LMFDB - Embedded newform 460.2.w.a.3.1

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			3.1
Character	$\chi$	$=$	460.3
Dual form			460.2.w.a.307.1

$q$-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 $\left(\mathbb{Z}/460\mathbb{Z}\right)^\times$.

$n$	$231$	$277$	$281$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{8}{11}\right)$

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	0.848303	+	0.529511i	$0.177625\pi$
$3$	0.959477	+	2.57246i	0.553954	+	1.48521i	−0.294349	+	0.955698i	$0.595103\pi$
$4$	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	0.342579	−	0.939489i	$-0.388700\pi$
$7$	0.698270	+	0.151899i	0.263921	+	0.0574125i	−0.0786575	+	0.996902i	$0.525063\pi$
$8$	−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	0.815759	−	0.578393i	$-0.196320\pi$
$11$	4.76108	+	0.684541i	1.43552	+	0.206397i	0.619763	+	0.784789i	$0.287229\pi$
$12$	1.91004	+	5.14823i	0.551381	+	1.48617i
$13$	−0.148722	−	0.683665i	−0.0412481	−	0.189615i	0.951913	−	0.306370i	$-0.0991144\pi$
$13$	−0.148722	−	0.683665i	−0.0412481	−	0.189615i	−0.993161	+	0.116755i	$0.962751\pi$
$14$	−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	−0.732384	−	0.680892i	$-0.761592\pi$
$17$	−2.29054	+	1.25073i	−0.555537	+	0.303346i	0.176846	+	0.984238i	$0.443410\pi$
$18$	4.85396	−	4.19862i	1.14409	−	0.989625i
$19$	6.83847	−	2.00795i	1.56885	−	0.460656i	0.622185	−	0.782870i	$-0.286245\pi$
$19$	6.83847	−	2.00795i	1.56885	−	0.460656i	0.946667	+	0.322214i	$0.104427\pi$
$20$	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	−0.966035	−	0.258411i	$-0.916801\pi$
$29$	−0.0734905	+	0.250286i	−0.0136468	+	0.0464769i	0.952388	+	0.304888i	$0.0986191\pi$
$30$	−7.41099	−	4.52312i	−1.35306	−	0.825805i
$31$	−7.34064	+	3.35236i	−1.31842	+	0.602101i	−0.945457	−	0.325746i	$-0.894385\pi$
$31$	−7.34064	+	3.35236i	−1.31842	+	0.602101i	−0.372961	+	0.927847i	$0.621657\pi$
$32$	−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	0.564763	−	0.825253i	$-0.308968\pi$
$37$	6.12127	+	0.437802i	1.00633	+	0.0719742i	0.441568	+	0.897228i	$0.354422\pi$
$38$	−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	−0.801569	−	0.597902i	$-0.796001\pi$
$41$	−0.612632	+	0.707015i	−0.0956771	+	0.110417i	0.705892	+	0.708320i	$0.250546\pi$
$42$	−0.392497	−	2.74676i	−0.0605636	−	0.423835i
$43$	3.62334	+	9.71456i	0.552554	+	1.48146i	0.850034	+	0.526728i	$0.176581\pi$
$43$	3.62334	+	9.71456i	0.552554	+	1.48146i	−0.297480	+	0.954728i	$0.596146\pi$
$44$	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	0.196610	−	0.980482i	$-0.437007\pi$
$47$	−5.37396	−	5.37396i	−0.783872	−	0.783872i	−0.980482	+	0.196610i	$0.937007\pi$
$48$	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	−0.802476	−	0.596685i	$-0.796484\pi$
$53$	−12.9608	−	2.81945i	−1.78031	−	0.387282i	−0.977829	+	0.209403i	$0.932848\pi$
$54$	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	0.754515	−	0.656282i	$-0.227872\pi$
$59$	3.61764	+	2.32492i	0.470977	+	0.302678i	−0.283539	+	0.958961i	$0.591508\pi$
$60$	10.4752	+	6.40573i	1.35234	+	0.826976i
$61$	−1.58180	−	3.46365i	−0.202528	−	0.443475i	0.780928	−	0.624621i	$-0.214747\pi$
$61$	−1.58180	−	3.46365i	−0.202528	−	0.443475i	−0.983456	+	0.181146i	$0.942019\pi$
$62$	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	−0.955206	−	0.295943i	$-0.904366\pi$
$67$	−3.29164	+	4.39711i	−0.402138	+	0.537193i	0.553068	+	0.833136i	$0.313457\pi$
$68$	−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	−0.316229	−	0.948683i	$-0.602417\pi$
$71$	−2.96916	+	0.426901i	−0.352375	+	0.0506638i	−0.0361452	+	0.999347i	$0.511508\pi$
$72$	9.72244	−	8.38042i	1.14580	−	0.987642i
$73$	8.00755	+	4.37245i	0.937213	+	0.511757i	0.873830	−	0.486232i	$-0.161629\pi$
$73$	8.00755	+	4.37245i	0.937213	+	0.511757i	0.0633832	+	0.997989i	$0.479811\pi$
$74$	−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	0.598512	−	0.801114i	$-0.295759\pi$
$79$	1.05258	+	0.676450i	0.118424	+	0.0761066i	−0.480088	+	0.877220i	$0.659395\pi$
