LMFDB - Embedded newform 88.2.k.b.51.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [88,2,Mod(19,88)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(88, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 5, 3]))

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

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

chi := DirichletCharacter("88.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 88 = 2^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	88.k (of order $10$, degree $4$, 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:	$0.702683537787$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$8$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			51.6
Character	$\chi$	$=$	88.51
Dual form			88.2.k.b.19.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.738473 + 1.20609i) q^{2} +(-0.303809 + 0.935028i) q^{3} +(-0.909315 + 1.78133i) q^{4} +(0.398383 + 0.548327i) q^{5} +(-1.35208 + 0.324071i) q^{6} +(-1.40393 - 4.32085i) q^{7} +(-2.81996 + 0.218749i) q^{8} +(1.64507 + 1.19522i) q^{9} +O(q^{10})$	\(q+(0.738473 + 1.20609i) q^{2} +(-0.303809 + 0.935028i) q^{3} +(-0.909315 + 1.78133i) q^{4} +(0.398383 + 0.548327i) q^{5} +(-1.35208 + 0.324071i) q^{6} +(-1.40393 - 4.32085i) q^{7} +(-2.81996 + 0.218749i) q^{8} +(1.64507 + 1.19522i) q^{9} +(-0.367138 + 0.885411i) q^{10} +(3.31396 + 0.132807i) q^{11} +(-1.38934 - 1.39142i) q^{12} +(1.90447 + 1.38368i) q^{13} +(4.17458 - 4.88410i) q^{14} +(-0.633734 + 0.205913i) q^{15} +(-2.34629 - 3.23959i) q^{16} +(-2.07445 - 2.85523i) q^{17} +(-0.226698 + 2.86675i) q^{18} +(-4.38980 - 1.42633i) q^{19} +(-1.33901 + 0.211051i) q^{20} +4.46665 q^{21} +(2.28710 + 4.09502i) q^{22} -1.11065i q^{23} +(0.652192 - 2.70319i) q^{24} +(1.40313 - 4.31839i) q^{25} +(-0.262443 + 3.31877i) q^{26} +(-4.00349 + 2.90871i) q^{27} +(8.97349 + 1.42815i) q^{28} +(0.379398 + 1.16767i) q^{29} +(-0.716345 - 0.612280i) q^{30} +(-3.46109 + 4.76378i) q^{31} +(2.17456 - 5.22219i) q^{32} +(-1.13099 + 3.05830i) q^{33} +(1.91175 - 4.61048i) q^{34} +(1.80994 - 2.49117i) q^{35} +(-3.62497 + 1.84360i) q^{36} +(-8.78677 + 2.85499i) q^{37} +(-1.52146 - 6.34781i) q^{38} +(-1.87237 + 1.36036i) q^{39} +(-1.24337 - 1.45911i) q^{40} +(1.88539 + 0.612601i) q^{41} +(3.29850 + 5.38718i) q^{42} +2.02637i q^{43} +(-3.25001 + 5.78251i) q^{44} +1.37819i q^{45} +(1.33955 - 0.820189i) q^{46} +(4.48649 + 1.45775i) q^{47} +(3.74193 - 1.20963i) q^{48} +(-11.0356 + 8.01786i) q^{49} +(6.24455 - 1.49671i) q^{50} +(3.29995 - 1.07222i) q^{51} +(-4.19655 + 2.13429i) q^{52} +(4.70018 - 6.46924i) q^{53} +(-6.46464 - 2.68058i) q^{54} +(1.24741 + 1.87005i) q^{55} +(4.90420 + 11.8775i) q^{56} +(2.66732 - 3.67125i) q^{57} +(-1.12814 + 1.31988i) q^{58} +(-0.400488 - 1.23257i) q^{59} +(0.209465 - 1.31613i) q^{60} +(-6.73720 + 4.89486i) q^{61} +(-8.30147 - 0.656467i) q^{62} +(2.85479 - 8.78613i) q^{63} +(7.90430 - 1.23372i) q^{64} +1.59551i q^{65} +(-4.52380 + 0.894394i) q^{66} -0.483683 q^{67} +(6.97244 - 1.09897i) q^{68} +(1.03849 + 0.337427i) q^{69} +(4.34117 + 0.343293i) q^{70} +(8.68470 + 11.9535i) q^{71} +(-4.90049 - 3.01060i) q^{72} +(8.79393 - 2.85732i) q^{73} +(-9.93218 - 8.48931i) q^{74} +(3.61153 + 2.62393i) q^{75} +(6.53249 - 6.52271i) q^{76} +(-4.07874 - 14.5056i) q^{77} +(-3.02341 - 1.25367i) q^{78} +(0.848366 + 0.616374i) q^{79} +(0.841630 - 2.57713i) q^{80} +(0.381661 + 1.17463i) q^{81} +(0.653458 + 2.72635i) q^{82} +(-4.37741 - 6.02499i) q^{83} +(-4.06159 + 7.95658i) q^{84} +(0.739176 - 2.27495i) q^{85} +(-2.44399 + 1.49642i) q^{86} -1.20707 q^{87} +(-9.37428 + 0.350415i) q^{88} +2.47072 q^{89} +(-1.66223 + 1.01776i) q^{90} +(3.30493 - 10.1715i) q^{91} +(1.97845 + 1.00994i) q^{92} +(-3.40275 - 4.68349i) q^{93} +(1.55497 + 6.48763i) q^{94} +(-0.966725 - 2.97527i) q^{95} +(4.22224 + 3.61983i) q^{96} +(-11.7932 - 8.56824i) q^{97} +(-17.8198 - 7.38902i) q^{98} +(5.29298 + 4.17938i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 5 q^{2} - 2 q^{3} - 5 q^{4} + 15 q^{6} - 5 q^{8} - 10 q^{9}+O(q^{10}) $ 32 * q - 5 * q^2 - 2 * q^3 - 5 * q^4 + 15 * q^6 - 5 * q^8 - 10 * q^9	$ 32 q - 5 q^{2} - 2 q^{3} - 5 q^{4} + 15 q^{6} - 5 q^{8} - 10 q^{9} - 18 q^{11} - 18 q^{12} + 8 q^{14} - q^{16} - 10 q^{17} - 20 q^{18} - 30 q^{20} + 17 q^{22} + 5 q^{24} + 6 q^{25} - 4 q^{26} - 32 q^{27} - 30 q^{28} + 30 q^{30} + 32 q^{33} - 14 q^{34} - 10 q^{35} + 16 q^{36} + 28 q^{38} + 30 q^{40} - 10 q^{41} + 64 q^{42} - 38 q^{44} + 40 q^{46} + 26 q^{48} - 18 q^{49} + 5 q^{50} + 60 q^{51} + 40 q^{52} + 76 q^{56} - 80 q^{57} - 56 q^{58} + 28 q^{59} + 34 q^{60} - 80 q^{62} + 55 q^{64} - 30 q^{66} - 28 q^{67} + 60 q^{68} - 44 q^{70} + 45 q^{72} - 10 q^{73} - 100 q^{74} + 4 q^{75} - 80 q^{78} - 76 q^{80} + 28 q^{81} + 13 q^{82} - 50 q^{84} - 39 q^{86} - 69 q^{88} + 20 q^{89} - 30 q^{90} + 78 q^{91} + 6 q^{92} - 30 q^{94} - 110 q^{96} - 52 q^{97} + 122 q^{99}+O(q^{100}) $ 32 * q - 5 * q^2 - 2 * q^3 - 5 * q^4 + 15 * q^6 - 5 * q^8 - 10 * q^9 - 18 * q^11 - 18 * q^12 + 8 * q^14 - q^16 - 10 * q^17 - 20 * q^18 - 30 * q^20 + 17 * q^22 + 5 * q^24 + 6 * q^25 - 4 * q^26 - 32 * q^27 - 30 * q^28 + 30 * q^30 + 32 * q^33 - 14 * q^34 - 10 * q^35 + 16 * q^36 + 28 * q^38 + 30 * q^40 - 10 * q^41 + 64 * q^42 - 38 * q^44 + 40 * q^46 + 26 * q^48 - 18 * q^49 + 5 * q^50 + 60 * q^51 + 40 * q^52 + 76 * q^56 - 80 * q^57 - 56 * q^58 + 28 * q^59 + 34 * q^60 - 80 * q^62 + 55 * q^64 - 30 * q^66 - 28 * q^67 + 60 * q^68 - 44 * q^70 + 45 * q^72 - 10 * q^73 - 100 * q^74 + 4 * q^75 - 80 * q^78 - 76 * q^80 + 28 * q^81 + 13 * q^82 - 50 * q^84 - 39 * q^86 - 69 * q^88 + 20 * q^89 - 30 * q^90 + 78 * q^91 + 6 * q^92 - 30 * q^94 - 110 * q^96 - 52 * q^97 + 122 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/88\mathbb{Z}\right)^\times$.

$n$	$23$	$45$	$57$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.738473	+	1.20609i	0.522179	+	0.852836i
$2$	0.738473	+	1.20609i	0.522179	+	0.852836i
$3$	−0.303809	+	0.935028i	−0.175404	+	0.539839i	−0.999652	−	0.0263911i	$-0.991598\pi$
$3$	−0.303809	+	0.935028i	−0.175404	+	0.539839i	0.824248	+	0.566230i	$0.191598\pi$
$4$	−0.909315	+	1.78133i	−0.454658	+	0.890666i
$5$	0.398383	+	0.548327i	0.178162	+	0.245219i	0.888753	−	0.458386i	$-0.151572\pi$
$5$	0.398383	+	0.548327i	0.178162	+	0.245219i	−0.710591	+	0.703605i	$0.751572\pi$
$6$	−1.35208	+	0.324071i	−0.551986	+	0.132302i
$7$	−1.40393	−	4.32085i	−0.530636	−	1.63313i	−0.752894	−	0.658142i	$-0.771343\pi$
$7$	−1.40393	−	4.32085i	−0.530636	−	1.63313i	0.222258	−	0.974988i	$-0.428657\pi$
$8$	−2.81996	+	0.218749i	−0.997005	+	0.0773394i
$9$	1.64507	+	1.19522i	0.548358	+	0.398405i
$10$	−0.367138	+	0.885411i	−0.116099	+	0.279992i
$11$	3.31396	+	0.132807i	0.999198	+	0.0400429i
$11$	3.31396	+	0.132807i	0.999198	+	0.0400429i
$12$	−1.38934	−	1.39142i	−0.401067	−	0.401668i
$13$	1.90447	+	1.38368i	0.528205	+	0.383763i	0.819686	−	0.572813i	$-0.194148\pi$
$13$	1.90447	+	1.38368i	0.528205	+	0.383763i	−0.291481	+	0.956577i	$0.594148\pi$
$14$	4.17458	−	4.88410i	1.11570	−	1.30533i
$15$	−0.633734	+	0.205913i	−0.163629	+	0.0531664i
$16$	−2.34629	−	3.23959i	−0.586573	−	0.809896i
$17$	−2.07445	−	2.85523i	−0.503127	−	0.692495i	0.479614	−	0.877479i	$-0.340777\pi$
$17$	−2.07445	−	2.85523i	−0.503127	−	0.692495i	−0.982741	+	0.184984i	$0.940777\pi$
$18$	−0.226698	+	2.86675i	−0.0534332	+	0.675698i
$19$	−4.38980	−	1.42633i	−1.00709	−	0.327223i	−0.241394	−	0.970427i	$-0.577605\pi$
$19$	−4.38980	−	1.42633i	−1.00709	−	0.327223i	−0.765695	+	0.643204i	$0.777605\pi$
$20$	−1.33901	+	0.211051i	−0.299412	+	0.0471923i
$21$	4.46665			0.974702
$22$	2.28710	+	4.09502i	0.487611	+	0.873061i
$23$		−	1.11065i		−	0.231588i	−0.993273	−	0.115794i	$-0.963059\pi$
$23$		−	1.11065i		−	0.231588i	0.993273	−	0.115794i	$-0.0369412\pi$
$24$	0.652192	−	2.70319i	0.133128	−	0.551787i
$25$	1.40313	−	4.31839i	0.280626	−	0.863679i
$26$	−0.262443	+	3.31877i	−0.0514694	+	0.650865i
$27$	−4.00349	+	2.90871i	−0.770473	+	0.559781i
$28$	8.97349	+	1.42815i	1.69583	+	0.269895i
$29$	0.379398	+	1.16767i	0.0704524	+	0.216830i	0.980083	−	0.198588i	$-0.0636354\pi$
$29$	0.379398	+	1.16767i	0.0704524	+	0.216830i	−0.909631	+	0.415418i	$0.863635\pi$
$30$	−0.716345	−	0.612280i	−0.130786	−	0.111787i
$31$	−3.46109	+	4.76378i	−0.621630	+	0.855600i	−0.997470	−	0.0710846i	$-0.977354\pi$
$31$	−3.46109	+	4.76378i	−0.621630	+	0.855600i	0.375841	+	0.926684i	$0.377354\pi$
$32$	2.17456	−	5.22219i	0.384412	−	0.923162i
$33$	−1.13099	+	3.05830i	−0.196880	+	0.532382i
$34$	1.91175	−	4.61048i	0.327862	−	0.790691i
$35$	1.80994	−	2.49117i	0.305936	−	0.421084i
$36$	−3.62497	+	1.84360i	−0.604161	+	0.307266i
$37$	−8.78677	+	2.85499i	−1.44454	+	0.469358i	−0.923308	−	0.384059i	$-0.874526\pi$
$37$	−8.78677	+	2.85499i	−1.44454	+	0.469358i	−0.521228	+	0.853418i	$0.674526\pi$
$38$	−1.52146	−	6.34781i	−0.246814	−	1.02975i
$39$	−1.87237	+	1.36036i	−0.299820	+	0.217832i
$40$	−1.24337	−	1.45911i	−0.196594	−	0.230706i
$41$	1.88539	+	0.612601i	0.294449	+	0.0956722i	0.452516	−	0.891756i	$-0.350526\pi$
$41$	1.88539	+	0.612601i	0.294449	+	0.0956722i	−0.158068	+	0.987428i	$0.550526\pi$
$42$	3.29850	+	5.38718i	0.508969	+	0.831261i
$43$			2.02637i			0.309019i	0.987991	+	0.154509i	$0.0493797\pi$
$43$			2.02637i			0.309019i	−0.987991	+	0.154509i	$0.950620\pi$
$44$	−3.25001	+	5.78251i	−0.489958	+	0.871746i
$45$			1.37819i			0.205449i
$46$	1.33955	−	0.820189i	0.197506	−	0.120930i
$47$	4.48649	+	1.45775i	0.654422	+	0.212634i	0.617363	−	0.786679i	$-0.288201\pi$
$47$	4.48649	+	1.45775i	0.654422	+	0.212634i	0.0370589	+	0.999313i	$0.488201\pi$
$48$	3.74193	−	1.20963i	0.540101	−	0.174596i
$49$	−11.0356	+	8.01786i	−1.57652	+	1.14541i
$50$	6.24455	−	1.49671i	0.883113	−	0.211667i
$51$	3.29995	−	1.07222i	0.462086	−	0.150141i
$52$	−4.19655	+	2.13429i	−0.581957	+	0.295973i
$53$	4.70018	−	6.46924i	0.645619	−	0.888619i	−0.353280	−	0.935517i	$-0.614934\pi$
