LMFDB - Embedded newform 460.2.w.a.307.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [460,2,Mod(3,460)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(460, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([22, 33, 32]))

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

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

chi := DirichletCharacter("460.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 460 = 2^{2} \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	460.w (of order $44$, degree $20$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.67311849298$
Analytic rank:	$0$
Dimension:	$1360$
Relative dimension:	$68$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			307.1
Character	$\chi$	$=$	460.307
Dual form			460.2.w.a.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41421 + 0.00122474i) q^{2} +(0.959477 - 2.57246i) q^{3} +(2.00000 - 0.00346408i) q^{4} +(1.75727 + 1.38275i) q^{5} +(-1.35375 + 3.63918i) q^{6} +(0.698270 - 0.151899i) q^{7} +(-2.82842 + 0.00734842i) q^{8} +(-3.42969 - 2.97185i) q^{9} +O(q^{10})$	\(q+(-1.41421 + 0.00122474i) q^{2} +(0.959477 - 2.57246i) q^{3} +(2.00000 - 0.00346408i) q^{4} +(1.75727 + 1.38275i) q^{5} +(-1.35375 + 3.63918i) q^{6} +(0.698270 - 0.151899i) q^{7} +(-2.82842 + 0.00734842i) q^{8} +(-3.42969 - 2.97185i) q^{9} +(-2.48685 - 1.95335i) q^{10} +(4.76108 - 0.684541i) q^{11} +(1.91004 - 5.14823i) q^{12} +(-0.148722 + 0.683665i) q^{13} +(-0.987316 + 0.215673i) q^{14} +(5.24313 - 3.19379i) q^{15} +(3.99998 - 0.0138563i) q^{16} +(-2.29054 - 1.25073i) q^{17} +(4.85396 + 4.19862i) q^{18} +(6.83847 + 2.00795i) q^{19} +(3.51933 + 2.75941i) q^{20} +(0.279219 - 1.94201i) q^{21} +(-6.73235 + 0.973917i) q^{22} +(-4.70701 + 0.918730i) q^{23} +(-2.69490 + 7.28304i) q^{24} +(1.17600 + 4.85973i) q^{25} +(0.209488 - 0.967030i) q^{26} +(-3.70648 + 2.02389i) q^{27} +(1.39601 - 0.306217i) q^{28} +(-0.0734905 - 0.250286i) q^{29} +(-7.41099 + 4.52312i) q^{30} +(-7.34064 - 3.35236i) q^{31} +(-5.65680 + 0.0244947i) q^{32} +(2.80720 - 12.9045i) q^{33} +(3.24084 + 1.76599i) q^{34} +(1.43709 + 0.698604i) q^{35} +(-6.86967 - 5.93180i) q^{36} +(6.12127 - 0.437802i) q^{37} +(-9.67351 - 2.83130i) q^{38} +(1.61600 + 1.03854i) q^{39} +(-4.98046 - 3.89808i) q^{40} +(-0.612632 - 0.707015i) q^{41} +(-0.392497 + 2.74676i) q^{42} +(3.62334 - 9.71456i) q^{43} +(9.51978 - 1.38557i) q^{44} +(-1.91758 - 9.96475i) q^{45} +(6.65559 - 1.30505i) q^{46} +(-5.37396 + 5.37396i) q^{47} +(3.80224 - 10.3031i) q^{48} +(-5.90292 + 2.69577i) q^{49} +(-1.66907 - 6.87126i) q^{50} +(-5.41517 + 4.69227i) q^{51} +(-0.295076 + 1.36784i) q^{52} +(-12.9608 + 2.81945i) q^{53} +(5.23928 - 2.86675i) q^{54} +(9.31307 + 5.38047i) q^{55} +(-1.97388 + 0.434766i) q^{56} +(11.7267 - 15.6651i) q^{57} +(0.104238 + 0.353867i) q^{58} +(3.61764 - 2.32492i) q^{59} +(10.4752 - 6.40573i) q^{60} +(-1.58180 + 3.46365i) q^{61} +(10.3853 + 4.73196i) q^{62} +(-2.84627 - 1.55418i) q^{63} +(7.99989 - 0.0415688i) q^{64} +(-1.20668 + 0.995739i) q^{65} +(-3.95417 + 18.2531i) q^{66} +(-3.29164 - 4.39711i) q^{67} +(-4.58540 - 2.49352i) q^{68} +(-2.15287 + 12.9901i) q^{69} +(-2.03320 - 0.986215i) q^{70} +(-2.96916 - 0.426901i) q^{71} +(9.72244 + 8.38042i) q^{72} +(8.00755 - 4.37245i) q^{73} +(-8.65625 + 0.626642i) q^{74} +(13.6298 + 1.63758i) q^{75} +(13.6839 + 3.99221i) q^{76} +(3.22054 - 1.20120i) q^{77} +(-2.28665 - 1.46674i) q^{78} +(1.05258 - 0.676450i) q^{79} +(7.04820 + 5.50662i) q^{80} +(-0.287439 - 1.99918i) q^{81} +(0.867258 + 0.999120i) q^{82} +(4.93702 - 0.353103i) q^{83} +(0.551710 - 3.88499i) q^{84} +(-2.29565 - 5.36511i) q^{85} +(-5.11228 + 13.7429i) q^{86} +(-0.714362 - 0.0510921i) q^{87} +(-13.4613 + 1.97115i) q^{88} +(-12.3441 + 5.63737i) q^{89} +(2.72407 + 14.0899i) q^{90} +0.499974i q^{91} +(-9.41082 + 1.85376i) q^{92} +(-15.6670 + 15.6670i) q^{93} +(7.59334 - 7.60650i) q^{94} +(9.24054 + 12.9844i) q^{95} +(-5.36456 + 14.5754i) q^{96} +(-0.687336 + 9.61022i) q^{97} +(8.34468 - 3.81963i) q^{98} +(-18.3634 - 11.8014i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	$ 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) $ 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{11}\right)$

Coefficient data

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

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

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

$2$	−1.41421	+	0.00122474i	−1.00000	+	0.000866020i
$2$	−1.41421	+	0.00122474i	−1.00000	+	0.000866020i
$3$	0.959477	−	2.57246i	0.553954	−	1.48521i	−0.294349	−	0.955698i	$-0.595103\pi$
$3$	0.959477	−	2.57246i	0.553954	−	1.48521i	0.848303	−	0.529511i	$-0.177625\pi$
$4$	2.00000	−	0.00346408i	0.999999	−	0.00173204i
$5$	1.75727	+	1.38275i	0.785876	+	0.618385i
$5$	1.75727	+	1.38275i	0.785876	+	0.618385i
$6$	−1.35375	+	3.63918i	−0.552668	+	1.48569i
$7$	0.698270	−	0.151899i	0.263921	−	0.0574125i	−0.0786575	−	0.996902i	$-0.525063\pi$
$7$	0.698270	−	0.151899i	0.263921	−	0.0574125i	0.342579	+	0.939489i	$0.388700\pi$
$8$	−2.82842	+	0.00734842i	−0.999997	+	0.00259806i
$9$	−3.42969	−	2.97185i	−1.14323	−	0.990615i
$10$	−2.48685	−	1.95335i	−0.786411	−	0.617704i
$11$	4.76108	−	0.684541i	1.43552	−	0.206397i	0.619763	−	0.784789i	$-0.287229\pi$
$11$	4.76108	−	0.684541i	1.43552	−	0.206397i	0.815759	+	0.578393i	$0.196320\pi$
$12$	1.91004	−	5.14823i	0.551381	−	1.48617i
$13$	−0.148722	+	0.683665i	−0.0412481	+	0.189615i	−0.993161	−	0.116755i	$-0.962751\pi$
$13$	−0.148722	+	0.683665i	−0.0412481	+	0.189615i	0.951913	+	0.306370i	$0.0991144\pi$
$14$	−0.987316	+	0.215673i	−0.263871	+	0.0576411i
$15$	5.24313	−	3.19379i	1.35377	−	0.824633i
$16$	3.99998	−	0.0138563i	0.999994	−	0.00346407i
$17$	−2.29054	−	1.25073i	−0.555537	−	0.303346i	0.176846	−	0.984238i	$-0.443410\pi$
$17$	−2.29054	−	1.25073i	−0.555537	−	0.303346i	−0.732384	+	0.680892i	$0.761592\pi$
$18$	4.85396	+	4.19862i	1.14409	+	0.989625i
$19$	6.83847	+	2.00795i	1.56885	+	0.460656i	0.946667	−	0.322214i	$-0.104427\pi$
$19$	6.83847	+	2.00795i	1.56885	+	0.460656i	0.622185	+	0.782870i	$0.286245\pi$
$20$	3.51933	+	2.75941i	0.786945	+	0.617023i
$21$	0.279219	−	1.94201i	0.0609306	−	0.423782i
$22$	−6.73235	+	0.973917i	−1.43534	+	0.207640i
$23$	−4.70701	+	0.918730i	−0.981479	+	0.191568i
$23$	−4.70701	+	0.918730i	−0.981479	+	0.191568i
$24$	−2.69490	+	7.28304i	−0.550094	+	1.48664i
$25$	1.17600	+	4.85973i	0.235201	+	0.971947i
$26$	0.209488	−	0.967030i	0.0410839	−	0.189650i
$27$	−3.70648	+	2.02389i	−0.713313	+	0.389498i
$28$	1.39601	−	0.306217i	0.263821	−	0.0578696i
$29$	−0.0734905	−	0.250286i	−0.0136468	−	0.0464769i	0.952388	−	0.304888i	$-0.0986191\pi$
$29$	−0.0734905	−	0.250286i	−0.0136468	−	0.0464769i	−0.966035	+	0.258411i	$0.916801\pi$
$30$	−7.41099	+	4.52312i	−1.35306	+	0.825805i
$31$	−7.34064	−	3.35236i	−1.31842	−	0.602101i	−0.372961	−	0.927847i	$-0.621657\pi$
$31$	−7.34064	−	3.35236i	−1.31842	−	0.602101i	−0.945457	+	0.325746i	$0.894385\pi$
$32$	−5.65680	+	0.0244947i	−0.999991	+	0.00433009i
$33$	2.80720	−	12.9045i	0.488671	−	2.24638i
$34$	3.24084	+	1.76599i	0.555800	+	0.302865i
$35$	1.43709	+	0.698604i	0.242912	+	0.118086i
$36$	−6.86967	−	5.93180i	−1.14495	−	0.988634i
$37$	6.12127	−	0.437802i	1.00633	−	0.0719742i	0.441568	−	0.897228i	$-0.354422\pi$
$37$	6.12127	−	0.437802i	1.00633	−	0.0719742i	0.564763	+	0.825253i	$0.308968\pi$
$38$	−9.67351	−	2.83130i	−1.56925	−	0.459298i
$39$	1.61600	+	1.03854i	0.258768	+	0.166300i
$40$	−4.98046	−	3.89808i	−0.787479	−	0.616341i
$41$	−0.612632	−	0.707015i	−0.0956771	−	0.110417i	0.705892	−	0.708320i	$-0.250546\pi$
$41$	−0.612632	−	0.707015i	−0.0956771	−	0.110417i	−0.801569	+	0.597902i	$0.796001\pi$
$42$	−0.392497	+	2.74676i	−0.0605636	+	0.423835i
$43$	3.62334	−	9.71456i	0.552554	−	1.48146i	−0.297480	−	0.954728i	$-0.596146\pi$
$43$	3.62334	−	9.71456i	0.552554	−	1.48146i	0.850034	−	0.526728i	$-0.176581\pi$
$44$	9.51978	−	1.38557i	1.43516	−	0.208883i
$45$	−1.91758	−	9.96475i	−0.285856	−	1.48546i
$46$	6.65559	−	1.30505i	0.981313	−	0.192418i
$47$	−5.37396	+	5.37396i	−0.783872	+	0.783872i	−0.980482	−	0.196610i	$-0.937007\pi$
$47$	−5.37396	+	5.37396i	−0.783872	+	0.783872i	0.196610	+	0.980482i	$0.437007\pi$
$48$	3.80224	−	10.3031i	0.548806	−	1.48712i
$49$	−5.90292	+	2.69577i	−0.843274	+	0.385110i
$50$	−1.66907	−	6.87126i	−0.236042	−	0.971743i
$51$	−5.41517	+	4.69227i	−0.758275	+	0.657049i
$52$	−0.295076	+	1.36784i	−0.0409197	+	0.189686i
$53$	−12.9608	+	2.81945i	−1.78031	+	0.387282i	−0.977829	−	0.209403i	$-0.932848\pi$
$53$	−12.9608	+	2.81945i	−1.78031	+	0.387282i	−0.802476	+	0.596685i	$0.796484\pi$
$54$	5.23928	−	2.86675i	0.712975	−	0.390116i
$55$	9.31307	+	5.38047i	1.25577	+	0.725502i
$56$	−1.97388	+	0.434766i	−0.263771	+	0.0580980i
$57$	11.7267	−	15.6651i	1.55324	−	2.07489i
$58$	0.104238	+	0.353867i	0.0136871	+	0.0464650i
$59$	3.61764	−	2.32492i	0.470977	−	0.302678i	−0.283539	−	0.958961i	$-0.591508\pi$
$59$	3.61764	−	2.32492i	0.470977	−	0.302678i	0.754515	+	0.656282i	$0.227872\pi$
$60$	10.4752	−	6.40573i	1.35234	−	0.826976i
$61$	−1.58180	+	3.46365i	−0.202528	+	0.443475i	−0.983456	−	0.181146i	$-0.942019\pi$
$61$	−1.58180	+	3.46365i	−0.202528	+	0.443475i	0.780928	+	0.624621i	$0.214747\pi$
$62$	10.3853	+	4.73196i	1.31894	+	0.600959i
$63$	−2.84627	−	1.55418i	−0.358597	−	0.195809i
$64$	7.99989	−	0.0415688i	0.999987	−	0.00519610i
$65$	−1.20668	+	0.995739i	−0.149671	+	0.123506i
$66$	−3.95417	+	18.2531i	−0.486725	+	2.24681i
$67$	−3.29164	−	4.39711i	−0.402138	−	0.537193i	0.553068	−	0.833136i	$-0.313457\pi$
$67$	−3.29164	−	4.39711i	−0.402138	−	0.537193i	−0.955206	+	0.295943i	$0.904366\pi$
$68$	−4.58540	−	2.49352i	−0.556062	−	0.302384i
$69$	−2.15287	+	12.9901i	−0.259175	+	1.56382i
