LMFDB - Embedded newform 168.2.ba.c.5.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [168,2,Mod(5,168)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(168, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 3, 5]))

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

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

chi := DirichletCharacter("168.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 168 = 2^{3} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	168.ba (of order $6$, degree $2$, 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:	$1.34148675396$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.18
Character	$\chi$	$=$	168.5
Dual form			168.2.ba.c.101.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.998351 - 1.00165i) q^{2} +(1.26610 + 1.18195i) q^{3} +(-0.00659077 - 1.99999i) q^{4} +(-1.54900 - 0.894317i) q^{5} +(2.44790 - 0.0881824i) q^{6} +(2.63573 + 0.230049i) q^{7} +(-2.00986 - 1.99009i) q^{8} +(0.206000 + 2.99292i) q^{9} +O(q^{10})$	\(q+(0.998351 - 1.00165i) q^{2} +(1.26610 + 1.18195i) q^{3} +(-0.00659077 - 1.99999i) q^{4} +(-1.54900 - 0.894317i) q^{5} +(2.44790 - 0.0881824i) q^{6} +(2.63573 + 0.230049i) q^{7} +(-2.00986 - 1.99009i) q^{8} +(0.206000 + 2.99292i) q^{9} +(-2.44224 + 0.658710i) q^{10} +(-0.501346 - 0.868358i) q^{11} +(2.35554 - 2.53997i) q^{12} -2.47302 q^{13} +(2.86181 - 2.41040i) q^{14} +(-0.904151 - 2.96313i) q^{15} +(-3.99991 + 0.0263630i) q^{16} +(3.32963 + 5.76708i) q^{17} +(3.20351 + 2.78164i) q^{18} +(-1.85941 + 3.22059i) q^{19} +(-1.77842 + 3.10388i) q^{20} +(3.06518 + 3.40656i) q^{21} +(-1.37031 - 0.364754i) q^{22} +(-6.85244 - 3.95626i) q^{23} +(-0.192497 - 4.89520i) q^{24} +(-0.900394 - 1.55953i) q^{25} +(-2.46894 + 2.47709i) q^{26} +(-3.27666 + 4.03281i) q^{27} +(0.442725 - 5.27295i) q^{28} -0.748403 q^{29} +(-3.87067 - 2.05261i) q^{30} +(2.87254 - 1.65846i) q^{31} +(-3.96691 + 4.03282i) q^{32} +(0.391600 - 1.69199i) q^{33} +(9.10071 + 2.42246i) q^{34} +(-3.87702 - 2.71353i) q^{35} +(5.98445 - 0.431724i) q^{36} +(3.22429 + 1.86155i) q^{37} +(1.36955 + 5.07775i) q^{38} +(-3.13108 - 2.92298i) q^{39} +(1.33351 + 4.88011i) q^{40} -2.01044 q^{41} +(6.47230 + 0.330713i) q^{42} -9.19651i q^{43} +(-1.73340 + 1.00841i) q^{44} +(2.35752 - 4.82027i) q^{45} +(-10.8039 + 2.91399i) q^{46} +(-1.19840 + 2.07569i) q^{47} +(-5.09544 - 4.69431i) q^{48} +(6.89415 + 1.21270i) q^{49} +(-2.46101 - 0.655080i) q^{50} +(-2.60076 + 11.2371i) q^{51} +(0.0162991 + 4.94601i) q^{52} +(6.33884 + 10.9792i) q^{53} +(0.768191 + 7.30821i) q^{54} +1.79345i q^{55} +(-4.83964 - 5.70771i) q^{56} +(-6.16075 + 1.87985i) q^{57} +(-0.747169 + 0.749635i) q^{58} +(7.34922 - 4.24308i) q^{59} +(-5.92027 + 1.82782i) q^{60} +(2.02442 - 3.50640i) q^{61} +(1.20661 - 4.53300i) q^{62} +(-0.145558 + 7.93592i) q^{63} +(0.0790881 + 7.99961i) q^{64} +(3.83071 + 2.21166i) q^{65} +(-1.30382 - 2.08144i) q^{66} +(6.89843 - 3.98281i) q^{67} +(11.5122 - 6.69723i) q^{68} +(-3.99976 - 13.1082i) q^{69} +(-6.58862 + 1.17435i) q^{70} -5.46843i q^{71} +(5.54214 - 6.42531i) q^{72} +(-5.68546 + 3.28250i) q^{73} +(5.08359 - 1.37113i) q^{74} +(0.703295 - 3.03873i) q^{75} +(6.45340 + 3.69757i) q^{76} +(-1.12165 - 2.40409i) q^{77} +(-6.05370 + 0.218077i) q^{78} +(2.53988 - 4.39920i) q^{79} +(6.21945 + 3.53635i) q^{80} +(-8.91513 + 1.23308i) q^{81} +(-2.00712 + 2.01375i) q^{82} -5.65457i q^{83} +(6.79288 - 6.15278i) q^{84} -11.9110i q^{85} +(-9.21165 - 9.18134i) q^{86} +(-0.947550 - 0.884573i) q^{87} +(-0.720472 + 2.74300i) q^{88} +(7.39495 - 12.8084i) q^{89} +(-2.47457 - 7.17372i) q^{90} +(-6.51821 - 0.568916i) q^{91} +(-7.86731 + 13.7309i) q^{92} +(5.59713 + 1.29542i) q^{93} +(0.882685 + 3.27265i) q^{94} +(5.76045 - 3.32580i) q^{95} +(-9.78907 + 0.417256i) q^{96} +1.75577i q^{97} +(8.09748 - 5.69481i) q^{98} +(2.49565 - 1.67937i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9}+O(q^{10}) $ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9	$ 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42} - 8 q^{46} - 36 q^{49} - 48 q^{52} + 60 q^{54} + 4 q^{57} + 30 q^{58} - 32 q^{60} - 6 q^{63} - 60 q^{64} + 54 q^{66} + 42 q^{70} + 42 q^{72} - 36 q^{73} - 68 q^{78} - 56 q^{79} + 42 q^{81} + 48 q^{82} + 48 q^{84} - 132 q^{87} + 6 q^{88} + 48 q^{94} + 90 q^{96}+O(q^{100}) $ 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

$n$	$73$	$85$	$113$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$-1$	$1$

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 $

$2$	0.998351	−	1.00165i	0.705941	−	0.708271i
$2$	0.998351	−	1.00165i	0.705941	−	0.708271i
$3$	1.26610	+	1.18195i	0.730981	+	0.682398i
$3$	1.26610	+	1.18195i	0.730981	+	0.682398i
$4$	−0.00659077	−	1.99999i	−0.00329539	−	0.999995i
$5$	−1.54900	−	0.894317i	−0.692735	−	0.399951i	0.111901	−	0.993719i	$-0.464306\pi$
$5$	−1.54900	−	0.894317i	−0.692735	−	0.399951i	−0.804636	+	0.593769i	$0.797639\pi$
$6$	2.44790	−	0.0881824i	0.999352	−	0.0360003i
$7$	2.63573	+	0.230049i	0.996213	+	0.0869505i
$7$	2.63573	+	0.230049i	0.996213	+	0.0869505i
$8$	−2.00986	−	1.99009i	−0.710593	−	0.703603i
$9$	0.206000	+	2.99292i	0.0686667	+	0.997640i
$10$	−2.44224	+	0.658710i	−0.772303	+	0.208303i
$11$	−0.501346	−	0.868358i	−0.151162	−	0.261820i	0.780493	−	0.625164i	$-0.214968\pi$
$11$	−0.501346	−	0.868358i	−0.151162	−	0.261820i	−0.931655	+	0.363345i	$0.881635\pi$
$12$	2.35554	−	2.53997i	0.679985	−	0.733226i
$13$	−2.47302			−0.685891			−0.342946	−	0.939355i	$-0.611425\pi$
$13$	−2.47302			−0.685891			−0.342946	+	0.939355i	$0.611425\pi$
$14$	2.86181	−	2.41040i	0.764852	−	0.644207i
$15$	−0.904151	−	2.96313i	−0.233451	−	0.765077i
$16$	−3.99991	+	0.0263630i	−0.999978	+	0.00659074i
$17$	3.32963	+	5.76708i	0.807553	+	1.39872i	0.914554	+	0.404464i	$0.132542\pi$
$17$	3.32963	+	5.76708i	0.807553	+	1.39872i	−0.107001	+	0.994259i	$0.534125\pi$
$18$	3.20351	+	2.78164i	0.755074	+	0.655640i
$19$	−1.85941	+	3.22059i	−0.426577	+	0.738854i	−0.996566	−	0.0827988i	$-0.973614\pi$
$19$	−1.85941	+	3.22059i	−0.426577	+	0.738854i	0.569989	+	0.821652i	$0.306947\pi$
$20$	−1.77842	+	3.10388i	−0.397666	+	0.694049i
$21$	3.06518	+	3.40656i	0.668878	+	0.743372i
$22$	−1.37031	−	0.364754i	−0.292150	−	0.0777658i
$23$	−6.85244	−	3.95626i	−1.42883	−	0.824936i	−0.431803	−	0.901968i	$-0.642123\pi$
$23$	−6.85244	−	3.95626i	−1.42883	−	0.824936i	−0.997029	+	0.0770314i	$0.975456\pi$
$24$	−0.192497	−	4.89520i	−0.0392934	−	0.999228i
$25$	−0.900394	−	1.55953i	−0.180079	−	0.311906i
$26$	−2.46894	+	2.47709i	−0.484199	+	0.485797i
$27$	−3.27666	+	4.03281i	−0.630593	+	0.776114i
$28$	0.442725	−	5.27295i	0.0836671	−	0.996494i
$29$	−0.748403			−0.138975			−0.0694875	−	0.997583i	$-0.522136\pi$
$29$	−0.748403			−0.138975			−0.0694875	+	0.997583i	$0.522136\pi$
$30$	−3.87067	−	2.05261i	−0.706684	−	0.374753i
$31$	2.87254	−	1.65846i	0.515924	−	0.297869i	−0.219341	−	0.975648i	$-0.570391\pi$
$31$	2.87254	−	1.65846i	0.515924	−	0.297869i	0.735265	+	0.677779i	$0.237058\pi$
$32$	−3.96691	+	4.03282i	−0.701257	+	0.712908i
$33$	0.391600	−	1.69199i	0.0681688	−	0.294538i
$34$	9.10071	+	2.42246i	1.56076	+	0.415449i
$35$	−3.87702	−	2.71353i	−0.655335	−	0.458670i
$36$	5.98445	−	0.431724i	0.997408	−	0.0719540i
$37$	3.22429	+	1.86155i	0.530071	+	0.306036i	0.741045	−	0.671455i	$-0.234330\pi$
$37$	3.22429	+	1.86155i	0.530071	+	0.306036i	−0.210975	+	0.977492i	$0.567664\pi$
$38$	1.36955	+	5.07775i	0.222170	+	0.823719i
$39$	−3.13108	−	2.92298i	−0.501374	−	0.468051i
$40$	1.33351	+	4.88011i	0.210846	+	0.771613i
$41$	−2.01044			−0.313978			−0.156989	−	0.987600i	$-0.550179\pi$
$41$	−2.01044			−0.313978			−0.156989	+	0.987600i	$0.550179\pi$
$42$	6.47230	+	0.330713i	0.998697	+	0.0510302i
$43$		−	9.19651i		−	1.40245i	−0.712938	−	0.701227i	$-0.752636\pi$
$43$		−	9.19651i		−	1.40245i	0.712938	−	0.701227i	$-0.247364\pi$
$44$	−1.73340	+	1.00841i	−0.261320	+	0.152024i
$45$	2.35752	−	4.82027i	0.351439	−	0.718563i
$46$	−10.8039	+	2.91399i	−1.59295	+	0.429644i
$47$	−1.19840	+	2.07569i	−0.174805	+	0.302771i	−0.940094	−	0.340916i	$-0.889263\pi$
$47$	−1.19840	+	2.07569i	−0.174805	+	0.302771i	0.765289	+	0.643687i	$0.222596\pi$
$48$	−5.09544	−	4.69431i	−0.735463	−	0.677565i
$49$	6.89415	+	1.21270i	0.984879	+	0.173242i
$50$	−2.46101	−	0.655080i	−0.348039	−	0.0926423i
$51$	−2.60076	+	11.2371i	−0.364179	+	1.57351i
$52$	0.0162991	+	4.94601i	0.00226028	+	0.685888i
$53$	6.33884	+	10.9792i	0.870707	+	1.50811i	0.861267	+	0.508153i	$0.169671\pi$
$53$	6.33884	+	10.9792i	0.870707	+	1.50811i	0.00943963	+	0.999955i	$0.496995\pi$
$54$	0.768191	+	7.30821i	0.104538	+	0.994521i
$55$			1.79345i			0.241829i
$56$	−4.83964	−	5.70771i	−0.646724	−	0.762725i
$57$	−6.16075	+	1.87985i	−0.816012	+	0.248993i
$58$	−0.747169	+	0.749635i	−0.0981081	+	0.0984319i
$59$	7.34922	−	4.24308i	0.956787	−	0.552401i	0.0616046	−	0.998101i	$-0.480378\pi$
$59$	7.34922	−	4.24308i	0.956787	−	0.552401i	0.895183	+	0.445699i	$0.147045\pi$
$60$	−5.92027	+	1.82782i	−0.764304	+	0.235971i
$61$	2.02442	−	3.50640i	0.259200	−	0.448948i	−0.706828	−	0.707386i	$-0.749874\pi$
$61$	2.02442	−	3.50640i	0.259200	−	0.448948i	0.966028	+	0.258438i	$0.0832077\pi$
$62$	1.20661	−	4.53300i	0.153240	−	0.575692i
$63$	−0.145558	+	7.93592i	−0.0183386	+	0.999832i
$64$	0.0790881	+	7.99961i	0.00988602	+	0.999951i
$65$	3.83071	+	2.21166i	0.475141	+	0.274323i
$66$	−1.30382	−	2.08144i	−0.160489	−	0.256208i
$67$	6.89843	−	3.98281i	0.842777	−	0.486577i	−0.0154303	−	0.999881i	$-0.504912\pi$
