LMFDB - Embedded newform 507.2.q.b.16.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [507,2,Mod(16,507)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(507, base_ring=CyclotomicField(78))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("507.16");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 507 = 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	507.q (of order $39$, 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:	$4.04841538248$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$16$ over $\Q(\zeta_{39})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{39}]$

Embedding invariants

Embedding label			16.12
Character	$\chi$	$=$	507.16
Dual form			507.2.q.b.412.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.45946 + 0.117820i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(0.142046 + 0.0230847i) q^{4} +(-0.575893 - 0.510197i) q^{5} +(-1.17055 - 0.879613i) q^{6} +(-2.84784 + 2.96491i) q^{7} +(-2.63873 - 0.650390i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})$	\(q+(1.45946 + 0.117820i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(0.142046 + 0.0230847i) q^{4} +(-0.575893 - 0.510197i) q^{5} +(-1.17055 - 0.879613i) q^{6} +(-2.84784 + 2.96491i) q^{7} +(-2.63873 - 0.650390i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-0.780383 - 0.812465i) q^{10} +(-0.187808 + 0.395798i) q^{11} +(-0.107718 - 0.0954295i) q^{12} +(-1.77100 - 3.14063i) q^{13} +(-4.50563 + 3.99164i) q^{14} +(0.214057 + 0.739009i) q^{15} +(-4.04751 - 1.35126i) q^{16} +(-3.36789 + 3.50635i) q^{17} +(0.519216 + 1.36906i) q^{18} +(-0.991167 + 1.71675i) q^{19} +(-0.0700255 - 0.0857656i) q^{20} +(3.99161 - 0.983843i) q^{21} +(-0.320732 + 0.555524i) q^{22} +(1.72465 + 2.98718i) q^{23} +(1.88262 + 1.96002i) q^{24} +(-0.531331 - 4.37591i) q^{25} +(-2.21468 - 4.79229i) q^{26} +(0.120537 - 0.992709i) q^{27} +(-0.472967 + 0.355412i) q^{28} +(-7.31886 - 0.590840i) q^{29} +(0.225337 + 1.10378i) q^{30} +(0.0172902 - 0.142398i) q^{31} +(-0.747511 - 0.318485i) q^{32} +(0.370274 - 0.234147i) q^{33} +(-5.32843 + 4.72057i) q^{34} +(3.15274 - 0.254516i) q^{35} +(0.0400381 + 0.138228i) q^{36} +(-2.97867 + 1.26909i) q^{37} +(-1.64884 + 2.38875i) q^{38} +(-0.181724 + 3.60097i) q^{39} +(1.18780 + 1.72083i) q^{40} +(4.86416 + 3.07591i) q^{41} +(5.94151 - 0.965590i) q^{42} +(11.3709 + 4.84470i) q^{43} +(-0.0358142 + 0.0518859i) q^{44} +(0.214057 - 0.739009i) q^{45} +(2.16511 + 4.56288i) q^{46} +(4.60010 - 12.1295i) q^{47} +(2.69871 + 3.30532i) q^{48} +(-0.398668 - 9.89285i) q^{49} +(-0.259889 - 6.44907i) q^{50} +(4.72053 - 1.16351i) q^{51} +(-0.179063 - 0.486996i) q^{52} +(-7.03562 - 1.73412i) q^{53} +(0.292880 - 1.43462i) q^{54} +(0.310092 - 0.132118i) q^{55} +(9.44303 - 5.97141i) q^{56} +(1.75527 - 0.921236i) q^{57} +(-10.6120 - 1.72462i) q^{58} +(-8.88042 + 2.96472i) q^{59} +(0.0133460 + 0.109914i) q^{60} +(-3.40778 + 11.7650i) q^{61} +(0.0420117 - 0.205787i) q^{62} +(-3.89950 - 1.30184i) q^{63} +(6.50323 + 3.41316i) q^{64} +(-0.582430 + 2.71223i) q^{65} +(0.567988 - 0.298103i) q^{66} +(8.35107 - 1.35718i) q^{67} +(-0.559338 + 0.420315i) q^{68} +(0.138889 - 3.44650i) q^{69} +4.63129 q^{70} +(0.390746 - 9.69626i) q^{71} +(-0.543611 - 2.66278i) q^{72} +(-9.67840 - 14.0216i) q^{73} +(-4.49678 + 1.50124i) q^{74} +(-1.88970 + 3.98245i) q^{75} +(-0.180422 + 0.220976i) q^{76} +(-0.638658 - 1.68400i) q^{77} +(-0.689486 + 5.23406i) q^{78} +(-0.551785 + 1.45494i) q^{79} +(1.64153 + 2.84321i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(6.73665 + 5.06227i) q^{82} +(-11.4186 - 5.99294i) q^{83} +(0.589703 - 0.0476057i) q^{84} +(3.72848 - 0.300994i) q^{85} +(16.0246 + 8.41038i) q^{86} +(5.87005 + 4.41105i) q^{87} +(0.752999 - 0.922256i) q^{88} +(3.05547 + 5.29224i) q^{89} +(0.399477 - 1.05333i) q^{90} +(14.3552 + 3.69313i) q^{91} +(0.176021 + 0.464130i) q^{92} +(-0.0907203 + 0.111112i) q^{93} +(8.14277 - 17.1605i) q^{94} +(1.44669 - 0.482975i) q^{95} +(0.461570 + 0.668699i) q^{96} +(-0.879791 - 4.30950i) q^{97} +(0.583734 - 14.4852i) q^{98} -0.438096 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9}+O(q^{10}) $ 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19} + q^{20} + 6 q^{21} - 86 q^{22} - 52 q^{23} + 9 q^{24} - 74 q^{25} - 64 q^{26} - 32 q^{27} - 16 q^{28} - 44 q^{29} + 3 q^{30} - 28 q^{31} + 74 q^{32} - 17 q^{33} - 83 q^{34} + 70 q^{35} + 17 q^{36} + 11 q^{37} - 29 q^{38} + q^{39} - 5 q^{40} + q^{41} + 118 q^{42} - 79 q^{43} - 19 q^{44} - 3 q^{45} + 314 q^{46} + 11 q^{48} - 69 q^{49} - 76 q^{50} + 6 q^{51} - 37 q^{52} - 102 q^{53} + q^{54} - 73 q^{55} - 36 q^{56} + 14 q^{57} - 51 q^{58} + 194 q^{59} + 76 q^{60} + 4 q^{61} - 89 q^{62} - 3 q^{63} - 184 q^{64} - 49 q^{65} - 36 q^{66} - 73 q^{67} + 4 q^{68} - 100 q^{70} + 106 q^{71} + 9 q^{72} - 132 q^{73} - 45 q^{74} + 11 q^{75} + 24 q^{76} - 54 q^{77} - 39 q^{78} - 2 q^{79} + 177 q^{80} + 16 q^{81} - 76 q^{82} - 58 q^{83} - 16 q^{84} - 123 q^{85} - 157 q^{86} - 57 q^{87} + 476 q^{88} + 18 q^{89} - 6 q^{90} + 233 q^{91} - 12 q^{92} + q^{93} - 111 q^{94} + 64 q^{95} - 83 q^{96} - 143 q^{97} - 79 q^{98} - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/507\mathbb{Z}\right)^\times$.

$n$	$170$	$340$
$\chi(n)$	$1$	$e\left(\frac{1}{39}\right)$

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 $

$2$	1.45946	+	0.117820i	1.03200	+	0.0833113i	0.584843	−	0.811147i	$-0.301156\pi$
$2$	1.45946	+	0.117820i	1.03200	+	0.0833113i	0.447152	+	0.894458i	$0.352438\pi$
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$3$	−0.845190	−	0.534466i	−0.487971	−	0.308574i
$4$	0.142046	+	0.0230847i	0.0710229	+	0.0115423i
$5$	−0.575893	−	0.510197i	−0.257547	−	0.228167i	0.524462	−	0.851434i	$-0.324267\pi$
$5$	−0.575893	−	0.510197i	−0.257547	−	0.228167i	−0.782009	+	0.623267i	$0.785805\pi$
$6$	−1.17055	−	0.879613i	−0.477876	−	0.359100i
$7$	−2.84784	+	2.96491i	−1.07638	+	1.12063i	−0.0841211	+	0.996456i	$0.526808\pi$
$7$	−2.84784	+	2.96491i	−1.07638	+	1.12063i	−0.992260	+	0.124176i	$0.960371\pi$
$8$	−2.63873	−	0.650390i	−0.932933	−	0.229947i
$9$	0.428693	+	0.903450i	0.142898	+	0.301150i
$10$	−0.780383	−	0.812465i	−0.246779	−	0.256924i
$11$	−0.187808	+	0.395798i	−0.0566264	+	0.119338i	−0.929791	−	0.368088i	$-0.880013\pi$
$11$	−0.187808	+	0.395798i	−0.0566264	+	0.119338i	0.873165	+	0.487425i	$0.162064\pi$
$12$	−0.107718	−	0.0954295i	−0.0310954	−	0.0275481i
$13$	−1.77100	−	3.14063i	−0.491188	−	0.871054i
$13$	−1.77100	−	3.14063i	−0.491188	−	0.871054i
$14$	−4.50563	+	3.99164i	−1.20418	+	1.06681i
$15$	0.214057	+	0.739009i	0.0552692	+	0.190811i
$16$	−4.04751	−	1.35126i	−1.01188	−	0.337814i
$17$	−3.36789	+	3.50635i	−0.816834	+	0.850414i	−0.990939	−	0.134313i	$-0.957117\pi$
$17$	−3.36789	+	3.50635i	−0.816834	+	0.850414i	0.174105	+	0.984727i	$0.444297\pi$
$18$	0.519216	+	1.36906i	0.122380	+	0.322690i
$19$	−0.991167	+	1.71675i	−0.227389	+	0.393850i	−0.957034	−	0.289977i	$-0.906352\pi$
$19$	−0.991167	+	1.71675i	−0.227389	+	0.393850i	0.729644	+	0.683827i	$0.239686\pi$
$20$	−0.0700255	−	0.0857656i	−0.0156582	−	0.0191778i
$21$	3.99161	−	0.983843i	0.871040	−	0.214692i
$22$	−0.320732	+	0.555524i	−0.0683803	+	0.118438i
$23$	1.72465	+	2.98718i	0.359615	+	0.622871i	0.987896	−	0.155115i	$-0.0495749\pi$
$23$	1.72465	+	2.98718i	0.359615	+	0.622871i	−0.628282	+	0.777986i	$0.716242\pi$
$24$	1.88262	+	1.96002i	0.384288	+	0.400087i
$25$	−0.531331	−	4.37591i	−0.106266	−	0.875181i
$26$	−2.21468	−	4.79229i	−0.434335	−	0.939845i
$27$	0.120537	−	0.992709i	0.0231973	−	0.191047i
$28$	−0.472967	+	0.355412i	−0.0893824	+	0.0671665i
$29$	−7.31886	−	0.590840i	−1.35908	−	0.109716i	−0.620671	−	0.784071i	$-0.713140\pi$
$29$	−7.31886	−	0.590840i	−1.35908	−	0.109716i	−0.738408	+	0.674355i	$0.764422\pi$
$30$	0.225337	+	1.10378i	0.0411408	+	0.201521i
$31$	0.0172902	−	0.142398i	0.00310542	−	0.0255754i	−0.991074	−	0.133314i	$-0.957438\pi$
$31$	0.0172902	−	0.142398i	0.00310542	−	0.0255754i	0.994179	+	0.107739i	$0.0343611\pi$
$32$	−0.747511	−	0.318485i	−0.132142	−	0.0563007i
$33$	0.370274	−	0.234147i	0.0644565	−	0.0407598i
$34$	−5.32843	+	4.72057i	−0.913818	+	0.809572i
$35$	3.15274	−	0.254516i	0.532910	−	0.0430210i
$36$	0.0400381	+	0.138228i	0.00667301	+	0.0230379i
$37$	−2.97867	+	1.26909i	−0.489690	+	0.208637i	−0.622675	−	0.782481i	$-0.713954\pi$
$37$	−2.97867	+	1.26909i	−0.489690	+	0.208637i	0.132985	+	0.991118i	$0.457544\pi$
$38$	−1.64884	+	2.38875i	−0.267477	+	0.387507i
$39$	−0.181724	+	3.60097i	−0.0290992	+	0.576616i
$40$	1.18780	+	1.72083i	0.187808	+	0.272087i
$41$	4.86416	+	3.07591i	0.759654	+	0.480376i	0.857282	−	0.514847i	$-0.172151\pi$
$41$	4.86416	+	3.07591i	0.759654	+	0.480376i	−0.0976279	+	0.995223i	$0.531126\pi$
$42$	5.94151	−	0.965590i	0.916796	−	0.148994i
$43$	11.3709	+	4.84470i	1.73405	+	0.738811i	0.998089	+	0.0617885i	$0.0196804\pi$
$43$	11.3709	+	4.84470i	1.73405	+	0.738811i	0.735963	+	0.677022i	$0.236730\pi$
$44$	−0.0358142	+	0.0518859i	−0.00539920	+	0.00782209i
$45$	0.214057	−	0.739009i	0.0319097	−	0.110165i
$46$	2.16511	+	4.56288i	0.319228	+	0.672759i
$47$	4.60010	−	12.1295i	0.670994	−	1.76927i	0.0327103	−	0.999465i	$-0.489586\pi$
$47$	4.60010	−	12.1295i	0.670994	−	1.76927i	0.638284	−	0.769801i	$-0.279645\pi$
$48$	2.69871	+	3.30532i	0.389526	+	0.477082i
$49$	−0.398668	−	9.89285i	−0.0569526	−	1.41326i
$50$	−0.259889	−	6.44907i	−0.0367538	−	0.912036i
$51$	4.72053	−	1.16351i	0.661007	−	0.162924i
$52$	−0.179063	−	0.486996i	−0.0248316	−	0.0675342i
$53$	−7.03562	−	1.73412i	−0.966416	−	0.238200i	−0.275634	−	0.961263i	$-0.588888\pi$
$53$	−7.03562	−	1.73412i	−0.966416	−	0.238200i	−0.690783	+	0.723063i	$0.742734\pi$
$54$	0.292880	−	1.43462i	0.0398559	−	0.195227i
$55$	0.310092	−	0.132118i	0.0418129	−	0.0178148i
$56$	9.44303	−	5.97141i	1.26188	−	0.797964i
$57$	1.75527	−	0.921236i	0.232491	−	0.122021i
$58$	−10.6120	−	1.72462i	−1.39342	−	0.226453i
$59$	−8.88042	+	2.96472i	−1.15613	+	0.385974i	−0.829133	−	0.559051i	$-0.811166\pi$
$59$	−8.88042	+	2.96472i	−1.15613	+	0.385974i	−0.326999	+	0.945025i	$0.606037\pi$