$70$	−2.03320	−	0.986215i	−0.243014	−	0.117875i
$71$	−2.96916	−	0.426901i	−0.352375	−	0.0506638i	−0.0361452	−	0.999347i	$-0.511508\pi$
$71$	−2.96916	−	0.426901i	−0.352375	−	0.0506638i	−0.316229	+	0.948683i	$0.602417\pi$
$72$	9.72244	+	8.38042i	1.14580	+	0.987642i
$73$	8.00755	−	4.37245i	0.937213	−	0.511757i	0.0633832	−	0.997989i	$-0.479811\pi$
$73$	8.00755	−	4.37245i	0.937213	−	0.511757i	0.873830	+	0.486232i	$0.161629\pi$
$74$	−8.65625	+	0.626642i	−1.00627	+	0.0728457i
$75$	13.6298	+	1.63758i	1.57383	+	0.189092i
$76$	13.6839	+	3.99221i	1.56965	+	0.457938i
$77$	3.22054	−	1.20120i	0.367015	−	0.136889i
$78$	−2.28665	−	1.46674i	−0.258912	−	0.166076i
$79$	1.05258	−	0.676450i	0.118424	−	0.0761066i	−0.480088	−	0.877220i	$-0.659395\pi$
$79$	1.05258	−	0.676450i	0.118424	−	0.0761066i	0.598512	+	0.801114i	$0.295759\pi$
$80$	7.04820	+	5.50662i	0.788013	+	0.615659i
$81$	−0.287439	−	1.99918i	−0.0319376	−	0.222131i
$82$	0.867258	+	0.999120i	0.0957727	+	0.110334i
$83$	4.93702	−	0.353103i	0.541908	−	0.0387580i	0.202298	−	0.979324i	$-0.435159\pi$
$83$	4.93702	−	0.353103i	0.541908	−	0.0387580i	0.339611	+	0.940566i	$0.389705\pi$
$84$	0.551710	−	3.88499i	0.0601966	−	0.423887i
$85$	−2.29565	−	5.36511i	−0.248998	−	0.581928i
$86$	−5.11228	+	13.7429i	−0.551271	+	1.48193i
$87$	−0.714362	−	0.0510921i	−0.0765876	−	0.00547765i
$88$	−13.4613	+	1.97115i	−1.43498	+	0.210126i
$89$	−12.3441	+	5.63737i	−1.30847	+	0.597560i	−0.942855	−	0.333204i	$-0.891870\pi$
$89$	−12.3441	+	5.63737i	−1.30847	+	0.597560i	−0.365620	+	0.930764i	$0.619143\pi$
$90$	2.72407	+	14.0899i	0.287142	+	1.48521i
$91$			0.499974i			0.0524115i
$92$	−9.41082	+	1.85376i	−0.981146	+	0.193268i
$93$	−15.6670	+	15.6670i	−1.62459	+	1.62459i
$94$	7.59334	−	7.60650i	0.783193	−	0.784551i
$95$	9.24054	+	12.9844i	0.948059	+	1.33217i
$96$	−5.36456	+	14.5754i	−0.547518	+	1.48759i
$97$	−0.687336	+	9.61022i	−0.0697884	+	0.975770i	0.835094	+	0.550108i	$0.185413\pi$
$97$	−0.687336	+	9.61022i	−0.0697884	+	0.975770i	−0.904882	+	0.425662i	$0.860041\pi$
$98$	8.34468	−	3.81963i	0.842940	−	0.385840i
$99$	−18.3634	−	11.8014i	−1.84559	−	1.18609i
$100$	2.36884	+	9.71538i	0.236884	+	0.971538i
$101$	−8.20088	+	9.46432i	−0.816018	+	0.941735i	−0.999145	−	0.0413541i	$-0.986833\pi$
$101$	−8.20088	+	9.46432i	−0.816018	+	0.941735i	0.183126	+	0.983089i	$0.441378\pi$
$102$	7.65245	−	6.64250i	0.757706	−	0.657705i
$103$	1.46819	−	1.96128i	0.144665	−	0.193250i	−0.722356	−	0.691522i	$-0.756941\pi$
$103$	1.46819	−	1.96128i	0.144665	−	0.193250i	0.867021	+	0.498271i	$0.166032\pi$
$104$	0.415625	−	1.93478i	0.0407554	−	0.189721i
$105$	3.17598	−	3.02655i	0.309944	−	0.295361i
$106$	18.3259	−	4.00318i	1.77997	−	0.388823i
$107$	2.04977	+	5.49564i	0.198158	+	0.531283i	0.997583	−	0.0694830i	$-0.0221349\pi$
$107$	2.04977	+	5.49564i	0.198158	+	0.531283i	−0.799425	+	0.600766i	$0.794862\pi$
$108$	−7.40594	+	4.06062i	−0.712637	+	0.390733i
$109$	−1.05669	−	3.59875i	−0.101212	−	0.344698i	0.893281	−	0.449499i	$-0.148398\pi$
$109$	−1.05669	−	3.59875i	−0.101212	−	0.344698i	−0.994493	+	0.104801i	$0.966579\pi$
$110$	−13.1772	−	7.59772i	−1.25640	−	0.724414i
$111$	4.74699	−	16.1668i	0.450565	−	1.53448i
$112$	2.79096	−	0.617269i	0.263721	−	0.0583264i
$113$	2.86617	+	3.82876i	0.269627	+	0.360179i	0.914835	−	0.403827i	$-0.132320\pi$
$113$	2.86617	+	3.82876i	0.269627	+	0.360179i	−0.645208	+	0.764007i	$0.723229\pi$
$114$	−16.5649	+	22.1681i	−1.55145	+	2.07623i
$115$	−9.54187	−	4.89416i	−0.889784	−	0.456383i
$116$	−0.147848	−	0.500316i	−0.0137273	−	0.0464532i
$117$	2.54182	−	1.90278i	0.234991	−	0.175912i
$118$	−5.11327	+	3.29236i	−0.470714	+	0.303086i
$119$	−1.78940	−	0.525415i	−0.164034	−	0.0481647i
$120$	−14.8063	+	9.07190i	−1.35162	+	0.828147i
$121$	11.6449	−	3.41925i	1.05863	−	0.310841i
$122$	2.23275	−	4.90028i	0.202144	−	0.443650i
$123$	−2.40657	+	0.897606i	−0.216993	+	0.0809344i
$124$	−14.6929	−	6.67928i	−1.31946	−	0.599817i
$125$	−4.65324	+	10.1660i	−0.416199	+	0.909274i
$126$	4.02714	+	2.19446i	0.358766	+	0.195498i
$127$	−0.850440	−	0.636631i	−0.0754643	−	0.0564919i	0.560879	−	0.827897i	$-0.310463\pi$
$127$	−0.850440	−	0.636631i	−0.0754643	−	0.0564919i	−0.636344	+	0.771406i	$0.719554\pi$
$128$	−11.3135	+	0.0685849i	−0.999982	+	0.00606210i
$129$	−21.5138	−	18.6418i	−1.89418	−	1.64132i
$130$	1.70529	−	1.40967i	0.149564	−	0.123636i
$131$	−3.74074	+	5.82071i	−0.326830	+	0.508558i	−0.965319	−	0.261073i	$-0.915924\pi$
$131$	−3.74074	+	5.82071i	−0.326830	+	0.508558i	0.638489	+	0.769631i	$0.279560\pi$
$132$	5.56969	−	25.8187i	0.484779	−	2.24723i
$133$	5.08010	+	0.363336i	0.440501	+	0.0315052i
$134$	4.66046	+	6.21443i	0.402603	+	0.536845i
$135$	−9.31183	−	1.56861i	−0.801435	−	0.135005i
$136$	6.48779	+	3.52075i	0.556323	+	0.301902i
$137$	11.1392	+	11.1392i	0.951689	+	0.951689i	0.998886	−	0.0471971i	$-0.0150289\pi$
$137$	11.1392	+	11.1392i	0.951689	+	0.951689i	−0.0471971	+	0.998886i	$0.515029\pi$
$138$	3.02871	−	18.3734i	0.257821	−	1.56405i
$139$	3.96625			0.336413			0.168207	−	0.985752i	$-0.446202\pi$
$139$	3.96625			0.336413			0.168207	+	0.985752i	$0.446202\pi$
$140$	2.87659	+	1.39223i	0.243116	+	0.117665i
$141$	8.66809	+	18.9805i	0.729985	+	1.59844i
$142$	4.19955	+	0.600093i	0.352418	+	0.0503586i
$143$	−0.240083	+	3.35679i	−0.0200767	+	0.280709i
$144$	−13.7599	−	11.8398i	−1.14666	−	0.986649i
$145$	0.216940	−	0.541439i	0.0180159	−	0.0449640i
$146$	−11.3190	+	6.19339i	−0.936769	+	0.512568i
$147$	1.27105	+	17.7715i	0.104834	+	1.46577i
$148$	12.2410	−	0.896807i	1.00620	−	0.0737171i
$149$	7.84795	−	1.12836i	0.642929	−	0.0924393i	0.186864	−	0.982386i	$-0.440168\pi$
$149$	7.84795	−	1.12836i	0.642929	−	0.0924393i	0.456065	+	0.889947i	$0.349258\pi$
$150$	−19.2775	−	2.29920i	−1.57400	−	0.187729i
$151$	7.30843	+	11.3721i	0.594752	+	0.925452i	0.999937	+	0.0112171i	$0.00357059\pi$
$151$	7.30843	+	11.3721i	0.594752	+	0.925452i	−0.405185	+	0.914235i	$0.632793\pi$
$152$	−19.3568	−	5.62908i	−1.57004	−	0.456579i
$153$	4.13887	+	11.0967i	0.334608	+	0.897118i
$154$	−4.55306	+	1.70270i	−0.366896	+	0.137207i
$155$	−8.26402	−	16.0413i	−0.663782	−	1.28847i
$156$	3.23560	+	2.07148i	0.259055	+	0.165852i
$157$	10.6480	+	19.5004i	0.849803	+	1.55630i	0.830863	+	0.556477i	$0.187847\pi$
$157$	10.6480	+	19.5004i	0.849803	+	1.55630i	0.0189402	+	0.999821i	$0.493971\pi$
$158$	−1.48774	+	0.957933i	−0.118358	+	0.0762091i
$159$	−5.18268	+	36.0464i	−0.411014	+	2.85866i
$160$	−9.97440	−	7.77890i	−0.788546	−	0.614976i
$161$	−3.14721	+	1.35651i	−0.248035	+	0.106908i
$162$	0.408948	+	2.82691i	0.0321300	+	0.222103i
$163$	−15.8229	+	11.8449i	−1.23935	+	0.927764i	−0.999078	−	0.0429416i	$-0.986327\pi$
$163$	−15.8229	+	11.8449i	−1.23935	+	0.927764i	−0.240271	+	0.970706i	$0.577236\pi$
$164$	−1.22771	−	1.41191i	−0.0958682	−	0.110251i
$165$	22.7767	−	18.7950i	1.77316	−	1.46319i
$166$	−6.98157	+	0.505409i	−0.541875	+	0.0392273i
$167$	10.4332	−	19.1069i	0.807343	−	1.47854i	−0.0694058	−	0.997589i	$-0.522110\pi$
$167$	10.4332	−	19.1069i	0.807343	−	1.47854i	0.876748	−	0.480949i	$-0.159708\pi$
$168$	−0.775478	+	5.49488i	−0.0598294	+	0.423939i
$169$	11.3799	+	5.19704i	0.875380	+	0.399773i
$170$	3.25311	+	7.58460i	0.249502	+	0.581712i
$171$	−17.4865	−	27.2095i	−1.33723	−	2.08077i
$172$	7.21302	−	19.4416i	0.549988	−	1.48241i
$173$	4.67051	+	3.49630i	0.355092	+	0.265819i	0.761900	−	0.647695i	$-0.224267\pi$
$173$	4.67051	+	3.49630i	0.355092	+	0.265819i	−0.406807	+	0.913514i	$0.633358\pi$
$174$	1.01032	+	0.0713803i	0.0765923	+	0.00541132i
$175$	1.55936	+	3.21477i	0.117876	+	0.243014i
$176$	19.0347	−	2.80412i	1.43480	−	0.211368i
$177$	−2.50971	−	11.5369i	−0.188641	−	0.867169i
$178$	17.4503	−	7.98756i	1.30796	−	0.598693i
$179$	2.32483	+	2.68300i	0.173766	+	0.200537i	0.835952	−	0.548803i	$-0.184916\pi$
$179$	2.32483	+	2.68300i	0.173766	+	0.200537i	−0.662185	+	0.749340i	$0.730371\pi$
$180$	−3.86967	−	19.9228i	−0.288428	−	1.48496i
$181$	−4.80743	−	10.5268i	−0.357333	−	0.782451i	−0.999869	−	0.0161949i	$-0.994845\pi$
$181$	−4.80743	−	10.5268i	−0.357333	−	0.782451i	0.642536	−	0.766256i	$-0.277882\pi$
$182$	−0.000612336	−	0.707069i	−4.53894e−5	−	0.0524114i
$183$	7.39240	+	7.39240i	0.546462	+	0.546462i
$184$	13.3066	−	2.63314i	0.980978	−	0.194118i
$185$	11.3621	+	7.69486i	0.835359	+	0.565737i
$186$	22.1373	−	22.1756i	1.62318	−	1.62600i
$187$	−11.7616	−	4.38686i	−0.860095	−	0.320799i
$188$	−10.7293	+	10.7665i	−0.782513	+	0.785229i
$189$	−2.28070	+	1.97623i	−0.165896	+	0.143750i
$190$	−13.0840	−	18.3514i	−0.949213	−	1.33135i
$191$	1.95023	−	3.03461i	0.141113	−	0.219577i	−0.763502	−	0.645805i	$-0.776522\pi$
$191$	1.95023	−	3.03461i	0.141113	−	0.219577i	0.904615	+	0.426229i	$0.140158\pi$
$192$	7.56878	−	20.6193i	0.546230	−	1.48807i
$193$	−0.282518	−	3.95011i	−0.0203361	−	0.284335i	−0.997437	−	0.0715568i	$-0.977203\pi$
$193$	−0.282518	−	3.95011i	−0.0203361	−	0.284335i	0.977100	−	0.212778i	$-0.0682513\pi$
$194$	0.960270	−	13.5917i	0.0689434	−	0.975830i
$195$	1.40371	+	4.05953i	0.100522	+	0.290709i
$196$	−11.7965	+	5.41198i	−0.842606	+	0.386570i
$197$	−10.6881	−	2.32506i	−0.761497	−	0.165654i	−0.184984	−	0.982742i	$-0.559223\pi$
$197$	−10.6881	−	2.32506i	−0.761497	−	0.165654i	−0.576513	+	0.817088i	$0.695587\pi$
$198$	25.9842	+	16.6673i	1.84662	+	1.18449i
$199$	2.50533	−	5.48591i	0.177598	−	0.388886i	−0.799808	−	0.600256i	$-0.795065\pi$
$199$	2.50533	−	5.48591i	0.177598	−	0.388886i	0.977406	+	0.211370i	$0.0677926\pi$
$200$	−3.36194	−	13.7367i	−0.237725	−	0.971332i
$201$	−14.4696	+	4.24867i	−1.02061	+	0.299678i
$202$	11.5862	−	13.3946i	0.815202	−	0.942442i
$203$	−0.0893344	−	0.163604i	−0.00627004	−	0.0114827i
$204$	−10.8141	+	9.40328i	−0.757136	+	0.658361i
$205$	−0.0989354	−	2.08954i	−0.00690995	−	0.145939i
