LMFDB - Embedded newform 168.2.ba.c.5.7

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			5.7
Character	$\chi$	$=$	168.5
Dual form			168.2.ba.c.101.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.998351 + 1.00165i) q^{2} +(0.390548 + 1.68745i) q^{3} +(-0.00659077 - 1.99999i) q^{4} +(1.54900 + 0.894317i) q^{5} +(-2.08013 - 1.29347i) q^{6} +(2.63573 + 0.230049i) q^{7} +(2.00986 + 1.99009i) q^{8} +(-2.69494 + 1.31806i) q^{9} +O(q^{10})$	\(q+(-0.998351 + 1.00165i) q^{2} +(0.390548 + 1.68745i) q^{3} +(-0.00659077 - 1.99999i) q^{4} +(1.54900 + 0.894317i) q^{5} +(-2.08013 - 1.29347i) q^{6} +(2.63573 + 0.230049i) q^{7} +(2.00986 + 1.99009i) q^{8} +(-2.69494 + 1.31806i) q^{9} +(-2.44224 + 0.658710i) q^{10} +(0.501346 + 0.868358i) q^{11} +(3.37230 - 0.792214i) 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} +(1.37027 - 4.01527i) q^{18} +(-1.85941 + 3.22059i) q^{19} +(1.77842 - 3.10388i) q^{20} +(0.641185 + 4.53750i) q^{21} +(-1.37031 - 0.364754i) q^{22} +(6.85244 + 3.95626i) q^{23} +(-2.57322 + 4.16876i) 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} +(-2.06535 - 3.86388i) q^{30} +(2.87254 - 1.65846i) q^{31} +(3.96691 - 4.03282i) q^{32} +(-1.26951 + 1.18513i) q^{33} +(9.10071 + 2.42246i) q^{34} +(3.87702 + 2.71353i) q^{35} +(2.65386 + 5.38117i) q^{36} +(3.22429 + 1.86155i) q^{37} +(-1.36955 - 5.07775i) q^{38} +(-0.965832 - 4.17308i) q^{39} +(1.33351 + 4.88011i) q^{40} +2.01044 q^{41} +(-5.18509 - 3.88777i) q^{42} -9.19651i q^{43} +(1.73340 - 1.00841i) q^{44} +(-5.35324 - 0.368459i) q^{45} +(-10.8039 + 2.91399i) q^{46} +(1.19840 - 2.07569i) q^{47} +(-1.60665 - 6.73934i) q^{48} +(6.89415 + 1.21270i) q^{49} +(2.46101 + 0.655080i) q^{50} +(8.43126 - 7.87089i) q^{51} +(0.0162991 + 4.94601i) q^{52} +(-6.33884 - 10.9792i) q^{53} +(7.31070 + 0.744103i) 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} +(5.93219 + 1.78876i) q^{60} +(2.02442 - 3.50640i) q^{61} +(-1.20661 + 4.53300i) q^{62} +(-7.40637 + 2.85408i) q^{63} +(0.0790881 + 7.99961i) q^{64} +(-3.83071 - 2.21166i) q^{65} +(0.0803309 - 2.45477i) 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} +(-8.03952 - 2.71406i) q^{72} +(-5.68546 + 3.28250i) q^{73} +(-5.08359 + 1.37113i) q^{74} +(2.27997 - 2.12844i) q^{75} +(6.45340 + 3.69757i) q^{76} +(1.12165 + 2.40409i) q^{77} +(5.14419 + 3.19878i) q^{78} +(2.53988 - 4.39920i) q^{79} +(-6.21945 - 3.53635i) q^{80} +(5.52545 - 7.10419i) q^{81} +(-2.00712 + 2.01375i) q^{82} +5.65457i q^{83} +(9.07072 - 1.31227i) q^{84} -11.9110i q^{85} +(9.21165 + 9.18134i) q^{86} +(0.292288 + 1.26289i) q^{87} +(-0.720472 + 2.74300i) q^{88} +(-7.39495 + 12.8084i) q^{89} +(5.71347 - 4.99420i) q^{90} +(-6.51821 - 0.568916i) q^{91} +(7.86731 - 13.7309i) q^{92} +(3.92043 + 4.19955i) q^{93} +(0.882685 + 3.27265i) q^{94} +(-5.76045 + 3.32580i) q^{95} +(8.35443 + 5.11893i) 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
$3$	0.390548	+	1.68745i	0.225483	+	0.974247i
$3$	0.390548	+	1.68745i	0.225483	+	0.974247i
$4$	−0.00659077	−	1.99999i	−0.00329539	−	0.999995i
$5$	1.54900	+	0.894317i	0.692735	+	0.399951i	0.804636	−	0.593769i	$-0.202361\pi$
$5$	1.54900	+	0.894317i	0.692735	+	0.399951i	−0.111901	+	0.993719i	$0.535694\pi$
$6$	−2.08013	−	1.29347i	−0.849209	−	0.528057i
$7$	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
$9$	−2.69494	+	1.31806i	−0.898315	+	0.439353i
$10$	−2.44224	+	0.658710i	−0.772303	+	0.208303i
$11$	0.501346	+	0.868358i	0.151162	+	0.261820i	0.931655	−	0.363345i	$-0.118365\pi$
$11$	0.501346	+	0.868358i	0.151162	+	0.261820i	−0.780493	+	0.625164i	$0.785032\pi$
$12$	3.37230	−	0.792214i	0.973499	−	0.228693i
$13$	−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	$-0.867458\pi$
$17$	−3.32963	−	5.76708i	−0.807553	−	1.39872i	0.107001	−	0.994259i	$-0.465875\pi$
$18$	1.37027	−	4.01527i	0.322976	−	0.946407i
$19$	−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
$21$	0.641185	+	4.53750i	0.139918	+	0.990163i
$22$	−1.37031	−	0.364754i	−0.292150	−	0.0777658i
$23$	6.85244	+	3.95626i	1.42883	+	0.824936i	0.997029	−	0.0770314i	$-0.0245442\pi$
$23$	6.85244	+	3.95626i	1.42883	+	0.824936i	0.431803	+	0.901968i	$0.357877\pi$
$24$	−2.57322	+	4.16876i	−0.525256	+	0.850944i
$25$	−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	$-0.477864\pi$
$29$	0.748403			0.138975			0.0694875	+	0.997583i	$0.477864\pi$
$30$	−2.06535	−	3.86388i	−0.377080	−	0.705446i
$31$	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
$33$	−1.26951	+	1.18513i	−0.220993	+	0.206305i
$34$	9.10071	+	2.42246i	1.56076	+	0.415449i
$35$	3.87702	+	2.71353i	0.655335	+	0.458670i
$36$	2.65386	+	5.38117i	0.442311	+	0.896862i
$37$	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
$39$	−0.965832	−	4.17308i	−0.154657	−	0.668228i
$40$	1.33351	+	4.88011i	0.210846	+	0.771613i
$41$	2.01044			0.313978			0.156989	−	0.987600i	$-0.449821\pi$
$41$	2.01044			0.313978			0.156989	+	0.987600i	$0.449821\pi$
$42$	−5.18509	−	3.88777i	−0.800078	−	0.599897i
$43$		−	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
$45$	−5.35324	−	0.368459i	−0.798013	−	0.0549266i
$46$	−10.8039	+	2.91399i	−1.59295	+	0.429644i
