LMFDB - Embedded newform 31.2.g.a.20.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [31,2,Mod(7,31)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(31, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([28]))

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

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

chi := DirichletCharacter("31.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	31.g (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:	$0.247536246266$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			20.2
Root			$-0.333129i$ of defining polynomial
Character	$\chi$	$=$	31.20
Dual form			31.2.g.a.14.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.640321 + 1.97070i) q^{2} +(-1.43153 - 1.58988i) q^{3} +(-1.85563 + 1.34820i) q^{4} +(-1.17396 - 2.03335i) q^{5} +(2.21654 - 3.83916i) q^{6} +(0.384094 + 3.65441i) q^{7} +(-0.492333 - 0.357701i) q^{8} +(-0.164841 + 1.56836i) q^{9} +O(q^{10})$	\(q+(0.640321 + 1.97070i) q^{2} +(-1.43153 - 1.58988i) q^{3} +(-1.85563 + 1.34820i) q^{4} +(-1.17396 - 2.03335i) q^{5} +(2.21654 - 3.83916i) q^{6} +(0.384094 + 3.65441i) q^{7} +(-0.492333 - 0.357701i) q^{8} +(-0.164841 + 1.56836i) q^{9} +(3.25543 - 3.61552i) q^{10} +(-3.91056 - 1.74109i) q^{11} +(4.79986 + 1.02024i) q^{12} +(2.04159 - 0.433953i) q^{13} +(-6.95582 + 3.09693i) q^{14} +(-1.55222 + 4.77725i) q^{15} +(-1.02791 + 3.16357i) q^{16} +(1.94411 - 0.865573i) q^{17} +(-3.19632 + 0.679399i) q^{18} +(0.606466 + 0.128908i) q^{19} +(4.91979 + 2.19043i) q^{20} +(5.26022 - 5.84207i) q^{21} +(0.927168 - 8.82142i) q^{22} +(2.71334 + 1.97136i) q^{23} +(0.136090 + 1.29481i) q^{24} +(-0.256344 + 0.444001i) q^{25} +(2.16247 + 3.74550i) q^{26} +(-2.46294 + 1.78943i) q^{27} +(-5.63960 - 6.26341i) q^{28} +(-0.425645 - 1.31000i) q^{29} -10.4085 q^{30} +(-1.44334 - 5.37743i) q^{31} -8.10976 q^{32} +(2.82997 + 8.70975i) q^{33} +(2.95064 + 3.27702i) q^{34} +(6.97979 - 5.07112i) q^{35} +(-1.80857 - 3.13253i) q^{36} +(-0.137239 + 0.237704i) q^{37} +(0.134293 + 1.27771i) q^{38} +(-3.61253 - 2.62466i) q^{39} +(-0.149354 + 1.42101i) q^{40} +(-2.86248 + 3.17911i) q^{41} +(14.8812 + 6.62555i) q^{42} +(-0.263799 - 0.0560722i) q^{43} +(9.60390 - 2.04137i) q^{44} +(3.38254 - 1.50600i) q^{45} +(-2.14756 + 6.60950i) q^{46} +(1.66225 - 5.11589i) q^{47} +(6.50117 - 2.89451i) q^{48} +(-6.36016 + 1.35189i) q^{49} +(-1.03914 - 0.220875i) q^{50} +(-4.15921 - 1.85180i) q^{51} +(-3.20338 + 3.55772i) q^{52} +(-0.993928 + 9.45659i) q^{53} +(-5.10351 - 3.70792i) q^{54} +(1.05057 + 9.99551i) q^{55} +(1.11808 - 1.93658i) q^{56} +(-0.663228 - 1.14874i) q^{57} +(2.30908 - 1.67764i) q^{58} +(-3.89932 - 4.33063i) q^{59} +(-3.56032 - 10.9575i) q^{60} +2.22719 q^{61} +(9.67313 - 6.28768i) q^{62} -5.79474 q^{63} +(-3.13704 - 9.65481i) q^{64} +(-3.27911 - 3.64182i) q^{65} +(-15.3522 + 11.1541i) q^{66} +(6.80719 + 11.7904i) q^{67} +(-2.44059 + 4.22722i) q^{68} +(-0.750018 - 7.13595i) q^{69} +(14.4630 + 10.5080i) q^{70} +(0.139642 - 1.32861i) q^{71} +(0.642159 - 0.713189i) q^{72} +(-12.9413 - 5.76184i) q^{73} +(-0.556321 - 0.118250i) q^{74} +(1.07287 - 0.228046i) q^{75} +(-1.29917 + 0.578429i) q^{76} +(4.86065 - 14.9595i) q^{77} +(2.85925 - 8.79986i) q^{78} +(7.92648 - 3.52910i) q^{79} +(7.63936 - 1.62380i) q^{80} +(10.9984 + 2.33777i) q^{81} +(-8.09799 - 3.60546i) q^{82} +(-3.46976 + 3.85356i) q^{83} +(-1.88479 + 17.9325i) q^{84} +(-4.04231 - 2.93691i) q^{85} +(-0.0584142 - 0.555774i) q^{86} +(-1.47342 + 2.55203i) q^{87} +(1.30251 + 2.25601i) q^{88} +(-4.05526 + 2.94632i) q^{89} +(5.13379 + 5.70166i) q^{90} +(2.37001 + 7.29413i) q^{91} -7.69274 q^{92} +(-6.48327 + 9.99270i) q^{93} +11.1463 q^{94} +(-0.449849 - 1.38449i) q^{95} +(11.6094 + 12.8935i) q^{96} +(-5.43173 + 3.94638i) q^{97} +(-6.73673 - 11.6684i) q^{98} +(3.37528 - 5.84615i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9}+O(q^{10}) $ 16 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9	\( 16 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9} - 2 q^{10} - 7 q^{11} + 5 q^{12} - 7 q^{13} - 6 q^{14} + 14 q^{15} - 2 q^{16} - 6 q^{17} - 3 q^{18} + 16 q^{19} + 37 q^{20} + 9 q^{21} + 9 q^{22} + q^{23} - 20 q^{24} - 13 q^{25} + 9 q^{26} + 9 q^{27} - 30 q^{28} - 14 q^{29} - 22 q^{30} + 15 q^{31} - 42 q^{32} - 13 q^{33} - 32 q^{34} - 9 q^{35} + q^{36} - 8 q^{37} + 8 q^{38} - 3 q^{39} - q^{40} - 8 q^{41} + 69 q^{42} + 23 q^{43} + 39 q^{44} + 65 q^{45} + 34 q^{46} + 14 q^{47} + 34 q^{48} + 2 q^{49} + 3 q^{50} - 42 q^{51} + 29 q^{52} + 6 q^{53} - 46 q^{54} - 7 q^{55} - 30 q^{56} - 17 q^{57} - 15 q^{58} + 4 q^{59} - 75 q^{60} - 60 q^{61} - 25 q^{62} - 46 q^{63} + 23 q^{64} - 12 q^{65} - 30 q^{66} + 13 q^{67} + 30 q^{68} + 38 q^{69} + 12 q^{70} - 14 q^{71} + 37 q^{72} + 2 q^{73} + 13 q^{74} + 13 q^{75} - 12 q^{76} + 18 q^{77} - 15 q^{78} + 18 q^{79} + 36 q^{80} + 23 q^{81} + 14 q^{82} - 16 q^{83} + 8 q^{84} + 37 q^{85} - 26 q^{86} + 15 q^{87} - 17 q^{88} + q^{89} - 23 q^{90} + 8 q^{91} - 64 q^{92} + 17 q^{93} + 44 q^{94} - 22 q^{95} + 8 q^{96} + 3 q^{97} - 10 q^{98} + 6 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9 - 2 * q^10 - 7 * q^11 + 5 * q^12 - 7 * q^13 - 6 * q^14 + 14 * q^15 - 2 * q^16 - 6 * q^17 - 3 * q^18 + 16 * q^19 + 37 * q^20 + 9 * q^21 + 9 * q^22 + q^23 - 20 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 - 30 * q^28 - 14 * q^29 - 22 * q^30 + 15 * q^31 - 42 * q^32 - 13 * q^33 - 32 * q^34 - 9 * q^35 + q^36 - 8 * q^37 + 8 * q^38 - 3 * q^39 - q^40 - 8 * q^41 + 69 * q^42 + 23 * q^43 + 39 * q^44 + 65 * q^45 + 34 * q^46 + 14 * q^47 + 34 * q^48 + 2 * q^49 + 3 * q^50 - 42 * q^51 + 29 * q^52 + 6 * q^53 - 46 * q^54 - 7 * q^55 - 30 * q^56 - 17 * q^57 - 15 * q^58 + 4 * q^59 - 75 * q^60 - 60 * q^61 - 25 * q^62 - 46 * q^63 + 23 * q^64 - 12 * q^65 - 30 * q^66 + 13 * q^67 + 30 * q^68 + 38 * q^69 + 12 * q^70 - 14 * q^71 + 37 * q^72 + 2 * q^73 + 13 * q^74 + 13 * q^75 - 12 * q^76 + 18 * q^77 - 15 * q^78 + 18 * q^79 + 36 * q^80 + 23 * q^81 + 14 * q^82 - 16 * q^83 + 8 * q^84 + 37 * q^85 - 26 * q^86 + 15 * q^87 - 17 * q^88 + q^89 - 23 * q^90 + 8 * q^91 - 64 * q^92 + 17 * q^93 + 44 * q^94 - 22 * q^95 + 8 * q^96 + 3 * q^97 - 10 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{4}{15}\right)$

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	$0.161696\pi$
$2$	0.640321	+	1.97070i	0.452775	+	1.39350i	−0.420952	+	0.907083i	$0.638304\pi$
$3$	−1.43153	−	1.58988i	−0.826496	−	0.917916i	0.171236	−	0.985230i	$-0.445224\pi$
$3$	−1.43153	−	1.58988i	−0.826496	−	0.917916i	−0.997732	+	0.0673137i	$0.978557\pi$
$4$	−1.85563	+	1.34820i	−0.927816	+	0.674098i
$5$	−1.17396	−	2.03335i	−0.525009	−	0.909342i	−0.999576	−	0.0291228i	$-0.990729\pi$
$5$	−1.17396	−	2.03335i	−0.525009	−	0.909342i	0.474567	−	0.880219i	$-0.342605\pi$
$6$	2.21654	−	3.83916i	0.904898	−	1.56733i
$7$	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
$9$	−0.164841	+	1.56836i	−0.0549470	+	0.522786i
$10$	3.25543	−	3.61552i	1.02946	−	1.14333i
$11$	−3.91056	−	1.74109i	−1.17908	−	0.524960i	−0.278832	−	0.960340i	$-0.589947\pi$
$11$	−3.91056	−	1.74109i	−1.17908	−	0.524960i	−0.900247	+	0.435380i	$0.856614\pi$
$12$	4.79986	+	1.02024i	1.38560	+	0.294519i
$13$	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
$15$	−1.55222	+	4.77725i	−0.400782	+	1.23348i
$16$	−1.02791	+	3.16357i	−0.256976	+	0.790892i
$17$	1.94411	−	0.865573i	0.471516	−	0.209932i	−0.157201	−	0.987567i	$-0.550247\pi$
$17$	1.94411	−	0.865573i	0.471516	−	0.209932i	0.628717	+	0.777634i	$0.283580\pi$
$18$	−3.19632	+	0.679399i	−0.753380	+	0.160136i
$19$	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
$21$	5.26022	−	5.84207i	1.14788	−	1.27484i
$22$	0.927168	−	8.82142i	0.197673	−	1.88073i
$23$	2.71334	+	1.97136i	0.565771	+	0.411057i	0.833567	−	0.552419i	$-0.186295\pi$
$23$	2.71334	+	1.97136i	0.565771	+	0.411057i	−0.267796	+	0.963476i	$0.586295\pi$
$24$	0.136090	+	1.29481i	0.0277792	+	0.264302i
$25$	−0.256344	+	0.444001i	−0.0512688	+	0.0888002i
$26$	2.16247	+	3.74550i	0.424094	+	0.734553i
$27$	−2.46294	+	1.78943i	−0.473993	+	0.344376i
$28$	−5.63960	−	6.26341i	−1.06578	−	1.18367i
$29$	−0.425645	−	1.31000i	−0.0790403	−	0.243261i	0.903727	−	0.428110i	$-0.140820\pi$
$29$	−0.425645	−	1.31000i	−0.0790403	−	0.243261i	−0.982767	+	0.184849i	$0.940820\pi$
$30$	−10.4085			−1.90032
$31$	−1.44334	−	5.37743i	−0.259231	−	0.965815i
$31$	−1.44334	−	5.37743i	−0.259231	−	0.965815i
$32$	−8.10976			−1.43362
$33$	2.82997	+	8.70975i	0.492634	+	1.51617i
$34$	2.95064	+	3.27702i	0.506031	+	0.562004i
$35$	6.97979	−	5.07112i	1.17980	−	0.857175i
$36$	−1.80857	−	3.13253i	−0.301428	−	0.522089i
$37$	−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