$206$	−2.07394	+	2.77546i	−0.144498	+	0.193376i
$207$	18.8739	+	10.8375i	1.31183	+	0.753261i
$208$	−0.585412	+	2.73671i	−0.0405911	+	0.189756i
$209$	33.9330	+	4.87884i	2.34720	+	0.337476i
$210$	−4.48781	+	4.28408i	−0.309688	+	0.295630i
$211$	−5.06714	+	17.2571i	−0.348836	+	1.18803i	0.579090	+	0.815264i	$0.303408\pi$
$211$	−5.06714	+	17.2571i	−0.348836	+	1.18803i	−0.927926	+	0.372764i	$0.878410\pi$
$212$	−25.9118	+	5.68380i	−1.77963	+	0.390365i
$213$	−3.94703	+	7.22844i	−0.270446	+	0.495285i
$214$	−2.90554	−	7.76949i	−0.198618	−	0.531112i
$215$	19.8000	−	12.0609i	1.35035	−	0.822549i
$216$	10.4686	−	5.75165i	0.712299	−	0.391350i
$217$	−5.63497	−	1.22581i	−0.382527	−	0.0832136i
$218$	1.49879	+	5.08811i	0.101511	+	0.344610i
$219$	−3.56489	−	24.7944i	−0.240893	−	1.67545i
$220$	18.6447	+	10.7287i	1.25703	+	0.723326i
$221$	1.19573	−	1.37995i	0.0804338	−	0.0928255i
$222$	−6.69346	+	22.8691i	−0.449236	+	1.53487i
$223$	1.05305	+	4.84080i	0.0705176	+	0.324164i	0.998869	−	0.0475385i	$-0.0151377\pi$
$223$	1.05305	+	4.84080i	0.0705176	+	0.324164i	−0.928352	+	0.371703i	$0.878774\pi$
$224$	−3.94625	+	0.876368i	−0.263670	+	0.0585548i
$225$	10.4091	−	20.1623i	0.693937	−	1.34415i
$226$	−4.05807	−	5.41117i	−0.269939	−	0.359945i
$227$	−2.94602	−	1.09881i	−0.195534	−	0.0729305i	0.249789	−	0.968300i	$-0.419639\pi$
$227$	−2.94602	−	1.09881i	−0.195534	−	0.0729305i	−0.445324	+	0.895370i	$0.646911\pi$
$228$	23.3992	−	31.3707i	1.54965	−	2.07758i
$229$		−	5.30243i		−	0.350395i	−0.984533	−	0.175197i	$-0.943944\pi$
$229$		−	5.30243i		−	0.350395i	0.984533	−	0.175197i	$-0.0560563\pi$
$230$	13.5002	+	6.90970i	0.890178	+	0.455612i
$231$		−	9.43723i		−	0.620924i
$232$	0.209701	+	0.707372i	0.0137675	+	0.0464413i
$233$	0.282881	+	0.105509i	0.0185321	+	0.00691213i	0.358713	−	0.933448i	$-0.383216\pi$
$233$	0.282881	+	0.105509i	0.0185321	+	0.00691213i	−0.340181	+	0.940360i	$0.610488\pi$
$234$	−3.59234	+	2.69405i	−0.234839	+	0.176116i
$235$	−16.8743	+	2.01266i	−1.10076	+	0.131291i
$236$	7.22722	−	4.66236i	0.470452	−	0.303494i
$237$	−0.730216	−	3.35675i	−0.0474326	−	0.218044i
$238$	2.53123	+	0.740857i	0.164076	+	0.0480226i
$239$	15.2710	−	17.6237i	0.987799	−	1.13998i	−0.00235445	−	0.999997i	$-0.500749\pi$
$239$	15.2710	−	17.6237i	0.987799	−	1.13998i	0.990154	−	0.139984i	$-0.0447051\pi$
$240$	20.9281	−	12.8477i	1.35091	−	0.829317i
$241$	3.04637	+	21.1880i	0.196234	+	1.36484i	0.815091	+	0.579333i	$0.196687\pi$
$241$	3.04637	+	21.1880i	0.196234	+	1.36484i	−0.618857	+	0.785504i	$0.712404\pi$
$242$	−16.4642	+	4.84982i	−1.05836	+	0.311758i
$243$	−17.7982	−	3.87177i	−1.14176	−	0.248374i
$244$	−3.15159	+	6.93277i	−0.201760	+	0.443825i
$245$	−14.1006	−	3.42506i	−0.900855	−	0.218819i
$246$	3.40231	−	1.27235i	0.216923	−	0.0811223i
$247$	−2.38980	+	4.37659i	−0.152059	+	0.278476i
$248$	20.7870	+	9.42793i	1.31998	+	0.598674i
$249$	3.82862	−	13.0391i	0.242629	−	0.826317i
$250$	6.56822	−	14.3826i	0.415411	−	0.909634i
$251$	−2.27348	−	0.326877i	−0.143501	−	0.0206323i	0.0701901	−	0.997534i	$-0.477639\pi$
$251$	−2.27348	−	0.326877i	−0.143501	−	0.0206323i	−0.213691	+	0.976901i	$0.568549\pi$
$252$	−5.69792	−	3.09850i	−0.358935	−	0.195187i
$253$	−21.7816	+	7.59629i	−1.36940	+	0.477575i
$254$	1.20348	+	0.899291i	0.0755132	+	0.0564265i
$255$	−16.0041	+	0.757765i	−1.00222	+	0.0474531i
$256$	15.9996	−	0.110850i	0.999976	−	0.00692811i
$257$	−9.53216	−	17.4569i	−0.594600	−	1.08893i	−0.985689	−	0.168576i	$-0.946083\pi$
$257$	−9.53216	−	17.4569i	−0.594600	−	1.08893i	0.391089	−	0.920353i	$-0.372099\pi$
$258$	30.4479	+	26.3371i	1.89560	+	1.63968i
$259$	4.20780	−	1.23552i	0.261460	−	0.0767715i
$260$	−2.40991	+	1.99566i	−0.149457	+	0.123765i
$261$	−0.491761	+	1.07681i	−0.0304392	+	0.0666526i
$262$	5.28308	−	8.23631i	0.326390	−	0.508841i
$263$	−21.9164	−	4.76762i	−1.35142	−	0.293984i	−0.522162	−	0.852847i	$-0.674874\pi$
$263$	−21.9164	−	4.76762i	−1.35142	−	0.293984i	−0.829260	+	0.558863i	$0.811238\pi$
$264$	−7.84511	+	36.5199i	−0.482833	+	2.24765i
$265$	−26.6743	−	12.9670i	−1.63859	−	0.796558i
$266$	−7.18479	−	0.507613i	−0.440528	−	0.0311237i
$267$	2.65800	+	37.1637i	0.162667	+	2.27438i
$268$	−6.59850	−	8.78281i	−0.403068	−	0.536496i
$269$	11.2767	−	17.5468i	0.687551	−	1.06985i	−0.305504	−	0.952191i	$-0.598825\pi$
$269$	11.2767	−	17.5468i	0.687551	−	1.06985i	0.993054	−	0.117659i	$-0.0375389\pi$
$270$	13.1708	+	2.20695i	0.801552	+	0.134310i
$271$	−8.39578	+	7.27499i	−0.510008	+	0.441924i	−0.871460	−	0.490466i	$-0.836826\pi$
$271$	−8.39578	+	7.27499i	−0.510008	+	0.441924i	0.361453	+	0.932391i	$0.382281\pi$
$272$	−9.17943	−	4.97115i	−0.556585	−	0.301420i
$273$	1.28616	+	0.479713i	0.0778420	+	0.0290336i
$274$	−15.7669	−	15.7396i	−0.952512	−	0.950864i
$275$	8.92574	+	22.3326i	0.538242	+	1.34671i
$276$	−4.26074	+	25.9876i	−0.256466	+	1.56427i
$277$	1.20755	+	1.20755i	0.0725544	+	0.0725544i	0.742453	−	0.669898i	$-0.233662\pi$
$277$	1.20755	+	1.20755i	0.0725544	+	0.0725544i	−0.669898	+	0.742453i	$0.733662\pi$
$278$	−5.60913	+	0.00485762i	−0.336413	+	0.000291341i
$279$	15.2135	+	33.3128i	0.910806	+	1.99439i
$280$	−4.06982	−	1.96538i	−0.243218	−	0.117454i
$281$	−13.7597	−	15.8796i	−0.820837	−	0.947297i	0.178491	−	0.983942i	$-0.442878\pi$
$281$	−13.7597	−	15.8796i	−0.820837	−	0.947297i	−0.999328	+	0.0366449i	$0.988333\pi$
$282$	−12.2818	−	26.8318i	−0.731369	−	1.59781i
$283$	−5.64319	−	25.9413i	−0.335453	−	1.54205i	−0.768006	−	0.640442i	$-0.778751\pi$
$283$	−5.64319	−	25.9413i	−0.335453	−	1.54205i	0.432554	−	0.901608i	$-0.357613\pi$
$284$	−5.93979	−	0.843515i	−0.352462	−	0.0500534i
$285$	42.2679	−	11.3127i	2.50374	−	0.670104i
$286$	0.335417	−	4.74752i	0.0198336	−	0.280727i
$287$	−0.535178	−	0.400629i	−0.0315905	−	0.0236484i
$288$	19.4739	+	16.7271i	1.14751	+	0.985656i
$289$	−5.50865	−	8.57163i	−0.324038	−	0.504213i
$290$	−0.306136	+	0.765975i	−0.0179769	+	0.0449796i
$291$	24.0624	+	10.9889i	1.41056	+	0.644182i
$292$	15.9999	−	8.77263i	0.936325	−	0.513379i
$293$	−1.34165	+	2.45706i	−0.0783803	+	0.143543i	−0.913930	−	0.405873i	$-0.866968\pi$
$293$	−1.34165	+	2.45706i	−0.0783803	+	0.143543i	0.835549	+	0.549415i	$0.185150\pi$
$294$	−1.81929	−	25.1312i	−0.106103	−	1.46568i
$295$	9.57195	+	0.916785i	0.557301	+	0.0533773i
$296$	−17.3103	+	1.28327i	−1.00614	+	0.0745885i
$297$	−16.2614	+	12.1732i	−0.943585	+	0.706359i
$298$	−11.0973	+	1.60536i	−0.642849	+	0.0929960i
$299$	0.0719332	−	3.35465i	0.00416000	−	0.194005i
$300$	27.2652	+	3.22795i	1.57416	+	0.186366i
$301$	1.05444	−	7.33376i	0.0607767	−	0.422711i
$302$	−10.3496	−	16.0737i	−0.595553	−	0.924936i
$303$	16.4780	+	30.1772i	0.946637	+	1.73364i
$304$	27.3815	+	7.93702i	1.57044	+	0.455219i
$305$	−7.56901	+	3.89934i	−0.433400	+	0.223276i
$306$	−5.86684	−	15.6881i	−0.335385	−	0.896828i
$307$	−5.37438	−	14.4093i	−0.306732	−	0.822380i	−0.995267	−	0.0971770i	$-0.969019\pi$
$307$	−5.37438	−	14.4093i	−0.306732	−	0.822380i	0.688535	−	0.725203i	$-0.258254\pi$
$308$	6.43691	−	2.41355i	0.366777	−	0.137525i
$309$	−3.63660	−	5.65866i	−0.206879	−	0.321910i
$310$	11.7067	+	22.6757i	0.664898	+	1.28789i
$311$	−4.74674	+	0.682478i	−0.269163	+	0.0386998i	−0.275575	−	0.961280i	$-0.588868\pi$
$311$	−4.74674	+	0.682478i	−0.269163	+	0.0386998i	0.00641189	+	0.999979i	$0.497959\pi$
$312$	−4.57837	−	2.92556i	−0.259199	−	0.165627i
$313$	1.73712	+	24.2881i	0.0981877	+	1.37284i	0.772790	+	0.634662i	$0.218861\pi$
$313$	1.73712	+	24.2881i	0.0981877	+	1.37284i	−0.674602	+	0.738182i	$0.735685\pi$
$314$	−15.0824	−	27.5646i	−0.851150	−	1.55556i
$315$	−2.85263	−	6.66680i	−0.160727	−	0.375632i
$316$	2.10281	−	1.35654i	0.118292	−	0.0763116i
$317$	−1.09532	+	15.3146i	−0.0615193	+	0.860153i	0.869210	+	0.494443i	$0.164628\pi$
$317$	−1.09532	+	15.3146i	−0.0615193	+	0.860153i	−0.930729	+	0.365709i	$0.880826\pi$
$318$	7.28527	−	50.9836i	0.408538	−	2.85902i
$319$	−0.521225	−	1.14132i	−0.0291830	−	0.0639019i
$320$	14.1155	+	10.9888i	0.789078	+	0.614293i
$321$	16.1040			0.898838
$322$	4.44916	−	1.92225i	0.247942	−	0.107123i
$323$	−13.1524	−	13.1524i	−0.731817	−	0.731817i
$324$	−0.581802	−	3.99736i	−0.0323223	−	0.222075i
$325$	−3.49733	+	0.0812420i	−0.193997	+	0.00450650i
$326$	22.3625	−	16.7706i	1.23854	−	0.928837i
$327$	−10.2715	−	0.734633i	−0.568016	−	0.0406253i
$328$	1.73798	+	1.99523i	0.0959636	+	0.110168i
$329$	−2.93617	+	4.56877i	−0.161876	+	0.251885i
$330$	−32.1881	+	26.6081i	−1.77190	+	1.46473i
$331$	−25.0283	−	21.6872i	−1.37568	−	1.19203i	−0.959145	−	0.282916i	$-0.908698\pi$
$331$	−25.0283	−	21.6872i	−1.37568	−	1.19203i	−0.416536	−	0.909119i	$-0.636756\pi$
$332$	9.87280	−	0.723306i	0.541840	−	0.0396966i
$333$	−22.2952	−	16.6900i	−1.22177	−	0.914604i
$334$	−14.7313	+	27.0340i	−0.806062	+	1.47924i
$335$	0.295810	−	12.2784i	0.0161618	−	0.670843i
$336$	1.08996	−	7.77187i	0.0594623	−	0.423990i
$337$	4.46110	−	1.66390i	0.243012	−	0.0906386i	−0.225007	−	0.974357i	$-0.572241\pi$
$337$	4.46110	−	1.66390i	0.243012	−	0.0906386i	0.468019	+	0.883718i	$0.344968\pi$
$338$	−16.1000	−	7.33579i	−0.875726	−	0.399014i
$339$	12.5993	−	3.69950i	0.684302	−	0.200929i
$340$	−4.60988	−	10.7223i	−0.250006	−	0.581496i
$341$	−37.2442	−	10.9359i	−2.01689	−	0.592212i
$342$	24.7630	+	38.4587i	1.33903	+	2.07961i
$343$	−7.71681	+	5.77673i	−0.416669	+	0.311914i
$344$	−10.1769	+	27.5034i	−0.548704	+	1.48289i
$345$	−21.7452	+	19.8502i	−1.17072	+	1.06870i
$346$	−6.60938	−	4.93879i	−0.355323	−	0.265511i
$347$	16.4802	+	22.0150i	0.884703	+	1.18182i	0.982434	+	0.186612i	$0.0597507\pi$
$347$	16.4802	+	22.0150i	0.884703	+	1.18182i	−0.0977307	+	0.995213i	$0.531158\pi$
$348$	−1.42890	−	0.0997095i	−0.0765970	−	0.00534499i
$349$	−1.10816	+	3.77406i	−0.0593186	+	0.202021i	−0.983821	−	0.179157i	$-0.942663\pi$
