LMFDB - Embedded newform 960.2.cn.a.11.108

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			11.108
Character	$\chi$	$=$	960.11
Dual form			960.2.cn.a.611.108

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.25987 + 0.642446i) q^{2} +(0.399961 + 1.68524i) q^{3} +(1.17453 + 1.61879i) q^{4} +(-0.831470 + 0.555570i) q^{5} +(-0.578777 + 2.38013i) q^{6} +(-0.496021 + 1.19750i) q^{7} +(0.439761 + 2.79403i) q^{8} +(-2.68006 + 1.34806i) q^{9} +O(q^{10})$	\(q+(1.25987 + 0.642446i) q^{2} +(0.399961 + 1.68524i) q^{3} +(1.17453 + 1.61879i) q^{4} +(-0.831470 + 0.555570i) q^{5} +(-0.578777 + 2.38013i) q^{6} +(-0.496021 + 1.19750i) q^{7} +(0.439761 + 2.79403i) q^{8} +(-2.68006 + 1.34806i) q^{9} +(-1.40446 + 0.165770i) q^{10} +(-0.701467 + 3.52651i) q^{11} +(-2.25829 + 2.62681i) q^{12} +(2.14761 - 3.21413i) q^{13} +(-1.39425 + 1.19002i) q^{14} +(-1.26882 - 1.17902i) q^{15} +(-1.24097 + 3.80263i) q^{16} +(-0.789972 - 0.789972i) q^{17} +(-4.24258 - 0.0234197i) q^{18} +(4.26717 - 6.38627i) q^{19} +(-1.87594 - 0.693444i) q^{20} +(-2.21646 - 0.356960i) q^{21} +(-3.14935 + 3.99228i) q^{22} +(1.68869 + 4.07686i) q^{23} +(-4.53272 + 1.85861i) q^{24} +(0.382683 - 0.923880i) q^{25} +(4.77060 - 2.66965i) q^{26} +(-3.34372 - 3.97738i) q^{27} +(-2.52109 + 0.603542i) q^{28} +(-7.54744 + 1.50128i) q^{29} +(-0.841093 - 2.30056i) q^{30} -2.10395 q^{31} +(-4.00644 + 3.99355i) q^{32} +(-6.22358 + 0.228328i) q^{33} +(-0.487745 - 1.50277i) q^{34} +(-0.252869 - 1.27126i) q^{35} +(-5.33003 - 2.75513i) q^{36} +(3.92809 - 2.62467i) q^{37} +(9.47889 - 5.30442i) q^{38} +(6.27553 + 2.33371i) q^{39} +(-1.91793 - 2.07883i) q^{40} +(-1.29011 + 0.534381i) q^{41} +(-2.56312 - 1.87368i) q^{42} +(-1.68478 + 8.46996i) q^{43} +(-6.53258 + 3.00646i) q^{44} +(1.47945 - 2.60983i) q^{45} +(-0.491637 + 6.22119i) q^{46} +(8.06060 - 8.06060i) q^{47} +(-6.90468 - 0.570433i) q^{48} +(3.76178 + 3.76178i) q^{49} +(1.07567 - 0.918111i) q^{50} +(1.01533 - 1.64725i) q^{51} +(7.72543 - 0.298544i) q^{52} +(-0.329760 - 0.0655933i) q^{53} +(-1.65740 - 7.15912i) q^{54} +(-1.37598 - 3.32190i) q^{55} +(-3.56398 - 0.859283i) q^{56} +(12.4691 + 4.63694i) q^{57} +(-10.4733 - 2.95741i) q^{58} +(6.16890 + 9.23241i) q^{59} +(0.418318 - 3.43875i) q^{60} +(2.71225 - 0.539500i) q^{61} +(-2.65070 - 1.35167i) q^{62} +(-0.284935 - 3.87804i) q^{63} +(-7.61322 + 2.45741i) q^{64} +3.86560i q^{65} +(-7.98757 - 3.71065i) q^{66} +(3.02134 + 15.1893i) q^{67} +(0.350957 - 2.20664i) q^{68} +(-6.19508 + 4.47643i) q^{69} +(0.498134 - 1.76407i) q^{70} +(0.620249 + 0.256916i) q^{71} +(-4.94511 - 6.89535i) q^{72} +(-0.564831 + 0.233961i) q^{73} +(6.63508 - 0.783145i) q^{74} +(1.71002 + 0.275397i) q^{75} +(15.3499 - 0.593188i) q^{76} +(-3.87506 - 2.58923i) q^{77} +(6.40705 + 6.97185i) q^{78} +(10.9463 - 10.9463i) q^{79} +(-1.08080 - 3.85122i) q^{80} +(5.36547 - 7.22577i) q^{81} +(-1.96868 - 0.155577i) q^{82} +(-12.8021 - 8.55406i) q^{83} +(-2.02545 - 4.00725i) q^{84} +(1.09572 + 0.217953i) q^{85} +(-7.56409 + 9.58864i) q^{86} +(-5.54870 - 12.1188i) q^{87} +(-10.1617 - 0.409097i) q^{88} +(2.34921 + 0.973073i) q^{89} +(3.54058 - 2.33758i) q^{90} +(2.78366 + 4.16604i) q^{91} +(-4.61618 + 7.52202i) q^{92} +(-0.841498 - 3.54566i) q^{93} +(15.3338 - 4.97678i) q^{94} +7.68070i q^{95} +(-8.33250 - 5.15455i) q^{96} -3.06732i q^{97} +(2.32260 + 7.15608i) q^{98} +(-2.87397 - 10.3969i) 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 $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{5}{16}\right)$

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 $

$2$	1.25987	+	0.642446i	0.890860	+	0.454278i
$2$	1.25987	+	0.642446i	0.890860	+	0.454278i
$3$	0.399961	+	1.68524i	0.230918	+	0.972973i
$3$	0.399961	+	1.68524i	0.230918	+	0.972973i
$4$	1.17453	+	1.61879i	0.587263	+	0.809396i
$5$	−0.831470	+	0.555570i	−0.371845	+	0.248459i
$5$	−0.831470	+	0.555570i	−0.371845	+	0.248459i
$6$	−0.578777	+	2.38013i	−0.236285	+	0.971684i
$7$	−0.496021	+	1.19750i	−0.187478	+	0.452612i	−0.989473	−	0.144719i	$-0.953772\pi$
$7$	−0.496021	+	1.19750i	−0.187478	+	0.452612i	0.801995	+	0.597331i	$0.203772\pi$
$8$	0.439761	+	2.79403i	0.155479	+	0.987839i
$9$	−2.68006	+	1.34806i	−0.893354	+	0.449353i
$10$	−1.40446	+	0.165770i	−0.444131	+	0.0524211i
$11$	−0.701467	+	3.52651i	−0.211500	+	1.06328i	0.718444	+	0.695584i	$0.244854\pi$
$11$	−0.701467	+	3.52651i	−0.211500	+	1.06328i	−0.929945	+	0.367699i	$0.880146\pi$
$12$	−2.25829	+	2.62681i	−0.651911	+	0.758295i
$13$	2.14761	−	3.21413i	0.595640	−	0.891438i	−0.404089	−	0.914720i	$-0.632411\pi$
$13$	2.14761	−	3.21413i	0.595640	−	0.891438i	0.999729	+	0.0232815i	$0.00741139\pi$
$14$	−1.39425	+	1.19002i	−0.372629	+	0.318047i
$15$	−1.26882	−	1.17902i	−0.327609	−	0.304421i
$16$	−1.24097	+	3.80263i	−0.310243	+	0.950657i
$17$	−0.789972	−	0.789972i	−0.191596	−	0.191596i	0.604789	−	0.796386i	$-0.293257\pi$
$17$	−0.789972	−	0.789972i	−0.191596	−	0.191596i	−0.796386	+	0.604789i	$0.793257\pi$
$18$	−4.24258	−	0.0234197i	−0.999985	−	0.00552008i
$19$	4.26717	−	6.38627i	0.978956	−	1.46511i	0.0961531	−	0.995367i	$-0.469346\pi$
$19$	4.26717	−	6.38627i	0.978956	−	1.46511i	0.882803	−	0.469744i	$-0.155654\pi$
$20$	−1.87594	−	0.693444i	−0.419472	−	0.155059i
$21$	−2.21646	−	0.356960i	−0.483672	−	0.0778952i
$22$	−3.14935	+	3.99228i	−0.671443	+	0.851157i
$23$	1.68869	+	4.07686i	0.352117	+	0.850084i	0.996359	+	0.0852627i	$0.0271730\pi$
$23$	1.68869	+	4.07686i	0.352117	+	0.850084i	−0.644242	+	0.764822i	$0.722827\pi$
$24$	−4.53272	+	1.85861i	−0.925238	+	0.379386i
$25$	0.382683	−	0.923880i	0.0765367	−	0.184776i
$26$	4.77060	−	2.66965i	0.935592	−	0.523561i
$27$	−3.34372	−	3.97738i	−0.643500	−	0.765446i
$28$	−2.52109	+	0.603542i	−0.476442	+	0.114059i
$29$	−7.54744	+	1.50128i	−1.40152	+	0.278781i	−0.837256	−	0.546811i	$-0.815842\pi$
$29$	−7.54744	+	1.50128i	−1.40152	+	0.278781i	−0.564268	+	0.825591i	$0.690842\pi$
$30$	−0.841093	−	2.30056i	−0.153562	−	0.420022i
$31$	−2.10395			−0.377881			−0.188940	−	0.981989i	$-0.560505\pi$
$31$	−2.10395			−0.377881			−0.188940	+	0.981989i	$0.560505\pi$
