LMFDB - Embedded newform 168.2.ba.c.101.18

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			101.18
Character	$\chi$	$=$	168.101
Dual form			168.2.ba.c.5.18

$q$-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 $\left(\mathbb{Z}/168\mathbb{Z}\right)^\times$.

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

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	−0.804636	−	0.593769i	$-0.797639\pi$
$5$	−1.54900	+	0.894317i	−0.692735	+	0.399951i	0.111901	+	0.993719i	$0.464306\pi$
$6$	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	−0.931655	−	0.363345i	$-0.881635\pi$
$11$	−0.501346	+	0.868358i	−0.151162	+	0.261820i	0.780493	+	0.625164i	$0.214968\pi$
$12$	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	−0.107001	−	0.994259i	$-0.534125\pi$
$17$	3.32963	−	5.76708i	0.807553	−	1.39872i	0.914554	−	0.404464i	$-0.132542\pi$
$18$	3.20351	−	2.78164i	0.755074	−	0.655640i
$19$	−1.85941	−	3.22059i	−0.426577	−	0.738854i	0.569989	−	0.821652i	$-0.306947\pi$
$19$	−1.85941	−	3.22059i	−0.426577	−	0.738854i	−0.996566	+	0.0827988i	$0.973614\pi$
$20$	−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	−0.997029	−	0.0770314i	$-0.975456\pi$
$23$	−6.85244	+	3.95626i	−1.42883	+	0.824936i	−0.431803	+	0.901968i	$0.642123\pi$
$24$	−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	0.735265	−	0.677779i	$-0.237058\pi$
$31$	2.87254	+	1.65846i	0.515924	+	0.297869i	−0.219341	+	0.975648i	$0.570391\pi$
$32$	−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	−0.210975	−	0.977492i	$-0.567664\pi$
$37$	3.22429	−	1.86155i	0.530071	−	0.306036i	0.741045	+	0.671455i	$0.234330\pi$
$38$	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	$0.247364\pi$
$43$			9.19651i			1.40245i	−0.712938	+	0.701227i	$0.752636\pi$
$44$	−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	0.765289	−	0.643687i	$-0.222596\pi$
$47$	−1.19840	−	2.07569i	−0.174805	−	0.302771i	−0.940094	+	0.340916i	$0.889263\pi$
$48$	−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	0.00943963	−	0.999955i	$-0.496995\pi$
$53$	6.33884	−	10.9792i	0.870707	−	1.50811i	0.861267	−	0.508153i	$-0.169671\pi$
$54$	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	0.895183	−	0.445699i	$-0.147045\pi$
$59$	7.34922	+	4.24308i	0.956787	+	0.552401i	0.0616046	+	0.998101i	$0.480378\pi$
$60$	−5.92027	−	1.82782i	−0.764304	−	0.235971i
$61$	2.02442	+	3.50640i	0.259200	+	0.448948i	0.966028	−	0.258438i	$-0.0832077\pi$
$61$	2.02442	+	3.50640i	0.259200	+	0.448948i	−0.706828	+	0.707386i	$0.749874\pi$
$62$	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	0.858207	−	0.513303i	$-0.171578\pi$
$67$	6.89843	+	3.98281i	0.842777	+	0.486577i	−0.0154303	+	0.999881i	$0.504912\pi$
$68$	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	$0.105193\pi$
$71$			5.46843i			0.648984i	−0.945889	+	0.324492i	$0.894807\pi$
$72$	5.54214	+	6.42531i	0.653148	+	0.757230i
$73$	−5.68546	−	3.28250i	−0.665433	−	0.384188i	0.128911	−	0.991656i	$-0.458852\pi$
$73$	−5.68546	−	3.28250i	−0.665433	−	0.384188i	−0.794344	+	0.607468i	$0.792185\pi$
$74$	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	0.972793	−	0.231676i	$-0.0744210\pi$
$79$	2.53988	+	4.39920i	0.285759	+	0.494949i	−0.687034	+	0.726625i	$0.741088\pi$
$80$	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	$0.100441\pi$
$83$			5.65457i			0.620669i	−0.950627	+	0.310335i	$0.899559\pi$
