LMFDB - Embedded newform 960.2.cn.a.611.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [960,2,Mod(11,960)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(960, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 5, 8, 0]))

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

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

chi := DirichletCharacter("960.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.cn (of order $16$, degree $8$, 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:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$1024$
Relative dimension:	$128$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			611.9
Character	$\chi$	$=$	960.611
Dual form			960.2.cn.a.11.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39036 + 0.258642i) q^{2} +(0.964034 - 1.43897i) q^{3} +(1.86621 - 0.719212i) q^{4} +(-0.831470 - 0.555570i) q^{5} +(-0.968177 + 2.25003i) q^{6} +(1.69186 + 4.08451i) q^{7} +(-2.40869 + 1.48264i) q^{8} +(-1.14128 - 2.77444i) q^{9} +O(q^{10})$	\(q+(-1.39036 + 0.258642i) q^{2} +(0.964034 - 1.43897i) q^{3} +(1.86621 - 0.719212i) q^{4} +(-0.831470 - 0.555570i) q^{5} +(-0.968177 + 2.25003i) q^{6} +(1.69186 + 4.08451i) q^{7} +(-2.40869 + 1.48264i) q^{8} +(-1.14128 - 2.77444i) q^{9} +(1.29974 + 0.557390i) q^{10} +(0.801441 + 4.02911i) q^{11} +(0.764164 - 3.37877i) q^{12} +(-0.795184 - 1.19008i) q^{13} +(-3.40872 - 5.24136i) q^{14} +(-1.60101 + 0.660872i) q^{15} +(2.96547 - 2.68440i) q^{16} +(-2.88827 + 2.88827i) q^{17} +(2.30437 + 3.56228i) q^{18} +(2.70435 + 4.04734i) q^{19} +(-1.95127 - 0.438807i) q^{20} +(7.50851 + 1.50307i) q^{21} +(-2.15639 - 5.39464i) q^{22} +(-2.41946 + 5.84108i) q^{23} +(-0.188573 + 4.89535i) q^{24} +(0.382683 + 0.923880i) q^{25} +(1.41340 + 1.44897i) q^{26} +(-5.09256 - 1.03239i) q^{27} +(6.09499 + 6.40575i) q^{28} +(-9.81291 - 1.95191i) q^{29} +(2.05506 - 1.33294i) q^{30} -7.34781 q^{31} +(-3.42877 + 4.49928i) q^{32} +(6.57040 + 2.73095i) q^{33} +(3.26871 - 4.76277i) q^{34} +(0.862503 - 4.33610i) q^{35} +(-4.12526 - 4.35686i) q^{36} +(-4.88878 - 3.26658i) q^{37} +(-4.80683 - 4.92781i) q^{38} +(-2.47907 - 0.00302822i) q^{39} +(2.82646 + 0.105420i) q^{40} +(3.77252 + 1.56263i) q^{41} +(-10.8283 - 0.147797i) q^{42} +(1.63266 + 8.20795i) q^{43} +(4.39344 + 6.94276i) q^{44} +(-0.592457 + 2.94092i) q^{45} +(1.85317 - 8.74699i) q^{46} +(2.83785 + 2.83785i) q^{47} +(-1.00396 - 6.85508i) q^{48} +(-8.87110 + 8.87110i) q^{49} +(-0.771022 - 1.18555i) q^{50} +(1.37175 + 6.94053i) q^{51} +(-2.33990 - 1.64903i) q^{52} +(4.81093 - 0.956954i) q^{53} +(7.34752 + 0.118241i) q^{54} +(1.57208 - 3.79534i) q^{55} +(-10.1310 - 7.32988i) q^{56} +(8.43109 + 0.0102987i) q^{57} +(14.1483 + 0.175827i) q^{58} +(5.35529 - 8.01475i) q^{59} +(-2.51252 + 2.38479i) q^{60} +(13.2916 + 2.64387i) q^{61} +(10.2161 - 1.90045i) q^{62} +(9.40134 - 9.35551i) q^{63} +(3.60353 - 7.14245i) q^{64} +1.43129i q^{65} +(-9.84156 - 2.09763i) q^{66} +(-0.792706 + 3.98520i) q^{67} +(-3.31284 + 7.46740i) q^{68} +(6.07271 + 9.11253i) q^{69} +(-0.0776939 + 6.25182i) q^{70} +(8.45413 - 3.50182i) q^{71} +(6.86247 + 4.99064i) q^{72} +(-0.865884 - 0.358661i) q^{73} +(7.64205 + 3.27728i) q^{74} +(1.69836 + 0.339981i) q^{75} +(7.95778 + 5.60819i) q^{76} +(-15.1010 + 10.0902i) q^{77} +(3.44759 - 0.636982i) q^{78} +(-12.2311 - 12.2311i) q^{79} +(-3.95707 + 0.584470i) q^{80} +(-6.39498 + 6.33279i) q^{81} +(-5.64933 - 1.19689i) q^{82} +(4.98973 - 3.33403i) q^{83} +(15.0935 - 2.59516i) q^{84} +(4.00615 - 0.796873i) q^{85} +(-4.39291 - 10.9897i) q^{86} +(-12.2687 + 12.2388i) q^{87} +(-7.90416 - 8.51662i) q^{88} +(4.54603 - 1.88303i) q^{89} +(0.0630849 - 4.24217i) q^{90} +(3.51554 - 5.26138i) q^{91} +(-0.314233 + 12.6408i) q^{92} +(-7.08354 + 10.5733i) q^{93} +(-4.67963 - 3.21165i) q^{94} -4.86770i q^{95} +(3.16888 + 9.27137i) q^{96} +13.3497i q^{97} +(10.0396 - 14.6285i) q^{98} +(10.2639 - 6.82188i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 1024 q+O(q^{10}) $ 1024 * q	$ 1024 q + 80 q^{24} + 80 q^{42} - 96 q^{52} - 288 q^{58} - 96 q^{64} + 256 q^{67} - 112 q^{76} - 48 q^{78} + 32 q^{79} - 112 q^{84} - 160 q^{88} - 144 q^{90} - 16 q^{94} - 272 q^{96}+O(q^{100}) $ 1024 * q + 80 * q^24 + 80 * q^42 - 96 * q^52 - 288 * q^58 - 96 * q^64 + 256 * q^67 - 112 * q^76 - 48 * q^78 + 32 * q^79 - 112 * q^84 - 160 * q^88 - 144 * q^90 - 16 * q^94 - 272 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{11}{16}\right)$

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 $

$2$	−1.39036	+	0.258642i	−0.983134	+	0.182888i
$2$	−1.39036	+	0.258642i	−0.983134	+	0.182888i
$3$	0.964034	−	1.43897i	0.556585	−	0.830790i
$3$	0.964034	−	1.43897i	0.556585	−	0.830790i
$4$	1.86621	−	0.719212i	0.933104	−	0.359606i
$5$	−0.831470	−	0.555570i	−0.371845	−	0.248459i
$5$	−0.831470	−	0.555570i	−0.371845	−	0.248459i
$6$	−0.968177	+	2.25003i	−0.395257	+	0.918571i
$7$	1.69186	+	4.08451i	0.639463	+	1.54380i	0.827396	+	0.561619i	$0.189821\pi$
$7$	1.69186	+	4.08451i	0.639463	+	1.54380i	−0.187933	+	0.982182i	$0.560179\pi$
$8$	−2.40869	+	1.48264i	−0.851599	+	0.524194i
$9$	−1.14128	−	2.77444i	−0.380425	−	0.924812i
$10$	1.29974	+	0.557390i	0.411013	+	0.176262i
$11$	0.801441	+	4.02911i	0.241643	+	1.21482i	0.890881	+	0.454238i	$0.150088\pi$
$11$	0.801441	+	4.02911i	0.241643	+	1.21482i	−0.649237	+	0.760586i	$0.724912\pi$
$12$	0.764164	−	3.37877i	0.220595	−	0.975365i
$13$	−0.795184	−	1.19008i	−0.220544	−	0.330068i	0.704655	−	0.709551i	$-0.251102\pi$
$13$	−0.795184	−	1.19008i	−0.220544	−	0.330068i	−0.925199	+	0.379483i	$0.876102\pi$
$14$	−3.40872	−	5.24136i	−0.911020	−	1.40081i
$15$	−1.60101	+	0.660872i	−0.413380	+	0.170636i
$16$	2.96547	−	2.68440i	0.741367	−	0.671100i
$17$	−2.88827	+	2.88827i	−0.700509	+	0.700509i	−0.964520	−	0.264011i	$-0.914955\pi$
$17$	−2.88827	+	2.88827i	−0.700509	+	0.700509i	0.264011	+	0.964520i	$0.414955\pi$
$18$	2.30437	+	3.56228i	0.543145	+	0.839639i
$19$	2.70435	+	4.04734i	0.620420	+	0.928524i	0.999994	+	0.00336299i	$0.00107047\pi$
$19$	2.70435	+	4.04734i	0.620420	+	0.928524i	−0.379574	+	0.925161i	$0.623930\pi$
$20$	−1.95127	−	0.438807i	−0.436317	−	0.0981203i
$21$	7.50851	+	1.50307i	1.63849	+	0.327997i
$22$	−2.15639	−	5.39464i	−0.459744	−	1.15014i
$23$	−2.41946	+	5.84108i	−0.504491	+	1.21795i	0.442523	+	0.896757i	$0.354084\pi$
$23$	−2.41946	+	5.84108i	−0.504491	+	1.21795i	−0.947014	+	0.321192i	$0.895916\pi$
$24$	−0.188573	+	4.89535i	−0.0384923	+	0.999259i
$25$	0.382683	+	0.923880i	0.0765367	+	0.184776i
$26$	1.41340	+	1.44897i	0.277190	+	0.284166i
$27$	−5.09256	−	1.03239i	−0.980064	−	0.198683i
$28$	6.09499	+	6.40575i	1.15185	+	1.21057i
$29$	−9.81291	−	1.95191i	−1.82221	−	0.362461i	−0.838886	−	0.544308i	$-0.816792\pi$
$29$	−9.81291	−	1.95191i	−1.82221	−	0.362461i	−0.983327	+	0.181847i	$0.941792\pi$
$30$	2.05506	−	1.33294i	0.375201	−	0.243361i
$31$	−7.34781			−1.31971			−0.659853	−	0.751395i	$-0.729381\pi$
$31$	−7.34781			−1.31971			−0.659853	+	0.751395i	$0.729381\pi$
$32$	−3.42877	+	4.49928i	−0.606127	+	0.795368i
$33$	6.57040	+	2.73095i	1.14376	+	0.475398i
$34$	3.26871	−	4.76277i	0.560580	−	0.816808i
$35$	0.862503	−	4.33610i	0.145790	−	0.732934i
$36$	−4.12526	−	4.35686i	−0.687544	−	0.726143i
$37$	−4.88878	−	3.26658i	−0.803711	−	0.537022i	0.0845189	−	0.996422i	$-0.473065\pi$
$37$	−4.88878	−	3.26658i	−0.803711	−	0.537022i	−0.888230	+	0.459399i	$0.848065\pi$
$38$	−4.80683	−	4.92781i	−0.779772	−	0.799396i
$39$	−2.47907	−	0.00302822i	−0.396969	−	0.000484904i
$40$	2.82646	+	0.105420i	0.446903	+	0.0166684i
$41$	3.77252	+	1.56263i	0.589169	+	0.244042i	0.657293	−	0.753635i	$-0.271701\pi$
$41$	3.77252	+	1.56263i	0.589169	+	0.244042i	−0.0681243	+	0.997677i	$0.521701\pi$
$42$	−10.8283	−	0.147797i	−1.67084	−	0.0228056i
$43$	1.63266	+	8.20795i	0.248979	+	1.25170i	0.879639	+	0.475642i	$0.157784\pi$
$43$	1.63266	+	8.20795i	0.248979	+	1.25170i	−0.630660	+	0.776059i	$0.717216\pi$
$44$	4.39344	+	6.94276i	0.662336	+	1.04666i
$45$	−0.592457	+	2.94092i	−0.0883183	+	0.438406i
$46$	1.85317	−	8.74699i	0.273235	−	1.28967i
$47$	2.83785	+	2.83785i	0.413944	+	0.413944i	0.883110	−	0.469166i	$-0.155445\pi$
$47$	2.83785	+	2.83785i	0.413944	+	0.413944i	−0.469166	+	0.883110i	$0.655445\pi$
$48$	−1.00396	−	6.85508i	−0.144909	−	0.989445i
$49$	−8.87110	+	8.87110i	−1.26730	+	1.26730i
$50$	−0.771022	−	1.18555i	−0.109039	−	0.167662i
$51$	1.37175	+	6.94053i	0.192083	+	0.971869i
$52$	−2.33990	−	1.64903i	−0.324485	−	0.228679i
$53$	4.81093	−	0.956954i	0.660833	−	0.131448i	0.146730	−	0.989177i	$-0.453125\pi$
$53$	4.81093	−	0.956954i	0.660833	−	0.131448i	0.514102	+	0.857729i	$0.328125\pi$
$54$	7.34752	+	0.118241i	0.999871	+	0.0160906i
$55$	1.57208	−	3.79534i	0.211980	−	0.511764i
$56$	−10.1310	−	7.32988i	−1.35382	−	0.979496i
$57$	8.43109	+	0.0102987i	1.11673	+	0.00136410i
$58$	14.1483	+	0.175827i	1.85777	+	0.0230873i
$59$	5.35529	−	8.01475i	0.697199	−	1.04343i	−0.298822	−	0.954309i	$-0.596594\pi$
$59$	5.35529	−	8.01475i	0.697199	−	1.04343i	0.996021	−	0.0891229i	$-0.0284064\pi$
$60$	−2.51252	+	2.38479i	−0.324365	+	0.307876i
$61$	13.2916	+	2.64387i	1.70182	+	0.338512i	0.947927	−	0.318489i	$-0.103175\pi$
$61$	13.2916	+	2.64387i	1.70182	+	0.338512i	0.753890	+	0.657001i	$0.228175\pi$
$62$	10.2161	−	1.90045i	1.29745	−	0.241358i
$63$	9.40134	−	9.35551i	1.18446	−	1.17868i
$64$	3.60353	−	7.14245i	0.450441	−	0.892806i
$65$			1.43129i			0.177530i
$66$	−9.84156	−	2.09763i	−1.21141	−	0.258201i
