LMFDB - Embedded newform 930.2.bs.a.107.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(107,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([30, 15, 44]))

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

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

chi := DirichletCharacter("930.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bs (of order $60$, degree $16$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$64$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			107.2
Character	$\chi$	$=$	930.107
Dual form			930.2.bs.a.113.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.453990 - 0.891007i) q^{2} +(-1.70228 - 0.319750i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(1.94583 + 1.10171i) q^{5} +(0.487920 + 1.66191i) q^{6} +(0.0931562 - 0.0754364i) q^{7} +(0.987688 + 0.156434i) q^{8} +(2.79552 + 1.08861i) q^{9} +O(q^{10})$	\(q+(-0.453990 - 0.891007i) q^{2} +(-1.70228 - 0.319750i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(1.94583 + 1.10171i) q^{5} +(0.487920 + 1.66191i) q^{6} +(0.0931562 - 0.0754364i) q^{7} +(0.987688 + 0.156434i) q^{8} +(2.79552 + 1.08861i) q^{9} +(0.0982390 - 2.23391i) q^{10} +(2.67115 + 5.99950i) q^{11} +(1.25926 - 1.18923i) q^{12} +(-3.05726 + 1.98541i) q^{13} +(-0.109506 - 0.0487554i) q^{14} +(-2.96008 - 2.49759i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-6.95114 + 2.66829i) q^{17} +(-0.299183 - 2.98504i) q^{18} +(-1.53203 - 7.20763i) q^{19} +(-2.03503 + 0.926642i) q^{20} +(-0.182699 + 0.0986273i) q^{21} +(4.13292 - 5.10373i) q^{22} +(-4.06017 - 0.643068i) q^{23} +(-1.63130 - 0.582108i) q^{24} +(2.57249 + 4.28746i) q^{25} +(3.15698 + 1.82268i) q^{26} +(-4.41068 - 2.74698i) q^{27} +(0.00627349 + 0.119705i) q^{28} +(1.21968 - 3.75378i) q^{29} +(-0.881522 + 3.77133i) q^{30} +(-2.74099 - 4.84634i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.62871 - 11.0669i) q^{33} +(5.53321 + 4.98213i) q^{34} +(0.264375 - 0.0441556i) q^{35} +(-2.52387 + 1.62176i) q^{36} +(-1.47504 + 5.50493i) q^{37} +(-5.72652 + 4.63724i) q^{38} +(5.83915 - 2.40217i) q^{39} +(1.74953 + 1.39254i) q^{40} +(-3.13504 + 2.82280i) q^{41} +(0.170821 + 0.118010i) q^{42} +(-1.38260 + 2.12902i) q^{43} +(-6.42376 - 1.36541i) q^{44} +(4.24028 + 5.19808i) q^{45} +(1.27030 + 3.90959i) q^{46} +(1.49165 + 0.760031i) q^{47} +(0.221934 + 1.71777i) q^{48} +(-1.45239 + 6.83298i) q^{49} +(2.65227 - 4.23857i) q^{50} +(12.6860 - 2.31956i) q^{51} +(0.190784 - 3.64037i) q^{52} +(-3.76784 + 4.65290i) q^{53} +(-0.445173 + 5.17705i) q^{54} +(-1.41208 + 14.6168i) q^{55} +(0.103810 - 0.0599348i) q^{56} +(0.303306 + 12.7593i) q^{57} +(-3.89837 + 0.617441i) q^{58} +(-4.48168 + 4.97742i) q^{59} +(3.76048 - 0.926705i) q^{60} -4.41331 q^{61} +(-3.07373 + 4.64243i) q^{62} +(0.342541 - 0.109473i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-8.13624 + 0.495063i) q^{65} +(-8.66731 + 7.36648i) q^{66} +(-1.01602 + 0.272242i) q^{67} +(1.92708 - 7.19197i) q^{68} +(6.70594 + 2.39292i) q^{69} +(-0.159367 - 0.215513i) q^{70} +(5.90613 - 0.620759i) q^{71} +(2.59081 + 1.51252i) q^{72} +(3.08405 - 8.03424i) q^{73} +(5.57458 - 1.18491i) q^{74} +(-3.00819 - 8.12101i) q^{75} +(6.73160 + 2.99710i) q^{76} +(0.701415 + 0.357389i) q^{77} +(-4.79127 - 4.11216i) q^{78} +(-1.11813 + 2.51137i) q^{79} +(0.446490 - 2.19104i) q^{80} +(6.62987 + 6.08645i) q^{81} +(3.93841 + 1.51182i) q^{82} +(0.221893 - 4.23397i) q^{83} +(0.0275965 - 0.205778i) q^{84} +(-16.4654 - 2.46607i) q^{85} +(2.52466 + 0.265353i) q^{86} +(-3.27651 + 6.00000i) q^{87} +(1.69974 + 6.34350i) q^{88} +(-7.88320 - 5.72748i) q^{89} +(2.70648 - 6.13799i) q^{90} +(-0.135031 + 0.415582i) q^{91} +(2.90676 - 2.90676i) q^{92} +(3.11632 + 9.12626i) q^{93} -1.67411i q^{94} +(4.95962 - 15.7126i) q^{95} +(1.42979 - 0.977597i) q^{96} +(2.53912 + 16.0314i) q^{97} +(6.74760 - 1.80801i) q^{98} +(0.936151 + 19.6796i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q - 8 q^{3} + 24 q^{7}+O(q^{10}) $ 1024 * q - 8 * q^3 + 24 * q^7	$ 1024 q - 8 q^{3} + 24 q^{7} + 8 q^{10} + 8 q^{12} - 8 q^{15} + 256 q^{16} + 44 q^{22} + 16 q^{25} - 20 q^{27} + 4 q^{28} + 48 q^{30} - 32 q^{31} - 52 q^{33} + 112 q^{37} + 12 q^{42} + 40 q^{45} + 24 q^{46} - 12 q^{48} + 16 q^{51} - 20 q^{55} - 40 q^{57} - 56 q^{58} - 12 q^{60} + 32 q^{61} + 224 q^{63} - 32 q^{66} + 24 q^{67} - 24 q^{70} - 88 q^{73} + 224 q^{75} - 96 q^{76} - 32 q^{78} + 48 q^{81} - 24 q^{85} + 20 q^{87} - 36 q^{88} + 8 q^{90} - 80 q^{91} - 252 q^{93} - 32 q^{97}+O(q^{100}) $ 1024 * q - 8 * q^3 + 24 * q^7 + 8 * q^10 + 8 * q^12 - 8 * q^15 + 256 * q^16 + 44 * q^22 + 16 * q^25 - 20 * q^27 + 4 * q^28 + 48 * q^30 - 32 * q^31 - 52 * q^33 + 112 * q^37 + 12 * q^42 + 40 * q^45 + 24 * q^46 - 12 * q^48 + 16 * q^51 - 20 * q^55 - 40 * q^57 - 56 * q^58 - 12 * q^60 + 32 * q^61 + 224 * q^63 - 32 * q^66 + 24 * q^67 - 24 * q^70 - 88 * q^73 + 224 * q^75 - 96 * q^76 - 32 * q^78 + 48 * q^81 - 24 * q^85 + 20 * q^87 - 36 * q^88 + 8 * q^90 - 80 * q^91 - 252 * q^93 - 32 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{11}{15}\right)$

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 $

$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$2$	−0.453990	−	0.891007i	−0.321020	−	0.630037i
$3$	−1.70228	−	0.319750i	−0.982812	−	0.184608i
$3$	−1.70228	−	0.319750i	−0.982812	−	0.184608i
$4$	−0.587785	+	0.809017i	−0.293893	+	0.404508i
$5$	1.94583	+	1.10171i	0.870201	+	0.492697i
$5$	1.94583	+	1.10171i	0.870201	+	0.492697i
$6$	0.487920	+	1.66191i	0.199193	+	0.678471i
$7$	0.0931562	−	0.0754364i	0.0352097	−	0.0285123i	−0.611554	−	0.791203i	$-0.709455\pi$
$7$	0.0931562	−	0.0754364i	0.0352097	−	0.0285123i	0.646764	+	0.762690i	$0.276122\pi$
$8$	0.987688	+	0.156434i	0.349201	+	0.0553079i
$9$	2.79552	+	1.08861i	0.931840	+	0.362869i
$10$	0.0982390	−	2.23391i	0.0310659	−	0.706424i
$11$	2.67115	+	5.99950i	0.805382	+	1.80892i	0.531218	+	0.847235i	$0.321735\pi$
$11$	2.67115	+	5.99950i	0.805382	+	1.80892i	0.274164	+	0.961683i	$0.411599\pi$
$12$	1.25926	−	1.18923i	0.363517	−	0.343301i
$13$	−3.05726	+	1.98541i	−0.847932	+	0.550653i	−0.893888	−	0.448290i	$-0.852033\pi$
$13$	−3.05726	+	1.98541i	−0.847932	+	0.550653i	0.0459562	+	0.998943i	$0.485367\pi$
$14$	−0.109506	−	0.0487554i	−0.0292668	−	0.0130304i
$15$	−2.96008	−	2.49759i	−0.764288	−	0.644875i
$16$	−0.309017	−	0.951057i	−0.0772542	−	0.237764i
$17$	−6.95114	+	2.66829i	−1.68590	+	0.647156i	−0.996978	−	0.0776821i	$-0.975248\pi$
$17$	−6.95114	+	2.66829i	−1.68590	+	0.647156i	−0.688920	+	0.724838i	$0.741915\pi$
$18$	−0.299183	−	2.98504i	−0.0705181	−	0.703582i
$19$	−1.53203	−	7.20763i	−0.351471	−	1.65354i	−0.698442	−	0.715667i	$-0.746123\pi$
$19$	−1.53203	−	7.20763i	−0.351471	−	1.65354i	0.346970	−	0.937876i	$-0.387210\pi$
$20$	−2.03503	+	0.926642i	−0.455046	+	0.207203i
$21$	−0.182699	+	0.0986273i	−0.0398682	+	0.0215222i
$22$	4.13292	−	5.10373i	0.881141	−	1.08812i
$23$	−4.06017	−	0.643068i	−0.846605	−	0.134089i	−0.281963	−	0.959425i	$-0.590986\pi$
$23$	−4.06017	−	0.643068i	−0.846605	−	0.134089i	−0.564642	+	0.825336i	$0.690986\pi$
$24$	−1.63130	−	0.582108i	−0.332988	−	0.118822i
$25$	2.57249	+	4.28746i	0.514498	+	0.857491i
$26$	3.15698	+	1.82268i	0.619135	+	0.357458i
$27$	−4.41068	−	2.74698i	−0.848835	−	0.528657i
$28$	0.00627349	+	0.119705i	0.00118558	+	0.0226222i
$29$	1.21968	−	3.75378i	0.226489	−	0.697060i	−0.771649	−	0.636049i	$-0.780568\pi$
$29$	1.21968	−	3.75378i	0.226489	−	0.697060i	0.998137	−	0.0610109i	$-0.0194324\pi$
$30$	−0.881522	+	3.77133i	−0.160943	+	0.688547i
$31$	−2.74099	−	4.84634i	−0.492297	−	0.870428i
$31$	−2.74099	−	4.84634i	−0.492297	−	0.870428i
$32$	−0.707107	+	0.707107i	−0.125000	+	0.125000i
$33$	−2.62871	−	11.0669i	−0.457600	−	1.92651i
$34$	5.53321	+	4.98213i	0.948938	+	0.854428i
$35$	0.264375	−	0.0441556i	0.0446875	−	0.00746366i
$36$	−2.52387	+	1.62176i	−0.420645	+	0.270293i
$37$	−1.47504	+	5.50493i	−0.242495	+	0.905005i	0.732130	+	0.681165i	$0.238526\pi$
$37$	−1.47504	+	5.50493i	−0.242495	+	0.905005i	−0.974626	+	0.223841i	$0.928140\pi$
$38$	−5.72652	+	4.63724i	−0.928964	+	0.752260i
$39$	5.83915	−	2.40217i	0.935013	−	0.384654i
$40$	1.74953	+	1.39254i	0.276624	+	0.220179i
$41$	−3.13504	+	2.82280i	−0.489611	+	0.440848i	−0.876588	−	0.481242i	$-0.840186\pi$
$41$	−3.13504	+	2.82280i	−0.489611	+	0.440848i	0.386977	+	0.922089i	$0.373519\pi$
$42$	0.170821	+	0.118010i	0.0263583	+	0.0182093i
$43$	−1.38260	+	2.12902i	−0.210845	+	0.324673i	−0.928232	−	0.372002i	$-0.878671\pi$
$43$	−1.38260	+	2.12902i	−0.210845	+	0.324673i	0.717387	+	0.696675i	$0.245338\pi$
$44$	−6.42376	−	1.36541i	−0.968419	−	0.205844i
$45$	4.24028	+	5.19808i	0.632103	+	0.774884i
$46$	1.27030	+	3.90959i	0.187296	+	0.576437i
$47$	1.49165	+	0.760031i	0.217579	+	0.110862i	0.559383	−	0.828909i	$-0.311038\pi$
$47$	1.49165	+	0.760031i	0.217579	+	0.110862i	−0.341804	+	0.939771i	$0.611038\pi$
$48$	0.221934	+	1.71777i	0.0320334	+	0.247939i
$49$	−1.45239	+	6.83298i	−0.207485	+	0.976140i
$50$	2.65227	−	4.23857i	0.375087	−	0.599425i
$51$	12.6860	−	2.31956i	1.77639	−	0.324803i
$52$	0.190784	−	3.64037i	0.0264570	−	0.504829i
$53$	−3.76784	+	4.65290i	−0.517553	+	0.639125i	−0.967180	−	0.254092i	$-0.918223\pi$
$53$	−3.76784	+	4.65290i	−0.517553	+	0.639125i	0.449627	+	0.893216i	$0.351557\pi$
$54$	−0.445173	+	5.17705i	−0.0605804	+	0.704507i
$55$	−1.41208	+	14.6168i	−0.190405	+	1.97093i
$56$	0.103810	−	0.0599348i	0.0138722	−	0.00800913i
$57$	0.303306	+	12.7593i	0.0401738	+	1.69001i
$58$	−3.89837	+	0.617441i	−0.511881	+	0.0810739i
$59$	−4.48168	+	4.97742i	−0.583466	+	0.648004i	−0.960528	−	0.278184i	$-0.910268\pi$
$59$	−4.48168	+	4.97742i	−0.583466	+	0.648004i	0.377062	+	0.926188i	$0.376934\pi$
$60$	3.76048	−	0.926705i	0.485476	−	0.119637i
$61$	−4.41331			−0.565066			−0.282533	−	0.959258i	$-0.591175\pi$