$349$	−1.10816	+	3.77406i	−0.0593186	+	0.202021i	0.924502	+	0.381177i	$0.124481\pi$
$350$	−2.20920	−	4.54446i	−0.118087	−	0.242912i
$351$	−0.832429	−	2.83499i	−0.0444318	−	0.151321i
$352$	−26.9157	+	3.98893i	−1.43461	+	0.212611i
$353$	−6.33978	−	16.9976i	−0.337432	−	0.904691i	−0.989239	−	0.146306i	$-0.953261\pi$
$353$	−6.33978	−	16.9976i	−0.337432	−	0.904691i	0.651807	−	0.758385i	$-0.274011\pi$
$354$	3.56339	+	16.3126i	0.189392	+	0.867005i
$355$	−4.62732	−	4.85579i	−0.245593	−	0.257719i
$356$	−24.6687	+	11.3175i	−1.30744	+	0.599826i
$357$	−3.06849	+	4.09903i	−0.162402	+	0.216944i
$358$	−3.29110	−	3.79149i	−0.173940	−	0.200386i
$359$	−18.2297	+	21.0382i	−0.962125	+	1.11035i	0.0317116	+	0.999497i	$0.489904\pi$
$359$	−18.2297	+	21.0382i	−0.962125	+	1.11035i	−0.993837	+	0.110854i	$0.964641\pi$
$360$	5.49694	+	28.1704i	0.289714	+	1.48471i
$361$	26.7489	+	17.1905i	1.40784	+	0.904763i
$362$	6.81162	+	14.8812i	0.358011	+	0.782141i
$363$	2.37714	−	33.2367i	0.124767	−	1.74448i
$364$	0.00173195	+	0.999946i	9.07787e−5	+	0.0524114i
$365$	20.1174	+	3.38886i	1.05300	+	0.177381i
$366$	−10.4635	−	10.4454i	−0.546935	−	0.545988i
$367$	−13.1040	+	13.1040i	−0.684023	+	0.684023i	−0.960904	−	0.276881i	$-0.910699\pi$
$367$	−13.1040	+	13.1040i	−0.684023	+	0.684023i	0.276881	+	0.960904i	$0.410699\pi$
$368$	−18.8152	+	3.74012i	−0.980810	+	0.194967i
$369$			4.24549i			0.221012i
$370$	−16.0779	−	10.8682i	−0.835848	−	0.565013i
$371$	−8.62187	+	3.93748i	−0.447625	+	0.204424i
$372$	−31.2796	+	31.3882i	−1.62177	+	1.62740i
$373$	28.0306	+	2.00479i	1.45137	+	0.103804i	0.774628	−	0.632418i	$-0.217937\pi$
$373$	28.0306	+	2.00479i	1.45137	+	0.103804i	0.676741	+	0.736222i	$0.263392\pi$
$374$	16.6388	+	6.18955i	0.860372	+	0.320054i
$375$	21.6869	+	21.7243i	1.11991	+	1.12184i
$376$	15.1603	−	15.2393i	0.781833	−	0.785906i
$377$	0.182041	−	0.0130198i	0.00937560	−	0.000670556i
$378$	3.22297	−	2.79761i	0.165772	−	0.143894i
$379$	−4.98238	−	34.6532i	−0.255928	−	1.78002i	−0.561128	−	0.827729i	$-0.689632\pi$
$379$	−4.98238	−	34.6532i	−0.255928	−	1.78002i	0.305200	−	0.952288i	$-0.401277\pi$
$380$	18.5260	+	25.9368i	0.950365	+	1.33053i
$381$	−2.45368	+	1.57689i	−0.125706	+	0.0807864i
$382$	−2.75432	+	4.29397i	−0.140923	+	0.219699i
$383$	−8.96637	+	3.34428i	−0.458160	+	0.170885i	−0.567938	−	0.823071i	$-0.692259\pi$
$383$	−8.96637	+	3.34428i	−0.458160	+	0.170885i	0.109778	+	0.993956i	$0.464986\pi$
$384$	−10.6786	+	29.1693i	−0.544941	+	1.48854i
$385$	7.32032	+	2.34237i	0.373078	+	0.119378i
$386$	0.404378	+	5.58595i	0.0205823	+	0.284318i
$387$	−41.2971	+	22.5499i	−2.09925	+	1.14628i
$388$	−1.34138	+	19.2228i	−0.0680983	+	0.975889i
$389$	−7.27003	−	1.04527i	−0.368605	−	0.0529975i	−0.0444766	−	0.999010i	$-0.514162\pi$
$389$	−7.27003	−	1.04527i	−0.368605	−	0.0529975i	−0.324129	+	0.946013i	$0.605071\pi$
$390$	−1.99012	−	5.73932i	−0.100774	−	0.290622i
$391$	11.9307	+	3.78280i	0.603360	+	0.191305i
$392$	16.6761	−	7.66815i	0.842270	−	0.387300i
$393$	11.3844	+	15.2077i	0.574266	+	0.767129i
$394$	15.1181	+	3.27504i	0.761640	+	0.164994i
$395$	2.78502	+	0.266745i	0.140130	+	0.0134214i
$396$	−36.7676	−	23.5392i	−1.84764	−	1.18289i
$397$	24.4721	+	13.3628i	1.22822	+	0.670658i	0.956504	−	0.291719i	$-0.0942273\pi$
$397$	24.4721	+	13.3628i	1.22822	+	0.670658i	0.271715	+	0.962378i	$0.412409\pi$
$398$	−3.53635	+	7.76132i	−0.177261	+	0.389040i
$399$	5.80891	−	12.7197i	0.290809	−	0.636783i
$400$	4.77132	+	19.4225i	0.238566	+	0.971126i
$401$	−29.3148	+	18.8394i	−1.46391	+	0.940797i	−0.465463	+	0.885067i	$0.654112\pi$
$401$	−29.3148	+	18.8394i	−1.46391	+	0.940797i	−0.998446	+	0.0557298i	$0.982251\pi$
$402$	20.4580	−	6.02625i	1.02035	−	0.300562i
$403$	3.38361	−	4.51997i	0.168550	−	0.225156i
$404$	−16.3690	+	18.9570i	−0.814386	+	0.943147i
$405$	2.25926	−	3.91056i	0.112263	−	0.194317i
$406$	0.126538	+	0.231261i	0.00627999	+	0.0114773i
$407$	28.8442	−	6.27467i	1.42975	−	0.311024i
$408$	15.2819	−	13.3115i	0.756565	−	0.659017i
$409$	−20.1766	+	17.4831i	−0.997666	+	0.864483i	−0.990778	−	0.135494i	$-0.956738\pi$
$409$	−20.1766	+	17.4831i	−0.997666	+	0.864483i	−0.00688804	+	0.999976i	$0.502193\pi$
$410$	0.142475	+	2.95493i	0.00703633	+	0.145933i
$411$	39.3430	−	17.9674i	1.94065	−	0.886264i
$412$	2.92959	−	3.92763i	0.144330	−	0.193501i
$413$	2.17294	−	2.17294i	0.106923	−	0.106923i
$414$	−26.7050	−	15.3035i	−1.31248	−	0.752125i
$415$	9.16393	+	6.20617i	0.449840	+	0.304649i
$416$	0.824546	−	3.87100i	0.0404267	−	0.189791i
$417$	3.80553	−	10.2030i	0.186358	−	0.499644i
$418$	−47.9945	−	6.85815i	−2.34749	−	0.335443i
$419$	−9.04149	−	10.4344i	−0.441706	−	0.509755i	0.490621	−	0.871373i	$-0.336770\pi$
$419$	−9.04149	−	10.4344i	−0.441706	−	0.509755i	−0.932326	+	0.361618i	$0.882225\pi$
$420$	6.34147	−	6.06410i	0.309432	−	0.295898i
$421$	−7.45919	−	4.79373i	−0.363538	−	0.233632i	0.346101	−	0.938197i	$-0.387506\pi$
$421$	−7.45919	−	4.79373i	−0.363538	−	0.233632i	−0.709639	+	0.704565i	$0.751142\pi$
$422$	7.14488	−	24.4114i	0.347807	−	1.18833i
$423$	34.4016	−	2.46045i	1.67266	−	0.119631i
$424$	36.6379	−	8.06983i	1.77929	−	0.391906i
$425$	3.38453	−	12.6023i	0.164174	−	0.611300i
$426$	5.57308	−	10.2274i	0.270017	−	0.495519i
$427$	−0.578394	+	2.65884i	−0.0279905	+	0.128670i
$428$	4.11856	+	10.9842i	0.199078	+	0.530939i
$429$	8.40486	+	3.83837i	0.405790	+	0.185318i
$430$	−27.9866	+	17.0810i	−1.34964	+	0.823718i
$431$	−6.96841	−	23.7322i	−0.335656	−	1.14314i	−0.938499	−	0.345281i	$-0.887784\pi$
$431$	−6.96841	−	23.7322i	−0.335656	−	1.14314i	0.602843	−	0.797860i	$-0.294035\pi$
$432$	−14.7978	+	8.14688i	−0.711959	+	0.391967i
$433$	1.94910	−	1.06429i	0.0936677	−	0.0511464i	−0.431732	−	0.902002i	$-0.642097\pi$
$433$	1.94910	−	1.06429i	0.0936677	−	0.0511464i	0.525400	+	0.850855i	$0.323916\pi$
$434$	7.97055	+	1.72666i	0.382599	+	0.0828823i
$435$	−1.18468	−	1.07757i	−0.0568010	−	0.0516654i
$436$	−2.12584	−	7.19383i	−0.101809	−	0.344522i
$437$	−34.0335	−	3.16876i	−1.62804	−	0.151582i
$438$	5.07188	+	35.0601i	0.242344	+	1.67524i
$439$	3.80146	−	26.4397i	0.181434	−	1.26190i	−0.671943	−	0.740603i	$-0.734540\pi$
$439$	3.80146	−	26.4397i	0.181434	−	1.26190i	0.853376	−	0.521295i	$-0.174551\pi$
$440$	−26.3808	−	15.1498i	−1.25765	−	0.722237i
$441$	28.2566	+	8.29689i	1.34555	+	0.395090i
$442$	−1.68933	+	1.95301i	−0.0803533	+	0.0928951i
$443$	26.5725	+	14.5097i	1.26250	+	0.689376i	0.964220	−	0.265103i	$-0.0854059\pi$
$443$	26.5725	+	14.5097i	1.26250	+	0.689376i	0.298278	+	0.954479i	$0.403588\pi$
$444$	9.43797	−	32.3499i	0.447906	−	1.53526i
$445$	−29.4870	−	7.16245i	−1.39782	−	0.339533i
$446$	−1.49517	−	6.84464i	−0.0707983	−	0.324103i
$447$	4.62726	−	21.2712i	0.218862	−	1.00609i
$448$	5.57977	−	1.24420i	0.263619	−	0.0587831i
$449$	19.6466	−	2.82475i	0.927178	−	0.133308i	0.337848	−	0.941201i	$-0.390301\pi$
$449$	19.6466	−	2.82475i	0.927178	−	0.133308i	0.589330	+	0.807893i	$0.299392\pi$
$450$	−14.6959	+	28.5265i	−0.692772	+	1.34475i
$451$	−3.40077	−	2.94679i	−0.160136	−	0.138759i
$452$	5.74560	+	7.64757i	0.270250	+	0.359712i
$453$	36.2666	−	7.88932i	1.70395	−	0.370673i
$454$	4.16765	+	1.55034i	0.195597	+	0.0727612i
$455$	−0.691338	+	0.878589i	−0.0324104	+	0.0411889i
$456$	−33.0530	+	44.3936i	−1.54785	+	2.07892i
$457$	0.902817	−	2.42055i	0.0422320	−	0.113228i	−0.914122	−	0.405440i	$-0.867118\pi$
$457$	0.902817	−	2.42055i	0.0422320	−	0.113228i	0.956354	+	0.292211i	$0.0943911\pi$
$458$	0.00649409	+	7.49877i	0.000303449	+	0.350395i
$459$	11.0212			0.514425
$460$	−19.1007	−	9.75525i	−0.890573	−	0.454841i
$461$	38.5807			1.79688			0.898442	−	0.439092i	$-0.144700\pi$
$461$	38.5807			1.79688			0.898442	+	0.439092i	$0.144700\pi$
$462$	0.0115581	+	13.3462i	0.000537732	+	0.620924i
$463$	−3.13288	+	8.39957i	−0.145597	+	0.390361i	−0.989193	−	0.146617i	$-0.953162\pi$
$463$	−3.13288	+	8.39957i	−0.145597	+	0.390361i	0.843596	+	0.536978i	$0.180434\pi$
$464$	−0.297428	−	1.00012i	−0.0138078	−	0.0464293i
$465$	−49.1947	+	5.86761i	−2.28135	+	0.272104i
$466$	−0.400183	−	0.148866i	−0.0185381	−	0.00689607i
$467$	−16.4106	+	3.56990i	−0.759391	+	0.165195i	−0.575557	−	0.817762i	$-0.695215\pi$
$467$	−16.4106	+	3.56990i	−0.759391	+	0.165195i	−0.183834	+	0.982957i	$0.558851\pi$
$468$	5.07704	−	3.81436i	0.234686	−	0.176319i
$469$	−2.96637	−	2.57037i	−0.136974	−	0.118689i
$470$	23.8614	−	2.86700i	1.10065	−	0.132245i
$471$	60.3804	−	8.68138i	2.78218	−	0.400017i
$472$	−10.2151	+	6.60242i	−0.470189	+	0.303901i
$473$	10.6010	−	48.7321i	0.487436	−	2.24071i
$474$	1.03679	+	4.74626i	0.0476214	+	0.218003i
$475$	−1.71607	+	35.5945i	−0.0787385	+	1.63319i
$476$	−3.58061	−	1.04463i	−0.164117	−	0.0478805i
$477$	52.8306	+	28.8477i	2.41895	+	1.32085i
$478$	−21.5749	+	24.9423i	−0.986812	+	1.14084i
$479$	22.8791	+	6.71790i	1.04537	+	0.306949i	0.758946	−	0.651154i	$-0.225715\pi$
$479$	22.8791	+	6.71790i	1.04537	+	0.306949i	0.286426	+	0.958102i	$0.407533\pi$
$480$	−29.5811	+	18.1951i	−1.35019	+	0.830487i
$481$	−0.611060	+	4.25001i	−0.0278619	+	0.193784i
$482$	−4.33417	−	29.9606i	−0.197416	−	1.36467i
$483$	0.469898	+	9.39760i	0.0213811	+	0.427606i
$484$	23.2779	−	6.87884i	1.05809	−	0.312674i
$485$	−14.4964	+	15.9373i	−0.658246	+	0.723678i
$486$	25.1752	+	5.45370i	1.14197	+	0.247385i
$487$	−24.2521	+	13.2426i	−1.09897	+	0.600081i	−0.923188	−	0.384348i	$-0.874426\pi$
$487$	−24.2521	+	13.2426i	−1.09897	+	0.600081i	−0.175779	+	0.984430i	$0.556244\pi$
$488$	4.44853	−	9.80827i	0.201375	−	0.444000i
$489$	15.2888	+	52.0687i	0.691382	+	2.35463i
$490$	19.9455	+	4.82649i	0.901044	+	0.218039i
$491$	15.1752	+	6.93028i	0.684847	+	0.312759i	0.727281	−	0.686340i	$-0.240784\pi$
$491$	15.1752	+	6.93028i	0.684847	+	0.312759i	−0.0424335	+	0.999099i	$0.513511\pi$
$492$	−4.81003	+	1.80354i	−0.216853	+	0.0813101i