$39$	−3.61253	−	2.62466i	−0.578468	−	0.420282i
$40$	−0.149354	+	1.42101i	−0.0236150	+	0.224681i
$41$	−2.86248	+	3.17911i	−0.447045	+	0.496494i	−0.923978	−	0.382446i	$-0.875082\pi$
$41$	−2.86248	+	3.17911i	−0.447045	+	0.496494i	0.476933	+	0.878940i	$0.341748\pi$
$42$	14.8812	+	6.62555i	2.29622	+	1.02234i
$43$	−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
$45$	3.38254	−	1.50600i	0.504239	−	0.224502i
$46$	−2.14756	+	6.60950i	−0.316640	+	0.974517i
$47$	1.66225	−	5.11589i	0.242464	−	0.746229i	−0.753579	−	0.657358i	$-0.771674\pi$
$47$	1.66225	−	5.11589i	0.242464	−	0.746229i	0.996043	−	0.0888711i	$-0.0283259\pi$
$48$	6.50117	−	2.89451i	0.938363	−	0.417786i
$49$	−6.36016	+	1.35189i	−0.908595	+	0.193128i
$50$	−1.03914	−	0.220875i	−0.146956	−	0.0312365i
$51$	−4.15921	−	1.85180i	−0.582406	−	0.259304i
$52$	−3.20338	+	3.55772i	−0.444229	+	0.493367i
$53$	−0.993928	+	9.45659i	−0.136527	+	1.29896i	0.684895	+	0.728642i	$0.259848\pi$
$53$	−0.993928	+	9.45659i	−0.136527	+	1.29896i	−0.821422	+	0.570321i	$0.806819\pi$
$54$	−5.10351	−	3.70792i	−0.694500	−	0.504584i
$55$	1.05057	+	9.99551i	0.141659	+	1.34779i
$56$	1.11808	−	1.93658i	0.149410	−	0.258786i
$57$	−0.663228	−	1.14874i	−0.0878467	−	0.152155i
$58$	2.30908	−	1.67764i	0.303196	−	0.220285i
$59$	−3.89932	−	4.33063i	−0.507648	−	0.563800i	0.433778	−	0.901020i	$-0.357180\pi$
$59$	−3.89932	−	4.33063i	−0.507648	−	0.563800i	−0.941426	+	0.337220i	$0.890513\pi$
$60$	−3.56032	−	10.9575i	−0.459635	−	1.41461i
$61$	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
$63$	−5.79474			−0.730068
$64$	−3.13704	−	9.65481i	−0.392130	−	1.20685i
$65$	−3.27911	−	3.64182i	−0.406724	−	0.451713i
$66$	−15.3522	+	11.1541i	−1.88973	+	1.37297i
$67$	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
$69$	−0.750018	−	7.13595i	−0.0902916	−	0.859067i
$70$	14.4630	+	10.5080i	1.72866	+	1.25594i
$71$	0.139642	−	1.32861i	0.0165725	−	0.157676i	−0.983106	−	0.183038i	$-0.941407\pi$
$71$	0.139642	−	1.32861i	0.0165725	−	0.157676i	0.999678	+	0.0253613i	$0.00807361\pi$
$72$	0.642159	−	0.713189i	0.0756791	−	0.0840502i
$73$	−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
$75$	1.07287	−	0.228046i	0.123885	−	0.0263325i
$76$	−1.29917	+	0.578429i	−0.149025	+	0.0663503i
$77$	4.86065	−	14.9595i	0.553922	−	1.70480i
$78$	2.85925	−	8.79986i	0.323746	−	0.996388i
$79$	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
$81$	10.9984	+	2.33777i	1.22204	+	0.259753i
$82$	−8.09799	−	3.60546i	−0.894274	−	0.398156i
$83$	−3.46976	+	3.85356i	−0.380856	+	0.422983i	−0.902843	−	0.429970i	$-0.858524\pi$
$83$	−3.46976	+	3.85356i	−0.380856	+	0.422983i	0.521987	+	0.852953i	$0.325191\pi$
$84$	−1.88479	+	17.9325i	−0.205647	+	1.95660i
$85$	−4.04231	−	2.93691i	−0.438450	−	0.318553i
$86$	−0.0584142	−	0.555774i	−0.00629897	−	0.0599307i
$87$	−1.47342	+	2.55203i	−0.157967	+	0.273607i
$88$	1.30251	+	2.25601i	0.138848	+	0.240491i
$89$	−4.05526	+	2.94632i	−0.429857	+	0.312309i	−0.781592	−	0.623790i	$-0.785592\pi$
$89$	−4.05526	+	2.94632i	−0.429857	+	0.312309i	0.351735	+	0.936100i	$0.385592\pi$
$90$	5.13379	+	5.70166i	0.541149	+	0.601007i
$91$	2.37001	+	7.29413i	0.248444	+	0.764632i
$92$	−7.69274			−0.802024
$93$	−6.48327	+	9.99270i	−0.672284	+	1.03619i
$94$	11.1463			1.14965
$95$	−0.449849	−	1.38449i	−0.0461535	−	0.142046i
$96$	11.6094	+	12.8935i	1.18488	+	1.31594i
$97$	−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
$99$	3.37528	−	5.84615i	0.339228	−	0.587560i
$100$	−0.122920	−	1.16950i	−0.0122920	−	0.116950i
$101$	14.6130	+	10.6169i	1.45404	+	1.05642i	0.984866	+	0.173320i	$0.0554495\pi$
$101$	14.6130	+	10.6169i	1.45404	+	1.05642i	0.469177	+	0.883104i	$0.344550\pi$
$102$	0.986121	−	9.38232i	0.0976406	−	0.928988i
$103$	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
$105$	−18.0543	−	3.83755i	−1.76191	−	0.374506i
$106$	−19.2726	+	4.09652i	−1.87192	+	0.397889i
$107$	10.1546	−	4.52113i	0.981685	−	0.437074i	0.147803	−	0.989017i	$-0.452780\pi$
$107$	10.1546	−	4.52113i	0.981685	−	0.437074i	0.833882	+	0.551943i	$0.186113\pi$
$108$	2.15781	−	6.64105i	0.207635	−	0.639036i
$109$	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
$111$	0.574382	−	0.122089i	0.0545179	−	0.0115881i
$112$	−11.9558	−	2.54128i	−1.12972	−	0.240129i
$113$	16.0224	+	7.13365i	1.50727	+	0.671078i	0.983520	−	0.180798i	$-0.0578679\pi$
$113$	16.0224	+	7.13365i	1.50727	+	0.671078i	0.523745	+	0.851875i	$0.324535\pi$
$114$	1.83916	−	2.04259i	0.172253	−	0.191306i
$115$	0.823120	−	7.83147i	0.0767564	−	0.730288i
$116$	2.55598	+	1.85703i	0.237317	+	0.172421i
$117$	0.344056	+	3.27347i	0.0318080	+	0.302633i
$118$	6.03758	−	10.4574i	0.555804	−	0.962681i
$119$	3.90988	+	6.77211i	0.358418	+	0.620798i
$120$	2.47304	−	1.79677i	0.225756	−	0.164022i
$121$	4.90064	+	5.44271i	0.445513	+	0.494792i
$122$	1.42611	+	4.38913i	0.129114	+	0.397373i
$123$	9.15213			0.825220
$124$	9.92814	+	8.03263i	0.891573	+	0.721352i
$125$	−10.5358			−0.942352
$126$	−3.71049	−	11.4197i	−0.330557	−	1.01735i
$127$	−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
$129$	0.288489	+	0.499677i	0.0254000	+	0.0439941i
$130$	5.07728	−	8.79410i	0.445307	−	0.771294i
$131$	−0.751404	−	7.14913i	−0.0656505	−	0.624623i	−0.977037	−	0.213071i	$-0.931654\pi$
$131$	−0.751404	−	7.14913i	−0.0656505	−	0.624623i	0.911386	−	0.411552i	$-0.135013\pi$
$132$	−16.9938	−	12.3467i	−1.47912	−	1.07465i
$133$	−0.238144	+	2.26579i	−0.0206497	+	0.196469i
$134$	−18.8766	+	20.9646i	−1.63069	+	1.81107i
$135$	6.52993	+	2.90731i	0.562007	+	0.250221i
$136$	−1.26676	−	0.269259i	−0.108624	−	0.0230888i
$137$	−7.41206	+	1.57548i	−0.633255	+	0.134603i	−0.513345	−	0.858182i	$-0.671594\pi$
$137$	−7.41206	+	1.57548i	−0.633255	+	0.134603i	−0.119910	+	0.992785i	$0.538261\pi$
$138$	13.5826	−	6.04736i	1.15623	−	0.514785i
$139$	−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
$141$	−10.5132	+	4.68078i	−0.885371	+	0.394193i
$142$	2.70771	−	0.575541i	0.227226	−	0.0482983i
$143$	−8.73931	−	1.85760i	−0.730818	−	0.155340i
$144$	−4.79216	−	2.13361i	−0.399347	−	0.177801i
$145$	−2.16400	+	2.40337i	−0.179711	+	0.199589i
$146$	3.06830	−	29.1929i	0.253934	−	2.41602i
$147$	11.2541	+	8.17660i	0.928225	+	0.674395i
$148$	−0.0658074	−	0.626116i	−0.00540934	−	0.0514664i
$149$	−6.15749	+	10.6651i	−0.504441	+	0.873717i	0.495546	+	0.868582i	$0.334968\pi$
$149$	−6.15749	+	10.6651i	−0.504441	+	0.873717i	−0.999987	+	0.00513554i	$0.998365\pi$
$150$	1.13639	+	1.96829i	0.0927862	+	0.160710i
$151$	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
$153$	1.03706	+	3.19174i	0.0838412	+	0.258037i
$154$	32.5932			2.62644
$155$	−9.23979	+	9.24768i	−0.742158	+	0.742792i
$156$	10.2421			0.820023
$157$	−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
$159$	16.4577	−	11.9572i	1.30518	−	0.948267i
$160$	9.52050	+	16.4900i	0.752662	+	1.30365i
$161$	−6.16198	+	10.6729i	−0.485632	+	0.841139i
$162$	2.43542	+	23.1714i	0.191344	+	1.82052i
$163$	−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
$165$	14.3877	−	15.9792i	1.12008	−	1.24398i
$166$	−9.81599	−	4.37036i	−0.761869	−	0.339206i
$167$	−2.13435	−	0.453670i	−0.165161	−	0.0351060i	0.124589	−	0.992208i	$-0.460239\pi$
$167$	−2.13435	−	0.453670i	−0.165161	−	0.0351060i	−0.289750	+	0.957102i	$0.593572\pi$
$168$	−4.67949	+	0.994657i	−0.361031	+	0.0767394i
$169$	−7.89632	+	3.51567i	−0.607409	+	0.270436i
$170$	3.19941	−	9.84677i	0.245383	−	0.755212i
$171$	−0.302145	+	0.929907i	−0.0231056	+	0.0711117i
$172$	0.565110	−	0.251603i	0.0430892	−	0.0191846i
$173$	5.38757	−	1.14516i	0.409609	−	0.0870651i	0.00150131	−	0.999999i	$-0.499522\pi$
$173$	5.38757	−	1.14516i	0.409609	−	0.0870651i	0.408108	+	0.912934i	$0.366189\pi$
$174$	−5.97276	−	1.26955i	−0.452794	−	0.0962443i
$175$	−1.72102	−	0.766249i	−0.130097	−	0.0579230i
$176$	9.52776	−	10.5816i	0.718182	−	0.797621i
$177$	−1.30317	+	12.3989i	−0.0979526	+	0.931956i
$178$	−8.40300	−	6.10514i	−0.629831	−	0.457599i
$179$	−1.26834	−	12.0674i	−0.0947999	−	0.901961i	−0.933792	−	0.357817i	$-0.883521\pi$
$179$	−1.26834	−	12.0674i	−0.0947999	−	0.901961i	0.838992	−	0.544144i	$-0.183146\pi$
$180$	−4.24636	+	7.35491i	−0.316505	+	0.548202i
$181$	−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
$183$	−3.18829	−	3.54096i	−0.235685	−	0.261755i
$184$	−0.630711	−	1.94113i	−0.0464966	−	0.143102i
$185$	0.644448			0.0473808
$186$	−23.8440	−	6.37808i	−1.74833	−	0.467663i
$187$	−9.10960			−0.666160
$188$	3.81269	+	11.7342i	0.278069	+	0.855808i
$189$	−7.48532	−	8.31329i	−0.544477	−	0.604703i
$190$	2.44038	−	1.77304i	0.177044	−	0.128630i
$191$	−5.23270	−	9.06331i	−0.378625	−	0.655798i	0.612237	−	0.790674i	$-0.290270\pi$
$191$	−5.23270	−	9.06331i	−0.378625	−	0.655798i	−0.990862	+	0.134876i	$0.956936\pi$