$60$	0.0133460	+	0.109914i	0.00172297	+	0.0141899i
$61$	−3.40778	+	11.7650i	−0.436321	+	1.50636i	0.377925	+	0.925836i	$0.376638\pi$
$61$	−3.40778	+	11.7650i	−0.436321	+	1.50636i	−0.814246	+	0.580520i	$0.802849\pi$
$62$	0.0420117	−	0.205787i	0.00533549	−	0.0261350i
$63$	−3.89950	−	1.30184i	−0.491291	−	0.164017i
$64$	6.50323	+	3.41316i	0.812904	+	0.426645i
$65$	−0.582430	+	2.71223i	−0.0722416	+	0.336410i
$66$	0.567988	−	0.298103i	0.0699145	−	0.0366940i
$67$	8.35107	−	1.35718i	1.02025	−	0.165806i	0.372795	−	0.927914i	$-0.378399\pi$
$67$	8.35107	−	1.35718i	1.02025	−	0.165806i	0.647450	+	0.762108i	$0.275835\pi$
$68$	−0.559338	+	0.420315i	−0.0678297	+	0.0509707i
$69$	0.138889	−	3.44650i	0.0167203	−	0.414910i
$70$	4.63129			0.553545
$71$	0.390746	−	9.69626i	0.0463730	−	1.15073i	−0.793717	−	0.608287i	$-0.791857\pi$
$71$	0.390746	−	9.69626i	0.0463730	−	1.15073i	0.840090	−	0.542447i	$-0.182502\pi$
$72$	−0.543611	−	2.66278i	−0.0640652	−	0.313812i
$73$	−9.67840	−	14.0216i	−1.13277	−	1.64110i	−0.629619	−	0.776904i	$-0.716789\pi$
$73$	−9.67840	−	14.0216i	−1.13277	−	1.64110i	−0.503151	−	0.864198i	$-0.667826\pi$
$74$	−4.49678	+	1.50124i	−0.522740	+	0.174516i
$75$	−1.88970	+	3.98245i	−0.218203	+	0.459854i
$76$	−0.180422	+	0.220976i	−0.0206958	+	0.0253477i
$77$	−0.638658	−	1.68400i	−0.0727818	−	0.191910i
$78$	−0.689486	+	5.23406i	−0.0780689	+	0.592641i
$79$	−0.551785	+	1.45494i	−0.0620807	+	0.163693i	−0.962467	−	0.271397i	$-0.912514\pi$
$79$	−0.551785	+	1.45494i	−0.0620807	+	0.163693i	0.900387	+	0.435090i	$0.143284\pi$
$80$	1.64153	+	2.84321i	0.183528	+	0.317880i
$81$	−0.632445	+	0.774605i	−0.0702717	+	0.0860672i
$82$	6.73665	+	5.06227i	0.743939	+	0.559034i
$83$	−11.4186	−	5.99294i	−1.25335	−	0.657811i	−0.298364	−	0.954452i	$-0.596441\pi$
$83$	−11.4186	−	5.99294i	−1.25335	−	0.657811i	−0.954989	+	0.296641i	$0.904133\pi$
$84$	0.589703	−	0.0476057i	0.0643418	−	0.00519421i
$85$	3.72848	−	0.300994i	0.404410	−	0.0326473i
$86$	16.0246	+	8.41038i	1.72798	+	0.906915i
$87$	5.87005	+	4.41105i	0.629335	+	0.472915i
$88$	0.752999	−	0.922256i	0.0802700	−	0.0983129i
$89$	3.05547	+	5.29224i	0.323880	+	0.560976i	0.981285	−	0.192561i	$-0.0616794\pi$
$89$	3.05547	+	5.29224i	0.323880	+	0.560976i	−0.657405	+	0.753537i	$0.728346\pi$
$90$	0.399477	−	1.05333i	0.0421086	−	0.111031i
$91$	14.3552	+	3.69313i	1.50484	+	0.387145i
$92$	0.176021	+	0.464130i	0.0183515	+	0.0483888i
$93$	−0.0907203	+	0.111112i	−0.00940725	+	0.0115218i
$94$	8.14277	−	17.1605i	0.839862	−	1.76997i
$95$	1.44669	−	0.482975i	0.148427	−	0.0495522i
$96$	0.461570	+	0.668699i	0.0471088	+	0.0682488i
$97$	−0.879791	−	4.30950i	−0.0893293	−	0.437564i	−0.999717	−	0.0238066i	$-0.992421\pi$
$97$	−0.879791	−	4.30950i	−0.0893293	−	0.437564i	0.910387	−	0.413757i	$-0.135784\pi$
$98$	0.583734	−	14.4852i	0.0589660	−	1.46323i
$99$	−0.438096			−0.0440303
$100$	0.0255431	−	0.633844i	0.00255431	−	0.0633844i
$101$	−7.61948	+	5.72567i	−0.758167	+	0.569725i	−0.907992	−	0.418987i	$-0.862385\pi$
$101$	−7.61948	+	5.72567i	−0.758167	+	0.569725i	0.149825	+	0.988712i	$0.452129\pi$
$102$	7.02652	−	1.14192i	0.695729	−	0.113067i
$103$	9.40505	−	4.93615i	0.926707	−	0.486373i	0.0673383	−	0.997730i	$-0.478549\pi$
$103$	9.40505	−	4.93615i	0.926707	−	0.486373i	0.859368	+	0.511357i	$0.170857\pi$
$104$	2.63057	+	9.43913i	0.257949	+	0.925582i
$105$	−2.80069	−	1.46992i	−0.273320	−	0.143449i
$106$	−10.0639	−	3.35982i	−0.977492	−	0.326335i
$107$	−2.34948	+	11.5085i	−0.227133	+	1.11257i	0.692992	+	0.720945i	$0.256292\pi$
$107$	−2.34948	+	11.5085i	−0.227133	+	1.11257i	−0.920125	+	0.391625i	$0.871913\pi$
$108$	0.0400381	−	0.138228i	0.00385267	−	0.0133009i
$109$	2.20217	+	18.1365i	0.210930	+	1.73716i	0.586130	+	0.810217i	$0.300651\pi$
$109$	2.20217	+	18.1365i	0.210930	+	1.73716i	−0.375200	+	0.926944i	$0.622426\pi$
$110$	0.468134	−	0.156286i	0.0446348	−	0.0149013i
$111$	3.19583	+	0.519373i	0.303335	+	0.0492967i
$112$	15.5330	−	8.15235i	1.46773	−	0.770325i
$113$	2.80593	−	1.77436i	0.263960	−	0.166918i	−0.395929	−	0.918281i	$-0.629578\pi$
$113$	2.80593	−	1.77436i	0.263960	−	0.166918i	0.659889	+	0.751363i	$0.270603\pi$
$114$	2.67029	−	1.13770i	0.250095	−	0.106556i
$115$	0.530837	−	2.60021i	0.0495008	−	0.242471i
$116$	−1.02597	−	0.252880i	−0.0952593	−	0.0234793i
$117$	2.07819	−	2.94638i	0.192128	−	0.272393i
$118$	−13.3099	+	3.28061i	−1.22528	+	0.302004i
$119$	−0.804804	−	19.9710i	−0.0737763	−	1.83074i
$120$	−0.0841946	−	2.08927i	−0.00768588	−	0.190723i
$121$	6.83552	+	8.37199i	0.621410	+	0.761090i
$122$	−6.35968	+	16.7691i	−0.575778	+	1.51820i
$123$	−2.46717	−	5.19946i	−0.222457	−	0.468819i
$124$	0.00574321	−	0.0198279i	0.000515755	−	0.00178059i
$125$	−4.11189	+	5.95710i	−0.367779	+	0.532819i
$126$	−5.53778	−	2.35943i	−0.493345	−	0.210195i
$127$	−11.6127	+	1.88725i	−1.03046	+	0.167467i	−0.652054	−	0.758172i	$-0.726093\pi$
$127$	−11.6127	+	1.88725i	−1.03046	+	0.167467i	−0.378409	+	0.925639i	$0.623529\pi$
$128$	10.4626	+	6.61613i	0.924769	+	0.584788i
$129$	−7.02128	−	10.1721i	−0.618189	−	0.895601i
$130$	−1.16959	+	3.88977i	−0.102580	+	0.341155i
$131$	−7.96746	+	11.5429i	−0.696120	+	1.00850i	0.302349	+	0.953197i	$0.402229\pi$
$131$	−7.96746	+	11.5429i	−0.696120	+	1.00850i	−0.998469	+	0.0553073i	$0.982386\pi$
$132$	0.0580011	−	0.0247120i	0.00504835	−	0.00215090i
$133$	−2.26734	−	7.82775i	−0.196603	−	0.678752i
$134$	12.3480	−	0.996831i	1.06670	−	0.0861131i
$135$	−0.575893	+	0.510197i	−0.0495650	+	0.0439108i
$136$	11.1675	−	7.06188i	0.957602	−	0.605551i
$137$	−6.86505	−	2.92493i	−0.586521	−	0.249893i	0.0782581	−	0.996933i	$-0.475064\pi$
$137$	−6.86505	−	2.92493i	−0.586521	−	0.249893i	−0.664779	+	0.747040i	$0.731474\pi$
$138$	0.608770	−	5.01368i	0.0518220	−	0.426792i
$139$	0.891731	+	4.36799i	0.0756356	+	0.370488i	0.999938	−	0.0111742i	$-0.00355694\pi$
$139$	0.891731	+	4.36799i	0.0756356	+	0.370488i	−0.924302	+	0.381662i	$0.875352\pi$
$140$	0.453709	+	0.0366272i	0.0383454	+	0.00309556i
$141$	−10.3708	+	7.79312i	−0.873375	+	0.656299i
$142$	1.71269	−	14.1053i	0.143726	−	1.18369i
$143$	1.57566	−	0.111123i	0.131764	−	0.00929255i
$144$	−0.514343	−	4.23600i	−0.0428619	−	0.353000i
$145$	3.91344	+	4.07432i	0.324994	+	0.338354i
$146$	−12.4732	−	21.6043i	−1.03229	−	1.78798i
$147$	−4.95044	+	8.57442i	−0.408306	+	0.707206i
$148$	−0.452404	+	0.111508i	−0.0371874	+	0.00916586i
$149$	0.816325	+	0.999817i	0.0668760	+	0.0819082i	0.806960	−	0.590607i	$-0.201112\pi$
$149$	0.816325	+	0.999817i	0.0668760	+	0.0819082i	−0.740084	+	0.672515i	$0.765214\pi$
$150$	−3.22715	+	5.58959i	−0.263496	+	0.456388i
$151$	5.68564	+	14.9918i	0.462691	+	1.22002i	0.939968	+	0.341263i	$0.110855\pi$
$151$	5.68564	+	14.9918i	0.462691	+	1.22002i	−0.477277	+	0.878753i	$0.658376\pi$
$152$	3.73198	−	3.88540i	0.302704	−	0.315148i
$153$	−4.61160	−	1.53958i	−0.372826	−	0.124468i
$154$	−0.733688	−	2.53298i	−0.0591222	−	0.204114i
$155$	−0.0826083	+	0.0731845i	−0.00663526	+	0.00587832i
$156$	−0.108940	+	0.507307i	−0.00872221	+	0.0406171i
$157$	6.23954	+	5.52775i	0.497970	+	0.441163i	0.874345	−	0.485304i	$-0.161291\pi$
$157$	6.23954	+	5.52775i	0.497970	+	0.441163i	−0.376375	+	0.926467i	$0.622830\pi$
$158$	−0.976730	+	2.05842i	−0.0777045	+	0.163759i
$159$	5.01960	+	5.22596i	0.398080	+	0.414446i
$160$	0.267997	+	0.564791i	0.0211870	+	0.0446507i
$161$	−13.7683	−	3.39357i	−1.08509	−	0.267451i
$162$	−1.01429	+	1.05599i	−0.0796904	+	0.0829665i
$163$	6.37804	+	4.79279i	0.499567	+	0.375400i	0.820450	−	0.571719i	$-0.193723\pi$
$163$	6.37804	+	4.79279i	0.499567	+	0.375400i	−0.320883	+	0.947119i	$0.603980\pi$
$164$	0.619927	+	0.549207i	0.0484082	+	0.0428859i
$165$	−0.332700	−	0.0540690i	−0.0259006	−	0.00420926i
$166$	−15.9589	−	10.0918i	−1.23865	−	0.783276i
$167$	−15.6105	−	1.26021i	−1.20798	−	0.0975180i	−0.539977	−	0.841680i	$-0.681567\pi$
$167$	−15.6105	−	1.26021i	−1.20798	−	0.0975180i	−0.667999	+	0.744162i	$0.732849\pi$
$168$	−11.1727			−0.861990
$169$	−6.72710	+	11.1241i	−0.517469	+	0.855702i
$170$	5.47703			0.420069
$171$	−1.97590	−	0.159512i	−0.151101	−	0.0121982i
$172$	1.50336	+	0.950664i	0.114630	+	0.0724875i
$173$	−21.0285	−	3.41746i	−1.59877	−	0.259825i	−0.705284	−	0.708925i	$-0.749181\pi$
$173$	−21.0285	−	3.41746i	−1.59877	−	0.259825i	−0.893481	+	0.449100i	$0.851745\pi$
$174$	8.04740	+	7.12937i	0.610072	+	0.540476i
$175$	14.4873	+	10.8865i	1.09514	+	0.822943i
$176$	1.29498	−	1.34822i	0.0976128	−	0.101626i
$177$	9.09019	+	2.24053i	0.683260	+	0.168409i
$178$	3.83582	+	8.08381i	0.287507	+	0.605907i
$179$	−4.76554	−	4.96145i	−0.356193	−	0.370837i	0.518863	−	0.854857i	$-0.326355\pi$
$179$	−4.76554	−	4.96145i	−0.356193	−	0.370837i	−0.875057	+	0.484021i	$0.839176\pi$
$180$	0.0474656	−	0.100032i	0.00353788	−	0.00745592i
$181$	1.15906	+	1.02684i	0.0861524	+	0.0763244i	0.705100	−	0.709108i	$-0.250902\pi$
$181$	1.15906	+	1.02684i	0.0861524	+	0.0763244i	−0.618947	+	0.785432i	$0.712441\pi$
$182$	20.5158	+	7.08131i	1.52073	+	0.524902i
$183$	9.16822	−	8.12234i	0.677734	−	0.600420i
$184$	−2.60806	−	9.00407i	−0.192269	−	0.663789i
$185$	2.36288	+	0.788846i	0.173723	+	0.0579971i
$186$	−0.145494	+	0.151475i	−0.0106681	+	0.0111067i
$187$	−0.755286	−	1.99153i	−0.0552320	−	0.145635i
$188$	0.933430	−	1.61675i	0.0680774	−	0.117914i
$189$	2.60003	+	3.18445i	0.189124	+	0.231635i
$190$	2.16829	−	0.534435i	0.157304	−	0.0387720i
$191$	1.89181	−	3.27672i	0.136887	−	0.237095i	−0.789430	−	0.613841i	$-0.789624\pi$
$191$	1.89181	−	3.27672i	0.136887	−	0.237095i	0.926317	+	0.376746i	$0.122957\pi$
$192$	−3.67225	−	6.36053i	−0.265022	−	0.459031i
$193$	−1.22778	−	1.27825i	−0.0883772	−	0.0920104i	0.675545	−	0.737319i	$-0.263908\pi$
$193$	−1.22778	−	1.27825i	−0.0883772	−	0.0920104i	−0.763922	+	0.645308i	$0.776729\pi$
$194$	−0.776276	−	6.39321i	−0.0557334	−	0.459006i
$195$	1.94186	−	1.98106i	0.139059	−	0.141867i
$196$	0.171744	−	1.41444i	0.0122674	−	0.101031i
$197$	−7.22722	+	5.43091i	−0.514918	+	0.386936i	−0.826196	−	0.563383i	$-0.809500\pi$