$84$	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	0.929676	+	0.368379i	$0.120087\pi$
$89$	7.39495	+	12.8084i	0.783863	+	1.35769i	−0.145812	+	0.989312i	$0.546580\pi$
$90$	−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	$-0.971590\pi$
$97$		−	1.75577i		−	0.178271i	0.996019	−	0.0891356i	$-0.0284105\pi$
$98$	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	−0.288330	−	0.957531i	$-0.593100\pi$
$101$	−12.6803	−	7.32100i	−1.26174	−	0.728467i	−0.973411	+	0.229064i	$0.926433\pi$
$102$	8.65916	−	13.8236i	0.857384	−	1.36874i
$103$	−8.54056	+	4.93089i	−0.841526	+	0.485855i	−0.857783	−	0.514013i	$-0.828158\pi$
$103$	−8.54056	+	4.93089i	−0.841526	+	0.485855i	0.0162566	+	0.999868i	$0.494825\pi$
$104$	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	0.983778	−	0.179392i	$-0.0574130\pi$
$107$	3.48110	+	6.02945i	0.336531	+	0.582889i	−0.647247	+	0.762281i	$0.724080\pi$
$108$	8.08716	−	6.52670i	0.778188	−	0.628032i
$109$	−2.36373	−	1.36470i	−0.226404	−	0.130715i	0.382508	−	0.923952i	$-0.375061\pi$
$109$	−2.36373	−	1.36470i	−0.226404	−	0.130715i	−0.608912	+	0.793238i	$0.708394\pi$
$110$	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	$-0.992047\pi$
$113$		−	0.531154i		−	0.0499667i	0.999688	−	0.0249834i	$-0.00795328\pi$
$114$	−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	0.216416	−	0.976301i	$-0.430563\pi$
$131$	13.3927	−	7.73228i	1.17013	−	0.675573i	0.953710	+	0.300729i	$0.0972298\pi$
$132$	−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	0.0240187	−	0.999712i	$-0.492354\pi$
$137$	−9.71195	−	5.60719i	−0.829748	−	0.479055i	−0.853766	+	0.520657i	$0.825687\pi$
$138$	−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	0.884348	−	0.466828i	$-0.154603\pi$
$149$	0.462495	+	0.801066i	0.0378891	+	0.0656258i	−0.846459	+	0.532454i	$0.821270\pi$
$150$	−2.34160	+	3.73817i	−0.191191	+	0.305221i
$151$	9.56720	−	16.5709i	0.778568	−	1.34852i	−0.154200	−	0.988040i	$-0.549280\pi$
$151$	9.56720	−	16.5709i	0.778568	−	1.34852i	0.932767	−	0.360479i	$-0.117387\pi$
$152$	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	−0.560961	−	0.827842i	$-0.689568\pi$
$157$	5.46873	−	9.47212i	0.436452	−	0.755957i	0.997413	+	0.0718851i	$0.0229015\pi$
$158$	−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	−0.0937855	−	0.995592i	$-0.529897\pi$
$163$	9.21188	−	5.31848i	0.721530	−	0.416576i	0.815316	+	0.579017i	$0.196563\pi$
$164$	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	−0.633974	−	0.773354i	$-0.718577\pi$
$173$	−3.69882	+	2.13552i	−0.281216	+	0.162360i	0.352758	+	0.935715i	$0.385244\pi$
$174$	−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	−0.971975	−	0.235083i	$-0.924464\pi$
$179$	−3.77825	+	6.54412i	−0.282399	+	0.489130i	0.689576	+	0.724214i	$0.257797\pi$
$180$	−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	−0.828923	−	0.559362i	$-0.811046\pi$
$191$	−10.4891	+	6.05587i	−0.758963	+	0.438188i	0.0699601	+	0.997550i	$0.477713\pi$
$192$	−9.35498	−	10.2218i	−0.675138	−	0.737692i
$193$	0.592437	−	1.02613i	0.0426445	−	0.0738625i	−0.843915	−	0.536476i	$-0.819755\pi$
$193$	0.592437	−	1.02613i	0.0426445	−	0.0738625i	0.886560	+	0.462614i	$0.153088\pi$
$194$	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	−0.0260186	−	0.999661i	$-0.508283\pi$
$199$	−12.7632	−	7.36884i	−0.904760	−	0.522363i	−0.878741	+	0.477298i	$0.841616\pi$
