LMFDB - Embedded newform 418.2.u.b.9.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [418,2,Mod(5,418)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(418, base_ring=CyclotomicField(90))

chi = DirichletCharacter(H, H._module([36, 80]))

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

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

chi := DirichletCharacter("418.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 418 = 2 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	418.u (of order $45$, degree $24$, 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:	$3.33774680449$
Analytic rank:	$0$
Dimension:	$264$
Relative dimension:	$11$ over $\Q(\zeta_{45})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{45}]$

Embedding invariants

Embedding label			9.8
Character	$\chi$	$=$	418.9
Dual form			418.2.u.b.93.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.990268 + 0.139173i) q^{2} +(0.276037 - 1.10712i) q^{3} +(0.961262 + 0.275637i) q^{4} +(-0.120793 + 3.45905i) q^{5} +(0.427432 - 1.05793i) q^{6} +(-4.47274 + 1.99139i) q^{7} +(0.913545 + 0.406737i) q^{8} +(1.49932 + 0.797201i) q^{9} +O(q^{10})$	\(q+(0.990268 + 0.139173i) q^{2} +(0.276037 - 1.10712i) q^{3} +(0.961262 + 0.275637i) q^{4} +(-0.120793 + 3.45905i) q^{5} +(0.427432 - 1.05793i) q^{6} +(-4.47274 + 1.99139i) q^{7} +(0.913545 + 0.406737i) q^{8} +(1.49932 + 0.797201i) q^{9} +(-0.601023 + 3.40857i) q^{10} +(1.37694 + 3.01729i) q^{11} +(0.570508 - 0.988149i) q^{12} +(3.43283 - 2.14507i) q^{13} +(-4.70636 + 1.34953i) q^{14} +(3.79625 + 1.08856i) q^{15} +(0.848048 + 0.529919i) q^{16} +(-3.76691 + 2.00290i) q^{17} +(1.37378 + 0.998108i) q^{18} +(-3.46103 - 2.64977i) q^{19} +(-1.06956 + 3.29175i) q^{20} +(0.970076 + 5.50158i) q^{21} +(0.943616 + 3.17956i) q^{22} +(6.13656 - 2.23352i) q^{23} +(0.702480 - 0.899133i) q^{24} +(-6.96258 - 0.486871i) q^{25} +(3.69796 - 1.64644i) q^{26} +(3.58693 - 3.98369i) q^{27} +(-4.84838 + 0.681395i) q^{28} +(6.58544 - 6.35948i) q^{29} +(3.60780 + 1.60630i) q^{30} +(-2.42998 - 2.69877i) q^{31} +(0.766044 + 0.642788i) q^{32} +(3.72060 - 0.691562i) q^{33} +(-4.00900 + 1.45916i) q^{34} +(-6.34805 - 15.7120i) q^{35} +(1.22150 + 1.17959i) q^{36} +(3.75169 + 2.72576i) q^{37} +(-3.05857 - 3.10567i) q^{38} +(-1.42727 - 4.39269i) q^{39} +(-1.51727 + 3.11086i) q^{40} +(-1.46659 + 5.88218i) q^{41} +(0.194964 + 5.58304i) q^{42} +(-5.59073 - 2.03486i) q^{43} +(0.491924 + 3.27994i) q^{44} +(-2.93866 + 5.08991i) q^{45} +(6.38768 - 1.35774i) q^{46} +(2.24096 + 4.59464i) q^{47} +(0.820778 - 0.792616i) q^{48} +(11.3559 - 12.6120i) q^{49} +(-6.82706 - 1.45114i) q^{50} +(1.17765 + 4.72330i) q^{51} +(3.89111 - 1.11576i) q^{52} +(-0.0488399 - 1.39859i) q^{53} +(4.10645 - 3.44572i) q^{54} +(-10.6033 + 4.39844i) q^{55} -4.89603 q^{56} +(-3.88900 + 3.10035i) q^{57} +(7.40642 - 5.38108i) q^{58} +(-0.653218 + 1.33930i) q^{59} +(3.34914 + 2.09277i) q^{60} +(3.32086 + 4.25051i) q^{61} +(-2.03074 - 3.01069i) q^{62} +(-8.29360 - 0.579945i) q^{63} +(0.669131 + 0.743145i) q^{64} +(7.00524 + 12.1334i) q^{65} +(3.78063 - 0.167024i) q^{66} +(0.955235 - 5.41741i) q^{67} +(-4.17306 + 0.887011i) q^{68} +(-0.778870 - 7.41046i) q^{69} +(-4.09959 - 16.4425i) q^{70} +(-0.0480678 + 1.37648i) q^{71} +(1.04544 + 1.33811i) q^{72} +(-1.75351 + 0.122617i) q^{73} +(3.33583 + 3.22137i) q^{74} +(-2.46096 + 7.57404i) q^{75} +(-2.59658 - 3.50111i) q^{76} +(-12.1673 - 10.7535i) q^{77} +(-0.802036 - 4.54857i) q^{78} +(2.69060 + 6.65948i) q^{79} +(-1.93545 + 2.86943i) q^{80} +(-0.571647 - 0.847501i) q^{81} +(-2.27096 + 5.62082i) q^{82} +(-8.43878 - 1.79372i) q^{83} +(-0.583943 + 5.55584i) q^{84} +(-6.47311 - 13.2718i) q^{85} +(-5.25312 - 2.79313i) q^{86} +(-5.22291 - 9.04634i) q^{87} +(0.0306572 + 3.31648i) q^{88} +(0.366969 + 0.307923i) q^{89} +(-3.61844 + 4.63139i) q^{90} +(-11.0825 + 16.4305i) q^{91} +(6.51448 - 0.455537i) q^{92} +(-3.65864 + 1.94533i) q^{93} +(1.57970 + 4.86181i) q^{94} +(9.58375 - 11.6518i) q^{95} +(0.923101 - 0.670672i) q^{96} +(2.19006 + 0.307794i) q^{97} +(13.0006 - 10.9088i) q^{98} +(-0.340913 + 5.62157i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9}+O(q^{10}) $ 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9	$ 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9} + 3 q^{11} - 6 q^{13} + 18 q^{14} - 39 q^{15} - 3 q^{17} - 78 q^{18} - 45 q^{19} - 24 q^{20} + 48 q^{21} + 6 q^{23} - 9 q^{24} + 30 q^{25} + 18 q^{26} - 24 q^{27} + 6 q^{28} - 3 q^{31} - 63 q^{33} - 36 q^{34} + 42 q^{35} - 9 q^{36} + 60 q^{37} - 3 q^{38} + 36 q^{39} + 39 q^{41} + 6 q^{42} - 60 q^{43} + 60 q^{44} - 108 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{48} + 6 q^{49} + 18 q^{50} + 96 q^{51} + 3 q^{52} - 117 q^{53} + 54 q^{54} + 102 q^{55} - 96 q^{57} - 60 q^{58} - 141 q^{59} + 36 q^{60} + 24 q^{61} - 27 q^{62} - 81 q^{63} + 33 q^{64} - 102 q^{65} + 72 q^{66} + 102 q^{67} - 21 q^{68} - 6 q^{69} - 33 q^{70} - 66 q^{71} - 12 q^{72} + 36 q^{73} + 18 q^{74} + 6 q^{76} - 174 q^{77} + 18 q^{78} + 36 q^{79} + 60 q^{81} - 36 q^{82} - 24 q^{83} + 48 q^{84} + 174 q^{85} - 21 q^{86} + 12 q^{87} + 3 q^{88} + 30 q^{89} - 48 q^{90} - 18 q^{91} + 18 q^{92} - 123 q^{93} - 120 q^{94} - 18 q^{95} - 24 q^{97} - 84 q^{98} - 141 q^{99}+O(q^{100}) $ 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9 + 3 * q^11 - 6 * q^13 + 18 * q^14 - 39 * q^15 - 3 * q^17 - 78 * q^18 - 45 * q^19 - 24 * q^20 + 48 * q^21 + 6 * q^23 - 9 * q^24 + 30 * q^25 + 18 * q^26 - 24 * q^27 + 6 * q^28 - 3 * q^31 - 63 * q^33 - 36 * q^34 + 42 * q^35 - 9 * q^36 + 60 * q^37 - 3 * q^38 + 36 * q^39 + 39 * q^41 + 6 * q^42 - 60 * q^43 + 60 * q^44 - 108 * q^45 - 12 * q^46 - 24 * q^47 - 12 * q^48 + 6 * q^49 + 18 * q^50 + 96 * q^51 + 3 * q^52 - 117 * q^53 + 54 * q^54 + 102 * q^55 - 96 * q^57 - 60 * q^58 - 141 * q^59 + 36 * q^60 + 24 * q^61 - 27 * q^62 - 81 * q^63 + 33 * q^64 - 102 * q^65 + 72 * q^66 + 102 * q^67 - 21 * q^68 - 6 * q^69 - 33 * q^70 - 66 * q^71 - 12 * q^72 + 36 * q^73 + 18 * q^74 + 6 * q^76 - 174 * q^77 + 18 * q^78 + 36 * q^79 + 60 * q^81 - 36 * q^82 - 24 * q^83 + 48 * q^84 + 174 * q^85 - 21 * q^86 + 12 * q^87 + 3 * q^88 + 30 * q^89 - 48 * q^90 - 18 * q^91 + 18 * q^92 - 123 * q^93 - 120 * q^94 - 18 * q^95 - 24 * q^97 - 84 * q^98 - 141 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/418\mathbb{Z}\right)^\times$.

$n$	$287$	$343$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.990268	+	0.139173i	0.700225	+	0.0984102i
$2$	0.990268	+	0.139173i	0.700225	+	0.0984102i
$3$	0.276037	−	1.10712i	0.159370	−	0.639198i	−0.836465	−	0.548021i	$-0.815381\pi$
$3$	0.276037	−	1.10712i	0.159370	−	0.639198i	0.995835	−	0.0911771i	$-0.0290629\pi$
$4$	0.961262	+	0.275637i	0.480631	+	0.137819i
$5$	−0.120793	+	3.45905i	−0.0540201	+	1.54693i	0.605866	+	0.795567i	$0.292827\pi$
$5$	−0.120793	+	3.45905i	−0.0540201	+	1.54693i	−0.659886	+	0.751365i	$0.729396\pi$
$6$	0.427432	−	1.05793i	0.174498	−	0.431899i
$7$	−4.47274	+	1.99139i	−1.69054	+	0.752676i	−0.690982	+	0.722872i	$0.742822\pi$
$7$	−4.47274	+	1.99139i	−1.69054	+	0.752676i	−0.999556	+	0.0298046i	$0.990512\pi$
$8$	0.913545	+	0.406737i	0.322987	+	0.143803i
$9$	1.49932	+	0.797201i	0.499772	+	0.265734i
$10$	−0.601023	+	3.40857i	−0.190060	+	1.07788i
$11$	1.37694	+	3.01729i	0.415164	+	0.909747i
$11$	1.37694	+	3.01729i	0.415164	+	0.909747i
$12$	0.570508	−	0.988149i	0.164692	−	0.285254i
$13$	3.43283	−	2.14507i	0.952096	−	0.594936i	0.0374966	−	0.999297i	$-0.488062\pi$
$13$	3.43283	−	2.14507i	0.952096	−	0.594936i	0.914599	+	0.404361i	$0.132506\pi$
$14$	−4.70636	+	1.34953i	−1.25783	+	0.360677i
$15$	3.79625	+	1.08856i	0.980186	+	0.281064i
$16$	0.848048	+	0.529919i	0.212012	+	0.132480i
$17$	−3.76691	+	2.00290i	−0.913609	+	0.485775i	−0.858562	−	0.512709i	$-0.828642\pi$
$17$	−3.76691	+	2.00290i	−0.913609	+	0.485775i	−0.0550467	+	0.998484i	$0.517531\pi$
$18$	1.37378	+	0.998108i	0.323802	+	0.235256i
$19$	−3.46103	−	2.64977i	−0.794014	−	0.607900i
$19$	−3.46103	−	2.64977i	−0.794014	−	0.607900i
$20$	−1.06956	+	3.29175i	−0.239160	+	0.736058i
$21$	0.970076	+	5.50158i	0.211688	+	1.20054i
$22$	0.943616	+	3.17956i	0.201180	+	0.677884i
$23$	6.13656	−	2.23352i	1.27956	−	0.465722i	0.389274	−	0.921122i	$-0.372726\pi$
$23$	6.13656	−	2.23352i	1.27956	−	0.465722i	0.890287	+	0.455400i	$0.150504\pi$
$24$	0.702480	−	0.899133i	0.143393	−	0.183535i
$25$	−6.96258	−	0.486871i	−1.39252	−	0.0973742i
$26$	3.69796	−	1.64644i	0.725229	−	0.322893i
$27$	3.58693	−	3.98369i	0.690306	−	0.766662i
$28$	−4.84838	+	0.681395i	−0.916258	+	0.128772i
$29$	6.58544	−	6.35948i	1.22289	−	1.18093i	0.245515	−	0.969393i	$-0.421043\pi$
$29$	6.58544	−	6.35948i	1.22289	−	1.18093i	0.977371	−	0.211534i	$-0.0678458\pi$
$30$	3.60780	+	1.60630i	0.658692	+	0.293268i
$31$	−2.42998	−	2.69877i	−0.436438	−	0.484713i	0.484296	−	0.874904i	$-0.339076\pi$
$31$	−2.42998	−	2.69877i	−0.436438	−	0.484713i	−0.920734	+	0.390191i	$0.872409\pi$
$32$	0.766044	+	0.642788i	0.135419	+	0.113630i
$33$	3.72060	−	0.691562i	0.647673	−	0.120385i
$34$	−4.00900	+	1.45916i	−0.687537	+	0.250243i
$35$	−6.34805	−	15.7120i	−1.07302	−	2.65581i
$36$	1.22150	+	1.17959i	0.203583	+	0.196598i
$37$	3.75169	+	2.72576i	0.616775	+	0.448113i	0.851793	−	0.523878i	$-0.175515\pi$
$37$	3.75169	+	2.72576i	0.616775	+	0.448113i	−0.235019	+	0.971991i	$0.575515\pi$
$38$	−3.05857	−	3.10567i	−0.496165	−	0.503806i
$39$	−1.42727	−	4.39269i	−0.228546	−	0.703393i
$40$	−1.51727	+	3.11086i	−0.239901	+	0.491871i
$41$	−1.46659	+	5.88218i	−0.229043	+	0.918642i	0.740170	+	0.672419i	$0.234745\pi$
$41$	−1.46659	+	5.88218i	−0.229043	+	0.918642i	−0.969213	+	0.246222i	$0.920811\pi$
$42$	0.194964	+	5.58304i	0.0300836	+	0.861482i
$43$	−5.59073	−	2.03486i	−0.852578	−	0.310313i	−0.121487	−	0.992593i	$-0.538766\pi$
$43$	−5.59073	−	2.03486i	−0.852578	−	0.310313i	−0.731091	+	0.682280i	$0.760988\pi$
$44$	0.491924	+	3.27994i	0.0741604	+	0.494470i
$45$	−2.93866	+	5.08991i	−0.438070	+	0.758759i
$46$	6.38768	−	1.35774i	0.941812	−	0.200188i
$47$	2.24096	+	4.59464i	0.326877	+	0.670198i	0.997429	−	0.0716653i	$-0.0228313\pi$
