LMFDB - Embedded newform 483.2.q.c.358.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [483,2,Mod(64,483)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(483, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 12]))

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

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

chi := DirichletCharacter("483.64");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 483 = 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	483.q (of order $11$, degree $10$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.85677441763$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 8 x^{19} + 40 x^{18} - 117 x^{17} + 295 x^{16} - 575 x^{15} + 1777 x^{14} - 1560 x^{13} + \cdots + 2374681 $ x^20 - 8x^19 + 40x^18 - 117x^17 + 295x^16 - 575x^15 + 1777x^14 - 1560x^13 + 4383x^12 - 6446x^11 + 7261x^10 + 7700x^9 + 7852x^8 - 39430x^7 - 101709x^6 + 156742x^5 + 999838x^4 + 2029154x^3 + 3616480x^2 + 4299390*x + 2374681
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			358.2
Root			$1.49752 - 1.72823i$ of defining polynomial
Character	$\chi$	$=$	483.358
Dual form			483.2.q.c.85.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.544078 - 0.627899i) q^{2} +(0.841254 + 0.540641i) q^{3} +(0.186393 - 1.29639i) q^{4} +(0.405886 - 0.888766i) q^{5} +(-0.118239 - 0.822373i) q^{6} +(-0.959493 - 0.281733i) q^{7} +(-2.31329 + 1.48666i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})$	\(q+(-0.544078 - 0.627899i) q^{2} +(0.841254 + 0.540641i) q^{3} +(0.186393 - 1.29639i) q^{4} +(0.405886 - 0.888766i) q^{5} +(-0.118239 - 0.822373i) q^{6} +(-0.959493 - 0.281733i) q^{7} +(-2.31329 + 1.48666i) q^{8} +(0.415415 + 0.909632i) q^{9} +(-0.778889 + 0.228702i) q^{10} +(3.57214 - 4.12247i) q^{11} +(0.857685 - 0.989821i) q^{12} +(-0.954742 + 0.280337i) q^{13} +(0.345139 + 0.755750i) q^{14} +(0.821956 - 0.528239i) q^{15} +(-0.321251 - 0.0943278i) q^{16} +(-0.595548 - 4.14213i) q^{17} +(0.345139 - 0.755750i) q^{18} +(0.0835672 - 0.581223i) q^{19} +(-1.07653 - 0.691846i) q^{20} +(-0.654861 - 0.755750i) q^{21} -4.53202 q^{22} +(-1.96432 - 4.37509i) q^{23} -2.74982 q^{24} +(2.64914 + 3.05727i) q^{25} +(0.695478 + 0.446956i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(-0.544078 + 1.19136i) q^{28} +(-0.113996 - 0.792858i) q^{29} +(-0.778889 - 0.228702i) q^{30} +(-3.31199 + 2.12849i) q^{31} +(2.40019 + 5.25568i) q^{32} +(5.23385 - 1.53680i) q^{33} +(-2.27682 + 2.62759i) q^{34} +(-0.639839 + 0.738413i) q^{35} +(1.25667 - 0.368991i) q^{36} +(-1.49833 - 3.28089i) q^{37} +(-0.410416 + 0.263759i) q^{38} +(-0.954742 - 0.280337i) q^{39} +(0.382363 + 2.65939i) q^{40} +(4.02324 - 8.80966i) q^{41} +(-0.118239 + 0.822373i) q^{42} +(9.13966 + 5.87370i) q^{43} +(-4.67851 - 5.39929i) q^{44} +0.977061 q^{45} +(-1.67837 + 3.61379i) q^{46} -11.5601 q^{47} +(-0.219256 - 0.253035i) q^{48} +(0.841254 + 0.540641i) q^{49} +(0.478320 - 3.32679i) q^{50} +(1.73840 - 3.80656i) q^{51} +(0.185470 + 1.28997i) q^{52} +(0.848176 + 0.249047i) q^{53} +(0.698939 - 0.449181i) q^{54} +(-2.21403 - 4.84805i) q^{55} +(2.63843 - 0.774713i) q^{56} +(0.384534 - 0.443776i) q^{57} +(-0.435813 + 0.502955i) q^{58} +(6.25110 - 1.83549i) q^{59} +(-0.531597 - 1.16404i) q^{60} +(1.25651 - 0.807508i) q^{61} +(3.13846 + 0.921535i) q^{62} +(-0.142315 - 0.989821i) q^{63} +(1.71597 - 3.75746i) q^{64} +(-0.138362 + 0.962327i) q^{65} +(-3.81258 - 2.45019i) q^{66} +(-0.874085 - 1.00875i) q^{67} -5.48082 q^{68} +(0.712860 - 4.74256i) q^{69} +0.811772 q^{70} +(7.26595 + 8.38535i) q^{71} +(-2.31329 - 1.48666i) q^{72} +(-1.33652 + 9.29567i) q^{73} +(-1.24486 + 2.72586i) q^{74} +(0.575714 + 4.00418i) q^{75} +(-0.737915 - 0.216671i) q^{76} +(-4.58888 + 2.94909i) q^{77} +(0.343430 + 0.752007i) q^{78} +(8.76905 - 2.57482i) q^{79} +(-0.214227 + 0.247231i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(-7.72054 + 2.26695i) q^{82} +(-1.31567 - 2.88091i) q^{83} +(-1.10181 + 0.708089i) q^{84} +(-3.92311 - 1.15193i) q^{85} +(-1.28459 - 8.93454i) q^{86} +(0.332752 - 0.728626i) q^{87} +(-2.13468 + 14.8470i) q^{88} +(3.21116 + 2.06369i) q^{89} +(-0.531597 - 0.613496i) q^{90} +0.995048 q^{91} +(-6.03796 + 1.73104i) q^{92} -3.93697 q^{93} +(6.28960 + 7.25858i) q^{94} +(-0.482652 - 0.310182i) q^{95} +(-0.822267 + 5.71900i) q^{96} +(-7.38495 + 16.1708i) q^{97} +(-0.118239 - 0.822373i) q^{98} +(5.23385 + 1.53680i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - q^5 - 4 * q^6 - 2 * q^7 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9} + 9 q^{10} + 3 q^{11} + 18 q^{12} - 2 q^{13} + 18 q^{14} - q^{15} + 8 q^{16} + 8 q^{17} + 18 q^{18} + 6 q^{19} - 2 q^{20} - 2 q^{21} + 6 q^{22} + 11 q^{23} + 9 q^{25} + 7 q^{26} - 2 q^{27} - 4 q^{28} + 23 q^{29} + 9 q^{30} + q^{31} - 28 q^{32} + 14 q^{33} - 28 q^{34} + 10 q^{35} - 4 q^{36} - 9 q^{37} + 34 q^{38} - 2 q^{39} - 15 q^{41} - 4 q^{42} - 23 q^{43} - 16 q^{44} - 12 q^{45} + 11 q^{46} - 66 q^{47} - 36 q^{48} - 2 q^{49} - 26 q^{50} - 14 q^{51} + 7 q^{52} + 9 q^{53} - 4 q^{54} - 62 q^{55} + 22 q^{56} - 27 q^{57} - 20 q^{58} + 49 q^{59} - 2 q^{60} + 46 q^{61} - 9 q^{62} - 2 q^{63} + 16 q^{64} + 11 q^{65} - 16 q^{66} + 14 q^{67} + 38 q^{68} + 11 q^{69} - 2 q^{70} + 36 q^{71} - q^{73} + 4 q^{74} - 2 q^{75} + 34 q^{76} - 8 q^{77} - 15 q^{78} - 22 q^{79} + 15 q^{80} - 2 q^{81} - 30 q^{82} + 8 q^{83} - 4 q^{84} - 32 q^{85} - 68 q^{86} + q^{87} - 11 q^{88} - 2 q^{89} - 2 q^{90} - 24 q^{91} + 11 q^{92} - 32 q^{93} + 33 q^{94} - 107 q^{95} + 16 q^{96} + 18 q^{97} - 4 q^{98} + 14 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - q^5 - 4 * q^6 - 2 * q^7 - 2 * q^9 + 9 * q^10 + 3 * q^11 + 18 * q^12 - 2 * q^13 + 18 * q^14 - q^15 + 8 * q^16 + 8 * q^17 + 18 * q^18 + 6 * q^19 - 2 * q^20 - 2 * q^21 + 6 * q^22 + 11 * q^23 + 9 * q^25 + 7 * q^26 - 2 * q^27 - 4 * q^28 + 23 * q^29 + 9 * q^30 + q^31 - 28 * q^32 + 14 * q^33 - 28 * q^34 + 10 * q^35 - 4 * q^36 - 9 * q^37 + 34 * q^38 - 2 * q^39 - 15 * q^41 - 4 * q^42 - 23 * q^43 - 16 * q^44 - 12 * q^45 + 11 * q^46 - 66 * q^47 - 36 * q^48 - 2 * q^49 - 26 * q^50 - 14 * q^51 + 7 * q^52 + 9 * q^53 - 4 * q^54 - 62 * q^55 + 22 * q^56 - 27 * q^57 - 20 * q^58 + 49 * q^59 - 2 * q^60 + 46 * q^61 - 9 * q^62 - 2 * q^63 + 16 * q^64 + 11 * q^65 - 16 * q^66 + 14 * q^67 + 38 * q^68 + 11 * q^69 - 2 * q^70 + 36 * q^71 - q^73 + 4 * q^74 - 2 * q^75 + 34 * q^76 - 8 * q^77 - 15 * q^78 - 22 * q^79 + 15 * q^80 - 2 * q^81 - 30 * q^82 + 8 * q^83 - 4 * q^84 - 32 * q^85 - 68 * q^86 + q^87 - 11 * q^88 - 2 * q^89 - 2 * q^90 - 24 * q^91 + 11 * q^92 - 32 * q^93 + 33 * q^94 - 107 * q^95 + 16 * q^96 + 18 * q^97 - 4 * q^98 + 14 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{7}{11}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.544078	−	0.627899i	−0.384721	−	0.443992i	0.530049	−	0.847967i	$-0.322174\pi$
$2$	−0.544078	−	0.627899i	−0.384721	−	0.443992i	−0.914770	+	0.403975i	$0.867628\pi$
$3$	0.841254	+	0.540641i	0.485698	+	0.312139i
$3$	0.841254	+	0.540641i	0.485698	+	0.312139i
$4$	0.186393	−	1.29639i	0.0931964	−	0.648195i
$5$	0.405886	−	0.888766i	0.181518	−	0.397468i	−0.796898	−	0.604114i	$-0.793527\pi$
$5$	0.405886	−	0.888766i	0.181518	−	0.397468i	0.978416	+	0.206645i	$0.0662546\pi$
$6$	−0.118239	−	0.822373i	−0.0482710	−	0.335733i
$7$	−0.959493	−	0.281733i	−0.362654	−	0.106485i
$7$	−0.959493	−	0.281733i	−0.362654	−	0.106485i
$8$	−2.31329	+	1.48666i	−0.817872	+	0.525615i
$9$	0.415415	+	0.909632i	0.138472	+	0.303211i
$10$	−0.778889	+	0.228702i	−0.246306	+	0.0723221i
$11$	3.57214	−	4.12247i	1.07704	−	1.24297i	0.108506	−	0.994096i	$-0.465393\pi$
$11$	3.57214	−	4.12247i	1.07704	−	1.24297i	0.968535	−	0.248876i	$-0.0800611\pi$
$12$	0.857685	−	0.989821i	0.247592	−	0.285737i
$13$	−0.954742	+	0.280337i	−0.264798	+	0.0777516i	−0.411436	−	0.911439i	$-0.634973\pi$
$13$	−0.954742	+	0.280337i	−0.264798	+	0.0777516i	0.146639	+	0.989190i	$0.453155\pi$
$14$	0.345139	+	0.755750i	0.0922423	+	0.201983i
$15$	0.821956	−	0.528239i	0.212228	−	0.136391i
$16$	−0.321251	−	0.0943278i	−0.0803127	−	0.0235819i
$17$	−0.595548	−	4.14213i	−0.144442	−	1.00461i	−0.925118	−	0.379679i	$-0.876034\pi$
$17$	−0.595548	−	4.14213i	−0.144442	−	1.00461i	0.780677	−	0.624935i	$-0.214875\pi$
$18$	0.345139	−	0.755750i	0.0813501	−	0.178132i
$19$	0.0835672	−	0.581223i	0.0191716	−	0.133342i	−0.977988	−	0.208662i	$-0.933089\pi$
$19$	0.0835672	−	0.581223i	0.0191716	−	0.133342i	0.997159	+	0.0753208i	$0.0239981\pi$
$20$	−1.07653	−	0.691846i	−0.240720	−	0.154701i
$21$	−0.654861	−	0.755750i	−0.142902	−	0.164918i
$22$	−4.53202			−0.966230
$23$	−1.96432	−	4.37509i	−0.409590	−	0.912270i
$23$	−1.96432	−	4.37509i	−0.409590	−	0.912270i
$24$	−2.74982			−0.561304
$25$	2.64914	+	3.05727i	0.529828	+	0.611455i
$26$	0.695478	+	0.446956i	0.136394	+	0.0876553i
$27$	−0.142315	+	0.989821i	−0.0273885	+	0.190491i
$28$	−0.544078	+	1.19136i	−0.102821	+	0.225147i
$29$	−0.113996	−	0.792858i	−0.0211685	−	0.147230i	0.976496	−	0.215536i	$-0.0691498\pi$
$29$	−0.113996	−	0.792858i	−0.0211685	−	0.147230i	−0.997664	+	0.0683056i	$0.978241\pi$
$30$	−0.778889	−	0.228702i	−0.142205	−	0.0417552i
$31$	−3.31199	+	2.12849i	−0.594851	+	0.382288i	−0.803149	−	0.595778i	$-0.796844\pi$
$31$	−3.31199	+	2.12849i	−0.594851	+	0.382288i	0.208298	+	0.978065i	$0.433208\pi$
$32$	2.40019	+	5.25568i	0.424297	+	0.929081i
$33$	5.23385	−	1.53680i	0.911097	−	0.267522i
$34$	−2.27682	+	2.62759i	−0.390471	+	0.450627i
$35$	−0.639839	+	0.738413i	−0.108153	+	0.124815i
$36$	1.25667	−	0.368991i	0.209445	−	0.0614985i
$37$	−1.49833	−	3.28089i	−0.246324	−	0.539375i	0.745572	−	0.666425i	$-0.232176\pi$
$37$	−1.49833	−	3.28089i	−0.246324	−	0.539375i	−0.991896	+	0.127050i	$0.959449\pi$
$38$	−0.410416	+	0.263759i	−0.0665783	+	0.0427873i
$39$	−0.954742	−	0.280337i	−0.152881	−	0.0448899i
$40$	0.382363	+	2.65939i	0.0604568	+	0.420487i
$41$	4.02324	−	8.80966i	0.628324	−	1.37584i	−0.280983	−	0.959713i	$-0.590660\pi$
