LMFDB - Embedded newform 279.2.y.c.82.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [279,2,Mod(10,279)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(279, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("279.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 279 = 3^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	279.y (of order $15$, degree $8$, 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:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{15})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 19x^{14} + 140x^{12} + 511x^{10} + 979x^{8} + 956x^{6} + 410x^{4} + 44x^{2} + 1 $ x^16 + 19x^14 + 140x^12 + 511x^10 + 979x^8 + 956x^6 + 410x^4 + 44*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			82.1
Root			$0.333129i$ of defining polynomial
Character	$\chi$	$=$	279.82
Dual form			279.2.y.c.262.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.640321 - 1.97070i) q^{2} +(-1.85563 + 1.34820i) q^{4} +(1.17396 + 2.03335i) q^{5} +(0.384094 + 3.65441i) q^{7} +(0.492333 + 0.357701i) q^{8} +(3.25543 - 3.61552i) q^{10} +(3.91056 + 1.74109i) q^{11} +(2.04159 - 0.433953i) q^{13} +(6.95582 - 3.09693i) q^{14} +(-1.02791 + 3.16357i) q^{16} +(-1.94411 + 0.865573i) q^{17} +(0.606466 + 0.128908i) q^{19} +(-4.91979 - 2.19043i) q^{20} +(0.927168 - 8.82142i) q^{22} +(-2.71334 - 1.97136i) q^{23} +(-0.256344 + 0.444001i) q^{25} +(-2.16247 - 3.74550i) q^{26} +(-5.63960 - 6.26341i) q^{28} +(0.425645 + 1.31000i) q^{29} +(-1.44334 - 5.37743i) q^{31} +8.10976 q^{32} +(2.95064 + 3.27702i) q^{34} +(-6.97979 + 5.07112i) q^{35} +(-0.137239 + 0.237704i) q^{37} +(-0.134293 - 1.27771i) q^{38} +(-0.149354 + 1.42101i) q^{40} +(2.86248 - 3.17911i) q^{41} +(-0.263799 - 0.0560722i) q^{43} +(-9.60390 + 2.04137i) q^{44} +(-2.14756 + 6.60950i) q^{46} +(-1.66225 + 5.11589i) q^{47} +(-6.36016 + 1.35189i) q^{49} +(1.03914 + 0.220875i) q^{50} +(-3.20338 + 3.55772i) q^{52} +(0.993928 - 9.45659i) q^{53} +(1.05057 + 9.99551i) q^{55} +(-1.11808 + 1.93658i) q^{56} +(2.30908 - 1.67764i) q^{58} +(3.89932 + 4.33063i) q^{59} +2.22719 q^{61} +(-9.67313 + 6.28768i) q^{62} +(-3.13704 - 9.65481i) q^{64} +(3.27911 + 3.64182i) q^{65} +(6.80719 + 11.7904i) q^{67} +(2.44059 - 4.22722i) q^{68} +(14.4630 + 10.5080i) q^{70} +(-0.139642 + 1.32861i) q^{71} +(-12.9413 - 5.76184i) q^{73} +(0.556321 + 0.118250i) q^{74} +(-1.29917 + 0.578429i) q^{76} +(-4.86065 + 14.9595i) q^{77} +(7.92648 - 3.52910i) q^{79} +(-7.63936 + 1.62380i) q^{80} +(-8.09799 - 3.60546i) q^{82} +(3.46976 - 3.85356i) q^{83} +(-4.04231 - 2.93691i) q^{85} +(0.0584142 + 0.555774i) q^{86} +(1.30251 + 2.25601i) q^{88} +(4.05526 - 2.94632i) q^{89} +(2.37001 + 7.29413i) q^{91} +7.69274 q^{92} +11.1463 q^{94} +(0.449849 + 1.38449i) q^{95} +(-5.43173 + 3.94638i) q^{97} +(6.73673 + 11.6684i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 6 q^{2} - 14 q^{4} + 3 q^{5} + 2 q^{7} - 17 q^{8} - 2 q^{10} + 7 q^{11} - 7 q^{13} + 6 q^{14} - 2 q^{16} + 6 q^{17} + 16 q^{19} - 37 q^{20} + 9 q^{22} - q^{23} - 13 q^{25} - 9 q^{26} - 30 q^{28}+ \cdots + 10 q^{98}+O(q^{100}) $ 16 * q + 6 * q^2 - 14 * q^4 + 3 * q^5 + 2 * q^7 - 17 * q^8 - 2 * q^10 + 7 * q^11 - 7 * q^13 + 6 * q^14 - 2 * q^16 + 6 * q^17 + 16 * q^19 - 37 * q^20 + 9 * q^22 - q^23 - 13 * q^25 - 9 * q^26 - 30 * q^28 + 14 * q^29 + 15 * q^31 + 42 * q^32 - 32 * q^34 + 9 * q^35 - 8 * q^37 - 8 * q^38 - q^40 + 8 * q^41 + 23 * q^43 - 39 * q^44 + 34 * q^46 - 14 * q^47 + 2 * q^49 - 3 * q^50 + 29 * q^52 - 6 * q^53 - 7 * q^55 + 30 * q^56 - 15 * q^58 - 4 * q^59 - 60 * q^61 + 25 * q^62 + 23 * q^64 + 12 * q^65 + 13 * q^67 - 30 * q^68 + 12 * q^70 + 14 * q^71 + 2 * q^73 - 13 * q^74 - 12 * q^76 - 18 * q^77 + 18 * q^79 - 36 * q^80 + 14 * q^82 + 16 * q^83 + 37 * q^85 + 26 * q^86 - 17 * q^88 - q^89 + 8 * q^91 + 64 * q^92 + 44 * q^94 + 22 * q^95 + 3 * q^97 + 10 * q^98

Character values

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

$n$	$127$	$218$
$\chi(n)$	$e\left(\frac{4}{15}\right)$	$1$

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 $

$2$	−0.640321	−	1.97070i	−0.452775	−	1.39350i	−0.873727	−	0.486416i	$-0.838304\pi$
$2$	−0.640321	−	1.97070i	−0.452775	−	1.39350i	0.420952	−	0.907083i	$-0.361696\pi$
$3$		0			0
$3$		0			0
$4$	−1.85563	+	1.34820i	−0.927816	+	0.674098i
$5$	1.17396	+	2.03335i	0.525009	+	0.909342i	0.999576	+	0.0291228i	$0.00927137\pi$
$5$	1.17396	+	2.03335i	0.525009	+	0.909342i	−0.474567	+	0.880219i	$0.657395\pi$
$6$		0			0
$7$	0.384094	+	3.65441i	0.145174	+	1.38124i	0.788212	+	0.615404i	$0.211007\pi$
$7$	0.384094	+	3.65441i	0.145174	+	1.38124i	−0.643038	+	0.765834i	$0.722326\pi$
$8$	0.492333	+	0.357701i	0.174066	+	0.126466i
$9$		0			0
$10$	3.25543	−	3.61552i	1.02946	−	1.14333i
$11$	3.91056	+	1.74109i	1.17908	+	0.524960i	0.900247	−	0.435380i	$-0.143386\pi$
$11$	3.91056	+	1.74109i	1.17908	+	0.524960i	0.278832	+	0.960340i	$0.410053\pi$
$12$		0			0
$13$	2.04159	−	0.433953i	0.566235	−	0.120357i	0.0841053	−	0.996457i	$-0.473197\pi$
$13$	2.04159	−	0.433953i	0.566235	−	0.120357i	0.482130	+	0.876100i	$0.339863\pi$
$14$	6.95582	−	3.09693i	1.85902	−	0.827690i
$15$		0			0
$16$	−1.02791	+	3.16357i	−0.256976	+	0.790892i
$17$	−1.94411	+	0.865573i	−0.471516	+	0.209932i	−0.628717	−	0.777634i	$-0.716420\pi$
$17$	−1.94411	+	0.865573i	−0.471516	+	0.209932i	0.157201	+	0.987567i	$0.449753\pi$
$18$		0			0
$19$	0.606466	+	0.128908i	0.139133	+	0.0295736i	0.276952	−	0.960884i	$-0.410676\pi$
$19$	0.606466	+	0.128908i	0.139133	+	0.0295736i	−0.137819	+	0.990457i	$0.544009\pi$
$20$	−4.91979	−	2.19043i	−1.10010	−	0.489795i
$21$		0			0
$22$	0.927168	−	8.82142i	0.197673	−	1.88073i
$23$	−2.71334	−	1.97136i	−0.565771	−	0.411057i	0.267796	−	0.963476i	$-0.413705\pi$
$23$	−2.71334	−	1.97136i	−0.565771	−	0.411057i	−0.833567	+	0.552419i	$0.813705\pi$
$24$		0			0
$25$	−0.256344	+	0.444001i	−0.0512688	+	0.0888002i
$26$	−2.16247	−	3.74550i	−0.424094	−	0.734553i
$27$		0			0
$28$	−5.63960	−	6.26341i	−1.06578	−	1.18367i
$29$	0.425645	+	1.31000i	0.0790403	+	0.243261i	0.982767	−	0.184849i	$-0.0591796\pi$
$29$	0.425645	+	1.31000i	0.0790403	+	0.243261i	−0.903727	+	0.428110i	$0.859180\pi$
$30$		0			0
$31$	−1.44334	−	5.37743i	−0.259231	−	0.965815i
$31$	−1.44334	−	5.37743i	−0.259231	−	0.965815i
$32$	8.10976			1.43362
$33$		0			0
$34$	2.95064	+	3.27702i	0.506031	+	0.562004i
$35$	−6.97979	+	5.07112i	−1.17980	+	0.857175i
$36$		0			0
$37$	−0.137239	+	0.237704i	−0.0225619	+	0.0390783i	−0.877086	−	0.480334i	$-0.840516\pi$
$37$	−0.137239	+	0.237704i	−0.0225619	+	0.0390783i	0.854524	+	0.519412i	$0.173849\pi$
$38$	−0.134293	−	1.27771i	−0.0217851	−	0.207272i
$39$		0			0
$40$	−0.149354	+	1.42101i	−0.0236150	+	0.224681i
$41$	2.86248	−	3.17911i	0.447045	−	0.496494i	−0.476933	−	0.878940i	$-0.658252\pi$
$41$	2.86248	−	3.17911i	0.447045	−	0.496494i	0.923978	+	0.382446i	$0.124918\pi$
$42$		0			0
$43$	−0.263799	−	0.0560722i	−0.0402290	−	0.00855093i	0.187753	−	0.982216i	$-0.439879\pi$
$43$	−0.263799	−	0.0560722i	−0.0402290	−	0.00855093i	−0.227982	+	0.973665i	$0.573213\pi$
$44$	−9.60390	+	2.04137i	−1.44784	+	0.307748i
$45$		0			0
$46$	−2.14756	+	6.60950i	−0.316640	+	0.974517i
$47$	−1.66225	+	5.11589i	−0.242464	+	0.746229i	0.753579	+	0.657358i	$0.228326\pi$
$47$	−1.66225	+	5.11589i	−0.242464	+	0.746229i	−0.996043	+	0.0888711i	$0.971674\pi$
$48$		0			0
$49$	−6.36016	+	1.35189i	−0.908595	+	0.193128i
$50$	1.03914	+	0.220875i	0.146956	+	0.0312365i
$51$		0			0
$52$	−3.20338	+	3.55772i	−0.444229	+	0.493367i
$53$	0.993928	−	9.45659i	0.136527	−	1.29896i	−0.684895	−	0.728642i	$-0.740152\pi$
$53$	0.993928	−	9.45659i	0.136527	−	1.29896i	0.821422	−	0.570321i	$-0.193181\pi$
$54$		0			0
$55$	1.05057	+	9.99551i	0.141659	+	1.34779i
$56$	−1.11808	+	1.93658i	−0.149410	+	0.258786i
$57$		0			0
$58$	2.30908	−	1.67764i	0.303196	−	0.220285i
$59$	3.89932	+	4.33063i	0.507648	+	0.563800i	0.941426	−	0.337220i	$-0.109487\pi$
$59$	3.89932	+	4.33063i	0.507648	+	0.563800i	−0.433778	+	0.901020i	$0.642820\pi$
$60$		0			0
$61$	2.22719			0.285162			0.142581	−	0.989783i	$-0.454460\pi$
$61$	2.22719			0.285162			0.142581	+	0.989783i	$0.454460\pi$
$62$	−9.67313	+	6.28768i	−1.22849	+	0.798536i
$63$		0			0
$64$	−3.13704	−	9.65481i	−0.392130	−	1.20685i