$32$	−4.00644	+	3.99355i	−0.708246	+	0.705966i
$33$	−6.22358	+	0.228328i	−1.08339	+	0.0397467i
$34$	−0.487745	−	1.50277i	−0.0836476	−	0.257723i
$35$	−0.252869	−	1.27126i	−0.0427427	−	0.214882i
$36$	−5.33003	−	2.75513i	−0.888339	−	0.459188i
$37$	3.92809	−	2.62467i	0.645775	−	0.431493i	−0.189081	−	0.981961i	$-0.560551\pi$
$37$	3.92809	−	2.62467i	0.645775	−	0.431493i	0.834856	+	0.550469i	$0.185551\pi$
$38$	9.47889	−	5.30442i	1.53768	−	0.860491i
$39$	6.27553	+	2.33371i	1.00489	+	0.373693i
$40$	−1.91793	−	2.07883i	−0.303251	−	0.328692i
$41$	−1.29011	+	0.534381i	−0.201481	+	0.0834563i	−0.481142	−	0.876643i	$-0.659778\pi$
$41$	−1.29011	+	0.534381i	−0.201481	+	0.0834563i	0.279661	+	0.960099i	$0.409778\pi$
$42$	−2.56312	−	1.87368i	−0.395498	−	0.289115i
$43$	−1.68478	+	8.46996i	−0.256927	+	1.29166i	0.609673	+	0.792653i	$0.291301\pi$
$43$	−1.68478	+	8.46996i	−0.256927	+	1.29166i	−0.866600	+	0.499004i	$0.833699\pi$
$44$	−6.53258	+	3.00646i	−0.984824	+	0.453240i
$45$	1.47945	−	2.60983i	0.220543	−	0.389051i
$46$	−0.491637	+	6.22119i	−0.0724879	+	0.917265i
$47$	8.06060	−	8.06060i	1.17576	−	1.17576i	0.194945	−	0.980814i	$-0.437547\pi$
$47$	8.06060	−	8.06060i	1.17576	−	1.17576i	0.980814	−	0.194945i	$-0.0624528\pi$
$48$	−6.90468	−	0.570433i	−0.996605	−	0.0823349i
$49$	3.76178	+	3.76178i	0.537397	+	0.537397i
$50$	1.07567	−	0.918111i	0.152123	−	0.129841i
$51$	1.01533	−	1.64725i	0.142175	−	0.230661i
$52$	7.72543	−	0.298544i	1.07132	−	0.0414006i
$53$	−0.329760	−	0.0655933i	−0.0452960	−	0.00900994i	0.172390	−	0.985029i	$-0.444851\pi$
$53$	−0.329760	−	0.0655933i	−0.0452960	−	0.00900994i	−0.217686	+	0.976019i	$0.569851\pi$
$54$	−1.65740	−	7.15912i	−0.225543	−	0.974233i
$55$	−1.37598	−	3.32190i	−0.185537	−	0.447925i
$56$	−3.56398	−	0.859283i	−0.476257	−	0.114827i
$57$	12.4691	+	4.63694i	1.65157	+	0.614178i
$58$	−10.4733	−	2.95741i	−1.37521	−	0.388327i
$59$	6.16890	+	9.23241i	0.803122	+	1.20196i	0.976162	+	0.217042i	$0.0696409\pi$
$59$	6.16890	+	9.23241i	0.803122	+	1.20196i	−0.173040	+	0.984915i	$0.555359\pi$
$60$	0.418318	−	3.43875i	0.0540046	−	0.443941i
$61$	2.71225	−	0.539500i	0.347268	−	0.0690759i	−0.0183747	−	0.999831i	$-0.505849\pi$
$61$	2.71225	−	0.539500i	0.347268	−	0.0690759i	0.365643	+	0.930755i	$0.380849\pi$
$62$	−2.65070	−	1.35167i	−0.336639	−	0.171663i
$63$	−0.284935	−	3.87804i	−0.0358984	−	0.488587i
$64$	−7.61322	+	2.45741i	−0.951652	+	0.307177i
$65$			3.86560i			0.479468i
$66$	−7.98757	−	3.71065i	−0.983201	−	0.456749i
$67$	3.02134	+	15.1893i	0.369115	+	1.85567i	0.502466	+	0.864597i	$0.332426\pi$
$67$	3.02134	+	15.1893i	0.369115	+	1.85567i	−0.133351	+	0.991069i	$0.542574\pi$
$68$	0.350957	−	2.20664i	0.0425597	−	0.267595i
$69$	−6.19508	+	4.47643i	−0.745800	+	0.538899i
$70$	0.498134	−	1.76407i	0.0595384	−	0.210847i
$71$	0.620249	+	0.256916i	0.0736100	+	0.0304903i	0.419185	−	0.907901i	$-0.362316\pi$
$71$	0.620249	+	0.256916i	0.0736100	+	0.0304903i	−0.345575	+	0.938391i	$0.612316\pi$
$72$	−4.94511	−	6.89535i	−0.582787	−	0.812625i