$67$	−0.792706	+	3.98520i	−0.0968444	+	0.486870i	0.901672	+	0.432420i	$0.142340\pi$
$67$	−0.792706	+	3.98520i	−0.0968444	+	0.486870i	−0.998517	+	0.0544493i	$0.982660\pi$
$68$	−3.31284	+	7.46740i	−0.401741	+	0.905555i
$69$	6.07271	+	9.11253i	0.731068	+	1.09702i
$70$	−0.0776939	+	6.25182i	−0.00928620	+	0.747235i
$71$	8.45413	−	3.50182i	1.00332	−	0.415589i	0.180307	−	0.983610i	$-0.442291\pi$
$71$	8.45413	−	3.50182i	1.00332	−	0.415589i	0.823014	+	0.568021i	$0.192291\pi$
$72$	6.86247	+	4.99064i	0.808750	+	0.588152i
$73$	−0.865884	−	0.358661i	−0.101344	−	0.0419781i	0.331435	−	0.943478i	$-0.392467\pi$
$73$	−0.865884	−	0.358661i	−0.101344	−	0.0419781i	−0.432779	+	0.901500i	$0.642467\pi$
$74$	7.64205	+	3.27728i	0.888370	+	0.380976i
$75$	1.69836	+	0.339981i	0.196109	+	0.0392576i
$76$	7.95778	+	5.60819i	0.912819	+	0.643303i
$77$	−15.1010	+	10.0902i	−1.72092	+	1.14988i
$78$	3.44759	−	0.636982i	0.390362	−	0.0721240i
$79$	−12.2311	−	12.2311i	−1.37611	−	1.37611i	−0.851088	−	0.525023i	$-0.824057\pi$
$79$	−12.2311	−	12.2311i	−1.37611	−	1.37611i	−0.525023	−	0.851088i	$-0.675943\pi$
$80$	−3.95707	+	0.584470i	−0.442414	+	0.0653457i
$81$	−6.39498	+	6.33279i	−0.710553	+	0.703643i
$82$	−5.64933	−	1.19689i	−0.623864	−	0.132174i
$83$	4.98973	−	3.33403i	0.547694	−	0.365958i	−0.250726	−	0.968058i	$-0.580669\pi$
$83$	4.98973	−	3.33403i	0.547694	−	0.365958i	0.798420	+	0.602101i	$0.205669\pi$
$84$	15.0935	−	2.59516i	1.64683	−	0.283155i
$85$	4.00615	−	0.796873i	0.434528	−	0.0864330i
$86$	−4.39291	−	10.9897i	−0.473700	−	1.18505i
$87$	−12.2687	+	12.2388i	−1.31535	+	1.31214i
$88$	−7.90416	−	8.51662i	−0.842587	−	0.907875i
$89$	4.54603	−	1.88303i	0.481878	−	0.199600i	−0.128502	−	0.991709i	$-0.541017\pi$
$89$	4.54603	−	1.88303i	0.481878	−	0.199600i	0.610380	+	0.792109i	$0.291017\pi$
$90$	0.0630849	−	4.24217i	0.00664973	−	0.447164i
$91$	3.51554	−	5.26138i	0.368529	−	0.551543i
$92$	−0.314233	+	12.6408i	−0.0327610	+	1.31789i
$93$	−7.08354	+	10.5733i	−0.734529	+	1.09640i
$94$	−4.67963	−	3.21165i	−0.482667	−	0.331257i
$95$		−	4.86770i		−	0.499415i
$96$	3.16888	+	9.27137i	0.323422	+	0.946255i
$97$			13.3497i			1.35546i	0.735313	+	0.677728i	$0.237035\pi$
$97$			13.3497i			1.35546i	−0.735313	+	0.677728i	$0.762965\pi$
$98$	10.0396	−	14.6285i	1.01415	−	1.47770i
$99$	10.2639	−	6.82188i	1.03156	−	0.685624i
$100$	1.37863	+	1.44892i	0.137863	+	0.144892i
$101$	−1.98305	+	2.96785i	−0.197321	+	0.295312i	−0.916914	−	0.399084i	$-0.869328\pi$
$101$	−1.98305	+	2.96785i	−0.197321	+	0.295312i	0.719593	+	0.694396i	$0.244328\pi$
$102$	−3.70234	−	9.29506i	−0.366586	−	0.920348i
$103$	−6.29175	+	2.60613i	−0.619945	+	0.256789i	−0.670474	−	0.741933i	$-0.733909\pi$
$103$	−6.29175	+	2.60613i	−0.619945	+	0.256789i	0.0505293	+	0.998723i	$0.483909\pi$
$104$	3.67981	+	1.68755i	0.360835	+	0.165477i
$105$	−5.40803	−	5.42126i	−0.527770	−	0.529061i
$106$	−6.44143	+	2.57482i	−0.625647	+	0.250089i
$107$	18.0491	−	3.59019i	1.74487	−	0.347077i	0.783303	−	0.621640i	$-0.213533\pi$
$107$	18.0491	−	3.59019i	1.74487	−	0.347077i	0.961569	+	0.274563i	$0.0885332\pi$
$108$	−10.2463	+	1.73598i	−0.985949	+	0.167045i
$109$	10.2864	−	6.87314i	0.985256	−	0.658327i	0.0450683	−	0.998984i	$-0.485649\pi$
$109$	10.2864	−	6.87314i	0.985256	−	0.658327i	0.940188	+	0.340657i	$0.110649\pi$
$110$	−1.20413	+	5.68350i	−0.114809	+	0.541901i
$111$	−9.41347	+	3.88572i	−0.893487	+	0.368816i
$112$	15.9816	+	7.57087i	1.51012	+	0.715380i
$113$	−1.30770	−	1.30770i	−0.123018	−	0.123018i	0.642917	−	0.765936i	$-0.277724\pi$
$113$	−1.30770	−	1.30770i	−0.123018	−	0.123018i	−0.765936	+	0.642917i	$0.777724\pi$
$114$	−11.7249	+	2.16632i	−1.09814	+	0.202894i
$115$	5.25683	−	3.51250i	0.490202	−	0.327543i
$116$	−19.7168	+	3.41489i	−1.83066	+	0.317065i
$117$	−2.39427	+	3.56439i	−0.221350	+	0.329528i
$118$	−5.37283	+	12.5285i	−0.494609	+	1.15334i
$119$	−16.6837	−	6.91063i	−1.52940	−	0.633496i
$120$	2.87650	−	3.96557i	0.262588	−	0.362005i
$121$	−5.42878	+	2.24868i	−0.493526	+	0.204425i
$122$	−19.1640	−	0.238158i	−1.73502	−	0.0215619i
$123$	5.88542	−	3.92212i	0.530670	−	0.353646i
$124$	−13.7126	+	5.28463i	−1.23142	+	0.474574i
$125$	0.195090	−	0.980785i	0.0174494	−	0.0877241i
$126$	−10.6515	+	15.4391i	−0.948913	+	1.37543i
$127$			17.7828i			1.57797i	0.614415	+	0.788983i	$0.289392\pi$
$127$			17.7828i			1.57797i	−0.614415	+	0.788983i	$0.710608\pi$
$128$	−3.16287	+	10.8626i	−0.279561	+	0.960128i
$129$	13.3850	+	5.56339i	1.17848	+	0.489829i
$130$	−0.370193	−	1.99001i	−0.0324680	−	0.174536i
$131$	1.22352	+	0.243374i	0.106900	+	0.0212637i	0.248250	−	0.968696i	$-0.420144\pi$
$131$	1.22352	+	0.243374i	0.106900	+	0.0212637i	−0.141351	+	0.989960i	$0.545144\pi$
$132$	14.2259	+	0.371024i	1.23820	+	0.0322935i
$133$	−11.9560	+	17.8935i	−1.03672	+	1.55156i
$134$	0.0714066	−	5.74589i	0.00616859	−	0.496370i
$135$	3.66075	+	3.68767i	0.315067	+	0.317384i
$136$	2.67466	−	11.2392i	0.229350	−	0.963755i
$137$	3.03354	−	7.32361i	0.259173	−	0.625699i	−0.739711	−	0.672924i	$-0.765038\pi$
$137$	3.03354	−	7.32361i	0.259173	−	0.625699i	0.998884	+	0.0472257i	$0.0150380\pi$
$138$	−10.8001	−	11.0990i	−0.919369	−	0.944814i
$139$	13.3824	−	2.66193i	1.13508	−	0.225782i	0.408431	−	0.912789i	$-0.366076\pi$
$139$	13.3824	−	2.66193i	1.13508	−	0.225782i	0.726650	+	0.687008i	$0.241076\pi$
$140$	−1.50896	−	8.71238i	−0.127530	−	0.736331i
$141$	6.81938	−	1.34780i	0.574295	−	0.113505i
$142$	−10.8486	+	7.05539i	−0.910393	+	0.592075i
$143$	4.15766	−	4.15766i	0.347681	−	0.347681i
$144$	−10.8321	−	5.16386i	−0.902676	−	0.430322i
$145$	7.07472	+	7.07472i	0.587523	+	0.587523i
$146$	1.29666	+	0.274714i	0.107312	+	0.0227355i
$147$	4.21321	+	21.3173i	0.347500	+	1.75822i
$148$	−11.4729	−	2.58005i	−0.943063	−	0.212079i
$149$	0.976107	+	4.90722i	0.0799658	+	0.402015i	0.999949	+	0.0100584i	$0.00320175\pi$
$149$	0.976107	+	4.90722i	0.0799658	+	0.402015i	−0.919984	+	0.391957i	$0.871798\pi$
$150$	−2.44926	−	0.0334303i	−0.199981	−	0.00272957i
$151$	−5.89186	−	2.44049i	−0.479473	−	0.198604i	0.129839	−	0.991535i	$-0.458554\pi$
$151$	−5.89186	−	2.44049i	−0.479473	−	0.198604i	−0.609311	+	0.792931i	$0.708554\pi$
$152$	−12.5147	−	5.73919i	−1.01508	−	0.465510i
$153$	11.3096	+	4.71701i	0.914330	+	0.381348i
$154$	18.3862	−	17.9348i	1.48160	−	1.44523i
$155$	6.10948	+	4.08223i	0.490725	+	0.327892i
$156$	−4.62864	+	1.77733i	−0.370588	+	0.142300i
$157$	−2.49058	+	12.5210i	−0.198770	+	0.999284i	0.744592	+	0.667520i	$0.232644\pi$
$157$	−2.49058	+	12.5210i	−0.198770	+	0.999284i	−0.943362	+	0.331765i	$0.892356\pi$
$158$	20.1692	+	13.8422i	1.60457	+	1.10123i
$159$	3.26088	−	7.84533i	0.258604	−	0.622175i
$160$	5.35059	−	1.83609i	0.423001	−	0.145156i
$161$	−27.9514			−2.20288
$162$	7.25341	−	10.4589i	0.569881	−	0.821727i
$163$	−7.87407	−	1.56625i	−0.616745	−	0.122678i	−0.123176	−	0.992385i	$-0.539308\pi$
$163$	−7.87407	−	1.56625i	−0.616745	−	0.122678i	−0.493569	+	0.869707i	$0.664308\pi$
$164$	8.16417	+	0.202950i	0.637515	+	0.0158478i
$165$	−3.94585	−	5.92102i	−0.307184	−	0.460951i
$166$	−6.07521	+	5.92606i	−0.471528	+	0.459952i
$167$	−0.832849	−	2.01068i	−0.0644478	−	0.155591i	0.888374	−	0.459120i	$-0.151835\pi$
$167$	−0.832849	−	2.01068i	−0.0644478	−	0.155591i	−0.952822	+	0.303529i	$0.901835\pi$
$168$	−20.3142	+	7.51202i	−1.56727	+	0.579565i
$169$	4.19092	−	10.1178i	0.322378	−	0.778290i
$170$	−5.36389	+	2.14410i	−0.411392	+	0.164445i
$171$	8.14268	−	12.1222i	0.622687	−	0.927006i
$172$	8.95015	+	14.1435i	0.682442	+	1.07843i
$173$	2.74355	+	4.10601i	0.208588	+	0.312174i	0.920982	−	0.389606i	$-0.127389\pi$
$173$	2.74355	+	4.10601i	0.208588	+	0.312174i	−0.712393	+	0.701780i	$0.752389\pi$
$174$	13.8925	−	20.1896i	1.05319	−	1.53057i
$175$	−3.12615	+	3.12615i	−0.236315	+	0.236315i
$176$	13.1924	+	9.79683i	0.994414	+	0.738464i
$177$	−6.37032	−	15.4326i	−0.478822	−	1.15999i
$178$	−5.83359	+	3.79388i	−0.437246	+	0.284363i
$179$	0.237509	+	0.355458i	0.0177523	+	0.0265682i	0.840240	−	0.542215i	$-0.182414\pi$
$179$	0.237509	+	0.355458i	0.0177523	+	0.0265682i	−0.822487	+	0.568783i	$0.807414\pi$
$180$	1.00949	+	5.91447i	0.0752432	+	0.440838i
$181$	−2.40057	−	12.0685i	−0.178433	−	0.897045i	−0.961436	−	0.275027i	$-0.911313\pi$
$181$	−2.40057	−	12.0685i	−0.178433	−	0.897045i	0.783003	−	0.622018i	$-0.213687\pi$
$182$	−3.52706	+	8.22449i	−0.261443	+	0.609640i
$183$	16.6180	−	16.5775i	1.22844	−	1.22544i
$184$	−2.83254	−	17.6565i	−0.208818	−	1.30166i
$185$	2.25006	+	5.43212i	0.165428	+	0.399378i
$186$	7.11399	−	16.5328i	0.521623	−	1.21224i
$187$	−13.9520	−	9.32240i	−1.02027	−	0.681722i
$188$	7.33705	+	3.25501i	0.535109	+	0.237396i
$189$	−4.39910	−	22.5473i	−0.319988	−	1.64007i
$190$	1.25899	+	6.76786i	0.0913369	+	0.490992i
$191$	−3.58575			−0.259456			−0.129728	−	0.991550i	$-0.541410\pi$
$191$	−3.58575			−0.259456			−0.129728	+	0.991550i	$0.541410\pi$
$192$	−6.80385	−	12.0709i	−0.491025	−	0.871145i
$193$	−10.8386			−0.780180			−0.390090	−	0.920777i	$-0.627556\pi$
$193$	−10.8386			−0.780180			−0.390090	+	0.920777i	$0.627556\pi$
$194$	−3.45279	−	18.5609i	−0.247896	−	1.33259i
$195$	2.05959	+	1.37982i	0.147490	+	0.0988107i
$196$	−10.1751	+	22.9355i	−0.726795	+	1.63825i
$197$	−12.4662	−	8.32965i	−0.888181	−	0.593463i	0.0255996	−	0.999672i	$-0.491850\pi$
$197$	−12.4662	−	8.32965i	−0.888181	−	0.593463i	−0.913780	+	0.406209i	$0.866850\pi$
$198$	−12.5060	+	12.1395i	−0.888765	+	0.862719i
$199$	1.38978	+	3.35523i	0.0985191	+	0.237846i	0.965453	−	0.260577i	$-0.0839127\pi$