$61$	−4.41331			−0.565066			−0.282533	+	0.959258i	$0.591175\pi$
$62$	−3.07373	+	4.64243i	−0.390364	+	0.589589i
$63$	0.342541	−	0.109473i	0.0431561	−	0.0137924i
$64$	0.951057	+	0.309017i	0.118882	+	0.0386271i
$65$	−8.13624	+	0.495063i	−1.00918	+	0.0614051i
$66$	−8.66731	+	7.36648i	−1.06687	+	0.906751i
$67$	−1.01602	+	0.272242i	−0.124127	+	0.0332596i	−0.320348	−	0.947300i	$-0.603800\pi$
$67$	−1.01602	+	0.272242i	−0.124127	+	0.0332596i	0.196221	+	0.980560i	$0.437133\pi$
$68$	1.92708	−	7.19197i	0.233693	−	0.872154i
$69$	6.70594	+	2.39292i	0.807300	+	0.288074i
$70$	−0.159367	−	0.215513i	−0.0190479	−	0.0257588i
$71$	5.90613	−	0.620759i	0.700929	−	0.0736706i	0.252641	−	0.967560i	$-0.418701\pi$
$71$	5.90613	−	0.620759i	0.700929	−	0.0736706i	0.448288	+	0.893889i	$0.352034\pi$
$72$	2.59081	+	1.51252i	0.305330	+	0.178252i
$73$	3.08405	−	8.03424i	0.360961	−	0.940336i	−0.626064	−	0.779772i	$-0.715335\pi$
$73$	3.08405	−	8.03424i	0.360961	−	0.940336i	0.987025	−	0.160565i	$-0.0513315\pi$
$74$	5.57458	−	1.18491i	0.648032	−	0.137744i
$75$	−3.00819	−	8.12101i	−0.347356	−	0.937733i
$76$	6.73160	+	2.99710i	0.772167	+	0.343791i
$77$	0.701415	+	0.357389i	0.0799337	+	0.0407283i
$78$	−4.79127	−	4.11216i	−0.542504	−	0.465611i
$79$	−1.11813	+	2.51137i	−0.125800	+	0.282551i	−0.965455	−	0.260568i	$-0.916090\pi$
$79$	−1.11813	+	2.51137i	−0.125800	+	0.282551i	0.839656	+	0.543119i	$0.182757\pi$
$80$	0.446490	−	2.19104i	0.0499191	−	0.244965i
$81$	6.62987	+	6.08645i	0.736652	+	0.676272i
$82$	3.93841	+	1.51182i	0.434925	+	0.166952i
$83$	0.221893	−	4.23397i	0.0243559	−	0.464738i	−0.959041	−	0.283269i	$-0.908581\pi$
$83$	0.221893	−	4.23397i	0.0243559	−	0.464738i	0.983397	−	0.181470i	$-0.0580854\pi$
$84$	0.0275965	−	0.205778i	0.00301103	−	0.0224522i
$85$	−16.4654	−	2.46607i	−1.78592	−	0.267482i
$86$	2.52466	+	0.265353i	0.272241	+	0.0286137i
$87$	−3.27651	+	6.00000i	−0.351278	+	0.643268i
$88$	1.69974	+	6.34350i	0.181192	+	0.676219i
$89$	−7.88320	−	5.72748i	−0.835617	−	0.607111i	0.0855259	−	0.996336i	$-0.472743\pi$
$89$	−7.88320	−	5.72748i	−0.835617	−	0.607111i	−0.921143	+	0.389225i	$0.872743\pi$
$90$	2.70648	−	6.13799i	0.285288	−	0.647001i
$91$	−0.135031	+	0.415582i	−0.0141551	+	0.0435648i
$92$	2.90676	−	2.90676i	0.303051	−	0.303051i
$93$	3.11632	+	9.12626i	0.323148	+	0.946349i
$94$		−	1.67411i		−	0.172672i
$95$	4.95962	−	15.7126i	0.508846	−	1.61208i
$96$	1.42979	−	0.977597i	0.145927	−	0.0997756i
$97$	2.53912	+	16.0314i	0.257809	+	1.62774i	0.688497	+	0.725239i	$0.258271\pi$
$97$	2.53912	+	16.0314i	0.257809	+	1.62774i	−0.430688	+	0.902501i	$0.641729\pi$
$98$	6.74760	−	1.80801i	0.681611	−	0.182637i
$99$	0.936151	+	19.6796i	0.0940867	+	1.97787i
$100$	−4.98070	−	0.438914i	−0.498070	−	0.0438914i
$101$	5.97690	+	8.22649i	0.594723	+	0.818567i	0.995212	−	0.0977350i	$-0.0311598\pi$
$101$	5.97690	+	8.22649i	0.594723	+	0.818567i	−0.400489	+	0.916302i	$0.631160\pi$
$102$	−7.82605	−	10.2502i	−0.774894	−	1.01492i
$103$	−7.47668	−	0.391836i	−0.736699	−	0.0386088i	−0.319704	−	0.947517i	$-0.603583\pi$
$103$	−7.47668	−	0.391836i	−0.736699	−	0.0386088i	−0.416995	+	0.908909i	$0.636917\pi$
$104$	−3.33021	+	1.48270i	−0.326554	+	0.145391i
$105$	−0.464159	−	0.00936848i	−0.0452972	−	0.000914270i
$106$	5.85633	+	1.24480i	0.568817	+	0.120906i
$107$	14.8327	−	5.69372i	1.43393	−	0.550433i	0.487435	−	0.873159i	$-0.337933\pi$
$107$	14.8327	−	5.69372i	1.43393	−	0.550433i	0.946492	+	0.322726i	$0.104599\pi$
$108$	4.81489	−	1.95368i	0.463313	−	0.187993i
$109$	16.7231	−	5.43366i	1.60178	−	0.520450i	0.634234	−	0.773141i	$-0.281315\pi$
$109$	16.7231	−	5.43366i	1.60178	−	0.520450i	0.967547	+	0.252691i	$0.0813155\pi$
$110$	13.6648	−	5.37772i	1.30288	−	0.512746i
$111$	4.27114	−	8.89930i	0.405398	−	0.844684i
$112$	−0.100531	−	0.0652857i	−0.00949930	−	0.00616892i
$113$	−0.996026	−	0.382338i	−0.0936982	−	0.0359674i	0.311067	−	0.950388i	$-0.399314\pi$
$113$	−0.996026	−	0.382338i	−0.0936982	−	0.0359674i	−0.404766	+	0.914421i	$0.632647\pi$
$114$	11.2309	−	6.06284i	1.05187	−	0.567837i
$115$	−7.19193	−	5.72441i	−0.670651	−	0.533804i
$116$	2.31997	+	3.19316i	0.215403	+	0.296477i
$117$	−10.7080	+	2.22209i	−0.989952	+	0.205433i
$118$	6.46955	+	1.73351i	0.595571	+	0.159583i
$119$	−0.446255	+	0.772937i	−0.0409081	+	0.0708550i
$120$	−2.53292	−	2.92990i	−0.231223	−	0.267462i
$121$	−21.4985	+	23.8766i	−1.95441	+	2.17060i
$122$	2.00360	+	3.93229i	0.181397	+	0.356012i
$123$	6.23931	−	3.80277i	0.562579	−	0.342885i
$124$	5.53188	+	0.631096i	0.496778	+	0.0566741i
$125$	0.282114	+	11.1768i	0.0252330	+	0.999682i
$126$	−0.253052	−	0.255506i	−0.0225436	−	0.0227623i
$127$	18.7971	−	0.985116i	1.66798	−	0.0874149i	0.805200	−	0.593003i	$-0.202058\pi$
$127$	18.7971	−	0.985116i	1.66798	−	0.0874149i	0.862775	+	0.505588i	$0.168724\pi$
$128$	−0.156434	−	0.987688i	−0.0138270	−	0.0873001i
$129$	3.03433	−	3.18211i	0.267158	−	0.280169i
$130$	4.13488	+	7.02469i	0.362653	+	0.616106i
$131$	−14.4790	−	1.52181i	−1.26504	−	0.132961i	−0.551856	−	0.833939i	$-0.686080\pi$
$131$	−14.4790	−	1.52181i	−1.26504	−	0.132961i	−0.713183	+	0.700978i	$0.752747\pi$
$132$	10.4985	+	4.37831i	0.913773	+	0.381083i
$133$	−0.686436	−	0.555865i	−0.0595215	−	0.0481996i
$134$	0.703833	+	0.781686i	0.0608019	+	0.0675273i
$135$	−5.55606	−	10.2044i	−0.478189	−	0.878257i
$136$	−7.28297	+	1.54804i	−0.624509	+	0.132744i
$137$	−6.38816	+	4.14852i	−0.545777	+	0.354432i	−0.787890	−	0.615816i	$-0.788826\pi$
$137$	−6.38816	+	4.14852i	−0.545777	+	0.354432i	0.242113	+	0.970248i	$0.422160\pi$
$138$	−0.912321	−	7.06140i	−0.0776620	−	0.601106i
$139$	−5.40041	+	1.75470i	−0.458057	+	0.148832i	−0.528951	−	0.848652i	$-0.677415\pi$
$139$	−5.40041	+	1.75470i	−0.458057	+	0.148832i	0.0708946	+	0.997484i	$0.477415\pi$
$140$	−0.119673	+	0.239838i	−0.0101142	+	0.0202700i
$141$	−2.29618	−	1.77074i	−0.193373	−	0.149123i
$142$	−3.23443	−	4.98058i	−0.271427	−	0.417961i
$143$	−20.0779	−	13.0387i	−1.67900	−	1.09035i
$144$	0.171464	−	2.99510i	0.0142887	−	0.249591i
$145$	6.50884	−	5.96049i	0.540530	−	0.494992i
$146$	−8.55869	+	0.899554i	−0.708322	+	0.0744476i
$147$	4.65723	−	11.1672i	0.384122	−	0.921059i
$148$	−3.58658	−	4.42905i	−0.294815	−	0.364066i
$149$	−1.65282	−	2.86276i	−0.135404	−	0.234527i	0.790348	−	0.612659i	$-0.209900\pi$
$149$	−1.65282	−	2.86276i	−0.135404	−	0.234527i	−0.925752	+	0.378132i	$0.876567\pi$
$150$	−5.87018	+	6.36718i	−0.479298	+	0.519878i
$151$	5.93218	+	4.30998i	0.482754	+	0.350741i	0.802391	−	0.596799i	$-0.203561\pi$
$151$	5.93218	+	4.30998i	0.482754	+	0.350741i	−0.319637	+	0.947540i	$0.603561\pi$
$152$	−0.385645	−	7.35855i	−0.0312800	−	0.596857i
$153$	−22.3368	−	0.107798i	−1.80582	−	0.00871497i
$154$		−	0.787217i		−	0.0634357i
$155$	0.00573435	−	12.4499i	0.000460594	−	1.00000i
$156$	−1.48878	+	6.13593i	−0.119197	+	0.491268i
$157$	7.97722	−	4.06460i	0.636651	−	0.324390i	−0.105703	−	0.994398i	$-0.533709\pi$
$157$	7.97722	−	4.06460i	0.636651	−	0.324390i	0.742354	+	0.670008i	$0.233709\pi$
$158$	2.74527	−	0.143873i	0.218402	−	0.0114459i
$159$	7.90169	−	6.71577i	0.626645	−	0.532595i
$160$	−2.15493	+	0.596885i	−0.170362	+	0.0471879i
$161$	−0.426741	+	0.246379i	−0.0336319	+	0.0194174i
$162$	2.41317	−	8.67044i	0.189597	−	0.681214i
$163$	2.12932	−	13.4440i	0.166781	−	1.05302i	−0.752264	−	0.658862i	$-0.771038\pi$
$163$	2.12932	−	13.4440i	0.166781	−	1.05302i	0.919045	−	0.394153i	$-0.128962\pi$
$164$	−0.440965	−	4.19550i	−0.0344336	−	0.327614i
$165$	7.07749	−	24.4304i	0.550982	−	1.90191i
$166$	−3.87323	+	1.72447i	−0.300621	+	0.133845i
$167$	2.32795	−	3.58473i	0.180142	−	0.277394i	−0.737051	−	0.675837i	$-0.763782\pi$
$167$	2.32795	−	3.58473i	0.180142	−	0.277394i	0.917193	+	0.398442i	$0.130449\pi$
$168$	−0.195878	+	0.0688326i	−0.0151123	+	0.00531055i
$169$	0.117426	−	0.263743i	0.00903278	−	0.0202879i
$170$	5.27785	+	15.7903i	0.404792	+	1.21106i
$171$	3.56346	−	21.8168i	0.272505	−	1.66838i
$172$	−0.909742	−	2.36996i	−0.0693671	−	0.180708i
$173$	3.85811	+	5.94098i	0.293327	+	0.451684i	0.954354	−	0.298678i	$-0.0965457\pi$
$173$	3.85811	+	5.94098i	0.293327	+	0.451684i	−0.661027	+	0.750362i	$0.729879\pi$
$174$	6.83354	+	0.195444i	0.518049	+	0.0148166i
$175$	0.563074	+	0.205344i	0.0425644	+	0.0155225i
$176$	4.88044	−	4.39436i	0.367877	−	0.331238i
$177$	9.22061	−	7.03994i	0.693064	−	0.529154i
$178$	−1.52432	+	9.62420i	−0.114253	+	0.721364i
$179$	−0.713517	+	6.78866i	−0.0533308	+	0.507408i	0.934952	+	0.354774i	$0.115442\pi$
$179$	−0.713517	+	6.78866i	−0.0533308	+	0.507408i	−0.988283	+	0.152634i	$0.951224\pi$
$180$	−6.69771	+	0.375100i	−0.499218	+	0.0279583i
$181$	−3.35559	+	5.81206i	−0.249419	+	0.432007i	−0.963365	−	0.268194i	$-0.913573\pi$
$181$	−3.35559	+	5.81206i	−0.249419	+	0.432007i	0.713946	+	0.700201i	$0.246906\pi$
$182$	0.431589	−	0.0683570i	0.0319915	−	0.00506696i
$183$	7.51269	+	1.41115i	0.555354	+	0.104315i
$184$	−3.90959	−	1.27030i	−0.288219	−	0.0936479i
$185$	−8.93499	+	9.08659i	−0.656913	+	0.668059i
$186$	6.71677	−	6.91990i	0.492498	−	0.507391i
$187$	−34.5759	−	34.5759i	−2.52844	−	2.52844i
$188$	−1.49165	+	0.760031i	−0.108789	+	0.0554310i
$189$	−0.618105	+	0.0768273i	−0.0449605	+	0.00558836i
$190$	−16.2517	+	2.71434i	−1.17902	+	0.196919i
$191$	−12.2193	−	7.05484i	−0.884160	−	0.510470i	−0.0121325	−	0.999926i	$-0.503862\pi$
$191$	−12.2193	−	7.05484i	−0.884160	−	0.510470i	−0.872028	+	0.489456i	$0.837195\pi$
$192$	−1.52016	−	0.830134i	−0.109708	−	0.0599097i
$193$	3.58999	+	4.43327i	0.258413	+	0.319114i	0.889797	−	0.456357i	$-0.150846\pi$
$193$	3.58999	+	4.43327i	0.258413	+	0.319114i	−0.631384	+	0.775471i	$0.717513\pi$
$194$	13.1313	−	9.54047i	0.942774	−	0.684966i
$195$	14.0085	+	1.75882i	1.00317	+	0.125952i
$196$	−4.67430	−	5.19134i	−0.333879	−	0.370810i
$197$	0.761576	−	1.98397i	0.0542601	−	0.141352i	−0.903771	−	0.428016i	$-0.859213\pi$
