LMFDB - Embedded newform 168.2.ba.c.101.7

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			101.7
Character	$\chi$	$=$	168.101
Dual form			168.2.ba.c.5.7

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

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

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
$3$	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	−0.111901	−	0.993719i	$-0.535694\pi$
$5$	1.54900	−	0.894317i	0.692735	−	0.399951i	0.804636	+	0.593769i	$0.202361\pi$
$6$	−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	−0.780493	−	0.625164i	$-0.785032\pi$
$11$	0.501346	−	0.868358i	0.151162	−	0.261820i	0.931655	+	0.363345i	$0.118365\pi$
$12$	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	0.107001	+	0.994259i	$0.465875\pi$
$17$	−3.32963	+	5.76708i	−0.807553	+	1.39872i	−0.914554	+	0.404464i	$0.867458\pi$
$18$	1.37027	+	4.01527i	0.322976	+	0.946407i
$19$	−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
$21$	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	0.431803	−	0.901968i	$-0.357877\pi$
$23$	6.85244	−	3.95626i	1.42883	−	0.824936i	0.997029	+	0.0770314i	$0.0245442\pi$
$24$	−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	0.735265	−	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
$33$	−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	−0.210975	−	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
$39$	−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	$0.247364\pi$
$43$			9.19651i			1.40245i	−0.712938	+	0.701227i	$0.752636\pi$
$44$	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	0.940094	−	0.340916i	$-0.110737\pi$
$47$	1.19840	+	2.07569i	0.174805	+	0.302771i	−0.765289	+	0.643687i	$0.777404\pi$
$48$	−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	−0.00943963	+	0.999955i	$0.503005\pi$
$53$	−6.33884	+	10.9792i	−0.870707	+	1.50811i	−0.861267	+	0.508153i	$0.830329\pi$
$54$	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	−0.0616046	−	0.998101i	$-0.519622\pi$
$59$	−7.34922	−	4.24308i	−0.956787	−	0.552401i	−0.895183	+	0.445699i	$0.852955\pi$
$60$	5.93219	−	1.78876i	0.765842	−	0.230928i
$61$	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
$63$	−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	0.858207	−	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	$-0.894807\pi$
$71$		−	5.46843i		−	0.648984i	0.945889	−	0.324492i	$-0.105193\pi$
$72$	−8.03952	+	2.71406i	−0.947466	+	0.319856i
$73$	−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
$75$	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	0.972793	−	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
$81$	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	$-0.899559\pi$
$83$		−	5.65457i		−	0.620669i	0.950627	−	0.310335i	$-0.100441\pi$
$84$	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	−0.929676	−	0.368379i	$-0.879913\pi$
$89$	−7.39495	−	12.8084i	−0.783863	−	1.35769i	0.145812	−	0.989312i	$-0.453420\pi$
$90$	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	$-0.971590\pi$
$97$		−	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	0.973411	−	0.229064i	$-0.0735667\pi$
$101$	12.6803	+	7.32100i	1.26174	+	0.728467i	0.288330	+	0.957531i	$0.406900\pi$
$102$	−0.533507	−	16.3030i	−0.0528251	−	1.61424i
$103$	−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
$105$	−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	0.647247	−	0.762281i	$-0.275920\pi$
$107$	−3.48110	−	6.02945i	−0.336531	−	0.582889i	−0.983778	+	0.179392i	$0.942587\pi$
