LMFDB - Embedded newform 189.2.be.a.20.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [189,2,Mod(20,189)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("189.20"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(189, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([7, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.be (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			20.19
Character	$\chi$	$=$	189.20
Dual form			189.2.be.a.104.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.735125 + 2.01974i) q^{2} +(-1.28358 + 1.16294i) q^{3} +(-2.00685 + 1.68395i) q^{4} +(0.0677816 + 0.384409i) q^{5} +(-3.29242 - 1.73760i) q^{6} +(0.618456 + 2.57245i) q^{7} +(-1.15362 - 0.666045i) q^{8} +(0.295160 - 2.98544i) q^{9} +(-0.726578 + 0.419490i) q^{10} +(-4.77807 - 0.842503i) q^{11} +(0.617633 - 4.49533i) q^{12} +(1.96127 - 5.38855i) q^{13} +(-4.74104 + 3.14020i) q^{14} +(-0.534046 - 0.414594i) q^{15} +(-0.412653 + 2.34027i) q^{16} +(3.57147 + 6.18597i) q^{17} +(6.24680 - 1.59853i) q^{18} +(0.398672 + 0.230173i) q^{19} +(-0.783352 - 0.657311i) q^{20} +(-3.78544 - 2.58273i) q^{21} +(-1.81084 - 10.2698i) q^{22} +(0.358944 + 0.427773i) q^{23} +(2.25534 - 0.486668i) q^{24} +(4.55529 - 1.65799i) q^{25} +12.3252 q^{26} +(3.09302 + 4.17531i) q^{27} +(-5.57303 - 4.12109i) q^{28} +(1.73522 + 4.76747i) q^{29} +(0.444781 - 1.38341i) q^{30} +(2.14159 + 2.55225i) q^{31} +(-7.65380 + 1.34957i) q^{32} +(7.11282 - 4.47517i) q^{33} +(-9.86858 + 11.7609i) q^{34} +(-0.946953 + 0.412105i) q^{35} +(4.43500 + 6.48838i) q^{36} +(-1.07348 - 1.85933i) q^{37} +(-0.171817 + 0.974420i) q^{38} +(3.74909 + 9.19747i) q^{39} +(0.177839 - 0.488609i) q^{40} +(0.917771 + 0.334041i) q^{41} +(2.43367 - 9.54423i) q^{42} +(1.16047 - 6.58138i) q^{43} +(11.0076 - 6.35525i) q^{44} +(1.16764 - 0.0888961i) q^{45} +(-0.600121 + 1.03944i) q^{46} +(-2.83834 - 2.38165i) q^{47} +(-2.19191 - 3.48382i) q^{48} +(-6.23502 + 3.18190i) q^{49} +(6.69741 + 7.98167i) q^{50} +(-11.7782 - 3.78680i) q^{51} +(5.13806 + 14.1167i) q^{52} -3.13310i q^{53} +(-6.15929 + 9.31647i) q^{54} -1.89384i q^{55} +(0.999904 - 3.37956i) q^{56} +(-0.779405 + 0.168184i) q^{57} +(-8.35346 + 7.00938i) q^{58} +(-0.715255 - 4.05641i) q^{59} +(1.76991 - 0.0672771i) q^{60} +(7.89549 - 9.40948i) q^{61} +(-3.58054 + 6.20168i) q^{62} +(7.86246 - 1.08708i) q^{63} +(-5.97591 - 10.3506i) q^{64} +(2.20434 + 0.388685i) q^{65} +(14.2675 + 11.0762i) q^{66} +(6.30401 + 2.29447i) q^{67} +(-17.5843 - 6.40016i) q^{68} +(-0.958206 - 0.131652i) q^{69} +(-1.52847 - 1.60965i) q^{70} +(6.08593 - 3.51371i) q^{71} +(-2.32894 + 3.24749i) q^{72} +(-6.55906 - 3.78687i) q^{73} +(2.96621 - 3.53499i) q^{74} +(-3.91895 + 7.42567i) q^{75} +(-1.18768 + 0.209419i) q^{76} +(-0.787728 - 12.8124i) q^{77} +(-15.8205 + 14.3335i) q^{78} +(-0.818714 + 0.297987i) q^{79} -0.927591 q^{80} +(-8.82576 - 1.76237i) q^{81} +2.09922i q^{82} +(6.78293 - 2.46878i) q^{83} +(11.9460 - 1.19133i) q^{84} +(-2.13586 + 1.79220i) q^{85} +(14.1458 - 2.49428i) q^{86} +(-7.77156 - 4.10149i) q^{87} +(4.95095 + 4.15434i) q^{88} +(2.65800 - 4.60379i) q^{89} +(1.03791 + 2.29297i) q^{90} +(15.0747 + 1.71270i) q^{91} +(-1.44070 - 0.254033i) q^{92} +(-5.71701 - 0.785485i) q^{93} +(2.72378 - 7.48351i) q^{94} +(-0.0614580 + 0.168854i) q^{95} +(8.25481 - 10.6332i) q^{96} +(10.7873 + 1.90209i) q^{97} +(-11.0101 - 10.2540i) q^{98} +(-3.92554 + 14.0160i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30}+ \cdots - 192 q^{99}+O(q^{100}) $ 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.735125	+	2.01974i	0.519812	+	1.42817i	0.870728	+	0.491765i	$0.163648\pi$
$2$	0.735125	+	2.01974i	0.519812	+	1.42817i	−0.350916	+	0.936407i	$0.614130\pi$
$3$	−1.28358	+	1.16294i	−0.741076	+	0.671421i
$3$	−1.28358	+	1.16294i	−0.741076	+	0.671421i
$4$	−2.00685	+	1.68395i	−1.00343	+	0.841975i
$5$	0.0677816	+	0.384409i	0.0303129	+	0.171913i	0.996206	−	0.0870291i	$-0.0277373\pi$
$5$	0.0677816	+	0.384409i	0.0303129	+	0.171913i	−0.965893	+	0.258942i	$0.916626\pi$
$6$	−3.29242	−	1.73760i	−1.34413	−	0.709371i
$7$	0.618456	+	2.57245i	0.233754	+	0.972296i
$7$	0.618456	+	2.57245i	0.233754	+	0.972296i
$8$	−1.15362	−	0.666045i	−0.407868	−	0.235483i
$9$	0.295160	−	2.98544i	0.0983867	−	0.995148i
$10$	−0.726578	+	0.419490i	−0.229764	+	0.132654i
$11$	−4.77807	−	0.842503i	−1.44064	−	0.254024i	−0.601909	−	0.798565i	$-0.705593\pi$
$11$	−4.77807	−	0.842503i	−1.44064	−	0.254024i	−0.838734	+	0.544541i	$0.816704\pi$
$12$	0.617633	−	4.49533i	0.178295	−	1.29769i
$13$	1.96127	−	5.38855i	0.543959	−	1.49451i	−0.297783	−	0.954634i	$-0.596247\pi$
$13$	1.96127	−	5.38855i	0.543959	−	1.49451i	0.841742	−	0.539881i	$-0.181531\pi$
$14$	−4.74104	+	3.14020i	−1.26710	+	0.839253i
$15$	−0.534046	−	0.414594i	−0.137890	−	0.107048i
$16$	−0.412653	+	2.34027i	−0.103163	+	0.585068i
$17$	3.57147	+	6.18597i	0.866209	+	1.50032i	0.865841	+	0.500319i	$0.166784\pi$
$17$	3.57147	+	6.18597i	0.866209	+	1.50032i	0.000368279		1.00000i	$0.499883\pi$
$18$	6.24680	−	1.59853i	1.47239	−	0.376777i
$19$	0.398672	+	0.230173i	0.0914616	+	0.0528054i	0.545033	−	0.838414i	$-0.316517\pi$
$19$	0.398672	+	0.230173i	0.0914616	+	0.0528054i	−0.453572	+	0.891220i	$0.649850\pi$
$20$	−0.783352	−	0.657311i	−0.175163	−	0.146979i
$21$	−3.78544	−	2.58273i	−0.826050	−	0.563597i
$22$	−1.81084	−	10.2698i	−0.386073	−	2.18953i
$23$	0.358944	+	0.427773i	0.0748450	+	0.0891968i	0.802168	−	0.597099i	$-0.203680\pi$
$23$	0.358944	+	0.427773i	0.0748450	+	0.0891968i	−0.727323	+	0.686296i	$0.759236\pi$
$24$	2.25534	−	0.486668i	0.460369	−	0.0993407i
$25$	4.55529	−	1.65799i	0.911057	−	0.331598i
$26$	12.3252			2.41718
$27$	3.09302	+	4.17531i	0.595252	+	0.803539i
$28$	−5.57303	−	4.12109i	−1.05320	−	0.778812i
$29$	1.73522	+	4.76747i	0.322222	+	0.885298i	0.990016	+	0.140952i	$0.0450163\pi$
$29$	1.73522	+	4.76747i	0.322222	+	0.885298i	−0.667794	+	0.744346i	$0.732761\pi$
$30$	0.444781	−	1.38341i	0.0812056	−	0.252575i
$31$	2.14159	+	2.55225i	0.384641	+	0.458398i	0.923273	−	0.384143i	$-0.125503\pi$
$31$	2.14159	+	2.55225i	0.384641	+	0.458398i	−0.538632	+	0.842541i	$0.681059\pi$
$32$	−7.65380	+	1.34957i	−1.35301	+	0.238573i
$33$	7.11282	−	4.47517i	1.23818	−	0.779027i
$34$	−9.86858	+	11.7609i	−1.69245	+	2.01698i
$35$	−0.946953	+	0.412105i	−0.160064	+	0.0696584i
$36$	4.43500	+	6.48838i	0.739166	+	1.08140i
$37$	−1.07348	−	1.85933i	−0.176479	−	0.305671i	0.764193	−	0.644988i	$-0.223138\pi$
$37$	−1.07348	−	1.85933i	−0.176479	−	0.305671i	−0.940672	+	0.339317i	$0.889804\pi$
$38$	−0.171817	+	0.974420i	−0.0278723	+	0.158072i
$39$	3.74909	+	9.19747i	0.600334	+	1.47277i
$40$	0.177839	−	0.488609i	0.0281188	−	0.0772558i
$41$	0.917771	+	0.334041i	0.143332	+	0.0521685i	0.412690	−	0.910872i	$-0.364589\pi$
$41$	0.917771	+	0.334041i	0.143332	+	0.0521685i	−0.269358	+	0.963040i	$0.586812\pi$
$42$	2.43367	−	9.54423i	0.375523	−	1.47271i
$43$	1.16047	−	6.58138i	0.176971	−	1.00365i	−0.758874	−	0.651238i	$-0.774250\pi$
$43$	1.16047	−	6.58138i	0.176971	−	1.00365i	0.935845	−	0.352413i	$-0.114639\pi$
$44$	11.0076	−	6.35525i	1.65946	−	0.958090i
$45$	1.16764	−	0.0888961i	0.174061	−	0.0132519i
$46$	−0.600121	+	1.03944i	−0.0884830	+	0.153257i
$47$	−2.83834	−	2.38165i	−0.414014	−	0.347399i	0.411867	−	0.911244i	$-0.364877\pi$
$47$	−2.83834	−	2.38165i	−0.414014	−	0.347399i	−0.825880	+	0.563845i	$0.809321\pi$
$48$	−2.19191	−	3.48382i	−0.316376	−	0.502846i
$49$	−6.23502	+	3.18190i	−0.890718	+	0.454557i
$50$	6.69741	+	7.98167i	0.947157	+	1.12878i
$51$	−11.7782	−	3.78680i	−1.64927	−	0.530258i
$52$	5.13806	+	14.1167i	0.712521	+	1.95763i
$53$		−	3.13310i		−	0.430364i	−0.976574	−	0.215182i	$-0.930966\pi$
$53$		−	3.13310i		−	0.430364i	0.976574	−	0.215182i	$-0.0690345\pi$
$54$	−6.15929	+	9.31647i	−0.838173	+	1.26781i
$55$		−	1.89384i		−	0.255365i
$56$	0.999904	−	3.37956i	0.133618	−	0.451613i
$57$	−0.779405	+	0.168184i	−0.103235	+	0.0222765i
$58$	−8.35346	+	7.00938i	−1.09686	+	0.920377i
$59$	−0.715255	−	4.05641i	−0.0931183	−	0.528100i	−0.995308	−	0.0967600i	$-0.969152\pi$
$59$	−0.715255	−	4.05641i	−0.0931183	−	0.528100i	0.902189	−	0.431340i	$-0.141959\pi$
$60$	1.76991	−	0.0672771i	0.228494	−	0.00868544i
$61$	7.89549	−	9.40948i	1.01091	−	1.20476i	0.0322101	−	0.999481i	$-0.489745\pi$
$61$	7.89549	−	9.40948i	1.01091	−	1.20476i	0.978704	−	0.205279i	$-0.0658101\pi$
$62$	−3.58054	+	6.20168i	−0.454730	+	0.787615i
$63$	7.86246	−	1.08708i	0.990577	−	0.136959i
$64$	−5.97591	−	10.3506i	−0.746989	−	1.29382i
$65$	2.20434	+	0.388685i	0.273415	+	0.0482104i
$66$	14.2675	+	11.0762i	1.75621	+	1.36339i
$67$	6.30401	+	2.29447i	0.770158	+	0.280314i	0.697062	−	0.717011i	$-0.254490\pi$
$67$	6.30401	+	2.29447i	0.770158	+	0.280314i	0.0730953	+	0.997325i	$0.476712\pi$
$68$	−17.5843	−	6.40016i	−2.13241	−	0.776133i
$69$	−0.958206	−	0.131652i	−0.115354	−	0.0158491i
$70$	−1.52847	−	1.60965i	−0.182688	−	0.192390i
$71$	6.08593	−	3.51371i	0.722267	−	0.417001i	−0.0933194	−	0.995636i	$-0.529748\pi$
$71$	6.08593	−	3.51371i	0.722267	−	0.417001i	0.815587	+	0.578635i	$0.196414\pi$
$72$	−2.32894	+	3.24749i	−0.274469	+	0.382720i
$73$	−6.55906	−	3.78687i	−0.767680	−	0.443220i	0.0643665	−	0.997926i	$-0.479497\pi$
$73$	−6.55906	−	3.78687i	−0.767680	−	0.443220i	−0.832046	+	0.554706i	$0.812831\pi$
$74$	2.96621	−	3.53499i	0.344815	−	0.410935i
$75$	−3.91895	+	7.42567i	−0.452521	+	0.857443i
