.9465i	−0.881244	+	2.71219i
$959$	−1.67012	−	5.14009i	−0.0539309	−	0.165982i
$960$		0			0
$961$	9.00221	−	29.6641i	0.290394	−	0.956907i
$962$	−29.7227			−0.958298
$963$		0			0
$964$	−3.65407	+	11.2461i	−0.117690	+	0.362212i
$965$	37.7491	−	27.4263i	1.21519	−	0.882884i
$966$		0			0
$967$	−8.79415			−0.282801			−0.141400	−	0.989952i	$-0.545161\pi$
$967$	−8.79415			−0.282801			−0.141400	+	0.989952i	$0.545161\pi$
$968$	−59.8288	+	43.4681i	−1.92297	+	1.39712i
$969$		0			0
$970$	118.798	+	86.3117i	3.81437	+	2.77130i
$971$	5.09820	+	15.6906i	0.163609	+	0.503536i	0.998931	−	0.0462243i	$-0.0147189\pi$
$971$	5.09820	+	15.6906i	0.163609	+	0.503536i	−0.835322	+	0.549761i	$0.814719\pi$
$972$		0			0
$973$	−1.22297	−	3.76393i	−0.0392067	−	0.120666i
$974$	−30.9233	+	95.1721i	−0.990847	+	3.04951i
$975$		0			0
$976$	−38.6795	+	119.043i	−1.23810	+	3.81048i
$977$	−16.9816	+	52.2641i	−0.543290	+	1.67208i	0.181731	+	0.983348i	$0.441830\pi$
$977$	−16.9816	+	52.2641i	−0.543290	+	1.67208i	−0.725021	+	0.688727i	$0.758170\pi$
$978$		0			0
$979$	−19.3810	+	59.6484i	−0.619418	+	1.90637i
$980$	5.77505	+	17.7738i	0.184477	+	0.567762i
$981$		0			0
$982$	24.0774	+	74.1028i	0.768342	+	2.36471i
$983$	−44.0280	−	31.9882i	−1.40427	−	1.02026i	−0.994124	−	0.108247i	$-0.965476\pi$
$983$	−44.0280	−	31.9882i	−1.40427	−	1.02026i	−0.410150	−	0.912018i	$-0.634524\pi$
$984$		0			0
$985$	9.70820	−	7.05342i	0.309329	−	0.224741i
$986$	−22.5881			−0.719353
$987$		0			0
$988$	26.2342	−	19.0603i	0.834622	−	0.606388i
$989$	3.85679	−	11.8700i	0.122639	−	0.377443i
$990$		0			0
$991$	−34.9449			−1.11006			−0.555031	−	0.831830i	$-0.687294\pi$
$991$	−34.9449			−1.11006			−0.555031	+	0.831830i	$0.687294\pi$
$992$	−81.2563	+	60.2566i	−2.57989	+	1.91315i
$993$		0			0
$994$	−4.65741	−	14.3340i	−0.147724	−	0.454648i
$995$	5.60870	−	17.2618i	0.177808	−	0.547236i
$996$		0			0
$997$	−36.9542			−1.17035			−0.585176	−	0.810906i	$-0.698975\pi$
$997$	−36.9542			−1.17035			−0.585176	+	0.810906i	$0.698975\pi$
$998$	72.1479			2.28380
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	279.2.i.d.190.6	yes	24
3.2	odd	2	inner	279.2.i.d.190.1	yes	24
31.8	even	5	inner	279.2.i.d.163.6	yes	24
31.15	odd	10		8649.2.a.bo.1.12		12
31.16	even	5		8649.2.a.bn.1.12		12
93.8	odd	10	inner	279.2.i.d.163.1	✓	24
93.47	odd	10		8649.2.a.bn.1.1		12
93.77	even	10		8649.2.a.bo.1.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
279.2.i.d.163.1	✓	24	93.8	odd	10	inner
279.2.i.d.163.6	yes	24	31.8	even	5	inner
279.2.i.d.190.1	yes	24	3.2	odd	2	inner
279.2.i.d.190.6	yes	24	1.1	even	1	trivial
8649.2.a.bn.1.1		12	93.47	odd	10
8649.2.a.bn.1.12		12	31.16	even	5
8649.2.a.bo.1.1		12	93.77	even	10
8649.2.a.bo.1.12		12	31.15	odd	10