$47$	2.24096	+	4.59464i	0.326877	+	0.670198i	−0.670551	+	0.741863i	$0.733942\pi$
$48$	0.820778	−	0.792616i	0.118469	−	0.114404i
$49$	11.3559	−	12.6120i	1.62227	−	1.80171i
$50$	−6.82706	−	1.45114i	−0.965493	−	0.205222i
$51$	1.17765	+	4.72330i	0.164904	+	0.661395i
$52$	3.89111	−	1.11576i	0.539600	−	0.154728i
$53$	−0.0488399	−	1.39859i	−0.00670868	−	0.192111i	−0.998118	−	0.0613178i	$-0.980470\pi$
$53$	−0.0488399	−	1.39859i	−0.00670868	−	0.192111i	0.991410	−	0.130794i	$-0.0417525\pi$
$54$	4.10645	−	3.44572i	0.558817	−	0.468903i
$55$	−10.6033	+	4.39844i	−1.42974	+	0.593085i
$56$	−4.89603			−0.654259
$57$	−3.88900	+	3.10035i	−0.515110	+	0.410651i
$58$	7.40642	−	5.38108i	0.972510	−	0.706570i
$59$	−0.653218	+	1.33930i	−0.0850418	+	0.174361i	−0.937077	−	0.349123i	$-0.886479\pi$
$59$	−0.653218	+	1.33930i	−0.0850418	+	0.174361i	0.852035	+	0.523485i	$0.175368\pi$
$60$	3.34914	+	2.09277i	0.432372	+	0.270176i
$61$	3.32086	+	4.25051i	0.425193	+	0.544222i	0.952135	−	0.305679i	$-0.0988835\pi$
$61$	3.32086	+	4.25051i	0.425193	+	0.544222i	−0.526941	+	0.849902i	$0.676661\pi$
$62$	−2.03074	−	3.01069i	−0.257904	−	0.382359i
$63$	−8.29360	−	0.579945i	−1.04490	−	0.0730662i
$64$	0.669131	+	0.743145i	0.0836413	+	0.0928931i
$65$	7.00524	+	12.1334i	0.868893	+	1.50497i
$66$	3.78063	−	0.167024i	0.465364	−	0.0205593i
$67$	0.955235	−	5.41741i	0.116701	−	0.661842i	−0.869194	−	0.494472i	$-0.835362\pi$
$67$	0.955235	−	5.41741i	0.116701	−	0.661842i	0.985894	−	0.167370i	$-0.0535274\pi$
$68$	−4.17306	+	0.887011i	−0.506057	+	0.107566i
$69$	−0.778870	−	7.41046i	−0.0937650	−	0.892114i
$70$	−4.09959	−	16.4425i	−0.489994	−	1.96526i
$71$	−0.0480678	+	1.37648i	−0.00570460	+	0.163358i	0.993195	+	0.116462i	$0.0371553\pi$
$71$	−0.0480678	+	1.37648i	−0.00570460	+	0.163358i	−0.998900	+	0.0468965i	$0.985067\pi$
$72$	1.04544	+	1.33811i	0.123207	+	0.157697i
$73$	−1.75351	+	0.122617i	−0.205232	+	0.0143512i	−0.172003	−	0.985096i	$-0.555024\pi$
$73$	−1.75351	+	0.122617i	−0.205232	+	0.0143512i	−0.0332297	+	0.999448i	$0.510579\pi$
$74$	3.33583	+	3.22137i	0.387782	+	0.374477i
$75$	−2.46096	+	7.57404i	−0.284167	+	0.874575i
$76$	−2.59658	−	3.50111i	−0.297848	−	0.401605i
$77$	−12.1673	−	10.7535i	−1.38659	−	1.22548i
$78$	−0.802036	−	4.54857i	−0.0908127	−	0.515025i
$79$	2.69060	+	6.65948i	0.302716	+	0.749250i	0.999489	+	0.0319577i	$0.0101742\pi$
$79$	2.69060	+	6.65948i	0.302716	+	0.749250i	−0.696773	+	0.717292i	$0.745381\pi$
$80$	−1.93545	+	2.86943i	−0.216390	+	0.320812i
$81$	−0.571647	−	0.847501i	−0.0635163	−	0.0941668i
$82$	−2.27096	+	5.62082i	−0.250785	+	0.620716i
$83$	−8.43878	−	1.79372i	−0.926277	−	0.196886i	−0.280009	−	0.959997i	$-0.590338\pi$
$83$	−8.43878	−	1.79372i	−0.926277	−	0.196886i	−0.646267	+	0.763111i	$0.723671\pi$
$84$	−0.583943	+	5.55584i	−0.0637134	+	0.606192i
$85$	−6.47311	−	13.2718i	−0.702107	−	1.43953i
$86$	−5.25312	−	2.79313i	−0.566458	−	0.301191i
$87$	−5.22291	−	9.04634i	−0.559955	−	0.969870i
$88$	0.0306572	+	3.31648i	0.00326807	+	0.353538i
$89$	0.366969	+	0.307923i	0.0388986	+	0.0326398i	0.662030	−	0.749478i	$-0.269695\pi$
$89$	0.366969	+	0.307923i	0.0388986	+	0.0326398i	−0.623131	+	0.782117i	$0.714140\pi$
$90$	−3.61844	+	4.63139i	−0.381417	+	0.488192i
$91$	−11.0825	+	16.4305i	−1.16176	+	1.72238i
$92$	6.51448	−	0.455537i	0.679181	−	0.0474930i
$93$	−3.65864	+	1.94533i	−0.379383	+	0.201721i
$94$	1.57970	+	4.86181i	0.162933	+	0.501457i
$95$	9.58375	−	11.6518i	0.983272	−	1.19545i
$96$	0.923101	−	0.670672i	0.0942137	−	0.0684502i
$97$	2.19006	+	0.307794i	0.222367	+	0.0312517i	0.249477	−	0.968381i	$-0.419741\pi$
$97$	2.19006	+	0.307794i	0.222367	+	0.0312517i	−0.0271094	+	0.999632i	$0.508630\pi$
$98$	13.0006	−	10.9088i	1.31326	−	1.10196i
$99$	−0.340913	+	5.62157i	−0.0342631	+	0.564989i
$100$	−6.55866	−	2.38716i	−0.655866	−	0.238716i
$101$	12.5933	−	7.86919i	1.25308	−	0.783014i	0.269420	−	0.963023i	$-0.413168\pi$
$101$	12.5933	−	7.86919i	1.25308	−	0.783014i	0.983665	+	0.180009i	$0.0576126\pi$
$102$	0.508834	+	4.84123i	0.0503821	+	0.479354i
$103$	1.60596	−	15.2797i	0.158240	−	1.50555i	−0.570803	−	0.821087i	$-0.693368\pi$
$103$	1.60596	−	15.2797i	0.158240	−	1.50555i	0.729043	−	0.684468i	$-0.239965\pi$
$104$	4.00853	−	0.563362i	0.393068	−	0.0552422i
$105$	−19.1474	+	2.69099i	−1.86859	+	0.262614i
$106$	0.146282	−	1.39178i	0.0142081	−	0.135181i
$107$	−0.686090	−	6.52771i	−0.0663268	−	0.631058i	−0.976305	−	0.216401i	$-0.930568\pi$
$107$	−0.686090	−	6.52771i	−0.0663268	−	0.631058i	0.909978	−	0.414657i	$-0.136098\pi$
$108$	4.54604	−	2.84068i	0.437443	−	0.273344i
$109$	0.665182	+	0.242107i	0.0637129	+	0.0231896i	0.373680	−	0.927558i	$-0.378096\pi$
$109$	0.665182	+	0.242107i	0.0637129	+	0.0231896i	−0.309967	+	0.950747i	$0.600318\pi$
$110$	−11.1122	+	2.87994i	−1.05951	+	0.274592i
$111$	4.05336	−	3.40117i	0.384728	−	0.322825i
$112$	−4.84838	−	0.681395i	−0.458129	−	0.0643858i
$113$	−1.82470	+	1.32572i	−0.171653	+	0.124713i	−0.670295	−	0.742095i	$-0.733832\pi$
$113$	−1.82470	+	1.32572i	−0.171653	+	0.124713i	0.498642	+	0.866808i	$0.333832\pi$
$114$	−4.28263	+	2.52893i	−0.401105	+	0.236856i
$115$	6.98461	+	21.4964i	0.651318	+	2.00455i
$116$	8.08324	−	4.29794i	0.750510	−	0.399053i
$117$	6.85696	−	0.479485i	0.633926	−	0.0443284i
$118$	−0.833255	+	1.23535i	−0.0767074	+	0.113723i
$119$	12.8598	−	16.4599i	1.17886	−	1.50887i
$120$	3.02529	+	2.53852i	0.276170	+	0.231734i
$121$	−7.20806	+	8.30926i	−0.655278	+	0.755388i
$122$	2.69699	+	4.67132i	0.244174	+	0.422922i
$123$	6.10746	+	3.24739i	0.550691	+	0.292808i
$124$	−1.59197	−	3.26402i	−0.142963	−	0.293118i
$125$	0.716192	−	6.81411i	0.0640582	−	0.609473i
$126$	−8.13218	−	1.72855i	−0.724472	−	0.153991i
$127$	4.95289	−	12.2588i	0.439498	−	1.08780i	−0.531147	−	0.847279i	$-0.678239\pi$
$127$	4.95289	−	12.2588i	0.439498	−	1.08780i	0.970645	−	0.240516i	$-0.0773166\pi$
$128$	0.559193	+	0.829038i	0.0494261	+	0.0732773i
$129$	−3.79608	+	5.62793i	−0.334227	+	0.495511i
$130$	5.24842	+	12.9903i	0.460317	+	1.13932i
$131$	−3.01418	−	17.0943i	−0.263351	−	1.49354i	−0.773691	−	0.633563i	$-0.781592\pi$
$131$	−3.01418	−	17.0943i	−0.263351	−	1.49354i	0.510341	−	0.859972i	$-0.329519\pi$
$132$	3.76709	+	0.360764i	0.327883	+	0.0314005i
$133$	20.7570	+	4.95949i	1.79986	+	0.430042i
$134$	1.69990	−	5.23174i	0.146849	−	0.451954i
$135$	13.3465	+	12.8886i	1.14868	+	1.10927i
$136$	−4.25589	+	0.297601i	−0.364940	+	0.0255191i
$137$	−7.42102	−	9.49847i	−0.634020	−	0.811509i	0.358508	−	0.933527i	$-0.383286\pi$
$137$	−7.42102	−	9.49847i	−0.634020	−	0.811509i	−0.992528	+	0.122018i	$0.961063\pi$
$138$	0.260046	−	7.44674i	0.0221366	−	0.633908i
$139$	4.73755	+	19.0013i	0.401834	+	1.61167i	0.741385	+	0.671080i	$0.234169\pi$
$139$	4.73755	+	19.0013i	0.401834	+	1.61167i	−0.339551	+	0.940588i	$0.610275\pi$
$140$	−1.77133	−	16.8531i	−0.149705	−	1.42434i
$141$	5.70542	−	1.21273i	0.480483	−	0.102130i
$142$	−0.239169	+	1.35640i	−0.0200706	+	0.113826i
$143$	11.1991	+	7.40420i	0.936516	+	0.619171i
$144$	0.849041	+	1.47058i	0.0707534	+	0.122549i
$145$	21.2023	+	23.5475i	1.76075	+	1.95551i
$146$	−1.75351	−	0.122617i	−0.145121	−	0.0101479i
$147$	−10.8284	−	16.0537i	−0.893109	−	1.32409i
$148$	2.85504	+	3.65428i	0.234683	+	0.300380i
$149$	11.0393	+	6.89810i	0.904372	+	0.565115i	0.900489	−	0.434878i	$-0.143208\pi$
$149$	11.0393	+	6.89810i	0.904372	+	0.565115i	0.00388299	+	0.999992i	$0.498764\pi$
$150$	−3.49111	+	7.15783i	−0.285048	+	0.584435i
$151$	−5.19349	+	3.77329i	−0.422640	+	0.307066i	−0.778699	−	0.627398i	$-0.784120\pi$
$151$	−5.19349	+	3.77329i	−0.422640	+	0.307066i	0.356059	+	0.934463i	$0.384120\pi$
$152$	−2.08404	−	3.82841i	−0.169038	−	0.310525i
$153$	−7.24450			−0.585683
$154$	−10.5523	−	12.3422i	−0.850329	−	0.994566i
$155$	9.62869	−	8.07943i	0.773395	−	0.648956i
$156$	−0.161192	−	4.61593i	−0.0129057	−	0.369570i
$157$	−9.54868	+	2.73804i	−0.762067	+	0.218519i	−0.634092	−	0.773258i	$-0.718626\pi$
$157$	−9.54868	+	2.73804i	−0.762067	+	0.218519i	−0.127976	+	0.991777i	$0.540848\pi$
$158$	1.73760	+	6.96913i	0.138236	+	0.554434i
$159$	−1.56190	−	0.331991i	−0.123866	−	0.0263286i
$160$	−2.31596	+	2.57214i	−0.183093	+	0.203345i
$161$	−22.9994	+	22.2103i	−1.81261	+	1.75042i
$162$	−0.448134	−	0.918811i	−0.0352087	−	0.0721886i
$163$	−10.4107	+	2.21286i	−0.815429	+	0.173325i	−0.596704	−	0.802462i	$-0.703523\pi$
$163$	−10.4107	+	2.21286i	−0.815429	+	0.173325i	−0.218725	+	0.975786i	$0.570190\pi$
$164$	−3.03113	+	5.25006i	−0.236691	+	0.409961i
$165$	1.94272	+	12.9532i	0.151241	+	1.00841i
$166$	−8.10702	−	2.95071i	−0.629227	−	0.229020i
$167$	−0.314899	−	9.01752i	−0.0243676	−	0.697797i	−0.948694	−	0.316195i	$-0.897595\pi$
$167$	−0.314899	−	9.01752i	−0.0243676	−	0.697797i	0.924327	−	0.381602i	$-0.124628\pi$
$168$	−1.35148	+	5.42051i	−0.104269	+	0.418201i
$169$	1.48418	−	3.04301i	0.114167	−	0.234078i
$170$	−4.56303	−	14.0436i	−0.349968	−	1.07709i
$171$	−3.07677	−	6.73199i	−0.235287	−	0.514808i
$172$	−4.81327	−	3.49704i	−0.367008	−	0.266647i
$173$	−17.4647	−	16.8655i	−1.32782	−	1.28226i	−0.931310	−	0.364228i	$-0.881333\pi$
$173$	−17.4647	−	16.8655i	−1.32782	−	1.28226i	−0.396508	−	0.918031i	$-0.629778\pi$
$174$	−3.91307	−	9.68519i	−0.296649	−	0.734233i
$175$	32.1114	−	11.6876i	2.42739	−	0.883499i
$176$	−0.431206	+	3.28847i	−0.0325034	+	0.247878i
$177$	1.30245	+	1.09289i	0.0978984	+	0.0821465i
$178$	0.320543	+	0.355999i	0.0240257	+	0.0266832i
$179$	5.87588	+	2.61611i	0.439184	+	0.195537i	0.614403	−	0.788992i	$-0.289397\pi$
$179$	5.87588	+	2.61611i	0.439184	+	0.195537i	−0.175220	+	0.984529i	$0.556064\pi$
$180$	−4.22779	+	4.08273i	−0.315121	+	0.304309i
$181$	−0.481525	+	0.0676740i	−0.0357915	+	0.00503017i	−0.157046	−	0.987591i	$-0.550197\pi$
$181$	−0.481525	+	0.0676740i	−0.0357915	+	0.00503017i	0.121255	+	0.992621i	$0.461308\pi$
$182$	−13.2613	+	14.7282i	−0.982994	+	1.09173i
$183$	5.62252	−	2.50331i	0.415629	−	0.185050i
$184$	6.51448	+	0.455537i	0.480254	+	0.0335826i
$185$	−9.88172	+	12.6480i	−0.726518	+	0.929901i
$186$	−3.89377	+	1.41722i	−0.285505	+	0.103915i