$80$	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	0.339611	−	0.940566i	$-0.389705\pi$
$83$	4.93702	+	0.353103i	0.541908	+	0.0387580i	0.202298	+	0.979324i	$0.435159\pi$
$84$	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	−0.365620	−	0.930764i	$-0.619143\pi$
$89$	−12.3441	−	5.63737i	−1.30847	−	0.597560i	−0.942855	+	0.333204i	$0.891870\pi$
$90$	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	−0.904882	−	0.425662i	$-0.860041\pi$
$97$	−0.687336	−	9.61022i	−0.0697884	−	0.975770i	0.835094	−	0.550108i	$-0.185413\pi$
$98$	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	0.183126	−	0.983089i	$-0.441378\pi$
$101$	−8.20088	−	9.46432i	−0.816018	−	0.941735i	−0.999145	+	0.0413541i	$0.986833\pi$
$102$	7.65245	+	6.64250i	0.757706	+	0.657705i
$103$	1.46819	+	1.96128i	0.144665	+	0.193250i	0.867021	−	0.498271i	$-0.166032\pi$
$103$	1.46819	+	1.96128i	0.144665	+	0.193250i	−0.722356	+	0.691522i	$0.756941\pi$
$104$	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	−0.799425	−	0.600766i	$-0.794862\pi$
$107$	2.04977	−	5.49564i	0.198158	−	0.531283i	0.997583	+	0.0694830i	$0.0221349\pi$
$108$	−7.40594	−	4.06062i	−0.712637	−	0.390733i
$109$	−1.05669	+	3.59875i	−0.101212	+	0.344698i	−0.994493	−	0.104801i	$-0.966579\pi$
$109$	−1.05669	+	3.59875i	−0.101212	+	0.344698i	0.893281	+	0.449499i	$0.148398\pi$
$110$	−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	−0.645208	−	0.764007i	$-0.723229\pi$
$113$	2.86617	−	3.82876i	0.269627	−	0.360179i	0.914835	+	0.403827i	$0.132320\pi$
$114$	−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	−0.636344	−	0.771406i	$-0.719554\pi$
$127$	−0.850440	+	0.636631i	−0.0754643	+	0.0564919i	0.560879	+	0.827897i	$0.310463\pi$
$128$	−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	0.638489	−	0.769631i	$-0.279560\pi$
$131$	−3.74074	−	5.82071i	−0.326830	−	0.508558i	−0.965319	+	0.261073i	$0.915924\pi$
$132$	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	−0.0471971	−	0.998886i	$-0.515029\pi$
$137$	11.1392	−	11.1392i	0.951689	−	0.951689i	0.998886	+	0.0471971i	$0.0150289\pi$
$138$	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	0.456065	−	0.889947i	$-0.349258\pi$
$149$	7.84795	+	1.12836i	0.642929	+	0.0924393i	0.186864	+	0.982386i	$0.440168\pi$
$150$	−19.2775	+	2.29920i	−1.57400	+	0.187729i
$151$	7.30843	−	11.3721i	0.594752	−	0.925452i	−0.405185	−	0.914235i	$-0.632793\pi$
$151$	7.30843	−	11.3721i	0.594752	−	0.925452i	0.999937	−	0.0112171i	$-0.00357059\pi$
$152$	−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	0.0189402	−	0.999821i	$-0.493971\pi$
$157$	10.6480	−	19.5004i	0.849803	−	1.55630i	0.830863	−	0.556477i	$-0.187847\pi$
$158$	−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	−0.240271	−	0.970706i	$-0.577236\pi$
$163$	−15.8229	−	11.8449i	−1.23935	−	0.927764i	−0.999078	+	0.0429416i	$0.986327\pi$
$164$	−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	0.876748	+	0.480949i	$0.159708\pi$
$167$	10.4332	+	19.1069i	0.807343	+	1.47854i	−0.0694058	+	0.997589i	$0.522110\pi$
$168$	−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	−0.406807	−	0.913514i	$-0.633358\pi$
$173$	4.67051	−	3.49630i	0.355092	−	0.265819i	0.761900	+	0.647695i	$0.224267\pi$
$174$	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	−0.662185	−	0.749340i	$-0.730371\pi$
$179$	2.32483	−	2.68300i	0.173766	−	0.200537i	0.835952	+	0.548803i	$0.184916\pi$
$180$	−3.86967	+	19.9228i	−0.288428	+	1.48496i
$181$	−4.80743	+	10.5268i	−0.357333	+	0.782451i	0.642536	+	0.766256i	$0.277882\pi$
$181$	−4.80743	+	10.5268i	−0.357333	+	0.782451i	−0.999869	+	0.0161949i	$0.994845\pi$
$182$	−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	0.904615	−	0.426229i	$-0.140158\pi$
$191$	1.95023	+	3.03461i	0.141113	+	0.219577i	−0.763502	+	0.645805i	$0.776522\pi$
$192$	7.56878	+	20.6193i	0.546230	+	1.48807i
$193$	−0.282518	+	3.95011i	−0.0203361	+	0.284335i	0.977100	+	0.212778i	$0.0682513\pi$
