LMFDB - Embedded newform 672.2.bo.a.125.2

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			125.2
Character	$\chi$	$=$	672.125
Dual form			672.2.bo.a.629.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41228 - 0.0740064i) q^{2} +(0.841142 - 1.51409i) q^{3} +(1.98905 + 0.209035i) q^{4} +(0.918980 + 2.21861i) q^{5} +(-1.29998 + 2.07607i) q^{6} +(-2.35812 + 1.19970i) q^{7} +(-2.79361 - 0.442417i) q^{8} +(-1.58496 - 2.54714i) q^{9} +O(q^{10})$	\(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} +(-2.35812 + 1.19970i) 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} +(3.41910 - 1.51979i) 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} +(-0.167061 + 4.57953i) 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} +(-4.94119 + 1.89332i) 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} +(-4.82873 - 4.12926i) 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} +(0.574851 - 6.45520i) 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} +(7.11844 - 2.30821i) 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} +(6.79331 + 4.10498i) 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} +(6.51390 + 6.18901i) 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} +(-5.89295 - 5.03933i) 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} +(-1.28957 + 9.07397i) 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} +(5.04687 - 0.394075i) 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} +(-6.23937 + 7.68572i) 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	$0.0554317\pi$
$5$	0.918980	+	2.21861i	0.410980	+	0.992194i	−0.573895	+	0.818929i	$0.694568\pi$
$6$	−1.29998	+	2.07607i	−0.530713	+	0.847551i
$7$	−2.35812	+	1.19970i	−0.891286	+	0.453442i
$7$	−2.35812	+	1.19970i	−0.891286	+	0.453442i
$8$	−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	0.123831	−	0.992303i	$-0.460482\pi$
$13$	−1.76770	−	0.732205i	−0.490271	−	0.203077i	−0.614103	+	0.789226i	$0.710482\pi$
$14$	3.41910	−	1.51979i	0.913793	−	0.406180i
$15$	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	$0.172732\pi$
$17$			4.25844i			1.03282i	−0.856341	+	0.516411i	$0.827268\pi$
$18$	2.04990	+	3.71456i	0.483165	+	0.875529i
$19$	5.27576	+	2.18529i	1.21034	+	0.501340i	0.894327	−	0.447414i	$-0.147655\pi$
$19$	5.27576	+	2.18529i	1.21034	+	0.501340i	0.316015	+	0.948754i	$0.397655\pi$
$20$	1.36413	+	4.60502i	0.305028	+	1.02971i
$21$	−0.167061	+	4.57953i	−0.0364558	+	0.999335i
$22$	−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
$28$	−4.94119	+	1.89332i	−0.933797	+	0.357804i
$29$	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	$0.216048\pi$
$31$			6.99097i			1.25562i	−0.778368	+	0.627808i	$0.783952\pi$
$32$	−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
$35$	−4.82873	−	4.12926i	−0.816204	−	0.697972i
$36$	−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	0.696691	−	0.717371i	$-0.254655\pi$
$41$	−0.132416	−	0.132416i	−0.0206800	−	0.0206800i	−0.717371	+	0.696691i	$0.754655\pi$
$42$	0.574851	−	6.45520i	0.0887015	−	0.996058i
$43$	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	$0.279235\pi$
$47$			10.5437i			1.53796i	−0.639273	+	0.768980i	$0.720765\pi$
$48$	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
$56$	7.11844	−	2.30821i	0.951241	−	0.308448i
$57$	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	0.963703	−	0.266977i	$-0.0860247\pi$
$59$	0.718041	+	1.73350i	0.0934810	+	0.225683i	−0.870222	+	0.492660i	$0.836025\pi$
$60$	8.11986	+	1.80806i	1.04827	+	0.233420i
$61$	−4.24533	+	10.2491i	−0.543559	+	1.31227i	0.378638	+	0.925545i	$0.376393\pi$
$61$	−4.24533	+	10.2491i	−0.543559	+	1.31227i	−0.922196	+	0.386722i	$0.873607\pi$
$62$	0.517377	−	9.87318i	0.0657069	−	1.25390i
$63$	6.79331	+	4.10498i	0.855877	+	0.517179i
$64$	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