$65$	3.27911	+	3.64182i	0.406724	+	0.451713i
$66$		0			0
$67$	6.80719	+	11.7904i	0.831631	+	1.44043i	0.896744	+	0.442550i	$0.145926\pi$
$67$	6.80719	+	11.7904i	0.831631	+	1.44043i	−0.0651129	+	0.997878i	$0.520741\pi$
$68$	2.44059	−	4.22722i	0.295965	−	0.512626i
$69$		0			0
$70$	14.4630	+	10.5080i	1.72866	+	1.25594i
$71$	−0.139642	+	1.32861i	−0.0165725	+	0.157676i	−0.999678	−	0.0253613i	$-0.991926\pi$
$71$	−0.139642	+	1.32861i	−0.0165725	+	0.157676i	0.983106	+	0.183038i	$0.0585931\pi$
$72$		0			0
$73$	−12.9413	−	5.76184i	−1.51466	−	0.674372i	−0.529868	−	0.848080i	$-0.677758\pi$
$73$	−12.9413	−	5.76184i	−1.51466	−	0.674372i	−0.984797	+	0.173708i	$0.944425\pi$
$74$	0.556321	+	0.118250i	0.0646710	+	0.0137463i
$75$		0			0
$76$	−1.29917	+	0.578429i	−0.149025	+	0.0663503i
$77$	−4.86065	+	14.9595i	−0.553922	+	1.70480i
$78$		0			0
$79$	7.92648	−	3.52910i	0.891799	−	0.397054i	0.0909042	−	0.995860i	$-0.471024\pi$
$79$	7.92648	−	3.52910i	0.891799	−	0.397054i	0.800895	+	0.598805i	$0.204358\pi$
$80$	−7.63936	+	1.62380i	−0.854106	+	0.181546i
$81$		0			0
$82$	−8.09799	−	3.60546i	−0.894274	−	0.398156i
$83$	3.46976	−	3.85356i	0.380856	−	0.422983i	−0.521987	−	0.852953i	$-0.674809\pi$
$83$	3.46976	−	3.85356i	0.380856	−	0.422983i	0.902843	+	0.429970i	$0.141476\pi$
$84$		0			0
$85$	−4.04231	−	2.93691i	−0.438450	−	0.318553i
$86$	0.0584142	+	0.555774i	0.00629897	+	0.0599307i
$87$		0			0
$88$	1.30251	+	2.25601i	0.138848	+	0.240491i
$89$	4.05526	−	2.94632i	0.429857	−	0.312309i	−0.351735	−	0.936100i	$-0.614408\pi$
$89$	4.05526	−	2.94632i	0.429857	−	0.312309i	0.781592	+	0.623790i	$0.214408\pi$
$90$		0			0
$91$	2.37001	+	7.29413i	0.248444	+	0.764632i
$92$	7.69274			0.802024
$93$		0			0
$94$	11.1463			1.14965
$95$	0.449849	+	1.38449i	0.0461535	+	0.142046i
$96$		0			0
$97$	−5.43173	+	3.94638i	−0.551508	+	0.400694i	−0.828341	−	0.560224i	$-0.810715\pi$
$97$	−5.43173	+	3.94638i	−0.551508	+	0.400694i	0.276833	+	0.960918i	$0.410715\pi$
$98$	6.73673	+	11.6684i	0.680512	+	1.17868i
$99$		0			0
$100$	−0.122920	−	1.16950i	−0.0122920	−	0.116950i
$101$	−14.6130	−	10.6169i	−1.45404	−	1.05642i	−0.984866	−	0.173320i	$-0.944550\pi$
$101$	−14.6130	−	10.6169i	−1.45404	−	1.05642i	−0.469177	−	0.883104i	$-0.655450\pi$
$102$		0			0
$103$	2.61986	−	2.90965i	0.258142	−	0.286696i	−0.600117	−	0.799912i	$-0.704879\pi$
$103$	2.61986	−	2.90965i	0.258142	−	0.286696i	0.858260	+	0.513216i	$0.171546\pi$
$104$	1.16037	+	0.516628i	0.113783	+	0.0506596i
$105$		0			0
$106$	−19.2726	+	4.09652i	−1.87192	+	0.397889i
$107$	−10.1546	+	4.52113i	−0.981685	+	0.437074i	−0.833882	−	0.551943i	$-0.813887\pi$
$107$	−10.1546	+	4.52113i	−0.981685	+	0.437074i	−0.147803	+	0.989017i	$0.547220\pi$
$108$		0			0
$109$	5.59116	−	17.2078i	0.535536	−	1.64821i	−0.206951	−	0.978351i	$-0.566354\pi$
$109$	5.59116	−	17.2078i	0.535536	−	1.64821i	0.742488	−	0.669860i	$-0.233646\pi$
$110$	19.0255	−	8.47070i	1.81401	−	0.807649i
$111$		0			0
$112$	−11.9558	−	2.54128i	−1.12972	−	0.240129i
$113$	−16.0224	−	7.13365i	−1.50727	−	0.671078i	−0.523745	−	0.851875i	$-0.675465\pi$
$113$	−16.0224	−	7.13365i	−1.50727	−	0.671078i	−0.983520	+	0.180798i	$0.942132\pi$
$114$		0			0
$115$	0.823120	−	7.83147i	0.0767564	−	0.730288i
$116$	−2.55598	−	1.85703i	−0.237317	−	0.172421i
$117$		0			0
$118$	6.03758	−	10.4574i	0.555804	−	0.962681i
$119$	−3.90988	−	6.77211i	−0.358418	−	0.620798i
$120$		0			0
$121$	4.90064	+	5.44271i	0.445513	+	0.494792i
$122$	−1.42611	−	4.38913i	−0.129114	−	0.397373i
$123$		0			0
$124$	9.92814	+	8.03263i	0.891573	+	0.721352i
$125$	10.5358			0.942352
$126$		0			0
$127$	−9.50050	−	10.5514i	−0.843033	−	0.936283i	0.155638	−	0.987814i	$-0.450257\pi$
$127$	−9.50050	−	10.5514i	−0.843033	−	0.936283i	−0.998671	+	0.0515308i	$0.983590\pi$
$128$	−3.89620	+	2.83075i	−0.344378	+	0.250205i
$129$		0			0
$130$	5.07728	−	8.79410i	0.445307	−	0.771294i
$131$	0.751404	+	7.14913i	0.0656505	+	0.624623i	0.977037	+	0.213071i	$0.0683465\pi$
$131$	0.751404	+	7.14913i	0.0656505	+	0.624623i	−0.911386	+	0.411552i	$0.864987\pi$
$132$		0			0
$133$	−0.238144	+	2.26579i	−0.0206497	+	0.196469i
$134$	18.8766	−	20.9646i	1.63069	−	1.81107i
$135$		0			0
$136$	−1.26676	−	0.269259i	−0.108624	−	0.0230888i
$137$	7.41206	−	1.57548i	0.633255	−	0.134603i	0.119910	−	0.992785i	$-0.461739\pi$
$137$	7.41206	−	1.57548i	0.633255	−	0.134603i	0.513345	+	0.858182i	$0.328406\pi$
$138$		0			0
$139$	−6.21069	+	19.1145i	−0.526784	+	1.62127i	0.233977	+	0.972242i	$0.424826\pi$
$139$	−6.21069	+	19.1145i	−0.526784	+	1.62127i	−0.760761	+	0.649032i	$0.775174\pi$
$140$	6.11507	−	18.8203i	0.516818	−	1.59060i
$141$		0			0
$142$	2.70771	−	0.575541i	0.227226	−	0.0482983i
$143$	8.73931	+	1.85760i	0.730818	+	0.155340i
$144$		0			0
$145$	−2.16400	+	2.40337i	−0.179711	+	0.199589i
$146$	−3.06830	+	29.1929i	−0.253934	+	2.41602i
$147$		0			0
$148$	−0.0658074	−	0.626116i	−0.00540934	−	0.0514664i
$149$	6.15749	−	10.6651i	0.504441	−	0.873717i	−0.495546	−	0.868582i	$-0.665032\pi$
$149$	6.15749	−	10.6651i	0.504441	−	0.873717i	0.999987	−	0.00513554i	$-0.00163470\pi$
$150$		0			0
$151$	16.0808	−	11.6834i	1.30864	−	0.950781i	0.308637	−	0.951180i	$-0.400127\pi$
$151$	16.0808	−	11.6834i	1.30864	−	0.950781i	1.00000		0.000399262i	$0.000127089\pi$
$152$	0.252473	+	0.280399i	0.0204782	+	0.0227434i
$153$		0			0
$154$	32.5932			2.62644
$155$	9.23979	−	9.24768i	0.742158	−	0.742792i
$156$		0			0
$157$	−1.79373	−	5.52052i	−0.143155	−	0.440585i	0.853614	−	0.520906i	$-0.174406\pi$
$157$	−1.79373	−	5.52052i	−0.143155	−	0.440585i	−0.996769	+	0.0803203i	$0.974406\pi$
$158$	−12.0303	−	13.3610i	−0.957079	−	1.06294i
$159$		0			0
$160$	9.52050	+	16.4900i	0.752662	+	1.30365i
$161$	6.16198	−	10.6729i	0.485632	−	0.841139i
$162$		0			0
$163$	−14.3870	−	10.4528i	−1.12688	−	0.818725i	−0.141640	−	0.989918i	$-0.545238\pi$
$163$	−14.3870	−	10.4528i	−1.12688	−	0.818725i	−0.985237	+	0.171194i	$0.945238\pi$
$164$	−1.02565	+	9.75845i	−0.0800901	+	0.762007i
$165$		0			0
$166$	−9.81599	−	4.37036i	−0.761869	−	0.339206i
$167$	2.13435	+	0.453670i	0.165161	+	0.0351060i	0.289750	−	0.957102i	$-0.406428\pi$
$167$	2.13435	+	0.453670i	0.165161	+	0.0351060i	−0.124589	+	0.992208i	$0.539761\pi$
$168$		0			0
$169$	−7.89632	+	3.51567i	−0.607409	+	0.270436i
$170$	−3.19941	+	9.84677i	−0.245383	+	0.755212i
$171$		0			0
$172$	0.565110	−	0.251603i	0.0430892	−	0.0191846i
$173$	−5.38757	+	1.14516i	−0.409609	+	0.0870651i	−0.408108	−	0.912934i	$-0.633811\pi$
$173$	−5.38757	+	1.14516i	−0.409609	+	0.0870651i	−0.00150131	+	0.999999i	$0.500478\pi$
$174$		0			0
$175$	−1.72102	−	0.766249i	−0.130097	−	0.0579230i
$176$	−9.52776	+	10.5816i	−0.718182	+	0.797621i
$177$		0			0
$178$	−8.40300	−	6.10514i	−0.629831	−	0.457599i
$179$	1.26834	+	12.0674i	0.0947999	+	0.901961i	0.933792	+	0.357817i	$0.116479\pi$
$179$	1.26834	+	12.0674i	0.0947999	+	0.901961i	−0.838992	+	0.544144i	$0.816854\pi$
$180$		0			0
$181$	−4.82344	−	8.35444i	−0.358523	−	0.620980i	0.629191	−	0.777251i	$-0.283386\pi$
$181$	−4.82344	−	8.35444i	−0.358523	−	0.620980i	−0.987714	+	0.156270i	$0.950053\pi$
$182$	12.8570	−	9.34116i	0.953025	−	0.692413i
$183$		0			0
$184$	−0.630711	−	1.94113i	−0.0464966	−	0.143102i
$185$	−0.644448			−0.0473808
$186$		0			0
$187$	−9.10960			−0.666160
$188$	−3.81269	−	11.7342i	−0.278069	−	0.855808i
$189$		0			0
$190$	2.44038	−	1.77304i	0.177044	−	0.128630i
$191$	5.23270	+	9.06331i	0.378625	+	0.655798i	0.990862	−	0.134876i	$-0.0430637\pi$
$191$	5.23270	+	9.06331i	0.378625	+	0.655798i	−0.612237	+	0.790674i	$0.709730\pi$
$192$		0			0
$193$	0.187174	+	1.78084i	0.0134731	+	0.128188i	0.999191	−	0.0402173i	$-0.0128050\pi$
$193$	0.187174	+	1.78084i	0.0134731	+	0.128188i	−0.985718	+	0.168405i	$0.946138\pi$
$194$	11.2552	+	8.17738i	0.808076	+	0.587102i
$195$		0			0
$196$	9.97950	−	11.0834i	0.712822	−	0.791669i
$197$	−5.84391	−	2.60188i	−0.416361	−	0.185376i	0.187854	−	0.982197i	$-0.439847\pi$
$197$	−5.84391	−	2.60188i	−0.416361	−	0.185376i	−0.604216	+	0.796821i	$0.706513\pi$
$198$		0			0
$199$	−0.906896	+	0.192767i	−0.0642881	+	0.0136649i	−0.239943	−	0.970787i	$-0.577129\pi$
$199$	−0.906896	+	0.192767i	−0.0642881	+	0.0136649i	0.175655	+	0.984452i	$0.443796\pi$