$193$	−0.282518	+	3.95011i	−0.0203361	+	0.284335i	−0.997437	+	0.0715568i	$0.977203\pi$
$194$	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	−0.576513	−	0.817088i	$-0.695587\pi$
$197$	−10.6881	+	2.32506i	−0.761497	+	0.165654i	−0.184984	+	0.982742i	$0.559223\pi$
$198$	25.9842	−	16.6673i	1.84662	−	1.18449i
$199$	2.50533	+	5.48591i	0.177598	+	0.388886i	0.977406	−	0.211370i	$-0.0677926\pi$
$199$	2.50533	+	5.48591i	0.177598	+	0.388886i	−0.799808	+	0.600256i	$0.795065\pi$
$200$	−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	−0.927926	−	0.372764i	$-0.878410\pi$
$211$	−5.06714	−	17.2571i	−0.348836	−	1.18803i	0.579090	−	0.815264i	$-0.303408\pi$
$212$	−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	−0.928352	−	0.371703i	$-0.878774\pi$
$223$	1.05305	−	4.84080i	0.0705176	−	0.324164i	0.998869	+	0.0475385i	$0.0151377\pi$
$224$	−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	−0.445324	−	0.895370i	$-0.646911\pi$
$227$	−2.94602	+	1.09881i	−0.195534	+	0.0729305i	0.249789	+	0.968300i	$0.419639\pi$
$228$	23.3992	+	31.3707i	1.54965	+	2.07758i
$229$			5.30243i			0.350395i	0.984533	+	0.175197i	$0.0560563\pi$
$229$			5.30243i			0.350395i	−0.984533	+	0.175197i	$0.943944\pi$
$230$	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	−0.340181	−	0.940360i	$-0.610488\pi$
$233$	0.282881	−	0.105509i	0.0185321	−	0.00691213i	0.358713	+	0.933448i	$0.383216\pi$
$234$	−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	0.990154	+	0.139984i	$0.0447051\pi$
$239$	15.2710	+	17.6237i	0.987799	+	1.13998i	−0.00235445	+	0.999997i	$0.500749\pi$
$240$	20.9281	+	12.8477i	1.35091	+	0.829317i
$241$	3.04637	−	21.1880i	0.196234	−	1.36484i	−0.618857	−	0.785504i	$-0.712404\pi$
$241$	3.04637	−	21.1880i	0.196234	−	1.36484i	0.815091	−	0.579333i	$-0.196687\pi$
$242$	−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	−0.213691	−	0.976901i	$-0.568549\pi$
$251$	−2.27348	+	0.326877i	−0.143501	+	0.0206323i	0.0701901	+	0.997534i	$0.477639\pi$
$252$	−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	0.391089	+	0.920353i	$0.372099\pi$
$257$	−9.53216	+	17.4569i	−0.594600	+	1.08893i	−0.985689	+	0.168576i	$0.946083\pi$
$258$	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	−0.829260	−	0.558863i	$-0.811238\pi$
$263$	−21.9164	+	4.76762i	−1.35142	+	0.293984i	−0.522162	+	0.852847i	$0.674874\pi$
$264$	−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	0.993054	+	0.117659i	$0.0375389\pi$
$269$	11.2767	+	17.5468i	0.687551	+	1.06985i	−0.305504	+	0.952191i	$0.598825\pi$
$270$	13.1708	−	2.20695i	0.801552	−	0.134310i
$271$	−8.39578	−	7.27499i	−0.510008	−	0.441924i	0.361453	−	0.932391i	$-0.382281\pi$
$271$	−8.39578	−	7.27499i	−0.510008	−	0.441924i	−0.871460	+	0.490466i	$0.836826\pi$
$272$	−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	−0.669898	−	0.742453i	$-0.733662\pi$
$277$	1.20755	−	1.20755i	0.0725544	−	0.0725544i	0.742453	+	0.669898i	$0.233662\pi$
$278$	−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	−0.999328	−	0.0366449i	$-0.988333\pi$
$281$	−13.7597	+	15.8796i	−0.820837	+	0.947297i	0.178491	+	0.983942i	$0.442878\pi$
$282$	−12.2818	+	26.8318i	−0.731369	+	1.59781i
$283$	−5.64319	+	25.9413i	−0.335453	+	1.54205i	0.432554	+	0.901608i	$0.357613\pi$
$283$	−5.64319	+	25.9413i	−0.335453	+	1.54205i	−0.768006	+	0.640442i	$0.778751\pi$
$284$	−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	0.835549	−	0.549415i	$-0.185150\pi$
$293$	−1.34165	−	2.45706i	−0.0783803	−	0.143543i	−0.913930	+	0.405873i	$0.866968\pi$
$294$	−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	0.688535	+	0.725203i	$0.258254\pi$
$307$	−5.37438	+	14.4093i	−0.306732	+	0.822380i	−0.995267	+	0.0971770i	$0.969019\pi$
$308$	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	0.00641189	−	0.999979i	$-0.497959\pi$
$311$	−4.74674	−	0.682478i	−0.269163	−	0.0386998i	−0.275575	+	0.961280i	$0.588868\pi$
$312$	−4.57837	+	2.92556i	−0.259199	+	0.165627i