$73$	−0.564831	+	0.233961i	−0.0661084	+	0.0273830i	−0.415493	−	0.909597i	$-0.636391\pi$
$73$	−0.564831	+	0.233961i	−0.0661084	+	0.0273830i	0.349384	+	0.936980i	$0.386391\pi$
$74$	6.63508	−	0.783145i	0.771313	−	0.0910387i
$75$	1.71002	+	0.275397i	0.197456	+	0.0318002i
$76$	15.3499	−	0.593188i	1.76076	−	0.0680434i
$77$	−3.87506	−	2.58923i	−0.441604	−	0.295070i
$78$	6.40705	+	6.97185i	0.725455	+	0.789407i
$79$	10.9463	−	10.9463i	1.23156	−	1.23156i	0.268190	−	0.963366i	$-0.413575\pi$
$79$	10.9463	−	10.9463i	1.23156	−	1.23156i	0.963366	−	0.268190i	$-0.0864255\pi$
$80$	−1.08080	−	3.85122i	−0.120837	−	0.430579i
$81$	5.36547	−	7.22577i	0.596163	−	0.802863i
$82$	−1.96868	−	0.155577i	−0.217404	−	0.0171806i
$83$	−12.8021	−	8.55406i	−1.40521	−	0.938930i	−0.999691	−	0.0248429i	$-0.992091\pi$
$83$	−12.8021	−	8.55406i	−1.40521	−	0.938930i	−0.405517	−	0.914087i	$-0.632909\pi$
$84$	−2.02545	−	4.00725i	−0.220995	−	0.437227i
$85$	1.09572	+	0.217953i	0.118848	+	0.0236403i
$86$	−7.56409	+	9.58864i	−0.815656	+	1.03397i
$87$	−5.54870	−	12.1188i	−0.594883	−	1.29927i
$88$	−10.1617	−	0.409097i	−1.08324	−	0.0436099i
$89$	2.34921	+	0.973073i	0.249015	+	0.103145i	0.503700	−	0.863879i	$-0.331972\pi$
$89$	2.34921	+	0.973073i	0.249015	+	0.103145i	−0.254685	+	0.967024i	$0.581972\pi$
$90$	3.54058	−	2.33758i	0.373210	−	0.246402i
$91$	2.78366	+	4.16604i	0.291807	+	0.436719i
$92$	−4.61618	+	7.52202i	−0.481270	+	0.784225i
$93$	−0.841498	−	3.54566i	−0.0872593	−	0.367668i
$94$	15.3338	−	4.97678i	1.58156	−	0.513316i
$95$			7.68070i			0.788023i
$96$	−8.33250	−	5.15455i	−0.850432	−	0.526084i
$97$		−	3.06732i		−	0.311439i	−0.987801	−	0.155720i	$-0.950230\pi$
$97$		−	3.06732i		−	0.311439i	0.987801	−	0.155720i	$-0.0497696\pi$
$98$	2.32260	+	7.15608i	0.234618	+	0.722873i
$99$	−2.87397	−	10.3969i	−0.288845	−	1.04493i
$100$	1.94504	−	0.465637i	0.194504	−	0.0465637i
$101$	4.59580	+	6.87810i	0.457299	+	0.684396i	0.986437	−	0.164139i	$-0.0524847\pi$
$101$	4.59580	+	6.87810i	0.457299	+	0.684396i	−0.529138	+	0.848536i	$0.677485\pi$
$102$	2.33745	−	1.42302i	0.231442	−	0.140900i
$103$	−3.98286	−	1.64975i	−0.392443	−	0.162555i	0.177731	−	0.984079i	$-0.443124\pi$
$103$	−3.98286	−	1.64975i	−0.392443	−	0.162555i	−0.570174	+	0.821524i	$0.693124\pi$
$104$	9.92480	+	4.58704i	0.973207	+	0.449796i
$105$	2.04124	−	0.934599i	0.199204	−	0.0912075i
$106$	−0.373313	−	0.294492i	−0.0362594	−	0.0286036i
$107$	15.7662	+	3.13610i	1.52418	+	0.303178i	0.884895	−	0.465791i	$-0.154230\pi$
$107$	15.7662	+	3.13610i	1.52418	+	0.303178i	0.639285	+	0.768970i	$0.279230\pi$
$108$	2.51125	−	10.0843i	0.241645	−	0.970365i
$109$	0.475997	+	0.318051i	0.0455923	+	0.0304638i	0.578158	−	0.815925i	$-0.303772\pi$
$109$	0.475997	+	0.318051i	0.0455923	+	0.0304638i	−0.532565	+	0.846389i	$0.678772\pi$
$110$	0.400595	−	5.06915i	0.0381952	−	0.483324i
$111$	5.99428	+	5.57001i	0.568952	+	0.528682i
$112$	−3.93810	−	3.37225i	−0.372115	−	0.318647i
$113$	−11.7543	+	11.7543i	−1.10575	+	1.10575i	−0.112048	+	0.993703i	$0.535741\pi$
$113$	−11.7543	+	11.7543i	−1.10575	+	1.10575i	−0.993703	+	0.112048i	$0.964259\pi$