$200$	−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	$-0.828273\pi$
$211$		−	14.9240i		−	1.02741i	0.857967	−	0.513704i	$-0.171727\pi$
$212$	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	$-0.917859\pi$
$223$		−	7.62187i		−	0.510398i	0.966889	−	0.255199i	$-0.0821410\pi$
$224$	−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	−0.0269870	−	0.999636i	$-0.508591\pi$
$227$	−13.6531	−	7.88264i	−0.906190	−	0.523189i	−0.879203	+	0.476446i	$0.841925\pi$
$228$	3.80029	−	12.3091i	0.251680	−	0.815187i
$229$	−8.82193	−	15.2800i	−0.582970	−	1.00973i	−0.995125	−	0.0986198i	$-0.968557\pi$
$229$	−8.82193	−	15.2800i	−0.582970	−	1.00973i	0.412155	−	0.911114i	$-0.364776\pi$
$230$	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	0.112344	−	0.993669i	$-0.464164\pi$
$233$	15.7079	−	9.06896i	1.02906	−	0.594127i	0.916715	+	0.399542i	$0.130831\pi$
$234$	−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	$-0.944012\pi$
$239$		−	5.41040i		−	0.349970i	0.984571	−	0.174985i	$-0.0559877\pi$
$240$	3.69464	−	11.8284i	0.238488	−	0.763522i
$241$	−18.6025	−	10.7401i	−1.19829	−	0.691834i	−0.238117	−	0.971236i	$-0.576530\pi$
$241$	−18.6025	−	10.7401i	−1.19829	−	0.691834i	−0.960174	+	0.279403i	$0.909863\pi$
$242$	−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	$0.215565\pi$
$251$			19.8553i			1.25325i	−0.779319	+	0.626627i	$0.784435\pi$
$252$	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	0.969464	−	0.245234i	$-0.0788647\pi$
$257$	4.36616	+	7.56240i	0.272353	+	0.471730i	−0.697111	+	0.716964i	$0.745531\pi$
$258$	−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	0.924623	−	0.380885i	$-0.124381\pi$
$263$	17.1429	+	9.89747i	1.05708	+	0.610304i	0.132455	+	0.991189i	$0.457714\pi$
$264$	−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	0.524357	−	0.851498i	$-0.324306\pi$
$269$	0.805574	+	0.465098i	0.0491167	+	0.0283575i	−0.475241	+	0.879856i	$0.657639\pi$
$270$	5.34592	+	12.0074i	0.325343	+	0.730749i
$271$	−7.45646	+	4.30499i	−0.452948	+	0.261509i	−0.709074	−	0.705134i	$-0.750887\pi$
$271$	−7.45646	+	4.30499i	−0.452948	+	0.261509i	0.256127	+	0.966643i	$0.417554\pi$
$272$	−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	0.999086	+	0.0427456i	$0.0136105\pi$
$277$	25.5583	+	14.7561i	1.53565	+	0.886607i	0.536562	+	0.843861i	$0.319723\pi$
$278$	−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	$-0.780546\pi$
$281$		−	21.3260i		−	1.27220i	0.771605	−	0.636102i	$-0.219454\pi$
$282$	−2.75053	−	5.18678i	−0.163792	−	0.308868i
$283$	−10.4247	+	18.0561i	−0.619684	+	1.07332i	0.369860	+	0.929088i	$0.379406\pi$
$283$	−10.4247	+	18.0561i	−0.619684	+	1.07332i	−0.989543	+	0.144236i	$0.953928\pi$
$284$	−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	$-0.874951\pi$
$293$		−	13.1058i		−	0.765652i	0.923821	−	0.382826i	$-0.125049\pi$
$294$	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	0.434211	+	0.900811i	$0.357027\pi$
$311$	−9.92896	+	17.1975i	−0.563020	+	0.975179i	−0.997231	+	0.0743677i	$0.976306\pi$
$312$	0.476049	−	12.1059i	0.0269510	−	0.685362i
$313$	2.33108	−	1.34585i	0.131760	−	0.0760718i	−0.432671	−	0.901552i	$-0.642429\pi$
$313$	2.33108	−	1.34585i	0.131760	−	0.0760718i	0.564431	+	0.825480i	$0.309096\pi$
$314$	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	0.976283	−	0.216499i	$-0.0694638\pi$