$199$	1.38978	+	3.35523i	0.0985191	+	0.237846i	−0.866934	+	0.498423i	$0.833913\pi$
$200$	−2.29155	−	1.65795i	−0.162037	−	0.117235i
$201$	4.97039	+	4.98255i	0.350584	+	0.351442i
$202$	1.98955	−	4.63928i	0.139984	−	0.326419i
$203$	−8.62948	−	43.3833i	−0.605671	−	3.04491i
$204$	7.55168	+	11.9659i	0.528723	+	0.837781i
$205$	−2.26859	−	3.39518i	−0.158445	−	0.237130i
$206$	8.07375	−	5.25077i	0.562525	−	0.365839i
$207$	18.9670	+	0.0463369i	1.31830	+	0.00322064i
$208$	−5.55273	−	1.39454i	−0.385013	−	0.0966943i
$209$	−14.1398	+	14.1398i	−0.978073	+	0.978073i
$210$	8.92129	+	6.13877i	0.615627	+	0.423615i
$211$	6.22707	+	9.31947i	0.428689	+	0.641579i	0.981440	−	0.191767i	$-0.0614219\pi$
$211$	6.22707	+	9.31947i	0.428689	+	0.641579i	−0.552751	+	0.833346i	$0.686422\pi$
$212$	8.28995	−	5.24596i	0.569356	−	0.360294i
$213$	3.11106	−	15.5411i	0.213166	−	1.06486i
$214$	−24.1662	+	9.65992i	−1.65197	+	0.660338i
$215$	3.20258	−	7.73172i	0.218414	−	0.527299i
$216$	13.7970	−	5.06376i	0.938770	−	0.344545i
$217$	−12.4315	−	30.0122i	−0.843903	−	2.03736i
$218$	−12.5241	+	12.2166i	−0.848239	+	0.827415i
$219$	−1.35084	+	0.900221i	−0.0912816	+	0.0608313i
$220$	0.204178	−	8.21356i	0.0137657	−	0.553758i
$221$	5.73397	+	1.14056i	0.385709	+	0.0767223i
$222$	12.0831	−	7.83728i	0.810965	−	0.526004i
$223$	11.9693			0.801526			0.400763	−	0.916182i	$-0.368745\pi$
$223$	11.9693			0.801526			0.400763	+	0.916182i	$0.368745\pi$
$224$	−24.1784	−	6.39272i	−1.61549	−	0.427131i
$225$	2.12650	−	2.11613i	0.141766	−	0.141075i
$226$	2.15641	+	1.47995i	0.143442	+	0.0984449i
$227$	−0.626063	+	3.14743i	−0.0415532	+	0.208902i	−0.995984	−	0.0895297i	$-0.971464\pi$
$227$	−0.626063	+	3.14743i	−0.0415532	+	0.208902i	0.954431	+	0.298432i	$0.0964636\pi$
$228$	15.7416	−	6.04452i	1.04251	−	0.400308i
$229$	−2.63273	−	1.75913i	−0.173975	−	0.116247i	0.465534	−	0.885030i	$-0.345862\pi$
$229$	−2.63273	−	1.75913i	−0.173975	−	0.116247i	−0.639509	+	0.768783i	$0.720862\pi$
$230$	−6.40042	+	6.24329i	−0.422031	+	0.411670i
$231$	−0.0384255	+	31.4573i	−0.00252821	+	2.06974i
$232$	26.5302	−	9.84752i	1.74179	−	0.646522i
$233$	1.27635	+	0.528681i	0.0836165	+	0.0346351i	0.424100	−	0.905616i	$-0.360591\pi$
$233$	1.27635	+	0.528681i	0.0836165	+	0.0346351i	−0.340483	+	0.940251i	$0.610591\pi$
$234$	2.40699	−	5.57505i	0.157350	−	0.364452i
$235$	−0.782962	−	3.93622i	−0.0510748	−	0.256771i
$236$	4.22978	−	18.8088i	0.275335	−	1.22435i
$237$	−29.3915	+	5.80902i	−1.90918	+	0.377336i
$238$	24.9838	+	5.29316i	1.61946	+	0.343104i
$239$	16.8988	+	16.8988i	1.09309	+	1.09309i	0.995197	+	0.0978968i	$0.0312115\pi$
$239$	16.8988	+	16.8988i	1.09309	+	1.09309i	0.0978968	+	0.995197i	$0.468788\pi$
$240$	−2.97372	+	6.25756i	−0.191952	+	0.403924i
$241$	11.2406	−	11.2406i	0.724070	−	0.724070i	−0.245362	−	0.969432i	$-0.578907\pi$
$241$	11.2406	−	11.2406i	0.724070	−	0.724070i	0.969432	+	0.245362i	$0.0789068\pi$
$242$	6.96637	−	4.53058i	0.447815	−	0.291237i
$243$	2.94772	+	15.3072i	0.189097	+	0.981959i
$244$	26.7064	−	4.62548i	1.70970	−	0.296116i
$245$	12.3046	−	2.44753i	0.786110	−	0.156367i
$246$	−7.16843	+	6.97538i	−0.457042	+	0.444734i
$247$	2.66620	−	6.43676i	0.169646	−	0.409562i
$248$	17.6986	−	10.8942i	1.12386	−	0.691782i
$249$	0.0126967	−	10.3942i	0.000804619	−	0.658706i
$250$	−0.0175737	+	1.41410i	−0.00111146	+	0.0894358i
$251$	−9.22931	+	13.8126i	−0.582549	+	0.871846i	−0.999309	−	0.0371703i	$-0.988166\pi$
$251$	−9.22931	+	13.8126i	−0.582549	+	0.871846i	0.416760	+	0.909017i	$0.363166\pi$
$252$	10.8163	−	24.2209i	0.681360	−	1.52577i
$253$	−25.4734	−	5.06698i	−1.60150	−	0.318558i
$254$	−4.59937	−	24.7245i	−0.288590	−	1.55135i
$255$	2.71539	−	6.53295i	0.170044	−	0.409109i
$256$	1.58801	−	15.9210i	0.0992505	−	0.995062i
$257$		−	16.1968i		−	1.01033i	−0.863024	−	0.505163i	$-0.831432\pi$
$257$		−	16.1968i		−	1.01033i	0.863024	−	0.505163i	$-0.168568\pi$
$258$	−20.0488	−	4.27321i	−1.24819	−	0.266039i
$259$	5.07125	−	25.4949i	0.315112	−	1.58418i
$260$	1.02940	+	2.67109i	0.0638409	+	0.165654i
$261$	5.78379	+	29.4530i	0.358008	+	1.82309i
$262$	−1.76409	−	0.0219230i	−0.108986	−	0.00135441i
$263$	1.41665	−	0.586797i	0.0873546	−	0.0361834i	−0.338578	−	0.940938i	$-0.609946\pi$
$263$	1.41665	−	0.586797i	0.0873546	−	0.0361834i	0.425933	+	0.904755i	$0.359946\pi$
$264$	−19.8751	+	3.16355i	−1.22322	+	0.194703i
$265$	−4.53180	−	1.87713i	−0.278386	−	0.115311i
$266$	11.9952	−	27.9707i	0.735474	−	1.71500i
$267$	1.67291	−	8.35690i	0.102380	−	0.511434i
$268$	1.38685	+	8.00734i	0.0847153	+	0.489126i
$269$	0.486704	−	0.325205i	0.0296749	−	0.0198281i	−0.540644	−	0.841251i	$-0.681820\pi$
$269$	0.486704	−	0.325205i	0.0296749	−	0.0198281i	0.570319	+	0.821423i	$0.306820\pi$
$270$	−6.04355	−	4.18038i	−0.367799	−	0.254410i
$271$	−12.7689	−	12.7689i	−0.775656	−	0.775656i	0.203433	−	0.979089i	$-0.434790\pi$
$271$	−12.7689	−	12.7689i	−0.775656	−	0.775656i	−0.979089	+	0.203433i	$0.934790\pi$
$272$	−0.811807	+	16.3184i	−0.0492230	+	0.989446i
$273$	−4.18187	−	10.1309i	−0.253098	−	0.613151i
$274$	−2.32352	+	10.9671i	−0.140369	+	0.662545i
$275$	−3.41572	+	2.28231i	−0.205976	+	0.137628i
$276$	17.8868	+	12.6383i	1.07666	+	0.760737i
$277$	22.2992	−	4.43558i	1.33983	−	0.266508i	0.527423	−	0.849603i	$-0.323158\pi$
$277$	22.2992	−	4.43558i	1.33983	−	0.266508i	0.812404	+	0.583095i	$0.198158\pi$
$278$	−17.9179	+	7.16229i	−1.07464	+	0.429566i
$279$	8.38588	+	20.3860i	0.502049	+	1.22048i
$280$	4.35139	+	11.7231i	0.260045	+	0.700588i
$281$	3.37584	−	1.39832i	0.201386	−	0.0834168i	−0.279711	−	0.960084i	$-0.590239\pi$
$281$	3.37584	−	1.39832i	0.201386	−	0.0834168i	0.481097	+	0.876668i	$0.340239\pi$
$282$	−9.13280	+	3.63771i	−0.543851	+	0.216622i
$283$	0.734354	−	1.09904i	0.0436528	−	0.0653310i	−0.809001	−	0.587807i	$-0.799992\pi$
$283$	0.734354	−	1.09904i	0.0436528	−	0.0653310i	0.852654	+	0.522476i	$0.174992\pi$
$284$	13.2586	−	12.6154i	0.786755	−	0.748588i
$285$	−7.00448	−	4.69263i	−0.414909	−	0.277967i
$286$	−4.70531	+	6.85600i	−0.278231	+	0.405404i
$287$			18.0527i			1.06561i
$288$	16.3961	+	4.37799i	0.966151	+	0.257976i
$289$			0.315764i			0.0185744i
$290$	−11.6662	−	8.00659i	−0.685065	−	0.470163i
$291$	19.2098	+	12.8696i	1.12610	+	0.754427i
$292$	−1.87387	−	0.0465820i	−0.109660	−	0.00272601i
$293$	2.56950	−	3.84552i	0.150112	−	0.224658i	−0.748791	−	0.662806i	$-0.769365\pi$
$293$	2.56950	−	3.84552i	0.150112	−	0.224658i	0.898903	+	0.438148i	$0.144365\pi$
$294$	−11.3714	−	28.5490i	−0.663196	−	1.66501i
$295$	−8.90552	+	3.68879i	−0.518499	+	0.214769i
$296$	16.6187	+	0.619838i	0.965943	+	0.0360274i
$297$	0.0782234	−	21.3459i	0.00453898	−	1.23862i
$298$	−2.62636	−	6.57035i	−0.152141	−	0.380610i
$299$	8.87525	−	1.76540i	0.513269	−	0.102096i
$300$	3.41400	−	0.587002i	0.197108	−	0.0338906i
$301$	−30.7632	+	20.5553i	−1.77316	+	1.18479i
$302$	8.82303	+	1.86928i	0.507708	+	0.107565i
$303$	2.35892	+	5.71466i	0.135516	+	0.328299i
$304$	18.8843	+	4.74272i	1.08309	+	0.272014i
$305$	−9.58272	−	9.58272i	−0.548705	−	0.548705i
$306$	−16.9445	−	3.63320i	−0.968653	−	0.207696i
$307$	20.3690	−	13.6102i	1.16252	−	0.776772i	0.184002	−	0.982926i	$-0.441095\pi$
$307$	20.3690	−	13.6102i	1.16252	−	0.776772i	0.978520	+	0.206153i	$0.0660946\pi$
$308$	−20.9247	+	29.6913i	−1.19230	+	1.69182i
$309$	−2.31532	+	11.5660i	−0.131714	+	0.657969i
$310$	−9.55022	−	4.09560i	−0.542416	−	0.232614i
$311$	−17.1564	−	7.10642i	−0.972851	−	0.402968i	−0.161078	−	0.986942i	$-0.551497\pi$
$311$	−17.1564	−	7.10642i	−0.972851	−	0.402968i	−0.811773	+	0.583974i	$0.801497\pi$
$312$	5.97579	−	3.66829i	0.338313	−	0.207676i
$313$	−8.99397	+	3.72542i	−0.508369	+	0.210573i	−0.622099	−	0.782938i	$-0.713720\pi$
$313$	−8.99397	+	3.72542i	−0.508369	+	0.210573i	0.113730	+	0.993512i	$0.463720\pi$
$314$	0.224351	−	18.0529i	0.0126608	−	1.01878i
$315$	−13.0146	+	2.55572i	−0.733288	+	0.143999i
$316$	−31.6226	−	14.0291i	−1.77891	−	0.789197i
$317$	−5.38782	+	27.0864i	−0.302610	+	1.52132i	0.467835	+	0.883816i	$0.345034\pi$
$317$	−5.38782	+	27.0864i	−0.302610	+	1.52132i	−0.770445	+	0.637507i	$0.779966\pi$
$318$	−2.50466	+	11.7512i	−0.140454	+	0.658977i
$319$		−	41.1017i		−	2.30125i
$320$	−6.96436	+	3.93671i	−0.389319	+	0.220069i
$321$	12.2338	−	29.4332i	0.682823	−	1.64280i
$322$	38.8625	−	7.22940i	2.16572	−	0.402878i
$323$	−19.5007	−	3.87894i	−1.08505	−	0.215830i
$324$	−7.37975	+	16.4177i	−0.409986	+	0.912092i
$325$	0.795184	−	1.19008i	0.0441089	−	0.0660136i
$326$	11.3529	+	0.141087i	0.628779	+	0.00781410i
$327$	0.0261743	−	21.4277i	0.00144744	−	1.18496i
$328$	−11.4036	+	1.82942i	−0.629660	+	0.101013i
$329$	−6.79000	+	16.3925i	−0.374345	+	0.903748i
$330$	7.01758	+	7.21180i	0.386305	+	0.396996i
$331$	−9.01138	+	1.79247i	−0.495310	+	0.0985233i	−0.436423	−	0.899741i	$-0.643755\pi$
$331$	−9.01138	+	1.79247i	−0.495310	+	0.0985233i	−0.0588866	+	0.998265i	$0.518755\pi$
$332$	6.91400	−	9.81067i	0.379455	−	0.538431i
$333$	−3.48347	+	17.2917i	−0.190893	+	0.947578i
$334$	1.67801	+	2.58015i	0.0918164	+	0.141180i
$335$	2.87317	−	2.87317i	0.156978	−	0.156978i
$336$	26.3011	−	15.6985i	1.43484	−	0.856424i
$337$	−9.79269	−	9.79269i	−0.533442	−	0.533442i	0.388153	−	0.921595i	$-0.373113\pi$
$337$	−9.79269	−	9.79269i	−0.533442	−	0.533442i	−0.921595	+	0.388153i	$0.873113\pi$
$338$	−3.21001	+	15.1513i	−0.174601	+	0.824123i
$339$	−3.14242	+	0.621076i	−0.170673	+	0.0337322i
$340$	6.90319	−	4.36840i	0.374378	−	0.236910i
$341$	−5.88884	−	29.6052i	−0.318898	−	1.60321i