$76$	−1.18768	+	0.209419i	−0.136236	+	0.0240221i
$77$	−0.787728	−	12.8124i	−0.0897700	−	1.46011i
$78$	−15.8205	+	14.3335i	−1.79131	+	1.62295i
$79$	−0.818714	+	0.297987i	−0.0921125	+	0.0335262i	−0.387665	−	0.921800i	$-0.626718\pi$
$79$	−0.818714	+	0.297987i	−0.0921125	+	0.0335262i	0.295553	+	0.955326i	$0.404496\pi$
$80$	−0.927591			−0.103708
$81$	−8.82576	−	1.76237i	−0.980640	−	0.195819i
$82$			2.09922i			0.231820i
$83$	6.78293	−	2.46878i	0.744523	−	0.270984i	0.0582238	−	0.998304i	$-0.481456\pi$
$83$	6.78293	−	2.46878i	0.744523	−	0.270984i	0.686299	+	0.727319i	$0.259234\pi$
$84$	11.9460	−	1.19133i	1.30341	−	0.129985i
$85$	−2.13586	+	1.79220i	−0.231667	+	0.194391i
$86$	14.1458	−	2.49428i	1.52538	−	0.268965i
$87$	−7.77156	−	4.10149i	−0.833199	−	0.439726i
$88$	4.95095	+	4.15434i	0.527773	+	0.442854i
$89$	2.65800	−	4.60379i	0.281748	−	0.488001i	−0.690068	−	0.723745i	$-0.742419\pi$
$89$	2.65800	−	4.60379i	0.281748	−	0.488001i	0.971815	+	0.235744i	$0.0757526\pi$
$90$	1.03791	+	2.29297i	0.109405	+	0.241701i
$91$	15.0747	+	1.71270i	1.58026	+	0.179539i
$92$	−1.44070	−	0.254033i	−0.150203	−	0.0264848i
$93$	−5.71701	−	0.785485i	−0.592826	−	0.0814510i
$94$	2.72378	−	7.48351i	0.280936	−	0.771865i
$95$	−0.0614580	+	0.168854i	−0.00630546	+	0.0173241i
$96$	8.25481	−	10.6332i	0.842503	−	1.08524i
$97$	10.7873	+	1.90209i	1.09528	+	0.193128i	0.691964	−	0.721932i	$-0.256746\pi$
$97$	10.7873	+	1.90209i	1.09528	+	0.193128i	0.403318	+	0.915060i	$0.367857\pi$
$98$	−11.0101	−	10.2540i	−1.11219	−	1.03581i
$99$	−3.92554	+	14.0160i	−0.394532	+	1.40866i
$100$	−6.34982	+	10.9982i	−0.634982	+	1.09982i
$101$	−10.5964	−	8.89141i	−1.05438	−	0.884728i	−0.0608307	−	0.998148i	$-0.519375\pi$
$101$	−10.5964	−	8.89141i	−1.05438	−	0.884728i	−0.993547	+	0.113420i	$0.963819\pi$
$102$	−1.01007	−	26.5726i	−0.100012	−	2.63108i
$103$	−12.0281	+	2.12089i	−1.18517	+	0.208977i	−0.731277	−	0.682080i	$-0.761075\pi$
$103$	−12.0281	+	2.12089i	−1.18517	+	0.208977i	−0.453890	+	0.891058i	$0.649964\pi$
$104$	−5.85159	+	4.91006i	−0.573795	+	0.481471i
$105$	0.736239	−	1.63022i	0.0718496	−	0.159093i
$106$	6.32804	−	2.30322i	0.614634	−	0.223708i
$107$			5.57017i			0.538489i	0.963072	+	0.269244i	$0.0867739\pi$
$107$			5.57017i			0.538489i	−0.963072	+	0.269244i	$0.913226\pi$
$108$	−13.2383	−	3.17075i	−1.27385	−	0.305106i
$109$	−3.73204			−0.357464			−0.178732	−	0.983898i	$-0.557200\pi$
$109$	−3.73204			−0.357464			−0.178732	+	0.983898i	$0.557200\pi$
$110$	3.82506	−	1.39221i	0.364705	−	0.132742i
$111$	3.54018	+	1.13820i	0.336019	+	0.108034i
$112$	−6.27545	+	0.385825i	−0.592974	+	0.0364570i
$113$	−9.56433	+	1.68645i	−0.899737	+	0.158648i	−0.604340	−	0.796727i	$-0.706563\pi$
$113$	−9.56433	+	1.68645i	−0.899737	+	0.158648i	−0.295397	+	0.955375i	$0.595452\pi$
$114$	−0.912648	−	1.45056i	−0.0854773	−	0.135857i
$115$	−0.140110	+	0.166976i	−0.0130653	+	0.0155706i
$116$	−11.5105	−	6.64560i	−1.06872	−	0.617028i
$117$	−15.5083	−	7.44575i	−1.43375	−	0.688360i
$118$	7.66710	−	4.42660i	0.705814	−	0.407502i
$119$	−13.7043	+	13.0132i	−1.25627	+	1.19292i
$120$	0.339950	+	0.833984i	0.0310330	+	0.0761320i
$121$	11.7835	+	4.28886i	1.07123	+	0.389896i
$122$	24.8089	+	9.02969i	2.24609	+	0.817510i
$123$	−1.56650	+	0.638540i	−0.141247	+	0.0575752i
$124$	−8.59572	−	1.51566i	−0.771919	−	0.136110i
$125$	1.92196	+	3.32893i	0.171905	+	0.297748i
$126$	7.97551	+	15.0810i	0.710515	+	1.34352i
$127$	5.60501	−	9.70817i	0.497365	−	0.861461i	−0.502631	−	0.864501i	$-0.667634\pi$
$127$	5.60501	−	9.70817i	0.497365	−	0.861461i	0.999995	+	0.00304049i	$0.000967819\pi$
$128$	6.52112	−	7.77157i	0.576391	−	0.686916i
$129$	6.16416	+	9.79729i	0.542724	+	0.862603i
$130$	0.835425	+	4.73793i	0.0732716	+	0.415544i
$131$	−16.2722	+	13.6540i	−1.42171	+	1.19296i	−0.471295	+	0.881976i	$0.656213\pi$
$131$	−16.2722	+	13.6540i	−1.42171	+	1.19296i	−0.950416	+	0.310982i	$0.899342\pi$
$132$	−6.73842	+	20.9586i	−0.586504	+	1.82422i
$133$	−0.345549	+	1.16792i	−0.0299629	+	0.101271i
$134$			14.4192i			1.24563i
$135$	−1.39538	+	1.47199i	−0.120095	+	0.126689i
$136$		−	9.51505i		−	0.815909i
$137$	−0.365575	−	1.00441i	−0.0312332	−	0.0858125i	0.923096	−	0.384570i	$-0.125650\pi$
$137$	−0.365575	−	1.00441i	−0.0312332	−	0.0858125i	−0.954329	+	0.298757i	$0.903428\pi$
$138$	−0.438498	−	2.03211i	−0.0373274	−	0.172984i
$139$	−3.73504	−	4.45125i	−0.316802	−	0.377550i	0.584020	−	0.811740i	$-0.301479\pi$
$139$	−3.73504	−	4.45125i	−0.316802	−	0.377550i	−0.900821	+	0.434190i	$0.857035\pi$
$140$	1.20643	−	2.42165i	0.101962	−	0.204667i
$141$	6.41294	−	0.243766i	0.540067	−	0.0205288i
$142$	11.5707	+	9.70898i	0.970993	+	0.814760i
$143$	−13.9110	+	24.0945i	−1.16329	+	2.01488i
$144$	6.86496	+	1.92271i	0.572080	+	0.160226i
$145$	−1.71504	+	0.990180i	−0.142427	+	0.0822300i
$146$	2.82677	−	16.0314i	0.233945	−	1.32677i
$147$	4.30282	−	11.3352i	0.354890	−	0.934908i
$148$	5.28533	+	1.92370i	0.434452	+	0.158127i
$149$	0.464232	−	1.27547i	0.0380314	−	0.104490i	−0.919223	−	0.393736i	$-0.871182\pi$
$149$	0.464232	−	1.27547i	0.0380314	−	0.104490i	0.957255	+	0.289246i	$0.0934045\pi$
$150$	−17.8788	−	2.45645i	−1.45980	−	0.200569i
$151$	−2.48969	+	14.1197i	−0.202608	+	1.14905i	0.698552	+	0.715559i	$0.253828\pi$
$151$	−2.48969	+	14.1197i	−0.202608	+	1.14905i	−0.901160	+	0.433487i	$0.857283\pi$
$152$	−0.306612	−	0.531067i	−0.0248695	−	0.0430752i
$153$	19.5220	−	8.83658i	1.57826	−	0.714395i
$154$	25.2987	−	11.0097i	2.03863	−	0.887190i
$155$	−0.835946	+	0.996242i	−0.0671448	+	0.0800201i
$156$	−23.0119	−	12.1447i	−1.84243	−	0.972354i
$157$	−1.93067	+	0.340430i	−0.154085	+	0.0271693i	−0.250158	−	0.968205i	$-0.580483\pi$
$157$	−1.93067	+	0.340430i	−0.154085	+	0.0271693i	0.0960737	+	0.995374i	$0.469372\pi$
$158$	−1.20371	−	1.43453i	−0.0957624	−	0.114125i
$159$	3.64359	+	4.02158i	0.288956	+	0.318932i
$160$	−1.03757	−	2.85071i	−0.0820274	−	0.225369i
$161$	−0.878434	+	1.18792i	−0.0692303	+	0.0936216i
$162$	−2.92851	−	19.1213i	−0.230086	−	1.50231i
$163$	14.8246			1.16115			0.580575	−	0.814207i	$-0.302828\pi$
$163$	14.8246			1.16115			0.580575	+	0.814207i	$0.302828\pi$
$164$	−2.40434	+	0.875109i	−0.187748	+	0.0683345i
$165$	2.20241	+	2.43089i	0.171458	+	0.189245i
$166$	9.97260	+	11.8849i	0.774024	+	0.922446i
$167$	−0.656828	−	3.72506i	−0.0508269	−	0.288254i	0.948791	−	0.315905i	$-0.102308\pi$
$167$	−0.656828	−	3.72506i	−0.0508269	−	0.288254i	−0.999618	+	0.0276516i	$0.991197\pi$
$168$	2.64676	+	5.50077i	0.204202	+	0.424393i
$169$	−15.2313	−	12.7806i	−1.17164	−	0.983121i
$170$	−5.18990	−	2.99639i	−0.398048	−	0.229813i
$171$	0.804842	−	1.12228i	0.0615478	−	0.0858225i
$172$	8.75381	+	15.1620i	0.667472	+	1.15609i
$173$	2.67149	−	15.1508i	0.203110	−	1.15189i	−0.697277	−	0.716802i	$-0.745605\pi$
$173$	2.67149	−	15.1508i	0.203110	−	1.15189i	0.900387	−	0.435090i	$-0.143284\pi$
$174$	2.57088	−	18.7116i	0.194898	−	1.41853i
$175$	7.08234	+	10.6929i	0.535375	+	0.808305i
$176$	3.94337	−	10.8343i	0.297243	−	0.816669i
$177$	5.63544	+	4.37494i	0.423585	+	0.328841i
$178$	11.2524	+	1.98411i	0.843405	+	0.148715i
$179$	14.0113	−	8.08943i	1.04725	−	0.604632i	0.125374	−	0.992109i	$-0.459987\pi$
$179$	14.0113	−	8.08943i	1.04725	−	0.604632i	0.921879	+	0.387477i	$0.126653\pi$
$180$	−2.19358	+	2.14464i	−0.163500	+	0.159852i
$181$	15.8886	+	9.17326i	1.18099	+	0.681843i	0.956243	−	0.292575i	$-0.0945121\pi$
$181$	15.8886	+	9.17326i	1.18099	+	0.681843i	0.224744	+	0.974418i	$0.427845\pi$
$182$	7.62262	+	31.7061i	0.565027	+	2.35021i
$183$	0.808119	+	21.2598i	0.0597379	+	1.57157i
$184$	−0.129170	−	0.732562i	−0.00952257	−	0.0540052i
$185$	0.641978	−	0.538684i	0.0471992	−	0.0396048i
$186$	−2.61624	−	12.1243i	−0.191832	−	0.888997i
$187$	−11.8531	−	32.5660i	−0.866781	−	2.38146i
$188$	9.70670			0.707934
$189$	−8.82790	+	10.5389i	−0.642135	+	0.766592i
$190$	−0.386222			−0.0280195
$191$	−6.87241	−	18.8818i	−0.497270	−	1.36624i	−0.893903	−	0.448261i	$-0.852044\pi$
$191$	−6.87241	−	18.8818i	−0.497270	−	1.36624i	0.396633	−	0.917977i	$-0.370179\pi$
$192$	19.7076	+	6.33621i	1.42228	+	0.457277i
$193$	−16.4758	+	13.8249i	−1.18596	+	0.995136i	−0.186037	+	0.982543i	$0.559564\pi$
$193$	−16.4758	+	13.8249i	−1.18596	+	0.995136i	−0.999921	+	0.0125936i	$0.995991\pi$
$194$	4.08827	+	23.1858i	0.293521	+	1.66464i
$195$	−3.28147	+	2.06460i	−0.234991	+	0.147849i
$196$	7.15462	−	16.8851i	0.511044	−	1.20608i
$197$	2.96839	+	1.71380i	0.211489	+	0.122103i	0.602003	−	0.798494i	$-0.294369\pi$
$197$	2.96839	+	1.71380i	0.211489	+	0.122103i	−0.390514	+	0.920597i	$0.627703\pi$
$198$	−31.1944	+	2.37494i	−2.21689	+	0.168779i
$199$	−9.32690	+	5.38489i	−0.661166	+	0.381725i	−0.792721	−	0.609584i	$-0.791336\pi$
$199$	−9.32690	+	5.38489i	−0.661166	+	0.381725i	0.131555	+	0.991309i	$0.458003\pi$
$200$	−6.35938	−	1.12133i	−0.449676	−	0.0792901i
$201$	−10.7600	+	4.38602i	−0.758954	+	0.309366i
$202$	10.1687	−	27.9382i	0.715466	−	1.96573i
$203$	−11.1909	+	7.41224i	−0.785450	+	0.520237i
$204$	30.0138	−	12.2343i	2.10139	−	0.856571i
$205$	−0.0662004	+	0.375441i	−0.00462364	+	0.0262219i
$206$	−13.1258	−	22.7346i	−0.914520	−	1.58399i
$207$	1.38304	−	0.945346i	0.0961278	−	0.0657061i
$208$	11.8014	+	6.81351i	0.818276	+	0.472432i
$209$	−1.71096	−	1.43567i	−0.118350	−	0.0993072i
$210$	3.83384	+	0.288600i	0.264560	+	0.0199153i
$211$	0.0518221	+	0.293898i	0.00356758	+	0.0202327i	0.986540	−	0.163523i	$-0.0522857\pi$
