LMFDB - Embedded newform 115.2.g.b.71.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(6,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 18]))

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

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

chi := DirichletCharacter("115.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.g (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 12 x^{18} - 12 x^{17} + 56 x^{16} - 155 x^{15} + 551 x^{14} - 1189 x^{13} + \cdots + 1437601 $ x^20 - x^19 + 12x^18 - 12x^17 + 56x^16 - 155x^15 + 551x^14 - 1189x^13 + 3851x^12 - 10594x^11 + 18470x^10 - 22715x^9 + 56089x^8 + 1474x^7 - 31240x^6 + 12001x^5 + 243089x^4 + 225907x^3 + 23958x^2 + 857285x + 1437601
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			71.1
Root			$1.52304 + 0.978800i$ of defining polynomial
Character	$\chi$	$=$	115.71
Dual form			115.2.g.b.81.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.698939 + 0.449181i) q^{2} +(-0.257653 - 1.79202i) q^{3} +(-0.544078 - 1.19136i) q^{4} +(0.959493 + 0.281733i) q^{5} +(0.624856 - 1.36824i) q^{6} +(-0.992315 + 1.14519i) q^{7} +(0.391340 - 2.72183i) q^{8} +(-0.266462 + 0.0782402i) q^{9} +O(q^{10})$	\(q+(0.698939 + 0.449181i) q^{2} +(-0.257653 - 1.79202i) q^{3} +(-0.544078 - 1.19136i) q^{4} +(0.959493 + 0.281733i) q^{5} +(0.624856 - 1.36824i) q^{6} +(-0.992315 + 1.14519i) q^{7} +(0.391340 - 2.72183i) q^{8} +(-0.266462 + 0.0782402i) q^{9} +(0.544078 + 0.627899i) q^{10} +(0.489927 - 0.314857i) q^{11} +(-1.99476 + 1.28196i) q^{12} +(1.92754 + 2.22450i) q^{13} +(-1.20797 + 0.354691i) q^{14} +(0.257653 - 1.79202i) q^{15} +(-0.219256 + 0.253035i) q^{16} +(-2.14614 + 4.69939i) q^{17} +(-0.221384 - 0.0650043i) q^{18} +(1.88662 + 4.13112i) q^{19} +(-0.186393 - 1.29639i) q^{20} +(2.30788 + 1.48318i) q^{21} +0.483856 q^{22} +(-4.00320 + 2.64090i) q^{23} -4.97839 q^{24} +(0.841254 + 0.540641i) q^{25} +(0.348031 + 2.42061i) q^{26} +(-2.04740 - 4.48317i) q^{27} +(1.90424 + 0.559135i) q^{28} +(0.778412 - 1.70448i) q^{29} +(0.985023 - 1.13678i) q^{30} +(1.31614 - 9.15396i) q^{31} +(-5.54376 + 1.62780i) q^{32} +(-0.690460 - 0.796833i) q^{33} +(-3.61089 + 2.32058i) q^{34} +(-1.27476 + 0.819236i) q^{35} +(0.238189 + 0.274884i) q^{36} +(1.36780 - 0.401622i) q^{37} +(-0.536988 + 3.73483i) q^{38} +(3.48971 - 4.02734i) q^{39} +(1.14231 - 2.50132i) q^{40} +(5.71074 + 1.67683i) q^{41} +(0.946848 + 2.07331i) q^{42} +(-0.212226 - 1.47606i) q^{43} +(-0.641667 - 0.412375i) q^{44} -0.277711 q^{45} +(-3.98424 + 0.0476677i) q^{46} -6.45514 q^{47} +(0.509935 + 0.327715i) q^{48} +(0.669427 + 4.65597i) q^{49} +(0.345139 + 0.755750i) q^{50} +(8.97435 + 2.63511i) q^{51} +(1.60146 - 3.50671i) q^{52} +(-3.92240 + 4.52669i) q^{53} +(0.582750 - 4.05311i) q^{54} +(0.558787 - 0.164075i) q^{55} +(2.72868 + 3.14907i) q^{56} +(6.91694 - 4.44525i) q^{57} +(1.30968 - 0.841683i) q^{58} +(5.66458 + 6.53728i) q^{59} +(-2.27513 + 0.668038i) q^{60} +(1.17999 - 8.20703i) q^{61} +(5.03168 - 5.80687i) q^{62} +(0.174814 - 0.382789i) q^{63} +(-3.96342 - 1.16377i) q^{64} +(1.22275 + 2.67745i) q^{65} +(-0.124667 - 0.867079i) q^{66} +(-6.20792 - 3.98959i) q^{67} +6.76635 q^{68} +(5.76398 + 6.49337i) q^{69} -1.25896 q^{70} +(-10.5240 - 6.76335i) q^{71} +(0.108679 + 0.755881i) q^{72} +(-1.38684 - 3.03677i) q^{73} +(1.13641 + 0.333680i) q^{74} +(0.752086 - 1.64684i) q^{75} +(3.89520 - 4.49530i) q^{76} +(-0.125590 + 0.873497i) q^{77} +(4.24810 - 1.24735i) q^{78} +(-2.37554 - 2.74152i) q^{79} +(-0.281663 + 0.181014i) q^{80} +(-8.20728 + 5.27450i) q^{81} +(3.23826 + 3.73715i) q^{82} +(-1.54995 + 0.455107i) q^{83} +(0.511346 - 3.55649i) q^{84} +(-3.38318 + 3.90439i) q^{85} +(0.514686 - 1.12701i) q^{86} +(-3.25503 - 0.955762i) q^{87} +(-0.665258 - 1.45671i) q^{88} +(-1.72200 - 11.9768i) q^{89} +(-0.194103 - 0.124742i) q^{90} -4.46021 q^{91} +(5.32433 + 3.33242i) q^{92} -16.7432 q^{93} +(-4.51175 - 2.89952i) q^{94} +(0.646327 + 4.49530i) q^{95} +(4.34541 + 9.51511i) q^{96} +(13.9977 + 4.11011i) q^{97} +(-1.62348 + 3.55493i) q^{98} +(-0.105912 + 0.122229i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9	\( 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9} + 4 q^{10} - 8 q^{11} + 2 q^{12} + 10 q^{13} + 3 q^{14} - q^{15} - 36 q^{16} - 9 q^{17} + 10 q^{18} + 24 q^{19} + 4 q^{20} + 25 q^{21} + 6 q^{22} + 11 q^{23} - 2 q^{25} - 2 q^{26} + 28 q^{27} - 8 q^{28} + 12 q^{29} - 2 q^{30} + 10 q^{31} - 50 q^{32} - 49 q^{33} - 7 q^{34} + 4 q^{35} + 43 q^{36} - 18 q^{37} - 29 q^{38} - 52 q^{39} + 22 q^{40} + 10 q^{41} - 5 q^{42} + 35 q^{43} + 6 q^{44} - 38 q^{45} - 33 q^{46} - 2 q^{47} - 4 q^{48} + 4 q^{49} + 18 q^{50} + 50 q^{51} + 9 q^{52} - 5 q^{53} + 23 q^{54} + 8 q^{55} + 33 q^{57} + 35 q^{58} + 41 q^{59} - 2 q^{60} - 13 q^{61} - 2 q^{62} - 46 q^{63} + 16 q^{64} - 10 q^{65} + 56 q^{66} - 9 q^{67} + 26 q^{68} - 45 q^{69} + 8 q^{70} - 19 q^{71} - 27 q^{73} + 8 q^{74} + q^{75} + 4 q^{76} - 64 q^{77} - 27 q^{78} - 83 q^{79} - 8 q^{80} + 12 q^{81} + 31 q^{82} + 67 q^{83} + 28 q^{84} - 13 q^{85} - 73 q^{86} + 69 q^{87} + 22 q^{88} - 5 q^{89} - 10 q^{90} - 84 q^{91} + 11 q^{92} + 28 q^{93} - 37 q^{94} - 2 q^{95} + 14 q^{96} + 18 q^{97} + 8 q^{98} + 62 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9 + 4 * q^10 - 8 * q^11 + 2 * q^12 + 10 * q^13 + 3 * q^14 - q^15 - 36 * q^16 - 9 * q^17 + 10 * q^18 + 24 * q^19 + 4 * q^20 + 25 * q^21 + 6 * q^22 + 11 * q^23 - 2 * q^25 - 2 * q^26 + 28 * q^27 - 8 * q^28 + 12 * q^29 - 2 * q^30 + 10 * q^31 - 50 * q^32 - 49 * q^33 - 7 * q^34 + 4 * q^35 + 43 * q^36 - 18 * q^37 - 29 * q^38 - 52 * q^39 + 22 * q^40 + 10 * q^41 - 5 * q^42 + 35 * q^43 + 6 * q^44 - 38 * q^45 - 33 * q^46 - 2 * q^47 - 4 * q^48 + 4 * q^49 + 18 * q^50 + 50 * q^51 + 9 * q^52 - 5 * q^53 + 23 * q^54 + 8 * q^55 + 33 * q^57 + 35 * q^58 + 41 * q^59 - 2 * q^60 - 13 * q^61 - 2 * q^62 - 46 * q^63 + 16 * q^64 - 10 * q^65 + 56 * q^66 - 9 * q^67 + 26 * q^68 - 45 * q^69 + 8 * q^70 - 19 * q^71 - 27 * q^73 + 8 * q^74 + q^75 + 4 * q^76 - 64 * q^77 - 27 * q^78 - 83 * q^79 - 8 * q^80 + 12 * q^81 + 31 * q^82 + 67 * q^83 + 28 * q^84 - 13 * q^85 - 73 * q^86 + 69 * q^87 + 22 * q^88 - 5 * q^89 - 10 * q^90 - 84 * q^91 + 11 * q^92 + 28 * q^93 - 37 * q^94 - 2 * q^95 + 14 * q^96 + 18 * q^97 + 8 * q^98 + 62 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$e\left(\frac{1}{11}\right)$

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 $

$2$	0.698939	+	0.449181i	0.494224	+	0.317619i	0.763902	−	0.645332i	$-0.223281\pi$
$2$	0.698939	+	0.449181i	0.494224	+	0.317619i	−0.269678	+	0.962951i	$0.586917\pi$
$3$	−0.257653	−	1.79202i	−0.148756	−	1.03462i	−0.918260	−	0.395979i	$-0.870405\pi$
$3$	−0.257653	−	1.79202i	−0.148756	−	1.03462i	0.769503	−	0.638643i	$-0.220504\pi$
$4$	−0.544078	−	1.19136i	−0.272039	−	0.595682i
$5$	0.959493	+	0.281733i	0.429098	+	0.125995i
$5$	0.959493	+	0.281733i	0.429098	+	0.125995i
$6$	0.624856	−	1.36824i	0.255096	−	0.558583i
$7$	−0.992315	+	1.14519i	−0.375060	+	0.432842i	−0.911629	−	0.411014i	$-0.865175\pi$
$7$	−0.992315	+	1.14519i	−0.375060	+	0.432842i	0.536569	+	0.843856i	$0.319720\pi$
$8$	0.391340	−	2.72183i	0.138359	−	0.962311i
$9$	−0.266462	+	0.0782402i	−0.0888206	+	0.0260801i
$10$	0.544078	+	0.627899i	0.172053	+	0.198559i
$11$	0.489927	−	0.314857i	0.147718	−	0.0949329i	−0.464694	−	0.885471i	$-0.653836\pi$
$11$	0.489927	−	0.314857i	0.147718	−	0.0949329i	0.612412	+	0.790539i	$0.290199\pi$
$12$	−1.99476	+	1.28196i	−0.575838	+	0.370069i
$13$	1.92754	+	2.22450i	0.534604	+	0.616966i	0.957226	−	0.289340i	$-0.0934358\pi$
$13$	1.92754	+	2.22450i	0.534604	+	0.616966i	−0.422622	+	0.906306i	$0.638890\pi$
$14$	−1.20797	+	0.354691i	−0.322842	+	0.0947950i
$15$	0.257653	−	1.79202i	0.0665258	−	0.462697i
$16$	−0.219256	+	0.253035i	−0.0548140	+	0.0632587i
$17$	−2.14614	+	4.69939i	−0.520515	+	1.13977i	0.448729	+	0.893668i	$0.351877\pi$
$17$	−2.14614	+	4.69939i	−0.520515	+	1.13977i	−0.969244	+	0.246101i	$0.920850\pi$
$18$	−0.221384	−	0.0650043i	−0.0521808	−	0.0153217i
$19$	1.88662	+	4.13112i	0.432820	+	0.947744i	0.992861	+	0.119279i	$0.0380582\pi$
$19$	1.88662	+	4.13112i	0.432820	+	0.947744i	−0.560041	+	0.828465i	$0.689215\pi$
$20$	−0.186393	−	1.29639i	−0.0416787	−	0.289882i
$21$	2.30788	+	1.48318i	0.503620	+	0.323657i
$22$	0.483856			0.103158
$23$	−4.00320	+	2.64090i	−0.834726	+	0.550666i
$23$	−4.00320	+	2.64090i	−0.834726	+	0.550666i
$24$	−4.97839			−1.01621
$25$	0.841254	+	0.540641i	0.168251	+	0.108128i
$26$	0.348031	+	2.42061i	0.0682544	+	0.474720i
$27$	−2.04740	−	4.48317i	−0.394021	−	0.862787i
$28$	1.90424	+	0.559135i	0.359867	+	0.105667i
$29$	0.778412	−	1.70448i	0.144548	−	0.316515i	−0.823486	−	0.567337i	$-0.807974\pi$
$29$	0.778412	−	1.70448i	0.144548	−	0.316515i	0.968033	+	0.250822i	$0.0807009\pi$
$30$	0.985023	−	1.13678i	0.179840	−	0.207546i
$31$	1.31614	−	9.15396i	0.236386	−	1.64410i	−0.433151	−	0.901321i	$-0.642598\pi$
$31$	1.31614	−	9.15396i	0.236386	−	1.64410i	0.669537	−	0.742779i	$-0.266493\pi$
$32$	−5.54376	+	1.62780i	−0.980008	+	0.287756i
$33$	−0.690460	−	0.796833i	−0.120194	−	0.138711i
$34$	−3.61089	+	2.32058i	−0.619263	+	0.397976i
$35$	−1.27476	+	0.819236i	−0.215473	+	0.138476i
$36$	0.238189	+	0.274884i	0.0396981	+	0.0458140i
$37$	1.36780	−	0.401622i	0.224865	−	0.0660263i	−0.167359	−	0.985896i	$-0.553524\pi$
$37$	1.36780	−	0.401622i	0.224865	−	0.0660263i	0.392224	+	0.919870i	$0.371706\pi$
$38$	−0.536988	+	3.73483i	−0.0871109	+	0.605870i
$39$	3.48971	−	4.02734i	0.558801	−	0.644890i
$40$	1.14231	−	2.50132i	0.180616	−	0.395494i
$41$	5.71074	+	1.67683i	0.891868	+	0.261876i	0.695390	−	0.718632i	$-0.255231\pi$
$41$	5.71074	+	1.67683i	0.891868	+	0.261876i	0.196478	+	0.980508i	$0.437050\pi$
$42$	0.946848	+	2.07331i	0.146102	+	0.319918i
$43$	−0.212226	−	1.47606i	−0.0323641	−	0.225098i	0.967220	−	0.253941i	$-0.0817268\pi$
$43$	−0.212226	−	1.47606i	−0.0323641	−	0.225098i	−0.999584	+	0.0288431i	$0.990818\pi$
