LMFDB - Embedded newform 672.2.bo.a.125.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,2,Mod(125,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 4, 4]))

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

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

chi := DirichletCharacter("672.125");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	672.bo (of order $8$, degree $4$, 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:	$5.36594701583$
Analytic rank:	$0$
Dimension:	$496$
Relative dimension:	$124$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			125.1
Character	$\chi$	$=$	672.125
Dual form			672.2.bo.a.629.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41228 - 0.0740064i) q^{2} +(-0.841142 + 1.51409i) q^{3} +(1.98905 + 0.209035i) q^{4} +(-0.918980 - 2.21861i) q^{5} +(1.29998 - 2.07607i) q^{6} +(-1.19970 + 2.35812i) q^{7} +(-2.79361 - 0.442417i) q^{8} +(-1.58496 - 2.54714i) q^{9} +O(q^{10})$	\(q+(-1.41228 - 0.0740064i) q^{2} +(-0.841142 + 1.51409i) q^{3} +(1.98905 + 0.209035i) q^{4} +(-0.918980 - 2.21861i) q^{5} +(1.29998 - 2.07607i) q^{6} +(-1.19970 + 2.35812i) q^{7} +(-2.79361 - 0.442417i) q^{8} +(-1.58496 - 2.54714i) q^{9} +(1.13366 + 3.20130i) q^{10} +(1.12152 + 2.70758i) q^{11} +(-1.98957 + 2.83577i) q^{12} +(1.76770 + 0.732205i) q^{13} +(1.86882 - 3.24153i) q^{14} +(4.13218 + 0.474747i) q^{15} +(3.91261 + 0.831560i) q^{16} -4.25844i q^{17} +(2.04990 + 3.71456i) q^{18} +(-5.27576 - 2.18529i) q^{19} +(-1.36413 - 4.60502i) q^{20} +(-2.56130 - 3.79997i) q^{21} +(-1.38351 - 3.90686i) q^{22} +(-5.72952 + 5.72952i) q^{23} +(3.01969 - 3.85765i) q^{24} +(-0.542186 + 0.542186i) q^{25} +(-2.44229 - 1.16490i) q^{26} +(5.18978 - 0.257275i) q^{27} +(-2.87918 + 4.43963i) q^{28} +(2.47058 - 5.96450i) q^{29} +(-5.80064 - 0.976282i) q^{30} -6.99097i q^{31} +(-5.46414 - 1.46395i) q^{32} +(-5.04289 - 0.579379i) q^{33} +(-0.315151 + 6.01409i) q^{34} +(6.33425 + 0.494597i) q^{35} +(-2.62012 - 5.39768i) q^{36} +(1.75471 + 4.23624i) q^{37} +(7.28910 + 3.47667i) q^{38} +(-2.59551 + 2.06057i) q^{39} +(1.58572 + 6.60452i) q^{40} +(0.132416 + 0.132416i) q^{41} +(3.33604 + 5.55615i) q^{42} +(0.813390 - 0.336917i) q^{43} +(1.66477 + 5.61995i) q^{44} +(-4.19456 + 5.85718i) q^{45} +(8.51569 - 7.66765i) q^{46} -10.5437i q^{47} +(-4.55012 + 5.22460i) q^{48} +(-4.12146 - 5.65805i) q^{49} +(0.805841 - 0.725591i) q^{50} +(6.44767 + 3.58195i) q^{51} +(3.36298 + 1.82590i) q^{52} +(-2.69882 - 6.51553i) q^{53} +(-7.34844 - 0.0207333i) q^{54} +(4.97643 - 4.97643i) q^{55} +(4.39476 - 6.05691i) q^{56} +(7.74639 - 6.14985i) q^{57} +(-3.93055 + 8.24068i) q^{58} +(-0.718041 - 1.73350i) q^{59} +(8.11986 + 1.80806i) q^{60} +(4.24533 - 10.2491i) q^{61} +(-0.517377 + 9.87318i) q^{62} +(7.90792 - 0.681737i) q^{63} +(7.60853 + 2.47188i) q^{64} -4.59472i q^{65} +(7.07908 + 1.19145i) q^{66} +(10.2684 + 4.25333i) q^{67} +(0.890162 - 8.47023i) q^{68} +(-3.85569 - 13.4944i) q^{69} +(-8.90911 - 1.16728i) q^{70} +(-3.71046 - 3.71046i) q^{71} +(3.30087 + 7.81692i) q^{72} +(1.25011 - 1.25011i) q^{73} +(-2.16462 - 6.11260i) q^{74} +(-0.364865 - 1.27698i) q^{75} +(-10.0369 - 5.44946i) q^{76} +(-7.73029 - 0.603604i) q^{77} +(3.81808 - 2.71801i) q^{78} -16.8392i q^{79} +(-1.75070 - 9.44475i) q^{80} +(-3.97580 + 8.07422i) q^{81} +(-0.177209 - 0.196808i) q^{82} +(2.55568 - 6.16997i) q^{83} +(-4.30022 - 8.09371i) q^{84} +(-9.44782 + 3.91342i) q^{85} +(-1.17366 + 0.415624i) q^{86} +(6.95271 + 8.75768i) q^{87} +(-1.93521 - 8.06012i) q^{88} +(-8.96098 + 8.96098i) q^{89} +(6.35735 - 7.96153i) q^{90} +(-3.84733 + 3.29002i) q^{91} +(-12.5940 + 10.1986i) q^{92} +(10.5850 + 5.88040i) q^{93} +(-0.780302 + 14.8906i) q^{94} +13.7131i q^{95} +(6.81268 - 7.04183i) q^{96} +9.83487i q^{97} +(5.40190 + 8.29575i) q^{98} +(5.11902 - 7.14807i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) $ 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9	$ 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9} - 48 q^{16} - 8 q^{18} - 4 q^{21} - 16 q^{22} - 16 q^{25} - 8 q^{28} - 64 q^{30} - 48 q^{36} - 16 q^{37} - 8 q^{39} + 56 q^{42} - 16 q^{43} - 16 q^{46} + 16 q^{51} - 8 q^{57} - 80 q^{58} + 24 q^{60} - 8 q^{63} - 112 q^{64} + 48 q^{67} - 8 q^{70} - 8 q^{72} - 160 q^{78} + 128 q^{84} + 64 q^{85} - 16 q^{88} - 56 q^{91} + 16 q^{93} - 8 q^{99}+O(q^{100}) $ 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9 - 48 * q^16 - 8 * q^18 - 4 * q^21 - 16 * q^22 - 16 * q^25 - 8 * q^28 - 64 * q^30 - 48 * q^36 - 16 * q^37 - 8 * q^39 + 56 * q^42 - 16 * q^43 - 16 * q^46 + 16 * q^51 - 8 * q^57 - 80 * q^58 + 24 * q^60 - 8 * q^63 - 112 * q^64 + 48 * q^67 - 8 * q^70 - 8 * q^72 - 160 * q^78 + 128 * q^84 + 64 * q^85 - 16 * q^88 - 56 * q^91 + 16 * q^93 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$	$-1$	$-1$

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 $

$2$	−1.41228	−	0.0740064i	−0.998630	−	0.0523304i
$2$	−1.41228	−	0.0740064i	−0.998630	−	0.0523304i
$3$	−0.841142	+	1.51409i	−0.485634	+	0.874162i
$3$	−0.841142	+	1.51409i	−0.485634	+	0.874162i
$4$	1.98905	+	0.209035i	0.994523	+	0.104517i
$5$	−0.918980	−	2.21861i	−0.410980	−	0.992194i	−0.984875	−	0.173265i	$-0.944568\pi$
$5$	−0.918980	−	2.21861i	−0.410980	−	0.992194i	0.573895	−	0.818929i	$-0.305432\pi$
$6$	1.29998	−	2.07607i	0.530713	−	0.847551i
$7$	−1.19970	+	2.35812i	−0.453442	+	0.891286i
$7$	−1.19970	+	2.35812i	−0.453442	+	0.891286i
$8$	−2.79361	−	0.442417i	−0.987691	−	0.156418i
$9$	−1.58496	−	2.54714i	−0.528320	−	0.849045i
$10$	1.13366	+	3.20130i	0.358495	+	1.01234i
$11$	1.12152	+	2.70758i	0.338151	+	0.816368i	0.997893	+	0.0648761i	$0.0206652\pi$
$11$	1.12152	+	2.70758i	0.338151	+	0.816368i	−0.659743	+	0.751491i	$0.729335\pi$
$12$	−1.98957	+	2.83577i	−0.574339	+	0.818618i
$13$	1.76770	+	0.732205i	0.490271	+	0.203077i	0.614103	−	0.789226i	$-0.289518\pi$
$13$	1.76770	+	0.732205i	0.490271	+	0.203077i	−0.123831	+	0.992303i	$0.539518\pi$
$14$	1.86882	−	3.24153i	0.499463	−	0.866335i
$15$	4.13218	+	0.474747i	1.06692	+	0.122579i
$16$	3.91261	+	0.831560i	0.978152	+	0.207890i
$17$		−	4.25844i		−	1.03282i	−0.856341	−	0.516411i	$-0.827268\pi$
$17$		−	4.25844i		−	1.03282i	0.856341	−	0.516411i	$-0.172732\pi$
$18$	2.04990	+	3.71456i	0.483165	+	0.875529i
$19$	−5.27576	−	2.18529i	−1.21034	−	0.501340i	−0.316015	−	0.948754i	$-0.602345\pi$
$19$	−5.27576	−	2.18529i	−1.21034	−	0.501340i	−0.894327	+	0.447414i	$0.852345\pi$
$20$	−1.36413	−	4.60502i	−0.305028	−	1.02971i
$21$	−2.56130	−	3.79997i	−0.558921	−	0.829221i
$22$	−1.38351	−	3.90686i	−0.294966	−	0.832945i
$23$	−5.72952	+	5.72952i	−1.19469	+	1.19469i	−0.218953	+	0.975736i	$0.570264\pi$
$23$	−5.72952	+	5.72952i	−1.19469	+	1.19469i	−0.975736	+	0.218953i	$0.929736\pi$
$24$	3.01969	−	3.85765i	0.616391	−	0.787441i
$25$	−0.542186	+	0.542186i	−0.108437	+	0.108437i
$26$	−2.44229	−	1.16490i	−0.478973	−	0.228455i
$27$	5.18978	−	0.257275i	0.998773	−	0.0495126i
$28$	−2.87918	+	4.43963i	−0.544114	+	0.839011i
$29$	2.47058	−	5.96450i	0.458775	−	1.10758i	−0.510119	−	0.860104i	$-0.670399\pi$
$29$	2.47058	−	5.96450i	0.458775	−	1.10758i	0.968894	−	0.247476i	$-0.0796012\pi$
$30$	−5.80064	−	0.976282i	−1.05905	−	0.178244i
$31$		−	6.99097i		−	1.25562i	−0.778368	−	0.627808i	$-0.783952\pi$
$31$		−	6.99097i		−	1.25562i	0.778368	−	0.627808i	$-0.216048\pi$
$32$	−5.46414	−	1.46395i	−0.965933	−	0.258792i
$33$	−5.04289	−	0.579379i	−0.877855	−	0.100857i
$34$	−0.315151	+	6.01409i	−0.0540480	+	1.03141i
$35$	6.33425	+	0.494597i	1.07068	+	0.0836022i
$36$	−2.62012	−	5.39768i	−0.436686	−	0.899614i
$37$	1.75471	+	4.23624i	0.288472	+	0.696434i	0.999981	−	0.00624412i	$-0.00198758\pi$
$37$	1.75471	+	4.23624i	0.288472	+	0.696434i	−0.711508	+	0.702678i	$0.751988\pi$
$38$	7.28910	+	3.47667i	1.18245	+	0.563991i
$39$	−2.59551	+	2.06057i	−0.415615	+	0.329956i
$40$	1.58572	+	6.60452i	0.250724	+	1.04427i
$41$	0.132416	+	0.132416i	0.0206800	+	0.0206800i	0.717371	−	0.696691i	$-0.245345\pi$
$41$	0.132416	+	0.132416i	0.0206800	+	0.0206800i	−0.696691	+	0.717371i	$0.745345\pi$
$42$	3.33604	+	5.55615i	0.514762	+	0.857333i
$43$	0.813390	−	0.336917i	0.124041	−	0.0513794i	−0.319800	−	0.947485i	$-0.603616\pi$
$43$	0.813390	−	0.336917i	0.124041	−	0.0513794i	0.443841	+	0.896106i	$0.353616\pi$
$44$	1.66477	+	5.61995i	0.250974	+	0.847239i
$45$	−4.19456	+	5.85718i	−0.625288	+	0.873137i
$46$	8.51569	−	7.66765i	1.25557	−	1.13053i
$47$		−	10.5437i		−	1.53796i	−0.639273	−	0.768980i	$-0.720765\pi$
$47$		−	10.5437i		−	1.53796i	0.639273	−	0.768980i	$-0.279235\pi$
$48$	−4.55012	+	5.22460i	−0.656753	+	0.754106i
$49$	−4.12146	−	5.65805i	−0.588780	−	0.808293i
$50$	0.805841	−	0.725591i	0.113963	−	0.102614i
$51$	6.44767	+	3.58195i	0.902855	+	0.501573i
$52$	3.36298	+	1.82590i	0.466361	+	0.253207i
$53$	−2.69882	−	6.51553i	−0.370711	−	0.894976i	−0.993630	−	0.112690i	$-0.964053\pi$
$53$	−2.69882	−	6.51553i	−0.370711	−	0.894976i	0.622919	−	0.782286i	$-0.285947\pi$
$54$	−7.34844	−	0.0207333i	−0.999996	−	0.00282144i
$55$	4.97643	−	4.97643i	0.671022	−	0.671022i
$56$	4.39476	−	6.05691i	0.587274	−	0.809388i
$57$	7.74639	−	6.14985i	1.02603	−	0.814568i
$58$	−3.93055	+	8.24068i	−0.516106	+	1.08205i
$59$	−0.718041	−	1.73350i	−0.0934810	−	0.225683i	0.870222	−	0.492660i	$-0.163975\pi$
$59$	−0.718041	−	1.73350i	−0.0934810	−	0.225683i	−0.963703	+	0.266977i	$0.913975\pi$
$60$	8.11986	+	1.80806i	1.04827	+	0.233420i
$61$	4.24533	−	10.2491i	0.543559	−	1.31227i	−0.378638	−	0.925545i	$-0.623607\pi$