$317$	5.35288	+	9.27147i	0.300648	+	0.520737i	−0.675635	+	0.737236i	$0.736130\pi$
$318$	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	−0.918762	−	0.394811i	$-0.870810\pi$
$331$	−18.8525	+	10.8845i	−1.03623	+	0.598266i	−0.117465	+	0.993077i	$0.537477\pi$
$332$	−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	−0.465604	−	0.884993i	$-0.654163\pi$
$347$	9.94032	−	17.2171i	0.533624	−	0.924265i	0.999229	−	0.0392715i	$-0.0125037\pi$
$348$	−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	−0.547057	−	0.837095i	$-0.684252\pi$
$353$	8.48135	−	14.6901i	0.451417	−	0.781877i	0.998474	+	0.0552182i	$0.0175854\pi$
$354$	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	−0.896608	−	0.442826i	$-0.853976\pi$
$359$	−18.2162	+	10.5171i	−0.961413	+	0.555072i	−0.0648056	+	0.997898i	$0.520643\pi$
$360$	−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	0.532238	−	0.846595i	$-0.321351\pi$
$367$	1.24875	+	0.720966i	0.0651842	+	0.0376341i	−0.467054	+	0.884229i	$0.654685\pi$
$368$	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	−0.900848	−	0.434134i	$-0.857055\pi$
$373$	−18.8362	+	10.8751i	−0.975302	+	0.563091i	−0.0744535	+	0.997224i	$0.523721\pi$
$374$	−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	$0.0149087\pi$
$379$			1.82298i			0.0936402i	−0.998903	+	0.0468201i	$0.985091\pi$
$380$	−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	0.962360	−	0.271777i	$-0.0876112\pi$
$383$	4.81069	+	8.33236i	0.245815	+	0.425763i	−0.716546	+	0.697540i	$0.754278\pi$
$384$	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	0.250703	+	0.968064i	$0.419338\pi$
$389$	−14.0629	+	24.3576i	−0.713017	+	1.23498i	−0.963719	+	0.266917i	$0.913995\pi$
$390$	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	0.999526	−	0.0307871i	$-0.00980139\pi$
$397$	9.42646	+	16.3271i	0.473101	+	0.819434i	−0.526425	+	0.850221i	$0.676468\pi$
$398$	−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	−0.363773	−	0.931488i	$-0.618512\pi$
$401$	5.22718	−	3.01791i	0.261033	−	0.150707i	0.624806	+	0.780780i	$0.285178\pi$
$402$	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	0.941556	−	0.336856i	$-0.109364\pi$
$409$	22.6629	+	13.0844i	1.12061	+	0.646984i	0.179052	+	0.983840i	$0.442697\pi$
$410$	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	$-0.980404\pi$
$419$		−	2.51866i		−	0.123045i	0.998106	−	0.0615223i	$-0.0195955\pi$
$420$	−16.0247	−	3.45569i	−0.781927	−	0.168620i
$421$		−	33.4873i		−	1.63207i	−0.578003	−	0.816034i	$-0.696168\pi$
$421$		−	33.4873i		−	1.63207i	0.578003	−	0.816034i	$-0.303832\pi$
$422$	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	0.760351	−	0.649512i	$-0.225027\pi$
$431$	12.0003	+	6.92836i	0.578033	+	0.333727i	−0.182319	+	0.983240i	$0.558360\pi$
$432$	13.0000	+	16.2173i	0.625464	+	0.780253i
$433$		−	9.79368i		−	0.470654i	−0.971916	−	0.235327i	$-0.924384\pi$
$433$		−	9.79368i		−	0.470654i	0.971916	−	0.235327i	$-0.0756161\pi$
$434$	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	−0.323707	−	0.946157i	$-0.604929\pi$
$439$	6.99463	−	4.03835i	0.333835	−	0.192740i	0.657543	+	0.753417i	$0.271596\pi$
$440$	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	0.575559	−	0.817760i	$-0.304784\pi$
$443$	−8.84884	−	15.3266i	−0.420421	−	0.728191i	−0.995981	+	0.0895692i	$0.971451\pi$
$444$	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	$0.151901\pi$