$200$	−0.285026	+	0.126902i	−0.0201544	+	0.00897331i
$201$		0			0
$202$	−11.5659	+	35.5961i	−0.813771	+	2.50453i
$203$	−4.62379	+	2.05865i	−0.324527	+	0.144489i
$204$		0			0
$205$	9.82467	+	2.08830i	0.686185	+	0.145853i
$206$	−7.41161	−	3.29986i	−0.516391	−	0.229912i
$207$		0			0
$208$	−0.725720	+	6.90477i	−0.0503197	+	0.478759i
$209$	2.14718	+	1.56002i	0.148524	+	0.107909i
$210$		0			0
$211$	3.09072	−	5.35328i	0.212774	−	0.368535i	−0.739808	−	0.672818i	$-0.765084\pi$
$211$	3.09072	−	5.35328i	0.212774	−	0.368535i	0.952582	+	0.304283i	$0.0984169\pi$
$212$	10.9050	+	18.8880i	0.748957	+	1.29723i
$213$		0			0
$214$	15.4120	+	17.1168i	1.05354	+	1.17008i
$215$	−0.195674	−	0.602222i	−0.0133448	−	0.0410712i
$216$		0			0
$217$	19.0970	−	7.34000i	1.29639	−	0.498272i
$218$	−37.4917			−2.53926
$219$		0			0
$220$	−15.4254	−	17.1316i	−1.03998	−	1.15501i
$221$	−3.59345	+	2.61080i	−0.241722	+	0.175621i
$222$		0			0
$223$	−7.94891	+	13.7679i	−0.532298	+	0.921968i	0.466991	+	0.884262i	$0.345338\pi$
$223$	−7.94891	+	13.7679i	−0.532298	+	0.921968i	−0.999289	+	0.0377054i	$0.987995\pi$
$224$	3.11491	+	29.6364i	0.208124	+	1.98017i
$225$		0			0
$226$	−3.79882	+	36.1433i	−0.252694	+	2.40422i
$227$	3.10808	−	3.45188i	0.206291	−	0.229109i	−0.631117	−	0.775688i	$-0.717403\pi$
$227$	3.10808	−	3.45188i	0.206291	−	0.229109i	0.837408	+	0.546578i	$0.184070\pi$
$228$		0			0
$229$	18.9940	+	4.03731i	1.25516	+	0.266793i	0.787057	−	0.616881i	$-0.211604\pi$
$229$	18.9940	+	4.03731i	1.25516	+	0.266793i	0.468104	+	0.883673i	$0.344937\pi$
$230$	−15.9606	+	3.39252i	−1.05241	+	0.223696i
$231$		0			0
$232$	−0.259029	+	0.797210i	−0.0170061	+	0.0523394i
$233$	4.40302	−	13.5511i	0.288452	−	0.887763i	−0.696891	−	0.717177i	$-0.745434\pi$
$233$	4.40302	−	13.5511i	0.288452	−	0.887763i	0.985343	−	0.170586i	$-0.0545660\pi$
$234$		0			0
$235$	−12.3538	+	2.62588i	−0.805873	+	0.171294i
$236$	−13.0742	−	2.77901i	−0.851060	−	0.180898i
$237$		0			0
$238$	−10.8423	+	12.0415i	−0.702799	+	0.780537i
$239$	−0.710952	+	6.76426i	−0.0459877	+	0.437544i	0.947167	+	0.320740i	$0.103932\pi$
$239$	−0.710952	+	6.76426i	−0.0459877	+	0.437544i	−0.993155	+	0.116804i	$0.962735\pi$
$240$		0			0
$241$	1.20261	+	11.4421i	0.0774671	+	0.737050i	0.962456	+	0.271438i	$0.0874992\pi$
$241$	1.20261	+	11.4421i	0.0774671	+	0.737050i	−0.884989	+	0.465612i	$0.845834\pi$
$242$	7.58800	−	13.1428i	0.487775	−	0.844851i
$243$		0			0
$244$	−4.13284	+	3.00269i	−0.264578	+	0.192227i
$245$	−10.2154	−	11.3454i	−0.652640	−	0.724830i
$246$		0			0
$247$	1.29410			0.0823413
$248$	1.21291	−	3.16377i	0.0770197	−	0.200899i
$249$		0			0
$250$	−6.74630	−	20.7630i	−0.426673	−	1.31317i
$251$	4.88091	+	5.42080i	0.308080	+	0.342158i	0.877225	−	0.480080i	$-0.159392\pi$
$251$	4.88091	+	5.42080i	0.308080	+	0.342158i	−0.569145	+	0.822237i	$0.692726\pi$
$252$		0			0
$253$	−7.17837	−	12.4333i	−0.451300	−	0.781675i
$254$	−14.7103	+	25.4790i	−0.923005	+	1.59869i
$255$		0			0
$256$	−8.35235	−	6.06834i	−0.522022	−	0.379271i
$257$	−2.57722	+	24.5206i	−0.160763	+	1.52955i	0.555378	+	0.831598i	$0.312574\pi$
$257$	−2.57722	+	24.5206i	−0.160763	+	1.52955i	−0.716140	+	0.697956i	$0.754093\pi$
$258$		0			0
$259$	−0.921381	−	0.410225i	−0.0572518	−	0.0254902i
$260$	−10.9947	−	2.33700i	−0.681864	−	0.144935i
$261$		0			0
$262$	13.6077	−	6.05853i	0.840686	−	0.374297i
$263$	8.12313	−	25.0004i	0.500894	−	1.54159i	−0.306672	−	0.951815i	$-0.599215\pi$
$263$	8.12313	−	25.0004i	0.500894	−	1.54159i	0.807566	−	0.589777i	$-0.200785\pi$
$264$		0			0
$265$	20.3954	−	9.08062i	1.25288	−	0.557818i
$266$	4.61769	−	0.981521i	0.283129	−	0.0601809i
$267$		0			0
$268$	−28.5274	−	12.7012i	−1.74259	−	0.775851i
$269$	13.9713	−	15.5167i	0.851846	−	0.946071i	−0.147228	−	0.989103i	$-0.547035\pi$
$269$	13.9713	−	15.5167i	0.851846	−	0.946071i	0.999074	+	0.0430321i	$0.0137018\pi$
$270$		0			0
$271$	16.9981	+	12.3499i	1.03256	+	0.750201i	0.968820	−	0.247765i	$-0.0796962\pi$
$271$	16.9981	+	12.3499i	1.03256	+	0.750201i	0.0637431	+	0.997966i	$0.479696\pi$
$272$	−0.739939	−	7.04005i	−0.0448654	−	0.426866i
$273$		0			0
$274$	−7.85091	−	13.5982i	−0.474291	−	0.821496i
$275$	−1.77550	+	1.28997i	−0.107066	+	0.0777883i
$276$		0			0
$277$	−1.47070	−	4.52635i	−0.0883657	−	0.271962i	0.897102	−	0.441823i	$-0.145668\pi$
$277$	−1.47070	−	4.52635i	−0.0883657	−	0.271962i	−0.985468	+	0.169861i	$0.945668\pi$
$278$	41.6459			2.49776
$279$		0			0
$280$	−5.25032			−0.313767
$281$	2.05645	+	6.32910i	0.122678	+	0.377563i	0.993471	−	0.114087i	$-0.0363942\pi$
$281$	2.05645	+	6.32910i	0.122678	+	0.377563i	−0.870793	+	0.491649i	$0.836394\pi$
$282$		0			0
$283$	5.86234	−	4.25924i	0.348480	−	0.253185i	−0.399751	−	0.916624i	$-0.630904\pi$
$283$	5.86234	−	4.25924i	0.348480	−	0.253185i	0.748231	+	0.663438i	$0.230904\pi$
$284$	−1.53210	−	2.65367i	−0.0909132	−	0.157466i
$285$		0			0
$286$	−1.93519	−	18.4121i	−0.114430	−	1.08873i
$287$	12.7172	+	9.23961i	0.750675	+	0.545397i
$288$		0			0
$289$	−8.34488	+	9.26793i	−0.490875	+	0.545172i
$290$	6.12199	+	2.72568i	0.359495	+	0.160058i
$291$		0			0
$292$	31.7824	−	6.75555i	1.85992	−	0.395339i
$293$	−12.3434	+	5.49563i	−0.721108	+	0.321058i	−0.734272	−	0.678855i	$-0.762476\pi$
$293$	−12.3434	+	5.49563i	−0.721108	+	0.321058i	0.0131637	+	0.999913i	$0.495810\pi$
$294$		0			0
$295$	−4.22807	+	13.0126i	−0.246168	+	0.757626i
$296$	−0.152594	+	0.0679392i	−0.00886934	+	0.00394888i
$297$		0			0
$298$	−24.9605	−	5.30552i	−1.44592	−	0.307340i
$299$	−6.39501	−	2.84724i	−0.369833	−	0.164660i
$300$		0			0
$301$	0.103587	−	0.985567i	0.00597067	−	0.0568071i
$302$	−33.3214	−	24.2094i	−1.91743	−	1.39309i
$303$		0			0
$304$	−1.03120	+	1.78609i	−0.0591434	+	0.102439i
$305$	2.61462	+	4.52866i	0.149713	+	0.259310i
$306$		0			0
$307$	−15.2065	−	16.8886i	−0.867883	−	0.963882i	0.131741	−	0.991284i	$-0.457943\pi$
$307$	−15.2065	−	16.8886i	−0.867883	−	0.963882i	−0.999624	+	0.0274020i	$0.991277\pi$
$308$	−11.1488	−	34.3125i	−0.635263	−	1.95514i
$309$		0			0
$310$	−24.1409	−	12.2874i	−1.37111	−	0.697878i
$311$	−9.49330			−0.538315			−0.269158	−	0.963096i	$-0.586745\pi$
$311$	−9.49330			−0.538315			−0.269158	+	0.963096i	$0.586745\pi$
$312$		0			0
$313$	18.8006	+	20.8802i	1.06267	+	1.18022i	0.983040	+	0.183393i	$0.0587082\pi$
$313$	18.8006	+	20.8802i	1.06267	+	1.18022i	0.0796330	+	0.996824i	$0.474625\pi$
$314$	−9.73075	+	7.06981i	−0.549138	+	0.398972i
$315$		0			0
$316$	−9.95072	+	17.2352i	−0.559772	+	0.969553i
$317$	−1.65331	−	15.7302i	−0.0928591	−	0.883495i	−0.937459	−	0.348096i	$-0.886828\pi$
$317$	−1.65331	−	15.7302i	−0.0928591	−	0.883495i	0.844600	−	0.535398i	$-0.179839\pi$
$318$		0			0
$319$	−0.616323	+	5.86393i	−0.0345075	+	0.328317i
$320$	15.9489	−	17.7130i	0.891569	−	0.990188i
$321$		0			0
$322$	−24.9787	−	5.30938i	−1.39201	−	0.295880i
$323$	−1.29062	+	0.274329i	−0.0718118	+	0.0152641i
$324$		0			0
$325$	−0.330674	+	1.01771i	−0.0183425	+	0.0564523i
$326$	−11.3870	+	35.0457i	−0.630669	+	1.94100i
$327$		0			0
$328$	2.54646	−	0.541267i	0.140605	−	0.0298865i
$329$	−19.3340	−	4.10957i	−1.06592	−	0.226568i
$330$		0			0
$331$	8.66131	−	9.61936i	0.476069	−	0.528728i	−0.456499	−	0.889724i	$-0.650897\pi$
$331$	8.66131	−	9.61936i	0.476069	−	0.528728i	0.932567	+	0.360996i	$0.117563\pi$
$332$	−1.24325	+	11.8287i	−0.0682321	+	0.649185i
$333$		0			0
$334$	−0.472618	−	4.49666i	−0.0258605	−	0.246046i
$335$	−15.9827	+	27.6828i	−0.873228	+	1.51247i
$336$		0			0
$337$	22.5443	−	16.3794i	1.22807	−	0.892243i	0.231323	−	0.972877i	$-0.425694\pi$
$337$	22.5443	−	16.3794i	1.22807	−	0.892243i	0.996744	+	0.0806338i	$0.0256944\pi$
$338$	11.9845	+	13.3102i	0.651872	+	0.723977i
$339$		0			0
$340$	11.4606			0.621537
$341$	3.71834	−	23.5418i	0.201360	−	1.27486i
$342$		0			0
$343$	0.565190	+	1.73948i	0.0305174	+	0.0939229i
$344$	−0.109820	−	0.121967i	−0.00592108	−	0.00657603i
$345$		0			0
$346$	5.70655	+	9.88403i	0.306786	+	0.531369i
$347$	2.66175	−	4.61029i	0.142890	−	0.247493i	−0.785693	−	0.618616i	$-0.787694\pi$
$347$	2.66175	−	4.61029i	0.142890	−	0.247493i	0.928584	+	0.371123i	$0.121027\pi$
$348$		0			0
$349$	3.31528	+	2.40869i	0.177463	+	0.128934i	0.672971	−	0.739669i	$-0.265018\pi$
$349$	3.31528	+	2.40869i	0.177463	+	0.128934i	−0.495508	+	0.868603i	$0.665018\pi$