$44$	−0.641667	−	0.412375i	−0.0967350	−	0.0621678i
$45$	−0.277711			−0.0413987
$46$	−3.98424	+	0.0476677i	−0.587444	+	0.00702821i
$47$	−6.45514			−0.941579			−0.470789	−	0.882246i	$-0.656031\pi$
$47$	−6.45514			−0.941579			−0.470789	+	0.882246i	$0.656031\pi$
$48$	0.509935	+	0.327715i	0.0736028	+	0.0473016i
$49$	0.669427	+	4.65597i	0.0956325	+	0.665138i
$50$	0.345139	+	0.755750i	0.0488101	+	0.106879i
$51$	8.97435	+	2.63511i	1.25666	+	0.368989i
$52$	1.60146	−	3.50671i	0.222083	−	0.486293i
$53$	−3.92240	+	4.52669i	−0.538783	+	0.621789i	−0.958233	−	0.285990i	$-0.907678\pi$
$53$	−3.92240	+	4.52669i	−0.538783	+	0.621789i	0.419450	+	0.907779i	$0.362223\pi$
$54$	0.582750	−	4.05311i	0.0793022	−	0.551559i
$55$	0.558787	−	0.164075i	0.0753468	−	0.0221238i
$56$	2.72868	+	3.14907i	0.364636	+	0.420812i
$57$	6.91694	−	4.44525i	0.916171	−	0.588788i
$58$	1.30968	−	0.841683i	0.171970	−	0.110518i
$59$	5.66458	+	6.53728i	0.737466	+	0.851081i	0.993291	−	0.115642i	$-0.0368925\pi$
$59$	5.66458	+	6.53728i	0.737466	+	0.851081i	−0.255825	+	0.966723i	$0.582347\pi$
$60$	−2.27513	+	0.668038i	−0.293718	+	0.0862434i
$61$	1.17999	−	8.20703i	0.151083	−	1.05080i	−0.763327	−	0.646012i	$-0.776435\pi$
$61$	1.17999	−	8.20703i	0.151083	−	1.05080i	0.914410	−	0.404790i	$-0.132655\pi$
$62$	5.03168	−	5.80687i	0.639025	−	0.737474i
$63$	0.174814	−	0.382789i	0.0220245	−	0.0482269i
$64$	−3.96342	−	1.16377i	−0.495428	−	0.145471i
$65$	1.22275	+	2.67745i	0.151663	+	0.332096i
$66$	−0.124667	−	0.867079i	−0.0153455	−	0.106730i
$67$	−6.20792	−	3.98959i	−0.758418	−	0.487406i	0.103390	−	0.994641i	$-0.467031\pi$
$67$	−6.20792	−	3.98959i	−0.758418	−	0.487406i	−0.861808	+	0.507235i	$0.830668\pi$
$68$	6.76635			0.820541
$69$	5.76398	+	6.49337i	0.693902	+	0.781710i
$70$	−1.25896			−0.150475
$71$	−10.5240	−	6.76335i	−1.24897	−	0.802662i	−0.262232	−	0.965005i	$-0.584459\pi$
$71$	−10.5240	−	6.76335i	−1.24897	−	0.802662i	−0.986734	+	0.162343i	$0.948095\pi$
$72$	0.108679	+	0.755881i	0.0128080	+	0.0890814i
$73$	−1.38684	−	3.03677i	−0.162318	−	0.355427i	0.810944	−	0.585123i	$-0.198954\pi$
$73$	−1.38684	−	3.03677i	−0.162318	−	0.355427i	−0.973262	+	0.229697i	$0.926227\pi$
$74$	1.13641	+	0.333680i	0.132105	+	0.0387895i
$75$	0.752086	−	1.64684i	0.0868434	−	0.190161i
$76$	3.89520	−	4.49530i	0.446810	−	0.515646i
$77$	−0.125590	+	0.873497i	−0.0143123	+	0.0995442i
$78$	4.24810	−	1.24735i	0.481002	−	0.141235i
$79$	−2.37554	−	2.74152i	−0.267269	−	0.308445i	0.606212	−	0.795303i	$-0.292688\pi$
$79$	−2.37554	−	2.74152i	−0.267269	−	0.308445i	−0.873481	+	0.486858i	$0.838143\pi$
$80$	−0.281663	+	0.181014i	−0.0314909	+	0.0202379i
$81$	−8.20728	+	5.27450i	−0.911920	+	0.586055i
$82$	3.23826	+	3.73715i	0.357606	+	0.412699i
$83$	−1.54995	+	0.455107i	−0.170129	+	0.0499545i	−0.365688	−	0.930738i	$-0.619166\pi$
$83$	−1.54995	+	0.455107i	−0.170129	+	0.0499545i	0.195558	+	0.980692i	$0.437348\pi$
$84$	0.511346	−	3.55649i	0.0557924	−	0.388045i
$85$	−3.38318	+	3.90439i	−0.366957	+	0.423491i
$86$	0.514686	−	1.12701i	0.0555000	−	0.121528i
$87$	−3.25503	−	0.955762i	−0.348975	−	0.102468i
$88$	−0.665258	−	1.45671i	−0.0709167	−	0.155286i
$89$	−1.72200	−	11.9768i	−0.182531	−	1.26953i	−0.850751	−	0.525569i	$-0.823852\pi$
$89$	−1.72200	−	11.9768i	−0.182531	−	1.26953i	0.668220	−	0.743964i	$-0.267057\pi$
$90$	−0.194103	−	0.124742i	−0.0204602	−	0.0131490i
$91$	−4.46021			−0.467557
$92$	5.32433	+	3.33242i	0.555100	+	0.347429i
$93$	−16.7432			−1.73619
$94$	−4.51175	−	2.89952i	−0.465351	−	0.299063i
$95$	0.646327	+	4.49530i	0.0663117	+	0.461208i
$96$	4.34541	+	9.51511i	0.443501	+	0.971132i
$97$	13.9977	+	4.11011i	1.42126	+	0.417318i	0.899928	−	0.436038i	$-0.143619\pi$
$97$	13.9977	+	4.11011i	1.42126	+	0.417318i	0.521327	+	0.853357i	$0.325437\pi$
$98$	−1.62348	+	3.55493i	−0.163996	+	0.359102i
$99$	−0.105912	+	0.122229i	−0.0106446	+	0.0122845i
$100$	0.186393	−	1.29639i	0.0186393	−	0.129639i
$101$	−15.9276	+	4.67676i	−1.58485	+	0.465355i	−0.951280	−	0.308329i	$-0.900230\pi$
$101$	−15.9276	+	4.67676i	−1.58485	+	0.465355i	−0.633573	+	0.773683i	$0.718412\pi$
$102$	5.08888	+	5.87288i	0.503874	+	0.581502i
$103$	16.3726	−	10.5220i	1.61324	−	1.03676i	0.653086	−	0.757284i	$-0.273474\pi$
$103$	16.3726	−	10.5220i	1.61324	−	1.03676i	0.960151	−	0.279480i	$-0.0901622\pi$
$104$	6.80903	−	4.37590i	0.667681	−	0.429092i
$105$	1.79653	+	2.07331i	0.175323	+	0.202334i
$106$	−4.77482	+	1.40201i	−0.463771	+	0.136176i
$107$	−1.72644	+	12.0077i	−0.166901	+	1.16082i	0.718340	+	0.695692i	$0.244902\pi$
$107$	−1.72644	+	12.0077i	−0.166901	+	1.16082i	−0.885241	+	0.465132i	$0.846007\pi$
$108$	−4.22715	+	4.87839i	−0.406758	+	0.469423i
$109$	−5.07171	+	11.1055i	−0.485781	+	1.06371i	0.495052	+	0.868863i	$0.335149\pi$
$109$	−5.07171	+	11.1055i	−0.485781	+	1.06371i	−0.980833	+	0.194849i	$0.937578\pi$
$110$	0.464257	+	0.136318i	0.0442651	+	0.0129974i
$111$	−1.07213	−	2.34764i	−0.101762	−	0.222828i
$112$	−0.0722027	−	0.502181i	−0.00682251	−	0.0474516i
$113$	−3.35883	−	2.15859i	−0.315972	−	0.203063i	0.373036	−	0.927817i	$-0.378317\pi$
$113$	−3.35883	−	2.15859i	−0.315972	−	0.203063i	−0.689007	+	0.724754i	$0.741953\pi$
$114$	6.83124			0.639804
$115$	−4.58507	+	1.40609i	−0.427560	+	0.131119i
$116$	−2.45418			−0.227865
$117$	−0.687662	−	0.441933i	−0.0635744	−	0.0408568i
$118$	1.02278	+	7.11358i	0.0941544	+	0.654858i
$119$	−3.25206	−	7.12101i	−0.298116	−	0.652782i
$120$	−4.77673	−	1.40257i	−0.436054	−	0.128037i
$121$	−4.42867	+	9.69744i	−0.402607	+	0.881585i
$122$	4.51118	−	5.20618i	0.408423	−	0.471345i
$123$	1.53351	−	10.6658i	0.138272	−	0.961702i
$124$	−11.6218	+	3.41247i	−1.04367	+	0.306448i
$125$	0.654861	+	0.755750i	0.0585725	+	0.0675963i
$126$	0.294125	−	0.189023i	0.0262028	−	0.0168395i
$127$	3.74014	−	2.40364i	0.331884	−	0.213289i	−0.364076	−	0.931369i	$-0.618615\pi$
$127$	3.74014	−	2.40364i	0.331884	−	0.213289i	0.695960	+	0.718080i	$0.254979\pi$
$128$	5.31987	+	6.13945i	0.470214	+	0.542656i
$129$	−2.59045	+	0.760625i	−0.228076	+	0.0669693i
$130$	−0.348031	+	2.42061i	−0.0305243	+	0.212301i
$131$	−9.10471	+	10.5074i	−0.795483	+	0.918036i	−0.998124	−	0.0612171i	$-0.980502\pi$
$131$	−9.10471	+	10.5074i	−0.795483	+	0.918036i	0.202642	+	0.979253i	$0.435047\pi$
$132$	−0.573655	+	1.25613i	−0.0499302	+	0.109332i
$133$	−6.60304	−	1.93883i	−0.572557	−	0.168118i
$134$	−2.54691	−	5.57695i	−0.220019	−	0.481775i
$135$	−0.701406	−	4.87839i	−0.0603675	−	0.419865i
$136$	11.9511	+	7.68048i	1.02479	+	0.658595i
$137$	−8.96972			−0.766335			−0.383168	−	0.923679i	$-0.625167\pi$
$137$	−8.96972			−0.766335			−0.383168	+	0.923679i	$0.625167\pi$
$138$	1.11197	+	7.12754i	0.0946574	+	0.606736i
$139$	19.6594			1.66749			0.833744	−	0.552152i	$-0.186193\pi$
$139$	19.6594			1.66749			0.833744	+	0.552152i	$0.186193\pi$
$140$	1.66958	+	1.07297i	0.141105	+	0.0906827i
$141$	1.66319	+	11.5677i	0.140066	+	0.974178i
$142$	−4.31765	−	9.45434i	−0.362329	−	0.793390i
$143$	1.64475	+	0.482943i	0.137541	+	0.0403857i
$144$	0.0386258	−	0.0845788i	0.00321882	−	0.00704823i
$145$	1.22709	−	1.41614i	0.101904	−	0.117604i
$146$	0.394737	−	2.74546i	0.0326687	−	0.227216i
$147$	8.17110	−	2.39925i	0.673941	−	0.197887i
$148$	−1.22267	−	1.41103i	−0.100503	−	0.115986i
$149$	3.72116	−	2.39144i	0.304849	−	0.195915i	−0.379268	−	0.925287i	$-0.623824\pi$
$149$	3.72116	−	2.39144i	0.304849	−	0.195915i	0.684117	+	0.729372i	$0.260188\pi$
$150$	1.26539	−	0.813217i	0.103319	−	0.0663989i
$151$	−4.11434	−	4.74820i	−0.334820	−	0.386403i	0.563227	−	0.826302i	$-0.309560\pi$
$151$	−4.11434	−	4.74820i	−0.334820	−	0.386403i	−0.898047	+	0.439899i	$0.855014\pi$
$152$	11.9825	−	3.51838i	0.971909	−	0.285378i
$153$	0.204183	−	1.42012i	0.0165072	−	0.114810i
$154$	−0.480138	+	0.554108i	−0.0386906	+	0.0446513i
$155$	3.84180	−	8.41236i	0.308581	−	0.675697i
$156$	−6.69670	−	1.96633i	−0.536165	−	0.157432i
$157$	−7.42658	−	16.2619i	−0.592705	−	1.29784i	−0.933793	−	0.357812i	$-0.883523\pi$
$157$	−7.42658	−	16.2619i	−0.592705	−	1.29784i	0.341088	−	0.940031i	$-0.389205\pi$
$158$	−0.428919	−	2.98320i	−0.0341230	−	0.237331i
$159$	9.12252	+	5.86269i	0.723463	+	0.464942i
$160$	−5.77780			−0.456776
$161$	0.948096	−	7.20504i	0.0747205	−	0.567837i
$162$	−8.10559			−0.636835
$163$	3.66437	+	2.35495i	0.287016	+	0.184454i	0.676224	−	0.736696i	$-0.263615\pi$
$163$	3.66437	+	2.35495i	0.287016	+	0.184454i	−0.389208	+	0.921150i	$0.627251\pi$
$164$	−1.10938	−	7.71590i	−0.0866279	−	0.602511i
$165$	−0.437998	−	0.959081i	−0.0340981	−	0.0746643i
$166$	−1.28775	−	0.378117i	−0.0999485	−	0.0293475i
$167$	1.39187	−	3.04777i	0.107706	−	0.235843i	−0.848103	−	0.529831i	$-0.822255\pi$
$167$	1.39187	−	3.04777i	0.107706	−	0.235843i	0.955809	+	0.293988i	$0.0949825\pi$
$168$	4.94013	−	5.70121i	0.381139	−	0.439858i
$169$	0.617101	−	4.29203i	0.0474693	−	0.330157i
$170$	−4.11841	+	1.20927i	−0.315868	+	0.0927471i
$171$	−0.825931	−	0.953175i	−0.0631605	−	0.0728912i
$172$	−1.64306	+	1.05593i	−0.125282	+	0.0805140i
$173$	14.8002	−	9.51152i	1.12524	−	0.723148i	0.160679	−	0.987007i	$-0.448632\pi$
$173$	14.8002	−	9.51152i	1.12524	−	0.723148i	0.964561	+	0.263859i	$0.0849954\pi$
$174$	−1.84575	−	2.13011i	−0.139926	−	0.161484i
$175$	−1.45393	+	0.426911i	−0.109906	+	0.0322714i
$176$	−0.0277496	+	0.193003i	−0.00209171	+	0.0145481i
$177$	10.2554	−	11.8354i	0.770844	−	0.889602i
$178$	4.17615	−	9.14450i	0.313016	−	0.685410i
$179$	−5.36189	−	1.57439i	−0.400766	−	0.117676i	0.0751369	−	0.997173i	$-0.476061\pi$
$179$	−5.36189	−	1.57439i	−0.400766	−	0.117676i	−0.475903	+	0.879498i	$0.657879\pi$
$180$	0.151096	+	0.330855i	0.0112621	+	0.0246605i
$181$	2.22040	+	15.4432i	0.165041	+	1.14788i	0.888955	+	0.457994i	$0.151432\pi$
$181$	2.22040	+	15.4432i	0.165041	+	1.14788i	−0.723914	+	0.689890i	$0.757659\pi$
$182$	−3.11741	−	2.00344i	−0.231078	−	0.148505i
$183$	−15.0112			−1.10966
$184$	5.62147	+	11.9295i	0.414420	+	0.879456i
$185$	1.42554			0.104808