$449$			19.4650i			0.918609i	−0.888279	+	0.459305i	$0.848099\pi$
$450$	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	0.988424	−	0.151715i	$-0.0484797\pi$
$457$	7.75626	+	13.4342i	0.362823	+	0.628427i	−0.625601	+	0.780143i	$0.715146\pi$
$458$	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	$0.00635516\pi$
$461$			0.857290i			0.0399280i	−0.999801	+	0.0199640i	$0.993645\pi$
$462$	−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	−0.687431	−	0.726249i	$-0.741262\pi$
$467$	−8.69155	+	5.01807i	−0.402197	+	0.232208i	0.285235	+	0.958458i	$0.407928\pi$
$468$	−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	−0.494663	−	0.869085i	$-0.664708\pi$
$479$	11.0594	−	19.1555i	0.505318	−	0.875237i	0.999981	−	0.00615194i	$-0.00195824\pi$
$480$	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	−0.489419	−	0.872049i	$-0.662791\pi$
$487$	11.2659	−	19.5131i	0.510506	−	0.884223i	0.999926	−	0.0121746i	$-0.00387541\pi$
$488$	−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	−0.691525	−	0.722353i	$-0.743061\pi$
$499$	−9.19695	+	5.30986i	−0.411712	+	0.237702i	0.279813	+	0.960054i	$0.409727\pi$
$500$	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	−0.876546	−	0.481318i	$-0.840158\pi$
$509$	−20.2595	+	11.6968i	−0.897985	+	0.518452i	−0.0214392	+	0.999770i	$0.506825\pi$
$510$	−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	−0.881691	−	0.471827i	$-0.843595\pi$
$521$	−0.735700	+	1.27427i	−0.0322316	+	0.0558267i	0.849460	+	0.527654i	$0.176928\pi$
$522$	−2.39751	+	2.08179i	−0.104936	+	0.0911175i
$523$	−5.30372	−	9.18631i	−0.231915	−	0.401689i	0.726456	−	0.687213i	$-0.241166\pi$
$523$	−5.30372	−	9.18631i	−0.231915	−	0.401689i	−0.958372	+	0.285523i	$0.907833\pi$
$524$	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	−0.167861	−	0.985811i	$-0.553686\pi$
$541$	14.0009	−	8.08343i	0.601946	−	0.347534i	0.769807	+	0.638277i	$0.220353\pi$
$542$	−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	$-0.914477\pi$
$547$		−	12.4170i		−	0.530914i	0.964123	−	0.265457i	$-0.0855228\pi$
$548$	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	−0.544554	−	0.838726i	$-0.683301\pi$
$557$	10.7167	−	18.5619i	0.454081	−	0.786492i	0.998635	+	0.0522341i	$0.0166342\pi$
$558$	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	0.827932	−	0.560829i	$-0.189517\pi$
$563$	17.9430	+	10.3594i	0.756205	+	0.436595i	−0.0717262	+	0.997424i	$0.522851\pi$
$564$	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	−0.908439	−	0.418018i	$-0.862725\pi$
$569$	−23.8691	+	13.7808i	−1.00064	+	0.577722i	−0.0922056	+	0.995740i	$0.529392\pi$
$570$	13.8077	+	8.64920i	0.578343	+	0.362275i
$571$	0.339940	+	0.196264i	0.0142260	+	0.00821340i	0.507096	−	0.861889i	$-0.330719\pi$
$571$	0.339940	+	0.196264i	0.0142260	+	0.00821340i	−0.492870	+	0.870103i	$0.664052\pi$
$572$	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	0.209493	−	0.977810i	$-0.432819\pi$
$577$	−12.7927	−	7.38589i	−0.532569	−	0.307479i	−0.742062	+	0.670331i	$0.766152\pi$
$578$	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	$-0.976895\pi$
$587$		−	3.51421i		−	0.145047i	0.997367	−	0.0725236i	$-0.0231052\pi$
$588$	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	−0.955012	−	0.296568i	$-0.904158\pi$
$593$	−17.8824	−	30.9732i	−0.734342	−	1.27192i	0.220670	−	0.975349i	$-0.429176\pi$