$70$	6.51390	+	6.18901i	0.778560	+	0.739728i
$71$	−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	−0.776469	−	0.630155i	$-0.782991\pi$
$73$	−1.25011	+	1.25011i	−0.146315	+	0.146315i	0.630155	+	0.776469i	$0.282991\pi$
$74$	−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
$77$	−5.89295	−	5.03933i	−0.671564	−	0.574285i
$78$	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	−0.999848	−	0.0174317i	$-0.994451\pi$
$83$	−2.55568	+	6.16997i	−0.280523	+	0.677242i	0.719325	+	0.694673i	$0.244451\pi$
$84$	−1.28957	+	9.07397i	−0.140704	+	0.990052i
$85$	−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	−0.0489396	−	0.998802i	$-0.515584\pi$
$89$	8.96098	−	8.96098i	0.949862	−	0.949862i	0.998802	+	0.0489396i	$0.0155842\pi$
$90$	−6.35735	+	7.96153i	−0.670123	+	0.839219i
$91$	5.04687	−	0.394075i	0.529056	−	0.0413102i
$92$	−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	$-0.833594\pi$
$97$		−	9.83487i		−	0.998579i	0.866435	−	0.499290i	$-0.166406\pi$
$98$	−6.23937	+	7.68572i	−0.630271	+	0.776375i
$99$	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	0.815121	−	0.579291i	$-0.196671\pi$
$101$	−1.71730	−	4.14593i	−0.170878	−	0.412535i	−0.985998	+	0.166756i	$0.946671\pi$
$102$	−8.84080	−	5.53587i	−0.875370	−	0.548133i
$103$	14.1619	+	14.1619i	1.39541	+	1.39541i	0.812632	+	0.582777i	$0.198034\pi$
$103$	14.1619	+	14.1619i	1.39541	+	1.39541i	0.582777	+	0.812632i	$0.301966\pi$
$104$	4.61432	+	2.82756i	0.452472	+	0.277265i
$105$	−10.3137	+	3.83785i	−1.00652	+	0.374536i
$106$	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
$112$	−10.2240	+	2.73302i	−0.966079	+	0.258246i
$113$	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
$119$	−5.10883	−	10.0419i	−0.468326	−	0.920540i
$120$	−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
$126$	−9.29024	−	6.30011i	−0.827640	−	0.561259i
$127$	−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	−0.0836584	−	0.996494i	$-0.526660\pi$
$131$	−9.69942	−	4.01763i	−0.847442	−	0.351022i	−0.763783	+	0.645473i	$0.776660\pi$
$132$	9.90944	+	2.20655i	0.862506	+	0.192056i
$133$	−15.0625	+	1.17613i	−1.30609	+	0.101983i
$134$	−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	0.739319	−	0.673356i	$-0.235148\pi$
$139$	−3.06055	−	7.38883i	−0.259593	−	0.626712i	−0.998912	+	0.0466431i	$0.985148\pi$
$140$	−8.74140	−	9.22266i	−0.738783	−	0.779457i
$141$	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
$147$	−5.10009	−	10.9995i	−0.420649	−	0.907224i
$148$	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
$154$	7.94953	+	7.55304i	0.640592	+	0.608641i
$155$	−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	−0.956843	−	0.290605i	$-0.906143\pi$
$157$	−0.936786	+	2.26160i	−0.0747637	+	0.180496i	0.882079	+	0.471101i	$0.156143\pi$
$158$	−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	−0.0422768	−	0.999106i	$-0.513461\pi$
$167$	12.3650	−	12.3650i	0.956829	−	0.956829i	0.999106	+	0.0422768i	$0.0134611\pi$
$168$	2.49277	−	12.7195i	0.192321	−	0.981332i
$169$	−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	$-0.544226\pi$
$173$	8.67738	−	20.9490i	0.659729	−	1.59273i	0.798223	−	0.602363i	$-0.205774\pi$
$174$	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	0.918517	−	0.395381i	$-0.129387\pi$
$181$	−0.141925	−	0.342638i	−0.0105492	−	0.0254681i	−0.929066	+	0.369913i	$0.879387\pi$
$182$	−7.15674	+	0.183041i	−0.530493	+	0.0135679i
$183$	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
$189$	11.9295	−	6.83284i	0.867741	−	0.497016i
$190$	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
$196$	9.38050	−	10.3926i	0.670036	−	0.742329i
$197$	−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	0.936210	−	0.351441i	$-0.114308\pi$
$199$	8.24918	+	8.24918i	0.584769	+	0.584769i	−0.351441	+	0.936210i	$0.614308\pi$