$67$	6.89843	−	3.98281i	0.842777	−	0.486577i	0.858207	+	0.513303i	$0.171578\pi$
$68$	11.5122	−	6.69723i	1.39605	−	0.812158i
$69$	−3.99976	−	13.1082i	−0.481514	−	1.57804i
$70$	−6.58862	+	1.17435i	−0.787490	+	0.140361i
$71$		−	5.46843i		−	0.648984i	−0.945889	−	0.324492i	$-0.894807\pi$
$71$		−	5.46843i		−	0.648984i	0.945889	−	0.324492i	$-0.105193\pi$
$72$	5.54214	−	6.42531i	0.653148	−	0.757230i
$73$	−5.68546	+	3.28250i	−0.665433	+	0.384188i	−0.794344	−	0.607468i	$-0.792185\pi$
$73$	−5.68546	+	3.28250i	−0.665433	+	0.384188i	0.128911	+	0.991656i	$0.458852\pi$
$74$	5.08359	−	1.37113i	0.590955	−	0.159390i
$75$	0.703295	−	3.03873i	0.0812095	−	0.350883i
$76$	6.45340	+	3.69757i	0.740255	+	0.424140i
$77$	−1.12165	−	2.40409i	−0.127824	−	0.273972i
$78$	−6.05370	+	0.218077i	−0.685447	+	0.0246923i
$79$	2.53988	−	4.39920i	0.285759	−	0.494949i	−0.687034	−	0.726625i	$-0.741088\pi$
$79$	2.53988	−	4.39920i	0.285759	−	0.494949i	0.972793	+	0.231676i	$0.0744210\pi$
$80$	6.21945	+	3.53635i	0.695356	+	0.395376i
$81$	−8.91513	+	1.23308i	−0.990570	+	0.137009i
$82$	−2.00712	+	2.01375i	−0.221650	+	0.222381i
$83$		−	5.65457i		−	0.620669i	−0.950627	−	0.310335i	$-0.899559\pi$
$83$		−	5.65457i		−	0.620669i	0.950627	−	0.310335i	$-0.100441\pi$
$84$	6.79288	−	6.15278i	0.741164	−	0.671324i
$85$		−	11.9110i		−	1.29193i
$86$	−9.21165	−	9.18134i	−0.993317	−	0.990049i
$87$	−0.947550	−	0.884573i	−0.101588	−	0.0948362i
$88$	−0.720472	+	2.74300i	−0.0768026	+	0.292405i
$89$	7.39495	−	12.8084i	0.783863	−	1.35769i	−0.145812	−	0.989312i	$-0.546580\pi$
$89$	7.39495	−	12.8084i	0.783863	−	1.35769i	0.929676	−	0.368379i	$-0.120087\pi$
$90$	−2.47457	−	7.17372i	−0.260842	−	0.756177i
$91$	−6.51821	−	0.568916i	−0.683294	−	0.0596386i
$92$	−7.86731	+	13.7309i	−0.820223	+	1.43154i
$93$	5.59713	+	1.29542i	0.580396	+	0.134329i
$94$	0.882685	+	3.27265i	0.0910420	+	0.337548i
$95$	5.76045	−	3.32580i	0.591010	−	0.341220i
$96$	−9.78907	+	0.417256i	−0.999093	+	0.0425860i
$97$			1.75577i			0.178271i	0.996019	+	0.0891356i	$0.0284105\pi$
$97$			1.75577i			0.178271i	−0.996019	+	0.0891356i	$0.971590\pi$
$98$	8.09748	−	5.69481i	0.817969	−	0.575262i
$99$	2.49565	−	1.67937i	0.250822	−	0.168783i
$100$	−3.11311	+	1.81106i	−0.311311	+	0.181106i
$101$	−12.6803	+	7.32100i	−1.26174	+	0.728467i	−0.973411	−	0.229064i	$-0.926433\pi$
$101$	−12.6803	+	7.32100i	−1.26174	+	0.728467i	−0.288330	+	0.957531i	$0.593100\pi$
$102$	8.65916	+	13.8236i	0.857384	+	1.36874i
$103$	−8.54056	−	4.93089i	−0.841526	−	0.485855i	0.0162566	−	0.999868i	$-0.494825\pi$
$103$	−8.54056	−	4.93089i	−0.841526	−	0.485855i	−0.857783	+	0.514013i	$0.828158\pi$
$104$	4.97042	+	4.92152i	0.487390	+	0.482595i
$105$	−1.70143	−	8.01802i	−0.166043	−	0.782478i
$106$	17.3257	+	4.61181i	1.68282	+	0.447939i
$107$	3.48110	−	6.02945i	0.336531	−	0.582889i	−0.647247	−	0.762281i	$-0.724080\pi$
$107$	3.48110	−	6.02945i	0.336531	−	0.582889i	0.983778	+	0.179392i	$0.0574130\pi$
$108$	8.08716	+	6.52670i	0.778188	+	0.628032i
$109$	−2.36373	+	1.36470i	−0.226404	+	0.130715i	−0.608912	−	0.793238i	$-0.708394\pi$
$109$	−2.36373	+	1.36470i	−0.226404	+	0.130715i	0.382508	+	0.923952i	$0.375061\pi$
$110$	1.79640	+	1.79049i	0.171280	+	0.170717i
$111$	1.88202	+	6.16785i	0.178633	+	0.585426i
$112$	−10.5488	−	0.850692i	−0.996764	−	0.0803828i
$113$			0.531154i			0.0499667i	0.999688	+	0.0249834i	$0.00795328\pi$
$113$			0.531154i			0.0499667i	−0.999688	+	0.0249834i	$0.992047\pi$
$114$	−4.26765	+	8.04765i	−0.399702	+	0.753731i
$115$	7.07629	+	12.2565i	0.659868	+	1.14292i
$116$	0.00493255	+	1.49680i	0.000457976	+	0.138974i
$117$	−0.509442	−	7.40154i	−0.0470979	−	0.684272i
$118$	3.08704	−	11.5974i	0.284185	−	1.06763i
$119$	7.44929	+	15.9665i	0.682875	+	1.46364i
$120$	−4.07968	+	7.75482i	−0.372422	+	0.707915i
$121$	4.99730	−	8.65558i	0.454300	−	0.786871i
$122$	−1.49109	−	5.52837i	−0.134997	−	0.500515i
$123$	−2.54541	−	2.37623i	−0.229512	−	0.214258i
$124$	−3.33584	−	5.73412i	−0.299567	−	0.514940i
$125$			12.1641i			1.08799i
$126$	7.80367	+	8.06863i	0.695206	+	0.718811i
$127$	−4.52393			−0.401434			−0.200717	−	0.979649i	$-0.564327\pi$
$127$	−4.52393			−0.401434			−0.200717	+	0.979649i	$0.564327\pi$
$128$	8.09174	+	7.90720i	0.715215	+	0.698904i
$129$	10.8698	−	11.6437i	0.957031	−	1.02517i
$130$	6.03969	−	1.62900i	0.529716	−	0.142873i
$131$	13.3927	+	7.73228i	1.17013	+	0.675573i	0.953710	−	0.300729i	$-0.0972298\pi$
$131$	13.3927	+	7.73228i	1.17013	+	0.675573i	0.216416	+	0.976301i	$0.430563\pi$
$132$	−3.38654	−	0.772044i	−0.294761	−	0.0671978i
$133$	−5.64179	+	8.06085i	−0.489205	+	0.698964i
$134$	2.89768	−	10.8860i	0.250322	−	0.940409i
$135$	8.68216	−	3.31646i	0.747241	−	0.285435i
$136$	4.78492	−	18.2173i	0.410304	−	1.56212i
$137$	−9.71195	+	5.60719i	−0.829748	+	0.479055i	−0.853766	−	0.520657i	$-0.825687\pi$
$137$	−9.71195	+	5.60719i	−0.829748	+	0.479055i	0.0240187	+	0.999712i	$0.492354\pi$
$138$	−17.1230	−	9.08026i	−1.45760	−	0.772963i
$139$	−17.9824			−1.52525			−0.762625	−	0.646840i	$-0.776090\pi$
$139$	−17.9824			−1.52525			−0.762625	+	0.646840i	$0.776090\pi$
$140$	−5.40147	+	7.77188i	−0.456508	+	0.656843i
$141$	−3.97066	+	1.21158i	−0.334390	+	0.102033i
$142$	−5.47744	−	5.45942i	−0.459656	−	0.458144i
$143$	1.23984	+	2.14746i	0.103680	+	0.179580i
$144$	−0.902885	−	11.9660i	−0.0752404	−	0.997165i
$145$	1.15928	+	0.669310i	0.0962728	+	0.0555831i
$146$	−2.38818	+	8.97191i	−0.197647	+	0.742520i
$147$	7.29532	+	9.68392i	0.601708	+	0.798716i
$148$	3.70182	−	6.46082i	0.304288	−	0.531076i
$149$	0.462495	−	0.801066i	0.0378891	−	0.0656258i	−0.846459	−	0.532454i	$-0.821270\pi$
$149$	0.462495	−	0.801066i	0.0378891	−	0.0656258i	0.884348	+	0.466828i	$0.154603\pi$
$150$	−2.34160	−	3.73817i	−0.191191	−	0.305221i
$151$	9.56720	+	16.5709i	0.778568	+	1.34852i	0.932767	+	0.360479i	$0.117387\pi$
$151$	9.56720	+	16.5709i	0.778568	+	1.34852i	−0.154200	+	0.988040i	$0.549280\pi$
$152$	10.1464	−	2.77255i	0.822982	−	0.224883i
$153$	−16.5745	+	11.1533i	−1.33997	+	0.901693i
$154$	−3.52785	−	1.27663i	−0.284282	−	0.102874i
$155$	−5.93277			−0.476531
$156$	−5.82528	+	6.28138i	−0.466396	+	0.502913i
$157$	5.46873	+	9.47212i	0.436452	+	0.755957i	0.997413	−	0.0718851i	$-0.0229015\pi$
$157$	5.46873	+	9.47212i	0.436452	+	0.755957i	−0.560961	+	0.827842i	$0.689568\pi$
$158$	−1.87075	−	6.93601i	−0.148829	−	0.551800i
$159$	−4.95125	+	21.3929i	−0.392659	+	1.69657i
$160$	9.75137	−	2.69917i	0.770914	−	0.213388i
$161$	−17.1510	−	12.0040i	−1.35169	−	0.946050i
$162$	−7.66531	+	10.1609i	−0.602244	+	0.798312i
$163$	9.21188	+	5.31848i	0.721530	+	0.416576i	0.815316	−	0.579017i	$-0.196563\pi$
$163$	9.21188	+	5.31848i	0.721530	+	0.416576i	−0.0937855	+	0.995592i	$0.529897\pi$
$164$	0.0132504	+	4.02086i	0.00103468	+	0.313976i
$165$	−2.11976	+	2.27068i	−0.165023	+	0.176772i
$166$	−5.66388	−	5.64524i	−0.439602	−	0.438156i
$167$	7.93040			0.613673			0.306836	−	0.951762i	$-0.400730\pi$
$167$	7.93040			0.613673			0.306836	+	0.951762i	$0.400730\pi$
$168$	0.618766	−	12.9467i	0.0477388	−	0.998860i
$169$	−6.88419			−0.529553
$170$	−11.9306	−	11.8913i	−0.915034	−	0.912023i
$171$	−10.0220	−	4.90161i	−0.766401	−	0.374836i
$172$	−18.3929	+	0.0606121i	−1.40245	+	0.00462163i
$173$	−3.69882	−	2.13552i	−0.281216	−	0.162360i	0.352758	−	0.935715i	$-0.385244\pi$
$173$	−3.69882	−	2.13552i	−0.281216	−	0.162360i	−0.633974	+	0.773354i	$0.718577\pi$
$174$	−1.83202	+	0.0659960i	−0.138885	+	0.00500314i
$175$	−2.01443	−	4.31763i	−0.152276	−	0.326382i
$176$	2.02823	+	3.46014i	0.152884	+	0.260818i
$177$	14.3199	+	3.31425i	1.07635	+	0.249115i
$178$	−5.44676	−	20.1944i	−0.408252	−	1.51364i
$179$	−3.77825	−	6.54412i	−0.282399	−	0.489130i	0.689576	−	0.724214i	$-0.257797\pi$
$179$	−3.77825	−	6.54412i	−0.282399	−	0.489130i	−0.971975	+	0.235083i	$0.924464\pi$
$180$	−9.65602	−	4.68325i	−0.719717	−	0.349069i
$181$	−5.00239			−0.371824			−0.185912	−	0.982566i	$-0.559524\pi$
$181$	−5.00239			−0.371824			−0.185912	+	0.982566i	$0.559524\pi$
$182$	−7.07731	+	5.96096i	−0.524605	+	0.441856i
$183$	6.70749	−	2.04668i	0.495832	−	0.151295i
$184$	5.89915	+	21.5885i	0.434891	+	1.59152i
$185$	−3.32963	−	5.76708i	−0.244799	−	0.424004i
$186$	6.88546	−	4.31306i	0.504866	−	0.316249i
$187$	3.33859	−	5.78261i	0.244142	−	0.422867i
$188$	4.15927	+	2.38311i	0.303346	+	0.173806i
$189$	−9.56413	+	9.87560i	−0.695688	+	0.718344i
$190$	2.41968	−	9.09025i	0.175542	−	0.659476i
$191$	−10.4891	−	6.05587i	−0.758963	−	0.438188i	0.0699601	−	0.997550i	$-0.477713\pi$
$191$	−10.4891	−	6.05587i	−0.758963	−	0.438188i	−0.828923	+	0.559362i	$0.811046\pi$
$192$	−9.35498	+	10.2218i	−0.675138	+	0.737692i
$193$	0.592437	+	1.02613i	0.0426445	+	0.0738625i	0.886560	−	0.462614i	$-0.153088\pi$
$193$	0.592437	+	1.02613i	0.0426445	+	0.0738625i	−0.843915	+	0.536476i	$0.819755\pi$
$194$	1.75866	+	1.75287i	0.126264	+	0.125849i
$195$	2.23598	+	7.32787i	0.160122	+	0.524760i
$196$	2.37994	−	13.7962i	0.169996	−	0.985445i
$197$	19.5111			1.39011			0.695054	−	0.718957i	$-0.255380\pi$
$197$	19.5111			1.39011			0.695054	+	0.718957i	$0.255380\pi$
$198$	0.809395	−	4.17636i	0.0575212	−	0.296801i
$199$	−12.7632	+	7.36884i	−0.904760	+	0.522363i	−0.878741	−	0.477298i	$-0.841616\pi$
$199$	−12.7632	+	7.36884i	−0.904760	+	0.522363i	−0.0260186	+	0.999661i	$0.508283\pi$
$200$	−1.29393	+	4.92630i	−0.0914949	+	0.348342i
$201$	13.4415	+	3.11096i	0.948093	+	0.219430i
$202$	−5.32638	+	20.0101i	−0.374763	+	1.40791i