$41$	4.02324	−	8.80966i	0.628324	−	1.37584i	0.909307	−	0.416126i	$-0.136612\pi$
$42$	−0.118239	+	0.822373i	−0.0182447	+	0.126895i
$43$	9.13966	+	5.87370i	1.39378	+	0.895731i	0.999727	−	0.0233550i	$-0.00743479\pi$
$43$	9.13966	+	5.87370i	1.39378	+	0.895731i	0.394057	+	0.919086i	$0.371071\pi$
$44$	−4.67851	−	5.39929i	−0.705312	−	0.813973i
$45$	0.977061			0.145652
$46$	−1.67837	+	3.61379i	−0.247463	+	0.532824i
$47$	−11.5601			−1.68621			−0.843107	−	0.537746i	$-0.819276\pi$
$47$	−11.5601			−1.68621			−0.843107	+	0.537746i	$0.819276\pi$
$48$	−0.219256	−	0.253035i	−0.0316469	−	0.0365225i
$49$	0.841254	+	0.540641i	0.120179	+	0.0772344i
$50$	0.478320	−	3.32679i	0.0676447	−	0.470479i
$51$	1.73840	−	3.80656i	0.243424	−	0.533025i
$52$	0.185470	+	1.28997i	0.0257200	+	0.178887i
$53$	0.848176	+	0.249047i	0.116506	+	0.0342092i	0.339466	−	0.940618i	$-0.389754\pi$
$53$	0.848176	+	0.249047i	0.116506	+	0.0342092i	−0.222960	+	0.974828i	$0.571572\pi$
$54$	0.698939	−	0.449181i	0.0951135	−	0.0611257i
$55$	−2.21403	−	4.84805i	−0.298540	−	0.653711i
$56$	2.63843	−	0.774713i	0.352575	−	0.103525i
$57$	0.384534	−	0.443776i	0.0509327	−	0.0587795i
$58$	−0.435813	+	0.502955i	−0.0572250	+	0.0660412i
$59$	6.25110	−	1.83549i	0.813824	−	0.238960i	0.151770	−	0.988416i	$-0.451503\pi$
$59$	6.25110	−	1.83549i	0.813824	−	0.238960i	0.662055	+	0.749456i	$0.269685\pi$
$60$	−0.531597	−	1.16404i	−0.0686289	−	0.150276i
$61$	1.25651	−	0.807508i	0.160879	−	0.103391i	−0.457724	−	0.889094i	$-0.651335\pi$
$61$	1.25651	−	0.807508i	0.160879	−	0.103391i	0.618603	+	0.785703i	$0.287699\pi$
$62$	3.13846	+	0.921535i	0.398585	+	0.117035i
$63$	−0.142315	−	0.989821i	−0.0179300	−	0.124706i
$64$	1.71597	−	3.75746i	0.214497	−	0.469682i
$65$	−0.138362	+	0.962327i	−0.0171617	+	0.119362i
$66$	−3.81258	−	2.45019i	−0.469296	−	0.301598i
$67$	−0.874085	−	1.00875i	−0.106786	−	0.123238i	0.699840	−	0.714299i	$-0.253255\pi$
$67$	−0.874085	−	1.00875i	−0.106786	−	0.123238i	−0.806627	+	0.591061i	$0.798709\pi$
$68$	−5.48082			−0.664648
$69$	0.712860	−	4.74256i	0.0858182	−	0.570937i
$70$	0.811772			0.0970253
$71$	7.26595	+	8.38535i	0.862309	+	0.995158i	0.999989	+	0.00468118i	$0.00149007\pi$
$71$	7.26595	+	8.38535i	0.862309	+	0.995158i	−0.137680	+	0.990477i	$0.543964\pi$
$72$	−2.31329	−	1.48666i	−0.272624	−	0.175205i
$73$	−1.33652	+	9.29567i	−0.156427	+	1.08798i	0.748723	+	0.662883i	$0.230667\pi$
$73$	−1.33652	+	9.29567i	−0.156427	+	1.08798i	−0.905150	+	0.425092i	$0.860242\pi$
$74$	−1.24486	+	2.72586i	−0.144712	+	0.316875i
$75$	0.575714	+	4.00418i	0.0664777	+	0.462362i
$76$	−0.737915	−	0.216671i	−0.0846447	−	0.0248539i
$77$	−4.58888	+	2.94909i	−0.522951	+	0.336080i
$78$	0.343430	+	0.752007i	0.0388858	+	0.0851480i
$79$	8.76905	−	2.57482i	0.986595	−	0.289690i	0.251651	−	0.967818i	$-0.419027\pi$
$79$	8.76905	−	2.57482i	0.986595	−	0.289690i	0.734944	+	0.678128i	$0.237208\pi$
$80$	−0.214227	+	0.247231i	−0.0239513	+	0.0276412i
$81$	−0.654861	+	0.755750i	−0.0727623	+	0.0839722i
$82$	−7.72054	+	2.26695i	−0.852591	+	0.250343i
$83$	−1.31567	−	2.88091i	−0.144413	−	0.316220i	0.823579	−	0.567202i	$-0.191974\pi$
$83$	−1.31567	−	2.88091i	−0.144413	−	0.316220i	−0.967992	+	0.250981i	$0.919247\pi$
$84$	−1.10181	+	0.708089i	−0.120217	+	0.0772588i
$85$	−3.92311	−	1.15193i	−0.425521	−	0.124944i
$86$	−1.28459	−	8.93454i	−0.138521	−	0.963436i
$87$	0.332752	−	0.728626i	0.0356748	−	0.0781169i
$88$	−2.13468	+	14.8470i	−0.227558	+	1.58270i
$89$	3.21116	+	2.06369i	0.340382	+	0.218750i	0.699653	−	0.714483i	$-0.253338\pi$
$89$	3.21116	+	2.06369i	0.340382	+	0.218750i	−0.359270	+	0.933233i	$0.616974\pi$
$90$	−0.531597	−	0.613496i	−0.0560353	−	0.0646682i
$91$	0.995048			0.104309
$92$	−6.03796	+	1.73104i	−0.629501	+	0.180474i
$93$	−3.93697			−0.408245
$94$	6.28960	+	7.25858i	0.648722	+	0.748665i
$95$	−0.482652	−	0.310182i	−0.0495191	−	0.0318240i
$96$	−0.822267	+	5.71900i	−0.0839223	+	0.583692i
$97$	−7.38495	+	16.1708i	−0.749828	+	1.64189i	0.0168467	+	0.999858i	$0.494637\pi$
$97$	−7.38495	+	16.1708i	−0.749828	+	1.64189i	−0.766675	+	0.642036i	$0.778090\pi$
$98$	−0.118239	−	0.822373i	−0.0119440	−	0.0830723i
$99$	5.23385	+	1.53680i	0.526022	+	0.154454i
$100$	4.45720	−	2.86447i	0.445720	−	0.286447i
$101$	3.46645	+	7.59047i	0.344925	+	0.755280i	1.00000		0.000283479i	$-9.02343e-5\pi$
$101$	3.46645	+	7.59047i	0.344925	+	0.755280i	−0.655075	+	0.755564i	$0.727363\pi$
$102$	−3.33596	+	0.979526i	−0.330309	+	0.0969876i
$103$	−0.122213	+	0.141041i	−0.0120420	+	0.0138972i	−0.761739	−	0.647884i	$-0.775654\pi$
$103$	−0.122213	+	0.141041i	−0.0120420	+	0.0138972i	0.749697	+	0.661782i	$0.230199\pi$
$104$	1.79183	−	2.06788i	0.175703	−	0.202772i
$105$	−0.937483	+	0.275270i	−0.0914890	+	0.0268636i
$106$	−0.305097	−	0.668070i	−0.0296337	−	0.0648887i
$107$	3.71790	−	2.38935i	0.359423	−	0.230987i	−0.348449	−	0.937328i	$-0.613292\pi$
$107$	3.71790	−	2.38935i	0.359423	−	0.230987i	0.707872	+	0.706341i	$0.249655\pi$
$108$	1.25667	+	0.368991i	0.120923	+	0.0355062i
$109$	2.59868	+	18.0742i	0.248909	+	1.73120i	0.604542	+	0.796573i	$0.293356\pi$
$109$	2.59868	+	18.0742i	0.248909	+	1.73120i	−0.355633	+	0.934626i	$0.615735\pi$
$110$	−1.83948	+	4.02790i	−0.175388	+	0.384046i
$111$	0.513306	−	3.57012i	0.0487208	−	0.338861i
$112$	0.281663	+	0.181014i	0.0266146	+	0.0171042i
$113$	7.02402	+	8.10616i	0.660765	+	0.762563i	0.982902	−	0.184130i	$-0.0589467\pi$
$113$	7.02402	+	8.10616i	0.660765	+	0.762563i	−0.322137	+	0.946693i	$0.604401\pi$
$114$	−0.487863			−0.0456925
$115$	−4.68572	−	0.0299643i	−0.436946	−	0.00279418i
$116$	−1.04910			−0.0974067
$117$	−0.651618	−	0.752007i	−0.0602421	−	0.0695231i
$118$	−4.55359	−	2.92641i	−0.419192	−	0.269398i
$119$	−0.595548	+	4.14213i	−0.0545938	+	0.379708i
$120$	−1.11611	+	2.44394i	−0.101887	+	0.223100i
$121$	−2.66911	−	18.5641i	−0.242646	−	1.68764i
$122$	−1.19067	−	0.349613i	−0.107798	−	0.0316525i
$123$	8.14743	−	5.23603i	0.734629	−	0.472117i
$124$	2.14202	+	4.69037i	0.192359	+	0.421208i
$125$	8.47987	−	2.48991i	0.758462	−	0.222705i
$126$	−0.544078	+	0.627899i	−0.0484703	+	0.0559377i
$127$	11.9843	−	13.8306i	1.06343	−	1.22726i	0.0905659	−	0.995890i	$-0.471132\pi$
$127$	11.9843	−	13.8306i	1.06343	−	1.22726i	0.972865	−	0.231374i	$-0.0743221\pi$
$128$	7.79460	−	2.28870i	0.688951	−	0.202294i
$129$	4.51321	+	9.88254i	0.397366	+	0.870109i
$130$	0.679524	−	0.436704i	0.0595982	−	0.0383014i
$131$	16.0496	+	4.71259i	1.40226	+	0.411741i	0.893460	−	0.449143i	$-0.148271\pi$
$131$	16.0496	+	4.71259i	1.40226	+	0.411741i	0.508801	+	0.860884i	$0.330089\pi$
$132$	−1.01674	−	7.07156i	−0.0884956	−	0.615501i
$133$	−0.243931	+	0.534135i	−0.0211515	+	0.0463154i
$134$	−0.157822	+	1.09767i	−0.0136337	+	0.0948246i
$135$	0.821956	+	0.528239i	0.0707427	+	0.0454636i
$136$	7.53563	+	8.69658i	0.646175	+	0.745726i
$137$	1.31005			0.111925			0.0559627	−	0.998433i	$-0.482177\pi$
$137$	1.31005			0.111925			0.0559627	+	0.998433i	$0.482177\pi$
$138$	−3.36570	+	2.13272i	−0.286507	+	0.181549i
$139$	−11.2805			−0.956802			−0.478401	−	0.878141i	$-0.658784\pi$
$139$	−11.2805			−0.956802			−0.478401	+	0.878141i	$0.658784\pi$
$140$	0.838011	+	0.967116i	0.0708248	+	0.0817362i
$141$	−9.72497	−	6.24986i	−0.818991	−	0.526333i
$142$	1.31191	−	9.12457i	0.110093	−	0.765717i
$143$	−2.25479	+	4.93730i	−0.188555	+	0.412878i
$144$	−0.0476489	−	0.331405i	−0.00397074	−	0.0276171i
$145$	−0.750935	−	0.220494i	−0.0623617	−	0.0183111i
$146$	6.56391	−	4.21837i	0.543233	−	0.349115i
$147$	0.415415	+	0.909632i	0.0342629	+	0.0750252i
$148$	−4.53259	+	1.33089i	−0.372577	+	0.109398i
$149$	−1.72101	+	1.98615i	−0.140991	+	0.162712i	−0.821853	−	0.569699i	$-0.807060\pi$
$149$	−1.72101	+	1.98615i	−0.140991	+	0.162712i	0.680862	+	0.732411i	$0.261605\pi$
$150$	2.20099	−	2.54007i	0.179710	−	0.207396i
$151$	6.14357	−	1.80392i	0.499957	−	0.146801i	−0.0220245	−	0.999757i	$-0.507011\pi$
$151$	6.14357	−	1.80392i	0.499957	−	0.146801i	0.521981	+	0.852957i	$0.325193\pi$
$152$	0.670767	+	1.46877i	0.0544064	+	0.119133i
$153$	3.52041	−	2.26243i	0.284609	−	0.182907i
$154$	4.34844	+	1.27682i	0.350407	+	0.102889i
$155$	0.547437	+	3.80751i	0.0439712	+	0.305827i
$156$	−0.541384	+	1.18547i	−0.0433454	+	0.0949132i
$157$	−2.59139	+	18.0235i	−0.206816	+	1.43843i	0.576646	+	0.816994i	$0.304361\pi$
$157$	−2.59139	+	18.0235i	−0.206816	+	1.43843i	−0.783462	+	0.621440i	$0.786548\pi$
$158$	−6.38778	−	4.10517i	−0.508184	−	0.326590i
$159$	0.578886	+	0.668070i	0.0459087	+	0.0529814i
$160$	5.64527			0.446298
$161$	0.652148	+	4.75128i	0.0513965	+	0.374454i
$162$	0.830830			0.0652762
$163$	2.18363	+	2.52005i	0.171035	+	0.197385i	0.834795	−	0.550560i	$-0.185586\pi$
$163$	2.18363	+	2.52005i	0.171035	+	0.197385i	−0.663760	+	0.747945i	$0.731040\pi$
$164$	−10.6709	−	6.85775i	−0.833254	−	0.535500i
$165$	0.758493	−	5.27543i	0.0590486	−	0.410692i
$166$	−1.09309	+	2.39354i	−0.0848406	+	0.185775i
$167$	−0.119468	−	0.830921i	−0.00924474	−	0.0642986i	0.984677	−	0.174389i	$-0.0557950\pi$
$167$	−0.119468	−	0.830921i	−0.00924474	−	0.0642986i	−0.993922	+	0.110090i	$0.964886\pi$
$168$	2.63843	+	0.774713i	0.203559	+	0.0597704i
$169$	−10.1034	+	6.49303i	−0.777181	+	0.499464i
$170$	1.41118	+	3.09006i	0.108233	+	0.236997i
$171$	0.563414	−	0.165433i	0.0430853	−	0.0126510i
$172$	9.31817	−	10.7537i	0.710504	−	0.819966i
$173$	−11.5403	+	13.3183i	−0.877395	+	1.01257i	0.122403	+	0.992480i	$0.460940\pi$
$173$	−11.5403	+	13.3183i	−0.877395	+	1.01257i	−0.999798	+	0.0200877i	$0.993605\pi$
$174$	−0.638547	+	0.187494i	−0.0484081	+	0.0142139i
$175$	−1.68050	−	3.67978i	−0.127034	−	0.278165i
$176$	−1.53642	+	0.987395i	−0.115812	+	0.0744277i
$177$	6.25110	+	1.83549i	0.469862	+	0.137964i
$178$	−0.451333	−	3.13909i	−0.0338289	−	0.235285i
$179$	−5.86921	+	12.8518i	−0.438686	+	0.960587i	0.553152	+	0.833080i	$0.313425\pi$
$179$	−5.86921	+	12.8518i	−0.438686	+	0.960587i	−0.991838	+	0.127507i	$0.959302\pi$
$180$	0.182117	−	1.26665i	0.0135742	−	0.0944107i