$342$	−8.18597	+	18.9602i	−0.442646	+	1.02525i
$343$	−22.6512	−	9.38244i	−1.22305	−	0.506604i
$344$	−16.1020	−	17.3497i	−0.868164	−	0.935434i
$345$	0.0133763	−	10.9506i	0.000720158	−	0.589561i
$346$	−4.87651	−	4.99924i	−0.262163	−	0.268761i
$347$	−6.71655	−	4.48786i	−0.360563	−	0.240921i	0.362072	−	0.932150i	$-0.382069\pi$
$347$	−6.71655	−	4.48786i	−0.360563	−	0.240921i	−0.722635	+	0.691229i	$0.757069\pi$
$348$	−14.0937	+	31.6640i	−0.755503	+	1.69737i
$349$	−2.94738	+	14.8175i	−0.157770	+	0.793163i	0.818145	+	0.575012i	$0.195003\pi$
$349$	−2.94738	+	14.8175i	−0.157770	+	0.793163i	−0.975915	+	0.218151i	$0.929997\pi$
$350$	3.53792	−	5.15503i	0.189110	−	0.275548i
$351$	2.82090	+	6.88148i	0.150569	+	0.367306i
$352$	−20.8761	−	10.2090i	−1.11270	−	0.544143i
$353$	−4.99675			−0.265950			−0.132975	−	0.991119i	$-0.542453\pi$
$353$	−4.99675			−0.265950			−0.132975	+	0.991119i	$0.542453\pi$
$354$	12.8486	+	19.8093i	0.682893	+	1.05285i
$355$	−8.97486	−	1.78521i	−0.476336	−	0.0947492i
$356$	7.12954	−	6.78368i	0.377865	−	0.359534i
$357$	−26.0279	+	17.3453i	−1.37754	+	0.918012i
$358$	−0.422160	−	0.432785i	−0.0223118	−	0.0228734i
$359$	4.72554	+	11.4085i	0.249404	+	0.602115i	0.998154	−	0.0607380i	$-0.0193454\pi$
$359$	4.72554	+	11.4085i	0.249404	+	0.602115i	−0.748750	+	0.662853i	$0.769345\pi$
$360$	−2.93329	−	7.96215i	−0.154598	−	0.419642i
$361$	−1.79650	+	4.33714i	−0.0945528	+	0.228271i
$362$	6.45909	+	16.1587i	0.339482	+	0.849282i
$363$	−1.99775	+	9.97967i	−0.104855	+	0.523797i
$364$	2.77669	−	12.3473i	0.145538	−	0.647172i
$365$	0.520695	+	0.779275i	0.0272544	+	0.0407891i
$366$	−18.8174	+	27.3468i	−0.983602	+	1.42944i
$367$	−17.7937	+	17.7937i	−0.928825	+	0.928825i	−0.997630	−	0.0688049i	$-0.978081\pi$
$367$	−17.7937	+	17.7937i	−0.928825	+	0.928825i	0.0688049	+	0.997630i	$0.478081\pi$
$368$	8.50497	+	23.8163i	0.443352	+	1.24151i
$369$	0.0299272	−	12.2500i	0.00155795	−	0.637710i
$370$	−4.53337	−	6.97065i	−0.235679	−	0.362387i
$371$	12.0481	+	18.0313i	0.625507	+	0.936138i
$372$	−5.61493	+	24.8265i	−0.291121	+	1.28720i
$373$	−5.39169	−	27.1059i	−0.279171	−	1.40349i	−0.824783	−	0.565450i	$-0.808703\pi$
$373$	−5.39169	−	27.1059i	−0.279171	−	1.40349i	0.545611	−	0.838038i	$-0.316297\pi$
$374$	21.8094	+	9.35294i	1.12774	+	0.483629i
$375$	−1.22325	−	1.22624i	−0.0631683	−	0.0633228i
$376$	−11.0430	−	2.62797i	−0.569501	−	0.135527i
$377$	5.48015	+	13.2303i	0.282242	+	0.681393i
$378$	11.9480	+	30.2111i	0.614540	+	1.55389i
$379$	−3.02860	−	2.02365i	−0.155569	−	0.103948i	0.475349	−	0.879797i	$-0.342322\pi$
$379$	−3.02860	−	2.02365i	−0.155569	−	0.103948i	−0.630918	+	0.775849i	$0.717322\pi$
$380$	−3.50091	−	9.08414i	−0.179593	−	0.466007i
$381$	25.5889	+	17.1432i	1.31096	+	0.878273i
$382$	4.98549	−	0.927427i	0.255080	−	0.0474513i
$383$	−18.7703			−0.959115			−0.479558	−	0.877510i	$-0.659203\pi$
$383$	−18.7703			−0.959115			−0.479558	+	0.877510i	$0.659203\pi$
$384$	12.5819	+	15.0232i	0.642065	+	0.766650i
$385$	18.1619			0.925615
$386$	15.0696	−	2.80332i	0.767021	−	0.142685i
$387$	20.9091	−	13.8973i	1.06287	−	0.706437i
$388$	9.60125	+	24.9133i	0.487430	+	1.26478i
$389$	21.2673	+	14.2103i	1.07829	+	0.720492i	0.962090	−	0.272733i	$-0.0879276\pi$
$389$	21.2673	+	14.2103i	1.07829	+	0.720492i	0.116203	+	0.993225i	$0.462928\pi$
$390$	−3.22045	−	1.38575i	−0.163074	−	0.0701700i
$391$	−9.88259	−	23.8587i	−0.499784	−	1.20659i
$392$	8.21501	−	34.5204i	0.414920	−	1.74354i
$393$	1.52973	−	1.52599i	0.0771645	−	0.0769762i
$394$	19.4869	+	8.35694i	0.981737	+	0.421017i
$395$	3.37456	+	16.9651i	0.169793	+	0.853606i
$396$	14.2481	−	20.1129i	0.715995	−	1.01071i
$397$	6.51990	+	9.75772i	0.327224	+	0.489726i	0.958209	−	0.286070i	$-0.0923489\pi$
$397$	6.51990	+	9.75772i	0.327224	+	0.489726i	−0.630985	+	0.775795i	$0.717349\pi$
$398$	−2.80010	−	4.30553i	−0.140357	−	0.215817i
$399$	14.2222	+	34.4543i	0.711999	+	1.72487i
$400$	3.61490	+	1.71246i	0.180745	+	0.0856230i
$401$	4.83106	−	4.83106i	0.241252	−	0.241252i	−0.576116	−	0.817368i	$-0.695432\pi$
$401$	4.83106	−	4.83106i	0.241252	−	0.241252i	0.817368	+	0.576116i	$0.195432\pi$
$402$	−8.19934	−	5.64199i	−0.408946	−	0.281397i
$403$	5.84286	+	8.74446i	0.291054	+	0.435593i
$404$	−1.56628	+	6.96486i	−0.0779253	+	0.346515i
$405$	8.83554	−	1.71266i	0.439042	−	0.0851029i
$406$	23.2189	+	58.0866i	1.15233	+	2.88279i
$407$	9.24336	−	22.3154i	0.458176	−	1.10614i
$408$	−13.5945	−	14.6838i	−0.673026	−	0.726954i
$409$	6.90986	+	16.6819i	0.341670	+	0.824865i	0.997547	+	0.0699973i	$0.0222991\pi$
$409$	6.90986	+	16.6819i	0.341670	+	0.824865i	−0.655877	+	0.754868i	$0.727701\pi$
$410$	4.03229	+	4.13377i	0.199141	+	0.204152i
$411$	−7.61403	−	11.4254i	−0.375572	−	0.563573i
$412$	−9.86736	+	9.38868i	−0.486130	+	0.462547i
$413$	41.7968	+	8.31389i	2.05668	+	0.409100i
$414$	−26.3829	+	4.84123i	−1.29665	+	0.237934i
$415$	−6.00110			−0.294582
$416$	8.08099	+	0.502751i	0.396203	+	0.0246494i
$417$	9.07067	−	21.8231i	0.444192	−	1.06868i
$418$	16.0023	−	23.3166i	0.782699	−	1.14045i
$419$	−3.05017	+	15.3342i	−0.149010	+	0.749126i	0.831940	+	0.554866i	$0.187230\pi$
$419$	−3.05017	+	15.3342i	−0.149010	+	0.749126i	−0.980950	+	0.194260i	$0.937770\pi$
$420$	−13.9916	−	6.22768i	−0.682718	−	0.303880i
$421$	26.5776	+	17.7586i	1.29531	+	0.865500i	0.996061	−	0.0886736i	$-0.0282628\pi$
$421$	26.5776	+	17.7586i	1.29531	+	0.865500i	0.299252	+	0.954174i	$0.403263\pi$
$422$	−11.0683	−	11.3469i	−0.538796	−	0.552356i
$423$	4.63467	−	11.1122i	0.225345	−	0.540295i
$424$	−10.1692	+	9.43791i	−0.493860	+	0.458345i
$425$	−3.77371	−	1.56312i	−0.183052	−	0.0758225i
$426$	−0.305910	+	22.4124i	−0.0148214	+	1.08589i
$427$	11.6886	+	58.7628i	0.565653	+	2.84373i
$428$	31.1013	−	19.6812i	1.50334	−	0.951325i
$429$	−1.97463	−	9.99089i	−0.0953359	−	0.482365i
$430$	−2.45300	+	11.5782i	−0.118294	+	0.558351i
$431$	−5.06471	−	5.06471i	−0.243959	−	0.243959i	0.574527	−	0.818486i	$-0.305186\pi$
$431$	−5.06471	−	5.06471i	−0.243959	−	0.243959i	−0.818486	+	0.574527i	$0.805186\pi$
$432$	−17.8732	+	10.6089i	−0.859923	+	0.510423i
$433$	−10.7183	+	10.7183i	−0.515088	+	0.515088i	−0.916081	−	0.400993i	$-0.868665\pi$
$433$	−10.7183	+	10.7183i	−0.515088	+	0.515088i	0.400993	+	0.916081i	$0.368665\pi$
$434$	25.0467	+	38.5125i	1.20228	+	1.84866i
$435$	17.0006	−	3.36004i	0.815116	−	0.161102i
$436$	14.2533	−	20.2248i	0.682608	−	0.968592i
$437$	−30.1839	+	6.00395i	−1.44389	+	0.287208i
$438$	1.64533	−	1.60102i	0.0786168	−	0.0764995i
$439$	−3.35772	+	8.10625i	−0.160255	+	0.386890i	−0.983528	−	0.180756i	$-0.942146\pi$
$439$	−3.35772	+	8.10625i	−0.160255	+	0.386890i	0.823273	+	0.567646i	$0.192146\pi$
$440$	1.84049	+	11.4726i	0.0877420	+	0.546936i
$441$	34.7367	+	14.4879i	1.65413	+	0.689901i
$442$	−8.26729	−	0.102741i	−0.393235	−	0.00488689i
$443$	19.0069	−	28.4459i	0.903046	−	1.35150i	−0.0329369	−	0.999457i	$-0.510486\pi$
$443$	19.0069	−	28.4459i	0.903046	−	1.35150i	0.935983	−	0.352046i	$-0.114514\pi$
$444$	−14.7728	+	14.0218i	−0.701088	+	0.665447i
$445$	−4.82604	−	0.959958i	−0.228776	−	0.0455064i
$446$	−16.6417	+	3.09577i	−0.788007	+	0.146589i
$447$	8.00235	+	3.32614i	0.378498	+	0.157321i
$448$	35.2701	+	2.63465i	1.66636	+	0.124475i
$449$			9.69119i			0.457356i	0.973502	+	0.228678i	$0.0734402\pi$
$449$			9.69119i			0.457356i	−0.973502	+	0.228678i	$0.926560\pi$
$450$	−2.40928	+	3.49219i	−0.113574	+	0.164623i
$451$	−3.27256	+	16.4523i	−0.154099	+	0.774707i
$452$	−3.38096	−	1.49993i	−0.159027	−	0.0705508i
$453$	−9.19175	+	6.12550i	−0.431866	+	0.287801i
$454$	0.0563955	−	4.53799i	0.00264677	−	0.212978i
$455$	−5.84614	+	2.42155i	−0.274071	+	0.113524i
$456$	−20.3231	+	12.4755i	−0.951718	+	0.584219i
$457$	−19.5074	−	8.08025i	−0.912520	−	0.377978i	−0.123499	−	0.992345i	$-0.539412\pi$
$457$	−19.5074	−	8.08025i	−0.912520	−	0.377978i	−0.789021	+	0.614367i	$0.789412\pi$
$458$	4.11543	+	1.76489i	0.192301	+	0.0824681i
$459$	17.6905	−	11.7269i	0.825723	−	0.547364i
$460$	7.28411	−	10.3358i	0.339624	−	0.481911i
$461$	−15.8464	+	10.5883i	−0.738042	+	0.493144i	−0.866877	−	0.498522i	$-0.833876\pi$
$461$	−15.8464	+	10.5883i	−0.738042	+	0.493144i	0.128835	+	0.991666i	$0.458876\pi$
$462$	−8.08275	−	43.7469i	−0.376043	−	2.03529i
$463$	−10.4988	−	10.4988i	−0.487922	−	0.487922i	0.419728	−	0.907650i	$-0.362126\pi$
$463$	−10.4988	−	10.4988i	−0.487922	−	0.487922i	−0.907650	+	0.419728i	$0.862126\pi$
$464$	−34.3396	+	20.5534i	−1.59418	+	0.954170i
$465$	11.7640	−	4.85596i	0.545540	−	0.225190i
$466$	−1.91133	−	0.404940i	−0.0885405	−	0.0187585i
$467$	23.4282	−	15.6543i	1.08413	−	0.724393i	0.120791	−	0.992678i	$-0.461457\pi$
$467$	23.4282	−	15.6543i	1.08413	−	0.724393i	0.963339	+	0.268285i	$0.0864571\pi$
$468$	−1.90465	+	8.37388i	−0.0880424	+	0.387083i
$469$	−17.6187	+	3.50459i	−0.813558	+	0.161827i
$470$	2.10667	+	5.27026i	0.0971735	+	0.243099i
$471$	15.6163	+	15.6545i	0.719563	+	0.721323i
$472$	−1.01617	+	27.2450i	−0.0467732	+	1.25405i
$473$	−31.7623	+	13.1564i	−1.46043	+	0.604931i
$474$	39.3623	−	15.6785i	1.80797	−	0.720138i
$475$	−2.70435	+	4.04734i	−0.124084	+	0.185705i
$476$	−36.1055	−	0.897536i	−1.65489	−	0.0411385i
$477$	−8.14561	−	12.2555i	−0.372962	−	0.561140i
$478$	−27.8662	−	19.1247i	−1.27457	−	0.874744i
$479$		−	27.7436i		−	1.26764i	−0.773481	−	0.633819i	$-0.781486\pi$
$479$		−	27.7436i		−	1.26764i	0.773481	−	0.633819i	$-0.218514\pi$
$480$	2.51607	−	9.46939i	0.114842	−	0.432217i
$481$			8.41556i			0.383716i
$482$	−12.7212	+	18.5358i	−0.579434	+	0.844281i