$47$	1.19840	−	2.07569i	0.174805	−	0.302771i	−0.765289	−	0.643687i	$-0.777404\pi$
$47$	1.19840	−	2.07569i	0.174805	−	0.302771i	0.940094	+	0.340916i	$0.110737\pi$
$48$	−1.60665	−	6.73934i	−0.231899	−	0.972740i
$49$	6.89415	+	1.21270i	0.984879	+	0.173242i
$50$	2.46101	+	0.655080i	0.348039	+	0.0926423i
$51$	8.43126	−	7.87089i	1.18061	−	1.10214i
$52$	0.0162991	+	4.94601i	0.00226028	+	0.685888i
$53$	−6.33884	−	10.9792i	−0.870707	−	1.50811i	−0.861267	−	0.508153i	$-0.830329\pi$
$53$	−6.33884	−	10.9792i	−0.870707	−	1.50811i	−0.00943963	−	0.999955i	$-0.503005\pi$
$54$	7.31070	+	0.744103i	0.994860	+	0.101260i
$55$			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	$-0.852955\pi$
$59$	−7.34922	+	4.24308i	−0.956787	+	0.552401i	−0.0616046	+	0.998101i	$0.519622\pi$
$60$	5.93219	+	1.78876i	0.765842	+	0.230928i
$61$	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
$63$	−7.40637	+	2.85408i	−0.933114	+	0.359580i
$64$	0.0790881	+	7.99961i	0.00988602	+	0.999951i
$65$	−3.83071	−	2.21166i	−0.475141	−	0.274323i
$66$	0.0803309	−	2.45477i	0.00988805	−	0.302162i
$67$	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	$0.105193\pi$
$71$			5.46843i			0.648984i	−0.945889	+	0.324492i	$0.894807\pi$
$72$	−8.03952	−	2.71406i	−0.947466	−	0.319856i
$73$	−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
$75$	2.27997	−	2.12844i	0.263268	−	0.245771i
$76$	6.45340	+	3.69757i	0.740255	+	0.424140i
$77$	1.12165	+	2.40409i	0.127824	+	0.273972i
$78$	5.14419	+	3.19878i	0.582465	+	0.362190i
$79$	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
$81$	5.52545	−	7.10419i	0.613938	−	0.789354i
$82$	−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	$0.899559\pi$
$84$	9.07072	−	1.31227i	0.989697	−	0.143180i
$85$		−	11.9110i		−	1.29193i
$86$	9.21165	+	9.18134i	0.993317	+	0.990049i
$87$	0.292288	+	1.26289i	0.0313365	+	0.135396i
$88$	−0.720472	+	2.74300i	−0.0768026	+	0.292405i
$89$	−7.39495	+	12.8084i	−0.783863	+	1.35769i	0.145812	+	0.989312i	$0.453420\pi$
$89$	−7.39495	+	12.8084i	−0.783863	+	1.35769i	−0.929676	+	0.368379i	$0.879913\pi$
$90$	5.71347	−	4.99420i	0.602253	−	0.526435i
$91$	−6.51821	−	0.568916i	−0.683294	−	0.0596386i
$92$	7.86731	−	13.7309i	0.820223	−	1.43154i
$93$	3.92043	+	4.19955i	0.406530	+	0.435473i
$94$	0.882685	+	3.27265i	0.0910420	+	0.337548i
$95$	−5.76045	+	3.32580i	−0.591010	+	0.341220i
$96$	8.35443	+	5.11893i	0.852670	+	0.522449i
$97$			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	0.288330	−	0.957531i	$-0.406900\pi$
$101$	12.6803	−	7.32100i	1.26174	−	0.728467i	0.973411	+	0.229064i	$0.0735667\pi$
$102$	−0.533507	+	16.3030i	−0.0528251	+	1.61424i
$103$	−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
$105$	−3.06476	+	7.60202i	−0.299090	+	0.741881i
$106$	17.3257	+	4.61181i	1.68282	+	0.447939i
$107$	−3.48110	+	6.02945i	−0.336531	+	0.582889i	−0.983778	−	0.179392i	$-0.942587\pi$
$107$	−3.48110	+	6.02945i	−0.336531	+	0.582889i	0.647247	+	0.762281i	$0.275920\pi$
$108$	−8.04397	+	6.57986i	−0.774031	+	0.633147i
$109$	−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	$-0.992047\pi$
$113$		−	0.531154i		−	0.0499667i	0.999688	−	0.0249834i	$-0.00795328\pi$
$114$	8.03354	−	4.29414i	0.752410	−	0.402183i
$115$	7.07629	+	12.2565i	0.659868	+	1.14292i
$116$	−0.00493255	−	1.49680i	−0.000457976	−	0.138974i
$117$	6.66464	−	3.25958i	0.616146	−	0.301348i
$118$	3.08704	−	11.5974i	0.284185	−	1.06763i
$119$	−7.44929	−	15.9665i	−0.682875	−	1.46364i
$120$	−7.71411	+	4.15614i	−0.704199	+	0.379402i
$121$	4.99730	−	8.65558i	0.454300	−	0.786871i
$122$	1.49109	+	5.52837i	0.134997	+	0.500515i
$123$	0.785174	+	3.39251i	0.0707967	+	0.305892i
$124$	−3.33584	−	5.73412i	−0.299567	−	0.514940i
$125$		−	12.1641i		−	1.08799i
$126$	4.53538	−	10.2679i	0.404043	−	0.914740i
$127$	−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
$129$	15.5186	−	3.59168i	1.36634	−	0.316230i
$130$	6.03969	−	1.62900i	0.529716	−	0.142873i
$131$	−13.3927	−	7.73228i	−1.17013	−	0.675573i	−0.216416	−	0.976301i	$-0.569437\pi$
$131$	−13.3927	−	7.73228i	−1.17013	−	0.675573i	−0.953710	+	0.300729i	$0.902770\pi$
$132$	2.37862	+	2.53119i	0.207032	+	0.220312i
$133$	−5.64179	+	8.06085i	−0.489205	+	0.698964i
$134$	−2.89768	+	10.8860i	−0.250322	+	0.940409i
$135$	−1.46894	−	9.17720i	−0.126427	−	0.789847i
$136$	4.78492	−	18.2173i	0.410304	−	1.56212i
$137$	9.71195	−	5.60719i	0.829748	−	0.479055i	−0.0240187	−	0.999712i	$-0.507646\pi$
$137$	9.71195	−	5.60719i	0.829748	−	0.479055i	0.853766	+	0.520657i	$0.174313\pi$
$138$	−9.13664	−	17.0929i	−0.777762	−	1.45505i
$139$	−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
$144$	10.7448	−	5.34316i	0.895399	−	0.445264i
$145$	1.15928	+	0.669310i	0.0962728	+	0.0555831i
$146$	2.38818	−	8.97191i	0.197647	−	0.742520i
$147$	0.646141	+	12.1071i	0.0532928	+	0.998579i
$148$	3.70182	−	6.46082i	0.304288	−	0.531076i
$149$	−0.462495	+	0.801066i	−0.0378891	+	0.0656258i	−0.884348	−	0.466828i	$-0.845397\pi$
$149$	−0.462495	+	0.801066i	−0.0378891	+	0.0656258i	0.846459	+	0.532454i	$0.178730\pi$
$150$	−0.144270	+	4.40865i	−0.0117796	+	0.359965i