$53$	4.70018	−	6.46924i	0.645619	−	0.888619i	0.998900	+	0.0468989i	$0.0149339\pi$
$54$	−6.46464	−	2.68058i	−0.879727	−	0.364781i
$55$	1.24741	+	1.87005i	0.168200	+	0.252157i
$56$	4.90420	+	11.8775i	0.655352	+	1.58720i
$57$	2.66732	−	3.67125i	0.353295	−	0.486269i
$58$	−1.12814	+	1.31988i	−0.148132	+	0.173309i
$59$	−0.400488	−	1.23257i	−0.0521391	−	0.160468i	0.921597	−	0.388149i	$-0.126885\pi$
$59$	−0.400488	−	1.23257i	−0.0521391	−	0.160468i	−0.973736	+	0.227682i	$0.926885\pi$
$60$	0.209465	−	1.31613i	0.0270418	−	0.169912i
$61$	−6.73720	+	4.89486i	−0.862610	+	0.626723i	−0.928594	−	0.371098i	$-0.878981\pi$
$61$	−6.73720	+	4.89486i	−0.862610	+	0.626723i	0.0659840	+	0.997821i	$0.478981\pi$
$62$	−8.30147	−	0.656467i	−1.05429	−	0.0833714i
$63$	2.85479	−	8.78613i	0.359669	−	1.10695i
$64$	7.90430	−	1.23372i	0.988037	−	0.154215i
$65$			1.59551i			0.197898i
$66$	−4.52380	+	0.894394i	−0.556841	+	0.110092i
$67$	−0.483683			−0.0590913			−0.0295457	−	0.999563i	$-0.509406\pi$
$67$	−0.483683			−0.0590913			−0.0295457	+	0.999563i	$0.509406\pi$
$68$	6.97244	−	1.09897i	0.845532	−	0.133270i
$69$	1.03849	+	0.337427i	0.125020	+	0.0406214i
$70$	4.34117	+	0.343293i	0.518869	+	0.0410313i
$71$	8.68470	+	11.9535i	1.03068	+	1.41862i	0.904432	+	0.426618i	$0.140295\pi$
$71$	8.68470	+	11.9535i	1.03068	+	1.41862i	0.126253	+	0.991998i	$0.459705\pi$
$72$	−4.90049	−	3.01060i	−0.577528	−	0.354802i
$73$	8.79393	−	2.85732i	1.02925	−	0.334424i	0.254758	−	0.967005i	$-0.418004\pi$
$73$	8.79393	−	2.85732i	1.02925	−	0.334424i	0.774495	+	0.632581i	$0.218004\pi$
$74$	−9.93218	−	8.48931i	−1.15459	−	0.986863i
$75$	3.61153	+	2.62393i	0.417024	+	0.302986i
$76$	6.53249	−	6.52271i	0.749327	−	0.748206i
$77$	−4.07874	−	14.5056i	−0.464815	−	1.65307i
$78$	−3.02341	−	1.25367i	−0.342334	−	0.141950i
$79$	0.848366	+	0.616374i	0.0954487	+	0.0693475i	0.634486	−	0.772934i	$-0.281212\pi$
$79$	0.848366	+	0.616374i	0.0954487	+	0.0693475i	−0.539037	+	0.842282i	$0.681212\pi$
$80$	0.841630	−	2.57713i	0.0940971	−	0.288132i
$81$	0.381661	+	1.17463i	0.0424067	+	0.130515i
$82$	0.653458	+	2.72635i	0.0721624	+	0.301075i
$83$	−4.37741	−	6.02499i	−0.480483	−	0.661328i	0.498115	−	0.867111i	$-0.334026\pi$
$83$	−4.37741	−	6.02499i	−0.480483	−	0.661328i	−0.978598	+	0.205783i	$0.934026\pi$
$84$	−4.06159	+	7.95658i	−0.443156	+	0.868134i
$85$	0.739176	−	2.27495i	0.0801749	−	0.246753i
$86$	−2.44399	+	1.49642i	−0.263542	+	0.161363i
$87$	−1.20707			−0.129411
$88$	−9.37428	+	0.350415i	−0.999302	+	0.0373544i
$89$	2.47072			0.261895			0.130948	−	0.991389i	$-0.458198\pi$
$89$	2.47072			0.261895			0.130948	+	0.991389i	$0.458198\pi$
$90$	−1.66223	+	1.01776i	−0.175214	+	0.107281i
$91$	3.30493	−	10.1715i	0.346451	−	1.06627i
$92$	1.97845	+	1.00994i	0.206267	+	0.105293i
$93$	−3.40275	−	4.68349i	−0.352849	−	0.485655i
$94$	1.55497	+	6.48763i	0.160383	+	0.669148i
$95$	−0.966725	−	2.97527i	−0.0991839	−	0.305257i
$96$	4.22224	+	3.61983i	0.430931	+	0.369447i
$97$	−11.7932	−	8.56824i	−1.19741	−	0.869973i	−0.203387	−	0.979098i	$-0.565195\pi$
$97$	−11.7932	−	8.56824i	−1.19741	−	0.869973i	−0.994028	+	0.109126i	$0.965195\pi$
$98$	−17.8198	−	7.38902i	−1.80007	−	0.746404i
$99$	5.29298	+	4.17938i	0.531965	+	0.420044i
$100$	6.41661	+	6.42622i	0.641661	+	0.642622i
$101$	−12.0780	−	8.77521i	−1.20181	−	0.873166i	−0.207348	−	0.978267i	$-0.566483\pi$
$101$	−12.0780	−	8.77521i	−1.20181	−	0.873166i	−0.994462	+	0.105101i	$0.966483\pi$
$102$	3.73012	+	3.18824i	0.369337	+	0.315683i
$103$	5.78997	−	1.88127i	0.570502	−	0.185367i	−0.00953889	−	0.999955i	$-0.503036\pi$
$103$	5.78997	−	1.88127i	0.570502	−	0.185367i	0.580041	+	0.814587i	$0.303036\pi$
$104$	−5.67320	−	3.48531i	−0.556303	−	0.341763i
$105$	1.77944	+	2.44918i	0.173655	+	0.239016i
$106$	11.2735	+	0.891487i	1.09497	+	0.0865889i
$107$	10.0872	+	3.27751i	0.975162	+	0.316849i	0.752898	−	0.658137i	$-0.228655\pi$
$107$	10.0872	+	3.27751i	0.975162	+	0.316849i	0.222264	+	0.974987i	$0.428655\pi$
$108$	−1.54094	−	9.77649i	−0.148277	−	0.940743i
$109$	15.7342			1.50706			0.753530	−	0.657413i	$-0.228349\pi$
$109$	15.7342			1.50706			0.753530	+	0.657413i	$0.228349\pi$
$110$	−1.33427	+	2.88546i	−0.127218	+	0.275118i
$111$		−	9.08325i		−	0.862144i
$112$	−10.7037	+	14.6861i	−1.01141	+	1.38771i
$113$	−4.68638	+	14.4232i	−0.440858	+	1.35682i	0.446105	+	0.894981i	$0.352811\pi$
$113$	−4.68638	+	14.4232i	−0.440858	+	1.35682i	−0.886963	+	0.461840i	$0.847189\pi$
$114$	6.39761	+	0.505913i	0.599191	+	0.0473831i
$115$	0.609002	−	0.442466i	0.0567898	−	0.0412602i
$116$	−2.42500	−	0.385943i	−0.225155	−	0.0358339i
$117$	1.47920	+	4.55251i	0.136752	+	0.420879i
$118$	1.19085	−	1.39325i	0.109627	−	0.128259i
$119$	−9.42465	+	12.9719i	−0.863957	+	1.18913i
$120$	1.74206	−	0.719292i	0.159027	−	0.0656621i
$121$	10.9647	+	0.880237i	0.996793	+	0.0800215i
$122$	−10.8789	−	4.51096i	−0.984928	−	0.408403i
$123$	−1.14560	+	1.57678i	−0.103295	+	0.142174i
$124$	−5.33865	−	10.4971i	−0.479425	−	0.942669i
$125$	6.14986	−	1.99821i	0.550061	−	0.178725i
$126$	12.7051	−	3.04518i	1.13186	−	0.271287i
$127$	−4.99525	+	3.62926i	−0.443257	+	0.322045i	−0.786928	−	0.617045i	$-0.788330\pi$
$127$	−4.99525	+	3.62926i	−0.443257	+	0.322045i	0.343671	+	0.939090i	$0.388330\pi$
$128$	7.32509	+	8.62224i	0.647453	+	0.762105i
$129$	−1.89471	−	0.615629i	−0.166820	−	0.0542032i
$130$	−1.92433	+	1.17824i	−0.168775	+	0.103338i
$131$			17.0297i			1.48789i	0.668242	+	0.743944i	$0.267047\pi$
$131$			17.0297i			1.48789i	−0.668242	+	0.743944i	$0.732953\pi$
$132$	−4.41942	−	4.79563i	−0.384662	−	0.417406i
$133$			20.9702i			1.81834i
$134$	−0.357187	−	0.583367i	−0.0308563	−	0.0503952i
$135$	−3.18985	−	1.03644i	−0.274538	−	0.0892030i
$136$	6.47442	+	7.59784i	0.555177	+	0.651509i
$137$	4.87931	−	3.54503i	0.416868	−	0.302872i	−0.359508	−	0.933142i	$-0.617056\pi$
$137$	4.87931	−	3.54503i	0.416868	−	0.302872i	0.776376	+	0.630270i	$0.217056\pi$
$138$	0.359931	+	1.50170i	0.0306394	+	0.127833i
$139$	−13.6321	+	4.42932i	−1.15626	+	0.375690i	−0.823496	−	0.567322i	$-0.807980\pi$
$139$	−13.6321	+	4.42932i	−1.15626	+	0.375690i	−0.332759	+	0.943012i	$0.607980\pi$
$140$	2.79179	+	5.48936i	0.235950	+	0.463936i
$141$	−2.72607	+	3.75211i	−0.229577	+	0.315985i
$142$	−8.00356	+	19.3019i	−0.671644	+	1.61978i
$143$	6.12758	+	4.83839i	0.512414	+	0.404606i
$144$	0.0121805	−	8.13368i	0.00101504	−	0.677807i
$145$	−0.489118	+	0.673213i	−0.0406190	+	0.0559073i
$146$	9.94028	+	8.49624i	0.822663	+	0.703154i
$147$	−4.14420	−	12.7545i	−0.341808	−	1.05198i
$148$	2.90425	−	18.2482i	0.238728	−	1.50000i
$149$	6.77687	−	4.92369i	0.555183	−	0.403364i	−0.274510	−	0.961584i	$-0.588516\pi$
$149$	6.77687	−	4.92369i	0.555183	−	0.403364i	0.829693	+	0.558220i	$0.188516\pi$
$150$	−0.497684	+	6.29355i	−0.0406357	+	0.513866i
$151$	4.67119	−	14.3764i	0.380136	−	1.16994i	−0.559812	−	0.828620i	$-0.689127\pi$
$151$	4.67119	−	14.3764i	0.380136	−	1.16994i	0.939948	−	0.341318i	$-0.110873\pi$
$152$	12.6911	+	3.06193i	1.02938	+	0.248355i
$153$		−	7.17648i		−	0.580184i
$154$	14.4831	−	15.6313i	1.16708	−	1.25961i
$155$	−3.99095			−0.320561
$156$	−0.720674	−	4.57231i	−0.0577001	−	0.366078i
$157$	−11.3904	−	3.70098i	−0.909057	−	0.295370i	−0.183087	−	0.983097i	$-0.558609\pi$
$157$	−11.3904	−	3.70098i	−0.909057	−	0.295370i	−0.725970	+	0.687726i	$0.758609\pi$
$158$	−0.116908	+	1.47838i	−0.00930072	+	0.117614i
$159$	4.62096	+	6.36021i	0.366466	+	0.504398i
$160$	3.72978	−	0.888060i	0.294865	−	0.0702073i
$161$	−4.79898	+	1.55928i	−0.378212	+	0.122889i
$162$	−1.13487	+	1.32775i	−0.0891635	+	0.104318i
$163$	0.263367	+	0.191347i	0.0206285	+	0.0149875i	0.598052	−	0.801457i	$-0.295942\pi$
$163$	0.263367	+	0.191347i	0.0206285	+	0.0149875i	−0.577423	+	0.816445i	$0.695942\pi$
$164$	−2.80566	+	2.80146i	−0.219085	+	0.218758i
$165$	−2.12752	+	0.598222i	−0.165627	+	0.0465716i
$166$	4.03409	−	9.72885i	0.313106	−	0.755105i
$167$	−8.95740	−	6.50793i	−0.693144	−	0.503599i	0.184548	−	0.982823i	$-0.440918\pi$
$167$	−8.95740	−	6.50793i	−0.693144	−	0.503599i	−0.877692	+	0.479225i	$0.840918\pi$
$168$	−12.5957	+	0.977073i	−0.971782	+	0.0753828i
$169$	−2.30478	−	7.09339i	−0.177291	−	0.545645i
$170$	3.28966	−	0.788475i	0.252305	−	0.0604733i
$171$	−5.51677	−	7.59318i	−0.421878	−	0.580665i
$172$	−3.60964	−	1.84261i	−0.275232	−	0.140498i
$173$	−6.26024	+	19.2670i	−0.475957	+	1.46485i	0.368705	+	0.929546i	$0.379801\pi$
$173$	−6.26024	+	19.2670i	−0.475957	+	1.46485i	−0.844662	+	0.535299i	$0.820199\pi$
$174$	−0.891385	−	1.45583i	−0.0675757	−	0.110366i
$175$	−20.6290			−1.55941
$176$	−7.34529	−	11.0475i	−0.553672	−	0.832735i
$177$	1.27416			0.0957720
$178$	1.82456	+	2.97991i	0.136756	+	0.223354i
$179$	−2.93358	+	9.02862i	−0.219266	+	0.674831i	0.779557	+	0.626331i	$0.215444\pi$
$179$	−2.93358	+	9.02862i	−0.219266	+	0.674831i	−0.998823	+	0.0484999i	$0.984556\pi$
$180$	−2.45502	−	1.25321i	−0.182986	−	0.0934089i
$181$	6.14986	+	8.46456i	0.457116	+	0.629166i	0.973908	−	0.226945i	$-0.0728739\pi$
$181$	6.14986	+	8.46456i	0.457116	+	0.629166i	−0.516792	+	0.856111i	$0.672874\pi$
$182$	14.7084	−	3.52535i	1.09026	−	0.261316i
$183$	−2.53001	−	7.78657i	−0.187024	−	0.575600i
$184$	0.242954	+	3.13200i	0.0179108	+	0.230894i
$185$	−5.06597	−	3.68064i	−0.372458	−	0.270606i
$186$	3.13588	−	7.56267i	0.229934	−	0.554522i
$187$	−6.49544	−	9.73763i	−0.474994	−	0.712086i
$188$	−6.67637	+	6.66638i	−0.486924	+	0.486196i
$189$	18.1887	+	13.2149i	1.32304	+	0.961242i
$190$	2.87455	−	3.36312i	0.208542	−	0.243986i
$191$	−1.39594	+	0.453568i	−0.101007	+	0.0328190i	−0.359084	−	0.933305i	$-0.616911\pi$
$191$	−1.39594	+	0.453568i	−0.101007	+	0.0328190i	0.258078	+	0.966124i	$0.416911\pi$
$192$	−1.24783	+	7.76555i	−0.0900544	+	0.560431i
$193$	−2.96615	−	4.08256i	−0.213508	−	0.293869i	0.688808	−	0.724944i	$-0.258134\pi$
$193$	−2.96615	−	4.08256i	−0.213508	−	0.293869i	−0.902316	+	0.431075i	$0.858134\pi$
$194$	1.62515	−	20.5511i	0.116679	−	1.47548i
$195$	−1.49184	−	0.484729i	−0.106833	−	0.0347122i
