LMFDB - Embedded newform 483.2.q.c.85.2

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			85.2
Root			$1.49752 + 1.72823i$ of defining polynomial
Character	$\chi$	$=$	483.85
Dual form			483.2.q.c.358.2

$q$-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 $\left(\mathbb{Z}/483\mathbb{Z}\right)^\times$.

$n$	$323$	$346$	$442$
$\chi(n)$	$1$	$1$	$e\left(\frac{4}{11}\right)$

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	−0.914770	−	0.403975i	$-0.867628\pi$
$2$	−0.544078	+	0.627899i	−0.384721	+	0.443992i	0.530049	+	0.847967i	$0.322174\pi$
$3$	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	0.978416	−	0.206645i	$-0.0662546\pi$
$5$	0.405886	+	0.888766i	0.181518	+	0.397468i	−0.796898	+	0.604114i	$0.793527\pi$
$6$	−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	0.968535	+	0.248876i	$0.0800611\pi$
$11$	3.57214	+	4.12247i	1.07704	+	1.24297i	0.108506	+	0.994096i	$0.465393\pi$
$12$	0.857685	+	0.989821i	0.247592	+	0.285737i
$13$	−0.954742	−	0.280337i	−0.264798	−	0.0777516i	0.146639	−	0.989190i	$-0.453155\pi$
$13$	−0.954742	−	0.280337i	−0.264798	−	0.0777516i	−0.411436	+	0.911439i	$0.634973\pi$
$14$	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	0.780677	+	0.624935i	$0.214875\pi$
$17$	−0.595548	+	4.14213i	−0.144442	+	1.00461i	−0.925118	+	0.379679i	$0.876034\pi$
$18$	0.345139	+	0.755750i	0.0813501	+	0.178132i
$19$	0.0835672	+	0.581223i	0.0191716	+	0.133342i	0.997159	−	0.0753208i	$-0.0239981\pi$
$19$	0.0835672	+	0.581223i	0.0191716	+	0.133342i	−0.977988	+	0.208662i	$0.933089\pi$
$20$	−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	−0.997664	−	0.0683056i	$-0.978241\pi$
$29$	−0.113996	+	0.792858i	−0.0211685	+	0.147230i	0.976496	+	0.215536i	$0.0691498\pi$
$30$	−0.778889	+	0.228702i	−0.142205	+	0.0417552i
$31$	−3.31199	−	2.12849i	−0.594851	−	0.382288i	0.208298	−	0.978065i	$-0.433208\pi$
$31$	−3.31199	−	2.12849i	−0.594851	−	0.382288i	−0.803149	+	0.595778i	$0.796844\pi$
$32$	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	−0.991896	−	0.127050i	$-0.959449\pi$
$37$	−1.49833	+	3.28089i	−0.246324	+	0.539375i	0.745572	+	0.666425i	$0.232176\pi$
$38$	−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	0.909307	+	0.416126i	$0.136612\pi$
$41$	4.02324	+	8.80966i	0.628324	+	1.37584i	−0.280983	+	0.959713i	$0.590660\pi$
$42$	−0.118239	−	0.822373i	−0.0182447	−	0.126895i
$43$	9.13966	−	5.87370i	1.39378	−	0.895731i	0.394057	−	0.919086i	$-0.371071\pi$
$43$	9.13966	−	5.87370i	1.39378	−	0.895731i	0.999727	+	0.0233550i	$0.00743479\pi$
$44$	−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	−0.222960	−	0.974828i	$-0.571572\pi$
$53$	0.848176	−	0.249047i	0.116506	−	0.0342092i	0.339466	+	0.940618i	$0.389754\pi$
$54$	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	0.662055	−	0.749456i	$-0.269685\pi$
$59$	6.25110	+	1.83549i	0.813824	+	0.238960i	0.151770	+	0.988416i	$0.451503\pi$
$60$	−0.531597	+	1.16404i	−0.0686289	+	0.150276i
$61$	1.25651	+	0.807508i	0.160879	+	0.103391i	0.618603	−	0.785703i	$-0.287699\pi$
$61$	1.25651	+	0.807508i	0.160879	+	0.103391i	−0.457724	+	0.889094i	$0.651335\pi$
$62$	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	−0.806627	−	0.591061i	$-0.798709\pi$
$67$	−0.874085	+	1.00875i	−0.106786	+	0.123238i	0.699840	+	0.714299i	$0.253255\pi$
$68$	−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	−0.137680	−	0.990477i	$-0.543964\pi$
$71$	7.26595	−	8.38535i	0.862309	−	0.995158i	0.999989	−	0.00468118i	$-0.00149007\pi$
$72$	−2.31329	+	1.48666i	−0.272624	+	0.175205i
$73$	−1.33652	−	9.29567i	−0.156427	−	1.08798i	−0.905150	−	0.425092i	$-0.860242\pi$
$73$	−1.33652	−	9.29567i	−0.156427	−	1.08798i	0.748723	−	0.662883i	$-0.230667\pi$