$350$	−0.408043	+	3.88227i	−0.0218108	+	0.207516i
$351$		0			0
$352$	31.7137	+	14.1199i	1.69035	+	0.752591i
$353$	21.3132	+	4.53026i	1.13439	+	0.241122i	0.736582	−	0.676348i	$-0.236438\pi$
$353$	21.3132	+	4.53026i	1.13439	+	0.241122i	0.397806	+	0.917470i	$0.369772\pi$
$354$		0			0
$355$	−2.86546	+	1.27578i	−0.152083	+	0.0677115i
$356$	−3.55286	+	10.9346i	−0.188301	+	0.579531i
$357$		0			0
$358$	22.9692	−	10.2265i	1.21396	−	0.540489i
$359$	−6.92668	+	1.47231i	−0.365576	+	0.0777057i	−0.387037	−	0.922064i	$-0.626502\pi$
$359$	−6.92668	+	1.47231i	−0.365576	+	0.0777057i	0.0214610	+	0.999770i	$0.493168\pi$
$360$		0			0
$361$	−17.0062	−	7.57164i	−0.895062	−	0.398507i
$362$	−13.3756	+	14.8551i	−0.703005	+	0.780766i
$363$		0			0
$364$	−14.2318	−	10.3400i	−0.745947	−	0.541963i
$365$	−3.47668	−	33.0784i	−0.181977	−	1.73140i
$366$		0			0
$367$	8.05884	+	13.9583i	0.420668	+	0.728619i	0.996005	−	0.0892980i	$-0.0284624\pi$
$367$	8.05884	+	13.9583i	0.420668	+	0.728619i	−0.575337	+	0.817917i	$0.695129\pi$
$368$	9.02559	−	6.55747i	0.470491	−	0.341832i
$369$		0			0
$370$	0.412653	+	1.27002i	0.0214528	+	0.0660250i
$371$	34.9401			1.81400
$372$		0			0
$373$	−9.81895			−0.508406			−0.254203	−	0.967151i	$-0.581813\pi$
$373$	−9.81895			−0.508406			−0.254203	+	0.967151i	$0.581813\pi$
$374$	5.83306	+	17.9523i	0.301621	+	0.928293i
$375$		0			0
$376$	−2.64834	+	1.92413i	−0.136578	+	0.0992294i
$377$	1.43747	+	2.48977i	0.0740335	+	0.128230i
$378$		0			0
$379$	1.44413	+	13.7399i	0.0741798	+	0.705773i	0.966899	+	0.255160i	$0.0821281\pi$
$379$	1.44413	+	13.7399i	0.0741798	+	0.705773i	−0.892719	+	0.450614i	$0.851205\pi$
$380$	−2.70132	−	1.96262i	−0.138575	−	0.100680i
$381$		0			0
$382$	14.5105	−	16.1155i	0.742421	−	0.824542i
$383$	−9.41502	−	4.19184i	−0.481085	−	0.214193i	0.151841	−	0.988405i	$-0.451480\pi$
$383$	−9.41502	−	4.19184i	−0.481085	−	0.214193i	−0.632926	+	0.774212i	$0.718146\pi$
$384$		0			0
$385$	−36.1242	+	7.67843i	−1.84106	+	0.391329i
$386$	3.38966	−	1.50917i	0.172529	−	0.0768149i
$387$		0			0
$388$	4.75879	−	14.6461i	0.241591	−	0.743541i
$389$	23.1725	−	10.3170i	1.17489	−	0.523095i	0.275952	−	0.961171i	$-0.411007\pi$
$389$	23.1725	−	10.3170i	1.17489	−	0.523095i	0.898938	+	0.438077i	$0.144340\pi$
$390$		0			0
$391$	6.98139	+	1.48394i	0.353064	+	0.0750460i
$392$	−3.61489	−	1.60945i	−0.182579	−	0.0812896i
$393$		0			0
$394$	−1.38555	+	13.1827i	−0.0698032	+	0.664133i
$395$	16.4812	+	11.9743i	0.829261	+	0.602493i
$396$		0			0
$397$	−8.37941	+	14.5136i	−0.420550	+	0.728415i	−0.995993	−	0.0894272i	$-0.971496\pi$
$397$	−8.37941	+	14.5136i	−0.420550	+	0.728415i	0.575443	+	0.817842i	$0.304830\pi$
$398$	0.960590	+	1.66379i	0.0481500	+	0.0833983i
$399$		0			0
$400$	−1.14113	−	1.26735i	−0.0570565	−	0.0633677i
$401$	8.53615	+	26.2716i	0.426275	+	1.31194i	0.901768	+	0.432220i	$0.142270\pi$
$401$	8.53615	+	26.2716i	0.426275	+	1.31194i	−0.475493	+	0.879720i	$0.657730\pi$
$402$		0			0
$403$	−5.28026	−	10.3522i	−0.263028	−	0.515678i
$404$	41.4300			2.06122
$405$		0			0
$406$	7.01769	+	7.79394i	0.348282	+	0.386807i
$407$	−0.950545	+	0.690611i	−0.0471168	+	0.0342323i
$408$		0			0
$409$	11.3053	−	19.5814i	0.559013	−	0.968239i	−0.438566	−	0.898699i	$-0.644514\pi$
$409$	11.3053	−	19.5814i	0.559013	−	0.968239i	0.997579	−	0.0695399i	$-0.0221531\pi$
$410$	−2.17552	−	20.6987i	−0.107441	−	1.02224i
$411$		0			0
$412$	−0.938720	+	8.93132i	−0.0462474	+	0.440015i
$413$	−14.3282	+	15.9131i	−0.705045	+	0.783031i
$414$		0			0
$415$	11.9090	+	2.53133i	0.584589	+	0.124258i
$416$	16.5568	−	3.51926i	0.811764	−	0.172546i
$417$		0			0
$418$	1.69945	−	5.23038i	0.0831229	−	0.255826i
$419$	1.91312	−	5.88796i	0.0934618	−	0.287646i	−0.893388	−	0.449286i	$-0.851678\pi$
$419$	1.91312	−	5.88796i	0.0934618	−	0.287646i	0.986850	+	0.161640i	$0.0516784\pi$
$420$		0			0
$421$	−6.41600	+	1.36376i	−0.312697	+	0.0664657i	−0.361587	−	0.932338i	$-0.617765\pi$
$421$	−6.41600	+	1.36376i	−0.312697	+	0.0664657i	0.0488901	+	0.998804i	$0.484432\pi$
$422$	−12.5288	−	2.66308i	−0.609892	−	0.129637i
$423$		0			0
$424$	3.87197	−	4.30026i	0.188040	−	0.208839i
$425$	0.114046	−	1.08507i	0.00553202	−	0.0526337i
$426$		0			0
$427$	0.855450	+	8.13906i	0.0413981	+	0.393877i
$428$	12.7479	−	22.0800i	0.616192	−	1.06728i
$429$		0			0
$430$	−1.06151	+	0.771231i	−0.0511905	+	0.0371920i
$431$	−15.7030	−	17.4399i	−0.756385	−	0.840051i	0.234868	−	0.972027i	$-0.424534\pi$
$431$	−15.7030	−	17.4399i	−0.756385	−	0.840051i	−0.991253	+	0.131977i	$0.957868\pi$
$432$		0			0
$433$	24.3130			1.16841			0.584203	−	0.811607i	$-0.301407\pi$
$433$	24.3130			1.16841			0.584203	+	0.811607i	$0.301407\pi$
$434$	−26.6932	−	32.9345i	−1.28131	−	1.58091i
$435$		0			0
$436$	12.8244	+	39.4694i	0.614176	+	1.89024i
$437$	−1.39143	−	1.54534i	−0.0665610	−	0.0739234i
$438$		0			0
$439$	−7.25318	−	12.5629i	−0.346175	−	0.599593i	0.639391	−	0.768881i	$-0.279186\pi$
$439$	−7.25318	−	12.5629i	−0.346175	−	0.599593i	−0.985567	+	0.169288i	$0.945853\pi$
$440$	−3.05817	+	5.29690i	−0.145792	+	0.252520i
$441$		0			0
$442$	7.44607	+	5.40989i	0.354173	+	0.257322i
$443$	−1.73162	+	16.4752i	−0.0822716	+	0.782762i	0.873137	+	0.487475i	$0.162082\pi$
$443$	−1.73162	+	16.4752i	−0.0822716	+	0.782762i	−0.955409	+	0.295287i	$0.904585\pi$
$444$		0			0
$445$	10.7516	+	4.78692i	0.509675	+	0.226922i
$446$	32.2223	+	6.84907i	1.52577	+	0.324313i
$447$		0			0
$448$	34.0777	−	15.1724i	1.61002	−	0.716828i
$449$	−2.10667	+	6.48365i	−0.0994197	+	0.305982i	−0.988380	−	0.152001i	$-0.951428\pi$
$449$	−2.10667	+	6.48365i	−0.0994197	+	0.305982i	0.888961	+	0.457984i	$0.151428\pi$
$450$		0			0
$451$	16.7290	−	7.44825i	0.787740	−	0.350724i
$452$	39.3493	−	8.36396i	1.85084	−	0.393408i
$453$		0			0
$454$	−8.79280	−	3.91481i	−0.412667	−	0.183731i
$455$	−12.0492	+	13.3820i	−0.564877	+	0.627359i
$456$		0			0
$457$	−17.3354	−	12.5949i	−0.810916	−	0.589165i	0.103180	−	0.994663i	$-0.467098\pi$
$457$	−17.3354	−	12.5949i	−0.810916	−	0.589165i	−0.914096	+	0.405497i	$0.867098\pi$
$458$	−4.20594	−	40.0168i	−0.196530	−	1.86986i
$459$		0			0
$460$	9.03094	+	15.6420i	0.421070	+	0.729314i
$461$	−7.01782	+	5.09875i	−0.326853	+	0.237472i	−0.739094	−	0.673602i	$-0.764746\pi$
$461$	−7.01782	+	5.09875i	−0.326853	+	0.237472i	0.412241	+	0.911075i	$0.364746\pi$
$462$		0			0
$463$	1.12787	+	3.47124i	0.0524167	+	0.161322i	0.973838	−	0.227243i	$-0.0729710\pi$
$463$	1.12787	+	3.47124i	0.0524167	+	0.161322i	−0.921421	+	0.388565i	$0.872971\pi$
$464$	−4.58180			−0.212705
$465$		0			0
$466$	−29.5246			−1.36770
$467$	0.952115	+	2.93031i	0.0440586	+	0.135599i	0.970666	−	0.240431i	$-0.0772889\pi$
$467$	0.952115	+	2.93031i	0.0440586	+	0.135599i	−0.926607	+	0.376030i	$0.877289\pi$
$468$		0			0
$469$	−40.4724	+	29.4049i	−1.86884	+	1.35779i
$470$	13.0852	+	22.6643i	0.603577	+	1.04543i
$471$		0			0
$472$	0.370692	+	3.52690i	0.0170625	+	0.162339i
$473$	−0.933975	−	0.678572i	−0.0429442	−	0.0312008i
$474$		0			0
$475$	−0.212700	+	0.236227i	−0.00975933	+	0.0108388i
$476$	16.3854	+	7.29526i	0.751025	+	0.334378i
$477$		0			0
$478$	13.7856	−	2.93022i	0.630538	−	0.134025i
$479$	15.9050	−	7.08138i	0.726720	−	0.323556i	−0.00981912	−	0.999952i	$-0.503126\pi$
$479$	15.9050	−	7.08138i	0.726720	−	0.323556i	0.736539	+	0.676395i	$0.236459\pi$
$480$		0			0
$481$	−0.177032	+	0.544849i	−0.00807197	+	0.0248430i
$482$	21.7789	−	9.69661i	0.992003	−	0.441668i
$483$		0			0
$484$	−16.4316	−	3.49265i	−0.746892	−	0.158757i
$485$	−14.4010	−	6.41173i	−0.653915	−	0.291142i
$486$		0			0
$487$	−3.00766	+	28.6160i	−0.136290	+	1.29671i	0.685981	+	0.727619i	$0.259373\pi$
$487$	−3.00766	+	28.6160i	−0.136290	+	1.29671i	−0.822272	+	0.569095i	$0.807294\pi$
$488$	1.09652	+	0.796666i	0.0496370	+	0.0360634i
$489$		0			0
$490$	−15.8172	+	27.3963i	−0.714550	+	1.23764i
$491$	−4.91284	−	8.50929i	−0.221713	−	0.384019i	0.733615	−	0.679565i	$-0.237832\pi$
$491$	−4.91284	−	8.50929i	−0.221713	−	0.384019i	−0.955328	+	0.295546i	$0.904498\pi$
$492$		0			0
$493$	−1.96140	−	2.17836i	−0.0883371	−	0.0981083i
$494$	−0.828636	−	2.55028i	−0.0372821	−	0.114743i
$495$		0			0
$496$	18.4955	+	0.961388i	0.830472	+	0.0431676i
$497$	−4.90891			−0.220195