$594$	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	−0.451284	−	0.892380i	$-0.649034\pi$
$599$	−35.4819	−	20.4855i	−1.44975	−	0.837014i	−0.998466	+	0.0553669i	$0.982367\pi$
$600$	−7.46087	−	4.70781i	−0.304589	−	0.192196i
$601$			36.1540i			1.47475i	0.675482	+	0.737377i	$0.263936\pi$
$601$			36.1540i			1.47475i	−0.675482	+	0.737377i	$0.736064\pi$
$602$	−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	−0.305182	−	0.952294i	$-0.598717\pi$
$607$	9.04038	−	5.21946i	0.366938	−	0.211851i	0.672120	+	0.740443i	$0.265384\pi$
$608$	−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	0.604684	−	0.796466i	$-0.293300\pi$
$613$	5.37925	+	3.10571i	0.217266	+	0.125439i	−0.387418	+	0.921904i	$0.626633\pi$
$614$	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	$0.149587\pi$
$617$			22.4963i			0.905669i	−0.891595	+	0.452834i	$0.850413\pi$
$618$	−21.3413	+	11.3172i	−0.858472	+	0.455245i
$619$	14.1624	−	24.5300i	0.569235	−	0.985943i	−0.427407	−	0.904059i	$-0.640573\pi$
$619$	14.1624	−	24.5300i	0.569235	−	0.985943i	0.996642	−	0.0818842i	$-0.0260938\pi$
$620$	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	0.498432	−	0.866929i	$-0.333909\pi$
$641$	−0.0793494	−	0.0458124i	−0.00313411	−	0.00180948i	−0.501566	+	0.865119i	$0.667243\pi$
$642$	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	−0.775139	−	0.631791i	$-0.782320\pi$
$647$	4.05903	−	7.03045i	0.159577	−	0.276396i	0.934716	+	0.355395i	$0.115654\pi$
$648$	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	−0.981959	−	0.189095i	$-0.939444\pi$
$653$	−16.7312	−	28.9792i	−0.654741	−	1.13404i	0.327218	−	0.944949i	$-0.393889\pi$
$654$	−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	0.393130	+	0.919483i	$0.371392\pi$
$661$	−15.4190	+	26.7065i	−0.599731	+	1.03876i	−0.992861	+	0.119281i	$0.961941\pi$
$662$	−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	−0.971305	−	0.237836i	$-0.923562\pi$
$677$	−32.5497	+	18.7926i	−1.25099	+	0.722257i	−0.279680	+	0.960093i	$0.590228\pi$
$678$	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	−0.884889	−	0.465802i	$-0.845766\pi$
$683$	−1.02051	+	1.76757i	−0.0390487	+	0.0676343i	0.845841	+	0.533436i	$0.179099\pi$
$684$	−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	0.998146	−	0.0608673i	$-0.0193866\pi$
$691$	11.7334	+	20.3229i	0.446360	+	0.773119i	−0.551786	+	0.833986i	$0.686053\pi$
$692$	−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	−0.570093	+	0.821580i	$0.693093\pi$
$709$	−41.7153	+	24.0843i	−1.56665	+	0.904505i	−0.996556	+	0.0829254i	$0.973574\pi$
$710$	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	0.719252	−	0.694749i	$-0.244484\pi$
$719$	−6.49021	−	11.2414i	−0.242044	−	0.419232i	−0.961296	+	0.275517i	$0.911151\pi$
$720$	−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	$0.0714880\pi$
$727$			12.0095i			0.445406i	−0.974886	+	0.222703i	$0.928512\pi$
$728$	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	0.934419	−	0.356175i	$-0.115919\pi$
$733$	4.29808	+	7.44449i	0.158753	+	0.274968i	−0.775666	+	0.631143i	$0.782586\pi$
$734$	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	0.457979	−	0.888963i	$-0.348574\pi$
$739$	−2.25350	−	1.30106i	−0.0828963	−	0.0478602i	−0.540875	+	0.841103i	$0.681907\pi$
$740$	−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	$-0.920913\pi$
$743$		−	13.4061i		−	0.491823i	0.969292	−	0.245911i	$-0.0790872\pi$