$196$	−4.24761	−	26.9489i	−0.303400	−	1.92492i
$197$	15.3763			1.09552			0.547759	−	0.836636i	$-0.315481\pi$
$197$	15.3763			1.09552			0.547759	+	0.836636i	$0.315481\pi$
$198$	−1.13199	+	9.47019i	−0.0804472	+	0.673017i
$199$		−	12.6770i		−	0.898652i	−0.893368	−	0.449326i	$-0.851664\pi$
$199$		−	12.6770i		−	0.898652i	0.893368	−	0.449326i	$-0.148336\pi$
$200$	−3.01212	+	12.4846i	−0.212989	+	0.882795i
$201$	0.146947	−	0.452257i	0.0103649	−	0.0318998i
$202$	1.66440	−	21.0475i	0.117107	−	1.48090i
$203$	4.51267	−	3.27865i	0.316727	−	0.230116i
$204$	−1.09072	+	6.85330i	−0.0763655	+	0.479827i
$205$	0.415203	+	1.27786i	0.0289990	+	0.0892497i
$206$	6.54473	+	5.59396i	0.455993	+	0.389750i
$207$	1.32747	−	1.82711i	0.0922657	−	0.126993i
$208$	0.0141011	−	9.41621i	0.000977734	−	0.652896i
$209$	−14.3582	−	5.30981i	−0.993179	−	0.367288i
$210$	−1.63987	+	3.95482i	−0.113162	+	0.272908i
$211$	−1.12319	+	1.54593i	−0.0773233	+	0.106426i	−0.845927	−	0.533299i	$-0.820952\pi$
$211$	−1.12319	+	1.54593i	−0.0773233	+	0.106426i	0.768603	+	0.639726i	$0.220952\pi$
$212$	7.24993	+	14.2552i	0.497927	+	0.979048i
$213$	−13.8153	+	4.48887i	−0.946610	+	0.307572i
$214$	3.49611	+	14.5864i	0.238989	+	0.997105i
$215$	−1.11111	+	0.807272i	−0.0757774	+	0.0550555i
$216$	10.6534	−	9.07819i	0.724872	−	0.617693i
$217$	25.4427	+	8.26684i	1.72716	+	0.561190i
$218$	11.6193	+	18.9769i	0.786956	+	1.28528i
$219$			9.09065i			0.614289i
$220$	−4.46546	+	0.521584i	−0.301061	+	0.0351652i
$221$		−	8.30806i		−	0.558861i
$222$	10.9552	−	6.70773i	0.735267	−	0.450194i
$223$	9.95822	+	3.23562i	0.666852	+	0.216673i	0.622830	−	0.782357i	$-0.285983\pi$
$223$	9.95822	+	3.23562i	0.666852	+	0.216673i	0.0440220	+	0.999031i	$0.485983\pi$
$224$	−25.6173	−	2.06438i	−1.71163	−	0.137932i
$225$	7.46967	−	5.42703i	0.497978	−	0.361802i
$226$	−20.8565	+	4.99894i	−1.38735	+	0.332525i
$227$	14.4585	−	4.69785i	0.959644	−	0.311807i	0.213016	−	0.977049i	$-0.431671\pi$
$227$	14.4585	−	4.69785i	0.959644	−	0.311807i	0.746628	+	0.665241i	$0.231671\pi$
$228$	4.11429	+	8.08971i	0.272475	+	0.535754i
$229$	15.5186	−	21.3595i	1.02550	−	1.41148i	0.117220	−	0.993106i	$-0.462602\pi$
$229$	15.5186	−	21.3595i	1.02550	−	1.41148i	0.908277	−	0.418370i	$-0.137398\pi$
$230$	0.983387	+	0.407763i	0.0648426	+	0.0268871i
$231$	14.8023	+	0.593203i	0.973920	+	0.0390299i
$232$	−1.32531	−	3.20978i	−0.0870109	−	0.210732i
$233$	−3.56834	+	4.91140i	−0.233770	+	0.321757i	−0.909745	−	0.415168i	$-0.863723\pi$
$233$	−3.56834	+	4.91140i	−0.233770	+	0.321757i	0.675975	+	0.736925i	$0.263723\pi$
$234$	−4.39839	+	5.14595i	−0.287532	+	0.336401i
$235$	0.988018	+	3.04081i	0.0644512	+	0.198360i
$236$	2.55979	+	0.407397i	0.166628	+	0.0265193i
$237$	−0.834068	+	0.605986i	−0.0541786	+	0.0393630i
$238$	−22.6052	−	1.78758i	−1.46528	−	0.115872i
$239$	−3.83978	+	11.8176i	−0.248375	+	0.764418i	0.746689	+	0.665174i	$0.231643\pi$
$239$	−3.83978	+	11.8176i	−0.248375	+	0.764418i	−0.995063	+	0.0992444i	$0.968357\pi$
$240$	2.15400	+	1.56990i	0.139040	+	0.101337i
$241$			8.63844i			0.556451i	0.960516	+	0.278225i	$0.0897462\pi$
$241$			8.63844i			0.556451i	−0.960516	+	0.278225i	$0.910254\pi$
$242$	7.03551	+	13.8745i	0.452260	+	0.891886i
$243$	−16.0600			−1.03025
$244$	−2.59314	−	16.4522i	−0.166009	−	1.05324i
$245$	−8.79282	−	2.85696i	−0.561753	−	0.182525i
$246$	−2.74774	−	0.217287i	−0.175189	−	0.0138537i
$247$	−6.38666	−	8.79048i	−0.406373	−	0.559325i
$248$	8.71804	−	14.1907i	0.553596	−	0.901113i
$249$	6.96343	−	2.26255i	0.441289	−	0.143384i
$250$	6.95154	+	5.94167i	0.439654	+	0.375784i
$251$	−0.223050	−	0.162055i	−0.0140788	−	0.0102288i	0.580724	−	0.814101i	$-0.302770\pi$
$251$	−0.223050	−	0.162055i	−0.0140788	−	0.0102288i	−0.594802	+	0.803872i	$0.702770\pi$
$252$	13.0551	+	13.0747i	0.822395	+	0.823627i
$253$	0.147503	−	3.68067i	0.00927343	−	0.231402i
$254$	−8.06608	−	3.34462i	−0.506111	−	0.209860i
$255$	1.90257	+	1.38230i	0.119144	+	0.0865630i
$256$	−4.98983	+	15.2020i	−0.311864	+	0.950127i
$257$	2.16006	+	6.64799i	0.134741	+	0.414690i	0.995550	−	0.0942387i	$-0.0300417\pi$
$257$	2.16006	+	6.64799i	0.134741	+	0.414690i	−0.860809	+	0.508929i	$0.830042\pi$
$258$	−0.656689	−	2.73982i	−0.0408836	−	0.170574i
$259$	24.6720	+	33.9581i	1.53305	+	2.11006i
$260$	−2.84213	−	1.45082i	−0.176261	−	0.0899759i
$261$	−0.771477	+	2.37436i	−0.0477532	+	0.146969i
$262$	−20.5393	+	12.5759i	−1.26892	+	0.776944i
$263$	−11.5402			−0.711602			−0.355801	−	0.934562i	$-0.615792\pi$
$263$	−11.5402			−0.711602			−0.355801	+	0.934562i	$0.615792\pi$
$264$	2.52034	−	8.87168i	0.155116	−	0.546014i
$265$	5.41973			0.332932
$266$	−25.2919	+	15.4859i	−1.55075	+	0.949501i
$267$	−0.750625	+	2.31019i	−0.0459375	+	0.141381i
$268$	0.439821	−	0.861601i	0.0268663	−	0.0526307i
$269$	−11.3719	−	15.6521i	−0.693356	−	0.954323i	−0.999997	−	0.00249771i	$-0.999205\pi$
$269$	−11.3719	−	15.6521i	−0.693356	−	0.954323i	0.306641	−	0.951825i	$-0.400795\pi$
$270$	−1.10557	−	4.61264i	−0.0672828	−	0.280716i
$271$	1.38625	+	4.26643i	0.0842086	+	0.259167i	0.984291	−	0.176551i	$-0.0564942\pi$
$271$	1.38625	+	4.26643i	0.0842086	+	0.259167i	−0.900083	+	0.435719i	$0.856494\pi$
$272$	−4.38250	+	13.4195i	−0.265728	+	0.813680i
$273$	8.50659	+	6.18040i	0.514842	+	0.374055i
$274$	7.87887	+	3.26699i	0.475980	+	0.197366i
$275$	5.22344	−	14.1247i	0.314985	−	0.851749i
$276$	−1.54539	+	1.54307i	−0.0930214	+	0.0928822i
$277$	−13.7180	−	9.96671i	−0.824235	−	0.598842i	0.0936874	−	0.995602i	$-0.470135\pi$
$277$	−13.7180	−	9.96671i	−0.824235	−	0.598842i	−0.917922	+	0.396760i	$0.870135\pi$
$278$	−15.4091	−	13.1706i	−0.924175	−	0.789919i
$279$	−11.3875	+	3.70002i	−0.681751	+	0.221514i
$280$	−4.55901	+	7.42091i	−0.272453	+	0.443484i
$281$	−4.32677	−	5.95529i	−0.258113	−	0.355263i	0.660219	−	0.751073i	$-0.270464\pi$
$281$	−4.32677	−	5.95529i	−0.258113	−	0.355263i	−0.918332	+	0.395811i	$0.870464\pi$
$282$	−6.53852	−	0.517056i	−0.389363	−	0.0307902i
$283$	−1.17501	−	0.381784i	−0.0698470	−	0.0226947i	0.273885	−	0.961762i	$-0.411691\pi$
$283$	−1.17501	−	0.381784i	−0.0698470	−	0.0226947i	−0.343732	+	0.939068i	$0.611691\pi$
$284$	−29.1902	+	4.60088i	−1.73212	+	0.273012i
$285$	3.07566			0.182187
$286$	−1.31049	+	10.9634i	−0.0774906	+	0.648282i
$287$		−	9.00655i		−	0.531640i
$288$	9.81896	−	5.99182i	0.578588	−	0.353071i
$289$	1.40428	−	4.32192i	0.0826046	−	0.254231i
$290$	−1.17316	−	0.0927714i	−0.0688901	−	0.00544772i
$291$	11.5944	−	8.42383i	0.679676	−	0.493814i
$292$	−2.90662	+	18.2631i	−0.170097	+	1.06877i
$293$	−0.464488	−	1.42955i	−0.0271357	−	0.0835150i	0.936572	−	0.350476i	$-0.113980\pi$
$293$	−0.464488	−	1.42955i	−0.0271357	−	0.0835150i	−0.963707	+	0.266961i	$0.913980\pi$
$294$	12.3228	−	14.4172i	0.718678	−	0.840826i
$295$	0.516307	−	0.710635i	0.0300605	−	0.0413748i
$296$	24.1538	−	9.97305i	1.40391	−	0.579672i
$297$	−13.6537	+	9.10767i	−0.792270	+	0.528480i
$298$	10.9430	+	4.53752i	0.633908	+	0.262852i
$299$	1.53679	−	2.11521i	0.0888748	−	0.122326i
$300$	−7.95812	+	4.04736i	−0.459462	+	0.233675i
$301$	8.75565	−	2.84488i	0.504667	−	0.163976i
$302$	20.7889	−	4.98273i	1.19626	−	0.286724i
$303$	11.8745	−	8.62732i	0.682171	−	0.495626i
$304$	5.67903	+	17.5677i	0.325715	+	1.00758i
$305$	−5.36797	−	1.74416i	−0.307369	−	0.0998703i
$306$	8.65549	−	5.29963i	0.494801	−	0.302960i
$307$		−	28.1622i		−	1.60730i	−0.595100	−	0.803652i	$-0.702888\pi$
$307$		−	28.1622i		−	1.60730i	0.595100	−	0.803652i	$-0.297112\pi$
$308$	29.5482	+	5.92458i	1.68366	+	0.337585i
$309$			5.98533i			0.340493i
$310$	−2.94721	−	4.81345i	−0.167390	−	0.273386i
$311$	29.7223	+	9.65736i	1.68540	+	0.547619i	0.985946	−	0.167062i	$-0.0534281\pi$
$311$	29.7223	+	9.65736i	1.68540	+	0.547619i	0.699451	+	0.714681i	$0.253428\pi$
$312$	4.98243	−	4.24573i	0.282075	−	0.240367i
$313$	−7.97204	+	5.79203i	−0.450606	+	0.327385i	−0.789835	−	0.613319i	$-0.789834\pi$
$313$	−7.97204	+	5.79203i	−0.450606	+	0.327385i	0.339229	+	0.940704i	$0.389834\pi$
$314$	−3.94782	−	16.4710i	−0.222788	−	0.929512i
$315$	5.95497	−	1.93489i	0.335525	−	0.109019i
$316$	−1.86940	+	0.950744i	−0.105162	+	0.0534835i
$317$	−1.47669	+	2.03248i	−0.0829389	+	0.114156i	−0.848470	−	0.529243i	$-0.822476\pi$
$317$	−1.47669	+	2.03248i	−0.0829389	+	0.114156i	0.765532	+	0.643398i	$0.222476\pi$
$318$	−4.25854	+	10.2702i	−0.238807	+	0.575921i
$319$	1.10224	+	3.91999i	0.0617134	+	0.219477i
$320$	3.82542	+	3.84265i	0.213848	+	0.214811i
$321$	−6.12913	+	8.43603i	−0.342095	+	0.470853i
$322$	−5.42455	−	4.63652i	−0.302299	−	0.258383i
$323$	5.03390	+	15.4927i	0.280093	+	0.862039i
$324$	−2.43946	−	0.388245i	−0.135525	−	0.0215692i
$325$	8.64749	−	6.28277i	0.479676	−	0.348505i
$326$	−0.0362930	+	0.458950i	−0.00201009	+	0.0254189i
$327$	−4.78018	+	14.7119i	−0.264345	+	0.813569i
$328$	−5.45073	−	1.31508i	−0.300966	−	0.0726132i
$329$		−	21.4320i		−	1.18159i
$330$	−2.29263	−	2.12421i	−0.126205	−	0.116934i
$331$	3.34398			0.183802			0.0919009	−	0.995768i	$-0.470706\pi$
$331$	3.34398			0.183802			0.0919009	+	0.995768i	$0.470706\pi$
$332$	14.7130	−	2.31901i	0.807478	−	0.127272i
$333$	−17.8672	−	5.80541i	−0.979118	−	0.318135i
$334$	1.23436	−	15.6094i	0.0675414	−	0.854107i
$335$	−0.192691	−	0.265217i	−0.0105279	−	0.0144903i
$336$	−10.4801	−	14.4701i	−0.571734	−	0.789407i
$337$	−15.8356	+	5.14531i	−0.862622	+	0.280283i	−0.706723	−	0.707490i	$-0.749827\pi$
$337$	−15.8356	+	5.14531i	−0.862622	+	0.280283i	−0.155899	+	0.987773i	$0.549827\pi$
$338$	6.85326	−	8.01805i	0.372768	−	0.436125i
$339$	−12.0623	−	8.76380i	−0.655136	−	0.475984i
$340$	3.38030	+	3.38537i	0.183322	+	0.183597i
$341$	−12.1026	+	15.3273i	−0.655392	+	0.830022i
$342$	5.08409	−	12.2611i	0.274916	−	0.663004i
$343$	24.4085	+	17.7338i	1.31794	+	0.957537i
$344$	−0.443266	−	5.71428i	−0.0238993	−	0.308093i
$345$	0.228698	+	0.703859i	0.0123127	+	0.0378945i
$346$	−27.8608	+	6.67776i	−1.49781	+	0.358999i
$347$	−11.7164	−	16.1263i	−0.628972	−	0.865705i	0.368996	−	0.929431i	$-0.379702\pi$