$197$	0.761576	−	1.98397i	0.0542601	−	0.141352i	0.958031	+	0.286663i	$0.0925461\pi$
$198$	17.1096	−	9.76845i	1.21593	−	0.694214i
$199$	−2.51767	+	11.8447i	−0.178473	+	0.839648i	0.794235	+	0.607611i	$0.207872\pi$
$199$	−2.51767	+	11.8447i	−0.178473	+	0.839648i	−0.972707	+	0.232036i	$0.925461\pi$
$200$	1.87011	+	4.63710i	0.132237	+	0.327892i
$201$	1.81660	−	0.138560i	0.128133	−	0.00977326i
$202$	4.61640	−	9.06020i	0.324809	−	0.637474i
$203$	−0.169551	−	0.441696i	−0.0119002	−	0.0310010i
$204$	−5.58007	+	11.6266i	−0.390683	+	0.814022i
$205$	−9.21014	+	2.03880i	−0.643264	+	0.142396i
$206$	3.04521	+	6.83966i	0.212170	+	0.476542i
$207$	−10.6502	−	6.21765i	−0.740243	−	0.432156i
$208$	2.83298	+	2.29410i	0.196432	+	0.159067i
$209$	39.1499	−	28.4441i	2.70806	−	1.96752i
$210$	0.202376	+	0.417822i	0.0139653	+	0.0288324i
$211$	7.58118	+	13.1310i	0.521910	+	0.903975i	0.999675	+	0.0254871i	$0.00811368\pi$
$211$	7.58118	+	13.1310i	0.521910	+	0.903975i	−0.477765	+	0.878488i	$0.658553\pi$
$212$	−1.54959	−	5.78315i	−0.106426	−	0.397189i
$213$	−10.2524	−	0.831777i	−0.702482	−	0.0569924i
$214$	−11.8070	−	10.6311i	−0.807112	−	0.726727i
$215$	−5.03586	+	2.61949i	−0.343443	+	0.178648i
$216$	−3.92665	−	3.40315i	−0.267175	−	0.231555i
$217$	−0.620931	−	0.244696i	−0.0421515	−	0.0166110i
$218$	−12.4336	−	12.4336i	−0.842106	−	0.842106i
$219$	−7.81887	+	12.6904i	−0.528350	+	0.857538i
$220$	−10.9953	−	9.73395i	−0.741300	−	0.656263i
$221$	15.9538	−	21.9585i	1.07317	−	1.47709i
$222$	−9.86839	+	0.234585i	−0.662323	+	0.0157443i
$223$	−5.13029	−	1.37466i	−0.343550	−	0.0920539i	0.0829187	−	0.996556i	$-0.473576\pi$
$223$	−5.13029	−	1.37466i	−0.343550	−	0.0920539i	−0.426468	+	0.904502i	$0.640242\pi$
$224$	−0.0125298	+	0.119213i	−0.000837182	+	0.00796525i
$225$	2.52409	+	14.7861i	0.168273	+	0.985740i
$226$	0.111520	+	1.06104i	0.00741821	+	0.0705796i
$227$	−4.93131	−	0.258439i	−0.327302	−	0.0171532i	−0.112023	−	0.993706i	$-0.535733\pi$
$227$	−4.93131	−	0.258439i	−0.327302	−	0.0171532i	−0.215280	+	0.976552i	$0.569066\pi$
$228$	−10.5007	−	7.25433i	−0.695429	−	0.480430i
$229$	4.57718	+	21.5339i	0.302468	+	1.42300i	0.822457	+	0.568828i	$0.192603\pi$
$229$	4.57718	+	21.5339i	0.302468	+	1.42300i	−0.519988	+	0.854173i	$0.674064\pi$
$230$	−1.83542	+	9.00688i	−0.121024	+	0.593896i
$231$	−1.07973	−	0.832654i	−0.0710411	−	0.0547846i
$232$	1.79188	−	3.51677i	0.117643	−	0.230887i
$233$	−2.76870	+	5.43387i	−0.181383	+	0.355985i	−0.963739	−	0.266847i	$-0.914018\pi$
$233$	−2.76870	+	5.43387i	−0.181383	+	0.355985i	0.782355	+	0.622832i	$0.214018\pi$
$234$	6.84122	+	8.53206i	0.447224	+	0.557758i
$235$	2.06516	+	3.12224i	0.134716	+	0.203673i
$236$	−1.39255	−	6.55141i	−0.0906470	−	0.426461i
$237$	2.70639	−	3.91753i	0.175799	−	0.254471i
$238$	0.891287	+	0.0467104i	0.0577736	+	0.00302778i
$239$	0.719970	+	6.85005i	0.0465710	+	0.443093i	0.992817	+	0.119645i	$0.0381756\pi$
$239$	0.719970	+	6.85005i	0.0465710	+	0.443093i	−0.946246	+	0.323448i	$0.895158\pi$
$240$	−1.46063	+	3.58700i	−0.0942836	+	0.231540i
$241$	0.221331	−	2.10582i	0.0142572	−	0.135648i	−0.985078	−	0.172109i	$-0.944942\pi$
$241$	0.221331	−	2.10582i	0.0142572	−	0.135648i	0.999335	+	0.0364611i	$0.0116085\pi$
$242$	31.0343	+	8.31562i	1.99496	+	0.534548i
$243$	−9.33975	−	12.4807i	−0.599146	−	0.800640i
$244$	2.59408	−	3.57044i	0.166069	−	0.228574i
$245$	−10.3540	+	11.6957i	−0.661495	+	0.747210i
$246$	−6.22088	−	3.83284i	−0.396629	−	0.244373i
$247$	18.9939	+	18.9939i	1.20855	+	1.20855i
$248$	−1.94911	−	5.21545i	−0.123769	−	0.331182i
$249$	−1.73153	+	7.13645i	−0.109731	+	0.452254i
$250$	9.83051	−	5.32552i	0.621736	−	0.336815i
$251$	−6.92642	−	6.23657i	−0.437191	−	0.393649i	0.420932	−	0.907092i	$-0.361703\pi$
$251$	−6.92642	−	6.23657i	−0.437191	−	0.393649i	−0.858124	+	0.513443i	$0.828370\pi$
$252$	−0.112775	+	0.341468i	−0.00710413	+	0.0215105i
$253$	−6.98725	−	26.0768i	−0.439284	−	1.63943i
$254$	−9.41146	−	16.3011i	−0.590528	−	1.02282i
$255$	27.2402	+	9.46274i	1.70585	+	0.592580i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	4.13979	+	3.35234i	0.258233	+	0.209113i	0.749690	−	0.661789i	$-0.230202\pi$
$257$	4.13979	+	3.35234i	0.258233	+	0.209113i	−0.491458	+	0.870902i	$0.663536\pi$
$258$	−4.21284	−	1.25896i	−0.262280	−	0.0783797i
$259$	0.277863	+	0.624090i	0.0172656	+	0.0387791i
$260$	4.38185	−	6.87335i	0.271751	−	0.426267i
$261$	7.49603	−	9.16602i	0.463993	−	0.567363i
$262$	5.21740	+	13.5918i	0.322332	+	0.839704i
$263$	−5.55832	+	10.9088i	−0.342741	+	0.672667i	−0.996460	−	0.0840708i	$-0.973208\pi$
$263$	−5.55832	+	10.9088i	−0.342741	+	0.672667i	0.653719	+	0.756737i	$0.273208\pi$
$264$	−0.865095	−	11.3419i	−0.0532429	−	0.698046i
$265$	−12.4577	+	4.90269i	−0.765270	+	0.301170i
$266$	−0.183644	+	0.863976i	−0.0112599	+	0.0529738i
$267$	11.5881	+	12.2704i	0.709177	+	0.750938i
$268$	0.376954	−	0.981997i	0.0230261	−	0.0599850i
$269$	6.02210	+	6.68822i	0.367174	+	0.407788i	0.898214	−	0.439559i	$-0.144865\pi$
$269$	6.02210	+	6.68822i	0.367174	+	0.407788i	−0.531040	+	0.847347i	$0.678199\pi$
$270$	−6.56981	+	9.58319i	−0.399826	+	0.583215i
$271$	0.355856	−	0.258545i	0.0216167	−	0.0157055i	−0.576924	−	0.816798i	$-0.695747\pi$
$271$	0.355856	−	0.258545i	0.0216167	−	0.0157055i	0.598541	+	0.801092i	$0.295747\pi$
$272$	4.68571	+	5.78638i	0.284113	+	0.350851i
$273$	0.362743	−	0.664261i	0.0219542	−	0.0402029i
$274$	6.59652	+	3.80850i	0.398510	+	0.230080i
$275$	−18.8511	+	26.8861i	−1.13676	+	1.62129i
$276$	−5.87756	+	4.01869i	−0.353788	+	0.241897i
$277$	−6.30121	+	3.21063i	−0.378603	+	0.192908i	−0.632928	−	0.774211i	$-0.718147\pi$
$277$	−6.30121	+	3.21063i	−0.378603	+	0.192908i	0.254324	+	0.967119i	$0.418147\pi$
$278$	4.01518	+	4.01518i	0.240815	+	0.240815i
$279$	−2.38674	−	16.5319i	−0.142890	−	0.989739i
$280$	0.268027	−	0.00225467i	0.0160177	−	0.000134742i
$281$	13.3522	+	4.33839i	0.796525	+	0.258807i	0.678880	−	0.734249i	$-0.262466\pi$
$281$	13.3522	+	4.33839i	0.796525	+	0.258807i	0.117645	+	0.993056i	$0.462466\pi$
$282$	−0.535297	+	2.84981i	−0.0318765	+	0.169704i
$283$	1.20743	−	0.191239i	0.0717744	−	0.0113680i	−0.120444	−	0.992720i	$-0.538432\pi$
$283$	1.20743	−	0.191239i	0.0717744	−	0.0113680i	0.192218	+	0.981352i	$0.438432\pi$
$284$	−2.96933	+	5.14303i	−0.176197	+	0.305183i
$285$	−13.4668	+	25.1615i	−0.797703	+	1.49044i
$286$	−2.50242	+	23.8090i	−0.147971	+	1.40785i
$287$	−0.0791063	+	0.499458i	−0.00466950	+	0.0294821i
$288$	−2.74649	+	1.20697i	−0.161839	+	0.0711214i
$289$	28.5650	−	25.7201i	1.68030	−	1.51295i
$290$	−8.26579	−	3.09342i	−0.485384	−	0.181652i
$291$	0.803732	−	28.1018i	0.0471156	−	1.64736i
$292$	4.68707	+	7.21746i	0.274290	+	0.422370i
$293$	−2.57069	−	6.69688i	−0.150181	−	0.391236i	0.837765	−	0.546031i	$-0.183862\pi$
$293$	−2.57069	−	6.69688i	−0.150181	−	0.391236i	−0.987947	+	0.154794i	$0.950528\pi$
$294$	−12.0644	+	0.920205i	−0.703612	+	0.0536674i
$295$	−14.2042	+	4.74770i	−0.827002	+	0.276422i
$296$	−2.31804	+	5.20641i	−0.134733	+	0.302616i
$297$	4.69894	−	33.7995i	0.272660	−	1.96124i
$298$	−1.80038	+	2.77234i	−0.104293	+	0.160597i
$299$	13.6898	−	6.09508i	0.791700	−	0.352487i
$300$	8.33820	+	2.33973i	0.481406	+	0.135084i
$301$	0.0318077	+	0.302630i	0.00183337	+	0.0174433i
$302$	1.14707	−	7.24230i	0.0660063	−	0.416748i
$303$	−7.54394	−	15.9149i	−0.433388	−	0.914288i
$304$	−6.38144	+	3.68432i	−0.366001	+	0.211311i
$305$	−8.58754	−	4.86216i	−0.491721	−	0.278407i
$306$	10.0446	+	19.9511i	0.574213	+	1.14053i
$307$	23.8364	−	1.24921i	1.36042	−	0.0712964i	0.641891	−	0.766796i	$-0.278150\pi$
$307$	23.8364	−	1.24921i	1.36042	−	0.0712964i	0.718526	+	0.695500i	$0.244817\pi$
$308$	−0.701415	+	0.357389i	−0.0399668	+	0.0203641i
$309$	12.6021	+	3.05768i	0.716909	+	0.173945i
$310$	−11.0955	+	5.64703i	−0.630185	+	0.320730i
$311$			25.1498i			1.42611i	0.701106	+	0.713057i	$0.252690\pi$
$311$			25.1498i			1.42611i	−0.701106	+	0.713057i	$0.747310\pi$
$312$	6.14304	−	1.45915i	0.347781	−	0.0826079i
$313$	0.639226	+	12.1972i	0.0361312	+	0.689425i	0.955314	+	0.295593i	$0.0955173\pi$
$313$	0.639226	+	12.1972i	0.0361312	+	0.689425i	−0.919183	+	0.393831i	$0.871149\pi$
$314$	−7.24316	−	5.26246i	−0.408755	−	0.296978i
$315$	0.787133	+	0.164362i	0.0443499	+	0.00926077i
$316$	−1.37452	−	2.38073i	−0.0773226	−	0.133927i
$317$	−22.1953	−	27.4089i	−1.24661	−	1.53944i	−0.730489	−	0.682925i	$-0.760708\pi$
$317$	−22.1953	−	27.4089i	−1.24661	−	1.53944i	−0.516124	−	0.856514i	$-0.672626\pi$
$318$	−9.57109	−	3.99156i	−0.536720	−	0.223835i
$319$	25.7788	−	2.70946i	1.44333	−	0.151701i
$320$	1.51015	+	1.64908i	0.0844198	+	0.0921862i
$321$	−27.0699	+	4.94958i	−1.51090	+	0.276259i
$322$	0.413262	+	0.268375i	0.0230302	+	0.0149560i
$323$	29.8814	+	46.0133i	1.66264	+	2.56025i
$324$	−8.82098	+	1.78615i	−0.490054	+	0.0992305i
$325$	−16.3771	−	8.00043i	−0.908440	−	0.443784i
$326$	−12.9454	+	4.20621i	−0.716978	+	0.232960i
$327$	−30.2048	+	3.90241i	−1.67033	+	0.215804i
$328$	−3.53803	+	2.29762i	−0.195355	+	0.126865i
$329$	0.196290	−	0.0417228i	0.0108218	−	0.00230025i
$330$	−24.9808	+	4.78509i	−1.37515	+	0.263411i
$331$	−14.0781	−	15.6353i	−0.773801	−	0.859393i	0.219420	−	0.975630i	$-0.429583\pi$
$331$	−14.0781	−	15.6353i	−0.773801	−	0.859393i	−0.993221	+	0.116237i	$0.962917\pi$
$332$	3.29493	+	2.66818i	0.180833	+	0.146435i
$333$	−10.1162	+	13.7834i	−0.554365	+	0.755326i
$334$	−4.25088	−	0.446785i	−0.232598	−	0.0244470i
$335$	−2.27693	−	0.589619i	−0.124402	−	0.0322143i
$336$	0.150257	+	0.143279i	0.00819720	+	0.00781653i
$337$	2.07524	+	13.1025i	0.113045	+	0.713740i	0.977485	+	0.211004i	$0.0676732\pi$
$337$	2.07524	+	13.1025i	0.113045	+	0.713740i	−0.864440	+	0.502736i	$0.832327\pi$
$338$	−0.288307	+	0.0151095i	−0.0156819	+	0.000821851i
$339$	1.57326	+	0.969326i	0.0854479	+	0.0526466i
$340$	11.6732	−	11.8713i	0.633068	−	0.643809i
$341$	21.7540	−	29.3899i	1.17805	−	1.59155i