$187$	−11.2301	−	8.60797i	−0.821229	−	0.629477i
$188$	0.887691	+	5.03435i	0.0647415	+	0.367167i
$189$	−8.11033	+	24.9610i	−0.589940	+	1.81565i
$190$	11.1121	−	10.2046i	0.806156	−	0.740318i
$191$	8.74676	+	6.35490i	0.632894	+	0.459824i	0.857401	−	0.514648i	$-0.172077\pi$
$191$	8.74676	+	6.35490i	0.632894	+	0.459824i	−0.224508	+	0.974472i	$0.572077\pi$
$192$	1.00746	−	0.535675i	0.0727070	−	0.0386590i
$193$	1.34543	+	0.840720i	0.0968464	+	0.0605163i	0.577478	−	0.816406i	$-0.304037\pi$
$193$	1.34543	+	0.840720i	0.0968464	+	0.0605163i	−0.480632	+	0.876923i	$0.659593\pi$
$194$	2.12591	+	0.609596i	0.152632	+	0.0437665i
$195$	15.3669	−	4.40639i	1.10045	−	0.315548i
$196$	14.3923	−	8.99330i	1.02802	−	0.642379i
$197$	−3.31807	+	5.74706i	−0.236402	+	0.409461i	−0.959679	−	0.281097i	$-0.909302\pi$
$197$	−3.31807	+	5.74706i	−0.236402	+	0.409461i	0.723277	+	0.690558i	$0.242635\pi$
$198$	−1.11997	+	5.51942i	−0.0795926	+	0.392248i
$199$	−1.06925	+	6.06399i	−0.0757968	+	0.429865i	0.923169	+	0.384395i	$0.125590\pi$
$199$	−1.06925	+	6.06399i	−0.0757968	+	0.429865i	−0.998966	+	0.0454704i	$0.985521\pi$
$200$	−6.16261	−	3.27672i	−0.435762	−	0.231699i
$201$	−5.73406	−	2.55297i	−0.404449	−	0.180072i
$202$	13.5660	−	6.03996i	0.954498	−	0.424970i
$203$	−16.7907	+	41.5585i	−1.17848	+	2.91684i
$204$	−0.169887	+	4.86494i	−0.0118945	+	0.340614i
$205$	−20.1696	−	5.78353i	−1.40870	−	0.403939i
$206$	3.71686	−	14.9075i	0.258966	−	1.03865i
$207$	10.9812	+	1.54331i	0.763247	+	0.107267i
$208$	4.04792			0.280673
$209$	3.22950	−	14.0915i	0.223389	−	0.974729i
$210$	−19.3356			−1.33428
$211$	19.7541	+	2.77625i	1.35992	+	0.191125i	0.781140	−	0.624356i	$-0.214638\pi$
$211$	19.7541	+	2.77625i	1.35992	+	0.191125i	0.578785	+	0.815480i	$0.303527\pi$
$212$	0.338556	−	1.35787i	0.0232521	−	0.0932592i
$213$	1.51067	+	0.433177i	0.103509	+	0.0296808i
$214$	0.229069	−	6.55967i	0.0156588	−	0.448410i
$215$	7.71398	−	19.0928i	0.526089	−	1.30212i
$216$	4.89714	−	2.18035i	0.333208	−	0.148354i
$217$	16.2430	+	7.23185i	1.10265	+	0.490930i
$218$	0.625014	+	0.332326i	0.0423313	+	0.0225079i
$219$	−0.348280	+	1.97519i	−0.0235346	+	0.133471i
$220$	−11.4049	+	1.30540i	−0.768917	+	0.0880097i
$221$	−8.63479	+	14.9559i	−0.580839	+	1.00604i
$222$	4.48727	−	2.80396i	0.301166	−	0.188189i
$223$	−12.7754	+	3.66328i	−0.855501	+	0.245311i	−0.674594	−	0.738189i	$-0.735681\pi$
$223$	−12.7754	+	3.66328i	−0.855501	+	0.245311i	−0.180907	+	0.983500i	$0.557903\pi$
$224$	−4.70636	−	1.34953i	−0.314457	−	0.0901691i
$225$	−10.0510	−	6.28055i	−0.670066	−	0.418704i
$226$	−1.99145	+	1.05887i	−0.132469	+	0.0704350i
$227$	0.466798	+	0.339149i	0.0309825	+	0.0225101i	0.603169	−	0.797614i	$-0.293905\pi$
$227$	0.466798	+	0.339149i	0.0309825	+	0.0225101i	−0.572186	+	0.820124i	$0.693905\pi$
$228$	−4.59291	+	1.90829i	−0.304173	+	0.126380i
$229$	−0.00249660	+	0.00768374i	−0.000164980	+	0.000507756i	−0.951139	−	0.308763i	$-0.900085\pi$
$229$	−0.00249660	+	0.00768374i	−0.000164980	+	0.000507756i	0.950974	+	0.309271i	$0.100085\pi$
$230$	3.92491	+	22.2593i	0.258801	+	1.46773i
$231$	−15.2641	+	10.5024i	−1.00430	+	0.691004i
$232$	8.60273	−	3.13114i	0.564797	−	0.205569i
$233$	−1.27820	+	1.63602i	−0.0837377	+	0.107179i	−0.828055	−	0.560646i	$-0.810553\pi$
$233$	−1.27820	+	1.63602i	−0.0837377	+	0.107179i	0.744318	+	0.667826i	$0.232775\pi$
$234$	6.85696	+	0.479485i	0.448253	+	0.0313449i
$235$	−16.1638	+	7.19658i	−1.05441	+	0.469453i
$236$	−0.997074	+	1.10736i	−0.0649040	+	0.0720832i
$237$	8.11557	−	1.14057i	0.527163	−	0.0740879i
$238$	15.0255	−	14.5099i	0.973956	−	0.940538i
$239$	−13.6096	−	6.05938i	−0.880332	−	0.391949i	−0.0837549	−	0.996486i	$-0.526691\pi$
$239$	−13.6096	−	6.05938i	−0.880332	−	0.391949i	−0.796577	+	0.604538i	$0.793358\pi$
$240$	2.64255	+	2.93485i	0.170576	+	0.189444i
$241$	−3.51978	−	2.95344i	−0.226729	−	0.190248i	0.522346	−	0.852734i	$-0.325057\pi$
$241$	−3.51978	−	2.95344i	−0.226729	−	0.190248i	−0.749074	+	0.662486i	$0.769501\pi$
$242$	−8.29434	+	7.22523i	−0.533180	+	0.464455i
$243$	14.0158	−	5.10135i	0.899116	−	0.327251i
$244$	2.02062	+	5.00121i	0.129357	+	0.320170i
$245$	42.2537	+	40.8039i	2.69949	+	2.60687i
$246$	5.59607	+	4.06578i	0.356793	+	0.259225i
$247$	−17.5651	−	1.67208i	−1.11764	−	0.106392i
$248$	−1.12221	−	3.45381i	−0.0712605	−	0.219317i
$249$	−4.31528	+	8.84764i	−0.273470	+	0.560696i
$250$	1.65756	−	6.64812i	0.104834	−	0.420464i
$251$	−0.0573532	−	1.64238i	−0.00362010	−	0.103666i	−0.999856	−	0.0169805i	$-0.994595\pi$
$251$	−0.0573532	−	1.64238i	−0.00362010	−	0.103666i	0.996236	−	0.0866856i	$-0.0276275\pi$
$252$	−7.81247	−	2.84351i	−0.492139	−	0.179124i
$253$	15.1889	+	15.4403i	0.954916	+	0.970725i
$254$	6.61079	−	11.4502i	0.414798	−	0.718451i
$255$	−16.4804	+	3.50301i	−1.03204	+	0.219367i
$256$	0.438371	+	0.898794i	0.0273982	+	0.0561746i
$257$	2.07761	−	2.00632i	0.129598	−	0.125151i	−0.627035	−	0.778991i	$-0.715732\pi$
$257$	2.07761	−	2.00632i	0.129598	−	0.125151i	0.756633	+	0.653840i	$0.226843\pi$
$258$	−4.54240	+	5.04484i	−0.282797	+	0.314078i
$259$	−22.2084	−	4.72055i	−1.37996	−	0.293321i
$260$	3.38944	+	13.5943i	0.210204	+	0.843083i
$261$	14.9435	−	4.28497i	0.924976	−	0.265233i
$262$	−0.605785	−	17.3474i	−0.0374255	−	1.07173i
$263$	10.9754	−	9.20946i	0.676773	−	0.567880i	−0.238289	−	0.971194i	$-0.576586\pi$
$263$	10.9754	−	9.20946i	0.676773	−	0.567880i	0.915061	+	0.403315i	$0.132142\pi$
$264$	3.68022	+	0.881530i	0.226502	+	0.0542544i
$265$	4.84369			0.297546
$266$	19.8648	+	7.80005i	1.21799	+	0.478251i
$267$	0.442206	−	0.321281i	0.0270626	−	0.0196621i
$268$	2.41147	−	4.94425i	0.147304	−	0.302018i
$269$	7.24150	+	4.52499i	0.441522	+	0.275894i	0.732410	−	0.680863i	$-0.238395\pi$
$269$	7.24150	+	4.52499i	0.441522	+	0.275894i	−0.290888	+	0.956757i	$0.593951\pi$
$270$	11.4229	+	14.6206i	0.695174	+	0.889782i
$271$	6.99705	+	10.3736i	0.425040	+	0.630148i	0.979352	−	0.202161i	$-0.0647963\pi$
$271$	6.99705	+	10.3736i	0.425040	+	0.630148i	−0.554312	+	0.832309i	$0.687019\pi$
$272$	−4.25589	−	0.297601i	−0.258051	−	0.0180447i
$273$	15.1314	+	16.8051i	0.915793	+	1.01709i
$274$	−6.02686	−	10.4388i	−0.364096	−	0.630633i
$275$	−8.11804	−	21.6785i	−0.489536	−	1.30726i
$276$	1.29390	−	7.33807i	0.0778837	−	0.441700i
$277$	6.98114	−	1.48389i	0.419456	−	0.0891581i	0.00665165	−	0.999978i	$-0.497883\pi$
$277$	6.98114	−	1.48389i	0.419456	−	0.0891581i	0.412804	+	0.910820i	$0.364549\pi$
$278$	2.04698	+	19.4757i	0.122770	+	1.16808i
$279$	−1.49185	−	5.98350i	−0.0893150	−	0.358223i
$280$	0.591403	−	16.9356i	0.0353431	−	1.01209i
$281$	−17.1123	−	21.9027i	−1.02083	−	1.30661i	−0.951047	−	0.309046i	$-0.899990\pi$
$281$	−17.1123	−	21.9027i	−1.02083	−	1.30661i	−0.0697868	−	0.997562i	$-0.522232\pi$
$282$	5.81868	−	0.406882i	0.346497	−	0.0242294i
$283$	1.89744	+	1.83234i	0.112791	+	0.108921i	0.748916	−	0.662665i	$-0.230575\pi$
$283$	1.89744	+	1.83234i	0.112791	+	0.108921i	−0.636125	+	0.771586i	$0.719464\pi$
$284$	−0.425616	+	1.30991i	−0.0252556	+	0.0777289i
$285$	−10.2545	−	13.8267i	−0.607423	−	0.819024i
$286$	10.0597	+	8.89076i	0.594840	+	0.525722i
$287$	−5.15404	−	29.2300i	−0.304233	−	1.72539i
$288$	0.636113	+	1.57443i	0.0374833	+	0.0927744i
$289$	0.671697	−	0.995832i	0.0395116	−	0.0585783i
$290$	17.7188	+	26.2691i	1.04048	+	1.54258i
$291$	0.945304	−	2.33971i	0.0554147	−	0.137156i
$292$	−1.71938	−	0.365465i	−0.100619	−	0.0213872i
$293$	1.79302	−	17.0595i	0.104750	−	0.996625i	−0.808298	−	0.588773i	$-0.799611\pi$
$293$	1.79302	−	17.0595i	0.104750	−	0.996625i	0.913048	−	0.407852i	$-0.133722\pi$
$294$	−8.48874	−	17.4045i	−0.495074	−	1.01505i
$295$	−4.55378	−	2.42129i	−0.265131	−	0.140973i
$296$	2.31867	+	4.01606i	0.134770	+	0.233429i
$297$	16.9590	+	5.33750i	0.984058	+	0.309713i
$298$	9.97181	+	8.36734i	0.577651	+	0.484707i
$299$	16.2747	−	20.8307i	0.941190	−	1.20467i
$300$	−4.45331	+	6.60231i	−0.257112	+	0.381184i
$301$	29.0581	−	2.03194i	1.67488	−	0.117119i
$302$	−5.66808	+	3.01377i	−0.326162	+	0.173423i
$303$	−5.23594	−	16.1146i	−0.300797	−	0.925758i
$304$	−1.53095	−	4.08120i	−0.0878060	−	0.234073i
$305$	−15.1038	+	10.9736i	−0.864844	+	0.628346i
$306$	−7.17400	−	1.00824i	−0.410110	−	0.0576372i
$307$	−18.9517	+	15.9024i	−1.08163	+	0.907598i	−0.996055	−	0.0887335i	$-0.971718\pi$
$307$	−18.9517	+	15.9024i	−1.08163	+	0.907598i	−0.0855778	+	0.996331i	$0.527274\pi$
$308$	−8.73190	−	13.6907i	−0.497546	−	0.780101i
$309$	−16.4732	−	5.99576i	−0.937128	−	0.341087i
$310$	10.6594	−	6.66075i	0.605415	−	0.378305i
$311$	0.257785	+	2.45266i	0.0146176	+	0.139078i	0.999397	−	0.0347338i	$-0.0110584\pi$
$311$	0.257785	+	2.45266i	0.0146176	+	0.139078i	−0.984779	+	0.173811i	$0.944392\pi$
$312$	0.482790	−	4.59344i	0.0273326	−	0.260052i
$313$	7.17566	−	1.00847i	0.405592	−	0.0570023i	0.0665727	−	0.997782i	$-0.478794\pi$
$313$	7.17566	−	1.00847i	0.405592	−	0.0570023i	0.339020	+	0.940779i	$0.389905\pi$
$314$	−9.83681	+	1.38247i	−0.555123	+	0.0780175i
$315$	3.00786	−	28.6179i	0.169474	−	1.61244i
$316$	0.750773	+	7.14313i	0.0422343	+	0.401832i
$317$	−27.8143	+	17.3803i	−1.56221	+	0.976176i	−0.574743	+	0.818334i	$0.694898\pi$
$317$	−27.8143	+	17.3803i	−1.56221	+	0.976176i	−0.987464	+	0.157841i	$0.949546\pi$
$318$	−1.50049	−	0.546134i	−0.0841433	−	0.0306257i
$319$	28.2562	+	11.1135i	1.58204	+	0.622238i
$320$	−2.65140	+	2.22479i	−0.148218	+	0.124369i
$321$	−7.41637	−	1.04230i	−0.413941	−	0.0581757i
$322$	−25.8667	+	18.7932i	−1.44149	+	1.04731i
$323$	18.3446	+	3.04936i	1.02072	+	0.169671i
$324$	−0.315899	−	0.972238i	−0.0175500	−	0.0540132i
$325$	−24.9457	+	13.2639i	−1.38374	+	0.735748i
$326$	−10.6174	+	0.742438i	−0.588041	+	0.0411198i
$327$	0.451657	−	0.669608i	0.0249767	−	0.0370294i
$328$	−3.73229	+	4.77712i	−0.206081	+	0.263772i
$329$	−19.1730	−	16.0880i	−1.05704	−	0.886962i
$330$	0.121073	+	13.0976i	0.00666483	+	0.720997i
$331$	10.7985	+	18.7035i	0.593539	+	1.02804i	0.993751	+	0.111617i	$0.0356031\pi$
$331$	10.7985	+	18.7035i	0.593539	+	1.02804i	−0.400212	+	0.916422i	$0.631064\pi$
$332$	−7.61746	−	4.05028i	−0.418063	−	0.222288i