$347$	−11.7164	−	16.1263i	−0.628972	−	0.865705i	−0.997967	+	0.0637258i	$0.979702\pi$
$348$	1.09760	−	2.15018i	0.0588377	−	0.115262i
$349$	−0.0914787	+	0.281543i	−0.00489674	+	0.0150706i	−0.953475	−	0.301472i	$-0.902522\pi$
$349$	−0.0914787	+	0.281543i	−0.00489674	+	0.0150706i	0.948578	+	0.316543i	$0.102522\pi$
$350$	−15.2340	−	24.8805i	−0.814291	−	1.32992i
$351$	−11.6493			−0.621791
$352$	7.89997	−	17.0174i	0.421070	−	0.907028i
$353$	12.3132			0.655366			0.327683	−	0.944788i	$-0.393732\pi$
$353$	12.3132			0.655366			0.327683	+	0.944788i	$0.393732\pi$
$354$	0.940935	+	1.53676i	0.0500101	+	0.0816777i
$355$	−3.09457	+	9.52412i	−0.164243	+	0.505488i
$356$	−2.24666	+	4.40117i	−0.119073	+	0.233261i
$357$	−9.26581	−	12.7533i	−0.490399	−	0.674976i
$358$	−13.0557	+	3.12923i	−0.690016	+	0.165385i
$359$	3.65694	+	11.2549i	0.193006	+	0.594011i	0.999994	+	0.00344333i	$0.00109605\pi$
$359$	3.65694	+	11.2549i	0.193006	+	0.594011i	−0.806988	+	0.590567i	$0.798904\pi$
$360$	−0.301478	−	3.88644i	−0.0158893	−	0.204833i
$361$	1.86460	+	1.35471i	0.0981371	+	0.0713008i
$362$	−5.66753	+	13.6682i	−0.297879	+	0.718382i
$363$	−4.15423	+	9.98490i	−0.218040	+	0.524071i
$364$	15.1136	+	15.1363i	0.792170	+	0.793358i
$365$	5.07010	+	3.68365i	0.265381	+	0.192811i
$366$	7.52297	−	8.80160i	0.393232	−	0.460067i
$367$	24.6571	−	8.01159i	1.28709	−	0.418202i	0.416020	−	0.909356i	$-0.363425\pi$
$367$	24.6571	−	8.01159i	1.28709	−	0.418202i	0.871073	+	0.491154i	$0.163425\pi$
$368$	−3.59806	+	2.60592i	−0.187562	+	0.135843i
$369$	2.36942	+	3.26123i	0.123347	+	0.169773i
$370$	0.698111	−	8.82808i	0.0362931	−	0.458950i
$371$	−34.5514	−	11.2264i	−1.79382	−	0.582847i
$372$	11.4370	−	1.80267i	0.592982	−	0.0934641i
$373$	−15.3985			−0.797305			−0.398652	−	0.917102i	$-0.630522\pi$
$373$	−15.3985			−0.797305			−0.398652	+	0.917102i	$0.630522\pi$
$374$	6.94777	−	15.0251i	0.359260	−	0.776928i
$375$			6.35737i			0.328293i
$376$	−12.9706	−	3.12937i	−0.668907	−	0.161385i
$377$	−0.893123	+	2.74875i	−0.0459982	+	0.141568i
$378$	−2.50648	+	31.6961i	−0.128919	+	1.63027i
$379$	6.68999	−	4.86056i	0.343642	−	0.249670i	−0.402555	−	0.915396i	$-0.631878\pi$
$379$	6.68999	−	4.86056i	0.343642	−	0.249670i	0.746197	+	0.665725i	$0.231878\pi$
$380$	6.17901	+	0.983402i	0.316977	+	0.0504475i
$381$	−1.87586	−	5.77330i	−0.0961032	−	0.295775i
$382$	−1.57791	−	1.34868i	−0.0807328	−	0.0690046i
$383$	−0.0941501	+	0.129586i	−0.00481085	+	0.00662156i	−0.811416	−	0.584470i	$-0.801303\pi$
$383$	−0.0941501	+	0.129586i	−0.00481085	+	0.00662156i	0.806605	+	0.591091i	$0.201303\pi$
$384$	−10.2875	+	4.22965i	−0.524980	+	0.215844i
$385$	6.32892	−	8.01527i	0.322552	−	0.408496i
$386$	2.73352	−	6.59231i	0.139132	−	0.335540i
$387$	−2.42195	+	3.33353i	−0.123115	+	0.169453i
$388$	25.9866	−	13.2163i	1.31927	−	0.670957i
$389$	14.1473	−	4.59673i	0.717295	−	0.233063i	0.0724452	−	0.997372i	$-0.476920\pi$
$389$	14.1473	−	4.59673i	0.717295	−	0.233063i	0.644850	+	0.764309i	$0.276920\pi$
$390$	−0.517058	−	2.15726i	−0.0261822	−	0.109237i
$391$	−3.17117	+	2.30399i	−0.160373	+	0.116518i
$392$	29.3661	−	25.0240i	1.48321	−	1.26391i
$393$	−15.9232	−	5.17376i	−0.803219	−	0.260982i
$394$	11.3550	+	18.5453i	0.572056	+	0.934296i
$395$			0.710735i			0.0357610i
$396$	−12.2579	+	5.62819i	−0.615981	+	0.282827i
$397$			14.1188i			0.708603i	0.935131	+	0.354301i	$0.115281\pi$
$397$			14.1188i			0.708603i	−0.935131	+	0.354301i	$0.884719\pi$
$398$	15.2897	−	9.36166i	0.766403	−	0.469257i
$399$	−19.6077	−	6.37092i	−0.981612	−	0.318945i
$400$	−17.2820	+	5.58665i	−0.864098	+	0.279333i
$401$	12.8915	−	9.36625i	0.643772	−	0.467728i	−0.217372	−	0.976089i	$-0.569748\pi$
$401$	12.8915	−	9.36625i	0.643772	−	0.467728i	0.861144	+	0.508361i	$0.169748\pi$
$402$	0.653981	−	0.156748i	0.0326176	−	0.00781788i
$403$	−13.1831	+	4.28344i	−0.656695	+	0.213373i
$404$	26.6143	−	13.5356i	1.32411	−	0.673420i
$405$	−0.492035	+	0.677228i	−0.0244494	+	0.0336517i
$406$	7.28683	+	3.02150i	0.361639	+	0.149955i
$407$	−29.4982	+	8.29441i	−1.46217	+	0.411138i
$408$	−9.07118	+	3.74547i	−0.449090	+	0.185429i
$409$	−11.8080	+	16.2524i	−0.583870	+	0.803629i	−0.994113	−	0.108348i	$-0.965444\pi$
$409$	−11.8080	+	16.2524i	−0.583870	+	0.803629i	0.410243	+	0.911976i	$0.365444\pi$
$410$	−1.23460	+	1.44444i	−0.0609727	+	0.0713358i
$411$	1.83232	+	5.63930i	0.0903817	+	0.278166i
$412$	−1.91373	+	12.0245i	−0.0942827	+	0.592406i
$413$	−4.76352	+	3.46090i	−0.234397	+	0.170300i
$414$	3.18396	+	0.251783i	0.156483	+	0.0123745i
$415$	1.55978	−	4.80051i	0.0765665	−	0.235648i
$416$	11.3672	−	6.93661i	0.557324	−	0.340095i
$417$		−	14.0920i		−	0.690089i
$418$	−4.19903	−	21.2385i	−0.205381	−	1.03881i
$419$	13.8395			0.676103			0.338052	−	0.941128i	$-0.390232\pi$
$419$	13.8395			0.676103			0.338052	+	0.941128i	$0.390232\pi$
$420$	−5.98088	+	0.942688i	−0.291837	+	0.0459985i
$421$	11.9971	+	3.89810i	0.584704	+	0.189982i	0.586407	−	0.810017i	$-0.300542\pi$
$421$	11.9971	+	3.89810i	0.584704	+	0.189982i	−0.00170305	+	0.999999i	$0.500542\pi$
$422$	−2.69398	−	0.213036i	−0.131141	−	0.0103704i
$423$	5.63828	+	7.76043i	0.274143	+	0.377325i
$424$	−11.8392	+	19.2711i	−0.574960	+	0.935889i
$425$	−15.2407	+	4.95201i	−0.739284	+	0.240208i
$426$	−15.6162	−	13.3476i	−0.756609	−	0.646695i
$427$	30.6085	+	22.2384i	1.48125	+	1.07619i
$428$	−15.0107	+	14.9883i	−0.725572	+	0.724486i
$429$	−6.38564	+	4.25951i	−0.308302	+	0.205651i
$430$	−1.79417	−	0.743957i	−0.0865226	−	0.0358768i
$431$	−12.6175	−	9.16714i	−0.607763	−	0.441566i	0.240863	−	0.970559i	$-0.422570\pi$
$431$	−12.6175	−	9.16714i	−0.607763	−	0.441566i	−0.848626	+	0.528993i	$0.822570\pi$
$432$	18.8164	+	6.14498i	0.905304	+	0.295651i
$433$	0.235781	+	0.725659i	0.0113309	+	0.0348729i	0.956562	−	0.291529i	$-0.0941638\pi$
$433$	0.235781	+	0.725659i	0.0113309	+	0.0348729i	−0.945231	+	0.326402i	$0.894164\pi$
$434$	8.81819	+	36.7911i	0.423287	+	1.76603i
$435$	−0.480874	−	0.661867i	−0.0230562	−	0.0317341i
$436$	−14.3073	+	28.0278i	−0.685196	+	1.34229i
$437$	−1.58416	+	4.87555i	−0.0757808	+	0.233229i
$438$	−10.9642	+	6.71320i	−0.523888	+	0.320769i
$439$	−1.62453			−0.0775344			−0.0387672	−	0.999248i	$-0.512343\pi$
$439$	−1.62453			−0.0775344			−0.0387672	+	0.999248i	$0.512343\pi$
$440$	−3.92670	−	5.00058i	−0.187198	−	0.238393i
$441$	−27.7375			−1.32083
$442$	10.0203	−	6.13528i	0.476616	−	0.291826i
$443$	10.2530	−	31.5554i	0.487134	−	1.49924i	−0.341732	−	0.939797i	$-0.611014\pi$
$443$	10.2530	−	31.5554i	0.487134	−	1.49924i	0.828866	−	0.559447i	$-0.188986\pi$
$444$	16.1803	+	8.25953i	0.767882	+	0.391980i
$445$	0.984291	+	1.35476i	0.0466599	+	0.0642218i
$446$	3.45142	+	14.4000i	0.163430	+	0.681857i
$447$	2.54491	+	7.83242i	0.120370	+	0.370461i
$448$	−16.4278	−	32.4213i	−0.776142	−	1.53176i
$449$	20.6014	+	14.9678i	0.972239	+	0.706373i	0.955961	−	0.293495i	$-0.0948183\pi$
$449$	20.6014	+	14.9678i	0.972239	+	0.706373i	0.0162782	+	0.999868i	$0.494818\pi$
$450$	12.0616	+	5.00139i	0.568592	+	0.235768i
$451$	6.16677	+	2.28053i	0.290382	+	0.107386i
$452$	−21.4311	−	21.4632i	−1.00804	−	1.00955i
$453$	12.0232	+	8.73538i	0.564900	+	0.410424i
$454$	16.3433	+	13.9690i	0.767027	+	0.655600i
$455$	6.89395	−	2.23998i	0.323193	−	0.105012i
$456$	−6.71865	+	10.9362i	−0.314629	+	0.512137i
$457$	20.3313	+	27.9836i	0.951058	+	1.30902i	0.951056	+	0.309019i	$0.100001\pi$
$457$	20.3313	+	27.9836i	0.951058	+	1.30902i	1.63349e−6		1.00000i	$0.499999\pi$
$458$	37.2216	+	2.94342i	1.73925	+	0.137537i
$459$	16.6101	+	5.39694i	0.775291	+	0.251907i
$460$	0.234404	+	1.48718i	0.0109292	+	0.0693400i
$461$	−11.5194			−0.536510			−0.268255	−	0.963348i	$-0.586447\pi$
$461$	−11.5194			−0.536510			−0.268255	+	0.963348i	$0.586447\pi$
$462$	10.2156	+	18.2910i	0.475275	+	0.850974i
$463$			11.0442i			0.513267i	0.966509	+	0.256634i	$0.0826133\pi$
$463$			11.0442i			0.513267i	−0.966509	+	0.256634i	$0.917387\pi$
$464$	2.89258	−	3.96878i	0.134285	−	0.184246i
$465$	1.21249	−	3.73165i	0.0562277	−	0.173051i
$466$	−8.55873	−	0.676811i	−0.396476	−	0.0313527i
$467$	−10.7423	+	7.80474i	−0.497095	+	0.361160i	−0.807906	−	0.589311i	$-0.799399\pi$
$467$	−10.7423	+	7.80474i	−0.497095	+	0.361160i	0.310812	+	0.950472i	$0.399399\pi$
$468$	−9.45459	−	1.50472i	−0.437038	−	0.0695556i
$469$	0.679058	+	2.08993i	0.0313560	+	0.0965038i
$470$	−2.93787	+	3.43719i	−0.135514	+	0.158546i
$471$	6.92104	−	9.52599i	0.318905	−	0.438935i
$472$	1.39898	+	3.38820i	0.0643934	+	0.155954i
$473$	−0.269117	+	6.71532i	−0.0123740	+	0.308771i
$474$	−1.34681	−	0.558458i	−0.0618611	−	0.0256508i
$475$	−12.3189	+	16.9556i	−0.565231	+	0.777974i
$476$	−14.5373	−	28.5840i	−0.666317	−	1.31015i
$477$	15.4643	−	5.02465i	0.708061	−	0.230063i
$478$	−17.0887	+	4.09587i	−0.781619	+	0.187341i
$479$	7.66139	−	5.56633i	0.350058	−	0.254332i	−0.398835	−	0.917023i	$-0.630586\pi$
$479$	7.66139	−	5.56633i	0.350058	−	0.254332i	0.748893	+	0.662691i	$0.230586\pi$
$480$	−0.302780	+	3.75725i	−0.0138199	+	0.171494i
$481$	−20.6845	−	6.72081i	−0.943133	−	0.306443i
$482$	−10.4187	+	6.37925i	−0.474561	+	0.290567i
$483$		−	4.96090i		−	0.225729i
$484$	−11.5384	+	18.7314i	−0.524472	+	0.851428i
$485$		−	9.87996i		−	0.448626i
$486$	−11.8599	−	19.3699i	−0.537976	−	0.878636i
$487$	−26.0060	−	8.44986i	−1.17844	−	0.382900i	−0.346656	−	0.937992i	$-0.612683\pi$
$487$	−26.0060	−	8.44986i	−1.17844	−	0.382900i	−0.831789	+	0.555092i	$0.812683\pi$
$488$	17.9279	−	15.2770i	0.811556	−	0.691559i
$489$	−0.258928	+	0.188123i	−0.0117091	+	0.00850719i
$490$	−3.04751	−	12.7147i	−0.137672	−	0.574394i
$491$	−22.5899	+	7.33990i	−1.01947	+	0.331245i	−0.770618	−	0.637297i	$-0.780052\pi$
$491$	−22.5899	+	7.33990i	−1.01947	+	0.331245i	−0.248849	+	0.968542i	$0.580052\pi$
$492$	−1.76706	−	3.47448i	−0.0796653	−	0.156642i
$493$	2.54692	−	3.50553i	0.114707	−	0.157881i
$494$	5.88575	−	14.1944i	0.264812	−	0.638637i
$495$	−0.183034	+	4.56728i	−0.00822676	+	0.205284i