$200$	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
$203$	1.32967	+	17.0289i	0.0933246	+	1.19520i
$204$	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
$210$	14.8499	−	4.65682i	1.02474	−	0.321351i
$211$	−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
$217$	−8.38704	−	16.4856i	−0.569350	−	1.11911i
$218$	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	$-0.911261\pi$
$223$		−	8.21873i		−	0.550367i	0.961392	−	0.275184i	$-0.0887386\pi$
$224$	14.6414	−	3.10314i	0.978270	−	0.207337i
$225$	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	−0.612321	−	0.790609i	$-0.709764\pi$
$227$	−24.1719	−	10.0123i	−1.60434	−	0.664540i	−0.992021	+	0.126069i	$0.959764\pi$
$228$	16.6935	−	10.6131i	1.10555	−	0.702868i
$229$	0.135918	−	0.0562990i	0.00898170	−	0.00372034i	−0.378188	−	0.925729i	$-0.623453\pi$
$229$	0.135918	−	0.0562990i	0.00898170	−	0.00372034i	0.387170	+	0.922008i	$0.373453\pi$
$230$	24.8373	+	11.8466i	1.63772	+	0.781142i
$231$	−12.5868	+	4.68369i	−0.828152	+	0.308164i
$232$	−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
$238$	6.47191	+	14.5600i	0.419512	+	0.943786i
$239$	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	$-0.584176\pi$
$241$	−8.11530			−0.522752			−0.261376	+	0.965237i	$0.584176\pi$
$242$	−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
$245$	16.3406	+	3.94429i	1.04396	+	0.251991i
$246$	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	$0.0236445\pi$
$251$	5.45889	+	13.1789i	0.344562	+	0.831847i	−0.652680	+	0.757633i	$0.726355\pi$
$252$	12.6541	+	9.58504i	0.797135	+	0.603801i
$253$	−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	$-0.480898\pi$
$257$	1.92294			0.119950			0.0599748	+	0.998200i	$0.480898\pi$
$258$	−0.357925	+	2.12664i	−0.0222835	+	0.132399i
$259$	−9.22001	−	7.88445i	−0.572904	−	0.489916i
$260$	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
$266$	21.3595	−	0.546293i	1.30964	−	0.0334954i
$267$	−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	$0.295247\pi$
$269$	−6.39834	+	15.4470i	−0.390114	+	0.941818i	−0.989914	+	0.141668i	$0.954753\pi$
$270$	6.70707	+	16.3224i	0.408179	+	0.993349i
$271$	2.63605			0.160128			0.0800642	−	0.996790i	$-0.474487\pi$
$271$	2.63605			0.160128			0.0800642	+	0.996790i	$0.474487\pi$
$272$	−3.54115	+	16.6616i	−0.214713	+	1.01026i
$273$	3.64847	−	7.97291i	0.220815	−	0.482542i
$274$	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
$280$	11.6627	+	13.6719i	0.696981	+	0.817050i
$281$	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	0.366269	−	0.930509i	$-0.380635\pi$
$283$	21.5873	−	8.94174i	1.28323	−	0.531531i	0.916961	+	0.398977i	$0.130635\pi$
$284$	−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	0.961179	−	0.275925i	$-0.0889840\pi$
$293$	1.47918	+	3.57106i	0.0864147	+	0.208624i	−0.874765	+	0.484548i	$0.838984\pi$
$294$	6.38870	+	15.9118i	0.372597	+	0.927993i
$295$	−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
$301$	−1.51387	+	1.77031i	−0.0872581	+	0.102039i
$302$	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	−0.181027	−	0.983478i	$-0.557942\pi$
$307$	−17.5995	−	7.28995i	−1.00446	−	0.416059i	−0.823429	+	0.567419i	$0.807942\pi$
$308$	−10.6680	−	11.2553i	−0.607864	−	0.641330i
$309$	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	0.855152	−	0.518378i	$-0.173464\pi$
$311$	5.93906	+	5.93906i	0.336773	+	0.336773i	−0.518378	+	0.855152i	$0.673464\pi$
$312$	8.16249	−	4.60814i	0.462110	−	0.260885i
$313$	15.8975	+	15.8975i	0.898577	+	0.898577i	0.995310	−	0.0967329i	$-0.0308393\pi$
$313$	15.8975	+	15.8975i	0.898577	+	0.898577i	−0.0967329	+	0.995310i	$0.530839\pi$
$314$	1.49037	−	3.12468i	0.0841067	−	0.176336i
$315$	−2.86445	+	18.8441i	−0.161393	+	1.06175i
$316$	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
$322$	−10.8822	+	28.2975i	−0.606440	+	1.57696i