$151$	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
$156$	−8.33975	+	1.95916i	−0.667714	+	0.156858i
$157$	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
$159$	16.0512	−	14.9844i	1.27294	−	1.18834i
$160$	9.75137	−	2.69917i	0.770914	−	0.213388i
$161$	17.1510	+	12.0040i	1.35169	+	0.946050i
$162$	1.59955	+	12.6270i	0.125672	+	0.992072i
$163$	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
$165$	−3.02635	+	0.700429i	−0.235601	+	0.0545283i
$166$	−5.66388	−	5.64524i	−0.439602	−	0.438156i
$167$	−7.93040			−0.613673			−0.306836	−	0.951762i	$-0.599270\pi$
$167$	−7.93040			−0.613673			−0.306836	+	0.951762i	$0.599270\pi$
$168$	−7.74133	+	10.3958i	−0.597257	+	0.802050i
$169$	−6.88419			−0.529553
$170$	11.9306	+	11.8913i	0.915034	+	0.912023i
$171$	0.766076	−	11.1301i	0.0585833	−	0.851141i
$172$	−18.3929	+	0.0606121i	−1.40245	+	0.00462163i
$173$	3.69882	+	2.13552i	0.281216	+	0.162360i	0.633974	−	0.773354i	$-0.281423\pi$
$173$	3.69882	+	2.13552i	0.281216	+	0.162360i	−0.352758	+	0.935715i	$0.614756\pi$
$174$	−1.55677	−	0.968038i	−0.118019	−	0.0733868i
$175$	−2.01443	−	4.31763i	−0.152276	−	0.326382i
$176$	−2.02823	−	3.46014i	−0.152884	−	0.260818i
$177$	−10.0302	−	10.7443i	−0.753915	−	0.807590i
$178$	−5.44676	−	20.1944i	−0.408252	−	1.51364i
$179$	3.77825	+	6.54412i	0.282399	+	0.489130i	0.971975	−	0.235083i	$-0.0755363\pi$
$179$	3.77825	+	6.54412i	0.282399	+	0.489130i	−0.689576	+	0.724214i	$0.742203\pi$
$180$	−0.701632	+	10.7088i	−0.0522965	+	0.798190i
$181$	−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
$186$	−8.12043	−	0.265736i	−0.595419	−	0.0194847i
$187$	3.33859	−	5.78261i	0.244142	−	0.422867i
$188$	−4.15927	−	2.38311i	−0.303346	−	0.173806i
$189$	−7.70864	−	11.3832i	−0.560721	−	0.828005i
$190$	2.41968	−	9.09025i	0.175542	−	0.659476i
$191$	10.4891	+	6.05587i	0.758963	+	0.438188i	0.828923	−	0.559362i	$-0.188954\pi$
$191$	10.4891	+	6.05587i	0.758963	+	0.438188i	−0.0699601	+	0.997550i	$0.522287\pi$
$192$	−13.4680	+	3.25769i	−0.971970	+	0.235104i
$193$	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	$-0.744620\pi$
$197$	−19.5111			−1.39011			−0.695054	+	0.718957i	$0.744620\pi$
$198$	4.17367	−	0.823153i	0.296610	−	0.0584990i
$199$	−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
$201$	9.41494	+	10.0852i	0.664079	+	0.711358i
$202$	−5.32638	+	20.0101i	−0.374763	+	1.40791i
$203$	1.97259	+	0.172170i	0.138449	+	0.0120839i
$204$	−15.7973	−	16.8105i	−1.10603	−	1.17697i
$205$	3.11418	+	1.79797i	0.217503	+	0.125576i
$206$	13.4655	−	3.63186i	0.938185	−	0.253043i
$207$	−23.6815	−	1.62998i	−1.64598	−	0.113291i
$208$	9.89185	−	0.0651960i	0.685876	−	0.00452053i
$209$	−3.72883			−0.257929
$210$	−4.55482	−	10.6593i	−0.314313	−	0.735561i
$211$			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
$213$	−9.22768	+	2.13569i	−0.632270	+	0.146335i
$214$	−2.56401	−	9.50634i	−0.175272	−	0.649840i
$215$	8.22459	−	14.2454i	0.560913	−	0.971529i
$216$	1.44002	−	14.6262i	0.0979807	−	0.995188i
$217$	7.95278	−	3.71044i	0.539870	−	0.251881i
$218$	0.992886	−	3.73007i	0.0672467	−	0.252633i
$219$	−7.75949	−	8.31193i	−0.524338	−	0.561668i
$220$	3.58688	−	0.0118202i	0.241828	−	0.000796920i
$221$	8.23422	+	14.2621i	0.553894	+	0.959372i
$222$	−4.29909	−	8.04279i	−0.288536	−	0.539797i
$223$			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	0.0269870	−	0.999636i	$-0.491409\pi$
$227$	13.6531	−	7.88264i	0.906190	−	0.523189i	0.879203	+	0.476446i	$0.158075\pi$
$228$	−3.71908	+	12.3338i	−0.246302	+	0.816828i
$229$	−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
$231$	−3.61871	+	2.83164i	−0.238094	+	0.186308i
$232$	1.50419	+	1.48939i	0.0987547	+	0.0977832i
$233$	−15.7079	−	9.06896i	−1.02906	−	0.594127i	−0.112344	−	0.993669i	$-0.535836\pi$
$233$	−15.7079	−	9.06896i	−1.02906	−	0.594127i	−0.916715	+	0.399542i	$0.869169\pi$
$234$	−3.38870	+	9.92982i	−0.221527	+	0.649132i
$235$	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	$-0.0559877\pi$
$240$	3.53841	−	11.8761i	0.228403	−	0.766599i
$241$	−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
$243$	14.1459	+	6.54936i	0.907459	+	0.420142i
$244$	−7.02610	−	4.02571i	−0.449800	−	0.257719i
$245$	9.59453	+	8.04403i	0.612972	+	0.513914i
$246$	−4.18197	−	2.60045i	−0.266633	−	0.165798i
$247$	4.59834	−	7.96457i	0.292586	−	0.506773i
$248$	9.07391	+	2.38334i	0.576194	+	0.151342i
$249$	−9.54177	+	2.20838i	−0.604685	+	0.139951i
$250$	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	$0.784435\pi$
$252$	5.75694	+	14.7938i	0.362653	+	0.931924i
$253$			7.93382i			0.498795i
$254$	4.51647	−	4.53138i	0.283389	−	0.284324i
$255$	20.0991	−	4.65181i	1.25865	−	0.291308i
$256$	15.9986	−	0.210899i	0.999913	−	0.0131812i
$257$	−4.36616	+	7.56240i	−0.272353	+	0.471730i	−0.969464	−	0.245234i	$-0.921135\pi$
$257$	−4.36616	+	7.56240i	−0.272353	+	0.471730i	0.697111	+	0.716964i	$0.254469\pi$
$258$	−11.8954	+	19.1299i	−0.740576	+	1.19098i
$259$	8.07012	+	5.64828i	0.501453	+	0.350967i
$260$	−4.39805	+	7.67595i	−0.272755	+	0.476042i
$261$	−2.01690	+	0.986439i	−0.124843	+	0.0610590i
$262$	21.1156	−	5.69522i	1.30453	−	0.351852i