$108$	−8.04397	−	6.57986i	−0.774031	−	0.633147i
$109$	−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	$0.00795328\pi$
$113$			0.531154i			0.0499667i	−0.999688	+	0.0249834i	$0.992047\pi$
$114$	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	−0.953710	−	0.300729i	$-0.902770\pi$
$131$	−13.3927	+	7.73228i	−1.17013	+	0.675573i	−0.216416	+	0.976301i	$0.569437\pi$
$132$	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	0.853766	−	0.520657i	$-0.174313\pi$
$137$	9.71195	+	5.60719i	0.829748	+	0.479055i	−0.0240187	+	0.999712i	$0.507646\pi$
$138$	−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	0.846459	−	0.532454i	$-0.178730\pi$
$149$	−0.462495	−	0.801066i	−0.0378891	−	0.0656258i	−0.884348	+	0.466828i	$0.845397\pi$
$150$	−0.144270	−	4.40865i	−0.0117796	−	0.359965i
$151$	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
$156$	−8.33975	−	1.95916i	−0.667714	−	0.156858i
$157$	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
$159$	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	−0.0937855	−	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
$165$	−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	−0.352758	−	0.935715i	$-0.614756\pi$
$173$	3.69882	−	2.13552i	0.281216	−	0.162360i	0.633974	+	0.773354i	$0.281423\pi$
$174$	−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	−0.689576	−	0.724214i	$-0.742203\pi$
$179$	3.77825	−	6.54412i	0.282399	−	0.489130i	0.971975	+	0.235083i	$0.0755363\pi$
$180$	−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	−0.0699601	−	0.997550i	$-0.522287\pi$
$191$	10.4891	−	6.05587i	0.758963	−	0.438188i	0.828923	+	0.559362i	$0.188954\pi$
$192$	−13.4680	−	3.25769i	−0.971970	−	0.235104i
$193$	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	$-0.744620\pi$
$197$	−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	−0.0260186	−	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
$201$	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	$-0.828273\pi$
$211$		−	14.9240i		−	1.02741i	0.857967	−	0.513704i	$-0.171727\pi$
$212$	−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	$-0.917859\pi$
$223$		−	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	0.879203	−	0.476446i	$-0.158075\pi$
$227$	13.6531	+	7.88264i	0.906190	+	0.523189i	0.0269870	+	0.999636i	$0.491409\pi$
$228$	−3.71908	−	12.3338i	−0.246302	−	0.816828i
$229$	−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
$231$	−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	−0.916715	−	0.399542i	$-0.869169\pi$
$233$	−15.7079	+	9.06896i	−1.02906	+	0.594127i	−0.112344	+	0.993669i	$0.535836\pi$
$234$	−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	$0.0559877\pi$
$239$			5.41040i			0.349970i	−0.984571	+	0.174985i	$0.944012\pi$
$240$	3.53841	+	11.8761i	0.228403	+	0.766599i
$241$	−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
$243$	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	$-0.784435\pi$
$251$		−	19.8553i		−	1.25325i	0.779319	−	0.626627i	$-0.215565\pi$
$252$	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	0.697111	−	0.716964i	$-0.254469\pi$
$257$	−4.36616	−	7.56240i	−0.272353	−	0.471730i	−0.969464	+	0.245234i	$0.921135\pi$
$258$	−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	−0.132455	−	0.991189i	$-0.542286\pi$
$263$	−17.1429	−	9.89747i	−1.05708	−	0.610304i	−0.924623	+	0.380885i	$0.875619\pi$
$264$	−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	0.475241	−	0.879856i	$-0.342361\pi$
$269$	−0.805574	−	0.465098i	−0.0491167	−	0.0283575i	−0.524357	+	0.851498i	$0.675694\pi$