$493$	−0.144707	+	0.665205i	−0.00651726	+	0.0299593i
$494$	3.37433	−	6.19236i	0.151818	−	0.278608i
$495$	−15.9510	−	46.1304i	−0.716946	−	2.07341i
$496$	−29.4088	−	13.3076i	−1.32050	−	0.597531i
$497$	−2.13812	+	0.152921i	−0.0959079	+	0.00685947i
$498$	−5.39851	+	18.4447i	−0.241913	+	0.826527i
$499$	−15.8660	−	10.1965i	−0.710261	−	0.456457i	0.134976	−	0.990849i	$-0.456904\pi$
$499$	−15.8660	−	10.1965i	−0.710261	−	0.456457i	−0.845237	+	0.534392i	$0.820541\pi$
$500$	−9.27125	+	20.3481i	−0.414623	+	0.909993i
$501$	−39.1414	−	45.1715i	−1.74871	−	2.01812i
$502$	3.21558	+	0.459489i	0.143518	+	0.0205080i
$503$	6.20409	−	16.6338i	0.276627	−	0.741665i	−0.722127	−	0.691760i	$-0.756836\pi$
$503$	6.20409	−	16.6338i	0.276627	−	0.741665i	0.998754	−	0.0499046i	$-0.0158917\pi$
$504$	8.06187	+	4.37496i	0.359104	+	0.194876i
$505$	−27.4980	+	5.29161i	−1.22364	+	0.235474i
$506$	30.7945	−	10.7695i	1.36898	−	0.478760i
$507$	24.2880	−	24.2880i	1.07867	−	1.07867i
$508$	−1.70308	−	1.27031i	−0.0755621	−	0.0563611i
$509$	23.4432	−	10.7062i	1.03910	−	0.474542i	0.178564	−	0.983928i	$-0.442855\pi$
$509$	23.4432	−	10.7062i	1.03910	−	0.474542i	0.860538	+	0.509386i	$0.170128\pi$
$510$	22.6323	−	1.09124i	1.00218	−	0.0483210i
$511$	4.92726	−	4.26949i	0.217969	−	0.188871i
$512$	−22.6267	+	0.176360i	−0.999970	+	0.00779410i
$513$	−29.4105	+	6.39787i	−1.29851	+	0.282473i
$514$	13.5019	+	24.6760i	0.595543	+	1.08841i
$515$	5.29197	−	1.41635i	0.233192	−	0.0624118i
$516$	−43.0920	−	37.2090i	−1.89702	−	1.63803i
$517$	−21.9072	+	29.2646i	−0.963476	+	1.28705i
$518$	−5.94921	+	1.75244i	−0.261393	+	0.0769979i
$519$	13.4753	−	8.66007i	0.591502	−	0.380135i
$520$	3.40569	−	2.82523i	0.149349	−	0.123895i
$521$	13.2425	−	28.9971i	0.580167	−	1.27039i	−0.361038	−	0.932551i	$-0.617578\pi$
$521$	13.2425	−	28.9971i	0.580167	−	1.27039i	0.941205	−	0.337837i	$-0.109695\pi$
$522$	0.694135	−	1.52343i	0.0303815	−	0.0666789i
$523$	14.7615	+	8.06041i	0.645477	+	0.352457i	0.768410	−	0.639958i	$-0.221048\pi$
$523$	14.7615	+	8.06041i	0.645477	+	0.352457i	−0.122933	+	0.992415i	$0.539230\pi$
$524$	−7.46131	+	11.6544i	−0.325949	+	0.509123i
$525$	9.76603	−	0.926882i	0.426224	−	0.0404525i
$526$	31.0003	+	6.71558i	1.35168	+	0.292813i
$527$	12.6211	+	16.8599i	0.549785	+	0.734427i
$528$	11.0499	−	51.6565i	0.480886	−	2.24806i
$529$	21.3119	−	8.64894i	0.926603	−	0.376041i
$530$	37.7390	+	18.3055i	1.63928	+	0.795139i
$531$	−19.3167	−	2.77732i	−0.838273	−	0.120525i
$532$	10.1614	+	0.709073i	0.440554	+	0.0307422i
$533$	0.574474	−	0.313686i	0.0248832	−	0.0135873i
$534$	−3.80449	−	52.5541i	−0.164636	−	2.27424i
$535$	−3.99710	+	12.4916i	−0.172810	+	0.540061i
$536$	9.34244	+	12.4127i	0.403532	+	0.536146i
$537$	9.13254	−	3.40626i	0.394098	−	0.146991i
$538$	−15.9261	+	24.8288i	−0.686624	+	1.07044i
$539$	−26.2589	+	16.8756i	−1.13105	+	0.726883i
$540$	−18.6291	−	3.10496i	−0.801668	−	0.133616i
$541$	−2.85008	−	19.8227i	−0.122535	−	0.852246i	−0.954668	−	0.297671i	$-0.903790\pi$
$541$	−2.85008	−	19.8227i	−0.122535	−	0.852246i	0.832134	−	0.554575i	$-0.187119\pi$
$542$	11.8645	−	10.2987i	0.509625	−	0.442366i
$543$	−31.6924	+	2.26668i	−1.36005	+	0.0972726i
$544$	12.9878	+	7.01902i	0.556845	+	0.300938i
$545$	3.11929	−	7.78512i	0.133616	−	0.333478i
$546$	−1.81949	−	0.676841i	−0.0778671	−	0.0289661i
$547$	−27.8486	−	1.99177i	−1.19072	−	0.0851621i	−0.538123	−	0.842866i	$-0.680866\pi$
$547$	−27.8486	−	1.99177i	−1.19072	−	0.0851621i	−0.652598	+	0.757704i	$0.726321\pi$
$548$	22.3170	+	22.2398i	0.953335	+	0.950039i
$549$	15.7185	−	7.17840i	0.670850	−	0.306367i
$550$	−12.6502	−	31.5721i	−0.539408	−	1.34624i
$551$		−	1.85914i		−	0.0792018i
$552$	5.99377	−	36.7572i	0.255112	−	1.56449i
$553$	0.632230	−	0.632230i	0.0268852	−	0.0268852i
$554$	−1.70921	−	1.70625i	−0.0726173	−	0.0724916i
$555$	30.6964	−	21.8455i	1.30299	−	0.927290i
$556$	7.93250	−	0.0137394i	0.336413	−	0.000582681i
$557$	−0.793632	+	11.0964i	−0.0336273	+	0.470171i	0.952540	+	0.304415i	$0.0984609\pi$
$557$	−0.793632	+	11.0964i	−0.0336273	+	0.470171i	−0.986167	+	0.165756i	$0.946994\pi$
$558$	−21.5559	−	47.0928i	−0.912533	−	1.99360i
$559$	6.10263	+	3.92192i	0.258114	+	0.165880i
$560$	5.75800	+	2.77449i	0.243320	+	0.117244i
$561$	−22.5700	+	26.0472i	−0.952907	+	1.09971i
$562$	19.4787	+	22.4403i	0.821657	+	0.946585i
$563$	16.8850	−	22.5557i	0.711617	−	0.950609i	−0.288359	−	0.957522i	$-0.593110\pi$
$563$	16.8850	−	22.5557i	0.711617	−	0.950609i	0.999976	+	0.00691326i	$0.00220058\pi$
$564$	17.4019	+	37.9309i	0.732752	+	1.59718i
$565$	−0.257574	+	10.6914i	−0.0108362	+	0.449789i
$566$	8.01244	+	36.6796i	0.336788	+	1.54176i
$567$	−0.504384	−	1.35231i	−0.0211821	−	0.0567915i
$568$	8.40117	+	1.18564i	0.352505	+	0.0497482i
$569$	1.51908	+	5.17352i	0.0636832	+	0.216885i	0.985187	−	0.171485i	$-0.0548565\pi$
$569$	1.51908	+	5.17352i	0.0636832	+	0.216885i	−0.921504	+	0.388370i	$0.873038\pi$
$570$	−59.7620	+	16.0503i	−2.50316	+	0.672272i
$571$	−0.359152	+	1.22316i	−0.0150300	+	0.0511876i	−0.966667	−	0.256039i	$-0.917583\pi$
$571$	−0.359152	+	1.22316i	−0.0150300	+	0.0511876i	0.951637	+	0.307226i	$0.0994008\pi$
$572$	−0.468536	+	6.71441i	−0.0195905	+	0.280744i
$573$	−5.93521	−	7.92851i	−0.247947	−	0.331218i
$574$	0.757346	+	0.565919i	0.0316110	+	0.0236210i
$575$	−10.0002	−	21.7944i	−0.417039	−	0.908889i
$576$	−27.5607	−	23.6319i	−1.14836	−	0.984662i
$577$	−1.85248	+	1.38675i	−0.0771198	+	0.0577311i	−0.637142	−	0.770746i	$-0.719884\pi$
$577$	−1.85248	+	1.38675i	−0.0771198	+	0.0577311i	0.560022	+	0.828478i	$0.310793\pi$
$578$	7.80090	+	12.1154i	0.324475	+	0.503933i
$579$	−10.4326	−	3.06328i	−0.433563	−	0.127305i
$580$	0.432003	−	1.08363i	0.0179380	−	0.0449952i
$581$	3.39374	−	0.996491i	0.140796	−	0.0413414i
$582$	−34.0428	−	15.5112i	−1.41112	−	0.642961i
$583$	−59.7775	+	22.2959i	−2.47573	+	0.923400i
$584$	−22.6166	+	12.4260i	−0.935880	+	0.514190i
$585$	7.09774	+	0.170997i	0.293455	+	0.00706987i
$586$	1.89438	−	3.47644i	0.0782560	−	0.143611i
$587$	5.23530	+	3.91909i	0.216084	+	0.161758i	0.701837	−	0.712338i	$-0.252364\pi$
$587$	5.23530	+	3.91909i	0.216084	+	0.161758i	−0.485753	+	0.874096i	$0.661455\pi$
$588$	2.60365	+	35.5386i	0.107373	+	1.46559i
$589$	−43.4674	−	37.6647i	−1.79104	−	1.55195i
$590$	−13.5379	−	1.28481i	−0.557347	−	0.0528946i
$591$	−16.2361	+	25.2639i	−0.667865	+	1.03922i
$592$	24.4789	−	1.83602i	1.00608	−	0.0754598i
$593$	−3.96795	−	0.283793i	−0.162944	−	0.0116540i	−0.0103712	−	0.999946i	$-0.503301\pi$
$593$	−3.96795	−	0.283793i	−0.162944	−	0.0116540i	−0.152573	+	0.988292i	$0.548756\pi$
$594$	22.9822	−	17.2354i	0.942972	−	0.707175i
$595$	−2.41794	−	3.39759i	−0.0991259	−	0.139287i
$596$	15.6920	−	2.28391i	0.642768	−	0.0935527i
$597$	−11.7085	−	11.7085i	−0.479196	−	0.479196i
$598$	−0.0976203	+	4.74428i	−0.00399199	+	0.194008i
$599$	−12.9910			−0.530799			−0.265400	−	0.964139i	$-0.585504\pi$
$599$	−12.9910			−0.530799			−0.265400	+	0.964139i	$0.585504\pi$
$600$	−38.5628	−	4.53162i	−1.57432	−	0.185002i
$601$	−4.11925	−	9.01991i	−0.168028	−	0.367930i	0.806821	−	0.590796i	$-0.201186\pi$
$601$	−4.11925	−	9.01991i	−0.168028	−	0.367930i	−0.974849	+	0.222866i	$0.928459\pi$
$602$	−1.48221	+	10.3728i	−0.0604106	+	0.422763i
$603$	−1.77824	+	24.8630i	−0.0724154	+	1.01250i
$604$	14.6562	+	22.7189i	0.596354	+	0.924420i
$605$	25.1912	+	10.0934i	1.02417	+	0.410357i
$606$	−23.3404	−	42.6568i	−0.948138	−	1.73282i
$607$	−1.52840	−	21.3698i	−0.0620358	−	0.867373i	−0.929253	−	0.369444i	$-0.879548\pi$
$607$	−1.52840	−	21.3698i	−0.0620358	−	0.867373i	0.867217	−	0.497930i	$-0.165906\pi$
$608$	−38.7330	−	11.1911i	−1.57083	−	0.453859i
$609$	−0.506578	+	0.0728349i	−0.0205276	+	0.00295142i
$610$	10.6994	−	5.52377i	0.433207	−	0.223651i
$611$	−2.87476	−	4.47322i	−0.116300	−	0.180967i
$612$	8.31617	+	22.1791i	0.336161	+	0.896538i
$613$	−11.1778	−	29.9689i	−0.451468	−	1.21043i	−0.940988	−	0.338441i	$-0.890101\pi$
$613$	−11.1778	−	29.9689i	−0.451468	−	1.21043i	0.489520	−	0.871992i	$-0.337172\pi$
$614$	7.61816	+	20.3712i	0.307444	+	0.822114i
$615$	−5.47017	−	1.75035i	−0.220578	−	0.0705811i
$616$	−9.10020	+	3.42116i	−0.366658	+	0.137842i
$617$	1.44685	+	2.64971i	0.0582481	+	0.106673i	0.905181	−	0.425027i	$-0.139735\pi$
$617$	1.44685	+	2.64971i	0.0582481	+	0.106673i	−0.846933	+	0.531700i	$0.821553\pi$
$618$	5.14986	+	7.99810i	0.207158	+	0.321731i
$619$	0.262996	−	1.82917i	0.0105707	−	0.0735207i	−0.983853	−	0.178977i	$-0.942721\pi$
$619$	0.262996	−	1.82917i	0.0105707	−	0.0735207i	0.994424	+	0.105456i	$0.0336303\pi$
$620$	−16.5836	−	32.0539i	−0.666013	−	1.28731i
$621$	15.5870	−	12.9317i	0.625486	−	0.518933i
$622$	6.71206	−	0.970982i	0.269129	−	0.0389328i
$623$	−7.76321	+	5.81147i	−0.311027	+	0.232832i
$624$	6.47837	+	4.13175i	0.259342	+	0.165403i
$625$	−22.2340	+	11.4301i	−0.889361	+	0.457205i
$626$	−2.48640	−	34.3464i	−0.0993766	−	1.37276i
$627$	45.1086	−	82.6102i	1.80146	−	3.29913i
$628$	21.3635	+	38.9638i	0.852497	+	1.55482i
$629$	−14.5686	−	6.65325i	−0.580887	−	0.265282i
$630$	4.04239	+	9.42479i	0.161053	+	0.375492i
$631$	13.9840	+	21.7595i	0.556693	+	0.866232i	0.999539	−	0.0303662i	$-0.00966735\pi$
$631$	13.9840	+	21.7595i	0.556693	+	0.866232i	−0.442846	+	0.896598i	$0.646031\pi$
$632$	−2.97216	+	1.92102i	−0.118226	+	0.0764140i
$633$	39.5313	+	29.5928i	1.57123	+	1.17621i
$634$	1.53026	−	21.6594i	0.0607744	−	0.860205i
$635$	−0.614151	−	2.29468i	−0.0243719	−	0.0910616i
$636$	−10.2405	+	72.1106i	−0.406062	+	2.85937i
$637$	−0.965110	−	4.43654i	−0.0382391	−	0.175782i
$638$	0.738521	+	1.61344i	0.0292383	+	0.0638766i
$639$	8.91463	+	10.2880i	0.352657	+	0.406988i
$640$	−19.9757	−	15.5232i	−0.789610	−	0.613609i
$641$	−17.2800	−	37.8378i	−0.682517	−	1.49450i	−0.859954	−	0.510372i	$-0.829508\pi$