$186$	−11.7024	−	7.52071i	−0.858065	−	0.551445i
$187$	0.428184	+	2.97808i	0.0313119	+	0.217779i
$188$	3.51210	+	7.69042i	0.256146	+	0.560882i
$189$	7.16575	+	2.10405i	0.521232	+	0.153047i
$190$	−1.56746	+	3.43226i	−0.113715	+	0.249002i
$191$	12.9302	−	14.9223i	0.935599	−	1.07974i	−0.0610663	−	0.998134i	$-0.519450\pi$
$191$	12.9302	−	14.9223i	0.935599	−	1.07974i	0.996665	−	0.0816045i	$-0.0260044\pi$
$192$	−1.06430	+	7.40237i	−0.0768092	+	0.534220i
$193$	23.3423	−	6.85391i	1.68021	−	0.493355i	0.704007	−	0.710193i	$-0.251393\pi$
$193$	23.3423	−	6.85391i	1.68021	−	0.493355i	0.976208	+	0.216838i	$0.0695744\pi$
$194$	7.93738	+	9.16023i	0.569871	+	0.657666i
$195$	4.48298	−	2.88104i	0.321033	−	0.206315i
$196$	5.18273	−	3.33074i	0.370195	−	0.237910i
$197$	1.87760	+	2.16686i	0.133773	+	0.154382i	0.818684	−	0.574245i	$-0.194704\pi$
$197$	1.87760	+	2.16686i	0.133773	+	0.154382i	−0.684911	+	0.728627i	$0.740159\pi$
$198$	−0.128929	+	0.0378570i	−0.00916260	+	0.00269038i
$199$	−2.90681	+	20.2173i	−0.206058	+	1.43317i	0.579799	+	0.814760i	$0.303131\pi$
$199$	−2.90681	+	20.2173i	−0.206058	+	1.43317i	−0.785857	+	0.618408i	$0.787778\pi$
$200$	1.80075	−	2.07817i	0.127332	−	0.146949i
$201$	−5.54992	+	12.1526i	−0.391461	+	0.857180i
$202$	−13.2331	−	3.88559i	−0.931078	−	0.273389i
$203$	1.17953	+	2.58282i	0.0827870	+	0.181278i
$204$	−1.74337	−	12.1254i	−0.122060	−	0.848949i
$205$	5.00700	+	3.21780i	0.349704	+	0.224741i
$206$	16.1697			1.12660
$207$	0.860076	−	1.01691i	0.0597794	−	0.0706802i
$208$	−0.985502			−0.0683323
$209$	2.22502	+	1.42993i	0.153908	+	0.0989104i
$210$	0.324376	+	2.25608i	0.0223840	+	0.155684i
$211$	−6.60476	−	14.4624i	−0.454691	−	0.995634i	−0.988666	−	0.150134i	$-0.952030\pi$
$211$	−6.60476	−	14.4624i	−0.454691	−	0.995634i	0.533975	−	0.845500i	$-0.320698\pi$
$212$	7.52703	+	2.21014i	0.516958	+	0.151793i
$213$	−9.40851	+	20.6018i	−0.644660	+	1.41161i
$214$	−6.60028	+	7.61713i	−0.451186	+	0.520696i
$215$	0.212226	−	1.47606i	0.0144737	−	0.100667i
$216$	−13.0036	+	3.81821i	−0.884786	+	0.259797i
$217$	9.17702	+	10.5908i	0.622977	+	0.718953i
$218$	−8.53318	+	5.48394i	−0.577940	+	0.371420i
$219$	−5.08461	+	3.26768i	−0.343586	+	0.220809i
$220$	−0.499496	−	0.576449i	−0.0336760	−	0.0388642i
$221$	−14.5906	+	4.28418i	−0.981468	+	0.288185i
$222$	0.305160	−	2.12244i	0.0204810	−	0.142449i
$223$	−10.2471	+	11.8258i	−0.686198	+	0.791915i	−0.986819	−	0.161829i	$-0.948261\pi$
$223$	−10.2471	+	11.8258i	−0.686198	+	0.791915i	0.300620	+	0.953744i	$0.402806\pi$
$224$	3.63702	−	7.96396i	0.243009	−	0.532114i
$225$	−0.266462	−	0.0782402i	−0.0177641	−	0.00521601i
$226$	−1.37802	−	3.01744i	−0.0916645	−	0.200717i
$227$	0.583887	+	4.06102i	0.0387539	+	0.269539i	0.999981	−	0.00621979i	$-0.00197983\pi$
$227$	0.583887	+	4.06102i	0.0387539	+	0.269539i	−0.961227	+	0.275759i	$0.911071\pi$
$228$	−9.05927	−	5.82204i	−0.599965	−	0.385574i
$229$	−25.5487			−1.68830			−0.844151	−	0.536105i	$-0.819895\pi$
$229$	−25.5487			−1.68830			−0.844151	+	0.536105i	$0.819895\pi$
$230$	−3.83628	−	1.07675i	−0.252957	−	0.0709989i
$231$	1.59768			0.105120
$232$	−4.33469	−	2.78574i	−0.284586	−	0.182892i
$233$	−1.58326	−	11.0118i	−0.103723	−	0.721408i	−0.973620	−	0.228175i	$-0.926724\pi$
$233$	−1.58326	−	11.0118i	−0.103723	−	0.721408i	0.869897	−	0.493233i	$-0.164185\pi$
$234$	−0.282125	−	0.617769i	−0.0184431	−	0.0403848i
$235$	−6.19366	−	1.81862i	−0.404030	−	0.118634i
$236$	4.70631	−	10.3054i	0.306354	−	0.670823i
$237$	−4.30078	+	4.96337i	−0.279366	+	0.322405i
$238$	0.925632	−	6.43791i	0.0599998	−	0.417308i
$239$	5.84982	−	1.71766i	0.378393	−	0.111106i	−0.0870045	−	0.996208i	$-0.527729\pi$
$239$	5.84982	−	1.71766i	0.378393	−	0.111106i	0.465398	+	0.885102i	$0.345911\pi$
$240$	0.396951	+	0.458106i	0.0256231	+	0.0295706i
$241$	23.5911	−	15.1611i	1.51964	−	0.976611i	0.527761	−	0.849393i	$-0.323032\pi$
$241$	23.5911	−	15.1611i	1.51964	−	0.976611i	0.991875	−	0.127218i	$-0.0406048\pi$
$242$	−7.45127	+	4.78864i	−0.478986	+	0.307826i
$243$	1.88407	+	2.17433i	0.120863	+	0.139484i
$244$	−10.4196	+	3.05946i	−0.667045	+	0.195862i
$245$	−0.669427	+	4.65597i	−0.0427681	+	0.297459i
$246$	5.86269	−	6.76591i	0.373792	−	0.431379i
$247$	−5.55315	+	12.1597i	−0.353338	+	0.773703i
$248$	−24.4004	−	7.16462i	−1.54943	−	0.454954i
$249$	1.21491	+	2.66028i	0.0769918	+	0.168588i
$250$	0.118239	+	0.822373i	0.00747812	+	0.0520115i
$251$	25.2310	+	16.2150i	1.59256	+	1.02348i	0.970682	+	0.240369i	$0.0772685\pi$
$251$	25.2310	+	16.2150i	1.59256	+	1.02348i	0.621883	+	0.783110i	$0.286368\pi$
$252$	−0.551153			−0.0347194
$253$	−1.12977	+	2.55428i	−0.0710280	+	0.160586i
$254$	3.69380			0.231770
$255$	7.86843	+	5.05673i	0.492740	+	0.316665i
$256$	2.13627	+	14.8581i	0.133517	+	0.928630i
$257$	−1.72148	−	3.76951i	−0.107383	−	0.235135i	0.848311	−	0.529498i	$-0.177620\pi$
$257$	−1.72148	−	3.76951i	−0.107383	−	0.235135i	−0.955694	+	0.294363i	$0.904893\pi$
$258$	−2.15222	−	0.631950i	−0.133992	−	0.0393435i
$259$	−0.897353	+	1.96493i	−0.0557588	+	0.122095i
$260$	2.52454	−	2.91348i	0.156566	−	0.180686i
$261$	−0.0740578	+	0.515083i	−0.00458406	+	0.0318828i
$262$	−11.0834	+	3.25437i	−0.684732	+	0.201055i
$263$	−5.24802	−	6.05654i	−0.323607	−	0.373462i	0.570514	−	0.821288i	$-0.306744\pi$
$263$	−5.24802	−	6.05654i	−0.323607	−	0.373462i	−0.894121	+	0.447826i	$0.852199\pi$
$264$	−2.43905	+	1.56748i	−0.150113	+	0.0964717i
$265$	−5.03883	+	3.23826i	−0.309533	+	0.198925i
$266$	−3.74424	−	4.32108i	−0.229574	−	0.264943i
$267$	−21.0189	+	6.17170i	−1.28633	+	0.377702i
$268$	−1.37546	+	9.56654i	−0.0840197	+	0.584370i
$269$	14.3501	−	16.5609i	0.874941	−	1.00974i	−0.124905	−	0.992169i	$-0.539862\pi$
$269$	14.3501	−	16.5609i	0.874941	−	1.00974i	0.999846	−	0.0175671i	$-0.00559208\pi$
$270$	1.70104	−	3.72475i	0.103522	−	0.226681i
$271$	8.46252	+	2.48482i	0.514061	+	0.150942i	0.528466	−	0.848954i	$-0.322767\pi$
$271$	8.46252	+	2.48482i	0.514061	+	0.150942i	−0.0144050	+	0.999896i	$0.504585\pi$
$272$	−0.718556	−	1.57342i	−0.0435688	−	0.0954025i
$273$	1.14919	+	7.99277i	0.0695520	+	0.483745i
$274$	−6.26929	−	4.02903i	−0.378741	−	0.243402i
$275$	0.582377			0.0351186
$276$	4.59992	−	10.3999i	0.276883	−	0.626001i
$277$	21.6227			1.29918			0.649590	−	0.760284i	$-0.274940\pi$
$277$	21.6227			1.29918			0.649590	+	0.760284i	$0.274940\pi$
$278$	13.7407	+	8.83061i	0.824113	+	0.529625i
$279$	0.365507	+	2.54216i	0.0218823	+	0.152195i
$280$	1.73096	+	3.79027i	0.103444	+	0.226512i
$281$	−8.23901	−	2.41919i	−0.491498	−	0.144317i	0.0265861	−	0.999647i	$-0.491536\pi$
$281$	−8.23901	−	2.41919i	−0.491498	−	0.144317i	−0.518084	+	0.855330i	$0.673355\pi$
$282$	−4.03353	+	8.83220i	−0.240193	+	0.525950i
$283$	−2.57964	+	2.97706i	−0.153344	+	0.176968i	−0.827224	−	0.561873i	$-0.810081\pi$
$283$	−2.57964	+	2.97706i	−0.153344	+	0.176968i	0.673880	+	0.738841i	$0.264626\pi$
$284$	−2.33175	+	16.2177i	−0.138364	+	0.962343i
$285$	7.88913	−	2.31646i	0.467312	−	0.137215i
$286$	0.932653	+	1.07634i	0.0551489	+	0.0636453i
$287$	−7.58714	+	4.87596i	−0.447855	+	0.287819i
$288$	1.34984	−	0.867490i	0.0795402	−	0.0511174i
$289$	−6.34571	−	7.32334i	−0.373277	−	0.430785i
$290$	1.49376	−	0.438608i	0.0877167	−	0.0257560i
$291$	3.75882	−	26.1432i	0.220346	−	1.53254i
$292$	−2.86334	+	3.30447i	−0.167565	+	0.193380i
$293$	2.61380	−	5.72342i	0.152700	−	0.334366i	−0.817787	−	0.575521i	$-0.804799\pi$
$293$	2.61380	−	5.72342i	0.152700	−	0.334366i	0.970486	+	0.241156i	$0.0775264\pi$
$294$	6.78879	+	1.99337i	0.395930	+	0.116256i
$295$	3.59336	+	7.86837i	0.209214	+	0.458114i
$296$	−0.557872	−	3.88008i	−0.0324256	−	0.225525i
$297$	−2.41463	−	1.55179i	−0.140111	−	0.0900439i
$298$	3.67505			0.212890
$299$	−13.5910	−	3.81468i	−0.785990	−	0.220609i
$300$	−2.37118			−0.136900
$301$	1.90097	+	1.22168i	0.109570	+	0.0704165i
$302$	−0.742872	−	5.16679i	−0.0427475	−	0.297315i
$303$	12.4846	+	27.3375i	0.717223	+	1.57050i
$304$	−1.45897	−	0.428392i	−0.0836777	−	0.0245700i
$305$	3.44438	−	7.54215i	0.197225	−	0.431862i
$306$	0.780602	−	0.900863i	0.0446241	−	0.0514989i
$307$	−3.38918	+	23.5723i	−0.193431	+	1.34534i	0.629413	+	0.777071i	$0.283296\pi$
$307$	−3.38918	+	23.5723i	−0.193431	+	1.34534i	−0.822843	+	0.568268i	$0.807614\pi$
$308$	1.10898	−	0.325627i	0.0631902	−	0.0185543i
$309$	−23.0741	−	26.6289i	−1.31264	−	1.51486i
$310$	6.46385	−	4.15407i	0.367122	−	0.235935i
$311$	11.9430	−	7.67532i	0.677227	−	0.435228i	−0.156297	−	0.987710i	$-0.549956\pi$
$311$	11.9430	−	7.67532i	0.677227	−	0.435228i	0.833524	+	0.552483i	$0.186319\pi$
$312$	−9.59606	−	11.0744i	−0.543270	−	0.626967i
$313$	11.9136	−	3.49815i	0.673397	−	0.197727i	0.0728816	−	0.997341i	$-0.476780\pi$
$313$	11.9136	−	3.49815i	0.673397	−	0.197727i	0.600515	+	0.799614i	$0.294962\pi$
$314$	2.11382	−	14.7020i	0.119290	−	0.829680i
$315$	0.275577	−	0.318032i	0.0155270	−	0.0179191i
$316$	−1.97367	+	4.32173i	−0.111028	+	0.243117i
$317$	−2.93332	−	0.861302i	−0.164752	−	0.0483755i	0.198316	−	0.980138i	$-0.436453\pi$
$317$	−2.93332	−	0.861302i	−0.164752	−	0.0483755i	−0.363068	+	0.931763i	$0.618271\pi$
$318$	3.74268	+	8.19532i	0.209879	+	0.459571i
$319$	−0.155304	−	1.08016i	−0.00869534	−	0.0604774i
$320$	−3.47501	−	2.23325i	−0.194259	−	0.124843i
$321$	21.9628			1.22584
$322$	3.89903	−	4.61002i	0.217284	−	0.256906i
$323$	−23.4627			−1.30550
$324$	10.7492	+	6.90812i	0.597180	+	0.383785i
$325$	0.418895	+	2.91348i	0.0232361	+	0.161611i
$326$	1.50338	+	3.29193i	0.0832642	+	0.182323i
$327$	21.2080	+	6.22722i	1.17280	+	0.344366i
$328$	6.79887	−	14.8874i	0.375405	−	0.822022i
$329$	6.40553	−	7.39238i	0.353148	−	0.407555i
$330$	0.124667	−	0.867079i	0.00686270	−	0.0477311i
$331$	−2.10185	+	0.617159i	−0.115528	+	0.0339221i	−0.338986	−	0.940792i	$-0.610084\pi$
$331$	−2.10185	+	0.617159i	−0.115528	+	0.0339221i	0.223457	+	0.974714i	$0.428266\pi$
$332$	1.38549	+	1.59894i	0.0760388	+	0.0877535i
$333$	−0.333043	+	0.214034i	−0.0182506	+	0.0117290i