$197$	−7.22722	+	5.43091i	−0.514918	+	0.386936i	0.311277	+	0.950319i	$0.399243\pi$
$198$	−0.639384	−	0.0516164i	−0.0454390	−	0.00366822i
$199$	−2.07277	−	10.1531i	−0.146935	−	0.719735i	−0.984777	−	0.173822i	$-0.944388\pi$
$199$	−2.07277	−	10.1531i	−0.146935	−	0.719735i	0.837842	−	0.545913i	$-0.183817\pi$
$200$	−1.44400	+	11.8924i	−0.102106	+	0.840921i
$201$	−7.78361	−	3.31629i	−0.549013	−	0.233913i
$202$	−11.7949	+	7.45867i	−0.829889	+	0.524790i
$203$	22.5947	−	20.0172i	1.58584	−	1.40493i
$204$	0.697391	−	0.0562992i	0.0488271	−	0.00394173i
$205$	−1.23192	−	4.25308i	−0.0860409	−	0.297048i
$206$	14.3079	−	6.09602i	0.996877	−	0.424730i
$207$	−1.95943	+	2.83872i	−0.136190	+	0.197305i
$208$	2.92435	+	15.1048i	0.202767	+	1.04733i
$209$	−0.493337	−	0.714722i	−0.0341248	−	0.0494383i
$210$	−3.91432	−	2.47527i	−0.270114	−	0.170810i
$211$	−12.1201	+	1.96972i	−0.834385	+	0.135601i	−0.562571	−	0.826749i	$-0.690188\pi$
$211$	−12.1201	+	1.96972i	−0.834385	+	0.135601i	−0.271814	+	0.962350i	$0.587624\pi$
$212$	−0.959348	−	0.408740i	−0.0658883	−	0.0280724i
$213$	−5.51257	+	7.98634i	−0.377715	+	0.547215i
$214$	−4.78491	+	16.5194i	−0.327089	+	1.12924i
$215$	−4.07670	−	8.59145i	−0.278028	−	0.585932i
$216$	−0.963712	+	2.54110i	−0.0655723	+	0.172900i
$217$	0.372957	+	0.456790i	0.0253180	+	0.0310089i
$218$	1.07714	+	26.7290i	0.0729532	+	1.81031i
$219$	0.686031	+	17.0237i	0.0463577	+	1.15035i
$220$	0.0470972	−	0.0116084i	0.00317529	−	0.000782640i
$221$	16.9767	+	4.36755i	1.14198	+	0.293793i
$222$	4.60300	+	1.13454i	0.308933	+	0.0761451i
$223$	5.06756	−	24.8225i	0.339349	−	1.66224i	−0.349198	−	0.937049i	$-0.613546\pi$
$223$	5.06756	−	24.8225i	0.339349	−	1.66224i	0.688547	−	0.725192i	$-0.258249\pi$
$224$	3.07307	−	1.30931i	0.205328	−	0.0874821i
$225$	3.72564	−	2.35595i	0.248376	−	0.157063i
$226$	4.30420	−	2.25902i	0.286311	−	0.150268i
$227$	−5.72032	−	0.929642i	−0.379671	−	0.0617025i	−0.0324189	−	0.999474i	$-0.510321\pi$
$227$	−5.72032	−	0.929642i	−0.379671	−	0.0617025i	−0.347252	+	0.937772i	$0.612885\pi$
$228$	0.270595	−	0.0903378i	0.0179206	−	0.00598277i
$229$	−1.25126	−	10.3051i	−0.0826857	−	0.680978i	−0.973833	−	0.227264i	$-0.927022\pi$
$229$	−1.25126	−	10.3051i	−0.0826857	−	0.680978i	0.891147	−	0.453714i	$-0.149901\pi$
$230$	1.08109	−	3.73236i	0.0712851	−	0.246105i
$231$	−0.360255	+	1.76464i	−0.0237030	+	0.116105i
$232$	18.9283	+	6.31918i	1.24270	+	0.414875i
$233$	−12.0925	−	6.34661i	−0.792203	−	0.415780i	0.0195296	−	0.999809i	$-0.493783\pi$
$233$	−12.0925	−	6.34661i	−0.792203	−	0.415780i	−0.811733	+	0.584029i	$0.801475\pi$
$234$	3.38017	−	4.05527i	0.220969	−	0.265101i
$235$	−8.83759	+	4.63833i	−0.576501	+	0.302571i
$236$	−1.32987	+	0.216124i	−0.0865669	+	0.0140685i
$237$	1.24398	−	0.934789i	0.0808051	−	0.0607211i
$238$	1.17840	−	29.2418i	0.0763845	−	1.89546i
$239$	−6.76534			−0.437613			−0.218807	−	0.975768i	$-0.570216\pi$
$239$	−6.76534			−0.437613			−0.218807	+	0.975768i	$0.570216\pi$
$240$	0.132195	−	3.28039i	0.00853316	−	0.211748i
$241$	1.04464	+	5.11699i	0.0672912	+	0.329614i	0.999476	−	0.0323686i	$-0.0103051\pi$
$241$	1.04464	+	5.11699i	0.0672912	+	0.329614i	−0.932185	+	0.361983i	$0.882100\pi$
$242$	8.98978	+	13.0240i	0.577885	+	0.837211i
$243$	0.948536	−	0.316668i	0.0608486	−	0.0203143i
$244$	−0.755652	+	1.59250i	−0.0483757	+	0.101950i
$245$	−4.81771	+	5.90063i	−0.307792	+	0.376977i
$246$	−2.98814	−	7.87909i	−0.190517	−	0.502352i
$247$	7.14704	+	0.0725150i	0.454755	+	0.00461402i
$248$	−0.138238	+	0.364504i	−0.00877814	+	0.0231461i
$249$	6.44786	+	11.1680i	0.408616	+	0.707745i
$250$	−6.70301	+	8.20969i	−0.423935	+	0.519227i
$251$	4.83366	+	3.63226i	0.305098	+	0.229266i	0.742253	−	0.670120i	$-0.233757\pi$
$251$	4.83366	+	3.63226i	0.305098	+	0.229266i	−0.437155	+	0.899386i	$0.644014\pi$
$252$	−0.523854	−	0.274940i	−0.0329997	−	0.0173196i
$253$	−1.50622	+	0.121595i	−0.0946955	+	0.00764461i
$254$	−17.1707	+	1.38616i	−1.07738	+	0.0869755i
$255$	−3.31214	−	1.73835i	−0.207414	−	0.108859i
$256$	2.74718	+	2.06437i	0.171699	+	0.129023i
$257$	1.44722	−	1.77252i	0.0902749	−	0.110567i	−0.727492	−	0.686116i	$-0.759314\pi$
$257$	1.44722	−	1.77252i	0.0902749	−	0.110567i	0.817767	+	0.575549i	$0.195212\pi$
$258$	−9.04881	−	15.6730i	−0.563354	−	0.975758i
$259$	4.72002	−	12.4457i	0.293288	−	0.773336i
$260$	−0.145343	+	0.371815i	−0.00901377	+	0.0230590i
$261$	−2.60375	−	6.86552i	−0.161168	−	0.424965i
$262$	−12.9882	+	15.9076i	−0.802413	+	0.982777i
$263$	−1.40637	+	2.96387i	−0.0867207	+	0.182760i	−0.942178	−	0.335114i	$-0.891225\pi$
$263$	−1.40637	+	2.96387i	−0.0867207	+	0.182760i	0.855457	+	0.517874i	$0.173276\pi$
$264$	−1.12934	+	0.377030i	−0.0695062	+	0.0232046i
$265$	3.16702	+	4.58822i	0.194549	+	0.281852i
$266$	−2.38682	−	11.6914i	−0.146346	−	0.716848i
$267$	0.246063	−	6.10599i	0.0150588	−	0.373681i
$268$	1.21756			0.0743745
$269$	−0.449008	+	11.1420i	−0.0273765	+	0.679342i	0.925994	+	0.377539i	$0.123229\pi$
$269$	−0.449008	+	11.1420i	−0.0273765	+	0.679342i	−0.953370	+	0.301803i	$0.902412\pi$
$270$	−0.900606	+	0.676761i	−0.0548091	+	0.0411864i
$271$	−6.93426	+	1.12693i	−0.421226	+	0.0684560i	−0.367330	−	0.930091i	$-0.619728\pi$
$271$	−6.93426	+	1.12693i	−0.421226	+	0.0684560i	−0.0538962	+	0.998547i	$0.517164\pi$
$272$	18.3696	−	9.64108i	1.11382	−	0.584577i
$273$	−10.1590	−	10.7938i	−0.614853	−	0.653269i
$274$	−9.67467	−	5.07766i	−0.584468	−	0.306752i
$275$	1.83176	+	0.611532i	0.110459	+	0.0368768i
$276$	0.0992901	−	0.486355i	0.00597656	−	0.0292751i
$277$	6.34434	−	21.9032i	0.381194	−	1.31604i	−0.509122	−	0.860694i	$-0.670030\pi$
$277$	6.34434	−	21.9032i	0.381194	−	1.31604i	0.890317	−	0.455342i	$-0.150483\pi$
$278$	0.786811	+	6.47997i	0.0471898	+	0.388643i
$279$	0.136062	−	0.0454240i	0.00814579	−	0.00271946i
$280$	−8.48478	−	1.37891i	−0.507062	−	0.0824057i
$281$	13.2950	−	6.97775i	0.793113	−	0.416258i	−0.0189554	−	0.999820i	$-0.506034\pi$
$281$	13.2950	−	6.97775i	0.793113	−	0.416258i	0.812068	+	0.583563i	$0.198342\pi$
$282$	−16.0539	+	10.1519i	−0.955996	+	0.604535i
$283$	0.884040	−	0.376654i	0.0525507	−	0.0223898i	−0.365531	−	0.930799i	$-0.619113\pi$
$283$	0.884040	−	0.376654i	0.0525507	−	0.0223898i	0.418082	+	0.908409i	$0.362702\pi$
$284$	0.279339	−	1.36829i	0.0165757	−	0.0811932i
$285$	−1.48086	−	0.364999i	−0.0877186	−	0.0216207i
$286$	2.31271	+	0.0234652i	0.136754	+	0.00138752i
$287$	−22.9721	+	5.66212i	−1.35600	+	0.334225i
$288$	−0.0327173	−	0.811871i	−0.00192788	−	0.0478400i
$289$	−0.267252	−	6.63180i	−0.0157207	−	0.390106i
$290$	5.23148	+	6.40740i	0.307203	+	0.376255i
$291$	−1.55969	+	4.11257i	−0.0914307	+	0.241083i
$292$	−1.05109	−	2.21513i	−0.0615105	−	0.129631i
$293$	6.16652	−	21.2893i	0.360252	−	1.24373i	−0.551910	−	0.833903i	$-0.686101\pi$
$293$	6.16652	−	21.2893i	0.360252	−	1.24373i	0.912162	−	0.409830i	$-0.134412\pi$
$294$	−8.23522	+	11.9308i	−0.480288	+	0.695817i
$295$	6.62677	+	2.82340i	0.385825	+	0.164385i
$296$	8.68532	−	1.41150i	0.504824	−	0.0820419i
$297$	0.370274	+	0.234147i	0.0214855	+	0.0135866i
$298$	1.07360	+	1.55537i	0.0621918	+	0.0901004i
$299$	6.32727	−	10.7068i	0.365915	−	0.619190i
$300$	−0.360357	+	0.522067i	−0.0208052	+	0.0301416i
$301$	−46.7467	+	19.9169i	−2.69444	+	1.14799i
$302$	6.53164	+	22.5499i	0.375854	+	1.29760i
$303$	9.50008	−	0.766926i	0.545766	−	0.0440588i
$304$	6.33153	−	5.60924i	0.363138	−	0.321712i
$305$	7.96500	−	5.03676i	0.456074	−	0.288404i
$306$	−6.54906	−	2.79029i	−0.374385	−	0.159511i
$307$	−1.46685	+	12.0806i	−0.0837176	+	0.689477i	0.889069	+	0.457773i	$0.151353\pi$
$307$	−1.46685	+	12.0806i	−0.0837176	+	0.689477i	−0.972787	+	0.231703i	$0.925570\pi$
$308$	−0.0518440	−	0.253949i	−0.00295409	−	0.0144701i
$309$	−10.5873	−	0.854692i	−0.602288	−	0.0486217i
$310$	−0.129186	+	0.0970771i	−0.00733728	+	0.00551361i
$311$	0.816904	−	6.72781i	0.0463224	−	0.381499i	−0.951049	−	0.309040i	$-0.899992\pi$
$311$	0.816904	−	6.72781i	0.0463224	−	0.381499i	0.997371	−	0.0724590i	$-0.0230847\pi$
$312$	2.82155	−	9.38381i	0.159739	−	0.531253i
$313$	1.61178	+	13.2742i	0.0911033	+	0.750303i	0.964645	+	0.263553i	$0.0848945\pi$
$313$	1.61178	+	13.2742i	0.0911033	+	0.750303i	−0.873542	+	0.486750i	$0.838182\pi$
$314$	8.45509	+	8.80269i	0.477149	+	0.496764i
$315$	1.58150	+	2.73924i	0.0891073	+	0.154338i
$316$	−0.111966	+	0.193930i	−0.00629855	+	0.0109094i
$317$	4.18141	−	1.03062i	0.234851	−	0.0578856i	−0.120133	−	0.992758i	$-0.538332\pi$
$317$	4.18141	−	1.03062i	0.234851	−	0.0578856i	0.354985	+	0.934872i	$0.384486\pi$
$318$	6.71020	+	8.21850i	0.376289	+	0.460871i
$319$	1.60840	−	2.78583i	0.0900530	−	0.155976i
$320$	−2.00379	−	5.28355i	−0.112015	−	0.295359i
$321$	8.13666	−	8.47116i	0.454144	−	0.472814i
$322$	−19.6944	−	6.57496i	−1.09753	−	0.366408i
$323$	−2.68138	−	9.25721i	−0.149196	−	0.515085i
$324$	−0.107718	+	0.0954295i	−0.00598432	+	0.00530164i
$325$	−12.8021	+	9.41846i	−0.710133	+	0.522442i
$326$	8.74382	+	7.74635i	0.484275	+	0.429030i
$327$	7.83208	−	16.5058i	0.433115	−	0.912771i
$328$	−10.8347	−	11.2801i	−0.598246	−	0.622840i
$329$	22.8625	+	48.1817i	1.26045	+	2.65634i
$330$	−0.479192	−	0.118110i	−0.0263786	−	0.00650175i
$331$	5.93592	−	6.17995i	0.326268	−	0.339681i	−0.537785	−	0.843082i	$-0.680739\pi$
$331$	5.93592	−	6.17995i	0.326268	−	0.339681i	0.864053	+	0.503401i	$0.167918\pi$
$332$	−1.48362	−	1.11487i	−0.0814241	−	0.0611862i
$333$	−2.42350	−	2.14703i	−0.132807	−	0.117656i
$334$	−22.6344	−	3.67845i	−1.23850	−	0.201276i
$335$	−5.50176	−	3.47910i	−0.300593	−	0.190084i
$336$	−17.4855	−	1.41157i	−0.953912	−	0.0770077i
$337$	5.75543			0.313518			0.156759	−	0.987637i	$-0.449895\pi$
$337$	5.75543			0.313518			0.156759	+	0.987637i	$0.449895\pi$
$338$	−11.1286	+	15.4426i	−0.605315	+	0.839969i
$339$	−3.31988			−0.180311
$340$	0.536562	+	0.0433158i	0.0290992	+	0.00234913i
$341$	0.0531135	+	0.0335869i	0.00287626	+	0.00181883i
$342$	−2.86496	−	0.465602i	−0.154919	−	0.0251769i
$343$	8.92654	+	7.90822i	0.481988	+	0.427004i
$344$	−26.8539	−	20.1794i	−1.44787	−	1.08800i
$345$	−1.83838	+	1.91396i	−0.0989751	+	0.103044i