$192$	−10.8592	+	18.8087i	−0.783695	+	1.35740i
$193$	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
$195$	−1.09590	+	10.4268i	−0.0784789	+	0.746677i
$196$	9.97950	−	11.0834i	0.712822	−	0.791669i
$197$	5.84391	+	2.60188i	0.416361	+	0.185376i	0.604216	−	0.796821i	$-0.293487\pi$
$197$	5.84391	+	2.60188i	0.416361	+	0.185376i	−0.187854	+	0.982197i	$0.560153\pi$
$198$	13.6823	+	2.90826i	0.972359	+	0.206681i
$199$	−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
$201$	9.00059	−	27.7010i	0.634852	−	1.95387i
$202$	−11.5659	+	35.5961i	−0.813771	+	2.50453i
$203$	4.62379	−	2.05865i	0.324527	−	0.144489i
$204$	10.2146	−	2.17117i	0.715162	−	0.152012i
$205$	9.82467	+	2.08830i	0.686185	+	0.145853i
$206$	7.41161	+	3.29986i	0.516391	+	0.229912i
$207$	−3.53906	+	3.93053i	−0.245982	+	0.273191i
$208$	−0.725720	+	6.90477i	−0.0503197	+	0.478759i
$209$	−2.14718	−	1.56002i	−0.148524	−	0.107909i
$210$	−3.99784	−	38.0369i	−0.275877	−	2.62479i
$211$	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
$213$	−2.31222	+	1.67993i	−0.158431	+	0.115107i
$214$	15.4120	+	17.1168i	1.05354	+	1.17008i
$215$	0.195674	+	0.602222i	0.0133448	+	0.0410712i
$216$	1.85267			0.126058
$217$	19.0970	−	7.34000i	1.29639	−	0.498272i
$218$	37.4917			2.53926
$219$	9.36527	+	28.8233i	0.632846	+	1.94770i
$220$	−15.4254	−	17.1316i	−1.03998	−	1.15501i
$221$	3.59345	−	2.61080i	0.241722	−	0.175621i
$222$	0.608389	+	1.05376i	0.0408324	+	0.0707238i
$223$	−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
$225$	−0.654096	−	0.475229i	−0.0436064	−	0.0316819i
$226$	−3.79882	+	36.1433i	−0.252694	+	2.40422i
$227$	−3.10808	+	3.45188i	−0.206291	+	0.229109i	−0.837408	−	0.546578i	$-0.815930\pi$
$227$	−3.10808	+	3.45188i	−0.206291	+	0.229109i	0.631117	+	0.775688i	$0.282597\pi$
$228$	2.77944	+	1.23749i	0.184073	+	0.0819545i
$229$	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
$231$	−30.7420	+	13.6872i	−2.02268	+	0.900554i
$232$	−0.259029	+	0.797210i	−0.0170061	+	0.0523394i
$233$	−4.40302	+	13.5511i	−0.288452	+	0.887763i	0.696891	+	0.717177i	$0.254566\pi$
$233$	−4.40302	+	13.5511i	−0.288452	+	0.887763i	−0.985343	+	0.170586i	$0.945434\pi$
$234$	−6.23074	+	2.77411i	−0.407316	+	0.181349i
$235$	−12.3538	+	2.62588i	−0.805873	+	0.171294i
$236$	13.0742	+	2.77901i	0.851060	+	0.180898i
$237$	−16.9578	−	7.55012i	−1.10153	−	0.490433i
$238$	−10.8423	+	12.0415i	−0.702799	+	0.780537i
$239$	0.710952	−	6.76426i	0.0459877	−	0.437544i	−0.947167	−	0.320740i	$-0.896068\pi$
$239$	0.710952	−	6.76426i	0.0459877	−	0.437544i	0.993155	−	0.116804i	$-0.0372648\pi$
$240$	−13.5176	−	9.82113i	−0.872559	−	0.633951i
$241$	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
$243$	−7.46119	−	12.9232i	−0.478636	−	0.829021i
$244$	−4.13284	+	3.00269i	−0.264578	+	0.192227i
$245$	10.2154	+	11.3454i	0.652640	+	0.724830i
$246$	5.86030	+	18.0362i	0.373639	+	1.14994i
$247$	1.29410			0.0823413
$248$	−1.21291	+	3.16377i	−0.0770197	+	0.200899i
$249$	11.0938			0.703039
$250$	−6.74630	−	20.7630i	−0.426673	−	1.31317i
$251$	−4.88091	−	5.42080i	−0.308080	−	0.342158i	0.569145	−	0.822237i	$-0.307274\pi$
$251$	−4.88091	−	5.42080i	−0.308080	−	0.342158i	−0.877225	+	0.480080i	$0.840608\pi$
$252$	10.7529	−	7.81244i	0.677369	−	0.492137i
$253$	−7.17837	−	12.4333i	−0.451300	−	0.781675i
$254$	14.7103	−	25.4790i	0.923005	−	1.59869i
$255$	1.11737	+	10.6311i	0.0699724	+	0.665743i
$256$	−8.35235	−	6.06834i	−0.522022	−	0.379271i
$257$	2.57722	−	24.5206i	0.160763	−	1.52955i	−0.555378	−	0.831598i	$-0.687426\pi$
$257$	2.57722	−	24.5206i	0.160763	−	1.52955i	0.716140	−	0.697956i	$-0.245907\pi$
$258$	−0.799991	+	0.888480i	−0.0498053	+	0.0553143i
$259$	−0.921381	−	0.410225i	−0.0572518	−	0.0254902i
$260$	10.9947	+	2.33700i	0.681864	+	0.144935i
$261$	2.12471	−	0.451622i	0.131516	−	0.0279547i
$262$	13.6077	−	6.05853i	0.840686	−	0.374297i
$263$	−8.12313	+	25.0004i	−0.500894	+	1.54159i	0.306672	+	0.951815i	$0.400785\pi$
$263$	−8.12313	+	25.0004i	−0.500894	+	1.54159i	−0.807566	+	0.589777i	$0.799215\pi$
$264$	1.72220	−	5.30037i	0.105994	−	0.326215i
$265$	20.3954	−	9.08062i	1.25288	−	0.557818i
$266$	−4.61769	+	0.981521i	−0.283129	+	0.0601809i
$267$	10.4895	+	2.22962i	0.641949	+	0.136450i
$268$	−28.5274	−	12.7012i	−1.74259	−	0.775851i
$269$	−13.9713	+	15.5167i	−0.851846	+	0.946071i	−0.999074	−	0.0430321i	$-0.986298\pi$
$269$	−13.9713	+	15.5167i	−0.851846	+	0.946071i	0.147228	+	0.989103i	$0.452965\pi$
$270$	−1.54820	+	14.7302i	−0.0942206	+	0.896450i
$271$	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
$273$	8.20403	−	14.2098i	0.496530	−	0.860016i
$274$	−7.85091	−	13.5982i	−0.474291	−	0.821496i
$275$	1.77550	−	1.28997i	0.107066	−	0.0777883i
$276$	11.0124	+	12.2305i	0.662869	+	0.736191i
$277$	−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
$279$	8.67165	−	1.37725i	0.519158	−	0.0824539i
$280$	−5.25032			−0.313767
$281$	−2.05645	−	6.32910i	−0.122678	−	0.377563i	0.870793	−	0.491649i	$-0.163606\pi$
$281$	−2.05645	−	6.32910i	−0.122678	−	0.377563i	−0.993471	+	0.114087i	$0.963606\pi$
$282$	−15.9563	−	17.7212i	−0.950181	−	1.05528i
$283$	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
$285$	−1.55720	+	2.69715i	−0.0922406	+	0.159765i
$286$	−1.93519	−	18.4121i	−0.114430	−	1.08873i
$287$	−12.7172	−	9.23961i	−0.750675	−	0.545397i
$288$	1.33682	−	12.7190i	0.0787729	−	0.749474i
$289$	−8.34488	+	9.26793i	−0.490875	+	0.545172i
$290$	−6.12199	−	2.72568i	−0.359495	−	0.160058i
$291$	14.0500	+	2.98641i	0.823623	+	0.175066i
$292$	31.7824	−	6.75555i	1.85992	−	0.395339i
$293$	12.3434	−	5.49563i	0.721108	−	0.321058i	−0.0131637	−	0.999913i	$-0.504190\pi$
$293$	12.3434	−	5.49563i	0.721108	−	0.321058i	0.734272	+	0.678855i	$0.237524\pi$
$294$	−8.90741	+	27.4142i	−0.519491	+	1.59883i
$295$	−4.22807	+	13.0126i	−0.246168	+	0.757626i
$296$	0.152594	−	0.0679392i	0.00886934	−	0.00394888i
$297$	12.7471	−	2.70947i	0.739659	−	0.157219i
$298$	−24.9605	−	5.30552i	−1.44592	−	0.307340i
$299$	6.39501	+	2.84724i	0.369833	+	0.164660i
$300$	−1.68341	+	1.86961i	−0.0971915	+	0.107942i
$301$	0.103587	−	0.985567i	0.00597067	−	0.0568071i
$302$	33.3214	+	24.2094i	1.91743	+	1.39309i
$303$	−4.03929	−	38.4313i	−0.232051	−	2.20782i
$304$	−1.03120	+	1.78609i	−0.0591434	+	0.102439i
$305$	−2.61462	−	4.52866i	−0.149713	−	0.259310i
$306$	−5.62592	+	4.08747i	−0.321613	+	0.233665i
$307$	−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
$309$	−8.37640			−0.476517
$310$	−24.1409	−	12.2874i	−1.37111	−	0.697878i
$311$	9.49330			0.538315			0.269158	−	0.963096i	$-0.413255\pi$
$311$	9.49330			0.538315			0.269158	+	0.963096i	$0.413255\pi$
$312$	0.839726	+	2.58441i	0.0475401	+	0.146313i
$313$	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
$315$	6.80276	+	11.7827i	0.383292	+	0.663882i
$316$	−9.95072	+	17.2352i	−0.559772	+	0.969553i
$317$	1.65331	+	15.7302i	0.0928591	+	0.883495i	0.937459	+	0.348096i	$0.113172\pi$
$317$	1.65331	+	15.7302i	0.0928591	+	0.883495i	−0.844600	+	0.535398i	$0.820161\pi$
$318$	34.1023	+	24.7768i	1.91236	+	1.38941i
$319$	−0.616323	+	5.86393i	−0.0345075	+	0.328317i
$320$	−15.9489	+	17.7130i	−0.891569	+	0.990188i
$321$	−21.7247	−	9.67247i	−1.21256	−	0.539865i
$322$	−24.9787	−	5.30938i	−1.39201	−	0.295880i
$323$	1.29062	−	0.274329i	0.0718118	−	0.0152641i
$324$	−23.5607	+	10.4899i	−1.30893	+	0.582772i
$325$	−0.330674	+	1.01771i	−0.0183425	+	0.0564523i
$326$	11.3870	−	35.0457i	0.630669	−	1.94100i
$327$	−35.3623	+	15.7443i	−1.95554	+	0.870662i
$328$	2.54646	−	0.541267i	0.140605	−	0.0298865i
$329$	19.3340	+	4.10957i	1.06592	+	0.226568i
$330$	40.7030	+	18.1221i	2.24063	+	0.997591i
$331$	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
$333$	−0.350182	−	0.254422i	−0.0191899	−	0.0139423i
$334$	−0.472618	−	4.49666i	−0.0258605	−	0.246046i
$335$	15.9827	−	27.6828i	0.873228	−	1.51247i
$336$	13.0748	+	22.6462i	0.713287	+	1.23545i
$337$	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
$339$	−11.5950	−	35.6858i	−0.629755	−	1.93819i
$340$	11.4606			0.621537
$341$	−3.71834	+	23.5418i	−0.201360	+	1.27486i
$342$	−2.02604			−0.109556
$343$	0.565190	+	1.73948i	0.0305174	+	0.0939229i
$344$	0.109820	+	0.121967i	0.00592108	+	0.00657603i
$345$	−13.6294	+	9.90233i	−0.733782	+	0.533124i
$346$	5.70655	+	9.88403i	0.306786	+	0.531369i
$347$	−2.66175	+	4.61029i	−0.142890	+	0.247493i	−0.928584	−	0.371123i	$-0.878973\pi$
$347$	−2.66175	+	4.61029i	−0.142890	+	0.247493i	0.785693	+	0.618616i	$0.212306\pi$
$348$	−0.706520	−	6.72209i	−0.0378734	−	0.360342i
$349$	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
$351$	−4.25178	+	4.72208i	−0.226943	+	0.252046i
$352$	31.7137	+	14.1199i	1.69035	+	0.752591i
$353$	−21.3132	−	4.53026i	−1.13439	−	0.241122i	−0.397806	−	0.917470i	$-0.630228\pi$