$483$	−26.9461	+	40.2212i	−1.22609	+	1.83013i
$484$	−8.51397	+	8.10095i	−0.386999	+	0.368225i
$485$	7.41669	−	11.0999i	0.336774	−	0.504019i
$486$	−8.05749	−	20.5202i	−0.365495	−	0.930813i
$487$	19.4066	−	8.03846i	0.879395	−	0.364257i	0.103133	−	0.994668i	$-0.467113\pi$
$487$	19.4066	−	8.03846i	0.879395	−	0.364257i	0.776262	+	0.630410i	$0.217113\pi$
$488$	−35.9352	+	13.3385i	−1.62671	+	0.603805i
$489$	−9.84466	+	9.82064i	−0.445191	+	0.444105i
$490$	−16.4748	+	6.58543i	−0.744254	+	0.297500i
$491$	−23.1689	+	4.60858i	−1.04560	+	0.207982i	−0.687862	−	0.725841i	$-0.741451\pi$
$491$	−23.1689	+	4.60858i	−1.04560	+	0.207982i	−0.357735	+	0.933823i	$0.616451\pi$
$492$	8.16258	−	11.5524i	0.367998	−	0.520820i
$493$	33.9800	−	22.7047i	1.53038	−	1.02257i
$494$	−2.04216	+	9.63902i	−0.0918810	+	0.433680i
$495$	−12.3241	−	0.0301082i	−0.553928	−	0.00135326i
$496$	−21.7897	+	19.7245i	−0.978387	+	0.885654i
$497$	28.6064	+	28.6064i	1.28317	+	1.28317i
$498$	2.67072	+	14.4550i	0.119678	+	0.647743i
$499$	−9.99118	+	6.67590i	−0.447267	+	0.298854i	−0.758731	−	0.651404i	$-0.774180\pi$
$499$	−9.99118	+	6.67590i	−0.447267	+	0.298854i	0.311465	+	0.950258i	$0.399180\pi$
$500$	−0.341313	−	1.97066i	−0.0152640	−	0.0881306i
$501$	−3.69620	−	0.739914i	−0.165134	−	0.0330569i
$502$	9.25955	−	21.5917i	0.413274	−	0.963683i
$503$	31.2503	+	12.9443i	1.39338	+	0.577157i	0.948025	−	0.318196i	$-0.103077\pi$
$503$	31.2503	+	12.9443i	1.39338	+	0.577157i	0.445356	+	0.895354i	$0.353077\pi$
$504$	−8.77396	+	36.4733i	−0.390823	+	1.62465i
$505$	3.29770	−	1.36595i	0.146746	−	0.0607840i
$506$	36.7278	+	0.456432i	1.63275	+	0.0202909i
$507$	−10.5190	−	15.7845i	−0.467165	−	0.701014i
$508$	12.7896	+	33.1864i	0.567446	+	1.47241i
$509$	1.72784	−	8.68643i	0.0765851	−	0.385019i	−0.923414	−	0.383805i	$-0.874613\pi$
$509$	1.72784	−	8.68643i	0.0765851	−	0.385019i	0.999999	−	0.00121434i	$-0.000386536\pi$
$510$	−2.08568	+	9.78547i	−0.0923553	+	0.433308i
$511$		−	4.14352i		−	0.183298i
$512$	1.90994	+	22.5467i	0.0844080	+	0.996431i
$513$	−9.59363	−	23.4033i	−0.423569	−	1.03328i
$514$	4.18916	+	22.5193i	0.184776	+	0.993285i
$515$	6.67929	+	1.32859i	0.294325	+	0.0585448i
$516$	28.9804	+	0.755836i	1.27579	+	0.0332738i
$517$	−9.15967	+	13.7084i	−0.402842	+	0.602895i
$518$	−0.456816	+	36.7587i	−0.0200714	+	1.61509i
$519$	8.55331	+	0.0104480i	0.375448	+	0.000458616i
$520$	−2.12210	−	3.44754i	−0.0930602	−	0.151184i
$521$	−4.01867	+	9.70192i	−0.176061	+	0.425049i	−0.987134	−	0.159896i	$-0.948884\pi$
$521$	−4.01867	+	9.70192i	−0.176061	+	0.425049i	0.811073	+	0.584945i	$0.198884\pi$
$522$	−15.6593	−	39.4543i	−0.685391	−	1.72687i
$523$	−28.6922	+	5.70723i	−1.25462	+	0.249560i	−0.777278	−	0.629158i	$-0.783400\pi$
$523$	−28.6922	+	5.70723i	−1.25462	+	0.249560i	−0.477343	+	0.878717i	$0.658400\pi$
$524$	2.45839	−	0.425786i	0.107395	−	0.0186005i
$525$	1.48472	+	7.51216i	0.0647987	+	0.327857i
$526$	−1.81789	+	1.18227i	−0.0792637	+	0.0515492i
$527$	21.2225	−	21.2225i	0.924466	−	0.924466i
$528$	26.8153	−	9.53900i	1.16699	−	0.415132i
$529$	−12.0010	−	12.0010i	−0.521783	−	0.521783i
$530$	6.78635	+	1.43778i	0.294780	+	0.0624531i
$531$	−28.3483	−	5.71085i	−1.23021	−	0.247830i
$532$	−9.44327	+	41.9919i	−0.409417	+	1.82058i
$533$	−1.14020	−	5.73217i	−0.0493875	−	0.248288i
$534$	−0.164497	+	12.0518i	−0.00711847	+	0.521532i
$535$	−17.0019	−	7.04241i	−0.735055	−	0.304470i
$536$	−3.99926	−	10.7744i	−0.172742	−	0.465383i
$537$	0.740460		0.000904484i	0.0319532		3.90313e-5i
$538$	−0.592583	+	0.578035i	−0.0255481	+	0.0249209i
$539$	−42.8524	−	28.6330i	−1.84578	−	1.23331i
$540$	9.48393	+	4.24912i	0.408124	+	0.182853i
$541$	1.03634	−	5.21001i	0.0445555	−	0.223996i	−0.952092	−	0.305812i	$-0.901072\pi$
$541$	1.03634	−	5.21001i	0.0445555	−	0.223996i	0.996647	+	0.0818163i	$0.0260721\pi$
$542$	21.0560	+	14.4508i	0.904431	+	0.620716i
$543$	−19.6805	−	8.18009i	−0.844569	−	0.351041i
$544$	−3.09191	−	22.8984i	−0.132564	−	0.981760i
$545$	−12.3713			−0.529929
$546$	8.43460	+	13.0040i	0.360967	+	0.556521i
$547$	43.9788	+	8.74793i	1.88040	+	0.374034i	0.995740	−	0.0922069i	$-0.0293921\pi$
$547$	43.9788	+	8.74793i	1.88040	+	0.374034i	0.884658	+	0.466241i	$0.154392\pi$
$548$	0.393989	−	15.8491i	0.0168304	−	0.677042i
$549$	−7.83416	−	39.8941i	−0.334354	−	1.70264i
$550$	4.15878	−	4.05668i	0.177331	−	0.172978i
$551$	−18.6375	−	44.9949i	−0.793984	−	1.91685i
$552$	−28.1379	−	12.9455i	−1.19763	−	0.550999i
$553$	29.2649	−	70.6516i	1.24447	−	3.00441i
$554$	−29.8567	+	11.9346i	−1.26849	+	0.507051i
$555$	9.98580	+	1.99898i	0.423874	+	0.0848521i
$556$	23.0599	−	14.5925i	0.977957	−	0.618860i
$557$	9.64995	+	14.4422i	0.408882	+	0.611935i	0.977568	−	0.210620i	$-0.0675482\pi$
$557$	9.64995	+	14.4422i	0.408882	+	0.611935i	−0.568686	+	0.822554i	$0.692548\pi$
$558$	−16.9321	−	26.1750i	−0.716792	−	1.10808i
$559$	8.46983	−	8.46983i	0.358236	−	0.358236i
$560$	−9.08208	−	15.1739i	−0.383788	−	0.641212i
$561$	−26.8648	+	11.0894i	−1.13423	+	0.468193i
$562$	−4.33198	+	2.81730i	−0.182733	+	0.118841i
$563$	−15.5615	−	23.2894i	−0.655839	−	0.981532i	−0.999105	−	0.0422940i	$-0.986533\pi$
$563$	−15.5615	−	23.2894i	−0.655839	−	0.981532i	0.343266	−	0.939238i	$-0.388467\pi$
$564$	11.7570	−	7.41986i	0.495060	−	0.312432i
$565$	0.360794	+	1.81384i	0.0151787	+	0.0763086i
$566$	−0.736760	+	1.71799i	−0.0309683	+	0.0722127i
$567$	−36.6858	−	15.4062i	−1.54066	−	0.646999i
$568$	−15.1714	+	20.9693i	−0.636578	+	0.879850i
$569$	12.2815	+	29.6502i	0.514868	+	1.24300i	0.941020	+	0.338350i	$0.109869\pi$
$569$	12.2815	+	29.6502i	0.514868	+	1.24300i	−0.426153	+	0.904651i	$0.640131\pi$
$570$	10.9525	+	4.71280i	0.458748	+	0.197397i
$571$	2.98631	+	1.99539i	0.124973	+	0.0835044i	0.616486	−	0.787366i	$-0.288556\pi$
$571$	2.98631	+	1.99539i	0.124973	+	0.0835044i	−0.491513	+	0.870871i	$0.663556\pi$
$572$	4.76883	−	10.7493i	0.199395	−	0.449451i
$573$	−3.45679	+	5.15980i	−0.144409	+	0.215554i
$574$	−4.66918	−	25.0997i	−0.194888	−	1.04764i
$575$	−6.32234			−0.263660
$576$	−23.9289	−	1.84626i	−0.997037	−	0.0769276i
$577$	2.42504			0.100956			0.0504780	−	0.998725i	$-0.483926\pi$
$577$	2.42504			0.100956			0.0504780	+	0.998725i	$0.483926\pi$
$578$	−0.0816699	−	0.439026i	−0.00339702	−	0.0182611i
$579$	−10.4488	+	15.5964i	−0.434237	+	0.648166i
$580$	18.2911	+	8.11468i	0.759497	+	0.336944i
$581$	22.0598	+	14.7399i	0.915196	+	0.611514i
$582$	−30.0372	−	12.9249i	−1.24508	−	0.535753i
$583$	7.71136	+	18.6169i	0.319372	+	0.771032i
$584$	2.61741	−	0.419897i	0.108309	−	0.0173754i
$585$	3.97103	−	1.63350i	0.164182	−	0.0675369i
$586$	−2.57791	+	6.01125i	−0.106493	+	0.248322i
$587$	4.97811	+	25.0266i	0.205468	+	1.03296i	0.936514	+	0.350631i	$0.114033\pi$
$587$	4.97811	+	25.0266i	0.205468	+	1.03296i	−0.731045	+	0.682329i	$0.760967\pi$
$588$	23.1944	+	36.7523i	0.956521	+	1.51564i
$589$	−19.8710	−	29.7391i	−0.818772	−	1.22538i
$590$	11.4278	−	7.43209i	0.470475	−	0.305974i
$591$	−24.0040	+	9.90844i	−0.987392	+	0.407579i
$592$	−23.2663	+	3.43650i	−0.956240	+	0.141239i
$593$	−2.93993	+	2.93993i	−0.120729	+	0.120729i	−0.764890	−	0.644161i	$-0.777207\pi$
$593$	−2.93993	+	2.93993i	−0.120729	+	0.120729i	0.644161	+	0.764890i	$0.277207\pi$
$594$	5.41219	+	29.6988i	0.222065	+	1.21855i
$595$	10.0327	+	15.0150i	0.411300	+	0.615554i
$596$	5.35095	+	8.45587i	0.219184	+	0.346366i
$597$	6.16788	+	1.23470i	0.252435	+	0.0505330i
$598$	−11.8832	+	4.75005i	−0.485940	+	0.194244i
$599$	−5.74359	+	13.8663i	−0.234677	+	0.566560i	−0.996717	−	0.0809704i	$-0.974198\pi$
$599$	−5.74359	+	13.8663i	−0.234677	+	0.566560i	0.762040	+	0.647530i	$0.224198\pi$
$600$	−4.59488	+	1.69915i	−0.187585	+	0.0693675i
$601$	11.2925	+	27.2624i	0.460629	+	1.11206i	0.968139	+	0.250412i	$0.0805660\pi$
$601$	11.2925	+	27.2624i	0.460629	+	1.11206i	−0.507510	+	0.861646i	$0.669434\pi$
$602$	37.4556	−	36.5360i	1.52657	−	1.48910i
$603$	11.9614	−	2.34890i	0.487105	−	0.0956547i
$604$	−12.7507	−	0.316965i	−0.518817	−	0.0128971i
$605$	5.76317	+	1.14637i	0.234306	+	0.0466064i
$606$	−4.75780	−	7.33533i	−0.193272	−	0.297977i
$607$	0.661065			0.0268318			0.0134159	−	0.999910i	$-0.495729\pi$
$607$	0.661065			0.0268318			0.0134159	+	0.999910i	$0.495729\pi$
$608$	−27.4827	−	1.70981i	−1.11457	−	0.0693419i
$609$	−70.7465	−	29.4054i	−2.86679	−	1.19157i
$610$	15.8019	+	10.8449i	0.639802	+	0.439099i
$611$	1.12065	−	5.63388i	0.0453366	−	0.227922i
$612$	24.4987	+	0.668896i	0.990300	+	0.0270385i
$613$	1.74648	+	1.16696i	0.0705396	+	0.0471331i	0.590340	−	0.807155i	$-0.298994\pi$
$613$	1.74648	+	1.16696i	0.0705396	+	0.0471331i	−0.519800	+	0.854288i	$0.673994\pi$
$614$	−24.8002	+	24.1913i	−1.00085	+	0.976282i
$615$	−7.07256	−	0.00863924i	−0.285193	−	0.000348368i
$616$	21.4135	−	46.6936i	0.862774	−	1.88134i
$617$	34.0568	+	14.1068i	1.37107	+	0.567918i	0.942080	−	0.335389i	$-0.108868\pi$
$617$	34.0568	+	14.1068i	1.37107	+	0.567918i	0.428995	+	0.903307i	$0.358868\pi$
$618$	0.227665	−	16.6798i	0.00915803	−	0.670961i
$619$	−2.37632	−	11.9466i	−0.0955125	−	0.480174i	−0.998702	−	0.0509320i	$-0.983781\pi$
$619$	−2.37632	−	11.9466i	−0.0955125	−	0.480174i	0.903190	−	0.429242i	$-0.141219\pi$
$620$	14.3376	+	3.22427i	0.575810	+	0.129490i
$621$	18.3515	−	27.2482i	0.736420	−	1.09343i
$622$	25.6916	+	5.44312i	1.03014	+	0.218249i
$623$	15.3825	+	15.3825i	0.616286	+	0.616286i
$624$	−7.35974	+	6.64583i	−0.294625	+	0.266046i
$625$	−0.707107	+	0.707107i	−0.0282843	+	0.0282843i
$626$	11.5413	−	7.50590i	0.461284	−	0.299996i