$346$	−30.2876	−	7.46523i	−1.62827	−	0.401333i
$347$	14.6722	+	30.9210i	0.787646	+	1.65993i	0.750730	+	0.660610i	$0.229702\pi$
$347$	14.6722	+	30.9210i	0.787646	+	1.65993i	0.0369160	+	0.999318i	$0.488247\pi$
$348$	0.731987	+	0.762080i	0.0392386	+	0.0408518i
$349$	9.39622	−	19.8021i	0.502968	−	1.05998i	−0.480180	−	0.877170i	$-0.659429\pi$
$349$	9.39622	−	19.8021i	0.502968	−	1.05998i	0.983148	−	0.182813i	$-0.0585201\pi$
$350$	19.8610	+	17.5953i	1.06162	+	0.940511i
$351$	−3.33120	+	1.37953i	−0.177806	+	0.0736338i
$352$	0.266444	−	0.236049i	0.0142015	−	0.0125815i
$353$	−4.70998	−	16.2607i	−0.250687	−	0.865471i	−0.982860	−	0.184353i	$-0.940981\pi$
$353$	−4.70998	−	16.2607i	−0.250687	−	0.865471i	0.732173	−	0.681118i	$-0.238506\pi$
$354$	13.0028	+	4.34097i	0.691091	+	0.230720i
$355$	−5.17203	+	5.38465i	−0.274503	+	0.285788i
$356$	0.311847	+	0.822274i	0.0165279	+	0.0435804i
$357$	−9.99361	+	17.3094i	−0.528918	+	0.916113i
$358$	−6.37057	−	7.80253i	−0.336695	−	0.412376i
$359$	6.15687	−	1.51753i	0.324947	−	0.0800923i	−0.0734677	−	0.997298i	$-0.523407\pi$
$359$	6.15687	−	1.51753i	0.324947	−	0.0800923i	0.398415	+	0.917205i	$0.369560\pi$
$360$	−1.04548	+	1.81083i	−0.0551017	+	0.0954390i
$361$	7.53518	+	13.0513i	0.396588	+	0.686911i
$362$	1.57062	+	1.63519i	0.0825502	+	0.0859438i
$363$	−1.30277	−	10.7293i	−0.0683776	−	0.563141i
$364$	1.95384	+	0.855979i	0.102409	+	0.0448655i
$365$	−1.58004	+	13.0128i	−0.0827032	+	0.681123i
$366$	14.3376	−	10.7740i	0.749440	−	0.563168i
$367$	−9.36666	−	0.756155i	−0.488935	−	0.0394709i	−0.166459	−	0.986048i	$-0.553233\pi$
$367$	−9.36666	−	0.756155i	−0.488935	−	0.0394709i	−0.322477	+	0.946577i	$0.604515\pi$
$368$	−2.94409	−	14.4211i	−0.153471	−	0.751751i
$369$	−0.693702	+	5.71315i	−0.0361127	+	0.297415i
$370$	3.35559	+	1.42969i	0.174449	+	0.0743258i
$371$	25.1778	−	15.9215i	1.30717	−	0.826602i
$372$	−0.0154514	+	0.0136888i	−0.000801119	+	0.000709729i
$373$	−17.4735	+	1.41060i	−0.904742	+	0.0730383i	−0.524073	−	0.851673i	$-0.675588\pi$
$373$	−17.4735	+	1.41060i	−0.904742	+	0.0730383i	−0.380669	+	0.924712i	$0.624306\pi$
$374$	−0.867670	−	2.99554i	−0.0448661	−	0.154896i
$375$	6.65919	−	2.83722i	0.343879	−	0.146513i
$376$	−20.0273	+	29.0146i	−1.03283	+	1.49631i
$377$	11.1061	+	24.0322i	0.571994	+	1.23772i
$378$	3.41945	+	4.95392i	0.175877	+	0.254802i
$379$	12.7679	+	8.07395i	0.655845	+	0.414731i	0.820521	−	0.571617i	$-0.193684\pi$
$379$	12.7679	+	8.07395i	0.655845	+	0.414731i	−0.164676	+	0.986348i	$0.552658\pi$
$380$	0.216645	−	0.0352083i	0.0111137	−	0.00180615i
$381$	10.8236	+	4.61152i	0.554512	+	0.236255i
$382$	3.14709	−	4.55935i	0.161019	−	0.233276i
$383$	−10.0975	+	34.8607i	−0.515960	+	1.78130i	0.101654	+	0.994820i	$0.467586\pi$
$383$	−10.0975	+	34.8607i	−0.515960	+	1.78130i	−0.617614	+	0.786481i	$0.711901\pi$
$384$	−5.30676	−	11.1838i	−0.270810	−	0.570719i
$385$	−0.491374	+	1.29565i	−0.0250428	+	0.0660323i
$386$	−1.64129	−	2.01021i	−0.0835393	−	0.102317i
$387$	0.497687	+	12.3500i	0.0252988	+	0.627784i
$388$	−0.0254871	−	0.632456i	−0.00129391	−	0.0321081i
$389$	10.6966	−	2.63647i	0.542338	−	0.133674i	0.0413759	−	0.999144i	$-0.486826\pi$
$389$	10.6966	−	2.63647i	0.542338	−	0.133674i	0.500962	+	0.865469i	$0.332980\pi$
$390$	3.06747	−	2.66249i	0.155328	−	0.134820i
$391$	−16.2825	−	4.01329i	−0.823443	−	0.202961i
$392$	−5.38223	+	26.3639i	−0.271844	+	1.33158i
$393$	12.9033	−	5.49758i	0.650885	−	0.277316i
$394$	−11.1877	+	7.07469i	−0.563629	+	0.356418i
$395$	1.06008	−	0.556370i	0.0533382	−	0.0279940i
$396$	−0.0622296	−	0.0101133i	−0.00312716	−	0.000508212i
$397$	−3.42887	+	1.14473i	−0.172090	+	0.0574521i	−0.401407	−	0.915900i	$-0.631479\pi$
$397$	−3.42887	+	1.14473i	−0.172090	+	0.0574521i	0.229317	+	0.973352i	$0.426351\pi$
$398$	−1.82889	−	15.0623i	−0.0916741	−	0.755004i
$399$	−2.26734	+	7.82775i	−0.113509	+	0.391878i
$400$	−3.76241	+	18.4295i	−0.188120	+	0.921474i
$401$	−23.9008	−	7.97928i	−1.19355	−	0.398466i	−0.350636	−	0.936512i	$-0.614034\pi$
$401$	−23.9008	−	7.97928i	−1.19355	−	0.398466i	−0.842916	+	0.538046i	$0.819163\pi$
$402$	−10.9692	−	5.75705i	−0.547092	−	0.287136i
$403$	−0.477840	+	0.197885i	−0.0238029	+	0.00985734i
$404$	−1.21449	+	0.637414i	−0.0604231	+	0.0317125i
$405$	0.759422	−	0.123418i	0.0377360	−	0.00613270i
$406$	35.3345	−	26.5522i	1.75362	−	1.31776i
$407$	0.0571151	−	1.41730i	0.00283109	−	0.0702528i
$408$	−13.2130			−0.654139
$409$	0.216745	−	5.37846i	0.0107173	−	0.265948i	−0.984943	−	0.172882i	$-0.944692\pi$
$409$	0.216745	−	5.37846i	0.0107173	−	0.265948i	0.995660	−	0.0930661i	$-0.0296668\pi$
$410$	−1.29684	−	6.35235i	−0.0640464	−	0.313720i
$411$	4.23900	+	6.14126i	0.209095	+	0.302926i
$412$	1.44990	−	0.484046i	0.0714313	−	0.0238473i
$413$	16.4999	−	34.7727i	0.811905	−	1.71105i
$414$	−3.19416	+	3.91214i	−0.156985	+	0.192271i
$415$	3.51831	+	9.27703i	0.172707	+	0.455391i
$416$	0.323602	+	2.91169i	0.0158659	+	0.142757i
$417$	1.58086	−	4.16838i	0.0774149	−	0.204126i
$418$	−0.635798	−	1.10123i	−0.0310979	−	0.0538631i
$419$	10.1495	−	12.4308i	0.495834	−	0.607286i	−0.464694	−	0.885472i	$-0.653836\pi$
$419$	10.1495	−	12.4308i	0.495834	−	0.607286i	0.960527	+	0.278185i	$0.0897329\pi$
$420$	−0.363894	−	0.273449i	−0.0177562	−	0.0133429i
$421$	−29.2049	−	15.3279i	−1.42336	−	0.747038i	−0.435183	−	0.900342i	$-0.643316\pi$
$421$	−29.2049	−	15.3279i	−1.42336	−	0.747038i	−0.988179	+	0.153304i	$0.951009\pi$
$422$	−17.9210	+	1.44673i	−0.872379	+	0.0704257i
$423$	12.9304	−	1.04385i	0.628698	−	0.0507538i
$424$	17.4373	+	9.15178i	0.846828	+	0.444450i
$425$	17.1329	+	12.8746i	0.831068	+	0.624507i
$426$	−8.98634	+	11.0063i	−0.435389	+	0.533255i
$427$	−25.1774	−	43.6086i	−1.21842	−	2.11037i
$428$	−0.599404	+	1.58050i	−0.0289733	+	0.0763963i
$429$	−1.39113	−	0.748218i	−0.0671642	−	0.0361243i
$430$	−4.93754	−	13.0192i	−0.238109	−	0.627842i
$431$	0.501068	−	0.613697i	0.0241356	−	0.0295608i	−0.762396	−	0.647111i	$-0.775977\pi$
$431$	0.501068	−	0.613697i	0.0241356	−	0.0295608i	0.786532	+	0.617550i	$0.211875\pi$
$432$	−1.82928	+	3.85512i	−0.0880112	+	0.185480i
$433$	−12.4367	+	4.15199i	−0.597671	+	0.199532i	−0.599377	−	0.800467i	$-0.704585\pi$
$433$	−12.4367	+	4.15199i	−0.597671	+	0.199532i	0.00170606	+	0.999999i	$0.499457\pi$
$434$	0.490498	+	0.710609i	0.0235446	+	0.0341103i
$435$	−1.13001	−	5.53518i	−0.0541801	−	0.265392i
$436$	−0.105866	+	2.62705i	−0.00507008	+	0.125813i
$437$	−6.83766			−0.327090
$438$	−1.00449	+	24.9262i	−0.0479965	+	1.19102i
$439$	26.1189	−	19.6271i	1.24659	−	0.936749i	0.247107	−	0.968988i	$-0.420520\pi$
$439$	26.1189	−	19.6271i	1.24659	−	0.936749i	0.999480	+	0.0322387i	$0.0102637\pi$
$440$	−0.904180	+	0.146944i	−0.0431051	+	0.00700526i
$441$	8.76680	−	4.60117i	0.417467	−	0.219103i
$442$	24.2622	+	8.37446i	1.15404	+	0.398332i
$443$	15.9632	+	8.37813i	0.758434	+	0.398057i	0.799164	−	0.601113i	$-0.205276\pi$
$443$	15.9632	+	8.37813i	0.758434	+	0.398057i	−0.0407299	+	0.999170i	$0.512968\pi$
$444$	0.441964	+	0.147549i	0.0209747	+	0.00700238i
$445$	0.940456	−	4.60666i	0.0445819	−	0.218377i
$446$	10.3205	−	35.6305i	0.488690	−	1.68715i
$447$	−0.155582	−	1.28133i	−0.00735878	−	0.0606050i
$448$	−28.6399	+	9.56140i	−1.35311	+	0.451734i
$449$	27.5338	+	4.47468i	1.29940	+	0.211173i	0.770462	−	0.637486i	$-0.220026\pi$
$449$	27.5338	+	4.47468i	1.29940	+	0.211173i	0.528940	+	0.848659i	$0.322590\pi$
$450$	5.71500	−	2.99946i	0.269408	−	0.141396i
$451$	−2.13097	+	1.34754i	−0.100343	+	0.0634533i
$452$	0.439531	−	0.187267i	0.0206738	−	0.00880828i
$453$	3.20716	−	15.7097i	0.150686	−	0.738107i
$454$	−8.23906	−	2.03074i	−0.386678	−	0.0953076i
$455$	−6.38285	−	9.45084i	−0.299233	−	0.443062i
$456$	−5.23085	+	1.28929i	−0.244957	+	0.0603765i
$457$	−1.43902	−	35.7088i	−0.0673143	−	1.67039i	−0.582136	−	0.813091i	$-0.697783\pi$
$457$	−1.43902	−	35.7088i	−0.0673143	−	1.67039i	0.514822	−	0.857297i	$-0.327858\pi$
$458$	−0.612026	−	15.1873i	−0.0285981	−	0.709655i
$459$	3.07483	+	3.76598i	0.143521	+	0.175781i
$460$	0.135428	−	0.357095i	0.00631437	−	0.0166496i
$461$	−13.1707	−	27.7566i	−0.613419	−	1.29275i	−0.937915	−	0.346866i	$-0.887246\pi$
$461$	−13.1707	−	27.7566i	−0.613419	−	1.29275i	0.324496	−	0.945887i	$-0.394805\pi$
$462$	−0.733688	+	2.53298i	−0.0341342	+	0.117845i
$463$	−5.72747	+	8.29768i	−0.266178	+	0.385626i	−0.933168	−	0.359441i	$-0.882967\pi$
$463$	−5.72747	+	8.29768i	−0.266178	+	0.385626i	0.666989	+	0.745067i	$0.267583\pi$
$464$	28.8248	+	12.2811i	1.33816	+	0.570135i
$465$	0.108934	−	0.0177035i	0.00505171	−	0.000820982i
$466$	−16.9007	−	10.6874i	−0.782911	−	0.495083i
$467$	10.2751	+	14.8860i	0.475473	+	0.688842i	0.985183	−	0.171504i	$-0.0548628\pi$
$467$	10.2751	+	14.8860i	0.475473	+	0.688842i	−0.509710	+	0.860346i	$0.670247\pi$
$468$	0.363214	−	0.370546i	0.0167896	−	0.0171285i
$469$	−19.7586	+	28.6252i	−0.912366	+	1.32179i
$470$	−13.4446	+	5.72821i	−0.620154	+	0.264223i
$471$	−2.31921	−	8.00683i	−0.106863	−	0.368935i
$472$	25.3613	−	2.04738i	1.16735	−	0.0942381i
$473$	−4.05308	+	3.59072i	−0.186361	+	0.165101i
$474$	1.92568	−	1.21772i	0.0884492	−	0.0559319i
$475$	8.03898	+	3.42509i	0.368854	+	0.157154i
$476$	0.346705	−	2.85538i	0.0158912	−	0.130876i
$477$	−1.44942	−	7.09974i	−0.0663645	−	0.325075i
$478$	−9.87375	−	0.797091i	−0.451615	−	0.0364581i
$479$	13.9035	−	10.4478i	0.635268	−	0.477373i	−0.233655	−	0.972319i	$-0.575069\pi$
$479$	13.9035	−	10.4478i	0.635268	−	0.477373i	0.868923	+	0.494947i	$0.164812\pi$
$480$	0.0753534	−	0.620591i	0.00343940	−	0.0283260i
$481$	9.26098	+	7.10733i	0.422264	+	0.324066i
$482$	0.921729	+	7.59112i	0.0419836	+	0.345766i
$483$	9.82305	+	10.2269i	0.446964	+	0.465339i
$484$	0.777691	+	1.34700i	0.0353496	+	0.0612273i
$485$	−1.69203	+	2.93068i	−0.0768311	+	0.133075i
$486$	1.42166	−	0.350408i	0.0644879	−	0.0158948i
$487$	18.8732	+	23.1155i	0.855226	+	1.04746i	0.998331	+	0.0577543i	$0.0183940\pi$
$487$	18.8732	+	23.1155i	0.855226	+	1.04746i	−0.143105	+	0.989708i	$0.545709\pi$
$488$	16.6441	−	28.8284i	0.753441	−	1.30500i
$489$	−2.82908	−	7.45966i	−0.127935	−	0.337337i