$496$	23.5534	+	0.0352720i	1.05758	+	0.00158376i
$497$	39.4565	−	54.3072i	1.76986	−	2.43601i
$498$	7.87115	+	6.72770i	0.352715	+	0.301475i
$499$	−1.99682	−	6.14559i	−0.0893901	−	0.275114i	0.896361	−	0.443325i	$-0.146201\pi$
$499$	−1.99682	−	6.14559i	−0.0893901	−	0.275114i	−0.985751	+	0.168210i	$0.946201\pi$
$500$	−2.03268	+	12.7720i	−0.0909044	+	0.571179i
$501$	8.80643	−	6.39825i	0.393442	−	0.285853i
$502$	0.0307372	−	0.388692i	0.00137187	−	0.0173482i
$503$	11.1405	−	34.2869i	0.496730	−	1.52878i	−0.317513	−	0.948254i	$-0.602848\pi$
$503$	11.1405	−	34.2869i	0.496730	−	1.52878i	0.814243	−	0.580524i	$-0.197152\pi$
$504$	−6.12841	+	25.4010i	−0.272981	+	1.13145i
$505$		−	10.1186i		−	0.450272i
$506$	4.54815	−	2.54017i	0.202190	−	0.112925i
$507$	7.33273			0.325658
$508$	−1.92267	−	12.1983i	−0.0853045	−	0.541214i
$509$	35.4254	+	11.5104i	1.57021	+	0.510191i	0.959510	−	0.281675i	$-0.0908900\pi$
$509$	35.4254	+	11.5104i	1.57021	+	0.510191i	0.610695	+	0.791866i	$0.290890\pi$
$510$	−0.262182	+	3.31547i	−0.0116096	+	0.146811i
$511$	−24.6921	−	33.9858i	−1.09232	−	1.50344i
$512$	−22.0199	+	5.20810i	−0.973151	+	0.230168i
$513$	21.7233	−	7.05834i	0.959109	−	0.311633i
$514$	−6.42293	+	7.51459i	−0.283304	+	0.331454i
$515$	3.33818	+	2.42533i	0.147098	+	0.106873i
$516$	2.81953	−	2.81531i	0.124123	−	0.123937i
$517$	14.6745	+	5.42677i	0.645382	+	0.238669i
$518$	−22.7370	+	54.8339i	−0.999006	+	2.40926i
$519$	−16.1133	−	11.7070i	−0.707295	−	0.513880i
$520$	−0.349015	−	4.49926i	−0.0153053	−	0.197305i
$521$	6.23908	+	19.2019i	0.273339	+	0.841251i	0.989654	+	0.143474i	$0.0458273\pi$
$521$	6.23908	+	19.2019i	0.273339	+	0.841251i	−0.716315	+	0.697777i	$0.754173\pi$
$522$	−3.43341	+	0.822930i	−0.150276	+	0.0360187i
$523$	−0.813147	−	1.11920i	−0.0355564	−	0.0489392i	0.790869	−	0.611986i	$-0.209629\pi$
$523$	−0.813147	−	1.11920i	−0.0355564	−	0.0489392i	−0.826425	+	0.563047i	$0.809629\pi$
$524$	−30.3355	−	15.4853i	−1.32521	−	0.676479i
$525$	6.26729	−	19.2887i	0.273527	−	0.841829i
$526$	−8.52216	−	13.9186i	−0.371584	−	0.606880i
$527$	20.7815			0.905257
$528$	12.5613	−	3.51173i	0.546659	−	0.152828i
$529$	21.7664			0.946367
$530$	4.00233	+	6.53670i	0.173850	+	0.283936i
$531$	0.814361	−	2.50635i	0.0353403	−	0.108766i
$532$	−37.3548	−	19.0685i	−1.61954	−	0.826724i
$533$	2.74303	+	3.77546i	0.118814	+	0.163533i
$534$	−3.34061	+	0.800688i	−0.144563	+	0.0346492i
$535$	2.22140	+	6.83677i	0.0960395	+	0.295579i
$536$	1.36397	−	0.105805i	0.0589144	−	0.00457009i
$537$	−7.55076	−	5.48595i	−0.325839	−	0.236736i
$538$	10.4800	−	25.2742i	0.451824	−	1.08965i
$539$	−37.6366	+	25.1053i	−1.62112	+	1.08136i
$540$	4.74683	−	4.73973i	0.204271	−	0.203965i
$541$	−20.6634	−	15.0128i	−0.888389	−	0.645452i	0.0470688	−	0.998892i	$-0.485012\pi$
$541$	−20.6634	−	15.0128i	−0.888389	−	0.645452i	−0.935457	+	0.353440i	$0.885012\pi$
$542$	−4.12200	+	4.82259i	−0.177055	+	0.207148i
$543$	−9.78298	+	3.17868i	−0.419828	+	0.136410i
$544$	−19.4216	+	4.62427i	−0.832693	+	0.198264i
$545$	6.26823	+	8.62748i	0.268501	+	0.369560i
$546$	−1.17224	+	14.8238i	−0.0501673	+	0.634400i
$547$	3.13486	+	1.01858i	0.134037	+	0.0435512i	0.375267	−	0.926917i	$-0.377551\pi$
$547$	3.13486	+	1.01858i	0.134037	+	0.0435512i	−0.241230	+	0.970468i	$0.577551\pi$
$548$	1.87804	+	11.9152i	0.0802260	+	0.508993i
$549$	−16.9336			−0.722709
$550$	20.8930	−	4.13073i	0.890881	−	0.176135i
$551$		−	5.66697i		−	0.241421i
$552$	−3.00232	−	0.724360i	−0.127787	−	0.0308308i
$553$	1.47222	−	4.53101i	0.0626050	−	0.192678i
$554$	1.89040	−	23.9053i	0.0803152	−	1.01564i
$555$	4.98059	−	3.61861i	0.211414	−	0.153602i
$556$	4.50573	−	28.3109i	0.191086	−	1.20065i
$557$	10.8949	+	33.5309i	0.461630	+	1.42075i	0.863172	+	0.504911i	$0.168475\pi$
$557$	10.8949	+	33.5309i	0.461630	+	1.42075i	−0.401542	+	0.915841i	$0.631525\pi$
$558$	−12.8719	−	11.0020i	−0.544912	−	0.465751i
$559$	−2.80384	+	3.85916i	−0.118590	+	0.163225i
$560$	−12.3170	−	0.0184451i	−0.520488	−	0.000779448i
$561$	11.0783	−	3.11504i	0.467727	−	0.131517i
$562$	3.98742	−	9.61630i	0.168199	−	0.405639i
$563$	21.2821	−	29.2923i	0.896934	−	1.23452i	−0.0745021	−	0.997221i	$-0.523737\pi$
$563$	21.2821	−	29.2923i	0.896934	−	1.23452i	0.971436	−	0.237303i	$-0.0762633\pi$
$564$	−4.20491	−	8.26789i	−0.177059	−	0.348141i
$565$	−9.77561	+	3.17629i	−0.411263	+	0.133627i
$566$	−0.407247	−	1.69911i	−0.0171178	−	0.0714188i
$567$	4.53958	−	3.29820i	0.190645	−	0.138511i
$568$	−27.1053	−	31.8085i	−1.13731	−	1.33465i
$569$	−31.6218	−	10.2745i	−1.32565	−	0.430731i	−0.441221	−	0.897398i	$-0.645455\pi$
$569$	−31.6218	−	10.2745i	−1.32565	−	0.430731i	−0.884433	+	0.466667i	$0.845455\pi$
$570$	2.27129	+	3.70953i	0.0951341	+	0.155375i
$571$		−	3.91193i		−	0.163709i	−0.996644	−	0.0818547i	$-0.973916\pi$
$571$		−	3.91193i		−	0.163709i	0.996644	−	0.0818547i	$-0.0260843\pi$
$572$	−14.1907	+	6.51564i	−0.593342	+	0.272433i
$573$		−	1.44304i		−	0.0602839i
$574$	10.8627	−	6.65110i	0.453402	−	0.277611i
$575$	−4.79625	−	1.55839i	−0.200017	−	0.0649896i
$576$	14.4777	+	7.41778i	0.603238	+	0.309074i
$577$	7.41867	−	5.38998i	0.308843	−	0.224388i	−0.422557	−	0.906337i	$-0.638867\pi$
$577$	7.41867	−	5.38998i	0.308843	−	0.224388i	0.731400	+	0.681949i	$0.238867\pi$
$578$	6.24966	−	1.49794i	0.259951	−	0.0623059i
$579$	4.71845	−	1.53312i	0.196092	−	0.0637142i
$580$	−0.754454	−	1.48344i	−0.0313270	−	0.0615967i
$581$	−19.8875	+	27.3728i	−0.825073	+	1.13562i
$582$	18.7221	+	7.76315i	0.776055	+	0.321793i
$583$	16.4354	−	20.8146i	0.680684	−	0.862053i
$584$	−24.1735	+	9.98118i	−1.00031	+	0.413024i
$585$	−1.90698	+	2.62473i	−0.0788437	+	0.108519i
$586$	1.38115	−	1.61590i	0.0570549	−	0.0667521i
$587$	6.32965	+	19.4807i	0.261253	+	0.804053i	0.992533	+	0.121976i	$0.0389231\pi$
$587$	6.32965	+	19.4807i	0.261253	+	0.804053i	−0.731280	+	0.682077i	$0.761077\pi$
$588$	26.4884	+	4.21569i	1.09236	+	0.173852i
$589$	21.9882	−	15.9754i	0.906009	−	0.658254i
$590$	1.23837	+	0.0979283i	0.0509829	+	0.00403165i
$591$	−4.67146	+	14.3773i	−0.192158	+	0.591402i
$592$	29.8653	+	21.7668i	1.22746	+	0.894612i
$593$			28.8970i			1.18666i	0.804961	+	0.593328i	$0.202186\pi$
$593$			28.8970i			1.18666i	−0.804961	+	0.593328i	$0.797814\pi$
$594$	−21.0676	−	9.74190i	−0.864414	−	0.399715i
$595$	−10.8675			−0.445523
$596$	2.60841	+	16.5490i	0.106845	+	0.677875i
$597$	11.8534	+	3.85140i	0.485127	+	0.157627i
$598$	3.68601	+	0.291484i	0.150732	+	0.0119197i
$599$	−21.8408	−	30.0612i	−0.892389	−	1.22827i	−0.972833	−	0.231509i	$-0.925634\pi$
$599$	−21.8408	−	30.0612i	−0.892389	−	1.22827i	0.0804433	−	0.996759i	$-0.474366\pi$
$600$	−10.7583	−	6.60936i	−0.439208	−	0.269826i
$601$	−2.38032	+	0.773413i	−0.0970953	+	0.0315482i	−0.357162	−	0.934043i	$-0.616256\pi$
$601$	−2.38032	+	0.773413i	−0.0970953	+	0.0315482i	0.260066	+	0.965591i	$0.416256\pi$
$602$	9.89700	+	8.45925i	0.403372	+	0.344773i
$603$	−0.795695	−	0.578106i	−0.0324032	−	0.0235423i
$604$	21.3616	+	21.3937i	0.869193	+	0.870496i
$605$	3.88550	+	6.36293i	0.157968	+	0.258690i
$606$	19.1743	+	7.95068i	0.778904	+	0.322974i
$607$	25.7355	+	18.6979i	1.04457	+	0.758925i	0.971173	−	0.238377i	$-0.0766155\pi$
$607$	25.7355	+	18.6979i	1.04457	+	0.758925i	0.0733985	+	0.997303i	$0.476616\pi$
$608$	−16.9945	+	19.8227i	−0.689217	+	0.803918i
$609$	1.69464	+	5.21555i	0.0686701	+	0.211345i
$610$	−1.86049	−	7.76228i	−0.0753289	−	0.314286i
$611$	6.52733	+	8.98410i	0.264067	+	0.363458i
$612$	12.7837	+	6.52568i	0.516750	+	0.263785i
$613$	0.969682	−	2.98437i	0.0391651	−	0.120538i	−0.929562	−	0.368665i	$-0.879815\pi$
$613$	0.969682	−	2.98437i	0.0391651	−	0.120538i	0.968728	+	0.248127i	$0.0798150\pi$
$614$	33.9662	−	20.7970i	1.37077	−	0.839301i
$615$	−1.32098			−0.0532670
$616$	14.6749	+	40.0130i	0.591270	+	1.61217i
$617$	−23.5622			−0.948577			−0.474289	−	0.880369i	$-0.657295\pi$
$617$	−23.5622			−0.948577			−0.474289	+	0.880369i	$0.657295\pi$
$618$	−7.21886	+	4.42000i	−0.290385	+	0.177799i
$619$	9.71231	−	29.8914i	0.390371	−	1.20144i	−0.542138	−	0.840289i	$-0.682385\pi$
$619$	9.71231	−	29.8914i	0.390371	−	1.20144i	0.932509	−	0.361148i	$-0.117615\pi$
$620$	3.62903	−	7.10920i	0.145745	−	0.285513i
$621$	3.23057	+	4.44650i	0.129638	+	0.178432i
$622$	10.3015	+	42.9795i	0.413051	+	1.72332i
$623$	−3.46871	−	10.6756i	−0.138971	−	0.427709i
$624$	8.80013	+	2.87391i	0.352287	+	0.115049i
$625$	−14.8216	−	10.7685i	−0.592862	−	0.430739i
$626$	−12.8729	−	5.33776i	−0.514503	−	0.213340i
$627$	9.32698	−	11.8122i	0.372484	−	0.471732i
$628$	16.9502	−	16.9248i	0.676386	−	0.675374i
$629$	26.3793	+	19.1657i	1.05181	+	0.764187i
$630$	6.73124	+	5.75338i	0.268179	+	0.229220i
$631$	−12.5873	+	4.08986i	−0.501092	+	0.162815i	−0.548647	−	0.836054i	$-0.684857\pi$
$631$	−12.5873	+	4.08986i	−0.501092	+	0.162815i	0.0475553	+	0.998869i	$0.484857\pi$
$632$	−2.52719	−	1.55257i	−0.100526	−	0.0617579i
$633$	−1.10426	−	1.51988i	−0.0438903	−	0.0604098i
$634$	−3.54185	−	0.280084i	−0.140665	−	0.0111236i
$635$	−3.98005	−	1.29320i	−0.157943	−	0.0513189i
$636$	−15.5316	+	2.44804i	−0.615867	+	0.0970710i
$637$	−32.1112			−1.27229
$638$	−3.91390	+	4.22421i	−0.154953	+	0.167238i
$639$			30.0444i			1.18854i
$640$	−1.80961	+	7.45150i	−0.0715313	+	0.294547i
$641$	1.84448	−	5.67673i	0.0728527	−	0.224217i	−0.907999	−	0.418971i	$-0.862391\pi$
$641$	1.84448	−	5.67673i	0.0728527	−	0.224217i	0.980852	+	0.194754i	$0.0623908\pi$
$642$	−14.7008	−	1.16252i	−0.580195	−	0.0458809i
$643$	−16.6320	+	12.0839i	−0.655903	+	0.476542i	−0.865277	−	0.501294i	$-0.832858\pi$
$643$	−16.6320	+	12.0839i	−0.655903	+	0.476542i	0.209374	+	0.977836i	$0.432858\pi$
$644$	1.58618	−	9.96646i	0.0625043	−	0.392733i
$645$	−0.417255	−	1.28418i	−0.0164294	−	0.0505645i
$646$	−14.9683	+	17.5123i	−0.588919	+	0.689013i
$647$	20.0669	−	27.6197i	0.788911	−	1.08584i	−0.205332	−	0.978692i	$-0.565827\pi$
$647$	20.0669	−	27.6197i	0.788911	−	1.08584i	0.994243	−	0.107150i	$-0.0341726\pi$