$333$	3.45200	+	7.07764i	0.189168	+	0.387852i
$334$	0.943162	−	8.97359i	0.0516076	−	0.491013i
$335$	18.6237	+	3.95858i	1.01752	+	0.216281i
$336$	−2.09272	+	5.17966i	−0.114167	+	0.282574i
$337$	−2.93370	−	4.34939i	−0.159809	−	0.236926i	0.740626	−	0.671918i	$-0.234529\pi$
$337$	−2.93370	−	4.34939i	−0.159809	−	0.236926i	−0.900435	+	0.434992i	$0.856751\pi$
$338$	1.89324	−	2.80684i	0.102979	−	0.152672i
$339$	0.964053	+	2.38611i	0.0523602	+	0.129596i
$340$	−2.56414	−	14.5419i	−0.139060	−	0.788647i
$341$	4.79702	−	11.0480i	0.259773	−	0.598283i
$342$	−2.10992	−	7.09467i	−0.114091	−	0.383636i
$343$	−15.0858	+	46.4293i	−0.814557	+	2.50695i
$344$	−4.27973	−	4.13289i	−0.230748	−	0.222830i
$345$	25.7272	−	1.79902i	1.38511	−	0.0968560i
$346$	−14.9475	−	19.1320i	−0.803584	−	1.02854i
$347$	−1.12011	+	32.0757i	−0.0601306	+	1.72191i	0.477414	+	0.878679i	$0.341574\pi$
$347$	−1.12011	+	32.0757i	−0.0601306	+	1.72191i	−0.537544	+	0.843236i	$0.680648\pi$
$348$	−2.52707	−	10.1355i	−0.135465	−	0.543322i
$349$	2.33612	+	22.2267i	0.125050	+	1.18977i	0.859511	+	0.511117i	$0.170768\pi$
$349$	2.33612	+	22.2267i	0.125050	+	1.18977i	−0.734462	+	0.678650i	$0.762565\pi$
$350$	33.4255	−	7.10481i	1.78667	−	0.379768i
$351$	3.76803	−	21.3696i	0.201123	−	1.14062i
$352$	−0.884677	+	3.19646i	−0.0471534	+	0.170372i
$353$	−4.47778	−	7.75574i	−0.238328	−	0.412796i	0.721907	−	0.691990i	$-0.243266\pi$
$353$	−4.47778	−	7.75574i	−0.238328	−	0.412796i	−0.960235	+	0.279194i	$0.909933\pi$
$354$	1.13768	+	1.26352i	0.0604669	+	0.0671553i
$355$	−4.75551	−	0.332538i	−0.252396	−	0.0176493i
$356$	0.267878	+	0.397145i	0.0141975	+	0.0210487i
$357$	−14.6733	−	18.7810i	−0.776593	−	0.993994i
$358$	5.45460	+	3.40841i	0.288285	+	0.180140i
$359$	−0.519933	+	1.06602i	−0.0274410	+	0.0562624i	−0.912074	−	0.410025i	$-0.865520\pi$
$359$	−0.519933	+	1.06602i	−0.0274410	+	0.0562624i	0.884633	+	0.466288i	$0.154409\pi$
$360$	−4.75485	+	3.45460i	−0.250603	+	0.182074i
$361$	4.95740	+	18.3419i	0.260916	+	0.965362i
$362$	−0.486257			−0.0255571
$363$	7.20969	+	10.2739i	0.378410	+	0.539239i
$364$	−15.1820	+	12.7392i	−0.795754	+	0.667717i
$365$	−0.212328	−	6.08027i	−0.0111137	−	0.318256i
$366$	5.91620	−	1.69644i	0.309245	−	0.0886744i
$367$	1.23674	+	4.96028i	0.0645571	+	0.258924i	0.993899	−	0.110297i	$-0.0351801\pi$
$367$	1.23674	+	4.96028i	0.0645571	+	0.258924i	−0.929342	+	0.369221i	$0.879625\pi$
$368$	6.38768	+	1.35774i	0.332981	+	0.0707773i
$369$	−6.88816	+	7.65008i	−0.358583	+	0.398247i
$370$	−11.5458	+	11.1497i	−0.600238	+	0.579643i
$371$	3.00360	+	6.15828i	0.155939	+	0.319722i
$372$	−4.05311	+	0.861516i	−0.210144	+	0.0446675i
$373$	−16.7033	+	28.9309i	−0.864864	+	1.49799i	0.00231886	+	0.999997i	$0.499262\pi$
$373$	−16.7033	+	28.9309i	−0.864864	+	1.49799i	−0.867183	+	0.497990i	$0.834071\pi$
$374$	−9.92285	−	10.0871i	−0.513098	−	0.521593i
$375$	−7.34637	−	2.67386i	−0.379365	−	0.138077i
$376$	0.178407	+	5.10890i	0.00920062	+	0.263471i
$377$	8.96515	−	35.9573i	0.461729	−	1.85189i
$378$	−11.5053	+	23.5894i	−0.591769	+	1.21331i
$379$	−9.46986	−	29.1452i	−0.486434	−	1.49709i	−0.829893	−	0.557922i	$-0.811599\pi$
$379$	−9.46986	−	29.1452i	−0.486434	−	1.49709i	0.343459	−	0.939168i	$-0.388401\pi$
$380$	12.4242	−	8.55876i	0.637346	−	0.439055i
$381$	−12.2049	−	8.86734i	−0.625274	−	0.454288i
$382$	7.77721	+	7.51037i	0.397917	+	0.384264i
$383$	−0.796160	−	1.97056i	−0.0406819	−	0.100691i	0.905475	−	0.424399i	$-0.139515\pi$
$383$	−0.796160	−	1.97056i	−0.0406819	−	0.100691i	−0.946157	+	0.323708i	$0.895070\pi$
$384$	1.07220	−	0.390251i	0.0547157	−	0.0199149i
$385$	38.6666	−	40.7884i	1.97063	−	2.07877i
$386$	1.21533	+	1.01979i	0.0618589	+	0.0519057i
$387$	−6.76008	−	7.50783i	−0.343634	−	0.381644i
$388$	2.02039	+	0.899534i	0.102570	+	0.0456669i
$389$	8.22397	−	7.94180i	0.416972	−	0.402665i	−0.456356	−	0.889797i	$-0.650846\pi$
$389$	8.22397	−	7.94180i	0.416972	−	0.402665i	0.873328	+	0.487132i	$0.161957\pi$
$390$	15.8306	−	2.22485i	0.801614	−	0.112659i
$391$	−18.6423	+	20.7044i	−0.942782	+	1.04707i
$392$	15.5039	−	6.90276i	0.783063	−	0.348642i
$393$	−19.7575	−	1.38158i	−0.996635	−	0.0696915i
$394$	−4.08561	+	5.22934i	−0.205830	+	0.263450i
$395$	−23.3604	+	8.50250i	−1.17539	+	0.427807i
$396$	−1.87722	+	5.30983i	−0.0943340	+	0.266829i
$397$	−3.84444	−	21.8029i	−0.192947	−	1.09426i	−0.915312	−	0.402745i	$-0.868056\pi$
$397$	−3.84444	−	21.8029i	−0.192947	−	1.09426i	0.722365	−	0.691512i	$-0.243055\pi$
$398$	−1.90278	+	5.85617i	−0.0953779	+	0.293543i
$399$	11.2205	−	21.6116i	0.561726	−	1.08193i
$400$	−5.64660	−	4.10250i	−0.282330	−	0.205125i
$401$	26.8223	−	14.2617i	1.33944	−	0.712194i	0.363783	−	0.931484i	$-0.381485\pi$
$401$	26.8223	−	14.2617i	1.33944	−	0.712194i	0.975660	+	0.219290i	$0.0703740\pi$
$402$	−5.32295	−	3.32615i	−0.265485	−	0.165893i
$403$	−14.1308	−	4.05193i	−0.703904	−	0.201841i
$404$	14.2745	−	4.09316i	0.710185	−	0.203642i
$405$	3.00060	−	1.87498i	0.149101	−	0.0931685i
$406$	−22.4112	+	38.8173i	−1.11225	+	1.92647i
$407$	−3.05855	+	15.0732i	−0.151607	+	0.747149i
$408$	−0.845302	+	4.79395i	−0.0418487	+	0.237336i
$409$	−34.2598	−	18.2163i	−1.69404	−	0.900736i	−0.979579	−	0.201059i	$-0.935562\pi$
$409$	−34.2598	−	18.2163i	−1.69404	−	0.900736i	−0.714459	−	0.699677i	$-0.753327\pi$
$410$	−19.1684	−	8.53430i	−0.946658	−	0.421479i
$411$	−12.5644	+	5.59405i	−0.619758	+	0.275934i
$412$	5.75541	−	14.2451i	0.283549	−	0.701808i
$413$	0.254612	−	7.29114i	0.0125287	−	0.358774i
$414$	10.6596	+	3.05658i	0.523889	+	0.150223i
$415$	7.22390	−	28.9735i	0.354607	−	1.42225i
$416$	4.00853	+	0.563362i	0.196534	+	0.0276211i
$417$	22.3445			1.09421
$418$	5.15923	−	13.5049i	0.252346	−	0.660546i
$419$	−6.05728			−0.295918			−0.147959	−	0.988994i	$-0.547270\pi$
$419$	−6.05728			−0.295918			−0.147959	+	0.988994i	$0.547270\pi$
$420$	−19.1474	−	2.69099i	−0.934296	−	0.131307i
$421$	6.98000	−	27.9953i	0.340185	−	1.36441i	−0.519888	−	0.854234i	$-0.674026\pi$
$421$	6.98000	−	27.9953i	0.340185	−	1.36441i	0.860073	−	0.510172i	$-0.170418\pi$
$422$	19.1754	+	5.49846i	0.933445	+	0.267661i
$423$	−0.302949	+	8.67532i	−0.0147299	+	0.421809i
$424$	0.524241	−	1.29754i	0.0254594	−	0.0630142i
$425$	27.2026	−	12.1114i	1.31952	−	0.587487i
$426$	1.43568	+	0.639205i	0.0695589	+	0.0309696i
$427$	−23.3178	−	12.3983i	−1.12843	−	0.599996i
$428$	1.13977	−	6.46395i	0.0550928	−	0.312447i
$429$	11.2887	−	10.3550i	0.545025	−	0.499942i
$430$	10.2961	−	17.8334i	0.496523	−	0.860002i
$431$	11.3088	−	7.06654i	0.544727	−	0.340383i	−0.229482	−	0.973313i	$-0.573703\pi$
$431$	11.3088	−	7.06654i	0.544727	−	0.340383i	0.774209	+	0.632930i	$0.218148\pi$
$432$	5.15293	−	1.47758i	0.247920	−	0.0710900i
$433$	−17.4853	−	5.01383i	−0.840291	−	0.240949i	−0.172230	−	0.985057i	$-0.555097\pi$
$433$	−17.4853	−	5.01383i	−0.840291	−	0.240949i	−0.668060	+	0.744107i	$0.732875\pi$
$434$	15.0785	+	9.42206i	0.723789	+	0.452273i
$435$	31.9226	−	16.9735i	1.53057	−	0.813819i
$436$	0.572681	+	0.416077i	0.0274264	+	0.0199265i
$437$	−27.1571	−	8.53020i	−1.29910	−	0.408055i
$438$	−0.619784	+	1.90750i	−0.0296144	+	0.0911439i
$439$	−2.17146	−	12.3150i	−0.103638	−	0.587762i	−0.991755	−	0.128145i	$-0.959098\pi$
$439$	−2.17146	−	12.3150i	−0.103638	−	0.587762i	0.888117	−	0.459617i	$-0.152013\pi$
$440$	−11.4756	−	0.294562i	−0.547076	−	0.0140427i
$441$	27.0803	−	9.85644i	1.28954	−	0.469354i
$442$	−10.6322	+	13.6086i	−0.505723	+	0.647296i
$443$	34.4135	+	2.40643i	1.63504	+	0.114333i	0.857493	−	0.514496i	$-0.172021\pi$
$443$	34.4135	+	2.40643i	1.63504	+	0.114333i	0.777544	+	0.628829i	$0.216465\pi$
$444$	4.83383	−	2.15216i	0.229404	−	0.102137i
$445$	−1.10945	+	1.23217i	−0.0525929	+	0.0584103i
$446$	−13.1609	+	1.84964i	−0.623185	+	0.0875829i
$447$	10.6843	−	10.3177i	0.505350	−	0.488011i
$448$	−4.47274	−	1.99139i	−0.211317	−	0.0940845i
$449$	−27.4260	−	30.4596i	−1.29431	−	1.43748i	−0.836043	−	0.548664i	$-0.815137\pi$
$449$	−27.4260	−	30.4596i	−1.29431	−	1.43748i	−0.458268	−	0.888814i	$-0.651530\pi$
$450$	−9.07909	−	7.61826i	−0.427992	−	0.359128i
$451$	−19.7676	+	3.67429i	−0.930822	+	0.173015i
$452$	−2.11943	+	0.771410i	−0.0996897	+	0.0362841i
$453$	2.74390	+	6.79140i	0.128920	+	0.319088i
$454$	0.415055	+	0.400814i	0.0194795	+	0.0188111i
$455$	−55.4951	−	40.3195i	−2.60165	−	1.89021i
$456$	−4.81380	+	1.25051i	−0.225427	+	0.0585605i
$457$	−11.0531	−	34.0181i	−0.517044	−	1.59130i	−0.779532	−	0.626363i	$-0.784543\pi$
$457$	−11.0531	−	34.0181i	−0.517044	−	1.59130i	0.262488	−	0.964935i	$-0.415457\pi$
$458$	−0.00354167	+	0.00726150i	−0.000165491	+	0.000339308i
$459$	−5.53270	+	22.1905i	−0.258245	+	1.03576i
$460$	0.788822	+	22.5889i	0.0367790	+	1.05321i
$461$	11.0137	+	4.00867i	0.512960	+	0.186702i	0.585514	−	0.810662i	$-0.300893\pi$
$461$	11.0137	+	4.00867i	0.512960	+	0.186702i	−0.0725539	+	0.997364i	$0.523115\pi$
$462$	−16.5772	+	8.27579i	−0.771241	+	0.385025i
$463$	0.128326	−	0.222267i	0.00596380	−	0.0103296i	−0.863028	−	0.505156i	$-0.831435\pi$
$463$	0.128326	−	0.222267i	0.00596380	−	0.0103296i	0.868992	+	0.494826i	$0.164768\pi$
$464$	8.95478	−	1.90340i	0.415715	−	0.0883630i
$465$	−6.28705	−	12.8904i	−0.291555	−	0.597776i
$466$	−1.49345	+	1.44221i	−0.0691828	+	0.0668091i
$467$	−22.5024	+	24.9915i	−1.04129	+	1.15647i	−0.0538365	+	0.998550i	$0.517145\pi$
$467$	−22.5024	+	24.9915i	−1.04129	+	1.15647i	−0.987452	+	0.157918i	$0.949522\pi$
$468$	6.72349	+	1.42912i	0.310794	+	0.0660612i
$469$	6.51567	+	26.1329i	0.300866	+	1.20671i
$470$	−17.0080	+	4.87698i	−0.784522	+	0.224958i
$471$	0.395560	+	11.3274i	0.0182265	+	0.521937i
$472$	−1.14149	+	0.957820i	−0.0525411	+	0.0440872i
$473$	−1.55835	−	19.6707i	−0.0716531	−	0.904460i
$474$	8.19532			0.376424
$475$	22.8076	+	20.1343i	1.04648	+	0.923827i
$476$	16.8986	−	12.2776i	0.774547	−	0.562741i
$477$	1.04173	−	2.13587i	0.0476977	−	0.0977947i
$478$	−12.6338	−	7.89450i	−0.577859	−	0.361086i
$479$	−10.3522	−	13.2502i	−0.473002	−	0.605415i	0.491049	−	0.871132i	$-0.336614\pi$
$479$	−10.3522	−	13.2502i	−0.473002	−	0.605415i	−0.964051	+	0.265717i	$0.914391\pi$
$480$	2.20838	+	3.27406i	0.100798	+	0.149440i