$641$	−17.2800	−	37.8378i	−0.682517	−	1.49450i	0.177436	−	0.984132i	$-0.443220\pi$
$642$	−22.7745	+	0.0197232i	−0.898837	+	0.000778411i
$643$	7.97088	+	7.97088i	0.314341	+	0.314341i	0.846589	−	0.532248i	$-0.178653\pi$
$643$	7.97088	+	7.97088i	0.314341	+	0.314341i	−0.532248	+	0.846589i	$0.678653\pi$
$644$	−6.28971	+	2.72392i	−0.247849	+	0.107338i
$645$	−12.0286	−	62.5068i	−0.473625	−	2.46120i
$646$	18.6164	+	18.5841i	0.732451	+	0.731183i
$647$	32.7081	+	12.1995i	1.28589	+	0.479611i	0.897146	−	0.441735i	$-0.145637\pi$
$647$	32.7081	+	12.1995i	1.28589	+	0.479611i	0.388743	+	0.921346i	$0.372910\pi$
$648$	0.827688	+	5.65240i	0.0325146	+	0.222047i
$649$	15.6324	−	13.5455i	0.613625	−	0.531709i
$650$	4.94587	−	0.119177i	0.193993	−	0.00467450i
$651$	−8.55997	+	13.3196i	−0.335492	+	0.522035i
$652$	−31.6048	+	23.7446i	−1.23774	+	0.929910i
$653$	−3.43962	−	48.0922i	−0.134603	−	1.88199i	−0.398114	−	0.917336i	$-0.630335\pi$
$653$	−3.43962	−	48.0922i	−0.134603	−	1.88199i	0.263511	−	0.964656i	$-0.415119\pi$
$654$	14.5270	+	1.02635i	0.568051	+	0.0401334i
$655$	−14.6221	+	5.05605i	−0.571332	+	0.197556i
$656$	−2.46031	−	2.81956i	−0.0960590	−	0.110085i
$657$	−40.4577	−	8.80103i	−1.57841	−	0.343361i
$658$	4.14678	−	6.46481i	0.161658	−	0.252025i
$659$	−9.86064	+	21.5918i	−0.384116	+	0.841096i	0.614521	+	0.788900i	$0.289349\pi$
$659$	−9.86064	+	21.5918i	−0.384116	+	0.841096i	−0.998637	+	0.0521959i	$0.983378\pi$
$660$	45.4882	−	37.6689i	1.77063	−	1.46626i
$661$	−28.3731	+	8.33110i	−1.10359	+	0.324042i	−0.782276	−	0.622932i	$-0.785941\pi$
$661$	−28.3731	+	8.33110i	−1.10359	+	0.324042i	−0.321310	+	0.946974i	$0.604123\pi$
$662$	35.4219	+	30.6396i	1.37671	+	1.19084i
$663$	−2.40258	−	4.40001i	−0.0933087	−	0.170882i
$664$	−13.9614	+	1.03500i	−0.541806	+	0.0401658i
$665$	8.42471	+	7.66299i	0.326696	+	0.297158i
$666$	31.5506	+	23.5758i	1.22256	+	0.913545i
$667$	0.575865	+	1.11058i	0.0222976	+	0.0430018i
$668$	20.8001	−	38.2499i	0.804781	−	1.47993i
$669$	13.4631	+	1.93571i	0.520515	+	0.0748388i
$670$	−0.403300	+	17.3647i	−0.0155808	+	0.670856i
$671$	−5.16006	+	17.5735i	−0.199202	+	0.678419i
$672$	−1.53192	+	10.9924i	−0.0590951	+	0.424042i
$673$	−20.5751	+	37.6805i	−0.793113	+	1.45248i	0.0962901	+	0.995353i	$0.469302\pi$
$673$	−20.5751	+	37.6805i	−0.793113	+	1.45248i	−0.889403	+	0.457124i	$0.848879\pi$
$674$	−6.30691	+	2.35858i	−0.242933	+	0.0908490i
$675$	−14.1944	−	15.6324i	−0.546343	−	0.601692i
$676$	22.7778	+	10.3546i	0.876071	+	0.398256i
$677$	47.6229	+	10.3597i	1.83030	+	0.398157i	0.989659	−	0.143441i	$-0.0458168\pi$
$677$	47.6229	+	10.3597i	1.83030	+	0.398157i	0.840638	+	0.541598i	$0.182180\pi$
$678$	−17.8136	+	5.24731i	−0.684128	+	0.201522i
$679$	0.979839	+	6.81493i	0.0376028	+	0.261533i
$680$	6.53249	+	15.1579i	0.250509	+	0.581279i
$681$	−5.65328	+	6.52423i	−0.216634	+	0.250009i
$682$	52.6847	+	15.4201i	2.01740	+	0.590465i
$683$	−0.0595864	−	0.273914i	−0.00228001	−	0.0104810i	0.975993	−	0.217803i	$-0.0698889\pi$
$683$	−0.0595864	−	0.273914i	−0.00228001	−	0.0104810i	−0.978273	+	0.207322i	$0.933525\pi$
$684$	−35.0672	−	54.3584i	−1.34083	−	2.07845i
$685$	4.17187	+	34.9774i	0.159399	+	1.33642i
$686$	10.9061	−	8.17898i	0.416398	−	0.312275i
$687$	−13.6403	−	5.08756i	−0.520409	−	0.194103i
$688$	14.3587	−	38.9082i	0.547419	−	1.48336i
$689$		−	9.28018i		−	0.353547i
$690$	30.7281	−	28.0991i	1.16980	−	1.06971i
$691$			16.0277i			0.609721i	0.952397	+	0.304861i	$0.0986099\pi$
$691$			16.0277i			0.609721i	−0.952397	+	0.304861i	$0.901390\pi$
$692$	9.35312	+	6.97641i	0.355552	+	0.265203i
$693$	−14.6152	−	5.45120i	−0.555187	−	0.207074i
$694$	−23.3335	−	31.1137i	−0.885726	−	1.18106i
$695$	6.96978	+	5.48434i	0.264379	+	0.208033i
$696$	2.02089	+	0.139261i	0.0766016	+	0.00527866i
$697$	0.518973	+	2.38568i	0.0196575	+	0.0903642i
$698$	1.56256	−	5.33868i	0.0591436	−	0.202072i
$699$	0.542835	−	0.626465i	0.0205319	−	0.0236951i
$700$	3.12985	+	6.42413i	0.118297	+	0.242809i
$701$	−0.969575	−	6.74355i	−0.0366204	−	0.254700i	0.963285	−	0.268482i	$-0.0865220\pi$
$701$	−0.969575	−	6.74355i	−0.0366204	−	0.254700i	−0.999905	+	0.0137819i	$0.995613\pi$
$702$	1.18070	+	4.00826i	0.0445628	+	0.151282i
$703$	42.7392	+	9.29735i	1.61194	+	0.350656i
$704$	38.0597	−	5.67416i	1.43443	−	0.213853i
$705$	−11.0131	+	45.3396i	−0.414776	+	1.70759i
$706$	8.98662	+	24.0305i	0.338216	+	0.904399i
$707$	−4.28880	+	7.85436i	−0.161297	+	0.295394i
$708$	−5.05937	−	23.0651i	−0.190143	−	0.866841i
$709$	9.77956	−	33.3061i	0.367279	−	1.25084i	−0.544013	−	0.839077i	$-0.683096\pi$
$709$	9.77956	−	33.3061i	0.367279	−	1.25084i	0.911292	−	0.411761i	$-0.135086\pi$
$710$	6.54997	+	6.86145i	0.245816	+	0.257506i
$711$	−5.62032	−	0.808080i	−0.210778	−	0.0303054i
$712$	34.8729	−	16.0356i	1.30692	−	0.600958i
$713$	37.6324	+	9.03552i	1.40934	+	0.338383i
$714$	4.33448	−	5.80066i	0.162214	−	0.217084i
$715$	−5.06350	+	5.56682i	−0.189364	+	0.208187i
$716$	4.65896	+	5.35794i	0.174113	+	0.200236i
$717$	−30.6840	−	56.1935i	−1.14591	−	2.09859i
$718$	25.7549	−	29.7748i	0.961163	−	1.11118i
$719$	−15.0329	+	4.41406i	−0.560633	+	0.164617i	−0.549757	−	0.835324i	$-0.685280\pi$
$719$	−15.0329	+	4.41406i	−0.560633	+	0.164617i	−0.0108750	+	0.999941i	$0.503462\pi$
$720$	−7.80835	−	39.8322i	−0.291000	−	1.48446i
$721$	0.727278	−	1.59252i	0.0270853	−	0.0593084i
$722$	−37.8497	−	24.2783i	−1.40862	−	0.903543i
$723$	57.4281	+	12.4927i	2.13577	+	0.464609i
$724$	−9.65131	−	21.0369i	−0.358688	−	0.781831i
$725$	1.12990	−	0.651481i	0.0419633	−	0.0241954i
$726$	−3.32107	+	47.0067i	−0.123257	+	1.74458i
$727$	0.376801	+	5.26837i	0.0139748	+	0.195393i	0.999643	+	0.0267003i	$0.00849999\pi$
$727$	0.376801	+	5.26837i	0.0139748	+	0.195393i	−0.985669	+	0.168693i	$0.946045\pi$
$728$	−0.00367401	−	1.41413i	−0.000136168	−	0.0524113i
$729$	−23.7611	+	36.9730i	−0.880040	+	1.36937i
$730$	−28.4545	−	4.76793i	−1.05315	−	0.176469i
$731$	−20.4497	+	17.7197i	−0.756359	+	0.655388i
$732$	14.8104	+	14.7592i	0.547407	+	0.545514i
$733$	7.20987	+	2.68914i	0.266303	+	0.0993258i	0.479069	−	0.877777i	$-0.340974\pi$
$733$	7.20987	+	2.68914i	0.266303	+	0.0993258i	−0.212766	+	0.977103i	$0.568247\pi$
$734$	18.5158	−	18.5479i	0.683431	−	0.684615i
$735$	−22.3400	+	32.9869i	−0.824024	+	1.21674i
$736$	26.6041	−	5.31237i	0.980641	−	0.195817i
$737$	−18.6818	−	18.6818i	−0.688152	−	0.688152i
$738$	−0.00519962	−	6.00403i	−0.000191400	−	0.221012i
$739$	8.49141	+	18.5936i	0.312361	+	0.683976i	0.999077	−	0.0429499i	$-0.0136756\pi$
$739$	8.49141	+	18.5936i	0.312361	+	0.683976i	−0.686716	+	0.726926i	$0.740948\pi$
$740$	22.7508	+	15.3503i	0.836337	+	0.564289i
$741$	8.96564	+	10.3469i	0.329361	+	0.380103i
$742$	12.1883	−	5.57899i	0.447448	−	0.204811i
$743$	3.54463	+	16.2944i	0.130040	+	0.597783i	0.995332	+	0.0965145i	$0.0307694\pi$
$743$	3.54463	+	16.2944i	0.130040	+	0.597783i	−0.865292	+	0.501268i	$0.832867\pi$
$744$	44.1976	−	44.4279i	1.62036	−	1.62881i
$745$	15.3512	+	8.86891i	0.562425	+	0.324932i
$746$	−39.6437	−	2.80087i	−1.45146	−	0.102547i
$747$	−17.9818	−	13.4610i	−0.657921	−	0.492513i
$748$	−23.5384	−	8.73296i	−0.860649	−	0.319309i
$749$	2.26607	+	3.52608i	0.0828005	+	0.128840i
$750$	−30.6965	−	30.6962i	−1.12088	−	1.12087i
$751$	17.6004	+	8.03783i	0.642248	+	0.293305i	0.709792	−	0.704412i	$-0.248789\pi$
$751$	17.6004	+	8.03783i	0.642248	+	0.293305i	−0.0675441	+	0.997716i	$0.521516\pi$
$752$	−21.4212	+	21.5702i	−0.781152	+	0.786583i
$753$	−3.02223	+	5.53480i	−0.110136	+	0.201699i
$754$	−0.257429	+	0.0186358i	−0.00937502	+	0.000678675i
$755$	−2.88194	+	30.0897i	−0.104884	+	1.09508i
$756$	−4.55454	+	3.96036i	−0.165647	+	0.144037i
$757$	−8.34777	+	6.24906i	−0.303405	+	0.227126i	−0.740122	−	0.672473i	$-0.765232\pi$
$757$	−8.34777	+	6.24906i	−0.303405	+	0.227126i	0.436717	+	0.899599i	$0.356141\pi$
$758$	7.08859	+	49.0010i	0.257469	+	1.77980i
$759$	−1.35777	+	63.3206i	−0.0492840	+	2.29839i
$760$	−26.2315	−	36.6574i	−0.951517	−	1.32971i
$761$	1.36391	−	9.48619i	0.0494416	−	0.343874i	−0.950053	−	0.312088i	$-0.898972\pi$
$761$	1.36391	−	9.48619i	0.0494416	−	0.343874i	0.999495	−	0.0317856i	$-0.0101194\pi$
$762$	3.46810	−	2.23306i	0.125636	−	0.0808952i
$763$	−1.28450	−	2.35239i	−0.0465021	−	0.0851622i
$764$	3.88993	−	6.07597i	0.140733	−	0.219821i
$765$	−8.07091	+	25.2230i	−0.291804	+	0.911940i
$766$	12.6763	−	4.74051i	0.458012	−	0.171282i
$767$	1.05144	+	2.81902i	0.0379653	+	0.101789i
$768$	15.0661	−	41.2647i	0.543651	−	1.48901i
$769$	−2.41714	−	3.76114i	−0.0871643	−	0.135630i	0.794934	−	0.606697i	$-0.207506\pi$
$769$	−2.41714	−	3.76114i	−0.0871643	−	0.135630i	−0.882098	+	0.471066i	$0.843869\pi$
$770$	−10.3554	−	3.30364i	−0.373181	−	0.119055i
$771$	−54.0529	+	7.77164i	−1.94667	+	0.279889i
$772$	−0.578718	−	7.89923i	−0.0208285	−	0.284300i
$773$	0.368531	+	5.15274i	0.0132551	+	0.185331i	0.999766	+	0.0216349i	$0.00688714\pi$
$773$	0.368531	+	5.15274i	0.0132551	+	0.185331i	−0.986511	+	0.163696i	$0.947658\pi$
$774$	58.3753	−	31.9410i	2.09826	−	1.14809i
$775$	7.65895	−	39.6160i	0.275118	−	1.42305i
$776$	1.87345	−	27.1868i	0.0672531	−	0.975948i
$777$	0.858960	−	12.0098i	0.0308150	−	0.430850i
$778$	10.2827	+	1.46934i	0.368651	+	0.0526782i
$779$	−2.76981	−	6.06504i	−0.0992388	−	0.217303i
$780$	2.82148	+	8.11419i	0.101025	+	0.290535i
$781$	−14.4287			−0.516298
$782$	−16.8771	−	5.33508i	−0.603525	−	0.190782i
$783$	0.778942	+	0.778942i	0.0278371	+	0.0278371i
$784$	−23.5742	+	10.8648i	−0.841935	+	0.388029i
$785$	−8.25270	+	48.9909i	−0.294551	+	1.74856i
$786$	−16.1186	−	21.4930i	−0.574930	−	0.766631i
$787$	37.5657	+	2.68675i	1.33907	+	0.0957723i	0.722415	−	0.691460i	$-0.243032\pi$
$787$	37.5657	+	2.68675i	1.33907	+	0.0957723i	0.616657	+	0.787232i	$0.288487\pi$
$788$	−21.3843	−	4.61309i	−0.761783	−	0.164334i