$744$	−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	0.686182	−	0.727430i	$-0.259285\pi$
$751$	−7.86182	−	13.6171i	−0.286882	−	0.496894i	−0.973064	+	0.230536i	$0.925952\pi$
$752$	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	$0.346633\pi$
$757$			48.7626i			1.77231i	−0.463391	+	0.886154i	$0.653367\pi$
$758$	−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	−0.927652	−	0.373447i	$-0.878176\pi$
$761$	−21.7170	−	37.6149i	−0.787240	−	1.36354i	0.140411	−	0.990093i	$-0.455158\pi$
$762$	−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	$-0.858043\pi$
$769$		−	23.9226i		−	0.862670i	0.902192	−	0.431335i	$-0.141957\pi$
$770$	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	0.219427	−	0.975629i	$-0.429581\pi$
$773$	−14.3402	−	8.27930i	−0.515780	−	0.297786i	−0.735206	+	0.677843i	$0.762915\pi$
$774$	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	−0.950819	−	0.309746i	$-0.899756\pi$
$787$	−5.81161	+	10.0660i	−0.207162	+	0.358814i	0.743658	+	0.668561i	$0.233089\pi$
$788$	−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	$-0.986709\pi$
$797$		−	2.35681i		−	0.0834824i	0.999128	−	0.0417412i	$-0.0132905\pi$
$798$	−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	0.993592	−	0.113024i	$-0.0360538\pi$
$809$	39.6070	+	22.8671i	1.39251	+	0.803964i	0.398914	+	0.916988i	$0.369387\pi$
$810$	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	0.984239	+	0.176845i	$0.0565892\pi$
$821$	18.4890	+	32.0239i	0.645272	+	1.11764i	−0.338967	+	0.940798i	$0.610078\pi$
$822$	−23.2794	−	14.5823i	−0.811964	−	0.508616i
$823$	−3.62518	+	6.27899i	−0.126366	+	0.218872i	−0.922266	−	0.386556i	$-0.873665\pi$
$823$	−3.62518	+	6.27899i	−0.126366	+	0.218872i	0.795900	+	0.605428i	$0.206998\pi$
$824$	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	−0.554139	−	0.832424i	$-0.686953\pi$
$829$	12.7789	−	22.1338i	0.443830	−	0.768737i	0.997970	+	0.0636869i	$0.0202859\pi$
$830$	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	−0.780691	−	0.624917i	$-0.785133\pi$
$857$	4.41603	−	7.64878i	0.150849	−	0.261277i	0.931540	+	0.363640i	$0.118466\pi$
$858$	3.22437	−	5.14745i	0.110078	−	0.175731i
$859$	−2.94564	−	5.10200i	−0.100504	−	0.174078i	0.811388	−	0.584507i	$-0.198712\pi$
$859$	−2.94564	−	5.10200i	−0.100504	−	0.174078i	−0.911892	+	0.410429i	$0.865379\pi$
$860$	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	−0.451439	−	0.892302i	$-0.649089\pi$
$863$	2.80835	−	1.62140i	0.0955974	−	0.0551932i	0.547037	+	0.837109i	$0.315756\pi$
$864$	−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	0.338028	−	0.941136i	$-0.390240\pi$
$877$	39.1526	−	22.6048i	1.32209	−	0.763309i	0.984062	+	0.177828i	$0.0569070\pi$
$878$	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	$0.0292367\pi$
$883$			5.45102i			0.183442i	−0.995785	+	0.0917208i	$0.970763\pi$
$884$	−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	0.879290	+	0.476287i	$0.158018\pi$
$887$	25.3783	+	43.9566i	0.852122	+	1.47592i	−0.0271684	+	0.999631i	$0.508649\pi$
$888$	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	0.636934	−	0.770918i	$-0.280202\pi$
$907$	8.66652	+	5.00362i	0.287767	+	0.166142i	−0.349167	+	0.937060i	$0.613536\pi$
$908$	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	$0.0777249\pi$
$911$			14.5940i			0.483521i	−0.970336	+	0.241761i	$0.922275\pi$