$74$	−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	0.734944	−	0.678128i	$-0.237208\pi$
$79$	8.76905	+	2.57482i	0.986595	+	0.289690i	0.251651	+	0.967818i	$0.419027\pi$
$80$	−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	−0.967992	−	0.250981i	$-0.919247\pi$
$83$	−1.31567	+	2.88091i	−0.144413	+	0.316220i	0.823579	+	0.567202i	$0.191974\pi$
$84$	−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	−0.359270	−	0.933233i	$-0.616974\pi$
$89$	3.21116	−	2.06369i	0.340382	−	0.218750i	0.699653	+	0.714483i	$0.253338\pi$
$90$	−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	−0.766675	−	0.642036i	$-0.778090\pi$
$97$	−7.38495	−	16.1708i	−0.749828	−	1.64189i	0.0168467	−	0.999858i	$-0.494637\pi$
$98$	−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	−0.655075	−	0.755564i	$-0.727363\pi$
$101$	3.46645	−	7.59047i	0.344925	−	0.755280i	1.00000		0.000283479i	$9.02343e-5\pi$
$102$	−3.33596	−	0.979526i	−0.330309	−	0.0969876i
$103$	−0.122213	−	0.141041i	−0.0120420	−	0.0138972i	0.749697	−	0.661782i	$-0.230199\pi$
$103$	−0.122213	−	0.141041i	−0.0120420	−	0.0138972i	−0.761739	+	0.647884i	$0.775654\pi$
$104$	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	0.707872	−	0.706341i	$-0.249655\pi$
$107$	3.71790	+	2.38935i	0.359423	+	0.230987i	−0.348449	+	0.937328i	$0.613292\pi$
$108$	1.25667	−	0.368991i	0.120923	−	0.0355062i
$109$	2.59868	−	18.0742i	0.248909	−	1.73120i	−0.355633	−	0.934626i	$-0.615735\pi$
$109$	2.59868	−	18.0742i	0.248909	−	1.73120i	0.604542	−	0.796573i	$-0.293356\pi$
$110$	−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	−0.322137	−	0.946693i	$-0.604401\pi$
$113$	7.02402	−	8.10616i	0.660765	−	0.762563i	0.982902	+	0.184130i	$0.0589467\pi$
$114$	−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	0.972865	+	0.231374i	$0.0743221\pi$
$127$	11.9843	+	13.8306i	1.06343	+	1.22726i	0.0905659	+	0.995890i	$0.471132\pi$
$128$	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	0.508801	−	0.860884i	$-0.330089\pi$
$131$	16.0496	−	4.71259i	1.40226	−	0.411741i	0.893460	+	0.449143i	$0.148271\pi$
$132$	−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	0.680862	−	0.732411i	$-0.261605\pi$
$149$	−1.72101	−	1.98615i	−0.140991	−	0.162712i	−0.821853	+	0.569699i	$0.807060\pi$
$150$	2.20099	+	2.54007i	0.179710	+	0.207396i
$151$	6.14357	+	1.80392i	0.499957	+	0.146801i	0.521981	−	0.852957i	$-0.325193\pi$
$151$	6.14357	+	1.80392i	0.499957	+	0.146801i	−0.0220245	+	0.999757i	$0.507011\pi$
$152$	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	−0.783462	−	0.621440i	$-0.786548\pi$
$157$	−2.59139	−	18.0235i	−0.206816	−	1.43843i	0.576646	−	0.816994i	$-0.304361\pi$
$158$	−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	−0.663760	−	0.747945i	$-0.731040\pi$
$163$	2.18363	−	2.52005i	0.171035	−	0.197385i	0.834795	+	0.550560i	$0.185586\pi$
$164$	−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	−0.993922	−	0.110090i	$-0.964886\pi$
$167$	−0.119468	+	0.830921i	−0.00924474	+	0.0642986i	0.984677	+	0.174389i	$0.0557950\pi$
$168$	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	−0.999798	−	0.0200877i	$-0.993605\pi$
$173$	−11.5403	−	13.3183i	−0.877395	−	1.01257i	0.122403	−	0.992480i	$-0.460940\pi$
$174$	−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	−0.991838	−	0.127507i	$-0.959302\pi$
$179$	−5.86921	−	12.8518i	−0.438686	−	0.960587i	0.553152	−	0.833080i	$-0.313425\pi$
$180$	0.182117	+	1.26665i	0.0135742	+	0.0944107i
$181$	0.228593	−	0.146908i	0.0169912	−	0.0109196i	−0.532118	−	0.846670i	$-0.678604\pi$
$181$	0.228593	−	0.146908i	0.0169912	−	0.0109196i	0.549109	+	0.835751i	$0.314967\pi$