$498$		0			0
$499$	−7.25874	−	8.06164i	−0.324946	−	0.360889i	0.558432	−	0.829550i	$-0.311403\pi$
$499$	−7.25874	−	8.06164i	−0.324946	−	0.360889i	−0.883378	+	0.468661i	$0.844736\pi$
$500$	−19.5506	+	14.2043i	−0.874329	+	0.635237i
$501$		0			0
$502$	7.55745	−	13.0899i	0.337305	−	0.584230i
$503$	0.894863	+	8.51405i	0.0399000	+	0.379623i	0.996190	+	0.0872044i	$0.0277933\pi$
$503$	0.894863	+	8.51405i	0.0399000	+	0.379623i	−0.956290	+	0.292418i	$0.905540\pi$
$504$		0			0
$505$	4.43299	−	42.1771i	0.197265	−	1.87685i
$506$	−19.9059	+	22.1077i	−0.884925	+	0.982809i
$507$		0			0
$508$	31.8548	+	6.77094i	1.41333	+	0.300412i
$509$	−38.7174	+	8.22963i	−1.71612	+	0.364772i	−0.957871	−	0.287197i	$-0.907276\pi$
$509$	−38.7174	+	8.22963i	−1.71612	+	0.364772i	−0.758245	+	0.651969i	$0.773943\pi$
$510$		0			0
$511$	16.0855	−	49.5059i	0.711579	−	2.19001i
$512$	−9.58715	+	29.5062i	−0.423696	+	1.30400i
$513$		0			0
$514$	49.9732	−	10.6221i	2.20422	−	0.468522i
$515$	8.99194	+	1.91130i	0.396232	+	0.0842217i
$516$		0			0
$517$	−15.4076	+	17.1119i	−0.677625	+	0.752578i
$518$	−0.218453	+	2.07845i	−0.00959830	+	0.0913217i
$519$		0			0
$520$	0.311732	+	2.96593i	0.0136703	+	0.130065i
$521$	−0.674660	+	1.16855i	−0.0295574	+	0.0511949i	−0.880426	−	0.474184i	$-0.842743\pi$
$521$	−0.674660	+	1.16855i	−0.0295574	+	0.0511949i	0.850868	+	0.525379i	$0.176076\pi$
$522$		0			0
$523$	−23.0351	+	16.7360i	−1.00725	+	0.731812i	−0.963631	−	0.267236i	$-0.913890\pi$
$523$	−23.0351	+	16.7360i	−1.00725	+	0.731812i	−0.0436219	+	0.999048i	$0.513890\pi$
$524$	−11.0328	−	12.2531i	−0.481968	−	0.535280i
$525$		0			0
$526$	−54.4699			−2.37500
$527$	7.46057	+	9.20499i	0.324987	+	0.400976i
$528$		0			0
$529$	−3.63142	−	11.1764i	−0.157888	−	0.485929i
$530$	−30.9548	−	34.3788i	−1.34459	−	1.49332i
$531$		0			0
$532$	−2.61282	−	4.52554i	−0.113280	−	0.196207i
$533$	4.46443	−	7.73262i	0.193376	−	0.334937i
$534$		0			0
$535$	−21.1141	−	15.3403i	−0.912843	−	0.663220i
$536$	−0.866031	+	8.23974i	−0.0374069	+	0.355902i
$537$		0			0
$538$	−39.5250	−	17.5977i	−1.70404	−	0.758689i
$539$	−27.2256	−	5.78697i	−1.17269	−	0.249263i
$540$		0			0
$541$	−13.0725	+	5.82024i	−0.562029	+	0.250232i	−0.668030	−	0.744134i	$-0.732862\pi$
$541$	−13.0725	+	5.82024i	−0.562029	+	0.250232i	0.106000	+	0.994366i	$0.466196\pi$
$542$	13.4537	−	41.4062i	0.577885	−	1.77855i
$543$		0			0
$544$	−15.7663	+	7.01959i	−0.675973	+	0.300962i
$545$	41.5533	−	8.83243i	1.77995	−	0.378340i
$546$		0			0
$547$	38.7041	+	17.2322i	1.65487	+	0.736795i	0.999823	−	0.0187957i	$-0.00598320\pi$
$547$	38.7041	+	17.2322i	1.65487	+	0.736795i	0.655044	+	0.755590i	$0.272650\pi$
$548$	−11.6300	+	12.9164i	−0.496809	+	0.551762i
$549$		0			0
$550$	3.67904	+	2.67298i	0.156875	+	0.113976i
$551$	0.0892693	+	0.849341i	0.00380300	+	0.0361831i
$552$		0			0
$553$	15.9413	+	27.6111i	0.677893	+	1.17414i
$554$	−7.97837	+	5.79663i	−0.338969	+	0.246275i
$555$		0			0
$556$	−14.2454	−	43.8428i	−0.604139	−	1.85935i
$557$	−27.3019			−1.15682			−0.578409	−	0.815747i	$-0.696326\pi$
$557$	−27.3019			−1.15682			−0.578409	+	0.815747i	$0.696326\pi$
$558$		0			0
$559$	−0.562902			−0.0238082
$560$	−8.86825	−	27.2937i	−0.374752	−	1.15337i
$561$		0			0
$562$	11.1560	−	8.10531i	0.470588	−	0.341902i
$563$	2.59399	+	4.49293i	0.109324	+	0.189354i	0.915497	−	0.402326i	$-0.131798\pi$
$563$	2.59399	+	4.49293i	0.109324	+	0.189354i	−0.806173	+	0.591680i	$0.798465\pi$
$564$		0			0
$565$	−4.30442	−	40.9539i	−0.181088	−	1.72294i
$566$	−12.1475	−	8.82566i	−0.510596	−	0.370970i
$567$		0			0
$568$	−0.543993	+	0.604166i	−0.0228255	+	0.0253502i
$569$	−2.16312	−	0.963083i	−0.0906827	−	0.0403746i	0.360894	−	0.932607i	$-0.382472\pi$
$569$	−2.16312	−	0.963083i	−0.0906827	−	0.0403746i	−0.451577	+	0.892232i	$0.649138\pi$
$570$		0			0
$571$	−19.9170	+	4.23348i	−0.833500	+	0.177166i	−0.604846	−	0.796342i	$-0.706765\pi$
$571$	−19.9170	+	4.23348i	−0.833500	+	0.177166i	−0.228653	+	0.973508i	$0.573432\pi$
$572$	−18.7214	+	8.33528i	−0.782779	+	0.348516i
$573$		0			0
$574$	10.0654	−	30.9782i	0.420123	−	1.29301i
$575$	1.57083	−	0.699381i	0.0655083	−	0.0291662i
$576$		0			0
$577$	−25.0227	−	5.31874i	−1.04171	−	0.221422i	−0.344871	−	0.938650i	$-0.612077\pi$
$577$	−25.0227	−	5.31874i	−1.04171	−	0.221422i	−0.696839	+	0.717228i	$0.745411\pi$
$578$	23.6077	+	10.5108i	0.981953	+	0.437194i
$579$		0			0
$580$	0.775382	−	7.37727i	0.0321960	−	0.306324i
$581$	15.4152	+	11.1998i	0.639531	+	0.464646i
$582$		0			0
$583$	20.3516	−	35.2501i	0.842879	−	1.45991i
$584$	−4.31041	−	7.46585i	−0.178366	−	0.308939i
$585$		0			0
$586$	18.7340	+	20.8062i	0.773894	+	0.859497i
$587$	−12.3489	−	38.0060i	−0.509694	−	1.56868i	−0.792733	−	0.609568i	$-0.791343\pi$
$587$	−12.3489	−	38.0060i	−0.509694	−	1.56868i	0.283040	−	0.959108i	$-0.408657\pi$
$588$		0			0
$589$	−0.182141	−	3.44729i	−0.00750499	−	0.142043i
$590$	28.3514			1.16721
$591$		0			0
$592$	−0.610925	−	0.678501i	−0.0251089	−	0.0278862i
$593$	−16.9709	+	12.3301i	−0.696911	+	0.506335i	−0.878925	−	0.476961i	$-0.841738\pi$
$593$	−16.9709	+	12.3301i	−0.696911	+	0.506335i	0.182014	+	0.983296i	$0.441738\pi$
$594$		0			0
$595$	9.18005	−	15.9003i	0.376345	−	0.651849i
$596$	2.95258	+	28.0920i	0.120943	+	1.15069i
$597$		0			0
$598$	−1.51621	+	14.4258i	−0.0620026	+	0.589915i
$599$	−14.0125	+	15.5625i	−0.572535	+	0.635865i	−0.957969	−	0.286870i	$-0.907385\pi$
$599$	−14.0125	+	15.5625i	−0.572535	+	0.635865i	0.385434	+	0.922735i	$0.374052\pi$
$600$		0			0
$601$	16.2555	+	3.45522i	0.663076	+	0.140941i	0.527143	−	0.849777i	$-0.323263\pi$
$601$	16.2555	+	3.45522i	0.663076	+	0.140941i	0.135933	+	0.990718i	$0.456597\pi$
$602$	−2.00859	+	0.426939i	−0.0818640	+	0.0174007i
$603$		0			0
$604$	−14.0886	+	43.3601i	−0.573256	+	1.76430i
$605$	−5.31381	+	16.3542i	−0.216037	+	0.664894i
$606$		0			0
$607$	−28.9056	+	6.14407i	−1.17324	+	0.249380i	−0.752993	−	0.658029i	$-0.771390\pi$
$607$	−28.9056	+	6.14407i	−1.17324	+	0.249380i	−0.420249	+	0.907409i	$0.638057\pi$
$608$	4.91830	+	1.04542i	0.199463	+	0.0423972i
$609$		0			0
$610$	7.25045	−	8.05244i	0.293562	−	0.326034i
$611$	−1.17358	+	11.1659i	−0.0474780	+	0.451723i
$612$		0			0
$613$	−3.87799	−	36.8966i	−0.156631	−	1.49024i	−0.737003	−	0.675889i	$-0.763760\pi$
$613$	−3.87799	−	36.8966i	−0.156631	−	1.49024i	0.580373	−	0.814351i	$-0.302907\pi$
$614$	−23.5453	+	40.7817i	−0.950212	+	1.64582i
$615$		0			0
$616$	−7.74409	+	5.62641i	−0.312018	+	0.226695i
$617$	17.6270	+	19.5768i	0.709636	+	0.788131i	0.984879	−	0.173244i	$-0.0554249\pi$
$617$	17.6270	+	19.5768i	0.709636	+	0.788131i	−0.275243	+	0.961375i	$0.588758\pi$
$618$		0			0
$619$	−26.3796			−1.06029			−0.530144	−	0.847908i	$-0.677862\pi$
$619$	−26.3796			−1.06029			−0.530144	+	0.847908i	$0.677862\pi$
$620$	−4.67796	+	29.6173i	−0.187871	+	1.18946i
$621$		0			0
$622$	6.07875	+	18.7085i	0.243736	+	0.750142i
$623$	12.3247	+	13.6879i	0.493778	+	0.548396i
$624$		0			0
$625$	13.6503	+	23.6430i	0.546012	+	0.945720i
$626$	29.1103	−	50.4204i	1.16348	−	2.01521i
$627$		0			0
$628$	10.7712	+	7.82576i	0.429819	+	0.312282i
$629$	0.0610564	−	0.580913i	0.00243448	−	0.0231625i
$630$		0			0
$631$	18.2446	+	8.12304i	0.726308	+	0.323373i	0.736372	−	0.676576i	$-0.236537\pi$
$631$	18.2446	+	8.12304i	0.726308	+	0.323373i	−0.0100649	+	0.999949i	$0.503204\pi$
$632$	5.16483	+	1.09782i	0.205446	+	0.0436688i
$633$		0			0
$634$	−29.9409	+	13.3305i	−1.18910	+	0.529423i
$635$	10.3015	−	31.7047i	0.408802	−	1.25816i
$636$		0			0
$637$	−12.3982	+	5.52002i	−0.491234	+	0.218711i
$638$	11.9507	−	2.54020i	0.473133	−	0.100568i
$639$		0			0
$640$	−10.3299	−	4.59916i	−0.408324	−	0.181798i
$641$	−15.5874	+	17.3115i	−0.615664	+	0.683764i	−0.967666	−	0.252235i	$-0.918834\pi$
$641$	−15.5874	+	17.3115i	−0.615664	+	0.683764i	0.352002	+	0.935999i	$0.385501\pi$
$642$		0			0
$643$	31.4658	+	22.8612i	1.24089	+	0.901559i	0.997657	−	0.0684089i	$-0.0217922\pi$
$643$	31.4658	+	22.8612i	1.24089	+	0.901559i	0.243232	+	0.969968i	$0.421792\pi$
$644$	2.95474	+	28.1124i	0.116433	+	1.10779i
$645$		0			0
$646$	1.36703	+	2.36777i	0.0537851	+	0.0931585i
$647$	−1.80444	+	1.31100i	−0.0709399	+	0.0515408i	−0.622690	−	0.782469i	$-0.713960\pi$