$789$	−33.2928	+	51.8045i	−1.18525	+	1.84429i
$790$	−3.93894	−	0.373823i	−0.140141	−	0.0133000i
$791$	2.58295	+	2.23814i	0.0918390	+	0.0795789i
$792$	52.0261	+	33.2445i	1.84867	+	1.18129i
$793$	−2.13273	−	1.59654i	−0.0757354	−	0.0566948i
$794$	−34.6251	−	18.8678i	−1.22880	−	0.669594i
$795$	−58.9505	+	56.1769i	−2.09076	+	1.99239i
$796$	4.99165	−	10.9805i	0.176924	−	0.389193i
$797$	13.7081	−	5.11287i	0.485567	−	0.181107i	−0.0947448	−	0.995502i	$-0.530203\pi$
$797$	13.7081	−	5.11287i	0.485567	−	0.181107i	0.580312	+	0.814395i	$0.302931\pi$
$798$	−8.19945	+	17.9955i	−0.290257	+	0.637035i
$799$	19.0306	−	5.58789i	0.673255	−	0.197685i
$800$	−6.77146	−	27.4617i	−0.239407	−	0.970919i
$801$	59.0900	+	17.3504i	2.08784	+	0.613045i
$802$	41.4342	−	26.6789i	1.46309	−	0.942065i
$803$	35.1315	−	26.2991i	1.23976	−	0.928076i
$804$	−28.9245	+	8.54745i	−1.02009	+	0.301445i
$805$	−7.40621	−	1.96804i	−0.261035	−	0.0693643i
$806$	−4.77961	+	6.39635i	−0.168354	+	0.225302i
$807$	−34.3188	−	45.8445i	−1.20808	−	1.61380i
$808$	23.1260	−	26.8293i	0.813569	−	0.943852i
$809$	−10.6367	+	36.2252i	−0.373966	+	1.27361i	0.530726	+	0.847544i	$0.321919\pi$
$809$	−10.6367	+	36.2252i	−0.373966	+	1.27361i	−0.904692	+	0.426067i	$0.859899\pi$
$810$	−3.19028	+	5.53313i	−0.112095	+	0.194414i
$811$	−3.35434	−	11.4238i	−0.117787	−	0.401145i	0.879402	−	0.476081i	$-0.157943\pi$
$811$	−3.35434	−	11.4238i	−0.117787	−	0.401145i	−0.997188	+	0.0749359i	$0.976125\pi$
$812$	−0.179235	−	0.326897i	−0.00628992	−	0.0114719i
$813$	10.6590	+	28.5780i	0.373829	+	1.00227i
$814$	−40.7842	+	8.90905i	−1.42948	+	0.312262i
$815$	−44.1837	−	1.06447i	−1.54769	−	0.0372866i
$816$	−21.5955	+	18.8440i	−0.755994	+	0.659672i
$817$	44.2845	−	59.1572i	1.54932	−	2.06965i
$818$	28.5125	−	24.7495i	0.996917	−	0.865346i
$819$	1.48584	−	1.71476i	0.0519196	−	0.0599184i
$820$	−0.205109	−	4.17872i	−0.00716271	−	0.145927i
$821$	−11.0783	−	7.11962i	−0.386637	−	0.248477i	0.332854	−	0.942978i	$-0.391988\pi$
$821$	−11.0783	−	7.11962i	−0.386637	−	0.248477i	−0.719491	+	0.694502i	$0.755625\pi$
$822$	−55.6174	+	25.4579i	−1.93988	+	0.887945i
$823$	3.92884	−	54.9324i	0.136951	−	1.91482i	−0.211298	−	0.977422i	$-0.567769\pi$
$823$	3.92884	−	54.9324i	0.136951	−	1.91482i	0.348249	−	0.937402i	$-0.386776\pi$
$824$	−4.13825	+	5.55810i	−0.144163	+	0.193625i
$825$	66.0137	−	1.53348i	2.29830	−	0.0533889i
$826$	−3.07033	+	3.07566i	−0.106831	+	0.107016i
$827$	24.2488	−	24.2488i	0.843213	−	0.843213i	−0.146062	−	0.989275i	$-0.546660\pi$
$827$	24.2488	−	24.2488i	0.843213	−	0.843213i	0.989275	+	0.146062i	$0.0466599\pi$
$828$	37.7853	+	21.6097i	1.31313	+	0.750988i
$829$		−	45.9815i		−	1.59700i	−0.601993	−	0.798502i	$-0.705626\pi$
$829$		−	45.9815i		−	1.59700i	0.601993	−	0.798502i	$-0.294374\pi$
$830$	−12.9674	−	8.76562i	−0.450104	−	0.304259i
$831$	4.26498	−	1.94775i	0.147950	−	0.0675667i
$832$	−1.16134	+	5.47543i	−0.0402623	+	0.189826i
$833$	16.8925	+	1.20818i	0.585292	+	0.0418609i
$834$	−5.36933	+	14.4339i	−0.185925	+	0.499805i
$835$	44.7540	−	19.1496i	1.54878	−	0.662698i
$836$	67.8829	+	9.64011i	2.34778	+	0.333410i
$837$	33.9928	−	2.43121i	1.17496	−	0.0840350i
$838$	12.7994	+	14.7454i	0.442147	+	0.509373i
$839$	1.52699	+	10.6204i	0.0527174	+	0.366658i	0.999054	+	0.0434763i	$0.0138433\pi$
$839$	1.52699	+	10.6204i	0.0527174	+	0.366658i	−0.946337	+	0.323181i	$0.895248\pi$
$840$	−8.96077	+	8.58369i	−0.309176	+	0.296166i
$841$	24.3391	−	15.6418i	0.839280	−	0.539372i
$842$	10.5547	+	6.77022i	0.363741	+	0.233317i
$843$	−54.0517	+	20.1602i	−1.86164	+	0.694356i
$844$	−10.0745	+	34.5317i	−0.346778	+	1.18863i
$845$	12.8114	+	24.8682i	0.440726	+	0.855493i
$846$	−48.6482	+	3.52174i	−1.67256	+	0.121080i
$847$	7.61190	−	4.15641i	0.261548	−	0.142816i
$848$	−51.8039	+	11.4573i	−1.77895	+	0.393447i
$849$	−72.1474	−	10.3732i	−2.47609	−	0.356008i
$850$	−4.77101	+	17.8264i	−0.163644	+	0.611442i
$851$	−28.4107	+	7.68454i	−0.973905	+	0.263423i
$852$	−7.86900	+	14.4705i	−0.269588	+	0.495752i
$853$	21.8879	+	29.2389i	0.749429	+	1.00112i	0.999459	+	0.0328815i	$0.0104684\pi$
$853$	21.8879	+	29.2389i	0.749429	+	1.00112i	−0.250031	+	0.968238i	$0.580441\pi$
$854$	0.814716	−	3.76087i	0.0278790	−	0.128694i
$855$	6.89546	−	71.9940i	0.235820	−	2.46214i
$856$	−5.83798	−	15.5289i	−0.199538	−	0.530767i
$857$	10.2772	+	5.61176i	0.351061	+	0.191694i	0.645097	−	0.764100i	$-0.276817\pi$
$857$	10.2772	+	5.61176i	0.351061	+	0.191694i	−0.294036	+	0.955794i	$0.594999\pi$
$858$	−11.8910	−	5.41798i	−0.405951	−	0.184967i
$859$	3.26854	−	7.15710i	0.111521	−	0.244197i	−0.845640	−	0.533754i	$-0.820781\pi$
$859$	3.26854	−	7.15710i	0.111521	−	0.244197i	0.957161	+	0.289557i	$0.0935080\pi$
$860$	39.5582	−	24.1904i	1.34892	−	0.824886i
$861$	−1.54409	+	0.992327i	−0.0526225	+	0.0338184i
$862$	9.88388	+	33.5539i	0.336646	+	1.14285i
$863$	25.4430	−	33.9879i	0.866090	−	1.15696i	−0.120333	−	0.992734i	$-0.538396\pi$
$863$	25.4430	−	33.9879i	0.866090	−	1.15696i	0.986423	−	0.164227i	$-0.0525128\pi$
$864$	20.9173	−	11.5395i	0.711620	−	0.392583i
$865$	3.37284	+	12.6021i	0.114680	+	0.428484i
$866$	−2.75514	+	1.50752i	−0.0936234	+	0.0512275i
$867$	−27.3356	+	5.94649i	−0.928365	+	0.201953i
$868$	−11.2742	−	2.43210i	−0.382670	−	0.0825509i
$869$	4.54835	−	3.94117i	0.154292	−	0.133695i
$870$	1.67671	+	1.52246i	0.0568457	+	0.0516161i
$871$	3.49569	−	1.59643i	0.118447	−	0.0540930i
$872$	3.01520	+	10.1710i	0.102108	+	0.344434i
$873$	30.9174	−	30.9174i	1.04640	−	1.04640i
$874$	48.1345	+	4.43962i	1.62817	+	0.150172i
$875$	−1.70501	+	7.80543i	−0.0576399	+	0.263872i
$876$	−7.21566	−	49.5763i	−0.243794	−	1.67503i
$877$	−10.8988	+	29.2209i	−0.368027	+	0.986718i	0.612524	+	0.790452i	$0.290154\pi$
$877$	−10.8988	+	29.2209i	−0.368027	+	0.986718i	−0.980551	+	0.196266i	$0.937118\pi$
$878$	−5.34369	+	37.3960i	−0.180341	+	1.26206i
$879$	5.03339	+	5.80884i	0.169772	+	0.195927i
$880$	37.3266	+	21.3927i	1.25828	+	0.721148i
$881$	21.1534	+	13.5945i	0.712676	+	0.458009i	0.846082	−	0.533052i	$-0.178955\pi$
$881$	21.1534	+	13.5945i	0.712676	+	0.458009i	−0.133406	+	0.991061i	$0.542591\pi$
$882$	−39.9710	−	11.6990i	−1.34589	−	0.393925i
$883$	−34.9152	+	2.49718i	−1.17499	+	0.0840369i	−0.645146	−	0.764059i	$-0.723204\pi$
$883$	−34.9152	+	2.49718i	−1.17499	+	0.0840369i	−0.529843	+	0.848096i	$0.677749\pi$
$884$	2.38668	−	2.76404i	0.0802729	−	0.0929647i
$885$	11.5425	−	23.7438i	0.387996	−	0.798140i
$886$	−37.5970	−	20.4872i	−1.26309	−	0.688283i
$887$	−0.934857	+	4.29747i	−0.0313894	+	0.144295i	−0.990174	−	0.139838i	$-0.955342\pi$
$887$	−0.934857	+	4.29747i	−0.0313894	+	0.144295i	0.958785	+	0.284133i	$0.0917056\pi$
$888$	−13.3077	+	45.7613i	−0.446577	+	1.53565i
$889$	−0.690540	−	0.315359i	−0.0231600	−	0.0105768i
$890$	41.7097	+	10.0931i	1.39811	+	0.338322i
$891$	−2.73704	−	9.32150i	−0.0916943	−	0.312282i
$892$	2.12287	+	9.67795i	0.0710790	+	0.324042i
$893$	−47.5403	+	25.9590i	−1.59088	+	0.868684i
$894$	−6.51788	+	30.0876i	−0.217990	+	1.00628i
$895$	0.375443	+	7.92943i	0.0125497	+	0.265052i
$896$	−7.88946	+	1.76640i	−0.263568	+	0.0590114i
$897$	−8.56069	−	3.40376i	−0.285833	−	0.113648i
$898$	−27.7809	+	4.01886i	−0.927062	+	0.134111i
$899$	−0.299580	+	2.08362i	−0.00999155	+	0.0694927i
$900$	20.7482	−	40.3606i	0.691608	−	1.34535i
$901$	33.2136	+	9.75240i	1.10651	+	0.324900i
$902$	4.81303	+	4.16322i	0.160256	+	0.138620i
$903$	−17.8541	−	9.74907i	−0.594147	−	0.324429i
$904$	−8.13486	−	10.8083i	−0.270562	−	0.359477i
$905$	6.10798	−	25.1459i	0.203036	−	0.835878i
$906$	−51.2791	+	11.2016i	−1.70363	+	0.372148i
$907$	8.88633	−	40.8498i	0.295066	−	1.35640i	−0.555933	−	0.831227i	$-0.687639\pi$
$907$	8.88633	−	40.8498i	0.295066	−	1.35640i	0.850998	−	0.525168i	$-0.175998\pi$
$908$	−5.89584	−	2.18741i	−0.195660	−	0.0725918i
$909$	56.2530	−	8.08796i	1.86579	−	0.268261i
$910$	0.976624	−	1.24336i	0.0323748	−	0.0412169i
$911$	−2.81931	−	2.44294i	−0.0934078	−	0.0809383i	0.606905	−	0.794774i	$-0.292411\pi$
$911$	−2.81931	−	2.44294i	−0.0934078	−	0.0809383i	−0.700313	+	0.713836i	$0.746956\pi$
$912$	46.6896	−	62.8224i	1.54605	−	2.08026i
$913$	23.2639	−	5.06074i	0.769921	−	0.167486i
$914$	−1.27381	+	3.42427i	−0.0421339	+	0.113265i
$915$	2.76861	+	23.2123i	0.0915273	+	0.767374i
$916$	−0.0183680	−	10.6049i	−0.000606897	−	0.350394i
$917$	−1.72789	+	4.63264i	−0.0570598	+	0.152983i
$918$	−15.5863	+	0.0134981i	−0.514424	+	0.000445502i
$919$	−54.4316			−1.79553			−0.897767	−	0.440471i	$-0.854811\pi$
$919$	−54.4316			−1.79553			−0.897767	+	0.440471i	$0.854811\pi$
$920$	27.0243	+	13.7726i	0.890966	+	0.454070i
$921$	−42.2238			−1.39132
$922$	−54.5614	+	0.0472513i	−1.79688	+	0.00155614i
$923$	0.733438	−	1.96642i	0.0241414	−	0.0647256i
$924$	−0.0326913	−	18.8744i	−0.00107546	−	0.620923i
$925$	9.32624	+	29.2329i	0.306645	+	0.961172i
$926$	4.42027	−	11.8826i	0.145259	−	0.390487i
$927$	−10.8641	+	2.36333i	−0.356823	+	0.0776220i
$928$	0.421852	+	1.41402i	0.0138480	+	0.0464173i
$929$	11.3687	+	9.85105i	0.372996	+	0.323202i	0.821106	−	0.570776i	$-0.193357\pi$
$929$	11.3687	+	9.85105i	0.372996	+	0.323202i	−0.448110	+	0.893978i	$0.647903\pi$
$930$	69.5645	−	8.35830i	2.28111	−	0.274080i
$931$	−45.7799	+	6.58215i	−1.50038	+	0.215721i
$932$	0.566126	+	0.210038i	0.0185441	+	0.00688002i
$933$	−2.79874	+	12.8656i	−0.0916266	+	0.421201i
$934$	23.2037	−	5.06870i	0.759247	−	0.165853i
$935$	−14.6024	−	23.9723i	−0.477550	−	0.783978i
$936$	−7.17535	+	5.40054i	−0.234533	+	0.176522i
$937$	−29.7193	−	16.2280i	−0.970887	−	0.530145i	−0.0861740	−	0.996280i	$-0.527464\pi$
$937$	−29.7193	−	16.2280i	−0.970887	−	0.530145i	−0.884713	+	0.466136i	$0.845646\pi$
$938$	4.19823	+	3.63142i	0.137077	+	0.118570i
$939$	64.1468	+	18.8352i	2.09335	+	0.614664i
$940$	−33.7417	+	4.08377i	−1.10053	+	0.133198i