$211$	0.0518221	+	0.293898i	0.00356758	+	0.0202327i	−0.982972	+	0.183755i	$0.941175\pi$
$212$	5.27598	+	6.28767i	0.362356	+	0.431839i
$213$	−3.72556	+	11.5877i	−0.255271	+	0.793975i
$214$	−11.2503	+	4.09477i	−0.769054	+	0.279913i
$215$	2.60860			0.177905
$216$	−0.787234	−	6.87683i	−0.0535645	−	0.467909i
$217$	−5.24106	+	7.08760i	−0.355786	+	0.481138i
$218$	−2.74352	−	7.53775i	−0.185814	−	0.510521i
$219$	12.8230	−	2.76701i	0.866496	−	0.186977i
$220$	3.18913	+	3.80065i	0.215011	+	0.256240i
$221$	40.3380	−	7.11269i	2.71343	−	0.478451i
$222$	0.303598	+	7.98696i	0.0203761	+	0.536050i
$223$	−1.84202	+	2.19524i	−0.123351	+	0.147004i	−0.824185	−	0.566320i	$-0.808367\pi$
$223$	−1.84202	+	2.19524i	−0.123351	+	0.147004i	0.700835	+	0.713324i	$0.252811\pi$
$224$	−8.20525	−	18.8544i	−0.548236	−	1.25976i
$225$	−3.60529	−	14.0889i	−0.240353	−	0.939262i
$226$	−10.4372	−	18.0777i	−0.694270	−	1.20251i
$227$	4.81038	−	27.2810i	0.319276	−	1.81070i	−0.227897	−	0.973685i	$-0.573185\pi$
$227$	4.81038	−	27.2810i	0.319276	−	1.81070i	0.547173	−	0.837019i	$-0.315704\pi$
$228$	1.28094	−	1.65000i	0.0848322	−	0.109274i
$229$	−8.06759	+	22.1655i	−0.533121	+	1.46474i	0.322216	+	0.946666i	$0.395572\pi$
$229$	−8.06759	+	22.1655i	−0.533121	+	1.46474i	−0.855337	+	0.518072i	$0.826650\pi$
$230$	−0.440247	−	0.160237i	−0.0290290	−	0.0105657i
$231$	15.9111	+	15.5297i	1.04688	+	1.02178i
$232$	1.17356	−	6.65561i	0.0770482	−	0.436962i
$233$	7.45007	−	4.30130i	0.488070	−	0.281787i	−0.235703	−	0.971825i	$-0.575739\pi$
$233$	7.45007	−	4.30130i	0.488070	−	0.281787i	0.723774	+	0.690038i	$0.242406\pi$
$234$	3.63792	−	36.7963i	0.237818	−	2.40545i
$235$	0.723139	−	1.25251i	0.0471724	−	0.0817049i
$236$	8.26621	+	6.93617i	0.538084	+	0.451506i
$237$	0.704345	−	1.33460i	0.0457521	−	0.0866918i
$238$	−36.3577	−	18.1128i	−2.35672	−	1.17408i
$239$	8.52364	+	10.1581i	0.551348	+	0.657071i	0.967692	−	0.252136i	$-0.0811331\pi$
$239$	8.52364	+	10.1581i	0.551348	+	0.657071i	−0.416344	+	0.909207i	$0.636689\pi$
$240$	1.19064	−	1.07873i	0.0768554	−	0.0696317i
$241$	3.73945	+	10.2740i	0.240879	+	0.661809i	0.999942	+	0.0107919i	$0.00343525\pi$
$241$	3.73945	+	10.2740i	0.240879	+	0.661809i	−0.759063	+	0.651017i	$0.774343\pi$
$242$			26.9525i			1.73258i
$243$	13.3781	−	8.00165i	0.858206	−	0.513306i
$244$			32.1790i			2.06005i
$245$	−1.64577	−	2.18112i	−0.105144	−	0.139347i
$246$	−2.44126	−	2.69452i	−0.155649	−	0.171796i
$247$	2.02220	−	1.69683i	0.128670	−	0.107967i
$248$	−0.770678	−	4.37073i	−0.0489381	−	0.277542i
$249$	−5.83540	+	11.0570i	−0.369803	+	0.700708i
$250$	−5.31069	+	6.32903i	−0.335877	+	0.400283i
$251$	−5.12956	+	8.88466i	−0.323775	+	0.560795i	−0.981264	−	0.192670i	$-0.938285\pi$
$251$	−5.12956	+	8.88466i	−0.323775	+	0.560795i	0.657489	+	0.753464i	$0.271619\pi$
$252$	−13.9482	+	15.4216i	−0.878655	+	0.971469i
$253$	−1.35466	−	2.34634i	−0.0851667	−	0.147513i
$254$	23.7284	+	4.18395i	1.48885	+	0.262524i
$255$	0.657337	−	4.78430i	0.0411640	−	0.299605i
$256$	−1.97169	−	0.717638i	−0.123231	−	0.0448524i
$257$	1.27159	+	0.462822i	0.0793198	+	0.0288700i	0.381375	−	0.924420i	$-0.375451\pi$
$257$	1.27159	+	0.462822i	0.0793198	+	0.0288700i	−0.302055	+	0.953290i	$0.597673\pi$
$258$	−15.2566	+	19.6522i	−0.949831	+	1.22349i
$259$	4.11913	−	3.91139i	0.255950	−	0.243042i
$260$	−5.07832	+	2.93197i	−0.314944	+	0.181833i
$261$	14.7452	−	3.77323i	0.912705	−	0.233557i
$262$	−39.5397	−	22.8283i	−2.44277	−	1.41033i
$263$	4.58008	−	5.45832i	0.282420	−	0.336575i	−0.606121	−	0.795372i	$-0.707275\pi$
$263$	4.58008	−	5.45832i	0.282420	−	0.336575i	0.888541	+	0.458798i	$0.151720\pi$
$264$	−11.1862	+	0.425206i	−0.688462	+	0.0261696i
$265$	1.20439	−	0.212366i	0.0739851	−	0.0130456i
$266$	−2.61291	+	0.160646i	−0.160208	+	0.00984984i
$267$	1.94216	+	9.00042i	0.118858	+	0.550817i
$268$	−16.5150	+	6.01097i	−1.00881	+	0.367178i
$269$	−6.69363			−0.408118			−0.204059	−	0.978959i	$-0.565413\pi$
$269$	−6.69363			−0.408118			−0.204059	+	0.978959i	$0.565413\pi$
$270$	−3.99882	−	1.73620i	−0.243360	−	0.105662i
$271$			15.0044i			0.911450i	0.890121	+	0.455725i	$0.150620\pi$
$271$			15.0044i			0.911450i	−0.890121	+	0.455725i	$0.849380\pi$
$272$	−15.9506	+	5.80556i	−0.967150	+	0.352014i
$273$	−21.3414	+	15.3326i	−1.29164	+	0.927970i
$274$	1.75990	−	1.47673i	0.106320	−	0.0892128i
$275$	−23.1624	+	4.08415i	−1.39674	+	0.246283i
$276$	2.14467	−	1.34936i	0.129094	−	0.0812222i
$277$	−19.7269	−	16.5529i	−1.18528	−	0.994566i	−0.999929	−	0.0118925i	$-0.996214\pi$
$277$	−19.7269	−	16.5529i	−1.18528	−	0.994566i	−0.185348	−	0.982673i	$-0.559341\pi$
$278$	6.24464	−	10.8160i	0.374529	−	0.648703i
$279$	8.25171	−	5.64028i	0.494017	−	0.337675i
$280$	1.36691	+	0.155299i	0.0816884	+	0.00928092i
$281$	−7.95320	−	1.40236i	−0.474448	−	0.0836580i	−0.0686892	−	0.997638i	$-0.521882\pi$
$281$	−7.95320	−	1.40236i	−0.474448	−	0.0836580i	−0.405759	+	0.913980i	$0.632993\pi$
$282$	5.20666	+	12.7733i	0.310052	+	0.760637i
$283$	2.15839	−	5.93013i	0.128303	−	0.352510i	−0.858863	−	0.512205i	$-0.828829\pi$
$283$	2.15839	−	5.93013i	0.128303	−	0.352510i	0.987166	+	0.159695i	$0.0510511\pi$
$284$	−6.29665	+	17.2999i	−0.373638	+	1.02656i
$285$	−0.117481	−	0.288210i	−0.00695895	−	0.0170721i
$286$	−58.8909	−	10.3841i	−3.48229	−	0.614022i
$287$	−0.291705	+	2.56751i	−0.0172188	+	0.151556i
$288$	1.76997	+	23.2483i	0.104297	+	1.36992i
$289$	−17.0108	+	29.4636i	−1.00064	+	1.73316i
$290$	−3.26068	−	2.73603i	−0.191474	−	0.160665i
$291$	−16.0583	+	10.1034i	−0.941357	+	0.592273i
$292$	19.5400	−	3.44542i	1.14349	−	0.201628i
$293$	6.25563	−	5.24910i	0.365458	−	0.306656i	−0.441504	−	0.897259i	$-0.645555\pi$
$293$	6.25563	−	5.24910i	0.365458	−	0.306656i	0.806962	+	0.590604i	$0.201110\pi$
$294$	26.0572	+	0.357809i	1.51969	+	0.0208678i
$295$	1.51084	−	0.549900i	0.0879644	−	0.0320164i
$296$			2.85995i			0.166231i
$297$	−11.2610	−	22.5558i	−0.653427	−	1.30882i
$298$	2.91738			0.168999
$299$	3.00906	−	1.09521i	0.174018	−	0.0633375i
$300$	−4.63971	−	21.5015i	−0.267874	−	1.24139i
$301$	17.6480	−	1.08503i	1.01721	−	0.0625399i
$302$	−30.3484	+	5.35124i	−1.74635	+	0.307929i
$303$	23.9414	−	0.910054i	1.37540	−	0.0522812i
$304$	−0.703182	+	0.838020i	−0.0403303	+	0.0480637i
$305$	4.15225	+	2.39730i	0.237757	+	0.137269i
$306$	32.1987	+	32.9335i	1.84068	+	1.88268i
$307$	−20.0345	+	11.5669i	−1.14343	+	0.660159i	−0.947277	−	0.320415i	$-0.896178\pi$
$307$	−20.0345	+	11.5669i	−1.14343	+	0.660159i	−0.196151	+	0.980574i	$0.562844\pi$
$308$	23.1563	+	24.3861i	1.31945	+	1.38953i
$309$	12.9726	−	16.7103i	0.737987	−	0.950615i
$310$	−2.62668	−	0.956032i	−0.149185	−	0.0542990i
$311$	22.1526	+	8.06290i	1.25616	+	0.457205i	0.882479	−	0.470352i	$-0.155873\pi$
$311$	22.1526	+	8.06290i	1.25616	+	0.457205i	0.373682	+	0.927557i	$0.378095\pi$
$312$	1.80090	−	13.1075i	0.101956	−	0.742065i
$313$	11.7748	+	2.07621i	0.665550	+	0.117354i	0.496209	−	0.868203i	$-0.334725\pi$
$313$	11.7748	+	2.07621i	0.665550	+	0.117354i	0.169341	+	0.985557i	$0.445836\pi$
$314$	−2.10687	−	3.64920i	−0.118897	−	0.205936i
$315$	0.950813	+	2.94871i	0.0535723	+	0.166141i
$316$	1.14124	−	1.97669i	0.0641999	−	0.111197i
$317$	−18.1039	+	21.5754i	−1.01682	+	1.21179i	−0.0396733	+	0.999213i	$0.512632\pi$
$317$	−18.1039	+	21.5754i	−1.01682	+	1.21179i	−0.977143	+	0.212582i	$0.931813\pi$
$318$	−5.44406	+	10.3155i	−0.305288	+	0.578463i
$319$	−4.27439	−	24.2413i	−0.239320	−	1.35725i
$320$	3.57380	−	2.99877i	0.199781	−	0.167636i
$321$	−6.47775	−	7.14976i	−0.361553	−	0.399061i
$322$	−3.04506	−	0.900935i	−0.169694	−	0.0502071i
$323$			3.28823i			0.182962i
$324$	20.6797	−	11.3253i	1.14887	−	0.629184i
$325$		−	27.7982i		−	1.54196i
$326$	10.8979	+	29.9418i	0.603580	+	1.65832i
$327$	4.79037	−	4.34012i	0.264908	−	0.240009i
$328$	−0.836276	−	0.996635i	−0.0461756	−	0.0550300i
$329$	4.37129	−	8.77443i	0.240997	−	0.483750i
$330$	−3.29073	+	6.23531i	−0.181149	+	0.343243i
$331$	−11.5569	−	9.69739i	−0.635224	−	0.533017i	0.267323	−	0.963607i	$-0.413861\pi$
$331$	−11.5569	−	9.69739i	−0.635224	−	0.533017i	−0.902547	+	0.430590i	$0.858305\pi$
$332$	−9.45503	+	16.3766i	−0.518912	+	0.898782i
$333$	−5.86776	+	2.65602i	−0.321551	+	0.145549i
$334$	7.04080	−	4.06501i	0.385255	−	0.222427i
$335$	−0.454719	+	2.57884i	−0.0248440	+	0.140897i
$336$	7.60636	−	7.79318i	0.414961	−	0.425153i
$337$	−15.3260	−	5.57821i	−0.834860	−	0.303864i	−0.111008	−	0.993819i	$-0.535408\pi$
$337$	−15.3260	−	5.57821i	−0.834860	−	0.303864i	−0.723852	+	0.689955i	$0.757630\pi$
$338$	14.6165	−	40.1586i	0.795034	−	2.18434i
$339$	10.3154	−	13.2874i	0.560253	−	0.721672i
$340$	1.26838	−	7.19337i	0.0687878	−	0.390115i
$341$	−8.08240	−	13.9991i	−0.437687	−	0.758096i
$342$	2.85836	+	0.800559i	0.154563	+	0.0432893i
$343$	−12.0414	−	14.0714i	−0.650173	−	0.759786i
$344$	−5.72225	+	6.81951i	−0.308523	+	0.367683i
$345$	−0.0143405	−	0.377266i	−0.000772067	−	0.0203113i
$346$	32.5645	−	5.74200i	1.75068	−	0.308692i
$347$	−23.3846	−	27.8687i	−1.25535	−	1.49607i	−0.792802	−	0.609480i	$-0.791378\pi$
$347$	−23.3846	−	27.8687i	−1.25535	−	1.49607i	−0.462552	−	0.886592i	$-0.653066\pi$
$348$	22.5031	−	4.85583i	1.20629	−	0.260300i
$349$	2.98415	+	8.19888i	0.159738	+	0.438876i	0.993581	−	0.113126i	$-0.0360863\pi$
$349$	2.98415	+	8.19888i	0.159738	+	0.438876i	−0.833843	+	0.552002i	$0.813864\pi$
$350$	−16.3904	+	22.1651i	−0.876104	+	1.18477i