$114$	12.7304	+	13.8526i	1.19231	+	1.29742i
$115$	−3.66908	−	2.45160i	−0.342143	−	0.228613i
$116$	−11.2949	−	10.4544i	−1.04871	−	0.970670i
$117$	−1.42290	+	11.5092i	−0.131547	+	1.06402i
$118$	1.84067	+	15.5948i	0.169447	+	1.43562i
$119$	1.33783	−	0.554149i	0.122639	−	0.0507987i
$120$	2.73624	−	4.06362i	0.249783	−	0.370956i
$121$	−1.78157	−	0.737950i	−0.161961	−	0.0670864i
$122$	3.76367	+	1.06278i	0.340747	+	0.0962192i
$123$	−1.41655	−	1.96041i	−0.127726	−	0.176764i
$124$	−2.47115	−	3.40586i	−0.221916	−	0.305855i
$125$	0.195090	+	0.980785i	0.0174494	+	0.0877241i
$126$	2.13245	−	5.06887i	0.189974	−	0.451571i
$127$		−	20.2578i		−	1.79759i	−0.438372	−	0.898794i	$-0.644445\pi$
$127$		−	20.2578i		−	1.79759i	0.438372	−	0.898794i	$-0.355555\pi$
$128$	−11.1704	−	1.79507i	−0.987333	−	0.158663i
$129$	−14.9478	+	0.548396i	−1.31608	+	0.0482835i
$130$	−2.48344	+	4.87014i	−0.217812	+	0.427139i
$131$	6.19162	−	1.23159i	0.540964	−	0.107604i	0.0829572	−	0.996553i	$-0.473564\pi$
$131$	6.19162	−	1.23159i	0.540964	−	0.107604i	0.458007	+	0.888949i	$0.348564\pi$
$132$	−7.67938	−	9.80650i	−0.668404	−	0.853546i
$133$	5.53095	+	8.27766i	0.479594	+	0.717764i
$134$	−5.95181	+	21.0775i	−0.514158	+	1.82082i
$135$	4.98992	+	1.44939i	0.429464	+	0.124744i
$136$	1.85981	−	2.55460i	0.159477	−	0.219056i
$137$	−6.61336	−	15.9661i	−0.565018	−	1.36407i	−0.905710	−	0.423898i	$-0.860661\pi$
$137$	−6.61336	−	15.9661i	−0.565018	−	1.36407i	0.340692	−	0.940175i	$-0.389339\pi$
$138$	−10.6808	+	1.65971i	−0.909213	+	0.141284i
$139$	5.63932	+	1.12173i	0.478321	+	0.0951439i	0.428362	−	0.903607i	$-0.359091\pi$
$139$	5.63932	+	1.12173i	0.478321	+	0.0951439i	0.0499591	+	0.998751i	$0.484091\pi$
$140$	1.76090	−	1.90247i	0.148823	−	0.160788i
$141$	16.8080	+	10.3601i	1.41549	+	0.872479i
$142$	0.616377	+	0.722156i	0.0517252	+	0.0606020i
$143$	9.82818	+	9.82818i	0.821874	+	0.821874i
$144$	−1.80029	−	11.8642i	−0.150024	−	0.988682i
$145$	5.44140	−	5.44140i	0.451884	−	0.451884i
$146$	−0.861918	−	0.0681140i	−0.0713329	−	0.00563716i
$147$	−4.83493	+	7.84406i	−0.398778	+	0.646967i
$148$	8.86245	+	3.27602i	0.728489	+	0.269287i
$149$	0.0775078	−	0.389658i	0.00634969	−	0.0319220i	−0.977481	−	0.211026i	$-0.932320\pi$
$149$	0.0775078	−	0.389658i	0.00634969	−	0.0319220i	0.983830	+	0.179103i	$0.0573197\pi$
$150$	1.97746	+	1.44556i	0.161459	+	0.118029i
$151$	20.6128	−	8.53809i	1.67744	−	0.694820i	0.678245	−	0.734836i	$-0.262741\pi$
$151$	20.6128	−	8.53809i	1.67744	−	0.694820i	0.999199	+	0.0400158i	$0.0127408\pi$
$152$	19.7200	+	9.11417i	1.59950	+	0.739257i
$153$	3.18210	+	1.05224i	0.257258	+	0.0850690i
$154$	−3.21862	−	5.75160i	−0.259363	−	0.463477i
$155$	1.74937	−	1.16889i	0.140513	−	0.0938877i
$156$	3.59299	+	12.8998i	0.287669	+	1.03281i
$157$	0.826145	+	4.15331i	0.0659335	+	0.331470i	0.999647	−	0.0265496i	$-0.00845201\pi$
$157$	0.826145	+	4.15331i	0.0659335	+	0.331470i	−0.933714	+	0.358020i	$0.883452\pi$
$158$	20.8233	−	6.75848i	1.65661	−	0.537676i
$159$	−0.0213506	−	0.581959i	−0.00169321	−	0.0461524i