$912$	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	0.846555	−	0.532302i	$-0.178673\pi$
$919$	−1.14316	−	1.98001i	−0.0377093	−	0.0653145i	−0.884264	+	0.466987i	$0.845339\pi$
$920$	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	0.661421	−	0.750015i	$-0.269954\pi$
$929$	−9.71753	−	16.8313i	−0.318822	−	0.552216i	−0.980242	+	0.197799i	$0.936621\pi$
$930$	−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	$-0.884916\pi$
$937$		−	21.6552i		−	0.707445i	0.935350	−	0.353723i	$-0.115084\pi$
$938$	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	0.402124	−	0.915585i	$-0.368272\pi$
$941$	−5.82024	−	3.36032i	−0.189735	−	0.109543i	−0.591858	+	0.806042i	$0.701605\pi$
$942$	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	0.985060	−	0.172210i	$-0.0550908\pi$
$947$	10.5673	+	18.3031i	0.343392	+	0.594772i	−0.641668	+	0.766982i	$0.721757\pi$
$948$	−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	$-0.988742\pi$
$953$		−	2.18327i		−	0.0707230i	0.999375	−	0.0353615i	$-0.0112583\pi$
$954$	−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	−0.897115	−	0.441797i	$-0.854341\pi$
$971$	−30.0100	+	17.3263i	−0.963065	+	0.556026i	−0.0659503	+	0.997823i	$0.521008\pi$
$972$	−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	0.447517	−	0.894275i	$-0.352308\pi$
$977$	−3.22538	−	1.86218i	−0.103189	−	0.0595763i	−0.550706	+	0.834699i	$0.685642\pi$
$978$	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	−0.00961355	+	0.999954i	$0.503060\pi$
$983$	−27.3018	+	47.2881i	−0.870792	+	1.50826i	−0.861179	+	0.508302i	$0.830273\pi$
$984$	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	0.119882	+	0.992788i	$0.461748\pi$
$991$	−25.1790	+	43.6114i	−0.799839	+	1.38536i	−0.919721	+	0.392573i	$0.871585\pi$
$992$	−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	−0.590080	−	0.807345i	$-0.700904\pi$
$997$	12.7609	−	22.1025i	0.404141	−	0.699993i	0.994221	+	0.107352i	$0.0342372\pi$
$998$	−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.101.18	yes	48
3.2	odd	2	inner	168.2.ba.c.101.7	yes	48
4.3	odd	2		672.2.bi.c.17.5		48
7.5	odd	6	inner	168.2.ba.c.5.15	yes	48
8.3	odd	2		672.2.bi.c.17.20		48
8.5	even	2	inner	168.2.ba.c.101.10	yes	48
12.11	even	2		672.2.bi.c.17.11		48
21.5	even	6	inner	168.2.ba.c.5.10	yes	48
24.5	odd	2	inner	168.2.ba.c.101.15	yes	48
24.11	even	2		672.2.bi.c.17.14		48
28.19	even	6		672.2.bi.c.593.14		48
56.5	odd	6	inner	168.2.ba.c.5.7	✓	48
56.19	even	6		672.2.bi.c.593.11		48
84.47	odd	6		672.2.bi.c.593.20		48
168.5	even	6	inner	168.2.ba.c.5.18	yes	48
168.131	odd	6		672.2.bi.c.593.5		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.2.ba.c.5.7	✓	48	56.5	odd	6	inner
168.2.ba.c.5.10	yes	48	21.5	even	6	inner
168.2.ba.c.5.15	yes	48	7.5	odd	6	inner
168.2.ba.c.5.18	yes	48	168.5	even	6	inner
168.2.ba.c.101.7	yes	48	3.2	odd	2	inner
168.2.ba.c.101.10	yes	48	8.5	even	2	inner
168.2.ba.c.101.15	yes	48	24.5	odd	2	inner
168.2.ba.c.101.18	yes	48	1.1	even	1	trivial
672.2.bi.c.17.5		48	4.3	odd	2
672.2.bi.c.17.11		48	12.11	even	2
672.2.bi.c.17.14		48	24.11	even	2
672.2.bi.c.17.20		48	8.3	odd	2
672.2.bi.c.593.5		48	168.131	odd	6
672.2.bi.c.593.11		48	56.19	even	6
672.2.bi.c.593.14		48	28.19	even	6
672.2.bi.c.593.20		48	84.47	odd	6

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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