$351$	28.5651	−	8.47796i	1.52469	−	0.452520i
$352$	37.7074			2.00981
$353$	−8.54968	+	3.11183i	−0.455053	+	0.165626i	−0.559370	−	0.828918i	$-0.688957\pi$
$353$	−8.54968	+	3.11183i	−0.455053	+	0.165626i	0.104316	+	0.994544i	$0.466735\pi$
$354$	−4.69349	+	14.5982i	−0.249456	+	0.775888i
$355$	1.76322	+	2.10132i	0.0935818	+	0.111526i
$356$	2.41834	+	13.7151i	0.128172	+	0.726897i
$357$	2.45709	−	32.6407i	0.130043	−	1.72753i
$358$	26.6386	+	22.3524i	1.40789	+	1.18136i
$359$	−0.444525	−	0.256647i	−0.0234611	−	0.0135453i	0.488224	−	0.872719i	$-0.337645\pi$
$359$	−0.444525	−	0.256647i	−0.0234611	−	0.0135453i	−0.511685	+	0.859173i	$0.670978\pi$
$360$	−1.40622	−	0.675146i	−0.0741145	−	0.0355833i
$361$	−9.39404	−	16.2710i	−0.494423	−	0.856366i
$362$	−6.84752	+	38.8342i	−0.359898	+	2.04108i
$363$	−20.1128	+	8.19841i	−1.05565	+	0.430305i
$364$	−33.1369	+	21.9480i	−1.73685	+	1.15039i
$365$	1.01112	−	2.77804i	0.0529246	−	0.145409i
$366$	−42.3451	+	17.2608i	−2.21342	+	0.902236i
$367$	30.6284	+	5.40061i	1.59879	+	0.281910i	0.900812	−	0.434210i	$-0.142972\pi$
$367$	30.6284	+	5.40061i	1.59879	+	0.281910i	0.697977	+	0.716120i	$0.254084\pi$
$368$	−1.14922	+	0.663505i	−0.0599075	+	0.0345876i
$369$	1.26815	−	2.64136i	0.0660174	−	0.137504i
$370$	1.55994	+	0.900630i	0.0810972	+	0.0468215i
$371$	8.05975	−	1.93768i	0.418441	−	0.100600i
$372$	12.7959	−	8.05080i	0.663437	−	0.417415i
$373$	4.53556	+	25.7224i	0.234842	+	1.33186i	0.842945	+	0.537999i	$0.180820\pi$
$373$	4.53556	+	25.7224i	0.234842	+	1.33186i	−0.608103	+	0.793858i	$0.708069\pi$
$374$	57.0614	−	47.8802i	2.95057	−	2.47583i
$375$	−6.33832	−	2.03783i	−0.327309	−	0.105233i
$376$	1.68809	+	4.63799i	0.0870565	+	0.239186i
$377$	29.0930			1.49837
$378$	−27.7754	−	10.0827i	−1.42861	−	0.518596i
$379$	−28.5024			−1.46407			−0.732035	−	0.681267i	$-0.761429\pi$
$379$	−28.5024			−1.46407			−0.732035	+	0.681267i	$0.761429\pi$
$380$	−0.161005	−	0.442358i	−0.00825940	−	0.0226925i
$381$	4.09549	+	18.9795i	0.209818	+	0.972349i
$382$	33.0842	−	27.7610i	1.69274	−	1.42037i
$383$	−2.37420	−	13.4648i	−0.121316	−	0.688017i	−0.983428	−	0.181299i	$-0.941970\pi$
$383$	−2.37420	−	13.4648i	−0.121316	−	0.688017i	0.862112	−	0.506718i	$-0.169141\pi$
$384$	0.667450	+	17.5591i	0.0340607	+	0.896058i
$385$	4.87181	−	1.17126i	0.248290	−	0.0596927i
$386$	−40.0345	−	23.1139i	−2.03770	−	1.17647i
$387$	−19.3058	−	5.40709i	−0.981370	−	0.274858i
$388$	−24.8515	+	14.3480i	−1.26164	+	0.728410i
$389$	24.7405	+	4.36241i	1.25439	+	0.221183i	0.761073	−	0.648666i	$-0.224673\pi$
$389$	24.7405	+	4.36241i	1.25439	+	0.221183i	0.493318	+	0.869849i	$0.335784\pi$
$390$	−6.58225	−	5.10997i	−0.333305	−	0.258754i
$391$	−1.36423	+	3.74820i	−0.0689922	+	0.189554i
$392$	9.31216	+	0.482094i	0.470335	+	0.0243494i
$393$	5.00797	−	36.4496i	0.252619	−	1.83864i
$394$	−1.27929	+	7.25523i	−0.0644498	+	0.365513i
$395$	−0.170043	−	0.294523i	−0.00855578	−	0.0148190i
$396$	−15.7242	−	34.7385i	−0.790173	−	1.74567i
$397$	6.75634	+	3.90078i	0.339091	+	0.195774i	0.659870	−	0.751380i	$-0.270611\pi$
$397$	6.75634	+	3.90078i	0.339091	+	0.195774i	−0.320779	+	0.947154i	$0.603945\pi$
$398$	−17.7325	−	14.8794i	−0.888851	−	0.745834i
$399$	−0.914672	−	1.90097i	−0.0457909	−	0.0951674i
$400$	2.00039	+	11.3448i	0.100020	+	0.567240i
$401$	0.935778	+	1.11522i	0.0467305	+	0.0556913i	0.788903	−	0.614517i	$-0.210649\pi$
$401$	0.935778	+	1.11522i	0.0467305	+	0.0556913i	−0.742173	+	0.670208i	$0.766205\pi$
$402$	−16.7686	−	18.5082i	−0.836342	−	0.923105i
$403$	17.9532	−	6.53442i	0.894311	−	0.325503i
$404$	36.2380			1.80291
$405$	0.0792456	−	3.51215i	0.00393775	−	0.174520i
$406$	−23.1975	−	17.1539i	−1.15128	−	0.851333i
$407$	3.56269	+	9.78840i	0.176596	+	0.485193i
$408$	11.0654	+	12.2133i	0.547819	+	0.604650i
$409$	−6.16526	−	7.34748i	−0.304853	−	0.363309i	0.591768	−	0.806108i	$-0.298430\pi$
$409$	−6.16526	−	7.34748i	−0.304853	−	0.363309i	−0.896621	+	0.442799i	$0.853986\pi$
$410$	−0.806959	+	0.142289i	−0.0398529	+	0.00702714i
$411$	1.63731	+	0.864101i	0.0807625	+	0.0426229i
$412$	20.5672	−	24.5111i	1.01328	−	1.20757i
$413$	9.99258	−	4.34867i	0.491702	−	0.213984i
$414$	2.92606	+	2.09843i	0.143808	+	0.103132i
$415$	1.40878	+	2.44008i	0.0691543	+	0.119779i
$416$	−7.73895	+	43.8898i	−0.379433	+	2.15187i
$417$	9.97074	+	1.36992i	0.488269	+	0.0670855i
$418$	1.64190	−	4.51109i	0.0803081	−	0.220645i
$419$	−20.7203	−	7.54159i	−1.01225	−	0.368431i	−0.217956	−	0.975959i	$-0.569939\pi$
$419$	−20.7203	−	7.54159i	−1.01225	−	0.368431i	−0.794298	+	0.607528i	$0.792161\pi$
$420$	1.26768	+	4.51139i	0.0618563	+	0.220133i
$421$	−4.79615	+	27.2003i	−0.233750	+	1.32566i	0.611481	+	0.791259i	$0.290574\pi$
$421$	−4.79615	+	27.2003i	−0.233750	+	1.32566i	−0.845230	+	0.534402i	$0.820537\pi$
$422$	−0.555501	+	0.320719i	−0.0270414	+	0.0156123i
$423$	−7.94804	+	7.77073i	−0.386447	+	0.377826i
$424$	−2.08678	+	3.61442i	−0.101343	+	0.175532i
$425$	26.5254	+	22.2574i	1.28667	+	1.07964i
$426$	−26.1429	+	0.993734i	−1.26663	+	0.0481466i
$427$	29.0884	+	14.4914i	1.40769	+	0.701289i
$428$	−9.37988	−	11.1785i	−0.453394	−	0.540334i
$429$	−10.1645	−	47.1048i	−0.490747	−	2.27424i
$430$	1.91765	+	5.26869i	0.0924771	+	0.254079i
$431$		−	13.9378i		−	0.671358i	−0.941976	−	0.335679i	$-0.891034\pi$
$431$		−	13.9378i		−	0.671358i	0.941976	−	0.335679i	$-0.108966\pi$
$432$	−11.0477	+	5.51555i	−0.531534	+	0.265367i
$433$		−	20.8489i		−	1.00193i	−0.865467	−	0.500966i	$-0.832978\pi$
$433$		−	20.8489i		−	1.00193i	0.865467	−	0.500966i	$-0.167022\pi$
$434$	−18.1679	−	5.37531i	−0.872089	−	0.258023i
$435$	1.04988	−	3.26546i	0.0503379	−	0.156567i
$436$	7.48965	−	6.28456i	0.358689	−	0.300976i
$437$	0.0446390	+	0.253160i	0.00213537	+	0.0121103i
$438$	15.0151	+	23.8650i	0.717451	+	1.14031i
$439$	2.39592	−	2.85534i	0.114351	−	0.136278i	−0.705833	−	0.708379i	$-0.749427\pi$
$439$	2.39592	−	2.85534i	0.114351	−	0.136278i	0.820183	+	0.572101i	$0.193871\pi$
$440$	−1.26138	+	2.18478i	−0.0601340	+	0.104155i
$441$	7.65905	+	19.5535i	0.364717	+	0.931119i
$442$	44.0193	+	76.2437i	2.09378	+	3.62654i
$443$	5.16917	+	0.911464i	0.245595	+	0.0433050i	0.295090	−	0.955469i	$-0.404650\pi$
$443$	5.16917	+	0.911464i	0.245595	+	0.0433050i	−0.0494956	+	0.998774i	$0.515761\pi$
$444$	−9.02130	+	3.67727i	−0.428132	+	0.174516i
$445$	1.94990	+	0.709706i	0.0924342	+	0.0336433i
$446$	−5.78792	−	2.10663i	−0.274066	−	0.0997519i
$447$	0.887407	+	2.17704i	0.0419729	+	0.102970i
$448$	22.9305	−	21.7741i	1.08337	−	1.02873i
$449$	−22.4516	+	12.9624i	−1.05956	+	0.611735i	−0.925310	−	0.379212i	$-0.876195\pi$
$449$	−22.4516	+	12.9624i	−1.05956	+	0.611735i	−0.134247	+	0.990948i	$0.542862\pi$
$450$	25.8056	−	17.6389i	1.21649	−	0.831505i
$451$	−4.10375	−	2.36930i	−0.193238	−	0.111566i
$452$	16.3543	−	19.4903i	0.769242	−	0.916747i
$453$	−13.2246	−	21.0191i	−0.621346	−	0.987565i
$454$	58.6368	−	10.3392i	2.75196	−	0.485245i
$455$	0.363415	+	5.91095i	0.0170372	+	0.277110i
$456$	1.01116	+	0.325098i	0.0473518	+	0.0152241i
$457$	19.4951	−	7.09562i	0.911940	−	0.331919i	0.156913	−	0.987612i	$-0.449846\pi$
$457$	19.4951	−	7.09562i	0.911940	−	0.331919i	0.755027	+	0.655693i	$0.227624\pi$
$458$	−50.6993			−2.36902
$459$	−14.7817	+	34.0453i	−0.689952	+	1.58910i
$460$		−	0.571034i		−	0.0266246i
$461$	0.166492	−	0.0605983i	0.00775433	−	0.00282234i	−0.338140	−	0.941096i	$-0.609798\pi$
$461$	0.166492	−	0.0605983i	0.00775433	−	0.00282234i	0.345894	+	0.938273i	$0.387576\pi$
$462$	−19.6693	+	43.5526i	−0.915097	+	2.02625i
$463$	22.1677	−	18.6009i	1.03022	−	0.864457i	0.0393425	−	0.999226i	$-0.487474\pi$
$463$	22.1677	−	18.6009i	1.03022	−	0.864457i	0.990877	+	0.134769i	$0.0430292\pi$
$464$	−11.8732	+	2.09357i	−0.551201	+	0.0971916i
$465$	−0.0855608	−	2.25091i	−0.00396779	−	0.104383i
$466$	14.1642	+	11.8852i	0.656146	+	0.550572i
$467$	−4.43621	+	7.68373i	−0.205283	+	0.355561i	−0.950223	−	0.311571i	$-0.899145\pi$
$467$	−4.43621	+	7.68373i	−0.205283	+	0.355561i	0.744940	+	0.667132i	$0.232478\pi$
$468$	43.6612	−	11.1727i	2.01824	−	0.516459i
$469$	−2.00367	+	17.6358i	−0.0925208	+	0.814346i
$470$	3.06135	+	0.539798i	0.141209	+	0.0248990i
$471$	2.08228	−	2.68222i	0.0959463	−	0.123590i
$472$	−1.87662	+	5.15597i	−0.0863784	+	0.237323i
$473$	−11.0897	+	30.4686i	−0.509903	+	1.40095i
$474$	3.21333	+	0.441494i	0.147593	+	0.0202785i
$475$	2.19769	+	0.387512i	0.100837	+	0.0177803i
$476$	5.58899	−	49.1930i	0.256171	−	2.25476i
$477$	−9.35369	−	0.924766i	−0.428276	−	0.0423421i
$478$	−14.2507	+	24.6830i	−0.651813	+	1.12897i
$479$	4.86205	+	4.07975i	0.222153	+	0.186408i	0.747071	−	0.664744i	$-0.231460\pi$
$479$	4.86205	+	4.07975i	0.222153	+	0.186408i	−0.524918	+	0.851153i	$0.675904\pi$
$480$	4.64700	+	2.45249i	0.212106	+	0.111940i
$481$	−12.1245	+	2.13787i	−0.552828	+	0.0974784i
$482$	−18.0019	+	15.1054i	−0.819966	+	0.688033i
$483$	−0.253939	−	2.54636i	−0.0115546	−	0.115863i
$484$	−30.8701	+	11.2358i	−1.40318	+	0.510717i
$485$			4.27565i			0.194147i
$486$	25.9958	+	21.1381i	1.17920	+	0.958843i
$487$	5.19850			0.235566			0.117783	−	0.993039i	$-0.462421\pi$
$487$	5.19850			0.235566			0.117783	+	0.993039i	$0.462421\pi$
$488$	−15.3756	+	5.59625i	−0.696019	+	0.253330i
$489$	−19.0285	+	17.2400i	−0.860500	+	0.779621i
$490$	3.19546	−	4.92742i	0.144356	−	0.222598i
$491$	−13.4965	+	2.37981i	−0.609091	+	0.107399i	−0.469682	−	0.882836i	$-0.655631\pi$