$182$	−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	−0.850872	−	0.525373i	$-0.823926\pi$
$191$	−17.7263	+	5.20492i	−1.28263	+	0.376615i	−0.431761	+	0.901988i	$0.642108\pi$
$192$	3.47501	+	2.23325i	0.250787	+	0.161171i
$193$	−8.52916	+	18.6762i	−0.613942	+	1.34435i	0.305902	+	0.952063i	$0.401042\pi$
$193$	−8.52916	+	18.6762i	−0.613942	+	1.34435i	−0.919845	+	0.392283i	$0.871685\pi$
$194$	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	0.653510	−	0.756918i	$-0.273296\pi$
$197$	11.1451	+	3.27250i	0.794057	+	0.233156i	0.140547	+	0.990074i	$0.455114\pi$
$198$	−1.88267	+	4.12247i	−0.133795	+	0.292971i
$199$	6.89107	+	4.42862i	0.488495	+	0.313937i	0.761600	−	0.648048i	$-0.224414\pi$
$199$	6.89107	+	4.42862i	0.488495	+	0.313937i	−0.273105	+	0.961984i	$0.588051\pi$
$200$	−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	0.355496	+	0.934678i	$0.384312\pi$
$211$	4.03425	+	28.0588i	0.277729	+	1.93165i	−0.0777665	+	0.996972i	$0.524779\pi$
$212$	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	−0.702540	−	0.711644i	$-0.747951\pi$
$223$	−13.5714	+	3.98493i	−0.908811	+	0.266851i	−0.206271	+	0.978495i	$0.566133\pi$
$224$	−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	−0.173683	−	0.984802i	$-0.555567\pi$
$227$	9.79284	−	6.29348i	0.649974	−	0.417713i	0.823657	+	0.567089i	$0.191930\pi$
$228$	−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	−0.954988	−	0.296646i	$-0.904132\pi$
$233$	−16.5140	+	10.6129i	−1.08187	+	0.695272i	−0.126878	+	0.991918i	$0.540496\pi$
$234$	−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	−0.975001	−	0.222201i	$-0.928676\pi$
$239$	−2.60622	+	5.70683i	−0.168582	+	0.369144i	0.806418	+	0.591345i	$0.201403\pi$
$240$	−0.313882	−	0.0921640i	−0.0202610	−	0.00594916i
$241$	2.46709	+	2.84717i	0.158919	+	0.183403i	0.829625	−	0.558321i	$-0.188554\pi$
$241$	2.46709	+	2.84717i	0.158919	+	0.183403i	−0.670706	+	0.741723i	$0.734009\pi$
$242$	−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	−0.0768135	+	0.997045i	$0.524475\pi$
$251$	−16.6792	+	19.2488i	−1.05278	+	1.21497i	−0.975965	+	0.217926i	$0.930071\pi$
$252$	−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	0.999716	−	0.0238326i	$-0.00758686\pi$
$257$	0.541552	+	3.76658i	0.0337811	+	0.234953i	−0.965935	+	0.258785i	$0.916678\pi$
$258$	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	0.259209	−	0.965821i	$-0.416538\pi$
$263$	−0.728046	−	0.213774i	−0.0448932	−	0.0131818i	−0.304102	+	0.952639i	$0.598356\pi$
$264$	−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	−0.674291	−	0.738466i	$-0.735551\pi$
$269$	−13.8147	+	4.05636i	−0.842296	+	0.247320i	−0.168005	+	0.985786i	$0.553733\pi$
$270$	−0.115527	+	0.803509i	−0.00703076	+	0.0489000i
$271$	−2.46886	−	5.40605i	−0.149973	−	0.328394i	0.819703	−	0.572788i	$-0.194138\pi$
$271$	−2.46886	−	5.40605i	−0.149973	−	0.328394i	−0.969676	+	0.244394i	$0.921411\pi$
$272$	−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	0.834104	−	0.551608i	$-0.185985\pi$
$281$	−2.16236	−	4.73490i	−0.128995	−	0.282461i	−0.963099	+	0.269147i	$0.913258\pi$
$282$	1.36686	−	9.50672i	0.0813953	−	0.566117i
$283$	24.8798	−	7.30537i	1.47895	−	0.434259i	0.559954	−	0.828524i	$-0.310819\pi$
$283$	24.8798	−	7.30537i	1.47895	−	0.434259i	0.918997	+	0.394265i	$0.129001\pi$
$284$	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	−0.991203	−	0.132353i	$-0.957747\pi$
$293$	−0.0489996	+	0.340800i	−0.00286259	+	0.0199097i	0.988340	+	0.152263i	$0.0486559\pi$
$294$	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	0.947380	−	0.320112i	$-0.103720\pi$
$307$	18.3931	+	11.8206i	1.04975	+	0.674635i	0.102372	+	0.994746i	$0.467357\pi$
$308$	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	0.999745	−	0.0225746i	$-0.00718634\pi$