$263$	−17.1429	+	9.89747i	−1.05708	+	0.610304i	−0.924623	−	0.380885i	$-0.875619\pi$
$263$	−17.1429	+	9.89747i	−1.05708	+	0.610304i	−0.132455	+	0.991189i	$0.542286\pi$
$264$	−4.91005	−	0.144482i	−0.302193	−	0.00889226i
$265$		−	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	$-0.675694\pi$
$269$	−0.805574	+	0.465098i	−0.0491167	+	0.0283575i	0.475241	+	0.879856i	$0.342361\pi$
$270$	10.6588	+	7.69070i	0.648675	+	0.468041i
$271$	−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
$273$	−1.58566	−	11.2213i	−0.0959685	−	0.679144i
$274$	−4.07950	+	15.3259i	−0.246452	+	0.925870i
$275$	0.902819	−	1.56373i	0.0544420	−	0.0942964i
$276$	26.2427	+	7.91308i	1.57962	+	0.476311i
$277$	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	$-0.780546\pi$
$281$		−	21.3260i		−	1.27220i	0.771605	−	0.636102i	$-0.219454\pi$
$282$	−5.17768	+	2.76761i	−0.308327	+	0.164809i
$283$	−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
$285$	−7.86184	−	8.42156i	−0.465695	−	0.498850i
$286$	3.38879	+	0.902042i	0.200383	+	0.0533389i
$287$	5.29898	+	0.462500i	0.312789	+	0.0273005i
$288$	−5.37511	+	16.0968i	−0.316732	+	0.948515i
$289$	−13.6728	+	23.6820i	−0.804284	+	1.39306i
$290$	−1.82778	+	0.492981i	−0.107331	+	0.0289488i
$291$	−2.96276	+	0.685712i	−0.173680	+	0.0401972i
$292$	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	$-0.125049\pi$
$294$	−12.7721	−	11.4400i	−0.744886	−	0.667192i
$295$	−15.1786			−0.883733
$296$	2.77574	+	10.1581i	0.161337	+	0.590427i
$297$	1.85918	−	4.86714i	0.107880	−	0.282420i
$298$	−0.340652	−	1.26300i	−0.0197334	−	0.0731637i
$299$	−16.9462	−	9.78389i	−0.980023	−	0.565817i
$300$	−4.27188	−	4.54589i	−0.246637	−	0.262457i
$301$	2.11565	−	24.2395i	0.121944	−	1.39714i
$302$	−26.1496	−	6.96060i	−1.50474	−	0.400537i
$303$	17.3061	+	18.5382i	0.994208	+	1.06499i
$304$	7.35256	−	12.9311i	0.421698	−	0.741649i
$305$	6.27166	−	3.62094i	0.359114	−	0.207335i
$306$	−27.7189	+	5.46686i	−1.58458	+	0.312520i
$307$	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	$0.0236939\pi$
$311$	9.92896	+	17.1975i	0.563020	+	0.975179i	−0.434211	+	0.900811i	$0.642973\pi$
$312$	6.36361	−	10.3094i	0.360269	−	0.583655i
$313$	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
$315$	−14.0249	−	2.20267i	−0.790215	−	0.124106i
$316$	−8.81510	−	5.05074i	−0.495888	−	0.284126i
$317$	−5.35288	+	9.27147i	−0.300648	+	0.520737i	−0.976283	−	0.216499i	$-0.930536\pi$
$317$	−5.35288	+	9.27147i	−0.300648	+	0.520737i	0.675635	+	0.737236i	$0.263870\pi$
$318$	−1.01567	+	31.0372i	−0.0569562	+	1.74048i
$319$	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
$324$	−14.2447	−	11.0040i	−0.791373	−	0.611334i
$325$	2.22669	+	3.85674i	0.123514	+	0.213933i
$326$	−14.5239	+	3.91733i	−0.804406	+	0.216961i
$327$	−3.22601	−	3.45569i	−0.178399	−	0.191100i
$328$	4.04071	+	4.00095i	0.223111	+	0.220916i
$329$	3.63618	−	5.19528i	0.200469	−	0.286425i
$330$	2.31978	−	3.73061i	0.127700	−	0.205363i
$331$	−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
$333$	−11.1429	−	0.766958i	−0.610628	−	0.0420290i
$334$	7.91732	−	7.94346i	0.433217	−	0.434647i
$335$	14.2476			0.778428
$336$	−2.68430	−	18.1327i	−0.146441	−	0.989219i
$337$	−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
$339$	0.896293	−	0.207441i	0.0486799	−	0.0112667i
$340$	−23.8218	+	0.0785025i	−1.29192	+	0.00425740i
$341$	2.88028	+	1.66293i	0.155976	+	0.0900527i
$342$	10.3836	+	11.8791i	0.561482	+	0.642348i
$343$	17.8922	+	4.78234i	0.966086	+	0.258222i
$344$	18.3019	−	18.4837i	0.986771	−	0.996575i
$345$	−17.9185	+	16.7276i	−0.964702	+	0.900585i
$346$	−5.83175	+	1.57292i	−0.313517	+	0.0845606i
$347$	−9.94032	−	17.2171i	−0.533624	−	0.924265i	−0.999229	−	0.0392715i	$-0.987496\pi$
$347$	−9.94032	−	17.2171i	−0.533624	−	0.924265i	0.465604	−	0.884993i	$-0.345837\pi$
$348$	2.52384	−	0.592895i	0.135292	−	0.0317825i
$349$	−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	$-0.315748\pi$
$353$	−8.48135	−	14.6901i	−0.451417	−	0.781877i	−0.998474	+	0.0552182i	$0.982415\pi$
$354$	20.7756	+	0.679869i	1.10421	+	0.0361346i
$355$	−4.89051	+	8.47062i	−0.259561	+	0.449574i
$356$	25.6655	+	14.7054i	1.36027	+	0.779385i
$357$	24.0332	−	18.8059i	1.27197	−	0.995316i
$358$	−10.3269	−	2.74886i	−0.545794	−	0.145282i
$359$	18.2162	+	10.5171i	0.961413	+	0.555072i	0.896608	−	0.442826i	$-0.146024\pi$
$359$	18.2162	+	10.5171i	0.961413	+	0.555072i	0.0648056	+	0.997898i	$0.479357\pi$
$360$	−10.0260	−	11.3940i	−0.528417	−	0.600515i
$361$	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
$366$	−8.74647	+	4.67522i	−0.457185	+	0.244378i
$367$	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
$369$	−5.41802	+	2.64988i	−0.282051	+	0.137947i
$370$	−9.10071	−	2.42246i	−0.473124	−	0.125938i
$371$	−14.1817	−	30.3964i	−0.736278	−	1.57810i
$372$	8.37321	−	7.86850i	0.434131	−	0.407963i
$373$	−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
$375$	20.5263	−	4.75068i	1.05997	−	0.245324i
$376$	6.53944	−	1.78693i	0.337246	−	0.0921539i
$377$	−1.85081			−0.0953217
$378$	19.0979	+	3.64308i	0.982288	+	0.187380i
$379$		−	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