$203$	−1.97259	−	0.172170i	−0.138449	−	0.0120839i
$204$	22.4913	+	5.12743i	1.57470	+	0.358992i
$205$	3.11418	+	1.79797i	0.217503	+	0.125576i
$206$	−13.4655	+	3.63186i	−0.938185	+	0.253043i
$207$	10.4292	−	21.3238i	0.724876	−	1.48211i
$208$	9.89185	−	0.0651960i	0.685876	−	0.00452053i
$209$	3.72883			0.257929
$210$	−9.72984	−	6.30056i	−0.671423	−	0.434780i
$211$			14.9240i			1.02741i	0.857967	+	0.513704i	$0.171727\pi$
$211$			14.9240i			1.02741i	−0.857967	+	0.513704i	$0.828273\pi$
$212$	21.9165	−	12.7500i	1.50523	−	0.875672i
$213$	6.46340	−	6.92356i	0.442865	−	0.474395i
$214$	−2.56401	−	9.50634i	−0.175272	−	0.649840i
$215$	−8.22459	+	14.2454i	−0.560913	+	0.971529i
$216$	14.6113	−	1.58454i	0.994171	−	0.107814i
$217$	7.95278	−	3.71044i	0.539870	−	0.251881i
$218$	−0.992886	+	3.73007i	−0.0672467	+	0.252633i
$219$	−11.0781	−	2.56395i	−0.748587	−	0.173256i
$220$	3.58688	−	0.0118202i	0.241828	−	0.000796920i
$221$	−8.23422	−	14.2621i	−0.553894	−	0.959372i
$222$	8.05691	+	4.27256i	0.540745	+	0.286755i
$223$			7.62187i			0.510398i	0.966889	+	0.255199i	$0.0821410\pi$
$223$			7.62187i			0.510398i	−0.966889	+	0.255199i	$0.917859\pi$
$224$	−11.3835	+	9.71684i	−0.760589	+	0.649233i
$225$	4.48206	−	3.01607i	0.298804	−	0.201071i
$226$	0.532028	+	0.530278i	0.0353900	+	0.0352735i
$227$	−13.6531	+	7.88264i	−0.906190	+	0.523189i	−0.879203	−	0.476446i	$-0.841925\pi$
$227$	−13.6531	+	7.88264i	−0.906190	+	0.523189i	−0.0269870	+	0.999636i	$0.508591\pi$
$228$	3.80029	+	12.3091i	0.251680	+	0.815187i
$229$	−8.82193	+	15.2800i	−0.582970	+	1.00973i	0.412155	+	0.911114i	$0.364776\pi$
$229$	−8.82193	+	15.2800i	−0.582970	+	1.00973i	−0.995125	+	0.0986198i	$0.968557\pi$
$230$	19.3413	+	5.14835i	1.27533	+	0.339472i
$231$	1.42139	−	4.36954i	0.0935208	−	0.287495i
$232$	1.50419	+	1.48939i	0.0987547	+	0.0977832i
$233$	15.7079	+	9.06896i	1.02906	+	0.594127i	0.916715	−	0.399542i	$-0.130831\pi$
$233$	15.7079	+	9.06896i	1.02906	+	0.594127i	0.112344	+	0.993669i	$0.464164\pi$
$234$	−7.92232	−	6.87905i	−0.517899	−	0.449698i
$235$	3.71266	−	2.14350i	0.242187	−	0.139827i
$236$	−8.53454	−	14.6704i	−0.555551	−	0.954962i
$237$	8.41536	−	2.56781i	0.546637	−	0.166797i
$238$	23.4297	+	8.47858i	1.51872	+	0.549585i
$239$			5.41040i			0.349970i	0.984571	+	0.174985i	$0.0559877\pi$
$239$			5.41040i			0.349970i	−0.984571	+	0.174985i	$0.944012\pi$
$240$	3.69464	+	11.8284i	0.238488	+	0.763522i
$241$	−18.6025	+	10.7401i	−1.19829	+	0.691834i	−0.960174	−	0.279403i	$-0.909863\pi$
$241$	−18.6025	+	10.7401i	−1.19829	+	0.691834i	−0.238117	+	0.971236i	$0.576530\pi$
$242$	−3.68077	−	13.6468i	−0.236609	−	0.877252i
$243$	−12.7449	−	8.97601i	−0.817583	−	0.575811i
$244$	−7.02610	−	4.02571i	−0.449800	−	0.257719i
$245$	−9.59453	−	8.04403i	−0.612972	−	0.513914i
$246$	−4.92136	+	0.177285i	−0.313774	+	0.0113033i
$247$	4.59834	−	7.96457i	0.292586	−	0.506773i
$248$	−9.07391	−	2.38334i	−0.576194	−	0.151342i
$249$	6.68340	−	7.15923i	0.423543	−	0.453698i
$250$	12.1841	+	12.1441i	0.770593	+	0.768058i
$251$		−	19.8553i		−	1.25325i	−0.779319	−	0.626627i	$-0.784435\pi$
$251$		−	19.8553i		−	1.25325i	0.779319	−	0.626627i	$-0.215565\pi$
$252$	15.8727	+	0.238811i	0.999887	+	0.0150437i
$253$			7.93382i			0.498795i
$254$	−4.51647	+	4.53138i	−0.283389	+	0.284324i
$255$	14.0781	−	15.0804i	0.881607	−	0.944373i
$256$	15.9986	−	0.210899i	0.999913	−	0.0131812i
$257$	4.36616	−	7.56240i	0.272353	−	0.471730i	−0.697111	−	0.716964i	$-0.745531\pi$
$257$	4.36616	−	7.56240i	0.272353	−	0.471730i	0.969464	+	0.245234i	$0.0788647\pi$
$258$	−0.810970	−	22.5121i	−0.0504888	−	1.40154i
$259$	8.07012	+	5.64828i	0.501453	+	0.350967i
$260$	4.39805	−	7.67595i	0.272755	−	0.476042i
$261$	−0.154171	−	2.23991i	−0.00954295	−	0.138647i
$262$	21.1156	−	5.69522i	1.30453	−	0.351852i
$263$	17.1429	−	9.89747i	1.05708	−	0.610304i	0.132455	−	0.991189i	$-0.457714\pi$
$263$	17.1429	−	9.89747i	1.05708	−	0.610304i	0.924623	+	0.380885i	$0.124381\pi$
$264$	−4.15427	+	2.62135i	−0.255678	+	0.161333i
$265$		−	22.6757i		−	1.39296i
$266$	2.44163	+	13.6986i	0.149706	+	0.839917i
$267$	24.5016	−	7.47627i	1.49947	−	0.457540i
$268$	−8.01104	−	13.7705i	−0.489352	−	0.841169i
$269$	0.805574	−	0.465098i	0.0491167	−	0.0283575i	−0.475241	−	0.879856i	$-0.657639\pi$
$269$	0.805574	−	0.465098i	0.0491167	−	0.0283575i	0.524357	+	0.851498i	$0.324306\pi$
$270$	5.34592	−	12.0074i	0.325343	−	0.730749i
$271$	−7.45646	−	4.30499i	−0.452948	−	0.261509i	0.256127	−	0.966643i	$-0.417554\pi$
$271$	−7.45646	−	4.30499i	−0.452948	−	0.261509i	−0.709074	+	0.705134i	$0.750887\pi$
$272$	−13.4703	−	22.9801i	−0.816754	−	1.39337i
$273$	−7.58025	−	8.42448i	−0.458777	−	0.509873i
$274$	−4.07950	+	15.3259i	−0.246452	+	0.925870i
$275$	−0.902819	+	1.56373i	−0.0544420	+	0.0942964i
$276$	−26.1899	+	8.08587i	−1.57645	+	0.486712i
$277$	25.5583	−	14.7561i	1.53565	−	0.886607i	0.536562	−	0.843861i	$-0.319723\pi$
$277$	25.5583	−	14.7561i	1.53565	−	0.886607i	0.999086	−	0.0427456i	$-0.0136105\pi$
$278$	−17.9528	+	18.0120i	−1.07674	+	1.08029i
$279$	5.55539	+	8.25565i	0.332593	+	0.494253i
$280$	2.39211	+	13.1694i	0.142956	+	0.787024i
$281$			21.3260i			1.27220i	0.771605	+	0.636102i	$0.219454\pi$
$281$			21.3260i			1.27220i	−0.771605	+	0.636102i	$0.780546\pi$
$282$	−2.75053	+	5.18678i	−0.163792	+	0.308868i
$283$	−10.4247	−	18.0561i	−0.619684	−	1.07332i	−0.989543	−	0.144236i	$-0.953928\pi$
$283$	−10.4247	−	18.0561i	−0.619684	−	1.07332i	0.369860	−	0.929088i	$-0.379406\pi$
$284$	−10.9368	+	0.0360412i	−0.648980	+	0.00213865i
$285$	11.2242	+	2.59777i	0.664865	+	0.153879i
$286$	3.38879	+	0.902042i	0.200383	+	0.0533389i
$287$	−5.29898	−	0.462500i	−0.312789	−	0.0273005i
$288$	−12.8871	−	11.0419i	−0.759379	−	0.650649i
$289$	−13.6728	+	23.6820i	−0.804284	+	1.39306i
$290$	1.82778	−	0.492981i	0.107331	−	0.0289488i
$291$	−2.07523	+	2.22297i	−0.121652	+	0.130313i
$292$	6.60244	+	11.3492i	0.386378	+	0.664163i
$293$			13.1058i			0.765652i	0.923821	+	0.382826i	$0.125049\pi$
$293$			13.1058i			0.765652i	−0.923821	+	0.382826i	$0.874951\pi$
$294$	16.9832	+	2.36062i	0.990478	+	0.137674i
$295$	−15.1786			−0.883733
$296$	−2.77574	−	10.1581i	−0.161337	−	0.590427i
$297$	5.14466	+	0.823477i	0.298523	+	0.0477830i
$298$	−0.340652	−	1.26300i	−0.0197334	−	0.0731637i
$299$	16.9462	+	9.78389i	0.980023	+	0.565817i
$300$	−6.08207	−	1.38655i	−0.351148	−	0.0800528i
$301$	2.11565	−	24.2395i	0.121944	−	1.39714i
$302$	26.1496	+	6.96060i	1.50474	+	0.400537i
$303$	−24.7076	−	5.71841i	−1.41941	−	0.328514i
$304$	7.35256	−	12.9311i	0.421698	−	0.741649i
$305$	−6.27166	+	3.62094i	−0.359114	+	0.207335i
$306$	−5.37549	+	27.7367i	−0.307296	+	1.58560i
$307$	18.6425			1.06398			0.531992	−	0.846750i	$-0.321444\pi$
$307$	18.6425			1.06398			0.531992	+	0.846750i	$0.321444\pi$
$308$	−4.80076	+	2.25913i	−0.273549	+	0.128726i
$309$	−4.98511	−	16.3375i	−0.283593	−	0.929406i
$310$	−5.92299	+	5.94254i	−0.336403	+	0.337513i
$311$	−9.92896	−	17.1975i	−0.563020	−	0.975179i	−0.997231	−	0.0743677i	$-0.976306\pi$
$311$	−9.92896	−	17.1975i	−0.563020	−	0.975179i	0.434211	−	0.900811i	$-0.357027\pi$
$312$	0.476049	+	12.1059i	0.0269510	+	0.685362i
$313$	2.33108	+	1.34585i	0.131760	+	0.0760718i	0.564431	−	0.825480i	$-0.309096\pi$
$313$	2.33108	+	1.34585i	0.131760	+	0.0760718i	−0.432671	+	0.901552i	$0.642429\pi$
$314$	14.9474	+	3.97876i	0.843532	+	0.224535i
$315$	7.32270	−	12.1626i	0.412587	−	0.685284i
$316$	−8.81510	−	5.05074i	−0.495888	−	0.284126i
$317$	5.35288	−	9.27147i	0.300648	−	0.520737i	−0.675635	−	0.737236i	$-0.736130\pi$
$317$	5.35288	−	9.27147i	0.300648	−	0.520737i	0.976283	+	0.216499i	$0.0694638\pi$
$318$	16.4850	+	26.3170i	0.924435	+	1.47578i
$319$	0.375209	+	0.649881i	0.0210077	+	0.0363864i
$320$	7.03168	−	12.4621i	0.393083	−	0.696655i
$321$	11.5339	−	3.51938i	0.643760	−	0.196433i
$322$	−29.1466	+	5.19505i	−1.62427	+	0.289509i
$323$	−24.7645			−1.37794
$324$	2.52491	+	17.8220i	0.140273	+	0.990113i
$325$	2.22669	+	3.85674i	0.123514	+	0.213933i
$326$	14.5239	−	3.91733i	0.804406	−	0.216961i
$327$	−4.60572	−	1.06596i	−0.254697	−	0.0589479i
$328$	4.04071	+	4.00095i	0.223111	+	0.220916i
$329$	−3.63618	+	5.19528i	−0.200469	+	0.286425i
$330$	0.158151	+	4.39019i	0.00870592	+	0.241672i
$331$	−18.8525	−	10.8845i	−1.03623	−	0.598266i	−0.117465	−	0.993077i	$-0.537477\pi$
$331$	−18.8525	−	10.8845i	−1.03623	−	0.598266i	−0.918762	+	0.394811i	$0.870810\pi$
$332$	−11.3091	+	0.0372680i	−0.620666	+	0.00204535i
$333$	−4.90725	+	10.0335i	−0.268916	+	0.549834i
$334$	7.91732	−	7.94346i	0.433217	−	0.434647i
$335$	−14.2476			−0.778428
$336$	−12.3503	−	13.5451i	−0.673763	−	0.738948i
$337$	−11.3104			−0.616116			−0.308058	−	0.951368i	$-0.599679\pi$
$337$	−11.3104			−0.616116			−0.308058	+	0.951368i	$0.599679\pi$
$338$	−6.87284	+	6.89552i	−0.373833	+	0.375067i
$339$	−0.627796	+	0.672492i	−0.0340972	+	0.0365247i
$340$	−23.8218	+	0.0785025i	−1.29192	+	0.00425740i
$341$	−2.88028	−	1.66293i	−0.155976	−	0.0900527i
$342$	−14.9152	+	5.14497i	−0.806519	+	0.278208i
$343$	17.8922	+	4.78234i	0.966086	+	0.258222i
$344$	−18.3019	+	18.4837i	−0.986771	+	0.996575i
$345$	−5.52727	+	23.8817i	−0.297578	+	1.28575i
$346$	−5.83175	+	1.57292i	−0.313517	+	0.0845606i
$347$	9.94032	+	17.2171i	0.533624	+	0.924265i	0.999229	+	0.0392715i	$0.0125037\pi$
$347$	9.94032	+	17.2171i	0.533624	+	0.924265i	−0.465604	+	0.884993i	$0.654163\pi$
$348$	−1.76289	+	1.90092i	−0.0945009	+	0.101900i
$349$	−9.45348			−0.506033			−0.253017	−	0.967462i	$-0.581423\pi$