$311$	14.7275	+	16.9965i	0.835122	+	0.963782i	−0.164623	+	0.986356i	$0.552641\pi$
$312$	2.62536	+	0.770876i	0.148632	+	0.0436423i
$313$	0.932104	−	2.04102i	0.0526856	−	0.115365i	−0.881458	−	0.472262i	$-0.843438\pi$
$313$	0.932104	−	2.04102i	0.0526856	−	0.115365i	0.934144	+	0.356896i	$0.116165\pi$
$314$	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	0.959703	−	0.281018i	$-0.0906720\pi$
$317$	2.11610	+	4.63361i	0.118852	+	0.260249i	−0.840851	+	0.541267i	$0.817945\pi$
$318$	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	0.226326	+	0.974052i	$0.427328\pi$
$331$	−11.9717	+	26.2144i	−0.658025	+	1.44087i	−0.884351	+	0.466822i	$0.845399\pi$
$332$	−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	0.988678	−	0.150053i	$-0.0479445\pi$
$337$	23.1837	+	14.8993i	1.26290	+	0.811614i	0.274219	+	0.961667i	$0.411581\pi$
$338$	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	−0.582689	−	0.812695i	$-0.697999\pi$
$347$	5.67518	−	6.54951i	0.304660	−	0.351596i	0.887349	+	0.461099i	$0.152545\pi$
$348$	−0.882561	+	0.567187i	−0.0473102	+	0.0304044i
$349$	−1.54134	−	10.7202i	−0.0825059	−	0.573841i	−0.988577	−	0.150716i	$-0.951842\pi$
$349$	−1.54134	−	10.7202i	−0.0825059	−	0.573841i	0.906071	−	0.423125i	$-0.139067\pi$
$350$	−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	−0.0773612	−	0.997003i	$-0.524649\pi$
$353$	−19.0965	−	12.2726i	−1.01640	−	0.653203i	−0.939043	+	0.343800i	$0.888286\pi$
$354$	−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	−0.981604	−	0.190926i	$-0.938851\pi$
$359$	−3.68521	+	8.06949i	−0.194498	+	0.425891i	0.787106	+	0.616817i	$0.211578\pi$
$360$	−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	0.963600	−	0.267346i	$-0.0861468\pi$
$373$	2.52094	+	5.52009i	0.130529	+	0.285820i	−0.833071	+	0.553166i	$0.813420\pi$
$374$	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	0.797477	−	0.603349i	$-0.206167\pi$
$379$	1.68937	+	1.94963i	0.0867769	+	0.100146i	−0.710700	+	0.703495i	$0.751622\pi$
$380$	−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	−0.990921	−	0.134446i	$-0.957075\pi$
$383$	−29.8421	−	19.1784i	−1.52486	−	0.979968i	−0.533940	−	0.845523i	$-0.679289\pi$
$384$	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	−0.411512	−	0.911404i	$-0.634999\pi$
$389$	10.8315	−	12.5002i	0.549180	−	0.633788i	0.960692	+	0.277617i	$0.0895446\pi$
$390$	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	0.895358	+	0.445348i	$0.146920\pi$
$397$	−1.77731	+	12.3615i	−0.0892006	+	0.620404i	−0.984558	+	0.175056i	$0.943989\pi$
$398$	−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	0.490462	−	0.871462i	$-0.336828\pi$
$401$	8.64913	+	2.53961i	0.431917	+	0.126822i	−0.0585451	+	0.998285i	$0.518646\pi$
$402$	−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	−0.973091	−	0.230420i	$-0.925990\pi$
$409$	−10.3139	−	22.5844i	−0.509992	−	1.11673i	0.463099	−	0.886306i	$-0.346737\pi$
$410$	−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	0.844995	−	0.534775i	$-0.179604\pi$
$419$	−2.30313	−	5.04314i	−0.112515	−	0.246374i	−0.957510	+	0.288401i	$0.906876\pi$
$420$	0.182117	−	1.26665i	0.00888641	−	0.0618063i
$421$	20.7815	−	6.10200i	1.01283	−	0.297393i	0.267118	−	0.963664i	$-0.413929\pi$
$421$	20.7815	−	6.10200i	1.01283	−	0.297393i	0.745710	+	0.666271i	$0.232110\pi$
$422$	−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	0.337461	+	0.941340i	$0.390432\pi$
$431$	−5.22203	+	36.3200i	−0.251536	+	1.74947i	−0.588997	+	0.808135i	$0.700477\pi$
$432$	0.139086	+	0.304557i	0.00669180	+	0.0146530i
$433$	−4.84971	−	33.7305i	−0.233062	−	1.62098i	−0.684730	−	0.728797i	$-0.740080\pi$