$334$	2.34183	−	1.50500i	0.128139	−	0.0823501i
$335$	−4.83246	−	5.57695i	−0.264025	−	0.304702i
$336$	−0.881313	+	0.258777i	−0.0480796	+	0.0141174i
$337$	3.56270	−	24.7791i	0.194073	−	1.34981i	−0.627016	−	0.779006i	$-0.715724\pi$
$337$	3.56270	−	24.7791i	0.194073	−	1.34981i	0.821089	−	0.570800i	$-0.193367\pi$
$338$	2.35921	−	2.72268i	0.128324	−	0.148094i
$339$	−3.00281	+	6.57524i	−0.163090	+	0.357118i
$340$	6.49227	+	1.90630i	0.352093	+	0.103384i
$341$	−2.23737	−	4.89917i	−0.121161	−	0.265305i
$342$	−0.149127	−	1.03720i	−0.00806388	−	0.0560855i
$343$	−14.9196	−	9.58822i	−0.805580	−	0.517715i
$344$	−4.10064			−0.221092
$345$	3.70110	+	7.85425i	0.199261	+	0.422858i
$346$	14.6168			0.785806
$347$	−6.36830	−	4.09266i	−0.341868	−	0.219705i	0.358429	−	0.933557i	$-0.383313\pi$
$347$	−6.36830	−	4.09266i	−0.341868	−	0.219705i	−0.700297	+	0.713852i	$0.746949\pi$
$348$	0.632327	+	4.39793i	0.0338963	+	0.235754i
$349$	2.75979	+	6.04309i	0.147728	+	0.323479i	0.969001	−	0.247056i	$-0.0794631\pi$
$349$	2.75979	+	6.04309i	0.147728	+	0.323479i	−0.821273	+	0.570535i	$0.806736\pi$
$350$	−1.20797	−	0.354691i	−0.0645685	−	0.0189590i
$351$	6.02638	−	13.1959i	0.321665	−	0.704347i
$352$	−2.20351	+	2.54299i	−0.117448	+	0.135542i
$353$	4.15026	−	28.8657i	0.220896	−	1.53637i	−0.513764	−	0.857932i	$-0.671749\pi$
$353$	4.15026	−	28.8657i	0.220896	−	1.53637i	0.734660	−	0.678435i	$-0.237342\pi$
$354$	12.4841	−	3.66567i	0.663524	−	0.194828i
$355$	−8.19223	−	9.45434i	−0.434798	−	0.501784i
$356$	−13.3318	+	8.56781i	−0.706583	+	0.454093i
$357$	−11.9231	+	7.66250i	−0.631036	+	0.405542i
$358$	−3.04045	−	3.50886i	−0.160693	−	0.185449i
$359$	−6.92894	+	2.03452i	−0.365696	+	0.107378i	−0.459417	−	0.888220i	$-0.651942\pi$
$359$	−6.92894	+	2.03452i	−0.365696	+	0.107378i	0.0937217	+	0.995598i	$0.470124\pi$
$360$	−0.108679	+	0.755881i	−0.00572790	+	0.0398384i
$361$	−1.06446	+	1.22845i	−0.0560240	+	0.0646552i
$362$	−5.38487	+	11.7912i	−0.283022	+	0.619732i
$363$	18.5190	+	5.43768i	0.971997	+	0.285404i
$364$	2.42670	+	5.31374i	0.127194	+	0.278516i
$365$	−0.475112	−	3.30447i	−0.0248685	−	0.172964i
$366$	−10.4919	−	6.74273i	−0.548420	−	0.352448i
$367$	−3.94449			−0.205901			−0.102950	−	0.994686i	$-0.532828\pi$
$367$	−3.94449			−0.205901			−0.102950	+	0.994686i	$0.532828\pi$
$368$	0.209486	−	1.59198i	0.0109202	−	0.0829879i
$369$	−1.65289			−0.0860460
$370$	0.996367	+	0.640327i	0.0517987	+	0.0332890i
$371$	−1.29168	−	8.98380i	−0.0670605	−	0.466416i
$372$	9.10959	+	19.9472i	0.472310	+	1.03421i
$373$	−30.8995	−	9.07292i	−1.59992	−	0.469778i	−0.644394	−	0.764694i	$-0.722890\pi$
$373$	−30.8995	−	9.07292i	−1.59992	−	0.469778i	−0.955523	+	0.294915i	$0.904709\pi$
$374$	−1.03842	+	2.27383i	−0.0536956	+	0.117577i
$375$	1.18559	−	1.36824i	0.0612236	−	0.0706558i
$376$	−2.52615	+	17.5698i	−0.130276	+	0.906092i
$377$	5.29205	−	1.55389i	0.272555	−	0.0800292i
$378$	4.06332	+	4.68932i	0.208995	+	0.241193i
$379$	−16.8360	+	10.8198i	−0.864805	+	0.555777i	−0.896160	−	0.443732i	$-0.853654\pi$
$379$	−16.8360	+	10.8198i	−0.864805	+	0.555777i	0.0313543	+	0.999508i	$0.490018\pi$
$380$	5.00389	−	3.21581i	0.256694	−	0.164967i
$381$	−5.27103	−	6.08309i	−0.270043	−	0.311646i
$382$	15.7402	−	4.62175i	0.805341	−	0.236469i
$383$	−5.47270	+	38.0635i	−0.279642	+	1.94495i	0.0446689	+	0.999002i	$0.485777\pi$
$383$	−5.47270	+	38.0635i	−0.279642	+	1.94495i	−0.324311	+	0.945951i	$0.605132\pi$
$384$	9.63133	−	11.1151i	0.491497	−	0.567217i
$385$	−0.366595	+	0.802732i	−0.0186834	+	0.0409110i
$386$	19.3935	+	5.69444i	0.987102	+	0.289839i
$387$	0.172038	+	0.376710i	0.00874516	+	0.0191492i
$388$	−2.71923	−	18.9126i	−0.138048	−	0.960144i
$389$	13.3578	+	8.58455i	0.677268	+	0.435254i	0.833539	−	0.552460i	$-0.186311\pi$
$389$	13.3578	+	8.58455i	0.677268	+	0.435254i	−0.156271	+	0.987714i	$0.549947\pi$
$390$	4.42744			0.224192
$391$	−3.81920	−	24.4804i	−0.193145	−	1.23802i
$392$	12.9347			0.653302
$393$	21.1753	+	13.6085i	1.06815	+	0.686460i
$394$	0.339012	+	2.35788i	0.0170792	+	0.118788i
$395$	−1.50694	−	3.29973i	−0.0758223	−	0.166028i
$396$	0.203244	+	0.0596778i	0.0102134	+	0.00299892i
$397$	−2.68195	+	5.87264i	−0.134603	+	0.294739i	−0.964916	−	0.262557i	$-0.915434\pi$
$397$	−2.68195	+	5.87264i	−0.134603	+	0.294739i	0.830313	+	0.557297i	$0.188161\pi$
$398$	−11.1129	+	12.8250i	−0.557040	+	0.642858i
$399$	−1.77312	+	12.3323i	−0.0887670	+	0.617388i
$400$	−0.321251	+	0.0943278i	−0.0160625	+	0.00471639i
$401$	12.9249	+	14.9161i	0.645437	+	0.744874i	0.980326	−	0.197384i	$-0.0632445\pi$
$401$	12.9249	+	14.9161i	0.645437	+	0.744874i	−0.334890	+	0.942257i	$0.608699\pi$
$402$	−9.33778	+	6.00103i	−0.465726	+	0.299304i
$403$	22.8999	−	14.7169i	1.14073	−	0.733101i
$404$	14.2376	+	16.4310i	0.708345	+	0.817474i
$405$	−9.36082	+	2.74859i	−0.465143	+	0.136578i
$406$	−0.335730	+	2.33505i	−0.0166620	+	0.115887i
$407$	0.543668	−	0.627426i	0.0269486	−	0.0311004i
$408$	10.6843	−	23.3954i	0.528953	−	1.15824i
$409$	0.368007	+	0.108057i	0.0181968	+	0.00534305i	0.290818	−	0.956778i	$-0.406072\pi$
$409$	0.368007	+	0.108057i	0.0181968	+	0.00534305i	−0.272622	+	0.962121i	$0.587891\pi$
$410$	2.05421	+	4.49810i	0.101450	+	0.222145i
$411$	2.31108	+	16.0739i	0.113997	+	0.792867i
$412$	−21.4435	−	13.7809i	−1.05645	−	0.678936i
$413$	−13.1075			−0.644977
$414$	1.05792	−	0.324429i	0.0519938	−	0.0159448i
$415$	−1.61539			−0.0792962
$416$	−14.3069	−	9.19447i	−0.701452	−	0.450796i
$417$	−5.06530	−	35.2300i	−0.248049	−	1.72522i
$418$	0.912852	+	1.99887i	0.0446491	+	0.0977678i
$419$	1.99315	+	0.585242i	0.0973718	+	0.0285909i	0.330056	−	0.943962i	$-0.392933\pi$
$419$	1.99315	+	0.585242i	0.0973718	+	0.0285909i	−0.232684	+	0.972552i	$0.574751\pi$
$420$	1.49261	−	3.26836i	0.0728320	−	0.159480i
$421$	−19.3641	+	22.3473i	−0.943747	+	1.08914i	0.0521497	+	0.998639i	$0.483393\pi$
$421$	−19.3641	+	22.3473i	−0.943747	+	1.08914i	−0.995896	+	0.0905023i	$0.971153\pi$
$422$	1.87991	−	13.0751i	0.0915127	−	0.636485i
$423$	1.72005	−	0.505052i	0.0836316	−	0.0245564i
$424$	10.7859	+	12.4476i	0.523808	+	0.604507i
$425$	−4.34613	+	2.79309i	−0.210818	+	0.135485i
$426$	−15.8299	+	10.1732i	−0.766960	+	0.492895i
$427$	8.22770	+	9.49527i	0.398166	+	0.459509i
$428$	15.2448	−	4.47628i	0.736886	−	0.216369i
$429$	0.441667	−	3.07186i	0.0213239	−	0.148311i
$430$	0.811352	−	0.936350i	0.0391269	−	0.0451548i
$431$	−8.95927	+	19.6181i	−0.431553	+	0.944969i	0.561519	+	0.827464i	$0.310217\pi$
$431$	−8.95927	+	19.6181i	−0.431553	+	0.944969i	−0.993072	+	0.117506i	$0.962510\pi$
$432$	1.58330	+	0.464900i	0.0761767	+	0.0223675i
$433$	4.53545	+	9.93125i	0.217960	+	0.477265i	0.986753	−	0.162233i	$-0.0518695\pi$
$433$	4.53545	+	9.93125i	0.217960	+	0.477265i	−0.768793	+	0.639498i	$0.779142\pi$
$434$	1.65697	+	11.5245i	0.0795372	+	0.553193i
$435$	−2.85391	−	1.83409i	−0.136834	−	0.0879381i
$436$	15.9901			0.765786
$437$	−18.4624	−	11.5553i	−0.883176	−	0.552766i
$438$	−5.02161			−0.239942
$439$	−19.0695	−	12.2553i	−0.910140	−	0.584911i	−0.000358817	−	1.00000i	$-0.500114\pi$
$439$	−19.0695	−	12.2553i	−0.910140	−	0.584911i	−0.909781	+	0.415089i	$0.863751\pi$
$440$	−0.227907	−	1.58513i	−0.0108650	−	0.0755681i
$441$	−0.542661	−	1.18826i	−0.0258410	−	0.0565839i
$442$	−12.1223	−	3.55942i	−0.576598	−	0.169305i
$443$	4.12813	−	9.03934i	0.196133	−	0.429472i	−0.785856	−	0.618410i	$-0.787777\pi$
$443$	4.12813	−	9.03934i	0.196133	−	0.429472i	0.981989	+	0.188938i	$0.0605045\pi$
$444$	−2.21357	+	2.55460i	−0.105051	+	0.121236i
$445$	1.72200	−	11.9768i	0.0816305	−	0.567753i
$446$	−12.4740	+	3.66271i	−0.590663	+	0.173434i
$447$	−5.24428	−	6.05222i	−0.248046	−	0.286260i
$448$	5.26570	−	3.38406i	0.248781	−	0.159882i
$449$	−33.9055	+	21.7897i	−1.60010	+	1.02832i	−0.632921	+	0.774217i	$0.718144\pi$
$449$	−33.9055	+	21.7897i	−1.60010	+	1.02832i	−0.967177	+	0.254104i	$0.918219\pi$
$450$	−0.151096	−	0.174375i	−0.00712275	−	0.00822010i
$451$	3.32580	−	0.976544i	0.156606	−	0.0459837i
$452$	−0.744201	+	5.17603i	−0.0350042	+	0.243460i
$453$	−7.44879	+	8.59636i	−0.349975	+	0.403892i
$454$	−1.41603	+	3.10068i	−0.0664576	+	0.145522i
$455$	−4.27954	−	1.25659i	−0.200628	−	0.0589097i
$456$	−9.39232	−	20.5663i	−0.439836	−	0.963106i
$457$	−1.70599	−	11.8654i	−0.0798030	−	0.555042i	−0.990022	−	0.140914i	$-0.954996\pi$
$457$	−1.70599	−	11.8654i	−0.0798030	−	0.555042i	0.910219	−	0.414128i	$-0.135913\pi$
$458$	−17.8569	−	11.4760i	−0.834400	−	0.536236i
$459$	25.4622			1.18847
$460$	4.16981	+	4.69747i	0.194418	+	0.219021i
$461$	−0.237183			−0.0110467			−0.00552335	−	0.999985i	$-0.501758\pi$
$461$	−0.237183			−0.0110467			−0.00552335	+	0.999985i	$0.501758\pi$
$462$	1.11668	+	0.717647i	0.0519527	+	0.0333880i
$463$	−1.46837	−	10.2127i	−0.0682409	−	0.474626i	−0.995073	−	0.0991490i	$-0.968388\pi$
$463$	−1.46837	−	10.2127i	−0.0682409	−	0.474626i	0.926832	−	0.375477i	$-0.122521\pi$
$464$	0.260623	+	0.570684i	0.0120991	+	0.0264933i
$465$	−16.0650	−	4.71710i	−0.744994	−	0.218750i
$466$	3.83969	−	8.40775i	0.177870	−	0.389482i
$467$	−6.96962	+	8.04337i	−0.322515	+	0.372203i	−0.893735	−	0.448594i	$-0.851925\pi$
$467$	−6.96962	+	8.04337i	−0.322515	+	0.372203i	0.571220	+	0.820797i	$0.306470\pi$
$468$	−0.152362	+	1.05970i	−0.00704294	+	0.0489847i
$469$	10.7291	−	3.15033i	0.495422	−	0.145469i
$470$	−3.51210	−	4.05318i	−0.162001	−	0.186959i
$471$	−27.2282	+	17.4985i	−1.25461	+	0.806288i
$472$	20.0101	−	12.8597i	0.921040	−	0.591917i
$473$	−0.568724	−	0.656342i	−0.0261499	−	0.0301786i
$474$	−5.23543	+	1.53726i	−0.240471	+	0.0706088i
$475$	−0.646327	+	4.49530i	−0.0296555	+	0.206259i
$476$	−6.71435	+	7.74877i	−0.307752	+	0.355164i
$477$	0.691000	−	1.51308i	0.0316387	−	0.0692791i
$478$	4.86021	+	1.42709i	0.222301	+	0.0652734i
$479$	5.86542	+	12.8435i	0.267998	+	0.586833i	0.995008	−	0.0997931i	$-0.0318181\pi$
$479$	5.86542	+	12.8435i	0.267998	+	0.586833i	−0.727010	+	0.686626i	$0.759091\pi$
$480$	1.48867	+	10.3539i	0.0679482	+	0.472590i