$349$	−9.45348			−0.506033			−0.253017	+	0.967462i	$0.581423\pi$
$350$	−6.33585	−	2.29277i	−0.338665	−	0.122554i
$351$	8.10323	−	9.97319i	0.432518	−	0.532330i
$352$	5.49072	+	1.42286i	0.292657	+	0.0758386i
$353$	8.48135	+	14.6901i	0.451417	+	0.781877i	0.998474	−	0.0552182i	$-0.0175854\pi$
$353$	8.48135	+	14.6901i	0.451417	+	0.781877i	−0.547057	+	0.837095i	$0.684252\pi$
$354$	17.6160	−	11.0347i	0.936281	−	0.586488i
$355$	−4.89051	+	8.47062i	−0.259561	+	0.449574i
$356$	−25.6655	−	14.7054i	−1.36027	−	0.779385i
$357$	−9.44000	+	29.0197i	−0.499618	+	1.53589i
$358$	−10.3269	−	2.74886i	−0.545794	−	0.145282i
$359$	−18.2162	−	10.5171i	−0.961413	−	0.555072i	−0.0648056	−	0.997898i	$-0.520643\pi$
$359$	−18.2162	−	10.5171i	−0.961413	−	0.555072i	−0.896608	+	0.442826i	$0.853976\pi$
$360$	−14.3311	+	4.99639i	−0.755313	+	0.263333i
$361$	2.58521	+	4.47771i	0.136064	+	0.235669i
$362$	−4.99414	+	5.01062i	−0.262486	+	0.263352i
$363$	16.5575	−	5.05225i	0.869044	−	0.265174i
$364$	−1.09487	+	13.0401i	−0.0573866	+	0.683486i
$365$	11.7424			0.614625
$366$	4.64638	−	8.76183i	0.242870	−	0.457988i
$367$	1.24875	−	0.720966i	0.0651842	−	0.0376341i	−0.467054	−	0.884229i	$-0.654685\pi$
$367$	1.24875	−	0.720966i	0.0651842	−	0.0376341i	0.532238	+	0.846595i	$0.321351\pi$
$368$	27.5135	+	15.6440i	1.43424	+	0.815501i
$369$	−0.414151	−	6.01708i	−0.0215598	−	0.313237i
$370$	−9.10071	−	2.42246i	−0.473124	−	0.125938i
$371$	14.1817	+	30.3964i	0.736278	+	1.57810i
$372$	2.55394	−	11.2027i	0.132415	−	0.580835i
$373$	−18.8362	−	10.8751i	−0.975302	−	0.563091i	−0.0744535	−	0.997224i	$-0.523721\pi$
$373$	−18.8362	−	10.8751i	−0.975302	−	0.563091i	−0.900848	+	0.434134i	$0.857055\pi$
$374$	−2.45905	−	9.11717i	−0.127154	−	0.471438i
$375$	−14.3774	+	15.4010i	−0.742443	+	0.795302i
$376$	6.53944	−	1.78693i	0.337246	−	0.0921539i
$377$	1.85081			0.0953217
$378$	0.343496	+	19.4392i	0.0176675	+	0.999844i
$379$		−	1.82298i		−	0.0936402i	−0.998903	−	0.0468201i	$-0.985091\pi$
$379$		−	1.82298i		−	0.0936402i	0.998903	−	0.0468201i	$-0.0149087\pi$
$380$	−6.68953	−	11.4989i	−0.343166	−	0.589882i
$381$	−5.72774	−	5.34705i	−0.293441	−	0.273938i
$382$	−16.5376	+	4.46046i	−0.846139	+	0.228217i
$383$	4.81069	−	8.33236i	0.245815	−	0.425763i	−0.716546	−	0.697540i	$-0.754278\pi$
$383$	4.81069	−	8.33236i	0.245815	−	0.425763i	0.962360	+	0.271777i	$0.0876112\pi$
$384$	0.899025	+	19.5753i	0.0458782	+	0.998947i
$385$	−0.412582	+	4.72705i	−0.0210271	+	0.240913i
$386$	1.61928	+	0.431026i	0.0824192	+	0.0219387i
$387$	27.5244	−	1.89448i	1.39914	−	0.0963019i
$388$	3.51152	−	0.0115719i	0.178270	−	0.000587473i
$389$	−14.0629	−	24.3576i	−0.713017	−	1.23498i	−0.963719	−	0.266917i	$-0.913995\pi$
$389$	−14.0629	−	24.3576i	−0.713017	−	1.23498i	0.250703	−	0.968064i	$-0.419338\pi$
$390$	9.57223	+	5.07613i	0.484709	+	0.257040i
$391$		−	52.6914i		−	2.66472i
$392$	−11.4429	−	16.1573i	−0.577955	−	0.816069i
$393$	7.81730	+	25.6193i	0.394331	+	1.29232i
$394$	19.4789	−	19.5432i	0.981334	−	0.984573i
$395$	−7.86857	+	4.54292i	−0.395911	+	0.228579i
$396$	−3.37517	−	4.98020i	−0.169609	−	0.250264i
$397$	9.42646	−	16.3271i	0.473101	−	0.819434i	−0.526425	−	0.850221i	$-0.676468\pi$
$397$	9.42646	−	16.3271i	0.473101	−	0.819434i	0.999526	+	0.0307871i	$0.00980139\pi$
$398$	−5.36119	+	20.1409i	−0.268732	+	1.00957i
$399$	−16.6706	+	3.53751i	−0.834571	+	0.177097i
$400$	3.64261	+	6.21424i	0.182131	+	0.310712i
$401$	5.22718	+	3.01791i	0.261033	+	0.150707i	0.624806	−	0.780780i	$-0.285178\pi$
$401$	5.22718	+	3.01791i	0.261033	+	0.150707i	−0.363773	+	0.931488i	$0.618512\pi$
$402$	16.5355	−	10.3578i	0.824714	−	0.516602i
$403$	−7.10385	+	4.10141i	−0.353868	+	0.204306i
$404$	14.7255	+	25.3123i	0.732621	+	1.25933i
$405$	14.9123	+	6.06290i	0.740999	+	0.301268i
$406$	−2.14179	+	1.80395i	−0.106295	+	0.0895286i
$407$		−	3.73312i		−	0.185044i
$408$	27.5901	−	17.4093i	1.36591	−	0.861890i
$409$	22.6629	−	13.0844i	1.12061	−	0.646984i	0.179052	−	0.983840i	$-0.442697\pi$
$409$	22.6629	−	13.0844i	1.12061	−	0.646984i	0.941556	+	0.336856i	$0.109364\pi$
$410$	4.90997	−	1.32430i	0.242486	−	0.0654024i
$411$	−18.9237	−	4.37976i	−0.933436	−	0.216038i
$412$	−9.80544	+	17.1135i	−0.483080	+	0.843123i
$413$	20.3467	−	9.49292i	1.00120	−	0.467116i
$414$	−10.9469	−	31.7349i	−0.538012	−	1.55969i
$415$	−5.05698	+	8.75894i	−0.248237	+	0.429959i
$416$	9.81023	−	9.97322i	0.480986	−	0.488978i
$417$	−22.7675	−	21.2543i	−1.11493	−	1.04083i
$418$	3.72268	−	3.73497i	0.182082	−	0.182683i
$419$			2.51866i			0.123045i	0.998106	+	0.0615223i	$0.0195955\pi$
$419$			2.51866i			0.123045i	−0.998106	+	0.0615223i	$0.980404\pi$
$420$	−16.0247	+	3.45569i	−0.781927	+	0.168620i
$421$			33.4873i			1.63207i	0.578003	+	0.816034i	$0.303832\pi$
$421$			33.4873i			1.63207i	−0.578003	+	0.816034i	$0.696168\pi$
$422$	14.9485	+	14.8994i	0.727684	+	0.725289i
$423$	−6.45926	−	3.15913i	−0.314060	−	0.153602i
$424$	9.10938	−	34.6815i	0.442391	−	1.68428i
$425$	5.99595	−	10.3853i	0.290846	−	0.503761i
$426$	−0.482220	−	13.3862i	−0.0233636	−	0.648563i
$427$	6.14247	−	8.77620i	0.297255	−	0.424710i
$428$	−12.0818	−	6.92243i	−0.583995	−	0.334608i
$429$	−0.968433	+	4.18432i	−0.0467564	+	0.202021i
$430$	6.05783	+	22.4601i	0.292135	+	1.08312i
$431$	12.0003	−	6.92836i	0.578033	−	0.333727i	−0.182319	−	0.983240i	$-0.558360\pi$
$431$	12.0003	−	6.92836i	0.578033	−	0.333727i	0.760351	+	0.649512i	$0.225027\pi$
$432$	13.0000	−	16.2173i	0.625464	−	0.780253i
$433$			9.79368i			0.470654i	0.971916	+	0.235327i	$0.0756161\pi$
$433$			9.79368i			0.470654i	−0.971916	+	0.235327i	$0.924384\pi$
$434$	4.22312	−	11.6702i	0.202716	−	0.560187i
$435$	0.676669	+	2.21762i	0.0324438	+	0.106327i
$436$	2.74497	+	4.71844i	0.131460	+	0.225973i
$437$	25.4829	−	14.7126i	1.21901	−	0.703798i
$438$	−13.6280	+	8.53660i	−0.651170	+	0.407894i
$439$	6.99463	+	4.03835i	0.333835	+	0.192740i	0.657543	−	0.753417i	$-0.271596\pi$
$439$	6.99463	+	4.03835i	0.333835	+	0.192740i	−0.323707	+	0.946157i	$0.604929\pi$
$440$	3.56913	−	3.60459i	0.170151	−	0.171842i
$441$	−2.20931	+	20.8835i	−0.105205	+	0.994451i
$442$	−22.5062	−	5.99079i	−1.07051	−	0.284953i
$443$	−8.84884	+	15.3266i	−0.420421	+	0.728191i	−0.995981	−	0.0895692i	$-0.971451\pi$
$443$	−8.84884	+	15.3266i	−0.420421	+	0.728191i	0.575559	+	0.817760i	$0.304784\pi$
$444$	12.3232	−	3.80466i	0.584834	−	0.180561i
$445$	−22.9096	+	13.2269i	−1.08602	+	0.627014i
$446$	7.63441	+	7.60930i	0.361500	+	0.360311i
$447$	1.53238	−	0.467581i	0.0724791	−	0.0221158i
$448$	−1.63185	+	21.1030i	−0.0770977	+	0.997024i
$449$		−	19.4650i		−	0.918609i	−0.888279	−	0.459305i	$-0.848099\pi$
$449$		−	19.4650i		−	0.918609i	0.888279	−	0.459305i	$-0.151901\pi$
$450$	1.45363	−	7.50054i	0.0685250	−	0.353579i
$451$	1.00793	+	1.74578i	0.0474614	+	0.0822056i
$452$	1.06230	−	0.00350071i	0.0499665	−	0.000164660i
$453$	−7.47291	+	32.2882i	−0.351108	+	1.51703i
$454$	−5.73500	+	21.5453i	−0.269157	+	1.01117i
$455$	9.58793	+	6.71059i	0.449489	+	0.314597i
$456$	16.1233	+	8.48221i	0.755045	+	0.397216i
$457$	7.75626	−	13.4342i	0.362823	−	0.628427i	−0.625601	−	0.780143i	$-0.715146\pi$
$457$	7.75626	−	13.4342i	0.362823	−	0.628427i	0.988424	+	0.151715i	$0.0484797\pi$
$458$	6.49781	+	24.0913i	0.303623	+	1.12571i
$459$	−34.1676	−	5.46902i	−1.59481	−	0.255272i
$460$	24.4662	−	14.2333i	1.14074	−	0.663631i
$461$		−	0.857290i		−	0.0399280i	−0.999801	−	0.0199640i	$-0.993645\pi$
$461$		−	0.857290i		−	0.0399280i	0.999801	−	0.0199640i	$-0.00635516\pi$
$462$	−2.95769	−	5.78607i	−0.137604	−	0.269192i
$463$	37.5731			1.74617			0.873086	−	0.487566i	$-0.162115\pi$
$463$	37.5731			1.74617			0.873086	+	0.487566i	$0.162115\pi$
$464$	2.99355	−	0.0197301i	0.138972	−	0.000915947i
$465$	−7.51146	−	7.01222i	−0.348335	−	0.325184i
$466$	24.7659	−	6.67975i	1.14726	−	0.309434i
$467$	−8.69155	−	5.01807i	−0.402197	−	0.232208i	0.285235	−	0.958458i	$-0.407928\pi$
$467$	−8.69155	−	5.01807i	−0.402197	−	0.232208i	−0.687431	+	0.726249i	$0.741262\pi$
$468$	−14.7996	+	1.06766i	−0.684113	+	0.0493526i
$469$	19.0986	−	8.91063i	0.881893	−	0.411455i
$470$	1.55950	−	5.85874i	0.0719345	−	0.270244i
$471$	−4.27161	+	18.4564i	−0.196825	+	0.850424i
$472$	−23.2150	−	6.09762i	−1.06856	−	0.280666i
$473$	−7.98586	+	4.61064i	−0.367190	+	0.211997i
$474$	5.82945	−	10.9928i	0.267755	−	0.504916i
$475$	6.69680			0.307270
$476$	31.8836	−	15.0037i	1.46138	−	0.687695i
$477$	−31.5540	+	21.2333i	−1.44476	+	0.972208i
$478$	5.41931	+	5.40148i	0.247873	+	0.247058i
$479$	11.0594	+	19.1555i	0.505318	+	0.875237i	0.999981	+	0.00615194i	$0.00195824\pi$
$479$	11.0594	+	19.1555i	0.505318	+	0.875237i	−0.494663	+	0.869085i	$0.664708\pi$
$480$	15.5365	+	8.10820i	0.709139	+	0.370087i
$481$	−7.97373	−	4.60364i	−0.363571	−	0.209908i
$482$	−7.81397	+	29.3555i	−0.355917	+	1.33711i
$483$	−7.52675	−	35.4699i	−0.342479	−	1.61394i
$484$	−17.3440	−	9.93751i	−0.788364	−	0.451705i
$485$	1.57021	−	2.71969i	0.0712997	−	0.123495i
$486$	−21.7146	+	3.80463i	−0.984995	+	0.172581i
$487$	11.2659	+	19.5131i	0.510506	+	0.884223i	0.999926	+	0.0121746i	$0.00387541\pi$
$487$	11.2659	+	19.5131i	0.510506	+	0.884223i	−0.489419	+	0.872049i	$0.662791\pi$
$488$	−11.0468	+	3.01860i	−0.500067	+	0.136645i
$489$	5.37696	+	17.6217i	0.243155	+	0.796879i
$490$	−17.6360	+	1.57956i	−0.796712	+	0.0713572i
$491$	−25.1085			−1.13313			−0.566565	−	0.824017i	$-0.691728\pi$
$491$	−25.1085			−1.13313			−0.566565	+	0.824017i	$0.691728\pi$