$490$	−7.72648	+	8.04412i	−0.349047	+	0.363396i
$491$	11.1633	+	3.72687i	0.503795	+	0.168191i	0.557195	−	0.830382i	$-0.311878\pi$
$491$	11.1633	+	3.72687i	0.503795	+	0.168191i	−0.0534000	+	0.998573i	$0.517006\pi$
$492$	−0.230424	−	0.795514i	−0.0103883	−	0.0358646i
$493$	26.7208	−	23.6726i	1.20345	−	1.06616i
$494$	10.4223	+	0.947896i	0.468921	+	0.0426479i
$495$	0.252296	+	0.223515i	0.0113399	+	0.0100463i
$496$	−0.262398	+	0.552993i	−0.0117820	+	0.0248301i
$497$	27.6358	+	28.7719i	1.23963	+	1.29060i
$498$	8.09459	+	17.0590i	0.362727	+	0.764431i
$499$	27.0692	+	6.67196i	1.21178	+	0.298678i	0.792894	−	0.609359i	$-0.208573\pi$
$499$	27.0692	+	6.67196i	1.21178	+	0.298678i	0.418890	+	0.908037i	$0.362419\pi$
$500$	−0.721594	+	0.751259i	−0.0322707	+	0.0335973i
$501$	12.5203	+	9.40839i	0.559366	+	0.420336i
$502$	6.62658	+	5.87064i	0.295759	+	0.262019i
$503$	−9.02441	−	1.46661i	−0.402378	−	0.0653928i	−0.0441455	−	0.999025i	$-0.514057\pi$
$503$	−9.02441	−	1.46661i	−0.402378	−	0.0653928i	−0.358233	+	0.933632i	$0.616621\pi$
$504$	9.44303	+	5.97141i	0.420626	+	0.265988i
$505$	7.30923	+	0.590062i	0.325256	+	0.0262574i
$506$	−2.21260			−0.0983622
$507$	11.6311	−	5.80660i	0.516557	−	0.257880i
$508$	−1.69311			−0.0751194
$509$	−35.1805	−	2.84006i	−1.55935	−	0.125884i	−0.729542	−	0.683936i	$-0.760267\pi$
$509$	−35.1805	−	2.84006i	−1.55935	−	0.125884i	−0.829805	+	0.558053i	$0.811549\pi$
$510$	−4.62913	−	2.92729i	−0.204981	−	0.129622i
$511$	69.1353	+	11.2356i	3.05836	+	0.497033i
$512$	−14.7654	−	13.0810i	−0.652544	−	0.578103i
$513$	1.58476	+	1.19087i	0.0699689	+	0.0525782i
$514$	2.32100	−	2.41641i	0.102375	−	0.106583i
$515$	−7.93471	−	1.95573i	−0.349645	−	0.0861798i
$516$	−0.762523	−	1.60698i	−0.0335682	−	0.0707435i
$517$	3.93688	+	4.09873i	0.173144	+	0.180262i
$518$	8.35503	−	17.6079i	0.367099	−	0.773645i
$519$	15.9465	+	14.1274i	0.699976	+	0.620124i
$520$	3.30088	−	6.77804i	0.144753	−	0.297237i
$521$	25.8939	−	22.9400i	1.13443	−	1.00502i	0.134532	−	0.990909i	$-0.457047\pi$
$521$	25.8939	−	22.9400i	1.13443	−	1.00502i	0.999900	−	0.0141099i	$-0.00449146\pi$
$522$	−2.99118	−	10.3267i	−0.130920	−	0.451989i
$523$	−1.13005	−	0.377266i	−0.0494136	−	0.0164967i	0.291854	−	0.956463i	$-0.405728\pi$
$523$	−1.13005	−	0.377266i	−0.0494136	−	0.0164967i	−0.341267	+	0.939966i	$0.610856\pi$
$524$	−1.39821	+	1.45569i	−0.0610810	+	0.0635920i
$525$	−6.42607	−	16.9442i	−0.280457	−	0.739504i
$526$	−2.40175	+	4.15995i	−0.104721	+	0.181383i
$527$	0.441065	+	0.540206i	0.0192131	+	0.0235317i
$528$	−1.81508	+	0.447377i	−0.0789912	+	0.0194696i
$529$	5.55116	−	9.61489i	0.241355	−	0.418039i
$530$	4.08156	+	7.06947i	0.177292	+	0.307078i
$531$	−6.48545	−	6.75207i	−0.281445	−	0.293015i
$532$	−0.141364	−	1.16424i	−0.00612892	−	0.0504762i
$533$	1.04584	−	20.7240i	0.0453005	−	0.897655i
$534$	1.07853	−	8.88247i	0.0466724	−	0.384382i
$535$	7.22466	−	5.42898i	0.312349	−	0.234715i
$536$	−22.9189	−	1.85021i	−0.989948	−	0.0799168i
$537$	1.37606	+	6.74039i	0.0593814	+	0.290869i
$538$	−1.96806	+	16.2085i	−0.0848492	+	0.698796i
$539$	3.99044	+	1.70017i	0.171881	+	0.0732315i
$540$	−0.0935809	+	0.0591770i	−0.00402708	+	0.00254657i
$541$	7.33986	−	6.50255i	0.315565	−	0.279567i	−0.490440	−	0.871475i	$-0.663164\pi$
$541$	7.33986	−	6.50255i	0.315565	−	0.279567i	0.806005	+	0.591909i	$0.201625\pi$
$542$	−10.2531	+	0.827713i	−0.440407	+	0.0355533i
$543$	−0.430817	−	1.48735i	−0.0184881	−	0.0638284i
$544$	3.63425	−	1.54841i	0.155817	−	0.0663876i
$545$	7.98497	−	11.5682i	0.342039	−	0.495528i
$546$	−13.5550	−	16.9500i	−0.580100	−	0.725394i
$547$	11.0003	+	15.9367i	0.470340	+	0.681405i	0.984319	−	0.176397i	$-0.0564444\pi$
$547$	11.0003	+	15.9367i	0.470340	+	0.681405i	−0.513979	+	0.857803i	$0.671829\pi$
$548$	−0.907631	−	0.573951i	−0.0387721	−	0.0245180i
$549$	−12.0900	+	1.96482i	−0.515989	+	0.0838563i
$550$	2.60134	+	1.10833i	0.110921	+	0.0472592i
$551$	8.26854	−	11.9790i	0.352252	−	0.510324i
$552$	−2.60806	+	9.00407i	−0.111006	+	0.383239i
$553$	−2.74237	−	5.77942i	−0.116617	−	0.245766i
$554$	11.8400	−	31.2194i	0.503031	−	1.32638i
$555$	−1.57547	−	1.92961i	−0.0668751	−	0.0819072i
$556$	0.0258330	+	0.641039i	0.00109556	+	0.0271861i
$557$	1.70579	+	42.3287i	0.0722765	+	1.79352i	0.476816	+	0.879003i	$0.341791\pi$
$557$	1.70579	+	42.3287i	0.0722765	+	1.79352i	−0.404539	+	0.914521i	$0.632568\pi$
$558$	0.203928	−	0.0502638i	0.00863298	−	0.00212784i
$559$	−4.92255	−	44.2919i	−0.208202	−	1.87335i
$560$	−13.1047	−	3.23001i	−0.553773	−	0.136493i
$561$	−0.426042	+	2.08689i	−0.0179875	+	0.0881087i
$562$	20.2256	−	8.61734i	0.853167	−	0.363501i
$563$	−29.4333	+	18.6125i	−1.24046	+	0.784422i	−0.983308	−	0.181948i	$-0.941760\pi$
$563$	−29.4333	+	18.6125i	−1.24046	+	0.784422i	−0.257156	+	0.966370i	$0.582785\pi$
$564$	−1.65302	+	0.867573i	−0.0696048	+	0.0365314i
$565$	−2.52119	−	0.409734i	−0.106067	−	0.0172376i
$566$	1.33460	−	0.445555i	0.0560974	−	0.0187281i
$567$	−0.495535	−	4.08109i	−0.0208105	−	0.171390i
$568$	−7.33742	+	25.3317i	−0.307871	+	1.06289i
$569$	−1.73992	+	8.52270i	−0.0729413	+	0.357290i	−0.999837	−	0.0180276i	$-0.994261\pi$
$569$	−1.73992	+	8.52270i	−0.0729413	+	0.357290i	0.926896	+	0.375318i	$0.122466\pi$
$570$	−2.11825	−	0.707177i	−0.0887239	−	0.0296204i
$571$	33.0874	+	17.3656i	1.38466	+	0.726727i	0.982046	−	0.188641i	$-0.0604084\pi$
$571$	33.0874	+	17.3656i	1.38466	+	0.726727i	0.402617	+	0.915369i	$0.368101\pi$
$572$	0.226381	+	0.0205892i	0.00946548	+	0.000860876i
$573$	−3.35023	+	1.75834i	−0.139958	+	0.0734556i
$574$	−34.1941	+	5.55708i	−1.42723	+	0.231948i
$575$	12.1553	−	9.13409i	0.506910	−	0.380918i
$576$	−0.295733	+	7.33855i	−0.0123222	+	0.305773i
$577$	15.1799			0.631945			0.315973	−	0.948768i	$-0.397669\pi$
$577$	15.1799			0.631945			0.315973	+	0.948768i	$0.397669\pi$
$578$	0.391313	−	9.71034i	0.0162765	−	0.403897i
$579$	0.354523	+	1.73657i	0.0147335	+	0.0721693i
$580$	0.461833	+	0.669081i	0.0191766	+	0.0277821i
$581$	50.2868	−	16.7882i	2.08625	−	0.696492i
$582$	−2.76085	+	5.81837i	−0.114441	+	0.241179i
$583$	2.00771	−	2.45900i	0.0831509	−	0.101841i
$584$	16.4192	+	43.2940i	0.679433	+	1.79152i
$585$	−2.70005	+	0.636515i	−0.111633	+	0.0263167i
$586$	11.5081	−	30.3443i	0.475395	−	1.25351i
$587$	4.99950	+	8.65940i	0.206352	+	0.357411i	0.950563	−	0.310533i	$-0.100508\pi$
$587$	4.99950	+	8.65940i	0.206352	+	0.357411i	−0.744211	+	0.667945i	$0.767174\pi$
$588$	−0.901127	+	1.10368i	−0.0371618	+	0.0455150i
$589$	0.227324	+	0.170823i	0.00936672	+	0.00703864i
$590$	9.33886	+	4.90141i	0.384475	+	0.201788i
$591$	9.01101	−	0.727444i	0.370663	−	0.0299230i
$592$	13.7711	−	1.11171i	0.565987	−	0.0456912i
$593$	−18.2566	−	9.58180i	−0.749708	−	0.393477i	0.0461703	−	0.998934i	$-0.485298\pi$
$593$	−18.2566	−	9.58180i	−0.749708	−	0.393477i	−0.795878	+	0.605456i	$0.792991\pi$
$594$	0.512814	+	0.385354i	0.0210410	+	0.0158113i
$595$	−9.72567	+	11.9118i	−0.398714	+	0.488336i
$596$	0.0928750	+	0.160864i	0.00380431	+	0.00658926i
$597$	−3.67460	+	9.68913i	−0.150392	+	0.396550i
$598$	10.4959	−	14.8807i	0.429208	−	0.608516i
$599$	7.38024	+	19.4601i	0.301548	+	0.795118i	0.997062	+	0.0766045i	$0.0244079\pi$
$599$	7.38024	+	19.4601i	0.301548	+	0.795118i	−0.695513	+	0.718513i	$0.744823\pi$
$600$	7.57655	−	9.27959i	0.309311	−	0.378838i
$601$	−0.693186	+	1.46086i	−0.0282757	+	0.0595897i	−0.917097	−	0.398665i	$-0.869474\pi$
$601$	−0.693186	+	1.46086i	−0.0282757	+	0.0595897i	0.888821	+	0.458254i	$0.151525\pi$
$602$	−70.5716	+	23.5603i	−2.87628	+	0.960245i
$603$	4.80619	+	6.96296i	0.195723	+	0.283554i
$604$	0.461540	+	2.26077i	0.0187798	+	0.0919896i
$605$	0.334834	−	8.30883i	0.0136130	−	0.337802i
$606$	13.9554			0.566898
$607$	1.40299	−	34.8148i	0.0569456	−	1.41309i	−0.678048	−	0.735017i	$-0.737174\pi$
$607$	1.40299	−	34.8148i	0.0569456	−	1.41309i	0.734994	−	0.678074i	$-0.237185\pi$
$608$	1.28767	−	0.967619i	0.0522218	−	0.0392421i
$609$	−29.7953	+	4.84221i	−1.20737	+	0.196216i
$610$	12.2180	−	6.41252i	0.494694	−	0.259635i
$611$	−46.2410	+	7.03412i	−1.87071	+	0.284570i
$612$	−0.619518	−	0.325148i	−0.0250425	−	0.0131433i
$613$	−6.95115	−	2.32063i	−0.280754	−	0.0937295i	0.172804	−	0.984956i	$-0.444717\pi$
$613$	−6.95115	−	2.32063i	−0.280754	−	0.0937295i	−0.453558	+	0.891227i	$0.649846\pi$
$614$	−3.56415	+	17.4584i	−0.143837	+	0.704562i
$615$	−1.23192	+	4.25308i	−0.0496758	+	0.171501i
$616$	0.589991	+	4.85901i	0.0237714	+	0.195775i
$617$	−19.0312	+	6.35354i	−0.766166	+	0.255784i	−0.672776	−	0.739846i	$-0.734898\pi$
$617$	−19.0312	+	6.35354i	−0.766166	+	0.255784i	−0.0933896	+	0.995630i	$0.529770\pi$
$618$	−15.3510	−	2.49478i	−0.617507	−	0.100355i
$619$	−31.6949	+	16.6348i	−1.27393	+	0.668608i	−0.959776	−	0.280765i	$-0.909412\pi$
$619$	−31.6949	+	16.6348i	−1.27393	+	0.668608i	−0.314150	+	0.949373i	$0.601719\pi$
$620$	−0.0134236	+	0.00848857i	−0.000539104	+	0.000340909i
$621$	3.17329	−	1.35201i	0.127340	−	0.0542543i
$622$	1.98491	−	9.72273i	0.0795876	−	0.389846i
$623$	−24.3925	−	6.01221i	−0.977265	−	0.240874i
$624$	5.60136	−	14.3294i	0.224234	−	0.573635i
$625$	−15.9925	+	3.94179i	−0.639699	+	0.157672i
$626$	0.788366	+	19.5631i	0.0315095	+	0.781899i
$627$	0.0349690	+	0.867747i	0.00139653	+	0.0346545i
$628$	0.758694	+	0.929232i	0.0302752	+	0.0370804i
$629$	5.58196	−	14.7184i	0.222567	−	0.586862i
$630$	1.98540	+	4.18414i	0.0791002	+	0.166700i
$631$	−12.4183	+	42.8729i	−0.494364	+	1.70674i	0.193671	+	0.981066i	$0.437960\pi$
$631$	−12.4183	+	42.8729i	−0.494364	+	1.70674i	−0.688036	+	0.725677i	$0.741527\pi$
$632$	2.40229	−	3.48032i	0.0955580	−	0.138440i
$633$	11.2966	+	4.81302i	0.448999	+	0.191300i
$634$	6.22403	−	1.01150i	0.247188	−	0.0401719i
$635$	7.65057	+	4.83792i	0.303603	+	0.191987i
$636$	0.592374	+	0.858201i	0.0234891	+	0.0340299i
$637$	−30.3637	+	18.7723i	−1.20306	+	0.743787i
$638$	2.67562	−	3.87630i	0.105929	−	0.153464i
$639$	8.92760	−	3.80369i	0.353170	−	0.150472i
$640$	−2.64980	−	9.14815i	−0.104742	−	0.361613i
$641$	−23.4836	+	1.89579i	−0.927545	+	0.0748791i	−0.534998	−	0.844853i	$-0.679688\pi$