$481$	18.7259	+	1.30944i	0.853827	+	0.0597054i
$482$	−3.07448	−	3.41456i	−0.140039	−	0.155529i
$483$	18.2408	+	31.5940i	0.829986	+	1.43758i
$484$	−9.21918	+	6.00057i	−0.419053	+	0.272753i
$485$	−1.32922	+	7.53835i	−0.0603566	+	0.342299i
$486$	14.5894	−	3.10107i	0.661789	−	0.140668i
$487$	−2.86591	−	27.2673i	−0.129867	−	1.23560i	−0.844290	−	0.535887i	$-0.819977\pi$
$487$	−2.86591	−	27.2673i	−0.129867	−	1.23560i	0.714423	−	0.699714i	$-0.246689\pi$
$488$	1.30492	+	5.23375i	0.0590710	+	0.236921i
$489$	−0.423825	+	12.1368i	−0.0191660	+	0.548843i
$490$	36.1637	+	46.2874i	1.63371	+	2.09105i
$491$	−40.0474	+	2.80038i	−1.80731	+	0.126380i	−0.933203	−	0.359350i	$-0.882998\pi$
$491$	−40.0474	+	2.80038i	−1.80731	+	0.126380i	−0.874109	+	0.485730i	$0.838554\pi$
$492$	4.97576	+	4.80504i	0.224325	+	0.216628i
$493$	−12.0693	+	37.1456i	−0.543575	+	1.67295i
$494$	−17.1614	−	4.10039i	−0.772129	−	0.184485i
$495$	−19.4041	−	1.85828i	−0.872149	−	0.0835234i
$496$	−0.630613	−	3.57638i	−0.0283153	−	0.160584i
$497$	−2.52612	−	6.25238i	−0.113312	−	0.280457i
$498$	−5.50464	+	8.16096i	−0.246669	+	0.365702i
$499$	−5.54187	−	8.21615i	−0.248088	−	0.367806i	0.684339	−	0.729164i	$-0.260091\pi$
$499$	−5.54187	−	8.21615i	−0.248088	−	0.367806i	−0.932427	+	0.361358i	$0.882313\pi$
$500$	2.56667	−	6.35274i	0.114785	−	0.284103i
$501$	−10.0704	−	2.14054i	−0.449914	−	0.0956321i
$502$	0.171780	−	1.63438i	0.00766692	−	0.0729459i
$503$	−0.0154939	−	0.0317672i	−0.000690838	−	0.00141643i	0.898448	−	0.439079i	$-0.144695\pi$
$503$	−0.0154939	−	0.0317672i	−0.000690838	−	0.00141643i	−0.899139	+	0.437663i	$0.855806\pi$
$504$	−7.34070	−	3.90312i	−0.326981	−	0.173859i
$505$	25.6987	+	44.5115i	1.14358	+	1.98074i
$506$	12.8922	+	17.4039i	0.573127	+	0.773700i
$507$	−2.95930	−	2.48315i	−0.131427	−	0.110280i
$508$	8.14001	−	10.4187i	0.361155	−	0.462257i
$509$	−9.13243	+	13.5394i	−0.404788	+	0.600123i	−0.975224	−	0.221219i	$-0.928996\pi$
$509$	−9.13243	+	13.5394i	−0.404788	+	0.600123i	0.570436	+	0.821342i	$0.306774\pi$
$510$	−16.8075	+	1.17530i	−0.744249	+	0.0520430i
$511$	7.59880	−	4.04035i	0.336151	−	0.178735i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	−22.9704	+	4.28310i	−1.01417	+	0.189104i
$514$	2.33661	−	1.69765i	0.103064	−	0.0748801i
$515$	52.6592	+	7.40077i	2.32044	+	0.326117i
$516$	−5.20030	+	4.36357i	−0.228930	+	0.192095i
$517$	−10.7777	+	13.0882i	−0.474003	+	0.575617i
$518$	−21.3353	−	7.76542i	−0.937421	−	0.341193i
$519$	−23.4931	+	14.6801i	−1.03123	+	0.644385i
$520$	1.46449	+	13.9337i	0.0642223	+	0.611034i
$521$	−0.975754	+	9.28368i	−0.0427485	+	0.406725i	0.952134	+	0.305682i	$0.0988846\pi$
$521$	−0.975754	+	9.28368i	−0.0427485	+	0.406725i	−0.994882	+	0.101043i	$0.967782\pi$
$522$	15.3944	−	2.16354i	0.673794	−	0.0946955i
$523$	−35.7919	+	5.03023i	−1.56507	+	0.219956i	−0.867823	−	0.496873i	$-0.834481\pi$
$523$	−35.7919	+	5.03023i	−1.56507	+	0.219956i	−0.697248	+	0.716830i	$0.745592\pi$
$524$	1.81440	−	17.2629i	0.0792626	−	0.754134i
$525$	−4.07568	−	38.7775i	−0.177877	−	1.69239i
$526$	12.1503	−	7.59235i	0.529778	−	0.331042i
$527$	14.5589	+	5.29900i	0.634195	+	0.230828i
$528$	3.52172	+	1.38514i	0.153263	+	0.0602804i
$529$	15.0497	−	12.6282i	0.654333	−	0.549051i
$530$	4.79655	+	0.674112i	0.208349	+	0.0292815i
$531$	−2.04707	+	1.48728i	−0.0888353	+	0.0645426i
$532$	18.5859	+	10.4888i	0.805801	+	0.454746i
$533$	7.58313	+	23.3385i	0.328462	+	1.01090i
$534$	0.482616	−	0.256612i	0.0208848	−	0.0111047i
$535$	22.6625	−	1.58472i	0.979786	−	0.0685133i
$536$	3.07611	−	4.56052i	0.132868	−	0.196984i
$537$	4.51831	−	5.78318i	0.194980	−	0.249562i
$538$	6.54127	+	5.48878i	0.282014	+	0.236638i
$539$	53.6903	+	16.8980i	2.31261	+	0.727848i
$540$	9.27691	+	16.0681i	0.399215	+	0.691460i
$541$	8.10208	+	4.30795i	0.348336	+	0.185213i	0.634415	−	0.772993i	$-0.281241\pi$
$541$	8.10208	+	4.30795i	0.348336	+	0.185213i	−0.286080	+	0.958206i	$0.592352\pi$
$542$	5.48523	+	11.2464i	0.235611	+	0.483074i
$543$	−0.0579953	+	0.551788i	−0.00248882	+	0.0236795i
$544$	−4.17306	−	0.887011i	−0.178918	−	0.0380303i
$545$	−0.917807	+	2.27165i	−0.0393145	+	0.0973068i
$546$	12.6453	+	18.7474i	0.541169	+	0.802316i
$547$	19.2176	−	28.4913i	0.821687	−	1.21820i	−0.151562	−	0.988448i	$-0.548430\pi$
$547$	19.2176	−	28.4913i	0.821687	−	1.21820i	0.973249	−	0.229754i	$-0.0737920\pi$
$548$	−4.51541	−	11.1760i	−0.192889	−	0.477416i
$549$	1.59052	+	9.02026i	0.0678816	+	0.384975i
$550$	−5.02197	−	22.5974i	−0.214138	−	0.963554i
$551$	−39.6436	+	4.56042i	−1.68887	+	0.194280i
$552$	2.30257	−	7.08659i	0.0980039	−	0.301625i
$553$	−25.2960	−	24.4281i	−1.07570	−	1.03879i
$554$	7.11971	−	0.497859i	0.302488	−	0.0211520i
$555$	11.2752	+	14.4316i	0.478606	+	0.612587i
$556$	−0.683436	+	19.5711i	−0.0289841	+	0.829997i
$557$	0.234150	+	0.939125i	0.00992126	+	0.0397920i	0.975052	−	0.221975i	$-0.0712503\pi$
$557$	0.234150	+	0.939125i	0.00992126	+	0.0397920i	−0.965131	+	0.261767i	$0.915695\pi$
$558$	−0.644593	−	6.13289i	−0.0272878	−	0.259626i
$559$	−23.5569	+	5.00718i	−0.996352	+	0.211781i
$560$	2.94263	−	16.6885i	0.124349	−	0.705216i
$561$	−12.6300	+	10.0570i	−0.533239	+	0.424608i
$562$	−13.8975	−	24.0712i	−0.586230	−	1.01538i
$563$	−5.56024	−	6.17527i	−0.234336	−	0.260257i	0.614495	−	0.788921i	$-0.289360\pi$
$563$	−5.56024	−	6.17527i	−0.234336	−	0.260257i	−0.848831	+	0.528664i	$0.822693\pi$
$564$	5.81868	+	0.406882i	0.245011	+	0.0171328i
$565$	−4.36532	−	6.47186i	−0.183650	−	0.272273i
$566$	1.62396	+	2.07858i	0.0682603	+	0.0873692i
$567$	4.24454	+	2.65228i	0.178254	+	0.111385i
$568$	−0.603778	+	1.23793i	−0.0253340	+	0.0519423i
$569$	−13.9209	+	10.1141i	−0.583593	+	0.424005i	−0.840018	−	0.542559i	$-0.817456\pi$
$569$	−13.9209	+	10.1141i	−0.583593	+	0.424005i	0.256424	+	0.966564i	$0.417456\pi$
$570$	−8.23038	−	15.1193i	−0.344733	−	0.633278i
$571$	3.19934			0.133888			0.0669442	−	0.997757i	$-0.478675\pi$
$571$	3.19934			0.133888			0.0669442	+	0.997757i	$0.478675\pi$
$572$	8.72440	+	10.2043i	0.364785	+	0.426662i
$573$	9.45008	−	7.92956i	0.394783	−	0.331262i
$574$	−1.03585	−	29.6629i	−0.0432355	−	1.23810i
$575$	−43.8137	+	12.5634i	−1.82716	+	0.523929i
$576$	0.410803	+	1.64764i	0.0171168	+	0.0686517i
$577$	19.0287	+	4.04468i	0.792177	+	0.168382i	0.586191	−	0.810173i	$-0.300627\pi$
$577$	19.0287	+	4.04468i	0.792177	+	0.168382i	0.205986	+	0.978555i	$0.433960\pi$
$578$	0.803753	−	0.892658i	0.0334317	−	0.0371297i
$579$	1.30217	−	1.25749i	0.0541163	−	0.0522595i
$580$	13.8904	+	28.4795i	0.576766	+	1.18255i
$581$	41.3165	−	8.78210i	1.71410	−	0.364343i
$582$	1.26173	−	2.18538i	0.0523003	−	0.0905868i
$583$	4.15271	−	2.07314i	0.171988	−	0.0858609i
$584$	−1.65178	−	0.601199i	−0.0683511	−	0.0248778i
$585$	0.830292	+	23.7764i	0.0343283	+	0.983035i
$586$	4.14979	−	16.6439i	0.171426	−	0.687554i
$587$	−19.9230	+	40.8481i	−0.822308	+	1.68598i	−0.0993899	+	0.995049i	$0.531689\pi$
$587$	−19.9230	+	40.8481i	−0.822308	+	1.68598i	−0.722918	+	0.690933i	$0.757200\pi$
$588$	−5.98389	−	18.4165i	−0.246772	−	0.759485i
$589$	1.25911	+	15.7794i	0.0518806	+	0.650180i
$590$	−4.17249	−	3.03149i	−0.171779	−	0.124804i
$591$	5.44679	+	5.25991i	0.224051	+	0.216364i
$592$	1.73718	+	4.29967i	0.0713977	+	0.176716i
$593$	26.0608	−	9.48537i	1.07019	−	0.389517i	0.253942	−	0.967219i	$-0.418273\pi$
$593$	26.0608	−	9.48537i	1.07019	−	0.389517i	0.816248	+	0.577702i	$0.196050\pi$
$594$	16.0511	+	7.64578i	0.658583	+	0.313710i
$595$	55.3820	+	46.4710i	2.27044	+	1.90513i
$596$	8.71025	+	9.67372i	0.356786	+	0.396251i
$597$	6.41843	+	2.85767i	0.262689	+	0.116957i
$598$	19.0154	−	18.3629i	0.777597	−	0.750916i
$599$	21.9316	−	3.08228i	0.896100	−	0.125939i	0.323937	−	0.946079i	$-0.394993\pi$
$599$	21.9316	−	3.08228i	0.896100	−	0.125939i	0.572163	+	0.820140i	$0.306104\pi$
$600$	−5.32884	+	5.91827i	−0.217549	+	0.241612i
$601$	−12.9650	+	5.77238i	−0.528852	+	0.235460i	−0.653752	−	0.756709i	$-0.726806\pi$
$601$	−12.9650	+	5.77238i	−0.528852	+	0.235460i	0.124899	+	0.992169i	$0.460139\pi$
$602$	29.0581	+	2.03194i	1.18432	+	0.0828157i
$603$	5.75096	−	7.36090i	0.234197	−	0.299759i
$604$	−6.03236	+	2.19560i	−0.245453	+	0.0893377i
$605$	−27.8714	−	25.9367i	−1.13314	−	1.05448i
$606$	−2.94227	−	16.6864i	−0.119522	−	0.677841i
$607$	−9.47860	+	29.1721i	−0.384725	+	1.18406i	0.551955	+	0.833874i	$0.313882\pi$
$607$	−9.47860	+	29.1721i	−0.384725	+	1.18406i	−0.936680	+	0.350187i	$0.886118\pi$
$608$	−0.948058	−	4.25455i	−0.0384488	−	0.172545i
$609$	41.3756	+	30.0611i	1.67662	+	1.21814i
$610$	−16.4841	+	8.76475i	−0.667421	+	0.354874i
$611$	17.5487	+	10.9656i	0.709943	+	0.443622i
$612$	−6.96386	−	1.99686i	−0.281497	−	0.0807181i
$613$	−18.5470	+	5.31827i	−0.749107	+	0.214803i	−0.628406	−	0.777886i	$-0.716292\pi$
$613$	−18.5470	+	5.31827i	−0.749107	+	0.214803i	−0.120701	+	0.992689i	$0.538514\pi$
$614$	−20.9805	+	13.1101i	−0.846704	+	0.529079i
$615$	−11.9706	+	20.7337i	−0.482702	+	0.836064i
$616$	−6.74155	−	14.7727i	−0.271625	−	0.595210i
$617$	−2.28040	+	12.9328i	−0.0918055	+	0.520655i	0.903874	+	0.427799i	$0.140711\pi$
$617$	−2.28040	+	12.9328i	−0.0918055	+	0.520655i	−0.995680	+	0.0928560i	$0.970400\pi$
$618$	−15.4785	−	8.23004i	−0.622635	−	0.331061i
$619$	24.6592	+	10.9790i	0.991135	+	0.441282i	0.837258	−	0.546808i	$-0.184157\pi$
$619$	24.6592	+	10.9790i	0.991135	+	0.441282i	0.153877	+	0.988090i	$0.450824\pi$
$620$	11.4827	−	5.11242i	0.461156	−	0.205320i
$621$	13.1137	−	32.4577i	0.526236	−	1.30248i
$622$	−0.0860681	+	2.46467i	−0.00345102	+	0.0988242i
$623$	−2.25455	−	0.646483i	−0.0903268	−	0.0259008i
$624$	1.11737	−	4.48155i	0.0447308	−	0.179405i
$625$	−11.0745	−	1.55642i	−0.442979	−	0.0622567i
$626$	7.24618			0.289616
$627$	−14.7096	−	7.46523i	−0.587443	−	0.298132i
$628$	−9.93348			−0.396389
$629$	−19.5917	−	2.75344i	−0.781173	−	0.109787i
$630$	6.96143	−	27.9208i	0.277350	−	1.11239i
$631$	−2.97709	−	0.853666i	−0.118516	−	0.0339839i	0.215855	−	0.976425i	$-0.430746\pi$
$631$	−2.97709	−	0.853666i	−0.118516	−	0.0339839i	−0.334371	+	0.942441i	$0.608524\pi$
$632$	−0.250665	+	7.17810i	−0.00997091	+	0.285530i