$61$	4.24533	−	10.2491i	0.543559	−	1.31227i	0.922196	−	0.386722i	$-0.126393\pi$
$62$	−0.517377	+	9.87318i	−0.0657069	+	1.25390i
$63$	7.90792	−	0.681737i	0.996305	−	0.0858908i
$64$	7.60853	+	2.47188i	0.951067	+	0.308985i
$65$		−	4.59472i		−	0.569905i
$66$	7.07908	+	1.19145i	0.871374	+	0.146657i
$67$	10.2684	+	4.25333i	1.25449	+	0.519627i	0.908214	−	0.418506i	$-0.137446\pi$
$67$	10.2684	+	4.25333i	1.25449	+	0.519627i	0.346276	+	0.938133i	$0.387446\pi$
$68$	0.890162	−	8.47023i	0.107948	−	1.02717i
$69$	−3.85569	−	13.4944i	−0.464171	−	1.62453i
$70$	−8.90911	−	1.16728i	−1.06484	−	0.139517i
$71$	−3.71046	−	3.71046i	−0.440350	−	0.440350i	0.451779	−	0.892130i	$-0.350789\pi$
$71$	−3.71046	−	3.71046i	−0.440350	−	0.440350i	−0.892130	+	0.451779i	$0.850789\pi$
$72$	3.30087	+	7.81692i	0.389011	+	0.921233i
$73$	1.25011	−	1.25011i	0.146315	−	0.146315i	−0.630155	−	0.776469i	$-0.717009\pi$
$73$	1.25011	−	1.25011i	0.146315	−	0.146315i	0.776469	+	0.630155i	$0.217009\pi$
$74$	−2.16462	−	6.11260i	−0.251632	−	0.710575i
$75$	−0.364865	−	1.27698i	−0.0421310	−	0.147452i
$76$	−10.0369	−	5.44946i	−1.15131	−	0.625096i
$77$	−7.73029	−	0.603604i	−0.880948	−	0.0687871i
$78$	3.81808	−	2.71801i	0.432312	−	0.307754i
$79$		−	16.8392i		−	1.89456i	−0.320403	−	0.947281i	$-0.603818\pi$
$79$		−	16.8392i		−	1.89456i	0.320403	−	0.947281i	$-0.396182\pi$
$80$	−1.75070	−	9.44475i	−0.195734	−	1.05596i
$81$	−3.97580	+	8.07422i	−0.441756	+	0.897135i
$82$	−0.177209	−	0.196808i	−0.0195694	−	0.0217338i
$83$	2.55568	−	6.16997i	0.280523	−	0.677242i	−0.719325	−	0.694673i	$-0.755549\pi$
$83$	2.55568	−	6.16997i	0.280523	−	0.677242i	0.999848	+	0.0174317i	$0.00554895\pi$
$84$	−4.30022	−	8.09371i	−0.469192	−	0.883096i
$85$	−9.44782	+	3.91342i	−1.02476	+	0.424470i
$86$	−1.17366	+	0.415624i	−0.126559	+	0.0448179i
$87$	6.95271	+	8.75768i	0.745408	+	0.938921i
$88$	−1.93521	−	8.06012i	−0.206294	−	0.859212i
$89$	−8.96098	+	8.96098i	−0.949862	+	0.949862i	−0.998802	−	0.0489396i	$-0.984416\pi$
$89$	−8.96098	+	8.96098i	−0.949862	+	0.949862i	0.0489396	+	0.998802i	$0.484416\pi$
$90$	6.35735	−	7.96153i	0.670123	−	0.839219i
$91$	−3.84733	+	3.29002i	−0.403310	+	0.344888i
$92$	−12.5940	+	10.1986i	−1.31301	+	1.06328i
$93$	10.5850	+	5.88040i	1.09761	+	0.609769i
$94$	−0.780302	+	14.8906i	−0.0804821	+	1.53585i
$95$			13.7131i			1.40693i
$96$	6.81268	−	7.04183i	0.695316	−	0.718704i
$97$			9.83487i			0.998579i	0.866435	+	0.499290i	$0.166406\pi$
$97$			9.83487i			0.998579i	−0.866435	+	0.499290i	$0.833594\pi$
$98$	5.40190	+	8.29575i	0.545675	+	0.837997i
$99$	5.11902	−	7.14807i	0.514481	−	0.718408i
$100$	−1.19177	+	0.965097i	−0.119177	+	0.0965097i
$101$	1.71730	+	4.14593i	0.170878	+	0.412535i	0.985998	−	0.166756i	$-0.0533293\pi$
$101$	1.71730	+	4.14593i	0.170878	+	0.412535i	−0.815121	+	0.579291i	$0.803329\pi$
$102$	−8.84080	−	5.53587i	−0.875370	−	0.548133i
$103$	−14.1619	−	14.1619i	−1.39541	−	1.39541i	−0.812632	−	0.582777i	$-0.801966\pi$
$103$	−14.1619	−	14.1619i	−1.39541	−	1.39541i	−0.582777	−	0.812632i	$-0.698034\pi$
$104$	−4.61432	−	2.82756i	−0.452472	−	0.277265i
$105$	−6.07687	+	9.17462i	−0.593042	+	0.895352i
$106$	3.32929	+	9.40145i	0.323369	+	0.913150i
$107$	0.447945	+	1.08143i	0.0433045	+	0.104546i	0.944052	−	0.329797i	$-0.106980\pi$
$107$	0.447945	+	1.08143i	0.0433045	+	0.104546i	−0.900747	+	0.434344i	$0.856980\pi$
$108$	10.3765	+	0.573113i	0.998478	+	0.0551478i
$109$	−0.311121	+	0.751112i	−0.0298000	+	0.0719435i	−0.938079	−	0.346421i	$-0.887397\pi$
$109$	−0.311121	+	0.751112i	−0.0298000	+	0.0719435i	0.908279	+	0.418365i	$0.137397\pi$
$110$	−7.39638	+	6.65980i	−0.705217	+	0.634987i
$111$	−7.89002	−	0.906487i	−0.748888	−	0.0860399i
$112$	−6.65486	+	8.22878i	−0.628825	+	0.777547i
$113$	8.33875			0.784443			0.392222	−	0.919871i	$-0.371707\pi$
$113$	8.33875			0.784443			0.392222	+	0.919871i	$0.371707\pi$
$114$	−11.3952	+	8.11200i	−1.06726	+	0.759759i
$115$	17.9769	+	7.44628i	1.67636	+	0.694369i
$116$	6.16088	−	11.3472i	0.572023	−	1.05356i
$117$	−0.936707	−	5.66308i	−0.0865986	−	0.523552i
$118$	0.885781	+	2.50133i	0.0815428	+	0.230266i
$119$	10.0419	+	5.10883i	0.920540	+	0.468326i
$120$	−11.3337	−	3.15441i	−1.03462	−	0.287957i
$121$	1.70496	−	1.70496i	0.154997	−	0.154997i
$122$	−6.75408	+	14.1604i	−0.611485	+	1.28202i
$123$	−0.311872	+	0.0891098i	−0.0281205	+	0.00803476i
$124$	1.46136	−	13.9054i	0.131234	−	1.24874i
$125$	−9.39191	−	3.89025i	−0.840038	−	0.347955i
$126$	−11.2186	+	0.377564i	−0.999434	+	0.0336361i
$127$	−7.52219			−0.667486			−0.333743	−	0.942664i	$-0.608312\pi$
$127$	−7.52219			−0.667486			−0.333743	+	0.942664i	$0.608312\pi$
$128$	−10.5624	−	4.05406i	−0.933594	−	0.358332i
$129$	−0.174052	+	1.51494i	−0.0153244	+	0.133383i
$130$	−0.340039	+	6.48901i	−0.0298234	+	0.569124i
$131$	9.69942	+	4.01763i	0.847442	+	0.351022i	0.763783	−	0.645473i	$-0.223340\pi$
$131$	9.69942	+	4.01763i	0.847442	+	0.351022i	0.0836584	+	0.996494i	$0.473340\pi$
$132$	−9.90944	−	2.20655i	−0.862506	−	0.192056i
$133$	11.4825	−	9.81918i	0.995657	−	0.851431i
$134$	−14.1871	−	6.76680i	−1.22558	−	0.584563i
$135$	−5.34010	−	11.2777i	−0.459602	−	0.970628i
$136$	−1.88400	+	11.8964i	−0.161552	+	1.02011i
$137$	−4.26743	+	4.26743i	−0.364591	+	0.364591i	−0.865500	−	0.500909i	$-0.832999\pi$
$137$	−4.26743	+	4.26743i	−0.364591	+	0.364591i	0.500909	+	0.865500i	$0.332999\pi$
$138$	4.44663	+	19.3431i	0.378522	+	1.64660i
$139$	3.06055	+	7.38883i	0.259593	+	0.626712i	0.998912	−	0.0466431i	$-0.0148523\pi$
$139$	3.06055	+	7.38883i	0.259593	+	0.626712i	−0.739319	+	0.673356i	$0.764852\pi$
$140$	12.4957	+	2.30786i	1.05608	+	0.195049i
$141$	15.9642	+	8.86876i	1.34443	+	0.746885i
$142$	4.96559	+	5.51479i	0.416703	+	0.462791i
$143$			5.60738i			0.468912i
$144$	−4.08323	−	11.2839i	−0.340269	−	0.940328i
$145$	−15.5033			−1.28748
$146$	−1.85802	+	1.67299i	−0.153771	+	0.138457i
$147$	12.0336	−	1.48105i	0.992511	−	0.122155i
$148$	2.60467	+	8.79287i	0.214103	+	0.722770i
$149$	4.76824	+	11.5116i	0.390630	+	0.943063i	0.989803	+	0.142444i	$0.0454961\pi$
$149$	4.76824	+	11.5116i	0.390630	+	0.943063i	−0.599173	+	0.800619i	$0.704504\pi$
$150$	0.420786	+	1.83044i	0.0343570	+	0.149455i
$151$	−8.55055	−	8.55055i	−0.695834	−	0.695834i	0.267675	−	0.963509i	$-0.413745\pi$
$151$	−8.55055	−	8.55055i	−0.695834	−	0.695834i	−0.963509	+	0.267675i	$0.913745\pi$
$152$	13.7716	+	8.43894i	1.11702	+	0.684488i
$153$	−10.8468	+	6.74945i	−0.876913	+	0.545661i
$154$	10.8726	+	1.42455i	0.876142	+	0.114793i
$155$	−15.5103	+	6.42456i	−1.24581	+	0.516033i
$156$	−5.59333	+	3.55602i	−0.447824	+	0.284710i
$157$	0.936786	−	2.26160i	0.0747637	−	0.180496i	−0.882079	−	0.471101i	$-0.843857\pi$
$157$	0.936786	−	2.26160i	0.0747637	−	0.180496i	0.956843	+	0.290605i	$0.0938567\pi$
$158$	−1.24621	+	23.7817i	−0.0991433	+	1.89197i
$159$	12.1352	+	1.39422i	0.962385	+	0.110569i
$160$	1.77350	+	13.4682i	0.140207	+	1.06475i
$161$	−6.63722	−	20.3846i	−0.523086	−	1.60653i
$162$	6.21247	−	11.1088i	0.488098	−	0.872789i
$163$	−1.89661	−	0.785602i	−0.148554	−	0.0615331i	0.307168	−	0.951655i	$-0.400619\pi$
$163$	−1.89661	−	0.785602i	−0.148554	−	0.0615331i	−0.455722	+	0.890122i	$0.650619\pi$
$164$	0.235702	+	0.291062i	0.0184053	+	0.0227281i
$165$	3.34890	+	11.7207i	0.260711	+	0.912453i
$166$	−4.06595	+	8.52456i	−0.315579	+	0.661634i
$167$	−12.3650	+	12.3650i	−0.956829	+	0.956829i	−0.999106	−	0.0422768i	$-0.986539\pi$
$167$	−12.3650	+	12.3650i	−0.956829	+	0.956829i	0.0422768	+	0.999106i	$0.486539\pi$
$168$	5.47411	+	11.7488i	0.422337	+	0.906439i
$169$	−6.60375	−	6.60375i	−0.507981	−	0.507981i
$170$	13.6325	−	4.82762i	1.04557	−	0.370262i
$171$	2.79563	+	16.9017i	0.213787	+	1.29250i
$172$	1.68830	−	0.500117i	0.128731	−	0.0381335i
$173$	−8.67738	+	20.9490i	−0.659729	+	1.59273i	0.138494	+	0.990363i	$0.455774\pi$
$173$	−8.67738	+	20.9490i	−0.659729	+	1.59273i	−0.798223	+	0.602363i	$0.794226\pi$
$174$	−9.17101	−	12.8828i	−0.695253	−	0.976643i
$175$	−0.628081	−	1.92900i	−0.0474785	−	0.145818i
$176$	2.13654	+	11.5263i	0.161048	+	0.868830i
$177$	3.22866	+	0.370942i	0.242681	+	0.0278817i
$178$	13.3185	−	11.9922i	0.998267	−	0.898854i
$179$	−11.9539	−	4.95147i	−0.893478	−	0.370091i	−0.111769	−	0.993734i	$-0.535652\pi$
$179$	−11.9539	−	4.95147i	−0.893478	−	0.370091i	−0.781709	+	0.623644i	$0.785652\pi$
$180$	−9.56753	+	10.7734i	−0.713122	+	0.803001i
$181$	0.141925	+	0.342638i	0.0105492	+	0.0254681i	0.929066	−	0.369913i	$-0.120613\pi$
$181$	0.141925	+	0.342638i	0.0105492	+	0.0254681i	−0.918517	+	0.395381i	$0.870613\pi$
$182$	5.67697	−	4.36169i	0.420805	−	0.323310i
$183$	11.9472	+	15.0488i	0.883164	+	1.11244i
$184$	18.5409	−	13.4712i	1.36685	−	0.993112i
$185$	7.78604	−	7.78604i	0.572441	−	0.572441i
$186$	−14.5137	−	9.08811i	−1.06420	−	0.666372i
$187$	11.5301	−	4.77591i	0.843163	−	0.349249i
$188$	2.20400	−	20.9719i	0.160744	−	1.52954i
$189$	−5.61947	+	12.5468i	−0.408756	+	0.912644i
$190$	1.01486	−	19.3667i	0.0736255	−	1.40501i
$191$		−	11.7754i		−	0.852036i	−0.904715	−	0.426018i	$-0.859916\pi$
$191$		−	11.7754i		−	0.852036i	0.904715	−	0.426018i	$-0.140084\pi$
$192$	−10.1425	+	9.44083i	−0.731973	+	0.681333i
$193$	−9.35365			−0.673290			−0.336645	−	0.941632i	$-0.609292\pi$
$193$	−9.35365			−0.673290			−0.336645	+	0.941632i	$0.609292\pi$
$194$	0.727843	−	13.8895i	0.0522561	−	0.997211i
$195$	6.95684	+	3.86481i	0.498190	+	0.276765i
$196$	−7.01504	−	12.1157i	−0.501074	−	0.865404i
$197$	−3.12621	+	1.29492i	−0.222733	+	0.0922592i	−0.491260	−	0.871013i	$-0.663463\pi$
$197$	−3.12621	+	1.29492i	−0.222733	+	0.0922592i	0.268526	+	0.963272i	$0.413463\pi$