$270$	10.6588	−	7.69070i	0.648675	−	0.468041i
$271$	−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
$273$	−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	0.999086	+	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	$0.219454\pi$
$281$			21.3260i			1.27220i	−0.771605	+	0.636102i	$0.780546\pi$
$282$	−5.17768	−	2.76761i	−0.308327	−	0.164809i
$283$	−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
$285$	−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	$0.125049\pi$
$293$			13.1058i			0.765652i	−0.923821	+	0.382826i	$0.874951\pi$
$294$	−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	−0.434211	−	0.900811i	$-0.642973\pi$
$311$	9.92896	−	17.1975i	0.563020	−	0.975179i	0.997231	−	0.0743677i	$-0.0236939\pi$
$312$	6.36361	+	10.3094i	0.360269	+	0.583655i
$313$	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
$315$	−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	0.675635	−	0.737236i	$-0.263870\pi$
$317$	−5.35288	−	9.27147i	−0.300648	−	0.520737i	−0.976283	+	0.216499i	$0.930536\pi$
$318$	−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	−0.918762	−	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
$333$	−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	0.465604	+	0.884993i	$0.345837\pi$
$347$	−9.94032	+	17.2171i	−0.533624	+	0.924265i	−0.999229	+	0.0392715i	$0.987496\pi$
$348$	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	−0.998474	−	0.0552182i	$-0.982415\pi$
$353$	−8.48135	+	14.6901i	−0.451417	+	0.781877i	0.547057	+	0.837095i	$0.315748\pi$
$354$	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	0.0648056	−	0.997898i	$-0.479357\pi$
$359$	18.2162	−	10.5171i	0.961413	−	0.555072i	0.896608	+	0.442826i	$0.146024\pi$
$360$	−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	0.532238	−	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
$369$	−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	−0.900848	−	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
$375$	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	$0.0149087\pi$
$379$			1.82298i			0.0936402i	−0.998903	+	0.0468201i	$0.985091\pi$
$380$	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	0.716546	−	0.697540i	$-0.245722\pi$
$383$	−4.81069	−	8.33236i	−0.245815	−	0.425763i	−0.962360	+	0.271777i	$0.912389\pi$
$384$	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	−0.250703	−	0.968064i	$-0.580662\pi$
$389$	14.0629	−	24.3576i	0.713017	−	1.23498i	0.963719	−	0.266917i	$-0.0860050\pi$
$390$	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	0.999526	−	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
$399$	−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	−0.624806	−	0.780780i	$-0.714822\pi$
$401$	−5.22718	+	3.01791i	−0.261033	+	0.150707i	0.363773	+	0.931488i	$0.381488\pi$
$402$	−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	0.941556	−	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
$411$	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	$0.0195955\pi$
$419$			2.51866i			0.123045i	−0.998106	+	0.0615223i	$0.980404\pi$
$420$	15.2242	−	6.07939i	0.742863	−	0.296644i
$421$		−	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
$423$	−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	0.182319	−	0.983240i	$-0.441640\pi$
$431$	−12.0003	−	6.92836i	−0.578033	−	0.333727i	−0.760351	+	0.649512i	$0.774973\pi$
$432$	13.2127	−	16.0445i	0.635694	−	0.771941i
$433$		−	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
$438$	16.0723	−	0.525956i	0.767964	−	0.0251312i