$633$	8.52650	−	21.1038i	0.338898	−	0.838801i
$634$	−29.9625	+	13.3402i	−1.18996	+	0.529806i
$635$	41.8056	+	18.6130i	1.65900	+	0.738636i
$636$	−1.40988	−	0.749647i	−0.0559054	−	0.0297254i
$637$	11.9292	−	67.6539i	0.472653	−	2.68055i
$638$	26.4345	+	14.9379i	1.04655	+	0.591396i
$639$	−1.16940	+	2.02546i	−0.0462608	+	0.0801261i
$640$	−2.93522	+	1.83413i	−0.116025	+	0.0725004i
$641$	−3.68568	+	1.05685i	−0.145576	+	0.0417432i	−0.347634	−	0.937630i	$-0.613015\pi$
$641$	−3.68568	+	1.05685i	−0.145576	+	0.0417432i	0.202058	+	0.979374i	$0.435237\pi$
$642$	−7.19913	−	2.06432i	−0.284127	−	0.0814721i
$643$	−0.183580	−	0.114713i	−0.00723968	−	0.00452385i	0.526295	−	0.850302i	$-0.323581\pi$
$643$	−0.183580	−	0.114713i	−0.00723968	−	0.00452385i	−0.533534	+	0.845778i	$0.679136\pi$
$644$	−28.2304	+	15.0104i	−1.11244	+	0.591492i
$645$	−19.0087	−	13.8106i	−0.748467	−	0.543793i
$646$	17.7417	+	5.57276i	0.698037	+	0.219257i
$647$	13.8459	−	42.6134i	0.544340	−	1.67531i	−0.178214	−	0.983992i	$-0.557032\pi$
$647$	13.8459	−	42.6134i	0.544340	−	1.67531i	0.722554	−	0.691315i	$-0.242968\pi$
$648$	−0.177516	−	1.00674i	−0.00697347	−	0.0395485i
$649$	−4.94049	−	0.126815i	−0.193931	−	0.00497794i
$650$	−26.5490	+	9.66303i	−1.04134	+	0.379015i
$651$	12.4902	−	15.9868i	0.489530	−	0.626570i
$652$	−10.6174	−	0.742438i	−0.415808	−	0.0290761i
$653$	25.4969	−	11.3519i	0.997769	−	0.444235i	0.158152	−	0.987415i	$-0.449446\pi$
$653$	25.4969	−	11.3519i	0.997769	−	0.444235i	0.839617	+	0.543179i	$0.182780\pi$
$654$	0.540453	−	0.600233i	0.0211334	−	0.0234710i
$655$	59.4940	−	8.36134i	2.32462	−	0.326705i
$656$	−4.36082	+	4.21119i	−0.170261	+	0.164419i
$657$	−2.72681	−	1.21405i	−0.106383	−	0.0473648i
$658$	−16.7474	−	18.5998i	−0.652880	−	0.725097i
$659$	23.2534	+	19.5119i	0.905825	+	0.760077i	0.971320	−	0.237776i	$-0.0764183\pi$
$659$	23.2534	+	19.5119i	0.905825	+	0.760077i	−0.0654954	+	0.997853i	$0.520863\pi$
$660$	−1.70293	+	12.9869i	−0.0662866	+	0.505516i
$661$	−31.2526	+	11.3750i	−1.21559	+	0.442437i	−0.868638	−	0.495447i	$-0.835004\pi$
$661$	−31.2526	+	11.3750i	−1.21559	+	0.442437i	−0.346948	+	0.937884i	$0.612782\pi$
$662$	8.09038	+	20.0244i	0.314441	+	0.778270i
$663$	14.1745	+	13.6882i	0.550492	+	0.531604i
$664$	−6.97964	−	5.07101i	−0.270863	−	0.196793i
$665$	−19.6624	+	71.2004i	−0.762475	+	2.76103i
$666$	2.43338	+	7.48919i	0.0942917	+	0.290200i
$667$	26.2079	−	53.7341i	1.01477	−	2.08059i
$668$	2.18287	−	8.75500i	0.0844576	−	0.338741i
$669$	0.529228	+	15.1551i	0.0204611	+	0.585930i
$670$	17.8915	+	6.51197i	0.691209	+	0.251579i
$671$	−8.25238	+	15.8727i	−0.318580	+	0.612759i
$672$	−2.79322	+	4.83800i	−0.107751	+	0.186630i
$673$	26.6964	−	5.67449i	1.02907	−	0.218735i	0.337713	−	0.941249i	$-0.390347\pi$
$673$	26.6964	−	5.67449i	1.02907	−	0.218735i	0.691357	+	0.722514i	$0.257013\pi$
$674$	−2.29983	−	4.71535i	−0.0885861	−	0.181629i
$675$	−26.9139	+	25.9904i	−1.03592	+	1.00037i
$676$	2.26545	−	2.51604i	0.0871326	−	0.0967706i
$677$	10.9771	+	2.33326i	0.421885	+	0.0896745i	0.413962	−	0.910294i	$-0.364145\pi$
$677$	10.9771	+	2.33326i	0.421885	+	0.0896745i	0.00792320	+	0.999969i	$0.497478\pi$
$678$	0.622588	+	2.49706i	0.0239103	+	0.0958992i
$679$	−10.4085	+	2.98460i	−0.399443	+	0.114538i
$680$	−0.515335	−	14.7573i	−0.0197622	−	0.565916i
$681$	0.504333	−	0.423185i	0.0193261	−	0.0162165i
$682$	6.28792	−	10.2729i	0.240777	−	0.393369i
$683$	1.01586			0.0388708			0.0194354	−	0.999811i	$-0.493813\pi$
$683$	1.01586			0.0388708			0.0194354	+	0.999811i	$0.493813\pi$
$684$	−1.10200	−	7.31927i	−0.0421360	−	0.279859i
$685$	33.7520	−	24.5223i	1.28960	−	0.936948i
$686$	−21.4007	+	43.8780i	−0.817083	+	1.67527i
$687$	0.00781769	+	0.00488503i	0.000298263	+	0.000186376i
$688$	−3.66289	−	4.68829i	−0.139647	−	0.178739i
$689$	−3.16774	−	4.69637i	−0.120681	−	0.178917i
$690$	25.7272	+	1.79902i	0.979417	+	0.0684875i
$691$	5.08791	+	5.65069i	0.193553	+	0.214962i	0.832108	−	0.554614i	$-0.187134\pi$
$691$	5.08791	+	5.65069i	0.193553	+	0.214962i	−0.638555	+	0.769576i	$0.720467\pi$
$692$	−12.1394	−	21.0261i	−0.461471	−	0.799291i
$693$	−9.66995	−	25.8227i	−0.367331	−	0.980925i
$694$	−5.57328	+	31.6077i	−0.211559	+	1.19981i
$695$	−66.2986	+	14.0922i	−2.51485	+	0.534547i
$696$	−1.09189	−	10.3886i	−0.0413878	−	0.393779i
$697$	−6.25690	−	25.0950i	−0.236997	−	0.950542i
$698$	−0.779973	+	22.3355i	−0.0295224	+	0.845411i
$699$	1.45845	+	1.86673i	0.0551636	+	0.0706061i
$700$	34.0890	−	2.38373i	1.28844	−	0.0900967i
$701$	9.96326	+	9.62141i	0.376307	+	0.363396i	0.858628	−	0.512599i	$-0.171317\pi$
$701$	9.96326	+	9.62141i	0.376307	+	0.363396i	−0.482321	+	0.875995i	$0.660206\pi$
$702$	6.70543	−	20.6372i	0.253080	−	0.778901i
$703$	−5.76205	−	19.3751i	−0.217320	−	0.730745i
$704$	−1.32093	+	3.04223i	−0.0497844	+	0.114658i
$705$	3.50570	+	19.8818i	0.132032	+	0.748792i
$706$	−3.35481	−	8.30345i	−0.126260	−	0.312504i
$707$	−40.6561	+	60.2752i	−1.52903	+	2.26688i
$708$	0.950758	+	1.40956i	0.0357317	+	0.0529744i
$709$	−11.3225	+	28.0242i	−0.425225	+	1.05247i	0.550766	+	0.834660i	$0.314336\pi$
$709$	−11.3225	+	28.0242i	−0.425225	+	1.05247i	−0.975991	+	0.217810i	$0.930109\pi$
$710$	−4.66295	−	0.991140i	−0.174997	−	0.0371968i
$711$	−1.27487	+	12.1296i	−0.0478115	+	0.454896i
$712$	0.209999	+	0.430562i	0.00787004	+	0.0161360i
$713$	−20.9395	−	11.1337i	−0.784190	−	0.416961i
$714$	−11.9167	−	20.6403i	−0.445971	−	0.772444i
$715$	−26.9642	+	37.8438i	−1.00841	+	1.41528i
$716$	4.92716	+	4.13438i	0.184137	+	0.154509i
$717$	−10.4652	+	13.3949i	−0.390831	+	0.500241i
$718$	−0.663234	+	0.983285i	−0.0247517	+	0.0366959i
$719$	−36.4394	+	2.54809i	−1.35896	+	0.0950278i	−0.730553	−	0.682856i	$-0.760738\pi$
$719$	−36.4394	+	2.54809i	−1.35896	+	0.0950278i	−0.628408	+	0.777884i	$0.716293\pi$
$720$	−5.18937	+	2.75924i	−0.193396	+	0.102831i
$721$	23.2449	+	71.5403i	0.865684	+	2.66430i
$722$	2.35646	+	18.8533i	0.0876984	+	0.701647i
$723$	−4.24141	+	3.08157i	−0.157740	+	0.114605i
$724$	−0.481525	−	0.0676740i	−0.0178957	−	0.00251508i
$725$	−48.9479	+	41.0722i	−1.81788	+	1.52538i
$726$	5.70968	+	11.1773i	0.211906	+	0.414828i
$727$	15.8974	+	5.78616i	0.589600	+	0.214597i	0.619554	−	0.784954i	$-0.287314\pi$
$727$	15.8974	+	5.78616i	0.589600	+	0.214597i	−0.0299533	+	0.999551i	$0.509536\pi$
$728$	−16.8072	+	10.5023i	−0.622918	+	0.389242i
$729$	−2.09950	−	19.9754i	−0.0777593	−	0.739830i
$730$	0.635948	−	6.05064i	0.0235375	−	0.223944i
$731$	25.1354	−	3.53254i	0.929665	−	0.130656i
$732$	6.09472	−	0.856557i	0.225267	−	0.0316593i
$733$	1.10845	−	10.5462i	0.0409415	−	0.389533i	−0.954793	−	0.297271i	$-0.903924\pi$
$733$	1.10845	−	10.5462i	0.0409415	−	0.389533i	0.995735	−	0.0922619i	$-0.0294097\pi$
$734$	0.534363	+	5.08413i	0.0197237	+	0.187659i
$735$	56.8385	−	35.5167i	2.09652	−	1.31005i
$736$	6.13656	+	2.23352i	0.226196	+	0.0823288i
$737$	17.6612	−	4.57724i	0.650558	−	0.168605i
$738$	−7.88581	+	6.61698i	−0.290281	+	0.243575i
$739$	−9.22160	−	1.29601i	−0.339222	−	0.0476745i	−0.0324944	−	0.999472i	$-0.510345\pi$
$739$	−9.22160	−	1.29601i	−0.339222	−	0.0476745i	−0.306727	+	0.951797i	$0.599234\pi$
$740$	−12.9852	+	9.43429i	−0.477345	+	0.346811i
$741$	−6.69980	+	18.9851i	−0.246123	+	0.697437i
$742$	2.11730	+	6.51637i	0.0777284	+	0.239224i
$743$	−0.643936	+	0.342387i	−0.0236237	+	0.0125609i	−0.481241	−	0.876588i	$-0.659814\pi$
$743$	−0.643936	+	0.342387i	−0.0236237	+	0.0125609i	0.457618	+	0.889149i	$0.348703\pi$
$744$	−4.13357	+	0.289047i	−0.151544	+	0.0105970i
$745$	−25.1943	+	37.3521i	−0.923048	+	1.36848i
$746$	−20.5671	+	26.3247i	−0.753017	+	0.963817i
$747$	−11.2225	−	9.41676i	−0.410608	−	0.344541i
$748$	−8.42242	−	11.3700i	−0.307954	−	0.415727i
$749$	16.0680	+	27.8305i	0.587110	+	1.01690i
$750$	−6.90274	−	3.67025i	−0.252053	−	0.134019i
$751$	17.2923	+	35.4546i	0.631007	+	1.29376i	0.939506	+	0.342531i	$0.111284\pi$
$751$	17.2923	+	35.4546i	0.631007	+	1.29376i	−0.308500	+	0.951224i	$0.599827\pi$
$752$	−0.534351	+	5.08401i	−0.0194858	+	0.185395i
$753$	−1.83415	−	0.389860i	−0.0668401	−	0.0142073i
$754$	13.8822	−	34.3596i	0.505560	−	1.25130i
$755$	−12.4246	−	18.4203i	−0.452179	−	0.670383i
$756$	−14.6763	+	21.7586i	−0.533773	+	0.791352i
$757$	−12.8006	−	31.6827i	−0.465247	−	1.15153i	−0.959374	−	0.282137i	$-0.908957\pi$
$757$	−12.8006	−	31.6827i	−0.465247	−	1.15153i	0.494127	−	0.869390i	$-0.335488\pi$
$758$	−5.32147	−	30.1795i	−0.193284	−	1.09617i
$759$	21.2870	−	12.5538i	0.772670	−	0.455676i
$760$	13.4944	−	6.74636i	0.489493	−	0.244716i
$761$	−6.17731	+	19.0118i	−0.223927	+	0.689178i	0.774471	+	0.632609i	$0.218016\pi$
$761$	−6.17731	+	19.0118i	−0.223927	+	0.689178i	−0.998399	+	0.0565687i	$0.981984\pi$
$762$	−10.8520	−	10.4796i	−0.393126	−	0.379637i
$763$	−3.45732	+	0.241759i	−0.125163	+	0.00875227i
$764$	6.65628	+	8.51965i	0.240816	+	0.308230i
$765$	0.875082	−	25.0591i	0.0316386	−	0.906012i
$766$	−0.514162	−	2.06219i	−0.0185774	−	0.0745100i
$767$	0.630497	+	5.99878i	0.0227659	+	0.216603i
$768$	1.11608	−	0.237231i	0.0402731	−	0.00856032i
$769$	5.15244	−	29.2210i	0.185802	−	1.05373i	−0.739119	−	0.673575i	$-0.764758\pi$
$769$	5.15244	−	29.2210i	0.185802	−	1.05373i	0.924921	−	0.380160i	$-0.124131\pi$
$770$	43.9670	−	35.0101i	1.58446	−	1.26167i
$771$	−1.64775	−	2.85399i	−0.0593423	−	0.102784i
$772$	1.06158	+	1.17900i	0.0382071	+	0.0424333i
$773$	21.4109	+	1.49720i	0.770097	+	0.0538504i	0.449399	−	0.893331i	$-0.351638\pi$
$773$	21.4109	+	1.49720i	0.770097	+	0.0538504i	0.320698	+	0.947181i	$0.396083\pi$
$774$	−5.64940	−	8.37559i	−0.203064	−	0.301054i
$775$	15.6050	+	19.9735i	0.560548	+	0.717469i
$776$	1.87553	+	1.17196i	0.0673277	+	0.0420710i
$777$	−11.3566	+	23.2844i	−0.407415	+	0.835324i
$778$	9.24922	−	6.71995i	0.331601	−	0.240922i
$779$	20.6623	−	16.4722i	0.740305	−	0.590179i
$780$	15.9862			0.572397
$781$	−4.21943	+	1.75030i	−0.150983	+	0.0626307i
$782$	−21.3424	+	17.9084i	−0.763202	+	0.640402i
$783$	−1.71270	−	49.0454i	−0.0612070	−	1.75274i
$784$	16.3137	−	4.67786i	0.582630	−	0.167067i
$785$	−8.31759	−	33.3600i	−0.296868	−	1.19067i