$198$	−7.75848	+	9.71621i	−0.551371	+	0.690501i
$199$	−8.24918	−	8.24918i	−0.584769	−	0.584769i	0.351441	−	0.936210i	$-0.385692\pi$
$199$	−8.24918	−	8.24918i	−0.584769	−	0.584769i	−0.936210	+	0.351441i	$0.885692\pi$
$200$	1.75453	−	1.27478i	0.124064	−	0.0901409i
$201$	−15.0772	+	11.9697i	−1.06346	+	0.844280i
$202$	−2.11847	−	5.98228i	−0.149055	−	0.420912i
$203$	11.1011	+	12.9815i	0.779142	+	0.911123i
$204$	12.0760	+	8.47245i	0.845487	+	0.593190i
$205$	0.172093	−	0.415468i	0.0120195	−	0.0290176i
$206$	18.9524	+	21.0485i	1.32047	+	1.46652i
$207$	23.6749	+	5.51281i	1.64552	+	0.383167i
$208$	6.30744	+	4.33478i	0.437342	+	0.300563i
$209$		−	16.7354i		−	1.15761i
$210$	9.26120	−	12.5074i	0.639083	−	0.863091i
$211$	−9.89616	+	23.8915i	−0.681280	+	1.64476i	0.0803686	+	0.996765i	$0.474390\pi$
$211$	−9.89616	+	23.8915i	−0.681280	+	1.64476i	−0.761649	+	0.647990i	$0.775610\pi$
$212$	−4.00610	−	13.5238i	−0.275140	−	0.928820i
$213$	8.73901	−	2.49696i	0.598787	−	0.171089i
$214$	−0.552589	−	1.56043i	−0.0377742	−	0.106669i
$215$	−1.49498	−	1.49498i	−0.101957	−	0.101957i
$216$	−14.6121	−	1.57732i	−0.994224	−	0.107323i
$217$	16.4856	+	8.38704i	1.11911	+	0.569350i
$218$	0.494976	−	1.03775i	0.0335240	−	0.0702855i
$219$	0.841265	+	2.94431i	0.0568474	+	0.198958i
$220$	10.9386	−	8.85810i	0.737480	−	0.597213i
$221$	3.11805	−	7.52763i	0.209743	−	0.506363i
$222$	11.0758	+	1.86412i	0.743359	+	0.125112i
$223$			8.21873i			0.550367i	0.961392	+	0.275184i	$0.0887386\pi$
$223$			8.21873i			0.550367i	−0.961392	+	0.275184i	$0.911261\pi$
$224$	10.0075	−	11.1288i	0.668653	−	0.743575i
$225$	2.24036	+	0.521678i	0.149358	+	0.0347785i
$226$	−11.7766	−	0.617121i	−0.783369	−	0.0410502i
$227$	24.1719	+	10.0123i	1.60434	+	0.664540i	0.992021	−	0.126069i	$-0.0402361\pi$
$227$	24.1719	+	10.0123i	1.60434	+	0.664540i	0.612321	+	0.790609i	$0.290236\pi$
$228$	16.6935	−	10.6131i	1.10555	−	0.702868i
$229$	−0.135918	+	0.0562990i	−0.00898170	+	0.00372034i	−0.387170	−	0.922008i	$-0.626547\pi$
$229$	−0.135918	+	0.0562990i	−0.00898170	+	0.00372034i	0.378188	+	0.925729i	$0.376547\pi$
$230$	−24.8373	−	11.8466i	−1.63772	−	0.781142i
$231$	7.41619	−	11.1967i	0.487949	−	0.736687i
$232$	−9.54063	+	15.5695i	−0.626373	+	1.02219i
$233$	2.76896	−	2.76896i	0.181401	−	0.181401i	−0.610565	−	0.791966i	$-0.709058\pi$
$233$	2.76896	−	2.76896i	0.181401	−	0.181401i	0.791966	+	0.610565i	$0.209058\pi$
$234$	0.903784	+	8.06716i	0.0590822	+	0.527367i
$235$	−23.3924	+	9.68946i	−1.52595	+	0.632071i
$236$	−1.06585	−	3.59812i	−0.0693812	−	0.234217i
$237$	25.4962	+	14.1642i	1.65616	+	0.920063i
$238$	−13.8039	−	7.95824i	−0.894771	−	0.515856i
$239$	0.455487			0.0294630			0.0147315	−	0.999891i	$-0.495311\pi$
$239$	0.455487			0.0294630			0.0147315	+	0.999891i	$0.495311\pi$
$240$	15.7728	+	5.29366i	1.01813	+	0.341704i
$241$	8.11530			0.522752			0.261376	−	0.965237i	$-0.415824\pi$
$241$	8.11530			0.522752			0.261376	+	0.965237i	$0.415824\pi$
$242$	−2.53405	+	2.28170i	−0.162895	+	0.146673i
$243$	−8.88091	−	12.8113i	−0.569711	−	0.821845i
$244$	10.5866	−	19.4986i	0.677736	−	1.24827i
$245$	−8.76550	+	14.3436i	−0.560007	+	0.916376i
$246$	0.447043	−	0.102767i	0.0285024	−	0.00655219i
$247$	−7.72587	−	7.72587i	−0.491585	−	0.491585i
$248$	−3.09293	+	19.5301i	−0.196401	+	1.24016i
$249$	7.19221	+	9.05936i	0.455788	+	0.574114i
$250$	12.9761	+	6.18917i	0.820678	+	0.391438i
$251$	−5.45889	−	13.1789i	−0.344562	−	0.831847i	−0.997242	−	0.0742132i	$-0.976355\pi$
$251$	−5.45889	−	13.1789i	−0.344562	−	0.831847i	0.652680	−	0.757633i	$-0.273645\pi$
$252$	15.8717	+	0.297025i	0.999825	+	0.0187108i
$253$	−21.9389	−	9.08740i	−1.37929	−	0.571320i
$254$	10.6234	+	0.556690i	0.666572	+	0.0349298i
$255$	2.02168	−	17.5966i	0.126603	−	1.10194i
$256$	14.6170	+	6.50714i	0.913563	+	0.406696i
$257$	−1.92294			−0.119950			−0.0599748	−	0.998200i	$-0.519102\pi$
$257$	−1.92294			−0.119950			−0.0599748	+	0.998200i	$0.519102\pi$
$258$	0.357925	−	2.12664i	0.0222835	−	0.132399i
$259$	−12.0947	−	0.944388i	−0.751527	−	0.0586814i
$260$	0.960457	−	9.13911i	0.0595650	−	0.566784i
$261$	−19.1082	+	3.16060i	−1.18277	+	0.195636i
$262$	−13.4009	−	6.39182i	−0.827912	−	0.394888i
$263$	−0.263735	−	0.263735i	−0.0162626	−	0.0162626i	0.698929	−	0.715191i	$-0.253660\pi$
$263$	−0.263735	−	0.263735i	−0.0162626	−	0.0162626i	−0.715191	+	0.698929i	$0.753660\pi$
$264$	13.8316	+	3.84962i	0.851274	+	0.236928i
$265$	−11.9753	+	11.9753i	−0.735635	+	0.735635i
$266$	−16.9431	+	13.0176i	−1.03885	+	0.798161i
$267$	−6.03031	−	21.1052i	−0.369049	−	1.29162i
$268$	19.5353	+	10.6065i	1.19331	+	0.647897i
$269$	6.39834	−	15.4470i	0.390114	−	0.941818i	−0.599801	−	0.800150i	$-0.704753\pi$
$269$	6.39834	−	15.4470i	0.390114	−	0.941818i	0.989914	−	0.141668i	$-0.0452466\pi$
$270$	6.70707	+	16.3224i	0.408179	+	0.993349i
$271$	−2.63605			−0.160128			−0.0800642	−	0.996790i	$-0.525513\pi$
$271$	−2.63605			−0.160128			−0.0800642	+	0.996790i	$0.525513\pi$
$272$	3.54115	−	16.6616i	0.214713	−	1.01026i
$273$	−1.74525	−	8.59259i	−0.105628	−	0.520047i
$274$	6.34261	−	5.71098i	0.383171	−	0.345013i
$275$	−2.07609	−	0.859943i	−0.125193	−	0.0518565i
$276$	−4.84835	−	27.6469i	−0.291837	−	1.66415i
$277$	−14.0371	+	5.81435i	−0.843406	+	0.349350i	−0.762196	−	0.647347i	$-0.775879\pi$
$277$	−14.0371	+	5.81435i	−0.843406	+	0.349350i	−0.0812107	+	0.996697i	$0.525879\pi$
$278$	−3.77553	−	10.6616i	−0.226441	−	0.639438i
$279$	−17.8070	+	11.0804i	−1.06607	+	0.663367i
$280$	−17.4766	−	4.18409i	−1.04443	−	0.250047i
$281$	3.81481	+	3.81481i	0.227572	+	0.227572i	0.811678	−	0.584105i	$-0.198555\pi$
$281$	3.81481	+	3.81481i	0.227572	+	0.227572i	−0.584105	+	0.811678i	$0.698555\pi$
$282$	−21.8895	−	13.7066i	−1.30350	−	0.816216i
$283$	−21.5873	+	8.94174i	−1.28323	+	0.531531i	−0.916961	−	0.398977i	$-0.869365\pi$
$283$	−21.5873	+	8.94174i	−1.28323	+	0.531531i	−0.366269	+	0.930509i	$0.619365\pi$
$284$	−6.60466	−	8.15589i	−0.391914	−	0.483963i
$285$	−20.7629	−	11.5347i	−1.22989	−	0.683254i
$286$	0.414982	−	7.91916i	0.0245384	−	0.468270i
$287$	−0.471113	+	0.153394i	−0.0278089	+	0.00905457i
$288$	4.93157	+	16.2382i	0.290595	+	0.956846i
$289$	−1.13428			−0.0667223
$290$	21.8950	+	1.14735i	1.28572	+	0.0673744i
$291$	−14.8909	−	8.27252i	−0.872921	−	0.484944i
$292$	2.74785	−	2.22521i	0.160806	−	0.130221i
$293$	−1.47918	−	3.57106i	−0.0864147	−	0.208624i	0.874765	−	0.484548i	$-0.161016\pi$
$293$	−1.47918	−	3.57106i	−0.0864147	−	0.208624i	−0.961179	+	0.275925i	$0.911016\pi$
$294$	−17.1043	+	1.20109i	−0.997544	+	0.0700489i
$295$	−3.18611	+	3.18611i	−0.185502	+	0.185502i
$296$	−3.02779	−	12.6107i	−0.175987	−	0.732983i
$297$	6.51703	+	13.7632i	0.378156	+	0.798624i
$298$	−5.88215	−	16.6104i	−0.340744	−	0.962213i
$299$	−14.3233	+	5.93289i	−0.828335	+	0.343108i
$300$	−0.458801	−	2.61623i	−0.0264889	−	0.151048i
$301$	−0.181330	+	2.32227i	−0.0104517	+	0.133853i
$302$	11.4429	+	12.7085i	0.658467	+	0.731294i
$303$	−7.72181	−	0.887161i	−0.443607	−	0.0509661i
$304$	−18.8248	−	12.9373i	−1.07967	−	0.742005i
$305$	−26.6402			−1.52541
$306$	15.8182	−	8.72935i	0.904266	−	0.499024i
$307$	17.5995	+	7.28995i	1.00446	+	0.416059i	0.823429	−	0.567419i	$-0.192058\pi$
$307$	17.5995	+	7.28995i	1.00446	+	0.416059i	0.181027	+	0.983478i	$0.442058\pi$
$308$	−15.2497	−	2.81650i	−0.868934	−	0.160485i
$309$	33.3545	−	9.53025i	1.89747	−	0.542157i
$310$	22.3802	−	7.92539i	1.27111	−	0.450132i
$311$	−5.93906	−	5.93906i	−0.336773	−	0.336773i	0.518378	−	0.855152i	$-0.326536\pi$
$311$	−5.93906	−	5.93906i	−0.336773	−	0.336773i	−0.855152	+	0.518378i	$0.826536\pi$
$312$	8.16249	−	4.60814i	0.462110	−	0.260885i
$313$	−15.8975	−	15.8975i	−0.898577	−	0.898577i	0.0967329	−	0.995310i	$-0.469161\pi$
$313$	−15.8975	−	15.8975i	−0.898577	−	0.898577i	−0.995310	+	0.0967329i	$0.969161\pi$
$314$	−1.49037	+	3.12468i	−0.0841067	+	0.176336i
$315$	−8.77973	−	16.9181i	−0.494682	−	0.953228i
$316$	3.51999	−	33.4940i	0.198015	−	1.88419i
$317$	6.55611	−	15.8278i	0.368228	−	0.888981i	−0.625813	−	0.779973i	$-0.715233\pi$
$317$	6.55611	−	15.8278i	0.368228	−	0.888981i	0.994041	−	0.109008i	$-0.0347673\pi$
$318$	−17.0351	−	2.86710i	−0.955280	−	0.160779i
$319$	18.9202			1.05933
$320$	−1.50794	−	19.1520i	−0.0842962	−	1.07063i
$321$	−2.01418	−	0.231409i	−0.112420	−	0.0129160i
$322$	7.86499	+	29.2799i	0.438299	+	1.63170i
$323$	−9.30592	+	22.4665i	−0.517795	+	1.25007i
$324$	−9.59585	+	15.2289i	−0.533103	+	0.846051i
$325$	−1.35541	+	0.561430i	−0.0751848	+	0.0311425i
$326$	2.62040	+	1.24985i	0.145130	+	0.0692227i
$327$	−0.875558	−	1.10286i	−0.0484184	−	0.0609882i
$328$	−0.311336	−	0.428503i	−0.0171907	−	0.0236601i
$329$	24.8634	+	12.6493i	1.37076	+	0.697376i
$330$	−3.86216	−	16.8007i	−0.212605	−	0.924846i
$331$	8.12112	−	3.36388i	0.446377	−	0.184895i	−0.148160	−	0.988963i	$-0.547335\pi$
$331$	8.12112	−	3.36388i	0.446377	−	0.184895i	0.594537	+	0.804068i	$0.297335\pi$
$332$	6.37311	−	11.7381i	0.349770	−	0.644213i
$333$	8.00914	−	11.1838i	0.438898	−	0.612866i
$334$	18.3778	−	16.5476i	1.00559	−	0.905447i
$335$		−	26.6904i		−	1.45825i
$336$	−6.86146	−	16.9977i	−0.374324	−	0.927298i
$337$			0.920733i			0.0501555i	0.999686	+	0.0250778i	$0.00798334\pi$
$337$			0.920733i			0.0501555i	−0.999686	+	0.0250778i	$0.992017\pi$
$338$	8.83760	+	9.81504i	0.480702	+	0.533868i
$339$	−7.01407	+	12.6256i	−0.380952	+	0.685731i
$340$	−19.6102	+	5.80904i	−1.06351	+	0.315039i
$341$	18.9287	−	7.84051i	1.02504	−	0.424587i
$342$	−2.69737	−	24.0767i	−0.145857	−	1.30192i