$181$	0.228593	+	0.146908i	0.0169912	+	0.0109196i	0.549109	−	0.835751i	$-0.314967\pi$
$181$	0.228593	+	0.146908i	0.0169912	+	0.0109196i	−0.532118	+	0.846670i	$0.678604\pi$
$182$	−0.541384	−	0.624790i	−0.0401300	−	0.0463125i
$183$	1.49361			0.110411
$184$	11.0483	+	7.20058i	0.814495	+	0.530834i
$185$	−3.52410			−0.259097
$186$	2.14202	+	2.47202i	0.157061	+	0.181258i
$187$	−19.2032	−	12.3411i	−1.40428	−	0.902474i
$188$	−2.15472	+	14.9864i	−0.157149	+	1.09300i
$189$	0.415415	−	0.909632i	0.0302170	−	0.0661660i
$190$	0.0678375	+	0.471820i	0.00492145	+	0.0342294i
$191$	−17.7263	−	5.20492i	−1.28263	−	0.376615i	−0.431761	−	0.901988i	$-0.642108\pi$
$191$	−17.7263	−	5.20492i	−1.28263	−	0.376615i	−0.850872	+	0.525373i	$0.823926\pi$
$192$	3.47501	−	2.23325i	0.250787	−	0.161171i
$193$	−8.52916	−	18.6762i	−0.613942	−	1.34435i	−0.919845	−	0.392283i	$-0.871685\pi$
$193$	−8.52916	−	18.6762i	−0.613942	−	1.34435i	0.305902	−	0.952063i	$-0.401042\pi$
$194$	14.1716	−	4.16116i	1.01746	−	0.298754i
$195$	−0.636671	+	0.734757i	−0.0455929	+	0.0526170i
$196$	0.857685	−	0.989821i	0.0612632	−	0.0707015i
$197$	11.1451	−	3.27250i	0.794057	−	0.233156i	0.140547	−	0.990074i	$-0.455114\pi$
$197$	11.1451	−	3.27250i	0.794057	−	0.233156i	0.653510	+	0.756918i	$0.273296\pi$
$198$	−1.88267	−	4.12247i	−0.133795	−	0.292971i
$199$	6.89107	−	4.42862i	0.488495	−	0.313937i	−0.273105	−	0.961984i	$-0.588051\pi$
$199$	6.89107	−	4.42862i	0.488495	−	0.313937i	0.761600	+	0.648048i	$0.224414\pi$
$200$	−10.6734	−	3.13399i	−0.754721	−	0.221606i
$201$	−0.189957	−	1.32118i	−0.0133985	−	0.0931887i
$202$	2.88003	−	6.30639i	0.202638	−	0.443716i
$203$	−0.113996	+	0.792858i	−0.00800094	+	0.0556478i
$204$	−4.61076	−	2.96316i	−0.322818	−	0.207463i
$205$	−6.19675	−	7.15144i	−0.432800	−	0.499478i
$206$	0.155053			0.0108031
$207$	3.16371	−	3.60429i	0.219893	−	0.250516i
$208$	0.333155			0.0231002
$209$	−2.09756	−	2.42071i	−0.145091	−	0.167444i
$210$	0.682906	+	0.438877i	0.0471250	+	0.0302854i
$211$	4.03425	−	28.0588i	0.277729	−	1.93165i	−0.0777665	−	0.996972i	$-0.524779\pi$
$211$	4.03425	−	28.0588i	0.277729	−	1.93165i	0.355496	−	0.934678i	$-0.384312\pi$
$212$	0.480956	−	1.05315i	0.0330322	−	0.0723304i
$213$	1.57904	+	10.9825i	0.108194	+	0.752507i
$214$	−3.52310	−	1.03447i	−0.240834	−	0.0707152i
$215$	8.93000	−	5.73896i	0.609021	−	0.391394i
$216$	−1.14231	−	2.50132i	−0.0777247	−	0.170193i
$217$	3.77750	−	1.10917i	0.256433	−	0.0752956i
$218$	9.93492	−	11.4655i	0.672878	−	0.776542i
$219$	−6.14997	+	7.09744i	−0.415576	+	0.479600i
$220$	−6.69764	+	1.96661i	−0.451555	+	0.132589i
$221$	1.72979	+	3.78771i	0.116358	+	0.254789i
$222$	−2.52095	+	1.62012i	−0.169195	+	0.108735i
$223$	−13.5714	−	3.98493i	−0.908811	−	0.266851i	−0.206271	−	0.978495i	$-0.566133\pi$
$223$	−13.5714	−	3.98493i	−0.908811	−	0.266851i	−0.702540	+	0.711644i	$0.747951\pi$
$224$	−0.822267	−	5.71900i	−0.0549400	−	0.382116i
$225$	−1.68050	+	3.67978i	−0.112033	+	0.245319i
$226$	1.26823	−	8.82076i	0.0843617	−	0.586748i
$227$	9.79284	+	6.29348i	0.649974	+	0.417713i	0.823657	−	0.567089i	$-0.191930\pi$
$227$	9.79284	+	6.29348i	0.649974	+	0.417713i	−0.173683	+	0.984802i	$0.555567\pi$
$228$	−0.503632	−	0.581223i	−0.0333539	−	0.0384924i
$229$	18.7885			1.24158			0.620788	−	0.783979i	$-0.286813\pi$
$229$	18.7885			1.24158			0.620788	+	0.783979i	$0.286813\pi$
$230$	2.53058	+	2.95847i	0.166862	+	0.195076i
$231$	−5.45481			−0.358900
$232$	1.44242	+	1.66464i	0.0946994	+	0.109289i
$233$	−16.5140	−	10.6129i	−1.08187	−	0.695272i	−0.126878	−	0.991918i	$-0.540496\pi$
$233$	−16.5140	−	10.6129i	−1.08187	−	0.695272i	−0.954988	+	0.296646i	$0.904132\pi$
$234$	−0.117654	+	0.818301i	−0.00769128	+	0.0534940i
$235$	−4.69208	+	10.2742i	−0.306078	+	0.670216i
$236$	−1.21435	−	8.44599i	−0.0790475	−	0.549787i
$237$	8.76905	+	2.57482i	0.569611	+	0.167253i
$238$	2.92487	−	1.87970i	0.189591	−	0.121843i
$239$	−2.60622	−	5.70683i	−0.168582	−	0.369144i	0.806418	−	0.591345i	$-0.201403\pi$
$239$	−2.60622	−	5.70683i	−0.168582	−	0.369144i	−0.975001	+	0.222201i	$0.928676\pi$
$240$	−0.313882	+	0.0921640i	−0.0202610	+	0.00594916i
$241$	2.46709	−	2.84717i	0.158919	−	0.183403i	−0.670706	−	0.741723i	$-0.734009\pi$
$241$	2.46709	−	2.84717i	0.158919	−	0.183403i	0.829625	+	0.558321i	$0.188554\pi$
$242$	−10.2042	+	11.7762i	−0.655948	+	0.757004i
$243$	−0.959493	+	0.281733i	−0.0615515	+	0.0180732i
$244$	−0.812642	−	1.77944i	−0.0520241	−	0.113917i
$245$	0.821956	−	0.528239i	0.0525128	−	0.0337480i
$246$	−7.72054	−	2.26695i	−0.492244	−	0.144536i
$247$	0.0831534	+	0.578344i	0.00529092	+	0.0367992i
$248$	4.49726	−	9.84763i	0.285576	−	0.625325i
$249$	0.450727	−	3.13487i	0.0285637	−	0.198665i
$250$	−6.17712	−	3.96980i	−0.390676	−	0.251072i
$251$	−16.6792	−	19.2488i	−1.05278	−	1.21497i	−0.975965	−	0.217926i	$-0.930071\pi$
$251$	−16.6792	−	19.2488i	−1.05278	−	1.21497i	−0.0768135	−	0.997045i	$-0.524475\pi$
$252$	−1.30972			−0.0825047
$253$	−25.0530	−	7.53058i	−1.57507	−	0.473444i
$254$	−15.2046			−0.954020
$255$	−2.67755	−	3.09006i	−0.167675	−	0.193507i
$256$	−12.6280	−	8.11549i	−0.789247	−	0.507218i
$257$	0.541552	−	3.76658i	0.0337811	−	0.234953i	−0.965935	−	0.258785i	$-0.916678\pi$
$257$	0.541552	−	3.76658i	0.0337811	−	0.234953i	0.999716	+	0.0238326i	$0.00758686\pi$
$258$	3.74971	−	8.21071i	0.233447	−	0.511177i
$259$	0.513306	+	3.57012i	0.0318953	+	0.221836i
$260$	1.22176	+	0.358742i	0.0757704	+	0.0222482i
$261$	0.673854	−	0.433060i	0.0417105	−	0.0268057i
$262$	−5.77321	−	12.6416i	−0.356670	−	0.780998i
$263$	−0.728046	+	0.213774i	−0.0448932	+	0.0131818i	−0.304102	−	0.952639i	$-0.598356\pi$
$263$	−0.728046	+	0.213774i	−0.0448932	+	0.0131818i	0.259209	+	0.965821i	$0.416538\pi$
$264$	−9.82273	+	11.3360i	−0.604547	+	0.697685i
$265$	0.565607	−	0.652745i	0.0347450	−	0.0400978i
$266$	0.468101	−	0.137447i	0.0287011	−	0.00842741i
$267$	1.58569	+	3.47217i	0.0970424	+	0.212493i
$268$	−1.47065	+	0.945132i	−0.0898345	+	0.0577331i
$269$	−13.8147	−	4.05636i	−0.842296	−	0.247320i	−0.168005	−	0.985786i	$-0.553733\pi$
$269$	−13.8147	−	4.05636i	−0.842296	−	0.247320i	−0.674291	+	0.738466i	$0.735551\pi$
$270$	−0.115527	−	0.803509i	−0.00703076	−	0.0489000i
$271$	−2.46886	+	5.40605i	−0.149973	+	0.328394i	−0.969676	−	0.244394i	$-0.921411\pi$
$271$	−2.46886	+	5.40605i	−0.149973	+	0.328394i	0.819703	+	0.572788i	$0.194138\pi$
$272$	−0.199398	+	1.38684i	−0.0120903	+	0.0840895i
$273$	0.837088	+	0.537964i	0.0506629	+	0.0325590i
$274$	−0.712771	−	0.822581i	−0.0430601	−	0.0496940i
$275$	22.0666			1.33067
$276$	−6.01533	−	1.80812i	−0.362080	−	0.108836i
$277$	−15.6271			−0.938942			−0.469471	−	0.882948i	$-0.655555\pi$
$277$	−15.6271			−0.938942			−0.469471	+	0.882948i	$0.655555\pi$
$278$	6.13749	+	7.08304i	0.368102	+	0.424813i
$279$	−3.31199	−	2.12849i	−0.198284	−	0.127429i
$280$	0.382363	−	2.65939i	0.0228505	−	0.158929i
$281$	−2.16236	+	4.73490i	−0.128995	+	0.282461i	−0.963099	−	0.269147i	$-0.913258\pi$
$281$	−2.16236	+	4.73490i	−0.128995	+	0.282461i	0.834104	+	0.551608i	$0.185985\pi$
$282$	1.36686	+	9.50672i	0.0813953	+	0.566117i
$283$	24.8798	+	7.30537i	1.47895	+	0.434259i	0.918997	−	0.394265i	$-0.129001\pi$
$283$	24.8798	+	7.30537i	1.47895	+	0.434259i	0.559954	+	0.828524i	$0.310819\pi$
$284$	12.2250	−	7.85654i	0.725421	−	0.466200i
$285$	−0.238336	−	0.521883i	−0.0141178	−	0.0309137i
$286$	4.32691	−	1.27049i	0.255855	−	0.0751259i
$287$	−6.34224	+	7.31933i	−0.374371	+	0.432047i
$288$	−3.78366	+	4.36657i	−0.222954	+	0.257303i
$289$	−0.491187	+	0.144226i	−0.0288934	+	0.00848386i
$290$	0.270119	+	0.591478i	0.0158619	+	0.0347328i
$291$	−14.9552	+	9.61112i	−0.876689	+	0.563414i
$292$	11.8017	+	3.46529i	0.690642	+	0.202791i
$293$	−0.0489996	−	0.340800i	−0.00286259	−	0.0199097i	0.988340	−	0.152263i	$-0.0486559\pi$
$293$	−0.0489996	−	0.340800i	−0.00286259	−	0.0199097i	−0.991203	+	0.132353i	$0.957747\pi$
$294$	0.345139	−	0.755750i	0.0201289	−	0.0440762i
$295$	0.905913	−	6.30077i	0.0527443	−	0.366845i
$296$	8.34366	+	5.36214i	0.484965	+	0.311668i
$297$	3.57214	+	4.12247i	0.207277	+	0.239210i
$298$	2.18347			0.126485
$299$	3.10192	+	3.62641i	0.179389	+	0.209721i
$300$	5.29828			0.305897
$301$	−7.11462	−	8.21071i	−0.410080	−	0.473258i
$302$	−4.47526	−	2.87608i	−0.257522	−	0.165500i
$303$	−1.18755	+	8.25962i	−0.0682232	+	0.474503i
$304$	−0.0816715	+	0.178836i	−0.00468418	+	0.0102569i
$305$	−0.207687	−	1.44450i	−0.0118921	−	0.0827117i
$306$	−3.33596	−	0.979526i	−0.190704	−	0.0559958i
$307$	18.3931	−	11.8206i	1.04975	−	0.674635i	0.102372	−	0.994746i	$-0.467357\pi$
$307$	18.3931	−	11.8206i	1.04975	−	0.674635i	0.947380	+	0.320112i	$0.103720\pi$
$308$	2.96784	+	6.49867i	0.169108	+	0.370296i
$309$	−0.179065	+	0.0525782i	−0.0101866	+	0.00299107i
$310$	2.09288	−	2.41532i	0.118868	−	0.137181i
$311$	14.7275	−	16.9965i	0.835122	−	0.963782i	−0.164623	−	0.986356i	$-0.552641\pi$
$311$	14.7275	−	16.9965i	0.835122	−	0.963782i	0.999745	+	0.0225746i	$0.00718634\pi$
$312$	2.62536	−	0.770876i	0.148632	−	0.0436423i
$313$	0.932104	+	2.04102i	0.0526856	+	0.115365i	0.934144	−	0.356896i	$-0.116165\pi$
$313$	0.932104	+	2.04102i	0.0526856	+	0.115365i	−0.881458	+	0.472262i	$0.843438\pi$
$314$	12.7269	−	8.17907i	0.718220	−	0.461572i
$315$	−0.937483	−	0.275270i	−0.0528212	−	0.0155097i
$316$	−1.70349	−	11.8480i	−0.0958288	−	0.666504i
$317$	2.11610	−	4.63361i	0.118852	−	0.260249i	−0.840851	−	0.541267i	$-0.817945\pi$
$317$	2.11610	−	4.63361i	0.118852	−	0.260249i	0.959703	+	0.281018i	$0.0906720\pi$
$318$	0.104522	−	0.726965i	0.00586129	−	0.0407662i
$319$	−3.67574	−	2.36226i	−0.205802	−	0.132261i
$320$	−2.64301	−	3.05020i	−0.147749	−	0.170511i
$321$	4.41947			0.246671
$322$	2.62851	−	2.99455i	0.146481	−	0.166880i
$323$	−2.45727			−0.136726
$324$	0.857685	+	0.989821i	0.0476492	+	0.0549901i
$325$	−3.38631	−	2.17625i	−0.187839	−	0.120717i
$326$	0.394269	−	2.74220i	0.0218365	−	0.151877i
$327$	−7.58552	+	16.6100i	−0.419480	+	0.918534i