$342$	−21.0567	+	6.72957i	−1.13862	+	0.363894i
$343$	0.761094	+	1.49373i	0.0410952	+	0.0806539i
$344$	−1.69863	+	1.88652i	−0.0915842	+	0.101715i
$345$	10.4123	+	12.0442i	0.560579	+	0.648437i
$346$	3.54190	−	6.13475i	0.190414	−	0.329806i
$347$	14.2225	+	3.81091i	0.763504	+	0.204580i	0.619500	−	0.784997i	$-0.287336\pi$
$347$	14.2225	+	3.81091i	0.763504	+	0.204580i	0.144004	+	0.989577i	$0.454002\pi$
$348$	−2.92822	−	6.17746i	−0.156969	−	0.331147i
$349$	−3.75747	−	5.17172i	−0.201133	−	0.276836i	0.696521	−	0.717536i	$-0.254730\pi$
$349$	−3.75747	−	5.17172i	−0.201133	−	0.276836i	−0.897654	+	0.440700i	$0.854730\pi$
$350$	−0.0726677	−	0.594927i	−0.00388425	−	0.0318002i
$351$	18.9385	−	0.358755i	1.01086	−	0.0191489i
$352$	−6.13108	−	2.35350i	−0.326788	−	0.125442i
$353$	20.1067	+	13.0574i	1.07017	+	0.694978i	0.954470	−	0.298306i	$-0.0964216\pi$
$353$	20.1067	+	13.0574i	1.07017	+	0.694978i	0.115702	+	0.993284i	$0.463088\pi$
$354$	−10.4587	−	5.01956i	−0.555874	−	0.266787i
$355$	12.1762	+	5.29892i	0.646246	+	0.281238i
$356$	9.26725	−	3.01111i	0.491163	−	0.159589i
$357$	1.00680	−	1.17307i	0.0532854	−	0.0620852i
$358$	6.37267	−	2.44624i	0.336806	−	0.129288i
$359$	−0.163128	−	0.0346739i	−0.00860956	−	0.00183002i	0.203605	−	0.979053i	$-0.434734\pi$
$359$	−0.163128	−	0.0346739i	−0.00860956	−	0.00183002i	−0.212214	+	0.977223i	$0.568068\pi$
$360$	3.37491	+	5.79741i	0.177874	+	0.305550i
$361$	−32.2454	+	14.3566i	−1.69713	+	0.755610i
$362$	6.70199	+	0.351236i	0.352249	+	0.0184606i
$363$	44.2311	−	33.7705i	2.32153	−	1.77249i
$364$	−0.256844	−	0.353515i	−0.0134623	−	0.0185292i
$365$	14.8524	−	12.2355i	0.777410	−	0.640436i
$366$	−2.15334	−	7.33451i	−0.112557	−	0.383381i
$367$	19.5083	−	5.22722i	1.01832	−	0.272859i	0.289220	−	0.957263i	$-0.406604\pi$
$367$	19.5083	−	5.22722i	1.01832	−	0.272859i	0.729103	+	0.684404i	$0.239937\pi$
$368$	0.643068	+	4.06017i	0.0335223	+	0.211651i
$369$	−11.8370	+	4.47837i	−0.616209	+	0.233135i
$370$	12.1526	+	3.83591i	0.631784	+	0.199419i
$371$			0.717679i			0.0372600i
$372$	−9.21502	−	2.84312i	−0.477777	−	0.147409i
$373$	2.87104	−	2.87104i	0.148657	−	0.148657i	−0.628861	−	0.777518i	$-0.716479\pi$
$373$	2.87104	−	2.87104i	0.148657	−	0.148657i	0.777518	+	0.628861i	$0.216479\pi$
$374$	−15.1102	+	46.5045i	−0.781332	+	2.40469i
$375$	3.09354	−	19.1162i	0.159749	−	0.987158i
$376$	1.35439	+	0.984019i	0.0698471	+	0.0507469i
$377$	3.72392	+	13.8979i	0.191792	+	0.715776i
$378$	0.349067	+	0.515856i	0.0179541	+	0.0265328i
$379$	−13.2046	−	1.38786i	−0.678274	−	0.0712895i	−0.240874	−	0.970556i	$-0.577434\pi$
$379$	−13.2046	−	1.38786i	−0.678274	−	0.0712895i	−0.437400	+	0.899267i	$0.644101\pi$
$380$	9.79661	+	13.2481i	0.502555	+	0.679612i
$381$	−32.3130	−	4.33343i	−1.65544	−	0.222009i
$382$	−0.738444	+	14.0903i	−0.0377821	+	0.720925i
$383$	27.8414	+	10.6873i	1.42263	+	0.546096i	0.943419	−	0.331604i	$-0.107590\pi$
$383$	27.8414	+	10.6873i	1.42263	+	0.546096i	0.479210	+	0.877700i	$0.340923\pi$
$384$	−0.0495177	+	1.73134i	−0.00252694	+	0.0883522i
$385$	0.971096	+	1.46817i	0.0494916	+	0.0748249i
$386$	2.32025	−	5.21137i	0.118098	−	0.265252i
$387$	−6.18277	+	4.44661i	−0.314288	+	0.226034i
$388$	−14.4621	−	7.36882i	−0.734203	−	0.374095i
$389$	−24.7132	−	11.0030i	−1.25301	−	0.557875i	−0.330483	−	0.943812i	$-0.607212\pi$
$389$	−24.7132	−	11.0030i	−1.25301	−	0.557875i	−0.922525	+	0.385936i	$0.873878\pi$
$390$	−4.79259	−	13.2801i	−0.242682	−	0.672465i
$391$	29.9387	−	6.36367i	1.51407	−	0.321825i
$392$	−2.50343	+	6.52165i	−0.126442	+	0.329393i
$393$	24.1608	+	7.22021i	1.21875	+	0.364211i
$394$	−2.11348	+	0.222136i	−0.106476	+	0.0111910i
$395$	−4.94248	+	3.65484i	−0.248683	+	0.183895i
$396$	−16.4714	−	10.8100i	−0.827717	−	0.543223i
$397$	8.52165	−	31.8032i	0.427689	−	1.59616i	−0.330290	−	0.943880i	$-0.607146\pi$
$397$	8.52165	−	31.8032i	0.427689	−	1.59616i	0.757979	−	0.652279i	$-0.226187\pi$
$398$	11.6967	−	3.13412i	0.586302	−	0.157099i
$399$	0.990769	+	1.16573i	0.0496005	+	0.0583593i
$400$	3.28267	−	3.77148i	0.164133	−	0.188574i
$401$	−10.3613	−	3.36660i	−0.517420	−	0.168120i	0.0386541	−	0.999253i	$-0.487693\pi$
$401$	−10.3613	−	3.36660i	−0.517420	−	0.168120i	−0.556074	+	0.831133i	$0.687693\pi$
$402$	−0.948177	−	1.55570i	−0.0472908	−	0.0775912i
$403$	18.0019	+	9.37453i	0.896738	+	0.466978i
$404$	−10.1685			−0.505902
$405$	6.19511	+	19.1473i	0.307837	+	0.951439i
$406$	−0.316580	+	0.351597i	−0.0157116	+	0.0174495i
$407$	−36.9669	+	5.85498i	−1.83238	+	0.290221i
$408$	12.8926	−	0.306476i	0.638281	−	0.0151728i
$409$	−1.33420	+	0.770299i	−0.0659718	+	0.0380888i	−0.532623	−	0.846353i	$-0.678794\pi$
$409$	−1.33420	+	0.770299i	−0.0659718	+	0.0380888i	0.466651	+	0.884441i	$0.345460\pi$
$410$	5.99790	+	7.28070i	0.296215	+	0.359568i
$411$	12.2009	−	5.01933i	0.601827	−	0.247585i
$412$	4.71168	−	5.81844i	0.232128	−	0.286654i
$413$	−0.0420184	+	0.801759i	−0.00206759	+	0.0394520i
$414$	−0.704852	+	12.3122i	−0.0346416	+	0.605111i
$415$	5.09635	−	7.99411i	0.250170	−	0.392415i
$416$	0.757914	−	3.56571i	0.0371598	−	0.174823i
$417$	9.75408	−	1.26021i	0.477659	−	0.0617128i
$418$	−43.1175	−	21.9695i	−2.10895	−	1.07456i
$419$	−10.2615	−	31.5818i	−0.501309	−	1.54287i	−0.806888	−	0.590704i	$-0.798850\pi$
$419$	−10.2615	−	31.5818i	−0.501309	−	1.54287i	0.305579	−	0.952167i	$-0.401150\pi$
$420$	0.280405	−	0.370006i	0.0136824	−	0.0180544i
$421$	19.9097	+	4.23193i	0.970337	+	0.206251i	0.665702	−	0.746218i	$-0.268132\pi$
$421$	19.9097	+	4.23193i	0.970337	+	0.206251i	0.304635	+	0.952469i	$0.401466\pi$
$422$	8.25801	−	12.7162i	0.401994	−	0.619016i
$423$	3.34255	+	3.74850i	0.162520	+	0.182258i
$424$	−4.44933	+	4.00619i	−0.216078	+	0.194558i
$425$	−29.3219	−	22.9385i	−1.42232	−	1.11268i
$426$	3.91337	+	9.51256i	0.189603	+	0.460885i
$427$	−0.411127	+	0.332924i	−0.0198958	+	0.0161113i
$428$	−4.11210	+	15.3466i	−0.198766	+	0.741804i
$429$	30.0091	+	28.6155i	1.44885	+	1.38157i
$430$	4.62022	+	3.29776i	0.222807	+	0.159032i
$431$	6.44866	+	5.80640i	0.310621	+	0.279684i	0.809665	−	0.586892i	$-0.199649\pi$
$431$	6.44866	+	5.80640i	0.310621	+	0.279684i	−0.499044	+	0.866577i	$0.666315\pi$
$432$	−1.24956	+	5.04367i	−0.0601195	+	0.242664i
$433$	19.1960	−	19.1960i	0.922501	−	0.922501i	−0.0747045	−	0.997206i	$-0.523801\pi$
$433$	19.1960	−	19.1960i	0.922501	−	0.922501i	0.997206	+	0.0747045i	$0.0238014\pi$
$434$	0.0638711	+	0.664343i	0.00306591	+	0.0318895i
$435$	−12.9857	+	8.06523i	−0.622619	+	0.386698i
$436$	−5.43366	+	16.7231i	−0.260225	+	0.800891i
$437$	1.58530	+	30.2494i	0.0758354	+	1.44703i
$438$	14.8569	+	1.20534i	0.709891	+	0.0575936i
$439$	26.9957	+	15.5859i	1.28843	+	0.743877i	0.978375	−	0.206841i	$-0.0663183\pi$
$439$	26.9957	+	15.5859i	1.28843	+	0.743877i	0.310058	+	0.950718i	$0.399652\pi$
$440$	−3.68127	+	14.2160i	−0.175498	+	0.677719i
$441$	−11.4986	+	17.5206i	−0.547554	+	0.834316i
$442$	−26.8080	−	4.24598i	−1.27513	−	0.201961i
$443$	−4.40798	+	5.44341i	−0.209430	+	0.258624i	−0.871027	−	0.491235i	$-0.836546\pi$
$443$	−4.40798	+	5.44341i	−0.209430	+	0.258624i	0.661597	+	0.749859i	$0.269879\pi$
$444$	4.68917	+	8.68630i	0.222538	+	0.412233i
$445$	−9.02935	−	19.8296i	−0.428032	−	0.940015i
$446$	1.10427	+	5.19520i	0.0522889	+	0.246000i
$447$	1.89819	+	5.40171i	0.0897813	+	0.255492i
$448$	0.111908	−	0.0429574i	0.00528715	−	0.00202955i
$449$	4.16720	+	12.8253i	0.196662	+	0.605264i	0.999953	+	0.00967706i	$0.00308035\pi$
$449$	4.16720	+	12.8253i	0.196662	+	0.605264i	−0.803291	+	0.595587i	$0.796920\pi$
$450$	12.0286	−	8.96174i	0.567034	−	0.422460i
$451$	−25.3096	−	11.2685i	−1.19178	−	0.530615i
$452$	0.894768	−	0.581069i	0.0420863	−	0.0273312i
$453$	−8.72012	−	9.23361i	−0.409707	−	0.433833i
$454$	2.00850	+	4.51115i	0.0942634	+	0.211719i
$455$	−0.720596	+	0.659887i	−0.0337820	+	0.0309360i
$456$	−1.69642	+	12.6496i	−0.0794421	+	0.592373i
$457$	34.2039	+	5.41736i	1.59999	+	0.253414i	0.891740	−	0.452548i	$-0.149485\pi$
$457$	34.2039	+	5.41736i	1.59999	+	0.253414i	0.708250	+	0.705962i	$0.249485\pi$
$458$	17.1089	−	13.8545i	0.799445	−	0.647378i
$459$	37.9890	+	7.32568i	1.77317	+	0.341933i
$460$	8.85846	−	2.45367i	0.413028	−	0.114403i
$461$	17.9960	−	24.7694i	0.838159	−	1.15363i	−0.148190	−	0.988959i	$-0.547345\pi$
$461$	17.9960	−	24.7694i	0.838159	−	1.15363i	0.986349	−	0.164668i	$-0.0526552\pi$
$462$	−0.251712	+	1.34006i	−0.0117107	+	0.0623454i
$463$	−11.1506	−	21.8843i	−0.518214	−	1.01705i	−0.990745	−	0.135738i	$-0.956660\pi$
$463$	−11.1506	−	21.8843i	−0.518214	−	1.01705i	0.472531	−	0.881314i	$-0.343340\pi$
$464$	−3.94696			−0.183233
$465$	−3.99061	+	21.1914i	−0.185060	+	0.982727i
$466$	6.09858			0.282511
$467$	−3.16280	−	6.20734i	−0.146357	−	0.287241i	0.806177	−	0.591675i	$-0.201533\pi$
$467$	−3.16280	−	6.20734i	−0.146357	−	0.287241i	−0.952534	+	0.304433i	$0.901533\pi$
$468$	4.49628	−	9.96904i	0.207840	−	0.460819i
$469$	−0.0741117	+	0.102006i	−0.00342216	+	0.00471020i
$470$	1.84438	−	3.25754i	0.0850749	−	0.150259i
$471$	−14.8791	+	4.36837i	−0.685594	+	0.201284i
$472$	−5.20515	+	4.21505i	−0.239586	+	0.194013i
$473$	−16.4662	−	2.60799i	−0.757118	−	0.119916i
$474$	−4.71922	−	0.632886i	−0.216761	−	0.0290694i
$475$	26.9613	−	25.1101i	1.23707	−	1.15213i
$476$	−0.363017	−	0.815349i	−0.0166388	−	0.0373714i
$477$	−15.5983	+	8.90557i	−0.714195	+	0.407758i
$478$	5.77658	−	3.75136i	0.264215	−	0.171583i
$479$	−30.1770	−	13.4356i	−1.37882	−	0.613890i	−0.422541	−	0.906344i	$-0.638862\pi$
$479$	−30.1770	−	13.4356i	−1.37882	−	0.613890i	−0.956280	+	0.292454i	$0.905528\pi$
$480$	3.85915	−	0.327027i	0.176145	−	0.0149267i
$481$	−6.41995	−	19.7586i	−0.292725	−	0.900914i
$482$	−1.97678	+	0.758816i	−0.0900400	+	0.0345631i
$483$	0.805213	−	0.282956i	0.0366385	−	0.0128750i
$484$	−6.68001	−	31.4270i	−0.303637	−	1.42850i
$485$	−12.7212	+	33.9917i	−0.577638	+	1.54348i
$486$	−6.88027	+	13.9879i	−0.312095	+	0.634505i