$343$	18.2869	−	2.93095i	0.987398	−	0.158256i
$344$	−2.42135	+	0.581358i	−0.130551	+	0.0313447i
$345$	−26.3955	+	20.9553i	−1.42109	+	1.12820i
$346$	13.8052	−	28.9436i	0.742173	−	1.55602i
$347$	19.2030	−	7.95414i	1.03087	−	0.427001i	0.197844	−	0.980233i	$-0.436606\pi$
$347$	19.2030	−	7.95414i	1.03087	−	0.427001i	0.833027	+	0.553233i	$0.186606\pi$
$348$	11.9986	+	18.8728i	0.643192	+	1.01169i
$349$	5.17842	−	12.5018i	0.277194	−	0.669206i	−0.722561	−	0.691307i	$-0.757035\pi$
$349$	5.17842	−	12.5018i	0.277194	−	0.669206i	0.999756	+	0.0221004i	$0.00703535\pi$
$350$	0.744265	+	2.77076i	0.0397827	+	0.148103i
$351$	9.36235	+	3.34520i	0.499725	+	0.178553i
$352$	−2.16437	−	16.4365i	−0.115361	−	0.876067i
$353$	−7.85492			−0.418075			−0.209038	−	0.977908i	$-0.567033\pi$
$353$	−7.85492			−0.418075			−0.209038	+	0.977908i	$0.567033\pi$
$354$	−4.53231	−	0.762814i	−0.240890	−	0.0405431i
$355$	−4.82224	+	11.6419i	−0.255938	+	0.617888i
$356$	−19.6970	+	15.9506i	−1.04394	+	0.845383i
$357$	−16.1819	+	10.9071i	−0.856438	+	0.577267i
$358$	16.5158	+	7.87751i	0.872886	+	0.416339i
$359$	8.21247	+	8.21247i	0.433438	+	0.433438i	0.889796	−	0.456358i	$-0.150847\pi$
$359$	8.21247	+	8.21247i	0.433438	+	0.433438i	−0.456358	+	0.889796i	$0.650847\pi$
$360$	14.3093	−	14.5069i	0.754166	−	0.764583i
$361$	9.62308	+	9.62308i	0.506478	+	0.506478i
$362$	−0.175080	−	0.494403i	−0.00920201	−	0.0259852i
$363$	1.14736	+	4.01559i	0.0602206	+	0.210764i
$364$	−8.34024	+	5.73978i	−0.437147	+	0.300846i
$365$	−3.92234	−	1.62469i	−0.205305	−	0.0850400i
$366$	−15.7591	−	22.1372i	−0.823739	−	1.15713i
$367$	−16.8850			−0.881390			−0.440695	−	0.897657i	$-0.645268\pi$
$367$	−16.8850			−0.881390			−0.440695	+	0.897657i	$0.645268\pi$
$368$	−27.1818	+	17.6529i	−1.41695	+	0.920223i
$369$	0.127408	−	0.547157i	0.00663258	−	0.0284838i
$370$	−11.5722	+	10.4198i	−0.601613	+	0.541700i
$371$	18.6022	+	1.45251i	0.965776	+	0.0754106i
$372$	19.8248	+	13.9090i	1.02787	+	0.721149i
$373$	30.7759	−	12.7478i	1.59351	−	0.660055i	0.603035	−	0.797715i	$-0.293958\pi$
$373$	30.7759	−	12.7478i	1.59351	−	0.660055i	0.990480	+	0.137659i	$0.0439578\pi$
$374$	−16.6371	+	5.89161i	−0.860284	+	0.304648i
$375$	13.7901	−	10.9480i	0.712120	−	0.565351i
$376$	−4.66472	+	29.4551i	−0.240565	+	1.51903i
$377$	8.73447	−	8.73447i	0.449848	−	0.449848i
$378$	8.86479	−	17.3036i	0.455955	−	0.890003i
$379$	−4.28723	−	10.3503i	−0.220220	−	0.531658i	0.774700	−	0.632329i	$-0.217901\pi$
$379$	−4.28723	−	10.3503i	−0.220220	−	0.531658i	−0.994920	+	0.100671i	$0.967901\pi$
$380$	−2.86652	+	27.2760i	−0.147049	+	1.39923i
$381$	6.32723	−	11.3893i	0.324154	−	0.583492i
$382$	−0.871453	+	16.6301i	−0.0445874	+	0.850869i
$383$	16.2526			0.830469			0.415234	−	0.909714i	$-0.363700\pi$
$383$	16.2526			0.830469			0.415234	+	0.909714i	$0.363700\pi$
$384$	15.0227	−	12.5824i	0.766625	−	0.642095i
$385$	5.76482	+	17.7052i	0.293802	+	0.902342i
$386$	13.2099	+	0.692230i	0.672368	+	0.0352336i
$387$	−2.14736	−	1.53781i	−0.109157	−	0.0781715i
$388$	−2.05583	+	19.5620i	−0.104369	+	0.993110i
$389$	20.3321	−	8.42184i	1.03088	−	0.427004i	0.197850	−	0.980232i	$-0.436604\pi$
$389$	20.3321	−	8.42184i	1.03088	−	0.427004i	0.833030	+	0.553228i	$0.186604\pi$
$390$	−9.53895	−	5.97303i	−0.483024	−	0.302456i
$391$	24.3988	+	24.3988i	1.23390	+	1.23390i
$392$	9.01054	+	17.6298i	0.455101	+	0.890440i
$393$	−14.2417	+	11.3064i	−0.718396	+	0.570334i
$394$	4.51091	−	1.59742i	0.227256	−	0.0804770i
$395$	−37.3598	+	15.4749i	−1.87977	+	0.778628i
$396$	11.6762	−	13.1478i	0.586750	−	0.660701i
$397$	2.19171	+	0.907836i	0.109999	+	0.0455630i	0.437004	−	0.899460i	$-0.356040\pi$
$397$	2.19171	+	0.907836i	0.109999	+	0.0455630i	−0.327005	+	0.945022i	$0.606040\pi$
$398$	11.0396	+	12.2606i	0.553366	+	0.614568i
$399$	5.20877	+	25.6449i	0.260765	+	1.28385i
$400$	−2.57222	+	1.67050i	−0.128611	+	0.0835251i
$401$	25.6786			1.28233			0.641163	−	0.767405i	$-0.278452\pi$
$401$	25.6786			1.28233			0.641163	+	0.767405i	$0.278452\pi$
$402$	22.1789	−	15.7888i	1.10619	−	0.787472i
$403$	5.11882	−	12.3579i	0.254987	−	0.615593i
$404$	2.54914	+	8.60541i	0.126825	+	0.428135i
$405$	21.5672	+	1.40073i	1.07169	+	0.0696027i
$406$	−14.7171	−	19.1550i	−0.730395	−	0.950647i
$407$	−9.50204	+	9.50204i	−0.470999	+	0.470999i
$408$	−16.4276	−	12.8591i	−0.813286	−	0.636622i
$409$	1.20802	+	1.20802i	0.0597328	+	0.0597328i	0.736342	−	0.676609i	$-0.236551\pi$
$409$	1.20802	+	1.20802i	0.0597328	+	0.0597328i	−0.676609	+	0.736342i	$0.736551\pi$
$410$	−0.273790	+	0.574020i	−0.0135215	+	0.0283488i
$411$	−2.87178	−	10.0508i	−0.141654	−	0.495770i
$412$	−25.2083	−	31.1289i	−1.24192	−	1.53361i
$413$	4.94924	+	0.386451i	0.243536	+	0.0190160i
$414$	−33.0276	−	9.53770i	−1.62322	−	0.468752i
$415$	−16.0374			−0.787244
$416$	−8.58705	−	6.58869i	−0.421015	−	0.323037i
$417$	−13.7617	−	1.58109i	−0.673915	−	0.0774263i
$418$	−1.23853	+	23.6350i	−0.0605783	+	1.15603i
$419$	−17.7515	−	7.35293i	−0.867220	−	0.359214i	−0.0956929	−	0.995411i	$-0.530507\pi$
$419$	−17.7515	−	7.35293i	−0.867220	−	0.359214i	−0.771527	+	0.636197i	$0.780507\pi$
$420$	−14.0050	+	16.9785i	−0.683374	+	0.828465i
$421$	2.07380	+	5.00660i	0.101071	+	0.244007i	0.966324	−	0.257329i	$-0.0828423\pi$
$421$	2.07380	+	5.00660i	0.101071	+	0.244007i	−0.865253	+	0.501335i	$0.832842\pi$
$422$	15.7442	−	33.0089i	0.766417	−	1.60685i
$423$	−26.8563	+	16.7114i	−1.30580	+	0.812535i
$424$	4.65687	+	19.3959i	0.226158	+	0.941946i
$425$	2.30886	+	2.30886i	0.111996	+	0.111996i
$426$	−12.5267	+	2.87965i	−0.606920	+	0.139520i
$427$	19.0756	+	22.3068i	0.923132	+	1.07950i
$428$	0.664925	+	2.24466i	0.0321404	+	0.108500i
$429$	−8.49009	−	4.71660i	−0.409906	−	0.227720i
$430$	2.00068	+	2.22196i	0.0964814	+	0.107152i
$431$	23.8734			1.14994			0.574970	−	0.818175i	$-0.305014\pi$
$431$	23.8734			1.14994			0.574970	+	0.818175i	$0.305014\pi$
$432$	20.5195	+	3.30900i	0.987246	+	0.159204i
$433$	−30.2072			−1.45167			−0.725833	−	0.687871i	$-0.758546\pi$
$433$	−30.2072			−1.45167			−0.725833	+	0.687871i	$0.758546\pi$
$434$	−22.6615	−	13.0649i	−1.08778	−	0.627133i
$435$	13.0405	−	23.4735i	0.625244	−	1.12547i
$436$	−0.775842	+	1.42896i	−0.0371561	+	0.0684349i
$437$	42.7482	−	17.7069i	2.04493	−	0.847036i
$438$	−0.970201	−	4.22044i	−0.0463580	−	0.201660i
$439$	3.35260	−	3.35260i	0.160011	−	0.160011i	−0.622561	−	0.782572i	$-0.713908\pi$
$439$	3.35260	−	3.35260i	0.160011	−	0.160011i	0.782572	+	0.622561i	$0.213908\pi$
$440$	−16.1039	+	11.7006i	−0.767722	+	0.557802i
$441$	−7.87949	+	19.4657i	−0.375214	+	0.926938i
$442$	−4.96064	+	10.4003i	−0.235953	+	0.494694i
$443$	7.14313	−	2.95878i	0.339380	−	0.140576i	−0.206483	−	0.978450i	$-0.566202\pi$
$443$	7.14313	−	2.95878i	0.339380	−	0.140576i	0.545863	+	0.837874i	$0.316202\pi$
$444$	−15.5041	−	3.45233i	−0.735794	−	0.163841i
$445$	28.1159	+	11.6460i	1.33282	+	0.552073i
$446$	0.608239	−	11.6071i	0.0288009	−	0.549613i
$447$	−21.4403	−	2.46329i	−1.01409	−	0.116509i
$448$	−14.9569	+	14.9763i	−0.706648	+	0.707565i
$449$			4.67146i			0.220460i	0.993906	+	0.110230i	$0.0351587\pi$
$449$			4.67146i			0.220460i	−0.993906	+	0.110230i	$0.964841\pi$
$450$	−3.12540	−	0.902555i	−0.147333	−	0.0425468i
$451$	−0.210021	+	0.507036i	−0.00988950	+	0.0238754i
$452$	16.5862	+	1.74309i	0.780147	+	0.0819880i
$453$	20.1386	−	5.75411i	0.946192	−	0.270352i
$454$	−33.3964	−	15.9290i	−1.56737	−	0.747586i
$455$	10.8349	+	5.51227i	0.507948	+	0.258419i
$456$	−24.3612	+	13.7532i	−1.14082	+	0.644051i
$457$	−4.88789	−	4.88789i	−0.228646	−	0.228646i	0.583481	−	0.812127i	$-0.301690\pi$
$457$	−4.88789	−	4.88789i	−0.228646	−	0.228646i	−0.812127	+	0.583481i	$0.801690\pi$
$458$	0.196120	−	0.0694510i	0.00916409	−	0.00324523i
$459$	−1.09559	−	22.1003i	−0.0511378	−	1.03156i
$460$	34.2004	+	18.5688i	1.59460	+	0.865774i
$461$	−7.05310	+	17.0277i	−0.328496	+	0.793058i	0.670209	+	0.742172i	$0.266204\pi$
$461$	−7.05310	+	17.0277i	−0.328496	+	0.793058i	−0.998704	+	0.0508859i	$0.983796\pi$
$462$	−11.3023	+	15.2639i	−0.525832	+	0.710143i
$463$			6.32769i			0.294073i	0.989131	+	0.147036i	$0.0469735\pi$
$463$			6.32769i			0.294073i	−0.989131	+	0.147036i	$0.953027\pi$
$464$	14.6262	−	21.2823i	0.679006	−	0.988007i
$465$	3.31895	−	28.8880i	0.153912	−	1.33965i
$466$	−4.11546	+	3.70561i	−0.190645	+	0.171659i
$467$	9.63693	−	23.2656i	0.445944	−	1.07660i	−0.527884	−	0.849317i	$-0.677014\pi$
$467$	9.63693	−	23.2656i	0.445944	−	1.07660i	0.973828	−	0.227288i	$-0.0729857\pi$
$468$	−0.679371	−	11.4599i	−0.0314039	−	0.529736i
$469$	−22.3489	+	19.1115i	−1.03197	+	0.882488i
$470$	33.7536	−	11.9530i	1.55694	−	0.551351i
$471$	2.63631	+	3.32071i	0.121475	+	0.153010i
$472$	1.23900	+	5.16041i	0.0570294	+	0.237527i
$473$	1.82446	+	1.82446i	0.0838889	+	0.0838889i
$474$	−34.9594	−	21.8906i	−1.60574	−	1.00547i
$475$	4.04527	−	1.67561i	0.185610	−	0.0768821i
$476$	18.9059	+	12.2608i	0.866550	+	0.561973i
$477$	−12.3184	+	17.2011i	−0.564021	+	0.787585i
$478$	−0.643273	−	0.0337090i	−0.0294226	−	0.00154181i
$479$	−38.5766			−1.76261			−0.881304	−	0.472549i	$-0.843334\pi$
$479$	−38.5766			−1.76261			−0.881304	+	0.472549i	$0.843334\pi$
$480$	−21.8838	−	8.64339i	−0.998855	−	0.394515i
$481$			8.77320i			0.400024i
$482$	−11.4610	−	0.600584i	−0.522036	−	0.0273558i
$483$	36.4470	+	7.09697i	1.65840	+	0.322923i
$484$	3.74764	−	3.03485i	0.170347	−	0.137948i
$485$	21.8198	−	9.03804i	0.990784	−	0.410396i
$486$	11.5942	+	18.7503i	0.525922	+	0.850533i
$487$	30.8230	−	30.8230i	1.39672	−	1.39672i	0.587492	−	0.809230i	$-0.300115\pi$