$433$	−4.84971	−	33.7305i	−0.233062	−	1.62098i	0.451668	−	0.892186i	$-0.350829\pi$
$434$	−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	−0.681341	−	0.731966i	$-0.738603\pi$
$439$	2.93626	−	3.38863i	0.140140	−	0.161730i	0.821481	+	0.570236i	$0.193148\pi$
$440$	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	−0.851398	−	0.524521i	$-0.824245\pi$
$443$	2.38442	−	16.5840i	0.113287	−	0.787928i	0.964685	−	0.263408i	$-0.0848464\pi$
$444$	−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	−0.999988	−	0.00484064i	$-0.998459\pi$
$449$	−18.2753	−	21.0909i	−0.862466	−	0.995339i	0.137522	−	0.990499i	$-0.456086\pi$
$450$	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	−0.407320	−	0.913285i	$-0.633537\pi$
$457$	5.43474	−	3.49270i	0.254226	−	0.163381i	0.661547	+	0.749904i	$0.269900\pi$
$458$	−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	−0.152400	−	0.988319i	$-0.548700\pi$
$463$	14.7028	−	9.44892i	0.683297	−	0.439128i	0.835697	+	0.549190i	$0.185064\pi$
$464$	−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	−0.835063	−	0.550155i	$-0.814569\pi$
$467$	−26.7994	+	7.86900i	−1.24013	+	0.364134i	−0.405063	+	0.914289i	$0.632751\pi$
$468$	−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	−0.954386	−	0.298574i	$-0.903489\pi$
$479$	−2.68712	−	18.6893i	−0.122777	−	0.853936i	0.831609	−	0.555362i	$-0.187420\pi$
$480$	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	0.991338	+	0.131333i	$0.0419257\pi$
$487$	1.70271	+	11.8426i	0.0771570	+	0.536638i	−0.914181	+	0.405305i	$0.867165\pi$
$488$	−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	0.181828	−	0.983330i	$-0.441799\pi$
$491$	−14.1174	−	9.07267i	−0.637107	−	0.409444i	−0.818935	+	0.573886i	$0.805435\pi$
$492$	−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	−0.569224	−	0.822183i	$-0.692756\pi$
$499$	−13.4829	+	3.95895i	−0.603579	+	0.177227i	−0.0343558	+	0.999410i	$0.510938\pi$
$500$	−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	0.0734579	−	0.997298i	$-0.476597\pi$
$503$	22.6777	−	14.5741i	1.01115	−	0.649825i	0.937690	+	0.347473i	$0.112960\pi$
$504$	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	−0.897008	−	0.442014i	$-0.854264\pi$
$509$	−19.5733	+	12.5790i	−0.867569	+	0.557553i	0.0294389	+	0.999567i	$0.490628\pi$
$510$	−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	0.923642	−	0.383257i	$-0.125198\pi$
$521$	21.8830	+	14.0634i	0.958713	+	0.616127i	0.0350714	+	0.999385i	$0.488834\pi$
$522$	−0.638547	+	0.187494i	−0.0279484	+	0.00820640i
$523$	−4.53565	+	31.5461i	−0.198330	+	1.37941i	0.610800	+	0.791785i	$0.290848\pi$
$523$	−4.53565	+	31.5461i	−0.198330	+	1.37941i	−0.809130	+	0.587630i	$0.800061\pi$
$524$	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	0.400209	−	0.916424i	$-0.368937\pi$
$541$	−13.1146	−	15.1351i	−0.563842	−	0.650709i	−0.964052	+	0.265715i	$0.914392\pi$
$542$	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	0.930023	−	0.367502i	$-0.119787\pi$
$547$	1.01148	+	2.21483i	0.0432477	+	0.0946993i	−0.886775	+	0.462202i	$0.847060\pi$
$548$	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	0.761874	−	0.647725i	$-0.224279\pi$
$557$	−5.34713	−	11.7086i	−0.226565	−	0.496108i	−0.988439	+	0.151617i	$0.951552\pi$
$558$	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	0.991389	+	0.130949i	$0.0418023\pi$
$563$	23.2511	+	26.8332i	0.979915	+	1.13088i	−0.0114737	+	0.999934i	$0.503652\pi$
$564$	−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	−0.945237	−	0.326384i	$-0.894170\pi$
$569$	1.28009	−	8.90324i	0.0536643	−	0.373243i	0.998902	−	0.0468591i	$-0.0149212\pi$
$570$	−0.198017	−	0.433596i	−0.00829400	−	0.0181613i