$641$	−23.4836	+	1.89579i	−0.927545	+	0.0748791i	−0.392546	+	0.919732i	$0.628406\pi$
$642$	12.8732	−	11.4047i	0.508065	−	0.450107i
$643$	22.6422	−	14.3181i	0.892922	−	0.564650i	−0.00735203	−	0.999973i	$-0.502340\pi$
$643$	22.6422	−	14.3181i	0.892922	−	0.564650i	0.900274	+	0.435323i	$0.143366\pi$
$644$	−1.87738	−	0.799878i	−0.0739793	−	0.0315196i
$645$	−1.14626	+	9.44027i	−0.0451338	+	0.371710i
$646$	−2.82269	−	13.8265i	−0.111057	−	0.543995i
$647$	29.5848	+	2.38833i	1.16310	+	0.0938949i	0.646900	−	0.762575i	$-0.276065\pi$
$647$	29.5848	+	2.38833i	1.16310	+	0.0938949i	0.516197	+	0.856470i	$0.327347\pi$
$648$	2.17265	−	1.63264i	0.0853498	−	0.0641362i
$649$	0.494388	−	4.07165i	0.0194064	−	0.159826i
$650$	−19.7939	+	12.2375i	−0.776379	+	0.479996i
$651$	−0.0710813	−	0.585407i	−0.00278590	−	0.0229439i
$652$	0.795333	+	0.828030i	0.0311477	+	0.0324282i
$653$	−13.0516	−	22.6061i	−0.510750	−	0.884645i	−0.999922	−	0.0124581i	$-0.996034\pi$
$653$	−13.0516	−	22.6061i	−0.510750	−	0.884645i	0.489172	−	0.872187i	$-0.337299\pi$
$654$	13.3753	−	23.1668i	0.523017	−	0.905892i
$655$	10.4775	−	2.58248i	0.409392	−	0.100906i
$656$	−15.5314	−	19.0225i	−0.606399	−	0.742704i
$657$	8.51875	−	14.7549i	0.332348	−	0.575644i
$658$	27.6902	+	73.0130i	1.07948	+	2.84634i
$659$	9.19886	−	9.57703i	0.358337	−	0.373068i	−0.517494	−	0.855687i	$-0.673135\pi$
$659$	9.19886	−	9.57703i	0.358337	−	0.373068i	0.875830	+	0.482619i	$0.160314\pi$
$660$	−0.0460104	−	0.0153605i	−0.00179095	−	0.000597908i
$661$	−4.20190	−	14.5066i	−0.163435	−	0.564243i	−0.999869	−	0.0161756i	$-0.994851\pi$
$661$	−4.20190	−	14.5066i	−0.163435	−	0.564243i	0.836434	−	0.548067i	$-0.184636\pi$
$662$	9.39137	−	8.32003i	0.365006	−	0.323367i
$663$	−12.0142	−	12.7649i	−0.466594	−	0.495746i
$664$	26.2329	+	23.2403i	1.01803	+	0.901899i
$665$	−2.68795	+	5.66474i	−0.104234	+	0.219669i
$666$	−3.28403	−	3.41904i	−0.127254	−	0.132485i
$667$	−10.8575	−	22.8818i	−0.420406	−	0.885986i
$668$	−2.18831	−	0.539371i	−0.0846684	−	0.0208689i
$669$	−17.5499	+	18.2713i	−0.678517	+	0.706411i
$670$	−7.61969	−	5.72583i	−0.294374	−	0.221208i
$671$	−4.01656	−	3.55836i	−0.155058	−	0.137369i
$672$	−3.29711	−	0.535832i	−0.127189	−	0.0206702i
$673$	−35.9791	−	22.7518i	−1.38689	−	0.877019i	−0.387893	−	0.921704i	$-0.626797\pi$
$673$	−35.9791	−	22.7518i	−1.38689	−	0.877019i	−0.999001	+	0.0446857i	$0.985771\pi$
$674$	8.39982	+	0.678104i	0.323549	+	0.0261196i
$675$	−4.40805			−0.169666
$676$	−1.21235	+	1.42484i	−0.0466289	+	0.0548016i
$677$	−13.2181			−0.508014			−0.254007	−	0.967202i	$-0.581749\pi$
$677$	−13.2181			−0.508014			−0.254007	+	0.967202i	$0.581749\pi$
$678$	−4.84524	−	0.391148i	−0.186080	−	0.0150220i
$679$	15.2828	+	9.66426i	0.586500	+	0.370880i
$680$	−10.0342	−	1.63072i	−0.384795	−	0.0625352i
$681$	4.33790	+	3.84304i	0.166229	+	0.147266i
$682$	0.0735599	+	0.0552767i	0.00281675	+	0.00211665i
$683$	−10.3727	+	10.7991i	−0.396899	+	0.413216i	−0.889424	−	0.457083i	$-0.848894\pi$
$683$	−10.3727	+	10.7991i	−0.396899	+	0.413216i	0.492525	+	0.870298i	$0.336074\pi$
$684$	−0.276987	−	0.0682711i	−0.0105908	−	0.00261041i
$685$	2.46125	+	5.18698i	0.0940396	+	0.198184i
$686$	12.0962	+	12.5935i	0.461835	+	0.480821i
$687$	−4.45015	+	9.37850i	−0.169784	+	0.357812i
$688$	−39.4775	−	34.9740i	−1.50507	−	1.33337i
$689$	7.01386	+	25.1674i	0.267207	+	0.958802i
$690$	−2.90855	+	2.57675i	−0.110727	+	0.0980952i
$691$	−2.24789	−	7.76062i	−0.0855138	−	0.295228i	0.906351	−	0.422526i	$-0.138857\pi$
$691$	−2.24789	−	7.76062i	−0.0855138	−	0.295228i	−0.991864	+	0.127298i	$0.959369\pi$
$692$	−2.90811	−	0.970871i	−0.110550	−	0.0369070i
$693$	1.24763	−	1.29892i	0.0473934	−	0.0493417i
$694$	17.7704	+	46.8567i	0.674556	+	1.77866i
$695$	1.71499	−	2.97045i	0.0650534	−	0.112676i
$696$	−12.6206	−	15.4574i	−0.478382	−	0.585912i
$697$	−27.1672	+	6.69611i	−1.02903	+	0.253633i
$698$	16.0465	−	27.7934i	0.607369	−	1.05199i
$699$	6.82838	+	11.8271i	0.258273	+	0.447342i
$700$	1.80655	+	1.88082i	0.0682812	+	0.0710883i
$701$	1.23966	+	10.2096i	0.0468215	+	0.385610i	0.997216	+	0.0745635i	$0.0237563\pi$
$701$	1.23966	+	10.2096i	0.0468215	+	0.385610i	−0.950395	+	0.311046i	$0.899321\pi$
$702$	−5.02430	+	1.62089i	−0.189630	+	0.0611765i
$703$	0.773642	−	6.37151i	0.0291785	−	0.240306i
$704$	−2.57228	+	1.93295i	−0.0969466	+	0.0728506i
$705$	9.94847	+	0.803124i	0.374681	+	0.0302474i
$706$	−4.95819	−	24.2868i	−0.186604	−	0.914047i
$707$	4.72293	−	38.8969i	0.177624	−	1.46287i
$708$	1.23950	+	0.528102i	0.0465833	+	0.0198473i
$709$	5.30687	−	3.35586i	0.199304	−	0.126032i	−0.431086	−	0.902311i	$-0.641869\pi$
$709$	5.30687	−	3.35586i	0.199304	−	0.126032i	0.630390	+	0.776279i	$0.282895\pi$
$710$	−8.18280	+	7.24933i	−0.307095	+	0.272062i
$711$	−1.55101	+	0.125211i	−0.0581675	+	0.00469576i
$712$	−4.62057	−	15.9521i	−0.173163	−	0.597828i
$713$	0.455188	−	0.193937i	0.0170469	−	0.00726301i
$714$	−16.6247	+	24.0850i	−0.622163	+	0.901359i
$715$	−0.964108	−	0.739904i	−0.0360556	−	0.0276708i
$716$	−0.562391	−	0.814765i	−0.0210176	−	0.0304492i
$717$	5.71800	+	3.61584i	0.213542	+	0.135036i
$718$	9.16451	−	1.48938i	0.342017	−	0.0555831i
$719$	−22.0842	−	9.40920i	−0.823602	−	0.350904i	−0.0612949	−	0.998120i	$-0.519523\pi$
$719$	−22.0842	−	9.40920i	−0.823602	−	0.350904i	−0.762307	+	0.647216i	$0.775933\pi$
$720$	−1.86499	+	2.70190i	−0.0695039	+	0.100694i
$721$	−12.1488	+	41.9425i	−0.452445	+	1.56202i
$722$	9.45960	+	19.9357i	0.352050	+	0.741929i
$723$	1.85193	−	4.88315i	0.0688742	−	0.181606i
$724$	0.140936	+	0.172615i	0.00523783	+	0.00641518i
$725$	1.30328	+	32.3406i	0.0484027	+	1.20110i
$726$	−0.637220	−	15.8124i	−0.0236494	−	0.586855i
$727$	−5.37668	+	1.32523i	−0.199410	+	0.0491502i	−0.337756	−	0.941234i	$-0.609668\pi$
$727$	−5.37668	+	1.32523i	−0.199410	+	0.0491502i	0.138346	+	0.990384i	$0.455822\pi$
$728$	−35.4776	−	19.0817i	−1.31489	−	0.707214i
$729$	−0.970942	−	0.239316i	−0.0359608	−	0.00886354i
$730$	−3.83918	+	18.8056i	−0.142095	+	0.696025i
$731$	−55.2833	+	23.5540i	−2.04473	+	0.871177i
$732$	1.48981	−	0.942098i	0.0550649	−	0.0348209i
$733$	−11.7832	+	6.18428i	−0.435221	+	0.228422i	−0.668081	−	0.744089i	$-0.732884\pi$
$733$	−11.7832	+	6.18428i	−0.435221	+	0.228422i	0.232860	+	0.972510i	$0.425192\pi$
$734$	−13.5812	−	2.20716i	−0.501291	−	0.0814676i
$735$	7.22557	−	2.41225i	0.266519	−	0.0889772i
$736$	−0.337823	−	2.78223i	−0.0124523	−	0.102554i
$737$	−1.03123	+	3.56022i	−0.0379859	+	0.131143i
$738$	−1.68555	+	8.25639i	−0.0620461	+	0.303922i
$739$	1.65766	+	0.553409i	0.0609781	+	0.0203575i	0.346993	−	0.937868i	$-0.387203\pi$
$739$	1.65766	+	0.553409i	0.0609781	+	0.0203575i	−0.286015	+	0.958225i	$0.592331\pi$
$740$	0.317427	+	0.166599i	0.0116689	+	0.00612429i
$741$	−6.00185	−	3.88114i	−0.220483	−	0.142577i
$742$	38.6219	−	20.2703i	1.41786	−	0.744148i
$743$	−3.12061	+	0.507148i	−0.114484	+	0.0186055i	−0.217383	−	0.976086i	$-0.569752\pi$
$743$	−3.12061	+	0.507148i	−0.114484	+	0.0186055i	0.102899	+	0.994692i	$0.467188\pi$
$744$	0.311653	−	0.234192i	0.0114257	−	0.00858589i
$745$	0.0399873	−	0.992275i	0.00146502	−	0.0363541i
$746$	−25.6681			−0.939774
$747$	0.519258	−	12.8853i	0.0189987	−	0.471447i
$748$	−0.0613114	−	0.300323i	−0.00224177	−	0.0109809i
$749$	−27.4308	−	39.7404i	−1.00230	−	1.45208i
$750$	10.0531	−	3.35622i	0.367088	−	0.122552i
$751$	−22.2798	+	46.9536i	−0.813001	+	1.71336i	−0.119587	+	0.992824i	$0.538157\pi$
$751$	−22.2798	+	46.9536i	−0.813001	+	1.71336i	−0.693414	+	0.720539i	$0.743894\pi$
$752$	−35.0090	+	42.8782i	−1.27665	+	1.56361i
$753$	−2.14404	−	5.65337i	−0.0781332	−	0.206020i
$754$	13.3775	+	36.3826i	0.487179	+	1.32498i
$755$	4.37445	−	11.5345i	0.159203	−	0.419783i
$756$	0.295811	+	0.512359i	0.0107585	+	0.0186343i
$757$	25.8425	−	31.6513i	0.939262	−	1.15039i	−0.0491805	−	0.998790i	$-0.515661\pi$
$757$	25.8425	−	31.6513i	0.939262	−	1.15039i	0.988442	−	0.151597i	$-0.0484416\pi$
$758$	17.6830	+	13.2879i	0.642277	+	0.482640i
$759$	1.33803	+	0.702254i	0.0485676	+	0.0254902i
$760$	−4.13155	+	0.333533i	−0.149867	+	0.0120985i
$761$	−19.8697	+	1.60405i	−0.720276	+	0.0581467i	−0.435169	−	0.900349i	$-0.643311\pi$
$761$	−19.8697	+	1.60405i	−0.720276	+	0.0581467i	−0.285107	+	0.958496i	$0.592029\pi$
$762$	15.2533	+	8.00558i	0.552571	+	0.290011i
$763$	−60.0445	−	45.1205i	−2.17376	−	1.63347i
$764$	0.344366	−	0.421772i	0.0124587	−	0.0152592i
$765$	1.87030	+	3.23946i	0.0676209	+	0.117123i
$766$	−18.8443	+	49.6882i	−0.680871	+	1.79531i
$767$	25.0383	+	22.6396i	0.904082	+	0.817468i
$768$	−1.21855	−	3.21306i	−0.0439708	−	0.115941i
$769$	17.7197	−	21.7026i	0.638987	−	0.782617i	−0.349005	−	0.937121i	$-0.613480\pi$
$769$	17.7197	−	21.7026i	0.638987	−	0.782617i	0.987992	+	0.154504i	$0.0493779\pi$
$770$	−0.869795	+	1.83305i	−0.0313452	+	0.0660587i
$771$	−2.17052	+	0.724627i	−0.0781695	+	0.0260968i
$772$	−0.144892	−	0.209913i	−0.00521479	−	0.00755492i
$773$	1.36568	+	6.68954i	0.0491201	+	0.240606i	0.996937	−	0.0782091i	$-0.0249202\pi$
$773$	1.36568	+	6.68954i	0.0491201	+	0.240606i	−0.947817	+	0.318815i	$0.896715\pi$
$774$	−0.728718	+	18.0829i	−0.0261932	+	0.649978i
$775$	−0.632306			−0.0227131
$776$	−0.481320	+	11.9438i	−0.0172784	+	0.428759i
$777$	−10.6411	+	7.99626i	−0.381747	+	0.286864i
$778$	15.9219	−	2.58755i	0.570826	−	0.0927683i
$779$	−10.1018	+	5.30181i	−0.361933	+	0.189957i
$780$	0.321565	−	0.236574i	0.0115139	−	0.00847070i
$781$	3.76437	+	1.97569i	0.134700	+	0.0706959i
$782$	−23.2909	−	7.77564i	−0.832881	−	0.278056i
$783$	−1.46872	+	7.19428i	−0.0524879	+	0.257103i
$784$	−11.7542	+	40.5801i	−0.419792	+	1.44929i
$785$	−0.773069	−	6.36679i	−0.0275920	−	0.227241i
$786$	19.4796	−	6.50324i	0.694813	−	0.231963i
$787$	−9.15339	−	1.48757i	−0.326283	−	0.0530261i	−0.00493643	−	0.999988i	$-0.501571\pi$
$787$	−9.15339	−	1.48757i	−0.326283	−	0.0530261i	−0.321347	+	0.946962i	$0.604135\pi$
$788$	−1.15197	+	0.604599i	−0.0410371	+	0.0215379i
$789$	2.77274	−	1.75337i	0.0987121	−	0.0624217i
$790$	1.61269	−	0.687103i	0.0573769	−	0.0244460i