$323$	−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
$329$	−12.6493	−	24.8634i	−0.697376	−	1.37076i
$330$	−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
$336$	−4.46180	+	17.7790i	−0.243411	+	0.969923i
$337$			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
$343$	−2.93095	+	18.2869i	−0.158256	+	0.987398i
$344$	−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	−0.999756	−	0.0221004i	$-0.992965\pi$
$349$	−5.17842	+	12.5018i	−0.277194	+	0.669206i	0.722561	+	0.691307i	$0.242965\pi$
$350$	−1.02978	+	2.67779i	−0.0550441	+	0.143134i
$351$	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	$-0.432967\pi$
$353$	7.85492			0.418075			0.209038	+	0.977908i	$0.432967\pi$
$354$	−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
$357$	−19.5016	−	0.711420i	−1.03214	−	0.0376524i
$358$	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
$364$	10.1208	+	0.271139i	0.530476	+	0.0142116i
$365$	−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	$-0.354732\pi$
$367$	16.8850			0.881390			0.440695	+	0.897657i	$0.354732\pi$
$368$	−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
$371$	14.1808	+	12.1266i	0.736230	+	0.629583i
$372$	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
$378$	−17.3534	+	8.76700i	−0.892561	+	0.450926i
$379$	−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	$-0.636300\pi$
$383$	−16.2526			−0.830469			−0.415234	+	0.909714i	$0.636300\pi$
$384$	−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
$392$	−14.0170	+	13.9830i	−0.707964	+	0.706248i
$393$	−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	0.327005	−	0.945022i	$-0.393960\pi$
$397$	−2.19171	−	0.907836i	−0.109999	−	0.0455630i	−0.437004	+	0.899460i	$0.643960\pi$
$398$	−11.0396	−	12.2606i	−0.553366	−	0.614568i
$399$	−10.8890	+	23.7954i	−0.545131	+	1.19126i
$400$	−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
$406$	−0.617611	−	24.1480i	−0.0306515	−	1.19844i
$407$	−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	0.676609	−	0.736342i	$-0.263449\pi$
$409$	−1.20802	−	1.20802i	−0.0597328	−	0.0597328i	−0.736342	+	0.676609i	$0.763449\pi$
$410$	−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
$413$	−3.77290	−	3.22638i	−0.185652	−	0.158760i
$414$	−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	0.771527	−	0.636197i	$-0.219493\pi$
$419$	17.7515	+	7.35293i	0.867220	+	0.359214i	0.0956929	+	0.995411i	$0.469493\pi$
$420$	−21.3167	+	5.47773i	−1.04015	+	0.267286i
$421$	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
$427$	−2.28485	−	29.2618i	−0.110571	−	1.41608i
$428$	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	$-0.241454\pi$
$433$	30.2072			1.45167			0.725833	+	0.687871i	$0.241454\pi$
$434$	10.6248	+	23.9028i	0.510006	+	1.14737i
$435$	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	−0.782572	−	0.622561i	$-0.786092\pi$
$439$	−3.35260	+	3.35260i	−0.160011	+	0.160011i	0.622561	+	0.782572i	$0.286092\pi$
$440$	16.1039	−	11.7006i	0.767722	−	0.557802i
$441$	−20.9442	−	1.53013i	−0.997342	−	0.0728631i
$442$	−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
$448$	−20.9073	+	3.29893i	−0.987779	+	0.155860i
$449$			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
$455$	5.51227	+	10.8349i	0.258419	+	0.507948i
$456$	−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	$-0.733796\pi$
$461$	7.05310	−	17.0277i	0.328496	−	0.793058i	0.998704	−	0.0508859i	$-0.0162045\pi$
$462$	18.1227	−	5.68316i	0.843144	−	0.264405i
$463$			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	$0.322986\pi$
$467$	−9.63693	+	23.2656i	−0.445944	+	1.07660i	−0.973828	+	0.227288i	$0.927014\pi$
$468$	0.679371	+	11.4599i	0.0314039	+	0.529736i
$469$	−29.3169	+	2.28915i	−1.35373	+	0.105703i
$470$	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
$476$	−8.06259	−	21.0417i	−0.369548	−	0.964446i