$571$	−0.826589	−	5.74905i	−0.0345917	−	0.240590i	0.965189	−	0.261555i	$-0.0842353\pi$
$571$	−0.826589	−	5.74905i	−0.0345917	−	0.240590i	−0.999780	+	0.0209647i	$0.993326\pi$
$572$	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	−0.891115	−	0.453778i	$-0.850076\pi$
$577$	−7.56986	+	8.73608i	−0.315137	+	0.363688i	0.575978	+	0.817465i	$0.304622\pi$
$578$	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	0.631293	−	0.775545i	$-0.282525\pi$
$587$	−5.48041	−	6.32473i	−0.226201	−	0.261049i	−0.857493	+	0.514495i	$0.827979\pi$
$588$	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	0.971263	+	0.238010i	$0.0764952\pi$
$593$	12.5434	+	27.4663i	0.515097	+	1.12791i	−0.456166	+	0.889895i	$0.650778\pi$
$594$	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	0.157673	−	0.987491i	$-0.449601\pi$
$601$	27.4921	−	17.6681i	1.12143	−	0.720697i	0.963754	+	0.266794i	$0.0859643\pi$
$602$	−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	−0.384673	−	0.923053i	$-0.625686\pi$
$607$	13.9159	−	30.4717i	0.564831	−	1.23681i	0.949504	−	0.313754i	$-0.101587\pi$
$608$	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	−0.310072	−	0.950713i	$-0.600353\pi$
$613$	−32.2776	−	20.7435i	−1.30368	−	0.837824i	−0.993608	+	0.112889i	$0.963990\pi$
$614$	−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	−0.969001	−	0.247058i	$-0.920536\pi$
$617$	−2.70392	−	18.8061i	−0.108856	−	0.757107i	0.860145	−	0.510049i	$-0.170373\pi$
$618$	0.130439	−	0.0838280i	0.00524703	−	0.00337206i
$619$	2.56152	−	2.95615i	0.102956	−	0.118818i	−0.701933	−	0.712243i	$-0.747679\pi$
$619$	2.56152	−	2.95615i	0.102956	−	0.118818i	0.804889	+	0.593425i	$0.202225\pi$
$620$	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	0.827130	−	0.562011i	$-0.189972\pi$
$631$	30.6237	+	8.99192i	1.21911	+	0.357963i	0.391979	+	0.919974i	$0.371790\pi$
$632$	−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	−0.794593	−	0.607142i	$-0.792316\pi$
$641$	−14.4921	+	9.31350i	−0.572403	+	0.367861i	0.222190	+	0.975003i	$0.428679\pi$
$642$	−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	−0.239128	−	0.970988i	$-0.576861\pi$
$647$	13.8571	−	8.90539i	0.544777	−	0.350107i	0.783905	+	0.620881i	$0.213225\pi$
$648$	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	−0.655767	−	0.754963i	$-0.727655\pi$
$653$	8.79647	−	19.2616i	0.344232	−	0.753764i	0.999999	+	0.00119955i	$0.000381828\pi$
$654$	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	0.457815	−	0.889047i	$-0.348632\pi$
$659$	−4.12553	−	2.65132i	−0.160708	−	0.103281i	−0.618523	+	0.785767i	$0.712269\pi$
$660$	−6.69764	+	1.96661i	−0.260705	+	0.0765500i
$661$	−3.10237	+	21.5774i	−0.120668	+	0.839265i	0.836134	+	0.548525i	$0.184811\pi$
$661$	−3.10237	+	21.5774i	−0.120668	+	0.839265i	−0.956802	+	0.290740i	$0.906099\pi$
$662$	−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	−0.250417	−	0.968138i	$-0.580568\pi$
$673$	6.81275	−	47.3837i	0.262612	−	1.82651i	0.513029	−	0.858371i	$-0.328523\pi$
$674$	−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	−0.0622403	−	0.998061i	$-0.519825\pi$
$677$	−17.0216	−	4.99799i	−0.654193	−	0.192088i	−0.591952	+	0.805973i	$0.701643\pi$
$678$	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	−0.485037	−	0.874494i	$-0.661194\pi$
$683$	−10.9840	+	3.22518i	−0.420289	+	0.123408i	0.0647478	+	0.997902i	$0.479376\pi$
$684$	−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	0.911439	−	0.411434i	$-0.134972\pi$
$701$	9.91493	+	11.4424i	0.374482	+	0.432175i	−0.536958	+	0.843609i	$0.680427\pi$
$702$	−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	−0.898116	−	0.439760i	$-0.855064\pi$
$709$	−4.26764	−	29.6821i	−0.160275	−	1.11473i	0.737841	−	0.674975i	$-0.235845\pi$