$941$	−0.998809	+	6.94687i	−0.0325602	+	0.226461i	−0.999604	−	0.0281499i	$-0.991038\pi$
$941$	−0.998809	+	6.94687i	−0.0325602	+	0.226461i	0.967043	+	0.254611i	$0.0819475\pi$
$942$	−85.3801	+	12.3513i	−2.78183	+	0.402426i
$943$	3.53322	+	2.76508i	0.115058	+	0.0900435i
$944$	14.4383	−	9.34974i	0.469925	−	0.304308i
$945$	−6.74044	+	0.319147i	−0.219267	+	0.0103818i
$946$	−14.9324	+	68.9306i	−0.485495	+	2.24113i
$947$	27.0607	−	14.7762i	0.879353	−	0.480163i	0.0248992	−	0.999690i	$-0.492074\pi$
$947$	27.0607	−	14.7762i	0.879353	−	0.480163i	0.854454	+	0.519527i	$0.173892\pi$
$948$	−1.47206	−	6.71095i	−0.0478102	−	0.217962i
$949$	1.79839	+	6.12476i	0.0583783	+	0.198818i
$950$	2.38329	−	50.3403i	0.0773241	−	1.63325i
$951$	38.3452	+	17.5117i	1.24343	+	0.567854i
$952$	5.06503	+	1.47294i	0.164158	+	0.0477384i
$953$	9.29486	−	42.7278i	0.301090	−	1.38409i	−0.539303	−	0.842112i	$-0.681312\pi$
$953$	9.29486	−	42.7278i	0.301090	−	1.38409i	0.840393	−	0.541977i	$-0.182324\pi$
$954$	−74.7491	−	40.7321i	−2.42009	−	1.31875i
$955$	7.62318	−	2.63596i	0.246680	−	0.0852976i
$956$	30.4809	−	35.3002i	0.985823	−	1.14169i
$957$	−3.43611	+	0.245755i	−0.111074	+	0.00794415i
$958$	−32.3641	−	9.47252i	−1.04564	−	0.306043i
$959$	9.47023	+	6.08614i	0.305810	+	0.196532i
$960$	41.8117	−	25.7679i	1.34947	−	0.831656i
$961$	22.3460	+	25.7887i	0.720840	+	0.831894i
$962$	0.858963	−	6.01117i	0.0276941	−	0.193808i
$963$	9.30212	−	24.9399i	0.299757	−	0.803678i
$964$	6.16613	+	42.3653i	0.198598	+	1.36449i
$965$	4.96556	−	7.33207i	0.159847	−	0.236028i
$966$	−0.676046	−	13.2896i	−0.0217514	−	0.427587i
$967$	26.6761	−	26.6761i	0.857844	−	0.857844i	−0.133239	−	0.991084i	$-0.542538\pi$
$967$	26.6761	−	26.6761i	0.857844	−	0.857844i	0.991084	+	0.133239i	$0.0425379\pi$
$968$	−32.9115	+	9.75665i	−1.05782	+	0.313591i
$969$	−46.4533	+	21.2145i	−1.49229	+	0.681508i
$970$	20.4814	−	22.5566i	0.657619	−	0.724247i
$971$	8.04441	−	6.97052i	0.258158	−	0.223695i	−0.516160	−	0.856492i	$-0.672639\pi$
$971$	8.04441	−	6.97052i	0.258158	−	0.223695i	0.774317	+	0.632798i	$0.218093\pi$
$972$	−35.6098	−	7.68187i	−1.14218	−	0.246396i
$973$	2.76952	−	0.602471i	0.0887866	−	0.0193143i
$974$	34.2814	−	18.7576i	1.09845	−	0.601033i
$975$	−3.14662	+	9.07468i	−0.100772	+	0.290622i
$976$	−6.27915	+	13.8764i	−0.200991	+	0.444174i
$977$	−11.8338	+	15.8081i	−0.378597	+	0.505746i	−0.948852	−	0.315722i	$-0.897753\pi$
$977$	−11.8338	+	15.8081i	−0.378597	+	0.505746i	0.570255	+	0.821468i	$0.306844\pi$
$978$	−21.6853	−	73.6176i	−0.693421	−	2.35403i
$979$	−54.9124	+	35.2901i	−1.75501	+	1.12788i
$980$	−28.2130	−	6.80126i	−0.901232	−	0.217258i
$981$	−7.07082	+	15.4829i	−0.225754	+	0.494332i
$982$	−21.4695	−	9.78231i	−0.685118	−	0.312166i
$983$	24.4334	+	13.3416i	0.779303	+	0.425532i	0.819082	−	0.573677i	$-0.194483\pi$
$983$	24.4334	+	13.3416i	0.779303	+	0.425532i	−0.0397784	+	0.999209i	$0.512665\pi$
$984$	6.80020	−	2.55649i	0.216782	−	0.0814979i
$985$	−15.5670	−	18.8648i	−0.496004	−	0.601081i
$986$	0.203831	−	0.940919i	0.00649131	−	0.0299650i
$987$	8.93578	+	11.9368i	0.284429	+	0.379953i
$988$	−4.76443	+	8.76145i	−0.151577	+	0.278739i
$989$	−8.13005	+	49.0554i	−0.258520	+	1.55987i
$990$	22.6147	+	65.2186i	0.718741	+	2.07278i
$991$	39.8560	+	5.73043i	1.26607	+	0.182033i	0.742439	−	0.669913i	$-0.233669\pi$
$991$	39.8560	+	5.73043i	1.26607	+	0.182033i	0.523629	+	0.851946i	$0.324578\pi$
$992$	41.6067	+	18.7838i	1.32101	+	0.596387i
$993$	−79.8034	+	43.5760i	−2.53249	+	1.38284i
$994$	3.02357	−	0.218882i	0.0959019	−	0.00694252i
$995$	11.9882	−	6.17599i	0.380051	−	0.195792i
$996$	7.61205	−	26.0914i	0.241197	−	0.826736i
$997$	−19.4407	+	7.25100i	−0.615693	+	0.229641i	−0.637909	−	0.770112i	$-0.720200\pi$
$997$	−19.4407	+	7.25100i	−0.615693	+	0.229641i	0.0222164	+	0.999753i	$0.492928\pi$
$998$	22.4504	+	14.4006i	0.710656	+	0.455842i
$999$	−21.8023	+	14.0115i	−0.689795	+	0.443304i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	460.2.w.a.307.1	yes	1360
4.3	odd	2	inner	460.2.w.a.307.28	yes	1360
5.3	odd	4	inner	460.2.w.a.123.35	yes	1360
20.3	even	4	inner	460.2.w.a.123.63	yes	1360
23.3	even	11	inner	460.2.w.a.187.63	yes	1360
92.3	odd	22	inner	460.2.w.a.187.35	yes	1360
115.3	odd	44	inner	460.2.w.a.3.28	yes	1360
460.3	even	44	inner	460.2.w.a.3.1	✓	1360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.w.a.3.1	✓	1360	460.3	even	44	inner
460.2.w.a.3.28	yes	1360	115.3	odd	44	inner
460.2.w.a.123.35	yes	1360	5.3	odd	4	inner
460.2.w.a.123.63	yes	1360	20.3	even	4	inner
460.2.w.a.187.35	yes	1360	92.3	odd	22	inner
460.2.w.a.187.63	yes	1360	23.3	even	11	inner
460.2.w.a.307.1	yes	1360	1.1	even	1	trivial
460.2.w.a.307.28	yes	1360	4.3	odd	2	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:	\( N \)	\(=\)	\( 460 = 2^{2} \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	460.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41421 + 0.00122474i) q^{2} +(0.959477 - 2.57246i) q^{3} +(2.00000 - 0.00346408i) q^{4} +(1.75727 + 1.38275i) q^{5} +(-1.35375 + 3.63918i) q^{6} +(0.698270 - 0.151899i) q^{7} +(-2.82842 + 0.00734842i) q^{8} +(-3.42969 - 2.97185i) q^{9} +O(q^{10})\)	\(q+(-1.41421 + 0.00122474i) q^{2} +(0.959477 - 2.57246i) q^{3} +(2.00000 - 0.00346408i) q^{4} +(1.75727 + 1.38275i) q^{5} +(-1.35375 + 3.63918i) q^{6} +(0.698270 - 0.151899i) q^{7} +(-2.82842 + 0.00734842i) q^{8} +(-3.42969 - 2.97185i) q^{9} +(-2.48685 - 1.95335i) q^{10} +(4.76108 - 0.684541i) q^{11} +(1.91004 - 5.14823i) q^{12} +(-0.148722 + 0.683665i) q^{13} +(-0.987316 + 0.215673i) q^{14} +(5.24313 - 3.19379i) q^{15} +(3.99998 - 0.0138563i) q^{16} +(-2.29054 - 1.25073i) q^{17} +(4.85396 + 4.19862i) q^{18} +(6.83847 + 2.00795i) q^{19} +(3.51933 + 2.75941i) q^{20} +(0.279219 - 1.94201i) q^{21} +(-6.73235 + 0.973917i) q^{22} +(-4.70701 + 0.918730i) q^{23} +(-2.69490 + 7.28304i) q^{24} +(1.17600 + 4.85973i) q^{25} +(0.209488 - 0.967030i) q^{26} +(-3.70648 + 2.02389i) q^{27} +(1.39601 - 0.306217i) q^{28} +(-0.0734905 - 0.250286i) q^{29} +(-7.41099 + 4.52312i) q^{30} +(-7.34064 - 3.35236i) q^{31} +(-5.65680 + 0.0244947i) q^{32} +(2.80720 - 12.9045i) q^{33} +(3.24084 + 1.76599i) q^{34} +(1.43709 + 0.698604i) q^{35} +(-6.86967 - 5.93180i) q^{36} +(6.12127 - 0.437802i) q^{37} +(-9.67351 - 2.83130i) q^{38} +(1.61600 + 1.03854i) q^{39} +(-4.98046 - 3.89808i) q^{40} +(-0.612632 - 0.707015i) q^{41} +(-0.392497 + 2.74676i) q^{42} +(3.62334 - 9.71456i) q^{43} +(9.51978 - 1.38557i) q^{44} +(-1.91758 - 9.96475i) q^{45} +(6.65559 - 1.30505i) q^{46} +(-5.37396 + 5.37396i) q^{47} +(3.80224 - 10.3031i) q^{48} +(-5.90292 + 2.69577i) q^{49} +(-1.66907 - 6.87126i) q^{50} +(-5.41517 + 4.69227i) q^{51} +(-0.295076 + 1.36784i) q^{52} +(-12.9608 + 2.81945i) q^{53} +(5.23928 - 2.86675i) q^{54} +(9.31307 + 5.38047i) q^{55} +(-1.97388 + 0.434766i) q^{56} +(11.7267 - 15.6651i) q^{57} +(0.104238 + 0.353867i) q^{58} +(3.61764 - 2.32492i) q^{59} +(10.4752 - 6.40573i) q^{60} +(-1.58180 + 3.46365i) q^{61} +(10.3853 + 4.73196i) q^{62} +(-2.84627 - 1.55418i) q^{63} +(7.99989 - 0.0415688i) q^{64} +(-1.20668 + 0.995739i) q^{65} +(-3.95417 + 18.2531i) q^{66} +(-3.29164 - 4.39711i) q^{67} +(-4.58540 - 2.49352i) q^{68} +(-2.15287 + 12.9901i) q^{69} +(-2.03320 - 0.986215i) q^{70} +(-2.96916 - 0.426901i) q^{71} +(9.72244 + 8.38042i) q^{72} +(8.00755 - 4.37245i) q^{73} +(-8.65625 + 0.626642i) q^{74} +(13.6298 + 1.63758i) q^{75} +(13.6839 + 3.99221i) q^{76} +(3.22054 - 1.20120i) q^{77} +(-2.28665 - 1.46674i) q^{78} +(1.05258 - 0.676450i) q^{79} +(7.04820 + 5.50662i) q^{80} +(-0.287439 - 1.99918i) q^{81} +(0.867258 + 0.999120i) q^{82} +(4.93702 - 0.353103i) q^{83} +(0.551710 - 3.88499i) q^{84} +(-2.29565 - 5.36511i) q^{85} +(-5.11228 + 13.7429i) q^{86} +(-0.714362 - 0.0510921i) q^{87} +(-13.4613 + 1.97115i) q^{88} +(-12.3441 + 5.63737i) q^{89} +(2.72407 + 14.0899i) q^{90} +0.499974i q^{91} +(-9.41082 + 1.85376i) q^{92} +(-15.6670 + 15.6670i) q^{93} +(7.59334 - 7.60650i) q^{94} +(9.24054 + 12.9844i) q^{95} +(-5.36456 + 14.5754i) q^{96} +(-0.687336 + 9.61022i) q^{97} +(8.34468 - 3.81963i) q^{98} +(-18.3634 - 11.8014i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8}+O(q^{10}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8	\( 1360 q - 18 q^{2} - 36 q^{5} - 44 q^{6} - 18 q^{8} - 18 q^{10} - 6 q^{12} - 36 q^{13} - 44 q^{16} - 36 q^{17} - 38 q^{18} - 14 q^{20} - 88 q^{21} - 28 q^{22} - 36 q^{25} - 36 q^{26} - 34 q^{28} + 2 q^{30} + 2 q^{32} - 60 q^{33} - 36 q^{36} - 36 q^{37} - 10 q^{38} + 2 q^{40} - 56 q^{41} - 202 q^{42} - 120 q^{45} - 44 q^{46} - 50 q^{48} - 34 q^{50} - 250 q^{52} - 84 q^{53} - 84 q^{56} - 44 q^{57} - 58 q^{58} - 42 q^{60} - 136 q^{61} - 82 q^{62} - 68 q^{65} - 84 q^{66} - 4 q^{68} + 16 q^{70} - 104 q^{72} - 36 q^{73} + 4 q^{76} - 44 q^{77} - 50 q^{78} + 204 q^{80} + 80 q^{81} - 10 q^{82} - 252 q^{85} + 44 q^{86} - 50 q^{88} + 264 q^{90} - 22 q^{92} - 88 q^{93} + 52 q^{96} - 36 q^{97} + 30 q^{98}+O(q^{100}) \) 1360 * q - 18 * q^2 - 36 * q^5 - 44 * q^6 - 18 * q^8 - 18 * q^10 - 6 * q^12 - 36 * q^13 - 44 * q^16 - 36 * q^17 - 38 * q^18 - 14 * q^20 - 88 * q^21 - 28 * q^22 - 36 * q^25 - 36 * q^26 - 34 * q^28 + 2 * q^30 + 2 * q^32 - 60 * q^33 - 36 * q^36 - 36 * q^37 - 10 * q^38 + 2 * q^40 - 56 * q^41 - 202 * q^42 - 120 * q^45 - 44 * q^46 - 50 * q^48 - 34 * q^50 - 250 * q^52 - 84 * q^53 - 84 * q^56 - 44 * q^57 - 58 * q^58 - 42 * q^60 - 136 * q^61 - 82 * q^62 - 68 * q^65 - 84 * q^66 - 4 * q^68 + 16 * q^70 - 104 * q^72 - 36 * q^73 + 4 * q^76 - 44 * q^77 - 50 * q^78 + 204 * q^80 + 80 * q^81 - 10 * q^82 - 252 * q^85 + 44 * q^86 - 50 * q^88 + 264 * q^90 - 22 * q^92 - 88 * q^93 + 52 * q^96 - 36 * q^97 + 30 * q^98

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