$353$	−21.3132	−	4.53026i	−1.13439	−	0.241122i	−0.736582	+	0.676348i	$0.763562\pi$
$354$	−25.2690	+	5.37109i	−1.34303	+	0.285470i
$355$	−2.86546	+	1.27578i	−0.152083	+	0.0677115i
$356$	3.55286	−	10.9346i	0.188301	−	0.579531i
$357$	5.16971	−	15.9107i	0.273610	−	0.842085i
$358$	22.9692	−	10.2265i	1.21396	−	0.540489i
$359$	6.92668	−	1.47231i	0.365576	−	0.0777057i	−0.0214610	−	0.999770i	$-0.506832\pi$
$359$	6.92668	−	1.47231i	0.365576	−	0.0777057i	0.387037	+	0.922064i	$0.373498\pi$
$360$	−2.20403	−	0.468481i	−0.116163	−	0.0246911i
$361$	−17.0062	−	7.57164i	−0.895062	−	0.398507i
$362$	13.3756	−	14.8551i	0.703005	−	0.780766i
$363$	1.63782	−	15.5828i	0.0859634	−	0.817887i
$364$	−14.2318	−	10.3400i	−0.745947	−	0.541963i
$365$	3.47668	+	33.0784i	0.181977	+	1.73140i
$366$	4.93665	−	8.55053i	0.258043	−	0.446943i
$367$	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
$369$	−4.51412	−	5.01344i	−0.234996	−	0.260989i
$370$	0.412653	+	1.27002i	0.0214528	+	0.0660250i
$371$	−34.9401			−1.81400
$372$	−1.44155	−	27.2835i	−0.0747409	−	1.41458i
$373$	−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
$375$	15.0824	+	16.7507i	0.778849	+	0.865000i
$376$	−2.64834	+	1.92413i	−0.136578	+	0.0992294i
$377$	−1.43747	−	2.48977i	−0.0740335	−	0.128230i
$378$	11.5900	−	20.0745i	0.596127	−	1.03252i
$379$	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
$381$	−3.17512	+	30.2093i	−0.162666	+	1.54767i
$382$	14.5105	−	16.1155i	0.742421	−	0.824542i
$383$	9.41502	+	4.19184i	0.481085	+	0.214193i	0.632926	−	0.774212i	$-0.281854\pi$
$383$	9.41502	+	4.19184i	0.481085	+	0.214193i	−0.151841	+	0.988405i	$0.548520\pi$
$384$	−10.0781	−	2.14216i	−0.514295	−	0.109317i
$385$	−36.1242	+	7.67843i	−1.84106	+	0.391329i
$386$	−3.38966	+	1.50917i	−0.172529	+	0.0768149i
$387$	0.131426	−	0.404488i	0.00668076	−	0.0205613i
$388$	4.75879	−	14.6461i	0.241591	−	0.743541i
$389$	−23.1725	+	10.3170i	−1.17489	+	0.523095i	−0.898938	−	0.438077i	$-0.855660\pi$
$389$	−23.1725	+	10.3170i	−1.17489	+	0.523095i	−0.275952	+	0.961171i	$0.588993\pi$
$390$	−21.2498	+	4.51679i	−1.07603	+	0.228717i
$391$	6.98139	+	1.48394i	0.353064	+	0.0750460i
$392$	3.61489	+	1.60945i	0.182579	+	0.0812896i
$393$	−10.2906	+	11.4289i	−0.519091	+	0.576509i
$394$	−1.38555	+	13.1827i	−0.0698032	+	0.664133i
$395$	−16.4812	−	11.9743i	−0.829261	−	0.602493i
$396$	1.61848	+	15.3988i	0.0813319	+	0.773821i
$397$	−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
$399$	3.94324	−	2.86493i	0.197409	−	0.143426i
$400$	−1.14113	−	1.26735i	−0.0570565	−	0.0633677i
$401$	−8.53615	−	26.2716i	−0.426275	−	1.31194i	−0.901768	−	0.432220i	$-0.857730\pi$
$401$	−8.53615	−	26.2716i	−0.426275	−	1.31194i	0.475493	−	0.879720i	$-0.342270\pi$
$402$	60.3537			3.01017
$403$	−5.28026	−	10.3522i	−0.263028	−	0.515678i
$404$	−41.4300			−2.06122
$405$	−8.15807	−	25.1080i	−0.405378	−	1.24763i
$406$	7.01769	+	7.79394i	0.348282	+	0.386807i
$407$	0.950545	−	0.690611i	0.0471168	−	0.0342323i
$408$	1.38532	+	2.39945i	0.0685838	+	0.118791i
$409$	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
$411$	13.1154	+	9.52892i	0.646936	+	0.470027i
$412$	−0.938720	+	8.93132i	−0.0462474	+	0.440015i
$413$	14.3282	−	15.9131i	0.705045	−	0.783031i
$414$	−10.0120	−	4.45765i	−0.492065	−	0.219082i
$415$	11.9090	+	2.53133i	0.584589	+	0.124258i
$416$	−16.5568	+	3.51926i	−0.811764	+	0.172546i
$417$	39.2806	−	17.4888i	1.92358	−	0.856432i
$418$	1.69945	−	5.23038i	0.0831229	−	0.255826i
$419$	−1.91312	+	5.88796i	−0.0934618	+	0.287646i	−0.986850	−	0.161640i	$-0.948322\pi$
$419$	−1.91312	+	5.88796i	−0.0934618	+	0.287646i	0.893388	+	0.449286i	$0.148322\pi$
$420$	38.6758	−	17.2196i	1.88719	−	0.840230i
$421$	−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
$423$	7.74953	+	3.45031i	0.376795	+	0.167760i
$424$	3.87197	−	4.30026i	0.188040	−	0.208839i
$425$	−0.114046	+	1.08507i	−0.00553202	+	0.0526337i
$426$	−4.79121	−	3.48102i	−0.232135	−	0.168656i
$427$	0.855450	+	8.13906i	0.0413981	+	0.393877i
$428$	−12.7479	+	22.0800i	−0.616192	+	1.06728i
$429$	9.55725	+	16.5536i	0.461428	+	0.799217i
$430$	−1.06151	+	0.771231i	−0.0511905	+	0.0371920i
$431$	15.7030	+	17.4399i	0.756385	+	0.840051i	0.991253	−	0.131977i	$-0.0421324\pi$
$431$	15.7030	+	17.4399i	0.756385	+	0.840051i	−0.234868	+	0.972027i	$0.575466\pi$
$432$	−3.12932	−	9.63105i	−0.150559	−	0.463374i
$433$	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
$435$	6.91890			0.331736
$436$	12.8244	+	39.4694i	0.614176	+	1.89024i
$437$	1.39143	+	1.54534i	0.0665610	+	0.0739234i
$438$	−50.8055	+	36.9124i	−2.42758	+	1.76374i
$439$	−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
$441$	−1.07184	−	10.1979i	−0.0510399	−	0.485612i
$442$	7.44607	+	5.40989i	0.354173	+	0.257322i
$443$	1.73162	−	16.4752i	0.0822716	−	0.782762i	−0.873137	−	0.487475i	$-0.837918\pi$
$443$	1.73162	−	16.4752i	0.0822716	−	0.782762i	0.955409	−	0.295287i	$-0.0954153\pi$
$444$	−0.901242	+	1.00093i	−0.0427711	+	0.0475021i
$445$	10.7516	+	4.78692i	0.509675	+	0.226922i
$446$	−32.2223	−	6.84907i	−1.52577	−	0.324313i
$447$	25.7708	−	5.47775i	1.21892	−	0.259089i
$448$	34.0777	−	15.1724i	1.61002	−	0.716828i
$449$	2.10667	−	6.48365i	0.0994197	−	0.305982i	−0.888961	−	0.457984i	$-0.848572\pi$
$449$	2.10667	−	6.48365i	0.0994197	−	0.305982i	0.988380	+	0.152001i	$0.0485718\pi$
$450$	0.517704	−	1.59333i	0.0244048	−	0.0751102i
$451$	16.7290	−	7.44825i	0.787740	−	0.350724i
$452$	−39.3493	+	8.36396i	−1.85084	+	0.393408i
$453$	−41.5953	−	8.84136i	−1.95432	−	0.415403i
$454$	−8.79280	−	3.91481i	−0.412667	−	0.183731i
$455$	12.0492	−	13.3820i	0.564877	−	0.627359i
$456$	−0.0843778	+	0.802801i	−0.00395135	+	0.0375946i
$457$	−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
$459$	−3.23934	+	5.61070i	−0.151200	+	0.261885i
$460$	9.03094	+	15.6420i	0.421070	+	0.729314i
$461$	7.01782	−	5.09875i	0.326853	−	0.237472i	−0.412241	−	0.911075i	$-0.635254\pi$
$461$	7.01782	−	5.09875i	0.326853	−	0.237472i	0.739094	+	0.673602i	$0.235254\pi$
$462$	−46.6582	−	51.8192i	−2.17074	−	2.41085i
$463$	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
$465$	27.9297	+	1.45178i	1.29521	+	0.0673245i
$466$	−29.5246			−1.36770
$467$	−0.952115	−	2.93031i	−0.0440586	−	0.135599i	0.926607	−	0.376030i	$-0.122711\pi$
$467$	−0.952115	−	2.93031i	−0.0440586	−	0.135599i	−0.970666	+	0.240431i	$0.922711\pi$
$468$	−5.05172	−	5.61051i	−0.233516	−	0.259346i
$469$	−40.4724	+	29.4049i	−1.86884	+	1.35779i
$470$	−13.0852	−	22.6643i	−0.603577	−	1.04543i
$471$	−6.20917	+	10.7546i	−0.286104	+	0.495546i
$472$	0.370692	+	3.52690i	0.0170625	+	0.162339i
$473$	0.933975	+	0.678572i	0.0429442	+	0.0312008i
$474$	4.02060	−	38.2534i	0.184672	−	1.75704i
$475$	−0.212700	+	0.236227i	−0.00975933	+	0.0108388i
$476$	−16.3854	−	7.29526i	−0.751025	−	0.334378i
$477$	−14.6675	−	3.11767i	−0.671578	−	0.142748i
$478$	13.7856	−	2.93022i	0.630538	−	0.134025i
$479$	−15.9050	+	7.08138i	−0.726720	+	0.323556i	−0.736539	−	0.676395i	$-0.763541\pi$
$479$	−15.9050	+	7.08138i	−0.726720	+	0.323556i	0.00981912	+	0.999952i	$0.496874\pi$
$480$	12.5882	−	38.7424i	0.574568	−	1.76834i
$481$	−0.177032	+	0.544849i	−0.00807197	+	0.0248430i
$482$	−21.7789	+	9.69661i	−0.992003	+	0.441668i
$483$	25.7896	−	5.48175i	1.17347	−	0.249428i
$484$	−16.4316	−	3.49265i	−0.746892	−	0.158757i
$485$	14.4010	+	6.41173i	0.653915	+	0.291142i
$486$	20.6902	−	22.9788i	0.938526	−	1.04234i
$487$	−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
$489$	3.97684	+	37.8371i	0.179839	+	1.71105i
$490$	−15.8172	+	27.3963i	−0.714550	+	1.23764i
$491$	4.91284	+	8.50929i	0.221713	+	0.384019i	0.955328	−	0.295546i	$-0.0955017\pi$
$491$	4.91284	+	8.50929i	0.221713	+	0.384019i	−0.733615	+	0.679565i	$0.762168\pi$
$492$	−16.9830	+	12.3389i	−0.765652	+	0.556279i
$493$	−1.96140	−	2.17836i	−0.0883371	−	0.0981083i
$494$	0.828636	+	2.55028i	0.0372821	+	0.114743i
$495$	−15.8497			−0.712391
$496$	18.4955	+	0.961388i	0.830472	+	0.0431676i
$497$	4.90891			0.220195
$498$	7.10357	+	21.8625i	0.318319	+	0.979684i
$499$	−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
$501$	2.33411	+	4.04280i	0.104280	+	0.180619i
$502$	7.55745	−	13.0899i	0.337305	−	0.584230i
$503$	−0.894863	−	8.51405i	−0.0399000	−	0.379623i	−0.996190	−	0.0872044i	$-0.972207\pi$
$503$	−0.894863	−	8.51405i	−0.0399000	−	0.379623i	0.956290	−	0.292418i	$-0.0944600\pi$
$504$	2.85294	+	2.07278i	0.127080	+	0.0923290i
$505$	4.43299	−	42.1771i	0.197265	−	1.87685i
$506$	19.9059	−	22.1077i	0.884925	−	0.982809i
$507$	16.8933	+	7.52139i	0.750259	+	0.334037i
$508$	31.8548	+	6.77094i	1.41333	+	0.300412i
$509$	38.7174	−	8.22963i	1.71612	−	0.364772i	0.758245	−	0.651969i	$-0.226057\pi$
$509$	38.7174	−	8.22963i	1.71612	−	0.364772i	0.957871	+	0.287197i	$0.0927236\pi$