$439$	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
$441$	−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	0.995981	−	0.0895692i	$-0.0285490\pi$
$443$	8.84884	+	15.3266i	0.420421	+	0.728191i	−0.575559	+	0.817760i	$0.695216\pi$
$444$	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	$-0.848099\pi$
$449$		−	19.4650i		−	0.918609i	0.888279	−	0.459305i	$-0.151901\pi$
$450$	−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	0.988424	−	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
$459$	−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	$-0.993645\pi$
$461$		−	0.857290i		−	0.0399280i	0.999801	−	0.0199640i	$-0.00635516\pi$
$462$	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	−0.285235	−	0.958458i	$-0.592072\pi$
$467$	8.69155	−	5.01807i	0.402197	−	0.232208i	0.687431	+	0.726249i	$0.258738\pi$
$468$	−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	0.494663	+	0.869085i	$0.335292\pi$
$479$	−11.0594	+	19.1555i	−0.505318	+	0.875237i	−0.999981	+	0.00615194i	$0.998042\pi$
$480$	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	−0.489419	−	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	$-0.308272\pi$
$491$	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	−0.691525	−	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
$501$	−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	0.0214392	−	0.999770i	$-0.493175\pi$
$509$	20.2595	−	11.6968i	0.897985	−	0.518452i	0.876546	+	0.481318i	$0.159842\pi$
$510$	−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	−0.849460	−	0.527654i	$-0.823072\pi$
$521$	0.735700	−	1.27427i	0.0322316	−	0.0558267i	0.881691	+	0.471827i	$0.156405\pi$
$522$	1.02552	+	3.00504i	0.0448856	+	0.131527i
$523$	−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
$525$	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	−0.167861	−	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
$543$	−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	$-0.914477\pi$
$547$		−	12.4170i		−	0.530914i	0.964123	−	0.265457i	$-0.0855228\pi$
$548$	−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	−0.998635	−	0.0522341i	$-0.983366\pi$
$557$	−10.7167	+	18.5619i	−0.454081	+	0.786492i	0.544554	+	0.838726i	$0.316699\pi$
$558$	−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	0.0717262	−	0.997424i	$-0.477149\pi$
$563$	−17.9430	−	10.3594i	−0.756205	−	0.436595i	−0.827932	+	0.560829i	$0.810483\pi$
$564$	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	0.0922056	−	0.995740i	$-0.470608\pi$
$569$	23.8691	−	13.7808i	1.00064	−	0.577722i	0.908439	+	0.418018i	$0.137275\pi$
$570$	16.2843	−	0.532894i	0.682074	−	0.0223205i
$571$	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
$576$	−10.7571	+	21.4543i	−0.448212	+	0.893927i
$577$	−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
$579$	−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	$0.0231052\pi$
$587$			3.51421i			0.145047i	−0.997367	+	0.0725236i	$0.976895\pi$
$588$	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	0.955012	+	0.296568i	$0.0958423\pi$
$593$	17.8824	+	30.9732i	0.734342	+	1.27192i	−0.220670	+	0.975349i	$0.570824\pi$
$594$	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	0.998466	−	0.0553669i	$-0.0176328\pi$
$599$	35.4819	+	20.4855i	1.44975	+	0.837014i	0.451284	+	0.892380i	$0.350966\pi$
$600$	8.81821	−	0.259483i	0.360002	−	0.0105933i
$601$			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
$606$	−35.8462	+	1.17305i	−1.45615	+	0.0476517i
$607$	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