$313$	1.73712	−	24.2881i	0.0981877	−	1.37284i	−0.674602	−	0.738182i	$-0.735685\pi$
$313$	1.73712	−	24.2881i	0.0981877	−	1.37284i	0.772790	−	0.634662i	$-0.218861\pi$
$314$	−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	−0.930729	−	0.365709i	$-0.880826\pi$
$317$	−1.09532	−	15.3146i	−0.0615193	−	0.860153i	0.869210	−	0.494443i	$-0.164628\pi$
$318$	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	−0.416536	+	0.909119i	$0.636756\pi$
$331$	−25.0283	+	21.6872i	−1.37568	+	1.19203i	−0.959145	+	0.282916i	$0.908698\pi$
$332$	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	0.468019	−	0.883718i	$-0.344968\pi$
$337$	4.46110	+	1.66390i	0.243012	+	0.0906386i	−0.225007	+	0.974357i	$0.572241\pi$
$338$	−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	−0.0977307	−	0.995213i	$-0.531158\pi$
$347$	16.4802	−	22.0150i	0.884703	−	1.18182i	0.982434	−	0.186612i	$-0.0597507\pi$
$348$	−1.42890	+	0.0997095i	−0.0765970	+	0.00534499i
$349$	−1.10816	−	3.77406i	−0.0593186	−	0.202021i	0.924502	−	0.381177i	$-0.124481\pi$
$349$	−1.10816	−	3.77406i	−0.0593186	−	0.202021i	−0.983821	+	0.179157i	$0.942663\pi$
$350$	−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	0.651807	+	0.758385i	$0.274011\pi$
$353$	−6.33978	+	16.9976i	−0.337432	+	0.904691i	−0.989239	+	0.146306i	$0.953261\pi$
$354$	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	−0.993837	−	0.110854i	$-0.964641\pi$
$359$	−18.2297	−	21.0382i	−0.962125	−	1.11035i	0.0317116	−	0.999497i	$-0.489904\pi$
$360$	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	0.276881	−	0.960904i	$-0.410699\pi$
$367$	−13.1040	−	13.1040i	−0.684023	−	0.684023i	−0.960904	+	0.276881i	$0.910699\pi$
$368$	−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	0.676741	−	0.736222i	$-0.263392\pi$
$373$	28.0306	−	2.00479i	1.45137	−	0.103804i	0.774628	+	0.632418i	$0.217937\pi$
$374$	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	0.305200	+	0.952288i	$0.401277\pi$
$379$	−4.98238	+	34.6532i	−0.255928	+	1.78002i	−0.561128	+	0.827729i	$0.689632\pi$
$380$	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	0.109778	−	0.993956i	$-0.464986\pi$
$383$	−8.96637	−	3.34428i	−0.458160	−	0.170885i	−0.567938	+	0.823071i	$0.692259\pi$
$384$	−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	−0.324129	−	0.946013i	$-0.605071\pi$
$389$	−7.27003	+	1.04527i	−0.368605	+	0.0529975i	−0.0444766	+	0.999010i	$0.514162\pi$
$390$	−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	0.271715	−	0.962378i	$-0.412409\pi$
$397$	24.4721	−	13.3628i	1.22822	−	0.670658i	0.956504	+	0.291719i	$0.0942273\pi$
$398$	−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	−0.998446	−	0.0557298i	$-0.982251\pi$
$401$	−29.3148	−	18.8394i	−1.46391	−	0.940797i	−0.465463	−	0.885067i	$-0.654112\pi$
$402$	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	−0.00688804	−	0.999976i	$-0.502193\pi$
$409$	−20.1766	−	17.4831i	−0.997666	−	0.864483i	−0.990778	+	0.135494i	$0.956738\pi$
$410$	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	−0.932326	−	0.361618i	$-0.882225\pi$
$419$	−9.04149	+	10.4344i	−0.441706	+	0.509755i	0.490621	+	0.871373i	$0.336770\pi$
$420$	6.34147	+	6.06410i	0.309432	+	0.295898i
$421$	−7.45919	+	4.79373i	−0.363538	+	0.233632i	−0.709639	−	0.704565i	$-0.751142\pi$
$421$	−7.45919	+	4.79373i	−0.363538	+	0.233632i	0.346101	+	0.938197i	$0.387506\pi$
$422$	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	0.602843	+	0.797860i	$0.294035\pi$
$431$	−6.96841	+	23.7322i	−0.335656	+	1.14314i	−0.938499	+	0.345281i	$0.887784\pi$
$432$	−14.7978	−	8.14688i	−0.711959	−	0.391967i
$433$	1.94910	+	1.06429i	0.0936677	+	0.0511464i	0.525400	−	0.850855i	$-0.323916\pi$
$433$	1.94910	+	1.06429i	0.0936677	+	0.0511464i	−0.431732	+	0.902002i	$0.642097\pi$
$434$	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	0.853376	+	0.521295i	$0.174551\pi$
$439$	3.80146	+	26.4397i	0.181434	+	1.26190i	−0.671943	+	0.740603i	$0.734540\pi$