$510$	−20.2352	+	9.00930i	−0.896030	+	0.398938i
$511$	16.0855	−	49.5059i	0.711579	−	2.19001i
$512$	9.58715	−	29.5062i	0.423696	−	1.30400i
$513$	−1.72436	+	0.767736i	−0.0761325	+	0.0338964i
$514$	49.9732	−	10.6221i	2.20422	−	0.468522i
$515$	−8.99194	−	1.91130i	−0.396232	−	0.0842217i
$516$	−1.20899	−	0.538278i	−0.0532229	−	0.0236964i
$517$	−15.4076	+	17.1119i	−0.677625	+	0.752578i
$518$	0.218453	−	2.07845i	0.00959830	−	0.0913217i
$519$	−9.53314	−	6.92623i	−0.418458	−	0.304028i
$520$	0.311732	+	2.96593i	0.0136703	+	0.130065i
$521$	0.674660	−	1.16855i	0.0295574	−	0.0511949i	−0.850868	−	0.525379i	$-0.823924\pi$
$521$	0.674660	−	1.16855i	0.0295574	−	0.0511949i	0.880426	+	0.474184i	$0.157257\pi$
$522$	2.25051	+	3.89800i	0.0985022	+	0.170611i
$523$	−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
$525$	1.24546	+	3.83313i	0.0543562	+	0.167291i
$526$	−54.4699			−2.37500
$527$	−7.46057	−	9.20499i	−0.324987	−	0.400976i
$528$	−30.4628			−1.32572
$529$	−3.63142	−	11.1764i	−0.157888	−	0.485929i
$530$	30.9548	+	34.3788i	1.34459	+	1.49332i
$531$	7.43474	−	5.40166i	0.322640	−	0.234412i
$532$	−2.61282	−	4.52554i	−0.113280	−	0.196207i
$533$	−4.46443	+	7.73262i	−0.193376	+	0.334937i
$534$	2.32274	+	22.0994i	0.100515	+	0.956336i
$535$	−21.1141	−	15.3403i	−0.912843	−	0.663220i
$536$	0.866031	−	8.23974i	0.0374069	−	0.355902i
$537$	−17.3701	+	19.2914i	−0.749573	+	0.832485i
$538$	−39.5250	−	17.5977i	−1.70404	−	0.758689i
$539$	27.2256	+	5.78697i	1.17269	+	0.249263i
$540$	−16.0368	+	3.40872i	−0.690113	+	0.146688i
$541$	−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
$543$	−6.37763	+	19.6283i	−0.273690	+	0.842332i
$544$	−15.7663	+	7.01959i	−0.675973	+	0.300962i
$545$	−41.5533	+	8.83243i	−1.77995	+	0.378340i
$546$	33.2565	+	7.06889i	1.42325	+	0.302521i
$547$	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
$549$	−0.367132	+	3.49303i	−0.0156688	+	0.149079i
$550$	3.67904	+	2.67298i	0.156875	+	0.113976i
$551$	−0.0892693	−	0.849341i	−0.00380300	−	0.0361831i
$552$	−2.18327	+	3.78154i	−0.0929263	+	0.160953i
$553$	15.9413	+	27.6111i	0.677893	+	1.17414i
$554$	7.97837	−	5.79663i	0.338969	−	0.246275i
$555$	−0.922548	−	1.02459i	−0.0391600	−	0.0434916i
$556$	−14.2454	−	43.8428i	−0.604139	−	1.85935i
$557$	27.3019			1.15682			0.578409	−	0.815747i	$-0.303674\pi$
$557$	27.3019			1.15682			0.578409	+	0.815747i	$0.303674\pi$
$558$	8.26679	+	16.2074i	0.349961	+	0.686113i
$559$	−0.562902			−0.0238082
$560$	8.86825	+	27.2937i	0.374752	+	1.15337i
$561$	13.0407	+	14.4831i	0.550578	+	0.611479i
$562$	11.1560	−	8.10531i	0.470588	−	0.341902i
$563$	−2.59399	−	4.49293i	−0.109324	−	0.189354i	0.806173	−	0.591680i	$-0.201535\pi$
$563$	−2.59399	−	4.49293i	−0.109324	−	0.189354i	−0.915497	+	0.402326i	$0.868202\pi$
$564$	13.1980	−	22.8597i	0.555737	−	0.962565i
$565$	−4.30442	−	40.9539i	−0.181088	−	1.72294i
$566$	12.1475	+	8.82566i	0.510596	+	0.370970i
$567$	−4.31878	+	41.0905i	−0.181372	+	1.72564i
$568$	−0.543993	+	0.604166i	−0.0228255	+	0.0253502i
$569$	2.16312	+	0.963083i	0.0906827	+	0.0403746i	0.451577	−	0.892232i	$-0.350862\pi$
$569$	2.16312	+	0.963083i	0.0906827	+	0.0403746i	−0.360894	+	0.932607i	$0.617528\pi$
$570$	−6.31239	−	1.34174i	−0.264397	−	0.0561993i
$571$	−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
$573$	−6.91877	+	21.2938i	−0.289036	+	0.889560i
$574$	10.0654	−	30.9782i	0.420123	−	1.29301i
$575$	−1.57083	+	0.699381i	−0.0655083	+	0.0291662i
$576$	15.6593	−	3.32849i	0.652471	−	0.138687i
$577$	−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
$579$	2.56337	−	2.84691i	0.106530	−	0.118314i
$580$	0.775382	−	7.37727i	0.0321960	−	0.306324i
$581$	−15.4152	−	11.1998i	−0.639531	−	0.464646i
$582$	3.11115	+	29.6006i	0.128961	+	1.22698i
$583$	20.3516	−	35.2501i	0.842879	−	1.45991i
$584$	4.31041	+	7.46585i	0.178366	+	0.308939i
$585$	6.25221	−	4.54250i	0.258497	−	0.187809i
$586$	18.7340	+	20.8062i	0.773894	+	0.859497i
$587$	12.3489	+	38.0060i	0.509694	+	1.56868i	0.792733	+	0.609568i	$0.208657\pi$
$587$	12.3489	+	38.0060i	0.509694	+	1.56868i	−0.283040	+	0.959108i	$0.591343\pi$
$588$	−31.9072			−1.31583
$589$	−0.182141	−	3.44729i	−0.00750499	−	0.142043i
$590$	−28.3514			−1.16721
$591$	−4.22908	−	13.0158i	−0.173961	−	0.535397i
$592$	−0.610925	−	0.678501i	−0.0251089	−	0.0278862i
$593$	16.9709	−	12.3301i	0.696911	−	0.506335i	−0.182014	−	0.983296i	$-0.558262\pi$
$593$	16.9709	−	12.3301i	0.696911	−	0.506335i	0.878925	+	0.476961i	$0.158262\pi$
$594$	13.5018	+	23.3857i	0.553984	+	0.959529i
$595$	9.18005	−	15.9003i	0.376345	−	0.651849i
$596$	−2.95258	−	28.0920i	−0.120943	−	1.15069i
$597$	1.60473	+	1.16590i	0.0656771	+	0.0477172i
$598$	−1.51621	+	14.4258i	−0.0620026	+	0.589915i
$599$	14.0125	−	15.5625i	0.572535	−	0.635865i	−0.385434	−	0.922735i	$-0.625948\pi$
$599$	14.0125	−	15.5625i	0.572535	−	0.635865i	0.957969	+	0.286870i	$0.0926149\pi$
$600$	−0.609782	−	0.271492i	−0.0248943	−	0.0110836i
$601$	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
$603$	−19.6137	+	8.73257i	−0.798730	+	0.355618i
$604$	−14.0886	+	43.3601i	−0.573256	+	1.76430i
$605$	5.31381	−	16.3542i	0.216037	−	0.664894i
$606$	73.1503	−	32.5686i	2.97153	−	1.32301i
$607$	−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
$609$	−9.89211	−	4.40425i	−0.400848	−	0.178469i
$610$	7.25045	−	8.05244i	0.293562	−	0.326034i
$611$	1.17358	−	11.1659i	0.0474780	−	0.451723i
$612$	−6.22749	−	4.52453i	−0.251731	−	0.182893i
$613$	−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
$615$	−10.7442	−	18.6095i	−0.433248	−	0.750407i
$616$	−7.74409	+	5.62641i	−0.312018	+	0.226695i
$617$	−17.6270	−	19.5768i	−0.709636	−	0.788131i	0.275243	−	0.961375i	$-0.411242\pi$
$617$	−17.6270	−	19.5768i	−0.709636	−	0.788131i	−0.984879	+	0.173244i	$0.944575\pi$
$618$	−5.36358	−	16.5074i	−0.215755	−	0.664026i
$619$	−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
$621$	−10.2104			−0.409730
$622$	6.07875	+	18.7085i	0.243736	+	0.750142i
$623$	−12.3247	−	13.6879i	−0.493778	−	0.548396i
$624$	12.0166	−	8.73059i	0.481050	−	0.349503i
$625$	13.6503	+	23.6430i	0.546012	+	0.945720i
$626$	−29.1103	+	50.4204i	−1.16348	+	2.01521i
$627$	0.593521	+	5.64698i	0.0237029	+	0.225518i
$628$	10.7712	+	7.82576i	0.429819	+	0.312282i
$629$	−0.0610564	+	0.580913i	−0.00243448	+	0.0231625i
$630$	−18.8643	+	20.9510i	−0.751573	+	0.834706i
$631$	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
$633$	−12.9355	+	2.74953i	−0.514141	+	0.109284i
$634$	−29.9409	+	13.3305i	−1.18910	+	0.529423i
$635$	−10.3015	+	31.7047i	−0.408802	+	1.25816i
$636$	−14.4187	+	44.3763i	−0.571740	+	1.75964i
$637$	−12.3982	+	5.52002i	−0.491234	+	0.218711i
$638$	−11.9507	+	2.54020i	−0.473133	+	0.100568i
$639$	2.06071	+	0.438017i	0.0815204	+	0.0173277i
$640$	−10.3299	−	4.59916i	−0.408324	−	0.181798i
$641$	15.5874	−	17.3115i	0.615664	−	0.683764i	−0.352002	−	0.935999i	$-0.614499\pi$
$641$	15.5874	−	17.3115i	0.615664	−	0.683764i	0.967666	+	0.252235i	$0.0811657\pi$
$642$	5.15079	−	49.0065i	0.203285	−	1.93413i
$643$	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
$645$	0.677346	−	1.17320i	0.0266705	−	0.0461946i
$646$	1.36703	+	2.36777i	0.0537851	+	0.0931585i
$647$	1.80444	−	1.31100i	0.0709399	−	0.0515408i	−0.551750	−	0.834009i	$-0.686040\pi$
$647$	1.80444	−	1.31100i	0.0709399	−	0.0515408i	0.622690	+	0.782469i	$0.286040\pi$
$648$	−4.57863	−	5.08508i	−0.179866	−	0.199761i
$649$	7.70848	+	23.7243i	0.302584	+	0.931259i
$650$	−2.21734			−0.0869713
$651$	−39.0076	−	19.8544i	−1.52883	−	0.778155i
$652$	40.7894			1.59744
$653$	−8.82960	−	27.1747i	−0.345529	−	1.06343i	−0.961300	−	0.275504i	$-0.911155\pi$
$653$	−8.82960	−	27.1747i	−0.345529	−	1.06343i	0.615771	−	0.787925i	$-0.288845\pi$
$654$	−53.6706	−	59.6072i	−2.09869	−	2.33083i
$655$	−13.6546	+	9.92063i	−0.533529	+	0.387631i
$656$	−7.11497	−	12.3235i	−0.277793	−	0.481151i
$657$	11.1699	−	19.3468i	0.435778	−	0.754790i
$658$	4.28122	+	40.7331i	0.166899	+	1.58794i
$659$	−4.15656	−	3.01991i	−0.161916	−	0.117639i	0.503877	−	0.863776i	$-0.331907\pi$
$659$	−4.15656	−	3.01991i	−0.161916	−	0.117639i	−0.665793	+	0.746136i	$0.731907\pi$
$660$	−5.15525	+	49.0489i	−0.200668	+	1.90923i
$661$	−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
$663$	−9.29499	−	1.97571i	−0.360987	−	0.0767302i
$664$	3.08670	−	0.656098i	0.119787	−	0.0254615i
$665$	4.88672	−	2.17571i	0.189499	−	0.0843703i
$666$	0.277162	−	0.853018i	0.0107398	−	0.0330538i
$667$	1.42756	−	4.39358i	0.0552754	−	0.170120i
$668$	4.57220	−	2.03567i	0.176904	−	0.0787626i
$669$	33.2684	−	7.07142i	1.28623	−	0.273397i
$670$	64.7887	+	13.7713i	2.50301	+	0.532031i
$671$	−8.70955	−	3.87774i	−0.336229	−	0.149699i
$672$	−42.6592	+	47.3778i	−1.64561	+	1.82764i