$609$	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	0.604684	−	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	$-0.850413\pi$
$617$		−	22.4963i		−	0.905669i	0.891595	−	0.452834i	$-0.149587\pi$
$618$	11.3875	−	21.3039i	0.458072	−	0.856967i
$619$	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
$621$	−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	0.501566	−	0.865119i	$-0.332757\pi$
$641$	0.0793494	+	0.0458124i	0.00313411	+	0.00180948i	−0.498432	+	0.866929i	$0.666091\pi$
$642$	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	−0.934716	−	0.355395i	$-0.884346\pi$
$647$	−4.05903	+	7.03045i	−0.159577	+	0.276396i	0.775139	+	0.631791i	$0.217680\pi$
$648$	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	0.981959	+	0.189095i	$0.0605555\pi$
$653$	16.7312	+	28.9792i	0.654741	+	1.13404i	−0.327218	+	0.944949i	$0.606111\pi$
$654$	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	0.393130	+	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
$663$	−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	0.279680	−	0.960093i	$-0.409772\pi$
$677$	32.5497	−	18.7926i	1.25099	−	0.722257i	0.971305	+	0.237836i	$0.0764382\pi$
$678$	−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	−0.845841	−	0.533436i	$-0.820901\pi$
$683$	1.02051	−	1.76757i	0.0390487	−	0.0676343i	0.884889	+	0.465802i	$0.154234\pi$
$684$	−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	0.998146	−	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
$693$	−6.19151	+	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	−0.570093	+	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
$711$	−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	0.961296	−	0.275517i	$-0.0888489\pi$
$719$	6.49021	+	11.2414i	0.242044	+	0.419232i	−0.719252	+	0.694749i	$0.755516\pi$
$720$	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	$0.0714880\pi$
$727$			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
$732$	4.04913	+	13.4284i	0.149660	+	0.496328i
$733$	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
$735$	−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	0.457979	−	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	$0.0790872\pi$
$743$			13.4061i			0.491823i	−0.969292	+	0.245911i	$0.920913\pi$
$744$	−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	0.686182	−	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
$753$	−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	$0.346633\pi$
$757$			48.7626i			1.77231i	−0.463391	+	0.886154i	$0.653367\pi$
$758$	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	0.927652	+	0.373447i	$0.121824\pi$
$761$	21.7170	+	37.6149i	0.787240	+	1.36354i	−0.140411	+	0.990093i	$0.544842\pi$
$762$	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	$-0.858043\pi$
$769$		−	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	0.735206	−	0.677843i	$-0.237085\pi$
$773$	14.3402	+	8.27930i	0.515780	+	0.297786i	−0.219427	+	0.975629i	$0.570419\pi$
$774$	−36.9264	+	12.6017i	−1.32729	+	0.452959i
$775$	−5.17284	+	2.98654i	−0.185814	+	0.107280i
$776$	−3.49414	−	3.52885i	−0.125432	−	0.126678i
$777$	−6.37940	−	15.8238i	−0.228860	−	0.567676i
$778$	−38.4374	+	10.2314i	−1.37805	+	0.366815i
$779$	−3.73823	−	6.47480i	−0.133936	−	0.231984i
$780$	−14.6704	+	4.42364i	−0.525285	+	0.158392i
$781$	−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
$786$	17.8571	−	33.4072i	0.636940	−	1.19160i
$787$	−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
$789$	−23.3966	+	25.0623i	−0.832940	+	0.892242i