$440$	−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	0.298278	−	0.954479i	$-0.403588\pi$
$443$	26.5725	−	14.5097i	1.26250	−	0.689376i	0.964220	+	0.265103i	$0.0854059\pi$
$444$	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	0.589330	−	0.807893i	$-0.299392\pi$
$449$	19.6466	+	2.82475i	0.927178	+	0.133308i	0.337848	+	0.941201i	$0.390301\pi$
$450$	−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	0.956354	−	0.292211i	$-0.0943911\pi$
$457$	0.902817	+	2.42055i	0.0422320	+	0.113228i	−0.914122	+	0.405440i	$0.867118\pi$
$458$	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	0.843596	−	0.536978i	$-0.180434\pi$
$463$	−3.13288	−	8.39957i	−0.145597	−	0.390361i	−0.989193	+	0.146617i	$0.953162\pi$
$464$	−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	−0.183834	−	0.982957i	$-0.558851\pi$
$467$	−16.4106	−	3.56990i	−0.759391	−	0.165195i	−0.575557	+	0.817762i	$0.695215\pi$
$468$	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	0.286426	−	0.958102i	$-0.407533\pi$
$479$	22.8791	−	6.71790i	1.04537	−	0.306949i	0.758946	+	0.651154i	$0.225715\pi$
$480$	−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	−0.175779	−	0.984430i	$-0.556244\pi$
$487$	−24.2521	−	13.2426i	−1.09897	−	0.600081i	−0.923188	+	0.384348i	$0.874426\pi$
$488$	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	−0.0424335	−	0.999099i	$-0.513511\pi$
$491$	15.1752	−	6.93028i	0.684847	−	0.312759i	0.727281	+	0.686340i	$0.240784\pi$
$492$	−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	−0.845237	−	0.534392i	$-0.820541\pi$
$499$	−15.8660	+	10.1965i	−0.710261	+	0.456457i	0.134976	+	0.990849i	$0.456904\pi$
$500$	−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	0.998754	+	0.0499046i	$0.0158917\pi$
$503$	6.20409	+	16.6338i	0.276627	+	0.741665i	−0.722127	+	0.691760i	$0.756836\pi$
$504$	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	0.860538	−	0.509386i	$-0.170128\pi$
$509$	23.4432	+	10.7062i	1.03910	+	0.474542i	0.178564	+	0.983928i	$0.442855\pi$
$510$	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	0.941205	+	0.337837i	$0.109695\pi$
$521$	13.2425	+	28.9971i	0.580167	+	1.27039i	−0.361038	+	0.932551i	$0.617578\pi$
$522$	0.694135	+	1.52343i	0.0303815	+	0.0666789i
$523$	14.7615	−	8.06041i	0.645477	−	0.352457i	−0.122933	−	0.992415i	$-0.539230\pi$
$523$	14.7615	−	8.06041i	0.645477	−	0.352457i	0.768410	+	0.639958i	$0.221048\pi$
$524$	−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	0.832134	+	0.554575i	$0.187119\pi$
$541$	−2.85008	+	19.8227i	−0.122535	+	0.852246i	−0.954668	+	0.297671i	$0.903790\pi$
$542$	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	−0.652598	−	0.757704i	$-0.726321\pi$
$547$	−27.8486	+	1.99177i	−1.19072	+	0.0851621i	−0.538123	+	0.842866i	$0.680866\pi$
$548$	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	−0.986167	−	0.165756i	$-0.946994\pi$
$557$	−0.793632	−	11.0964i	−0.0336273	−	0.470171i	0.952540	−	0.304415i	$-0.0984609\pi$
$558$	−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	0.999976	−	0.00691326i	$-0.00220058\pi$
$563$	16.8850	+	22.5557i	0.711617	+	0.950609i	−0.288359	+	0.957522i	$0.593110\pi$
$564$	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	−0.921504	−	0.388370i	$-0.873038\pi$
$569$	1.51908	−	5.17352i	0.0636832	−	0.216885i	0.985187	+	0.171485i	$0.0548565\pi$
$570$	−59.7620	−	16.0503i	−2.50316	−	0.672272i
$571$	−0.359152	−	1.22316i	−0.0150300	−	0.0511876i	0.951637	−	0.307226i	$-0.0994008\pi$
$571$	−0.359152	−	1.22316i	−0.0150300	−	0.0511876i	−0.966667	+	0.256039i	$0.917583\pi$
$572$	−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	0.560022	−	0.828478i	$-0.310793\pi$
$577$	−1.85248	−	1.38675i	−0.0771198	−	0.0577311i	−0.637142	+	0.770746i	$0.719884\pi$
$578$	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	−0.485753	−	0.874096i	$-0.661455\pi$
$587$	5.23530	−	3.91909i	0.216084	−	0.161758i	0.701837	+	0.712338i	$0.252364\pi$
$588$	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	−0.152573	−	0.988292i	$-0.548756\pi$