$328$	3.79007	+	26.3605i	0.209272	+	1.45552i
$329$	11.0918	+	3.25686i	0.611513	+	0.179556i
$330$	−3.72512	+	2.39399i	−0.205061	+	0.131785i
$331$	−11.9717	−	26.2144i	−0.658025	−	1.44087i	−0.884351	−	0.466822i	$-0.845399\pi$
$331$	−11.9717	−	26.2144i	−0.658025	−	1.44087i	0.226326	−	0.974052i	$-0.427328\pi$
$332$	−3.98001	+	1.16864i	−0.218431	+	0.0641372i
$333$	2.36197	−	2.72586i	0.129435	−	0.149376i
$334$	−0.456735	+	0.527100i	−0.0249914	+	0.0288416i
$335$	−1.25132	+	0.367420i	−0.0683669	+	0.0200743i
$336$	0.139086	+	0.304557i	0.00758779	+	0.0166149i
$337$	23.1837	−	14.8993i	1.26290	−	0.811614i	0.274219	−	0.961667i	$-0.411581\pi$
$337$	23.1837	−	14.8993i	1.26290	−	0.811614i	0.988678	+	0.150053i	$0.0479445\pi$
$338$	9.57398	+	2.81117i	0.520756	+	0.152908i
$339$	1.52647	+	10.6168i	0.0829063	+	0.576626i
$340$	−2.22459	+	4.87117i	−0.120645	+	0.264176i
$341$	−3.05627	+	21.2569i	−0.165506	+	1.15112i
$342$	−0.410416	−	0.263759i	−0.0221928	−	0.0142624i
$343$	−0.654861	−	0.755750i	−0.0353592	−	0.0408066i
$344$	−29.8749			−1.61075
$345$	−3.92568	−	2.55850i	−0.211352	−	0.137745i
$346$	14.6414			0.787125
$347$	5.67518	+	6.54951i	0.304660	+	0.351596i	0.887349	−	0.461099i	$-0.152545\pi$
$347$	5.67518	+	6.54951i	0.304660	+	0.351596i	−0.582689	+	0.812695i	$0.697999\pi$
$348$	−0.882561	−	0.567187i	−0.0473102	−	0.0304044i
$349$	−1.54134	+	10.7202i	−0.0825059	+	0.573841i	0.906071	+	0.423125i	$0.139067\pi$
$349$	−1.54134	+	10.7202i	−0.0825059	+	0.573841i	−0.988577	+	0.150716i	$0.951842\pi$
$350$	−1.39621	+	3.05727i	−0.0746305	+	0.163418i
$351$	−0.141610	−	0.984920i	−0.00755859	−	0.0525711i
$352$	30.2402	+	8.87932i	1.61181	+	0.473269i
$353$	−19.0965	+	12.2726i	−1.01640	+	0.653203i	−0.939043	−	0.343800i	$-0.888286\pi$
$353$	−19.0965	+	12.2726i	−1.01640	+	0.653203i	−0.0773612	+	0.997003i	$0.524649\pi$
$354$	−2.24858	−	4.92371i	−0.119511	−	0.261692i
$355$	10.4018	−	3.05423i	0.552068	−	0.162102i
$356$	3.27388	−	3.77826i	0.173515	−	0.200247i
$357$	−2.74041	+	3.16260i	−0.145038	+	0.167383i
$358$	11.2629	−	3.30710i	0.595265	−	0.174785i
$359$	−3.68521	−	8.06949i	−0.194498	−	0.425891i	0.787106	−	0.616817i	$-0.211578\pi$
$359$	−3.68521	−	8.06949i	−0.194498	−	0.425891i	−0.981604	+	0.190926i	$0.938851\pi$
$360$	−2.26023	+	1.45256i	−0.119124	+	0.0765566i
$361$	17.8995	+	5.25578i	0.942081	+	0.276620i
$362$	−0.0321291	−	0.223463i	−0.00168867	−	0.0117450i
$363$	7.79109	−	17.0601i	0.408926	−	0.895423i
$364$	0.185470	−	1.28997i	0.00972126	−	0.0676128i
$365$	7.71920	+	4.96083i	0.404041	+	0.259662i
$366$	−0.812642	−	0.937839i	−0.0424775	−	0.0490216i
$367$	−32.6808			−1.70592			−0.852961	−	0.521974i	$-0.825196\pi$
$367$	−32.6808			−1.70592			−0.852961	+	0.521974i	$0.825196\pi$
$368$	0.218348	+	1.59079i	0.0113822	+	0.0829258i
$369$	9.68487			0.504174
$370$	1.91738	+	2.21278i	0.0996800	+	0.115037i
$371$	−0.743654	−	0.477918i	−0.0386086	−	0.0248122i
$372$	−0.733823	+	5.10385i	−0.0380470	+	0.264623i
$373$	2.52094	−	5.52009i	0.130529	−	0.285820i	−0.833071	−	0.553166i	$-0.813420\pi$
$373$	2.52094	−	5.52009i	0.130529	−	0.285820i	0.963600	+	0.267346i	$0.0861468\pi$
$374$	2.69904	+	18.7722i	0.139564	+	0.970688i
$375$	8.47987	+	2.48991i	0.437898	+	0.128579i
$376$	26.7419	−	17.1860i	1.37911	−	0.886299i
$377$	0.331104	+	0.725018i	0.0170527	+	0.0373403i
$378$	−0.797176	+	0.234072i	−0.0410023	+	0.0120394i
$379$	1.68937	−	1.94963i	0.0867769	−	0.100146i	−0.710700	−	0.703495i	$-0.751622\pi$
$379$	1.68937	−	1.94963i	0.0867769	−	0.100146i	0.797477	+	0.603349i	$0.206167\pi$
$380$	−0.492079	+	0.567890i	−0.0252431	+	0.0291321i
$381$	17.5592	−	5.15584i	0.899583	−	0.264142i
$382$	6.37634	+	13.9622i	0.326242	+	0.714371i
$383$	−29.8421	+	19.1784i	−1.52486	+	0.979968i	−0.533940	+	0.845523i	$0.679289\pi$
$383$	−29.8421	+	19.1784i	−1.52486	+	0.979968i	−0.990921	+	0.134446i	$0.957075\pi$
$384$	7.79460	+	2.28870i	0.397766	+	0.116795i
$385$	0.758493	+	5.27543i	0.0386564	+	0.268861i
$386$	−7.08628	+	15.5168i	−0.360682	+	0.789784i
$387$	−1.54616	+	10.7537i	−0.0785955	+	0.546644i
$388$	19.5871	+	12.5879i	0.994387	+	0.639053i
$389$	10.8315	+	12.5002i	0.549180	+	0.633788i	0.960692	−	0.277617i	$-0.0895446\pi$
$389$	10.8315	+	12.5002i	0.549180	+	0.633788i	−0.411512	+	0.911404i	$0.634999\pi$
$390$	0.807752			0.0409021
$391$	−16.9524	+	10.7421i	−0.857317	+	0.543249i
$392$	−2.74982			−0.138887
$393$	10.9540	+	12.6416i	0.552555	+	0.637682i
$394$	−8.11862	−	5.21752i	−0.409010	−	0.262855i
$395$	1.27082	−	8.83872i	0.0639417	−	0.444724i
$396$	2.96784	−	6.49867i	0.149140	−	0.326570i
$397$	−1.77731	−	12.3615i	−0.0892006	−	0.620404i	−0.984558	−	0.175056i	$-0.943989\pi$
$397$	−1.77731	−	12.3615i	−0.0892006	−	0.620404i	0.895358	−	0.445348i	$-0.146920\pi$
$398$	−6.53001	−	1.91738i	−0.327320	−	0.0961097i
$399$	−0.493984	+	0.317464i	−0.0247301	+	0.0158931i
$400$	−0.562654	−	1.23204i	−0.0281327	−	0.0616020i
$401$	8.64913	−	2.53961i	0.431917	−	0.126822i	−0.0585451	−	0.998285i	$-0.518646\pi$
$401$	8.64913	−	2.53961i	0.431917	−	0.126822i	0.490462	+	0.871462i	$0.336828\pi$
$402$	−0.726216	+	0.838098i	−0.0362204	+	0.0418005i
$403$	2.56540	−	2.96063i	0.127792	−	0.147480i
$404$	10.4863	−	3.07907i	0.521715	−	0.153189i
$405$	0.405886	+	0.888766i	0.0201686	+	0.0441631i
$406$	0.559858	−	0.359799i	0.0277853	−	0.0178565i
$407$	−18.8776	−	5.54297i	−0.935729	−	0.274755i
$408$	1.63765	+	11.3901i	0.0810757	+	0.563894i
$409$	−10.3139	+	22.5844i	−0.509992	+	1.11673i	0.463099	+	0.886306i	$0.346737\pi$
$409$	−10.3139	+	22.5844i	−0.509992	+	1.11673i	−0.973091	+	0.230420i	$0.925990\pi$
$410$	−1.11886	+	7.78188i	−0.0552568	+	0.384320i
$411$	1.10209	+	0.708268i	0.0543619	+	0.0349363i
$412$	0.160065	+	0.184725i	0.00788583	+	0.00910074i
$413$	−6.51501			−0.320582
$414$	−3.98444	−	0.0254797i	−0.195825	−	0.00125226i
$415$	−3.09446			−0.151901
$416$	−3.76492	−	4.34495i	−0.184590	−	0.213029i
$417$	−9.48979	−	6.09872i	−0.464717	−	0.298655i
$418$	−0.378728	+	2.63411i	−0.0185242	+	0.128839i
$419$	−2.30313	+	5.04314i	−0.112515	+	0.246374i	−0.957510	−	0.288401i	$-0.906876\pi$
$419$	−2.30313	+	5.04314i	−0.112515	+	0.246374i	0.844995	+	0.534775i	$0.179604\pi$
$420$	0.182117	+	1.26665i	0.00888641	+	0.0618063i
$421$	20.7815	+	6.10200i	1.01283	+	0.297393i	0.745710	−	0.666271i	$-0.232110\pi$
$421$	20.7815	+	6.10200i	1.01283	+	0.297393i	0.267118	+	0.963664i	$0.413929\pi$
$422$	−19.8131	+	12.7331i	−0.964485	+	0.619837i
$423$	−4.80224	−	10.5154i	−0.233493	−	0.511278i
$424$	−2.33233	+	0.684833i	−0.113268	+	0.0332584i
$425$	11.0859	−	12.7938i	0.537747	−	0.620593i
$426$	6.03677	−	6.96680i	0.292482	−	0.337543i
$427$	−1.43311	+	0.420800i	−0.0693531	+	0.0203639i
$428$	−2.40454	−	5.26520i	−0.116228	−	0.254503i
$429$	−4.56615	+	2.93449i	−0.220456	+	0.141678i
$430$	−8.46211	−	2.48470i	−0.408079	−	0.119823i
$431$	−5.22203	−	36.3200i	−0.251536	−	1.74947i	−0.588997	−	0.808135i	$-0.700477\pi$
$431$	−5.22203	−	36.3200i	−0.251536	−	1.74947i	0.337461	−	0.941340i	$-0.390432\pi$
$432$	0.139086	−	0.304557i	0.00669180	−	0.0146530i
$433$	−4.84971	+	33.7305i	−0.233062	+	1.62098i	0.451668	+	0.892186i	$0.350829\pi$
$433$	−4.84971	+	33.7305i	−0.233062	+	1.62098i	−0.684730	+	0.728797i	$0.740080\pi$
$434$	−2.75170	−	1.76841i	−0.132086	−	0.0848865i
$435$	−0.512518	−	0.591478i	−0.0245734	−	0.0283592i
$436$	23.9157			1.14535
$437$	−2.70706	+	0.776095i	−0.129496	+	0.0371257i
$438$	7.80254			0.372820
$439$	2.93626	+	3.38863i	0.140140	+	0.161730i	0.821481	−	0.570236i	$-0.193148\pi$
$439$	2.93626	+	3.38863i	0.140140	+	0.161730i	−0.681341	+	0.731966i	$0.738603\pi$
$440$	12.3291	+	7.92344i	0.587767	+	0.377735i
$441$	−0.142315	+	0.989821i	−0.00677690	+	0.0471344i
$442$	1.43716	−	3.14694i	0.0683588	−	0.149685i
$443$	2.38442	+	16.5840i	0.113287	+	0.787928i	0.964685	+	0.263408i	$0.0848464\pi$
$443$	2.38442	+	16.5840i	0.113287	+	0.787928i	−0.851398	+	0.524521i	$0.824245\pi$
$444$	−4.53259	−	1.33089i	−0.215107	−	0.0631612i
$445$	3.13750	−	2.01635i	0.148732	−	0.0955841i
$446$	4.88178	+	10.6896i	0.231159	+	0.506168i
$447$	−2.52160	+	0.740409i	−0.119268	+	0.0350202i
$448$	−2.70506	+	3.12181i	−0.127802	+	0.147492i
$449$	−18.2753	+	21.0909i	−0.862466	+	0.995339i	0.137522	+	0.990499i	$0.456086\pi$
$449$	−18.2753	+	21.0909i	−0.862466	+	0.995339i	−0.999988	+	0.00484064i	$0.998459\pi$
$450$	3.22486	−	0.946903i	0.152021	−	0.0446374i
$451$	−21.9460	−	48.0550i	−1.03340	−	2.26282i
$452$	11.8180	−	7.59495i	0.555871	−	0.357236i
$453$	6.14357	+	1.80392i	0.288650	+	0.0847554i
$454$	−1.37640	−	9.57306i	−0.0645976	−	0.449286i
$455$	0.403876	−	0.884365i	0.0189340	−	0.0414597i
$456$	−0.229794	+	1.59826i	−0.0107611	+	0.0748451i
$457$	5.43474	+	3.49270i	0.254226	+	0.163381i	0.661547	−	0.749904i	$-0.269900\pi$
$457$	5.43474	+	3.49270i	0.254226	+	0.163381i	−0.407320	+	0.913285i	$0.633537\pi$
$458$	−10.2224	−	11.7973i	−0.477661	−	0.551250i
$459$	4.18473			0.195326
$460$	−0.912231	+	6.06894i	−0.0425330	+	0.282966i
$461$	−28.4302			−1.32413			−0.662063	−	0.749448i	$-0.730319\pi$
$461$	−28.4302			−1.32413			−0.662063	+	0.749448i	$0.730319\pi$
$462$	2.96784	+	3.42507i	0.138076	+	0.159349i
$463$	14.7028	+	9.44892i	0.683297	+	0.439128i	0.835697	−	0.549190i	$-0.185064\pi$
$463$	14.7028	+	9.44892i	0.683297	+	0.439128i	−0.152400	+	0.988319i	$0.548700\pi$
$464$	−0.0381673	+	0.265460i	−0.00177187	+	0.0123236i
$465$	−1.59796	+	3.49905i	−0.0741037	+	0.162264i
$466$	2.32106	+	16.1433i	0.107521	+	0.747825i
$467$	−26.7994	−	7.86900i	−1.24013	−	0.364134i	−0.405063	−	0.914289i	$-0.632751\pi$
$467$	−26.7994	−	7.86900i	−1.24013	−	0.364134i	−0.835063	+	0.550155i	$0.814569\pi$
$468$	−1.09635	+	0.704583i	−0.0506789	+	0.0325693i
$469$	0.554481	+	1.21414i	0.0256036	+	0.0560640i
$470$	9.00404	−	2.64382i	0.415325	−	0.121950i
$471$	−11.9243	+	13.7613i	−0.549442	+	0.634089i
$472$	−11.7319	+	13.5393i	−0.540003	+	0.623197i
$473$	56.8623	−	16.6963i	2.61453	−	0.767696i
$474$	−3.15431	−	6.90699i	−0.144882	−	0.317248i