$790$	−3.30519	−	12.4169i	−0.117593	−	0.441775i
$791$	0.122192	+	1.39998i	0.00434463	+	0.0497775i
$792$	−1.67381	+	8.34186i	−0.0594761	+	0.296415i
$793$	−5.00642	−	8.67137i	−0.177783	−	0.307930i
$794$	6.94307	−	25.7422i	0.246400	−	0.913555i
$795$	38.2641	+	8.85597i	1.35709	+	0.314089i
$796$	14.8217	−	25.4777i	0.525342	−	0.903034i
$797$			2.35681i			0.0834824i	0.999128	+	0.0417412i	$0.0132905\pi$
$797$			2.35681i			0.0834824i	−0.999128	+	0.0417412i	$0.986709\pi$
$798$	22.1621	+	9.47010i	0.784531	+	0.335238i
$799$	−15.9609			−0.564657
$800$	−9.86108	+	2.55538i	−0.348642	+	0.0903465i
$801$	3.04672	+	44.2650i	0.107651	+	1.56403i
$802$	8.24144	+	2.22285i	0.291015	+	0.0784915i
$803$	−5.70077	+	3.29134i	−0.201176	+	0.116149i
$804$	20.1083	+	18.8962i	0.709166	+	0.666419i
$805$	15.8316	−	33.9327i	0.557991	−	1.19597i
$806$	2.98397	+	11.2102i	0.105106	+	0.394862i
$807$	−1.09944	+	1.17772i	−0.0387022	+	0.0414576i
$808$	40.0552	−	10.5208i	1.40914	−	0.370121i
$809$	−39.6070	−	22.8671i	−1.39251	−	0.803964i	−0.398914	−	0.916988i	$-0.630613\pi$
$809$	−39.6070	−	22.8671i	−1.39251	−	0.803964i	−0.993592	+	0.113024i	$0.963946\pi$
$810$	−8.81485	−	20.9898i	−0.309722	−	0.737506i
$811$	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
$816$	−33.5168	−	31.7051i	−1.17332	−	1.10990i
$817$	29.6182	−	17.1000i	1.03621	−	0.598255i
$818$	−9.51956	−	35.7631i	−0.332844	−	1.25043i
$819$	18.3161	+	7.05818i	0.640015	+	0.246633i
$820$	3.57540	+	6.24017i	0.124858	+	0.217916i
$821$	−18.4890	−	32.0239i	−0.645272	−	1.11764i	−0.984239	−	0.176845i	$-0.943411\pi$
$821$	−18.4890	−	32.0239i	−0.645272	−	1.11764i	0.338967	−	0.940798i	$-0.389922\pi$
$822$	−27.4548	+	0.898442i	−0.957597	+	0.0313368i
$823$	−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	$-0.227827\pi$
$827$	43.4014			1.50921			0.754607	+	0.656176i	$0.227827\pi$
$828$	−3.10386	−	47.3735i	−0.107867	−	1.64634i
$829$	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
$831$	34.8818	−	37.3652i	1.21004	−	1.29619i
$832$	−0.195586	+	19.7832i	−0.00678073	+	0.685858i
$833$	−15.9612	+	43.7970i	−0.553024	+	1.51748i
$834$	37.4058	−	23.2598i	1.29526	−	0.805420i
$835$	−12.2842	+	7.09229i	−0.425113	+	0.245439i
$836$	0.0245759	−	7.45762i	0.000849974	−	0.257927i
$837$	−16.1006	+	6.15019i	−0.556518	+	0.212582i
$838$	2.52281	−	2.51451i	0.0871489	−	0.0868622i
$839$	19.2288			0.663854			0.331927	−	0.943305i	$-0.392301\pi$
$839$	19.2288			0.663854			0.331927	+	0.943305i	$0.392301\pi$
$840$	−21.2884	−	9.17985i	−0.734521	−	0.316735i
$841$	−28.4399			−0.980686
$842$	−33.5424	+	33.4320i	−1.15595	+	1.15214i
$843$	35.9865	+	8.32884i	1.23944	+	0.286860i
$844$	29.8478	+	0.0983605i	1.02740	+	0.00338571i
$845$	−10.6636	+	6.15665i	−0.366840	+	0.211795i
$846$	−6.69233	+	7.65617i	−0.230087	+	0.263225i
$847$	15.1628	+	21.6642i	0.520999	+	0.744389i
$848$	25.6443	−	43.7487i	0.880627	−	1.50234i
$849$	26.3973	+	24.6429i	0.905954	+	0.845741i
$850$	−4.41633	+	16.3740i	−0.151479	+	0.561623i
$851$	14.7295	−	25.5123i	0.504921	−	0.874549i
$852$	4.33217	−	18.4412i	0.148418	−	0.631785i
$853$	43.5472			1.49103			0.745514	−	0.666489i	$-0.232204\pi$
$853$	43.5472			1.49103			0.745514	+	0.666489i	$0.232204\pi$
$854$	2.65831	−	14.9143i	0.0909655	−	0.510357i
$855$	11.1405	+	16.5555i	0.380997	+	0.566185i
$856$	−18.9957	−	5.19065i	−0.649259	−	0.177413i
$857$	−4.41603	+	7.64878i	−0.150849	+	0.261277i	−0.931540	−	0.363640i	$-0.881534\pi$
$857$	−4.41603	+	7.64878i	−0.150849	+	0.261277i	0.780691	+	0.624917i	$0.214867\pi$
$858$	−0.198660	−	6.07069i	−0.00678213	−	0.207250i