$492$	−4.73567	+	5.10645i	−0.213500	+	0.230217i
$493$	−2.49190	−	4.31610i	−0.112230	−	0.194387i
$494$	−3.38692	−	12.5573i	−0.152385	−	0.564982i
$495$	−5.36765	+	0.369451i	−0.241258	+	0.0166056i
$496$	−11.4462	+	6.70944i	−0.513950	+	0.301263i
$497$	1.25801	−	14.4133i	0.0564295	−	0.646526i
$498$	−0.498633	−	13.8418i	−0.0223443	−	0.620267i
$499$	−9.19695	−	5.30986i	−0.411712	−	0.237702i	0.279813	−	0.960054i	$-0.409727\pi$
$499$	−9.19695	−	5.30986i	−0.411712	−	0.237702i	−0.691525	+	0.722353i	$0.743061\pi$
$500$	24.3281	−	0.0801710i	1.08799	−	0.00358535i
$501$	10.0407	+	9.37332i	0.448583	+	0.418769i
$502$	−19.8880	−	19.8225i	−0.887643	−	0.884723i
$503$	13.3046			0.593223			0.296612	−	0.954998i	$-0.404143\pi$
$503$	13.3046			0.593223			0.296612	+	0.954998i	$0.404143\pi$
$504$	16.0857	−	15.6604i	0.716516	−	0.697571i
$505$	26.1892			1.16540
$506$	7.94688	+	7.92074i	0.353282	+	0.352120i
$507$	−8.71605	−	8.13675i	−0.387093	−	0.361366i
$508$	0.0298162	+	9.04782i	0.00132288	+	0.401432i
$509$	−20.2595	−	11.6968i	−0.897985	−	0.518452i	−0.0214392	−	0.999770i	$-0.506825\pi$
$509$	−20.2595	−	11.6968i	−0.897985	−	0.518452i	−0.876546	+	0.481318i	$0.840158\pi$
$510$	−1.05034	−	29.1569i	−0.0465097	−	1.29109i
$511$	−15.7405	+	7.34385i	−0.696318	+	0.324873i
$512$	15.7610	−	16.2355i	0.696544	−	0.717515i
$513$	−6.89536	−	18.0514i	−0.304438	−	0.796988i
$514$	−3.21590	−	11.9233i	−0.141847	−	0.525913i
$515$	8.81956	+	15.2759i	0.388636	+	0.673138i
$516$	−23.3588	−	21.6627i	−1.02832	−	0.953648i
$517$	2.40326			0.105695
$518$	13.7144	−	2.44444i	0.602576	−	0.107403i
$519$	−2.15900	−	7.07558i	−0.0947695	−	0.310584i
$520$	−3.29779	−	12.0686i	−0.144618	−	0.529242i
$521$	−0.735700	−	1.27427i	−0.0322316	−	0.0558267i	0.849460	−	0.527654i	$-0.176928\pi$
$521$	−0.735700	−	1.27427i	−0.0322316	−	0.0558267i	−0.881691	+	0.471827i	$0.843595\pi$
$522$	−2.39751	−	2.08179i	−0.104936	−	0.0911175i
$523$	−5.30372	+	9.18631i	−0.231915	+	0.401689i	−0.958372	−	0.285523i	$-0.907833\pi$
$523$	−5.30372	+	9.18631i	−0.231915	+	0.401689i	0.726456	+	0.687213i	$0.241166\pi$
$524$	15.3762	−	26.8362i	0.671713	−	1.17235i
$525$	2.55275	−	7.84749i	0.111411	−	0.342492i
$526$	7.20089	−	27.0523i	0.313974	−	1.17954i
$527$	19.1290	+	11.0441i	0.833272	+	0.481090i
$528$	−1.52176	+	6.77814i	−0.0662261	+	0.294980i
$529$	19.8039	+	34.3014i	0.861040	+	1.49137i
$530$	−22.7131	−	22.6383i	−0.986592	−	0.983347i
$531$	14.2131	+	21.1216i	0.616797	+	0.916597i
$532$	16.1588	+	11.2304i	0.700572	+	0.486899i
$533$	4.97185			0.215355
$534$	16.9726	−	32.0059i	0.734478	−	1.38503i
$535$	−10.7845	+	6.22642i	−0.466254	+	0.269192i
$536$	−21.7910	−	5.72359i	−0.941229	−	0.247221i
$537$	2.95118	−	12.7512i	0.127353	−	0.550254i
$538$	0.338381	−	1.27123i	0.0145887	−	0.0548067i
$539$	−2.40331	−	6.59457i	−0.103518	−	0.284048i
$540$	−6.69010	−	17.3424i	−0.287896	−	0.746296i
$541$	14.0009	+	8.08343i	0.601946	+	0.347534i	0.769807	−	0.638277i	$-0.220353\pi$
$541$	14.0009	+	8.08343i	0.601946	+	0.347534i	−0.167861	+	0.985811i	$0.553686\pi$
$542$	−11.7562	+	3.17085i	−0.504974	+	0.136199i
$543$	−6.33350	−	5.91256i	−0.271797	−	0.253732i
$544$	−36.4659	−	9.44972i	−1.56346	−	0.405154i
$545$	4.88190			0.209118
$546$	−16.0061	−	0.817859i	−0.684998	−	0.0350011i
$547$			12.4170i			0.530914i	0.964123	+	0.265457i	$0.0855228\pi$
$547$			12.4170i			0.530914i	−0.964123	+	0.265457i	$0.914477\pi$
$548$	11.2783	+	19.3868i	0.481787	+	0.828164i
$549$	10.9114	+	5.33660i	0.465687	+	0.227761i
$550$	0.664972	+	2.46545i	0.0283545	+	0.105127i
$551$	1.39159	−	2.41030i	0.0592836	−	0.102682i
$552$	−18.0476	+	34.3056i	−0.768156	+	1.46014i
$553$	7.70648	−	11.0108i	0.327713	−	0.468228i
$554$	10.7358	−	40.3321i	0.456119	−	1.71355i
$555$	2.60076	−	11.2371i	0.110396	−	0.476989i
$556$	0.118518	+	35.9647i	0.00502629	+	1.52524i
$557$	10.7167	+	18.5619i	0.454081	+	0.786492i	0.998635	−	0.0522341i	$-0.0166342\pi$
$557$	10.7167	+	18.5619i	0.454081	+	0.786492i	−0.544554	+	0.838726i	$0.683301\pi$
$558$	13.8155	+	2.67749i	0.584855	+	0.113347i
$559$			22.7431i			0.961931i
$560$	15.5793	+	10.7517i	0.658344	+	0.454341i
$561$	11.0617	−	3.37530i	0.467026	−	0.142505i
$562$	21.3611	+	21.2908i	0.901064	+	0.898100i
$563$	17.9430	−	10.3594i	0.756205	−	0.436595i	−0.0717262	−	0.997424i	$-0.522851\pi$
$563$	17.9430	−	10.3594i	0.756205	−	0.436595i	0.827932	+	0.560829i	$0.189517\pi$
$564$	2.44932	+	7.93328i	0.103135	+	0.334051i
$565$	0.475020	−	0.822758i	0.0199842	−	0.0346137i
$566$	−28.4933	−	7.58447i	−1.19766	−	0.318799i
$567$	−23.7815	+	1.19916i	−0.998731	+	0.0503598i
$568$	−10.8827	+	10.9908i	−0.456627	+	0.461164i
$569$	−23.8691	−	13.7808i	−1.00064	−	0.577722i	−0.0922056	−	0.995740i	$-0.529392\pi$
$569$	−23.8691	−	13.7808i	−1.00064	−	0.577722i	−0.908439	+	0.418018i	$0.862725\pi$
$570$	13.8077	−	8.64920i	0.578343	−	0.362275i
$571$	0.339940	−	0.196264i	0.0142260	−	0.00821340i	−0.492870	−	0.870103i	$-0.664052\pi$
$571$	0.339940	−	0.196264i	0.0142260	−	0.00821340i	0.507096	+	0.861889i	$0.330719\pi$
$572$	4.28673	−	2.49382i	0.179237	−	0.104272i
$573$	−6.12246	−	20.0649i	−0.255770	−	0.838222i
$574$	−5.75350	+	4.84596i	−0.240146	+	0.202267i
$575$			14.2488i			0.594214i
$576$	−23.9259	+	1.88463i	−0.996912	+	0.0785260i
$577$	−12.7927	+	7.38589i	−0.532569	+	0.307479i	−0.742062	−	0.670331i	$-0.766152\pi$
$577$	−12.7927	+	7.38589i	−0.532569	+	0.307479i	0.209493	+	0.977810i	$0.432819\pi$
$578$	10.0707	+	37.3383i	0.418888	+	1.55307i
$579$	−0.462751	+	1.99941i	−0.0192313	+	0.0830926i
$580$	1.33097	−	2.32296i	0.0552656	−	0.0964555i
$581$	1.30083	−	14.9039i	0.0539675	−	0.618319i
$582$	0.154828	+	4.29795i	0.00641782	+	0.178156i
$583$	6.35591	−	11.0088i	0.263235	−	0.455936i
$584$	17.9595	+	4.71720i	0.743168	+	0.195199i
$585$	−5.83019	+	11.9206i	−0.241049	+	0.492856i
$586$	13.1274	+	13.0842i	0.542289	+	0.540505i
$587$			3.51421i			0.145047i	0.997367	+	0.0725236i	$0.0231052\pi$
$587$			3.51421i			0.145047i	−0.997367	+	0.0725236i	$0.976895\pi$
$588$	19.3197	−	14.6544i	0.796729	−	0.604337i
$589$			12.3350i			0.508256i
$590$	−15.1536	+	15.2036i	−0.623863	+	0.625923i
$591$	24.7029	+	23.0611i	1.01614	+	0.948607i
$592$	−12.9460	−	7.36103i	−0.532076	−	0.302536i
$593$	−17.8824	+	30.9732i	−0.734342	+	1.27192i	0.220670	+	0.975349i	$0.429176\pi$
$593$	−17.8824	+	30.9732i	−0.734342	+	1.27192i	−0.955012	+	0.296568i	$0.904158\pi$
$594$	5.96101	−	4.33101i	0.244583	−	0.177703i
$595$	2.74011	−	31.3941i	0.112334	−	1.28703i
$596$	−1.60517	−	0.919706i	−0.0657504	−	0.0376726i
$597$	−24.8690	−	5.75578i	−1.01782	−	0.235568i
$598$	26.7182	−	7.20633i	1.09259	−	0.294689i
$599$	−35.4819	+	20.4855i	−1.44975	+	0.837014i	−0.998466	−	0.0553669i	$-0.982367\pi$
$599$	−35.4819	+	20.4855i	−1.44975	+	0.837014i	−0.451284	+	0.892380i	$0.649034\pi$
$600$	−7.46087	+	4.70781i	−0.304589	+	0.192196i
$601$		−	36.1540i		−	1.47475i	−0.675482	−	0.737377i	$-0.736064\pi$
$601$		−	36.1540i		−	1.47475i	0.675482	−	0.737377i	$-0.263936\pi$
$602$	−22.1673	−	26.3187i	−0.903470	−	1.07267i
$603$	13.3413	+	19.8260i	0.543300	+	0.807376i
$604$	33.0785	−	19.2435i	1.34595	−	0.783007i
$605$	−15.4817	+	8.93835i	−0.629419	+	0.363395i
$606$	−30.3947	+	19.0393i	−1.23470	+	0.773418i
$607$	9.04038	+	5.21946i	0.366938	+	0.211851i	0.672120	−	0.740443i	$-0.265384\pi$
$607$	9.04038	+	5.21946i	0.366938	+	0.211851i	−0.305182	+	0.952294i	$0.598717\pi$
$608$	−5.61194	−	20.2744i	−0.227594	−	0.822237i
$609$	−2.29399	−	2.54948i	−0.0929573	−	0.103310i
$610$	−2.63441	+	9.89696i	−0.106664	+	0.400716i
$611$	2.96367	−	5.13323i	0.119897	−	0.207668i
$612$	22.4158	+	33.0753i	0.906104	+	1.33699i
$613$	5.37925	−	3.10571i	0.217266	−	0.125439i	−0.387418	−	0.921904i	$-0.626633\pi$
$613$	5.37925	−	3.10571i	0.217266	−	0.125439i	0.604684	+	0.796466i	$0.293300\pi$
$614$	18.6117	−	18.6732i	0.751109	−	0.753588i
$615$	1.81774	+	5.95720i	0.0732984	+	0.240217i
$616$	−2.53000	+	7.06407i	−0.101936	+	0.284620i
$617$		−	22.4963i		−	0.905669i	−0.891595	−	0.452834i	$-0.850413\pi$
$617$		−	22.4963i		−	0.905669i	0.891595	−	0.452834i	$-0.149587\pi$
$618$	−21.3413	−	11.3172i	−0.858472	−	0.455245i
$619$	14.1624	+	24.5300i	0.569235	+	0.985943i	0.996642	+	0.0818842i	$0.0260938\pi$
$619$	14.1624	+	24.5300i	0.569235	+	0.985943i	−0.427407	+	0.904059i	$0.640573\pi$
$620$	0.0391015	+	11.8655i	0.00157036	+	0.476529i
$621$	38.4079	−	14.6712i	1.54126	−	0.588737i
$622$	−27.1384	−	7.22380i	−1.08815	−	0.289648i
$623$	22.4377	−	32.0584i	0.898947	−	1.28439i
$624$	12.6011	+	11.6091i	0.504447	+	0.464736i
$625$	6.37661	−	11.0446i	0.255064	−	0.441785i
$626$	3.67529	−	0.991285i	0.146894	−	0.0396197i
$627$	4.72106	+	4.40728i	0.188541	+	0.176010i
$628$	18.9081	−	10.9998i	0.754515	−	0.438941i
$629$			24.7930i			0.988563i
$630$	−4.87199	−	19.4773i	−0.194105	−	0.775993i
$631$	8.51542			0.338993			0.169497	−	0.985531i	$-0.445786\pi$
$631$	8.51542			0.338993			0.169497	+	0.985531i	$0.445786\pi$
$632$	−13.8596	+	3.78720i	−0.551306	+	0.150647i
$633$	−17.6393	+	18.8952i	−0.701101	+	0.751016i
$634$	−3.94267	−	14.6179i	−0.156584	−	0.580550i
$635$	7.00758	+	4.04583i	0.278087	+	0.160554i
$636$	42.8182	+	9.76145i	1.69785	+	0.387066i
$637$	−17.0494	−	2.99902i	−0.675520	−	0.118825i
$638$	1.02554	+	0.272983i	0.0406016	+	0.0108075i
$639$	16.3666	−	1.12650i	0.647452	−	0.0445636i
$640$	−5.46258	−	19.4848i	−0.215927	−	0.770206i
$641$	−0.0793494	+	0.0458124i	−0.00313411	+	0.00180948i	−0.501566	−	0.865119i	$-0.667243\pi$