$481$	3.52990	+	2.26853i	0.160950	+	0.103436i
$482$	23.2988			1.06123
$483$	−13.1558	+	0.157397i	−0.598611	+	0.00716183i
$484$	13.9627			0.634669
$485$	12.2728	+	7.88724i	0.557278	+	0.358141i
$486$	0.340181	+	2.36601i	0.0154309	+	0.107325i
$487$	−2.43737	−	5.33709i	−0.110448	−	0.241847i	0.846335	−	0.532651i	$-0.178804\pi$
$487$	−2.43737	−	5.33709i	−0.110448	−	0.241847i	−0.956782	+	0.290805i	$0.906077\pi$
$488$	−21.8763	−	6.42347i	−0.990295	−	0.290777i
$489$	3.27597	−	7.17338i	0.148145	−	0.324392i
$490$	−2.55926	+	2.95354i	−0.115616	+	0.133427i
$491$	−3.80640	+	26.4741i	−0.171780	+	1.19476i	0.703340	+	0.710853i	$0.251691\pi$
$491$	−3.80640	+	26.4741i	−0.171780	+	1.19476i	−0.875121	+	0.483905i	$0.839218\pi$
$492$	−13.5412	+	3.97605i	−0.610484	+	0.179254i
$493$	6.33946	+	7.31612i	0.285515	+	0.329502i
$494$	−9.34321	+	6.00451i	−0.420371	+	0.270156i
$495$	−0.136058	+	0.0874392i	−0.00611535	+	0.00393010i
$496$	2.02770	+	2.34009i	0.0910465	+	0.105073i
$497$	18.1884	−	5.34061i	0.815863	−	0.239559i
$498$	−0.345799	+	2.40509i	−0.0154956	+	0.107775i
$499$	1.39389	−	1.60863i	0.0623990	−	0.0720122i	−0.723692	−	0.690123i	$-0.757556\pi$
$499$	1.39389	−	1.60863i	0.0623990	−	0.0720122i	0.786091	+	0.618111i	$0.212102\pi$
$500$	0.544078	−	1.19136i	0.0243319	−	0.0532794i
$501$	−5.82028	−	1.70899i	−0.260031	−	0.0763519i
$502$	10.3515	+	22.6665i	0.462008	+	1.01166i
$503$	5.70391	+	39.6716i	0.254325	+	1.76887i	0.571597	+	0.820534i	$0.306324\pi$
$503$	5.70391	+	39.6716i	0.254325	+	1.76887i	−0.317273	+	0.948334i	$0.602767\pi$
$504$	−0.973473	−	0.625613i	−0.0433619	−	0.0278670i
$505$	−16.6000			−0.738690
$506$	−1.93697	+	1.27782i	−0.0861090	+	0.0568059i
$507$	−7.85040			−0.348648
$508$	−4.89854	−	3.14810i	−0.217338	−	0.139674i
$509$	−4.33542	−	30.1535i	−0.192164	−	1.33653i	−0.826265	−	0.563282i	$-0.809539\pi$
$509$	−4.33542	−	30.1535i	−0.192164	−	1.33653i	0.634101	−	0.773250i	$-0.281370\pi$
$510$	3.22816	+	7.06869i	0.142945	+	0.313007i
$511$	4.85387	+	1.42522i	0.214722	+	0.0630482i
$512$	1.56854	−	3.43462i	0.0693203	−	0.151790i
$513$	14.6579	−	16.9161i	0.647160	−	0.746863i
$514$	0.489983	−	3.40791i	0.0216122	−	0.150316i
$515$	18.6738	−	5.48311i	0.822864	−	0.241615i
$516$	2.31559	+	2.67233i	0.101938	+	0.117643i
$517$	−3.16254	+	2.03244i	−0.139089	+	0.0893868i
$518$	−1.50980	+	0.970291i	−0.0663369	+	0.0426321i
$519$	−20.8581	−	24.0716i	−0.915571	−	1.05662i
$520$	7.76605	−	2.28032i	0.340564	−	0.0999986i
$521$	0.940764	−	6.54316i	0.0412156	−	0.286661i	−0.958781	−	0.284145i	$-0.908290\pi$
$521$	0.940764	−	6.54316i	0.0412156	−	0.286661i	0.999997	−	0.00251563i	$-0.000800750\pi$
$522$	−0.283127	+	0.326746i	−0.0123921	+	0.0143013i
$523$	9.29979	−	20.3637i	0.406651	−	0.890442i	−0.589901	−	0.807476i	$-0.700833\pi$
$523$	9.29979	−	20.3637i	0.406651	−	0.890442i	0.996552	−	0.0829666i	$-0.0264395\pi$
$524$	17.4718	+	5.13019i	0.763260	+	0.224113i
$525$	1.13964	+	2.49547i	0.0497380	+	0.108911i
$526$	−0.947565	−	6.59046i	−0.0413158	−	0.287358i
$527$	40.1934	+	25.8307i	1.75085	+	1.12520i
$528$	0.353014			0.0153630
$529$	9.05127	−	21.1441i	0.393533	−	0.919310i
$530$	−4.97640			−0.216161
$531$	−2.02087	−	1.29874i	−0.0876984	−	0.0563604i
$532$	1.28272	+	8.92151i	0.0556129	+	0.386796i
$533$	7.27760	+	15.9357i	0.315228	+	0.690252i
$534$	−17.4631	−	5.12763i	−0.755703	−	0.221894i
$535$	−5.03946	+	11.0349i	−0.217875	+	0.477079i
$536$	−13.2884	+	15.3356i	−0.573970	+	0.662397i
$537$	−1.43983	+	10.0142i	−0.0621333	+	0.432147i
$538$	17.4687	−	5.12927i	0.753128	−	0.221138i
$539$	1.79393	+	2.07031i	0.0772702	+	0.0891745i
$540$	−5.43032	+	3.48985i	−0.233684	+	0.150179i
$541$	−21.8322	+	14.0307i	−0.938638	+	0.603226i	−0.918008	−	0.396561i	$-0.870203\pi$
$541$	−21.8322	+	14.0307i	−0.938638	+	0.603226i	−0.0206298	+	0.999787i	$0.506567\pi$
$542$	4.79865	+	5.53794i	0.206120	+	0.237875i
$543$	27.1024	−	7.95798i	1.16308	−	0.341510i
$544$	4.24804	−	29.5458i	0.182133	−	1.26676i
$545$	−7.99504	+	9.22677i	−0.342470	+	0.395232i
$546$	−2.78699	+	6.10265i	−0.119272	+	0.261169i
$547$	39.0340	+	11.4614i	1.66897	+	0.490054i	0.973536	−	0.228534i	$-0.0733933\pi$
$547$	39.0340	+	11.4614i	1.66897	+	0.490054i	0.695435	+	0.718589i	$0.255212\pi$
$548$	4.88023	+	10.6862i	0.208473	+	0.456492i
$549$	0.327697	+	2.27918i	0.0139858	+	0.0972731i
$550$	0.407046	+	0.261592i	0.0173565	+	0.0111543i
$551$	8.51000			0.362538
$552$	19.9295	−	13.1474i	0.848256	−	0.559592i
$553$	5.49685			0.233750
$554$	15.1129	+	9.71249i	0.642087	+	0.412644i
$555$	−0.367296	−	2.55460i	−0.0155908	−	0.108437i
$556$	−10.6962	−	23.4215i	−0.453622	−	0.993293i
$557$	−18.1134	−	5.31858i	−0.767490	−	0.225356i	−0.125526	−	0.992090i	$-0.540062\pi$
$557$	−18.1134	−	5.31858i	−0.767490	−	0.225356i	−0.641964	+	0.766735i	$0.721880\pi$
$558$	−0.886420	+	1.94099i	−0.0375252	+	0.0821686i
$559$	2.87443	−	3.31727i	0.121576	−	0.140306i
$560$	0.0722027	−	0.502181i	0.00305112	−	0.0212210i
$561$	5.22645	−	1.53462i	0.220661	−	0.0647919i
$562$	−4.67191	−	5.39167i	−0.197073	−	0.227434i
$563$	−2.48078	+	1.59430i	−0.104553	+	0.0671918i	−0.591872	−	0.806032i	$-0.701611\pi$
$563$	−2.48078	+	1.59430i	−0.104553	+	0.0671918i	0.487320	+	0.873224i	$0.337975\pi$
$564$	12.8765	−	8.27520i	0.542197	−	0.348449i
$565$	−2.61463	−	3.01744i	−0.109998	−	0.126945i
$566$	−3.14025	+	0.922060i	−0.131994	+	0.0387571i
$567$	2.10389	−	14.6329i	0.0883550	−	0.614523i
$568$	−22.5271	+	25.9977i	−0.945217	+	1.09084i
$569$	4.94269	−	10.8230i	0.207209	−	0.453723i	−0.777284	−	0.629150i	$-0.783403\pi$
$569$	4.94269	−	10.8230i	0.207209	−	0.453723i	0.984493	+	0.175427i	$0.0561304\pi$
$570$	6.55453	+	1.92458i	0.274539	+	0.0806119i
$571$	−10.0624	−	22.0336i	−0.421098	−	0.922077i	−0.994688	−	0.102934i	$-0.967177\pi$
$571$	−10.0624	−	22.0336i	−0.421098	−	0.922077i	0.573590	−	0.819143i	$-0.305550\pi$
$572$	−0.319513	−	2.22226i	−0.0133595	−	0.0929174i
$573$	−30.0725	−	19.3264i	−1.25630	−	0.807373i
$574$	−7.49313			−0.312757
$575$	−4.79549	+	0.0573735i	−0.199986	+	0.00239264i
$576$	1.14715			0.0477981
$577$	0.526575	+	0.338409i	0.0219216	+	0.0140882i	0.551556	−	0.834138i	$-0.314034\pi$
$577$	0.526575	+	0.338409i	0.0219216	+	0.0140882i	−0.529634	+	0.848226i	$0.677671\pi$
$578$	−1.14576	−	7.96894i	−0.0476573	−	0.331464i
$579$	−18.2965	−	40.0638i	−0.760378	−	1.66500i
$580$	−2.35477	−	0.691422i	−0.0977764	−	0.0287097i
$581$	1.01686	−	2.22660i	0.0421863	−	0.0923750i
$582$	14.3702	−	16.5841i	0.595664	−	0.687433i
$583$	−0.496429	+	3.45274i	−0.0205600	+	0.142998i
$584$	−8.80828	+	2.58634i	−0.364489	+	0.107024i
$585$	−0.535300	−	0.617769i	−0.0221319	−	0.0255416i
$586$	4.39773	−	2.82625i	0.181669	−	0.116751i
$587$	−14.7412	+	9.47359i	−0.608434	+	0.391017i	−0.808270	−	0.588812i	$-0.799596\pi$
$587$	−14.7412	+	9.47359i	−0.608434	+	0.391017i	0.199835	+	0.979830i	$0.435959\pi$
$588$	−7.30409	−	8.42937i	−0.301216	−	0.347622i
$589$	40.2992	−	11.8329i	1.66050	−	0.487566i
$590$	−1.02278	+	7.11358i	−0.0421071	+	0.292861i
$591$	3.39928	−	3.92298i	0.139828	−	0.161370i
$592$	−0.198274	+	0.434159i	−0.00814900	+	0.0178438i
$593$	27.8704	+	8.18348i	1.14450	+	0.336055i	0.798391	−	0.602140i	$-0.205685\pi$
$593$	27.8704	+	8.18348i	1.14450	+	0.336055i	0.346108	+	0.938195i	$0.387503\pi$
$594$	−0.990645	−	2.16921i	−0.0406467	−	0.0890038i
$595$	−1.11411	−	7.74877i	−0.0456739	−	0.317669i
$596$	−4.87368	−	3.13213i	−0.199634	−	0.128297i
$597$	36.9787			1.51344
$598$	−7.78582	−	8.77106i	−0.318386	−	0.358675i
$599$	2.42049			0.0988986			0.0494493	−	0.998777i	$-0.484253\pi$
$599$	2.42049			0.0988986			0.0494493	+	0.998777i	$0.484253\pi$
$600$	−4.18809	−	2.69152i	−0.170978	−	0.109881i
$601$	−4.51283	−	31.3874i	−0.184082	−	1.28032i	−0.846986	−	0.531615i	$-0.821585\pi$
$601$	−4.51283	−	31.3874i	−0.184082	−	1.28032i	0.662904	−	0.748704i	$-0.269324\pi$
$602$	0.779907	+	1.70776i	0.0317866	+	0.0696030i
$603$	1.96632	+	0.577363i	0.0800747	+	0.0235121i
$604$	−3.41832	+	7.48508i	−0.139089	+	0.304563i
$605$	−6.98136	+	8.05692i	−0.283833	+	0.327561i
$606$	−3.55349	+	24.7151i	−0.144351	+	1.00398i
$607$	17.7945	−	5.22492i	0.722254	−	0.212073i	0.100111	−	0.994976i	$-0.468080\pi$
$607$	17.7945	−	5.22492i	0.722254	−	0.212073i	0.622143	+	0.782903i	$0.286262\pi$
$608$	−17.1836	−	19.8309i	−0.696886	−	0.804250i
$609$	4.32454	−	2.77921i	0.175239	−	0.112619i
$610$	5.79520	−	3.72435i	0.234641	−	0.150794i
$611$	−12.4426	−	14.3595i	−0.503372	−	0.580922i
$612$	−1.80297	+	0.529401i	−0.0728809	+	0.0213998i
$613$	0.907201	−	6.30972i	0.0366415	−	0.254847i	−0.963265	−	0.268554i	$-0.913454\pi$
$613$	0.907201	−	6.30972i	0.0366415	−	0.254847i	0.999906	+	0.0137071i	$0.00436324\pi$
$614$	−12.9570	+	14.9532i	−0.522903	+	0.603462i
$615$	4.47629	−	9.80171i	0.180501	−	0.395243i
$616$	2.32836	+	0.683668i	0.0938123	+	0.0275458i
$617$	−19.0925	−	41.8068i	−0.768636	−	1.68308i	−0.729634	−	0.683838i	$-0.760309\pi$
$617$	−19.0925	−	41.8068i	−0.768636	−	1.68308i	−0.0390019	−	0.999239i	$-0.512418\pi$
$618$	−4.16618	−	28.9764i	−0.167588	−	1.16560i
$619$	1.76675	+	1.13542i	0.0710115	+	0.0456363i	0.575665	−	0.817686i	$-0.304743\pi$
$619$	1.76675	+	1.13542i	0.0710115	+	0.0456363i	−0.504653	+	0.863322i	$0.668380\pi$
$620$	−12.1124			−0.486447
$621$	20.0358	+	12.5401i	0.804007	+	0.503216i
$622$	11.7951			0.472939
$623$	15.4244	+	9.91269i	0.617967	+	0.397144i
$624$	0.253918	+	1.76604i	0.0101648	+	0.0706981i
$625$	0.415415	+	0.909632i	0.0166166	+	0.0363853i
$626$	9.89818	+	2.90637i	0.395611	+	0.116162i
$627$	1.98918	−	4.35569i	0.0794401	−	0.173950i
$628$	−15.3333	+	17.6955i	−0.611864	+	0.706128i
$629$	−1.04811	+	7.28976i	−0.0417908	+	0.290662i
$630$	0.335465	−	0.0985015i	0.0133653	−	0.00392439i
$631$	2.47493	+	2.85622i	0.0985254	+	0.113704i	0.802871	−	0.596153i	$-0.203305\pi$
$631$	2.47493	+	2.85622i	0.0985254	+	0.113704i	−0.704345	+	0.709857i	$0.748759\pi$
$632$	−8.39158	+	5.39294i	−0.333799	+	0.214520i
$633$	−24.2152	+	15.5621i	−0.962466	+	0.618540i