$648$	−1.33322	−	3.22892i	−0.0523736	−	0.126844i
$649$	−1.16351	−	4.13790i	−0.0456717	−	0.162427i
$650$	13.9635	+	5.79001i	0.547695	+	0.227103i
$651$	−15.4594	+	21.2781i	−0.605903	+	0.833955i
$652$	−0.580337	+	0.295149i	−0.0227278	+	0.0115589i
$653$	−21.8273	+	7.09213i	−0.854169	+	0.277536i	−0.703191	−	0.711001i	$-0.748242\pi$
$653$	−21.8273	+	7.09213i	−0.854169	+	0.277536i	−0.150978	+	0.988537i	$0.548242\pi$
$654$	−21.2739	+	5.09899i	−0.831876	+	0.199386i
$655$	−9.33782	+	6.78433i	−0.364859	+	0.265086i
$656$	−2.43911	−	7.54523i	−0.0952312	−	0.294592i
$657$	17.8818	+	5.81015i	0.697635	+	0.226675i
$658$	25.8490	−	15.8270i	1.00770	−	0.617000i
$659$		−	11.3191i		−	0.440930i	−0.975395	−	0.220465i	$-0.929242\pi$
$659$		−	11.3191i		−	0.440930i	0.975395	−	0.220465i	$-0.0707575\pi$
$660$	0.868950	−	4.33379i	0.0338238	−	0.168692i
$661$		−	29.7411i		−	1.15680i	−0.815755	−	0.578398i	$-0.803678\pi$
$661$		−	29.7411i		−	1.15680i	0.815755	−	0.578398i	$-0.196322\pi$
$662$	2.46944	+	4.03315i	0.0959775	+	0.156753i
$663$	7.76827	+	2.52406i	0.301695	+	0.0980265i
$664$	13.6621	+	16.0326i	0.530191	+	0.622187i
$665$	−11.4985	+	8.35416i	−0.445893	+	0.323960i
$666$	−6.19260	−	25.8367i	−0.239958	−	1.00115i
$667$	1.29687	−	0.421380i	0.0502152	−	0.0163159i
$668$	19.7379	−	10.0383i	0.763682	−	0.388395i
$669$	−6.05079	+	8.32820i	−0.233937	+	0.321987i
$670$	0.177579	−	0.428259i	0.00686046	−	0.0165451i
$671$	−22.9769	+	15.3266i	−0.887014	+	0.591679i
$672$	9.71300	−	23.3257i	0.374687	−	0.899807i
$673$	−14.6339	+	20.1418i	−0.564095	+	0.776410i	−0.991840	−	0.127489i	$-0.959308\pi$
$673$	−14.6339	+	20.1418i	−0.564095	+	0.776410i	0.427745	+	0.903899i	$0.359308\pi$
$674$	−17.8999	−	15.2996i	−0.689479	−	0.589317i
$675$	6.94352	+	21.3700i	0.267256	+	0.822530i
$676$	14.7315	+	2.34454i	0.566595	+	0.0901747i
$677$	−31.1545	+	22.6351i	−1.19736	+	0.869936i	−0.994023	−	0.109172i	$-0.965180\pi$
$677$	−31.1545	+	22.6351i	−1.19736	+	0.869936i	−0.203341	+	0.979108i	$0.565180\pi$
$678$	1.66224	−	21.0201i	0.0638378	−	0.807272i
$679$	−20.4653	+	62.9858i	−0.785387	+	2.41717i
$680$	−1.58680	+	6.57695i	−0.0608511	+	0.252215i
$681$			14.9463i			0.572745i
$682$	−27.4236	−	3.27800i	−1.05010	−	0.125521i
$683$	32.8926			1.25860			0.629299	−	0.777163i	$-0.283342\pi$
$683$	32.8926			1.25860			0.629299	+	0.777163i	$0.283342\pi$
$684$	18.5425	−	2.92261i	0.708989	−	0.111749i
$685$	3.88767	+	1.26318i	0.148540	+	0.0482637i
$686$	−3.36359	+	42.5349i	−0.128422	+	1.62399i
$687$	15.2570	+	20.9995i	0.582093	+	0.801182i
$688$	6.56460	−	4.75446i	0.250273	−	0.181262i
$689$	17.9027	−	5.81694i	0.682038	−	0.221608i
$690$	−0.680032	+	0.795612i	−0.0258884	+	0.0302884i
$691$	−35.0702	−	25.4800i	−1.33413	−	0.969303i	−0.999638	−	0.0269051i	$-0.991435\pi$
$691$	−35.0702	−	25.4800i	−1.33413	−	0.969303i	−0.334493	−	0.942398i	$-0.608565\pi$
$692$	−28.6285	−	28.6714i	−1.08829	−	1.08992i
$693$	10.6275	−	28.7378i	0.403706	−	1.09166i
$694$	10.7975	−	26.0399i	0.409868	−	0.988463i
$695$	−7.85950	−	5.71026i	−0.298128	−	0.216602i
$696$	3.40387	−	0.264044i	0.129023	−	0.0100086i
$697$	−2.16203	−	6.65404i	−0.0818926	−	0.252040i
$698$	−0.407121	+	0.0975799i	−0.0154097	+	0.00369345i
$699$	−3.50820	−	4.82863i	−0.132692	−	0.182636i
$700$	18.7583	−	36.7472i	0.708997	−	1.38891i
$701$	−0.458220	+	1.41026i	−0.0173067	+	0.0532647i	−0.959337	−	0.282263i	$-0.908915\pi$
$701$	−0.458220	+	1.41026i	−0.0173067	+	0.0532647i	0.942030	+	0.335528i	$0.108915\pi$
$702$	−8.60266	−	14.0501i	−0.324686	−	0.530286i
$703$	42.6443			1.60836
$704$	26.3584	−	3.03877i	0.993420	−	0.114528i
$705$	−3.14341			−0.118388
$706$	9.09298	+	14.8509i	0.342219	+	0.558920i
$707$	−20.9597	+	64.5072i	−0.788270	+	2.42604i
$708$	−1.15862	+	2.26971i	−0.0435434	+	0.0853009i
$709$	−4.74019	−	6.52432i	−0.178022	−	0.245026i	0.710676	−	0.703519i	$-0.248389\pi$
$709$	−4.74019	−	6.52432i	−0.178022	−	0.245026i	−0.888698	+	0.458494i	$0.848389\pi$
$710$	−13.7722	+	3.30097i	−0.516862	+	0.123883i
$711$	0.658925	+	2.02796i	0.0247116	+	0.0760545i
$712$	−6.96731	+	0.540466i	−0.261111	+	0.0202548i
$713$	5.29091	+	3.84407i	0.198146	+	0.143962i
$714$	8.53909	−	20.5934i	0.319568	−	0.770688i
$715$	−0.211895	+	5.28745i	−0.00792441	+	0.197740i
$716$	−13.4154	−	13.4355i	−0.501358	−	0.502109i
$717$	−9.88324	−	7.18060i	−0.369096	−	0.268164i
$718$	−10.8739	+	12.7220i	−0.405810	+	0.474782i
$719$	−8.47135	+	2.75251i	−0.315928	+	0.102651i	−0.462689	−	0.886521i	$-0.653115\pi$
$719$	−8.47135	+	2.75251i	−0.315928	+	0.102651i	0.146761	+	0.989172i	$0.453115\pi$
$720$	4.46477	−	3.23364i	0.166392	−	0.120511i
$721$	−16.2574	−	22.3764i	−0.605458	−	0.833342i
$722$	−0.256950	+	3.24930i	−0.00956269	+	0.120927i
$723$	−8.07718	−	2.62443i	−0.300393	−	0.0976037i
$724$	−20.6704	+	3.25800i	−0.768208	+	0.121083i
$725$	5.57479			0.207043
$726$	−15.1105	+	2.36320i	−0.560803	+	0.0877065i
$727$			34.2174i			1.26905i	0.772901	+	0.634527i	$0.218805\pi$
$727$			34.2174i			1.26905i	−0.772901	+	0.634527i	$0.781195\pi$
$728$	−7.09474	+	29.4062i	−0.262949	+	1.08987i
$729$	3.73420	−	11.4927i	0.138304	−	0.425655i
$730$	−0.698680	+	8.83528i	−0.0258593	+	0.327008i
$731$	5.78575	−	4.20360i	0.213994	−	0.155476i
$732$	16.1710	+	2.57366i	0.597699	+	0.0951250i
$733$	−10.4338	−	32.1121i	−0.385383	−	1.18609i	−0.936202	−	0.351462i	$-0.885685\pi$
$733$	−10.4338	−	32.1121i	−0.385383	−	1.18609i	0.550820	−	0.834624i	$-0.314315\pi$
$734$	27.8714	+	23.8224i	1.02875	+	0.879302i
$735$	5.34268	−	7.35356i	0.197068	−	0.271240i
$736$	−5.80005	−	2.41519i	−0.213793	−	0.0890251i
$737$	−1.60291	−	0.0642366i	−0.0590439	−	0.00236619i
$738$	−2.18359	+	5.26606i	−0.0803789	+	0.193847i
$739$	17.0290	−	23.4384i	0.626421	−	0.862195i	−0.371379	−	0.928481i	$-0.621115\pi$
$739$	17.0290	−	23.4384i	0.626421	−	0.862195i	0.997801	+	0.0662863i	$0.0211151\pi$
$740$	11.1630	−	5.67732i	0.410361	−	0.208702i
$741$	10.1597	−	3.30108i	0.373225	−	0.121268i
$742$	−11.9752	−	49.9625i	−0.439622	−	1.83418i
$743$	7.72726	−	5.61419i	0.283486	−	0.205964i	−0.436951	−	0.899486i	$-0.643942\pi$
$743$	7.72726	−	5.61419i	0.283486	−	0.205964i	0.720436	+	0.693521i	$0.243942\pi$
$744$	10.6201	+	12.4629i	0.389353	+	0.456912i
$745$	5.39958	+	1.75443i	0.197825	+	0.0642774i
$746$	−11.3714	−	18.5720i	−0.416336	−	0.679970i
$747$		−	15.1435i		−	0.554072i
$748$	23.2524	−	2.71597i	0.850191	−	0.0993058i
$749$		−	48.1865i		−	1.76070i
$750$	−7.66757	+	4.69474i	−0.279980	+	0.171428i
$751$	−7.57353	−	2.46079i	−0.276362	−	0.0897955i	0.167557	−	0.985862i	$-0.446412\pi$
$751$	−7.57353	−	2.46079i	−0.276362	−	0.0897955i	−0.443919	+	0.896067i	$0.646412\pi$
$752$	−5.80411	−	17.9547i	−0.211654	−	0.654739i
$753$	0.219291	−	0.159324i	0.00799140	−	0.00580609i
$754$	−3.97479	+	0.952690i	−0.144753	+	0.0346949i
$755$	9.74392	−	3.16599i	0.354617	−	0.115222i
$756$	−40.0794	+	20.3837i	−1.45767	+	0.741348i
$757$	−8.25126	+	11.3569i	−0.299897	+	0.412773i	−0.932197	−	0.361950i	$-0.882111\pi$
$757$	−8.25126	+	11.3569i	−0.299897	+	0.412773i	0.632300	+	0.774724i	$0.282111\pi$
$758$	10.8027	+	4.47935i	0.392371	+	0.162697i
$759$	3.39672	+	1.25614i	0.123293	+	0.0455950i
$760$	3.37696	+	8.17867i	0.122495	+	0.296672i
$761$	−17.6554	+	24.3006i	−0.640008	+	0.880895i	−0.998616	−	0.0525928i	$-0.983251\pi$
$761$	−17.6554	+	24.3006i	−0.640008	+	0.880895i	0.358608	+	0.933488i	$0.383251\pi$
$762$	5.57786	−	6.52588i	0.202065	−	0.236408i
$763$	−22.0897	−	67.9851i	−0.799700	−	2.46122i
$764$	0.461393	−	2.89907i	0.0166926	−	0.104885i
$765$	3.93506	−	2.85899i	0.142272	−	0.103367i
$766$	−0.225821	−	0.0178575i	−0.00815923	−	0.000645219i
$767$	0.942770	−	2.90155i	0.0340414	−	0.104769i
$768$	−12.6984	−	9.28414i	−0.458213	−	0.335012i
$769$		−	9.64819i		−	0.347923i	−0.984752	−	0.173961i	$-0.944343\pi$
$769$		−	9.64819i		−	0.347923i	0.984752	−	0.173961i	$-0.0556568\pi$
$770$	14.3409	+	1.71420i	0.516810	+	0.0617754i
$771$	−6.87230			−0.247500
$772$	9.96956	−	1.57137i	0.358812	−	0.0565549i
$773$	−26.9139	−	8.74484i	−0.968024	−	0.314530i	−0.218006	−	0.975947i	$-0.569955\pi$
$773$	−26.9139	−	8.74484i	−0.968024	−	0.314530i	−0.750018	+	0.661417i	$0.769955\pi$
$774$	−5.80909	−	0.459374i	−0.208803	−	0.0165118i
$775$	15.7155	+	21.6305i	0.564518	+	0.776992i
$776$	35.1305	+	21.5823i	1.26111	+	0.774760i
$777$	−39.2474	+	12.7522i	−1.40799	+	0.457484i
$778$	15.9915	+	13.6684i	0.573322	+	0.490034i
$779$	−7.40272	−	5.37839i	−0.265230	−	0.192701i
$780$	2.22002	−	2.21670i	0.0794894	−	0.0793705i
$781$	27.1933	+	40.7668i	0.973053	+	1.45875i
$782$	−5.12066	−	2.12329i	−0.183114	−	0.0759287i
$783$	−4.91532	−	3.57119i	−0.175659	−	0.127624i
$784$	51.8674	+	16.9387i	1.85241	+	0.604952i
$785$	−2.50841	−	7.72010i	−0.0895291	−	0.275542i
$786$	−5.51882	−	23.0255i	−0.196850	−	0.821293i
$787$	8.29975	+	11.4236i	0.295854	+	0.407208i	0.930905	−	0.365262i	$-0.119021\pi$
$787$	8.29975	+	11.4236i	0.295854	+	0.407208i	−0.635051	+	0.772471i	$0.719021\pi$
$788$	−13.9819	+	27.3903i	−0.498085	+	0.975740i
$789$	3.50603	−	10.7905i	0.124818	−	0.384150i
$790$	−0.857212	+	0.524859i	−0.0304982	+	0.0186736i
$791$	68.8999			2.44980
$792$	−15.8402	−	10.6278i	−0.562857	−	0.377644i
$793$	−19.6037			−0.696148
$794$	−17.0286	+	10.4264i	−0.604322	+	0.370018i
$795$	−1.64656	+	5.06760i	−0.0583976	+	0.179729i
$796$	22.5820	+	11.5274i	0.800399	+	0.408579i
$797$	19.7252	+	27.1494i	0.698703	+	0.961683i	0.999967	+	0.00814175i	$0.00259163\pi$
$797$	19.7252	+	27.1494i	0.698703	+	0.961683i	−0.301263	+	0.953541i	$0.597408\pi$
$798$	−6.79583	−	28.3534i	−0.240570	−	1.00370i
$799$	−5.14477	−	15.8340i	−0.182009	−	0.560166i
$800$	−19.5003	−	16.7180i	−0.689439	−	0.591072i
$801$	4.06451	+	2.95304i	0.143612	+	0.104340i
$802$	20.8166	+	8.63165i	0.735060	+	0.304794i
$803$	29.5223	−	8.30117i	1.04182	−	0.292942i
$804$	0.672000	+	0.673007i	0.0236996	+	0.0237351i
$805$	−2.76683	−	2.01022i	−0.0975179	−	0.0708509i
$806$	−14.9016	−	12.7368i	−0.524885	−	0.448634i