$710$	−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	0.675847	+	0.737042i	$0.263778\pi$
$719$	−4.83385	+	33.6202i	−0.180272	+	1.25382i	−0.856119	+	0.516779i	$0.827131\pi$
$720$	−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	−0.955097	−	0.296293i	$-0.904249\pi$
$727$	−2.85047	+	6.24166i	−0.105718	+	0.231490i	0.849379	+	0.527783i	$0.176977\pi$
$728$	−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	−0.990486	−	0.137616i	$-0.956056\pi$
$733$	−34.5672	+	22.2150i	−1.27677	+	0.820529i	−0.286283	+	0.958145i	$0.592420\pi$
$734$	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	−0.622579	−	0.782557i	$-0.713915\pi$
$739$	−4.60423	+	2.95896i	−0.169369	+	0.108847i	0.453210	+	0.891404i	$0.350279\pi$
$740$	−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	−0.101023	−	0.994884i	$-0.532211\pi$
$743$	9.59119	−	2.81623i	0.351867	−	0.103317i	0.452889	+	0.891567i	$0.350393\pi$
$744$	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	0.678158	−	0.734916i	$-0.262778\pi$
$751$	7.98488	+	5.13157i	0.291372	+	0.187254i	−0.386786	+	0.922170i	$0.626415\pi$
$752$	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	−0.469991	−	0.882671i	$-0.655743\pi$
$757$	12.9474	−	14.9421i	0.470583	−	0.543082i	0.940574	+	0.339590i	$0.110288\pi$
$758$	−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	−0.997454	−	0.0713111i	$-0.977282\pi$
$761$	−21.6529	+	24.9888i	−0.784916	+	0.905842i	0.212538	+	0.977153i	$0.431827\pi$
$762$	−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	−0.106290	−	0.994335i	$-0.533897\pi$
$769$	−20.3346	−	5.97079i	−0.733285	−	0.215312i	−0.626995	+	0.779023i	$0.715715\pi$
$770$	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	−0.936388	−	0.350967i	$-0.885853\pi$
$773$	−1.61093	+	3.52745i	−0.0579411	+	0.126873i	0.878447	+	0.477840i	$0.158580\pi$
$774$	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	0.999945	+	0.0104966i	$0.00334123\pi$
$787$	9.90438	+	21.6876i	0.353053	+	0.773078i	−0.646892	+	0.762582i	$0.723932\pi$
$788$	−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	0.818517	−	0.574482i	$-0.194796\pi$
$797$	17.9543	+	11.5385i	0.635975	+	0.408716i	−0.182543	+	0.983198i	$0.558433\pi$
$798$	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	0.927724	+	0.373267i	$0.121763\pi$
$809$	4.05997	+	28.2377i	0.142741	+	0.992785i	−0.784983	+	0.619517i	$0.787328\pi$
$810$	0.337222	+	0.738413i	0.0118488	+	0.0259452i
$811$	3.71955	−	25.8700i	0.130611	−	0.908419i	−0.814149	−	0.580656i	$-0.802796\pi$
$811$	3.71955	−	25.8700i	0.130611	−	0.908419i	0.944760	−	0.327763i	$-0.106295\pi$
$812$	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	−0.905670	−	0.423983i	$-0.860632\pi$
$821$	−41.2131	+	12.1012i	−1.43835	+	0.422337i	−0.532676	+	0.846319i	$0.678813\pi$
$822$	−0.154900	+	1.07735i	−0.00540276	+	0.0375770i
$823$	−18.1505	−	39.7440i	−0.632686	−	1.38539i	−0.905923	−	0.423442i	$-0.860822\pi$
$823$	−18.1505	−	39.7440i	−0.632686	−	1.38539i	0.273237	−	0.961947i	$-0.411906\pi$
$824$	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	0.999169	+	0.0407525i	$0.0129755\pi$
$839$	25.9910	+	29.9953i	0.897310	+	1.03555i	−0.101859	+	0.994799i	$0.532479\pi$
$840$	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	−0.995940	−	0.0900235i	$-0.971306\pi$
$853$	−22.3455	+	25.7881i	−0.765095	+	0.882967i	0.230844	+	0.972991i	$0.425851\pi$
$854$	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	−0.342314	−	0.939585i	$-0.611211\pi$
$857$	7.34340	−	51.0745i	0.250846	−	1.74467i	0.593160	−	0.805085i	$-0.297880\pi$
$858$	4.32691	−	1.27049i	0.147718	−	0.0433740i
$859$	14.7952	+	9.50829i	0.504805	+	0.324419i	0.768136	−	0.640287i	$-0.221185\pi$