$634$	−1.66333	−	1.91959i	−0.0660594	−	0.0762366i
$635$	4.26582	−	1.25256i	0.169284	−	0.0497063i
$636$	2.02124	−	14.0580i	0.0801473	−	0.557436i
$637$	−9.06686	+	10.4637i	−0.359242	+	0.414588i
$638$	0.376640	−	0.824726i	0.0149113	−	0.0326512i
$639$	3.33340	+	0.978776i	0.131867	+	0.0387198i
$640$	3.37469	+	7.38954i	0.133396	+	0.292097i
$641$	4.22074	+	29.3559i	0.166709	+	1.15949i	0.885629	+	0.464394i	$0.153728\pi$
$641$	4.22074	+	29.3559i	0.166709	+	1.15949i	−0.718919	+	0.695093i	$0.755363\pi$
$642$	15.3506	+	9.86524i	0.605841	+	0.389350i
$643$	−19.5504			−0.770993			−0.385496	−	0.922709i	$-0.625970\pi$
$643$	−19.5504			−0.770993			−0.385496	+	0.922709i	$0.625970\pi$
$644$	−9.09967	+	2.79058i	−0.358577	+	0.109964i
$645$	−2.69981			−0.106305
$646$	−16.3990	−	10.5390i	−0.645209	−	0.414651i
$647$	0.608965	+	4.23544i	0.0239409	+	0.166512i	0.998284	−	0.0585543i	$-0.0186491\pi$
$647$	0.608965	+	4.23544i	0.0239409	+	0.166512i	−0.974343	+	0.225067i	$0.927740\pi$
$648$	11.1444	+	24.4029i	0.437795	+	0.958637i
$649$	4.83354	+	1.41925i	0.189733	+	0.0557106i
$650$	−1.01590	+	2.22450i	−0.0398467	+	0.0872522i
$651$	16.6145	−	19.1741i	0.651173	−	0.751494i
$652$	0.811899	−	5.64688i	0.0317964	−	0.221149i
$653$	22.9041	−	6.72524i	0.896306	−	0.263179i	0.199040	−	0.979991i	$-0.436218\pi$
$653$	22.9041	−	6.72524i	0.896306	−	0.263179i	0.697266	+	0.716812i	$0.254400\pi$
$654$	12.0259	+	13.8787i	0.470251	+	0.542698i
$655$	−11.6962	+	7.51668i	−0.457008	+	0.293701i
$656$	−1.67641	+	1.07736i	−0.0654528	+	0.0420640i
$657$	0.607138	+	0.700675i	0.0236867	+	0.0273359i
$658$	7.79758	−	2.28958i	0.303981	−	0.0892570i
$659$	−4.10743	+	28.5678i	−0.160003	+	1.11284i	0.738620	+	0.674122i	$0.235478\pi$
$659$	−4.10743	+	28.5678i	−0.160003	+	1.11284i	−0.898623	+	0.438722i	$0.855431\pi$
$660$	−0.904310	+	1.04363i	−0.0352002	+	0.0406232i
$661$	−16.8646	+	36.9283i	−0.655957	+	1.43635i	0.230285	+	0.973123i	$0.426034\pi$
$661$	−16.8646	+	36.9283i	−0.655957	+	1.43635i	−0.886242	+	0.463222i	$0.846693\pi$
$662$	−1.74628	−	0.512754i	−0.0678711	−	0.0199288i
$663$	11.4366	+	25.0427i	0.444162	+	0.972579i
$664$	0.632165	+	4.39680i	0.0245328	+	0.170629i
$665$	−5.78934	−	3.72058i	−0.224501	−	0.144278i
$666$	−0.328917			−0.0127453
$667$	1.38524	+	8.87911i	0.0536366	+	0.343800i
$668$	−4.38829			−0.169788
$669$	23.8323	+	15.3161i	0.921409	+	0.592154i
$670$	−0.872532	−	6.06860i	−0.0337089	−	0.234450i
$671$	−2.00593	−	4.39237i	−0.0774380	−	0.169566i
$672$	−15.2086	−	4.46566i	−0.586686	−	0.172267i
$673$	−13.2154	+	28.9378i	−0.509418	+	1.11547i	0.463874	+	0.885901i	$0.346459\pi$
$673$	−13.2154	+	28.9378i	−0.509418	+	1.11547i	−0.973292	+	0.229569i	$0.926268\pi$
$674$	13.6204	−	15.7188i	0.524639	−	0.605466i
$675$	0.701406	−	4.87839i	0.0269971	−	0.187769i
$676$	−5.44913	+	1.60001i	−0.209582	+	0.0615388i
$677$	−26.4739	−	30.5525i	−1.01748	−	1.17423i	−0.984609	−	0.174770i	$-0.944082\pi$
$677$	−26.4739	−	30.5525i	−1.01748	−	1.17423i	−0.0328665	−	0.999460i	$-0.510464\pi$
$678$	−5.05225	+	3.24689i	−0.194031	+	0.124696i
$679$	−18.5970	+	11.9516i	−0.713688	+	0.458660i
$680$	9.30311	+	10.7364i	0.356758	+	0.411721i
$681$	7.12698	−	2.09267i	0.273106	−	0.0801913i
$682$	0.636823	−	4.42920i	0.0243852	−	0.169603i
$683$	12.1173	−	13.9842i	0.463657	−	0.535089i	−0.474979	−	0.879997i	$-0.657544\pi$
$683$	12.1173	−	13.9842i	0.463657	−	0.535089i	0.938636	+	0.344908i	$0.112090\pi$
$684$	−0.686208	+	1.50259i	−0.0262378	+	0.0574528i
$685$	−8.60639	−	2.52706i	−0.328833	−	0.0965541i
$686$	−6.12101	−	13.4032i	−0.233701	−	0.511735i
$687$	6.58269	+	45.7836i	0.251145	+	1.74675i
$688$	0.420027	+	0.269935i	0.0160134	+	0.0102912i
$689$	−17.6302			−0.671658
$690$	−0.941130	+	7.15210i	−0.0358282	+	0.272276i
$691$	15.0176			0.571297			0.285648	−	0.958334i	$-0.407791\pi$
$691$	15.0176			0.571297			0.285648	+	0.958334i	$0.407791\pi$
$692$	−19.3842	−	12.4574i	−0.736875	−	0.473561i
$693$	−0.0348777	−	0.242580i	−0.00132489	−	0.00921484i
$694$	−2.61271	−	5.72104i	−0.0991771	−	0.217168i
$695$	18.8630	+	5.53869i	0.715516	+	0.210094i
$696$	−3.87524	+	8.48559i	−0.146891	+	0.321645i
$697$	−20.1361	+	23.2383i	−0.762709	+	0.880213i
$698$	−0.785518	+	5.46340i	−0.0297323	+	0.206793i
$699$	−19.3254	+	5.67446i	−0.730955	+	0.214628i
$700$	1.29966	+	1.49988i	0.0491224	+	0.0566902i
$701$	−15.6842	+	10.0796i	−0.592384	+	0.380702i	−0.802215	−	0.597036i	$-0.796345\pi$
$701$	−15.6842	+	10.0796i	−0.592384	+	0.380702i	0.209831	+	0.977738i	$0.432709\pi$
$702$	10.1394	−	6.51622i	0.382688	−	0.245939i
$703$	4.23966	+	4.89283i	0.159902	+	0.184537i
$704$	−2.30821	+	0.677750i	−0.0869938	+	0.0255437i
$705$	−1.66319	+	11.5677i	−0.0626393	+	0.435666i
$706$	15.8667	−	18.3111i	0.597151	−	0.689149i
$707$	10.4494	−	22.8809i	0.392989	−	0.860526i
$708$	−19.6800	−	5.77857i	−0.739620	−	0.217172i
$709$	6.59888	+	14.4495i	0.247826	+	0.542664i	0.992135	−	0.125172i	$-0.0399482\pi$
$709$	6.59888	+	14.4495i	0.247826	+	0.542664i	−0.744309	+	0.667836i	$0.767221\pi$
$710$	−1.47916	−	10.2878i	−0.0555119	−	0.386094i
$711$	0.847487	+	0.544647i	0.0317833	+	0.0204259i
$712$	−33.2725			−1.24694
$713$	18.9059	+	40.1210i	0.708033	+	1.50254i
$714$	−11.7753			−0.440681
$715$	1.44207	+	0.926761i	0.0539303	+	0.0346589i
$716$	1.04161	+	7.24456i	0.0389268	+	0.270742i
$717$	−4.58530	−	10.0404i	−0.171241	−	0.374966i
$718$	−5.75678	−	1.69034i	−0.214841	−	0.0630830i
$719$	5.00121	−	10.9511i	0.186513	−	0.408408i	−0.793158	−	0.609016i	$-0.791565\pi$
$719$	5.00121	−	10.9511i	0.186513	−	0.408408i	0.979672	+	0.200608i	$0.0642919\pi$
$720$	0.0608898	−	0.0702706i	0.00226923	−	0.00261883i
$721$	−4.19701	+	29.1909i	−0.156305	+	1.08713i
$722$	−1.29579	+	0.380477i	−0.0482241	+	0.0141599i
$723$	−33.2472	−	38.3693i	−1.23648	−	1.42697i
$724$	17.1904	−	11.0476i	0.638877	−	0.410581i
$725$	1.57636	−	1.01306i	0.0585444	−	0.0376242i
$726$	10.5012	+	12.1190i	0.389735	+	0.449778i
$727$	−32.9808	+	9.68403i	−1.22319	+	0.359161i	−0.828676	−	0.559729i	$-0.810905\pi$
$727$	−32.9808	+	9.68403i	−1.22319	+	0.359161i	−0.394514	+	0.918890i	$0.629087\pi$
$728$	−1.74546	+	12.1399i	−0.0646909	+	0.449935i
$729$	−15.7555	+	18.1828i	−0.583536	+	0.673437i
$730$	1.15223	−	2.52304i	0.0426460	−	0.0933818i
$731$	7.39206	+	2.17051i	0.273405	+	0.0802790i
$732$	8.16725	+	17.8838i	0.301870	+	0.661003i
$733$	1.87113	+	13.0140i	0.0691119	+	0.480684i	0.994755	+	0.102286i	$0.0326158\pi$
$733$	1.87113	+	13.0140i	0.0691119	+	0.480684i	−0.925643	+	0.378398i	$0.876475\pi$
$734$	−2.75696	−	1.77179i	−0.101761	−	0.0653979i
$735$	8.51606			0.314119
$736$	17.8940	−	21.1569i	0.659580	−	0.779855i
$737$	−4.29757			−0.158303
$738$	−1.15527	−	0.742446i	−0.0425260	−	0.0273298i
$739$	2.98369	+	20.7520i	0.109757	+	0.763376i	0.968148	+	0.250379i	$0.0805554\pi$
$739$	2.98369	+	20.7520i	0.109757	+	0.763376i	−0.858391	+	0.512996i	$0.828536\pi$
$740$	−0.775607	−	1.69834i	−0.0285119	−	0.0624323i
$741$	23.2212	+	6.81835i	0.853051	+	0.250478i
$742$	3.13255	−	6.85932i	0.114999	−	0.251814i
$743$	12.1599	−	14.0332i	0.446102	−	0.514829i	−0.487509	−	0.873118i	$-0.662094\pi$
$743$	12.1599	−	14.0332i	0.446102	−	0.514829i	0.933611	+	0.358289i	$0.116640\pi$
$744$	−6.55226	+	45.5720i	−0.240218	+	1.67075i
$745$	4.24417	−	1.24620i	0.155494	−	0.0456573i
$746$	−17.5215	−	20.2209i	−0.641508	−	0.740339i
$747$	0.377395	−	0.242537i	0.0138082	−	0.00887397i
$748$	3.31502	−	2.13043i	0.121209	−	0.0778963i
$749$	−12.0379	−	13.8925i	−0.439855	−	0.507620i
$750$	1.44324	−	0.423774i	0.0526998	−	0.0154740i
$751$	3.81081	−	26.5048i	0.139059	−	0.967174i	−0.794120	−	0.607761i	$-0.792068\pi$
$751$	3.81081	−	26.5048i	0.139059	−	0.967174i	0.933179	−	0.359413i	$-0.117023\pi$
$752$	1.41533	−	1.63338i	0.0516117	−	0.0595631i
$753$	22.5566	−	49.3922i	0.822010	−	1.79995i
$754$	4.39680	+	1.29102i	0.160122	+	0.0470160i
$755$	−2.60996	−	5.71501i	−0.0949861	−	0.207991i
$756$	−1.39203	−	9.68179i	−0.0506277	−	0.352123i
$757$	17.0997	+	10.9893i	0.621500	+	0.399414i	0.813154	−	0.582049i	$-0.197749\pi$
$757$	17.0997	+	10.9893i	0.621500	+	0.399414i	−0.191654	+	0.981463i	$0.561385\pi$
$758$	−16.6274			−0.603933
$759$	4.86841	+	1.36645i	0.176712	+	0.0495989i
$760$	12.4884			0.453001
$761$	−11.4883	−	7.38311i	−0.416452	−	0.267638i	0.315592	−	0.948895i	$-0.397797\pi$
$761$	−11.4883	−	7.38311i	−0.416452	−	0.267638i	−0.732044	+	0.681258i	$0.761433\pi$
$762$	−0.951719	−	6.61935i	−0.0344771	−	0.239794i
$763$	−7.68519	−	16.8282i	−0.278223	−	0.609222i
$764$	−24.8129	−	7.28573i	−0.897700	−	0.263589i
$765$	0.596006	−	1.30507i	0.0215487	−	0.0471850i
$766$	−20.9225	+	24.1458i	−0.755959	+	0.872423i
$767$	−3.62347	+	25.2018i	−0.130836	+	0.909983i
$768$	26.0755	−	7.65647i	0.940920	−	0.276279i
$769$	−8.52034	−	9.83300i	−0.307251	−	0.354587i	0.581034	−	0.813879i	$-0.302648\pi$
$769$	−8.52034	−	9.83300i	−0.307251	−	0.354587i	−0.888285	+	0.459293i	$0.848103\pi$
$770$	−0.616799	+	0.396393i	−0.0222279	+	0.0142850i
$771$	−6.31148	+	4.05614i	−0.227302	+	0.146078i
$772$	−20.8655	−	24.0801i	−0.750967	−	0.866662i
$773$	−8.48441	+	2.49125i	−0.305163	+	0.0896039i	−0.430729	−	0.902481i	$-0.641744\pi$
$773$	−8.48441	+	2.49125i	−0.305163	+	0.0896039i	0.125566	+	0.992085i	$0.459925\pi$
$774$	−0.0489670	+	0.340573i	−0.00176008	+	0.0122416i
$775$	6.05621	−	6.98924i	0.217546	−	0.251061i
$776$	16.6649	−	36.4910i	0.598234	−	1.30995i
$777$	3.75239	+	1.10180i	0.134616	+	0.0395269i
$778$	5.48028	+	12.0001i	0.196478	+	0.430226i
$779$	3.84683	+	26.7553i	0.137827	+	0.958608i
$780$	−5.87146	−	3.77336i	−0.210232	−	0.135108i
$781$	−7.28547			−0.260694
$782$	8.32671	−	18.8258i	0.297763	−	0.673208i
$783$	−9.23521			−0.330040
$784$	−1.32490	−	0.851461i	−0.0473178	−	0.0304093i
$785$	−2.54423	−	17.6955i	−0.0908075	−	0.631580i
$786$	8.68754	+	19.0231i	0.309874	+	0.678530i
$787$	−15.6538	−	4.59638i	−0.557999	−	0.163843i	−0.00944035	−	0.999955i	$-0.503005\pi$