$593$	−3.96795	+	0.283793i	−0.162944	+	0.0116540i	−0.0103712	+	0.999946i	$0.503301\pi$
$594$	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	−0.974849	−	0.222866i	$-0.928459\pi$
$601$	−4.11925	+	9.01991i	−0.168028	+	0.367930i	0.806821	+	0.590796i	$0.201186\pi$
$602$	−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	0.867217	+	0.497930i	$0.165906\pi$
$607$	−1.52840	+	21.3698i	−0.0620358	+	0.867373i	−0.929253	+	0.369444i	$0.879548\pi$
$608$	−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	0.489520	+	0.871992i	$0.337172\pi$
$613$	−11.1778	+	29.9689i	−0.451468	+	1.21043i	−0.940988	+	0.338441i	$0.890101\pi$
$614$	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	−0.846933	−	0.531700i	$-0.821553\pi$
$617$	1.44685	−	2.64971i	0.0582481	−	0.106673i	0.905181	+	0.425027i	$0.139735\pi$
$618$	5.14986	−	7.99810i	0.207158	−	0.321731i
$619$	0.262996	+	1.82917i	0.0105707	+	0.0735207i	0.994424	−	0.105456i	$-0.0336303\pi$
$619$	0.262996	+	1.82917i	0.0105707	+	0.0735207i	−0.983853	+	0.178977i	$0.942721\pi$
$620$	−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	−0.442846	−	0.896598i	$-0.646031\pi$
$631$	13.9840	−	21.7595i	0.556693	−	0.866232i	0.999539	+	0.0303662i	$0.00966735\pi$
$632$	−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	0.177436	+	0.984132i	$0.443220\pi$
$641$	−17.2800	+	37.8378i	−0.682517	+	1.49450i	−0.859954	+	0.510372i	$0.829508\pi$
$642$	−22.7745	−	0.0197232i	−0.898837	−	0.000778411i
$643$	7.97088	−	7.97088i	0.314341	−	0.314341i	−0.532248	−	0.846589i	$-0.678653\pi$
$643$	7.97088	−	7.97088i	0.314341	−	0.314341i	0.846589	+	0.532248i	$0.178653\pi$
$644$	−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	0.388743	−	0.921346i	$-0.372910\pi$
$647$	32.7081	−	12.1995i	1.28589	−	0.479611i	0.897146	+	0.441735i	$0.145637\pi$
$648$	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	0.263511	+	0.964656i	$0.415119\pi$
$653$	−3.43962	+	48.0922i	−0.134603	+	1.88199i	−0.398114	+	0.917336i	$0.630335\pi$
$654$	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	−0.998637	−	0.0521959i	$-0.983378\pi$
$659$	−9.86064	−	21.5918i	−0.384116	−	0.841096i	0.614521	−	0.788900i	$-0.289349\pi$
$660$	45.4882	+	37.6689i	1.77063	+	1.46626i
$661$	−28.3731	−	8.33110i	−1.10359	−	0.324042i	−0.321310	−	0.946974i	$-0.604123\pi$
$661$	−28.3731	−	8.33110i	−1.10359	−	0.324042i	−0.782276	+	0.622932i	$0.785941\pi$
$662$	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	−0.889403	−	0.457124i	$-0.848879\pi$
$673$	−20.5751	−	37.6805i	−0.793113	−	1.45248i	0.0962901	−	0.995353i	$-0.469302\pi$
$674$	−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	0.840638	−	0.541598i	$-0.182180\pi$
$677$	47.6229	−	10.3597i	1.83030	−	0.398157i	0.989659	+	0.143441i	$0.0458168\pi$
$678$	−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	−0.978273	−	0.207322i	$-0.933525\pi$
$683$	−0.0595864	+	0.273914i	−0.00228001	+	0.0104810i	0.975993	+	0.217803i	$0.0698889\pi$
$684$	−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	$-0.901390\pi$
$691$		−	16.0277i		−	0.609721i	0.952397	−	0.304861i	$-0.0986099\pi$
$692$	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	−0.999905	−	0.0137819i	$-0.995613\pi$
$701$	−0.969575	+	6.74355i	−0.0366204	+	0.254700i	0.963285	+	0.268482i	$0.0865220\pi$
$702$	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	0.911292	+	0.411761i	$0.135086\pi$
$709$	9.77956	+	33.3061i	0.367279	+	1.25084i	−0.544013	+	0.839077i	$0.683096\pi$
$710$	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	−0.0108750	−	0.999941i	$-0.503462\pi$
$719$	−15.0329	−	4.41406i	−0.560633	−	0.164617i	−0.549757	+	0.835324i	$0.685280\pi$
$720$	−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	−0.985669	−	0.168693i	$-0.946045\pi$
$727$	0.376801	−	5.26837i	0.0139748	−	0.195393i	0.999643	−	0.0267003i	$-0.00849999\pi$
$728$	−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	−0.212766	−	0.977103i	$-0.568247\pi$