$807$	18.0900	−	5.87780i	0.636798	−	0.206908i
$808$	35.9791	+	22.1036i	1.26574	+	0.777604i
$809$	−19.0271	−	26.1886i	−0.668959	−	0.920743i	0.330778	−	0.943709i	$-0.392689\pi$
$809$	−19.0271	−	26.1886i	−0.668959	−	0.920743i	−0.999736	+	0.0229661i	$0.992689\pi$
$810$	−1.18015	−	0.0933247i	−0.0414664	−	0.00327910i
$811$	48.3019	+	15.6943i	1.69611	+	0.551100i	0.987926	−	0.154927i	$-0.0495143\pi$
$811$	48.3019	+	15.6943i	1.69611	+	0.551100i	0.708185	+	0.706027i	$0.249514\pi$
$812$	1.73692	+	11.0199i	0.0609540	+	0.386722i
$813$	−4.41039			−0.154679
$814$	−31.7874	−	29.4524i	−1.11415	−	1.03230i
$815$			0.220641i			0.00772872i
$816$	−11.2162	−	8.17474i	−0.392646	−	0.286173i
$817$	2.89028	−	8.89536i	0.101118	−	0.311209i
$818$	−28.3218	−	2.23964i	−0.990248	−	0.0783073i
$819$	17.5940	−	12.7828i	0.614785	−	0.446667i
$820$	−2.65385	−	0.422365i	−0.0926764	−	0.0147496i
$821$	−6.41880	−	19.7550i	−0.224018	−	0.689455i	−0.998390	−	0.0567249i	$-0.981934\pi$
$821$	−6.41880	−	19.7550i	−0.224018	−	0.689455i	0.774372	−	0.632730i	$-0.218066\pi$
$822$	−5.44840	+	6.37442i	−0.190035	+	0.222334i
$823$	−25.5250	+	35.1322i	−0.889746	+	1.22463i	0.0838787	+	0.996476i	$0.473269\pi$
$823$	−25.5250	+	35.1322i	−0.889746	+	1.22463i	−0.973625	+	0.228155i	$0.926731\pi$
$824$	−15.9159	+	6.57166i	−0.554458	+	0.228935i
$825$	11.6200	+	9.17526i	0.404557	+	0.319442i
$826$	−7.69189	−	3.18946i	−0.267635	−	0.110975i
$827$	−4.54817	+	6.26002i	−0.158155	+	0.217682i	−0.880740	−	0.473600i	$-0.842954\pi$
$827$	−4.54817	+	6.26002i	−0.158155	+	0.217682i	0.722584	+	0.691283i	$0.242954\pi$
$828$	2.04760	+	4.02609i	0.0711590	+	0.139916i
$829$	−42.6182	+	13.8475i	−1.48019	+	0.480944i	−0.934170	−	0.356827i	$-0.883859\pi$
$829$	−42.6182	+	13.8475i	−1.48019	+	0.480944i	−0.546022	+	0.837771i	$0.683859\pi$
$830$	6.94171	−	1.66381i	0.240950	−	0.0577516i
$831$	13.4868	−	9.79874i	0.467852	−	0.339914i
$832$	16.7606	+	8.58742i	0.581068	+	0.297715i
$833$	45.7857	+	14.8767i	1.58638	+	0.515446i
$834$	16.9963	−	10.4066i	0.588533	−	0.360350i
$835$		−	7.50423i		−	0.259695i
$836$	22.5147	−	20.7485i	0.778687	−	0.717601i
$837$		−	29.1391i		−	1.00719i
$838$	10.2201	+	16.6917i	0.353047	+	0.576605i
$839$	−39.1351	−	12.7158i	−1.35109	−	0.438997i	−0.458035	−	0.888934i	$-0.651446\pi$
$839$	−39.1351	−	12.7158i	−1.35109	−	0.438997i	−0.893060	+	0.449937i	$0.851446\pi$
$840$	−5.55369	−	6.51734i	−0.191620	−	0.224870i
$841$	22.2420	−	16.1598i	0.766965	−	0.557233i
$842$	4.15808	+	17.3483i	0.143297	+	0.597861i
$843$	6.88287	−	2.23638i	0.237059	−	0.0770250i
$844$	−1.73249	−	3.40651i	−0.0596348	−	0.117257i
$845$	2.97131	−	4.08966i	0.102216	−	0.140689i
$846$	−5.19607	+	12.5312i	−0.178645	+	0.430830i
$847$	−11.5903	−	48.6128i	−0.398249	−	1.67035i
$848$	−31.9857	−	0.0478996i	−1.09839	−	0.00164488i
$849$	0.713957	−	0.982677i	0.0245029	−	0.0337254i
$850$	−17.2274	−	14.7248i	−0.590897	−	0.505056i
$851$	3.17091	+	9.75907i	0.108698	+	0.334537i
$852$	4.56631	−	28.6915i	0.156439	−	0.982954i
$853$	−13.8750	+	10.0808i	−0.475071	+	0.345159i	−0.799414	−	0.600780i	$-0.794857\pi$
$853$	−13.8750	+	10.0808i	−0.475071	+	0.345159i	0.324343	+	0.945939i	$0.394857\pi$
$854$	−4.21798	+	53.3392i	−0.144336	+	1.82523i
$855$	1.96576	−	6.04999i	0.0672276	−	0.206905i
$856$	−29.1623	−	7.03589i	−0.996746	−	0.240482i
$857$			55.4066i			1.89265i	0.323210	+	0.946327i	$0.395238\pi$
$857$			55.4066i			1.89265i	−0.323210	+	0.946327i	$0.604762\pi$
$858$	−9.85299	−	4.55613i	−0.336376	−	0.155544i
$859$	4.87871			0.166459			0.0832297	−	0.996530i	$-0.473476\pi$
$859$	4.87871			0.166459			0.0832297	+	0.996530i	$0.473476\pi$
$860$	−0.427667	−	2.71333i	−0.0145833	−	0.0925237i
$861$	8.42138	+	2.73627i	0.287000	+	0.0932519i
$862$	1.73874	−	21.9875i	0.0592217	−	0.748899i
$863$	−0.0613516	−	0.0844432i	−0.00208843	−	0.00287448i	0.807972	−	0.589222i	$-0.200565\pi$
$863$	−0.0613516	−	0.0844432i	−0.00208843	−	0.00287448i	−0.810060	+	0.586347i	$0.800565\pi$
$864$	6.48398	+	27.2322i	0.220589	+	0.926458i
$865$	−13.0586	+	4.24300i	−0.444006	+	0.144266i
$866$	−0.701094	+	0.820253i	−0.0238241	+	0.0278733i
$867$	3.61449	+	2.62608i	0.122754	+	0.0891863i
$868$	−37.8614	+	37.8048i	−1.28510	+	1.28318i
$869$	2.72960	+	2.15531i	0.0925952	+	0.0731139i
$870$	0.443159	−	1.06875i	0.0150245	−	0.0362340i
$871$	−0.921160	−	0.669262i	−0.0312123	−	0.0226771i
$872$	−44.3697	+	3.44183i	−1.50255	+	0.116555i
$873$	−9.15974	−	28.1908i	−0.310010	−	0.954113i
$874$	−7.05023	+	1.68982i	−0.238478	+	0.0571590i
$875$	−17.2680	−	23.7673i	−0.583764	−	0.803482i
$876$	−16.1935	−	8.26627i	−0.547127	−	0.279291i
$877$	12.2636	−	37.7435i	0.414113	−	1.27451i	−0.498929	−	0.866643i	$-0.666273\pi$
$877$	12.2636	−	37.7435i	0.414113	−	1.27451i	0.913042	−	0.407866i	$-0.133727\pi$
$878$	−1.19967	−	1.95933i	−0.0404869	−	0.0661241i
$879$	1.47778			0.0498443
$880$	3.13139	−	8.42875i	0.105559	−	0.284133i
$881$	45.8159			1.54358			0.771789	−	0.635879i	$-0.219362\pi$
$881$	45.8159			1.54358			0.771789	+	0.635879i	$0.219362\pi$
$882$	−20.4834	−	33.4540i	−0.689712	−	1.12645i
$883$	−15.4974	+	47.6960i	−0.521528	+	1.60510i	0.249552	+	0.968361i	$0.419717\pi$
$883$	−15.4974	+	47.6960i	−0.521528	+	1.60510i	−0.771081	+	0.636738i	$0.780283\pi$
$884$	14.7994	+	7.55465i	0.497759	+	0.254090i
$885$	0.507605	+	0.698658i	0.0170630	+	0.0234851i
$886$	45.6303	−	10.9368i	1.53298	−	0.367429i
$887$	1.87115	+	5.75880i	0.0628270	+	0.193362i	0.977543	−	0.210735i	$-0.0675858\pi$
$887$	1.87115	+	5.75880i	0.0628270	+	0.193362i	−0.914716	+	0.404097i	$0.867586\pi$
$888$	1.98695	+	25.6144i	0.0666776	+	0.859561i
$889$	22.6945	+	16.4885i	0.761149	+	0.553007i
$890$	−0.907093	+	2.18760i	−0.0304058	+	0.0733285i
$891$	1.10881	+	3.94337i	0.0371466	+	0.132108i
$892$	−14.8189	+	14.7967i	−0.496173	+	0.495430i
$893$	−17.6156	−	12.7985i	−0.589482	−	0.428284i
$894$	−7.56727	+	8.85343i	−0.253088	+	0.296103i
$895$	−6.11932	+	1.98829i	−0.204546	+	0.0664612i
$896$	26.9715	−	43.7557i	0.901055	−	1.46178i
$897$	1.51089	+	2.07956i	0.0504471	+	0.0694345i
$898$	−2.83895	+	35.9004i	−0.0947370	+	1.19801i
$899$	−6.87563	−	2.23403i	−0.229315	−	0.0745090i
$900$	2.87507	+	18.2408i	0.0958356	+	0.608028i
$901$	−28.2214			−0.940192
$902$	1.80346	+	9.12180i	0.0600486	+	0.303723i
$903$			9.05108i			0.301201i
$904$	10.0603	−	41.6979i	0.334602	−	1.38685i
$905$	−2.19135	+	6.74428i	−0.0728429	+	0.224187i
$906$	−1.65685	+	20.9520i	−0.0550451	+	0.696082i
$907$	−48.4559	+	35.2053i	−1.60895	+	1.16897i	−0.742290	+	0.670079i	$0.766260\pi$
$907$	−48.4559	+	35.2053i	−1.60895	+	1.16897i	−0.866663	+	0.498894i	$0.833740\pi$
$908$	−4.77890	+	30.0272i	−0.158593	+	0.996489i
$909$	−9.38100	−	28.8717i	−0.311148	−	0.957615i
$910$	7.79262	+	6.66057i	0.258323	+	0.220796i
$911$	26.1407	−	35.9795i	0.866079	−	1.19206i	−0.114007	−	0.993480i	$-0.536369\pi$
$911$	26.1407	−	35.9795i	0.866079	−	1.19206i	0.980086	−	0.198575i	$-0.0636315\pi$
$912$	−18.1517	−	0.0271827i	−0.601061	−	0.000900109i
$913$	−13.7064	−	20.5479i	−0.453616	−	0.680038i
$914$	−18.7367	+	45.1866i	−0.619755	+	1.49464i
$915$	3.26167	−	4.48931i	0.107828	−	0.148412i
$916$	23.9371	+	47.0663i	0.790904	+	1.55511i
$917$	73.5827	−	23.9085i	2.42991	−	0.789527i
$918$	5.75688	+	24.0188i	0.190005	+	0.792737i
$919$	−6.54928	+	4.75833i	−0.216041	+	0.156963i	−0.690543	−	0.723292i	$-0.742628\pi$
$919$	−6.54928	+	4.75833i	−0.216041	+	0.156963i	0.474502	+	0.880255i	$0.342628\pi$
$920$	−1.62057	+	1.38095i	−0.0534286	+	0.0455287i
$921$	26.3325	+	8.55594i	0.867684	+	0.281928i
$922$	−8.50674	−	13.8934i	−0.280155	−	0.457555i
$923$			34.7819i			1.14486i
$924$	−14.5166	+	25.8284i	−0.477563	+	0.849693i
$925$			41.9507i			1.37933i
$926$	−13.3203	+	8.15584i	−0.437733	+	0.268017i
$927$	11.7735	+	3.82543i	0.386691	+	0.125644i
$928$	6.92280	+	0.557877i	0.227252	+	0.0183132i
$929$	−3.99231	+	2.90059i	−0.130984	+	0.0951651i	−0.651348	−	0.758779i	$-0.725796\pi$
$929$	−3.99231	+	2.90059i	−0.130984	+	0.0951651i	0.520364	+	0.853944i	$0.325796\pi$
$930$	5.39610	−	1.29335i	0.176945	−	0.0424107i
$931$	59.8804	−	19.4563i	1.96250	−	0.637655i
$932$	−5.50410	−	10.8224i	−0.180293	−	0.354500i
$933$	−18.0598	+	24.8572i	−0.591251	+	0.813788i
$934$	−17.3461	−	7.19261i	−0.567583	−	0.235350i
$935$	2.75173	−	7.44094i	0.0899913	−	0.243345i
$936$	−5.16713	−	12.5143i	−0.168893	−	0.409042i
$937$	−1.64936	+	2.27015i	−0.0538822	+	0.0741625i	−0.835108	−	0.550086i	$-0.814595\pi$
$937$	−1.64936	+	2.27015i	−0.0538822	+	0.0741625i	0.781226	+	0.624249i	$0.214595\pi$
$938$	−2.01918	+	2.36236i	−0.0659284	+	0.0771338i
$939$	−2.99373	−	9.21375i	−0.0976966	−	0.300679i
$940$	−6.31511	−	1.00506i	−0.205976	−	0.0327815i
$941$	−25.4946	+	18.5229i	−0.831102	+	0.603831i	−0.919871	−	0.392222i	$-0.871707\pi$
$941$	−25.4946	+	18.5229i	−0.831102	+	0.603831i	0.0887691	+	0.996052i	$0.471707\pi$
$942$	16.6002	+	1.31272i	0.540864	+	0.0427707i
$943$	0.680388	−	2.09402i	0.0221565	−	0.0681907i
$944$	−3.05337	+	4.18939i	−0.0993787	+	0.136353i
$945$			15.2380i			0.495691i
$946$	−8.29803	+	4.63450i	−0.269792	+	0.150681i
$947$	−35.0634			−1.13941			−0.569703	−	0.821850i	$-0.692942\pi$
$947$	−35.0634			−1.13941			−0.569703	+	0.821850i	$0.692942\pi$
$948$	−0.321032	−	2.03679i	−0.0104266	−	0.0661517i
$949$	20.7014	+	6.72629i	0.671996	+	0.218345i
$950$	−29.5472	−	2.33654i	−0.958637	−	0.0758075i
$951$	−1.45180	−	1.99823i	−0.0470778	−	0.0647970i
$952$	23.7395	−	38.6419i	0.769402	−	1.25239i
$953$	23.1273	−	7.51452i	0.749167	−	0.243419i	0.0905443	−	0.995892i	$-0.471139\pi$
$953$	23.1273	−	7.51452i	0.749167	−	0.243419i	0.658623	+	0.752473i	$0.271139\pi$
$954$	17.4801	+	14.9408i	0.565941	+	0.483726i
$955$	−0.804822	−	0.584738i	−0.0260434	−	0.0189217i
$956$	−17.5595	−	17.5859i	−0.567916	−	0.568767i
$957$	−4.00017	−	0.160307i	−0.129307	−	0.00518199i
$958$	12.3712	+	5.12976i	0.399696	+	0.165735i
$959$	−22.1678	−	16.1058i	−0.715835	−	0.520084i
$960$	−4.75518	+	2.40945i	−0.153473	+	0.0777645i
$961$	−1.13493	−	3.49294i	−0.0366105	−	0.112676i