$491$	−13.4965	+	2.37981i	−0.609091	+	0.107399i	−0.139409	+	0.990235i	$0.544520\pi$
$492$	2.06847	−	3.91937i	0.0932539	−	0.176699i
$493$	−23.2942	+	27.7609i	−1.04912	+	1.25029i
$494$	4.91373	+	2.83694i	0.221079	+	0.127640i
$495$	−5.65395	−	0.558986i	−0.254126	−	0.0251245i
$496$	−6.85670	+	3.95872i	−0.307875	+	0.177752i
$497$	12.8027	+	13.4827i	0.574282	+	0.604781i
$498$	−26.6220	−	3.65772i	−1.19296	−	0.163906i
$499$	−32.4000	−	11.7926i	−1.45042	−	0.527911i	−0.507714	−	0.861526i	$-0.669509\pi$
$499$	−32.4000	−	11.7926i	−1.45042	−	0.527911i	−0.942709	+	0.333615i	$0.891732\pi$
$500$	−9.46283	−	3.44419i	−0.423191	−	0.154029i
$501$	5.17510	+	4.01757i	0.231206	+	0.179492i
$502$	−21.7156	−	3.82904i	−0.969213	−	0.170898i
$503$	19.0162	+	32.9370i	0.847891	+	1.46859i	0.883087	+	0.469209i	$0.155461\pi$
$503$	19.0162	+	32.9370i	0.847891	+	1.46859i	−0.0351966	+	0.999380i	$0.511206\pi$
$504$	−9.79437	−	3.98267i	−0.436276	−	0.177402i
$505$	2.69969	−	4.67601i	0.120135	−	0.208080i
$506$	3.74315	−	4.46092i	0.166403	−	0.198312i
$507$	34.4136	−	1.30812i	1.52836	−	0.0580955i
$508$	5.09963	+	28.9214i	0.226259	+	1.28318i
$509$	−2.43971	+	2.04716i	−0.108138	+	0.0907387i	−0.695254	−	0.718765i	$-0.744708\pi$
$509$	−2.43971	+	2.04716i	−0.108138	+	0.0907387i	0.587115	+	0.809503i	$0.300263\pi$
$510$	10.1463	−	2.18941i	0.449285	−	0.0969489i
$511$	5.68507	−	19.2149i	0.251492	−	0.850016i
$512$		−	24.8000i		−	1.09601i
$513$	0.272054	+	2.37651i	0.0120115	+	0.104926i
$514$			2.90852i			0.128289i
$515$	−1.63057	−	4.47996i	−0.0718516	−	0.197411i
$516$	−28.8687	−	9.28159i	−1.27087	−	0.408599i
$517$	11.5552	+	13.7710i	0.508198	+	0.605647i
$518$	10.9281	+	5.44420i	0.480152	+	0.239204i
$519$	14.1903	+	22.5540i	0.622885	+	0.990011i
$520$	−2.28410	−	1.91659i	−0.100164	−	0.0840479i
$521$	13.0875	−	22.6683i	0.573375	−	0.993115i	−0.422841	−	0.906204i	$-0.638967\pi$
$521$	13.0875	−	22.6683i	0.573375	−	0.993115i	0.996216	−	0.0869113i	$-0.0276997\pi$
$522$	18.4605	+	27.0077i	0.807995	+	1.18209i
$523$	14.0356	−	8.10349i	0.613736	−	0.354341i	−0.160690	−	0.987005i	$-0.551372\pi$
$523$	14.0356	−	8.10349i	0.613736	−	0.354341i	0.774426	+	0.632664i	$0.218039\pi$
$524$	9.66329	−	54.8032i	0.422143	−	2.39409i
$525$	−21.5259	−	5.48885i	−0.939466	−	0.239553i
$526$	14.3913	+	5.23801i	0.627492	+	0.228388i
$527$	−8.13951	+	22.3631i	−0.354563	+	0.974153i
$528$	7.53799	+	18.4926i	0.328049	+	0.804789i
$529$	3.93976	−	22.3435i	0.171294	−	0.971456i
$530$	1.31430	+	2.27644i	0.0570897	+	0.0988822i
$531$	−12.3213	+	0.938063i	−0.534699	+	0.0407084i
$532$	−1.27325	−	2.92572i	−0.0552023	−	0.126846i
$533$	3.60000	−	4.29031i	0.155933	−	0.185834i
$534$	−16.7508	+	10.5391i	−0.724878	+	0.456071i
$535$	−2.14122	+	0.377555i	−0.0925731	+	0.0163231i
$536$	−5.74424	−	6.84572i	−0.248113	−	0.295690i
$537$	−8.57715	+	26.6777i	−0.370131	+	1.15123i
$538$	−4.92065	−	13.5194i	−0.212144	−	0.582862i
$539$	32.4722	−	9.95031i	1.39867	−	0.428590i
$540$	0.321554	−	5.30382i	0.0138375	−	0.228240i
$541$	9.50292			0.408562			0.204281	−	0.978912i	$-0.434514\pi$
$541$	9.50292			0.408562			0.204281	+	0.978912i	$0.434514\pi$
$542$	−30.3049	+	11.0301i	−1.30171	+	0.473783i
$543$	−31.0622	+	6.70274i	−1.33300	+	0.287642i
$544$	−35.6838	−	42.5263i	−1.52993	−	1.82330i
$545$	−0.252964	−	1.43463i	−0.0108358	−	0.0614527i
$546$	−46.6564	−	31.8327i	−1.99671	−	1.36232i
$547$	−7.11504	−	5.97023i	−0.304217	−	0.255269i	0.477880	−	0.878425i	$-0.341405\pi$
$547$	−7.11504	−	5.97023i	−0.304217	−	0.255269i	−0.782097	+	0.623157i	$0.785850\pi$
$548$	2.42503	+	1.40009i	0.103592	+	0.0598090i
$549$	−25.7610	−	26.3488i	−1.09945	−	1.12454i
$550$	−25.2762	−	43.7796i	−1.07778	−	1.86677i
$551$	−0.405563	+	2.30006i	−0.0172775	+	0.0979858i
$552$	1.01772	+	0.790085i	0.0433172	+	0.0336283i
$553$	−1.27290	−	1.92181i	−0.0541291	−	0.0817237i
$554$	18.9307	−	52.0117i	0.804289	−	2.20977i
$555$	−0.197577	+	1.43802i	−0.00838666	+	0.0610407i
$556$	14.9913	+	2.64338i	0.635775	+	0.112104i
$557$	10.3816	−	5.99382i	0.439882	−	0.253966i	−0.263665	−	0.964614i	$-0.584931\pi$
$557$	10.3816	−	5.99382i	0.439882	−	0.253966i	0.703548	+	0.710648i	$0.251598\pi$
$558$	17.4580	+	12.5200i	0.739054	+	0.530014i
$559$	−33.1881	−	19.1611i	−1.40371	−	0.810430i
$560$	−0.573675	−	2.38619i	−0.0242422	−	0.100835i
$561$	53.0865	+	28.0168i	2.24131	+	1.18287i
$562$	−3.01419	−	17.0943i	−0.127146	−	0.721080i
$563$	0.0744631	−	0.0624819i	0.00313824	−	0.00263330i	−0.641217	−	0.767359i	$-0.721570\pi$
$563$	0.0744631	−	0.0624819i	0.00313824	−	0.00263330i	0.644355	+	0.764726i	$0.277126\pi$
$564$	−12.4593	+	11.2883i	−0.524633	+	0.475322i
$565$	−1.29657	−	3.56230i	−0.0545472	−	0.149867i
$566$	13.5640			0.570138
$567$	−0.924734	−	23.7938i	−0.0388352	−	0.999246i
$568$	−9.36117			−0.392786
$569$	6.26646	+	17.2169i	0.262704	+	0.721772i	0.998983	+	0.0450941i	$0.0143588\pi$
$569$	6.26646	+	17.2169i	0.262704	+	0.721772i	−0.736279	+	0.676678i	$0.763419\pi$
$570$	0.495747	−	0.449151i	0.0207645	−	0.0188129i
$571$	11.0847	−	9.30116i	0.463880	−	0.389241i	−0.380676	−	0.924708i	$-0.624309\pi$
$571$	11.0847	−	9.30116i	0.463880	−	0.389241i	0.844556	+	0.535467i	$0.179864\pi$
$572$	−12.6567	−	71.7795i	−0.529201	−	3.00125i
$573$	30.7796	+	16.2441i	1.28584	+	0.678608i
$574$	−5.40015	+	1.29828i	−0.225398	+	0.0541890i
$575$	2.34434	+	1.35350i	0.0977655	+	0.0564450i
$576$	−32.6650	+	14.7857i	−1.36104	+	0.616070i
$577$	21.6982	−	12.5275i	0.903309	−	0.521526i	0.0250367	−	0.999687i	$-0.492030\pi$
$577$	21.6982	−	12.5275i	0.903309	−	0.521526i	0.878272	+	0.478161i	$0.158696\pi$
$578$	−72.0140	−	12.6980i	−2.99539	−	0.528168i
$579$	5.07064	−	36.9057i	0.210729	−	1.53375i
$580$	1.77442	−	4.87519i	0.0736790	−	0.202431i
$581$	10.5458	+	15.9219i	0.437512	+	0.660553i
$582$	−32.2112	−	25.0064i	−1.33520	−	1.03655i
$583$	−2.63964	+	14.9702i	−0.109323	+	0.620001i
$584$	5.04446	+	8.73726i	0.208741	+	0.361550i
$585$	1.81103	−	6.46622i	0.0748770	−	0.267345i
$586$	15.2005	+	8.77601i	0.627927	+	0.362534i
$587$	−21.3062	−	17.8781i	−0.879402	−	0.737906i	0.0866537	−	0.996238i	$-0.472383\pi$
$587$	−21.3062	−	17.8781i	−0.879402	−	0.737906i	−0.966056	+	0.258332i	$0.916827\pi$
$588$	10.4527	+	29.9937i	0.431063	+	1.23692i
$589$	0.266333	+	1.51045i	0.0109741	+	0.0622369i
$590$	2.22131	+	2.64726i	0.0914500	+	0.108986i
$591$	−5.80320	+	1.25224i	−0.238712	+	0.0515104i
$592$	4.79431	−	1.74498i	0.197045	−	0.0717184i
$593$	−43.7366			−1.79605			−0.898023	−	0.439949i	$-0.854996\pi$
$593$	−43.7366			−1.79605			−0.898023	+	0.439949i	$0.854996\pi$
$594$	37.2787	−	39.3256i	1.52956	−	1.61355i
$595$	−5.93129	−	4.38600i	−0.243159	−	0.179809i
$596$	1.21618	+	3.34142i	0.0498165	+	0.136870i
$597$	5.70955	−	17.7585i	0.233676	−	0.726808i
$598$	4.42407	+	5.27240i	0.180914	+	0.215605i
$599$	9.06627	−	1.59863i	0.370438	−	0.0653181i	0.0146695	−	0.999892i	$-0.495330\pi$
$599$	9.06627	−	1.59863i	0.370438	−	0.0653181i	0.355768	+	0.934574i	$0.384219\pi$
$600$	9.46682	−	5.95624i	0.386481	−	0.243162i
$601$	−25.8812	+	30.8440i	−1.05571	+	1.25815i	−0.0907219	+	0.995876i	$0.528917\pi$
$601$	−25.8812	+	30.8440i	−1.05571	+	1.25815i	−0.964993	+	0.262276i	$0.915527\pi$
$602$	15.1650	+	34.8467i	0.618077	+	1.42025i
$603$	8.71072	−	18.1430i	0.354728	−	0.738842i
$604$	−18.7804	−	32.5287i	−0.764166	−	1.32357i
$605$	−0.849967	+	4.82040i	−0.0345561	+	0.195977i
$606$	19.4380	+	47.6865i	0.789616	+	1.93713i
$607$	0.602537	−	1.65546i	0.0244562	−	0.0671930i	−0.926864	−	0.375398i	$-0.877506\pi$
$607$	0.602537	−	1.65546i	0.0244562	−	0.0671930i	0.951320	+	0.308205i	$0.0997283\pi$
$608$	−3.36199	−	1.22367i	−0.136347	−	0.0496262i
$609$	5.74452	−	22.5286i	0.232780	−	0.912903i
$610$	−1.78951	+	10.1488i	−0.0724550	+	0.410913i
$611$	−18.4004	+	10.6235i	−0.744399	+	0.429779i
$612$	−24.2975	+	50.6079i	−0.982168	+	2.04570i
$613$	−11.2627	+	19.5075i	−0.454895	+	0.787901i	−0.998682	−	0.0513222i	$-0.983656\pi$
$613$	−11.2627	+	19.5075i	−0.454895	+	0.787901i	0.543787	+	0.839223i	$0.316990\pi$
$614$	−38.0900	−	31.9613i	−1.53719	−	1.28985i
$615$	−0.351640	−	0.558896i	−0.0141795	−	0.0225369i
$616$	−7.62490	+	15.3054i	−0.307216	+	0.616671i
$617$	12.7802	+	15.2309i	0.514513	+	0.613173i	0.959274	−	0.282476i	$-0.0911558\pi$
$617$	12.7802	+	15.2309i	0.514513	+	0.613173i	−0.444761	+	0.895649i	$0.646711\pi$
$618$	43.2869	+	13.9172i	1.74126	+	0.559832i
$619$	1.43450	+	3.94126i	0.0576575	+	0.158413i	0.965177	−	0.261597i	$-0.0842490\pi$
$619$	1.43450	+	3.94126i	0.0576575	+	0.158413i	−0.907520	+	0.420009i	$0.862027\pi$
$620$		−	3.40700i		−	0.136829i
$621$	−0.675864	+	2.82181i	−0.0271215	+	0.113235i
$622$			50.6698i			2.03167i
$623$	13.4869	+	3.99034i	0.540341	+	0.159870i
$624$	−23.0717	+	4.97852i	−0.923606	+	0.199300i
$625$	17.4181	−	14.6155i	0.696725	−	0.584622i
$626$	4.46253	+	25.3083i	0.178359	+	1.01152i
$627$	3.86575	−	0.146943i	0.154383	−	0.00586836i
$628$	3.30131	−	3.93435i	0.131737	−	0.156998i
$629$	7.66783	−	13.2811i	0.305736	−	0.529551i
$630$	−5.25667	+	4.08807i	−0.209431	+	0.162873i
$631$	7.09781	+	12.2938i	0.282559	+	0.489407i	0.972014	−	0.234921i	$-0.0754833\pi$
$631$	7.09781	+	12.2938i	0.282559	+	0.489407i	−0.689455	+	0.724328i	$0.742150\pi$
$632$	1.14296	+	0.201535i	0.0454645	+	0.00801663i
$633$	−0.408302	−	0.316976i	−0.0162285	−	0.0125986i
$634$	−56.8853	−	20.7046i	−2.25920	−	0.822283i
$635$	4.11182	+	1.49658i	0.163173	+	0.0593900i