$381$	−1.76681	−	7.63389i	−0.0905167	−	0.391096i
$382$	−16.5376	+	4.46046i	−0.846139	+	0.228217i
$383$	−4.81069	+	8.33236i	−0.245815	+	0.425763i	−0.962360	−	0.271777i	$-0.912389\pi$
$383$	−4.81069	+	8.33236i	−0.245815	+	0.425763i	0.716546	+	0.697540i	$0.245722\pi$
$384$	10.1828	−	16.7425i	0.519636	−	0.854388i
$385$	−0.412582	+	4.72705i	−0.0210271	+	0.240913i
$386$	−1.61928	−	0.431026i	−0.0824192	−	0.0219387i
$387$	12.1215	+	24.7841i	0.616172	+	1.25984i
$388$	3.51152	−	0.0115719i	0.178270	−	0.000587473i
$389$	14.0629	+	24.3576i	0.713017	+	1.23498i	0.963719	+	0.266917i	$0.0860050\pi$
$389$	14.0629	+	24.3576i	0.713017	+	1.23498i	−0.250703	+	0.968064i	$0.580662\pi$
$390$	5.10764	+	9.55545i	0.258636	+	0.483859i
$391$		−	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
$396$	−3.34228	+	5.00233i	−0.167956	+	0.251377i
$397$	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
$399$	−15.8056	−	6.37206i	−0.791271	−	0.319002i
$400$	3.64261	+	6.21424i	0.182131	+	0.310712i
$401$	−5.22718	−	3.01791i	−0.261033	−	0.150707i	0.363773	−	0.931488i	$-0.381488\pi$
$401$	−5.22718	−	3.01791i	−0.261033	−	0.150707i	−0.624806	+	0.780780i	$0.714822\pi$
$402$	−19.5013	−	0.638166i	−0.972634	−	0.0318288i
$403$	−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
$408$	32.6094	+	0.959559i	1.61441	+	0.0475052i
$409$	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
$411$	13.2548	+	14.1985i	0.653812	+	0.700360i
$412$	−9.80544	+	17.1135i	−0.483080	+	0.843123i
$413$	−20.3467	+	9.49292i	−1.00120	+	0.467116i
$414$	25.2751	−	22.0932i	1.24220	−	1.08582i
$415$	−5.05698	+	8.75894i	−0.248237	+	0.429959i
$416$	−9.81023	+	9.97322i	−0.480986	+	0.488978i
$417$	−7.02301	−	30.3444i	−0.343918	−	1.48597i
$418$	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	$-0.0195955\pi$
$420$	15.2242	+	6.07939i	0.742863	+	0.296644i
$421$			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
$423$	−0.493742	+	7.17345i	−0.0240066	+	0.348785i
$424$	9.10938	−	34.6815i	0.442391	−	1.68428i
$425$	−5.99595	+	10.3853i	−0.290846	+	0.503761i
$426$	7.07326	−	11.3750i	0.342701	−	0.551123i
$427$	6.14247	−	8.77620i	0.297255	−	0.424710i
$428$	12.0818	+	6.92243i	0.583995	+	0.334608i
$429$	3.13951	−	2.93085i	0.151577	−	0.141503i
$430$	6.05783	+	22.4601i	0.292135	+	1.08312i
$431$	−12.0003	+	6.92836i	−0.578033	+	0.333727i	−0.760351	−	0.649512i	$-0.774973\pi$
$431$	−12.0003	+	6.92836i	−0.578033	+	0.333727i	0.182319	+	0.983240i	$0.441640\pi$
$432$	13.2127	+	16.0445i	0.635694	+	0.771941i
$433$			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
$438$	16.0723	+	0.525956i	0.767964	+	0.0251312i
$439$	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
$441$	−20.1778	+	5.81875i	−0.960846	+	0.277083i
$442$	−22.5062	−	5.99079i	−1.07051	−	0.284953i
$443$	8.84884	−	15.3266i	0.420421	−	0.728191i	−0.575559	−	0.817760i	$-0.695216\pi$
$443$	8.84884	−	15.3266i	0.420421	−	0.728191i	0.995981	+	0.0895692i	$0.0285490\pi$
$444$	12.3480	+	3.72336i	0.586011	+	0.176703i
$445$	−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	$0.848099\pi$
$450$	−7.49570	+	1.47834i	−0.353351	+	0.0696898i
$451$	1.00793	+	1.74578i	0.0474614	+	0.0822056i
$452$	−1.06230	+	0.00350071i	−0.0499665	+	0.000164660i
$453$	−24.2260	+	22.6159i	−1.13824	+	1.06259i
$454$	−5.73500	+	21.5453i	−0.269157	+	1.01117i
$455$	−9.58793	−	6.71059i	−0.449489	−	0.314597i
$456$	−8.64119	−	16.0387i	−0.404661	−	0.751081i
$457$	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
$459$	−12.3475	+	32.3245i	−0.576331	+	1.50878i
$460$	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	$0.993645\pi$
$462$	0.776449	−	6.45164i	0.0361237	−	0.300157i
$463$	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
$465$	2.31703	+	10.0112i	0.107450	+	0.464259i
$466$	24.7659	−	6.67975i	1.14726	−	0.309434i
$467$	8.69155	+	5.01807i	0.402197	+	0.232208i	0.687431	−	0.726249i	$-0.258738\pi$
$467$	8.69155	+	5.01807i	0.402197	+	0.232208i	−0.285235	+	0.958458i	$0.592072\pi$
$468$	−6.56305	−	13.3077i	−0.303377	−	0.615150i
$469$	19.0986	−	8.91063i	0.881893	−	0.411455i
$470$	−1.55950	+	5.85874i	−0.0719345	+	0.270244i
$471$	−13.8479	+	12.9275i	−0.638076	+	0.595668i
$472$	−23.2150	−	6.09762i	−1.06856	−	0.280666i
$473$	7.98586	−	4.61064i	0.367190	−	0.211997i
$474$	−10.9735	+	5.86564i	−0.504031	+	0.269418i
$475$	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	$-0.998042\pi$
$479$	−11.0594	−	19.1555i	−0.505318	−	0.875237i	0.494663	−	0.869085i	$-0.335292\pi$
$480$	8.36308	+	15.4008i	0.381721	+	0.702945i
$481$	−7.97373	−	4.60364i	−0.363571	−	0.209908i
$482$	7.81397	−	29.3555i	0.355917	−	1.33711i
$483$	−13.5578	+	33.6296i	−0.616902	+	1.53020i
$484$	−17.3440	−	9.93751i	−0.788364	−	0.451705i
$485$	−1.57021	+	2.71969i	−0.0712997	+	0.123495i
$486$	−20.6827	+	7.63061i	−0.938186	+	0.346131i
$487$	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	$-0.308272\pi$
$491$	25.1085			1.13313			0.566565	+	0.824017i	$0.308272\pi$
$492$	6.77980	−	1.59270i	0.305657	−	0.0718044i
$493$	−2.49190	−	4.31610i	−0.112230	−	0.194387i
$494$	3.38692	+	12.5573i	0.152385	+	0.564982i
$495$	−2.36387	−	4.83325i	−0.106248	−	0.217238i