$487$	−12.2714	+	15.1540i	−0.556072	+	0.686691i	−0.975223	−	0.221225i	$-0.928994\pi$
$487$	−12.2714	+	15.1540i	−0.556072	+	0.686691i	0.419151	+	0.907917i	$0.362328\pi$
$488$	−4.35897	−	0.690393i	−0.197321	−	0.0312526i
$489$	−7.92342	+	22.2046i	−0.358309	+	1.00413i
$490$	15.1216	+	3.91578i	0.683123	+	0.176897i
$491$	15.2879	+	8.82649i	0.689935	+	0.398334i	0.803588	−	0.595187i	$-0.202922\pi$
$491$	15.2879	+	8.82649i	0.689935	+	0.398334i	−0.113653	+	0.993521i	$0.536255\pi$
$492$	−0.590864	+	7.28292i	−0.0266382	+	0.328339i
$493$	1.53804	+	29.3475i	0.0692697	+	1.32175i
$494$	8.30064	−	25.5467i	0.373463	−	1.14940i
$495$	−19.8595	+	39.3244i	−0.892618	+	1.76750i
$496$	−3.76213	+	4.10444i	−0.168924	+	0.184295i
$497$	0.503365	−	0.503365i	0.0225790	−	0.0225790i
$498$	7.14472	−	1.69707i	0.320163	−	0.0760477i
$499$	−4.11853	−	3.70834i	−0.184371	−	0.166008i	0.571777	−	0.820409i	$-0.306254\pi$
$499$	−4.11853	−	3.70834i	−0.184371	−	0.166008i	−0.756148	+	0.654401i	$0.772921\pi$
$500$	−9.20803	−	6.34131i	−0.411795	−	0.283592i
$501$	−5.10904	+	5.35785i	−0.228255	+	0.239371i
$502$	−2.41230	+	9.00283i	−0.107666	+	0.401816i
$503$	−24.9582	+	20.2107i	−1.11283	+	0.901151i	−0.995762	−	0.0919726i	$-0.970683\pi$
$503$	−24.9582	+	20.2107i	−1.11283	+	0.901151i	−0.117068	+	0.993124i	$0.537349\pi$
$504$	0.355449	−	0.0545405i	0.0158330	−	0.00242943i
$505$	2.56684	+	22.5921i	0.114223	+	1.00534i
$506$	−20.0624	+	18.0643i	−0.891883	+	0.803055i
$507$	−0.284224	+	0.411418i	−0.0126228	+	0.0182717i
$508$	−10.2517	+	15.7862i	−0.454846	+	0.700401i
$509$	−25.2494	−	5.36692i	−1.11916	−	0.237884i	−0.389050	−	0.921217i	$-0.627197\pi$
$509$	−25.2494	−	5.36692i	−1.11916	−	0.237884i	−0.730108	+	0.683332i	$0.760530\pi$
$510$	−3.93542	−	28.5672i	−0.174263	−	1.26498i
$511$	−0.318775	−	0.981089i	−0.0141018	−	0.0434008i
$512$	0.891007	+	0.453990i	0.0393773	+	0.0200637i
$513$	−13.0419	+	35.9990i	−0.575816	+	1.58939i
$514$	1.10753	−	5.21051i	0.0488509	−	0.229826i
$515$	−14.1166	−	8.99954i	−0.622054	−	0.396567i
$516$	0.790842	+	4.32522i	0.0348149	+	0.190407i
$517$	−0.575400	+	10.9793i	−0.0253061	+	0.482869i
$518$	0.429922	−	0.530909i	0.0188897	−	0.0233268i
$519$	−4.66797	−	11.3468i	−0.204901	−	0.498071i
$520$	−8.11352	−	0.783820i	−0.355801	−	0.0343728i
$521$	31.9177	−	18.4277i	1.39834	−	0.807332i	0.404121	−	0.914705i	$-0.367577\pi$
$521$	31.9177	−	18.4277i	1.39834	−	0.807332i	0.994219	+	0.107374i	$0.0342441\pi$
$522$	−11.5701	−	2.51772i	−0.506410	−	0.110198i
$523$	36.1747	−	5.72950i	1.58181	−	0.250534i	0.697202	−	0.716874i	$-0.254428\pi$
$523$	36.1747	−	5.72950i	1.58181	−	0.250534i	0.884605	+	0.466341i	$0.154428\pi$
$524$	9.74173	−	10.8193i	0.425569	−	0.472643i
$525$	−0.892852	−	0.529595i	−0.0389672	−	0.0231134i
$526$	12.2433			0.533831
$527$	31.9844	+	26.3738i	1.39326	+	1.14886i
$528$	−9.71297	+	5.91992i	−0.422703	+	0.257632i
$529$	−5.80282	−	1.88545i	−0.252297	−	0.0819762i
$530$	10.0240	+	8.87411i	0.435415	+	0.385467i
$531$	−17.9471	+	9.03567i	−0.778838	+	0.392115i
$532$	0.853181	−	0.228609i	0.0369901	−	0.00991146i
$533$	3.98022	−	14.8544i	0.172402	−	0.643415i
$534$	5.67216	−	15.8957i	0.245458	−	0.687874i
$535$	35.1346	+	5.26221i	1.51900	+	0.227505i
$536$	−1.04610	+	0.109949i	−0.0451846	+	0.00474909i
$537$	3.38528	−	11.3281i	0.146086	−	0.488842i
$538$	3.22527	−	8.40212i	0.139051	−	0.362241i
$539$	−44.8740	+	9.53827i	−1.93286	+	0.410842i
$540$	11.5213	+	1.50307i	0.495799	+	0.0646816i
$541$	−26.5243	−	11.8094i	−1.14037	−	0.507725i	−0.252398	−	0.967623i	$-0.581219\pi$
$541$	−26.5243	−	11.8094i	−1.14037	−	0.507725i	−0.887972	+	0.459898i	$0.847886\pi$
$542$	−0.391921	−	0.199693i	−0.0168344	−	0.00857757i
$543$	7.57057	−	8.82081i	0.324884	−	0.378537i
$544$	3.02843	−	6.80196i	0.129843	−	0.291632i
$545$	38.5265	+	7.85094i	1.65030	+	0.336297i
$546$	−0.756543	−	0.0216377i	−0.0323771	−	0.000926008i
$547$	−10.7066	−	4.10988i	−0.457781	−	0.175726i	0.118539	−	0.992949i	$-0.462179\pi$
$547$	−10.7066	−	4.10988i	−0.457781	−	0.175726i	−0.576321	+	0.817224i	$0.695512\pi$
$548$	0.398643	−	7.60657i	0.0170292	−	0.324936i
$549$	−12.3375	−	4.80436i	−0.526551	−	0.205045i
$550$	32.5139	+	4.59041i	1.38640	+	0.195736i
$551$	−28.9244	−	3.04008i	−1.23222	−	0.129512i
$552$	6.24904	+	3.41250i	0.265977	+	0.145246i
$553$	0.0852876	+	0.318298i	0.00362680	+	0.0135354i
$554$	5.72138	+	4.15683i	0.243078	+	0.176607i
$555$	18.1153	−	12.6110i	0.768951	−	0.535306i
$556$	1.75470	−	5.40041i	0.0744158	−	0.229028i
$557$	−0.844294	+	0.844294i	−0.0357739	+	0.0357739i	−0.724767	−	0.688994i	$-0.758053\pi$
$557$	−0.844294	+	0.844294i	−0.0357739	+	0.0357739i	0.688994	+	0.724767i	$0.258053\pi$
$558$	−13.6465	+	9.63192i	−0.577701	+	0.407752i
$559$		−	9.25401i		−	0.391403i
$560$	−0.123691	−	0.237790i	−0.00522689	−	0.0100485i
$561$	47.8023	+	69.9136i	2.01822	+	2.95176i
$562$	−2.19623	−	13.8665i	−0.0926426	−	0.584922i
$563$	−40.2148	+	10.7755i	−1.69485	+	0.454134i	−0.971635	−	0.236487i	$-0.924004\pi$
$563$	−40.2148	+	10.7755i	−1.69485	+	0.454134i	−0.723217	+	0.690621i	$0.757337\pi$
$564$	2.78222	−	0.816834i	0.117153	−	0.0343949i
$565$	−1.51687	−	1.84129i	−0.0638152	−	0.0774637i
$566$	−0.718558	−	0.989010i	−0.0302032	−	0.0415712i
$567$	1.07675	+	0.0668572i	0.0452194	+	0.00280774i
$568$	5.93053	+	0.310806i	0.248839	+	0.0130411i
$569$	18.9511	−	8.43755i	0.794469	−	0.353721i	0.0309628	−	0.999521i	$-0.490143\pi$
$569$	18.9511	−	8.43755i	0.794469	−	0.353721i	0.763507	+	0.645800i	$0.223476\pi$
$570$	28.5328	+	0.575901i	1.19511	+	0.0241218i
$571$	10.0465	+	2.13546i	0.420434	+	0.0893661i	0.413271	−	0.910608i	$-0.364386\pi$
$571$	10.0465	+	2.13546i	0.420434	+	0.0893661i	0.00716374	+	0.999974i	$0.497720\pi$
$572$	22.3500	−	8.57937i	0.934502	−	0.358722i
$573$	18.5450	+	15.9164i	0.774727	+	0.664919i
$574$	0.480934	−	0.156265i	0.0200738	−	0.00652237i
$575$	−7.68764	−	19.0621i	−0.320597	−	0.794945i
$576$	2.32230	+	1.89919i	0.0967625	+	0.0791329i
$577$	16.2684	+	10.5648i	0.677261	+	0.439818i	0.836899	−	0.547357i	$-0.184366\pi$
$577$	16.2684	+	10.5648i	0.677261	+	0.439818i	−0.159638	+	0.987176i	$0.551033\pi$
$578$	−35.8850	−	13.7750i	−1.49262	−	0.572963i
$579$	−4.69364	−	8.69457i	−0.195061	−	0.361334i
$580$	0.996334	+	8.76925i	0.0413705	+	0.364123i
$581$	−0.298725	−	0.411159i	−0.0123932	−	0.0170578i
$582$	−25.4038	+	12.0418i	−1.05302	+	0.499149i
$583$	−37.9795	−	10.1766i	−1.57295	−	0.421471i
$584$	4.30292	−	7.45287i	0.178056	−	0.308402i
$585$	−23.2840	−	7.47322i	−0.962673	−	0.308979i
$586$	−4.79990	+	5.33083i	−0.198282	+	0.220214i
$587$	3.53578	+	6.93936i	0.145937	+	0.286418i	0.952391	−	0.304879i	$-0.0986161\pi$
$587$	3.53578	+	6.93936i	0.145937	+	0.286418i	−0.806454	+	0.591297i	$0.798616\pi$
$588$	6.29704	+	10.3317i	0.259686	+	0.426073i
$589$	−30.7313	+	27.1808i	−1.26626	+	1.11996i
$590$	10.6788	+	10.5007i	0.439640	+	0.432305i
$591$	−1.93079	+	3.13377i	−0.0794222	+	0.128906i
$592$	5.69131	−	0.298269i	0.233912	−	0.0122588i
$593$	4.89697	+	30.9183i	0.201094	+	1.26966i	0.857197	+	0.514989i	$0.172204\pi$
$593$	4.89697	+	30.9183i	0.201094	+	1.26966i	−0.656103	+	0.754672i	$0.727796\pi$
$594$	−32.2488	+	11.1579i	−1.32319	+	0.457812i
$595$	−1.71988	+	1.01236i	−0.0705084	+	0.0415027i
$596$	3.28752	+	0.345533i	0.134662	+	0.0141536i
$597$	8.07311	−	19.3580i	0.330410	−	0.792269i
$598$	−11.6458	−	9.43057i	−0.476231	−	0.385645i
$599$	7.31303	+	8.12194i	0.298802	+	0.331854i	0.873785	−	0.486312i	$-0.161658\pi$
$599$	7.31303	+	8.12194i	0.298802	+	0.331854i	−0.574983	+	0.818165i	$0.694991\pi$
$600$	−1.70075	−	8.49161i	−0.0694328	−	0.346669i
$601$	42.3148	−	8.99429i	1.72606	−	0.366885i	0.765171	−	0.643828i	$-0.222655\pi$
$601$	42.3148	−	8.99429i	1.72606	−	0.366885i	0.960886	+	0.276943i	$0.0893213\pi$
$602$	0.255205	−	0.165732i	0.0104014	−	0.00675474i
$603$	−3.13667	−	0.344990i	−0.127735	−	0.0140491i
$604$	−6.97369	+	2.26589i	−0.283756	+	0.0921978i
$605$	−68.1374	+	22.7746i	−2.77018	+	0.925920i
$606$	−10.7554	+	13.9469i	−0.436909	+	0.566555i
$607$	23.4020	+	36.0360i	0.949860	+	1.46266i	0.885451	+	0.464732i	$0.153849\pi$
$607$	23.4020	+	36.0360i	0.949860	+	1.46266i	0.0644087	+	0.997924i	$0.479484\pi$
$608$	6.17987	+	4.01325i	0.250627	+	0.162759i
$609$	0.147392	+	0.806105i	0.00597261	+	0.0326650i
$610$	−0.433559	+	9.85893i	−0.0175543	+	0.399176i
$611$	−6.06933	+	0.637912i	−0.245539	+	0.0258072i
$612$	13.2164	−	18.0075i	0.534242	−	0.727908i
$613$	−1.99580	−	2.46460i	−0.0806094	−	0.0995443i	0.735246	−	0.677801i	$-0.237067\pi$
$613$	−1.99580	−	2.46460i	−0.0806094	−	0.0995443i	−0.815855	+	0.578256i	$0.803733\pi$
$614$	−11.9346	−	20.6713i	−0.481640	−	0.834225i
$615$	16.3302	−	0.525667i	0.658495	−	0.0211969i
$616$	0.636872	+	0.462714i	0.0256603	+	0.0186433i
$617$	−1.81433	−	34.6195i	−0.0730421	−	1.39373i	−0.751813	−	0.659377i	$-0.770820\pi$
$617$	−1.81433	−	34.6195i	−0.0730421	−	1.39373i	0.678771	−	0.734350i	$-0.262513\pi$
$618$	−2.99683	−	12.6167i	−0.120550	−	0.507519i
$619$			7.66095i			0.307920i	0.988077	+	0.153960i	$0.0492027\pi$
$619$			7.66095i			0.307920i	−0.988077	+	0.153960i	$0.950797\pi$
$620$	10.0688	+	7.32251i	0.404373	+	0.294079i
$621$	16.1416	+	13.9896i	0.647741	+	0.561383i
$622$	22.4086	−	11.4178i	0.898504	−	0.457811i
$623$	−1.16643	+	0.0611300i	−0.0467320	+	0.00244912i
$624$	−4.08899	−	4.81105i	−0.163691	−	0.192596i
$625$	−11.7646	+	22.0589i	−0.470583	+	0.882356i
$626$	10.5776	−	6.10695i	0.422764	−	0.244083i
$627$	−75.7391	+	35.9016i	−3.02473	+	1.43377i
$628$	−1.40056	+	8.84281i	−0.0558886	+	0.352867i
$629$	−4.43554	−	42.2014i	−0.176857	−	1.68268i
$630$	−0.210903	−	0.775959i	−0.00840257	−	0.0309150i
$631$	15.1871	−	6.76172i	0.604588	−	0.269180i	−0.0815294	−	0.996671i	$-0.525980\pi$
$631$	15.1871	−	6.76172i	0.604588	−	0.269180i	0.686117	+	0.727491i	$0.259314\pi$
$632$	−1.49723	+	2.30553i	−0.0595567	+	0.0917092i