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:	\( N \)	\(=\)	\( 279 = 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	279.i (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.833573 + 2.56547i) q^{2} +(-4.26878 + 3.10145i) q^{4} -3.42101 q^{5} +(1.97584 - 1.43553i) q^{7} +(-7.15039 - 5.19506i) q^{8} +O(q^{10})\)	\(q+(0.833573 + 2.56547i) q^{2} +(-4.26878 + 3.10145i) q^{4} -3.42101 q^{5} +(1.97584 - 1.43553i) q^{7} +(-7.15039 - 5.19506i) q^{8} +(-2.85166 - 8.77652i) q^{10} +(-3.56034 + 2.58674i) q^{11} +(-1.31674 + 4.05251i) q^{13} +(5.32982 + 3.87234i) q^{14} +(4.10637 - 12.6381i) q^{16} +(3.00472 + 2.18306i) q^{17} +(0.445686 + 1.37168i) q^{19} +(14.6036 - 10.6101i) q^{20} +(-9.60401 - 6.97772i) q^{22} +(1.84983 + 1.34398i) q^{23} +6.70333 q^{25} -11.4942 q^{26} +(-3.98219 + 12.2559i) q^{28} +(0.696715 + 2.14427i) q^{29} +(-4.47226 + 3.31646i) q^{31} +18.1689 q^{32} +(-3.09592 + 9.52827i) q^{34} +(-6.75937 + 4.91097i) q^{35} +2.58589 q^{37} +(-3.14750 + 2.28679i) q^{38} +(24.4616 + 17.7724i) q^{40} +(-1.47558 - 4.54136i) q^{41} +(-1.68675 - 5.19129i) q^{43} +(7.17566 - 22.0844i) q^{44} +(-1.90598 + 5.86600i) q^{46} +(-0.0697791 + 0.214758i) q^{47} +(-0.319930 + 0.984642i) q^{49} +(5.58772 + 17.1972i) q^{50} +(-6.94778 - 21.3831i) q^{52} +(8.96191 + 6.51121i) q^{53} +(12.1800 - 8.84926i) q^{55} -21.5857 q^{56} +(-4.92031 + 3.57481i) q^{58} +(-1.10051 + 3.38703i) q^{59} -9.41939 q^{61} +(-12.2362 - 8.70896i) q^{62} +(6.93241 + 21.3358i) q^{64} +(4.50458 - 13.8637i) q^{65} +8.78757 q^{67} -19.5971 q^{68} +(-18.2334 - 13.2473i) q^{70} +(-1.85082 - 1.34470i) q^{71} +(4.92762 - 3.58012i) q^{73} +(2.15553 + 6.63402i) q^{74} +(-6.15674 - 4.47313i) q^{76} +(-3.32131 + 10.2219i) q^{77} +(13.6289 + 9.90196i) q^{79} +(-14.0479 + 43.2351i) q^{80} +(10.4207 - 7.57112i) q^{82} +(-2.26010 - 6.95586i) q^{83} +(-10.2792 - 7.46826i) q^{85} +(11.9121 - 8.65464i) q^{86} +38.8961 q^{88} +(11.5297 - 8.37680i) q^{89} +(3.21583 + 9.89732i) q^{91} -12.0648 q^{92} -0.609122 q^{94} +(-1.52470 - 4.69254i) q^{95} +(-12.8734 + 9.35306i) q^{97} -2.79276 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} + 2 q^{7}+O(q^{10}) \) 24 * q - 12 * q^4 + 2 * q^7	\( 24 q - 12 q^{4} + 2 q^{7} - 2 q^{10} - 10 q^{13} + 12 q^{16} + 4 q^{19} - 20 q^{22} + 28 q^{25} + 12 q^{28} - 16 q^{31} + 8 q^{34} - 28 q^{37} + 86 q^{40} + 32 q^{43} + 14 q^{46} - 36 q^{49} - 116 q^{52} + 8 q^{55} - 2 q^{58} - 44 q^{61} - 6 q^{64} - 76 q^{67} - 126 q^{70} - 22 q^{73} + 72 q^{79} + 18 q^{82} - 44 q^{85} + 120 q^{88} + 34 q^{91} + 172 q^{94} - 24 q^{97}+O(q^{100}) \) 24 * q - 12 * q^4 + 2 * q^7 - 2 * q^10 - 10 * q^13 + 12 * q^16 + 4 * q^19 - 20 * q^22 + 28 * q^25 + 12 * q^28 - 16 * q^31 + 8 * q^34 - 28 * q^37 + 86 * q^40 + 32 * q^43 + 14 * q^46 - 36 * q^49 - 116 * q^52 + 8 * q^55 - 2 * q^58 - 44 * q^61 - 6 * q^64 - 76 * q^67 - 126 * q^70 - 22 * q^73 + 72 * q^79 + 18 * q^82 - 44 * q^85 + 120 * q^88 + 34 * q^91 + 172 * q^94 - 24 * q^97

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