$475$	1.99834	−	1.28425i	0.0916900	−	0.0589256i
$476$	5.25881	+	1.54413i	0.241037	+	0.0707749i
$477$	0.125804	+	0.874986i	0.00576017	+	0.0400629i
$478$	−2.16533	+	4.74140i	−0.0990397	+	0.216867i
$479$	−2.68712	+	18.6893i	−0.122777	+	0.853936i	0.831609	+	0.555362i	$0.187420\pi$
$479$	−2.68712	+	18.6893i	−0.122777	+	0.853936i	−0.954386	+	0.298574i	$0.903489\pi$
$480$	4.74910	+	3.05206i	0.216766	+	0.139307i
$481$	2.35028	+	2.71236i	0.107163	+	0.123673i
$482$	−3.13003			−0.142569
$483$	−2.02012	+	4.34961i	−0.0919185	+	0.197914i
$484$	−24.5638			−1.11653
$485$	11.3746	+	13.1270i	0.516494	+	0.596066i
$486$	0.698939	+	0.449181i	0.0317045	+	0.0203752i
$487$	1.70271	−	11.8426i	0.0771570	−	0.536638i	−0.914181	−	0.405305i	$-0.867165\pi$
$487$	1.70271	−	11.8426i	0.0771570	−	0.536638i	0.991338	−	0.131333i	$-0.0419257\pi$
$488$	−1.70618	+	3.73601i	−0.0772350	+	0.169121i
$489$	0.474548	+	3.30056i	0.0214598	+	0.149256i
$490$	−0.778889	−	0.228702i	−0.0351866	−	0.0103317i
$491$	−14.1174	+	9.07267i	−0.637107	+	0.409444i	−0.818935	−	0.573886i	$-0.805435\pi$
$491$	−14.1174	+	9.07267i	−0.637107	+	0.409444i	0.181828	+	0.983330i	$0.441799\pi$
$492$	−5.26932	−	11.5382i	−0.237559	−	0.520183i
$493$	−3.21623	+	0.944371i	−0.144852	+	0.0425323i
$494$	0.317900	−	0.366876i	0.0143030	−	0.0165065i
$495$	3.49020	−	4.02790i	0.156873	−	0.181041i
$496$	1.26476	−	0.371366i	0.0567892	−	0.0166748i
$497$	−4.60920	−	10.0927i	−0.206751	−	0.452721i
$498$	−2.21362	+	1.42260i	−0.0991945	+	0.0637484i
$499$	−13.4829	−	3.95895i	−0.603579	−	0.177227i	−0.0343558	−	0.999410i	$-0.510938\pi$
$499$	−13.4829	−	3.95895i	−0.603579	−	0.177227i	−0.569224	+	0.822183i	$0.692756\pi$
$500$	−1.64731	−	11.4573i	−0.0736701	−	0.512387i
$501$	0.348726	−	0.763604i	0.0155799	−	0.0341153i
$502$	−3.01153	+	20.9457i	−0.134411	+	0.934851i
$503$	22.6777	+	14.5741i	1.01115	+	0.649825i	0.937690	−	0.347473i	$-0.112960\pi$
$503$	22.6777	+	14.5741i	1.01115	+	0.649825i	0.0734579	+	0.997298i	$0.476597\pi$
$504$	1.80075	+	2.07817i	0.0802116	+	0.0925691i
$505$	8.15314			0.362810
$506$	8.90235	+	19.8280i	0.395758	+	0.881462i
$507$	−12.0099			−0.533377
$508$	−15.6960	−	18.1142i	−0.696399	−	0.803687i
$509$	−19.5733	−	12.5790i	−0.867569	−	0.557553i	0.0294389	−	0.999567i	$-0.490628\pi$
$509$	−19.5733	−	12.5790i	−0.867569	−	0.557553i	−0.897008	+	0.442014i	$0.854264\pi$
$510$	−0.483449	+	3.36246i	−0.0214075	+	0.148892i
$511$	3.90127	−	8.54259i	0.172582	−	0.377902i
$512$	−0.537357	−	3.73740i	−0.0237481	−	0.165171i
$513$	0.563414	+	0.165433i	0.0248753	+	0.00730405i
$514$	−2.65968	+	1.70927i	−0.117313	+	0.0753928i
$515$	0.0757482	+	0.165865i	0.00333786	+	0.00730890i
$516$	13.6529	−	4.00884i	0.601034	−	0.176479i
$517$	−41.2943	+	47.6562i	−1.81612	+	2.09592i
$518$	1.96240	−	2.26473i	0.0862228	−	0.0995064i
$519$	−16.9087	+	4.96485i	−0.742211	+	0.217933i
$520$	−1.11058	−	2.43184i	−0.0487024	−	0.106643i
$521$	21.8830	−	14.0634i	0.958713	−	0.616127i	0.0350714	−	0.999385i	$-0.488834\pi$
$521$	21.8830	−	14.0634i	0.958713	−	0.616127i	0.923642	+	0.383257i	$0.125198\pi$
$522$	−0.638547	−	0.187494i	−0.0279484	−	0.00820640i
$523$	−4.53565	−	31.5461i	−0.198330	−	1.37941i	−0.809130	−	0.587630i	$-0.800061\pi$
$523$	−4.53565	−	31.5461i	−0.198330	−	1.37941i	0.610800	−	0.791785i	$-0.290848\pi$
$524$	9.10089	−	19.9282i	0.397574	−	0.870566i
$525$	0.575714	−	4.00418i	0.0251262	−	0.174757i
$526$	0.530342	+	0.340830i	0.0231240	+	0.0148609i
$527$	10.7889	+	12.4511i	0.469973	+	0.542378i
$528$	−1.82634			−0.0794814
$529$	−15.2829	+	17.1882i	−0.664473	+	0.747313i
$530$	−0.717593			−0.0311702
$531$	4.26642	+	4.92371i	0.185147	+	0.213671i
$532$	0.646981	+	0.415789i	0.0280502	+	0.0180268i
$533$	−1.37147	+	9.53882i	−0.0594052	+	0.413172i
$534$	1.31744	−	2.88478i	0.0570110	−	0.124837i
$535$	−0.614529	−	4.27414i	−0.0265684	−	0.184787i
$536$	3.52168	+	1.03406i	0.152113	+	0.0446645i
$537$	−11.8857	+	7.63847i	−0.512906	+	0.329624i
$538$	4.96928	+	10.8812i	0.214241	+	0.469122i
$539$	5.23385	−	1.53680i	0.225438	−	0.0661946i
$540$	0.838011	−	0.967116i	0.0360622	−	0.0416180i
$541$	−13.1146	+	15.1351i	−0.563842	+	0.650709i	−0.964052	−	0.265715i	$-0.914392\pi$
$541$	−13.1146	+	15.1351i	−0.563842	+	0.650709i	0.400209	+	0.916424i	$0.368937\pi$
$542$	4.73771	−	1.39112i	0.203502	−	0.0597536i
$543$	0.112880	+	0.247174i	0.00484416	+	0.0106072i
$544$	20.3403	−	13.0719i	0.872082	−	0.560453i
$545$	17.1185	+	5.02646i	0.733278	+	0.215310i
$546$	−0.117654	−	0.818301i	−0.00503512	−	0.0350201i
$547$	1.01148	−	2.21483i	0.0432477	−	0.0946993i	−0.886775	−	0.462202i	$-0.847060\pi$
$547$	1.01148	−	2.21483i	0.0432477	−	0.0946993i	0.930023	+	0.367502i	$0.119787\pi$
$548$	0.244184	−	1.69834i	0.0104310	−	0.0725495i
$549$	1.25651	+	0.807508i	0.0536264	+	0.0344636i
$550$	−12.0060	−	13.8556i	−0.511936	−	0.590806i
$551$	−0.470354			−0.0200377
$552$	5.40153	+	12.0307i	0.229904	+	0.512061i
$553$	−9.13925			−0.388641
$554$	8.50236	+	9.81225i	0.361231	+	0.416883i
$555$	−2.96466	−	1.90527i	−0.125843	−	0.0808742i
$556$	−2.10261	+	14.6240i	−0.0891705	+	0.620195i
$557$	−5.34713	+	11.7086i	−0.226565	+	0.496108i	−0.988439	−	0.151617i	$-0.951552\pi$
$557$	−5.34713	+	11.7086i	−0.226565	+	0.496108i	0.761874	+	0.647725i	$0.224279\pi$
$558$	0.465505	+	3.23766i	0.0197064	+	0.137061i
$559$	−10.3726	−	3.04568i	−0.438715	−	0.128818i
$560$	0.275202	−	0.176861i	0.0116294	−	0.00747376i
$561$	−9.48263	−	20.7641i	−0.400357	−	0.876659i
$562$	4.14953	−	1.21841i	0.175037	−	0.0513956i
$563$	23.2511	−	26.8332i	0.979915	−	1.13088i	−0.0114737	−	0.999934i	$-0.503652\pi$
$563$	23.2511	−	26.8332i	0.979915	−	1.13088i	0.991389	−	0.130949i	$-0.0418023\pi$
$564$	−9.91493	+	11.4424i	−0.417494	+	0.481813i
$565$	10.0554	−	2.95254i	0.423035	−	0.124214i
$566$	−8.94951	−	19.5967i	−0.376176	−	0.823711i
$567$	0.841254	−	0.540641i	0.0353293	−	0.0227048i
$568$	−29.2744	−	8.59575i	−1.22833	−	0.360670i
$569$	1.28009	+	8.90324i	0.0536643	+	0.373243i	0.998902	+	0.0468591i	$0.0149212\pi$
$569$	1.28009	+	8.90324i	0.0536643	+	0.373243i	−0.945237	+	0.326384i	$0.894170\pi$
$570$	−0.198017	+	0.433596i	−0.00829400	+	0.0181613i
$571$	−0.826589	+	5.74905i	−0.0345917	+	0.240590i	−0.999780	−	0.0209647i	$-0.993326\pi$
$571$	−0.826589	+	5.74905i	−0.0345917	+	0.240590i	0.965189	+	0.261555i	$0.0842353\pi$
$572$	5.98039	+	3.84336i	0.250053	+	0.160699i
$573$	−12.0984	−	13.9622i	−0.505416	−	0.583281i
$574$	8.04648			0.335853
$575$	8.17208	−	17.5957i	0.340799	−	0.733792i
$576$	4.13075			0.172114
$577$	−7.56986	−	8.73608i	−0.315137	−	0.363688i	0.575978	−	0.817465i	$-0.304622\pi$
$577$	−7.56986	−	8.73608i	−0.315137	−	0.363688i	−0.891115	+	0.453778i	$0.850076\pi$
$578$	0.357803	+	0.229946i	0.0148827	+	0.00956450i
$579$	2.92196	−	20.3227i	0.121432	−	0.844581i
$580$	−0.425816	+	0.932406i	−0.0176810	+	0.0387161i
$581$	0.450727	+	3.13487i	0.0186993	+	0.130057i
$582$	14.1716	+	4.16116i	0.587432	+	0.172486i
$583$	4.05649	−	2.60695i	0.168003	−	0.107969i
$584$	−10.7278	−	23.4905i	−0.443918	−	0.972046i
$585$	−0.932841	+	0.273907i	−0.0385682	+	0.0113247i
$586$	−0.187328	+	0.216188i	−0.00773846	+	0.00893066i
$587$	−5.48041	+	6.32473i	−0.226201	+	0.261049i	−0.857493	−	0.514495i	$-0.827979\pi$
$587$	−5.48041	+	6.32473i	−0.226201	+	0.261049i	0.631293	+	0.775545i	$0.282525\pi$
$588$	1.25667	−	0.368991i	0.0518241	−	0.0152169i
$589$	0.960352	+	2.10288i	0.0395706	+	0.0866475i
$590$	−4.44913	+	2.85929i	−0.183168	+	0.117715i
$591$	11.1451	+	3.27250i	0.458449	+	0.134613i
$592$	0.171862	+	1.19532i	0.00706347	+	0.0491275i
$593$	12.5434	−	27.4663i	0.515097	−	1.12791i	−0.456166	−	0.889895i	$-0.650778\pi$
$593$	12.5434	−	27.4663i	0.515097	−	1.12791i	0.971263	−	0.238010i	$-0.0764952\pi$
$594$	0.644974	−	4.48589i	0.0264636	−	0.184058i
$595$	3.43966	+	2.21054i	0.141012	+	0.0906231i
$596$	2.25405	+	2.60131i	0.0923293	+	0.106554i
$597$	8.19143			0.335253
$598$	0.589332	−	3.92075i	0.0240996	−	0.160331i
$599$	28.8614			1.17925			0.589623	−	0.807678i	$-0.299276\pi$
$599$	28.8614			1.17925			0.589623	+	0.807678i	$0.299276\pi$
$600$	−7.28465	−	8.40694i	−0.297395	−	0.343212i
$601$	27.4921	+	17.6681i	1.12143	+	0.720697i	0.963754	−	0.266794i	$-0.0859643\pi$
$601$	27.4921	+	17.6681i	1.12143	+	0.720697i	0.157673	+	0.987491i	$0.449601\pi$
$602$	−1.28459	+	8.93454i	−0.0523561	+	0.364144i
$603$	0.554481	−	1.21414i	0.0225802	−	0.0494438i
$604$	−1.19346	−	8.30071i	−0.0485613	−	0.337751i
$605$	−17.5825	−	5.16267i	−0.714828	−	0.209893i
$606$	5.83233	−	3.74821i	0.236922	−	0.152261i
$607$	13.9159	+	30.4717i	0.564831	+	1.23681i	0.949504	+	0.313754i	$0.101587\pi$
$607$	13.9159	+	30.4717i	0.564831	+	1.23681i	−0.384673	+	0.923053i	$0.625686\pi$
$608$	3.25529	−	0.955841i	0.132020	−	0.0387645i
$609$	−0.524551	+	0.605364i	−0.0212559	+	0.0245306i
$610$	−0.794001	+	0.916326i	−0.0321482	+	0.0371010i
$611$	11.0369	−	3.24073i	0.446506	−	0.131106i
$612$	−2.27682	−	4.98553i	−0.0920349	−	0.201528i
$613$	−32.2776	+	20.7435i	−1.30368	+	0.837824i	−0.993608	−	0.112889i	$-0.963990\pi$
$613$	−32.2776	+	20.7435i	−1.30368	+	0.837824i	−0.310072	+	0.950713i	$0.600353\pi$
$614$	−17.4294	−	5.11774i	−0.703394	−	0.206535i
$615$	−1.34668	−	9.36639i	−0.0543035	−	0.377689i
$616$	6.23111	−	13.6442i	0.251059	−	0.549742i
$617$	−2.70392	+	18.8061i	−0.108856	+	0.757107i	0.860145	+	0.510049i	$0.170373\pi$
$617$	−2.70392	+	18.8061i	−0.108856	+	0.757107i	−0.969001	+	0.247058i	$0.920536\pi$
$618$	0.130439	+	0.0838280i	0.00524703	+	0.00337206i
$619$	2.56152	+	2.95615i	0.102956	+	0.118818i	0.804889	−	0.593425i	$-0.202225\pi$
$619$	2.56152	+	2.95615i	0.102956	+	0.118818i	−0.701933	+	0.712243i	$0.747679\pi$
$620$	5.03806			0.202333
$621$	4.61011	−	1.32169i	0.184997	−	0.0530375i
$622$	−18.6850			−0.749200
$623$	−2.49968	−	2.88478i	−0.100147	−	0.115576i
$624$	0.280268	+	0.180117i	0.0112197	+	0.00721046i
$625$	−1.64966	+	11.4736i	−0.0659864	+	0.458946i
$626$	0.774420	−	1.69574i	0.0309520	−	0.0677755i
$627$	−0.455843	−	3.17046i	−0.0182046	−	0.126616i