$791$	−2.73000	+	13.3724i	−0.0970677	+	0.475469i
$792$	1.15602	+	0.284933i	0.0410773	+	0.0101246i
$793$	42.9847	−	10.1333i	1.52643	−	0.359845i
$794$	−5.13918	+	1.26669i	−0.182383	+	0.0449533i
$795$	−0.224487	−	5.57058i	−0.00796173	−	0.197568i
$796$	−0.0600472	−	1.49006i	−0.00212832	−	0.0528136i
$797$	−22.7846	−	27.9061i	−0.807072	−	0.988484i	−0.999974	−	0.00726562i	$-0.997687\pi$
$797$	−22.7846	−	27.9061i	−0.807072	−	0.988484i	0.192902	−	0.981218i	$-0.438210\pi$
$798$	−4.23135	+	11.1572i	−0.149788	+	0.394959i
$799$	27.0375	+	56.9803i	0.956518	+	2.01582i
$800$	−0.996483	+	3.44026i	−0.0352310	+	0.121631i
$801$	−3.47141	+	5.02921i	−0.122656	+	0.177698i
$802$	−33.9422	−	14.4614i	−1.19854	−	0.510651i
$803$	7.36739	−	1.19732i	0.259990	−	0.0422524i
$804$	−1.02907	−	0.650746i	−0.0362926	−	0.0229501i
$805$	6.19766	+	8.97886i	0.218439	+	0.316463i
$806$	−0.720703	+	0.232506i	−0.0253857	+	0.00818968i
$807$	6.33453	−	9.17715i	0.222986	−	0.323051i
$808$	23.8297	−	10.1529i	0.838326	−	0.357177i
$809$	−3.47292	−	11.9899i	−0.122101	−	0.421543i	0.876057	−	0.482208i	$-0.160165\pi$
$809$	−3.47292	−	11.9899i	−0.122101	−	0.421543i	−0.998158	+	0.0606652i	$0.980678\pi$
$810$	1.12289	−	0.0906490i	0.0394543	−	0.00318508i
$811$	−15.3963	+	13.6399i	−0.540636	+	0.478962i	−0.888687	−	0.458514i	$-0.848382\pi$
$811$	−15.3963	+	13.6399i	−0.540636	+	0.478962i	0.348051	+	0.937476i	$0.386844\pi$
$812$	3.67157	−	2.32176i	0.128847	−	0.0814779i
$813$	6.46307	+	2.75366i	0.226670	+	0.0965750i
$814$	0.250343	−	2.06176i	0.00877452	−	0.0722647i
$815$	−1.22781	−	6.01419i	−0.0430082	−	0.210668i
$816$	−20.6786	−	1.66935i	−0.723895	−	0.0584389i
$817$	−19.5876	+	14.7192i	−0.685285	+	0.514958i
$818$	0.950020	−	7.82412i	0.0332167	−	0.273564i
$819$	2.81742	+	14.5524i	0.0984485	+	0.508504i
$820$	−0.0768079	−	0.632570i	−0.00268225	−	0.0220903i
$821$	−18.2436	−	18.9935i	−0.636704	−	0.662879i	0.322179	−	0.946679i	$-0.395585\pi$
$821$	−18.2436	−	18.9935i	−0.636704	−	0.662879i	−0.958884	+	0.283799i	$0.908405\pi$
$822$	5.46310	+	9.46236i	0.190547	+	0.330038i
$823$	−4.55138	+	7.88322i	−0.158651	+	0.274792i	−0.934382	−	0.356272i	$-0.884048\pi$
$823$	−4.55138	+	7.88322i	−0.158651	+	0.274792i	0.775731	+	0.631063i	$0.217381\pi$
$824$	−28.0278	+	6.90824i	−0.976396	+	0.240660i
$825$	−1.22134	−	1.49588i	−0.0425218	−	0.0520797i
$826$	28.1778	−	48.8054i	0.980432	−	1.69816i
$827$	−1.72801	−	4.55638i	−0.0600887	−	0.158441i	0.901610	−	0.432550i	$-0.142386\pi$
$827$	−1.72801	−	4.55638i	−0.0600887	−	0.158441i	−0.961699	+	0.274109i	$0.911617\pi$
$828$	−0.343859	+	0.357995i	−0.0119499	+	0.0124412i
$829$	48.5812	+	16.2188i	1.68729	+	0.563301i	0.988393	−	0.151918i	$-0.0485449\pi$
$829$	48.5812	+	16.2188i	1.68729	+	0.563301i	0.698900	+	0.715219i	$0.253673\pi$
$830$	4.04182	+	13.9540i	0.140294	+	0.484350i
$831$	−17.0687	+	15.1215i	−0.592106	+	0.524560i
$832$	−0.797778	−	26.4690i	−0.0276580	−	0.917646i
$833$	36.0305	+	31.9202i	1.24838	+	1.10597i
$834$	2.79832	−	5.89733i	0.0968979	−	0.204208i
$835$	8.34703	+	8.69018i	0.288861	+	0.300736i
$836$	−0.0535773	−	0.112912i	−0.00185301	−	0.00390513i
$837$	−0.139275	−	0.0343283i	−0.00481406	−	0.00118656i
$838$	16.2774	−	16.9465i	0.562292	−	0.585408i
$839$	−34.4930	−	25.9198i	−1.19083	−	0.894851i	−0.194539	−	0.980895i	$-0.562321\pi$
$839$	−34.4930	−	25.9198i	−1.19083	−	0.894851i	−0.996291	+	0.0860442i	$0.972577\pi$
$840$	6.43427	+	5.70027i	0.222003	+	0.196678i
$841$	24.5922	+	3.99663i	0.848008	+	0.137815i
$842$	−40.8176	−	25.8115i	−1.40667	−	0.889521i
$843$	−14.9662	−	1.20819i	−0.515462	−	0.0416124i
$844$	−1.76709			−0.0608256
$845$	9.54959	−	2.97417i	0.328516	−	0.102314i
$846$	18.9944			0.653042
$847$	−44.2886	−	3.57535i	−1.52178	−	0.122850i
$848$	26.1335	+	16.5258i	0.897427	+	0.567499i
$849$	−0.948491	−	0.154145i	−0.0325521	−	0.00529023i
$850$	23.4880	+	20.8085i	0.805630	+	0.713726i
$851$	−8.92817	−	6.70909i	−0.306054	−	0.229985i
$852$	−0.967399	+	1.00717i	−0.0331426	+	0.0345051i
$853$	−30.2787	−	7.46304i	−1.03672	−	0.255530i	−0.316005	−	0.948757i	$-0.602342\pi$
$853$	−30.2787	−	7.46304i	−1.03672	−	0.255530i	−0.720718	+	0.693228i	$0.756188\pi$
$854$	−31.6076	−	66.6115i	−1.08159	−	2.27940i
$855$	1.05653	+	1.09996i	0.0361325	+	0.0376179i
$856$	13.6847	−	28.8398i	0.467732	−	0.985725i
$857$	22.5786	+	20.0029i	0.771269	+	0.683285i	0.953976	−	0.299883i	$-0.0969475\pi$
$857$	22.5786	+	20.0029i	0.771269	+	0.683285i	−0.182707	+	0.983167i	$0.558486\pi$
$858$	−1.94214	−	1.25590i	−0.0663036	−	0.0428757i
$859$	−28.8635	+	25.5708i	−0.984810	+	0.872466i	−0.991837	−	0.127510i	$-0.959302\pi$
$859$	−28.8635	+	25.5708i	−0.984810	+	0.872466i	0.00702718	+	0.999975i	$0.497763\pi$
$860$	−0.380746	−	1.31449i	−0.0129833	−	0.0448237i
$861$	22.4420	+	7.49225i	0.764823	+	0.255335i
$862$	0.803596	−	0.836632i	0.0273706	−	0.0284958i
$863$	−9.36995	−	24.7065i	−0.318957	−	0.841020i	−0.994599	−	0.103791i	$-0.966903\pi$
$863$	−9.36995	−	24.7065i	−0.318957	−	0.841020i	0.675642	−	0.737230i	$-0.263866\pi$
$864$	−0.406265	+	0.703672i	−0.0138214	+	0.0239394i
$865$	10.3666	+	12.6968i	0.352474	+	0.431703i
$866$	−18.6401	+	4.59438i	−0.633417	+	0.156123i
$867$	−3.31859	+	5.74796i	−0.112705	+	0.195211i
$868$	0.0424321	+	0.0734946i	0.00144024	+	0.00249457i
$869$	−0.472232	−	0.491645i	−0.0160194	−	0.0166779i
$870$	−0.997059	−	8.21152i	−0.0338035	−	0.278397i
$871$	−19.0522	−	23.8240i	−0.645558	−	0.807247i
$872$	5.98485	−	49.2896i	0.202672	−	1.66916i
$873$	3.51626	−	2.64230i	0.119007	−	0.0894283i
$874$	−9.97931	−	0.805613i	−0.337555	−	0.0272503i
$875$	−5.95229	−	29.1562i	−0.201224	−	0.985661i
$876$	−0.295538	+	2.43398i	−0.00998532	+	0.0822365i
$877$	−3.31470	−	1.41226i	−0.111929	−	0.0476887i	0.335276	−	0.942120i	$-0.391170\pi$
$877$	−3.31470	−	1.41226i	−0.111929	−	0.0476887i	−0.447205	+	0.894431i	$0.647581\pi$
$878$	40.4320	−	25.5676i	1.36451	−	0.862866i
$879$	−16.5903	+	14.6977i	−0.559576	+	0.495741i
$880$	−1.43363	+	0.115734i	−0.0483276	+	0.00390140i
$881$	−0.799592	−	2.76051i	−0.0269389	−	0.0930040i	0.945922	−	0.324393i	$-0.105160\pi$
$881$	−0.799592	−	2.76051i	−0.0269389	−	0.0930040i	−0.972861	+	0.231389i	$0.925673\pi$
$882$	13.3369	−	5.68233i	0.449077	−	0.191334i
$883$	−4.95441	+	7.17771i	−0.166729	+	0.241549i	−0.897438	−	0.441140i	$-0.854574\pi$
$883$	−4.95441	+	7.17771i	−0.166729	+	0.241549i	0.730709	+	0.682689i	$0.239190\pi$
$884$	2.31064	+	1.01229i	0.0777153	+	0.0340471i
$885$	−4.09187	−	5.92809i	−0.137547	−	0.199271i
$886$	22.3105	+	14.1083i	0.749537	+	0.473979i
$887$	29.0674	−	4.72391i	0.975987	−	0.158613i	0.348558	−	0.937287i	$-0.386671\pi$
$887$	29.0674	−	4.72391i	0.975987	−	0.158613i	0.627429	+	0.778674i	$0.284107\pi$
$888$	−8.09514	−	3.44902i	−0.271655	−	0.115741i
$889$	27.4756	−	39.8053i	0.921503	−	1.33503i
$890$	1.91532	−	6.61243i	0.0642015	−	0.221649i
$891$	−0.187808	−	0.395798i	−0.00629182	−	0.0132597i
$892$	1.29285	−	3.40895i	0.0432877	−	0.114140i
$893$	16.2638	+	19.9196i	0.544248	+	0.666583i
$894$	−0.0760994	−	1.88839i	−0.00254514	−	0.0631571i
$895$	0.213125	+	5.28863i	0.00712397	+	0.176780i
$896$	−49.4119	+	12.1789i	−1.65074	+	0.406870i
$897$	−11.0702	+	5.66757i	−0.369622	+	0.189235i
$898$	39.6574	+	9.77466i	1.32338	+	0.326185i
$899$	−0.210679	+	1.03197i	−0.00702654	+	0.0344183i
$900$	0.583597	−	0.248647i	0.0194532	−	0.00828825i
$901$	29.7756	−	18.8290i	0.991971	−	0.627284i
$902$	−3.26883	+	1.71562i	−0.108840	+	0.0571238i
$903$	50.1548	+	8.15094i	1.66905	+	0.271246i
$904$	−8.55813	+	2.85712i	−0.284639	+	0.0950265i
$905$	−0.143606	−	1.18270i	−0.00477362	−	0.0393143i
$906$	6.53164	−	22.5499i	0.216999	−	0.749169i
$907$	−0.00456845	+	0.0223778i	−0.000151693	+	0.000743042i	−0.979866	−	0.199654i	$-0.936018\pi$
$907$	−0.00456845	+	0.0223778i	−0.000151693	+	0.000743042i	0.979715	+	0.200397i	$0.0642233\pi$
$908$	−0.791087	−	0.264103i	−0.0262531	−	0.00876458i
$909$	−8.43927	−	4.42927i	−0.279913	−	0.146910i
$910$	−8.20203	−	14.5452i	−0.271895	−	0.482167i
$911$	−13.9536	+	7.32343i	−0.462304	+	0.242636i	−0.679761	−	0.733434i	$-0.737916\pi$
$911$	−13.9536	+	7.32343i	−0.462304	+	0.242636i	0.217456	+	0.976070i	$0.430224\pi$
$912$	−8.34929	+	1.35689i	−0.276473	+	0.0449312i
$913$	4.51650	−	3.39393i	0.149474	−	0.112323i
$914$	2.10702	−	52.2852i	0.0696941	−	1.72944i
$915$	−9.42391			−0.311545
$916$	0.0601528	−	1.49268i	0.00198750	−	0.0493194i
$917$	−11.5335	−	56.4950i	−0.380871	−	1.86563i
$918$	4.04389	+	5.85858i	0.133468	+	0.193362i
$919$	−18.9262	+	6.31850i	−0.624318	+	0.208428i	−0.611188	−	0.791486i	$-0.709308\pi$
$919$	−18.9262	+	6.31850i	−0.624318	+	0.208428i	−0.0131307	+	0.999914i	$0.504180\pi$
$920$	−3.09189	+	6.51601i	−0.101936	+	0.214827i
$921$	7.69644	−	9.42643i	0.253606	−	0.310611i
$922$	−15.9518	−	42.0614i	−0.525344	−	1.38522i
$923$	−31.1444	+	15.9449i	−1.02513	+	0.524833i
$924$	−0.0919089	+	0.242344i	−0.00302358	+	0.00797252i
$925$	7.13609	+	12.3601i	0.234633	+	0.406397i
$926$	−9.33666	+	11.4353i	−0.306822	+	0.375788i
$927$	8.49144	+	6.38090i	0.278895	+	0.209576i
$928$	5.28276	+	2.77260i	0.173415	+	0.0910152i
$929$	−5.26733	+	0.425223i	−0.172815	+	0.0139511i	−0.166571	−	0.986029i	$-0.553270\pi$
$929$	−5.26733	+	0.425223i	−0.172815	+	0.0139511i	−0.00624407	+	0.999981i	$0.501988\pi$
$930$	0.161071	−	0.0130030i	0.00528173	−	0.000426386i
$931$	17.3787	+	9.12105i	0.569564	+	0.298930i
$932$	−1.57117	−	1.18066i	−0.0514655	−	0.0386738i
$933$	−4.28622	+	5.24967i	−0.140325	+	0.171867i
$934$	13.2422	+	22.9361i	0.433298	+	0.750493i
$935$	−0.581106	+	1.53225i	−0.0190042	+	0.0501100i
$936$	−7.40007	+	6.42308i	−0.241879	+	0.209945i
$937$	−17.1951	−	45.3396i	−0.561738	−	1.48118i	−0.851641	−	0.524125i	$-0.824392\pi$
$937$	−17.1951	−	45.3396i	−0.561738	−	1.48118i	0.289903	−	0.957056i	$-0.406377\pi$
$938$	−32.2095	+	39.4495i	−1.05168	+	1.28807i
$939$	5.73235	−	12.0807i	0.187068	−	0.394238i
$940$	−1.36242	+	0.454842i	−0.0444371	+	0.0148353i
$941$	18.1021	+	26.2254i	0.590111	+	0.854923i	0.998319	−	0.0579659i	$-0.0184615\pi$
$941$	18.1021	+	26.2254i	0.590111	+	0.854923i	−0.408208	+	0.912889i	$0.633846\pi$