$641$	−0.0793494	+	0.0458124i	−0.00313411	+	0.00180948i	0.498432	+	0.866929i	$0.333909\pi$
$642$	7.98971	−	15.0665i	0.315329	−	0.594626i
$643$	−5.89351			−0.232417			−0.116209	−	0.993225i	$-0.537074\pi$
$643$	−5.89351			−0.232417			−0.116209	+	0.993225i	$0.537074\pi$
$644$	−23.8949	+	34.3810i	−0.941590	+	1.35480i
$645$	−27.2505	+	8.31503i	−1.07299	+	0.327404i
$646$	−24.7237	+	24.8053i	−0.972741	+	0.975951i
$647$	4.05903	+	7.03045i	0.159577	+	0.276396i	0.934716	−	0.355395i	$-0.115654\pi$
$647$	4.05903	+	7.03045i	0.159577	+	0.276396i	−0.775139	+	0.631791i	$0.782320\pi$
$648$	20.3721	+	15.2636i	0.800292	+	0.599610i
$649$	−7.36901	−	4.25450i	−0.289259	−	0.167004i
$650$	6.08611	+	1.62002i	0.238717	+	0.0635426i
$651$	14.4545	+	4.70200i	0.566518	+	0.184286i
$652$	10.5762	−	18.4587i	0.414196	−	0.722899i
$653$	−16.7312	+	28.9792i	−0.654741	+	1.13404i	0.327218	+	0.944949i	$0.393889\pi$
$653$	−16.7312	+	28.9792i	−0.654741	+	1.13404i	−0.981959	+	0.189095i	$0.939444\pi$
$654$	−5.66584	+	3.54910i	−0.221552	+	0.138781i
$655$	−13.8302	−	23.9547i	−0.540392	−	0.935986i
$656$	8.04158	−	0.0530011i	0.313971	−	0.00206935i
$657$	−10.9955	−	16.3399i	−0.428974	−	0.637481i
$658$	1.57365	+	8.82888i	0.0613473	+	0.344186i
$659$	15.5448			0.605540			0.302770	−	0.953064i	$-0.402089\pi$
$659$	15.5448			0.605540			0.302770	+	0.953064i	$0.402089\pi$
$660$	4.55531	+	4.22454i	0.177315	+	0.164440i
$661$	−15.4190	−	26.7065i	−0.599731	−	1.03876i	−0.992861	−	0.119281i	$-0.961941\pi$
$661$	−15.4190	−	26.7065i	−0.599731	−	1.03876i	0.393130	−	0.919483i	$-0.371392\pi$
$662$	−29.7238	+	8.01699i	−1.15525	+	0.311589i
$663$	6.43172	−	27.7896i	0.249787	−	1.07926i
$664$	−11.2531	+	11.3649i	−0.436705	+	0.441044i
$665$	15.9481	−	7.44072i	0.618441	−	0.288539i
$666$	5.15089	+	14.9323i	0.199593	+	0.578616i
$667$	5.12838	+	2.96087i	0.198572	+	0.114646i
$668$	−0.0522675	−	15.8607i	−0.00202229	−	0.613670i
$669$	−9.00865	+	9.65002i	−0.348294	+	0.373091i
$670$	−14.2241	+	14.2710i	−0.549524	+	0.551338i
$671$	−4.05974			−0.156725
$672$	−25.8973	−	1.15220i	−0.999012	−	0.0444469i
$673$	3.84855			0.148351			0.0741753	−	0.997245i	$-0.476368\pi$
$673$	3.84855			0.148351			0.0741753	+	0.997245i	$0.476368\pi$
$674$	−11.2917	+	11.3290i	−0.434941	+	0.436377i
$675$	9.23956	+	1.47893i	0.355631	+	0.0569239i
$676$	0.0453721	+	13.7683i	0.00174508	+	0.529550i
$677$	−32.5497	−	18.7926i	−1.25099	−	0.722257i	−0.279680	−	0.960093i	$-0.590228\pi$
$677$	−32.5497	−	18.7926i	−1.25099	−	0.722257i	−0.971305	+	0.237836i	$0.923562\pi$
$678$	0.0468384	+	1.30021i	0.00179882	+	0.0499343i
$679$	−0.403913	+	4.62773i	−0.0155008	+	0.177596i
$680$	−23.7039	+	23.9394i	−0.909003	+	0.918034i
$681$	−26.6031	−	6.15711i	−1.01943	−	0.235941i
$682$	−4.54120	+	1.22483i	−0.173891	+	0.0469013i
$683$	−1.02051	−	1.76757i	−0.0390487	−	0.0676343i	0.845841	−	0.533436i	$-0.179099\pi$
$683$	−1.02051	−	1.76757i	−0.0390487	−	0.0676343i	−0.884889	+	0.465802i	$0.845766\pi$
$684$	−9.73712	+	20.0762i	−0.372308	+	0.767632i
$685$	20.0584			0.766394
$686$	22.6529	−	13.1472i	0.864890	−	0.501961i
$687$	−29.2296	+	8.91894i	−1.11518	+	0.340279i
$688$	0.242447	+	36.7852i	0.00924321	+	1.40242i
$689$	−15.6761	−	27.1517i	−0.597210	−	1.03440i
$690$	18.4029	+	29.3787i	0.700586	+	1.11843i
$691$	11.7334	−	20.3229i	0.446360	−	0.773119i	−0.551786	−	0.833986i	$-0.686053\pi$
$691$	11.7334	−	20.3229i	0.446360	−	0.773119i	0.998146	+	0.0608673i	$0.0193866\pi$
$692$	−4.24663	+	7.41168i	−0.161433	+	0.281750i
$693$	6.96419	−	3.85225i	0.264548	−	0.146335i
$694$	27.1694	+	7.23206i	1.03134	+	0.274525i
$695$	27.8548	+	16.0820i	1.05659	+	0.610025i
$696$	0.144066	+	3.66358i	0.00546079	+	0.138868i
$697$	−6.69401	−	11.5944i	−0.253554	−	0.439168i
$698$	−9.43789	+	9.46905i	−0.357230	+	0.358409i
$699$	9.16868	+	30.0481i	0.346791	+	1.13652i
$700$	−8.62194	+	4.05729i	−0.325879	+	0.153351i
$701$	15.4603			0.583926			0.291963	−	0.956430i	$-0.405692\pi$
$701$	15.4603			0.583926			0.291963	+	0.956430i	$0.405692\pi$
$702$	−1.89975	−	18.0733i	−0.0717014	−	0.682133i
$703$	−11.9906	+	6.92275i	−0.452232	+	0.261096i
$704$	6.90687	−	4.07925i	0.260312	−	0.153743i
$705$	7.23409	+	1.67428i	0.272452	+	0.0630572i
$706$	23.1817	+	6.17059i	0.872454	+	0.232233i
$707$	−35.1062	+	16.3791i	−1.32030	+	0.615999i
$708$	6.53409	−	28.6615i	0.245566	−	1.07717i
$709$	−41.7153	−	24.0843i	−1.56665	−	0.904505i	−0.996556	−	0.0829254i	$-0.973574\pi$
$709$	−41.7153	−	24.0843i	−1.56665	−	0.904505i	−0.570093	−	0.821580i	$-0.693093\pi$
$710$	3.60211	+	13.3552i	0.135185	+	0.501212i
$711$	13.6897	+	6.69542i	0.513403	+	0.251098i
$712$	−40.3528	+	11.0266i	−1.51228	+	0.413238i
$713$	−26.2452			−0.982891
$714$	19.6431	+	38.4274i	0.735124	+	1.43811i
$715$		−	4.43523i		−	0.165868i
$716$	−13.0633	+	7.59958i	−0.488197	+	0.284010i
$717$	−6.39481	+	6.85009i	−0.238819	+	0.255821i
$718$	−28.7206	+	7.74640i	−1.07184	+	0.289093i
$719$	−6.49021	+	11.2414i	−0.242044	+	0.419232i	−0.961296	−	0.275517i	$-0.911151\pi$
$719$	−6.49021	+	11.2414i	−0.242044	+	0.419232i	0.719252	+	0.694749i	$0.244484\pi$
$720$	−9.30281	+	19.3428i	−0.346695	+	0.720864i
$721$	−21.3763	−	14.9613i	−0.796094	−	0.557186i
$722$	7.06603	+	1.88086i	0.262970	+	0.0699985i
$723$	−36.2468	−	8.38909i	−1.34803	−	0.311994i
$724$	0.0329696	+	10.0047i	0.00122531	+	0.371822i
$725$	0.673858	+	1.16716i	0.0250264	+	0.0433471i
$726$	11.4696	−	21.6287i	0.425678	−	0.802716i
$727$		−	12.0095i		−	0.445406i	−0.974886	−	0.222703i	$-0.928512\pi$
$727$		−	12.0095i		−	0.445406i	0.974886	−	0.222703i	$-0.0714880\pi$
$728$	11.9685	+	14.1153i	0.443582	+	0.523146i
$729$	−5.52704	−	26.4282i	−0.204705	−	0.978824i
$730$	11.7230	−	11.7617i	0.433889	−	0.435321i
$731$	53.0370	−	30.6209i	1.96164	−	1.13256i
$732$	−4.13754	−	13.4014i	−0.152928	−	0.495330i
$733$	4.29808	−	7.44449i	0.158753	−	0.274968i	−0.775666	−	0.631143i	$-0.782586\pi$
$733$	4.29808	−	7.44449i	0.158753	−	0.274968i	0.934419	+	0.356175i	$0.115919\pi$
$734$	0.524538	−	1.97058i	0.0193610	−	0.0727355i
$735$	−2.63998	−	21.5247i	−0.0973770	−	0.793952i
$736$	43.1379	−	11.9405i	1.59008	−	0.440133i
$737$	−6.91700	−	3.99353i	−0.254791	−	0.147104i
$738$	−6.44046	−	5.59233i	−0.237076	−	0.205856i
$739$	−2.25350	+	1.30106i	−0.0828963	+	0.0478602i	−0.540875	−	0.841103i	$-0.681907\pi$
$739$	−2.25350	+	1.30106i	−0.0828963	+	0.0478602i	0.457979	+	0.888963i	$0.348574\pi$
$740$	−11.5122	+	6.69723i	−0.423195	+	0.246195i
$741$	15.2356	−	4.64891i	0.559695	−	0.170782i
$742$	44.6048	+	16.1413i	1.63749	+	0.592564i
$743$			13.4061i			0.491823i	0.969292	+	0.245911i	$0.0790872\pi$
$743$			13.4061i			0.491823i	−0.969292	+	0.245911i	$0.920913\pi$
$744$	−8.67146	−	13.7424i	−0.317911	−	0.503821i
$745$	−1.43281	+	0.827235i	−0.0524942	+	0.0303075i
$746$	−29.6981	+	8.01006i	−1.08733	+	0.293269i
$747$	16.9237	−	1.16484i	0.619204	−	0.0426193i
$748$	−11.5872	−	6.63904i	−0.423669	−	0.242747i
$749$	10.5623	−	15.0912i	0.385939	−	0.551420i
$750$	1.07266	+	29.7766i	0.0391681	+	1.08729i
$751$	−7.86182	+	13.6171i	−0.286882	+	0.496894i	−0.973064	−	0.230536i	$-0.925952\pi$
$751$	−7.86182	+	13.6171i	−0.286882	+	0.496894i	0.686182	+	0.727430i	$0.259285\pi$
$752$	4.73879	−	8.33419i	0.172806	−	0.303917i
$753$	23.4679	−	25.1387i	0.855218	−	0.916105i
$754$	1.84776	−	1.85386i	0.0672915	−	0.0675136i
$755$		−	34.2244i		−	1.24555i
$756$	19.8141	+	19.0631i	0.720633	+	0.693317i
$757$		−	48.7626i		−	1.77231i	−0.463391	−	0.886154i	$-0.653367\pi$
$757$		−	48.7626i		−	1.77231i	0.463391	−	0.886154i	$-0.346633\pi$
$758$	−1.82598	−	1.81997i	−0.0663226	−	0.0661044i
$759$	−9.37736	+	10.0450i	−0.340377	+	0.364610i
$760$	−18.1964	−	4.77942i	−0.660051	−	0.173368i
$761$	−21.7170	+	37.6149i	−0.787240	+	1.36354i	0.140411	+	0.990093i	$0.455158\pi$
$761$	−21.7170	+	37.6149i	−0.787240	+	1.36354i	−0.927652	+	0.373447i	$0.878176\pi$
$762$	−11.0741	+	0.398931i	−0.401174	+	0.0144518i
$763$	−6.54411	+	3.05321i	−0.236913	+	0.110534i
$764$	−12.0426	+	21.0180i	−0.435684	+	0.760403i
$765$	35.6486	−	2.45366i	1.28888	−	0.0887123i
$766$	−3.54332	−	13.1372i	−0.128025	−	0.474667i
$767$	−18.1747	+	10.4932i	−0.656252	+	0.378887i
$768$	20.5051	+	18.6425i	0.739912	+	0.672703i
$769$			23.9226i			0.862670i	0.902192	+	0.431335i	$0.141957\pi$
$769$			23.9226i			0.862670i	−0.902192	+	0.431335i	$0.858043\pi$
$770$	4.32293	+	5.13252i	0.155788	+	0.184963i
$771$	14.4663	−	4.41417i	0.520993	−	0.158972i
$772$	2.04835	−	1.19163i	0.0737216	−	0.0428877i
$773$	−14.3402	+	8.27930i	−0.515780	+	0.297786i	−0.735206	−	0.677843i	$-0.762915\pi$
$773$	−14.3402	+	8.27930i	−0.515780	+	0.297786i	0.219427	+	0.975629i	$0.429581\pi$
$774$	25.5814	−	29.4611i	0.919505	−	1.05896i
$775$	−5.17284	−	2.98654i	−0.185814	−	0.107280i
$776$	3.49414	−	3.52885i	0.125432	−	0.126678i
$777$	3.54158	+	16.6897i	0.127053	+	0.598741i
$778$	−38.4374	−	10.2314i	−1.37805	−	0.366815i
$779$	3.73823	−	6.47480i	0.133936	−	0.231984i
$780$	14.6409	−	4.52023i	0.524229	−	0.161850i
$781$	−4.74856	+	2.74158i	−0.169917	+	0.0981014i
$782$	−52.7782	−	52.6045i	−1.88734	−	1.88113i
$783$	2.45226	−	3.01816i	0.0876366	−	0.107860i
$784$	−27.6080	−	4.66893i	−0.986000	−	0.166748i
$785$		−	19.5631i		−	0.698237i
$786$	33.4659	+	17.7469i	1.19369	+	0.633010i
$787$	−5.81161	−	10.0660i	−0.207162	−	0.358814i	0.743658	−	0.668561i	$-0.233089\pi$
$787$	−5.81161	−	10.0660i	−0.207162	−	0.358814i	−0.950819	+	0.309746i	$0.899756\pi$
$788$	−0.128593	−	39.0220i	−0.00458094	−	1.39010i
$789$	33.4029	+	7.73088i	1.18917	+	0.275227i