$627$	6.71553	+	33.9781i	0.268192	+	1.35695i
$628$	4.35730	+	25.1580i	0.173875	+	1.00392i
$629$	23.5549	−	4.68536i	0.939196	−	0.186818i
$630$	17.4339	−	6.91949i	0.694585	−	0.275679i
$631$	11.7999	−	28.4876i	0.469748	−	1.13407i	−0.494525	−	0.869163i	$-0.664658\pi$
$631$	11.7999	−	28.4876i	0.469748	−	1.13407i	0.964273	−	0.264909i	$-0.0853421\pi$
$632$	47.5954	+	11.3265i	1.89324	+	0.450546i
$633$	19.4136	+	0.0237140i	0.771620	+	0.000942546i
$634$	0.485332	−	39.0534i	0.0192750	−	1.55101i
$635$	9.87958	−	14.7858i	0.392059	−	0.586758i
$636$	0.443019	−	16.9863i	0.0175668	−	0.673550i
$637$	17.6115	+	3.50314i	0.697791	+	0.138799i
$638$	10.6306	+	57.1462i	0.420871	+	2.26244i
$639$	−19.3641	−	19.4589i	−0.766030	−	0.769783i
$640$	8.66477	−	7.27473i	0.342505	−	0.287559i
$641$			3.65530i			0.144376i	0.997391	+	0.0721878i	$0.0229981\pi$
$641$			3.65530i			0.144376i	−0.997391	+	0.0721878i	$0.977002\pi$
$642$	−9.39670	+	44.0869i	−0.370858	+	1.73997i
$643$	−1.23326	+	6.20000i	−0.0486349	+	0.244504i	−0.997454	−	0.0713168i	$-0.977280\pi$
$643$	−1.23326	+	6.20000i	−0.0486349	+	0.244504i	0.948819	+	0.315821i	$0.102280\pi$
$644$	−52.1631	+	20.1029i	−2.05551	+	0.792167i
$645$	−8.03832	−	12.0621i	−0.316509	−	0.474944i
$646$	28.1163	+	0.349413i	1.10622	+	0.0137475i
$647$	−28.9512	+	11.9920i	−1.13819	+	0.471453i	−0.870556	−	0.492069i	$-0.836241\pi$
$647$	−28.9512	+	11.9920i	−1.13819	+	0.471453i	−0.267631	+	0.963521i	$0.586241\pi$
$648$	6.01422	−	24.7352i	0.236261	−	0.971690i
$649$	36.5843	+	15.1537i	1.43606	+	0.594835i
$650$	−0.797789	+	1.86030i	−0.0312919	+	0.0729672i
$651$	−55.1711	−	11.0443i	−2.16233	−	0.432860i
$652$	−15.8211	+	2.74018i	−0.619603	+	0.107314i
$653$	−13.7063	+	9.15827i	−0.536370	+	0.358391i	−0.794062	−	0.607836i	$-0.792038\pi$
$653$	−13.7063	+	9.15827i	−0.536370	+	0.358391i	0.257693	+	0.966227i	$0.417038\pi$
$654$	5.50572	+	29.7991i	0.215291	+	1.16524i
$655$	−0.882111	−	0.882111i	−0.0344669	−	0.0344669i
$656$	15.3820	−	5.49302i	0.600567	−	0.214466i
$657$	−0.00686900	+	2.81167i	−0.000267985	+	0.109694i
$658$	5.20076	−	24.5477i	0.202747	−	0.956968i
$659$	−13.8495	+	9.25392i	−0.539499	+	0.360482i	−0.795270	−	0.606256i	$-0.792671\pi$
$659$	−13.8495	+	9.25392i	−0.539499	+	0.360482i	0.255771	+	0.966737i	$0.417671\pi$
$660$	−11.6222	−	8.21196i	−0.452395	−	0.319650i
$661$	−10.3795	+	2.06460i	−0.403714	+	0.0803037i	−0.392771	−	0.919636i	$-0.628483\pi$
$661$	−10.3795	+	2.06460i	−0.403714	+	0.0803037i	−0.0109432	+	0.999940i	$0.503483\pi$
$662$	12.0655	−	4.82291i	0.468937	−	0.187448i
$663$	7.16898	−	7.15149i	0.278420	−	0.277741i
$664$	−7.07551	+	15.4286i	−0.274583	+	0.598747i
$665$	19.8822	−	8.23547i	0.770998	−	0.319358i
$666$	0.370920	−	24.9426i	0.0143728	−	0.966508i
$667$	35.1432	−	52.5955i	1.36075	−	2.03651i
$668$	−3.00037	−	3.15334i	−0.116088	−	0.122007i
$669$	11.5389	−	17.2235i	0.446118	−	0.665900i
$670$	−3.25162	+	4.73787i	−0.125621	+	0.183040i
$671$			55.6723i			2.14921i
$672$	−32.5077	+	28.6292i	−1.25401	+	1.10439i
$673$		−	20.0074i		−	0.771228i	−0.922660	−	0.385614i	$-0.873990\pi$
$673$		−	20.0074i		−	0.771228i	0.922660	−	0.385614i	$-0.126010\pi$
$674$	16.1482	+	11.0826i	0.622005	+	0.426885i
$675$	−0.995037	−	5.09999i	−0.0382990	−	0.196299i
$676$	0.544306	−	21.8960i	0.0209349	−	0.842155i
$677$	10.2656	−	15.3635i	0.394538	−	0.590467i	−0.580021	−	0.814602i	$-0.696955\pi$
$677$	10.2656	−	15.3635i	0.394538	−	0.590467i	0.974558	+	0.224134i	$0.0719555\pi$
$678$	4.20846	−	1.67628i	0.161625	−	0.0643772i
$679$	−54.5270	+	22.5858i	−2.09255	+	0.866764i
$680$	−8.46807	+	7.85911i	−0.324736	+	0.301383i
$681$	3.92551	+	3.93512i	0.150426	+	0.150794i
$682$	15.8448	+	39.6388i	0.606727	+	1.51785i
$683$	21.0736	−	4.19180i	0.806358	−	0.160395i	0.225335	−	0.974281i	$-0.427652\pi$
$683$	21.0736	−	4.19180i	0.806358	−	0.160395i	0.581023	+	0.813887i	$0.302652\pi$
$684$	6.47754	−	28.4788i	0.247675	−	1.08891i
$685$	−6.59108	+	4.40402i	−0.251832	+	0.168269i
$686$	33.9201	+	7.18642i	1.29507	+	0.274379i
$687$	−5.06938	+	2.09255i	−0.193409	+	0.0798359i
$688$	26.8750	+	19.9577i	1.02460	+	0.760881i
$689$	−4.96443	−	4.96443i	−0.189130	−	0.189130i
$690$	2.81369	+	15.2288i	0.107115	+	0.579749i
$691$	14.2072	−	9.49296i	0.540468	−	0.361129i	−0.255175	−	0.966895i	$-0.582133\pi$
$691$	14.2072	−	9.49296i	0.540468	−	0.361129i	0.795643	+	0.605766i	$0.207133\pi$
$692$	8.07313	+	5.68948i	0.306894	+	0.216282i
$693$	45.2290	+	30.3812i	1.71811	+	1.15409i
$694$	10.4992	+	4.50256i	0.398543	+	0.170915i
$695$	−12.6060	−	5.22156i	−0.478171	−	0.198065i
$696$	11.4057	−	47.6696i	0.432333	−	1.80691i
$697$	−15.4094	+	6.38277i	−0.583671	+	0.241765i
$698$	0.265499	−	21.3640i	0.0100493	−	0.808639i
$699$	1.99120	−	1.32696i	0.0753142	−	0.0501904i
$700$	−3.58568	+	8.08241i	−0.135526	+	0.305487i
$701$	−6.51786	+	32.7675i	−0.246176	+	1.23761i	0.637845	+	0.770164i	$0.279826\pi$
$701$	−6.51786	+	32.7675i	−0.246176	+	1.23761i	−0.884021	+	0.467446i	$0.845174\pi$
$702$	−5.70191	−	8.83813i	−0.215205	−	0.333574i
$703$		−	28.6206i		−	1.07944i
$704$	31.6658	+	8.79479i	1.19345	+	0.331466i
$705$	−6.41891	−	2.66799i	−0.241750	−	0.100482i
$706$	6.94729	−	1.29237i	0.261465	−	0.0486390i
$707$	−15.4773	−	3.07862i	−0.582082	−	0.115783i
$708$	−22.9876	−	24.2188i	−0.863929	−	0.910200i
$709$	−9.46261	+	14.1618i	−0.355376	+	0.531858i	−0.965485	−	0.260460i	$-0.916126\pi$
$709$	−9.46261	+	14.1618i	−0.355376	+	0.531858i	0.610109	+	0.792318i	$0.291126\pi$
$710$	12.9400	+	0.160811i	0.485631	+	0.00603513i
$711$	−19.9754	+	47.8936i	−0.749136	+	1.79615i
$712$	−8.15809	+	11.2758i	−0.305737	+	0.422577i
$713$	17.7777	−	42.9192i	0.665780	−	1.60734i
$714$	31.7019	−	30.8482i	1.18642	−	1.15446i
$715$	−5.76685	+	1.14710i	−0.215668	+	0.0428990i
$716$	0.698891	+	0.492539i	0.0261188	+	0.0184070i
$717$	40.6079	−	8.02587i	1.51653	−	0.299732i
$718$	−9.52091	−	14.6396i	−0.355317	−	0.546347i
$719$	0.276062	−	0.276062i	0.0102954	−	0.0102954i	−0.701940	−	0.712236i	$-0.747683\pi$
$719$	0.276062	−	0.276062i	0.0102954	−	0.0102954i	0.712236	+	0.701940i	$0.247683\pi$
$720$	6.13768	+	10.3116i	0.228738	+	0.384290i
$721$	−21.2895	−	21.2895i	−0.792863	−	0.792863i
$722$	1.37602	−	6.49485i	0.0512102	−	0.241713i
$723$	−5.33857	−	27.0112i	−0.198543	−	1.00456i
$724$	−13.1598	−	20.7958i	−0.489079	−	0.772871i
$725$	−1.95191	−	9.81291i	−0.0724921	−	0.364443i
$726$	0.196439	−	14.3920i	0.00729053	−	0.534139i
$727$	33.6290	+	13.9296i	1.24723	+	0.516620i	0.905967	−	0.423348i	$-0.139145\pi$
$727$	33.6290	+	13.9296i	1.24723	+	0.516620i	0.341264	+	0.939968i	$0.389145\pi$
$728$	−0.667080	+	17.8853i	−0.0247236	+	0.662874i
$729$	24.8684	+	10.5150i	0.921050	+	0.389444i
$730$	−0.925507	−	0.948800i	−0.0342546	−	0.0351167i
$731$	−28.4224	−	18.9912i	−1.05124	−	0.702416i
$732$	19.0900	−	42.8889i	0.705586	−	1.58522i
$733$	1.45051	−	7.29221i	0.0535759	−	0.269344i	−0.944707	−	0.327914i	$-0.893654\pi$
$733$	1.45051	−	7.29221i	0.0535759	−	0.269344i	0.998283	+	0.0585704i	$0.0186542\pi$
$734$	20.1375	−	29.3419i	0.743289	−	1.08303i
$735$	8.34010	−	20.0654i	0.307629	−	0.740124i
$736$	−17.9849	−	30.9136i	−0.662932	−	1.13949i
$737$	−16.6921			−0.614863
$738$	3.12676	+	17.0397i	0.115097	+	0.627239i
$739$	22.8446	+	4.54408i	0.840354	+	0.167157i	0.596458	−	0.802645i	$-0.296574\pi$
$739$	22.8446	+	4.54408i	0.840354	+	0.167157i	0.243896	+	0.969801i	$0.421574\pi$
$740$	8.10593	+	8.51921i	0.297980	+	0.313172i
$741$	−6.69201	−	10.0418i	−0.245837	−	0.368896i
$742$	−21.4149	−	21.9539i	−0.786165	−	0.805951i
$743$	1.74498	+	4.21275i	0.0640171	+	0.154551i	0.952651	−	0.304067i	$-0.0983447\pi$
$743$	1.74498	+	4.21275i	0.0640171	+	0.154551i	−0.888634	+	0.458618i	$0.848345\pi$
$744$	1.38560	−	35.9701i	0.0507986	−	1.31873i
$745$	1.91470	−	4.62250i	0.0701493	−	0.169355i
$746$	14.5071	+	36.2924i	0.531143	+	1.32876i
$747$	−14.9447	−	10.0386i	−0.546798	−	0.367294i
$748$	−32.7421	−	7.36313i	−1.19717	−	0.269223i
$749$	45.2007	+	67.6477i	1.65160	+	2.47179i
$750$	2.01791	+	1.38853i	0.0736838	+	0.0507021i
$751$	3.23996	−	3.23996i	0.118228	−	0.118228i	−0.645518	−	0.763745i	$-0.723358\pi$
$751$	3.23996	−	3.23996i	0.118228	−	0.118228i	0.763745	+	0.645518i	$0.223358\pi$
$752$	16.0335	+	0.797636i	0.584682	+	0.0290868i
$753$	10.9786	+	26.5966i	0.400083	+	0.969233i
$754$	−11.0413	−	16.9774i	−0.402100	−	0.618282i
$755$	3.54304	+	5.30253i	0.128944	+	0.192979i
$756$	−24.4259	−	38.9140i	−0.888362	−	1.41529i
$757$	−6.96553	−	35.0181i	−0.253166	−	1.27275i	−0.872884	−	0.487929i	$-0.837753\pi$
$757$	−6.96553	−	35.0181i	−0.253166	−	1.27275i	0.619717	−	0.784825i	$-0.287247\pi$
$758$	4.73425	+	2.03028i	0.171956	+	0.0737430i
$759$	−31.8485	+	31.7708i	−1.15603	+	1.15321i
$760$	7.21707	+	11.7248i	0.261790	+	0.425302i
$761$	−0.993427	−	2.39834i	−0.0360117	−	0.0869399i	0.904850	−	0.425730i	$-0.139983\pi$
$761$	−0.993427	−	2.39834i	−0.0360117	−	0.0869399i	−0.940862	+	0.338790i	$0.889983\pi$
$762$	−40.0118	−	17.2169i	−1.44947	−	0.623702i
$763$	45.4765	+	30.3864i	1.64636	+	1.10006i
$764$	−6.69177	+	2.57892i	−0.242100	+	0.0933020i
$765$	−6.78299	−	10.2053i	−0.245240	−	0.368975i
$766$	26.0974	−	4.85478i	0.942939	−	0.175410i
$767$	−13.7966			−0.498167
$768$	−21.3790	−	17.6335i	−0.771447	−	0.636294i
$769$	36.9195			1.33135			0.665675	−	0.746242i	$-0.268144\pi$
$769$	36.9195			1.33135			0.665675	+	0.746242i	$0.268144\pi$
$770$	−25.2516	+	4.69742i	−0.910003	+	0.169283i
$771$	−23.3067	−	15.6142i	−0.839369	−	0.562333i