$496$	−11.4462	+	6.70944i	−0.513950	+	0.301263i
$497$	−1.25801	+	14.4133i	−0.0564295	+	0.646526i
$498$	7.31402	−	11.7622i	0.327749	−	0.527078i
$499$	−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
$501$	−3.09721	−	13.3821i	−0.138373	−	0.597869i
$502$	−19.8880	−	19.8225i	−0.887643	−	0.884723i
$503$	−13.3046			−0.593223			−0.296612	−	0.954998i	$-0.595857\pi$
$503$	−13.3046			−0.593223			−0.296612	+	0.954998i	$0.595857\pi$
$504$	−20.5656	−	9.00303i	−0.916066	−	0.401027i
$505$	26.1892			1.16540
$506$	−7.94688	−	7.92074i	−0.353282	−	0.352120i
$507$	−2.68861	−	11.6167i	−0.119405	−	0.515916i
$508$	0.0298162	+	9.04782i	0.00132288	+	0.401432i
$509$	20.2595	+	11.6968i	0.897985	+	0.518452i	0.876546	−	0.481318i	$-0.159842\pi$
$509$	20.2595	+	11.6968i	0.897985	+	0.518452i	0.0214392	+	0.999770i	$0.493175\pi$
$510$	−15.4065	+	24.7763i	−0.682211	+	1.09711i
$511$	−15.7405	+	7.34385i	−0.696318	+	0.324873i
$512$	−15.7610	+	16.2355i	−0.696544	+	0.717515i
$513$	19.0806	−	3.05413i	0.842431	−	0.134843i
$514$	−3.21590	−	11.9233i	−0.141847	−	0.525913i
$515$	−8.81956	−	15.2759i	−0.388636	−	0.673138i
$516$	−7.28560	−	31.0134i	−0.320731	−	1.36529i
$517$	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	$-0.156405\pi$
$521$	0.735700	+	1.27427i	0.0322316	+	0.0558267i	−0.849460	+	0.527654i	$0.823072\pi$
$522$	1.02552	−	3.00504i	0.0448856	−	0.131527i
$523$	−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
$525$	6.49904	−	5.08548i	0.283641	−	0.221949i
$526$	7.20089	−	27.0523i	0.313974	−	1.17954i
$527$	−19.1290	−	11.0441i	−0.833272	−	0.481090i
$528$	5.04667	−	4.77389i	0.219628	−	0.207757i
$529$	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
$534$	31.9498	−	17.0780i	1.38260	−	0.739038i
$535$	−10.7845	+	6.22642i	−0.466254	+	0.269192i
$536$	21.7910	+	5.72359i	0.941229	+	0.247221i
$537$	−9.56725	+	8.93138i	−0.412857	+	0.385417i
$538$	0.338381	−	1.27123i	0.0145887	−	0.0548067i
$539$	2.40331	+	6.59457i	0.103518	+	0.284048i
$540$	−18.3446	+	2.99836i	−0.789426	+	0.129029i
$541$	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
$543$	−1.95367	−	8.44125i	−0.0838402	−	0.362249i
$544$	−36.4659	−	9.44972i	−1.56346	−	0.405154i
$545$	−4.88190			−0.209118
$546$	12.8228	+	9.61453i	0.548766	+	0.411464i
$547$			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
$549$	−0.834061	+	12.1178i	−0.0355969	+	0.517177i
$550$	0.664972	+	2.46545i	0.0283545	+	0.105127i
$551$	−1.39159	+	2.41030i	−0.0592836	+	0.102682i
$552$	−34.1255	+	18.3858i	−1.45248	+	0.782553i
$553$	7.70648	−	11.0108i	0.327713	−	0.468228i
$554$	−10.7358	+	40.3321i	−0.456119	+	1.71355i
$555$	−8.43126	+	7.87089i	−0.357887	+	0.334101i
$556$	0.118518	+	35.9647i	0.00502629	+	1.52524i
$557$	−10.7167	−	18.5619i	−0.454081	−	0.786492i	0.544554	−	0.838726i	$-0.316699\pi$
$557$	−10.7167	−	18.5619i	−0.454081	−	0.786492i	−0.998635	+	0.0522341i	$0.983366\pi$
$558$	−2.72301	−	13.8066i	−0.115274	−	0.584479i
$559$			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	$-0.810483\pi$
$563$	−17.9430	+	10.3594i	−0.756205	+	0.436595i	0.0717262	+	0.997424i	$0.477149\pi$
$564$	2.39698	−	7.94925i	0.100931	−	0.334724i
$565$	0.475020	−	0.822758i	0.0199842	−	0.0346137i
$566$	28.4933	+	7.58447i	1.19766	+	0.318799i
$567$	16.1979	−	17.4536i	0.680248	−	0.732982i
$568$	−10.8827	+	10.9908i	−0.456627	+	0.461164i
$569$	23.8691	+	13.7808i	1.00064	+	0.577722i	0.908439	−	0.418018i	$-0.137275\pi$
$569$	23.8691	+	13.7808i	1.00064	+	0.577722i	0.0922056	+	0.995740i	$0.470608\pi$
$570$	16.2843	+	0.532894i	0.682074	+	0.0223205i
$571$	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
$576$	−10.7571	−	21.4543i	−0.448212	−	0.893927i
$577$	−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
$579$	−1.50016	+	1.40046i	−0.0623447	+	0.0582011i
$580$	1.33097	−	2.32296i	0.0552656	−	0.0964555i
$581$	−1.30083	+	14.9039i	−0.0539675	+	0.618319i
$582$	2.27104	−	3.65222i	0.0941375	−	0.151389i
$583$	6.35591	−	11.0088i	0.263235	−	0.455936i
$584$	−17.9595	−	4.71720i	−0.743168	−	0.195199i
$585$	13.2386	+	0.911205i	0.547350	+	0.0376737i
$586$	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	$-0.0231052\pi$
$588$	24.2099	−	1.37207i	0.998398	−	0.0565833i
$589$			12.3350i			0.508256i
$590$	15.1536	−	15.2036i	0.623863	−	0.625923i
$591$	−7.62003	−	32.9239i	−0.313446	−	1.35431i
$592$	−12.9460	−	7.36103i	−0.532076	−	0.302536i
$593$	17.8824	−	30.9732i	0.734342	−	1.27192i	−0.220670	−	0.975349i	$-0.570824\pi$
$593$	17.8824	−	30.9732i	0.734342	−	1.27192i	0.955012	−	0.296568i	$-0.0958423\pi$
$594$	3.01905	+	6.72135i	0.123873	+	0.275781i
$595$	2.74011	−	31.3941i	0.112334	−	1.28703i
$596$	1.60517	+	0.919706i	0.0657504	+	0.0376726i
$597$	−17.4192	−	18.6593i	−0.712919	−	0.763676i
$598$	26.7182	−	7.20633i	1.09259	−	0.294689i
$599$	35.4819	−	20.4855i	1.44975	−	0.837014i	0.451284	−	0.892380i	$-0.350966\pi$
$599$	35.4819	−	20.4855i	1.44975	−	0.837014i	0.998466	+	0.0553669i	$0.0176328\pi$
$600$	8.81821	+	0.259483i	0.360002	+	0.0105933i
$601$		−	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
$606$	−35.8462	−	1.17305i	−1.45615	−	0.0476517i