$859$	−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
$861$	1.28906	−	9.12236i	0.0439311	−	0.310889i
$862$	5.04071	+	18.9370i	0.171687	+	0.644995i
$863$	−2.80835	+	1.62140i	−0.0955974	+	0.0551932i	−0.547037	−	0.837109i	$-0.684244\pi$
$863$	−2.80835	+	1.62140i	−0.0955974	+	0.0551932i	0.451439	+	0.892302i	$0.350911\pi$
$864$	−29.2618	+	2.78362i	−0.995506	+	0.0947006i
$865$	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
$870$	−1.54571	+	2.89174i	−0.0524046	+	0.0980393i
$871$	−17.0599	−	9.84955i	−0.578053	−	0.333739i
$872$	−7.46665	+	1.96118i	−0.252853	+	0.0664138i
$873$	−2.31420	+	4.73170i	−0.0783240	+	0.160144i
$874$	10.7041	+	40.2132i	0.362072	+	1.36023i
$875$	2.79835	+	32.0614i	0.0946015	+	1.08387i
$876$	−16.5726	−	15.5737i	−0.559937	−	0.526186i
$877$	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
$879$	22.1154	+	5.11847i	0.745934	+	0.172642i
$880$	−0.0472807	+	7.17365i	−0.00159383	+	0.241824i
$881$	−28.1014			−0.946759			−0.473380	−	0.880859i	$-0.656966\pi$
$881$	−28.1014			−0.946759			−0.473380	+	0.880859i	$0.656966\pi$
$882$	14.3162	+	26.0201i	0.482050	+	0.876144i
$883$			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
$885$	−5.92799	+	25.6131i	−0.199267	+	0.860975i
$886$	6.51763	−	24.1648i	0.218964	−	0.811832i
$887$	−25.3783	−	43.9566i	−0.852122	−	1.47592i	−0.879290	−	0.476287i	$-0.841982\pi$
$887$	−25.3783	−	43.9566i	−0.852122	−	1.47592i	0.0271684	−	0.999631i	$-0.491351\pi$
$888$	−16.0572	−	8.65113i	−0.538843	−	0.290313i
$889$	−11.9239	+	1.04073i	−0.399914	+	0.0349049i
$890$	9.62318	+	36.1524i	0.322570	+	1.21183i
$891$	8.93914	−	1.23640i	0.299472	−	0.0414211i
$892$	15.2437	+	0.0502340i	0.510395	+	0.00168196i
$893$	4.45664	−	7.71912i	0.149136	−	0.258311i
$894$	1.99820	+	1.06809i	0.0668300	+	0.0357224i
$895$		−	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
$900$	6.00257	+	8.98395i	0.200086	+	0.299465i
$901$	−42.2119	−	73.1132i	−1.40628	−	2.43575i
$902$	−2.75492	+	0.733315i	−0.0917288	+	0.0244167i
$903$	41.7291	+	5.89666i	1.38866	+	0.196228i
$904$	1.05704	+	1.06755i	0.0351567	+	0.0355060i
$905$	−7.74871	+	4.47372i	−0.257576	+	0.148711i
$906$	1.53295	+	46.8444i	0.0509290	+	1.55630i
$907$	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	$-0.922275\pi$
$911$		−	14.5940i		−	0.483521i	0.970336	−	0.241761i	$-0.0777249\pi$
$912$	24.6920	−	7.35683i	0.817635	−	0.243609i
$913$	−4.91019	−	2.83490i	−0.162503	−	0.0938214i
$914$	5.71289	−	21.1811i	0.188966	−	0.700609i
$915$	8.55953	−	9.16893i	0.282969	−	0.303115i
$916$	30.6181	−	17.5431i	1.01165	−	0.579639i
$917$	−33.5208	+	23.4612i	−1.10695	+	0.774757i
$918$	−20.0506	+	44.6390i	−0.661768	+	1.47331i
$919$	−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
$921$	7.28079	−	31.4582i	0.239910	−	1.03658i
$922$	−0.858701	+	0.855876i	−0.0282798	+	0.0281868i
$923$			13.5235i			0.445132i
$924$	5.68709	−	7.21873i	0.187092	−	0.237479i
$925$			6.70450i			0.220443i
$926$	−37.5112	−	37.6350i	−1.23269	−	1.23676i
$927$	29.5155	−	2.03153i	0.969417	−	0.0667242i
$928$	2.96885	+	3.01817i	0.0974572	+	0.0990764i
$929$	9.71753	+	16.8313i	0.318822	+	0.552216i	0.980242	−	0.197799i	$-0.0633795\pi$
$929$	9.71753	+	16.8313i	0.318822	+	0.552216i	−0.661421	+	0.750015i	$0.730046\pi$
$930$	−12.3409	+	7.67387i	−0.404675	+	0.251636i
$931$	−16.7246	−	19.9483i	−0.548128	−	0.653780i
$932$	−18.0343	−	31.4754i	−0.590733	−	1.03101i
$933$	−25.1420	−	23.4710i	−0.823114	−	0.768407i
$934$	−13.7035	−	3.69606i	−0.448394	−	0.120939i
$935$	10.3430	+	5.97152i	0.338252	+	0.195290i