$160$	1.11254	−	5.54637i	0.0879540	−	0.438479i
$161$	−5.71967			−0.450773
$162$	11.4019	−	5.65648i	0.895821	−	0.444415i
$163$	−11.2915	+	2.24602i	−0.884420	+	0.175922i	−0.616345	−	0.787476i	$-0.711387\pi$
$163$	−11.2915	+	2.24602i	−0.884420	+	0.175922i	−0.268075	+	0.963398i	$0.586387\pi$
$164$	−2.38032	−	1.46077i	−0.185872	−	0.114067i
$165$	5.04786	−	3.64748i	0.392976	−	0.283956i
$166$	−10.6334	−	19.0016i	−0.825309	−	1.47481i
$167$	1.95543	−	4.72083i	0.151316	−	0.365309i	−0.829986	−	0.557784i	$-0.811652\pi$
$167$	1.95543	−	4.72083i	0.151316	−	0.365309i	0.981302	+	0.192475i	$0.0616516\pi$
$168$	0.0226439	−	6.34984i	0.00174701	−	0.489901i
$169$	−0.743492	−	1.79495i	−0.0571917	−	0.138073i
$170$	1.24044	+	0.978533i	0.0951375	+	0.0750501i
$171$	−2.82721	+	22.8680i	−0.216202	+	1.74876i
$172$	−15.6899	+	7.22089i	−1.19635	+	0.550588i
$173$	−11.1598	+	16.7019i	−0.848468	+	1.26982i	0.112637	+	0.993636i	$0.464070\pi$
$173$	−11.1598	+	16.7019i	−0.848468	+	1.26982i	−0.961104	+	0.276185i	$0.910930\pi$
$174$	0.795049	−	18.8328i	0.0602725	−	1.42771i
$175$	0.916527	+	0.916527i	0.0692829	+	0.0692829i
$176$	−12.5395	−	7.04373i	−0.945202	−	0.530941i
$177$	−13.0915	+	14.0887i	−0.984017	+	1.05897i
$178$	2.33454	+	2.73518i	0.174981	+	0.205010i
$179$	4.79841	−	7.18133i	0.358650	−	0.536758i	−0.607640	−	0.794212i	$-0.707884\pi$
$179$	4.79841	−	7.18133i	0.358650	−	0.536758i	0.966290	+	0.257455i	$0.0828838\pi$
$180$	5.96243	−	0.670400i	0.444413	−	0.0499687i
$181$	−0.422281	+	2.12295i	−0.0313879	+	0.157798i	−0.993301	−	0.115559i	$-0.963134\pi$
$181$	−0.422281	+	2.12295i	−0.0313879	+	0.157798i	0.961913	+	0.273357i	$0.0881340\pi$
$182$	0.830583	+	7.03700i	0.0615669	+	0.521617i
$183$	1.99398	+	4.35501i	0.147399	+	0.321932i
$184$	−10.6483	+	6.51110i	−0.785000	+	0.480005i
$185$	−1.80790	+	4.36467i	−0.132920	+	0.320897i
$186$	1.21772	−	5.00768i	0.0892876	−	0.367181i
$187$	3.33999	−	2.23171i	0.244244	−	0.163199i
$188$	22.5158	+	3.58104i	1.64214	+	0.261174i
$189$	6.42146	−	2.03125i	0.467093	−	0.147752i
$190$	−4.93443	+	9.67666i	−0.357981	+	0.702019i
$191$	12.9032			0.933640			0.466820	−	0.884352i	$-0.345400\pi$
$191$	12.9032			0.933640			0.466820	+	0.884352i	$0.345400\pi$
$192$	−7.18632	−	11.8472i	−0.518628	−	0.855000i
$193$	−20.0824			−1.44556			−0.722782	−	0.691076i	$-0.757137\pi$
$193$	−20.0824			−1.44556			−0.722782	+	0.691076i	$0.757137\pi$
$194$	1.97059	−	3.86441i	0.141480	−	0.277449i
$195$	−6.51446	+	1.54609i	−0.466510	+	0.110718i
$196$	−1.67122	+	10.5078i	−0.119373	+	0.750560i
$197$	10.6526	−	7.11783i	0.758966	−	0.507125i	−0.114849	−	0.993383i	$-0.536639\pi$
$197$	10.6526	−	7.11783i	0.758966	−	0.507125i	0.873815	+	0.486258i	$0.161639\pi$
$198$	3.05862	−	14.9451i	0.217367	−	1.06210i
$199$	2.69503	−	6.50637i	0.191045	−	0.461224i	−0.799112	−	0.601182i	$-0.794697\pi$
$199$	2.69503	−	6.50637i	0.191045	−	0.461224i	0.990157	+	0.139958i	$0.0446967\pi$
$200$	2.74964	+	0.662943i	0.194429	+	0.0468771i
$201$	−24.3892	+	11.1668i	−1.72028	+	0.787645i