$647$	−1.80444	+	1.31100i	−0.0709399	+	0.0515408i	0.551750	+	0.834009i	$0.313960\pi$
$648$		0			0
$649$	7.70848	+	23.7243i	0.302584	+	0.931259i
$650$	2.21734			0.0869713
$651$		0			0
$652$	40.7894			1.59744
$653$	8.82960	+	27.1747i	0.345529	+	1.06343i	0.961300	+	0.275504i	$0.0888446\pi$
$653$	8.82960	+	27.1747i	0.345529	+	1.06343i	−0.615771	+	0.787925i	$0.711155\pi$
$654$		0			0
$655$	−13.6546	+	9.92063i	−0.533529	+	0.387631i
$656$	7.11497	+	12.3235i	0.277793	+	0.481151i
$657$		0			0
$658$	4.28122	+	40.7331i	0.166899	+	1.58794i
$659$	4.15656	+	3.01991i	0.161916	+	0.117639i	0.665793	−	0.746136i	$-0.268093\pi$
$659$	4.15656	+	3.01991i	0.161916	+	0.117639i	−0.503877	+	0.863776i	$0.668093\pi$
$660$		0			0
$661$	−3.94482	+	4.38117i	−0.153436	+	0.170408i	−0.814962	−	0.579514i	$-0.803242\pi$
$661$	−3.94482	+	4.38117i	−0.153436	+	0.170408i	0.661526	+	0.749922i	$0.269909\pi$
$662$	−24.5029	−	10.9094i	−0.952333	−	0.424006i
$663$		0			0
$664$	3.08670	−	0.656098i	0.119787	−	0.0254615i
$665$	−4.88672	+	2.17571i	−0.189499	+	0.0843703i
$666$		0			0
$667$	1.42756	−	4.39358i	0.0552754	−	0.170120i
$668$	−4.57220	+	2.03567i	−0.176904	+	0.0787626i
$669$		0			0
$670$	64.7887	+	13.7713i	2.50301	+	0.532031i
$671$	8.70955	+	3.87774i	0.336229	+	0.149699i
$672$		0			0
$673$	−2.84979	+	27.1140i	−0.109851	+	1.04517i	0.791231	+	0.611518i	$0.209441\pi$
$673$	−2.84979	+	27.1140i	−0.109851	+	1.04517i	−0.901082	+	0.433649i	$0.857226\pi$
$674$	−46.7146	−	33.9401i	−1.79938	−	1.30732i
$675$		0			0
$676$	9.91286	−	17.1696i	0.381264	−	0.660368i
$677$	−1.31511	−	2.27784i	−0.0505438	−	0.0875444i	0.839647	−	0.543133i	$-0.182762\pi$
$677$	−1.31511	−	2.27784i	−0.0505438	−	0.0875444i	−0.890190	+	0.455589i	$0.849429\pi$
$678$		0			0
$679$	−16.5080	−	18.3340i	−0.633519	−	0.703594i
$680$	−0.939627	−	2.89187i	−0.0360330	−	0.110898i
$681$		0			0
$682$	−48.7748	+	7.74652i	−1.86768	+	0.296630i
$683$	−29.5859			−1.13207			−0.566037	−	0.824380i	$-0.691524\pi$
$683$	−29.5859			−1.13207			−0.566037	+	0.824380i	$0.691524\pi$
$684$		0			0
$685$	11.9049	+	13.2218i	0.454864	+	0.505178i
$686$	3.06609	−	2.22765i	0.117064	−	0.0850519i
$687$		0			0
$688$	0.448549	−	0.776909i	0.0171008	−	0.0296194i
$689$	−2.07453	−	19.7378i	−0.0790331	−	0.751950i
$690$		0			0
$691$	−1.76087	+	16.7535i	−0.0669866	+	0.637334i	0.908592	+	0.417684i	$0.137158\pi$
$691$	−1.76087	+	16.7535i	−0.0669866	+	0.637334i	−0.975579	+	0.219650i	$0.929508\pi$
$692$	8.45344	−	9.38849i	0.321351	−	0.356897i
$693$		0			0
$694$	−10.7899	−	2.29346i	−0.409579	−	0.0870587i
$695$	−46.1576	+	9.81111i	−1.75086	+	0.372157i
$696$		0			0
$697$	−2.81323	+	8.65822i	−0.106559	+	0.327954i
$698$	2.62397	−	8.07576i	0.0993189	−	0.305672i
$699$		0			0
$700$	4.22664	−	0.898400i	0.159752	−	0.0339563i
$701$	20.7605	+	4.41279i	0.784114	+	0.166669i	0.582537	−	0.812804i	$-0.302060\pi$
$701$	20.7605	+	4.41279i	0.784114	+	0.166669i	0.201577	+	0.979473i	$0.435393\pi$
$702$		0			0
$703$	−0.113873	+	0.126468i	−0.00429479	+	0.00476985i
$704$	4.54235	−	43.2176i	0.171196	−	1.62882i
$705$		0			0
$706$	−4.71948	−	44.9029i	−0.177620	−	1.68994i
$707$	33.1859	−	57.4796i	1.24808	−	2.16174i
$708$		0			0
$709$	−41.5383	+	30.1794i	−1.56001	+	1.13341i	−0.624000	+	0.781424i	$0.714494\pi$
$709$	−41.5383	+	30.1794i	−1.56001	+	1.13341i	−0.936005	+	0.351986i	$0.885506\pi$
$710$	4.34900	+	4.83006i	0.163215	+	0.181269i
$711$		0			0
$712$	3.05044			0.114320
$713$	−6.68457	+	17.4362i	−0.250339	+	0.652989i
$714$		0			0
$715$	6.48241	+	19.9508i	0.242429	+	0.746118i
$716$	−18.6228	−	20.6827i	−0.695967	−	0.772950i
$717$		0			0
$718$	7.33679	+	12.7077i	0.273807	+	0.474247i
$719$	−20.0999	+	34.8141i	−0.749601	+	1.29835i	0.198413	+	0.980119i	$0.436421\pi$
$719$	−20.0999	+	34.8141i	−0.749601	+	1.29835i	−0.948014	+	0.318229i	$0.896912\pi$
$720$		0			0
$721$	11.6393	+	8.45647i	0.433471	+	0.314935i
$722$	−4.03205	+	38.3624i	−0.150058	+	1.42770i
$723$		0			0
$724$	20.2139	+	8.99983i	0.751245	+	0.334476i
$725$	−0.690753	−	0.146824i	−0.0256539	−	0.00545291i
$726$		0			0
$727$	−19.6265	+	8.73827i	−0.727906	+	0.324084i	−0.737017	−	0.675874i	$-0.763766\pi$
$727$	−19.6265	+	8.73827i	−0.727906	+	0.324084i	0.00911160	+	0.999958i	$0.497100\pi$
$728$	−1.44228	+	4.43889i	−0.0534545	+	0.164516i
$729$		0			0
$730$	−62.9615	+	28.0323i	−2.33031	+	1.03752i
$731$	0.561388	−	0.119327i	0.0207637	−	0.00441346i
$732$		0			0
$733$	20.5286	+	9.13991i	0.758241	+	0.337590i	0.749178	−	0.662368i	$-0.230449\pi$
$733$	20.5286	+	9.13991i	0.758241	+	0.337590i	0.00906234	+	0.999959i	$0.497115\pi$
$734$	22.3475	−	24.8194i	0.824861	−	0.916101i
$735$		0			0
$736$	−22.0046	−	15.9872i	−0.811099	−	0.589298i
$737$	6.09174	+	57.9591i	0.224392	+	2.13495i
$738$		0			0
$739$	−26.2750	−	45.5097i	−0.966542	−	1.67410i	−0.705413	−	0.708797i	$-0.749238\pi$
$739$	−26.2750	−	45.5097i	−0.966542	−	1.67410i	−0.261129	−	0.965304i	$-0.584095\pi$
$740$	1.19586	−	0.868842i	0.0439606	−	0.0319393i
$741$		0			0
$742$	−22.3728	−	68.8565i	−0.821333	−	2.52780i
$743$	17.4032			0.638460			0.319230	−	0.947677i	$-0.396576\pi$
$743$	17.4032			0.638460			0.319230	+	0.947677i	$0.396576\pi$
$744$		0			0
$745$	28.9145			1.05934
$746$	6.28728	+	19.3503i	0.230194	+	0.708463i
$747$		0			0
$748$	16.9041	−	12.2815i	0.618074	−	0.449057i
$749$	−20.4224	−	35.3727i	−0.746219	−	1.29249i
$750$		0			0
$751$	2.34603	+	22.3210i	0.0856080	+	0.814505i	0.950118	+	0.311890i	$0.100962\pi$
$751$	2.34603	+	22.3210i	0.0856080	+	0.814505i	−0.864510	+	0.502615i	$0.832371\pi$
$752$	−14.4758	−	10.5173i	−0.527879	−	0.383526i
$753$		0			0
$754$	3.98616	−	4.42708i	0.145168	−	0.161225i
$755$	42.6346	+	18.9821i	1.55163	+	0.690831i
$756$		0			0
$757$	14.4696	−	3.07560i	0.525906	−	0.111785i	0.0626946	−	0.998033i	$-0.480031\pi$
$757$	14.4696	−	3.07560i	0.525906	−	0.111785i	0.463211	+	0.886248i	$0.346697\pi$
$758$	26.1527	−	11.6439i	0.949907	−	0.422926i
$759$		0			0
$760$	−0.273758	+	0.842542i	−0.00993026	+	0.0305622i
$761$	18.1807	−	8.09457i	0.659050	−	0.293428i	−0.0498293	−	0.998758i	$-0.515868\pi$
$761$	18.1807	−	8.09457i	0.659050	−	0.293428i	0.708879	+	0.705330i	$0.249201\pi$
$762$		0			0
$763$	65.0320	+	13.8230i	2.35432	+	0.500426i
$764$	−21.9291	−	9.76346i	−0.793366	−	0.353229i
$765$		0			0
$766$	−2.23224	+	21.2383i	−0.0806541	+	0.767373i
$767$	9.84009	+	7.14925i	0.355305	+	0.258144i
$768$		0			0
$769$	−2.09853	+	3.63477i	−0.0756751	+	0.131073i	−0.901380	−	0.433030i	$-0.857445\pi$
$769$	−2.09853	+	3.63477i	−0.0756751	+	0.131073i	0.825705	+	0.564103i	$0.190778\pi$
$770$	38.2630	+	66.2734i	1.37890	+	2.38833i
$771$		0			0
$772$	−2.74825	−	3.05224i	−0.0989116	−	0.109852i
$773$	−3.67070	−	11.2973i	−0.132026	−	0.406334i	0.863090	−	0.505051i	$-0.168526\pi$
$773$	−3.67070	−	11.2973i	−0.132026	−	0.406334i	−0.995116	+	0.0987167i	$0.968526\pi$
$774$		0			0
$775$	2.75758	+	0.737629i	0.0990551	+	0.0264964i
$776$	−4.08584			−0.146673
$777$		0			0
$778$	−35.1696	−	39.0598i	−1.26089	−	1.40036i
$779$	2.14581	−	1.55903i	0.0768818	−	0.0558579i
$780$		0			0
$781$	−2.85931	+	4.95246i	−0.102314	+	0.177213i
$782$	−1.54592	−	14.7084i	−0.0552820	−	0.525973i
$783$		0			0
$784$	2.26084	−	21.5104i	0.0807442	−	0.768230i
$785$	9.11940	−	10.1281i	0.325485	−	0.361488i
$786$		0			0
$787$	−1.94067	−	0.412503i	−0.0691776	−	0.0147042i	0.173193	−	0.984888i	$-0.444592\pi$
$787$	−1.94067	−	0.412503i	−0.0691776	−	0.0147042i	−0.242370	+	0.970184i	$0.577925\pi$
$788$	14.3520	−	3.05061i	0.511269	−	0.108673i
$789$		0			0
$790$	13.0446	−	40.1470i	0.464105	−	1.42837i
$791$	19.9152	−	61.2926i	0.708102	−	2.17931i
$792$		0			0
$793$	4.54700	−	0.966495i	0.161469	−	0.0343212i
$794$	33.9675	+	7.22001i	1.20546	+	0.256228i
$795$		0			0
$796$	1.42298	−	1.58038i	0.0504361	−	0.0560150i
$797$	−5.26681	+	50.1103i	−0.186560	+	1.77500i	0.355517	+	0.934670i	$0.384305\pi$
$797$	−5.26681	+	50.1103i	−0.186560	+	1.77500i	−0.542077	+	0.840329i	$0.682362\pi$
$798$		0			0
$799$	−1.19657	−	11.3846i	−0.0423317	−	0.402760i
$800$	−2.07889	+	3.60074i	−0.0734998	+	0.127305i
$801$		0			0
$802$	46.3076	−	33.6445i	1.63518	−	1.18803i
$803$	−40.5758	−	45.0640i	−1.43189	−	1.59028i
$804$		0			0
$805$	28.9356			1.01984
$806$	−17.0200	+	17.0345i	−0.599504	+	0.600016i
$807$		0			0