$772$	−20.2271	+	7.79525i	−0.727989	+	0.280557i
$773$	−14.3958	−	9.61896i	−0.517781	−	0.345970i	0.269063	−	0.963123i	$-0.413286\pi$
$773$	−14.3958	−	9.61896i	−0.517781	−	0.345970i	−0.786844	+	0.617153i	$0.788286\pi$
$774$	−25.4768	+	24.7302i	−0.915745	+	0.888908i
$775$	−2.81189	−	6.78849i	−0.101006	−	0.243850i
$776$	−19.7928	−	32.1552i	−0.710521	−	1.15430i
$777$	−31.7976	−	31.8753i	−1.14073	−	1.14352i
$778$	−33.2446	−	14.2569i	−1.19188	−	0.511134i
$779$	3.87771	+	19.4946i	0.138933	+	0.698466i
$780$	4.83600	+	1.09374i	0.173157	+	0.0391623i
$781$	20.8847	+	31.2562i	0.747314	+	1.11843i
$782$	19.9112	+	30.6161i	0.712024	+	1.09483i
$783$	47.9577	+	20.0710i	1.71387	+	0.717277i
$784$	−2.49340	+	50.1206i	−0.0890500	+	1.79002i
$785$	9.02713	−	9.02713i	0.322192	−	0.322192i
$786$	−1.73219	+	2.51733i	−0.0617850	+	0.0897903i
$787$	23.9347	+	35.8208i	0.853179	+	1.27687i	0.959263	+	0.282516i	$0.0911689\pi$
$787$	23.9347	+	35.8208i	0.853179	+	1.27687i	−0.106084	+	0.994357i	$0.533831\pi$
$788$	−29.2553	−	6.57903i	−1.04218	−	0.234368i
$789$	0.521318	−	2.60421i	0.0185594	−	0.0927125i
$790$	−9.07975	−	22.7148i	−0.323043	−	0.808156i
$791$	3.12888	−	7.55378i	0.111250	−	0.268581i
$792$	−14.6080	+	31.6494i	−0.519072	+	1.12461i
$793$	−7.42287	−	17.9204i	−0.263594	−	0.636372i
$794$	−11.5888	−	11.8804i	−0.411270	−	0.421621i
$795$	−7.06995	+	4.71151i	−0.250745	+	0.167100i
$796$	5.00675	+	5.26202i	0.177459	+	0.186507i
$797$	10.0844	+	2.00592i	0.357209	+	0.0710533i	0.370433	−	0.928859i	$-0.379209\pi$
$797$	10.0844	+	2.00592i	0.357209	+	0.0710533i	−0.0132236	+	0.999913i	$0.504209\pi$
$798$	−28.6853	−	44.2255i	−1.01545	−	1.56557i
$799$	−16.3930			−0.579943
$800$	−5.46893	−	1.44597i	−0.193356	−	0.0511229i
$801$	−10.4126	−	10.4636i	−0.367911	−	0.369713i
$802$	−5.46741	+	7.96644i	−0.193061	+	0.281305i
$803$	0.751131	−	3.77619i	0.0265068	−	0.133259i
$804$	12.8593	+	5.72371i	0.453512	+	0.201860i
$805$	23.2407	+	15.5289i	0.819127	+	0.547323i
$806$	−10.3854	−	10.6467i	−0.365809	−	0.375016i
$807$	0.00123845	−	1.01386i	4.35955e−5	−	0.0356897i
$808$	0.376287	−	10.0888i	0.0132377	−	0.354922i
$809$	−10.0950	−	4.18147i	−0.354920	−	0.147013i	0.198097	−	0.980182i	$-0.436524\pi$
$809$	−10.0950	−	4.18147i	−0.354920	−	0.147013i	−0.553018	+	0.833170i	$0.686524\pi$
$810$	−11.8416	+	4.66646i	−0.416072	+	0.163963i
$811$	8.69166	+	43.6959i	0.305206	+	1.53437i	0.763639	+	0.645644i	$0.223411\pi$
$811$	8.69166	+	43.6959i	0.305206	+	1.53437i	−0.458433	+	0.888729i	$0.651589\pi$
$812$	−47.3062	−	74.7559i	−1.66012	−	2.62342i
$813$	−30.6837	+	6.06442i	−1.07613	+	0.212689i
$814$	−7.07989	+	33.4172i	−0.248150	+	1.17127i
$815$	5.67689	+	5.67689i	0.198853	+	0.198853i
$816$	22.6990	+	16.8996i	0.794625	+	0.591605i
$817$	−28.8051	+	28.8051i	−1.00776	+	1.00776i
$818$	−13.9218	−	21.4066i	−0.486765	−	0.748466i
$819$	−18.6096	−	3.74896i	−0.650271	−	0.130999i
$820$	−6.67551	−	4.70452i	−0.233119	−	0.164289i
$821$	6.81899	−	1.35638i	0.237985	−	0.0473381i	−0.0746569	−	0.997209i	$-0.523786\pi$
$821$	6.81899	−	1.35638i	0.237985	−	0.0473381i	0.312641	+	0.949871i	$0.398786\pi$
$822$	13.5413	+	13.9161i	0.472309	+	0.485380i
$823$	0.951348	−	2.29676i	0.0331619	−	0.0800599i	−0.906431	−	0.422354i	$-0.861204\pi$
$823$	0.951348	−	2.29676i	0.0331619	−	0.0800599i	0.939593	+	0.342294i	$0.111204\pi$
$824$	11.2909	−	15.6058i	0.393337	−	0.543653i
$825$	−0.00869150	+	7.11535i	−0.000302599	+	0.247725i
$826$	−60.2629	−	0.748912i	−2.09681	−	0.0260580i
$827$	−0.302650	+	0.452948i	−0.0105242	+	0.0157505i	−0.836694	−	0.547670i	$-0.815515\pi$
$827$	−0.302650	+	0.452948i	−0.0105242	+	0.0157505i	0.826170	+	0.563421i	$0.190515\pi$
$828$	35.4296	−	13.5548i	1.23127	−	0.471062i
$829$	−25.6077	−	5.09368i	−0.889391	−	0.176911i	−0.270811	−	0.962633i	$-0.587292\pi$
$829$	−25.6077	−	5.09368i	−0.889391	−	0.176911i	−0.618580	+	0.785722i	$0.712292\pi$
$830$	8.34369	−	1.55214i	0.289614	−	0.0538755i
$831$	15.1145	−	36.3639i	0.524316	−	1.26145i
$832$	−11.3655	+	1.39108i	−0.394029	+	0.0482270i
$833$		−	51.2443i		−	1.77551i
$834$	−6.96713	+	32.6880i	−0.241252	+	1.13189i
$835$	−0.424583	+	2.13452i	−0.0146933	+	0.0738682i
$836$	−16.2183	+	36.5574i	−0.560923	+	1.26436i
$837$	37.4192	+	7.58579i	1.29340	+	0.262203i
$838$	0.274758	−	22.1090i	0.00949135	−	0.763743i
$839$	17.5262	−	7.25959i	0.605072	−	0.250629i	−0.0590481	−	0.998255i	$-0.518807\pi$
$839$	17.5262	−	7.25959i	0.605072	−	0.250629i	0.664120	+	0.747626i	$0.268807\pi$
$840$	21.0641	+	5.03992i	0.726779	+	0.173894i
$841$	65.6908	+	27.2100i	2.26520	+	0.938277i
$842$	−41.5456	−	17.8168i	−1.43176	−	0.614006i
$843$	1.24229	−	6.20577i	0.0427866	−	0.213738i
$844$	18.3237	+	12.9135i	0.630728	+	0.444501i
$845$	−9.10576	+	6.08427i	−0.313248	+	0.209305i
$846$	−3.56978	+	16.6487i	−0.122731	+	0.572395i
$847$	−18.3695	−	18.3695i	−0.631183	−	0.631183i
$848$	11.6978	−	15.7523i	0.401705	−	0.540936i
$849$	−0.873542	−	2.11622i	−0.0299799	−	0.0726286i
$850$	5.65111	+	1.19726i	0.193831	+	0.0410658i
$851$	30.9086	−	20.6524i	1.05953	−	0.707956i
$852$	−5.37147	−	31.2405i	−0.184024	−	1.07028i
$853$	24.0551	−	4.78486i	0.823632	−	0.163831i	0.234756	−	0.972054i	$-0.424571\pi$
$853$	24.0551	−	4.78486i	0.823632	−	0.163831i	0.588876	+	0.808224i	$0.299571\pi$
$854$	−31.4500	−	78.6783i	−1.07620	−	2.69232i
$855$	−13.5051	+	5.55539i	−0.461865	+	0.189990i
$856$	−38.1516	+	35.4080i	−1.30400	+	1.21022i
$857$	−17.8143	+	7.37891i	−0.608524	+	0.252059i	−0.665597	−	0.746311i	$-0.731823\pi$
$857$	−17.8143	+	7.37891i	−0.608524	+	0.252059i	0.0570734	+	0.998370i	$0.481823\pi$
$858$	5.32951	+	13.3802i	0.181946	+	0.456793i
$859$	14.1279	−	21.1439i	0.482038	−	0.721420i	−0.508134	−	0.861278i	$-0.669664\pi$
$859$	14.1279	−	21.1439i	0.482038	−	0.721420i	0.990172	+	0.139858i	$0.0446645\pi$
$860$	0.415944	−	16.7323i	0.0141836	−	0.570568i
$861$	25.9772	+	17.4034i	0.885302	+	0.593106i
$862$	8.35173	+	5.73183i	0.284461	+	0.195227i
$863$		−	9.02063i		−	0.307066i	−0.988144	−	0.153533i	$-0.950935\pi$
$863$		−	9.02063i		−	0.307066i	0.988144	−	0.153533i	$-0.0490651\pi$
$864$	22.1062	−	19.3730i	0.752070	−	0.659084i
$865$		−	4.93826i		−	0.167906i
$866$	12.1301	−	17.6745i	0.412198	−	0.600604i
$867$	0.454375	+	0.304407i	0.0154314	+	0.0103382i
$868$	−44.7849	−	47.0682i	−1.52010	−	1.59760i
$869$	39.4781	−	59.0832i	1.33920	−	2.00426i
$870$	−22.7679	+	9.06874i	−0.771904	+	0.307459i
$871$	5.37304	−	2.22559i	0.182059	−	0.0754111i
$872$	−14.5862	+	31.8063i	−0.493952	+	1.07710i
$873$	37.0378	−	15.2357i	1.25354	−	0.515649i
$874$	40.4137	−	16.1545i	1.36701	−	0.546434i
$875$	4.33610	−	0.862503i	0.146587	−	0.0291579i
$876$	−1.87351	+	2.65154i	−0.0633000	+	0.0895873i
$877$	−2.04201	+	1.36443i	−0.0689537	+	0.0460734i	−0.589569	−	0.807718i	$-0.700702\pi$
$877$	−2.04201	+	1.36443i	−0.0689537	+	0.0460734i	0.520616	+	0.853791i	$0.325702\pi$
$878$	2.57182	−	12.1391i	0.0867948	−	0.409673i
$879$	−3.05651	−	7.40465i	−0.103094	−	0.249753i
$880$	−5.52625	−	15.4751i	−0.186290	−	0.521664i
$881$	−14.2829	−	14.2829i	−0.481203	−	0.481203i	0.424313	−	0.905516i	$-0.360516\pi$
$881$	−14.2829	−	14.2829i	−0.481203	−	0.481203i	−0.905516	+	0.424313i	$0.860516\pi$
$882$	−52.0437	−	11.1591i	−1.75240	−	0.375746i
$883$	11.0809	−	7.40403i	0.372902	−	0.249165i	−0.354970	−	0.934878i	$-0.615509\pi$
$883$	11.0809	−	7.40403i	0.372902	−	0.249165i	0.727873	+	0.685712i	$0.240509\pi$
$884$	11.5211	−	1.99542i	0.387496	−	0.0671133i
$885$	−3.27717	+	16.3709i	−0.110161	+	0.550302i
$886$	−19.0692	+	44.4660i	−0.640642	+	1.49386i
$887$	−41.0437	−	17.0009i	−1.37811	−	0.570833i	−0.434137	−	0.900847i	$-0.642947\pi$
$887$	−41.0437	−	17.0009i	−1.37811	−	0.570833i	−0.943976	+	0.330014i	$0.892947\pi$
$888$	16.9129	−	23.3163i	0.567561	−	0.782444i
$889$	−72.6340	+	30.0860i	−2.43606	+	1.00905i
$890$	6.95822	+	0.0864727i	0.233240	+	0.00289857i
$891$	−30.6407	−	20.6908i	−1.02650	−	0.693166i
$892$	22.3373	−	8.60849i	0.747907	−	0.288234i
$893$	−3.81122	+	19.1603i	−0.127538	+	0.641176i
$894$	−11.9864	−	2.55479i	−0.400886	−	0.0854450i
$895$		−	0.427505i		−	0.0142899i
$896$	−49.7196	+	5.45922i	−1.66102	+	0.182380i
$897$	6.01569	−	14.4731i	0.200858	−	0.483244i
$898$	−2.50655	−	13.4743i	−0.0836447	−	0.449642i
$899$	72.1035	+	14.3423i	2.40478	+	0.478341i
$900$	2.44654	−	5.47854i	0.0815513	−	0.182618i
$901$	−11.1313	+	16.6592i	−0.370839	+	0.555000i
$902$	0.294791	−	23.7210i	0.00981547	−	0.789824i
$903$	−0.0782790	+	64.0835i	−0.00260496	+	2.13256i
$904$	5.08870	+	1.21099i	0.169248	+	0.0402768i
$905$	−4.70890	+	11.3683i	−0.156529	+	0.377894i
$906$	11.1955	−	10.8940i	0.371947	−	0.361930i
$907$	−40.9945	+	8.15432i	−1.36120	+	0.270760i	−0.821073	−	0.570823i	$-0.806624\pi$
$907$	−40.9945	+	8.15432i	−1.36120	+	0.270760i	−0.540128	+	0.841583i	$0.681624\pi$
$908$	1.09531	+	6.32403i	0.0363490	+	0.209870i
$909$	10.4973	+	2.11472i	0.348174	+	0.0701408i
$910$	7.50193	−	4.87888i	0.248686	−	0.161733i
$911$	29.6269	−	29.6269i	0.981583	−	0.981583i	−0.0182500	−	0.999833i	$-0.505809\pi$
$911$	29.6269	−	29.6269i	0.981583	−	0.981583i	0.999833	+	0.0182500i	$0.00580947\pi$
$912$	25.0298	−	22.6019i	0.828819	−	0.748423i
$913$	17.4322	+	17.4322i	0.576921	+	0.576921i
$914$	29.2123	+	6.18902i	0.966256	+	0.204714i
$915$	−23.0273	+	4.55119i	−0.761260	+	0.150458i
$916$	−6.17841	−	1.38942i	−0.204140	−	0.0459077i
$917$	1.07597	+	5.40925i	0.0355316	+	0.178629i
$918$	−21.5631	+	20.8801i	−0.711690	+	0.689147i
$919$	22.9345	+	9.49980i	0.756541	+	0.313369i	0.727407	−	0.686206i	$-0.240725\pi$