$487$	30.8230	−	30.8230i	1.39672	−	1.39672i	0.809230	−	0.587492i	$-0.199885\pi$
$488$	−16.3942	+	26.7539i	−0.742130	+	1.21109i
$489$	2.78479	−	2.21084i	0.125933	−	0.0999778i
$490$	13.4408	−	19.6084i	0.607194	−	0.885815i
$491$	−0.672892	−	1.62451i	−0.0303672	−	0.0733129i	0.907968	−	0.419039i	$-0.137633\pi$
$491$	−0.672892	−	1.62451i	−0.0303672	−	0.0733129i	−0.938336	+	0.345726i	$0.887633\pi$
$492$	−0.638954	+	0.112051i	−0.0288063	+	0.00505167i
$493$	−25.3994	−	10.5208i	−1.14393	−	0.473833i
$494$	10.3393	+	11.4828i	0.465187	+	0.516637i
$495$	−20.5631	−	4.78820i	−0.924242	−	0.215214i
$496$	5.81341	−	27.3529i	0.261030	−	1.22818i
$497$	13.2011	−	4.29828i	0.592152	−	0.192804i
$498$	−9.48694	−	13.3266i	−0.425120	−	0.597179i
$499$	−11.3021	+	27.2857i	−0.505953	+	1.22148i	0.440242	+	0.897879i	$0.354893\pi$
$499$	−11.3021	+	27.2857i	−0.505953	+	1.22148i	−0.946195	+	0.323598i	$0.895107\pi$
$500$	−17.8677	−	9.70113i	−0.799069	−	0.433848i
$501$	−8.32102	−	29.1224i	−0.371756	−	1.30109i
$502$	6.73414	+	19.0163i	0.300559	+	0.848738i
$503$	22.4266	+	22.4266i	0.999955	+	0.999955i	1.00000		4.54584e-5i	$-1.44699e-5\pi$
$503$	22.4266	+	22.4266i	0.999955	+	0.999955i	−4.54584e−5		1.00000i	$0.500014\pi$
$504$	−22.3933	−	1.59409i	−0.997476	−	0.0710064i
$505$	7.62004	−	7.62004i	0.339087	−	0.339087i
$506$	30.3113	+	14.4575i	1.34750	+	0.642716i
$507$	15.5534	−	4.44401i	0.690751	−	0.197365i
$508$	−14.9620	−	1.57240i	−0.663831	−	0.0697640i
$509$	−2.76365	−	1.14474i	−0.122497	−	0.0507398i	0.320593	−	0.947217i	$-0.396118\pi$
$509$	−2.76365	−	1.14474i	−0.122497	−	0.0507398i	−0.443090	+	0.896477i	$0.646118\pi$
$510$	−4.15743	+	24.7017i	−0.184094	+	1.09381i
$511$	1.44816	+	4.44767i	0.0640628	+	0.196753i
$512$	−20.1617	−	10.2716i	−0.891029	−	0.453946i
$513$	−27.9422	−	9.98385i	−1.23368	−	0.440798i
$514$	2.71572	+	0.142310i	0.119785	+	0.00627701i
$515$	−18.4052	+	44.4341i	−0.811031	+	1.95800i
$516$	−0.662874	+	2.97691i	−0.0291814	+	0.131051i
$517$	28.5480	−	11.8250i	1.25554	−	0.520062i
$518$	17.0111	+	2.22882i	0.747426	+	0.0979288i
$519$	−24.4199	−	30.7595i	−1.07191	−	1.35019i
$520$	−2.03278	+	12.8359i	−0.0891434	+	0.562890i
$521$	25.3111	+	25.3111i	1.10890	+	1.10890i	0.993295	+	0.115605i	$0.0368807\pi$
$521$	25.3111	+	25.3111i	1.10890	+	1.10890i	0.115605	+	0.993295i	$0.463119\pi$
$522$	27.2199	−	3.04951i	1.19138	−	0.133474i
$523$	−7.85797	−	18.9708i	−0.343605	−	0.829536i	−0.997345	−	0.0728169i	$-0.976801\pi$
$523$	−7.85797	−	18.9708i	−0.343605	−	0.829536i	0.653740	−	0.756719i	$-0.273199\pi$
$524$	18.4528	+	10.0188i	0.806113	+	0.437672i
$525$	3.44899	+	0.671587i	0.150526	+	0.0293105i
$526$	0.352948	+	0.391984i	0.0153893	+	0.0170913i
$527$	−29.7706			−1.29683
$528$	−19.2491	−	6.46035i	−0.837709	−	0.281151i
$529$		−	42.6549i		−	1.85456i
$530$	17.7986	−	16.0261i	0.773123	−	0.696131i
$531$	−3.27740	+	4.57648i	−0.142227	+	0.198602i
$532$	24.8917	−	17.1306i	1.07919	−	0.742704i
$533$	0.137116	+	0.331028i	0.00593917	+	0.0143384i
$534$	6.95454	+	30.2527i	0.300952	+	1.30916i
$535$	1.98763	−	1.98763i	0.0859328	−	0.0859328i
$536$	−26.8043	−	16.4251i	−1.15777	−	0.709456i
$537$	17.5519	−	13.9345i	0.757422	−	0.601316i
$538$	−10.1794	+	21.3418i	−0.438865	+	0.920112i
$539$	10.6974	−	17.5048i	0.460768	−	0.753986i
$540$	−8.26427	−	23.5481i	−0.355637	−	1.01335i
$541$	−20.5129	−	8.49671i	−0.881917	−	0.365302i	−0.104677	−	0.994506i	$-0.533381\pi$
$541$	−20.5129	−	8.49671i	−0.881917	−	0.365302i	−0.777240	+	0.629204i	$0.783381\pi$
$542$	3.72283	+	0.195084i	0.159909	+	0.00837959i
$543$	−0.638165	−	0.0733190i	−0.0273863	−	0.00314642i
$544$	−6.23414	+	23.2687i	−0.267286	+	0.997637i
$545$	1.95234			0.0836291
$546$	1.82887	+	12.2643i	0.0782685	+	0.524862i
$547$	−30.0885	−	12.4631i	−1.28649	−	0.532883i	−0.368555	−	0.929606i	$-0.620147\pi$
$547$	−30.0885	−	12.4631i	−1.28649	−	0.532883i	−0.917938	+	0.396723i	$0.870147\pi$
$548$	−9.38017	+	7.59608i	−0.400701	+	0.324488i
$549$	−32.8346	+	5.43103i	−1.40135	+	0.231791i
$550$	2.86836	+	1.36812i	0.122307	+	0.0583368i
$551$	−26.0683	+	26.0683i	−1.11055	+	1.11055i
$552$	4.80117	+	39.4039i	0.204351	+	1.67714i
$553$	39.7089	+	20.2020i	1.68860	+	0.859075i
$554$	20.2545	−	7.17263i	0.860532	−	0.304736i
$555$	5.23963	+	18.3380i	0.222410	+	0.778403i
$556$	4.54306	+	15.3365i	0.192669	+	0.650412i
$557$	−20.7782	−	8.60662i	−0.880401	−	0.364674i	−0.103749	−	0.994604i	$-0.533084\pi$
$557$	−20.7782	−	8.60662i	−0.880401	−	0.364674i	−0.776652	+	0.629929i	$0.783084\pi$
$558$	25.9684	−	14.3308i	1.09933	−	0.606670i
$559$	1.68452			0.0712476
$560$	24.3722	+	7.20248i	1.02991	+	0.304360i
$561$	−2.46725	+	21.4748i	−0.104167	+	0.906669i
$562$	−5.10524	−	5.66988i	−0.215352	−	0.239169i
$563$	−1.44517	+	3.48895i	−0.0609067	+	0.147042i	−0.951403	−	0.307949i	$-0.900357\pi$
$563$	−1.44517	+	3.48895i	−0.0609067	+	0.147042i	0.890496	+	0.454991i	$0.150357\pi$
$564$	29.8996	+	20.9775i	1.25900	+	0.883310i
$565$	−7.66314	−	18.5005i	−0.322391	−	0.778320i
$566$	31.1489	−	11.0306i	1.30929	−	0.463651i
$567$	−14.2702	−	19.0620i	−0.599293	−	0.800530i
$568$	8.72401	+	12.0072i	0.366051	+	0.503809i
$569$	0.289498	+	0.289498i	0.0121364	+	0.0121364i	0.713149	−	0.701013i	$-0.247268\pi$
$569$	0.289498	+	0.289498i	0.0121364	+	0.0121364i	−0.701013	+	0.713149i	$0.747268\pi$
$570$	28.4693	+	17.8267i	1.19245	+	0.746679i
$571$	11.7643	+	28.4015i	0.492320	+	1.18857i	0.953536	+	0.301278i	$0.0974132\pi$
$571$	11.7643	+	28.4015i	0.492320	+	1.18857i	−0.461216	+	0.887288i	$0.652587\pi$
$572$	−1.17214	+	11.1533i	−0.0490095	+	0.466344i
$573$	17.8290	+	9.90476i	0.744818	+	0.413777i
$574$	0.676693	−	0.181770i	0.0282446	−	0.00758691i
$575$		−	6.21293i		−	0.259097i
$576$	−5.76300	−	23.2978i	−0.240125	−	0.970742i
$577$			12.4923i			0.520060i	0.965601	+	0.260030i	$0.0837324\pi$
$577$			12.4923i			0.520060i	−0.965601	+	0.260030i	$0.916268\pi$
$578$	1.60191	+	0.0839439i	0.0666309	+	0.00349160i
$579$	7.86775	−	14.1623i	0.326972	−	0.588565i
$580$	−30.8368	−	3.24074i	−1.28043	−	0.134564i
$581$	11.4835	+	13.4287i	0.476415	+	0.557116i
$582$	20.4179	+	12.7851i	0.846347	+	0.529960i
$583$	14.6146	−	14.6146i	0.605273	−	0.605273i
$584$	−4.04540	+	2.93926i	−0.167400	+	0.121627i
$585$	−11.7034	+	7.28245i	−0.483875	+	0.301092i
$586$	1.82473	+	5.15279i	0.0753790	+	0.212860i
$587$	−35.3756	+	14.6531i	−1.46011	+	0.604797i	−0.964579	−	0.263795i	$-0.915026\pi$
$587$	−35.3756	+	14.6531i	−1.46011	+	0.604797i	−0.495529	+	0.868591i	$0.665026\pi$
$588$	24.2449	−	0.430440i	0.999842	−	0.0177510i
$589$	−15.2773	+	36.8827i	−0.629490	+	1.51972i
$590$	4.73546	−	4.26387i	0.194956	−	0.175541i
$591$	0.668959	−	5.82259i	0.0275173	−	0.239509i
$592$	3.34280	+	18.0339i	0.137388	+	0.741189i
$593$			14.6858i			0.603073i	0.953455	+	0.301536i	$0.0974994\pi$
$593$			14.6858i			0.603073i	−0.953455	+	0.301536i	$0.902501\pi$
$594$	−8.18527	−	19.9198i	−0.335846	−	0.817318i
$595$	2.10621	−	26.9740i	0.0863462	−	1.10583i
$596$	7.07794	+	23.8937i	0.289924	+	0.978726i
$597$	19.4288	−	5.55130i	0.795166	−	0.227199i
$598$	20.6675	−	7.31886i	0.845155	−	0.299290i
$599$	−31.1980	+	31.1980i	−1.27472	+	1.27472i	−0.331130	+	0.943585i	$0.607430\pi$
$599$	−31.1980	+	31.1980i	−1.27472	+	1.27472i	−0.943585	+	0.331130i	$0.892570\pi$
$600$	0.454335	+	3.72880i	0.0185482	+	0.152227i
$601$	5.24221	+	5.24221i	0.213834	+	0.213834i	0.805894	−	0.592060i	$-0.201685\pi$
$601$	5.24221	+	5.24221i	0.213834	+	0.213834i	−0.592060	+	0.805894i	$0.701685\pi$
$602$	0.427950	−	3.26626i	0.0174419	−	0.133123i
$603$	−5.44127	−	32.8965i	−0.221586	−	1.33965i
$604$	−15.2201	−	18.7948i	−0.619296	−	0.764750i
$605$	−5.34948	−	2.21583i	−0.217487	−	0.0900861i
$606$	10.8397	+	1.82438i	0.440332	+	0.0741104i
$607$			1.09521i			0.0444533i	0.999753	+	0.0222266i	$0.00707554\pi$
$607$			1.09521i			0.0444533i	−0.999753	+	0.0222266i	$0.992924\pi$
$608$	25.6283	+	19.6642i	1.03937	+	0.797488i
$609$	−28.9928	+	5.88877i	−1.17485	+	0.238625i
$610$	37.6233	+	1.97155i	1.52332	+	0.0798256i
$611$	7.72016	−	18.6381i	0.312324	−	0.754018i
$612$	−22.9857	+	11.1576i	−0.929141	+	0.451020i
$613$	−5.14508	−	12.4213i	−0.207808	−	0.501692i	0.785270	−	0.619154i	$-0.212524\pi$
$613$	−5.14508	−	12.4213i	−0.207808	−	0.501692i	−0.993077	+	0.117462i	$0.962524\pi$
$614$	−24.3158	−	11.5979i	−0.981307	−	0.468053i
$615$	0.484304	+	0.610032i	0.0195290	+	0.0245989i
$616$	21.3284	+	5.10625i	0.859345	+	0.205737i
$617$	15.5531	−	15.5531i	0.626143	−	0.626143i	−0.320952	−	0.947095i	$-0.604003\pi$
$617$	15.5531	−	15.5531i	0.626143	−	0.626143i	0.947095	+	0.320952i	$0.104003\pi$
$618$	−47.8111	+	10.9909i	−1.92324	+	0.442118i
$619$	−0.528903	−	1.27689i	−0.0212584	−	0.0513224i	0.912894	−	0.408197i	$-0.133842\pi$
$619$	−0.528903	−	1.27689i	−0.0212584	−	0.0513224i	−0.934152	+	0.356875i	$0.883842\pi$
$620$	−32.1936	+	9.53656i	−1.29293	+	0.382998i
$621$	−28.2609	+	31.2090i	−1.13407	+	1.25237i
$622$	7.94807	+	8.82712i	0.318688	+	0.353935i
$623$	−10.3806	−	31.8815i	−0.415891	−	1.27731i
$624$	−11.8687	+	5.90389i	−0.475129	+	0.236345i
$625$			28.2459i			1.12984i
$626$	21.2751	+	23.6281i	0.850323	+	0.944369i
$627$	25.3390	+	14.0768i	1.01194	+	0.562175i
$628$	2.33607	−	4.30261i	0.0932191	−	0.171693i
$629$	18.0398	−	7.47231i	0.719292	−	0.297941i
$630$	11.1474	+	24.5428i	0.444121	+	0.977809i
$631$	21.6318	+	21.6318i	0.861148	+	0.861148i	0.991471	−	0.130324i	$-0.0416017\pi$
$631$	21.6318	+	21.6318i	0.861148	+	0.861148i	−0.130324	+	0.991471i	$0.541602\pi$
$632$	−7.44997	+	47.0423i	−0.296344	+	1.87124i
$633$	−27.8498	−	35.0798i	−1.10693	−	1.39430i