$808$	−3.39675	−	10.4541i	−0.119497	−	0.367775i
$809$	10.4200	+	11.5726i	0.366347	+	0.406870i	0.897931	−	0.440136i	$-0.145070\pi$
$809$	10.4200	+	11.5726i	0.366347	+	0.406870i	−0.531584	+	0.847005i	$0.678403\pi$
$810$		0			0
$811$	−10.3694	−	17.9604i	−0.364119	−	0.630673i	0.624515	−	0.781013i	$-0.285297\pi$
$811$	−10.3694	−	17.9604i	−0.364119	−	0.630673i	−0.988634	+	0.150340i	$0.951963\pi$
$812$	5.80460	−	10.0539i	0.203702	−	0.352822i
$813$		0			0
$814$	1.96964	+	1.43103i	0.0690360	+	0.0501576i
$815$	4.36445	−	41.5249i	0.152880	−	1.45456i
$816$		0			0
$817$	−0.152757	−	0.0680118i	−0.00534429	−	0.00237943i
$818$	−45.8282	−	9.74109i	−1.60235	−	0.340589i
$819$		0			0
$820$	−21.0464	+	9.37047i	−0.734973	+	0.327231i
$821$	−6.05511	+	18.6357i	−0.211325	+	0.650391i	0.788069	+	0.615587i	$0.211081\pi$
$821$	−6.05511	+	18.6357i	−0.211325	+	0.650391i	−0.999394	+	0.0348044i	$0.988919\pi$
$822$		0			0
$823$	1.91901	−	0.854399i	0.0668925	−	0.0297825i	−0.373018	−	0.927824i	$-0.621677\pi$
$823$	1.91901	−	0.854399i	0.0668925	−	0.0297825i	0.439910	+	0.898042i	$0.355010\pi$
$824$	2.33063	−	0.495390i	0.0811912	−	0.0172577i
$825$		0			0
$826$	40.5346	+	18.0472i	1.41038	+	0.627942i
$827$	2.34540	−	2.60483i	0.0815575	−	0.0905787i	−0.700985	−	0.713176i	$-0.747256\pi$
$827$	2.34540	−	2.60483i	0.0815575	−	0.0905787i	0.782542	+	0.622597i	$0.213923\pi$
$828$		0			0
$829$	1.68971	+	1.22765i	0.0586860	+	0.0426379i	0.616742	−	0.787166i	$-0.288452\pi$
$829$	1.68971	+	1.22765i	0.0586860	+	0.0426379i	−0.558056	+	0.829804i	$0.688452\pi$
$830$	−2.63706	−	25.0900i	−0.0915338	−	0.870886i
$831$		0			0
$832$	−10.5943	−	18.3498i	−0.367290	−	0.636166i
$833$	11.1947	−	8.13341i	0.387873	−	0.281806i
$834$		0			0
$835$	1.58316	+	4.87247i	0.0547875	+	0.168619i
$836$	−6.08759			−0.210544
$837$		0			0
$838$	−12.8284			−0.443151
$839$	3.32915	+	10.2461i	0.114935	+	0.353734i	0.991933	−	0.126759i	$-0.0404576\pi$
$839$	3.32915	+	10.2461i	0.114935	+	0.353734i	−0.876998	+	0.480493i	$0.840458\pi$
$840$		0			0
$841$	21.9266	−	15.9306i	0.756088	−	0.549330i
$842$	6.79587	+	11.7708i	0.234201	+	0.405648i
$843$		0			0
$844$	1.48203	+	14.1006i	0.0510137	+	0.485363i
$845$	−16.4185	−	11.9288i	−0.564814	−	0.410362i
$846$		0			0
$847$	−18.0076	+	19.9995i	−0.618749	+	0.687190i
$848$	28.8949	+	12.8648i	0.992256	+	0.441781i
$849$		0			0
$850$	−2.21138	+	0.470043i	−0.0758497	+	0.0161224i
$851$	0.840975	−	0.374426i	0.0288283	−	0.0128352i
$852$		0			0
$853$	10.0895	−	31.0524i	0.345459	−	1.06321i	−0.615879	−	0.787841i	$-0.711199\pi$
$853$	10.0895	−	31.0524i	0.345459	−	1.06321i	0.961338	−	0.275372i	$-0.0888010\pi$
$854$	15.4919	−	6.89745i	0.530123	−	0.236026i
$855$		0			0
$856$	−6.61667	−	1.40642i	−0.226153	−	0.0480703i
$857$	39.9528	+	17.7881i	1.36476	+	0.607631i	0.952808	−	0.303573i	$-0.0981798\pi$
$857$	39.9528	+	17.7881i	1.36476	+	0.607631i	0.411954	+	0.911205i	$0.364846\pi$
$858$		0			0
$859$	2.54697	−	24.2328i	0.0869016	−	0.826813i	−0.861076	−	0.508476i	$-0.830209\pi$
$859$	2.54697	−	24.2328i	0.0869016	−	0.826813i	0.947978	−	0.318337i	$-0.103124\pi$
$860$	1.17501	+	0.853696i	0.0400676	+	0.0291108i
$861$		0			0
$862$	−24.3140	+	42.1130i	−0.828137	+	1.43438i
$863$	−21.7570	−	37.6842i	−0.740616	−	1.28279i	−0.952215	−	0.305429i	$-0.901200\pi$
$863$	−21.7570	−	37.6842i	−0.740616	−	1.28279i	0.211599	−	0.977357i	$-0.432133\pi$
$864$		0			0
$865$	−8.65328	−	9.61044i	−0.294220	−	0.326765i
$866$	−15.5681	−	47.9137i	−0.529025	−	1.62817i
$867$		0			0
$868$	−25.5412	+	39.3668i	−0.866925	+	1.33620i
$869$	37.1415			1.25994
$870$		0			0
$871$	19.0140	+	21.1172i	0.644264	+	0.715528i
$872$	8.90796	−	6.47201i	0.301662	−	0.219170i
$873$		0			0
$874$	−2.15444	+	3.73160i	−0.0728751	+	0.126223i
$875$	4.04674	+	38.5022i	0.136805	+	1.30161i
$876$		0			0
$877$	3.99757	−	38.0343i	0.134988	−	1.28433i	−0.691913	−	0.721981i	$-0.743232\pi$
$877$	3.99757	−	38.0343i	0.134988	−	1.28433i	0.826901	−	0.562347i	$-0.190101\pi$
$878$	−20.1133	+	22.3381i	−0.678793	+	0.753876i
$879$		0			0
$880$	−32.7014	−	6.95089i	−1.10236	−	0.234314i
$881$	39.8511	−	8.47062i	1.34262	−	0.285382i	0.520092	−	0.854110i	$-0.325898\pi$
$881$	39.8511	−	8.47062i	1.34262	−	0.285382i	0.822526	+	0.568728i	$0.192564\pi$
$882$		0			0
$883$	10.2334	−	31.4952i	0.344382	−	1.05990i	−0.617532	−	0.786546i	$-0.711867\pi$
$883$	10.2334	−	31.4952i	0.344382	−	1.05990i	0.961914	−	0.273353i	$-0.0881327\pi$
$884$	3.14826	−	9.68935i	0.105888	−	0.325888i
$885$		0			0
$886$	33.5766	−	7.13693i	1.12803	−	0.239770i
$887$	12.1951	+	2.59214i	0.409470	+	0.0870356i	0.408042	−	0.912963i	$-0.366212\pi$
$887$	12.1951	+	2.59214i	0.409470	+	0.0870356i	0.00142883	+	0.999999i	$0.499545\pi$
$888$		0			0
$889$	34.9100	−	38.7715i	1.17084	−	1.30035i
$890$	2.54914	−	24.2534i	0.0854472	−	0.812976i
$891$		0			0
$892$	−3.81159	−	36.2649i	−0.127622	−	1.21424i
$893$	−1.66758	+	2.88834i	−0.0558035	+	0.0966545i
$894$		0			0
$895$	−23.0483	+	16.7456i	−0.770421	+	0.559743i
$896$	−11.8412	−	13.1510i	−0.395588	−	0.439345i
$897$		0			0
$898$	14.1263			0.471401
$899$	6.43009	−	4.17965i	0.214455	−	0.139399i
$900$		0			0
$901$	6.25307	+	19.2450i	0.208320	+	0.641143i
$902$	−25.3903	−	28.1987i	−0.845403	−	0.938915i
$903$		0			0
$904$	−5.33666	−	9.24337i	−0.177495	−	0.307430i
$905$	11.3250	−	19.6155i	0.376456	−	0.652041i
$906$		0			0
$907$	−13.6734	−	9.93431i	−0.454018	−	0.329863i	0.337162	−	0.941447i	$-0.390533\pi$
$907$	−13.6734	−	9.93431i	−0.454018	−	0.329863i	−0.791180	+	0.611583i	$0.790533\pi$
$908$	−1.11365	+	10.5957i	−0.0369579	+	0.351631i
$909$		0			0
$910$	34.0874	+	15.1767i	1.12999	+	0.503103i
$911$	−53.2794	−	11.3249i	−1.76522	−	0.375210i	−0.792992	−	0.609232i	$-0.791478\pi$
$911$	−53.2794	−	11.3249i	−1.76522	−	0.375210i	−0.972231	+	0.234022i	$0.924811\pi$
$912$		0			0
$913$	20.2781	−	9.02841i	0.671108	−	0.298797i
$914$	−13.7206	+	42.2278i	−0.453838	+	1.39677i
$915$		0			0
$916$	−40.6890	+	18.1159i	−1.34440	+	0.598567i
$917$	−25.8373	+	5.49188i	−0.853222	+	0.181358i
$918$		0			0
$919$	−8.00934	−	3.56599i	−0.264204	−	0.117631i	0.270360	−	0.962759i	$-0.412857\pi$
$919$	−8.00934	−	3.56599i	−0.264204	−	0.117631i	−0.534564	+	0.845128i	$0.679524\pi$
$920$	3.20657	−	3.56125i	0.105717	−	0.117411i
$921$		0			0
$922$	14.5418	+	10.5652i	0.478908	+	0.347947i
$923$	0.291461	+	2.77306i	0.00959355	+	0.0912765i
$924$		0			0
$925$	−0.0703606	−	0.121868i	−0.00231344	−	0.00400700i
$926$	6.11858	−	4.44541i	0.201069	−	0.146085i
$927$		0			0
$928$	3.45188	+	10.6238i	0.113313	+	0.348743i
$929$	44.2868			1.45300			0.726501	−	0.687165i	$-0.241145\pi$
$929$	44.2868			1.45300			0.726501	+	0.687165i	$0.241145\pi$
$930$		0			0
$931$	−4.03150			−0.132127
$932$	10.0992	+	31.0820i	0.330809	+	1.01813i
$933$		0			0
$934$	5.16512	−	3.75268i	0.169008	−	0.122791i
$935$	−10.6943	−	18.5230i	−0.349740	−	0.605767i
$936$		0			0
$937$	5.38495	+	51.2343i	0.175919	+	1.67375i	0.625278	+	0.780402i	$0.284986\pi$
$937$	5.38495	+	51.2343i	0.175919	+	1.67375i	−0.449359	+	0.893351i	$0.648348\pi$
$938$	83.8637	+	60.9306i	2.73825	+	1.98945i
$939$		0			0
$940$	19.3839	−	21.5280i	0.632234	−	0.702167i
$941$	−35.8083	−	15.9429i	−1.16732	−	0.519722i	−0.270757	−	0.962648i	$-0.587274\pi$
$941$	−35.8083	−	15.9429i	−1.16732	−	0.519722i	−0.896559	+	0.442925i	$0.853941\pi$
$942$		0			0
$943$	−14.0341	+	2.98303i	−0.457012	+	0.0971409i
$944$	−17.7084	+	7.88428i	−0.576358	+	0.256611i
$945$		0			0
$946$	−0.739222	+	2.27509i	−0.0240342	+	0.0739696i
$947$	−51.9956	+	23.1500i	−1.68963	+	0.752272i	−0.690038	+	0.723773i	$0.742406\pi$
$947$	−51.9956	+	23.1500i	−1.68963	+	0.752272i	−0.999594	+	0.0284989i	$0.990927\pi$
$948$		0			0
$949$	−28.9212	−	6.14739i	−0.938821	−	0.199553i
$950$	0.601729	+	0.267907i	0.0195227	+	0.00869206i
$951$		0			0
$952$	0.497427	−	4.73270i	0.0161217	−	0.153388i
$953$	−12.3568	−	8.97773i	−0.400275	−	0.290817i	0.369378	−	0.929279i	$-0.379571\pi$
$953$	−12.3568	−	8.97773i	−0.400275	−	0.290817i	−0.769653	+	0.638462i	$0.779571\pi$
$954$		0			0
$955$	−12.2859	+	21.2798i	−0.397563	+	0.688599i
$956$	−7.80028	−	13.5105i	−0.252279	−	0.436960i
$957$		0			0
$958$	−24.1396	−	26.8098i	−0.779916	−	0.866184i
$959$	8.60439	+	26.4816i	0.277850	+	0.855135i
$960$		0			0