$919$	22.9345	+	9.49980i	0.756541	+	0.313369i	0.0291335	+	0.999576i	$0.490725\pi$
$920$	−7.45427	+	16.2545i	−0.245760	+	0.535896i
$921$	0.0518302	−	42.4311i	0.00170786	−	1.39815i
$922$	19.2937	−	18.8200i	0.635404	−	0.619805i
$923$	−10.8900	−	7.27648i	−0.358449	−	0.239508i
$924$	22.5527	+	58.7334i	0.741930	+	1.93219i
$925$	1.14707	−	5.76671i	0.0377154	−	0.189608i
$926$	17.3126	+	11.8817i	0.568928	+	0.390458i
$927$	14.4112	+	14.4817i	0.473324	+	0.475643i
$928$	42.4285	−	37.4584i	1.39278	−	1.22963i
$929$	21.7894			0.714886			0.357443	−	0.933935i	$-0.383649\pi$
$929$	21.7894			0.714886			0.357443	+	0.933935i	$0.383649\pi$
$930$	−15.1002	+	9.79420i	−0.495155	+	0.321164i
$931$	−59.8949	−	11.9138i	−1.96298	−	0.390461i
$932$	2.76217	+	0.0686639i	0.0904779	+	0.00224916i
$933$	−26.7653	+	17.8367i	−0.876256	+	0.583949i
$934$	−28.5249	+	27.8246i	−0.933363	+	0.910449i
$935$	6.42138	+	15.5026i	0.210002	+	0.506989i
$936$	0.482310	−	12.1353i	0.0157648	−	0.396656i
$937$	1.65020	−	3.98394i	0.0539098	−	0.130150i	−0.894630	−	0.446808i	$-0.852561\pi$
$937$	1.65020	−	3.98394i	0.0539098	−	0.130150i	0.948540	+	0.316658i	$0.102561\pi$
$938$	23.5900	−	9.42959i	0.770240	−	0.307887i
$939$	−3.30972	+	16.5335i	−0.108009	+	0.539550i
$940$	−4.29215	−	6.78269i	−0.139994	−	0.221227i
$941$	−21.6784	−	32.4441i	−0.706697	−	1.05765i	−0.994977	−	0.100101i	$-0.968083\pi$
$941$	−21.6784	−	32.4441i	−0.706697	−	1.05765i	0.288280	−	0.957546i	$-0.406917\pi$
$942$	−25.7613	−	17.7264i	−0.839348	−	0.577558i
$943$	−18.2549	+	18.2549i	−0.594461	+	0.594461i
$944$	−5.63386	−	38.1432i	−0.183366	−	1.24146i
$945$	−8.86888	+	21.1914i	−0.288505	+	0.689356i
$946$	40.7583	−	26.5072i	1.32517	−	0.861823i
$947$	13.3919	+	20.0424i	0.435178	+	0.651289i	0.982636	−	0.185543i	$-0.0594046\pi$
$947$	13.3919	+	20.0424i	0.435178	+	0.651289i	−0.547458	+	0.836833i	$0.684405\pi$
$948$	−50.6727	+	31.9796i	−1.64577	+	1.03865i
$949$	0.261703	+	1.31567i	0.00849524	+	0.0427084i
$950$	2.71321	−	6.32673i	0.0880281	−	0.205266i
$951$	33.7825	+	33.8651i	1.09547	+	1.09815i
$952$	50.4319	−	8.09051i	1.63451	−	0.262215i
$953$	−7.78366	−	18.7914i	−0.252138	−	0.608714i	0.746239	−	0.665679i	$-0.231858\pi$
$953$	−7.78366	−	18.7914i	−0.252138	−	0.608714i	−0.998376	+	0.0569645i	$0.981858\pi$
$954$	14.4951	+	14.9327i	0.469297	+	0.483465i
$955$	2.98145	+	1.99214i	0.0964773	+	0.0644641i
$956$	43.6905	+	19.3829i	1.41305	+	0.626887i
$957$	−59.1442	−	39.6235i	−1.91186	−	1.28084i
$958$	7.17567	+	38.5737i	0.231835	+	1.24626i
$959$	35.0457			1.13169
$960$	−1.04906	+	13.8166i	−0.0338584	+	0.445930i
$961$	22.9903			0.741624
$962$	−2.17662	−	11.7007i	−0.0701770	−	0.377245i
$963$	−30.5597	−	45.9787i	−0.984774	−	1.48164i
$964$	12.8929	−	29.0616i	0.415253	−	0.936012i
$965$	9.01197	+	6.02161i	0.290106	+	0.193842i
$966$	27.0619	−	62.8914i	0.870701	−	2.02350i
$967$	−6.20730	−	14.9858i	−0.199613	−	0.481910i	0.792098	−	0.610394i	$-0.208989\pi$
$967$	−6.20730	−	14.9858i	−0.199613	−	0.481910i	−0.991712	+	0.128484i	$0.958989\pi$
$968$	9.74225	−	13.4653i	0.313128	−	0.432791i
$969$	−24.3810	+	24.3216i	−0.783232	+	0.781321i
$970$	−7.44098	+	17.3511i	−0.238916	+	0.557110i
$971$	6.87613	+	34.5686i	0.220665	+	1.10936i	0.919202	+	0.393786i	$0.128835\pi$
$971$	6.87613	+	34.5686i	0.220665	+	1.10936i	−0.698537	+	0.715574i	$0.746165\pi$
$972$	16.5102	+	26.4464i	0.529565	+	0.848269i
$973$	33.5138	+	50.1570i	1.07440	+	1.60796i
$974$	−24.9030	+	16.1957i	−0.797945	+	0.518944i
$975$	−0.945902	−	2.29152i	−0.0302931	−	0.0733874i
$976$	46.5130	−	27.8397i	1.48885	−	0.891126i
$977$	30.6853	−	30.6853i	0.981709	−	0.981709i	−0.0181267	−	0.999836i	$-0.505770\pi$
$977$	30.6853	−	30.6853i	0.981709	−	0.981709i	0.999836	+	0.0181267i	$0.00577023\pi$
$978$	11.1476	−	16.2005i	0.356461	−	0.518034i
$979$	11.2303	+	16.8073i	0.358922	+	0.537165i
$980$	21.2026	−	13.4172i	0.677292	−	0.428597i
$981$	−30.8087	−	20.6947i	−0.983645	−	0.660732i
$982$	31.0211	−	12.4000i	0.989924	−	0.395701i
$983$	−8.92135	+	21.5381i	−0.284547	+	0.686957i	−0.999931	−	0.0117746i	$-0.996252\pi$
$983$	−8.92135	+	21.5381i	−0.284547	+	0.686957i	0.715384	+	0.698732i	$0.246252\pi$
$984$	−8.36101	+	18.1731i	−0.266539	+	0.579338i
$985$	5.73757	+	13.8517i	0.182814	+	0.441352i
$986$	−41.3721	+	40.3564i	−1.31756	+	1.28521i
$987$	17.0426	+	25.5736i	0.542470	+	0.814015i
$988$	0.346279	−	13.9299i	0.0110166	−	0.443169i
$989$	−51.8935	−	10.3223i	−1.65012	−	0.328229i
$990$	17.1428	−	3.14567i	0.544833	−	0.0999761i
$991$	−21.3984			−0.679742			−0.339871	−	0.940472i	$-0.610383\pi$
$991$	−21.3984			−0.679742			−0.339871	+	0.940472i	$0.610383\pi$
$992$	25.1940	−	33.0599i	0.799910	−	1.04965i
$993$	−6.10796	+	14.6951i	−0.193830	+	0.466335i
$994$	−47.1721	−	32.3744i	−1.49621	−	1.02686i
$995$	0.708505	−	3.56190i	0.0224611	−	0.112920i
$996$	−7.45194	−	19.4069i	−0.236124	−	0.614930i
$997$	−44.3693	−	29.6466i	−1.40519	−	0.938918i	−0.999692	−	0.0248216i	$-0.992098\pi$
$997$	−44.3693	−	29.6466i	−1.40519	−	0.938918i	−0.405498	−	0.914096i	$-0.632902\pi$
$998$	12.1647	−	11.8660i	0.385066	−	0.375613i
$999$	21.5240	+	21.6824i	0.680991	+	0.686000i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.cn.a.611.9	yes	1024
3.2	odd	2	inner	960.2.cn.a.611.120	yes	1024
64.11	odd	16	inner	960.2.cn.a.11.120	yes	1024
192.11	even	16	inner	960.2.cn.a.11.9	✓	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
960.2.cn.a.11.9	✓	1024	192.11	even	16	inner
960.2.cn.a.11.120	yes	1024	64.11	odd	16	inner
960.2.cn.a.611.9	yes	1024	1.1	even	1	trivial
960.2.cn.a.611.120	yes	1024	3.2	odd	2	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:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.cn (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39036 + 0.258642i) q^{2} +(0.964034 - 1.43897i) q^{3} +(1.86621 - 0.719212i) q^{4} +(-0.831470 - 0.555570i) q^{5} +(-0.968177 + 2.25003i) q^{6} +(1.69186 + 4.08451i) q^{7} +(-2.40869 + 1.48264i) q^{8} +(-1.14128 - 2.77444i) q^{9} +O(q^{10})\)	\(q+(-1.39036 + 0.258642i) q^{2} +(0.964034 - 1.43897i) q^{3} +(1.86621 - 0.719212i) q^{4} +(-0.831470 - 0.555570i) q^{5} +(-0.968177 + 2.25003i) q^{6} +(1.69186 + 4.08451i) q^{7} +(-2.40869 + 1.48264i) q^{8} +(-1.14128 - 2.77444i) q^{9} +(1.29974 + 0.557390i) q^{10} +(0.801441 + 4.02911i) q^{11} +(0.764164 - 3.37877i) q^{12} +(-0.795184 - 1.19008i) q^{13} +(-3.40872 - 5.24136i) q^{14} +(-1.60101 + 0.660872i) q^{15} +(2.96547 - 2.68440i) q^{16} +(-2.88827 + 2.88827i) q^{17} +(2.30437 + 3.56228i) q^{18} +(2.70435 + 4.04734i) q^{19} +(-1.95127 - 0.438807i) q^{20} +(7.50851 + 1.50307i) q^{21} +(-2.15639 - 5.39464i) q^{22} +(-2.41946 + 5.84108i) q^{23} +(-0.188573 + 4.89535i) q^{24} +(0.382683 + 0.923880i) q^{25} +(1.41340 + 1.44897i) q^{26} +(-5.09256 - 1.03239i) q^{27} +(6.09499 + 6.40575i) q^{28} +(-9.81291 - 1.95191i) q^{29} +(2.05506 - 1.33294i) q^{30} -7.34781 q^{31} +(-3.42877 + 4.49928i) q^{32} +(6.57040 + 2.73095i) q^{33} +(3.26871 - 4.76277i) q^{34} +(0.862503 - 4.33610i) q^{35} +(-4.12526 - 4.35686i) q^{36} +(-4.88878 - 3.26658i) q^{37} +(-4.80683 - 4.92781i) q^{38} +(-2.47907 - 0.00302822i) q^{39} +(2.82646 + 0.105420i) q^{40} +(3.77252 + 1.56263i) q^{41} +(-10.8283 - 0.147797i) q^{42} +(1.63266 + 8.20795i) q^{43} +(4.39344 + 6.94276i) q^{44} +(-0.592457 + 2.94092i) q^{45} +(1.85317 - 8.74699i) q^{46} +(2.83785 + 2.83785i) q^{47} +(-1.00396 - 6.85508i) q^{48} +(-8.87110 + 8.87110i) q^{49} +(-0.771022 - 1.18555i) q^{50} +(1.37175 + 6.94053i) q^{51} +(-2.33990 - 1.64903i) q^{52} +(4.81093 - 0.956954i) q^{53} +(7.34752 + 0.118241i) q^{54} +(1.57208 - 3.79534i) q^{55} +(-10.1310 - 7.32988i) q^{56} +(8.43109 + 0.0102987i) q^{57} +(14.1483 + 0.175827i) q^{58} +(5.35529 - 8.01475i) q^{59} +(-2.51252 + 2.38479i) q^{60} +(13.2916 + 2.64387i) q^{61} +(10.2161 - 1.90045i) q^{62} +(9.40134 - 9.35551i) q^{63} +(3.60353 - 7.14245i) q^{64} +1.43129i q^{65} +(-9.84156 - 2.09763i) q^{66} +(-0.792706 + 3.98520i) q^{67} +(-3.31284 + 7.46740i) q^{68} +(6.07271 + 9.11253i) q^{69} +(-0.0776939 + 6.25182i) q^{70} +(8.45413 - 3.50182i) q^{71} +(6.86247 + 4.99064i) q^{72} +(-0.865884 - 0.358661i) q^{73} +(7.64205 + 3.27728i) q^{74} +(1.69836 + 0.339981i) q^{75} +(7.95778 + 5.60819i) q^{76} +(-15.1010 + 10.0902i) q^{77} +(3.44759 - 0.636982i) q^{78} +(-12.2311 - 12.2311i) q^{79} +(-3.95707 + 0.584470i) q^{80} +(-6.39498 + 6.33279i) q^{81} +(-5.64933 - 1.19689i) q^{82} +(4.98973 - 3.33403i) q^{83} +(15.0935 - 2.59516i) q^{84} +(4.00615 - 0.796873i) q^{85} +(-4.39291 - 10.9897i) q^{86} +(-12.2687 + 12.2388i) q^{87} +(-7.90416 - 8.51662i) q^{88} +(4.54603 - 1.88303i) q^{89} +(0.0630849 - 4.24217i) q^{90} +(3.51554 - 5.26138i) q^{91} +(-0.314233 + 12.6408i) q^{92} +(-7.08354 + 10.5733i) q^{93} +(-4.67963 - 3.21165i) q^{94} -4.86770i q^{95} +(3.16888 + 9.27137i) q^{96} +13.3497i q^{97} +(10.0396 - 14.6285i) q^{98} +(10.2639 - 6.82188i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 1024 q+O(q^{10}) \) 1024 * q	\( 1024 q + 80 q^{24} + 80 q^{42} - 96 q^{52} - 288 q^{58} - 96 q^{64} + 256 q^{67} - 112 q^{76} - 48 q^{78} + 32 q^{79} - 112 q^{84} - 160 q^{88} - 144 q^{90} - 16 q^{94} - 272 q^{96}+O(q^{100}) \) 1024 * q + 80 * q^24 + 80 * q^42 - 96 * q^52 - 288 * q^58 - 96 * q^64 + 256 * q^67 - 112 * q^76 - 48 * q^78 + 32 * q^79 - 112 * q^84 - 160 * q^88 - 144 * q^90 - 16 * q^94 - 272 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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