$633$	−8.70667	−	24.7767i	−0.346059	−	0.984786i
$634$	−14.3451	+	32.2196i	−0.569716	+	1.27960i
$635$	37.6613	+	18.7920i	1.49454	+	0.745739i
$636$	0.788678	+	10.3400i	0.0312731	+	0.410009i
$637$	−9.12591	−	23.7738i	−0.361582	−	0.941952i
$638$	−14.1175	−	21.7390i	−0.558916	−	0.860655i
$639$	17.1865	+	4.69411i	0.679886	+	0.185696i
$640$	0.783747	−	2.09422i	0.0309803	−	0.0827812i
$641$	28.3478	−	25.5245i	1.11967	−	1.00816i	0.119788	−	0.992800i	$-0.461779\pi$
$641$	28.3478	−	25.5245i	1.11967	−	1.00816i	0.999882	−	0.0153558i	$-0.00488810\pi$
$642$	16.6996	+	21.8724i	0.659080	+	0.863235i
$643$	−5.59617	+	35.3328i	−0.220691	+	1.39339i	0.589757	+	0.807581i	$0.299224\pi$
$643$	−5.59617	+	35.3328i	−0.220691	+	1.39339i	−0.810448	+	0.585810i	$0.800776\pi$
$644$	0.0515073	−	0.490059i	0.00202967	−	0.0193110i
$645$	9.41004	−	2.84889i	0.370520	−	0.112175i
$646$	27.4323	−	47.5141i	1.07931	−	1.86942i
$647$	−7.96588	+	1.26167i	−0.313171	+	0.0496014i	−0.311042	−	0.950396i	$-0.600678\pi$
$647$	−7.96588	+	1.26167i	−0.313171	+	0.0496014i	−0.00212944	+	0.999998i	$0.500678\pi$
$648$	5.59611	+	7.04865i	0.219836	+	0.276897i
$649$	−41.8333	−	13.5925i	−1.64210	−	0.533550i
$650$	0.306630	+	18.2243i	0.0120270	+	0.714814i
$651$	0.978757	+	0.615083i	0.0383605	+	0.0241070i
$652$	9.62484	+	9.62484i	0.376938	+	0.376938i
$653$	27.5067	−	14.0154i	1.07642	−	0.548464i	0.176404	−	0.984318i	$-0.443554\pi$
$653$	27.5067	−	14.0154i	1.07642	−	0.548464i	0.900017	+	0.435854i	$0.143554\pi$
$654$	17.1898	+	25.1410i	0.672173	+	0.983092i
$655$	−26.4971	−	18.9128i	−1.03533	−	0.738984i
$656$	3.65342	+	2.10931i	0.142642	+	0.0823546i
$657$	17.3677	−	19.1025i	0.677577	−	0.745261i
$658$	−0.126289	−	0.155954i	−0.00492326	−	0.00607972i
$659$	−1.56805	+	1.13926i	−0.0610826	+	0.0443791i	−0.617908	−	0.786251i	$-0.712019\pi$
$659$	−1.56805	+	1.13926i	−0.0610826	+	0.0443791i	0.556825	+	0.830630i	$0.312019\pi$
$660$	15.6046	+	20.0856i	0.607408	+	0.781833i
$661$	−19.7321	−	21.9148i	−0.767491	−	0.852385i	0.225043	−	0.974349i	$-0.427748\pi$
$661$	−19.7321	−	21.9148i	−0.767491	−	0.852385i	−0.992535	+	0.121963i	$0.961081\pi$
$662$	−7.53983	+	19.6419i	−0.293044	+	0.763405i
$663$	−34.1791	+	32.2783i	−1.32740	+	1.25359i
$664$	0.881499	−	4.14713i	0.0342088	−	0.160940i
$665$	−0.723287	−	1.83787i	−0.0280479	−	0.0712694i
$666$	16.8738	+	2.75608i	0.653845	+	0.106796i
$667$	−7.36604	+	14.4567i	−0.285214	+	0.559765i
$668$	1.53177	+	3.99040i	0.0592660	+	0.154393i
$669$	8.29365	+	3.98046i	0.320651	+	0.153894i
$670$	0.508351	+	2.29644i	0.0196393	+	0.0887193i
$671$	−11.7886	−	26.4776i	−0.455094	−	1.02216i
$672$	0.0594475	−	0.198928i	0.00229324	−	0.00767380i
$673$	−18.0715	−	14.6340i	−0.696604	−	0.564099i	0.214274	−	0.976774i	$-0.431261\pi$
$673$	−18.0715	−	14.6340i	−0.696604	−	0.564099i	−0.910879	+	0.412674i	$0.864595\pi$
$674$	10.7323	−	7.79747i	0.413393	−	0.300347i
$675$	0.431135	−	25.9772i	0.0165944	−	0.999862i
$676$	0.144351	+	0.250024i	0.00555198	+	0.00961631i
$677$	4.88880	+	18.2453i	0.187892	+	0.701222i	0.993993	+	0.109444i	$0.0349071\pi$
$677$	4.88880	+	18.2453i	0.187892	+	0.701222i	−0.806101	+	0.591778i	$0.798426\pi$
$678$	0.149430	−	1.84185i	0.00573881	−	0.0707359i
$679$	1.44588	+	1.30188i	0.0554880	+	0.0499616i
$680$	−15.8769	−	5.01146i	−0.608851	−	0.192181i
$681$	8.31183	+	2.01672i	0.318510	+	0.0772809i
$682$	−36.0627	−	6.04023i	−1.38091	−	0.231292i
$683$	−28.4770	−	28.4770i	−1.08964	−	1.08964i	−0.995565	−	0.0940780i	$-0.970010\pi$
$683$	−28.4770	−	28.4770i	−1.08964	−	1.08964i	−0.0940780	−	0.995565i	$-0.529990\pi$
$684$	15.5556	+	15.7065i	0.594785	+	0.600554i
$685$	−17.0007	+	1.03444i	−0.649563	+	0.0395238i
$686$	0.985394	−	1.35628i	0.0376225	−	0.0517830i
$687$	−0.906174	−	38.1203i	−0.0345727	−	1.45438i
$688$	2.45207	+	0.657030i	0.0934842	+	0.0250490i
$689$	2.28138	−	21.7058i	0.0869135	−	0.826926i
$690$	6.00436	−	14.7454i	0.228582	−	0.561347i
$691$	−1.10865	−	10.5481i	−0.0421751	−	0.401269i	−0.995161	−	0.0982554i	$-0.968674\pi$
$691$	−1.10865	−	10.5481i	−0.0421751	−	0.401269i	0.952986	−	0.303014i	$-0.0979929\pi$
$692$	−7.07409	−	0.370738i	−0.268917	−	0.0140933i
$693$	1.57176	+	1.76265i	0.0597064	+	0.0669577i
$694$	−3.06134	−	14.4025i	−0.116207	−	0.546710i
$695$	−12.4414	−	2.53532i	−0.471930	−	0.0961700i
$696$	−4.17477	+	5.41357i	−0.158244	+	0.205201i
$697$	14.2600	−	27.9869i	0.540137	−	1.06008i
$698$	−2.90218	+	5.69584i	−0.109849	+	0.215591i
$699$	6.45058	−	8.36469i	0.243983	−	0.316382i
$700$	−0.497093	+	0.334838i	−0.0187884	+	0.0126557i
$701$	10.1075	+	47.5520i	0.381754	+	1.79601i	0.578636	+	0.815586i	$0.303585\pi$
$701$	10.1075	+	47.5520i	0.381754	+	1.79601i	−0.196882	+	0.980427i	$0.563081\pi$
$702$	−8.91755	−	16.7114i	−0.336571	−	0.630733i
$703$	41.9373	+	2.19784i	1.58170	+	0.0828931i
$704$	0.686467	+	6.53130i	0.0258722	+	0.246158i
$705$	−2.51714	−	5.97527i	−0.0948009	−	0.225042i
$706$	2.50602	−	23.8432i	0.0943152	−	0.897349i
$707$	1.17736	+	0.315473i	0.0442793	+	0.0118646i
$708$	0.275691	+	11.5976i	0.0103611	+	0.435865i
$709$	−17.9717	+	24.7359i	−0.674940	+	0.928975i	−0.999859	−	0.0167667i	$-0.994663\pi$
$709$	−17.9717	+	24.7359i	−0.674940	+	0.928975i	0.324920	+	0.945742i	$0.394663\pi$
$710$	−0.806507	−	13.2547i	−0.0302677	−	0.497442i
$711$	−5.85966	+	5.80337i	−0.219754	+	0.217643i
$712$	−6.89017	−	6.89017i	−0.258220	−	0.258220i
$713$	8.01238	+	21.4396i	0.300066	+	0.802920i
$714$	−1.50229	−	0.364503i	−0.0562216	−	0.0136412i
$715$	−24.7033	−	47.4910i	−0.923850	−	1.77606i
$716$	−5.07275	−	4.56752i	−0.189577	−	0.170696i
$717$	0.964712	−	11.8909i	0.0360278	−	0.444075i
$718$	0.0431638	+	0.161090i	0.00161086	+	0.00601181i
$719$	22.9545	+	39.7584i	0.856059	+	1.48274i	0.875659	+	0.482930i	$0.160427\pi$
$719$	22.9545	+	39.7584i	0.856059	+	1.48274i	−0.0195998	+	0.999808i	$0.506239\pi$
$720$	3.63335	−	5.63904i	0.135407	−	0.210155i
$721$	−0.726058	+	0.527512i	−0.0270398	+	0.0196456i
$722$	27.4309	+	22.2131i	1.02087	+	0.826687i
$723$	−1.05010	+	3.51393i	−0.0390538	+	0.130684i
$724$	−2.72969	−	6.13097i	−0.101448	−	0.227856i
$725$	19.2318	−	4.42726i	0.714251	−	0.164424i
$726$	−50.1702	−	24.0787i	−1.86199	−	0.893645i
$727$	−12.8550	−	33.4885i	−0.476766	−	1.24202i	−0.935463	−	0.353426i	$-0.885017\pi$
$727$	−12.8550	−	33.4885i	−0.476766	−	1.24202i	0.458696	−	0.888593i	$-0.348317\pi$
$728$	−0.198380	+	0.389342i	−0.00735244	+	0.0144300i
$729$	11.9082	+	24.2321i	0.441043	+	0.897486i
$730$	−17.6448	−	7.67877i	−0.653063	−	0.284204i
$731$	3.92981	−	18.4883i	0.145349	−	0.683815i
$732$	−5.55750	+	5.24844i	−0.205411	+	0.193988i
$733$	−7.55693	+	19.6865i	−0.279122	+	0.727137i	0.720317	+	0.693645i	$0.243996\pi$
$733$	−7.55693	+	19.6865i	−0.279122	+	0.727137i	−0.999439	+	0.0334920i	$0.989337\pi$
$734$	−13.5141	−	15.0089i	−0.498813	−	0.553988i
$735$	21.3652	−	16.5986i	0.788066	−	0.612250i
$736$	3.32569	−	2.41626i	0.122587	−	0.0890645i
$737$	−4.34726	−	5.36842i	−0.160133	−	0.197748i
$738$	9.36414	+	8.51370i	0.344699	+	0.313394i
$739$	−27.6202	−	15.9465i	−1.01603	−	0.586602i	−0.103075	−	0.994674i	$-0.532868\pi$
$739$	−27.6202	−	15.9465i	−1.01603	−	0.586602i	−0.912950	+	0.408071i	$0.866201\pi$
$740$	−2.09935	−	12.5695i	−0.0771736	−	0.462065i
$741$	−26.2597	−	38.4063i	−0.964673	−	1.41089i
$742$	0.639456	−	0.325819i	0.0234752	−	0.0119612i
$743$	7.29641	+	7.29641i	0.267679	+	0.267679i	0.828164	−	0.560485i	$-0.189385\pi$
$743$	7.29641	+	7.29641i	0.267679	+	0.267679i	−0.560485	+	0.828164i	$0.689385\pi$
$744$	1.65030	+	9.50140i	0.0605028	+	0.348338i
$745$	−0.0621768	−	7.39136i	−0.00227798	−	0.270798i
$746$	−3.86154	−	1.25469i	−0.141381	−	0.0459375i
$747$	5.22943	−	11.5946i	0.191335	−	0.424224i
$748$	48.2958	−	7.64930i	1.76587	−	0.279686i
$749$	0.952240	−	1.64933i	0.0347941	−	0.0602652i
$750$	−18.4371	+	5.92222i	−0.673228	+	0.216249i
$751$	2.46241	−	23.4283i	0.0898547	−	0.854910i	−0.853046	−	0.521836i	$-0.825247\pi$
$751$	2.46241	−	23.4283i	0.0898547	−	0.854910i	0.942901	−	0.333074i	$-0.108086\pi$
$752$	0.261889	−	1.65350i	0.00955011	−	0.0602970i
$753$	9.79656	+	12.8311i	0.357007	+	0.467592i
$754$	10.6925	−	9.62753i	0.389396	−	0.350614i
$755$	6.79467	+	14.9220i	0.247283	+	0.543067i
$756$	0.301158	−	0.545215i	0.0109530	−	0.0198293i
$757$	−10.0268	−	15.4400i	−0.364431	−	0.561175i	0.608126	−	0.793841i	$-0.291922\pi$
$757$	−10.0268	−	15.4400i	−0.364431	−	0.561175i	−0.972557	+	0.232666i	$0.925255\pi$
$758$	4.75817	+	12.3955i	0.172824	+	0.450223i
$759$	3.55622	+	46.6241i	0.129083	+	1.69235i
$760$	7.35655	−	14.7433i	0.266850	−	0.534797i
$761$	−9.97874	+	22.4126i	−0.361729	+	0.812457i	0.637392	+	0.770540i	$0.280013\pi$
$761$	−9.97874	+	22.4126i	−0.361729	+	0.812457i	−0.999121	+	0.0419171i	$0.986653\pi$
$762$	10.8087	+	30.7584i	0.391557	+	1.11426i
$763$	1.14796	−	1.76771i	0.0415591	−	0.0639954i
$764$	12.8898	−	5.73892i	0.466338	−	0.207627i
$765$	−43.3447	−	24.8183i	−1.56713	−	0.897307i
$766$	−3.11727	−	29.6588i	−0.112631	−	1.07162i
$767$	3.81948	−	24.1152i	0.137913	−	0.870751i
$768$	1.56512	−	0.741893i	0.0564763	−	0.0267707i
$769$	4.36024	−	2.51739i	0.157234	−	0.0907793i	−0.419318	−	0.907839i	$-0.637731\pi$
$769$	4.36024	−	2.51739i	0.157234	−	0.0907793i	0.576553	+	0.817060i	$0.304398\pi$
$770$	0.867281	−	1.53179i	0.0312546	−	0.0552018i
$771$	−5.97518	−	7.03031i	−0.215191	−	0.253191i
$772$	−5.69674	+	0.298553i	−0.205030	+	0.0107452i
$773$	−7.93396	+	4.04255i	−0.285365	+	0.145401i	−0.590814	−	0.806808i	$-0.701193\pi$
$773$	−7.93396	+	4.04255i	−0.285365	+	0.145401i	0.305449	+	0.952208i	$0.401193\pi$
$774$	6.76888	+	3.49017i	0.243302	+	0.125451i
$775$	13.7273	−	24.2190i	0.493098	−	0.869974i
$776$			16.2312i			0.582667i
$777$	−0.273448	−	1.15122i	−0.00980990	−	0.0412999i
$778$	1.41579	+	27.0149i	0.0507585	+	0.968531i
$779$	25.1487	+	18.2716i	0.901045	+	0.654647i
$780$	−9.65689	+	10.2993i	−0.345772	+	0.368773i