$673$	−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
$675$	−0.163149	−	1.55226i	−0.00627961	−	0.0597465i
$676$	9.91286	−	17.1696i	0.381264	−	0.660368i
$677$	1.31511	+	2.27784i	0.0505438	+	0.0875444i	0.890190	−	0.455589i	$-0.150571\pi$
$677$	1.31511	+	2.27784i	0.0505438	+	0.0875444i	−0.839647	+	0.543133i	$0.817238\pi$
$678$	62.9016	−	45.7007i	2.41572	−	1.75512i
$679$	−16.5080	−	18.3340i	−0.633519	−	0.703594i
$680$	0.939627	+	2.89187i	0.0360330	+	0.110898i
$681$	9.93738			0.380801
$682$	−48.7748	+	7.74652i	−1.86768	+	0.296630i
$683$	29.5859			1.13207			0.566037	−	0.824380i	$-0.308476\pi$
$683$	29.5859			1.13207			0.566037	+	0.824380i	$0.308476\pi$
$684$	−0.693026	−	2.13292i	−0.0264985	−	0.0815540i
$685$	11.9049	+	13.2218i	0.454864	+	0.505178i
$686$	−3.06609	+	2.22765i	−0.117064	+	0.0850519i
$687$	−20.7717	−	35.9777i	−0.792492	−	1.37264i
$688$	0.448549	−	0.776909i	0.0171008	−	0.0296194i
$689$	2.07453	+	19.7378i	0.0790331	+	0.751950i
$690$	−28.2418	−	20.5188i	−1.07515	−	0.781139i
$691$	−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
$693$	22.6607	+	10.0892i	0.860808	+	0.383256i
$694$	−10.7899	−	2.29346i	−0.409579	−	0.0870587i
$695$	46.1576	−	9.81111i	1.75086	−	0.372157i
$696$	1.63827	−	0.729407i	0.0620986	−	0.0276481i
$697$	−2.81323	+	8.65822i	−0.106559	+	0.327954i
$698$	−2.62397	+	8.07576i	−0.0993189	+	0.305672i
$699$	27.8477	−	12.3986i	1.05330	−	0.468957i
$700$	4.22664	−	0.898400i	0.159752	−	0.0339563i
$701$	−20.7605	−	4.41279i	−0.784114	−	0.166669i	−0.201577	−	0.979473i	$-0.564607\pi$
$701$	−20.7605	−	4.41279i	−0.784114	−	0.166669i	−0.582537	+	0.812804i	$0.697940\pi$
$702$	−12.0283	−	5.35536i	−0.453980	−	0.202125i
$703$	−0.113873	+	0.126468i	−0.00429479	+	0.00476985i
$704$	−4.54235	+	43.2176i	−0.171196	+	1.62882i
$705$	21.8597	+	15.8820i	0.823284	+	0.598151i
$706$	−4.71948	−	44.9029i	−0.177620	−	1.68994i
$707$	−33.1859	+	57.4796i	−1.24808	+	2.16174i
$708$	−14.2979	−	24.7647i	−0.537348	−	0.930714i
$709$	−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
$711$	4.22828	+	13.0133i	0.158573	+	0.488037i
$712$	3.05044			0.114320
$713$	6.68457	−	17.4362i	0.250339	−	0.652989i
$714$	34.6656			1.29733
$715$	6.48241	+	19.9508i	0.242429	+	0.746118i
$716$	18.6228	+	20.6827i	0.695967	+	0.772950i
$717$	−11.7721	+	8.55293i	−0.439637	+	0.319415i
$718$	7.33679	+	12.7077i	0.273807	+	0.474247i
$719$	20.0999	−	34.8141i	0.749601	−	1.29835i	−0.198413	−	0.980119i	$-0.563579\pi$
$719$	20.0999	−	34.8141i	0.749601	−	1.29835i	0.948014	−	0.318229i	$-0.103088\pi$
$720$	1.28741	+	12.2489i	0.0479790	+	0.456490i
$721$	11.6393	+	8.45647i	0.433471	+	0.314935i
$722$	4.03205	−	38.3624i	0.150058	−	1.42770i
$723$	16.4700	−	18.2917i	0.612524	−	0.680277i
$724$	20.2139	+	8.99983i	0.751245	+	0.334476i
$725$	0.690753	+	0.146824i	0.0256539	+	0.00545291i
$726$	31.7579	−	6.75035i	1.17865	−	0.250529i
$727$	−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
$729$	0.558517	−	1.71894i	0.0206858	−	0.0636644i
$730$	−62.9615	+	28.0323i	−2.33031	+	1.03752i
$731$	−0.561388	+	0.119327i	−0.0207637	+	0.00441346i
$732$	10.6902	+	2.27227i	0.395121	+	0.0839856i
$733$	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
$735$	3.41405	−	32.4826i	0.125929	−	1.19814i
$736$	−22.0046	−	15.9872i	−0.811099	−	0.589298i
$737$	−6.09174	−	57.9591i	−0.224392	−	2.13495i
$738$	6.98953	−	12.1062i	0.257288	−	0.445636i
$739$	−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
$741$	−1.85254	−	2.05745i	−0.0680547	−	0.0755824i
$742$	−22.3728	−	68.8565i	−0.821333	−	2.52780i
$743$	−17.4032			−0.638460			−0.319230	−	0.947677i	$-0.603424\pi$
$743$	−17.4032			−0.638460			−0.319230	+	0.947677i	$0.603424\pi$
$744$	6.76632	−	2.60066i	0.248065	−	0.0953449i
$745$	28.9145			1.05934
$746$	−6.28728	−	19.3503i	−0.230194	−	0.708463i
$747$	−5.47180	−	6.07705i	−0.200203	−	0.222348i
$748$	16.9041	−	12.2815i	0.618074	−	0.449057i
$749$	20.4224	+	35.3727i	0.746219	+	1.29249i
$750$	−23.3530	+	40.4487i	−0.852732	+	1.47698i
$751$	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
$753$	−1.63123	+	15.5201i	−0.0594453	+	0.565584i
$754$	3.98616	−	4.42708i	0.145168	−	0.161225i
$755$	−42.6346	−	18.9821i	−1.55163	−	0.690831i
$756$	25.0979	+	5.33473i	0.912804	+	0.194022i
$757$	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
$759$	−9.49136	+	29.2114i	−0.344515	+	1.06031i
$760$	−0.273758	+	0.842542i	−0.00993026	+	0.0305622i
$761$	−18.1807	+	8.09457i	−0.659050	+	0.293428i	−0.708879	−	0.705330i	$-0.750799\pi$
$761$	−18.1807	+	8.09457i	−0.659050	+	0.293428i	0.0498293	+	0.998758i	$0.484132\pi$
$762$	−61.5667	+	13.0864i	−2.23032	+	0.474070i
$763$	65.0320	+	13.8230i	2.35432	+	0.500426i
$764$	21.9291	+	9.76346i	0.793366	+	0.353229i
$765$	5.27246	−	5.85566i	0.190626	−	0.211712i
$766$	−2.23224	+	21.2383i	−0.0806541	+	0.767373i
$767$	−9.84009	−	7.14925i	−0.355305	−	0.258144i
$768$	2.30874	+	21.9662i	0.0833096	+	0.792638i
$769$	−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
$771$	−42.6742	+	31.0046i	−1.53687	+	1.11660i
$772$	−2.74825	−	3.05224i	−0.0989116	−	0.109852i
$773$	3.67070	+	11.2973i	0.132026	+	0.406334i	0.995116	−	0.0987167i	$-0.0314738\pi$
$773$	3.67070	+	11.2973i	0.132026	+	0.406334i	−0.863090	+	0.505051i	$0.831474\pi$
$774$	0.881281			0.0316770
$775$	2.75758	+	0.737629i	0.0990551	+	0.0264964i
$776$	4.08584			0.146673
$777$	0.666779	+	2.05213i	0.0239206	+	0.0736199i
$778$	−35.1696	−	39.0598i	−1.26089	−	1.40036i
$779$	−2.14581	+	1.55903i	−0.0768818	+	0.0558579i
$780$	−12.0238	−	20.8258i	−0.430519	−	0.745682i
$781$	−2.85931	+	4.95246i	−0.102314	+	0.177213i
$782$	1.54592	+	14.7084i	0.0552820	+	0.525973i
$783$	3.39250	+	2.46479i	0.121238	+	0.0880845i
$784$	2.26084	−	21.5104i	0.0807442	−	0.768230i
$785$	−9.11940	+	10.1281i	−0.325485	+	0.361488i
$786$	−29.1122	−	12.9616i	−1.03840	−	0.462324i
$787$	−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
$789$	51.3762	−	22.8741i	1.82904	−	0.814341i
$790$	13.0446	−	40.1470i	0.464105	−	1.42837i
$791$	−19.9152	+	61.2926i	−0.708102	+	2.17931i
$792$	−3.75293	+	1.67091i	−0.133355	+	0.0593733i
$793$	4.54700	−	0.966495i	0.161469	−	0.0343212i
$794$	−33.9675	−	7.22001i	−1.20546	−	0.256228i
$795$	−43.6338	−	19.4270i	−1.54753	−	0.689005i
$796$	1.42298	−	1.58038i	0.0504361	−	0.0560150i
$797$	5.26681	−	50.1103i	0.186560	−	1.77500i	−0.355517	−	0.934670i	$-0.615695\pi$
$797$	5.26681	−	50.1103i	0.186560	−	1.77500i	0.542077	−	0.840329i	$-0.317638\pi$
$798$	8.17088	+	5.93649i	0.289246	+	0.210149i
$799$	−1.19657	−	11.3846i	−0.0423317	−	0.402760i
$800$	2.07889	−	3.60074i	0.0734998	−	0.127305i
$801$	−3.95241	−	6.84577i	−0.139652	−	0.241884i
$802$	46.3076	−	33.6445i	1.63518	−	1.18803i
$803$	40.5758	+	45.0640i	1.43189	+	1.59028i
$804$	20.6445	+	63.5373i	0.728077	+	2.24079i
$805$	28.9356			1.01984
$806$	17.0200	−	17.0345i	0.599504	−	0.600016i
$807$	44.6701			1.57246
$808$	−3.39675	−	10.4541i	−0.119497	−	0.367775i
$809$	−10.4200	−	11.5726i	−0.366347	−	0.406870i	0.531584	−	0.847005i	$-0.321597\pi$
$809$	−10.4200	−	11.5726i	−0.366347	−	0.406870i	−0.897931	+	0.440136i	$0.854930\pi$
$810$	44.2566	−	32.1543i	1.55502	−	1.12979i
$811$	−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
$813$	−4.69860	−	44.7042i	−0.164787	−	1.56784i
$814$	1.96964	+	1.43103i	0.0690360	+	0.0501576i
$815$	−4.36445	+	41.5249i	−0.152880	+	1.45456i
$816$	10.1336	−	11.2545i	0.354746	−	0.393985i
$817$	−0.152757	−	0.0680118i	−0.00534429	−	0.00237943i
$818$	45.8282	+	9.74109i	1.60235	+	0.340589i
$819$	−11.8305	+	2.51464i	−0.413390	+	0.0878688i
$820$	−21.0464	+	9.37047i	−0.734973	+	0.327231i
$821$	6.05511	−	18.6357i	0.211325	−	0.650391i	−0.788069	−	0.615587i	$-0.788919\pi$
$821$	6.05511	−	18.6357i	0.211325	−	0.650391i	0.999394	−	0.0348044i	$-0.0110808\pi$
$822$	−10.3806	+	31.9482i	−0.362065	+	1.11432i
$823$	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
$825$	−4.59258	−	0.976183i	−0.159893	−	0.0339863i
$826$	40.5346	+	18.0472i	1.41038	+	0.627942i
$827$	−2.34540	+	2.60483i	−0.0815575	+	0.0905787i	−0.782542	−	0.622597i	$-0.786077\pi$
$827$	−2.34540	+	2.60483i	−0.0815575	+	0.0905787i	0.700985	+	0.713176i	$0.252744\pi$
$828$	1.26808	−	12.0650i	0.0440688	−	0.419287i
$829$	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
$831$	−5.09098	+	8.81784i	−0.176604	+	0.305888i
$832$	−10.5943	−	18.3498i	−0.367290	−	0.636166i
$833$	−11.1947	+	8.13341i	−0.387873	+	0.281806i
$834$	59.6175	+	66.2120i	2.06439	+	2.29273i
$835$	1.58316	+	4.87247i	0.0547875	+	0.168619i
$836$	6.08759			0.210544
$837$	13.1774	+	10.6615i	0.455478	+	0.368517i
$838$	−12.8284			−0.443151
$839$	−3.32915	−	10.2461i	−0.114935	−	0.353734i	0.876998	−	0.480493i	$-0.159542\pi$