$936$	19.8819	−	6.71193i	0.649859	−	0.219386i
$937$		−	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	0.591858	−	0.806042i	$-0.298395\pi$
$941$	5.82024	+	3.36032i	0.189735	+	0.109543i	−0.402124	+	0.915585i	$0.631728\pi$
$942$	0.876256	+	26.7769i	0.0285500	+	0.872437i
$943$	13.7764	−	7.95381i	0.448622	−	0.259012i
$944$	29.2844	+	17.1657i	0.953126	+	0.558695i
$945$	−1.76053	+	24.5265i	−0.0572701	+	0.797849i
$946$	−3.35446	−	12.6020i	−0.109063	−	0.409728i
$947$	−10.5673	−	18.3031i	−0.343392	−	0.594772i	0.641668	−	0.766982i	$-0.278243\pi$
$947$	−10.5673	−	18.3031i	−0.343392	−	0.594772i	−0.985060	+	0.172210i	$0.944909\pi$
$948$	5.08013	+	16.8476i	0.164995	+	0.547183i
$949$	14.0602	+	8.11768i	0.456414	+	0.263511i
$950$	−6.68575	−	6.70782i	−0.216914	−	0.217630i
$951$	−17.7357	+	5.41174i	−0.575118	+	0.175488i
$952$	16.8026	+	46.9151i	0.544577	+	1.52053i
$953$			2.18327i			0.0707230i	0.999375	+	0.0353615i	$0.0112583\pi$
$953$			2.18327i			0.0707230i	−0.999375	+	0.0353615i	$0.988742\pi$
$954$	−52.7703	−	10.4076i	−1.70850	−	0.336960i
$955$	10.8317	−	18.7611i	0.350507	−	0.607096i
$956$	−10.8207	−	0.0356587i	−0.349968	−	0.00115329i
$957$	−0.950102	−	0.886955i	−0.0307124	−	0.0286712i
$958$	30.2282	−	8.04627i	0.976630	−	0.259963i
$959$	26.8880	+	12.5448i	0.868259	+	0.405094i
$960$	−23.7754	+	6.99850i	−0.767348	+	0.225876i
$961$	−9.99900	−	17.3188i	−0.322548	−	0.558670i
$962$	12.5718	+	3.39081i	0.405331	+	0.109324i
$963$	1.43422	+	20.8373i	0.0462170	+	0.671473i
$964$	21.6028	−	37.1340i	0.695779	−	1.19600i
$965$		−	2.11931i		−	0.0682229i
$966$	−20.1495	+	47.1543i	−0.648300	+	1.51716i
$967$	−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
$969$	9.67175	−	41.7888i	0.310701	−	1.34245i
$970$	−1.15654	+	4.28800i	−0.0371344	+	0.137679i
$971$	30.0100	−	17.3263i	0.963065	−	0.556026i	0.0659503	−	0.997823i	$-0.478992\pi$
$971$	30.0100	−	17.3263i	0.963065	−	0.556026i	0.897115	+	0.441797i	$0.145659\pi$
$972$	13.0054	+	28.3348i	0.417149	+	0.908838i
$973$	−47.3969	+	4.13685i	−1.51947	+	0.132621i
$974$	−30.7925	+	8.19648i	−0.986657	+	0.262632i
$975$	−5.63841	−	5.26366i	−0.180574	−	0.168572i
$976$	−8.00506	−	14.0787i	−0.256236	−	0.450647i
$977$	3.22538	+	1.86218i	0.103189	+	0.0595763i	0.550706	−	0.834699i	$-0.314358\pi$
$977$	3.22538	+	1.86218i	0.103189	+	0.0595763i	−0.447517	+	0.894275i	$0.647692\pi$
$978$	−12.2826	+	22.9784i	−0.392754	+	0.734769i
$979$	−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	$-0.496940\pi$
$983$	27.3018	−	47.2881i	0.870792	−	1.50826i	0.861179	−	0.508302i	$-0.169727\pi$
$984$	−5.17330	−	8.38104i	−0.164919	−	0.267178i
$985$	−30.2227	+	17.4491i	−0.962977	+	0.555975i
$986$	6.81100	−	1.81298i	0.216906	−	0.0577370i
$987$	10.1869	−	4.10685i	0.324251	−	0.130722i
$988$	−15.9594	+	9.14415i	−0.507735	+	0.290914i
$989$	36.3837	+	63.0185i	1.15694	+	2.00387i
$990$	7.20118	−	2.45752i	0.228869	−	0.0781050i
$991$	−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
$996$	4.47963	−	19.0689i	0.141942	−	0.604221i
$997$	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
$999$	−3.05765	+	19.1026i	−0.0967398	+	0.604380i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.998351 - 1.00165i) q^{2} +(0.390548 - 1.68745i) q^{3} +(-0.00659077 + 1.99999i) q^{4} +(1.54900 - 0.894317i) q^{5} +(-2.08013 + 1.29347i) q^{6} +(2.63573 - 0.230049i) q^{7} +(2.00986 - 1.99009i) q^{8} +(-2.69494 - 1.31806i) q^{9} +O(q^{10})\)	\(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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