$781$	19.5004	+	33.7757i	0.697780	+	1.20859i
$782$	−19.2620	−	23.7865i	−0.688806	−	0.850605i
$783$	−15.6912	+	13.2063i	−0.560757	+	0.471954i
$784$	6.94736	−	0.730197i	0.248120	−	0.0260785i
$785$	20.0003	+	0.879538i	0.713840	+	0.0313921i
$786$	−4.53551	−	24.8053i	−0.161776	−	0.884777i
$787$	−12.7752	−	8.29629i	−0.455386	−	0.295731i	0.296490	−	0.955036i	$-0.404184\pi$
$787$	−12.7752	−	8.29629i	−0.455386	−	0.295731i	−0.751876	+	0.659305i	$0.770851\pi$
$788$	1.15743	+	1.78228i	0.0412316	+	0.0634911i
$789$	12.9499	−	16.7926i	0.461029	−	0.597832i
$790$	5.50032	+	2.74452i	0.195693	+	0.0976457i
$791$	−0.121628	+	0.0395194i	−0.00432460	+	0.00140515i
$792$	−2.15394	+	19.5837i	−0.0765368	+	0.695877i
$793$	13.4926	−	8.76222i	0.479138	−	0.311156i
$794$	−32.2056	+	6.84552i	−1.14294	+	0.242938i
$795$	22.7741	−	4.36241i	0.807715	−	0.154719i
$796$	−8.10271	−	8.99897i	−0.287193	−	0.318960i
$797$	21.6679	+	17.5463i	0.767517	+	0.621523i	0.930998	−	0.365024i	$-0.118939\pi$
$797$	21.6679	+	17.5463i	0.767517	+	0.621523i	−0.163482	+	0.986546i	$0.552272\pi$
$798$	0.588869	−	1.41201i	0.0208457	−	0.0499846i
$799$	−12.3966	−	1.30294i	−0.438561	−	0.0460946i
$800$	−4.85072	−	1.21266i	−0.171499	−	0.0428741i
$801$	−15.8027	−	24.5930i	−0.558359	−	0.868950i
$802$	1.70428	+	10.7604i	0.0601803	+	0.379964i
$803$	56.4394	−	2.95786i	1.99170	−	0.104381i
$804$	−0.955674	+	1.55110i	−0.0337040	+	0.0547032i
$805$	−1.10180	+	0.00926847i	−0.0388334	+	0.000326671i
$806$	0.180079	−	20.2957i	0.00634300	−	0.714887i
$807$	−8.11275	−	13.3108i	−0.285582	−	0.468562i
$808$	4.61640	+	9.06020i	0.162405	+	0.318737i
$809$	−11.1135	+	12.3428i	−0.390730	+	0.433950i	−0.906130	−	0.423000i	$-0.860977\pi$
$809$	−11.1135	+	12.3428i	−0.390730	+	0.433950i	0.515399	+	0.856950i	$0.327644\pi$
$810$	14.2479	−	14.2126i	0.500620	−	0.499380i
$811$	−26.2672	+	45.4961i	−0.922366	+	1.59758i	−0.126623	+	0.991951i	$0.540414\pi$
$811$	−26.2672	+	45.4961i	−0.922366	+	1.59758i	−0.795743	+	0.605634i	$0.792920\pi$
$812$	0.457000	+	0.122453i	0.0160375	+	0.00429725i
$813$	−0.688437	+	0.326331i	−0.0241445	+	0.0114449i
$814$	21.9995	+	30.2797i	0.771080	+	1.06130i
$815$	18.9546	−	23.8138i	0.663951	−	0.834162i
$816$	−6.12621	−	11.3483i	−0.214460	−	0.397270i
$817$	17.4634	+	6.70357i	0.610967	+	0.234528i
$818$	1.29205	+	0.839069i	0.0451756	+	0.0293374i
$819$	−0.829887	+	1.01477i	−0.0289986	+	0.0354590i
$820$	3.76416	−	8.64954i	0.131450	−	0.302055i
$821$	12.8926	−	4.18905i	0.449954	−	0.146199i	−0.0752694	−	0.997163i	$-0.523982\pi$
$821$	12.8926	−	4.18905i	0.449954	−	0.146199i	0.525224	+	0.850964i	$0.323982\pi$
$822$	−10.0114	−	8.59238i	−0.349186	−	0.299694i
$823$	−4.93265	+	1.89347i	−0.171941	+	0.0660021i	−0.442816	−	0.896613i	$-0.646020\pi$
$823$	−4.93265	+	1.89347i	−0.171941	+	0.0660021i	0.270875	+	0.962615i	$0.412687\pi$
$824$	−7.32333	−	1.55662i	−0.255120	−	0.0542275i
$825$	40.6867	−	39.7401i	1.41653	−	1.38357i
$826$	0.733449	−	0.326552i	0.0255200	−	0.0113622i
$827$	−7.51239	−	0.393708i	−0.261232	−	0.0136906i	−0.0787294	−	0.996896i	$-0.525086\pi$
$827$	−7.51239	−	0.393708i	−0.261232	−	0.0136906i	−0.182502	+	0.983205i	$0.558420\pi$
$828$	11.2902	−	4.96159i	0.392363	−	0.172427i
$829$	−0.462209	−	0.636176i	−0.0160532	−	0.0220953i	0.800915	−	0.598778i	$-0.204347\pi$
$829$	−0.462209	−	0.636176i	−0.0160532	−	0.0220953i	−0.816968	+	0.576683i	$0.804347\pi$
$830$	−9.43650	−	0.911629i	−0.327546	−	0.0316431i
$831$	11.7530	−	3.45058i	0.407708	−	0.119699i
$832$	−3.52115	+	0.943490i	−0.122074	+	0.0327096i
$833$	−8.13658	−	51.3724i	−0.281916	−	1.77995i
$834$	−5.55112	−	8.11882i	−0.192219	−	0.281132i
$835$	8.47910	−	4.41055i	0.293431	−	0.152633i
$836$			48.3919i			1.67367i
$837$	−1.22317	+	28.9051i	−0.0422788	+	0.999106i
$838$	−23.4809	+	23.4809i	−0.811135	+	0.811135i
$839$	−8.20765	+	25.2605i	−0.283359	+	0.872091i	0.703526	+	0.710669i	$0.251608\pi$
$839$	−8.20765	+	25.2605i	−0.283359	+	0.872091i	−0.986886	+	0.161421i	$0.948392\pi$
$840$	−0.456979	−	0.0818635i	−0.0157673	−	0.00282456i
$841$	10.8582	+	7.88896i	0.374421	+	0.272033i
$842$	−5.26812	−	19.6609i	−0.181551	−	0.677559i
$843$	−21.3420	−	11.6545i	−0.735057	−	0.401403i
$844$	−15.0793	−	1.58490i	−0.519051	−	0.0545545i
$845$	0.519058	−	0.383830i	0.0178561	−	0.0132042i
$846$	1.82245	−	4.68002i	0.0626572	−	0.160902i
$847$	−0.201562	+	3.84602i	−0.00692574	+	0.132151i
$848$	5.58950	+	2.14561i	0.191944	+	0.0736804i
$849$	−2.11654	−	0.0605346i	−0.0726394	−	0.00207754i
$850$	−7.12651	+	36.5399i	−0.244437	+	1.25331i
$851$	9.52897	−	21.4024i	0.326649	−	0.733666i
$852$	6.69912	−	7.80545i	0.229508	−	0.267410i
$853$	16.5349	+	8.42498i	0.566146	+	0.288466i	0.713543	−	0.700612i	$-0.247089\pi$
$853$	16.5349	+	8.42498i	0.566146	+	0.288466i	−0.147397	+	0.989077i	$0.547089\pi$
$854$	0.483285	+	0.215172i	0.0165377	+	0.00736305i
$855$	30.9696	−	38.5259i	1.05914	−	1.31756i
$856$	15.5407	−	3.30329i	0.531172	−	0.112904i
$857$	17.5642	−	45.7564i	0.599982	−	1.56301i	−0.210719	−	0.977547i	$-0.567580\pi$
$857$	17.5642	−	45.7564i	0.599982	−	1.56301i	0.810701	−	0.585460i	$-0.199086\pi$
$858$	11.8727	−	39.7294i	0.405329	−	1.35634i
$859$	−45.8594	+	4.82002i	−1.56470	+	0.164457i	−0.846885	−	0.531775i	$-0.821525\pi$
$859$	−45.8594	+	4.82002i	−1.56470	+	0.164457i	−0.717817	+	0.696232i	$0.754858\pi$
$860$	0.840794	−	5.61380i	0.0286708	−	0.191429i
$861$	0.294363	−	0.824923i	0.0100319	−	0.0281133i
$862$	2.24591	−	8.38184i	0.0764959	−	0.285487i
$863$	35.8971	−	9.61861i	1.22195	−	0.327421i	0.410512	−	0.911855i	$-0.365350\pi$
$863$	35.8971	−	9.61861i	1.22195	−	0.327421i	0.811441	+	0.584434i	$0.198683\pi$
$864$	5.06123	−	1.17641i	0.172187	−	0.0400223i
$865$	0.962024	+	15.8106i	0.0327098	+	0.537577i
$866$	−25.8186	−	8.38896i	−0.877351	−	0.285069i
$867$	−56.8497	+	34.6491i	−1.93072	+	1.17675i
$868$	0.562937	−	0.358515i	0.0191073	−	0.0121688i
$869$	−18.0537			−0.612429
$870$	13.0816	+	7.90885i	0.443507	+	0.268135i
$871$	2.56573	−	2.84953i	0.0869364	−	0.0965527i
$872$	17.3672	−	2.75070i	0.588128	−	0.0931503i
$873$	−10.3537	+	47.5802i	−0.350420	+	1.61034i
$874$	26.2327	−	15.1455i	0.887335	−	0.512303i
$875$	0.869417	+	1.01990i	0.0293917	+	0.0344791i
$876$	−5.67093	−	13.7848i	−0.191603	−	0.465746i
$877$	−32.7736	+	40.4721i	−1.10669	+	1.36664i	−0.183173	+	0.983081i	$0.558637\pi$
$877$	−32.7736	+	40.4721i	−1.10669	+	1.36664i	−0.923514	+	0.383564i	$0.874697\pi$
$878$	1.63141	−	31.1292i	0.0550575	−	1.05056i
$879$	2.23471	+	12.2220i	0.0753751	+	0.412236i
$880$	14.3378	−	3.17387i	0.483326	−	0.106991i
$881$	0.853802	−	4.01682i	0.0287653	−	0.135330i	−0.961422	−	0.275079i	$-0.911296\pi$
$881$	0.853802	−	4.01682i	0.0287653	−	0.135330i	0.990187	+	0.139749i	$0.0446294\pi$
$882$	20.8313	+	2.29115i	0.701426	+	0.0771470i
$883$	4.94559	+	2.51990i	0.166432	+	0.0848015i	0.535222	−	0.844711i	$-0.320228\pi$
$883$	4.94559	+	2.51990i	0.166432	+	0.0848015i	−0.368790	+	0.929513i	$0.620228\pi$
$884$	8.38741	+	25.8138i	0.282099	+	0.868211i
$885$	25.6977	−	3.54012i	0.863818	−	0.119000i
$886$	6.85130	+	1.45629i	0.230174	+	0.0489249i
$887$	21.9219	−	33.7568i	0.736066	−	1.13344i	−0.250187	−	0.968198i	$-0.580492\pi$
$887$	21.9219	−	33.7568i	0.736066	−	1.13344i	0.986253	−	0.165244i	$-0.0528413\pi$
$888$	5.61071	−	8.12158i	0.188283	−	0.272542i
$889$	1.67676	−	1.50976i	0.0562366	−	0.0506357i
$890$	−13.5691	+	17.0477i	−0.454837	+	0.571439i
$891$	−18.8063	+	56.0337i	−0.630035	+	1.87720i
$892$	4.12763	−	3.34249i	0.138203	−	0.111915i
$893$	3.19278	−	11.9156i	0.106842	−	0.398741i
$894$	3.95120	−	4.14363i	0.132148	−	0.138584i
$895$	−8.86748	+	12.4235i	−0.296407	+	0.415271i
$896$	−0.0890805	−	0.0802085i	−0.00297597	−	0.00267958i
$897$	−25.2527	+	5.99824i	−0.843164	+	0.200275i
$898$	9.53557	−	9.53557i	0.318206	−	0.318206i
$899$	−21.5352	+	4.37812i	−0.718240	+	0.146018i
$900$	−13.4458	−	6.64902i	−0.448195	−	0.221634i
$901$	13.7755	−	42.3966i	0.458928	−	1.41244i
$902$	1.44996	+	27.6668i	0.0482783	+	0.921204i
$903$	0.0426203	−	0.525332i	0.00141831	−	0.0174820i
$904$	−0.923952	−	0.533444i	−0.0307302	−	0.0177421i
$905$	−12.9326	+	7.61239i	−0.429894	+	0.253044i
$906$	−4.26835	+	11.9617i	−0.141807	+	0.397399i
$907$	−23.0850	−	3.65631i	−0.766526	−	0.121406i	−0.239086	−	0.970998i	$-0.576848\pi$
$907$	−23.0850	−	3.65631i	−0.766526	−	0.121406i	−0.527439	+	0.849593i	$0.676848\pi$
$908$	3.10763	−	3.83760i	0.103130	−	0.127355i
$909$	7.75311	+	29.5038i	0.257154	+	0.978580i
$910$	0.915107	+	0.342473i	0.0303355	+	0.0113529i
$911$	−0.900934	−	4.23856i	−0.0298493	−	0.140430i	0.960700	−	0.277590i	$-0.0895357\pi$
$911$	−0.900934	−	4.23856i	−0.0298493	−	0.140430i	−0.990549	+	0.137160i	$0.956202\pi$
$912$	12.0411	−	4.23129i	0.398719	−	0.140112i
$913$	25.9944	−	9.97832i	0.860289	−	0.330234i
$914$	−10.7013	−	32.9353i	−0.353969	−	1.08940i
$915$	13.0637	+	11.0226i	0.431873	+	0.364397i
$916$	−20.1117	−	8.95431i	−0.664509	−	0.295859i
$917$	−1.46361	+	0.950481i	−0.0483327	+	0.0313876i
$918$	−10.7194	−	37.1742i	−0.353793	−	1.22693i
$919$	9.62278	+	21.6131i	0.317426	+	0.712951i	0.999838	−	0.0180172i	$-0.00573537\pi$
$919$	9.62278	+	21.6131i	0.317426	+	0.712951i	−0.682411	+	0.730968i	$0.739069\pi$
$920$	−6.20789	−	6.77900i	−0.204668	−	0.223497i
$921$	−40.9757	−	5.49518i	−1.35020	−	0.181072i
$922$	−30.2397	−	4.78950i	−0.995893	−	0.157734i
$923$	−16.8241	+	13.6239i	−0.553773	+	0.448437i
$924$	1.30828	−	0.384099i	0.0430393	−	0.0126359i
$925$	−27.3967	+	7.83721i	−0.900798	+	0.257686i
$926$	−14.4368	+	19.8706i	−0.474423	+	0.652987i
$927$	−20.4746	−	9.23456i	−0.672476	−	0.303303i
$928$	1.79188	+	3.51677i	0.0588214	+	0.115444i
$929$	−31.6934			−1.03983			−0.519913	−	0.854219i	$-0.674036\pi$
$929$	−31.6934			−1.03983			−0.519913	+	0.854219i	$0.674036\pi$
$930$	20.6934	−	6.06503i	0.678562	−	0.198880i
$931$	51.4747			1.68701