$202$	1.37129	+	11.6180i	0.0964834	+	0.817442i
$203$	1.94591	−	9.78273i	0.136576	−	0.686613i
$204$	3.85909	−	0.291125i	0.270190	−	0.0203828i
$205$	0.775801	−	1.16107i	0.0541843	−	0.0810925i
$206$	−3.95799	−	4.63724i	−0.275766	−	0.323092i
$207$	−10.0217	−	8.64979i	−0.696553	−	0.601202i
$208$	9.55700	+	12.1552i	0.662659	+	0.842812i
$209$	19.5280	+	19.5280i	1.35078	+	1.35078i
$210$	3.17212	+	0.133915i	0.218897	+	0.00924100i
$211$	−7.89663	+	11.8181i	−0.543626	+	0.813594i	−0.996974	−	0.0777396i	$-0.975230\pi$
$211$	−7.89663	+	11.8181i	−0.543626	+	0.813594i	0.453347	+	0.891334i	$0.350230\pi$
$212$	−0.281130	−	0.610854i	−0.0193081	−	0.0419536i
$213$	−0.184889	+	1.14802i	−0.0126684	+	0.0786613i
$214$	17.8486	+	14.0800i	1.22010	+	0.962490i
$215$	−3.30481	−	7.97853i	−0.225386	−	0.544131i
$216$	9.64247	−	11.0916i	0.656087	−	0.754685i
$217$	1.04360	−	2.51948i	0.0708444	−	0.171034i
$218$	0.395362	+	0.706504i	0.0267773	+	0.0478505i
$219$	−0.620190	−	0.858300i	−0.0419085	−	0.0579985i
$220$	3.76135	−	6.12909i	0.253590	−	0.413223i
$221$	−4.23562	+	0.842517i	−0.284919	+	0.0566739i
$222$	3.97356	+	10.8685i	0.266688	+	0.729444i
$223$	14.4285			0.966207			0.483103	−	0.875563i	$-0.339510\pi$
$223$	14.4285			0.966207			0.483103	+	0.875563i	$0.339510\pi$
$224$	−2.79499	−	6.77860i	−0.186748	−	0.452914i
$225$	0.219829	+	2.99194i	0.0146553	+	0.199462i
$226$	−22.3603	+	7.25735i	−1.48739	+	0.482751i
$227$	−4.30608	−	21.6481i	−0.285805	−	1.43684i	−0.810595	−	0.585607i	$-0.800856\pi$
$227$	−4.30608	−	21.6481i	−0.285805	−	1.43684i	0.524791	−	0.851231i	$-0.324144\pi$
$228$	7.13904	+	25.6311i	0.472795	+	1.69746i
$229$	12.2114	−	8.15942i	0.806955	−	0.539190i	−0.0822972	−	0.996608i	$-0.526226\pi$
$229$	12.2114	−	8.15942i	0.806955	−	0.539190i	0.889252	+	0.457418i	$0.151226\pi$
$230$	−3.04753	−	5.44587i	−0.200948	−	0.359090i
$231$	2.81360	−	7.56599i	0.185121	−	0.497806i
$232$	−7.51369	−	20.4276i	−0.493298	−	1.34114i
$233$	9.73576	−	4.03268i	0.637811	−	0.264190i	−0.0402568	−	0.999189i	$-0.512818\pi$
$233$	9.73576	−	4.03268i	0.637811	−	0.264190i	0.678068	+	0.734999i	$0.262818\pi$
$234$	−9.18667	+	13.5859i	−0.600552	+	0.888137i
$235$	−2.22391	+	11.1804i	−0.145072	+	0.729327i
$236$	−7.69981	+	20.8299i	−0.501215	+	1.35591i
$237$	22.8252	+	14.0691i	1.48266	+	0.913883i
$238$	2.04150	+	0.161332i	0.132331	+	0.0104576i
$239$	−1.27236	+	1.27236i	−0.0823022	+	0.0823022i	−0.747059	−	0.664757i	$-0.768535\pi$
$239$	−1.27236	+	1.27236i	−0.0823022	+	0.0823022i	0.664757	+	0.747059i	$0.268535\pi$
$240$	6.05795	−	3.36174i	0.391039	−	0.216999i
$241$	2.89073	+	2.89073i	0.186208	+	0.186208i	0.794055	−	0.607847i	$-0.207966\pi$
$241$	2.89073	+	2.89073i	0.186208	+	0.186208i	−0.607847	+	0.794055i	$0.707966\pi$
$242$	−1.77045	−	2.07428i	−0.113809	−	0.133340i
$243$	14.3231	+	6.15208i	0.918829	+	0.394656i
$244$	4.05895	+	3.75691i	0.259848	+	0.240512i
$245$	−5.21774	−	1.03787i	−0.333349	−	0.0663072i
$246$	−0.525209	−	3.37992i	−0.0334861	−	0.215496i
$247$	−11.3621	−	27.4304i	−0.722951	−	1.74536i
$248$	−0.925237	−	5.87851i	−0.0587526	−	0.373286i