$628$	22.8825	+	6.71891i	0.913112	+	0.268114i
$629$	−12.6975	+	8.16022i	−0.506284	+	0.325369i
$630$	0.337222	+	0.738413i	0.0134353	+	0.0294191i
$631$	30.6237	−	8.99192i	1.21911	−	0.357963i	0.391979	−	0.919974i	$-0.371790\pi$
$631$	30.6237	−	8.99192i	1.21911	−	0.357963i	0.827130	+	0.562011i	$0.189972\pi$
$632$	−16.4575	+	18.9929i	−0.654643	+	0.755499i
$633$	18.5636	−	21.4235i	0.737836	−	0.851508i
$634$	−4.06076	+	1.19235i	−0.161274	+	0.0473542i
$635$	−7.42790	−	16.2648i	−0.294767	−	0.645450i
$636$	0.973980	−	0.625939i	0.0386208	−	0.0248201i
$637$	−0.954742	−	0.280337i	−0.0378282	−	0.0111074i
$638$	0.516631	+	3.59325i	0.0204536	+	0.142258i
$639$	−4.60920	+	10.0927i	−0.182337	+	0.399263i
$640$	1.12960	−	7.85652i	0.0446513	−	0.310556i
$641$	−14.4921	−	9.31350i	−0.572403	−	0.367861i	0.222190	−	0.975003i	$-0.428679\pi$
$641$	−14.4921	−	9.31350i	−0.572403	−	0.367861i	−0.794593	+	0.607142i	$0.792316\pi$
$642$	−2.40454	−	2.77498i	−0.0948995	−	0.109520i
$643$	−13.2525			−0.522626			−0.261313	−	0.965254i	$-0.584156\pi$
$643$	−13.2525			−0.522626			−0.261313	+	0.965254i	$0.584156\pi$
$644$	6.28108	+	0.0401662i	0.247509	+	0.00158277i
$645$	10.6151			0.417970
$646$	1.33695	+	1.54292i	0.0526014	+	0.0607053i
$647$	13.8571	+	8.90539i	0.544777	+	0.350107i	0.783905	−	0.620881i	$-0.213225\pi$
$647$	13.8571	+	8.90539i	0.544777	+	0.350107i	−0.239128	+	0.970988i	$0.576861\pi$
$648$	0.391340	−	2.72183i	0.0153733	−	0.106923i
$649$	14.7631	−	32.3266i	0.579501	−	1.26893i
$650$	0.475952	+	3.31032i	0.0186684	+	0.129841i
$651$	3.77750	+	1.10917i	0.148052	+	0.0434719i
$652$	3.67398	−	2.36112i	0.143884	−	0.0924686i
$653$	8.79647	+	19.2616i	0.344232	+	0.753764i	0.999999	−	0.00119955i	$-0.000381828\pi$
$653$	8.79647	+	19.2616i	0.344232	+	0.753764i	−0.655767	+	0.754963i	$0.727655\pi$
$654$	14.5565	−	4.27418i	0.569205	−	0.167134i
$655$	10.7027	−	12.3516i	0.418189	−	0.482616i
$656$	−2.12347	+	2.45061i	−0.0829074	+	0.0956802i
$657$	−9.01085	+	2.64582i	−0.351547	+	0.103223i
$658$	−3.98984	−	8.73654i	−0.155540	−	0.340586i
$659$	−4.12553	+	2.65132i	−0.160708	+	0.103281i	−0.618523	−	0.785767i	$-0.712269\pi$
$659$	−4.12553	+	2.65132i	−0.160708	+	0.103281i	0.457815	+	0.889047i	$0.348632\pi$
$660$	−6.69764	−	1.96661i	−0.260705	−	0.0765500i
$661$	−3.10237	−	21.5774i	−0.120668	−	0.839265i	−0.956802	−	0.290740i	$-0.906099\pi$
$661$	−3.10237	−	21.5774i	−0.120668	−	0.839265i	0.836134	−	0.548525i	$-0.184811\pi$
$662$	−9.94646	+	21.7797i	−0.386580	+	0.846492i
$663$	−0.592599	+	4.12162i	−0.0230147	+	0.160070i
$664$	7.32645	+	4.70843i	0.284322	+	0.182722i
$665$	0.375713	+	0.433596i	0.0145695	+	0.0168141i
$666$	−2.99666			−0.116118
$667$	−3.24490	+	2.05617i	−0.125643	+	0.0796153i
$668$	−1.09947			−0.0425396
$669$	−9.26260	−	10.6896i	−0.358113	−	0.413284i
$670$	0.911518	+	0.585797i	0.0352150	+	0.0226313i
$671$	1.15949	−	8.06445i	0.0447617	−	0.311325i
$672$	2.40019	−	5.25568i	0.0925892	−	0.202742i
$673$	6.81275	+	47.3837i	0.262612	+	1.82651i	0.513029	+	0.858371i	$0.328523\pi$
$673$	6.81275	+	47.3837i	0.262612	+	1.82651i	−0.250417	+	0.968138i	$0.580568\pi$
$674$	−21.9690	−	6.45067i	−0.846213	−	0.248471i
$675$	−3.40317	+	2.18708i	−0.130988	+	0.0841808i
$676$	6.53431	+	14.3081i	0.251320	+	0.550313i
$677$	−17.0216	+	4.99799i	−0.654193	+	0.192088i	−0.591952	−	0.805973i	$-0.701643\pi$
$677$	−17.0216	+	4.99799i	−0.654193	+	0.192088i	−0.0622403	+	0.998061i	$0.519825\pi$
$678$	5.83577	−	6.73484i	0.224121	−	0.258650i
$679$	11.6416	−	13.4352i	0.446765	−	0.515595i
$680$	10.7878	−	3.16759i	0.413694	−	0.121472i
$681$	4.83575	+	10.5888i	0.185306	+	0.405765i
$682$	15.0100	−	9.64635i	0.574763	−	0.369378i
$683$	−10.9840	−	3.22518i	−0.420289	−	0.123408i	0.0647478	−	0.997902i	$-0.479376\pi$
$683$	−10.9840	−	3.22518i	−0.420289	−	0.123408i	−0.485037	+	0.874494i	$0.661194\pi$
$684$	−0.109450	−	0.761240i	−0.00418492	−	0.0291067i
$685$	0.531732	−	1.16433i	0.0203164	−	0.0444868i
$686$	−0.118239	+	0.822373i	−0.00451440	+	0.0313984i
$687$	15.8059	+	10.1578i	0.603031	+	0.387544i
$688$	−2.38207	−	2.74906i	−0.0908156	−	0.104807i
$689$	−0.879606			−0.0335103
$690$	0.529396	+	3.85696i	0.0201537	+	0.146832i
$691$	−27.0982			−1.03086			−0.515432	−	0.856931i	$-0.672368\pi$
$691$	−27.0982			−1.03086			−0.515432	+	0.856931i	$0.672368\pi$
$692$	15.1146	+	17.4432i	0.574572	+	0.663091i
$693$	−4.58888	−	2.94909i	−0.174317	−	0.112027i
$694$	1.02469	−	7.12689i	0.0388968	−	0.270533i
$695$	−4.57861	+	10.0258i	−0.173677	+	0.380299i
$696$	0.313468	+	2.18021i	0.0118820	+	0.0826408i
$697$	−38.8868	−	11.4182i	−1.47294	−	0.432495i
$698$	7.56983	−	4.86484i	0.286522	−	0.184137i
$699$	−8.15467	−	17.8562i	−0.308438	−	0.675385i
$700$	−5.08367	+	1.49270i	−0.192145	+	0.0564187i
$701$	9.91493	−	11.4424i	0.374482	−	0.432175i	−0.536958	−	0.843609i	$-0.680427\pi$
$701$	9.91493	−	11.4424i	0.374482	−	0.432175i	0.911439	+	0.411434i	$0.134972\pi$
$702$	−0.541384	+	0.624790i	−0.0204332	+	0.0235812i
$703$	−2.03214	+	0.596690i	−0.0766436	+	0.0225046i
$704$	−9.36031	−	20.4962i	−0.352780	−	0.772481i
$705$	−9.50189	+	6.10650i	−0.357862	+	0.229984i
$706$	18.0959	+	5.31344i	0.681049	+	0.199974i
$707$	−1.18755	−	8.25962i	−0.0446626	−	0.310635i
$708$	3.54467	−	7.76175i	0.133217	−	0.291704i
$709$	−4.26764	+	29.6821i	−0.160275	+	1.11473i	0.737841	+	0.674975i	$0.235845\pi$
$709$	−4.26764	+	29.6821i	−0.160275	+	1.11473i	−0.898116	+	0.439760i	$0.855064\pi$
$710$	−7.57712	−	4.86952i	−0.284364	−	0.182750i
$711$	5.98494	+	6.90699i	0.224453	+	0.259032i
$712$	−10.4964			−0.393368
$713$	15.8182	+	10.3092i	0.592395	+	0.386084i
$714$	3.47680			0.130116
$715$	3.47292	+	4.00796i	0.129880	+	0.149889i
$716$	15.5669	+	10.0043i	0.581764	+	0.373877i
$717$	0.892851	−	6.20992i	0.0333441	−	0.231914i
$718$	−3.06178	+	6.70437i	−0.114265	+	0.250205i
$719$	−4.83385	−	33.6202i	−0.180272	−	1.25382i	−0.856119	−	0.516779i	$-0.827131\pi$
$719$	−4.83385	−	33.6202i	−0.180272	−	1.25382i	0.675847	−	0.737042i	$-0.263778\pi$
$720$	−0.313882	−	0.0921640i	−0.0116977	−	0.00343475i
$721$	0.156998	−	0.100897i	0.00584693	−	0.00375759i
$722$	−6.43864	−	14.0987i	−0.239621	−	0.524698i
$723$	3.61475	−	1.06139i	0.134434	−	0.0394733i
$724$	0.233058	−	0.268964i	0.00866154	−	0.00999595i
$725$	2.12199	−	2.44891i	0.0788089	−	0.0909503i
$726$	−14.9510	+	4.39001i	−0.554883	+	0.162928i
$727$	−2.85047	−	6.24166i	−0.105718	−	0.231490i	0.849379	−	0.527783i	$-0.176977\pi$
$727$	−2.85047	−	6.24166i	−0.105718	−	0.231490i	−0.955097	+	0.296293i	$0.904249\pi$
$728$	−2.30184	+	1.47930i	−0.0853118	+	0.0548265i
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$	−1.08495	−	7.54596i	−0.0401556	−	0.279288i
$731$	18.8865	−	41.3557i	0.698543	−	1.52960i
$732$	0.278399	−	1.93631i	0.0102899	−	0.0715679i
$733$	−34.5672	−	22.2150i	−1.27677	−	0.820529i	−0.286283	−	0.958145i	$-0.592420\pi$
$733$	−34.5672	−	22.2150i	−1.27677	−	0.820529i	−0.990486	+	0.137616i	$0.956056\pi$
$734$	17.7809	+	20.5202i	0.656305	+	0.757416i
$735$	0.977061			0.0360394
$736$	18.2793	−	20.8249i	0.673785	−	0.767616i
$737$	−7.28089			−0.268195
$738$	−5.26932	−	6.08112i	−0.193966	−	0.223849i
$739$	−4.60423	−	2.95896i	−0.169369	−	0.108847i	0.453210	−	0.891404i	$-0.350279\pi$
$739$	−4.60423	−	2.95896i	−0.169369	−	0.108847i	−0.622579	+	0.782557i	$0.713915\pi$
$740$	−0.656866	+	4.56860i	−0.0241469	+	0.167945i
$741$	−0.242724	+	0.531490i	−0.00891667	+	0.0195248i
$742$	0.104522	+	0.726965i	0.00383711	+	0.0266877i
$743$	9.59119	+	2.81623i	0.351867	+	0.103317i	0.452889	−	0.891567i	$-0.350393\pi$
$743$	9.59119	+	2.81623i	0.351867	+	0.103317i	−0.101023	+	0.994884i	$0.532211\pi$
$744$	9.10737	−	5.85295i	0.333892	−	0.214580i
$745$	1.06669	+	2.33573i	0.0390805	+	0.0855744i
$746$	−4.83765	+	1.42046i	−0.177119	+	0.0520068i
$747$	2.07402	−	2.39354i	0.0758843	−	0.0875751i
$748$	−19.5783	+	22.5945i	−0.715853	+	0.826138i
$749$	−4.24045	+	1.24511i	−0.154943	+	0.0454953i
$750$	−3.05029	−	6.67921i	−0.111381	−	0.243890i
$751$	7.98488	−	5.13157i	0.291372	−	0.187254i	−0.386786	−	0.922170i	$-0.626415\pi$
$751$	7.98488	−	5.13157i	0.291372	−	0.187254i	0.678158	+	0.734916i	$0.262778\pi$
$752$	3.71369	+	1.09044i	0.135424	+	0.0397642i
$753$	−3.62473	−	25.2105i	−0.132092	−	0.918723i
$754$	0.275092	−	0.602366i	0.0100182	−	0.0219369i
$755$	0.890330	−	6.19238i	0.0324024	−	0.225364i
$756$	−1.10181	−	0.708089i	−0.0400724	−	0.0257529i
$757$	12.9474	+	14.9421i	0.470583	+	0.543082i	0.940574	−	0.339590i	$-0.110288\pi$
$757$	12.9474	+	14.9421i	0.470583	+	0.543082i	−0.469991	+	0.882671i	$0.655743\pi$
$758$	−2.14332			−0.0778489
$759$	−17.0046	−	19.8798i	−0.617228	−	0.721592i
$760$	1.57765			0.0572274
$761$	−21.6529	−	24.9888i	−0.784916	−	0.905842i	0.212538	−	0.977153i	$-0.431827\pi$
$761$	−21.6529	−	24.9888i	−0.784916	−	0.905842i	−0.997454	+	0.0713111i	$0.977282\pi$
$762$	−12.7909	−	8.22021i	−0.463366	−	0.297787i
$763$	2.59868	−	18.0742i	0.0940787	−	0.654332i
$764$	−10.0517	+	22.0101i	−0.363657	+	0.796298i
$765$	−0.581887	−	4.04711i	−0.0210382	−	0.146324i
$766$	28.2785	+	8.30332i	1.02174	+	0.300011i
$767$	−5.45363	+	3.50484i	−0.196919	+	0.126552i
$768$	−6.23574	−	13.6544i	−0.225013	−	0.492710i
$769$	−20.3346	+	5.97079i	−0.733285	+	0.215312i	−0.626995	−	0.779023i	$-0.715715\pi$
$769$	−20.3346	+	5.97079i	−0.733285	+	0.215312i	−0.106290	+	0.994335i	$0.533897\pi$
$770$	2.89976	−	3.34650i	0.104500	−	0.120600i
$771$	2.49195	−	2.87586i	0.0897454	−	0.103572i
$772$	−25.8015	+	7.57600i	−0.928616	+	0.272666i
$773$	−1.61093	−	3.52745i	−0.0579411	−	0.126873i	0.878447	−	0.477840i	$-0.158580\pi$
$773$	−1.61093	−	3.52745i	−0.0579411	−	0.126873i	−0.936388	+	0.350967i	$0.885853\pi$
$774$	7.59350	−	4.88005i	0.272943	−	0.175410i
$775$	−15.2813	−	4.48700i	−0.548921	−	0.161178i
$776$	−6.95695	−	48.3867i	−0.249740	−	1.73698i
$777$	−1.49833	+	3.28089i	−0.0537524	+	0.117701i
$778$	1.95570	−	13.6022i	0.0701154	−	0.487663i
$779$	−4.78416	−	3.07460i	−0.171410	−	0.110159i