$786$	−19.3730	−	4.11785i	−0.691010	−	0.146879i
$787$	3.99410	−	4.43589i	0.142374	−	0.158122i	−0.667740	−	0.744394i	$-0.732738\pi$
$787$	3.99410	−	4.43589i	0.142374	−	0.158122i	0.810114	+	0.586272i	$0.199405\pi$
$788$	−4.77363	+	4.60984i	−0.170054	+	0.164219i
$789$	−7.16639	−	14.6933i	−0.255130	−	0.523095i
$790$	−24.3164	+	5.16861i	−0.865139	+	0.183891i
$791$	5.52138	−	9.56331i	0.196318	−	0.340032i
$792$	−2.59794	+	4.99690i	−0.0923138	+	0.177557i
$793$	20.5176	+	7.46780i	0.728602	+	0.265189i
$794$	−0.772649	−	22.1258i	−0.0274203	−	0.785214i
$795$	1.33704	−	5.36256i	0.0474198	−	0.190191i
$796$	−2.69929	+	5.53436i	−0.0956737	+	0.196160i
$797$	−2.74040	−	8.43407i	−0.0970698	−	0.298750i	0.890718	−	0.454557i	$-0.150202\pi$
$797$	−2.74040	−	8.43407i	−0.0970698	−	0.298750i	−0.987788	+	0.155807i	$0.950202\pi$
$798$	14.1190	−	19.8397i	0.499808	−	0.702317i
$799$	−17.6441	−	12.8192i	−0.624203	−	0.453510i
$800$	−5.02069	−	4.84843i	−0.177508	−	0.171418i
$801$	0.304726	+	0.754223i	0.0107670	+	0.0266492i
$802$	28.5461	−	10.3899i	1.00800	−	0.366881i
$803$	−2.78445	−	5.12200i	−0.0982610	−	0.180751i
$804$	−4.80824	−	4.03459i	−0.169573	−	0.142289i
$805$	−74.0482	−	82.2389i	−2.60986	−	2.89854i
$806$	−13.4293	−	5.97913i	−0.473028	−	0.210606i
$807$	7.00864	−	6.76817i	0.246716	−	0.238251i
$808$	14.7053	−	2.06669i	0.517330	−	0.0727060i
$809$	27.5558	−	30.6038i	0.968809	−	1.07597i	−0.0282708	−	0.999600i	$-0.509000\pi$
$809$	27.5558	−	30.6038i	0.968809	−	1.07597i	0.997079	−	0.0763708i	$-0.0243333\pi$
$810$	3.23234	−	1.43913i	0.113573	−	0.0505659i
$811$	−35.6890	−	2.49562i	−1.25321	−	0.0876329i	−0.572327	−	0.820026i	$-0.693959\pi$
$811$	−35.6890	−	2.49562i	−1.25321	−	0.0876329i	−0.680882	+	0.732393i	$0.738404\pi$
$812$	−27.5954	+	35.3205i	−0.968408	+	1.23951i
$813$	13.4162	−	4.88311i	0.470528	−	0.171258i
$814$	−5.12657	+	14.5008i	−0.179686	+	0.508253i
$815$	−6.39686	−	36.2784i	−0.224072	−	1.27078i
$816$	−1.50426	+	4.62965i	−0.0526598	+	0.162070i
$817$	13.9577	+	21.8569i	0.488319	+	0.764674i
$818$	−31.3912	−	22.8070i	−1.09757	−	0.797429i
$819$	−29.7146	+	15.7995i	−1.03831	+	0.552080i
$820$	−17.7941	−	11.1190i	−0.621396	−	0.388291i
$821$	41.3505	+	11.8571i	1.44314	+	0.413814i	0.903685	−	0.428198i	$-0.140852\pi$
$821$	41.3505	+	11.8571i	1.44314	+	0.413814i	0.539458	+	0.842013i	$0.318629\pi$
$822$	−13.2207	+	3.79098i	−0.461125	+	0.132226i
$823$	−7.26435	+	4.53927i	−0.253219	+	0.158229i	−0.650590	−	0.759429i	$-0.725478\pi$
$823$	−7.26435	+	4.53927i	−0.253219	+	0.158229i	0.397371	+	0.917658i	$0.369923\pi$
$824$	7.68194	−	13.3055i	0.267613	−	0.463519i
$825$	−26.2417	+	3.00360i	−0.913617	+	0.104572i
$826$	1.26687	−	7.18475i	0.0440799	−	0.249989i
$827$	26.1966	+	13.9290i	0.910946	+	0.484359i	0.857658	−	0.514220i	$-0.171919\pi$
$827$	26.1966	+	13.9290i	0.910946	+	0.484359i	0.0532884	+	0.998579i	$0.483030\pi$
$828$	10.1304	+	4.51036i	0.352057	+	0.156746i
$829$	−40.3416	+	17.9612i	−1.40112	+	0.623819i	−0.961610	−	0.274419i	$-0.911514\pi$
$829$	−40.3416	+	17.9612i	−1.40112	+	0.623819i	−0.439510	+	0.898238i	$0.644848\pi$
$830$	11.1859	−	27.6861i	0.388269	−	0.960999i
$831$	0.284206	−	8.13859i	0.00985899	−	0.282324i
$832$	3.89111	+	1.11576i	0.134900	+	0.0386820i
$833$	−17.5160	+	70.2528i	−0.606893	+	2.43412i
$834$	22.1270	+	3.10975i	0.766197	+	0.107682i
$835$	31.2301			1.08076
$836$	6.98854	−	12.6554i	0.241704	−	0.437698i
$837$	−19.4673			−0.672887
$838$	−5.99833	−	0.843011i	−0.207209	−	0.0291213i
$839$	9.29038	−	37.2617i	0.320739	−	1.28642i	−0.566100	−	0.824337i	$-0.691548\pi$
$839$	9.29038	−	37.2617i	0.320739	−	1.28642i	0.886839	−	0.462079i	$-0.152896\pi$
$840$	−18.5865	−	5.32960i	−0.641296	−	0.183889i
$841$	1.91288	−	54.7777i	0.0659613	−	1.88888i
$842$	10.8083	−	26.7514i	0.372477	−	0.921914i
$843$	−28.9727	+	12.8995i	−0.997871	+	0.444281i
$844$	18.2236	+	8.11366i	0.627281	+	0.279284i
$845$	10.3466	+	5.50140i	0.355935	+	0.189254i
$846$	−1.50737	+	8.54873i	−0.0518245	+	0.293912i
$847$	15.6928	−	51.5193i	0.539211	−	1.77022i
$848$	0.699722	−	1.21195i	0.0240286	−	0.0416187i
$849$	2.55239	−	1.59491i	0.0875978	−	0.0547372i
$850$	28.6234	−	8.20763i	0.981774	−	0.281519i
$851$	29.1105	+	8.34731i	0.997896	+	0.286142i
$852$	1.33275	+	0.832793i	0.0456592	+	0.0285310i
$853$	44.5040	−	23.6632i	1.52379	−	0.810213i	0.524635	−	0.851327i	$-0.324202\pi$
$853$	44.5040	−	23.6632i	1.52379	−	0.810213i	0.999154	+	0.0411140i	$0.0130907\pi$
$854$	−21.3654	−	15.5229i	−0.731108	−	0.531181i
$855$	23.6579	−	9.82953i	0.809083	−	0.336163i
$856$	2.02829	−	6.24242i	0.0693254	−	0.213362i
$857$	1.35707	+	7.69631i	0.0463566	+	0.262901i	0.999174	−	0.0406438i	$-0.0129409\pi$
$857$	1.35707	+	7.69631i	0.0463566	+	0.262901i	−0.952817	+	0.303545i	$0.901830\pi$
$858$	12.6200	−	8.68310i	0.430840	−	0.296436i
$859$	−16.6011	+	6.04229i	−0.566421	+	0.206160i	−0.609327	−	0.792919i	$-0.708560\pi$
$859$	−16.6011	+	6.04229i	−0.566421	+	0.206160i	0.0429066	+	0.999079i	$0.486338\pi$
$860$	12.6778	−	16.2269i	0.432311	−	0.553332i
$861$	−33.7839	−	2.36240i	−1.15135	−	0.0805105i
$862$	12.1822	−	5.42388i	0.414929	−	0.184738i
$863$	−6.89156	+	7.65385i	−0.234591	+	0.260540i	−0.848934	−	0.528500i	$-0.822755\pi$
$863$	−6.89156	+	7.65385i	−0.234591	+	0.260540i	0.614342	+	0.789040i	$0.289421\pi$
$864$	5.30842	−	0.746050i	0.180596	−	0.0253811i
$865$	60.4481	−	58.3740i	2.05530	−	1.98478i
$866$	−16.6174	−	7.39853i	−0.564681	−	0.251412i
$867$	−0.917095	−	1.01854i	−0.0311462	−	0.0345913i
$868$	13.6204	+	11.4289i	0.462307	+	0.387922i
$869$	−16.3888	+	17.2880i	−0.555951	+	0.586457i
$870$	33.9742	−	12.3656i	1.15183	−	0.419233i
$871$	−8.34156	−	20.6461i	−0.282643	−	0.699566i
$872$	0.509201	+	0.491729i	0.0172437	+	0.0166521i
$873$	3.03823	+	2.20740i	0.102828	+	0.0747093i
$874$	−25.7056	−	12.2267i	−0.869506	−	0.413575i
$875$	10.3662	+	31.9040i	0.350443	+	1.07855i
$876$	−0.879225	+	1.80268i	−0.0297063	+	0.0609069i
$877$	0.880035	−	3.52963i	0.0297167	−	0.119187i	−0.953606	−	0.301059i	$-0.902660\pi$
$877$	0.880035	−	3.52963i	0.0297167	−	0.119187i	0.983322	+	0.181872i	$0.0582155\pi$
$878$	−0.436417	−	12.4973i	−0.0147283	−	0.421765i
$879$	−18.3920	−	6.69414i	−0.620347	−	0.225788i
$880$	−11.3229	−	1.88879i	−0.381695	−	0.0636709i
$881$	−6.29084	+	10.8961i	−0.211944	+	0.367098i	−0.952323	−	0.305092i	$-0.901313\pi$
$881$	−6.29084	+	10.8961i	−0.211944	+	0.367098i	0.740379	+	0.672190i	$0.234646\pi$
$882$	28.1885	−	5.99166i	0.949158	−	0.201750i
$883$	−1.94216	−	3.98202i	−0.0653589	−	0.134006i	0.863614	−	0.504154i	$-0.168196\pi$
$883$	−1.94216	−	3.98202i	−0.0653589	−	0.134006i	−0.928973	+	0.370149i	$0.879307\pi$
$884$	−12.4227	+	11.9965i	−0.417821	+	0.403485i
$885$	−3.93768	+	4.37323i	−0.132364	+	0.147005i
$886$	33.7437	+	7.17245i	1.13364	+	0.240963i
$887$	12.1790	+	48.8474i	0.408932	+	1.64014i	0.723082	+	0.690762i	$0.242725\pi$
$887$	12.1790	+	48.8474i	0.408932	+	1.64014i	−0.314150	+	0.949373i	$0.601720\pi$
$888$	5.08631	−	1.45848i	0.170686	−	0.0489433i
$889$	2.25916	+	64.6937i	0.0757696	+	2.16976i
$890$	−1.27014	+	1.06577i	−0.0425750	+	0.0357247i
$891$	1.77003	−	2.89178i	0.0592983	−	0.0968784i
$892$	−13.2902			−0.444989
$893$	4.41875	−	21.8402i	0.147868	−	0.730855i
$894$	12.0163	−	8.73033i	0.401884	−	0.291986i
$895$	−9.75900	+	20.0089i	−0.326207	+	0.668824i
$896$	−4.15207	−	2.59450i	−0.138711	−	0.0866761i
$897$	−18.5697	−	23.7681i	−0.620024	−	0.793594i
$898$	−22.9199	−	33.9801i	−0.764847	−	1.13393i
$899$	−33.1653	−	2.31914i	−1.10612	−	0.0773478i
$900$	−7.93047	−	8.80768i	−0.264349	−	0.293589i
$901$	2.98521	+	5.17054i	0.0994519	+	0.172256i
$902$	−20.0866	+	0.887405i	−0.668811	+	0.0295474i
$903$	5.77149	−	32.7318i	0.192063	−	1.08925i
$904$	−2.20617	+	0.468935i	−0.0733760	+	0.0155965i
$905$	−0.175923	−	1.67379i	−0.00584787	−	0.0556387i
$906$	1.77202	+	7.10718i	0.0588714	+	0.236120i
$907$	0.644016	−	18.4422i	0.0213842	−	0.612363i	−0.940641	−	0.339403i	$-0.889775\pi$
$907$	0.644016	−	18.4422i	0.0213842	−	0.612363i	0.962025	−	0.272960i	$-0.0880027\pi$
$908$	0.355233	+	0.454677i	0.0117888	+	0.0150890i
$909$	25.1548	−	1.75899i	0.834330	−	0.0583421i
$910$	−49.3436	−	47.6506i	−1.63572	−	1.57960i
$911$	−12.5049	+	38.4863i	−0.414307	+	1.27511i	0.498562	+	0.866854i	$0.333862\pi$
$911$	−12.5049	+	38.4863i	−0.414307	+	1.27511i	−0.912869	+	0.408252i	$0.866138\pi$
$912$	−4.94099	+	0.568390i	−0.163613	+	0.0188213i
$913$	−6.20755	−	27.9321i	−0.205440	−	0.924417i
$914$	−6.21117	−	35.2253i	−0.205447	−	1.16515i
$915$	7.97990	+	19.7509i	0.263807	+	0.652946i
$916$	−0.00451781	+	0.00669793i	−0.000149273	+	0.000221306i
$917$	47.5231	+	70.4559i	1.56935	+	2.32666i
$918$	−8.56718	+	21.2045i	−0.282759	+	0.699853i
$919$	11.8328	+	2.51514i	0.390328	+	0.0829667i	0.398895	−	0.916997i	$-0.369394\pi$
$919$	11.8328	+	2.51514i	0.390328	+	0.0829667i	−0.00856741	+	0.999963i	$0.502727\pi$
$920$	−2.36262	+	22.4789i	−0.0778934	+	0.741106i
$921$	12.3745	+	25.3716i	0.407755	+	0.836021i
$922$	10.3486	+	5.50247i	0.340814	+	0.181214i
$923$	2.78764	+	4.82834i	0.0917564	+	0.158927i
$924$	−17.5676	+	5.88815i	−0.577933	+	0.193706i
$925$	−24.7944	−	20.8050i	−0.815234	−	0.684063i
$926$	0.158010	−	0.202244i	0.00519255	−	0.00664616i
$927$	14.5889	−	21.6289i	0.479161	−	0.710385i
$928$	9.13254	−	0.638609i	0.299790	−	0.0209634i
$929$	9.79360	−	5.20735i	0.321318	−	0.170848i	−0.300976	−	0.953632i	$-0.597312\pi$
$929$	9.79360	−	5.20735i	0.321318	−	0.170848i	0.622293	+	0.782784i	$0.286201\pi$
$930$	−4.43187	−	13.6399i	−0.145327	−	0.447270i
$931$	−72.7218	+	13.5599i	−2.38336	+	0.444407i
$932$	−1.67963	+	1.22033i	−0.0550182	+	0.0399731i
$933$	2.78655	+	0.391625i	0.0912277	+	0.0128212i
$934$	−25.7616	+	21.6165i	−0.842945	+	0.707315i
$935$	31.1319	−	37.8058i	1.01812	−	1.23638i
$936$	6.45917	+	2.35094i	0.211124	+	0.0768430i
$937$	32.3880	−	20.2383i	1.05807	−	0.661155i	0.114870	−	0.993381i	$-0.463355\pi$
$937$	32.3880	−	20.2383i	1.05807	−	0.661155i	0.943200	+	0.332225i	$0.107799\pi$
$938$	2.81526	+	26.7854i	0.0919215	+	0.874575i
$939$	0.864242	−	8.22272i	0.0282035	−	0.268338i
$940$	−17.5213	+	2.46245i	−0.571481	+	0.0803163i