$634$	−10.4304	+	21.8681i	−0.414244	+	0.868493i
$635$	6.91274	+	16.6888i	0.274324	+	0.662276i
$636$	23.8460	+	5.30984i	0.945557	+	0.210549i
$637$	−3.14264	−	13.0195i	−0.124516	−	0.515851i
$638$	−26.7205	−	1.40021i	−1.05788	−	0.0554350i
$639$	−3.57011	+	15.3320i	−0.141232	+	0.606524i
$640$	0.712252	+	27.1595i	0.0281542	+	1.07357i
$641$			31.6262i			1.24916i	0.780960	+	0.624581i	$0.214730\pi$
$641$			31.6262i			1.24916i	−0.780960	+	0.624581i	$0.785270\pi$
$642$	2.82745	+	0.475876i	0.111591	+	0.0187813i
$643$	16.9924	−	41.0234i	0.670116	−	1.61780i	−0.111295	−	0.993787i	$-0.535500\pi$
$643$	16.9924	−	41.0234i	0.670116	−	1.61780i	0.781411	−	0.624016i	$-0.214500\pi$
$644$	−8.94064	−	41.9333i	−0.352311	−	1.65240i
$645$	3.52102	−	1.00605i	0.138640	−	0.0396131i
$646$	14.8052	−	31.0402i	0.582502	−	1.22126i
$647$	−24.8248	+	24.8248i	−0.975965	+	0.975965i	−0.999718	−	0.0237528i	$-0.992439\pi$
$647$	−24.8248	+	24.8248i	−0.975965	+	0.975965i	0.0237528	+	0.999718i	$0.492439\pi$
$648$	14.6790	−	20.7973i	0.576646	−	0.816994i
$649$	3.88831	−	3.88831i	0.152630	−	0.152630i
$650$	1.95577	−	0.692585i	0.0767114	−	0.0271654i
$651$	−26.5655	+	17.9060i	−1.04118	+	0.701791i
$652$	−3.60823	−	1.95906i	−0.141309	−	0.0767226i
$653$	−30.7313	−	12.7293i	−1.20261	−	0.498137i	−0.310768	−	0.950486i	$-0.600586\pi$
$653$	−30.7313	−	12.7293i	−1.20261	−	0.498137i	−0.891841	+	0.452349i	$0.850586\pi$
$654$	1.15491	+	1.62234i	0.0451606	+	0.0634384i
$655$		−	25.2114i		−	0.985090i
$656$	0.407981	+	0.628205i	0.0159290	+	0.0245273i
$657$	−5.16558	−	1.20283i	−0.201529	−	0.0469268i
$658$	−34.1778	−	19.7043i	−1.33239	−	0.768153i
$659$	−23.1719	−	9.59812i	−0.902650	−	0.373890i	−0.117411	−	0.993083i	$-0.537460\pi$
$659$	−23.1719	−	9.59812i	−0.902650	−	0.373890i	−0.785238	+	0.619194i	$0.787460\pi$
$660$	4.21108	+	24.0130i	0.163916	+	0.934704i
$661$	−9.86920	−	23.8264i	−0.383867	−	0.926738i	−0.991210	−	0.132298i	$-0.957764\pi$
$661$	−9.86920	−	23.8264i	−0.383867	−	0.926738i	0.607343	−	0.794440i	$-0.292236\pi$
$662$	−11.7182	+	4.14971i	−0.455441	+	0.161283i
$663$	8.77482	+	11.0528i	0.340786	+	0.429256i
$664$	−9.86928	+	16.1058i	−0.383003	+	0.625027i
$665$	−32.3371	−	16.4515i	−1.25398	−	0.637964i
$666$	−12.1388	+	15.2018i	−0.470368	+	0.589058i
$667$	20.0185	+	48.3290i	0.775120	+	1.87130i
$668$	−27.1792	+	22.0098i	−1.05159	+	0.851583i
$669$	−12.4439	−	6.91312i	−0.481110	−	0.267277i
$670$	−1.97526	+	37.6942i	−0.0763110	+	1.45626i
$671$	32.5116			1.25510
$672$	8.43235	+	24.5132i	0.325285	+	0.945616i
$673$	37.8628			1.45950			0.729751	−	0.683713i	$-0.239636\pi$
$673$	37.8628			1.45950			0.729751	+	0.683713i	$0.239636\pi$
$674$	0.0681401	−	1.30033i	0.00262466	−	0.0500868i
$675$	−2.67433	+	2.95332i	−0.102935	+	0.113673i
$676$	−11.7548	−	14.5156i	−0.452106	−	0.558292i
$677$	−9.78269	−	23.6175i	−0.375979	−	0.907694i	−0.992711	−	0.120521i	$-0.961544\pi$
$677$	−9.78269	−	23.6175i	−0.375979	−	0.907694i	0.616732	−	0.787174i	$-0.288456\pi$
$678$	10.8402	−	17.3118i	0.416315	−	0.664856i
$679$	−23.1918	−	11.7989i	−0.890019	−	0.452798i
$680$	28.1249	−	6.75269i	1.07854	−	0.258954i
$681$	−35.4915	+	28.1767i	−1.36004	+	1.07973i
$682$	−27.3127	+	9.67211i	−1.04586	+	0.370364i
$683$	−16.8729	−	40.7348i	−0.645624	−	1.55867i	−0.818984	−	0.573816i	$-0.805462\pi$
$683$	−16.8729	−	40.7348i	−0.645624	−	1.55867i	0.173360	−	0.984858i	$-0.444538\pi$
$684$	2.02761	+	34.2026i	0.0775274	+	1.30777i
$685$	13.3895	+	5.54610i	0.511585	+	0.211906i
$686$	−26.0430	+	2.78596i	−0.994327	+	0.106369i
$687$	0.0290842	−	0.253148i	0.00110963	−	0.00965819i
$688$	3.46264	−	0.641842i	0.132012	−	0.0244700i
$689$		−	13.4936i		−	0.514064i
$690$	38.8286	−	27.6413i	1.47818	−	1.05229i
$691$	−0.00449366	−	0.00186133i	−0.000170947	−	7.08085e-5i	0.382598	−	0.923915i	$-0.375029\pi$
$691$	−0.00449366	−	0.00186133i	−0.000170947	−	7.08085e-5i	−0.382769	+	0.923844i	$0.625029\pi$
$692$	−21.6388	+	39.8547i	−0.822583	+	1.51505i
$693$	10.7147	+	20.6468i	0.407019	+	0.784307i
$694$	−27.7086	+	9.81230i	−1.05180	+	0.372470i
$695$	13.5804	−	13.5804i	0.515133	−	0.515133i
$696$	−15.5486	−	27.5415i	−0.589369	−	1.04396i
$697$	0.563886	−	0.563886i	0.0213587	−	0.0213587i
$698$	−8.23857	+	17.2728i	−0.311834	+	0.653784i
$699$	1.86338	+	6.52155i	0.0704794	+	0.246668i
$700$	−0.846054	−	3.96816i	−0.0319778	−	0.149982i
$701$	0.981051	−	2.36847i	0.0370538	−	0.0894558i	−0.904269	−	0.426963i	$-0.859584\pi$
$701$	0.981051	−	2.36847i	0.0370538	−	0.0894558i	0.941323	+	0.337507i	$0.109584\pi$
$702$	−12.9746	−	5.41721i	−0.489697	−	0.204460i
$703$		−	26.1839i		−	0.987545i
$704$	1.84028	+	23.3730i	0.0693581	+	0.880904i
$705$	5.00560	−	43.5685i	0.188522	−	1.64089i
$706$	11.0933	+	0.581314i	0.417502	+	0.0218780i
$707$	−11.8368	−	0.924255i	−0.445170	−	0.0347602i
$708$	6.34442	+	1.41272i	0.238438	+	0.0530934i
$709$	1.13463	+	2.73923i	0.0426117	+	0.102874i	0.943752	−	0.330653i	$-0.107269\pi$
$709$	1.13463	+	2.73923i	0.0426117	+	0.102874i	−0.901141	+	0.433527i	$0.857269\pi$
$710$	7.67190	−	16.0847i	0.287921	−	0.603648i
$711$	−42.8918	+	26.6895i	−1.60857	+	1.00094i
$712$	28.9980	−	21.0690i	1.08675	−	0.789595i
$713$	40.0549	+	40.0549i	1.50007	+	1.50007i
$714$	23.6605	−	14.2063i	0.885473	−	0.531658i
$715$	12.4406	−	5.15306i	0.465252	−	0.192714i
$716$	−22.7419	−	12.3475i	−0.849903	−	0.461448i
$717$	−0.383129	+	0.689650i	−0.0143082	+	0.0257555i
$718$	−10.9905	−	12.2060i	−0.410162	−	0.455526i
$719$		−	37.0977i		−	1.38351i	−0.722132	−	0.691755i	$-0.756838\pi$
$719$		−	37.0977i		−	1.38351i	0.722132	−	0.691755i	$-0.243162\pi$
$720$	−21.2823	+	19.4288i	−0.793144	+	0.724069i
$721$	50.3853	−	16.4054i	1.87645	−	0.610970i
$722$	−12.8783	−	14.3026i	−0.479280	−	0.532288i
$723$	−6.82612	+	12.2873i	−0.253866	+	0.456970i
$724$	0.210673	+	0.711190i	0.00782959	+	0.0264312i
$725$	1.89436	+	4.57338i	0.0703546	+	0.169851i
$726$	−1.32321	−	5.75603i	−0.0491088	−	0.213626i
$727$	−16.4771	+	16.4771i	−0.611100	+	0.611100i	−0.943233	−	0.332133i	$-0.892232\pi$
$727$	−16.4771	+	16.4771i	−0.611100	+	0.611100i	0.332133	+	0.943233i	$0.392232\pi$
$728$	12.2035	−	7.48892i	0.452292	−	0.277558i
$729$	26.8676	−	2.67040i	0.995097	−	0.0989038i
$730$	5.41919	+	2.58479i	0.200573	+	0.0956672i
$731$	−1.43474	−	3.46377i	−0.0530658	−	0.128112i
$732$	20.6178	+	32.4301i	0.762058	+	1.19865i
$733$	−7.06369	+	17.0533i	−0.260903	+	0.629877i	−0.998995	−	0.0448241i	$-0.985727\pi$
$733$	−7.06369	+	17.0533i	−0.260903	+	0.629877i	0.738091	+	0.674701i	$0.235727\pi$
$734$	23.8463	+	1.24960i	0.880183	+	0.0461235i
$735$	−14.3445	−	25.3368i	−0.529104	−	0.934560i
$736$	39.6947	−	22.9192i	1.46316	−	0.844813i
$737$			32.5729i			1.19984i
$738$	−0.220428	+	0.763307i	−0.00811407	+	0.0280977i
$739$	37.9790	+	15.7314i	1.39708	+	0.578689i	0.948992	−	0.315301i	$-0.102106\pi$
$739$	37.9790	+	15.7314i	1.39708	+	0.578689i	0.448087	+	0.893990i	$0.352106\pi$
$740$	17.1143	−	13.8592i	0.629136	−	0.509476i
$741$	18.1962	−	5.19914i	0.668456	−	0.190995i
$742$	−26.1639	−	3.42803i	−0.960506	−	0.125847i
$743$	24.7248	+	24.7248i	0.907065	+	0.907065i	0.996034	−	0.0889696i	$-0.0283574\pi$
$743$	24.7248	+	24.7248i	0.907065	+	0.907065i	−0.0889696	+	0.996034i	$0.528357\pi$
$744$	−26.9688	−	21.1105i	−0.988723	−	0.773950i
$745$	21.1578	−	21.1578i	0.775161	−	0.775161i
$746$	−44.4075	+	15.7258i	−1.62587	+	0.575762i
$747$	−19.7664	+	3.26948i	−0.723215	+	0.119624i
$748$	23.9322	−	7.08933i	0.875047	−	0.259211i
$749$	−3.08755	−	0.241085i	−0.112817	−	0.00880905i
$750$	−20.2857	+	14.4410i	−0.740729	+	0.527311i
$751$			17.5309i			0.639711i	0.947466	+	0.319856i	$0.103634\pi$
$751$			17.5309i			0.639711i	−0.947466	+	0.319856i	$0.896366\pi$
$752$	8.76773	−	41.2534i	0.319726	−	1.50436i
$753$	24.5458	+	2.82008i	0.894500	+	0.102769i
$754$	−12.9819	+	11.6891i	−0.472773	+	0.425691i
$755$	−11.1126	+	26.8281i	−0.404428	+	0.976376i
$756$	−13.8001	+	23.7814i	−0.501905	+	0.864923i
$757$	−16.3318	+	6.76485i	−0.593589	+	0.245873i	−0.659194	−	0.751973i	$-0.729102\pi$
$757$	−16.3318	+	6.76485i	−0.593589	+	0.245873i	0.0656050	+	0.997846i	$0.479102\pi$
$758$	5.28876	+	14.9347i	0.192096	+	0.542454i
$759$	32.2129	−	25.5738i	1.16926	−	0.928270i
$760$	6.06691	−	38.3091i	0.220070	−	1.38962i
$761$	−36.0655	+	36.0655i	−1.30737	+	1.30737i	−0.384069	+	0.923304i	$0.625478\pi$
$761$	−36.0655	+	36.0655i	−1.30737	+	1.30737i	−0.923304	+	0.384069i	$0.874522\pi$
$762$	−9.77867	+	15.6166i	−0.354244	+	0.565729i
$763$	−1.39796	−	1.63477i	−0.0506096	−	0.0591825i
$764$	2.46146	−	23.4218i	0.0890526	−	0.847370i
$765$	24.9424	+	17.8623i	0.901795	+	0.645812i
$766$	−22.9531	−	1.20280i	−0.829331	−	0.0434588i
$767$		−	3.59007i		−	0.129630i
$768$	−22.1474	+	16.6581i	−0.799176	+	0.601098i
$769$		−	36.1347i		−	1.30305i	−0.758627	−	0.651525i	$-0.774129\pi$
$769$		−	36.1347i		−	1.30305i	0.758627	−	0.651525i	$-0.225871\pi$
$770$	−6.83121	−	25.4313i	−0.246180	−	0.916480i
$771$	1.61746	−	2.91151i	0.0582515	−	0.104855i
$772$	−18.6048	−	1.95524i	−0.669603	−	0.0703706i
$773$	−3.91476	−	9.45106i	−0.140804	−	0.339931i	0.837709	−	0.546117i	$-0.183895\pi$
$773$	−3.91476	−	9.45106i	−0.140804	−	0.339931i	−0.978513	+	0.206186i	$0.933895\pi$
$774$	2.91886	+	2.33074i	0.104916	+	0.0837766i
$775$	3.79041	+	3.79041i	0.136155	+	0.136155i
$776$	4.35111	−	27.4748i	0.156196	−	0.986288i
$777$	11.6032	−	17.5181i	0.416264	−	0.628459i
$778$	−29.3378	+	10.3893i	−1.05181	+	0.372473i
$779$	−0.409228	−	0.987964i	−0.0146621	−	0.0353975i
$780$	13.0296	+	9.14151i	0.466534	+	0.327319i