$942$	−2.44143	−	11.9589i	−0.0795460	−	0.389642i
$943$	−0.799323	+	19.8350i	−0.0260296	+	0.645917i
$944$	39.9497			1.30025
$945$	0.127361	−	3.16043i	0.00414306	−	0.102809i
$946$	−6.33837	+	4.76298i	−0.206078	+	0.154858i
$947$	34.8004	−	5.65562i	1.13086	−	0.183783i	0.433948	−	0.900938i	$-0.357120\pi$
$947$	34.8004	−	5.65562i	1.13086	−	0.183783i	0.696914	+	0.717155i	$0.254556\pi$
$948$	0.198281	−	0.104066i	0.00643987	−	0.00337991i
$949$	−26.8961	+	55.2285i	−0.873085	+	1.79279i
$950$	11.3290	+	5.94594i	0.367562	+	0.192912i
$951$	−4.08492	−	1.36375i	−0.132462	−	0.0442225i
$952$	−10.8653	+	53.2216i	−0.352146	+	1.72492i
$953$	−15.4420	+	53.3120i	−0.500216	+	1.72695i	0.170616	+	0.985338i	$0.445424\pi$
$953$	−15.4420	+	53.3120i	−0.500216	+	1.72695i	−0.670832	+	0.741609i	$0.734063\pi$
$954$	−1.27888	−	10.5326i	−0.0414054	−	0.341004i
$955$	−2.76125	+	0.921842i	−0.0893521	+	0.0298301i
$956$	−0.960987	−	0.156176i	−0.0310805	−	0.00505108i
$957$	−2.84833	+	1.49492i	−0.0920734	+	0.0483239i
$958$	21.5226	−	13.6101i	0.695364	−	0.439722i
$959$	28.2227	−	12.0246i	0.911359	−	0.388294i
$960$	−1.13030	+	5.53656i	−0.0364802	+	0.178692i
$961$	30.0792	+	7.41386i	0.970297	+	0.239157i
$962$	12.6787	+	11.4640i	0.408776	+	0.369614i
$963$	−11.4046	+	2.81098i	−0.367507	+	0.0905824i
$964$	0.0302627	+	0.750961i	0.000974696	+	0.0241868i
$965$	0.0549086	+	1.36254i	0.00176757	+	0.0438618i
$966$	13.1314	+	16.0831i	0.422497	+	0.517465i
$967$	18.8141	−	49.6088i	0.605022	−	1.59531i	−0.185341	−	0.982674i	$-0.559339\pi$
$967$	18.8141	−	49.6088i	0.605022	−	1.59531i	0.790363	−	0.612638i	$-0.209892\pi$
$968$	−12.5921	−	26.5372i	−0.404724	−	0.852938i
$969$	−2.68138	+	9.25721i	−0.0861384	+	0.297384i
$970$	−2.81474	+	4.07786i	−0.0903760	+	0.130932i
$971$	−30.4676	−	12.9810i	−0.977753	−	0.416582i	−0.156833	−	0.987625i	$-0.550129\pi$
$971$	−30.4676	−	12.9810i	−0.977753	−	0.416582i	−0.820920	+	0.571043i	$0.806539\pi$
$972$	0.142046	−	0.0230847i	0.00455612	−	0.000740441i
$973$	−15.4902	−	9.79541i	−0.496593	−	0.314027i
$974$	24.8212	+	35.9598i	0.795324	+	1.15223i
$975$	15.8541	−	1.11810i	0.507736	−	0.0358078i
$976$	29.6906	−	43.0142i	0.950372	−	1.37685i
$977$	−40.4631	+	17.2397i	−1.29453	+	0.551548i	−0.925809	−	0.377992i	$-0.876615\pi$
$977$	−40.4631	+	17.2397i	−1.29453	+	0.551548i	−0.368722	+	0.929540i	$0.620204\pi$
$978$	−3.25003	−	11.2204i	−0.103925	−	0.358789i
$979$	−2.66850	+	0.215423i	−0.0852856	+	0.00688496i
$980$	−0.820550	+	0.726944i	−0.0262115	+	0.0232214i
$981$	−15.4414	+	9.76453i	−0.493005	+	0.311757i
$982$	15.8534	+	6.75449i	0.505902	+	0.215545i
$983$	−6.38345	+	52.5725i	−0.203600	+	1.67680i	0.429759	+	0.902943i	$0.358598\pi$
$983$	−6.38345	+	52.5725i	−0.203600	+	1.67680i	−0.633360	+	0.773857i	$0.718325\pi$
$984$	3.12854	+	15.3246i	0.0997342	+	0.488531i
$985$	6.93294	+	0.559685i	0.220902	+	0.0178330i
$986$	41.7871	−	31.4010i	1.33077	−	1.00001i
$987$	6.42831	−	52.9419i	0.204615	−	1.68516i
$988$	1.01353	+	0.175287i	0.0322447	+	0.00557664i
$989$	5.13888	+	42.3225i	0.163407	+	1.34578i
$990$	0.341882	+	0.355937i	0.0108657	+	0.0113124i
$991$	30.7766	+	53.3067i	0.977652	+	1.69334i	0.670891	+	0.741556i	$0.265912\pi$
$991$	30.7766	+	53.3067i	0.977652	+	1.69334i	0.306760	+	0.951787i	$0.400755\pi$
$992$	−0.0582761	+	0.100937i	−0.00185027	+	0.00320476i
$993$	−8.31995	+	2.05068i	−0.264026	+	0.0650765i
$994$	36.9434	+	45.2475i	1.17177	+	1.43516i
$995$	−3.98639	+	6.90463i	−0.126377	+	0.218892i
$996$	0.658081	+	1.73522i	0.0208521	+	0.0549824i
$997$	6.66221	−	6.93609i	0.210994	−	0.219668i	−0.607293	−	0.794478i	$-0.707745\pi$
$997$	6.66221	−	6.93609i	0.210994	−	0.219668i	0.818287	+	0.574810i	$0.194924\pi$
$998$	38.7204	+	12.9268i	1.22567	+	0.409190i
$999$	0.900800	+	3.10992i	0.0285001	+	0.0983936i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	507.2.q.b.16.12	✓	384
169.74	even	39	inner	507.2.q.b.412.12	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
507.2.q.b.16.12	✓	384	1.1	even	1	trivial
507.2.q.b.412.12	yes	384	169.74	even	39	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:	\( N \)	\(=\)	\( 507 = 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	507.q (of order \(39\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(1.45946 + 0.117820i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(0.142046 + 0.0230847i) q^{4} +(-0.575893 - 0.510197i) q^{5} +(-1.17055 - 0.879613i) q^{6} +(-2.84784 + 2.96491i) q^{7} +(-2.63873 - 0.650390i) q^{8} +(0.428693 + 0.903450i) q^{9} +O(q^{10})\)	\(q+(1.45946 + 0.117820i) q^{2} +(-0.845190 - 0.534466i) q^{3} +(0.142046 + 0.0230847i) q^{4} +(-0.575893 - 0.510197i) q^{5} +(-1.17055 - 0.879613i) q^{6} +(-2.84784 + 2.96491i) q^{7} +(-2.63873 - 0.650390i) q^{8} +(0.428693 + 0.903450i) q^{9} +(-0.780383 - 0.812465i) q^{10} +(-0.187808 + 0.395798i) q^{11} +(-0.107718 - 0.0954295i) q^{12} +(-1.77100 - 3.14063i) q^{13} +(-4.50563 + 3.99164i) q^{14} +(0.214057 + 0.739009i) q^{15} +(-4.04751 - 1.35126i) q^{16} +(-3.36789 + 3.50635i) q^{17} +(0.519216 + 1.36906i) q^{18} +(-0.991167 + 1.71675i) q^{19} +(-0.0700255 - 0.0857656i) q^{20} +(3.99161 - 0.983843i) q^{21} +(-0.320732 + 0.555524i) q^{22} +(1.72465 + 2.98718i) q^{23} +(1.88262 + 1.96002i) q^{24} +(-0.531331 - 4.37591i) q^{25} +(-2.21468 - 4.79229i) q^{26} +(0.120537 - 0.992709i) q^{27} +(-0.472967 + 0.355412i) q^{28} +(-7.31886 - 0.590840i) q^{29} +(0.225337 + 1.10378i) q^{30} +(0.0172902 - 0.142398i) q^{31} +(-0.747511 - 0.318485i) q^{32} +(0.370274 - 0.234147i) q^{33} +(-5.32843 + 4.72057i) q^{34} +(3.15274 - 0.254516i) q^{35} +(0.0400381 + 0.138228i) q^{36} +(-2.97867 + 1.26909i) q^{37} +(-1.64884 + 2.38875i) q^{38} +(-0.181724 + 3.60097i) q^{39} +(1.18780 + 1.72083i) q^{40} +(4.86416 + 3.07591i) q^{41} +(5.94151 - 0.965590i) q^{42} +(11.3709 + 4.84470i) q^{43} +(-0.0358142 + 0.0518859i) q^{44} +(0.214057 - 0.739009i) q^{45} +(2.16511 + 4.56288i) q^{46} +(4.60010 - 12.1295i) q^{47} +(2.69871 + 3.30532i) q^{48} +(-0.398668 - 9.89285i) q^{49} +(-0.259889 - 6.44907i) q^{50} +(4.72053 - 1.16351i) q^{51} +(-0.179063 - 0.486996i) q^{52} +(-7.03562 - 1.73412i) q^{53} +(0.292880 - 1.43462i) q^{54} +(0.310092 - 0.132118i) q^{55} +(9.44303 - 5.97141i) q^{56} +(1.75527 - 0.921236i) q^{57} +(-10.6120 - 1.72462i) q^{58} +(-8.88042 + 2.96472i) q^{59} +(0.0133460 + 0.109914i) q^{60} +(-3.40778 + 11.7650i) q^{61} +(0.0420117 - 0.205787i) q^{62} +(-3.89950 - 1.30184i) q^{63} +(6.50323 + 3.41316i) q^{64} +(-0.582430 + 2.71223i) q^{65} +(0.567988 - 0.298103i) q^{66} +(8.35107 - 1.35718i) q^{67} +(-0.559338 + 0.420315i) q^{68} +(0.138889 - 3.44650i) q^{69} +4.63129 q^{70} +(0.390746 - 9.69626i) q^{71} +(-0.543611 - 2.66278i) q^{72} +(-9.67840 - 14.0216i) q^{73} +(-4.49678 + 1.50124i) q^{74} +(-1.88970 + 3.98245i) q^{75} +(-0.180422 + 0.220976i) q^{76} +(-0.638658 - 1.68400i) q^{77} +(-0.689486 + 5.23406i) q^{78} +(-0.551785 + 1.45494i) q^{79} +(1.64153 + 2.84321i) q^{80} +(-0.632445 + 0.774605i) q^{81} +(6.73665 + 5.06227i) q^{82} +(-11.4186 - 5.99294i) q^{83} +(0.589703 - 0.0476057i) q^{84} +(3.72848 - 0.300994i) q^{85} +(16.0246 + 8.41038i) q^{86} +(5.87005 + 4.41105i) q^{87} +(0.752999 - 0.922256i) q^{88} +(3.05547 + 5.29224i) q^{89} +(0.399477 - 1.05333i) q^{90} +(14.3552 + 3.69313i) q^{91} +(0.176021 + 0.464130i) q^{92} +(-0.0907203 + 0.111112i) q^{93} +(8.14277 - 17.1605i) q^{94} +(1.44669 - 0.482975i) q^{95} +(0.461570 + 0.668699i) q^{96} +(-0.879791 - 4.30950i) q^{97} +(0.583734 - 14.4852i) q^{98} -0.438096 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9}+O(q^{10}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9	\( 384 q + q^{2} + 16 q^{3} + 17 q^{4} + 6 q^{5} + q^{6} - 3 q^{7} - 18 q^{8} + 16 q^{9} + 3 q^{10} - 4 q^{11} - 34 q^{12} - 15 q^{13} + 24 q^{14} - 3 q^{15} + 11 q^{16} - 3 q^{17} - 2 q^{18} + 6 q^{19} + q^{20} + 6 q^{21} - 86 q^{22} - 52 q^{23} + 9 q^{24} - 74 q^{25} - 64 q^{26} - 32 q^{27} - 16 q^{28} - 44 q^{29} + 3 q^{30} - 28 q^{31} + 74 q^{32} - 17 q^{33} - 83 q^{34} + 70 q^{35} + 17 q^{36} + 11 q^{37} - 29 q^{38} + q^{39} - 5 q^{40} + q^{41} + 118 q^{42} - 79 q^{43} - 19 q^{44} - 3 q^{45} + 314 q^{46} + 11 q^{48} - 69 q^{49} - 76 q^{50} + 6 q^{51} - 37 q^{52} - 102 q^{53} + q^{54} - 73 q^{55} - 36 q^{56} + 14 q^{57} - 51 q^{58} + 194 q^{59} + 76 q^{60} + 4 q^{61} - 89 q^{62} - 3 q^{63} - 184 q^{64} - 49 q^{65} - 36 q^{66} - 73 q^{67} + 4 q^{68} - 100 q^{70} + 106 q^{71} + 9 q^{72} - 132 q^{73} - 45 q^{74} + 11 q^{75} + 24 q^{76} - 54 q^{77} - 39 q^{78} - 2 q^{79} + 177 q^{80} + 16 q^{81} - 76 q^{82} - 58 q^{83} - 16 q^{84} - 123 q^{85} - 157 q^{86} - 57 q^{87} + 476 q^{88} + 18 q^{89} - 6 q^{90} + 233 q^{91} - 12 q^{92} + q^{93} - 111 q^{94} + 64 q^{95} - 83 q^{96} - 143 q^{97} - 79 q^{98} - 18 q^{99}+O(q^{100}) \) 384 * q + q^2 + 16 * q^3 + 17 * q^4 + 6 * q^5 + q^6 - 3 * q^7 - 18 * q^8 + 16 * q^9 + 3 * q^10 - 4 * q^11 - 34 * q^12 - 15 * q^13 + 24 * q^14 - 3 * q^15 + 11 * q^16 - 3 * q^17 - 2 * q^18 + 6 * q^19 + q^20 + 6 * q^21 - 86 * q^22 - 52 * q^23 + 9 * q^24 - 74 * q^25 - 64 * q^26 - 32 * q^27 - 16 * q^28 - 44 * q^29 + 3 * q^30 - 28 * q^31 + 74 * q^32 - 17 * q^33 - 83 * q^34 + 70 * q^35 + 17 * q^36 + 11 * q^37 - 29 * q^38 + q^39 - 5 * q^40 + q^41 + 118 * q^42 - 79 * q^43 - 19 * q^44 - 3 * q^45 + 314 * q^46 + 11 * q^48 - 69 * q^49 - 76 * q^50 + 6 * q^51 - 37 * q^52 - 102 * q^53 + q^54 - 73 * q^55 - 36 * q^56 + 14 * q^57 - 51 * q^58 + 194 * q^59 + 76 * q^60 + 4 * q^61 - 89 * q^62 - 3 * q^63 - 184 * q^64 - 49 * q^65 - 36 * q^66 - 73 * q^67 + 4 * q^68 - 100 * q^70 + 106 * q^71 + 9 * q^72 - 132 * q^73 - 45 * q^74 + 11 * q^75 + 24 * q^76 - 54 * q^77 - 39 * q^78 - 2 * q^79 + 177 * q^80 + 16 * q^81 - 76 * q^82 - 58 * q^83 - 16 * q^84 - 123 * q^85 - 157 * q^86 - 57 * q^87 + 476 * q^88 + 18 * q^89 - 6 * q^90 + 233 * q^91 - 12 * q^92 + q^93 - 111 * q^94 + 64 * q^95 - 83 * q^96 - 143 * q^97 - 79 * q^98 - 18 * q^99

Introduction

L-functions

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