$780$	0.833861	+	0.962327i	0.0298570	+	0.0344568i
$781$	60.5233			2.16570
$782$	15.9683	+	4.79985i	0.571027	+	0.171642i
$783$	0.801012			0.0286258
$784$	−0.219256	−	0.253035i	−0.00783057	−	0.00903696i
$785$	14.9669	+	9.61864i	0.534191	+	0.343304i
$786$	1.97781	−	13.7560i	0.0705462	−	0.490660i
$787$	9.90438	−	21.6876i	0.353053	−	0.773078i	−0.646892	−	0.762582i	$-0.723932\pi$
$787$	9.90438	−	21.6876i	0.353053	−	0.773078i	0.999945	−	0.0104966i	$-0.00334123\pi$
$788$	−2.16507	−	15.0584i	−0.0771275	−	0.536433i
$789$	−0.728046	−	0.213774i	−0.0259191	−	0.00761054i
$790$	−6.24125	+	4.01101i	−0.222054	+	0.142705i
$791$	−4.45573	−	9.75670i	−0.158428	−	0.346908i
$792$	−14.3921	+	4.22591i	−0.511402	+	0.150161i
$793$	−0.973265	+	1.12321i	−0.0345617	+	0.0398863i
$794$	−6.79476	+	7.84157i	−0.241137	+	0.278287i
$795$	0.828720	−	0.243334i	0.0293917	−	0.00863017i
$796$	−4.45678	−	9.75898i	−0.157966	−	0.345898i
$797$	17.9543	−	11.5385i	0.635975	−	0.408716i	−0.182543	−	0.983198i	$-0.558433\pi$
$797$	17.9543	−	11.5385i	0.635975	−	0.408716i	0.818517	+	0.574482i	$0.194796\pi$
$798$	0.468101	+	0.137447i	0.0165706	+	0.00486557i
$799$	6.88460	+	47.8834i	0.243560	+	1.69399i
$800$	−9.70960	+	21.2611i	−0.343286	+	0.751692i
$801$	−0.543232	+	3.77826i	−0.0191942	+	0.133498i
$802$	−6.30043	−	4.04904i	−0.222476	−	0.142976i
$803$	33.5469	+	38.7152i	1.18384	+	1.36623i
$804$	−1.74817			−0.0616532
$805$	4.48748	+	1.34887i	0.158163	+	0.0475415i
$806$	−3.25476			−0.114644
$807$	−9.42862	−	10.8812i	−0.331903	−	0.383037i
$808$	−19.3034	−	12.4055i	−0.679091	−	0.436425i
$809$	4.05997	−	28.2377i	0.142741	−	0.992785i	−0.784983	−	0.619517i	$-0.787328\pi$
$809$	4.05997	−	28.2377i	0.142741	−	0.992785i	0.927724	−	0.373267i	$-0.121763\pi$
$810$	0.337222	−	0.738413i	0.0118488	−	0.0259452i
$811$	3.71955	+	25.8700i	0.130611	+	0.908419i	0.944760	+	0.327763i	$0.106295\pi$
$811$	3.71955	+	25.8700i	0.130611	+	0.908419i	−0.814149	+	0.580656i	$0.802796\pi$
$812$	1.00661	+	0.295566i	0.0353249	+	0.0103723i
$813$	−4.99967	+	3.21309i	−0.175346	+	0.112688i
$814$	6.79047	+	14.8691i	0.238006	+	0.521160i
$815$	3.12604	−	0.917887i	0.109500	−	0.0321522i
$816$	−0.917526	+	1.05888i	−0.0321198	+	0.0370683i
$817$	4.17770	−	4.82133i	0.146159	−	0.168677i
$818$	19.7923	−	5.81155i	0.692022	−	0.203196i
$819$	0.413358	+	0.905128i	0.0144439	+	0.0316277i
$820$	−10.4261	+	6.70044i	−0.364095	+	0.233989i
$821$	−41.2131	−	12.1012i	−1.43835	−	0.422337i	−0.532676	−	0.846319i	$-0.678813\pi$
$821$	−41.2131	−	12.1012i	−1.43835	−	0.422337i	−0.905670	+	0.423983i	$0.860632\pi$
$822$	−0.154900	−	1.07735i	−0.00540276	−	0.0375770i
$823$	−18.1505	+	39.7440i	−0.632686	+	1.38539i	0.273237	+	0.961947i	$0.411906\pi$
$823$	−18.1505	+	39.7440i	−0.632686	+	1.38539i	−0.905923	+	0.423442i	$0.860822\pi$
$824$	0.0730335	−	0.507959i	0.00254424	−	0.0176956i
$825$	18.5636	+	11.9301i	0.646302	+	0.415353i
$826$	3.54467	+	4.09077i	0.123335	+	0.142336i
$827$	7.03475			0.244622			0.122311	−	0.992492i	$-0.460969\pi$
$827$	7.03475			0.244622			0.122311	+	0.992492i	$0.460969\pi$
$828$	−4.08287	−	4.77322i	−0.141890	−	0.165881i
$829$	−10.5106			−0.365050			−0.182525	−	0.983201i	$-0.558427\pi$
$829$	−10.5106			−0.365050			−0.182525	+	0.983201i	$0.558427\pi$
$830$	1.68363	+	1.94301i	0.0584396	+	0.0674429i
$831$	−13.1464	−	8.44865i	−0.456042	−	0.293080i
$832$	−0.584956	+	4.06846i	−0.0202797	+	0.141048i
$833$	1.73840	−	3.80656i	0.0602319	−	0.131889i
$834$	1.33380	+	9.27681i	0.0461859	+	0.321230i
$835$	−0.786985	−	0.231080i	−0.0272347	−	0.00799684i
$836$	−3.52916	+	2.26805i	−0.122058	+	0.0784422i
$837$	−1.63548	−	3.58120i	−0.0565304	−	0.123784i
$838$	4.41967	−	1.29773i	0.152675	−	0.0448294i
$839$	25.9910	−	29.9953i	0.897310	−	1.03555i	−0.101859	−	0.994799i	$-0.532479\pi$
$839$	25.9910	−	29.9953i	0.897310	−	1.03555i	0.999169	−	0.0407525i	$-0.0129755\pi$
$840$	1.75944	−	2.03050i	0.0607064	−	0.0700589i
$841$	27.2097	−	7.98948i	0.938264	−	0.275499i
$842$	−7.47531	−	16.3687i	−0.257616	−	0.564101i
$843$	−4.37897	+	2.81419i	−0.150820	+	0.0969260i
$844$	−35.6232	−	10.4599i	−1.22620	−	0.360046i
$845$	1.66998	+	11.6149i	0.0574490	+	0.399566i
$846$	−3.98984	+	8.73654i	−0.137174	+	0.300368i
$847$	−2.66911	+	18.5641i	−0.0917116	+	0.637868i
$848$	−0.248985	−	0.160013i	−0.00855019	−	0.00549487i
$849$	16.9806	+	19.5967i	0.582774	+	0.672557i
$850$	−14.0649			−0.482421
$851$	−11.4110	+	13.0001i	−0.391164	+	0.445637i
$852$	14.5319			0.497855
$853$	−22.3455	−	25.7881i	−0.765095	−	0.882967i	0.230844	−	0.972991i	$-0.425851\pi$
$853$	−22.3455	−	25.7881i	−0.765095	−	0.882967i	−0.995940	+	0.0900235i	$0.971306\pi$
$854$	1.04394	+	0.670902i	0.0357230	+	0.0229578i
$855$	0.0816502	−	0.567890i	0.00279238	−	0.0194214i
$856$	−5.04843	+	11.0545i	−0.172552	+	0.377836i
$857$	7.34340	+	51.0745i	0.250846	+	1.74467i	0.593160	+	0.805085i	$0.297880\pi$
$857$	7.34340	+	51.0745i	0.250846	+	1.74467i	−0.342314	+	0.939585i	$0.611211\pi$
$858$	4.32691	+	1.27049i	0.147718	+	0.0433740i
$859$	14.7952	−	9.50829i	0.504805	−	0.324419i	−0.263331	−	0.964706i	$-0.584821\pi$
$859$	14.7952	−	9.50829i	0.504805	−	0.324419i	0.768136	+	0.640287i	$0.221185\pi$
$860$	−5.77545	−	12.6465i	−0.196941	−	0.431241i
$861$	−9.29256	+	2.72854i	−0.316690	+	0.0929885i
$862$	−19.9641	+	23.0398i	−0.679981	+	0.784740i
$863$	−23.8886	+	27.5689i	−0.813176	+	0.938455i	−0.999026	−	0.0441229i	$-0.985951\pi$
$863$	−23.8886	+	27.5689i	−0.813176	+	0.938455i	0.185850	+	0.982578i	$0.440496\pi$
$864$	−5.54376	+	1.62780i	−0.188603	+	0.0553787i
$865$	7.15275	+	15.6623i	0.243201	+	0.532536i
$866$	23.8180	−	15.3069i	0.809367	−	0.520149i
$867$	−0.491187	−	0.144226i	−0.0166816	−	0.00489816i
$868$	−0.733823	−	5.10385i	−0.0249076	−	0.173236i
$869$	20.7096	−	45.3478i	0.702526	−	1.53832i
$870$	−0.0925386	+	0.643620i	−0.00313735	+	0.0218208i
$871$	1.11731	+	0.718055i	0.0378588	+	0.0243304i
$872$	−32.8818	−	37.9477i	−1.11352	−	1.28507i
$873$	−17.7773			−0.601670
$874$	1.96016	+	1.27750i	0.0663034	+	0.0432122i
$875$	−8.83786			−0.298774
$876$	8.05474	+	9.29567i	0.272145	+	0.314072i
$877$	−12.2499	−	7.87251i	−0.413649	−	0.265836i	0.317223	−	0.948351i	$-0.397250\pi$
$877$	−12.2499	−	7.87251i	−0.413649	−	0.265836i	−0.730871	+	0.682515i	$0.760886\pi$
$878$	0.530162	−	3.68735i	0.0178921	−	0.124442i
$879$	0.143029	−	0.313190i	0.00482425	−	0.0105636i
$880$	0.253953	+	1.76629i	0.00856077	+	0.0595415i
$881$	−28.4352	−	8.34932i	−0.958005	−	0.281296i	−0.234889	−	0.972022i	$-0.575473\pi$
$881$	−28.4352	−	8.34932i	−0.958005	−	0.281296i	−0.723116	+	0.690727i	$0.757291\pi$
$882$	0.698939	−	0.449181i	0.0235345	−	0.0151247i
$883$	12.1047	+	26.5056i	0.407355	+	0.891983i	0.996471	+	0.0839348i	$0.0267488\pi$
$883$	12.1047	+	26.5056i	0.407355	+	0.891983i	−0.589116	+	0.808048i	$0.700524\pi$
$884$	5.23277	−	1.53648i	0.175997	−	0.0516774i
$885$	4.16855	−	4.81077i	0.140124	−	0.161712i
$886$	9.11576	−	10.5201i	0.306250	−	0.353431i
$887$	9.84151	−	2.88973i	0.330446	−	0.0970276i	−0.112301	−	0.993674i	$-0.535822\pi$
$887$	9.84151	−	2.88973i	0.330446	−	0.0970276i	0.442747	+	0.896647i	$0.354004\pi$
$888$	4.12014	+	9.02184i	0.138263	+	0.302753i
$889$	−15.3953	+	9.89398i	−0.516343	+	0.331833i
$890$	−2.97311	−	0.872983i	−0.0996588	−	0.0292625i
$891$	0.776300	+	5.39929i	0.0260070	+	0.180883i
$892$	−7.69565	+	16.8511i	−0.257669	+	0.564217i
$893$	−0.966045	+	6.71899i	−0.0323275	+	0.224842i
$894$	1.83685	+	1.18047i	0.0614335	+	0.0394809i
$895$	9.04000	+	10.4327i	0.302174	+	0.348727i
$896$	−8.12366			−0.271392
$897$	0.648919	+	4.72776i	0.0216668	+	0.157855i
$898$	23.1861			0.773732
$899$	2.06514	+	2.38330i	0.0688764	+	0.0794876i
$900$	4.45720	+	2.86447i	0.148573	+	0.0954823i
$901$	0.526455	−	3.66158i	0.0175388	−	0.121985i
$902$	−18.2334	+	39.9256i	−0.607106	+	1.32938i
$903$	−1.54616	−	10.7537i	−0.0514528	−	0.357862i
$904$	−28.2997	−	8.30955i	−0.941235	−	0.276372i
$905$	0.223350	−	0.143538i	0.00742439	−	0.00477137i
$906$	−2.20991	−	4.83902i	−0.0734192	−	0.160766i
$907$	57.0669	−	16.7564i	1.89488	−	0.556386i	0.902919	−	0.429810i	$-0.141420\pi$
$907$	57.0669	−	16.7564i	1.89488	−	0.556386i	0.991957	−	0.126576i	$-0.0403987\pi$
$908$	9.98412	−	11.5223i	0.331335	−	0.382381i
$909$	−5.46452	+	6.30639i	−0.181247	+	0.209170i
$910$	−0.775032	+	0.227570i	−0.0256921	+	0.00754387i
$911$	−6.18078	−	13.5340i	−0.204779	−	0.448402i	0.779180	−	0.626800i	$-0.215636\pi$
$911$	−6.18078	−	13.5340i	−0.204779	−	0.448402i	−0.983958	+	0.178398i	$0.942909\pi$
$912$	−0.165392	+	0.106291i	−0.00547668	+	0.00351965i
$913$	−16.5762	−	4.86721i	−0.548592	−	0.161081i
$914$	−0.763861	−	5.31277i	−0.0252663	−	0.175731i
$915$	0.606237	−	1.32747i	0.0200416	−	0.0438849i
$916$	3.50203	−	24.3572i	0.115710	−	0.804783i
$917$	−14.0718	−	9.04340i	−0.464692	−	0.298639i
$918$	−2.27682	−	2.62759i	−0.0751461	−	0.0867233i
$919$	53.3876			1.76110			0.880548	−	0.473958i	$-0.157175\pi$
$919$	53.3876			1.76110			0.880548	+	0.473958i	$0.157175\pi$
$920$	10.8840	−	6.89678i	0.358835	−	0.227380i
$921$	21.8640			0.720442
$922$	15.4682	+	17.8513i	0.509420	+	0.587902i
$923$	−9.28783	−	5.96893i	−0.305713	−	0.196470i
$924$	−1.01674	+	7.07156i	−0.0334482	+	0.232637i
$925$	6.06128	−	13.2724i	0.199294	−	0.436392i
$926$	−2.06650	−	14.3728i	−0.0679094	−	0.472320i
$927$	−0.179065	−	0.0525782i	−0.00588126	−	0.00172689i
$928$	3.89340	−	2.50213i	0.127807	−	0.0821366i
$929$	0.510054	+	1.11686i	0.0167343	+	0.0366431i	0.917815	−	0.397009i	$-0.129952\pi$
$929$	0.510054	+	1.11686i	0.0167343	+	0.0366431i	−0.901080	+	0.433652i	$0.857225\pi$
$930$	3.06647	−	0.900396i	0.100553	−	0.0295251i
$931$	0.384534	−	0.443776i	0.0126026	−	0.0145442i
$932$	−16.8365	+	19.4304i	−0.551498	+	0.636463i
$933$	21.5786	−	6.33604i	0.706451	−	0.207433i
$934$	9.64000	+	21.1086i	0.315430	+	0.690696i
$935$	−18.7627	+	12.0580i	−0.613606	+	0.394340i
$936$	2.62536	+	0.770876i	0.0858127	+	0.0251969i
$937$	7.85114	+	54.6059i	0.256486	+	1.78390i	0.557399	+	0.830245i	$0.311799\pi$