$477$	−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	$-0.156666\pi$
$479$	38.5766			1.76261			0.881304	+	0.472549i	$0.156666\pi$
$480$	−21.8838	−	8.64339i	−0.998855	−	0.394515i
$481$		−	8.77320i		−	0.400024i
$482$	11.4610	+	0.600584i	0.522036	+	0.0273558i
$483$	−25.2813	−	27.1957i	−1.15034	−	1.23745i
$484$	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
$490$	−22.7855	−	6.77973i	−1.02934	−	0.306277i
$491$	−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	4.54584e−5	−	1.00000i	$-0.499986\pi$
$503$	−22.4266	−	22.4266i	−0.999955	−	0.999955i	−1.00000		4.54584e-5i	$0.999986\pi$
$504$	−17.1618	−	14.4732i	−0.764446	−	0.644688i
$505$	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	0.443090	−	0.896477i	$-0.353882\pi$
$509$	2.76365	+	1.14474i	0.122497	+	0.0507398i	−0.320593	+	0.947217i	$0.603882\pi$
$510$	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
$518$	12.4377	+	11.8174i	0.546481	+	0.519225i
$519$	−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	$-0.963119\pi$
$521$	−25.3111	−	25.3111i	−1.10890	−	1.10890i	−0.115605	−	0.993295i	$-0.536881\pi$
$522$	27.2199	−	3.04951i	1.19138	−	0.133474i
$523$	7.85797	+	18.9708i	0.343605	+	0.829536i	0.997345	+	0.0728169i	$0.0231989\pi$
$523$	7.85797	+	18.9708i	0.343605	+	0.829536i	−0.653740	+	0.756719i	$0.726801\pi$
$524$	−18.4528	−	10.0188i	−0.806113	−	0.437672i
$525$	−2.39238	−	2.57353i	−0.104412	−	0.112318i
$526$	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
$532$	−30.2060	−	0.809224i	−1.30959	−	0.0350843i
$533$	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
$539$	19.9420	+	4.81359i	0.858961	+	0.207336i
$540$	−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
$546$	−5.74269	+	10.9899i	−0.245764	+	0.470326i
$547$	−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
$553$	20.2020	+	39.7089i	0.859075	+	1.68860i
$554$	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
$560$	−15.4592	−	20.1716i	−0.653270	−	0.852404i
$561$	−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	−0.890496	−	0.454991i	$-0.849643\pi$
$563$	1.44517	−	3.48895i	0.0609067	−	0.147042i	0.951403	+	0.307949i	$0.0996426\pi$
$564$	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
$567$	−0.311187	−	23.8097i	−0.0130686	−	0.999915i
$568$	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
$574$	−0.653989	−	0.251500i	−0.0272970	−	0.0104974i
$575$		−	6.21293i		−	0.259097i
$576$	−5.76300	−	23.2978i	−0.240125	−	0.970742i
$577$		−	12.4923i		−	0.520060i	−0.965601	−	0.260030i	$-0.916268\pi$
$577$		−	12.4923i		−	0.520060i	0.965601	−	0.260030i	$-0.0837324\pi$
$578$	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
$581$	−1.37548	−	17.6156i	−0.0570643	−	0.730817i
$582$	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	0.495529	−	0.868591i	$-0.334974\pi$
$587$	35.3756	−	14.6531i	1.46011	−	0.604797i	0.964579	+	0.263795i	$0.0849741\pi$
$588$	−7.84504	−	22.9446i	−0.323524	−	0.946220i
$589$	−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	$-0.902501\pi$
$593$		−	14.6858i		−	0.603073i	0.953455	−	0.301536i	$-0.0974994\pi$
$594$	8.18527	+	19.9198i	0.335846	+	0.817318i
$595$	17.5842	−	20.5628i	0.720881	−	0.842993i
$596$	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	0.592060	−	0.805894i	$-0.298315\pi$
$601$	−5.24221	−	5.24221i	−0.213834	−	0.213834i	−0.805894	+	0.592060i	$0.798315\pi$
$602$	2.26902	−	2.38813i	0.0924783	−	0.0973330i
$603$	−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	$-0.992924\pi$
$607$		−	1.09521i		−	0.0444533i	0.999753	−	0.0222266i	$-0.00707554\pi$
$608$	−25.6283	−	19.6642i	−1.03937	−	0.797488i
$609$	26.9019	+	12.3105i	1.09012	+	0.498847i
$610$	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
$616$	14.2331	+	16.6851i	0.573470	+	0.672261i