$636$	−14.0843	−	1.93510i	−0.558479	−	0.0767319i
$637$	4.91724	+	39.8383i	0.194828	+	1.57845i
$638$	45.8188	−	26.4535i	1.81399	−	1.04730i
$639$	−8.69367	−	19.2063i	−0.343916	−	0.759790i
$640$	3.42947	+	1.98001i	0.135562	+	0.0782666i
$641$	16.7592	−	19.9729i	0.661949	−	0.788881i	−0.325715	−	0.945468i	$-0.605605\pi$
$641$	16.7592	−	19.9729i	0.661949	−	0.788881i	0.987664	+	0.156588i	$0.0500493\pi$
$642$	9.67871	−	18.3393i	0.381988	−	0.723796i
$643$	35.5086	−	6.26113i	1.40032	−	0.246915i	0.578048	−	0.816003i	$-0.303815\pi$
$643$	35.5086	−	6.26113i	1.40032	−	0.246915i	0.822277	+	0.569088i	$0.192704\pi$
$644$	−0.237518	−	3.86323i	−0.00935951	−	0.152233i
$645$	−3.34835	+	3.03363i	−0.131841	+	0.119449i
$646$	−6.64138	+	2.41726i	−0.261301	+	0.0951059i
$647$	14.1360			0.555744			0.277872	−	0.960618i	$-0.410371\pi$
$647$	14.1360			0.555744			0.277872	+	0.960618i	$0.410371\pi$
$648$	9.00779	+	7.91147i	0.353860	+	0.310792i
$649$			19.9844i			0.784458i
$650$	56.1451	−	20.4351i	2.20219	−	0.801532i
$651$	−1.51510	−	15.1925i	−0.0593813	−	0.595442i
$652$	−29.7507	+	24.9638i	−1.16513	+	0.977659i
$653$	33.8858	−	5.97498i	1.32605	−	0.233819i	0.534629	−	0.845087i	$-0.320451\pi$
$653$	33.8858	−	5.97498i	1.32605	−	0.233819i	0.791424	+	0.611268i	$0.209340\pi$
$654$	12.2874	+	6.48478i	0.480477	+	0.253575i
$655$	−6.35168	−	5.32969i	−0.248181	−	0.208248i
$656$	−1.16047	+	2.00999i	−0.0453087	+	0.0784770i
$657$	−13.2415	+	18.4640i	−0.516599	+	0.720348i
$658$	20.9355	+	2.37856i	0.816151	+	0.0927259i
$659$	−38.1009	−	6.71821i	−1.48420	−	0.261704i	−0.627944	−	0.778258i	$-0.716104\pi$
$659$	−38.1009	−	6.71821i	−1.48420	−	0.261704i	−0.856255	+	0.516554i	$0.827215\pi$
$660$	−8.51342	−	1.16970i	−0.331385	−	0.0455304i
$661$	−10.2109	+	28.0542i	−0.397158	+	1.09118i	0.566504	+	0.824059i	$0.308296\pi$
$661$	−10.2109	+	28.0542i	−0.397158	+	1.09118i	−0.963662	+	0.267124i	$0.913927\pi$
$662$	11.0904	−	30.4707i	0.431042	−	1.18428i
$663$	−43.5055	+	56.0403i	−1.68962	+	2.17642i
$664$	−9.46927	−	1.66969i	−0.367479	−	0.0647964i
$665$	−0.472379	−	0.0536687i	−0.0183181	−	0.00208118i
$666$	−9.67802	−	9.89885i	−0.375016	−	0.383573i
$667$	−1.41655	+	2.45353i	−0.0548490	+	0.0950013i
$668$	7.59097	+	6.36958i	0.293703	+	0.246446i
$669$	−0.188535	−	4.95992i	−0.00728917	−	0.191761i
$670$	−5.54286	+	0.977356i	−0.214139	+	0.0377586i
$671$	−45.6527	+	38.3072i	−1.76240	+	1.47883i
$672$	32.4586	+	14.6590i	1.25212	+	0.565482i
$673$	20.3275	−	7.39859i	0.783566	−	0.285195i	0.0809075	−	0.996722i	$-0.474218\pi$
$673$	20.3275	−	7.39859i	0.783566	−	0.285195i	0.702659	+	0.711527i	$0.251996\pi$
$674$		−	35.0552i		−	1.35028i
$675$	21.0122	+	13.8916i	0.808760	+	0.534686i
$676$	52.0888			2.00342
$677$	7.25316	−	2.63993i	0.278761	−	0.101461i	−0.198856	−	0.980029i	$-0.563723\pi$
$677$	7.25316	−	2.63993i	0.278761	−	0.101461i	0.477618	+	0.878568i	$0.341500\pi$
$678$	34.4202	+	11.0664i	1.32190	+	0.425004i
$679$	1.77842	+	28.9261i	0.0682497	+	1.11008i
$680$	3.65767	−	0.644945i	0.140265	−	0.0247325i
$681$	25.5516	+	40.6116i	0.979138	+	1.55624i
$682$	22.3330	−	26.6155i	0.855176	−	1.01916i
$683$	7.78254	+	4.49325i	0.297791	+	0.171930i	0.641450	−	0.767165i	$-0.278333\pi$
$683$	7.78254	+	4.49325i	0.297791	+	0.171930i	−0.343659	+	0.939094i	$0.611667\pi$
$684$	0.274655	+	3.60755i	0.0105017	+	0.137938i
$685$	0.361325	−	0.208611i	0.0138055	−	0.00797061i
$686$	19.5687	−	34.6647i	0.747138	−	1.32350i
$687$	−15.4217	−	37.8333i	−0.588374	−	1.44343i
$688$	14.9234	+	5.43166i	0.568947	+	0.207080i
$689$	−16.8828	−	6.14485i	−0.643185	−	0.234100i
$690$	0.751438	−	0.306302i	0.0286067	−	0.0116607i
$691$	−34.0362	−	6.00150i	−1.29480	−	0.228308i	−0.516546	−	0.856259i	$-0.672783\pi$
$691$	−34.0362	−	6.00150i	−1.29480	−	0.228308i	−0.778253	+	0.627951i	$0.783894\pi$
$692$	20.1518	+	34.9040i	0.766058	+	1.32685i
$693$	−38.4833	−	1.43000i	−1.46186	−	0.0543210i
$694$	39.0970	−	67.7179i	1.48410	−	2.57054i
$695$	1.45793	−	1.73749i	0.0553025	−	0.0659069i
$696$	6.23368	+	9.90779i	0.236287	+	0.375554i
$697$	1.21142	+	6.87033i	0.0458860	+	0.260232i
$698$	−14.3659	+	12.0544i	−0.543757	+	0.456266i
$699$	−4.56063	+	14.1850i	−0.172499	+	0.536527i
$700$	−32.2195	−	9.53270i	−1.21778	−	0.360302i
$701$			23.2192i			0.876977i	0.898737	+	0.438488i	$0.144486\pi$
$701$			23.2192i			0.876977i	−0.898737	+	0.438488i	$0.855514\pi$
$702$	38.1222	+	51.4618i	1.43883	+	1.94230i
$703$		−	0.988348i		−	0.0372763i
$704$	19.8329	+	54.4906i	0.747482	+	2.05369i
$705$	0.528385	+	2.44867i	0.0199001	+	0.0922221i
$706$	−12.5702	−	14.9805i	−0.473085	−	0.563800i
$707$	16.3193	−	32.7576i	0.613752	−	1.23198i
$708$	−18.6767	+	0.709931i	−0.701912	+	0.0266809i
$709$	27.0985	+	22.7383i	1.01770	+	0.853955i	0.989337	−	0.145643i	$-0.0465250\pi$
$709$	27.0985	+	22.7383i	1.01770	+	0.853955i	0.0283665	+	0.999598i	$0.490969\pi$
$710$	−2.94793	+	5.10597i	−0.110634	+	0.191624i
$711$	0.647973	+	2.53218i	0.0243009	+	0.0949641i
$712$	−6.13267	+	3.54070i	−0.229831	+	0.132693i
$713$	−0.323071	+	1.83223i	−0.0120991	+	0.0686175i
$714$	67.7321	−	19.0323i	2.53481	−	0.712268i
$715$	−10.2050	−	3.71433i	−0.381647	−	0.138908i
$716$	−14.4964	+	39.8286i	−0.541757	+	1.48847i
$717$	−22.7540	−	3.12627i	−0.849762	−	0.116753i
$718$	0.191578	−	1.08649i	0.00714963	−	0.0405476i
$719$	−16.5681	−	28.6967i	−0.617884	−	1.07021i	−0.989871	−	0.141969i	$-0.954657\pi$
$719$	−16.5681	−	28.6967i	−0.617884	−	1.07021i	0.371987	−	0.928238i	$-0.378677\pi$
$720$	−0.273788	+	2.76927i	−0.0102035	+	0.103205i
$721$	−12.8948	−	29.6301i	−0.480226	−	1.10348i
$722$	25.9573	−	30.9347i	0.966031	−	1.15127i
$723$	−16.7479	−	8.83883i	−0.622862	−	0.328720i
$724$	−47.3333	+	8.34614i	−1.75913	+	0.310182i
$725$	15.8088	+	18.8402i	0.587126	+	0.699709i
$726$	−31.3441	−	34.5958i	−1.16329	−	1.28397i
$727$	−2.36915	−	6.50919i	−0.0878670	−	0.241413i	0.887974	−	0.459893i	$-0.152112\pi$
$727$	−2.36915	−	6.50919i	−0.0878670	−	0.241413i	−0.975841	+	0.218480i	$0.929890\pi$
$728$	−16.2499	−	12.0163i	−0.602260	−	0.445353i
$729$	−7.86647	+	25.8286i	−0.291351	+	0.956616i
$730$	6.35422			0.235180
$731$	44.8568	−	16.3266i	1.65909	−	0.603859i
$732$	−37.4222	−	41.3044i	−1.38316	−	1.52665i
$733$	−18.5983	−	22.1646i	−0.686943	−	0.818666i	0.304040	−	0.952659i	$-0.401664\pi$
$733$	−18.5983	−	22.1646i	−0.686943	−	0.818666i	−0.990982	+	0.133993i	$0.957220\pi$
$734$	11.6079	+	65.8315i	0.428454	+	2.42989i
$735$	4.64898	+	0.885724i	0.171480	+	0.0326704i
$736$	−3.32460	−	2.78967i	−0.122546	−	0.102828i
$737$	−28.1879	−	16.2743i	−1.03832	−	0.599472i
$738$	6.26711	+	0.619607i	0.230696	+	0.0228080i
$739$	8.46122	+	14.6553i	0.311251	+	0.539103i	0.978633	−	0.205613i	$-0.0659187\pi$
$739$	8.46122	+	14.6553i	0.311251	+	0.539103i	−0.667382	+	0.744715i	$0.732585\pi$
$740$	−0.381240	+	2.16212i	−0.0140147	+	0.0794811i
$741$	−0.622357	+	4.52971i	−0.0228629	+	0.166403i
$742$	9.83854	+	14.8542i	0.361184	+	0.545313i
$743$	−4.26829	+	11.7270i	−0.156588	+	0.430223i	−0.993034	−	0.117827i	$-0.962407\pi$
$743$	−4.26829	+	11.7270i	−0.156588	+	0.430223i	0.836446	+	0.548049i	$0.184629\pi$
$744$	6.07211	+	4.71394i	0.222614	+	0.172821i
$745$	0.521767	+	0.0920016i	0.0191161	+	0.00337068i
$746$	−48.6184	+	28.0699i	−1.78005	+	1.02771i
$747$	−5.36837	−	20.9787i	−0.196418	−	0.767572i
$748$	78.6268	+	45.3952i	2.87488	+	1.65981i
$749$	−14.3290	+	3.44490i	−0.523570	+	0.125874i
$750$	−0.543560	−	14.2998i	−0.0198480	−	0.522155i
$751$	−2.59871	−	14.7380i	−0.0948283	−	0.537798i	−0.994800	−	0.101849i	$-0.967524\pi$
$751$	−2.59871	−	14.7380i	−0.0948283	−	0.537798i	0.899972	−	0.435949i	$-0.143587\pi$
$752$	6.74495	−	5.65969i	0.245963	−	0.206388i
$753$	−3.74808	−	17.3695i	−0.136588	−	0.632981i
$754$	21.3870	+	58.7603i	0.778869	+	2.13992i
$755$	−5.59649			−0.203677
$756$	−0.0306699	−	36.0157i	−0.00111546	−	1.30988i
$757$	−48.2688			−1.75436			−0.877180	−	0.480162i	$-0.840578\pi$
$757$	−48.2688			−1.75436			−0.877180	+	0.480162i	$0.840578\pi$
$758$	−20.9528	−	57.5674i	−0.761041	−	2.09094i
$759$	4.46746	+	1.43633i	0.162158	+	0.0521356i
$760$	0.183364	−	0.153861i	0.00665132	−	0.00558112i
$761$	7.10296	+	40.2829i	0.257482	+	1.46025i	0.789620	+	0.613596i	$0.210278\pi$
$761$	7.10296	+	40.2829i	0.257482	+	1.46025i	−0.532138	+	0.846657i	$0.678611\pi$
$762$	−35.3229	+	22.2241i	−1.27962	+	0.805095i
$763$	−2.30810	−	9.60049i	−0.0835589	−	0.347561i
$764$	45.5879	+	26.3202i	1.64931	+	0.952231i
$765$	4.72009	+	6.90548i	0.170655	+	0.249668i
$766$	25.4500	−	14.6936i	0.919545	−	0.530900i
$767$	−23.2610	−	4.10154i	−0.839905	−	0.148098i
$768$	3.36539	−	1.37181i	0.121438	−	0.0495008i
$769$	7.22183	−	19.8418i	0.260426	−	0.715514i	−0.738713	−	0.674020i	$-0.764566\pi$
$769$	7.22183	−	19.8418i	0.260426	−	0.715514i	0.999139	−	0.0414940i	$-0.0132118\pi$
$770$	5.94702	+	8.97877i	0.214316	+	0.323572i
$771$	−2.17043	+	0.884712i	−0.0781660	+	0.0318621i
$772$	9.78421	−	55.4890i	0.352141	−	1.99709i
$773$	0.539761	+	0.934893i	0.0194138	+	0.0336258i	0.875569	−	0.483093i	$-0.160487\pi$
$773$	0.539761	+	0.934893i	0.0194138	+	0.0336258i	−0.856155	+	0.516719i	$0.827153\pi$
$774$	−3.27127	−	42.9676i	−0.117583	−	1.54444i
$775$	13.9872	+	8.07550i	0.502434	+	0.290080i
$776$	−11.1776	−	9.37910i	−0.401252	−	0.336690i
$777$	−0.738532	+	9.81087i	−0.0264947	+	0.351963i
$778$	9.37640	+	53.1762i	0.336160	+	1.90646i
$779$	0.289002	+	0.344420i	0.0103546	+	0.0123401i