$790$	−3.30519	+	12.4169i	−0.117593	+	0.441775i
$791$	−0.122192	+	1.39998i	−0.00434463	+	0.0497775i
$792$	−8.35800	−	1.59126i	−0.296989	−	0.0565428i
$793$	−5.00642	+	8.67137i	−0.177783	+	0.307930i
$794$	−6.94307	−	25.7422i	−0.246400	−	0.913555i
$795$	26.8015	−	28.7097i	0.950552	−	1.01823i
$796$	14.8217	+	25.4777i	0.525342	+	0.903034i
$797$			2.35681i			0.0834824i	0.999128	+	0.0417412i	$0.0132905\pi$
$797$			2.35681i			0.0834824i	−0.999128	+	0.0417412i	$0.986709\pi$
$798$	−13.0997	+	20.2297i	−0.463725	+	0.716123i
$799$	−15.9609			−0.564657
$800$	9.86108	+	2.55538i	0.348642	+	0.0903465i
$801$	39.8580	+	19.4940i	1.40831	+	0.688785i
$802$	8.24144	−	2.22285i	0.291015	−	0.0784915i
$803$	5.70077	+	3.29134i	0.201176	+	0.116149i
$804$	6.13329	−	26.9034i	0.216305	−	0.948811i
$805$	15.8316	+	33.9327i	0.557991	+	1.19597i
$806$	−2.98397	+	11.2102i	−0.105106	+	0.394862i
$807$	1.56966	+	0.363287i	0.0552545	+	0.0127883i
$808$	40.0552	+	10.5208i	1.40914	+	0.370121i
$809$	39.6070	−	22.8671i	1.39251	−	0.803964i	0.398914	−	0.916988i	$-0.369387\pi$
$809$	39.6070	−	22.8671i	1.39251	−	0.803964i	0.993592	+	0.113024i	$0.0360538\pi$
$810$	20.9606	−	8.88397i	0.736481	−	0.312151i
$811$	0.844573			0.0296570			0.0148285	−	0.999890i	$-0.495280\pi$
$811$	0.844573			0.0296570			0.0148285	+	0.999890i	$0.495280\pi$
$812$	−0.331337	+	3.94629i	−0.0116276	+	0.138488i
$813$	−4.35233	−	14.2637i	−0.152643	−	0.500249i
$814$	−3.73927	−	3.72696i	−0.131061	−	0.130630i
$815$	−9.51282	−	16.4767i	−0.333219	−	0.577153i
$816$	10.1066	−	45.0161i	0.353801	−	1.57588i
$817$	29.6182	+	17.1000i	1.03621	+	0.598255i
$818$	9.51956	−	35.7631i	0.332844	−	1.25043i
$819$	0.359968	−	19.6257i	0.0125783	−	0.685776i
$820$	3.57540	−	6.24017i	0.124858	−	0.217916i
$821$	18.4890	−	32.0239i	0.645272	−	1.11764i	−0.338967	−	0.940798i	$-0.610078\pi$
$821$	18.4890	−	32.0239i	0.645272	−	1.11764i	0.984239	−	0.176845i	$-0.0565892\pi$
$822$	−23.2794	+	14.5823i	−0.811964	+	0.508616i
$823$	−3.62518	−	6.27899i	−0.126366	−	0.218872i	0.795900	−	0.605428i	$-0.206998\pi$
$823$	−3.62518	−	6.27899i	−0.126366	−	0.218872i	−0.922266	+	0.386556i	$0.873665\pi$
$824$	7.35242	+	26.9069i	0.256134	+	0.937346i
$825$	−2.99130	+	0.912746i	−0.104144	+	0.0317777i
$826$	10.8046	−	29.8575i	0.375940	−	1.03887i
$827$	−43.4014			−1.50921			−0.754607	−	0.656176i	$-0.772173\pi$
$827$	−43.4014			−1.50921			−0.754607	+	0.656176i	$0.772173\pi$
$828$	−42.7161	−	20.7176i	−1.48449	−	0.719988i
$829$	12.7789	+	22.1338i	0.443830	+	0.768737i	0.997970	−	0.0636869i	$-0.0202859\pi$
$829$	12.7789	+	22.1338i	0.443830	+	0.768737i	−0.554139	+	0.832424i	$0.686953\pi$
$830$	3.72472	+	13.8098i	0.129287	+	0.479345i
$831$	49.8001	+	11.5259i	1.72755	+	0.399830i
$832$	−0.195586	−	19.7832i	−0.00678073	−	0.685858i
$833$	15.9612	+	43.7970i	0.553024	+	1.51748i
$834$	−44.0193	+	1.58573i	−1.52426	+	0.0549095i
$835$	−12.2842	−	7.09229i	−0.425113	−	0.245439i
$836$	−0.0245759	−	7.45762i	−0.000849974	−	0.257927i
$837$	−2.72408	+	17.0186i	−0.0941579	+	0.588250i
$838$	2.52281	+	2.51451i	0.0871489	+	0.0868622i
$839$	−19.2288			−0.663854			−0.331927	−	0.943305i	$-0.607699\pi$
$839$	−19.2288			−0.663854			−0.331927	+	0.943305i	$0.607699\pi$
$840$	−12.5369	+	19.5011i	−0.432565	+	0.672852i
$841$	−28.4399			−0.980686
$842$	33.5424	+	33.4320i	1.15595	+	1.15214i
$843$	−25.2062	+	27.0008i	−0.868149	+	0.929956i
$844$	29.8478	−	0.0983605i	1.02740	−	0.00338571i
$845$	10.6636	+	6.15665i	0.366840	+	0.211795i
$846$	−9.61294	+	3.31597i	−0.330500	+	0.114005i
$847$	15.1628	−	21.6642i	0.520999	−	0.744389i
$848$	−25.6443	−	43.7487i	−0.880627	−	1.50234i
$849$	8.14269	−	35.1822i	0.279457	−	1.20745i
$850$	−4.41633	−	16.3740i	−0.151479	−	0.561623i
$851$	−14.7295	−	25.5123i	−0.504921	−	0.874549i
$852$	−13.8897	−	12.8811i	−0.475852	−	0.441299i
$853$	43.5472			1.49103			0.745514	−	0.666489i	$-0.232204\pi$
$853$	43.5472			1.49103			0.745514	+	0.666489i	$0.232204\pi$
$854$	−2.65831	−	14.9143i	−0.0909655	−	0.510357i
$855$	11.1405	+	16.5555i	0.380997	+	0.566185i
$856$	−18.9957	+	5.19065i	−0.649259	+	0.177413i
$857$	4.41603	+	7.64878i	0.150849	+	0.261277i	0.931540	−	0.363640i	$-0.118466\pi$
$857$	4.41603	+	7.64878i	0.150849	+	0.261277i	−0.780691	+	0.624917i	$0.785133\pi$
$858$	3.22437	+	5.14745i	0.110078	+	0.175731i
$859$	−2.94564	+	5.10200i	−0.100504	+	0.174078i	−0.911892	−	0.410429i	$-0.865379\pi$
$859$	−2.94564	+	5.10200i	−0.100504	+	0.174078i	0.811388	+	0.584507i	$0.198712\pi$
$860$	28.5449	+	16.3552i	0.973372	+	0.557708i
$861$	−6.16237	−	6.84868i	−0.210013	−	0.233403i
$862$	5.04071	−	18.9370i	0.171687	−	0.644995i
$863$	2.80835	+	1.62140i	0.0955974	+	0.0551932i	0.547037	−	0.837109i	$-0.315756\pi$
$863$	2.80835	+	1.62140i	0.0955974	+	0.0551932i	−0.451439	+	0.892302i	$0.649089\pi$
$864$	−3.26536	−	29.2119i	−0.111090	−	0.993810i
$865$	3.81966	+	6.61584i	0.129872	+	0.224945i
$866$	9.80980	+	9.77753i	0.333351	+	0.332254i
$867$	−45.3020	+	13.8232i	−1.53854	+	0.469460i
$868$	−7.47325	−	15.8810i	−0.253659	−	0.539037i
$869$	−5.09344			−0.172783
$870$	2.89682	+	1.53618i	0.0982114	+	0.0520813i
$871$	−17.0599	+	9.84955i	−0.578053	+	0.333739i
$872$	7.46665	+	1.96118i	0.252853	+	0.0664138i
$873$	−5.25487	+	0.361689i	−0.177850	+	0.0122413i
$874$	10.7041	−	40.2132i	0.362072	−	1.36023i
$875$	−2.79835	+	32.0614i	−0.0946015	+	1.08387i
$876$	−5.05486	+	22.1729i	−0.170788	+	0.749154i
$877$	39.1526	+	22.6048i	1.32209	+	0.763309i	0.984062	−	0.177828i	$-0.0569070\pi$
$877$	39.1526	+	22.6048i	1.32209	+	0.763309i	0.338028	+	0.941136i	$0.390240\pi$
$878$	11.0281	−	2.97445i	0.372180	−	0.100383i
$879$	−15.4904	+	16.5933i	−0.522479	+	0.559677i
$880$	−0.0472807	−	7.17365i	−0.00159383	−	0.241824i
$881$	28.1014			0.946759			0.473380	−	0.880859i	$-0.343034\pi$
$881$	28.1014			0.946759			0.473380	+	0.880859i	$0.343034\pi$
$882$	18.7122	+	23.0620i	0.630072	+	0.776537i
$883$		−	5.45102i		−	0.183442i	−0.995785	−	0.0917208i	$-0.970763\pi$
$883$		−	5.45102i		−	0.183442i	0.995785	−	0.0917208i	$-0.0292367\pi$
$884$	−28.4698	+	16.5624i	−0.957541	+	0.557052i
$885$	−19.2176	−	17.9403i	−0.645992	−	0.603058i
$886$	6.51763	+	24.1648i	0.218964	+	0.811832i
$887$	25.3783	−	43.9566i	0.852122	−	1.47592i	−0.0271684	−	0.999631i	$-0.508649\pi$
$887$	25.3783	−	43.9566i	0.852122	−	1.47592i	0.879290	−	0.476287i	$-0.158018\pi$
$888$	8.49197	−	16.1419i	0.284972	−	0.541687i
$889$	−11.9239	−	1.04073i	−0.399914	−	0.0349049i
$890$	−9.62318	+	36.1524i	−0.322570	+	1.21183i
$891$	5.54033	+	7.12332i	0.185608	+	0.238640i
$892$	15.2437	−	0.0502340i	0.510395	−	0.00168196i
$893$	−4.45664	−	7.71912i	−0.149136	−	0.258311i
$894$	1.06150	−	2.00171i	0.0355020	−	0.0669473i
$895$			13.5158i			0.451783i
$896$	19.5086	+	22.7027i	0.651736	+	0.758446i
$897$	9.89147	+	32.4168i	0.330266	+	1.08237i
$898$	−19.4970	−	19.4329i	−0.650624	−	0.648484i
$899$	−2.14982	+	1.24120i	−0.0717005	+	0.0413963i
$900$	−6.06165	−	8.94419i	−0.202055	−	0.298140i
$901$	−42.2119	+	73.1132i	−1.40628	+	2.43575i
$902$	2.75492	+	0.733315i	0.0917288	+	0.0244167i
$903$	31.3285	−	28.1890i	1.04255	−	0.938070i
$904$	1.05704	−	1.06755i	0.0351567	−	0.0355060i
$905$	7.74871	+	4.47372i	0.257576	+	0.148711i
$906$	24.8808	+	39.7202i	0.826610	+	1.31962i
$907$	8.66652	−	5.00362i	0.287767	−	0.166142i	−0.349167	−	0.937060i	$-0.613536\pi$
$907$	8.66652	−	5.00362i	0.287767	−	0.166142i	0.636934	+	0.770918i	$0.280202\pi$
$908$	15.8552	+	27.2542i	0.526173	+	0.904461i
$909$	−24.5233	−	36.4431i	−0.813387	−	1.20874i
$910$	16.2938	−	2.90418i	0.540133	−	0.0962727i
$911$		−	14.5940i		−	0.483521i	−0.970336	−	0.241761i	$-0.922275\pi$
$911$		−	14.5940i		−	0.483521i	0.970336	−	0.241761i	$-0.0777249\pi$
$912$	24.5929	−	7.68166i	0.814353	−	0.254365i
$913$	−4.91019	+	2.83490i	−0.162503	+	0.0938214i
$914$	−5.71289	−	21.1811i	−0.188966	−	0.700609i
$915$	−12.2203	−	2.82831i	−0.403990	−	0.0935010i
$916$	30.6181	+	17.5431i	1.01165	+	0.579639i
$917$	33.5208	+	23.4612i	1.10695	+	0.774757i
$918$	−39.5892	+	28.7638i	−1.30664	+	0.949348i
$919$	−1.14316	+	1.98001i	−0.0377093	+	0.0653145i	−0.884264	−	0.466987i	$-0.845339\pi$
$919$	−1.14316	+	1.98001i	−0.0377093	+	0.0653145i	0.846555	+	0.532302i	$0.178673\pi$
$920$	10.1692	−	38.7163i	0.335267	−	1.27644i
$921$	23.6032	+	22.0344i	0.777751	+	0.726060i
$922$	−0.858701	−	0.855876i	−0.0282798	−	0.0281868i
$923$			13.5235i			0.445132i
$924$	−8.74840	−	2.81397i	−0.287801	−	0.0925729i
$925$		−	6.70450i		−	0.220443i
$926$	37.5112	−	37.6350i	1.23269	−	1.23676i
$927$	12.9984	−	26.5770i	0.426924	−	0.872902i
$928$	2.96885	−	3.01817i	0.0974572	−	0.0990764i
$929$	−9.71753	+	16.8313i	−0.318822	+	0.552216i	−0.980242	−	0.197799i	$-0.936621\pi$
$929$	−9.71753	+	16.8313i	−0.318822	+	0.552216i	0.661421	+	0.750015i	$0.269954\pi$
$930$	−14.5228	+	0.523166i	−0.476223	+	0.0171553i
$931$	−16.7246	+	19.9483i	−0.548128	+	0.653780i
$932$	18.0343	−	31.4754i	0.590733	−	1.03101i
$933$	7.75548	−	33.5092i	0.253903	−	1.09704i
$934$	−13.7035	+	3.69606i	−0.448394	+	0.120939i
$935$	−10.3430	+	5.97152i	−0.338252	+	0.195290i
$936$	−13.7058	+	15.8899i	−0.447989	+	0.519378i
$937$			21.6552i			0.707445i	0.935350	+	0.353723i	$0.115084\pi$
$937$			21.6552i			0.707445i	−0.935350	+	0.353723i	$0.884916\pi$
$938$	10.1418	−	28.0260i	0.331143	−	0.915082i
$939$	1.36065	+	4.45918i	0.0444030	+	0.145520i
$940$	−4.31145	−	7.41115i	−0.140624	−	0.241725i
$941$	−5.82024	+	3.36032i	−0.189735	+	0.109543i	−0.591858	−	0.806042i	$-0.701605\pi$