$617$	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	0.934152	−	0.356875i	$-0.116158\pi$
$619$	0.528903	+	1.27689i	0.0212584	+	0.0513224i	−0.912894	+	0.408197i	$0.866158\pi$
$620$	−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
$630$	5.43998	−	26.4011i	0.216734	−	1.05185i
$631$	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
$637$	−11.4284	+	6.98398i	−0.452808	+	0.276716i
$638$	−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	$0.464500\pi$
$643$	−16.9924	+	41.0234i	−0.670116	+	1.61780i	−0.781411	+	0.624016i	$0.785500\pi$
$644$	17.4628	−	39.1585i	0.688131	−	1.54306i
$645$	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	−0.0237528	−	0.999718i	$-0.507561\pi$
$647$	24.8248	−	24.8248i	0.975965	−	0.975965i	0.999718	+	0.0237528i	$0.00756147\pi$
$648$	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
$651$	−32.0154	−	1.16792i	−1.25478	−	0.0457745i
$652$	−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
$658$	16.0242	+	36.0500i	0.624688	+	1.40538i
$659$	−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	$0.0422355\pi$
$661$	9.86920	+	23.8264i	0.383867	+	0.926738i	−0.607343	+	0.794440i	$0.707764\pi$
$662$	−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
$665$	−16.4515	−	32.3371i	−0.637964	−	1.25398i
$666$	−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
$672$	7.61705	−	24.7786i	0.293834	−	0.955856i
$673$	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	$0.0384564\pi$
$677$	9.78269	+	23.6175i	0.375979	+	0.907694i	−0.616732	+	0.787174i	$0.711544\pi$
$678$	−10.8402	+	17.3118i	−0.416315	+	0.664856i
$679$	11.7989	+	23.1918i	0.452798	+	0.890019i
$680$	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
$686$	5.49265	−	25.6092i	0.209710	−	0.977764i
$687$	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	0.382769	−	0.923844i	$-0.374971\pi$
$691$	0.00449366	+	0.00186133i	0.000170947	+	7.08085e-5i	−0.382598	+	0.923915i	$0.624971\pi$
$692$	21.6388	−	39.8547i	0.822583	−	1.51505i
$693$	−3.49576	+	22.9973i	−0.132793	+	0.873595i
$694$	−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
$700$	1.65251	−	3.70557i	0.0624590	−	0.140058i
$701$	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
$707$	9.02345	+	7.71635i	0.339362	+	0.290203i
$708$	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
$714$	27.4890	+	2.44797i	1.02875	+	0.0916129i
$715$	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	$0.243162\pi$
$719$			37.0977i			1.38351i	−0.722132	+	0.691755i	$0.756838\pi$
$720$	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	−0.332133	−	0.943233i	$-0.607768\pi$
$727$	16.4771	−	16.4771i	0.611100	−	0.611100i	0.943233	+	0.332133i	$0.107768\pi$
$728$	−14.2733	−	1.13193i	−0.529005	−	0.0419521i
$729$	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	−0.738091	−	0.674701i	$-0.764273\pi$
$733$	7.06369	−	17.0533i	0.260903	−	0.629877i	0.998995	+	0.0448241i	$0.0142727\pi$
$734$	−23.8463	−	1.24960i	−0.880183	−	0.0461235i
$735$	19.7168	−	21.4234i	0.727264	−	0.790216i
$736$	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
$742$	−19.1297	−	18.1756i	−0.702275	−	0.667248i
$743$	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
$749$	−2.35370	−	2.01275i	−0.0860023	−	0.0735444i
$750$	−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
$756$	25.1566	−	11.0972i	0.914936	−	0.403600i
$757$	−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	$-0.374522\pi$
$761$	36.0655	−	36.0655i	1.30737	−	1.30737i	0.923304	−	0.384069i	$-0.125478\pi$
$762$	9.77867	−	15.6166i	0.354244	−	0.565729i
$763$	−0.167446	−	2.14446i	−0.00606195	−	0.0776348i
$764$	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	$0.225871\pi$
$769$			36.1347i			1.30305i	−0.758627	+	0.651525i	$0.774129\pi$
$770$	−9.45181	+	24.5780i	−0.340620	+	0.885731i
$771$	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	0.978513	−	0.206186i	$-0.0661053\pi$