$962$	−7.16905	−	29.9106i	−0.231140	−	0.964356i
$963$	12.6768	+	17.4481i	0.408503	+	0.562257i
$964$	−15.3879	−	7.85506i	−0.495612	−	0.252994i
$965$	1.05691	−	3.25284i	0.0340232	−	0.104713i
$966$	5.98330	−	3.66349i	0.192510	−	0.117871i
$967$	−11.0350			−0.354861			−0.177431	−	0.984133i	$-0.556779\pi$
$967$	−11.0350			−0.354861			−0.177431	+	0.984133i	$0.556779\pi$
$968$	−31.1126	−	0.0837087i	−0.999996	−	0.00269050i
$969$	−16.0155			−0.514491
$970$	11.9161	−	7.29608i	0.382604	−	0.234263i
$971$	4.23253	−	13.0264i	0.135828	−	0.418037i	−0.859890	−	0.510480i	$-0.829468\pi$
$971$	4.23253	−	13.0264i	0.135828	−	0.418037i	0.995718	+	0.0924434i	$0.0294677\pi$
$972$	14.6036	−	28.6083i	0.468412	−	0.917611i
$973$	38.2769	+	52.6837i	1.22710	+	1.68896i
$974$	−9.01342	−	37.6056i	−0.288809	−	1.20496i
$975$	3.24738	+	9.99440i	0.103999	+	0.320077i
$976$	31.6648	+	10.3410i	1.01356	+	0.331006i
$977$	1.23456	+	0.896963i	0.0394972	+	0.0286964i	0.607359	−	0.794428i	$-0.292229\pi$
$977$	1.23456	+	0.896963i	0.0394972	+	0.0286964i	−0.567862	+	0.823124i	$0.692229\pi$
$978$	−0.418105	−	0.173368i	−0.0133695	−	0.00554370i
$979$	8.18786	+	0.328129i	0.261685	+	0.0104870i
$980$	13.0846	−	13.0651i	0.417974	−	0.417348i
$981$	25.8839	+	18.8057i	0.826409	+	0.600421i
$982$	−25.5346	−	21.8252i	−0.814843	−	0.696469i
$983$	−39.0389	+	12.6845i	−1.24515	+	0.404572i	−0.856179	−	0.516679i	$-0.827168\pi$
$983$	−39.0389	+	12.6845i	−1.24515	+	0.404572i	−0.388967	+	0.921252i	$0.627168\pi$
$984$	2.88562	−	4.69705i	0.0919901	−	0.149736i
$985$	6.12566	+	8.43125i	0.195180	+	0.268642i
$986$	6.10882	+	0.483076i	0.194544	+	0.0153843i
$987$	20.0396	+	6.51125i	0.637866	+	0.207255i
$988$	21.4663	−	3.38345i	0.682932	−	0.107642i
$989$	2.25060			0.0715649
$990$	−5.64373	+	3.15206i	−0.179369	+	0.100179i
$991$			0.742581i			0.0235889i	0.999930	+	0.0117944i	$0.00375437\pi$
$991$			0.742581i			0.0235889i	−0.999930	+	0.0117944i	$0.996246\pi$
$992$	17.3510	+	28.4336i	0.550895	+	0.902767i
$993$	−1.01593	+	3.12672i	−0.0322396	+	0.0992233i
$994$	94.6370	+	7.48374i	3.00170	+	0.237370i
$995$	6.95117	−	5.05032i	0.220367	−	0.160106i
$996$	−2.30159	+	14.4616i	−0.0729286	+	0.458232i
$997$	5.30363	+	16.3229i	0.167967	+	0.516951i	0.999243	−	0.0389103i	$-0.0123887\pi$
$997$	5.30363	+	16.3229i	0.167967	+	0.516951i	−0.831275	+	0.555861i	$0.812389\pi$
$998$	5.93754	−	6.94670i	0.187950	−	0.219894i
$999$	26.8734	−	36.9881i	0.850238	−	1.17025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	88.2.k.b.51.6	yes	32
3.2	odd	2		792.2.bp.b.667.3		32
4.3	odd	2		352.2.s.b.271.6		32
8.3	odd	2	inner	88.2.k.b.51.1	yes	32
8.5	even	2		352.2.s.b.271.5		32
11.2	odd	10		968.2.k.e.699.5		32
11.3	even	5		968.2.k.h.723.8		32
11.4	even	5		968.2.k.e.475.3		32
11.5	even	5		968.2.g.e.483.7		32
11.6	odd	10		968.2.g.e.483.26		32
11.7	odd	10		968.2.k.i.475.6		32
11.8	odd	10	inner	88.2.k.b.19.1	✓	32
11.9	even	5		968.2.k.i.699.4		32
11.10	odd	2		968.2.k.h.403.3		32
24.11	even	2		792.2.bp.b.667.8		32
33.8	even	10		792.2.bp.b.19.8		32
44.19	even	10		352.2.s.b.239.5		32
44.27	odd	10		3872.2.g.d.1935.24		32
44.39	even	10		3872.2.g.d.1935.23		32
88.3	odd	10		968.2.k.h.723.3		32
88.5	even	10		3872.2.g.d.1935.22		32
88.19	even	10	inner	88.2.k.b.19.6	yes	32
88.27	odd	10		968.2.g.e.483.25		32
88.35	even	10		968.2.k.e.699.3		32
88.43	even	2		968.2.k.h.403.8		32
88.51	even	10		968.2.k.i.475.4		32
88.59	odd	10		968.2.k.e.475.5		32
88.61	odd	10		3872.2.g.d.1935.21		32
88.75	odd	10		968.2.k.i.699.6		32
88.83	even	10		968.2.g.e.483.8		32
88.85	odd	10		352.2.s.b.239.6		32
264.107	odd	10		792.2.bp.b.19.3		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
88.2.k.b.19.1	✓	32	11.8	odd	10	inner
88.2.k.b.19.6	yes	32	88.19	even	10	inner
88.2.k.b.51.1	yes	32	8.3	odd	2	inner
88.2.k.b.51.6	yes	32	1.1	even	1	trivial
352.2.s.b.239.5		32	44.19	even	10
352.2.s.b.239.6		32	88.85	odd	10
352.2.s.b.271.5		32	8.5	even	2
352.2.s.b.271.6		32	4.3	odd	2
792.2.bp.b.19.3		32	264.107	odd	10
792.2.bp.b.19.8		32	33.8	even	10
792.2.bp.b.667.3		32	3.2	odd	2
792.2.bp.b.667.8		32	24.11	even	2
968.2.g.e.483.7		32	11.5	even	5
968.2.g.e.483.8		32	88.83	even	10
968.2.g.e.483.25		32	88.27	odd	10
968.2.g.e.483.26		32	11.6	odd	10
968.2.k.e.475.3		32	11.4	even	5
968.2.k.e.475.5		32	88.59	odd	10
968.2.k.e.699.3		32	88.35	even	10
968.2.k.e.699.5		32	11.2	odd	10
968.2.k.h.403.3		32	11.10	odd	2
968.2.k.h.403.8		32	88.43	even	2
968.2.k.h.723.3		32	88.3	odd	10
968.2.k.h.723.8		32	11.3	even	5
968.2.k.i.475.4		32	88.51	even	10
968.2.k.i.475.6		32	11.7	odd	10
968.2.k.i.699.4		32	11.9	even	5
968.2.k.i.699.6		32	88.75	odd	10
3872.2.g.d.1935.21		32	88.61	odd	10
3872.2.g.d.1935.22		32	88.5	even	10
3872.2.g.d.1935.23		32	44.39	even	10
3872.2.g.d.1935.24		32	44.27	odd	10

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:	\( N \)	\(=\)	\( 88 = 2^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	88.k (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.738473 + 1.20609i) q^{2} +(-0.303809 + 0.935028i) q^{3} +(-0.909315 + 1.78133i) q^{4} +(0.398383 + 0.548327i) q^{5} +(-1.35208 + 0.324071i) q^{6} +(-1.40393 - 4.32085i) q^{7} +(-2.81996 + 0.218749i) q^{8} +(1.64507 + 1.19522i) q^{9} +O(q^{10})\)	\(q+(0.738473 + 1.20609i) q^{2} +(-0.303809 + 0.935028i) q^{3} +(-0.909315 + 1.78133i) q^{4} +(0.398383 + 0.548327i) q^{5} +(-1.35208 + 0.324071i) q^{6} +(-1.40393 - 4.32085i) q^{7} +(-2.81996 + 0.218749i) q^{8} +(1.64507 + 1.19522i) q^{9} +(-0.367138 + 0.885411i) q^{10} +(3.31396 + 0.132807i) q^{11} +(-1.38934 - 1.39142i) q^{12} +(1.90447 + 1.38368i) q^{13} +(4.17458 - 4.88410i) q^{14} +(-0.633734 + 0.205913i) q^{15} +(-2.34629 - 3.23959i) q^{16} +(-2.07445 - 2.85523i) q^{17} +(-0.226698 + 2.86675i) q^{18} +(-4.38980 - 1.42633i) q^{19} +(-1.33901 + 0.211051i) q^{20} +4.46665 q^{21} +(2.28710 + 4.09502i) q^{22} -1.11065i q^{23} +(0.652192 - 2.70319i) q^{24} +(1.40313 - 4.31839i) q^{25} +(-0.262443 + 3.31877i) q^{26} +(-4.00349 + 2.90871i) q^{27} +(8.97349 + 1.42815i) q^{28} +(0.379398 + 1.16767i) q^{29} +(-0.716345 - 0.612280i) q^{30} +(-3.46109 + 4.76378i) q^{31} +(2.17456 - 5.22219i) q^{32} +(-1.13099 + 3.05830i) q^{33} +(1.91175 - 4.61048i) q^{34} +(1.80994 - 2.49117i) q^{35} +(-3.62497 + 1.84360i) q^{36} +(-8.78677 + 2.85499i) q^{37} +(-1.52146 - 6.34781i) q^{38} +(-1.87237 + 1.36036i) q^{39} +(-1.24337 - 1.45911i) q^{40} +(1.88539 + 0.612601i) q^{41} +(3.29850 + 5.38718i) q^{42} +2.02637i q^{43} +(-3.25001 + 5.78251i) q^{44} +1.37819i q^{45} +(1.33955 - 0.820189i) q^{46} +(4.48649 + 1.45775i) q^{47} +(3.74193 - 1.20963i) q^{48} +(-11.0356 + 8.01786i) q^{49} +(6.24455 - 1.49671i) q^{50} +(3.29995 - 1.07222i) q^{51} +(-4.19655 + 2.13429i) q^{52} +(4.70018 - 6.46924i) q^{53} +(-6.46464 - 2.68058i) q^{54} +(1.24741 + 1.87005i) q^{55} +(4.90420 + 11.8775i) q^{56} +(2.66732 - 3.67125i) q^{57} +(-1.12814 + 1.31988i) q^{58} +(-0.400488 - 1.23257i) q^{59} +(0.209465 - 1.31613i) q^{60} +(-6.73720 + 4.89486i) q^{61} +(-8.30147 - 0.656467i) q^{62} +(2.85479 - 8.78613i) q^{63} +(7.90430 - 1.23372i) q^{64} +1.59551i q^{65} +(-4.52380 + 0.894394i) q^{66} -0.483683 q^{67} +(6.97244 - 1.09897i) q^{68} +(1.03849 + 0.337427i) q^{69} +(4.34117 + 0.343293i) q^{70} +(8.68470 + 11.9535i) q^{71} +(-4.90049 - 3.01060i) q^{72} +(8.79393 - 2.85732i) q^{73} +(-9.93218 - 8.48931i) q^{74} +(3.61153 + 2.62393i) q^{75} +(6.53249 - 6.52271i) q^{76} +(-4.07874 - 14.5056i) q^{77} +(-3.02341 - 1.25367i) q^{78} +(0.848366 + 0.616374i) q^{79} +(0.841630 - 2.57713i) q^{80} +(0.381661 + 1.17463i) q^{81} +(0.653458 + 2.72635i) q^{82} +(-4.37741 - 6.02499i) q^{83} +(-4.06159 + 7.95658i) q^{84} +(0.739176 - 2.27495i) q^{85} +(-2.44399 + 1.49642i) q^{86} -1.20707 q^{87} +(-9.37428 + 0.350415i) q^{88} +2.47072 q^{89} +(-1.66223 + 1.01776i) q^{90} +(3.30493 - 10.1715i) q^{91} +(1.97845 + 1.00994i) q^{92} +(-3.40275 - 4.68349i) q^{93} +(1.55497 + 6.48763i) q^{94} +(-0.966725 - 2.97527i) q^{95} +(4.22224 + 3.61983i) q^{96} +(-11.7932 - 8.56824i) q^{97} +(-17.8198 - 7.38902i) q^{98} +(5.29298 + 4.17938i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 5 q^{2} - 2 q^{3} - 5 q^{4} + 15 q^{6} - 5 q^{8} - 10 q^{9}+O(q^{10}) \) 32 * q - 5 * q^2 - 2 * q^3 - 5 * q^4 + 15 * q^6 - 5 * q^8 - 10 * q^9	\( 32 q - 5 q^{2} - 2 q^{3} - 5 q^{4} + 15 q^{6} - 5 q^{8} - 10 q^{9} - 18 q^{11} - 18 q^{12} + 8 q^{14} - q^{16} - 10 q^{17} - 20 q^{18} - 30 q^{20} + 17 q^{22} + 5 q^{24} + 6 q^{25} - 4 q^{26} - 32 q^{27} - 30 q^{28} + 30 q^{30} + 32 q^{33} - 14 q^{34} - 10 q^{35} + 16 q^{36} + 28 q^{38} + 30 q^{40} - 10 q^{41} + 64 q^{42} - 38 q^{44} + 40 q^{46} + 26 q^{48} - 18 q^{49} + 5 q^{50} + 60 q^{51} + 40 q^{52} + 76 q^{56} - 80 q^{57} - 56 q^{58} + 28 q^{59} + 34 q^{60} - 80 q^{62} + 55 q^{64} - 30 q^{66} - 28 q^{67} + 60 q^{68} - 44 q^{70} + 45 q^{72} - 10 q^{73} - 100 q^{74} + 4 q^{75} - 80 q^{78} - 76 q^{80} + 28 q^{81} + 13 q^{82} - 50 q^{84} - 39 q^{86} - 69 q^{88} + 20 q^{89} - 30 q^{90} + 78 q^{91} + 6 q^{92} - 30 q^{94} - 110 q^{96} - 52 q^{97} + 122 q^{99}+O(q^{100}) \) 32 * q - 5 * q^2 - 2 * q^3 - 5 * q^4 + 15 * q^6 - 5 * q^8 - 10 * q^9 - 18 * q^11 - 18 * q^12 + 8 * q^14 - q^16 - 10 * q^17 - 20 * q^18 - 30 * q^20 + 17 * q^22 + 5 * q^24 + 6 * q^25 - 4 * q^26 - 32 * q^27 - 30 * q^28 + 30 * q^30 + 32 * q^33 - 14 * q^34 - 10 * q^35 + 16 * q^36 + 28 * q^38 + 30 * q^40 - 10 * q^41 + 64 * q^42 - 38 * q^44 + 40 * q^46 + 26 * q^48 - 18 * q^49 + 5 * q^50 + 60 * q^51 + 40 * q^52 + 76 * q^56 - 80 * q^57 - 56 * q^58 + 28 * q^59 + 34 * q^60 - 80 * q^62 + 55 * q^64 - 30 * q^66 - 28 * q^67 + 60 * q^68 - 44 * q^70 + 45 * q^72 - 10 * q^73 - 100 * q^74 + 4 * q^75 - 80 * q^78 - 76 * q^80 + 28 * q^81 + 13 * q^82 - 50 * q^84 - 39 * q^86 - 69 * q^88 + 20 * q^89 - 30 * q^90 + 78 * q^91 + 6 * q^92 - 30 * q^94 - 110 * q^96 - 52 * q^97 + 122 * q^99

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