$787$	−15.6538	−	4.59638i	−0.557999	−	0.163843i	−0.548558	+	0.836112i	$0.684823\pi$
$788$	1.55996	−	3.41584i	0.0555714	−	0.121684i
$789$	−9.50125	+	10.9650i	−0.338253	+	0.390365i
$790$	0.428919	−	2.98320i	0.0152603	−	0.106137i
$791$	5.80501	−	1.70451i	0.206402	−	0.0606052i
$792$	0.291239	+	0.336108i	0.0103487	+	0.0119431i
$793$	20.5310	−	13.1945i	0.729079	−	0.468550i
$794$	−4.51239	+	2.89994i	−0.160139	+	0.102915i
$795$	7.10129	+	8.19532i	0.251857	+	0.290658i
$796$	25.6677	−	7.53673i	0.909769	−	0.267132i
$797$	1.40770	−	9.79077i	0.0498633	−	0.346807i	−0.949582	−	0.313517i	$-0.898493\pi$
$797$	1.40770	−	9.79077i	0.0498633	−	0.346807i	0.999446	−	0.0332894i	$-0.0105983\pi$
$798$	−6.77874	+	7.82308i	−0.239965	+	0.276934i
$799$	13.8536	−	30.3352i	0.490106	−	1.07318i
$800$	−5.54376	−	1.62780i	−0.196002	−	0.0575513i
$801$	1.39591	+	3.05662i	0.0493221	+	0.108000i
$802$	2.33367	+	16.2310i	0.0824047	+	0.573137i
$803$	−1.63560	−	1.05114i	−0.0577190	−	0.0370938i
$804$	17.4978			0.617100
$805$	2.93959	−	6.64608i	0.103607	−	0.234243i
$806$	22.6162			0.796621
$807$	−33.3748	−	21.4487i	−1.17485	−	0.755029i
$808$	6.49623	+	45.1823i	0.228537	+	1.58951i
$809$	12.3963	+	27.1440i	0.435829	+	0.954333i	0.992345	+	0.123496i	$0.0394105\pi$
$809$	12.3963	+	27.1440i	0.435829	+	0.954333i	−0.556516	+	0.830837i	$0.687862\pi$
$810$	−7.77725	−	2.28361i	−0.273265	−	0.0802378i
$811$	−15.2212	+	33.3297i	−0.534488	+	1.17036i	0.429170	+	0.903224i	$0.358806\pi$
$811$	−15.2212	+	33.3297i	−0.534488	+	1.17036i	−0.963657	+	0.267141i	$0.913921\pi$
$812$	2.43532	−	2.81051i	0.0854629	−	0.0986295i
$813$	2.27245	−	15.8052i	0.0796981	−	0.554313i
$814$	0.661818	−	0.194327i	0.0231967	−	0.00681117i
$815$	2.85248	+	3.29193i	0.0999179	+	0.115311i
$816$	−2.63445	+	1.69306i	−0.0922243	+	0.0592690i
$817$	5.69740	−	3.66150i	0.199327	−	0.128100i
$818$	0.208677	+	0.240827i	0.00729623	+	0.00842030i
$819$	1.18848	−	0.348968i	0.0415287	−	0.0121939i
$820$	1.10938	−	7.71590i	0.0387412	−	0.269451i
$821$	28.2071	−	32.5527i	0.984434	−	1.13610i	−0.00625838	−	0.999980i	$-0.501992\pi$
$821$	28.2071	−	32.5527i	0.984434	−	1.13610i	0.990693	−	0.136117i	$-0.0434624\pi$
$822$	−5.60478	+	12.2728i	−0.195489	+	0.428062i
$823$	−10.9244	−	3.20768i	−0.380799	−	0.111813i	0.0857303	−	0.996318i	$-0.472678\pi$
$823$	−10.9244	−	3.20768i	−0.380799	−	0.111813i	−0.466529	+	0.884506i	$0.654496\pi$
$824$	−22.2319	−	48.6810i	−0.774483	−	1.69588i
$825$	−0.150051	−	1.04363i	−0.00522411	−	0.0363345i
$826$	−9.16133	−	5.88763i	−0.318764	−	0.204857i
$827$	56.5332			1.96585			0.982925	−	0.184005i	$-0.0589062\pi$
$827$	56.5332			1.96585			0.982925	+	0.184005i	$0.0589062\pi$
$828$	−1.67946	−	0.471385i	−0.0583653	−	0.0163818i
$829$	28.3441			0.984430			0.492215	−	0.870474i	$-0.336187\pi$
$829$	28.3441			0.984430			0.492215	+	0.870474i	$0.336187\pi$
$830$	−1.12906	−	0.725600i	−0.0391901	−	0.0251860i
$831$	−5.57115	−	38.7482i	−0.193261	−	1.34416i
$832$	−5.05086	−	11.0599i	−0.175107	−	0.383431i
$833$	−23.3169	−	6.84646i	−0.807882	−	0.237216i
$834$	12.2843	−	26.8988i	0.425370	−	0.931430i
$835$	2.19415	−	2.53218i	0.0759315	−	0.0876296i
$836$	0.492987	−	3.42880i	0.0170503	−	0.118587i
$837$	−43.7334	+	12.8413i	−1.51165	+	0.443860i
$838$	1.13021	+	1.30433i	0.0390425	+	0.0450574i
$839$	−0.995123	+	0.639526i	−0.0343554	+	0.0220789i	−0.557706	−	0.830039i	$-0.688318\pi$
$839$	−0.995123	+	0.639526i	−0.0343554	+	0.0220789i	0.523350	+	0.852118i	$0.324682\pi$
$840$	6.34624	−	4.07848i	0.218966	−	0.140721i
$841$	16.6916	+	19.2632i	0.575573	+	0.664247i
$842$	−23.5723	+	6.92144i	−0.812354	+	0.238529i
$843$	−2.21243	+	15.3878i	−0.0762000	+	0.529983i
$844$	−13.6365	+	15.7374i	−0.469388	+	0.541702i
$845$	1.80131	−	3.94432i	0.0619670	−	0.135689i
$846$	1.42907	+	0.419612i	0.0491323	+	0.0144266i
$847$	−6.71079	−	14.6946i	−0.230586	−	0.504912i
$848$	−0.285401	−	1.98501i	−0.00980071	−	0.0681655i
$849$	5.99960	+	3.85571i	0.205906	+	0.132328i
$850$	−4.29228			−0.147224
$851$	−4.41493	+	5.22000i	−0.151342	+	0.178939i
$852$	29.6632			1.01624
$853$	48.7187	+	31.3096i	1.66810	+	1.07202i	0.904657	+	0.426141i	$0.140127\pi$
$853$	48.7187	+	31.3096i	1.66810	+	1.07202i	0.763440	+	0.645879i	$0.223509\pi$
$854$	1.48557	+	10.3323i	0.0508350	+	0.353565i
$855$	−0.523935	−	1.14726i	−0.0179182	−	0.0392354i
$856$	32.0071	+	9.39814i	1.09398	+	0.321222i
$857$	−5.92063	+	12.9644i	−0.202245	+	0.442855i	−0.983392	−	0.181492i	$-0.941907\pi$
$857$	−5.92063	+	12.9644i	−0.202245	+	0.442855i	0.781148	+	0.624347i	$0.214635\pi$
$858$	1.68852	−	1.94865i	0.0576450	−	0.0665259i
$859$	4.81932	−	33.5191i	0.164433	−	1.14366i	−0.725718	−	0.687992i	$-0.758492\pi$
$859$	4.81932	−	33.5191i	0.164433	−	1.14366i	0.890151	−	0.455665i	$-0.150599\pi$
$860$	−1.87400	+	0.550255i	−0.0639028	+	0.0187635i
$861$	10.6927	+	12.3400i	0.364405	+	0.420545i
$862$	−15.0740	+	9.68750i	−0.513424	+	0.329957i
$863$	28.7251	−	18.4605i	0.977813	−	0.628402i	0.0489405	−	0.998802i	$-0.484416\pi$
$863$	28.7251	−	18.4605i	0.977813	−	0.628402i	0.928873	+	0.370399i	$0.120779\pi$
$864$	18.6480	+	21.5209i	0.634417	+	0.732156i
$865$	16.8804	−	4.95654i	0.573951	−	0.168527i
$866$	−1.29092	+	8.97857i	−0.0438674	+	0.305104i
$867$	−11.4886	+	13.2585i	−0.390172	+	0.450282i
$868$	7.62454	−	16.6954i	0.258794	−	0.566680i
$869$	−2.02703	−	0.595188i	−0.0687621	−	0.0201904i
$870$	−1.17087	−	2.56384i	−0.0396961	−	0.0869223i
$871$	−3.09118	−	21.4996i	−0.104741	−	0.728487i
$872$	28.2425	+	18.1503i	0.956410	+	0.614648i
$873$	−4.05144			−0.137120
$874$	−7.71365	−	16.3694i	−0.260918	−	0.553704i
$875$	−1.51531			−0.0512267
$876$	6.65943	+	4.27975i	0.225001	+	0.144599i
$877$	6.43418	+	44.7507i	0.217267	+	1.51112i	0.748065	+	0.663626i	$0.230983\pi$
$877$	6.43418	+	44.7507i	0.217267	+	1.51112i	−0.530798	+	0.847498i	$0.678108\pi$
$878$	−7.82362	−	17.1313i	−0.264034	−	0.578155i
$879$	−10.9299	−	3.20931i	−0.368657	−	0.108247i
$880$	−0.0810007	+	0.177367i	−0.00273053	+	0.00597904i
$881$	15.7171	−	18.1385i	0.529524	−	0.611103i	−0.426466	−	0.904504i	$-0.640242\pi$
$881$	15.7171	−	18.1385i	0.529524	−	0.611103i	0.955990	+	0.293401i	$0.0947870\pi$
$882$	0.154457	−	1.07427i	0.00520085	−	0.0361727i
$883$	1.88175	−	0.552532i	0.0633260	−	0.0185942i	−0.249916	−	0.968267i	$-0.580403\pi$
$883$	1.88175	−	0.552532i	0.0633260	−	0.0185942i	0.313242	+	0.949673i	$0.398585\pi$
$884$	13.0424	+	15.0518i	0.438664	+	0.506246i
$885$	13.1744	−	8.46668i	0.442853	−	0.284604i
$886$	6.94561	−	4.46367i	0.233342	−	0.149960i
$887$	−15.5264	−	17.9184i	−0.521324	−	0.601640i	0.432638	−	0.901568i	$-0.357583\pi$
$887$	−15.5264	−	17.9184i	−0.521324	−	0.601640i	−0.953962	+	0.299927i	$0.903038\pi$
$888$	−6.80944	+	1.99943i	−0.228510	+	0.0670965i
$889$	−0.958764	+	6.66835i	−0.0321559	+	0.223649i
$890$	6.58330	−	7.59753i	0.220673	−	0.254670i
$891$	−2.36025	+	5.16823i	−0.0790715	+	0.173142i
$892$	19.6641	+	5.77390i	0.658403	+	0.193324i
$893$	−12.1784	−	26.6669i	−0.407534	−	0.892375i
$894$	−0.946889	−	6.58576i	−0.0316687	−	0.220261i
$895$	−4.70114	−	3.02124i	−0.157142	−	0.100989i
$896$	−12.3098			−0.411243
$897$	−3.33420	+	25.3382i	−0.111326	+	0.846019i
$898$	−33.4854			−1.11742
$899$	−14.5783	−	9.36890i	−0.486213	−	0.312470i
$900$	0.0517633	+	0.360022i	0.00172544	+	0.0120007i
$901$	−12.8547	−	28.1478i	−0.428251	−	0.937739i
$902$	2.76318	+	0.811342i	0.0920038	+	0.0270147i
$903$	1.69948	−	3.72134i	0.0565552	−	0.123839i
$904$	−7.18974	+	8.29741i	−0.239127	+	0.275968i
$905$	−2.22040	+	15.4432i	−0.0738085	+	0.513349i
$906$	−9.06757	+	2.66248i	−0.301250	+	0.0884549i
$907$	8.39668	+	9.69029i	0.278807	+	0.321761i	0.877831	−	0.478971i	$-0.158990\pi$
$907$	8.39668	+	9.69029i	0.278807	+	0.321761i	−0.599024	+	0.800731i	$0.704444\pi$
$908$	4.52048	−	2.90513i	0.150017	−	0.0964103i
$909$	3.87818	−	2.49235i	0.128631	−	0.0826661i
$910$	−2.42670	−	2.80056i	−0.0804444	−	0.0928378i
$911$	20.2902	−	5.95774i	0.672244	−	0.197389i	0.0722419	−	0.997387i	$-0.476985\pi$
$911$	20.2902	−	5.95774i	0.672244	−	0.197389i	0.600002	+	0.799999i	$0.295166\pi$
$912$	−0.391778	+	2.72488i	−0.0129731	+	0.0902297i
$913$	−0.616069	+	0.710982i	−0.0203889	+	0.0235301i
$914$	4.13734	−	9.05951i	0.136851	−	0.299662i
$915$	−14.4031	−	4.22913i	−0.476152	−	0.139811i
$916$	13.9005	+	30.4378i	0.459284	+	1.00569i
$917$	−2.99825	−	20.8533i	−0.0990110	−	0.688636i
$918$	17.7965	+	11.4371i	0.587372	+	0.377481i
$919$	−14.2788			−0.471013			−0.235506	−	0.971873i	$-0.575675\pi$
$919$	−14.2788			−0.471013			−0.235506	+	0.971873i	$0.575675\pi$
$920$	2.03283	+	13.0300i	0.0670203	+	0.429588i
$921$	43.1151			1.42069
$922$	−0.165776	−	0.106538i	−0.00545955	−	0.00350864i
$923$	−5.24033	−	36.4473i	−0.172487	−	1.19968i
$924$	−0.869263	−	1.90342i	−0.0285966	−	0.0626179i
$925$	1.36780	+	0.401622i	0.0449730	+	0.0132053i
$926$	3.56106	−	7.79764i	0.117024	−	0.256246i
$927$	−3.53942	+	4.08471i	−0.116250	+	0.134159i
$928$	−1.54078	+	10.7164i	−0.0505786	+	0.351782i
$929$	−37.2195	+	10.9286i	−1.22113	+	0.358556i	−0.827896	−	0.560882i	$-0.810462\pi$
$929$	−37.2195	+	10.9286i	−1.22113	+	0.358556i	−0.393235	+	0.919438i	$0.628644\pi$
$930$	−9.10959	−	10.5130i	−0.298715	−	0.344736i
$931$	−17.9714	+	11.5495i	−0.588989	+	0.378520i
$932$	−12.2577	+	7.87753i	−0.401513	+	0.258037i
$933$	−16.8315	−	19.4245i	−0.551038	−	0.635931i
$934$	−8.48426	+	2.49120i	−0.277613	+	0.0815147i
$935$	−0.428184	+	2.97808i	−0.0140031	+	0.0973937i
$936$	−1.47198	+	1.69875i	−0.0481130	+	0.0555254i
$937$	−8.47617	+	18.5602i	−0.276904	+	0.606336i	−0.996077	−	0.0884959i	$-0.971794\pi$
$937$	−8.47617	+	18.5602i	−0.276904	+	0.606336i	0.719172	+	0.694832i	$0.244521\pi$
$938$	8.91402	+	2.61739i	0.291053	+	0.0854609i
$939$	−9.33832	−	20.4481i	−0.304745	−	0.667297i
$940$	1.20319	+	8.36838i	0.0392438	+	0.272946i
$941$	5.35574	+	3.44192i	0.174592	+	0.112203i	0.625018	−	0.780610i	$-0.285092\pi$
$941$	5.35574	+	3.44192i	0.174592	+	0.112203i	−0.450426	+	0.892814i	$0.648728\pi$
$942$	−26.8908			−0.876150