$773$	3.91476	+	9.45106i	0.140804	+	0.339931i	−0.837709	+	0.546117i	$0.816105\pi$
$774$	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
$777$	−19.6931	+	7.32803i	−0.706487	+	0.262891i
$778$	−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
$784$	20.8307	−	18.7105i	0.743952	−	0.668233i
$785$	−5.87851			−0.209813
$786$	20.9499	−	14.9138i	0.747258	−	0.531958i
$787$	28.7299	+	11.9003i	1.02411	+	0.424200i	0.830583	−	0.556895i	$-0.188008\pi$
$787$	28.7299	+	11.9003i	1.02411	+	0.424200i	0.193526	+	0.981095i	$0.438008\pi$
$788$	−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
$791$	−19.6638	+	10.0040i	−0.699163	+	0.355700i
$792$	−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	0.167208	−	0.985922i	$-0.446525\pi$
$797$	−11.6231	−	4.81444i	−0.411711	−	0.170536i	−0.578918	+	0.815386i	$0.696525\pi$
$798$	17.1392	−	32.7998i	0.606723	−	1.16110i
$799$	−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
$805$	51.3250	−	4.00761i	1.80897	−	0.141250i
$806$	−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	$0.110825\pi$
$811$	14.7108	+	35.5150i	0.516566	+	1.24710i	−0.423433	+	0.905927i	$0.639175\pi$
$812$	−0.914867	+	34.1493i	−0.0321055	+	1.19841i
$813$	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
$819$	−9.00285	−	12.2305i	−0.314585	−	0.427367i
$820$	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
$826$	5.08961	+	4.83576i	0.177090	+	0.168258i
$827$	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	−0.914229	−	0.405198i	$-0.867203\pi$
$829$	0.539755	−	1.30308i	0.0187465	−	0.0452579i	0.932976	+	0.359940i	$0.117203\pi$
$830$	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	−0.530937	−	0.847411i	$-0.678160\pi$
$839$	9.16683	−	9.16683i	0.316474	−	0.316474i	0.847411	+	0.530937i	$0.178160\pi$
$840$	30.5105	−	6.15849i	1.05271	−	0.212488i
$841$	−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	$-0.932821\pi$
$853$	−12.6907	−	30.6381i	−0.434522	−	1.04903i	0.543290	−	0.839545i	$-0.317179\pi$
$854$	1.06128	+	41.4948i	0.0363161	+	1.41992i
$855$	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	$0.662069\pi$
$857$	−39.8309	+	39.8309i	−1.36060	+	1.36060i	−0.873157	+	0.487439i	$0.837931\pi$
$858$	11.6413	+	7.28946i	0.397427	+	0.248858i
$859$	16.7972	−	6.95764i	0.573114	−	0.237392i	−0.0772534	−	0.997011i	$-0.524615\pi$
$859$	16.7972	−	6.95764i	0.573114	−	0.237392i	0.650367	+	0.759620i	$0.274615\pi$
$860$	2.66108	+	3.28608i	0.0907419	+	0.112054i
$861$	0.628526	−	0.584283i	0.0214201	−	0.0199123i
$862$	−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
$868$	−13.2362	−	34.5437i	−0.449265	−	1.17249i
$869$	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
$875$	−26.8144	+	2.09375i	−0.906491	+	0.0707815i
$876$	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	$0.278773\pi$
$881$			45.5940i			1.53610i	−0.640389	+	0.768051i	$0.721227\pi$
$882$	29.4657	+	3.71096i	0.992162	+	0.124955i
$883$	−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	0.996941	−	0.0781593i	$-0.0249043\pi$
$887$	27.3637	+	27.3637i	0.918782	+	0.918782i	−0.0781593	+	0.996941i	$0.524904\pi$
$888$	−21.6406	−	6.02305i	−0.726212	−	0.202120i
$889$	17.7382	−	9.02434i	0.594921	−	0.302667i
$890$	−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
$896$	29.7711	−	3.11173i	0.994582	−	0.103955i
$897$	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
$903$	1.40704	+	3.78123i	0.0468232	+	0.125831i
$904$	−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
$910$	−6.98299	−	15.7098i	−0.231484	−	0.520775i
$911$	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
$917$	27.6923	−	2.16230i	0.914481	−	0.0714054i
$918$	−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
$924$	−26.0148	+	6.68500i	−0.855825	+	0.219920i