$859$	14.7952	+	9.50829i	0.504805	+	0.324419i	−0.263331	+	0.964706i	$0.584821\pi$
$860$	−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	0.185850	−	0.982578i	$-0.440496\pi$
$863$	−23.8886	−	27.5689i	−0.813176	−	0.938455i	−0.999026	+	0.0441229i	$0.985951\pi$
$864$	−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	−0.730871	−	0.682515i	$-0.760886\pi$
$877$	−12.2499	+	7.87251i	−0.413649	+	0.265836i	0.317223	+	0.948351i	$0.397250\pi$
$878$	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	−0.723116	−	0.690727i	$-0.757291\pi$
$881$	−28.4352	+	8.34932i	−0.958005	+	0.281296i	−0.234889	+	0.972022i	$0.575473\pi$
$882$	0.698939	+	0.449181i	0.0235345	+	0.0151247i
$883$	12.1047	−	26.5056i	0.407355	−	0.891983i	−0.589116	−	0.808048i	$-0.700524\pi$
$883$	12.1047	−	26.5056i	0.407355	−	0.891983i	0.996471	−	0.0839348i	$-0.0267488\pi$
$884$	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	0.442747	−	0.896647i	$-0.354004\pi$
$887$	9.84151	+	2.88973i	0.330446	+	0.0970276i	−0.112301	+	0.993674i	$0.535822\pi$
$888$	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	0.991957	+	0.126576i	$0.0403987\pi$
$907$	57.0669	+	16.7564i	1.89488	+	0.556386i	0.902919	+	0.429810i	$0.141420\pi$
$908$	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	−0.983958	−	0.178398i	$-0.942909\pi$
$911$	−6.18078	+	13.5340i	−0.204779	+	0.448402i	0.779180	+	0.626800i	$0.215636\pi$
$912$	−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	−0.901080	−	0.433652i	$-0.857225\pi$
$929$	0.510054	−	1.11686i	0.0167343	−	0.0366431i	0.917815	+	0.397009i	$0.129952\pi$
$930$	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	−0.300914	−	0.953651i	$-0.597292\pi$
$937$	7.85114	−	54.6059i	0.256486	−	1.78390i	0.557399	−	0.830245i	$-0.311799\pi$
$938$	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	−0.350812	−	0.936446i	$-0.614094\pi$
$941$	19.2039	−	22.1625i	0.626029	−	0.722475i	0.976840	+	0.213971i	$0.0686397\pi$
$942$	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	0.994853	−	0.101328i	$-0.0323093\pi$
$947$	0.361618	+	2.51511i	0.0117510	+	0.0817301i	−0.983102	+	0.183059i	$0.941400\pi$
$948$	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	0.885897	−	0.463882i	$-0.153544\pi$
$953$	42.6129	+	12.5123i	1.38037	+	0.405313i	0.494471	+	0.869194i	$0.335362\pi$
$954$	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	−0.887977	−	0.459889i	$-0.847889\pi$
$971$	−20.3803	−	44.6267i	−0.654036	−	1.43214i	0.233940	−	0.972251i	$-0.424838\pi$
$972$	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	0.927537	+	0.373730i	$0.121921\pi$
$977$	36.4288	+	42.0411i	1.16546	+	1.34501i	0.237924	+	0.971284i	$0.423533\pi$
$978$	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	−0.806119	−	0.591754i	$-0.798436\pi$
$983$	4.20325	−	29.2342i	0.134063	−	0.932428i	0.940182	−	0.340674i	$-0.110655\pi$
$984$	−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	−0.573066	−	0.819509i	$-0.694246\pi$
$991$	10.0629	−	11.6132i	0.319657	−	0.368904i	0.892723	+	0.450605i	$0.148792\pi$
$992$	−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	0.988103	+	0.153796i	$0.0491499\pi$
$997$	48.5778	+	31.2190i	1.53847	+	0.988717i	0.550371	+	0.834920i	$0.314486\pi$
$998$	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.85.2	✓	20
23.13	even	11	inner	483.2.q.c.358.2	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
483.2.q.c.85.2	✓	20	1.1	even	1	trivial
483.2.q.c.358.2	yes	20	23.13	even	11	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:	\( N \)	\(=\)	\( 483 = 3 \cdot 7 \cdot 23 \)
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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