$607$	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
$609$	0.479865	+	3.39588i	0.0194451	+	0.137608i
$610$	−2.63441	+	9.89696i	−0.106664	+	0.400716i
$611$	−2.96367	+	5.13323i	−0.119897	+	0.207668i
$612$	22.1973	−	33.2223i	0.897272	−	1.34293i
$613$	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	$0.149587\pi$
$617$			22.4963i			0.905669i	−0.891595	+	0.452834i	$0.850413\pi$
$618$	11.3875	+	21.3039i	0.458072	+	0.856967i
$619$	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
$621$	−6.49827	−	40.5978i	−0.260767	−	1.62914i
$622$	−27.1384	−	7.22380i	−1.08815	−	0.289648i
$623$	−22.4377	+	32.0584i	−0.898947	+	1.28439i
$624$	3.97326	+	16.6665i	0.159058	+	0.667194i
$625$	6.37661	−	11.0446i	0.255064	−	0.441785i
$626$	−3.67529	+	0.991285i	−0.146894	+	0.0396197i
$627$	−1.45629	−	6.29220i	−0.0581585	−	0.251286i
$628$	18.9081	−	10.9998i	0.754515	−	0.438941i
$629$		−	24.7930i		−	0.988563i
$630$	16.2081	−	11.8490i	0.645746	−	0.472075i
$631$	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
$633$	−25.1834	+	5.82853i	−1.00095	+	0.231663i
$634$	−3.94267	−	14.6179i	−0.156584	−	0.580550i
$635$	−7.00758	−	4.04583i	−0.278087	−	0.160554i
$636$	−30.0743	−	32.0034i	−1.19252	−	1.26902i
$637$	−17.0494	−	2.99902i	−0.675520	−	0.118825i
$638$	−1.02554	−	0.272983i	−0.0406016	−	0.0108075i
$639$	−7.20771	−	14.7371i	−0.285133	−	0.582992i
$640$	−5.46258	−	19.4848i	−0.215927	−	0.770206i
$641$	0.0793494	−	0.0458124i	0.00313411	−	0.00180948i	−0.498432	−	0.866929i	$-0.666091\pi$
$641$	0.0793494	−	0.0458124i	0.00313411	−	0.00180948i	0.501566	+	0.865119i	$0.332757\pi$
$642$	15.0401	−	8.03932i	0.593584	−	0.317287i
$643$	−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	$-0.217680\pi$
$647$	−4.05903	−	7.03045i	−0.159577	−	0.276396i	−0.934716	+	0.355395i	$0.884346\pi$
$648$	25.2433	−	3.28230i	0.991652	−	0.128941i
$649$	−7.36901	−	4.25450i	−0.289259	−	0.167004i
$650$	−6.08611	−	1.62002i	−0.238717	−	0.0635426i
$651$	9.36710	+	11.9708i	0.367126	+	0.469172i
$652$	10.5762	−	18.4587i	0.414196	−	0.722899i
$653$	16.7312	−	28.9792i	0.654741	−	1.13404i	−0.327218	−	0.944949i	$-0.606111\pi$
$653$	16.7312	−	28.9792i	0.654741	−	1.13404i	0.981959	−	0.189095i	$-0.0605555\pi$
$654$	6.68207	+	0.218666i	0.261290	+	0.00855054i
$655$	−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	$-0.597911\pi$
$659$	−15.5448			−0.605540			−0.302770	+	0.953064i	$0.597911\pi$
$660$	1.42080	+	6.04805i	0.0553044	+	0.235420i
$661$	−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
$663$	−20.8506	+	19.4648i	−0.809772	+	0.755952i
$664$	−11.2531	+	11.3649i	−0.436705	+	0.441044i
$665$	−15.9481	+	7.44072i	−0.618441	+	0.288539i
$666$	11.8928	−	10.3956i	0.460835	−	0.402820i
$667$	5.12838	+	2.96087i	0.198572	+	0.114646i
$668$	0.0522675	+	15.8607i	0.00202229	+	0.613670i
$669$	−12.8615	+	2.97671i	−0.497254	+	0.115086i
$670$	−14.2241	+	14.2710i	−0.549524	+	0.551338i
$671$	4.05974			0.156725
$672$	20.8424	+	15.4141i	0.804014	+	0.594611i
$673$	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
$675$	−3.33899	+	8.74115i	−0.128518	+	0.336447i
$676$	0.0453721	+	13.7683i	0.00174508	+	0.529550i
$677$	32.5497	+	18.7926i	1.25099	+	0.722257i	0.971305	−	0.237836i	$-0.0764382\pi$
$677$	32.5497	+	18.7926i	1.25099	+	0.722257i	0.279680	+	0.960093i	$0.409772\pi$
$678$	−0.687032	+	1.10487i	−0.0263853	+	0.0424322i
$679$	−0.403913	+	4.62773i	−0.0155008	+	0.177596i
$680$	23.7039	−	23.9394i	0.909003	−	0.918034i
$681$	18.6337	+	19.9604i	0.714046	+	0.764883i
$682$	−4.54120	+	1.22483i	−0.173891	+	0.0469013i
$683$	1.02051	+	1.76757i	0.0390487	+	0.0676343i	0.884889	−	0.465802i	$-0.154234\pi$
$683$	1.02051	+	1.76757i	0.0390487	+	0.0676343i	−0.845841	+	0.533436i	$0.820901\pi$
$684$	−22.2651	−	1.45879i	−0.851329	−	0.0557782i
$685$	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
$690$	1.13384	−	34.6481i	0.0431644	−	1.31903i
$691$	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
$693$	−6.19151	−	5.00049i	−0.235196	−	0.189953i
$694$	27.1694	+	7.23206i	1.03134	+	0.274525i
$695$	−27.8548	−	16.0820i	−1.05659	−	0.610025i
$696$	−1.92580	+	3.11991i	−0.0729974	+	0.118260i
$697$	−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	$-0.594308\pi$
$701$	−15.4603			−0.583926			−0.291963	+	0.956430i	$0.594308\pi$
$702$	−18.0795	−	1.84018i	−0.682366	−	0.0694531i
$703$	−11.9906	+	6.92275i	−0.452232	+	0.261096i
$704$	−6.90687	+	4.07925i	−0.260312	+	0.153743i
$705$	5.06702	+	5.42777i	0.190835	+	0.204421i
$706$	23.1817	+	6.17059i	0.872454	+	0.232233i
$707$	35.1062	−	16.3791i	1.32030	−	0.615999i
$708$	−21.4223	+	20.1311i	−0.805101	+	0.756572i
$709$	−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
$711$	−1.04643	+	15.2033i	−0.0392443	+	0.570169i
$712$	−40.3528	+	11.0266i	−1.51228	+	0.413238i
$713$	26.2452			0.982891
$714$	−5.15669	+	42.8477i	−0.192984	+	1.60354i
$715$		−	4.43523i		−	0.165868i
$716$	13.0633	−	7.59958i	0.488197	−	0.284010i
$717$	9.12976	−	2.11302i	0.340957	−	0.0789123i
$718$	−28.7206	+	7.74640i	−1.07184	+	0.289093i
$719$	6.49021	−	11.2414i	0.242044	−	0.419232i	−0.719252	−	0.694749i	$-0.755516\pi$