$781$	5.88504	−	14.2077i	0.210583	−	0.508393i
$782$	−32.6522	−	36.2635i	−1.16764	−	1.29678i
$783$	11.2872	−	31.5901i	0.403373	−	1.12894i
$784$	−11.4206	−	25.5650i	−0.407880	−	0.913035i
$785$	−5.87851			−0.209813
$786$	20.9499	−	14.9138i	0.747258	−	0.531958i
$787$	−28.7299	−	11.9003i	−1.02411	−	0.424200i	−0.193526	−	0.981095i	$-0.561992\pi$
$787$	−28.7299	−	11.9003i	−1.02411	−	0.424200i	−0.830583	+	0.556895i	$0.811992\pi$
$788$	−6.48886	+	1.92217i	−0.231156	+	0.0684744i
$789$	0.621158	−	0.177481i	0.0221138	−	0.00631848i
$790$	53.9075	−	19.0900i	1.91794	−	0.679191i
$791$	−10.0040	+	19.6638i	−0.355700	+	0.699163i
$792$	−17.4630	+	17.7042i	−0.620521	+	0.629091i
$793$	15.0089	−	15.0089i	0.532983	−	0.532983i
$794$	−3.02811	−	1.44431i	−0.107464	−	0.0512568i
$795$	−8.05878	−	28.2046i	−0.285815	−	1.00031i
$796$	−14.6836	−	18.1324i	−0.520447	−	0.642684i
$797$	11.6231	+	4.81444i	0.411711	+	0.170536i	0.578918	−	0.815386i	$-0.303475\pi$
$797$	11.6231	+	4.81444i	0.411711	+	0.170536i	−0.167208	+	0.985922i	$0.553475\pi$
$798$	−5.45833	−	36.6031i	−0.193223	−	1.29574i
$799$	−44.8997			−1.58844
$800$	3.75631	−	2.16885i	0.132806	−	0.0766803i
$801$	37.0276	+	8.62204i	1.30831	+	0.304645i
$802$	−36.2652	−	1.90038i	−1.28057	−	0.0671046i
$803$	4.78681	+	1.98276i	0.168923	+	0.0699701i
$804$	−32.4913	+	20.6567i	−1.14588	+	0.728506i
$805$	−39.1260	+	33.4584i	−1.37901	+	1.17925i
$806$	−8.14376	+	17.0740i	−0.286852	+	0.601406i
$807$	18.0062	+	22.6808i	0.633849	+	0.798401i
$808$	−2.96324	−	12.3419i	−0.104246	−	0.434186i
$809$	33.7797	−	33.7797i	1.18763	−	1.18763i	0.209909	−	0.977721i	$-0.432683\pi$
$809$	33.7797	−	33.7797i	1.18763	−	1.18763i	0.977721	−	0.209909i	$-0.0673168\pi$
$810$	−30.3552	−	3.57433i	−1.06657	−	0.125589i
$811$	−14.7108	−	35.5150i	−0.516566	−	1.24710i	−0.940000	−	0.341175i	$-0.889175\pi$
$811$	−14.7108	−	35.5150i	−0.516566	−	1.24710i	0.423433	−	0.905927i	$-0.360825\pi$
$812$	19.3669	+	28.1413i	0.679646	+	0.987567i
$813$	2.21729	−	3.99122i	0.0777638	−	0.139978i
$814$	14.1227	−	12.7163i	0.495001	−	0.445706i
$815$			4.92980i			0.172683i
$816$	22.2486	+	19.3764i	0.778857	+	0.678309i
$817$	−5.02751			−0.175890
$818$	−1.61666	−	1.79546i	−0.0565251	−	0.0627768i
$819$	14.4780	+	4.58511i	0.505902	+	0.160217i
$820$	0.429148	−	0.790412i	0.0149865	−	0.0276024i
$821$	19.6013	+	47.3217i	0.684089	+	1.65154i	0.756362	+	0.654153i	$0.226975\pi$
$821$	19.6013	+	47.3217i	0.684089	+	1.65154i	−0.0722729	+	0.997385i	$0.523025\pi$
$822$	3.31192	+	14.4071i	0.115516	+	0.502504i
$823$	−30.6403	−	30.6403i	−1.06805	−	1.06805i	−0.997509	−	0.0705437i	$-0.977527\pi$
$823$	−30.6403	−	30.6403i	−1.06805	−	1.06805i	−0.0705437	−	0.997509i	$-0.522473\pi$
$824$	33.2973	+	45.8282i	1.15997	+	1.59650i
$825$	3.04832	−	2.42005i	0.106129	−	0.0842555i
$826$	−6.96109	−	0.912052i	−0.242207	−	0.0317343i
$827$	39.3013	−	16.2791i	1.36664	−	0.566080i	0.425764	−	0.904834i	$-0.360006\pi$
$827$	39.3013	−	16.2791i	1.36664	−	0.566080i	0.940875	+	0.338754i	$0.110006\pi$
$828$	45.9382	+	15.9141i	1.59646	+	0.553054i
$829$	−0.539755	+	1.30308i	−0.0187465	+	0.0452579i	−0.932976	−	0.359940i	$-0.882797\pi$
$829$	−0.539755	+	1.30308i	−0.0187465	+	0.0452579i	0.914229	+	0.405198i	$0.132797\pi$
$830$	22.6492	+	1.18687i	0.786166	+	0.0411968i
$831$	3.00371	−	26.1442i	0.104197	−	0.906931i
$832$	11.6397	+	9.94055i	0.403533	+	0.344627i
$833$	−24.0945	+	17.5510i	−0.834824	+	0.608105i
$834$	19.3184	+	3.25139i	0.668940	+	0.112587i
$835$	38.7962	+	16.0699i	1.34260	+	0.556122i
$836$	3.49828	−	33.2875i	0.120991	−	1.15127i
$837$	−1.79860	−	36.2816i	−0.0621689	−	1.25408i
$838$	24.5259	+	11.6981i	0.847234	+	0.404104i
$839$	−9.16683	+	9.16683i	−0.316474	+	0.316474i	−0.847411	−	0.530937i	$-0.821840\pi$
$839$	−9.16683	+	9.16683i	−0.316474	+	0.316474i	0.530937	+	0.847411i	$0.321840\pi$
$840$	21.0354	−	22.9418i	0.725791	−	0.791568i
$841$	−8.96541	−	8.96541i	−0.309152	−	0.309152i
$842$	−2.55826	−	7.22418i	−0.0881635	−	0.248962i
$843$	−8.98477	+	2.56718i	−0.309452	+	0.0884184i
$844$	−24.6781	+	45.4526i	−0.849454	+	1.56454i
$845$	−8.58246	+	20.7199i	−0.295246	+	0.712786i
$846$	39.1652	−	21.6135i	1.34653	−	0.743089i
$847$	1.97507	+	6.06594i	0.0678642	+	0.208428i
$848$	−5.14137	−	27.7369i	−0.176555	−	0.952490i
$849$	4.61933	−	40.2064i	0.158535	−	1.37988i
$850$	−3.08988	−	3.43162i	−0.105982	−	0.117704i
$851$	−34.3253	−	14.2180i	−1.17666	−	0.487387i
$852$	17.9042	−	3.13981i	0.613389	−	0.107568i
$853$	12.6907	+	30.6381i	0.434522	+	1.04903i	0.977812	+	0.209485i	$0.0671786\pi$
$853$	12.6907	+	30.6381i	0.434522	+	1.04903i	−0.543290	+	0.839545i	$0.682821\pi$
$854$	−25.2891	−	32.9151i	−0.865376	−	1.12633i
$855$	34.9291	−	21.7347i	1.19455	−	0.743312i
$856$	−0.772939	−	3.21929i	−0.0264185	−	0.110033i
$857$	39.8309	−	39.8309i	1.36060	−	1.36060i	0.487439	−	0.873157i	$-0.337931\pi$
$857$	39.8309	−	39.8309i	1.36060	−	1.36060i	0.873157	−	0.487439i	$-0.162069\pi$
$858$	11.6413	+	7.28946i	0.397427	+	0.248858i
$859$	−16.7972	+	6.95764i	−0.573114	+	0.237392i	−0.650367	−	0.759620i	$-0.725385\pi$
$859$	−16.7972	+	6.95764i	−0.573114	+	0.237392i	0.0772534	+	0.997011i	$0.475385\pi$
$860$	−2.66108	−	3.28608i	−0.0907419	−	0.112054i
$861$	0.164020	−	0.842335i	0.00558977	−	0.0287067i
$862$	−33.7158	−	1.76678i	−1.14836	−	0.0601768i
$863$		−	43.0671i		−	1.46602i	−0.680218	−	0.733010i	$-0.738115\pi$
$863$		−	43.0671i		−	1.46602i	0.680218	−	0.733010i	$-0.261885\pi$
$864$	−28.7343	−	6.19179i	−0.977562	−	0.210649i
$865$	54.4521			1.85143
$866$	42.6609	+	2.23553i	1.44968	+	0.0759663i
$867$	0.954089	−	1.71740i	0.0324026	−	0.0583261i
$868$	31.0373	+	20.1283i	1.05348	+	0.683198i
$869$	45.5937	−	18.8855i	1.54666	−	0.640647i
$870$	−20.1540	+	32.1860i	−0.683284	+	1.09121i
$871$	15.0372	+	15.0372i	0.509516	+	0.509516i
$872$	1.20146	−	1.96067i	0.0406864	−	0.0663967i
$873$	25.0507	−	15.5879i	0.847839	−	0.527570i
$874$	−61.6827	+	21.8434i	−2.08645	+	0.738863i
$875$	20.4411	−	17.4801i	0.691036	−	0.590936i
$876$	1.05785	+	6.03222i	0.0357415	+	0.203810i
$877$	−0.921553	+	2.22483i	−0.0311186	+	0.0751270i	−0.938675	−	0.344803i	$-0.887946\pi$
$877$	−0.921553	+	2.22483i	−0.0311186	+	0.0751270i	0.907556	+	0.419930i	$0.137946\pi$
$878$	−4.98291	+	4.48668i	−0.168165	+	0.151418i
$879$	6.65112	+	0.764150i	0.224337	+	0.0257741i
$880$	23.6090	−	15.3326i	0.795860	−	0.516863i
$881$		−	45.5940i		−	1.53610i	−0.640389	−	0.768051i	$-0.721227\pi$
$881$		−	45.5940i		−	1.53610i	0.640389	−	0.768051i	$-0.278773\pi$
$882$	12.5686	−	26.9078i	0.423207	−	0.906033i
$883$	−9.04179	+	21.8288i	−0.304280	+	0.734598i	0.695589	+	0.718440i	$0.255143\pi$
$883$	−9.04179	+	21.8288i	−0.304280	+	0.734598i	−0.999869	+	0.0161580i	$0.994857\pi$
$884$	7.77548	−	14.3210i	0.261518	−	0.481668i
$885$	−2.14410	−	7.50404i	−0.0720731	−	0.252246i
$886$	−10.3070	+	3.64998i	−0.346272	+	0.122623i
$887$	−27.3637	−	27.3637i	−0.918782	−	0.918782i	0.0781593	−	0.996941i	$-0.475096\pi$
$887$	−27.3637	−	27.3637i	−0.918782	−	0.918782i	−0.996941	+	0.0781593i	$0.975096\pi$
$888$	21.6406	+	6.02305i	0.726212	+	0.202120i
$889$	9.02434	−	17.7382i	0.302667	−	0.594921i
$890$	−38.8455	−	18.5281i	−1.30211	−	0.621064i
$891$	−26.3206	−	1.70944i	−0.881772	−	0.0572684i
$892$	−1.71800	+	16.3474i	−0.0575230	+	0.547353i
$893$	−23.0411	+	55.6261i	−0.771040	+	1.86146i
$894$	30.0974	+	5.06556i	1.00661	+	0.169418i
$895$			31.0714i			1.03860i
$896$	22.2316	−	20.0438i	0.742707	−	0.669616i
$897$	3.06495	−	26.6772i	0.102336	−	0.890724i
$898$	0.345718	−	6.59739i	0.0115368	−	0.220158i
$899$	−41.6977	−	17.2717i	−1.39069	−	0.576045i
$900$	4.34714	+	1.50596i	0.144905	+	0.0501985i
$901$	−27.7460	+	11.4927i	−0.924352	+	0.382879i
$902$	0.334132	−	0.700531i	0.0111254	−	0.0233251i
$903$	−3.36361	−	2.22791i	−0.111934	−	0.0741401i
$904$	−23.2952	−	3.68920i	−0.774788	−	0.122701i
$905$	0.629754	−	0.629754i	0.0209337	−	0.0209337i
$906$	−28.8670	+	6.63601i	−0.959043	+	0.220467i
$907$	7.67991	−	3.18112i	0.255007	−	0.105627i	−0.251518	−	0.967853i	$-0.580930\pi$
$907$	7.67991	−	3.18112i	0.255007	−	0.105627i	0.506525	+	0.862225i	$0.330930\pi$
$908$	45.9860	+	24.9677i	1.52610	+	0.828582i
$909$	7.83839	−	10.9453i	0.259983	−	0.363033i
$910$	−14.8939	−	8.58670i	−0.493729	−	0.284646i
$911$	17.9728			0.595465			0.297733	−	0.954649i	$-0.403770\pi$
$911$	17.9728			0.595465			0.297733	+	0.954649i	$0.403770\pi$
$912$	35.4226	−	17.6204i	1.17296	−	0.583469i
$913$	19.5719			0.647737
$914$	6.54132	+	7.26479i	0.216368	+	0.240298i
$915$	22.4082	−	40.3358i	0.740793	−	1.33346i
$916$	−0.282115	+	0.0835698i	−0.00932135	+	0.00276122i
$917$	−21.1104	+	18.0524i	−0.697127	+	0.596144i
$918$	−0.0882914	+	31.2929i	−0.00291405	+	1.03282i
$919$	−17.6890	−	17.6890i	−0.583507	−	0.583507i	0.352358	−	0.935865i	$-0.385380\pi$
$919$	−17.6890	−	17.6890i	−0.583507	−	0.583507i	−0.935865	+	0.352358i	$0.885380\pi$
$920$	−46.9261	−	28.7553i	−1.54711	−	0.948034i
$921$	−25.8413	+	20.5154i	−0.851501	+	0.676006i
$922$	11.2211	−	23.5258i	0.369547	−	0.774781i
$923$	−3.84216	−	9.27579i	−0.126466	−	0.305316i
$924$	17.0916	−	20.7204i	0.562273	−	0.681653i
$925$	−3.24821	−	1.34545i	−0.106800	−	0.0442382i
$926$	0.468290	−	8.93645i	0.0153890	−	0.293670i
$927$	−13.6262	+	58.5181i	−0.447543	+	1.92199i
$928$	−22.2313	+	28.9741i	−0.729779	+	0.951121i
$929$	−8.05622			−0.264316			−0.132158	−	0.991229i	$-0.542191\pi$
$929$	−8.05622			−0.264316			−0.132158	+	0.991229i	$0.542191\pi$
$930$	−6.82516	+	40.5521i	−0.223806	+	1.32976i
$931$	9.37932	+	38.8571i	0.307395	+	1.27349i
$932$	6.08640	−	4.92878i	0.199367	−	0.161448i