$780$	3.10874	−	9.66918i	0.111311	−	0.346212i
$781$	−32.0393	+	11.6614i	−1.14646	+	0.417276i
$782$	−8.57326			−0.306579
$783$	−14.5386	+	21.9910i	−0.519568	+	0.785893i
$784$	−4.87361	−	15.9047i	−0.174057	−	0.568024i
$785$	−0.261728	−	0.719093i	−0.00934149	−	0.0256655i
$786$	77.3002	−	16.6802i	2.75721	−	0.594964i
$787$	−22.2373	−	26.5014i	−0.792674	−	0.944673i	0.206757	−	0.978392i	$-0.433709\pi$
$787$	−22.2373	−	26.5014i	−0.792674	−	0.944673i	−0.999431	+	0.0337197i	$0.989265\pi$
$788$	−8.84307	+	1.55927i	−0.315021	+	0.0555467i
$789$	0.468780	+	12.3325i	0.0166890	+	0.439050i
$790$	0.469856	−	0.559953i	0.0167167	−	0.0199222i
$791$	−10.2534	−	23.5608i	−0.364570	−	0.837725i
$792$	13.8639	−	13.5546i	0.492632	−	0.481642i
$793$	−35.2182	−	60.9998i	−1.25064	−	2.16616i
$794$	−2.91180	+	16.5136i	−0.103336	+	0.586046i
$795$	−1.29896	+	1.67322i	−0.0460695	+	0.0593429i
$796$	9.64984	−	26.5127i	0.342029	−	0.939718i
$797$	13.7273	+	4.99634i	0.486247	+	0.176980i	0.573498	−	0.819207i	$-0.305586\pi$
$797$	13.7273	+	4.99634i	0.486247	+	0.176980i	−0.0872509	+	0.996186i	$0.527808\pi$
$798$	3.16706	−	3.24485i	0.112113	−	0.114866i
$799$	4.59576	−	26.0639i	0.162586	−	0.922073i
$800$	−32.6277	+	18.8376i	−1.15356	+	0.666010i
$801$	−12.9598	−	9.29417i	−0.457913	−	0.328393i
$802$	−1.56453	+	2.70985i	−0.0552456	+	0.0956882i
$803$	28.1492	+	23.6200i	0.993364	+	0.833531i
$804$	14.2080	−	26.9215i	0.501076	−	0.949446i
$805$	−0.516190	−	0.257158i	−0.0181933	−	0.00906363i
$806$	26.3957	+	31.4571i	0.929747	+	1.10803i
$807$	8.59181	−	7.78426i	0.302446	−	0.274019i
$808$	6.30214	+	17.3150i	0.221709	+	0.609140i
$809$			19.4950i			0.685407i	0.939444	+	0.342704i	$0.111343\pi$
$809$			19.4950i			0.685407i	−0.939444	+	0.342704i	$0.888657\pi$
$810$	7.15190	−	2.42182i	0.251292	−	0.0850940i
$811$			8.74742i			0.307163i	0.988136	+	0.153582i	$0.0490808\pi$
$811$			8.74742i			0.307163i	−0.988136	+	0.153582i	$0.950919\pi$
$812$	9.97674	−	33.7203i	0.350115	−	1.18335i
$813$	−17.4491	−	19.2593i	−0.611967	−	0.675453i
$814$	−17.1510	+	14.3914i	−0.601143	+	0.504419i
$815$	1.00483	+	5.69869i	0.0351978	+	0.199617i
$816$	13.7225	−	26.0015i	0.480382	−	0.910234i
$817$	1.97751	−	2.35670i	0.0691842	−	0.0824505i
$818$	10.3078	−	17.8535i	0.360402	−	0.624235i
$819$	9.56263	−	44.4993i	0.334145	−	1.55493i
$820$	−0.499369	−	0.864933i	−0.0174387	−	0.0302048i
$821$	−14.8604	−	2.62030i	−0.518633	−	0.0914490i	−0.0917964	−	0.995778i	$-0.529261\pi$
$821$	−14.8604	−	2.62030i	−0.518633	−	0.0914490i	−0.426836	+	0.904329i	$0.640372\pi$
$822$	−0.541631	+	3.94216i	−0.0188916	+	0.137499i
$823$	45.4998	+	16.5606i	1.58602	+	0.577265i	0.976503	−	0.215505i	$-0.0691396\pi$
$823$	45.4998	+	16.5606i	1.58602	+	0.577265i	0.609521	+	0.792770i	$0.291362\pi$
$824$	15.2886	+	5.56458i	0.532602	+	0.193851i
$825$	24.9812	−	32.1787i	0.869732	−	1.12032i
$826$	16.1290	+	16.9856i	0.561199	+	0.591004i
$827$	1.87534	−	1.08273i	0.0652119	−	0.0376501i	−0.467040	−	0.884236i	$-0.654679\pi$
$827$	1.87534	−	1.08273i	0.0652119	−	0.0376501i	0.532251	+	0.846586i	$0.321346\pi$
$828$	−1.18364	+	4.22614i	−0.0411343	+	0.146868i
$829$	34.8737	+	20.1344i	1.21121	+	0.699295i	0.963024	−	0.269416i	$-0.0868307\pi$
$829$	34.8737	+	20.1344i	1.21121	+	0.699295i	0.248191	+	0.968711i	$0.420164\pi$
$830$	−3.89269	+	4.63913i	−0.135117	+	0.161027i
$831$	44.5711	−	1.69422i	1.54615	−	0.0587718i
$832$	−67.4950	+	11.9012i	−2.33997	+	0.412600i
$833$	−41.9514	−	27.2056i	−1.45353	−	0.942619i
$834$	4.56285	+	21.1454i	0.157999	+	0.732204i
$835$	1.38742	−	0.504981i	0.0480138	−	0.0174756i
$836$	5.85124			0.202369
$837$	−4.03246	+	16.8360i	−0.139382	+	0.581936i
$838$		−	47.3937i		−	1.63719i
$839$	−8.35277	+	3.04016i	−0.288370	+	0.104958i	−0.482155	−	0.876086i	$-0.660146\pi$
$839$	−8.35277	+	3.04016i	−0.288370	+	0.104958i	0.193785	+	0.981044i	$0.437924\pi$
$840$	−1.93514	+	1.39029i	−0.0667687	+	0.0479695i
$841$	2.49746	−	2.09562i	0.0861194	−	0.0722628i
$842$	−58.4633	+	10.3087i	−2.01478	+	0.355260i
$843$	11.8394	−	7.44902i	0.407772	−	0.256558i
$844$	−0.598908	−	0.502543i	−0.0206153	−	0.0172983i
$845$	3.88056	−	6.72133i	0.133495	−	0.231221i
$846$	−21.5377	−	10.3405i	−0.740480	−	0.355514i
$847$	−3.74528	+	32.9651i	−0.128689	+	1.13269i
$848$	7.33230	+	1.29288i	0.251792	+	0.0443978i
$849$	4.12589	+	10.1219i	0.141600	+	0.347382i
$850$	−25.4547	+	69.9363i	−0.873091	+	2.39880i
$851$	0.410049	−	1.12660i	0.0140563	−	0.0386194i
$852$	−12.0364	−	29.5284i	−0.412361	−	1.01163i
$853$	−7.05528	−	1.24404i	−0.241568	−	0.0425950i	0.0515532	−	0.998670i	$-0.483583\pi$
$853$	−7.05528	−	1.24404i	−0.241568	−	0.0425950i	−0.293121	+	0.956075i	$0.594694\pi$
$854$	−7.88525	+	69.4041i	−0.269828	+	2.37496i
$855$	0.485966	+	0.233319i	0.0166197	+	0.00797933i
$856$	3.70998	−	6.42588i	0.126805	−	0.219632i
$857$	27.4777	+	23.0565i	0.938619	+	0.787595i	0.977344	−	0.211655i	$-0.0678852\pi$
$857$	27.4777	+	23.0565i	0.938619	+	0.787595i	−0.0387252	+	0.999250i	$0.512330\pi$
$858$	87.6673	−	55.1576i	2.99291	−	1.88305i
$859$	4.46217	−	0.786801i	0.152247	−	0.0268453i	−0.0970050	−	0.995284i	$-0.530926\pi$
$859$	4.46217	−	0.786801i	0.152247	−	0.0268453i	0.249252	+	0.968439i	$0.419815\pi$
$860$	−5.23507	+	4.39275i	−0.178514	+	0.149791i
$861$	−2.61143	−	3.63484i	−0.0889972	−	0.123875i
$862$	28.1506	−	10.2460i	0.958815	−	0.348980i
$863$			33.0683i			1.12566i	0.826573	+	0.562830i	$0.190287\pi$
$863$			33.0683i			1.12566i	−0.826573	+	0.562830i	$0.809713\pi$
$864$	−29.3082	−	27.7828i	−0.997086	−	0.945189i
$865$	6.00516			0.204182
$866$	42.1093	−	15.3265i	1.43093	−	0.520817i
$867$	−12.4295	−	57.6015i	−0.422129	−	1.95625i
$868$	−1.41712	−	23.0495i	−0.0481001	−	0.782349i
$869$	4.16293	−	0.734037i	0.141218	−	0.0249005i
$870$	7.36718	−	0.280039i	0.249771	−	0.00949420i
$871$	24.7278	−	29.4694i	0.837868	−	0.998532i
$872$	4.30537	+	2.48571i	0.145798	+	0.0841766i
$873$	8.86255	−	31.6434i	0.299952	−	1.07097i
$874$	−0.478503	+	0.276264i	−0.0161856	+	0.00934476i
$875$	−7.37486	+	7.00294i	−0.249316	+	0.236743i
$876$	−21.0743	+	27.1462i	−0.712036	+	0.917186i
$877$	−12.0002	−	4.36773i	−0.405219	−	0.147488i	0.131366	−	0.991334i	$-0.458064\pi$
$877$	−12.0002	−	4.36773i	−0.405219	−	0.147488i	−0.536585	+	0.843846i	$0.680286\pi$
$878$	7.52835	+	2.74009i	0.254069	+	0.0924737i
$879$	−1.92525	+	14.0125i	−0.0649369	+	0.472631i
$880$	4.43210	+	0.781499i	0.149406	+	0.0263443i
$881$	−8.46605	−	14.6636i	−0.285229	−	0.494030i	0.687436	−	0.726245i	$-0.258736\pi$
$881$	−8.46605	−	14.6636i	−0.285229	−	0.494030i	−0.972665	+	0.232215i	$0.925403\pi$
$882$	−33.8626	+	29.8436i	−1.14021	+	1.00488i
$883$	4.01408	−	6.95260i	0.135085	−	0.233973i	−0.790545	−	0.612404i	$-0.790203\pi$
$883$	4.01408	−	6.95260i	0.135085	−	0.233973i	0.925630	+	0.378430i	$0.123536\pi$
$884$	−68.9751	+	82.2013i	−2.31988	+	2.76473i
$885$	−1.29979	+	2.46285i	−0.0436918	+	0.0827878i
$886$	1.95907	+	11.1104i	0.0658161	+	0.373262i
$887$	23.0852	−	19.3708i	0.775125	−	0.650408i	−0.166891	−	0.985975i	$-0.553373\pi$
$887$	23.0852	−	19.3708i	0.775125	−	0.650408i	0.942016	+	0.335568i	$0.108928\pi$
$888$	−3.32594	−	3.67098i	−0.111611	−	0.123190i
$889$	28.4403	+	8.41456i	0.953856	+	0.282215i
$890$			4.46002i			0.149500i
$891$	40.6853	+	15.8565i	1.36301	+	0.531211i
$892$		−	7.50739i		−	0.251366i
$893$	−0.583374	−	1.60281i	−0.0195218	−	0.0536358i
$894$	−3.74469	+	3.39273i	−0.125241	+	0.113470i
$895$	4.05935	+	4.83775i	0.135689	+	0.161708i
$896$	24.0250	+	11.9689i	0.802620	+	0.399853i
$897$	−2.58872	+	4.90513i	−0.0864347	+	0.163778i
$898$	−42.6855	−	35.8174i	−1.42443	−	1.19524i
$899$	−8.45166	+	14.6387i	−0.281879	+	0.488228i
$900$	30.9603	+	22.2033i	1.03201	+	0.740109i
$901$	19.3813	−	11.1898i	0.645683	−	0.372785i
$902$	1.76860	−	10.0302i	0.0588880	−	0.333970i
$903$	−21.3908	+	21.9162i	−0.711841	+	0.729325i
$904$	12.1569	+	4.42475i	0.404332	+	0.147165i
$905$	−2.44933	+	6.72947i	−0.0814184	+	0.223695i
$906$	32.7315	−	42.1620i	1.08743	−	1.40074i
$907$	−4.40531	+	24.9838i	−0.146276	+	0.829572i	0.820058	+	0.572281i	$0.193941\pi$
$907$	−4.40531	+	24.9838i	−0.146276	+	0.829572i	−0.966334	+	0.257292i	$0.917170\pi$
$908$	36.2861	+	62.8494i	1.20420	+	2.08573i
$909$	−29.6724	+	29.0105i	−0.984172	+	0.962217i
$910$	−11.6714	+	5.07929i	−0.386904	+	0.168377i
$911$	−0.815474	+	0.971845i	−0.0270179	+	0.0321986i	−0.779384	−	0.626546i	$-0.784468\pi$
$911$	−0.815474	+	0.971845i	−0.0270179	+	0.0321986i	0.752366	+	0.658745i	$0.228912\pi$
$912$	−0.0719721	−	1.89342i	−0.00238323	−	0.0626975i
$913$	−34.4893	+	6.08139i	−1.14143	+	0.201265i
$914$	28.6626	+	34.1588i	0.948075	+	1.12987i
$915$	−8.11766	+	1.75167i	−0.268362	+	0.0579084i
$916$	−21.1352	−	58.0683i	−0.698325	−	1.91863i
$917$	−45.1880	−	33.4151i	−1.49224	−	1.10346i
$918$	−79.6292	−	4.82767i	−2.62816	−	0.159337i
$919$	38.7081			1.27686			0.638430	−	0.769680i	$-0.279584\pi$
$919$	38.7081			1.27686			0.638430	+	0.769680i	$0.279584\pi$
$920$	0.272848	−	0.0993084i	0.00899552	−	0.00327410i
$921$	12.2643	−	38.1459i	0.404123	−	1.25695i
$922$	0.244786	+	0.291724i	0.00806159	+	0.00960743i
$923$	−6.99766	−	39.6857i	−0.230331	−	1.30627i
$924$	−58.0825	−	4.37227i	−1.91077	−	0.143837i
$925$	−7.97276	−	6.68994i	−0.262143	−	0.219964i
$926$	53.8650	+	31.0990i	1.77011	+	1.02198i
$927$	2.78156	+	36.5353i	0.0913583	+	1.19998i
$928$	−19.7151	−	34.1475i	−0.647179	−	1.12095i