$961$	−26.8335	+	15.5229i	−0.865598	+	0.500739i
$962$	1.18709			0.0382735
$963$		0			0
$964$	−17.6578	−	19.6110i	−0.568719	−	0.631627i
$965$	−3.40134	+	2.47122i	−0.109493	+	0.0795513i
$966$		0			0
$967$	−5.64979	+	9.78573i	−0.181685	+	0.314688i	−0.942455	−	0.334334i	$-0.891489\pi$
$967$	−5.64979	+	9.78573i	−0.181685	+	0.314688i	0.760769	+	0.649022i	$0.224822\pi$
$968$	0.465884	+	4.43259i	0.0149741	+	0.142469i
$969$		0			0
$970$	−3.41438	+	32.4857i	−0.109629	+	1.04305i
$971$	10.6179	−	11.7924i	0.340745	−	0.378436i	−0.548280	−	0.836295i	$-0.684717\pi$
$971$	10.6179	−	11.7924i	0.340745	−	0.378436i	0.889025	+	0.457859i	$0.151384\pi$
$972$		0			0
$973$	−72.2379	−	15.3546i	−2.31584	−	0.492247i
$974$	58.3195	−	12.3962i	1.86868	−	0.397200i
$975$		0			0
$976$	−2.28934	+	7.04586i	−0.0732800	+	0.225533i
$977$	5.11731	−	15.7495i	0.163717	−	0.503870i	−0.835222	−	0.549913i	$-0.814661\pi$
$977$	5.11731	−	15.7495i	0.163717	−	0.503870i	0.998939	+	0.0460426i	$0.0146610\pi$
$978$		0			0
$979$	20.9882	−	4.46117i	0.670785	−	0.142580i
$980$	34.2519	+	7.28046i	1.09414	+	0.232566i
$981$		0			0
$982$	−13.6235	+	15.1304i	−0.434743	+	0.482832i
$983$	2.26302	−	21.5312i	0.0721792	−	0.686739i	−0.897276	−	0.441470i	$-0.854457\pi$
$983$	2.26302	−	21.5312i	0.0721792	−	0.686739i	0.969455	−	0.245269i	$-0.0788763\pi$
$984$		0			0
$985$	−1.56996	−	14.9372i	−0.0500232	−	0.475939i
$986$	−3.03697	+	5.26019i	−0.0967169	+	0.167519i
$987$		0			0
$988$	−2.40137	+	1.74469i	−0.0763976	+	0.0555061i
$989$	0.605238	+	0.672185i	0.0192455	+	0.0213743i
$990$		0			0
$991$	32.3028			1.02613			0.513066	−	0.858349i	$-0.328510\pi$
$991$	32.3028			1.02613			0.513066	+	0.858349i	$0.328510\pi$
$992$	−11.7051	−	43.6097i	−0.371639	−	1.38461i
$993$		0			0
$994$	3.14328	+	9.67401i	0.0996987	+	0.306841i
$995$	−1.45662	−	1.61774i	−0.0461779	−	0.0512857i
$996$		0			0
$997$	5.74360	+	9.94821i	0.181902	+	0.315063i	0.942528	−	0.334127i	$-0.108441\pi$
$997$	5.74360	+	9.94821i	0.181902	+	0.315063i	−0.760626	+	0.649190i	$0.775108\pi$
$998$	−11.2392	+	19.4669i	−0.355771	+	0.616213i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	279.2.y.c.82.1		16
3.2	odd	2		31.2.g.a.20.2	yes	16
12.11	even	2		496.2.bg.c.113.2		16
15.2	even	4		775.2.ck.a.299.2		32
15.8	even	4		775.2.ck.a.299.3		32
15.14	odd	2		775.2.bl.a.51.1		16
31.13	odd	30		8649.2.a.be.1.2		8
31.14	even	15	inner	279.2.y.c.262.1		16
31.18	even	15		8649.2.a.bf.1.2		8
93.2	odd	10		961.2.g.s.235.1		16
93.5	odd	6		961.2.d.o.531.4		16
93.8	odd	10		961.2.g.k.846.2		16
93.11	even	30		961.2.d.q.374.1		16
93.14	odd	30		31.2.g.a.14.2	✓	16
93.17	even	30		961.2.g.l.448.2		16
93.20	odd	30		961.2.d.p.374.1		16
93.23	even	10		961.2.g.j.846.2		16
93.26	even	6		961.2.d.n.531.4		16
93.29	even	10		961.2.g.m.235.1		16
93.35	odd	10		961.2.g.t.816.1		16
93.38	odd	30		961.2.g.s.732.1		16
93.41	odd	30		961.2.d.p.388.1		16
93.44	even	30		961.2.a.j.1.7		8
93.47	odd	10		961.2.c.j.439.7		16
93.50	odd	30		961.2.g.t.338.1		16
93.53	even	30		961.2.d.n.628.4		16
93.56	odd	6		961.2.g.k.844.2		16
93.59	odd	30		961.2.c.j.521.7		16
93.65	even	30		961.2.c.i.521.7		16
93.68	even	6		961.2.g.j.844.2		16
93.71	odd	30		961.2.d.o.628.4		16
93.74	even	30		961.2.g.n.338.1		16
93.77	even	10		961.2.c.i.439.7		16
93.80	odd	30		961.2.a.i.1.7		8
93.83	even	30		961.2.d.q.388.1		16
93.86	even	30		961.2.g.m.732.1		16
93.89	even	10		961.2.g.n.816.1		16
93.92	even	2		961.2.g.l.547.2		16
372.107	even	30		496.2.bg.c.417.2		16
465.14	odd	30		775.2.bl.a.76.1		16
465.107	even	60		775.2.ck.a.324.3		32
465.293	even	60		775.2.ck.a.324.2		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.g.a.14.2	✓	16	93.14	odd	30
31.2.g.a.20.2	yes	16	3.2	odd	2
279.2.y.c.82.1		16	1.1	even	1	trivial
279.2.y.c.262.1		16	31.14	even	15	inner
496.2.bg.c.113.2		16	12.11	even	2
496.2.bg.c.417.2		16	372.107	even	30
775.2.bl.a.51.1		16	15.14	odd	2
775.2.bl.a.76.1		16	465.14	odd	30
775.2.ck.a.299.2		32	15.2	even	4
775.2.ck.a.299.3		32	15.8	even	4
775.2.ck.a.324.2		32	465.293	even	60
775.2.ck.a.324.3		32	465.107	even	60
961.2.a.i.1.7		8	93.80	odd	30
961.2.a.j.1.7		8	93.44	even	30
961.2.c.i.439.7		16	93.77	even	10
961.2.c.i.521.7		16	93.65	even	30
961.2.c.j.439.7		16	93.47	odd	10
961.2.c.j.521.7		16	93.59	odd	30
961.2.d.n.531.4		16	93.26	even	6
961.2.d.n.628.4		16	93.53	even	30
961.2.d.o.531.4		16	93.5	odd	6
961.2.d.o.628.4		16	93.71	odd	30
961.2.d.p.374.1		16	93.20	odd	30
961.2.d.p.388.1		16	93.41	odd	30
961.2.d.q.374.1		16	93.11	even	30
961.2.d.q.388.1		16	93.83	even	30
961.2.g.j.844.2		16	93.68	even	6
961.2.g.j.846.2		16	93.23	even	10
961.2.g.k.844.2		16	93.56	odd	6
961.2.g.k.846.2		16	93.8	odd	10
961.2.g.l.448.2		16	93.17	even	30
961.2.g.l.547.2		16	93.92	even	2
961.2.g.m.235.1		16	93.29	even	10
961.2.g.m.732.1		16	93.86	even	30
961.2.g.n.338.1		16	93.74	even	30
961.2.g.n.816.1		16	93.89	even	10
961.2.g.s.235.1		16	93.2	odd	10
961.2.g.s.732.1		16	93.38	odd	30
961.2.g.t.338.1		16	93.50	odd	30
961.2.g.t.816.1		16	93.35	odd	10
8649.2.a.be.1.2		8	31.13	odd	30
8649.2.a.bf.1.2		8	31.18	even	15

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.y (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.640321 - 1.97070i) q^{2} +(-1.85563 + 1.34820i) q^{4} +(1.17396 + 2.03335i) q^{5} +(0.384094 + 3.65441i) q^{7} +(0.492333 + 0.357701i) q^{8} +(3.25543 - 3.61552i) q^{10} +(3.91056 + 1.74109i) q^{11} +(2.04159 - 0.433953i) q^{13} +(6.95582 - 3.09693i) q^{14} +(-1.02791 + 3.16357i) q^{16} +(-1.94411 + 0.865573i) q^{17} +(0.606466 + 0.128908i) q^{19} +(-4.91979 - 2.19043i) q^{20} +(0.927168 - 8.82142i) q^{22} +(-2.71334 - 1.97136i) q^{23} +(-0.256344 + 0.444001i) q^{25} +(-2.16247 - 3.74550i) q^{26} +(-5.63960 - 6.26341i) q^{28} +(0.425645 + 1.31000i) q^{29} +(-1.44334 - 5.37743i) q^{31} +8.10976 q^{32} +(2.95064 + 3.27702i) q^{34} +(-6.97979 + 5.07112i) q^{35} +(-0.137239 + 0.237704i) q^{37} +(-0.134293 - 1.27771i) q^{38} +(-0.149354 + 1.42101i) q^{40} +(2.86248 - 3.17911i) q^{41} +(-0.263799 - 0.0560722i) q^{43} +(-9.60390 + 2.04137i) q^{44} +(-2.14756 + 6.60950i) q^{46} +(-1.66225 + 5.11589i) q^{47} +(-6.36016 + 1.35189i) q^{49} +(1.03914 + 0.220875i) q^{50} +(-3.20338 + 3.55772i) q^{52} +(0.993928 - 9.45659i) q^{53} +(1.05057 + 9.99551i) q^{55} +(-1.11808 + 1.93658i) q^{56} +(2.30908 - 1.67764i) q^{58} +(3.89932 + 4.33063i) q^{59} +2.22719 q^{61} +(-9.67313 + 6.28768i) q^{62} +(-3.13704 - 9.65481i) q^{64} +(3.27911 + 3.64182i) q^{65} +(6.80719 + 11.7904i) q^{67} +(2.44059 - 4.22722i) q^{68} +(14.4630 + 10.5080i) q^{70} +(-0.139642 + 1.32861i) q^{71} +(-12.9413 - 5.76184i) q^{73} +(0.556321 + 0.118250i) q^{74} +(-1.29917 + 0.578429i) q^{76} +(-4.86065 + 14.9595i) q^{77} +(7.92648 - 3.52910i) q^{79} +(-7.63936 + 1.62380i) q^{80} +(-8.09799 - 3.60546i) q^{82} +(3.46976 - 3.85356i) q^{83} +(-4.04231 - 2.93691i) q^{85} +(0.0584142 + 0.555774i) q^{86} +(1.30251 + 2.25601i) q^{88} +(4.05526 - 2.94632i) q^{89} +(2.37001 + 7.29413i) q^{91} +7.69274 q^{92} +11.1463 q^{94} +(0.449849 + 1.38449i) q^{95} +(-5.43173 + 3.94638i) q^{97} +(6.73673 + 11.6684i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 6 q^{2} - 14 q^{4} + 3 q^{5} + 2 q^{7} - 17 q^{8} - 2 q^{10} + 7 q^{11} - 7 q^{13} + 6 q^{14} - 2 q^{16} + 6 q^{17} + 16 q^{19} - 37 q^{20} + 9 q^{22} - q^{23} - 13 q^{25} - 9 q^{26} - 30 q^{28}+ \cdots + 10 q^{98}+O(q^{100}) \) 16 * q + 6 * q^2 - 14 * q^4 + 3 * q^5 + 2 * q^7 - 17 * q^8 - 2 * q^10 + 7 * q^11 - 7 * q^13 + 6 * q^14 - 2 * q^16 + 6 * q^17 + 16 * q^19 - 37 * q^20 + 9 * q^22 - q^23 - 13 * q^25 - 9 * q^26 - 30 * q^28 + 14 * q^29 + 15 * q^31 + 42 * q^32 - 32 * q^34 + 9 * q^35 - 8 * q^37 - 8 * q^38 - q^40 + 8 * q^41 + 23 * q^43 - 39 * q^44 + 34 * q^46 - 14 * q^47 + 2 * q^49 - 3 * q^50 + 29 * q^52 - 6 * q^53 - 7 * q^55 + 30 * q^56 - 15 * q^58 - 4 * q^59 - 60 * q^61 + 25 * q^62 + 23 * q^64 + 12 * q^65 + 13 * q^67 - 30 * q^68 + 12 * q^70 + 14 * q^71 + 2 * q^73 - 13 * q^74 - 12 * q^76 - 18 * q^77 + 18 * q^79 - 36 * q^80 + 14 * q^82 + 16 * q^83 + 37 * q^85 + 26 * q^86 - 17 * q^88 - q^89 + 8 * q^91 + 64 * q^92 + 44 * q^94 + 22 * q^95 + 3 * q^97 + 10 * q^98

Introduction

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