$933$	13.9879	−	3.99670i	0.457943	−	0.130846i
$934$	−15.3318	+	32.1443i	−0.501672	+	1.05179i
$935$	−21.1918	−	21.1918i	−0.693046	−	0.693046i
$936$	0.111351	+	16.2349i	0.00363961	+	0.530654i
$937$	−21.1032	+	21.1032i	−0.689413	+	0.689413i	−0.962102	−	0.272690i	$-0.912087\pi$
$937$	−21.1032	+	21.1032i	−0.689413	+	0.689413i	0.272690	+	0.962102i	$0.412087\pi$
$938$	32.9771	−	25.3368i	1.07674	−	0.827275i
$939$	37.4423	−	10.6982i	1.22188	−	0.349123i
$940$	−48.5541	+	14.3830i	−1.58366	+	0.469120i
$941$	4.34229	−	10.4832i	0.141555	−	0.341743i	−0.837163	−	0.546953i	$-0.815788\pi$
$941$	4.34229	−	10.4832i	0.141555	−	0.341743i	0.978718	+	0.205210i	$0.0657877\pi$
$942$	−3.47744	−	4.88486i	−0.113301	−	0.159157i
$943$	−1.51736			−0.0494122
$944$	−1.36790	−	7.37962i	−0.0445214	−	0.240186i
$945$	33.0006	+	0.937204i	1.07351	+	0.0304873i
$946$	−2.44162	−	2.71167i	−0.0793840	−	0.0881639i
$947$	10.3075	+	4.26949i	0.334948	+	0.138740i	0.543817	−	0.839204i	$-0.316978\pi$
$947$	10.3075	+	4.26949i	0.334948	+	0.138740i	−0.208870	+	0.977944i	$0.566978\pi$
$948$	47.7523	+	33.5028i	1.55092	+	1.08812i
$949$	3.12516	−	1.29448i	0.101447	−	0.0420207i
$950$	−5.83705	+	2.06704i	−0.189379	+	0.0670637i
$951$	18.4502	+	23.2400i	0.598290	+	0.753610i
$952$	−25.7929	−	18.7148i	−0.835954	−	0.606550i
$953$	−34.1430	−	34.1430i	−1.10600	−	1.10600i	−0.993671	−	0.112328i	$-0.964169\pi$
$953$	−34.1430	−	34.1430i	−1.10600	−	1.10600i	−0.112328	−	0.993671i	$-0.535831\pi$
$954$	18.6700	−	23.3811i	0.604463	−	0.756990i
$955$	−26.1250	+	10.8213i	−0.845385	+	0.350170i
$956$	0.905985	+	0.0952127i	0.0293016	+	0.00307940i
$957$	−15.9146	+	28.6469i	−0.514445	+	0.926024i
$958$	54.4808	+	2.85491i	1.76019	+	0.0922380i
$959$	−4.94350	−	15.1827i	−0.159634	−	0.490276i
$960$	30.2663	+	13.8264i	0.976841	+	0.446245i
$961$	−17.8737			−0.576571
$962$	0.649273	−	12.3902i	0.0209334	−	0.399476i
$963$	2.04459	−	2.85501i	0.0658858	−	0.0920013i
$964$	16.1417	+	1.69638i	0.519889	+	0.0546367i
$965$	8.59581	+	20.7521i	0.276709	+	0.668035i
$966$	−50.9480	−	12.7202i	−1.63923	−	0.409265i
$967$	1.75330	−	1.75330i	0.0563823	−	0.0563823i	−0.678353	−	0.734736i	$-0.737306\pi$
$967$	1.75330	−	1.75330i	0.0563823	−	0.0563823i	0.734736	+	0.678353i	$0.237306\pi$
$968$	−5.51731	+	4.00870i	−0.177333	+	0.128844i
$969$	−26.1887	−	32.9875i	−0.841304	−	1.05971i
$970$	−31.4844	+	11.1494i	−1.01090	+	0.357986i
$971$	42.7144	−	17.6929i	1.37077	−	0.567792i	0.428774	−	0.903412i	$-0.358946\pi$
$971$	42.7144	−	17.6929i	1.37077	−	0.567792i	0.941998	+	0.335620i	$0.108946\pi$
$972$	−14.9865	−	27.3387i	−0.480693	−	0.876889i
$973$	−21.0955	−	1.64720i	−0.676290	−	0.0528067i
$974$	−45.8116	+	41.2494i	−1.46790	+	1.32172i
$975$	0.290036	−	2.52446i	0.00928860	−	0.0808476i
$976$	25.1331	−	36.5706i	0.804490	−	1.17060i
$977$	−57.8990			−1.85235			−0.926177	−	0.377089i	$-0.876925\pi$
$977$	−57.8990			−1.85235			−0.926177	+	0.377089i	$0.876925\pi$
$978$	−4.09651	+	2.91623i	−0.130992	+	0.0932507i
$979$	−34.3125	−	14.2127i	−1.09663	−	0.454240i
$980$	−20.4333	+	26.6977i	−0.652717	+	0.852827i
$981$	2.40630	−	0.398016i	0.0768272	−	0.0127077i
$982$	0.830086	+	2.34405i	0.0264891	+	0.0748016i
$983$	−1.99489	−	1.99489i	−0.0636270	−	0.0636270i	0.674577	−	0.738204i	$-0.264326\pi$
$983$	−1.99489	−	1.99489i	−0.0636270	−	0.0636270i	−0.738204	+	0.674577i	$0.764326\pi$
$984$	0.910672	−	0.110961i	0.0290312	−	0.00353730i
$985$	5.74585	+	5.74585i	0.183078	+	0.183078i
$986$	35.0924	+	16.7380i	1.11757	+	0.533046i
$987$	−40.0658	+	27.0056i	−1.27531	+	0.859598i
$988$	−13.7521	−	16.9821i	−0.437514	−	0.540272i
$989$	−2.72996	+	6.59071i	−0.0868077	+	0.209572i
$990$	28.6864	+	8.28406i	0.911713	+	0.263285i
$991$	14.7543			0.468685			0.234342	−	0.972154i	$-0.424706\pi$
$991$	14.7543			0.468685			0.234342	+	0.972154i	$0.424706\pi$
$992$	−10.2344	+	38.1997i	−0.324944	+	1.21284i
$993$	−1.73779	+	15.1256i	−0.0551470	+	0.479998i
$994$	−18.9617	+	5.09340i	−0.601430	+	0.161553i
$995$	−10.7209	+	25.8826i	−0.339875	+	0.820532i
$996$	12.4119	+	19.5229i	0.393287	+	0.618607i
$997$	−4.39948	+	1.82232i	−0.139333	+	0.0577135i	−0.451260	−	0.892392i	$-0.649025\pi$
$997$	−4.39948	+	1.82232i	−0.139333	+	0.0577135i	0.311927	+	0.950106i	$0.399025\pi$
$998$	17.9810	−	37.6986i	0.569180	−	1.19333i
$999$	10.1964	+	21.5337i	0.322601	+	0.681296i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.2.bo.a.125.1	✓	496
3.2	odd	2	inner	672.2.bo.a.125.123	yes	496
7.6	odd	2	inner	672.2.bo.a.125.2	yes	496
21.20	even	2	inner	672.2.bo.a.125.124	yes	496
32.21	even	8	inner	672.2.bo.a.629.124	yes	496
96.53	odd	8	inner	672.2.bo.a.629.2	yes	496
224.181	odd	8	inner	672.2.bo.a.629.123	yes	496
672.629	even	8	inner	672.2.bo.a.629.1	yes	496

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.2.bo.a.125.1	✓	496	1.1	even	1	trivial
672.2.bo.a.125.2	yes	496	7.6	odd	2	inner
672.2.bo.a.125.123	yes	496	3.2	odd	2	inner
672.2.bo.a.125.124	yes	496	21.20	even	2	inner
672.2.bo.a.629.1	yes	496	672.629	even	8	inner
672.2.bo.a.629.2	yes	496	96.53	odd	8	inner
672.2.bo.a.629.123	yes	496	224.181	odd	8	inner
672.2.bo.a.629.124	yes	496	32.21	even	8	inner

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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.bo (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41228 - 0.0740064i) q^{2} +(-0.841142 + 1.51409i) q^{3} +(1.98905 + 0.209035i) q^{4} +(-0.918980 - 2.21861i) q^{5} +(1.29998 - 2.07607i) q^{6} +(-1.19970 + 2.35812i) q^{7} +(-2.79361 - 0.442417i) q^{8} +(-1.58496 - 2.54714i) q^{9} +O(q^{10})\)	\(q+(-1.41228 - 0.0740064i) q^{2} +(-0.841142 + 1.51409i) q^{3} +(1.98905 + 0.209035i) q^{4} +(-0.918980 - 2.21861i) q^{5} +(1.29998 - 2.07607i) q^{6} +(-1.19970 + 2.35812i) q^{7} +(-2.79361 - 0.442417i) q^{8} +(-1.58496 - 2.54714i) q^{9} +(1.13366 + 3.20130i) q^{10} +(1.12152 + 2.70758i) q^{11} +(-1.98957 + 2.83577i) q^{12} +(1.76770 + 0.732205i) q^{13} +(1.86882 - 3.24153i) q^{14} +(4.13218 + 0.474747i) q^{15} +(3.91261 + 0.831560i) q^{16} -4.25844i q^{17} +(2.04990 + 3.71456i) q^{18} +(-5.27576 - 2.18529i) q^{19} +(-1.36413 - 4.60502i) q^{20} +(-2.56130 - 3.79997i) q^{21} +(-1.38351 - 3.90686i) q^{22} +(-5.72952 + 5.72952i) q^{23} +(3.01969 - 3.85765i) q^{24} +(-0.542186 + 0.542186i) q^{25} +(-2.44229 - 1.16490i) q^{26} +(5.18978 - 0.257275i) q^{27} +(-2.87918 + 4.43963i) q^{28} +(2.47058 - 5.96450i) q^{29} +(-5.80064 - 0.976282i) q^{30} -6.99097i q^{31} +(-5.46414 - 1.46395i) q^{32} +(-5.04289 - 0.579379i) q^{33} +(-0.315151 + 6.01409i) q^{34} +(6.33425 + 0.494597i) q^{35} +(-2.62012 - 5.39768i) q^{36} +(1.75471 + 4.23624i) q^{37} +(7.28910 + 3.47667i) q^{38} +(-2.59551 + 2.06057i) q^{39} +(1.58572 + 6.60452i) q^{40} +(0.132416 + 0.132416i) q^{41} +(3.33604 + 5.55615i) q^{42} +(0.813390 - 0.336917i) q^{43} +(1.66477 + 5.61995i) q^{44} +(-4.19456 + 5.85718i) q^{45} +(8.51569 - 7.66765i) q^{46} -10.5437i q^{47} +(-4.55012 + 5.22460i) q^{48} +(-4.12146 - 5.65805i) q^{49} +(0.805841 - 0.725591i) q^{50} +(6.44767 + 3.58195i) q^{51} +(3.36298 + 1.82590i) q^{52} +(-2.69882 - 6.51553i) q^{53} +(-7.34844 - 0.0207333i) q^{54} +(4.97643 - 4.97643i) q^{55} +(4.39476 - 6.05691i) q^{56} +(7.74639 - 6.14985i) q^{57} +(-3.93055 + 8.24068i) q^{58} +(-0.718041 - 1.73350i) q^{59} +(8.11986 + 1.80806i) q^{60} +(4.24533 - 10.2491i) q^{61} +(-0.517377 + 9.87318i) q^{62} +(7.90792 - 0.681737i) q^{63} +(7.60853 + 2.47188i) q^{64} -4.59472i q^{65} +(7.07908 + 1.19145i) q^{66} +(10.2684 + 4.25333i) q^{67} +(0.890162 - 8.47023i) q^{68} +(-3.85569 - 13.4944i) q^{69} +(-8.90911 - 1.16728i) q^{70} +(-3.71046 - 3.71046i) q^{71} +(3.30087 + 7.81692i) q^{72} +(1.25011 - 1.25011i) q^{73} +(-2.16462 - 6.11260i) q^{74} +(-0.364865 - 1.27698i) q^{75} +(-10.0369 - 5.44946i) q^{76} +(-7.73029 - 0.603604i) q^{77} +(3.81808 - 2.71801i) q^{78} -16.8392i q^{79} +(-1.75070 - 9.44475i) q^{80} +(-3.97580 + 8.07422i) q^{81} +(-0.177209 - 0.196808i) q^{82} +(2.55568 - 6.16997i) q^{83} +(-4.30022 - 8.09371i) q^{84} +(-9.44782 + 3.91342i) q^{85} +(-1.17366 + 0.415624i) q^{86} +(6.95271 + 8.75768i) q^{87} +(-1.93521 - 8.06012i) q^{88} +(-8.96098 + 8.96098i) q^{89} +(6.35735 - 7.96153i) q^{90} +(-3.84733 + 3.29002i) q^{91} +(-12.5940 + 10.1986i) q^{92} +(10.5850 + 5.88040i) q^{93} +(-0.780302 + 14.8906i) q^{94} +13.7131i q^{95} +(6.81268 - 7.04183i) q^{96} +9.83487i q^{97} +(5.40190 + 8.29575i) q^{98} +(5.11902 - 7.14807i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9}+O(q^{10}) \) 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9	\( 496 q - 16 q^{4} - 8 q^{7} - 8 q^{9} - 48 q^{16} - 8 q^{18} - 4 q^{21} - 16 q^{22} - 16 q^{25} - 8 q^{28} - 64 q^{30} - 48 q^{36} - 16 q^{37} - 8 q^{39} + 56 q^{42} - 16 q^{43} - 16 q^{46} + 16 q^{51} - 8 q^{57} - 80 q^{58} + 24 q^{60} - 8 q^{63} - 112 q^{64} + 48 q^{67} - 8 q^{70} - 8 q^{72} - 160 q^{78} + 128 q^{84} + 64 q^{85} - 16 q^{88} - 56 q^{91} + 16 q^{93} - 8 q^{99}+O(q^{100}) \) 496 * q - 16 * q^4 - 8 * q^7 - 8 * q^9 - 48 * q^16 - 8 * q^18 - 4 * q^21 - 16 * q^22 - 16 * q^25 - 8 * q^28 - 64 * q^30 - 48 * q^36 - 16 * q^37 - 8 * q^39 + 56 * q^42 - 16 * q^43 - 16 * q^46 + 16 * q^51 - 8 * q^57 - 80 * q^58 + 24 * q^60 - 8 * q^63 - 112 * q^64 + 48 * q^67 - 8 * q^70 - 8 * q^72 - 160 * q^78 + 128 * q^84 + 64 * q^85 - 16 * q^88 - 56 * q^91 + 16 * q^93 - 8 * q^99

Introduction

L-functions

Modular forms

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Database

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