$929$	6.02005	−	34.1414i	0.197512	−	1.12014i	−0.711285	−	0.702904i	$-0.751886\pi$
$929$	6.02005	−	34.1414i	0.197512	−	1.12014i	0.908796	−	0.417240i	$-0.137002\pi$
$930$	4.48335	−	1.82751i	0.147015	−	0.0599265i
$931$	−3.21812	−	0.166603i	−0.105470	−	0.00546020i
$932$	−7.70802	+	21.1776i	−0.252485	+	0.693696i
$933$	−37.8113	+	15.4127i	−1.23789	+	0.504589i
$934$	−18.7803	−	3.31148i	−0.614511	−	0.108355i
$935$	11.7152	−	6.76379i	0.383129	−	0.221200i
$936$	12.9316	+	18.9188i	0.422682	+	0.618382i
$937$	−24.7426	−	14.2852i	−0.808307	−	0.466676i	0.0380609	−	0.999275i	$-0.487882\pi$
$937$	−24.7426	−	14.2852i	−0.808307	−	0.466676i	−0.846367	+	0.532599i	$0.821215\pi$
$938$	−37.0927	+	8.91764i	−1.21112	+	0.291171i
$939$	−17.5284	+	11.0283i	−0.572018	+	0.359896i
$940$	0.657936	+	3.73134i	0.0214595	+	0.121703i
$941$	−37.2620	+	31.2666i	−1.21471	+	1.01926i	−0.215623	+	0.976477i	$0.569178\pi$
$941$	−37.2620	+	31.2666i	−1.21471	+	1.01926i	−0.999084	+	0.0427842i	$0.986377\pi$
$942$	6.94812	+	2.23389i	0.226382	+	0.0727842i
$943$	0.186535	+	0.512500i	0.00607440	+	0.0166893i
$944$	9.78827			0.318581
$945$	−4.64961	−	2.67918i	−0.151252	−	0.0871536i
$946$	−69.6909			−2.26585
$947$	−6.23321	−	17.1256i	−0.202552	−	0.556508i	0.796275	−	0.604935i	$-0.206801\pi$
$947$	−6.23321	−	17.1256i	−0.202552	−	0.556508i	−0.998827	+	0.0484279i	$0.984579\pi$
$948$	0.833886	+	3.86443i	0.0270834	+	0.125511i
$949$	−33.2698	+	27.9167i	−1.07999	+	0.906215i
$950$	0.832904	+	4.72363i	0.0270230	+	0.153255i
$951$	−1.85297	−	48.7474i	−0.0600867	−	1.58074i
$952$	24.4770	−	5.88464i	0.793305	−	0.190722i
$953$	28.1743	+	16.2665i	0.912656	+	0.526922i	0.881285	−	0.472586i	$-0.156679\pi$
$953$	28.1743	+	16.2665i	0.912656	+	0.526922i	0.0313712	+	0.999508i	$0.490013\pi$
$954$	−5.00835	−	19.5718i	−0.162151	−	0.633662i
$955$	6.79250	−	3.92165i	0.219800	−	0.126902i
$956$	−34.2114	−	6.03239i	−1.10647	−	0.195101i
$957$	33.6776	+	26.1448i	1.08864	+	0.845141i
$958$	−4.66581	+	12.8192i	−0.150746	+	0.414170i
$959$	2.35770	−	1.56161i	0.0761343	−	0.0504270i
$960$	−1.09988	+	8.00526i	−0.0354984	+	0.258369i
$961$	3.45553	−	19.5973i	0.111469	−	0.632170i
$962$	−13.2309	−	22.9167i	−0.426582	−	0.738863i
$963$	16.6294	+	1.64409i	0.535876	+	0.0529801i
$964$	−24.8055	−	14.3215i	−0.798931	−	0.461263i
$965$	−6.43116	−	5.39639i	−0.207026	−	0.173716i
$966$	4.95631	−	2.38479i	0.159467	−	0.0767292i
$967$	0.197163	+	1.11816i	0.00634032	+	0.0359577i	0.987814	−	0.155640i	$-0.0497441\pi$
$967$	0.197163	+	1.11816i	0.00634032	+	0.0359577i	−0.981473	+	0.191598i	$0.938633\pi$
$968$	−10.7372	−	12.7961i	−0.345107	−	0.411282i
$969$	−3.82400	−	4.22071i	−0.122845	−	0.135589i
$970$	−8.63569	+	3.14314i	−0.277275	+	0.100920i
$971$	−37.6895			−1.20951			−0.604757	−	0.796410i	$-0.706730\pi$
$971$	−37.6895			−1.20951			−0.604757	+	0.796410i	$0.706730\pi$
$972$	−13.3735	+	38.5862i	−0.428955	+	1.23765i
$973$	9.14066	−	12.3611i	0.293036	−	0.396279i
$974$	3.82155	+	10.4996i	0.122450	+	0.336429i
$975$	32.3275	+	35.6812i	1.03531	+	1.14271i
$976$	18.7626	+	22.3604i	0.600578	+	0.715741i
$977$	−29.2666	+	5.16050i	−0.936323	+	0.165099i	−0.620933	−	0.783863i	$-0.713246\pi$
$977$	−29.2666	+	5.16050i	−0.936323	+	0.165099i	−0.315390	+	0.948962i	$0.602135\pi$
$978$	−48.8088	−	25.7591i	−1.56073	−	0.823686i
$979$	−16.5788	+	19.7579i	−0.529862	+	0.631465i
$980$	6.97572	+	1.60580i	0.222831	+	0.0512954i
$981$	−1.10155	+	11.1418i	−0.0351698	+	0.355730i
$982$	−14.7282	−	25.5101i	−0.469997	−	0.814059i
$983$	0.460838	−	2.61354i	0.0146984	−	0.0833590i	−0.976576	−	0.215172i	$-0.930969\pi$
$983$	0.460838	−	2.61354i	0.0146984	−	0.0833590i	0.991275	+	0.131813i	$0.0420799\pi$
$984$	2.23245	+	0.306726i	0.0711680	+	0.00977808i
$985$	−0.457597	+	1.25724i	−0.0145803	+	0.0400589i
$986$	−73.1940	−	26.6404i	−2.33097	−	0.848404i
$987$	4.59320	+	16.3462i	0.146203	+	0.520306i
$988$	−1.20089	+	6.81058i	−0.0382054	+	0.216673i
$989$	3.23188	−	1.86593i	0.102768	−	0.0593330i
$990$	−3.02736	−	11.8304i	−0.0962157	−	0.375996i
$991$	−16.1884	+	28.0391i	−0.514242	+	0.890693i	0.485622	+	0.874169i	$0.338593\pi$
$991$	−16.1884	+	28.0391i	−0.514242	+	0.890693i	−0.999863	+	0.0165236i	$0.994740\pi$
$992$	−19.8358	−	16.6442i	−0.629786	−	0.528453i
$993$	26.1116	−	0.992547i	0.828628	−	0.0314975i
$994$	−17.8199	+	35.7697i	−0.565213	+	1.13455i
$995$	−2.70219	−	3.22034i	−0.0856652	−	0.102092i
$996$	−6.90863	−	32.0163i	−0.218908	−	1.01447i
$997$	3.04666	+	8.37063i	0.0964887	+	0.265100i	0.978541	−	0.206050i	$-0.0660610\pi$
$997$	3.04666	+	8.37063i	0.0964887	+	0.265100i	−0.882053	+	0.471151i	$0.843839\pi$
$998$		−	74.1087i		−	2.34587i
$999$	4.44297	−	10.2331i	0.140569	−	0.323759i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.be.a.20.19	✓	132
3.2	odd	2		567.2.be.a.62.3		132
7.6	odd	2	inner	189.2.be.a.20.20	yes	132
21.20	even	2		567.2.be.a.62.4		132
27.4	even	9		567.2.be.a.503.4		132
27.23	odd	18	inner	189.2.be.a.104.20	yes	132
189.104	even	18	inner	189.2.be.a.104.19	yes	132
189.139	odd	18		567.2.be.a.503.3		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.be.a.20.19	✓	132	1.1	even	1	trivial
189.2.be.a.20.20	yes	132	7.6	odd	2	inner
189.2.be.a.104.19	yes	132	189.104	even	18	inner
189.2.be.a.104.20	yes	132	27.23	odd	18	inner
567.2.be.a.62.3		132	3.2	odd	2
567.2.be.a.62.4		132	21.20	even	2
567.2.be.a.503.3		132	189.139	odd	18
567.2.be.a.503.4		132	27.4	even	9

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.735125 + 2.01974i) q^{2} +(-1.28358 + 1.16294i) q^{3} +(-2.00685 + 1.68395i) q^{4} +(0.0677816 + 0.384409i) q^{5} +(-3.29242 - 1.73760i) q^{6} +(0.618456 + 2.57245i) q^{7} +(-1.15362 - 0.666045i) q^{8} +(0.295160 - 2.98544i) q^{9} +(-0.726578 + 0.419490i) q^{10} +(-4.77807 - 0.842503i) q^{11} +(0.617633 - 4.49533i) q^{12} +(1.96127 - 5.38855i) q^{13} +(-4.74104 + 3.14020i) q^{14} +(-0.534046 - 0.414594i) q^{15} +(-0.412653 + 2.34027i) q^{16} +(3.57147 + 6.18597i) q^{17} +(6.24680 - 1.59853i) q^{18} +(0.398672 + 0.230173i) q^{19} +(-0.783352 - 0.657311i) q^{20} +(-3.78544 - 2.58273i) q^{21} +(-1.81084 - 10.2698i) q^{22} +(0.358944 + 0.427773i) q^{23} +(2.25534 - 0.486668i) q^{24} +(4.55529 - 1.65799i) q^{25} +12.3252 q^{26} +(3.09302 + 4.17531i) q^{27} +(-5.57303 - 4.12109i) q^{28} +(1.73522 + 4.76747i) q^{29} +(0.444781 - 1.38341i) q^{30} +(2.14159 + 2.55225i) q^{31} +(-7.65380 + 1.34957i) q^{32} +(7.11282 - 4.47517i) q^{33} +(-9.86858 + 11.7609i) q^{34} +(-0.946953 + 0.412105i) q^{35} +(4.43500 + 6.48838i) q^{36} +(-1.07348 - 1.85933i) q^{37} +(-0.171817 + 0.974420i) q^{38} +(3.74909 + 9.19747i) q^{39} +(0.177839 - 0.488609i) q^{40} +(0.917771 + 0.334041i) q^{41} +(2.43367 - 9.54423i) q^{42} +(1.16047 - 6.58138i) q^{43} +(11.0076 - 6.35525i) q^{44} +(1.16764 - 0.0888961i) q^{45} +(-0.600121 + 1.03944i) q^{46} +(-2.83834 - 2.38165i) q^{47} +(-2.19191 - 3.48382i) q^{48} +(-6.23502 + 3.18190i) q^{49} +(6.69741 + 7.98167i) q^{50} +(-11.7782 - 3.78680i) q^{51} +(5.13806 + 14.1167i) q^{52} -3.13310i q^{53} +(-6.15929 + 9.31647i) q^{54} -1.89384i q^{55} +(0.999904 - 3.37956i) q^{56} +(-0.779405 + 0.168184i) q^{57} +(-8.35346 + 7.00938i) q^{58} +(-0.715255 - 4.05641i) q^{59} +(1.76991 - 0.0672771i) q^{60} +(7.89549 - 9.40948i) q^{61} +(-3.58054 + 6.20168i) q^{62} +(7.86246 - 1.08708i) q^{63} +(-5.97591 - 10.3506i) q^{64} +(2.20434 + 0.388685i) q^{65} +(14.2675 + 11.0762i) q^{66} +(6.30401 + 2.29447i) q^{67} +(-17.5843 - 6.40016i) q^{68} +(-0.958206 - 0.131652i) q^{69} +(-1.52847 - 1.60965i) q^{70} +(6.08593 - 3.51371i) q^{71} +(-2.32894 + 3.24749i) q^{72} +(-6.55906 - 3.78687i) q^{73} +(2.96621 - 3.53499i) q^{74} +(-3.91895 + 7.42567i) q^{75} +(-1.18768 + 0.209419i) q^{76} +(-0.787728 - 12.8124i) q^{77} +(-15.8205 + 14.3335i) q^{78} +(-0.818714 + 0.297987i) q^{79} -0.927591 q^{80} +(-8.82576 - 1.76237i) q^{81} +2.09922i q^{82} +(6.78293 - 2.46878i) q^{83} +(11.9460 - 1.19133i) q^{84} +(-2.13586 + 1.79220i) q^{85} +(14.1458 - 2.49428i) q^{86} +(-7.77156 - 4.10149i) q^{87} +(4.95095 + 4.15434i) q^{88} +(2.65800 - 4.60379i) q^{89} +(1.03791 + 2.29297i) q^{90} +(15.0747 + 1.71270i) q^{91} +(-1.44070 - 0.254033i) q^{92} +(-5.71701 - 0.785485i) q^{93} +(2.72378 - 7.48351i) q^{94} +(-0.0614580 + 0.168854i) q^{95} +(8.25481 - 10.6332i) q^{96} +(10.7873 + 1.90209i) q^{97} +(-11.0101 - 10.2540i) q^{98} +(-3.92554 + 14.0160i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 12 q^{2} - 12 q^{4} - 6 q^{7} - 18 q^{8} - 6 q^{9} - 18 q^{11} + 3 q^{14} - 24 q^{15} - 24 q^{16} - 12 q^{18} - 12 q^{21} - 12 q^{22} + 12 q^{23} - 12 q^{25} - 12 q^{28} - 48 q^{29} + 42 q^{30}+ \cdots - 192 q^{99}+O(q^{100}) \) 132 * q - 12 * q^2 - 12 * q^4 - 6 * q^7 - 18 * q^8 - 6 * q^9 - 18 * q^11 + 3 * q^14 - 24 * q^15 - 24 * q^16 - 12 * q^18 - 12 * q^21 - 12 * q^22 + 12 * q^23 - 12 * q^25 - 12 * q^28 - 48 * q^29 + 42 * q^30 - 6 * q^32 - 36 * q^35 - 36 * q^36 - 6 * q^37 - 18 * q^39 - 12 * q^43 - 18 * q^44 - 6 * q^46 - 24 * q^49 + 18 * q^50 + 24 * q^51 + 57 * q^56 - 12 * q^58 - 6 * q^60 + 21 * q^63 + 18 * q^64 + 78 * q^65 - 12 * q^67 - 69 * q^70 + 18 * q^71 + 114 * q^72 - 6 * q^74 - 57 * q^77 + 12 * q^78 + 24 * q^79 - 42 * q^81 - 48 * q^84 + 54 * q^85 - 42 * q^86 - 72 * q^88 + 6 * q^91 - 120 * q^92 - 60 * q^93 + 126 * q^95 + 126 * q^98 - 192 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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