$932$	−2.76870	−	5.43387i	−0.0906917	−	0.177992i
$933$	8.04164	−	42.8120i	0.263272	−	1.40160i
$934$	−4.09490	+	5.63614i	−0.133989	+	0.184420i
$935$	−29.1863	−	105.371i	−0.954496	−	3.44601i
$936$	−10.9237	+	0.519639i	−0.357054	+	0.0169849i
$937$	27.6632	−	22.4012i	0.903717	−	0.731815i	−0.0601530	−	0.998189i	$-0.519159\pi$
$937$	27.6632	−	22.4012i	0.903717	−	0.731815i	0.963870	+	0.266374i	$0.0858255\pi$
$938$	0.124534	+	0.0197242i	0.00406618	+	0.000644019i
$939$	2.81190	−	20.9674i	0.0917628	−	0.684245i
$940$	−3.73982	−	0.164463i	−0.121979	−	0.00536420i
$941$	−19.4624	−	43.7132i	−0.634455	−	1.42501i	−0.888981	−	0.457943i	$-0.848586\pi$
$941$	−19.4624	−	43.7132i	−0.634455	−	1.42501i	0.254526	−	0.967066i	$-0.418080\pi$
$942$	10.6472	+	11.2742i	0.346905	+	0.367333i
$943$	14.5441	−	9.44502i	0.473620	−	0.307572i
$944$	6.11872	+	2.72423i	0.199147	+	0.0886661i
$945$	−1.28737	−	0.531476i	−0.0418780	−	0.0172889i
$946$	5.15177	+	15.8555i	0.167498	+	0.515507i
$947$	17.6004	−	6.75617i	0.571937	−	0.219546i	−0.0551731	−	0.998477i	$-0.517571\pi$
$947$	17.6004	−	6.75617i	0.571937	−	0.219546i	0.627110	+	0.778931i	$0.284238\pi$
$948$	1.57858	+	4.49218i	0.0512697	+	0.145899i
$949$	6.52248	+	30.6859i	0.211729	+	0.996106i
$950$	−34.6134	−	12.6229i	−1.12301	−	0.409542i
$951$	29.0187	+	53.7546i	0.940994	+	1.74311i
$952$	−0.561675	+	0.693611i	−0.0182040	+	0.0224801i
$953$	−29.7048	−	4.70478i	−0.962233	−	0.152403i	−0.344496	−	0.938788i	$-0.611950\pi$
$953$	−29.7048	−	4.70478i	−0.962233	−	0.152403i	−0.617737	+	0.786385i	$0.711950\pi$
$954$	15.0164	+	9.85511i	0.486173	+	0.319071i
$955$	−16.0044	−	27.1896i	−0.517890	−	0.879835i
$956$	−5.96500	−	3.44389i	−0.192922	−	0.111383i
$957$	−44.7491	−	3.63050i	−1.44653	−	0.117357i
$958$	1.72880	+	32.9875i	0.0558551	+	1.06578i
$959$	−0.282147	+	0.868360i	−0.00911101	+	0.0280408i
$960$	−2.04340	−	3.29006i	−0.0659505	−	0.106186i
$961$	−15.9739	+	26.5675i	−0.515288	+	0.857017i
$962$	−14.6904	+	14.6904i	−0.473638	+	0.473638i
$963$	47.6632	+	0.230025i	1.53593	+	0.00741245i
$964$	1.57355	+	1.41683i	0.0506807	+	0.0456331i
$965$	2.10135	+	12.5815i	0.0676448	+	0.405013i
$966$	−0.617675	−	0.588991i	−0.0198734	−	0.0189505i
$967$	−2.30657	+	8.60823i	−0.0741742	+	0.276822i	−0.993045	−	0.117737i	$-0.962436\pi$
$967$	−2.30657	+	8.60823i	−0.0741742	+	0.276822i	0.918871	+	0.394559i	$0.129103\pi$
$968$	−24.9690	+	20.2195i	−0.802534	+	0.649879i
$969$	−36.1538	−	87.8821i	−1.16143	−	2.82318i
$970$	36.0621	−	4.09726i	1.15788	−	0.131555i
$971$	27.9380	−	25.1555i	0.896574	−	0.807279i	−0.0853900	−	0.996348i	$-0.527214\pi$
$971$	27.9380	−	25.1555i	0.896574	−	0.807279i	0.981964	+	0.189069i	$0.0605470\pi$
$972$	15.5869	−	0.220022i	0.499950	−	0.00705722i
$973$	−0.370713	+	0.570849i	−0.0118845	+	0.0183006i
$974$	19.0734	+	4.05417i	0.611151	+	0.129904i
$975$	25.3204	+	18.8556i	0.810900	+	0.603861i
$976$	1.36379	+	4.19730i	0.0436538	+	0.134352i
$977$	12.2171	+	6.22494i	0.390861	+	0.199153i	0.638366	−	0.769733i	$-0.279611\pi$
$977$	12.2171	+	6.22494i	0.390861	+	0.199153i	−0.247505	+	0.968887i	$0.579611\pi$
$978$	23.3816	−	3.02087i	0.747661	−	0.0965967i
$979$	13.3048	−	62.5942i	0.425224	−	2.00052i
$980$	−3.37606	−	15.2511i	−0.107844	−	0.487180i
$981$	52.6649	+	3.01497i	1.68146	+	0.0962607i
$982$	0.923886	−	17.6288i	0.0294824	−	0.562557i
$983$	−9.45413	+	11.6749i	−0.301540	+	0.372371i	−0.905284	−	0.424808i	$-0.860342\pi$
$983$	−9.45413	+	11.6749i	−0.301540	+	0.372371i	0.603744	+	0.797179i	$0.293675\pi$
$984$	6.75738	−	2.77991i	0.215417	−	0.0886204i
$985$	3.66765	−	3.02144i	0.116861	−	0.0962711i
$986$	25.4506	−	14.6939i	0.810511	−	0.467949i
$987$	−0.347482	+	0.00826013i	−0.0110605	+	0.000262923i
$988$	−26.5307	+	4.20205i	−0.844055	+	0.133685i
$989$	6.98272	−	7.75509i	0.222038	−	0.246598i
$990$	44.0543	−	0.157975i	1.40014	−	0.00502076i
$991$	−25.8918			−0.822479			−0.411240	−	0.911527i	$-0.634904\pi$
$991$	−25.8918			−0.822479			−0.411240	+	0.911527i	$0.634904\pi$
$992$	5.36505	+	1.48870i	0.170341	+	0.0472664i
$993$	18.9655	+	31.1171i	0.601851	+	0.987472i
$994$	−0.677024	−	0.219979i	−0.0214739	−	0.00697730i
$995$	−17.9483	+	20.2740i	−0.568999	+	0.642729i
$996$	−4.75574	−	5.59554i	−0.150691	−	0.177301i
$997$	−43.8304	+	11.7443i	−1.38812	+	0.371947i	−0.874065	−	0.485809i	$-0.838525\pi$
$997$	−43.8304	+	11.7443i	−1.38812	+	0.371947i	−0.514058	+	0.857755i	$0.671859\pi$
$998$	−1.43438	+	5.35319i	−0.0454046	+	0.169452i
$999$	21.6279	−	20.2286i	0.684276	−	0.640004i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bs.a.107.2	✓	1024
3.2	odd	2	inner	930.2.bs.a.107.61	yes	1024
5.3	odd	4	inner	930.2.bs.a.293.18	yes	1024
15.8	even	4	inner	930.2.bs.a.293.50	yes	1024
31.20	even	15	inner	930.2.bs.a.857.50	yes	1024
93.20	odd	30	inner	930.2.bs.a.857.18	yes	1024
155.113	odd	60	inner	930.2.bs.a.113.61	yes	1024
465.113	even	60	inner	930.2.bs.a.113.2	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bs.a.107.2	✓	1024	1.1	even	1	trivial
930.2.bs.a.107.61	yes	1024	3.2	odd	2	inner
930.2.bs.a.113.2	yes	1024	465.113	even	60	inner
930.2.bs.a.113.61	yes	1024	155.113	odd	60	inner
930.2.bs.a.293.18	yes	1024	5.3	odd	4	inner
930.2.bs.a.293.50	yes	1024	15.8	even	4	inner
930.2.bs.a.857.18	yes	1024	93.20	odd	30	inner
930.2.bs.a.857.50	yes	1024	31.20	even	15	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bs (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.453990 - 0.891007i) q^{2} +(-1.70228 - 0.319750i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(1.94583 + 1.10171i) q^{5} +(0.487920 + 1.66191i) q^{6} +(0.0931562 - 0.0754364i) q^{7} +(0.987688 + 0.156434i) q^{8} +(2.79552 + 1.08861i) q^{9} +O(q^{10})\)	\(q+(-0.453990 - 0.891007i) q^{2} +(-1.70228 - 0.319750i) q^{3} +(-0.587785 + 0.809017i) q^{4} +(1.94583 + 1.10171i) q^{5} +(0.487920 + 1.66191i) q^{6} +(0.0931562 - 0.0754364i) q^{7} +(0.987688 + 0.156434i) q^{8} +(2.79552 + 1.08861i) q^{9} +(0.0982390 - 2.23391i) q^{10} +(2.67115 + 5.99950i) q^{11} +(1.25926 - 1.18923i) q^{12} +(-3.05726 + 1.98541i) q^{13} +(-0.109506 - 0.0487554i) q^{14} +(-2.96008 - 2.49759i) q^{15} +(-0.309017 - 0.951057i) q^{16} +(-6.95114 + 2.66829i) q^{17} +(-0.299183 - 2.98504i) q^{18} +(-1.53203 - 7.20763i) q^{19} +(-2.03503 + 0.926642i) q^{20} +(-0.182699 + 0.0986273i) q^{21} +(4.13292 - 5.10373i) q^{22} +(-4.06017 - 0.643068i) q^{23} +(-1.63130 - 0.582108i) q^{24} +(2.57249 + 4.28746i) q^{25} +(3.15698 + 1.82268i) q^{26} +(-4.41068 - 2.74698i) q^{27} +(0.00627349 + 0.119705i) q^{28} +(1.21968 - 3.75378i) q^{29} +(-0.881522 + 3.77133i) q^{30} +(-2.74099 - 4.84634i) q^{31} +(-0.707107 + 0.707107i) q^{32} +(-2.62871 - 11.0669i) q^{33} +(5.53321 + 4.98213i) q^{34} +(0.264375 - 0.0441556i) q^{35} +(-2.52387 + 1.62176i) q^{36} +(-1.47504 + 5.50493i) q^{37} +(-5.72652 + 4.63724i) q^{38} +(5.83915 - 2.40217i) q^{39} +(1.74953 + 1.39254i) q^{40} +(-3.13504 + 2.82280i) q^{41} +(0.170821 + 0.118010i) q^{42} +(-1.38260 + 2.12902i) q^{43} +(-6.42376 - 1.36541i) q^{44} +(4.24028 + 5.19808i) q^{45} +(1.27030 + 3.90959i) q^{46} +(1.49165 + 0.760031i) q^{47} +(0.221934 + 1.71777i) q^{48} +(-1.45239 + 6.83298i) q^{49} +(2.65227 - 4.23857i) q^{50} +(12.6860 - 2.31956i) q^{51} +(0.190784 - 3.64037i) q^{52} +(-3.76784 + 4.65290i) q^{53} +(-0.445173 + 5.17705i) q^{54} +(-1.41208 + 14.6168i) q^{55} +(0.103810 - 0.0599348i) q^{56} +(0.303306 + 12.7593i) q^{57} +(-3.89837 + 0.617441i) q^{58} +(-4.48168 + 4.97742i) q^{59} +(3.76048 - 0.926705i) q^{60} -4.41331 q^{61} +(-3.07373 + 4.64243i) q^{62} +(0.342541 - 0.109473i) q^{63} +(0.951057 + 0.309017i) q^{64} +(-8.13624 + 0.495063i) q^{65} +(-8.66731 + 7.36648i) q^{66} +(-1.01602 + 0.272242i) q^{67} +(1.92708 - 7.19197i) q^{68} +(6.70594 + 2.39292i) q^{69} +(-0.159367 - 0.215513i) q^{70} +(5.90613 - 0.620759i) q^{71} +(2.59081 + 1.51252i) q^{72} +(3.08405 - 8.03424i) q^{73} +(5.57458 - 1.18491i) q^{74} +(-3.00819 - 8.12101i) q^{75} +(6.73160 + 2.99710i) q^{76} +(0.701415 + 0.357389i) q^{77} +(-4.79127 - 4.11216i) q^{78} +(-1.11813 + 2.51137i) q^{79} +(0.446490 - 2.19104i) q^{80} +(6.62987 + 6.08645i) q^{81} +(3.93841 + 1.51182i) q^{82} +(0.221893 - 4.23397i) q^{83} +(0.0275965 - 0.205778i) q^{84} +(-16.4654 - 2.46607i) q^{85} +(2.52466 + 0.265353i) q^{86} +(-3.27651 + 6.00000i) q^{87} +(1.69974 + 6.34350i) q^{88} +(-7.88320 - 5.72748i) q^{89} +(2.70648 - 6.13799i) q^{90} +(-0.135031 + 0.415582i) q^{91} +(2.90676 - 2.90676i) q^{92} +(3.11632 + 9.12626i) q^{93} -1.67411i q^{94} +(4.95962 - 15.7126i) q^{95} +(1.42979 - 0.977597i) q^{96} +(2.53912 + 16.0314i) q^{97} +(6.74760 - 1.80801i) q^{98} +(0.936151 + 19.6796i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q - 8 q^{3} + 24 q^{7}+O(q^{10}) \) 1024 * q - 8 * q^3 + 24 * q^7	\( 1024 q - 8 q^{3} + 24 q^{7} + 8 q^{10} + 8 q^{12} - 8 q^{15} + 256 q^{16} + 44 q^{22} + 16 q^{25} - 20 q^{27} + 4 q^{28} + 48 q^{30} - 32 q^{31} - 52 q^{33} + 112 q^{37} + 12 q^{42} + 40 q^{45} + 24 q^{46} - 12 q^{48} + 16 q^{51} - 20 q^{55} - 40 q^{57} - 56 q^{58} - 12 q^{60} + 32 q^{61} + 224 q^{63} - 32 q^{66} + 24 q^{67} - 24 q^{70} - 88 q^{73} + 224 q^{75} - 96 q^{76} - 32 q^{78} + 48 q^{81} - 24 q^{85} + 20 q^{87} - 36 q^{88} + 8 q^{90} - 80 q^{91} - 252 q^{93} - 32 q^{97}+O(q^{100}) \) 1024 * q - 8 * q^3 + 24 * q^7 + 8 * q^10 + 8 * q^12 - 8 * q^15 + 256 * q^16 + 44 * q^22 + 16 * q^25 - 20 * q^27 + 4 * q^28 + 48 * q^30 - 32 * q^31 - 52 * q^33 + 112 * q^37 + 12 * q^42 + 40 * q^45 + 24 * q^46 - 12 * q^48 + 16 * q^51 - 20 * q^55 - 40 * q^57 - 56 * q^58 - 12 * q^60 + 32 * q^61 + 224 * q^63 - 32 * q^66 + 24 * q^67 - 24 * q^70 - 88 * q^73 + 224 * q^75 - 96 * q^76 - 32 * q^78 + 48 * q^81 - 24 * q^85 + 20 * q^87 - 36 * q^88 + 8 * q^90 - 80 * q^91 - 252 * q^93 - 32 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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