$941$	−5.82024	+	3.36032i	−0.189735	+	0.109543i	0.402124	+	0.915585i	$0.368272\pi$
$942$	14.2222	+	22.7046i	0.463384	+	0.739755i
$943$	13.7764	+	7.95381i	0.448622	+	0.259012i
$944$	−29.2844	+	17.1657i	−0.953126	+	0.558695i
$945$	23.6468	−	6.74396i	0.769230	−	0.219381i
$946$	−3.35446	+	12.6020i	−0.109063	+	0.409728i
$947$	10.5673	−	18.3031i	0.343392	−	0.594772i	−0.641668	−	0.766982i	$-0.721757\pi$
$947$	10.5673	−	18.3031i	0.343392	−	0.594772i	0.985060	+	0.172210i	$0.0550908\pi$
$948$	−5.19106	−	16.8137i	−0.168598	−	0.546084i
$949$	14.0602	−	8.11768i	0.456414	−	0.263511i
$950$	6.68575	−	6.70782i	0.216914	−	0.217630i
$951$	17.7357	−	5.41174i	0.575118	−	0.175488i
$952$	16.8026	−	46.9151i	0.544577	−	1.52053i
$953$			2.18327i			0.0707230i	0.999375	+	0.0353615i	$0.0112583\pi$
$953$			2.18327i			0.0707230i	−0.999375	+	0.0353615i	$0.988742\pi$
$954$	−10.2337	+	52.8043i	−0.331328	+	1.70960i
$955$	10.8317	+	18.7611i	0.350507	+	0.607096i
$956$	10.8207	−	0.0356587i	0.349968	−	0.00115329i
$957$	−0.293075	+	1.26629i	−0.00947376	+	0.0409333i
$958$	30.2282	+	8.04627i	0.976630	+	0.259963i
$959$	−26.8880	+	12.5448i	−0.868259	+	0.405094i
$960$	23.6324	−	7.46720i	0.762732	−	0.241003i
$961$	−9.99900	+	17.3188i	−0.322548	+	0.558670i
$962$	−12.5718	+	3.39081i	−0.405331	+	0.109324i
$963$	18.7628	+	9.17660i	0.604622	+	0.295712i
$964$	21.6028	+	37.1340i	0.695779	+	1.19600i
$965$		−	2.11931i		−	0.0682229i
$966$	−43.0426	−	27.8723i	−1.38487	−	0.896775i
$967$	−25.1413			−0.808490			−0.404245	−	0.914651i	$-0.632466\pi$
$967$	−25.1413			−0.808490			−0.404245	+	0.914651i	$0.632466\pi$
$968$	−27.2693	+	7.45144i	−0.876468	+	0.239499i
$969$	−31.3543	−	29.2704i	−1.00724	−	0.940300i
$970$	−1.15654	−	4.28800i	−0.0371344	−	0.137679i
$971$	−30.0100	−	17.3263i	−0.963065	−	0.556026i	−0.0659503	−	0.997823i	$-0.521008\pi$
$971$	−30.0100	−	17.3263i	−0.963065	−	0.556026i	−0.897115	+	0.441797i	$0.854341\pi$
$972$	−17.8679	+	25.5487i	−0.573114	+	0.819476i
$973$	−47.3969	−	4.13685i	−1.51947	−	0.132621i
$974$	30.7925	+	8.19648i	0.986657	+	0.262632i
$975$	−1.73926	+	7.51483i	−0.0557009	+	0.240667i
$976$	−8.00506	+	14.0787i	−0.256236	+	0.450647i
$977$	−3.22538	+	1.86218i	−0.103189	+	0.0595763i	−0.550706	−	0.834699i	$-0.685642\pi$
$977$	−3.22538	+	1.86218i	−0.103189	+	0.0595763i	0.447517	+	0.894275i	$0.352308\pi$
$978$	23.0188	+	12.2068i	0.736059	+	0.390330i
$979$	−14.8297			−0.473960
$980$	−16.0247	+	19.2420i	−0.511891	+	0.614662i
$981$	−4.57137	−	6.79333i	−0.145953	−	0.216894i
$982$	−25.0671	+	25.1498i	−0.799923	+	0.802564i
$983$	−27.3018	−	47.2881i	−0.870792	−	1.50826i	−0.861179	−	0.508302i	$-0.830273\pi$
$983$	−27.3018	−	47.2881i	−0.870792	−	1.50826i	−0.00961355	−	0.999954i	$-0.503060\pi$
$984$	0.387004	+	9.84150i	0.0123372	+	0.313735i
$985$	−30.2227	−	17.4491i	−0.962977	−	0.555975i
$986$	−6.81100	−	1.81298i	−0.216906	−	0.0577370i
$987$	−10.7443	+	2.27995i	−0.341995	+	0.0725717i
$988$	−15.9594	−	9.14415i	−0.507735	−	0.290914i
$989$	−36.3837	+	63.0185i	−1.15694	+	2.00387i
$990$	−4.98874	+	5.74533i	−0.158553	+	0.182599i
$991$	−25.1790	−	43.6114i	−0.799839	−	1.38536i	−0.919721	−	0.392573i	$-0.871585\pi$
$991$	−25.1790	−	43.6114i	−0.799839	−	1.38536i	0.119882	−	0.992788i	$-0.461748\pi$
$992$	−4.70684	+	18.1634i	−0.149442	+	0.576689i
$993$	−11.0042	−	36.0635i	−0.349207	−	1.14444i
$994$	−13.1811	−	15.6496i	−0.418080	−	0.496376i
$995$	26.3603			0.835679
$996$	−14.3624	−	13.3195i	−0.455091	−	0.422046i
$997$	12.7609	+	22.1025i	0.404141	+	0.699993i	0.994221	−	0.107352i	$-0.0342372\pi$
$997$	12.7609	+	22.1025i	0.404141	+	0.699993i	−0.590080	+	0.807345i	$0.700904\pi$
$998$	−14.5004	+	3.91098i	−0.459002	+	0.123800i
$999$	−18.0722	+	6.90330i	−0.571778	+	0.218411i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	168.2.ba.c.5.18	yes	48
3.2	odd	2	inner	168.2.ba.c.5.7	✓	48
4.3	odd	2		672.2.bi.c.593.5		48
7.3	odd	6	inner	168.2.ba.c.101.15	yes	48
8.3	odd	2		672.2.bi.c.593.20		48
8.5	even	2	inner	168.2.ba.c.5.10	yes	48
12.11	even	2		672.2.bi.c.593.11		48
21.17	even	6	inner	168.2.ba.c.101.10	yes	48
24.5	odd	2	inner	168.2.ba.c.5.15	yes	48
24.11	even	2		672.2.bi.c.593.14		48
28.3	even	6		672.2.bi.c.17.14		48
56.3	even	6		672.2.bi.c.17.11		48
56.45	odd	6	inner	168.2.ba.c.101.7	yes	48
84.59	odd	6		672.2.bi.c.17.20		48
168.59	odd	6		672.2.bi.c.17.5		48
168.101	even	6	inner	168.2.ba.c.101.18	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.7	✓	48	3.2	odd	2	inner
168.2.ba.c.5.10	yes	48	8.5	even	2	inner
168.2.ba.c.5.15	yes	48	24.5	odd	2	inner
168.2.ba.c.5.18	yes	48	1.1	even	1	trivial
168.2.ba.c.101.7	yes	48	56.45	odd	6	inner
168.2.ba.c.101.10	yes	48	21.17	even	6	inner
168.2.ba.c.101.15	yes	48	7.3	odd	6	inner
168.2.ba.c.101.18	yes	48	168.101	even	6	inner
672.2.bi.c.17.5		48	168.59	odd	6
672.2.bi.c.17.11		48	56.3	even	6
672.2.bi.c.17.14		48	28.3	even	6
672.2.bi.c.17.20		48	84.59	odd	6
672.2.bi.c.593.5		48	4.3	odd	2
672.2.bi.c.593.11		48	12.11	even	2
672.2.bi.c.593.14		48	24.11	even	2
672.2.bi.c.593.20		48	8.3	odd	2

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:	\( N \)	\(=\)	\( 168 = 2^{3} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	168.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.998351 - 1.00165i) q^{2} +(1.26610 + 1.18195i) q^{3} +(-0.00659077 - 1.99999i) q^{4} +(-1.54900 - 0.894317i) q^{5} +(2.44790 - 0.0881824i) q^{6} +(2.63573 + 0.230049i) q^{7} +(-2.00986 - 1.99009i) q^{8} +(0.206000 + 2.99292i) q^{9} +O(q^{10})\)	\(q+(0.998351 - 1.00165i) q^{2} +(1.26610 + 1.18195i) q^{3} +(-0.00659077 - 1.99999i) q^{4} +(-1.54900 - 0.894317i) q^{5} +(2.44790 - 0.0881824i) q^{6} +(2.63573 + 0.230049i) q^{7} +(-2.00986 - 1.99009i) q^{8} +(0.206000 + 2.99292i) q^{9} +(-2.44224 + 0.658710i) q^{10} +(-0.501346 - 0.868358i) q^{11} +(2.35554 - 2.53997i) q^{12} -2.47302 q^{13} +(2.86181 - 2.41040i) q^{14} +(-0.904151 - 2.96313i) q^{15} +(-3.99991 + 0.0263630i) q^{16} +(3.32963 + 5.76708i) q^{17} +(3.20351 + 2.78164i) q^{18} +(-1.85941 + 3.22059i) q^{19} +(-1.77842 + 3.10388i) q^{20} +(3.06518 + 3.40656i) q^{21} +(-1.37031 - 0.364754i) q^{22} +(-6.85244 - 3.95626i) q^{23} +(-0.192497 - 4.89520i) q^{24} +(-0.900394 - 1.55953i) q^{25} +(-2.46894 + 2.47709i) q^{26} +(-3.27666 + 4.03281i) q^{27} +(0.442725 - 5.27295i) q^{28} -0.748403 q^{29} +(-3.87067 - 2.05261i) q^{30} +(2.87254 - 1.65846i) q^{31} +(-3.96691 + 4.03282i) q^{32} +(0.391600 - 1.69199i) q^{33} +(9.10071 + 2.42246i) q^{34} +(-3.87702 - 2.71353i) q^{35} +(5.98445 - 0.431724i) q^{36} +(3.22429 + 1.86155i) q^{37} +(1.36955 + 5.07775i) q^{38} +(-3.13108 - 2.92298i) q^{39} +(1.33351 + 4.88011i) q^{40} -2.01044 q^{41} +(6.47230 + 0.330713i) q^{42} -9.19651i q^{43} +(-1.73340 + 1.00841i) q^{44} +(2.35752 - 4.82027i) q^{45} +(-10.8039 + 2.91399i) q^{46} +(-1.19840 + 2.07569i) q^{47} +(-5.09544 - 4.69431i) q^{48} +(6.89415 + 1.21270i) q^{49} +(-2.46101 - 0.655080i) q^{50} +(-2.60076 + 11.2371i) q^{51} +(0.0162991 + 4.94601i) q^{52} +(6.33884 + 10.9792i) q^{53} +(0.768191 + 7.30821i) q^{54} +1.79345i q^{55} +(-4.83964 - 5.70771i) q^{56} +(-6.16075 + 1.87985i) q^{57} +(-0.747169 + 0.749635i) q^{58} +(7.34922 - 4.24308i) q^{59} +(-5.92027 + 1.82782i) q^{60} +(2.02442 - 3.50640i) q^{61} +(1.20661 - 4.53300i) q^{62} +(-0.145558 + 7.93592i) q^{63} +(0.0790881 + 7.99961i) q^{64} +(3.83071 + 2.21166i) q^{65} +(-1.30382 - 2.08144i) q^{66} +(6.89843 - 3.98281i) q^{67} +(11.5122 - 6.69723i) q^{68} +(-3.99976 - 13.1082i) q^{69} +(-6.58862 + 1.17435i) q^{70} -5.46843i q^{71} +(5.54214 - 6.42531i) q^{72} +(-5.68546 + 3.28250i) q^{73} +(5.08359 - 1.37113i) q^{74} +(0.703295 - 3.03873i) q^{75} +(6.45340 + 3.69757i) q^{76} +(-1.12165 - 2.40409i) q^{77} +(-6.05370 + 0.218077i) q^{78} +(2.53988 - 4.39920i) q^{79} +(6.21945 + 3.53635i) q^{80} +(-8.91513 + 1.23308i) q^{81} +(-2.00712 + 2.01375i) q^{82} -5.65457i q^{83} +(6.79288 - 6.15278i) q^{84} -11.9110i q^{85} +(-9.21165 - 9.18134i) q^{86} +(-0.947550 - 0.884573i) q^{87} +(-0.720472 + 2.74300i) q^{88} +(7.39495 - 12.8084i) q^{89} +(-2.47457 - 7.17372i) q^{90} +(-6.51821 - 0.568916i) q^{91} +(-7.86731 + 13.7309i) q^{92} +(5.59713 + 1.29542i) q^{93} +(0.882685 + 3.27265i) q^{94} +(5.76045 - 3.32580i) q^{95} +(-9.78907 + 0.417256i) q^{96} +1.75577i q^{97} +(8.09748 - 5.69481i) q^{98} +(2.49565 - 1.67937i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9}+O(q^{10}) \) 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9	\( 48 q + 6 q^{4} - 4 q^{7} - 14 q^{9} - 30 q^{10} - 18 q^{12} + 4 q^{15} + 6 q^{16} - 36 q^{22} - 12 q^{24} - 8 q^{25} - 10 q^{28} + 22 q^{30} + 48 q^{31} - 42 q^{33} + 52 q^{36} - 8 q^{39} - 18 q^{40} + 12 q^{42} - 8 q^{46} - 36 q^{49} - 48 q^{52} + 60 q^{54} + 4 q^{57} + 30 q^{58} - 32 q^{60} - 6 q^{63} - 60 q^{64} + 54 q^{66} + 42 q^{70} + 42 q^{72} - 36 q^{73} - 68 q^{78} - 56 q^{79} + 42 q^{81} + 48 q^{82} + 48 q^{84} - 132 q^{87} + 6 q^{88} + 48 q^{94} + 90 q^{96}+O(q^{100}) \) 48 * q + 6 * q^4 - 4 * q^7 - 14 * q^9 - 30 * q^10 - 18 * q^12 + 4 * q^15 + 6 * q^16 - 36 * q^22 - 12 * q^24 - 8 * q^25 - 10 * q^28 + 22 * q^30 + 48 * q^31 - 42 * q^33 + 52 * q^36 - 8 * q^39 - 18 * q^40 + 12 * q^42 - 8 * q^46 - 36 * q^49 - 48 * q^52 + 60 * q^54 + 4 * q^57 + 30 * q^58 - 32 * q^60 - 6 * q^63 - 60 * q^64 + 54 * q^66 + 42 * q^70 + 42 * q^72 - 36 * q^73 - 68 * q^78 - 56 * q^79 + 42 * q^81 + 48 * q^82 + 48 * q^84 - 132 * q^87 + 6 * q^88 + 48 * q^94 + 90 * q^96

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