$941$	49.6456	−	6.97723i	1.61840	−	0.227451i	0.728977	−	0.684538i	$-0.239996\pi$
$941$	49.6456	−	6.97723i	1.61840	−	0.227451i	0.889422	+	0.457087i	$0.151107\pi$
$942$	−1.18475	+	11.2722i	−0.0386014	+	0.367267i
$943$	4.13816	+	39.3720i	0.134757	+	1.28213i
$944$	−1.26368	+	0.789635i	−0.0411293	+	0.0257004i
$945$	−85.3617	−	31.0691i	−2.77682	−	1.01068i
$946$	1.19445	−	19.6962i	0.0388349	−	0.640377i
$947$	3.43641	−	2.88349i	0.111668	−	0.0937008i	−0.585244	−	0.810857i	$-0.699001\pi$
$947$	3.43641	−	2.88349i	0.111668	−	0.0937008i	0.696912	+	0.717157i	$0.254557\pi$
$948$	8.11557	+	1.14057i	0.263581	+	0.0370439i
$949$	−5.75647	+	4.18232i	−0.186863	+	0.135764i
$950$	19.7835	+	23.1126i	0.641860	+	0.749872i
$951$	11.5644	+	35.5915i	0.375000	+	1.15413i
$952$	18.4429	−	9.80625i	0.597737	−	0.317822i
$953$	−11.7183	+	0.819423i	−0.379593	+	0.0265437i	−0.258279	−	0.966070i	$-0.583155\pi$
$953$	−11.7183	+	0.819423i	−0.379593	+	0.0265437i	−0.121314	+	0.992614i	$0.538711\pi$
$954$	1.32885	−	1.97010i	0.0430231	−	0.0637844i
$955$	−23.0384	+	29.4878i	−0.745506	+	0.954204i
$956$	−11.4122	−	9.57596i	−0.369097	−	0.309709i
$957$	20.1038	−	28.2153i	0.649863	−	0.912072i
$958$	−8.40735	−	14.5620i	−0.271629	−	0.470475i
$959$	52.1075	+	27.7060i	1.68264	+	0.894675i
$960$	1.73123	+	3.54955i	0.0558752	+	0.114561i
$961$	1.86184	−	17.7142i	0.0600594	−	0.571427i
$962$	18.3614	+	3.90284i	0.591996	+	0.125833i
$963$	4.17523	−	10.3341i	0.134545	−	0.333011i
$964$	−2.56935	−	3.80921i	−0.0827531	−	0.122686i
$965$	−3.07061	+	4.55236i	−0.0988463	+	0.146546i
$966$	13.6663	+	33.8252i	0.439705	+	1.08831i
$967$	2.34400	+	13.2935i	0.0753780	+	0.427490i	0.999021	+	0.0442361i	$0.0140854\pi$
$967$	2.34400	+	13.2935i	0.0753780	+	0.427490i	−0.923643	+	0.383254i	$0.874803\pi$
$968$	−9.96457	+	4.65911i	−0.320274	+	0.149749i
$969$	8.43980	−	19.4680i	0.271125	−	0.625402i
$970$	−2.36542	+	7.28000i	−0.0759489	+	0.233747i
$971$	2.36030	+	2.27932i	0.0757458	+	0.0731468i	0.731568	−	0.681769i	$-0.238789\pi$
$971$	2.36030	+	2.27932i	0.0757458	+	0.0731468i	−0.655822	+	0.754916i	$0.727678\pi$
$972$	14.8790	−	1.04044i	0.477244	−	0.0333722i
$973$	−59.0289	−	75.5535i	−1.89238	−	2.42214i
$974$	0.956858	−	27.4008i	0.0306597	−	0.877979i
$975$	7.79881	+	31.2793i	0.249762	+	1.00174i
$976$	0.563824	+	5.36443i	0.0180476	+	0.171711i
$977$	−14.1473	+	3.00710i	−0.452611	+	0.0962055i	−0.428576	−	0.903506i	$-0.640985\pi$
$977$	−14.1473	+	3.00710i	−0.452611	+	0.0962055i	−0.0240351	+	0.999711i	$0.507651\pi$
$978$	−2.10881	+	11.9597i	−0.0674323	+	0.382428i
$979$	−0.423799	+	1.53124i	−0.0135447	+	0.0489388i
$980$	29.3698	+	50.8699i	0.938183	+	1.62498i
$981$	0.804312	+	0.893279i	0.0256797	+	0.0285202i
$982$	−40.0474	−	2.80038i	−1.27796	−	0.0893638i
$983$	−16.5733	−	24.5710i	−0.528607	−	0.783692i	0.466285	−	0.884634i	$-0.345592\pi$
$983$	−16.5733	−	24.5710i	−0.528607	−	0.783692i	−0.994892	+	0.100942i	$0.967814\pi$
$984$	4.25861	+	5.45077i	0.135759	+	0.173764i
$985$	−19.4785	−	12.1715i	−0.620638	−	0.387818i
$986$	−17.1215	+	35.1043i	−0.545260	+	1.11795i
$987$	−23.1039	+	16.7860i	−0.735405	+	0.534303i
$988$	−16.4237	−	6.44889i	−0.522509	−	0.205167i
$989$	−38.8527			−1.23544
$990$	−18.9566	−	4.54072i	−0.602481	−	0.144314i
$991$	−35.6429	+	29.9080i	−1.13224	+	0.950058i	−0.999157	−	0.0410472i	$-0.986931\pi$
$991$	−35.6429	+	29.9080i	−1.13224	+	0.950058i	−0.133078	+	0.991106i	$0.542486\pi$
$992$	−0.126739	−	3.62934i	−0.00402398	−	0.115232i
$993$	23.6879	−	6.79240i	0.751713	−	0.215550i
$994$	−1.63138	−	6.54310i	−0.0517441	−	0.207534i
$995$	−20.8465	−	4.43105i	−0.660877	−	0.140474i
$996$	−6.58686	+	7.31544i	−0.208713	+	0.231799i
$997$	10.6845	−	10.3179i	0.338380	−	0.326770i	−0.505981	−	0.862545i	$-0.668869\pi$
$997$	10.6845	−	10.3179i	0.338380	−	0.326770i	0.844361	+	0.535775i	$0.179980\pi$
$998$	−4.34447	−	8.90747i	−0.137522	−	0.281961i
$999$	24.3157	−	5.16846i	0.769314	−	0.163523i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	418.2.u.b.9.8	✓	264
11.5	even	5	inner	418.2.u.b.313.8	yes	264
19.17	even	9	inner	418.2.u.b.207.8	yes	264
209.93	even	45	inner	418.2.u.b.93.8	yes	264

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.u.b.9.8	✓	264	1.1	even	1	trivial
418.2.u.b.93.8	yes	264	209.93	even	45	inner
418.2.u.b.207.8	yes	264	19.17	even	9	inner
418.2.u.b.313.8	yes	264	11.5	even	5	inner

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:	\( N \)	\(=\)	\( 418 = 2 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	418.u (of order \(45\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(0.990268 + 0.139173i) q^{2} +(0.276037 - 1.10712i) q^{3} +(0.961262 + 0.275637i) q^{4} +(-0.120793 + 3.45905i) q^{5} +(0.427432 - 1.05793i) q^{6} +(-4.47274 + 1.99139i) q^{7} +(0.913545 + 0.406737i) q^{8} +(1.49932 + 0.797201i) q^{9} +O(q^{10})\)	\(q+(0.990268 + 0.139173i) q^{2} +(0.276037 - 1.10712i) q^{3} +(0.961262 + 0.275637i) q^{4} +(-0.120793 + 3.45905i) q^{5} +(0.427432 - 1.05793i) q^{6} +(-4.47274 + 1.99139i) q^{7} +(0.913545 + 0.406737i) q^{8} +(1.49932 + 0.797201i) q^{9} +(-0.601023 + 3.40857i) q^{10} +(1.37694 + 3.01729i) q^{11} +(0.570508 - 0.988149i) q^{12} +(3.43283 - 2.14507i) q^{13} +(-4.70636 + 1.34953i) q^{14} +(3.79625 + 1.08856i) q^{15} +(0.848048 + 0.529919i) q^{16} +(-3.76691 + 2.00290i) q^{17} +(1.37378 + 0.998108i) q^{18} +(-3.46103 - 2.64977i) q^{19} +(-1.06956 + 3.29175i) q^{20} +(0.970076 + 5.50158i) q^{21} +(0.943616 + 3.17956i) q^{22} +(6.13656 - 2.23352i) q^{23} +(0.702480 - 0.899133i) q^{24} +(-6.96258 - 0.486871i) q^{25} +(3.69796 - 1.64644i) q^{26} +(3.58693 - 3.98369i) q^{27} +(-4.84838 + 0.681395i) q^{28} +(6.58544 - 6.35948i) q^{29} +(3.60780 + 1.60630i) q^{30} +(-2.42998 - 2.69877i) q^{31} +(0.766044 + 0.642788i) q^{32} +(3.72060 - 0.691562i) q^{33} +(-4.00900 + 1.45916i) q^{34} +(-6.34805 - 15.7120i) q^{35} +(1.22150 + 1.17959i) q^{36} +(3.75169 + 2.72576i) q^{37} +(-3.05857 - 3.10567i) q^{38} +(-1.42727 - 4.39269i) q^{39} +(-1.51727 + 3.11086i) q^{40} +(-1.46659 + 5.88218i) q^{41} +(0.194964 + 5.58304i) q^{42} +(-5.59073 - 2.03486i) q^{43} +(0.491924 + 3.27994i) q^{44} +(-2.93866 + 5.08991i) q^{45} +(6.38768 - 1.35774i) q^{46} +(2.24096 + 4.59464i) q^{47} +(0.820778 - 0.792616i) q^{48} +(11.3559 - 12.6120i) q^{49} +(-6.82706 - 1.45114i) q^{50} +(1.17765 + 4.72330i) q^{51} +(3.89111 - 1.11576i) q^{52} +(-0.0488399 - 1.39859i) q^{53} +(4.10645 - 3.44572i) q^{54} +(-10.6033 + 4.39844i) q^{55} -4.89603 q^{56} +(-3.88900 + 3.10035i) q^{57} +(7.40642 - 5.38108i) q^{58} +(-0.653218 + 1.33930i) q^{59} +(3.34914 + 2.09277i) q^{60} +(3.32086 + 4.25051i) q^{61} +(-2.03074 - 3.01069i) q^{62} +(-8.29360 - 0.579945i) q^{63} +(0.669131 + 0.743145i) q^{64} +(7.00524 + 12.1334i) q^{65} +(3.78063 - 0.167024i) q^{66} +(0.955235 - 5.41741i) q^{67} +(-4.17306 + 0.887011i) q^{68} +(-0.778870 - 7.41046i) q^{69} +(-4.09959 - 16.4425i) q^{70} +(-0.0480678 + 1.37648i) q^{71} +(1.04544 + 1.33811i) q^{72} +(-1.75351 + 0.122617i) q^{73} +(3.33583 + 3.22137i) q^{74} +(-2.46096 + 7.57404i) q^{75} +(-2.59658 - 3.50111i) q^{76} +(-12.1673 - 10.7535i) q^{77} +(-0.802036 - 4.54857i) q^{78} +(2.69060 + 6.65948i) q^{79} +(-1.93545 + 2.86943i) q^{80} +(-0.571647 - 0.847501i) q^{81} +(-2.27096 + 5.62082i) q^{82} +(-8.43878 - 1.79372i) q^{83} +(-0.583943 + 5.55584i) q^{84} +(-6.47311 - 13.2718i) q^{85} +(-5.25312 - 2.79313i) q^{86} +(-5.22291 - 9.04634i) q^{87} +(0.0306572 + 3.31648i) q^{88} +(0.366969 + 0.307923i) q^{89} +(-3.61844 + 4.63139i) q^{90} +(-11.0825 + 16.4305i) q^{91} +(6.51448 - 0.455537i) q^{92} +(-3.65864 + 1.94533i) q^{93} +(1.57970 + 4.86181i) q^{94} +(9.58375 - 11.6518i) q^{95} +(0.923101 - 0.670672i) q^{96} +(2.19006 + 0.307794i) q^{97} +(13.0006 - 10.9088i) q^{98} +(-0.340913 + 5.62157i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9}+O(q^{10}) \) 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9	\( 264 q + 6 q^{3} - 9 q^{6} - 15 q^{7} + 33 q^{8} + 6 q^{9} + 3 q^{11} - 6 q^{13} + 18 q^{14} - 39 q^{15} - 3 q^{17} - 78 q^{18} - 45 q^{19} - 24 q^{20} + 48 q^{21} + 6 q^{23} - 9 q^{24} + 30 q^{25} + 18 q^{26} - 24 q^{27} + 6 q^{28} - 3 q^{31} - 63 q^{33} - 36 q^{34} + 42 q^{35} - 9 q^{36} + 60 q^{37} - 3 q^{38} + 36 q^{39} + 39 q^{41} + 6 q^{42} - 60 q^{43} + 60 q^{44} - 108 q^{45} - 12 q^{46} - 24 q^{47} - 12 q^{48} + 6 q^{49} + 18 q^{50} + 96 q^{51} + 3 q^{52} - 117 q^{53} + 54 q^{54} + 102 q^{55} - 96 q^{57} - 60 q^{58} - 141 q^{59} + 36 q^{60} + 24 q^{61} - 27 q^{62} - 81 q^{63} + 33 q^{64} - 102 q^{65} + 72 q^{66} + 102 q^{67} - 21 q^{68} - 6 q^{69} - 33 q^{70} - 66 q^{71} - 12 q^{72} + 36 q^{73} + 18 q^{74} + 6 q^{76} - 174 q^{77} + 18 q^{78} + 36 q^{79} + 60 q^{81} - 36 q^{82} - 24 q^{83} + 48 q^{84} + 174 q^{85} - 21 q^{86} + 12 q^{87} + 3 q^{88} + 30 q^{89} - 48 q^{90} - 18 q^{91} + 18 q^{92} - 123 q^{93} - 120 q^{94} - 18 q^{95} - 24 q^{97} - 84 q^{98} - 141 q^{99}+O(q^{100}) \) 264 * q + 6 * q^3 - 9 * q^6 - 15 * q^7 + 33 * q^8 + 6 * q^9 + 3 * q^11 - 6 * q^13 + 18 * q^14 - 39 * q^15 - 3 * q^17 - 78 * q^18 - 45 * q^19 - 24 * q^20 + 48 * q^21 + 6 * q^23 - 9 * q^24 + 30 * q^25 + 18 * q^26 - 24 * q^27 + 6 * q^28 - 3 * q^31 - 63 * q^33 - 36 * q^34 + 42 * q^35 - 9 * q^36 + 60 * q^37 - 3 * q^38 + 36 * q^39 + 39 * q^41 + 6 * q^42 - 60 * q^43 + 60 * q^44 - 108 * q^45 - 12 * q^46 - 24 * q^47 - 12 * q^48 + 6 * q^49 + 18 * q^50 + 96 * q^51 + 3 * q^52 - 117 * q^53 + 54 * q^54 + 102 * q^55 - 96 * q^57 - 60 * q^58 - 141 * q^59 + 36 * q^60 + 24 * q^61 - 27 * q^62 - 81 * q^63 + 33 * q^64 - 102 * q^65 + 72 * q^66 + 102 * q^67 - 21 * q^68 - 6 * q^69 - 33 * q^70 - 66 * q^71 - 12 * q^72 + 36 * q^73 + 18 * q^74 + 6 * q^76 - 174 * q^77 + 18 * q^78 + 36 * q^79 + 60 * q^81 - 36 * q^82 - 24 * q^83 + 48 * q^84 + 174 * q^85 - 21 * q^86 + 12 * q^87 + 3 * q^88 + 30 * q^89 - 48 * q^90 - 18 * q^91 + 18 * q^92 - 123 * q^93 - 120 * q^94 - 18 * q^95 - 24 * q^97 - 84 * q^98 - 141 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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