$733$	7.20987	−	2.68914i	0.266303	−	0.0993258i	0.479069	+	0.877777i	$0.340974\pi$
$734$	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	−0.686716	−	0.726926i	$-0.740948\pi$
$739$	8.49141	−	18.5936i	0.312361	−	0.683976i	0.999077	+	0.0429499i	$0.0136756\pi$
$740$	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	−0.865292	−	0.501268i	$-0.832867\pi$
$743$	3.54463	−	16.2944i	0.130040	−	0.597783i	0.995332	−	0.0965145i	$-0.0307694\pi$
$744$	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	−0.0675441	−	0.997716i	$-0.521516\pi$
$751$	17.6004	−	8.03783i	0.642248	−	0.293305i	0.709792	+	0.704412i	$0.248789\pi$
$752$	−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	0.436717	−	0.899599i	$-0.356141\pi$
$757$	−8.34777	−	6.24906i	−0.303405	−	0.227126i	−0.740122	+	0.672473i	$0.765232\pi$
$758$	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	0.999495	+	0.0317856i	$0.0101194\pi$
$761$	1.36391	+	9.48619i	0.0494416	+	0.343874i	−0.950053	+	0.312088i	$0.898972\pi$
$762$	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	−0.882098	−	0.471066i	$-0.843869\pi$
$769$	−2.41714	+	3.76114i	−0.0871643	+	0.135630i	0.794934	+	0.606697i	$0.207506\pi$
$770$	−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	−0.986511	−	0.163696i	$-0.947658\pi$
$773$	0.368531	−	5.15274i	0.0132551	−	0.185331i	0.999766	−	0.0216349i	$-0.00688714\pi$
$774$	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	0.616657	−	0.787232i	$-0.288487\pi$
$787$	37.5657	−	2.68675i	1.33907	−	0.0957723i	0.722415	+	0.691460i	$0.243032\pi$
$788$	−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	0.580312	−	0.814395i	$-0.302931\pi$
$797$	13.7081	+	5.11287i	0.485567	+	0.181107i	−0.0947448	+	0.995502i	$0.530203\pi$
$798$	−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	−0.904692	−	0.426067i	$-0.859899\pi$
$809$	−10.6367	−	36.2252i	−0.373966	−	1.27361i	0.530726	−	0.847544i	$-0.321919\pi$
$810$	−3.19028	−	5.53313i	−0.112095	−	0.194414i
$811$	−3.35434	+	11.4238i	−0.117787	+	0.401145i	−0.997188	−	0.0749359i	$-0.976125\pi$
$811$	−3.35434	+	11.4238i	−0.117787	+	0.401145i	0.879402	+	0.476081i	$0.157943\pi$
$812$	−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	−0.719491	−	0.694502i	$-0.755625\pi$
$821$	−11.0783	+	7.11962i	−0.386637	+	0.248477i	0.332854	+	0.942978i	$0.391988\pi$
$822$	−55.6174	−	25.4579i	−1.93988	−	0.887945i
$823$	3.92884	+	54.9324i	0.136951	+	1.91482i	0.348249	+	0.937402i	$0.386776\pi$
$823$	3.92884	+	54.9324i	0.136951	+	1.91482i	−0.211298	+	0.977422i	$0.567769\pi$
$824$	−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	0.989275	−	0.146062i	$-0.0466599\pi$
$827$	24.2488	+	24.2488i	0.843213	+	0.843213i	−0.146062	+	0.989275i	$0.546660\pi$
$828$	37.7853	−	21.6097i	1.31313	−	0.750988i
$829$			45.9815i			1.59700i	0.601993	+	0.798502i	$0.294374\pi$
$829$			45.9815i			1.59700i	−0.601993	+	0.798502i	$0.705626\pi$
$830$	−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	−0.946337	−	0.323181i	$-0.895248\pi$
$839$	1.52699	−	10.6204i	0.0527174	−	0.366658i	0.999054	−	0.0434763i	$-0.0138433\pi$
$840$	−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	−0.250031	−	0.968238i	$-0.580441\pi$
$853$	21.8879	−	29.2389i	0.749429	−	1.00112i	0.999459	−	0.0328815i	$-0.0104684\pi$
$854$	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	−0.294036	−	0.955794i	$-0.594999\pi$
$857$	10.2772	−	5.61176i	0.351061	−	0.191694i	0.645097	+	0.764100i	$0.276817\pi$
$858$	−11.8910	+	5.41798i	−0.405951	+	0.184967i
$859$	3.26854	+	7.15710i	0.111521	+	0.244197i	0.957161	−	0.289557i	$-0.0935080\pi$
$859$	3.26854	+	7.15710i	0.111521	+	0.244197i	−0.845640	+	0.533754i	$0.820781\pi$
$860$	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	0.986423	+	0.164227i	$0.0525128\pi$
$863$	25.4430	+	33.9879i	0.866090	+	1.15696i	−0.120333	+	0.992734i	$0.538396\pi$
$864$	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	−0.980551	−	0.196266i	$-0.937118\pi$