$839$	−3.32915	−	10.2461i	−0.114935	−	0.353734i	−0.991933	+	0.126759i	$0.959542\pi$
$840$	7.51600	+	8.34737i	0.259327	+	0.288011i
$841$	21.9266	−	15.9306i	0.756088	−	0.549330i
$842$	−6.79587	−	11.7708i	−0.234201	−	0.405648i
$843$	−7.11863	+	12.3298i	−0.245178	+	0.424662i
$844$	1.48203	+	14.1006i	0.0510137	+	0.485363i
$845$	16.4185	+	11.9288i	0.564814	+	0.410362i
$846$	−1.83736	+	17.4813i	−0.0631698	+	0.601021i
$847$	−18.0076	+	19.9995i	−0.618749	+	0.687190i
$848$	−28.8949	−	12.8648i	−0.992256	−	0.441781i
$849$	−15.1638	−	3.22316i	−0.520420	−	0.110619i
$850$	−2.21138	+	0.470043i	−0.0758497	+	0.0161224i
$851$	−0.840975	+	0.374426i	−0.0288283	+	0.0128352i
$852$	2.02576	−	6.23466i	0.0694015	−	0.213596i
$853$	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
$855$	2.24553	−	0.477302i	0.0767955	−	0.0163234i
$856$	−6.61667	−	1.40642i	−0.226153	−	0.0480703i
$857$	−39.9528	−	17.7881i	−1.36476	−	0.607631i	−0.411954	−	0.911205i	$-0.635154\pi$
$857$	−39.9528	−	17.7881i	−1.36476	−	0.607631i	−0.952808	+	0.303573i	$0.901820\pi$
$858$	−26.5026	+	29.4342i	−0.904785	+	1.00487i
$859$	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
$861$	3.51528	+	33.4457i	0.119800	+	1.13983i
$862$	−24.3140	+	42.1130i	−0.828137	+	1.43438i
$863$	21.7570	+	37.6842i	0.740616	+	1.28279i	0.952215	+	0.305429i	$0.0987997\pi$
$863$	21.7570	+	37.6842i	0.740616	+	1.28279i	−0.211599	+	0.977357i	$0.567867\pi$
$864$	19.9739	−	14.5119i	0.679525	−	0.493704i
$865$	−8.65328	−	9.61044i	−0.294220	−	0.326765i
$866$	15.5681	+	47.9137i	0.529025	+	1.62817i
$867$	26.6808			0.906129
$868$	−25.5412	+	39.3668i	−0.866925	+	1.33620i
$869$	−37.1415			−1.25994
$870$	4.43032	+	13.6351i	0.150202	+	0.462274i
$871$	19.0140	+	21.1172i	0.644264	+	0.715528i
$872$	−8.90796	+	6.47201i	−0.301662	+	0.219170i
$873$	−5.29396	−	9.16941i	−0.179173	−	0.310338i
$874$	−2.15444	+	3.73160i	−0.0728751	+	0.126223i
$875$	−4.04674	−	38.5022i	−0.136805	−	1.30161i
$876$	−56.2380	−	40.8593i	−1.90011	−	1.38051i
$877$	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
$879$	−26.4073	−	11.7573i	−0.890697	−	0.396564i
$880$	−32.7014	−	6.95089i	−1.10236	−	0.234314i
$881$	−39.8511	+	8.47062i	−1.34262	+	0.285382i	−0.822526	−	0.568728i	$-0.807436\pi$
$881$	−39.8511	+	8.47062i	−1.34262	+	0.285382i	−0.520092	+	0.854110i	$0.674102\pi$
$882$	19.4106	−	8.64217i	0.653590	−	0.290997i
$883$	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
$885$	26.7411	−	11.9059i	0.898893	−	0.400213i
$886$	33.5766	−	7.13693i	1.12803	−	0.239770i
$887$	−12.1951	−	2.59214i	−0.409470	−	0.0870356i	−0.00142883	−	0.999999i	$-0.500455\pi$
$887$	−12.1951	−	2.59214i	−0.409470	−	0.0870356i	−0.408042	+	0.912963i	$0.633788\pi$
$888$	−0.326458	−	0.145349i	−0.0109552	−	0.00487758i
$889$	34.9100	−	38.7715i	1.17084	−	1.30035i
$890$	−2.54914	+	24.2534i	−0.0854472	+	0.812976i
$891$	−38.9395	−	28.2912i	−1.30452	−	0.947790i
$892$	−3.81159	−	36.2649i	−0.127622	−	1.21424i
$893$	1.66758	−	2.88834i	0.0558035	−	0.0966545i
$894$	27.2966	+	47.2791i	0.912936	+	1.58125i
$895$	−23.0483	+	16.7456i	−0.770421	+	0.559743i
$896$	11.8412	+	13.1510i	0.395588	+	0.439345i
$897$	−4.62789	−	14.2432i	−0.154521	−	0.475566i
$898$	14.1263			0.471401
$899$	−6.43009	+	4.17965i	−0.214455	+	0.139399i
$900$	1.85446			0.0618154
$901$	6.25307	+	19.2450i	0.208320	+	0.641143i
$902$	25.3903	+	28.1987i	0.845403	+	0.938915i
$903$	−1.71522	+	1.24618i	−0.0570789	+	0.0414703i
$904$	−5.33666	−	9.24337i	−0.177495	−	0.307430i
$905$	−11.3250	+	19.6155i	−0.376456	+	0.652041i
$906$	−9.21065	−	87.6335i	−0.306003	−	2.91143i
$907$	−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
$909$	−19.0599	+	21.1682i	−0.632179	+	0.702105i
$910$	34.0874	+	15.1767i	1.12999	+	0.503103i
$911$	53.2794	+	11.3249i	1.76522	+	0.375210i	0.972231	−	0.234022i	$-0.0751887\pi$
$911$	53.2794	+	11.3249i	1.76522	+	0.375210i	0.792992	+	0.609232i	$0.208522\pi$
$912$	4.31587	−	0.917366i	0.142913	−	0.0303770i
$913$	20.2781	−	9.02841i	0.671108	−	0.298797i
$914$	13.7206	−	42.2278i	0.453838	−	1.39677i
$915$	−3.45709	+	10.6398i	−0.114288	+	0.351742i
$916$	−40.6890	+	18.1159i	−1.34440	+	0.598567i
$917$	25.8373	−	5.49188i	0.853222	−	0.181358i
$918$	−13.1313	−	2.79114i	−0.433396	−	0.0921212i
$919$	−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
$921$	−5.08212	+	48.3531i	−0.167461	+	1.59329i
$922$	14.5418	+	10.5652i	0.478908	+	0.347947i
$923$	−0.291461	−	2.77306i	−0.00959355	−	0.0912765i
$924$	38.5928	−	66.8447i	1.26961	−	2.19903i
$925$	−0.0703606	−	0.121868i	−0.00231344	−	0.00400700i
$926$	−6.11858	+	4.44541i	−0.201069	+	0.146085i
$927$	4.13151	+	4.58851i	0.135697	+	0.150706i
$928$	3.45188	+	10.6238i	0.113313	+	0.348743i
$929$	−44.2868			−1.45300			−0.726501	−	0.687165i	$-0.758855\pi$
$929$	−44.2868			−1.45300			−0.726501	+	0.687165i	$0.758855\pi$
$930$	15.0230	+	55.9709i	0.492623	+	1.83536i
$931$	−4.03150			−0.132127
$932$	−10.0992	−	31.0820i	−0.330809	−	1.01813i
$933$	−13.5900	−	15.0932i	−0.444915	−	0.494129i
$934$	5.16512	−	3.75268i	0.169008	−	0.122791i
$935$	10.6943	+	18.5230i	0.349740	+	0.605767i
$936$	1.00153	−	1.73471i	0.0327361	−	0.0567006i
$937$	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
$939$	6.28327	−	59.7813i	0.205047	−	1.95089i
$940$	19.3839	−	21.5280i	0.632234	−	0.702167i
$941$	35.8083	+	15.9429i	1.16732	+	0.519722i	0.896559	−	0.442925i	$-0.146059\pi$
$941$	35.8083	+	15.9429i	1.16732	+	0.519722i	0.270757	+	0.962648i	$0.412726\pi$
$942$	−25.1700	−	5.35005i	−0.820083	−	0.174314i
$943$	−14.0341	+	2.98303i	−0.457012	+	0.0971409i
$944$	17.7084	−	7.88428i	0.576358	−	0.256611i
$945$	−8.11640	+	24.9797i	−0.264027	+	0.812590i
$946$	−0.739222	+	2.27509i	−0.0240342	+	0.0739696i
$947$	51.9956	−	23.1500i	1.68963	−	0.752272i	0.690038	−	0.723773i	$-0.257594\pi$
$947$	51.9956	−	23.1500i	1.68963	−	0.752272i	0.999594	−	0.0284989i	$-0.00907271\pi$
$948$	41.6466	−	8.85225i	1.35262	−	0.287508i
$949$	−28.9212	−	6.14739i	−0.938821	−	0.199553i
$950$	−0.601729	−	0.267907i	−0.0195227	−	0.00869206i
$951$	22.6423	−	25.1468i	0.734227	−	0.815441i
$952$	0.497427	−	4.73270i	0.0161217	−	0.153388i
$953$	12.3568	+	8.97773i	0.400275	+	0.290817i	0.769653	−	0.638462i	$-0.220429\pi$
$953$	12.3568	+	8.97773i	0.400275	+	0.290817i	−0.369378	+	0.929279i	$0.620429\pi$
$954$	−3.24789	−	30.9016i	−0.105154	−	1.00048i
$955$	−12.2859	+	21.2798i	−0.397563	+	0.688599i
$956$	7.80028	+	13.5105i	0.252279	+	0.436960i
$957$	10.2052	−	7.41452i	0.329888	−	0.239677i
$958$	−24.1396	−	26.8098i	−0.779916	−	0.866184i
$959$	−8.60439	−	26.4816i	−0.277850	−	0.855135i
$960$	50.9928			1.64579
$961$	−26.8335	+	15.5229i	−0.865598	+	0.500739i
$962$	−1.18709			−0.0382735
$963$	5.41685	+	16.6713i	0.174556	+	0.537227i
$964$	−17.6578	−	19.6110i	−0.568719	−	0.631627i
$965$	3.40134	−	2.47122i	0.109493	−	0.0795513i
$966$	27.3165	+	47.3136i	0.878895	+	1.52229i
$967$	−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
$969$	−2.28371	−	1.65921i	−0.0733633	−	0.0533015i
$970$	−3.41438	+	32.4857i	−0.109629	+	1.04305i
$971$	−10.6179	+	11.7924i	−0.340745	+	0.378436i	−0.889025	−	0.457859i	$-0.848616\pi$
$971$	−10.6179	+	11.7924i	−0.340745	+	0.378436i	0.548280	+	0.836295i	$0.315283\pi$
$972$	31.2682	+	13.9215i	1.00293	+	0.446532i
$973$	−72.2379	−	15.3546i	−2.31584	−	0.492247i
$974$	−58.3195	+	12.3962i	−1.86868	+	0.397200i
$975$	2.09140	−	0.931152i	0.0669785	−	0.0298207i
$976$	−2.28934	+	7.04586i	−0.0732800	+	0.225533i
$977$	−5.11731	+	15.7495i	−0.163717	+	0.503870i	−0.998939	−	0.0460426i	$-0.985339\pi$
$977$	−5.11731	+	15.7495i	−0.163717	+	0.503870i	0.835222	+	0.549913i	$0.185339\pi$
$978$	−72.0193	+	32.0650i	−2.30292	+	1.02533i
$979$	20.9882	−	4.46117i	0.670785	−	0.142580i
$980$	−34.2519	−	7.28046i	−1.09414	−	0.232566i
$981$	26.0664	+	11.6055i	0.832235	+	0.370535i
$982$	−13.6235	+	15.1304i	−0.434743	+	0.482832i
$983$	−2.26302	+	21.5312i	−0.0721792	+	0.686739i	0.897276	+	0.441470i	$0.145543\pi$
$983$	−2.26302	+	21.5312i	−0.0721792	+	0.686739i	−0.969455	+	0.245269i	$0.921124\pi$
$984$	−4.50589	−	3.27372i	−0.143643	−	0.104362i
$985$	−1.56996	−	14.9372i	−0.0500232	−	0.475939i
$986$	3.03697	−	5.26019i	0.0967169	−	0.167519i
$987$	−21.1436	−	36.6217i	−0.673007	−	1.16568i
$988$	−2.40137	+	1.74469i	−0.0763976	+	0.0555061i
$989$	−0.605238	−	0.672185i	−0.0192455	−	0.0213743i
$990$	−10.1489	−	31.2351i	−0.322553	−	0.992716i
$991$	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
$993$	−27.6925			−0.878796
$994$	3.14328	+	9.67401i	0.0996987	+	0.306841i
$995$	1.45662	+	1.61774i	0.0461779	+	0.0512857i
$996$	−20.5860	+	14.9566i	−0.652291	+	0.473917i
$997$	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
$999$	−0.0873448	−	0.831030i	−0.00276347	−	0.0262926i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.2.g.a.20.2	yes	16