$943$	−27.2896	+	8.36884i	−0.888671	+	0.272527i
$944$	−2.89615			−0.0942618
$945$	6.28271	+	4.03765i	0.204377	+	0.131345i
$946$	−0.102687	−	0.714202i	−0.00333864	−	0.0232207i
$947$	6.29292	+	13.7796i	0.204493	+	0.447776i	0.983895	−	0.178747i	$-0.0572045\pi$
$947$	6.29292	+	13.7796i	0.204493	+	0.447776i	−0.779402	+	0.626524i	$0.784477\pi$
$948$	8.25314	+	2.42334i	0.268050	+	0.0787065i
$949$	4.08209	−	8.93853i	0.132510	−	0.290157i
$950$	−2.47094	+	2.85162i	−0.0801680	+	0.0925188i
$951$	−0.787687	+	5.47849i	−0.0255425	+	0.177652i
$952$	−20.6548	+	6.06480i	−0.669427	+	0.196561i
$953$	11.9289	+	13.7667i	0.386416	+	0.445948i	0.915316	−	0.402736i	$-0.131941\pi$
$953$	11.9289	+	13.7667i	0.386416	+	0.445948i	−0.528900	+	0.848684i	$0.677395\pi$
$954$	1.16261	−	0.747166i	0.0376410	−	0.0241904i
$955$	16.6106	−	10.6750i	0.537505	−	0.345433i
$956$	−5.22912	−	6.03473i	−0.169122	−	0.195177i
$957$	−1.89565	+	0.556614i	−0.0612777	+	0.0179928i
$958$	−1.66947	+	11.6114i	−0.0539382	+	0.375148i
$959$	8.90079	−	10.2721i	0.287421	−	0.331702i
$960$	−3.10668	+	6.80267i	−0.100268	+	0.219555i
$961$	−52.3185	−	15.3621i	−1.68769	−	0.495552i
$962$	1.44820	+	3.17112i	0.0466920	+	0.102241i
$963$	−0.479451	−	3.33466i	−0.0154501	−	0.107458i
$964$	−30.8978	−	19.8568i	−0.995150	−	0.639544i
$965$	24.3277			0.783137
$966$	−9.26583	−	5.79934i	−0.298123	−	0.186591i
$967$	7.04671			0.226607			0.113304	−	0.993560i	$-0.463857\pi$
$967$	7.04671			0.226607			0.113304	+	0.993560i	$0.463857\pi$
$968$	24.6616	+	15.8491i	0.792655	+	0.509408i
$969$	6.04523	+	42.0455i	0.194201	+	1.35070i
$970$	5.03513	+	11.0254i	0.161668	+	0.354004i
$971$	53.7374	+	15.7787i	1.72452	+	0.506364i	0.985839	−	0.167696i	$-0.0536326\pi$
$971$	53.7374	+	15.7787i	1.72452	+	0.506364i	0.738677	+	0.674059i	$0.235451\pi$
$972$	1.56534	−	3.42762i	0.0502084	−	0.109941i
$973$	−19.5083	+	22.5138i	−0.625407	+	0.721758i
$974$	0.693747	−	4.82512i	0.0222291	−	0.154607i
$975$	5.11307	−	1.50133i	0.163749	−	0.0480812i
$976$	1.81795	+	2.09802i	0.0581910	+	0.0671560i
$977$	15.0723	−	9.68638i	0.482205	−	0.309895i	−0.276859	−	0.960911i	$-0.589293\pi$
$977$	15.0723	−	9.68638i	0.482205	−	0.309895i	0.759064	+	0.651016i	$0.225657\pi$
$978$	5.51185	−	3.54225i	0.176250	−	0.113269i
$979$	−4.61461	−	5.32555i	−0.147484	−	0.170205i
$980$	5.91118	−	1.73568i	0.188826	−	0.0554442i
$981$	0.482520	−	3.35600i	0.0154057	−	0.107149i
$982$	−14.5521	+	16.7940i	−0.464376	+	0.535918i
$983$	1.82621	−	3.99885i	0.0582471	−	0.127543i	−0.878270	−	0.478165i	$-0.841302\pi$
$983$	1.82621	−	3.99885i	0.0582471	−	0.127543i	0.936517	+	0.350621i	$0.114030\pi$
$984$	−28.4303	−	8.34789i	−0.906325	−	0.266121i
$985$	1.19106	+	2.60807i	0.0379505	+	0.0830999i
$986$	1.14463	+	7.96108i	0.0364525	+	0.253533i
$987$	−14.8977	−	9.57415i	−0.474198	−	0.304749i
$988$	17.5080			0.557003
$989$	4.74772	+	5.34851i	0.150969	+	0.170073i
$990$	−0.134372			−0.00427063
$991$	−15.1174	−	9.71539i	−0.480221	−	0.308619i	0.278041	−	0.960569i	$-0.410315\pi$
$991$	−15.1174	−	9.71539i	−0.480221	−	0.308619i	−0.758262	+	0.651950i	$0.773951\pi$
$992$	7.60441	+	52.8898i	0.241440	+	1.67925i
$993$	1.64751	+	3.60754i	0.0522821	+	0.114482i
$994$	15.1115	+	4.43714i	0.479308	+	0.140737i
$995$	−8.48494	+	18.5794i	−0.268991	+	0.589008i
$996$	2.50836	−	2.89480i	0.0794804	−	0.0917253i
$997$	6.39326	−	44.4661i	0.202476	−	1.40825i	−0.594428	−	0.804149i	$-0.702621\pi$
$997$	6.39326	−	44.4661i	0.202476	−	1.40825i	0.796904	−	0.604106i	$-0.206470\pi$
$998$	1.69681	−	0.498228i	0.0537115	−	0.0157711i
$999$	−4.60097	−	5.30980i	−0.145568	−	0.167995i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.g.b.71.1	✓	20
5.2	odd	4		575.2.p.c.324.1		40
5.3	odd	4		575.2.p.c.324.4		40
5.4	even	2		575.2.k.c.301.2		20
23.9	even	11		2645.2.a.t.1.8		10
23.12	even	11	inner	115.2.g.b.81.1	yes	20
23.14	odd	22		2645.2.a.u.1.8		10
115.12	odd	44		575.2.p.c.449.4		40
115.58	odd	44		575.2.p.c.449.1		40
115.104	even	22		575.2.k.c.426.2		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.g.b.71.1	✓	20	1.1	even	1	trivial
115.2.g.b.81.1	yes	20	23.12	even	11	inner
575.2.k.c.301.2		20	5.4	even	2
575.2.k.c.426.2		20	115.104	even	22
575.2.p.c.324.1		40	5.2	odd	4
575.2.p.c.324.4		40	5.3	odd	4
575.2.p.c.449.1		40	115.58	odd	44
575.2.p.c.449.4		40	115.12	odd	44
2645.2.a.t.1.8		10	23.9	even	11
2645.2.a.u.1.8		10	23.14	odd	22

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.698939 + 0.449181i) q^{2} +(-0.257653 - 1.79202i) q^{3} +(-0.544078 - 1.19136i) q^{4} +(0.959493 + 0.281733i) q^{5} +(0.624856 - 1.36824i) q^{6} +(-0.992315 + 1.14519i) q^{7} +(0.391340 - 2.72183i) q^{8} +(-0.266462 + 0.0782402i) q^{9} +O(q^{10})\)	\(q+(0.698939 + 0.449181i) q^{2} +(-0.257653 - 1.79202i) q^{3} +(-0.544078 - 1.19136i) q^{4} +(0.959493 + 0.281733i) q^{5} +(0.624856 - 1.36824i) q^{6} +(-0.992315 + 1.14519i) q^{7} +(0.391340 - 2.72183i) q^{8} +(-0.266462 + 0.0782402i) q^{9} +(0.544078 + 0.627899i) q^{10} +(0.489927 - 0.314857i) q^{11} +(-1.99476 + 1.28196i) q^{12} +(1.92754 + 2.22450i) q^{13} +(-1.20797 + 0.354691i) q^{14} +(0.257653 - 1.79202i) q^{15} +(-0.219256 + 0.253035i) q^{16} +(-2.14614 + 4.69939i) q^{17} +(-0.221384 - 0.0650043i) q^{18} +(1.88662 + 4.13112i) q^{19} +(-0.186393 - 1.29639i) q^{20} +(2.30788 + 1.48318i) q^{21} +0.483856 q^{22} +(-4.00320 + 2.64090i) q^{23} -4.97839 q^{24} +(0.841254 + 0.540641i) q^{25} +(0.348031 + 2.42061i) q^{26} +(-2.04740 - 4.48317i) q^{27} +(1.90424 + 0.559135i) q^{28} +(0.778412 - 1.70448i) q^{29} +(0.985023 - 1.13678i) q^{30} +(1.31614 - 9.15396i) q^{31} +(-5.54376 + 1.62780i) q^{32} +(-0.690460 - 0.796833i) q^{33} +(-3.61089 + 2.32058i) q^{34} +(-1.27476 + 0.819236i) q^{35} +(0.238189 + 0.274884i) q^{36} +(1.36780 - 0.401622i) q^{37} +(-0.536988 + 3.73483i) q^{38} +(3.48971 - 4.02734i) q^{39} +(1.14231 - 2.50132i) q^{40} +(5.71074 + 1.67683i) q^{41} +(0.946848 + 2.07331i) q^{42} +(-0.212226 - 1.47606i) q^{43} +(-0.641667 - 0.412375i) q^{44} -0.277711 q^{45} +(-3.98424 + 0.0476677i) q^{46} -6.45514 q^{47} +(0.509935 + 0.327715i) q^{48} +(0.669427 + 4.65597i) q^{49} +(0.345139 + 0.755750i) q^{50} +(8.97435 + 2.63511i) q^{51} +(1.60146 - 3.50671i) q^{52} +(-3.92240 + 4.52669i) q^{53} +(0.582750 - 4.05311i) q^{54} +(0.558787 - 0.164075i) q^{55} +(2.72868 + 3.14907i) q^{56} +(6.91694 - 4.44525i) q^{57} +(1.30968 - 0.841683i) q^{58} +(5.66458 + 6.53728i) q^{59} +(-2.27513 + 0.668038i) q^{60} +(1.17999 - 8.20703i) q^{61} +(5.03168 - 5.80687i) q^{62} +(0.174814 - 0.382789i) q^{63} +(-3.96342 - 1.16377i) q^{64} +(1.22275 + 2.67745i) q^{65} +(-0.124667 - 0.867079i) q^{66} +(-6.20792 - 3.98959i) q^{67} +6.76635 q^{68} +(5.76398 + 6.49337i) q^{69} -1.25896 q^{70} +(-10.5240 - 6.76335i) q^{71} +(0.108679 + 0.755881i) q^{72} +(-1.38684 - 3.03677i) q^{73} +(1.13641 + 0.333680i) q^{74} +(0.752086 - 1.64684i) q^{75} +(3.89520 - 4.49530i) q^{76} +(-0.125590 + 0.873497i) q^{77} +(4.24810 - 1.24735i) q^{78} +(-2.37554 - 2.74152i) q^{79} +(-0.281663 + 0.181014i) q^{80} +(-8.20728 + 5.27450i) q^{81} +(3.23826 + 3.73715i) q^{82} +(-1.54995 + 0.455107i) q^{83} +(0.511346 - 3.55649i) q^{84} +(-3.38318 + 3.90439i) q^{85} +(0.514686 - 1.12701i) q^{86} +(-3.25503 - 0.955762i) q^{87} +(-0.665258 - 1.45671i) q^{88} +(-1.72200 - 11.9768i) q^{89} +(-0.194103 - 0.124742i) q^{90} -4.46021 q^{91} +(5.32433 + 3.33242i) q^{92} -16.7432 q^{93} +(-4.51175 - 2.89952i) q^{94} +(0.646327 + 4.49530i) q^{95} +(4.34541 + 9.51511i) q^{96} +(13.9977 + 4.11011i) q^{97} +(-1.62348 + 3.55493i) q^{98} +(-0.105912 + 0.122229i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9	\( 20 q - 4 q^{2} + q^{3} - 4 q^{4} + 2 q^{5} - 9 q^{6} - 4 q^{7} - 17 q^{9} + 4 q^{10} - 8 q^{11} + 2 q^{12} + 10 q^{13} + 3 q^{14} - q^{15} - 36 q^{16} - 9 q^{17} + 10 q^{18} + 24 q^{19} + 4 q^{20} + 25 q^{21} + 6 q^{22} + 11 q^{23} - 2 q^{25} - 2 q^{26} + 28 q^{27} - 8 q^{28} + 12 q^{29} - 2 q^{30} + 10 q^{31} - 50 q^{32} - 49 q^{33} - 7 q^{34} + 4 q^{35} + 43 q^{36} - 18 q^{37} - 29 q^{38} - 52 q^{39} + 22 q^{40} + 10 q^{41} - 5 q^{42} + 35 q^{43} + 6 q^{44} - 38 q^{45} - 33 q^{46} - 2 q^{47} - 4 q^{48} + 4 q^{49} + 18 q^{50} + 50 q^{51} + 9 q^{52} - 5 q^{53} + 23 q^{54} + 8 q^{55} + 33 q^{57} + 35 q^{58} + 41 q^{59} - 2 q^{60} - 13 q^{61} - 2 q^{62} - 46 q^{63} + 16 q^{64} - 10 q^{65} + 56 q^{66} - 9 q^{67} + 26 q^{68} - 45 q^{69} + 8 q^{70} - 19 q^{71} - 27 q^{73} + 8 q^{74} + q^{75} + 4 q^{76} - 64 q^{77} - 27 q^{78} - 83 q^{79} - 8 q^{80} + 12 q^{81} + 31 q^{82} + 67 q^{83} + 28 q^{84} - 13 q^{85} - 73 q^{86} + 69 q^{87} + 22 q^{88} - 5 q^{89} - 10 q^{90} - 84 q^{91} + 11 q^{92} + 28 q^{93} - 37 q^{94} - 2 q^{95} + 14 q^{96} + 18 q^{97} + 8 q^{98} + 62 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 + q^3 - 4 * q^4 + 2 * q^5 - 9 * q^6 - 4 * q^7 - 17 * q^9 + 4 * q^10 - 8 * q^11 + 2 * q^12 + 10 * q^13 + 3 * q^14 - q^15 - 36 * q^16 - 9 * q^17 + 10 * q^18 + 24 * q^19 + 4 * q^20 + 25 * q^21 + 6 * q^22 + 11 * q^23 - 2 * q^25 - 2 * q^26 + 28 * q^27 - 8 * q^28 + 12 * q^29 - 2 * q^30 + 10 * q^31 - 50 * q^32 - 49 * q^33 - 7 * q^34 + 4 * q^35 + 43 * q^36 - 18 * q^37 - 29 * q^38 - 52 * q^39 + 22 * q^40 + 10 * q^41 - 5 * q^42 + 35 * q^43 + 6 * q^44 - 38 * q^45 - 33 * q^46 - 2 * q^47 - 4 * q^48 + 4 * q^49 + 18 * q^50 + 50 * q^51 + 9 * q^52 - 5 * q^53 + 23 * q^54 + 8 * q^55 + 33 * q^57 + 35 * q^58 + 41 * q^59 - 2 * q^60 - 13 * q^61 - 2 * q^62 - 46 * q^63 + 16 * q^64 - 10 * q^65 + 56 * q^66 - 9 * q^67 + 26 * q^68 - 45 * q^69 + 8 * q^70 - 19 * q^71 - 27 * q^73 + 8 * q^74 + q^75 + 4 * q^76 - 64 * q^77 - 27 * q^78 - 83 * q^79 - 8 * q^80 + 12 * q^81 + 31 * q^82 + 67 * q^83 + 28 * q^84 - 13 * q^85 - 73 * q^86 + 69 * q^87 + 22 * q^88 - 5 * q^89 - 10 * q^90 - 84 * q^91 + 11 * q^92 + 28 * q^93 - 37 * q^94 - 2 * q^95 + 14 * q^96 + 18 * q^97 + 8 * q^98 + 62 * q^99

Introduction

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