$877$	−10.8988	−	29.2209i	−0.368027	−	0.986718i	0.612524	−	0.790452i	$-0.290154\pi$
$878$	−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	−0.133406	−	0.991061i	$-0.542591\pi$
$881$	21.1534	−	13.5945i	0.712676	−	0.458009i	0.846082	+	0.533052i	$0.178955\pi$
$882$	−39.9710	+	11.6990i	−1.34589	+	0.393925i
$883$	−34.9152	−	2.49718i	−1.17499	−	0.0840369i	−0.529843	−	0.848096i	$-0.677749\pi$
$883$	−34.9152	−	2.49718i	−1.17499	−	0.0840369i	−0.645146	+	0.764059i	$0.723204\pi$
$884$	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	0.958785	−	0.284133i	$-0.0917056\pi$
$887$	−0.934857	−	4.29747i	−0.0313894	−	0.144295i	−0.990174	+	0.139838i	$0.955342\pi$
$888$	−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	0.850998	+	0.525168i	$0.175998\pi$
$907$	8.88633	+	40.8498i	0.295066	+	1.35640i	−0.555933	+	0.831227i	$0.687639\pi$
$908$	−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	−0.700313	−	0.713836i	$-0.746956\pi$
$911$	−2.81931	+	2.44294i	−0.0934078	+	0.0809383i	0.606905	+	0.794774i	$0.292411\pi$
$912$	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	−0.448110	−	0.893978i	$-0.647903\pi$
$929$	11.3687	−	9.85105i	0.372996	−	0.323202i	0.821106	+	0.570776i	$0.193357\pi$
$930$	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	−0.884713	−	0.466136i	$-0.845646\pi$
$937$	−29.7193	+	16.2280i	−0.970887	+	0.530145i	−0.0861740	+	0.996280i	$0.527464\pi$
$938$	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	0.967043	−	0.254611i	$-0.0819475\pi$
$941$	−0.998809	−	6.94687i	−0.0325602	−	0.226461i	−0.999604	+	0.0281499i	$0.991038\pi$
$942$	−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	0.854454	−	0.519527i	$-0.173892\pi$
$947$	27.0607	+	14.7762i	0.879353	+	0.480163i	0.0248992	+	0.999690i	$0.492074\pi$
$948$	−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	0.840393	+	0.541977i	$0.182324\pi$
$953$	9.29486	+	42.7278i	0.301090	+	1.38409i	−0.539303	+	0.842112i	$0.681312\pi$
$954$	−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	0.991084	−	0.133239i	$-0.0425379\pi$
$967$	26.6761	+	26.6761i	0.857844	+	0.857844i	−0.133239	+	0.991084i	$0.542538\pi$
$968$	−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	0.774317	−	0.632798i	$-0.218093\pi$
$971$	8.04441	+	6.97052i	0.258158	+	0.223695i	−0.516160	+	0.856492i	$0.672639\pi$
$972$	−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	0.570255	−	0.821468i	$-0.306844\pi$
$977$	−11.8338	−	15.8081i	−0.378597	−	0.505746i	−0.948852	+	0.315722i	$0.897753\pi$
$978$	−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	−0.0397784	−	0.999209i	$-0.512665\pi$
$983$	24.4334	−	13.3416i	0.779303	−	0.425532i	0.819082	+	0.573677i	$0.194483\pi$
$984$	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	0.523629	−	0.851946i	$-0.324578\pi$
$991$	39.8560	−	5.73043i	1.26607	−	0.182033i	0.742439	+	0.669913i	$0.233669\pi$
$992$	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	0.0222164	−	0.999753i	$-0.492928\pi$
$997$	−19.4407	−	7.25100i	−0.615693	−	0.229641i	−0.637909	+	0.770112i	$0.720200\pi$
$998$	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.3.1	✓	1360
4.3	odd	2	inner	460.2.w.a.3.28	yes	1360
5.2	odd	4	inner	460.2.w.a.187.35	yes	1360
20.7	even	4	inner	460.2.w.a.187.63	yes	1360
23.8	even	11	inner	460.2.w.a.123.63	yes	1360
92.31	odd	22	inner	460.2.w.a.123.35	yes	1360
115.77	odd	44	inner	460.2.w.a.307.28	yes	1360
460.307	even	44	inner	460.2.w.a.307.1	yes	1360

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
460.2.w.a.3.1	✓	1360	1.1	even	1	trivial
460.2.w.a.3.28	yes	1360	4.3	odd	2	inner
460.2.w.a.123.35	yes	1360	92.31	odd	22	inner
460.2.w.a.123.63	yes	1360	23.8	even	11	inner
460.2.w.a.187.35	yes	1360	5.2	odd	4	inner
460.2.w.a.187.63	yes	1360	20.7	even	4	inner
460.2.w.a.307.1	yes	1360	460.307	even	44	inner
460.2.w.a.307.28	yes	1360	115.77	odd	44	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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