$937$	7.85114	+	54.6059i	0.256486	+	1.78390i	−0.300914	+	0.953651i	$0.597292\pi$
$938$	0.460680	−	1.00875i	0.0150417	−	0.0329368i
$939$	−0.319324	+	2.22095i	−0.0104208	+	0.0724780i
$940$	12.4448	+	7.99781i	0.405906	+	0.260860i
$941$	19.2039	+	22.1625i	0.626029	+	0.722475i	0.976840	−	0.213971i	$-0.0686397\pi$
$941$	19.2039	+	22.1625i	0.626029	+	0.722475i	−0.350812	+	0.936446i	$0.614094\pi$
$942$	15.1285			0.492912
$943$	−46.4460	−	0.297013i	−1.51249	−	0.00967207i
$944$	−2.18131			−0.0709956
$945$	−0.639839	−	0.738413i	−0.0208140	−	0.0240206i
$946$	−41.4211	−	26.6197i	−1.34672	−	0.865482i
$947$	0.361618	−	2.51511i	0.0117510	−	0.0817301i	−0.983102	−	0.183059i	$-0.941400\pi$
$947$	0.361618	−	2.51511i	0.0117510	−	0.0817301i	0.994853	+	0.101328i	$0.0323093\pi$
$948$	4.97247	−	10.8882i	0.161498	−	0.353632i
$949$	−1.32990	−	9.24964i	−0.0431703	−	0.300256i
$950$	−1.89363	−	0.556021i	−0.0614376	−	0.0180397i
$951$	4.28529	−	2.75399i	0.138960	−	0.0893043i
$952$	−4.78027	−	10.4673i	−0.154930	−	0.339248i
$953$	42.6129	−	12.5123i	1.38037	−	0.405313i	0.494471	−	0.869194i	$-0.335362\pi$
$953$	42.6129	−	12.5123i	1.38037	−	0.405313i	0.885897	+	0.463882i	$0.153544\pi$
$954$	0.480956	−	0.555053i	0.0155715	−	0.0179705i
$955$	−11.8208	+	13.6420i	−0.382513	+	0.441444i
$956$	−7.88406	+	2.31497i	−0.254989	+	0.0748714i
$957$	−1.81510	−	3.97451i	−0.0586739	−	0.128478i
$958$	13.1970	−	8.48120i	0.426376	−	0.274015i
$959$	−1.25699	−	0.369085i	−0.0405902	−	0.0119184i
$960$	−0.574382	−	3.99491i	−0.0185381	−	0.128935i
$961$	−6.43903	+	14.0995i	−0.207711	+	0.454823i
$962$	0.424358	−	2.95147i	0.0136819	−	0.0951594i
$963$	3.71790	+	2.38935i	0.119808	+	0.0769957i
$964$	−3.23120	−	3.72900i	−0.104070	−	0.120103i
$965$	−20.0607			−0.645776
$966$	3.83022	−	1.09810i	0.123235	−	0.0353307i
$967$	−9.44888			−0.303855			−0.151928	−	0.988392i	$-0.548548\pi$
$967$	−9.44888			−0.303855			−0.151928	+	0.988392i	$0.548548\pi$
$968$	33.7729	+	38.9760i	1.08550	+	1.25274i
$969$	−2.06719	−	1.32850i	−0.0664076	−	0.0426775i
$970$	2.05376	−	14.2842i	0.0659422	−	0.458638i
$971$	−20.3803	+	44.6267i	−0.654036	+	1.43214i	0.233940	+	0.972251i	$0.424838\pi$
$971$	−20.3803	+	44.6267i	−0.654036	+	1.43214i	−0.887977	+	0.459889i	$0.847889\pi$
$972$	0.186393	+	1.29639i	0.00597855	+	0.0415817i
$973$	10.8236	+	3.17809i	0.346988	+	0.101885i
$974$	−8.36235	+	5.37416i	−0.267947	+	0.172199i
$975$	−1.67218	−	3.66156i	−0.0535526	−	0.117264i
$976$	−0.479825	+	0.140889i	−0.0153588	+	0.00450976i
$977$	36.4288	−	42.0411i	1.16546	−	1.34501i	0.237924	−	0.971284i	$-0.423533\pi$
$977$	36.4288	−	42.0411i	1.16546	−	1.34501i	0.927537	−	0.373730i	$-0.121921\pi$
$978$	1.81423	−	2.09373i	0.0580126	−	0.0669501i
$979$	19.9782	−	5.86613i	0.638506	−	0.187482i
$980$	−0.531597	−	1.16404i	−0.0169813	−	0.0371838i
$981$	−15.3614	+	9.87216i	−0.490451	+	0.315194i
$982$	13.3777	+	3.92804i	0.426899	+	0.125349i
$983$	4.20325	+	29.2342i	0.134063	+	0.932428i	0.940182	+	0.340674i	$0.110655\pi$
$983$	4.20325	+	29.2342i	0.134063	+	0.932428i	−0.806119	+	0.591754i	$0.798436\pi$
$984$	−11.0632	+	24.2250i	−0.352681	+	0.772263i
$985$	1.61516	−	11.2337i	0.0514632	−	0.357934i
$986$	2.34285	+	1.50566i	0.0746116	+	0.0479500i
$987$	7.57025	+	8.73654i	0.240964	+	0.278087i
$988$	0.765259			0.0243461
$989$	7.74474	−	51.5247i	0.246268	−	1.63839i
$990$	−4.42806			−0.140733
$991$	10.0629	+	11.6132i	0.319657	+	0.368904i	0.892723	−	0.450605i	$-0.148792\pi$
$991$	10.0629	+	11.6132i	0.319657	+	0.368904i	−0.573066	+	0.819509i	$0.694246\pi$
$992$	−19.1360	−	12.2980i	−0.607570	−	0.390462i
$993$	4.10133	−	28.5254i	0.130152	−	0.905225i
$994$	−3.82946	+	8.38535i	−0.121463	+	0.265967i
$995$	−1.13902	−	7.92206i	−0.0361094	−	0.251146i
$996$	−3.98001	−	1.16864i	−0.126111	−	0.0370296i
$997$	48.5778	−	31.2190i	1.53847	−	0.988717i	0.550371	−	0.834920i	$-0.314486\pi$
$997$	48.5778	−	31.2190i	1.53847	−	0.988717i	0.988103	−	0.153796i	$-0.0491499\pi$
$998$	4.84995	+	10.6199i	0.153522	+	0.336167i
$999$	3.46073	−	1.01616i	0.109493	−	0.0321499i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	483.2.q.c.358.2	yes	20
23.16	even	11	inner	483.2.q.c.85.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.c.85.2	✓	20	23.16	even	11	inner
483.2.q.c.358.2	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	483.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.544078 - 0.627899i) q^{2} +(0.841254 + 0.540641i) q^{3} +(0.186393 - 1.29639i) q^{4} +(0.405886 - 0.888766i) q^{5} +(-0.118239 - 0.822373i) q^{6} +(-0.959493 - 0.281733i) q^{7} +(-2.31329 + 1.48666i) q^{8} +(0.415415 + 0.909632i) q^{9} +O(q^{10})\)	\(q+(-0.544078 - 0.627899i) q^{2} +(0.841254 + 0.540641i) q^{3} +(0.186393 - 1.29639i) q^{4} +(0.405886 - 0.888766i) q^{5} +(-0.118239 - 0.822373i) q^{6} +(-0.959493 - 0.281733i) q^{7} +(-2.31329 + 1.48666i) q^{8} +(0.415415 + 0.909632i) q^{9} +(-0.778889 + 0.228702i) q^{10} +(3.57214 - 4.12247i) q^{11} +(0.857685 - 0.989821i) q^{12} +(-0.954742 + 0.280337i) q^{13} +(0.345139 + 0.755750i) q^{14} +(0.821956 - 0.528239i) q^{15} +(-0.321251 - 0.0943278i) q^{16} +(-0.595548 - 4.14213i) q^{17} +(0.345139 - 0.755750i) q^{18} +(0.0835672 - 0.581223i) q^{19} +(-1.07653 - 0.691846i) q^{20} +(-0.654861 - 0.755750i) q^{21} -4.53202 q^{22} +(-1.96432 - 4.37509i) q^{23} -2.74982 q^{24} +(2.64914 + 3.05727i) q^{25} +(0.695478 + 0.446956i) q^{26} +(-0.142315 + 0.989821i) q^{27} +(-0.544078 + 1.19136i) q^{28} +(-0.113996 - 0.792858i) q^{29} +(-0.778889 - 0.228702i) q^{30} +(-3.31199 + 2.12849i) q^{31} +(2.40019 + 5.25568i) q^{32} +(5.23385 - 1.53680i) q^{33} +(-2.27682 + 2.62759i) q^{34} +(-0.639839 + 0.738413i) q^{35} +(1.25667 - 0.368991i) q^{36} +(-1.49833 - 3.28089i) q^{37} +(-0.410416 + 0.263759i) q^{38} +(-0.954742 - 0.280337i) q^{39} +(0.382363 + 2.65939i) q^{40} +(4.02324 - 8.80966i) q^{41} +(-0.118239 + 0.822373i) q^{42} +(9.13966 + 5.87370i) q^{43} +(-4.67851 - 5.39929i) q^{44} +0.977061 q^{45} +(-1.67837 + 3.61379i) q^{46} -11.5601 q^{47} +(-0.219256 - 0.253035i) q^{48} +(0.841254 + 0.540641i) q^{49} +(0.478320 - 3.32679i) q^{50} +(1.73840 - 3.80656i) q^{51} +(0.185470 + 1.28997i) q^{52} +(0.848176 + 0.249047i) q^{53} +(0.698939 - 0.449181i) q^{54} +(-2.21403 - 4.84805i) q^{55} +(2.63843 - 0.774713i) q^{56} +(0.384534 - 0.443776i) q^{57} +(-0.435813 + 0.502955i) q^{58} +(6.25110 - 1.83549i) q^{59} +(-0.531597 - 1.16404i) q^{60} +(1.25651 - 0.807508i) q^{61} +(3.13846 + 0.921535i) q^{62} +(-0.142315 - 0.989821i) q^{63} +(1.71597 - 3.75746i) q^{64} +(-0.138362 + 0.962327i) q^{65} +(-3.81258 - 2.45019i) q^{66} +(-0.874085 - 1.00875i) q^{67} -5.48082 q^{68} +(0.712860 - 4.74256i) q^{69} +0.811772 q^{70} +(7.26595 + 8.38535i) q^{71} +(-2.31329 - 1.48666i) q^{72} +(-1.33652 + 9.29567i) q^{73} +(-1.24486 + 2.72586i) q^{74} +(0.575714 + 4.00418i) q^{75} +(-0.737915 - 0.216671i) q^{76} +(-4.58888 + 2.94909i) q^{77} +(0.343430 + 0.752007i) q^{78} +(8.76905 - 2.57482i) q^{79} +(-0.214227 + 0.247231i) q^{80} +(-0.654861 + 0.755750i) q^{81} +(-7.72054 + 2.26695i) q^{82} +(-1.31567 - 2.88091i) q^{83} +(-1.10181 + 0.708089i) q^{84} +(-3.92311 - 1.15193i) q^{85} +(-1.28459 - 8.93454i) q^{86} +(0.332752 - 0.728626i) q^{87} +(-2.13468 + 14.8470i) q^{88} +(3.21116 + 2.06369i) q^{89} +(-0.531597 - 0.613496i) q^{90} +0.995048 q^{91} +(-6.03796 + 1.73104i) q^{92} -3.93697 q^{93} +(6.28960 + 7.25858i) q^{94} +(-0.482652 - 0.310182i) q^{95} +(-0.822267 + 5.71900i) q^{96} +(-7.38495 + 16.1708i) q^{97} +(-0.118239 - 0.822373i) q^{98} +(5.23385 + 1.53680i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - q^5 - 4 * q^6 - 2 * q^7 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 4 q^{4} - q^{5} - 4 q^{6} - 2 q^{7} - 2 q^{9} + 9 q^{10} + 3 q^{11} + 18 q^{12} - 2 q^{13} + 18 q^{14} - q^{15} + 8 q^{16} + 8 q^{17} + 18 q^{18} + 6 q^{19} - 2 q^{20} - 2 q^{21} + 6 q^{22} + 11 q^{23} + 9 q^{25} + 7 q^{26} - 2 q^{27} - 4 q^{28} + 23 q^{29} + 9 q^{30} + q^{31} - 28 q^{32} + 14 q^{33} - 28 q^{34} + 10 q^{35} - 4 q^{36} - 9 q^{37} + 34 q^{38} - 2 q^{39} - 15 q^{41} - 4 q^{42} - 23 q^{43} - 16 q^{44} - 12 q^{45} + 11 q^{46} - 66 q^{47} - 36 q^{48} - 2 q^{49} - 26 q^{50} - 14 q^{51} + 7 q^{52} + 9 q^{53} - 4 q^{54} - 62 q^{55} + 22 q^{56} - 27 q^{57} - 20 q^{58} + 49 q^{59} - 2 q^{60} + 46 q^{61} - 9 q^{62} - 2 q^{63} + 16 q^{64} + 11 q^{65} - 16 q^{66} + 14 q^{67} + 38 q^{68} + 11 q^{69} - 2 q^{70} + 36 q^{71} - q^{73} + 4 q^{74} - 2 q^{75} + 34 q^{76} - 8 q^{77} - 15 q^{78} - 22 q^{79} + 15 q^{80} - 2 q^{81} - 30 q^{82} + 8 q^{83} - 4 q^{84} - 32 q^{85} - 68 q^{86} + q^{87} - 11 q^{88} - 2 q^{89} - 2 q^{90} - 24 q^{91} + 11 q^{92} - 32 q^{93} + 33 q^{94} - 107 q^{95} + 16 q^{96} + 18 q^{97} - 4 q^{98} + 14 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 4 * q^4 - q^5 - 4 * q^6 - 2 * q^7 - 2 * q^9 + 9 * q^10 + 3 * q^11 + 18 * q^12 - 2 * q^13 + 18 * q^14 - q^15 + 8 * q^16 + 8 * q^17 + 18 * q^18 + 6 * q^19 - 2 * q^20 - 2 * q^21 + 6 * q^22 + 11 * q^23 + 9 * q^25 + 7 * q^26 - 2 * q^27 - 4 * q^28 + 23 * q^29 + 9 * q^30 + q^31 - 28 * q^32 + 14 * q^33 - 28 * q^34 + 10 * q^35 - 4 * q^36 - 9 * q^37 + 34 * q^38 - 2 * q^39 - 15 * q^41 - 4 * q^42 - 23 * q^43 - 16 * q^44 - 12 * q^45 + 11 * q^46 - 66 * q^47 - 36 * q^48 - 2 * q^49 - 26 * q^50 - 14 * q^51 + 7 * q^52 + 9 * q^53 - 4 * q^54 - 62 * q^55 + 22 * q^56 - 27 * q^57 - 20 * q^58 + 49 * q^59 - 2 * q^60 + 46 * q^61 - 9 * q^62 - 2 * q^63 + 16 * q^64 + 11 * q^65 - 16 * q^66 + 14 * q^67 + 38 * q^68 + 11 * q^69 - 2 * q^70 + 36 * q^71 - q^73 + 4 * q^74 - 2 * q^75 + 34 * q^76 - 8 * q^77 - 15 * q^78 - 22 * q^79 + 15 * q^80 - 2 * q^81 - 30 * q^82 + 8 * q^83 - 4 * q^84 - 32 * q^85 - 68 * q^86 + q^87 - 11 * q^88 - 2 * q^89 - 2 * q^90 - 24 * q^91 + 11 * q^92 - 32 * q^93 + 33 * q^94 - 107 * q^95 + 16 * q^96 + 18 * q^97 - 4 * q^98 + 14 * q^99

Introduction

L-functions

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