$719$	6.49021	−	11.2414i	0.242044	−	0.419232i	0.961296	+	0.275517i	$0.0888489\pi$
$720$	21.4222	+	1.33268i	0.798358	+	0.0496659i
$721$	−21.3763	−	14.9613i	−0.796094	−	0.557186i
$722$	−7.06603	−	1.88086i	−0.262970	−	0.0699985i
$723$	−25.3886	−	27.1961i	−0.944211	−	1.01143i
$724$	0.0329696	+	10.0047i	0.00122531	+	0.371822i
$725$	−0.673858	−	1.16716i	−0.0250264	−	0.0433471i
$726$	−21.5908	+	11.5409i	−0.801309	+	0.428321i
$727$		−	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
$732$	4.04913	−	13.4284i	0.149660	−	0.496328i
$733$	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
$735$	−9.82673	+	19.3318i	−0.362465	+	0.713065i
$736$	43.1379	−	11.9405i	1.59008	−	0.440133i
$737$	6.91700	+	3.99353i	0.254791	+	0.147104i
$738$	2.75485	−	8.07245i	0.101407	−	0.297151i
$739$	−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	$-0.920913\pi$
$743$		−	13.4061i		−	0.491823i	0.969292	−	0.245911i	$-0.0790872\pi$
$744$	−0.477949	+	16.2425i	−0.0175225	+	0.595480i
$745$	−1.43281	+	0.827235i	−0.0524942	+	0.0303075i
$746$	29.6981	−	8.01006i	1.08733	−	0.293269i
$747$	−7.45305	−	15.2387i	−0.272693	−	0.557556i
$748$	−11.5872	−	6.63904i	−0.423669	−	0.242747i
$749$	−10.5623	+	15.0912i	−0.385939	+	0.551420i
$750$	−15.7339	+	25.3029i	−0.574522	+	0.923932i
$751$	−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
$753$	−33.5047	+	7.75445i	−1.22098	+	0.282588i
$754$	1.84776	−	1.85386i	0.0672915	−	0.0675136i
$755$			34.2244i			1.24555i
$756$	−22.7154	+	15.4922i	−0.826152	+	0.563447i
$757$		−	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
$759$	−13.3879	+	3.09854i	−0.485950	+	0.112470i
$760$	−18.1964	−	4.77942i	−0.660051	−	0.173368i
$761$	21.7170	−	37.6149i	0.787240	−	1.36354i	−0.140411	−	0.990093i	$-0.544842\pi$
$761$	21.7170	−	37.6149i	0.787240	−	1.36354i	0.927652	−	0.373447i	$-0.121824\pi$
$762$	9.41036	+	5.85158i	0.340901	+	0.211980i
$763$	−6.54411	+	3.05321i	−0.236913	+	0.110534i
$764$	12.0426	−	21.0180i	0.435684	−	0.760403i
$765$	15.6993	+	32.0994i	0.567611	+	1.16056i
$766$	−3.54332	−	13.1372i	−0.128025	−	0.474667i
$767$	18.1747	−	10.4932i	0.656252	−	0.378887i
$768$	6.60411	+	26.9144i	0.238305	+	0.971190i
$769$			23.9226i			0.862670i	0.902192	+	0.431335i	$0.141957\pi$
$769$			23.9226i			0.862670i	−0.902192	+	0.431335i	$0.858043\pi$

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)

\(f(q)\)	\(=\)	\(q+(-0.998351 + 1.00165i) q^{2} +(0.390548 + 1.68745i) q^{3} +(-0.00659077 - 1.99999i) q^{4} +(1.54900 + 0.894317i) q^{5} +(-2.08013 - 1.29347i) q^{6} +(2.63573 + 0.230049i) q^{7} +(2.00986 + 1.99009i) q^{8} +(-2.69494 + 1.31806i) q^{9} +O(q^{10})\)	\(q+(-0.998351 + 1.00165i) q^{2} +(0.390548 + 1.68745i) q^{3} +(-0.00659077 - 1.99999i) q^{4} +(1.54900 + 0.894317i) q^{5} +(-2.08013 - 1.29347i) q^{6} +(2.63573 + 0.230049i) q^{7} +(2.00986 + 1.99009i) q^{8} +(-2.69494 + 1.31806i) q^{9} +(-2.44224 + 0.658710i) q^{10} +(0.501346 + 0.868358i) q^{11} +(3.37230 - 0.792214i) 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} +(1.37027 - 4.01527i) q^{18} +(-1.85941 + 3.22059i) q^{19} +(1.77842 - 3.10388i) q^{20} +(0.641185 + 4.53750i) q^{21} +(-1.37031 - 0.364754i) q^{22} +(6.85244 + 3.95626i) q^{23} +(-2.57322 + 4.16876i) 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} +(-2.06535 - 3.86388i) q^{30} +(2.87254 - 1.65846i) q^{31} +(3.96691 - 4.03282i) q^{32} +(-1.26951 + 1.18513i) q^{33} +(9.10071 + 2.42246i) q^{34} +(3.87702 + 2.71353i) q^{35} +(2.65386 + 5.38117i) q^{36} +(3.22429 + 1.86155i) q^{37} +(-1.36955 - 5.07775i) q^{38} +(-0.965832 - 4.17308i) q^{39} +(1.33351 + 4.88011i) q^{40} +2.01044 q^{41} +(-5.18509 - 3.88777i) q^{42} -9.19651i q^{43} +(1.73340 - 1.00841i) q^{44} +(-5.35324 - 0.368459i) q^{45} +(-10.8039 + 2.91399i) q^{46} +(1.19840 - 2.07569i) q^{47} +(-1.60665 - 6.73934i) q^{48} +(6.89415 + 1.21270i) q^{49} +(2.46101 + 0.655080i) q^{50} +(8.43126 - 7.87089i) q^{51} +(0.0162991 + 4.94601i) q^{52} +(-6.33884 - 10.9792i) q^{53} +(7.31070 + 0.744103i) 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} +(5.93219 + 1.78876i) q^{60} +(2.02442 - 3.50640i) q^{61} +(-1.20661 + 4.53300i) q^{62} +(-7.40637 + 2.85408i) q^{63} +(0.0790881 + 7.99961i) q^{64} +(-3.83071 - 2.21166i) q^{65} +(0.0803309 - 2.45477i) 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} +(-8.03952 - 2.71406i) q^{72} +(-5.68546 + 3.28250i) q^{73} +(-5.08359 + 1.37113i) q^{74} +(2.27997 - 2.12844i) q^{75} +(6.45340 + 3.69757i) q^{76} +(1.12165 + 2.40409i) q^{77} +(5.14419 + 3.19878i) q^{78} +(2.53988 - 4.39920i) q^{79} +(-6.21945 - 3.53635i) q^{80} +(5.52545 - 7.10419i) q^{81} +(-2.00712 + 2.01375i) q^{82} +5.65457i q^{83} +(9.07072 - 1.31227i) q^{84} -11.9110i q^{85} +(9.21165 + 9.18134i) q^{86} +(0.292288 + 1.26289i) q^{87} +(-0.720472 + 2.74300i) q^{88} +(-7.39495 + 12.8084i) q^{89} +(5.71347 - 4.99420i) q^{90} +(-6.51821 - 0.568916i) q^{91} +(7.86731 - 13.7309i) q^{92} +(3.92043 + 4.19955i) q^{93} +(0.882685 + 3.27265i) q^{94} +(-5.76045 + 3.32580i) q^{95} +(8.35443 + 5.11893i) 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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