$925$	−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	$-0.457809\pi$
$929$	8.05622			0.264316			0.132158	+	0.991229i	$0.457809\pi$
$930$	6.82516	−	40.5521i	0.223806	−	1.32976i
$931$	34.1083	−	20.8439i	1.11785	−	0.683132i
$932$	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	−0.272690	−	0.962102i	$-0.587913\pi$
$937$	21.1032	−	21.1032i	0.689413	−	0.689413i	0.962102	+	0.272690i	$0.0879132\pi$
$938$	41.5730	−	1.06328i	1.35741	−	0.0347172i
$939$	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	−0.978718	−	0.205210i	$-0.934212\pi$
$941$	−4.34229	+	10.4832i	−0.141555	+	0.341743i	0.837163	+	0.546953i	$0.184212\pi$
$942$	−3.47744	−	4.88486i	−0.113301	−	0.159157i
$943$	1.51736			0.0494122
$944$	1.36790	+	7.37962i	0.0445214	+	0.240186i
$945$	26.1224	+	20.1876i	0.849761	+	0.656704i
$946$	−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
$952$	9.82938	+	30.3134i	0.318572	+	0.982463i
$953$	−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
$966$	33.6916	+	40.2788i	1.08401	+	1.29595i
$967$	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	−0.941998	−	0.335620i	$-0.891054\pi$
$971$	−42.7144	+	17.6929i	−1.37077	+	0.567792i	−0.428774	+	0.903412i	$0.641054\pi$
$972$	14.9865	+	27.3387i	0.480693	+	0.876889i
$973$	16.0815	+	13.7520i	0.515549	+	0.440869i
$974$	−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
$980$	31.6777	+	11.2611i	1.01191	+	0.359723i
$981$	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	0.738204	−	0.674577i	$-0.235674\pi$
$983$	1.99489	+	1.99489i	0.0636270	+	0.0636270i	−0.674577	+	0.738204i	$0.735674\pi$
$984$	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
$987$	−48.2853	−	1.76145i	−1.53694	−	0.0560675i
$988$	−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
$994$	−18.3255	−	7.04733i	−0.581251	−	0.223528i
$995$	−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	−0.311927	−	0.950106i	$-0.600975\pi$
$997$	4.39948	−	1.82232i	0.139333	−	0.0577135i	0.451260	+	0.892392i	$0.350975\pi$
$998$	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.125.2	yes	496
3.2	odd	2	inner	672.2.bo.a.125.124	yes	496
7.6	odd	2	inner	672.2.bo.a.125.1	✓	496
21.20	even	2	inner	672.2.bo.a.125.123	yes	496
32.21	even	8	inner	672.2.bo.a.629.123	yes	496
96.53	odd	8	inner	672.2.bo.a.629.1	yes	496
224.181	odd	8	inner	672.2.bo.a.629.124	yes	496
672.629	even	8	inner	672.2.bo.a.629.2	yes	496

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

\(f(q)\)	\(=\)	\(q+(-1.41228 - 0.0740064i) q^{2} +(0.841142 - 1.51409i) q^{3} +(1.98905 + 0.209035i) q^{4} +(0.918980 + 2.21861i) q^{5} +(-1.29998 + 2.07607i) q^{6} +(-2.35812 + 1.19970i) q^{7} +(-2.79361 - 0.442417i) q^{8} +(-1.58496 - 2.54714i) q^{9} +O(q^{10})\)	\(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} +(-2.35812 + 1.19970i) 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} +(3.41910 - 1.51979i) 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} +(-0.167061 + 4.57953i) 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} +(-4.94119 + 1.89332i) 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} +(-4.82873 - 4.12926i) 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} +(0.574851 - 6.45520i) 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} +(7.11844 - 2.30821i) 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} +(6.79331 + 4.10498i) 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} +(6.51390 + 6.18901i) 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} +(-5.89295 - 5.03933i) 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} +(-1.28957 + 9.07397i) 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} +(5.04687 - 0.394075i) 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} +(-6.23937 + 7.68572i) 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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