3.2	odd	2		279.2.y.c.82.1		16
4.3	odd	2		496.2.bg.c.113.2		16
5.2	odd	4		775.2.ck.a.299.2		32
5.3	odd	4		775.2.ck.a.299.3		32
5.4	even	2		775.2.bl.a.51.1		16
31.2	even	5		961.2.g.s.235.1		16
31.3	odd	30		961.2.c.i.521.7		16
31.4	even	5		961.2.g.t.816.1		16
31.5	even	3		961.2.d.o.531.4		16
31.6	odd	6		961.2.g.j.844.2		16
31.7	even	15		961.2.g.s.732.1		16
31.8	even	5		961.2.g.k.846.2		16
31.9	even	15		961.2.d.o.628.4		16
31.10	even	15		961.2.d.p.388.1		16
31.11	odd	30		961.2.d.q.374.1		16
31.12	odd	30		961.2.g.n.338.1		16
31.13	odd	30		961.2.a.j.1.7		8
31.14	even	15	inner	31.2.g.a.14.2	✓	16
31.15	odd	10		961.2.c.i.439.7		16
31.16	even	5		961.2.c.j.439.7		16
31.17	odd	30		961.2.g.l.448.2		16
31.18	even	15		961.2.a.i.1.7		8
31.19	even	15		961.2.g.t.338.1		16
31.20	even	15		961.2.d.p.374.1		16
31.21	odd	30		961.2.d.q.388.1		16
31.22	odd	30		961.2.d.n.628.4		16
31.23	odd	10		961.2.g.j.846.2		16
31.24	odd	30		961.2.g.m.732.1		16
31.25	even	3		961.2.g.k.844.2		16
31.26	odd	6		961.2.d.n.531.4		16
31.27	odd	10		961.2.g.n.816.1		16
31.28	even	15		961.2.c.j.521.7		16
31.29	odd	10		961.2.g.m.235.1		16
31.30	odd	2		961.2.g.l.547.2		16
93.14	odd	30		279.2.y.c.262.1		16
93.44	even	30		8649.2.a.be.1.2		8
93.80	odd	30		8649.2.a.bf.1.2		8
124.107	odd	30		496.2.bg.c.417.2		16
155.14	even	30		775.2.bl.a.76.1		16
155.107	odd	60		775.2.ck.a.324.3		32
155.138	odd	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	31.14	even	15	inner
31.2.g.a.20.2	yes	16	1.1	even	1	trivial
279.2.y.c.82.1		16	3.2	odd	2
279.2.y.c.262.1		16	93.14	odd	30
496.2.bg.c.113.2		16	4.3	odd	2
496.2.bg.c.417.2		16	124.107	odd	30
775.2.bl.a.51.1		16	5.4	even	2
775.2.bl.a.76.1		16	155.14	even	30
775.2.ck.a.299.2		32	5.2	odd	4
775.2.ck.a.299.3		32	5.3	odd	4
775.2.ck.a.324.2		32	155.138	odd	60
775.2.ck.a.324.3		32	155.107	odd	60
961.2.a.i.1.7		8	31.18	even	15
961.2.a.j.1.7		8	31.13	odd	30
961.2.c.i.439.7		16	31.15	odd	10
961.2.c.i.521.7		16	31.3	odd	30
961.2.c.j.439.7		16	31.16	even	5
961.2.c.j.521.7		16	31.28	even	15
961.2.d.n.531.4		16	31.26	odd	6
961.2.d.n.628.4		16	31.22	odd	30
961.2.d.o.531.4		16	31.5	even	3
961.2.d.o.628.4		16	31.9	even	15
961.2.d.p.374.1		16	31.20	even	15
961.2.d.p.388.1		16	31.10	even	15
961.2.d.q.374.1		16	31.11	odd	30
961.2.d.q.388.1		16	31.21	odd	30
961.2.g.j.844.2		16	31.6	odd	6
961.2.g.j.846.2		16	31.23	odd	10
961.2.g.k.844.2		16	31.25	even	3
961.2.g.k.846.2		16	31.8	even	5
961.2.g.l.448.2		16	31.17	odd	30
961.2.g.l.547.2		16	31.30	odd	2
961.2.g.m.235.1		16	31.29	odd	10
961.2.g.m.732.1		16	31.24	odd	30
961.2.g.n.338.1		16	31.12	odd	30
961.2.g.n.816.1		16	31.27	odd	10
961.2.g.s.235.1		16	31.2	even	5
961.2.g.s.732.1		16	31.7	even	15
961.2.g.t.338.1		16	31.19	even	15
961.2.g.t.816.1		16	31.4	even	5
8649.2.a.be.1.2		8	93.44	even	30
8649.2.a.bf.1.2		8	93.80	odd	30

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:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	31.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.640321 + 1.97070i) q^{2} +(-1.43153 - 1.58988i) q^{3} +(-1.85563 + 1.34820i) q^{4} +(-1.17396 - 2.03335i) q^{5} +(2.21654 - 3.83916i) q^{6} +(0.384094 + 3.65441i) q^{7} +(-0.492333 - 0.357701i) q^{8} +(-0.164841 + 1.56836i) q^{9} +O(q^{10})\)	\(q+(0.640321 + 1.97070i) q^{2} +(-1.43153 - 1.58988i) q^{3} +(-1.85563 + 1.34820i) q^{4} +(-1.17396 - 2.03335i) q^{5} +(2.21654 - 3.83916i) q^{6} +(0.384094 + 3.65441i) q^{7} +(-0.492333 - 0.357701i) q^{8} +(-0.164841 + 1.56836i) q^{9} +(3.25543 - 3.61552i) q^{10} +(-3.91056 - 1.74109i) q^{11} +(4.79986 + 1.02024i) q^{12} +(2.04159 - 0.433953i) q^{13} +(-6.95582 + 3.09693i) q^{14} +(-1.55222 + 4.77725i) q^{15} +(-1.02791 + 3.16357i) q^{16} +(1.94411 - 0.865573i) q^{17} +(-3.19632 + 0.679399i) q^{18} +(0.606466 + 0.128908i) q^{19} +(4.91979 + 2.19043i) q^{20} +(5.26022 - 5.84207i) q^{21} +(0.927168 - 8.82142i) q^{22} +(2.71334 + 1.97136i) q^{23} +(0.136090 + 1.29481i) q^{24} +(-0.256344 + 0.444001i) q^{25} +(2.16247 + 3.74550i) q^{26} +(-2.46294 + 1.78943i) q^{27} +(-5.63960 - 6.26341i) q^{28} +(-0.425645 - 1.31000i) q^{29} -10.4085 q^{30} +(-1.44334 - 5.37743i) q^{31} -8.10976 q^{32} +(2.82997 + 8.70975i) q^{33} +(2.95064 + 3.27702i) q^{34} +(6.97979 - 5.07112i) q^{35} +(-1.80857 - 3.13253i) q^{36} +(-0.137239 + 0.237704i) q^{37} +(0.134293 + 1.27771i) q^{38} +(-3.61253 - 2.62466i) q^{39} +(-0.149354 + 1.42101i) q^{40} +(-2.86248 + 3.17911i) q^{41} +(14.8812 + 6.62555i) q^{42} +(-0.263799 - 0.0560722i) q^{43} +(9.60390 - 2.04137i) q^{44} +(3.38254 - 1.50600i) q^{45} +(-2.14756 + 6.60950i) q^{46} +(1.66225 - 5.11589i) q^{47} +(6.50117 - 2.89451i) q^{48} +(-6.36016 + 1.35189i) q^{49} +(-1.03914 - 0.220875i) q^{50} +(-4.15921 - 1.85180i) q^{51} +(-3.20338 + 3.55772i) q^{52} +(-0.993928 + 9.45659i) q^{53} +(-5.10351 - 3.70792i) q^{54} +(1.05057 + 9.99551i) q^{55} +(1.11808 - 1.93658i) q^{56} +(-0.663228 - 1.14874i) q^{57} +(2.30908 - 1.67764i) q^{58} +(-3.89932 - 4.33063i) q^{59} +(-3.56032 - 10.9575i) q^{60} +2.22719 q^{61} +(9.67313 - 6.28768i) q^{62} -5.79474 q^{63} +(-3.13704 - 9.65481i) q^{64} +(-3.27911 - 3.64182i) q^{65} +(-15.3522 + 11.1541i) q^{66} +(6.80719 + 11.7904i) q^{67} +(-2.44059 + 4.22722i) q^{68} +(-0.750018 - 7.13595i) q^{69} +(14.4630 + 10.5080i) q^{70} +(0.139642 - 1.32861i) q^{71} +(0.642159 - 0.713189i) q^{72} +(-12.9413 - 5.76184i) q^{73} +(-0.556321 - 0.118250i) q^{74} +(1.07287 - 0.228046i) q^{75} +(-1.29917 + 0.578429i) q^{76} +(4.86065 - 14.9595i) q^{77} +(2.85925 - 8.79986i) q^{78} +(7.92648 - 3.52910i) q^{79} +(7.63936 - 1.62380i) q^{80} +(10.9984 + 2.33777i) q^{81} +(-8.09799 - 3.60546i) q^{82} +(-3.46976 + 3.85356i) q^{83} +(-1.88479 + 17.9325i) q^{84} +(-4.04231 - 2.93691i) q^{85} +(-0.0584142 - 0.555774i) q^{86} +(-1.47342 + 2.55203i) q^{87} +(1.30251 + 2.25601i) q^{88} +(-4.05526 + 2.94632i) q^{89} +(5.13379 + 5.70166i) q^{90} +(2.37001 + 7.29413i) q^{91} -7.69274 q^{92} +(-6.48327 + 9.99270i) q^{93} +11.1463 q^{94} +(-0.449849 - 1.38449i) q^{95} +(11.6094 + 12.8935i) q^{96} +(-5.43173 + 3.94638i) q^{97} +(-6.73673 - 11.6684i) q^{98} +(3.37528 - 5.84615i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9}+O(q^{10}) \) 16 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9	\( 16 q - 6 q^{2} - 12 q^{3} - 14 q^{4} - 3 q^{5} + 11 q^{6} + 2 q^{7} + 17 q^{8} - 10 q^{9} - 2 q^{10} - 7 q^{11} + 5 q^{12} - 7 q^{13} - 6 q^{14} + 14 q^{15} - 2 q^{16} - 6 q^{17} - 3 q^{18} + 16 q^{19} + 37 q^{20} + 9 q^{21} + 9 q^{22} + q^{23} - 20 q^{24} - 13 q^{25} + 9 q^{26} + 9 q^{27} - 30 q^{28} - 14 q^{29} - 22 q^{30} + 15 q^{31} - 42 q^{32} - 13 q^{33} - 32 q^{34} - 9 q^{35} + q^{36} - 8 q^{37} + 8 q^{38} - 3 q^{39} - q^{40} - 8 q^{41} + 69 q^{42} + 23 q^{43} + 39 q^{44} + 65 q^{45} + 34 q^{46} + 14 q^{47} + 34 q^{48} + 2 q^{49} + 3 q^{50} - 42 q^{51} + 29 q^{52} + 6 q^{53} - 46 q^{54} - 7 q^{55} - 30 q^{56} - 17 q^{57} - 15 q^{58} + 4 q^{59} - 75 q^{60} - 60 q^{61} - 25 q^{62} - 46 q^{63} + 23 q^{64} - 12 q^{65} - 30 q^{66} + 13 q^{67} + 30 q^{68} + 38 q^{69} + 12 q^{70} - 14 q^{71} + 37 q^{72} + 2 q^{73} + 13 q^{74} + 13 q^{75} - 12 q^{76} + 18 q^{77} - 15 q^{78} + 18 q^{79} + 36 q^{80} + 23 q^{81} + 14 q^{82} - 16 q^{83} + 8 q^{84} + 37 q^{85} - 26 q^{86} + 15 q^{87} - 17 q^{88} + q^{89} - 23 q^{90} + 8 q^{91} - 64 q^{92} + 17 q^{93} + 44 q^{94} - 22 q^{95} + 8 q^{96} + 3 q^{97} - 10 q^{98} + 6 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 12 * q^3 - 14 * q^4 - 3 * q^5 + 11 * q^6 + 2 * q^7 + 17 * q^8 - 10 * q^9 - 2 * q^10 - 7 * q^11 + 5 * q^12 - 7 * q^13 - 6 * q^14 + 14 * q^15 - 2 * q^16 - 6 * q^17 - 3 * q^18 + 16 * q^19 + 37 * q^20 + 9 * q^21 + 9 * q^22 + q^23 - 20 * q^24 - 13 * q^25 + 9 * q^26 + 9 * q^27 - 30 * q^28 - 14 * q^29 - 22 * q^30 + 15 * q^31 - 42 * q^32 - 13 * q^33 - 32 * q^34 - 9 * q^35 + q^36 - 8 * q^37 + 8 * q^38 - 3 * q^39 - q^40 - 8 * q^41 + 69 * q^42 + 23 * q^43 + 39 * q^44 + 65 * q^45 + 34 * q^46 + 14 * q^47 + 34 * q^48 + 2 * q^49 + 3 * q^50 - 42 * q^51 + 29 * q^52 + 6 * q^53 - 46 * q^54 - 7 * q^55 - 30 * q^56 - 17 * q^57 - 15 * q^58 + 4 * q^59 - 75 * q^60 - 60 * q^61 - 25 * q^62 - 46 * q^63 + 23 * q^64 - 12 * q^65 - 30 * q^66 + 13 * q^67 + 30 * q^68 + 38 * q^69 + 12 * q^70 - 14 * q^71 + 37 * q^72 + 2 * q^73 + 13 * q^74 + 13 * q^75 - 12 * q^76 + 18 * q^77 - 15 * q^78 + 18 * q^79 + 36 * q^80 + 23 * q^81 + 14 * q^82 - 16 * q^83 + 8 * q^84 + 37 * q^85 - 26 * q^86 + 15 * q^87 - 17 * q^88 + q^89 - 23 * q^90 + 8 * q^91 - 64 * q^92 + 17 * q^93 + 44 * q^94 - 22 * q^95 + 8 * q^96 + 3 * q^97 - 10 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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