$249$	9.29532	−	24.9958i	0.589067	−	1.58405i
$250$	−0.384314	+	1.36099i	−0.0243061	+	0.0860768i
$251$	−1.68335	−	2.51931i	−0.106252	−	0.159018i	0.774533	−	0.632533i	$-0.217985\pi$
$251$	−1.68335	−	2.51931i	−0.106252	−	0.159018i	−0.880785	+	0.473516i	$0.842985\pi$
$252$	5.94308	−	5.01611i	0.374379	−	0.315985i
$253$	−15.5617	+	3.09541i	−0.978354	+	0.194607i
$254$	13.0145	−	25.5221i	0.816604	−	1.60140i
$255$	0.0709436	+	1.93373i	0.00444266	+	0.121095i
$256$	−12.9200	−	9.43792i	−0.807498	−	0.589870i
$257$		−	3.59905i		−	0.224502i	−0.993680	−	0.112251i	$-0.964194\pi$
$257$		−	3.59905i		−	0.224502i	0.993680	−	0.112251i	$-0.0358061\pi$
$258$	−19.1845	−	8.91222i	−1.19437	−	0.554850i
$259$	1.19462	+	6.00578i	0.0742304	+	0.373181i
$260$	−6.25760	+	4.54025i	−0.388080	+	0.281574i
$261$	18.2038	−	14.1979i	1.12679	−	0.878829i
$262$	8.59184	+	2.42614i	0.530806	+	0.149887i
$263$	−11.3711	−	4.71008i	−0.701175	−	0.290436i	0.00347235	−	0.999994i	$-0.498895\pi$
$263$	−11.3711	−	4.71008i	−0.701175	−	0.290436i	−0.704647	+	0.709558i	$0.748895\pi$
$264$	−3.37484	−	17.2885i	−0.207707	−	1.06403i
$265$	0.310627	−	0.128666i	0.0190817	−	0.00790389i
$266$	1.65032	+	13.9821i	0.101187	+	0.857296i
$267$	−0.700270	+	4.34816i	−0.0428558	+	0.266103i
$268$	−21.0396	+	22.7311i	−1.28520	+	1.38852i
$269$	−6.99023	−	4.67072i	−0.426202	−	0.284779i	0.323913	−	0.946087i	$-0.395002\pi$
$269$	−6.99023	−	4.67072i	−0.426202	−	0.284779i	−0.750114	+	0.661308i	$0.770002\pi$
$270$	5.35547	+	5.03179i	0.325924	+	0.306225i
$271$	−15.4182	+	15.4182i	−0.936588	+	0.936588i	−0.998106	−	0.0615180i	$-0.980406\pi$
$271$	−15.4182	+	15.4182i	−0.936588	+	0.936588i	0.0615180	+	0.998106i	$0.480406\pi$
$272$	3.98430	−	2.02364i	0.241584	−	0.122701i
$273$	−5.90741	+	6.35738i	−0.357533	+	0.384766i
$274$	1.92538	−	24.3638i	0.116316	−	1.47187i
$275$	2.98963	+	1.99761i	0.180282	+	0.120460i
$276$	−14.5227	−	4.77085i	−0.874164	−	0.287171i
$277$	−14.8237	−	2.94862i	−0.890672	−	0.177166i	−0.271516	−	0.962434i	$-0.587525\pi$
$277$	−14.8237	−	2.94862i	−0.890672	−	0.177166i	−0.619156	+	0.785268i	$0.712525\pi$
$278$	6.38414	+	5.03619i	0.382895	+	0.302050i
$279$	5.63872	−	2.83625i	0.337582	−	0.169802i
$280$	3.44074	−	1.26558i	0.205623	−	0.0756326i
$281$	9.82990	+	4.07168i	0.586403	+	0.242896i	0.656102	−	0.754672i	$-0.272204\pi$
$281$	9.82990	+	4.07168i	0.586403	+	0.242896i	−0.0696995	+	0.997568i	$0.522204\pi$
$282$	14.5200	+	23.8506i	0.864652	+	1.42028i
$283$	−5.30360	−	7.93740i	−0.315266	−	0.471829i	0.639666	−	0.768653i	$-0.279073\pi$
$283$	−5.30360	−	7.93740i	−0.315266	−	0.471829i	−0.954932	+	0.296824i	$0.904073\pi$
$284$	0.312607	+	1.30581i	0.0185498	+	0.0774855i
$285$	−12.9438	+	3.07198i	−0.766726	+	0.181968i
$286$	6.06812	+	18.6963i	0.358816	+	1.10553i
$287$		−	1.80997i		−	0.106839i
$288$	5.35398	−	16.1039i	0.315486	−	0.948930i
$289$		−	15.7519i		−	0.926582i
$290$	10.3512	−	3.35963i	0.607846	−	0.197285i
$291$	5.16917	−	1.22681i	0.303022	−	0.0719168i
$292$	−1.04214	−	0.639550i	−0.0609868	−	0.0374268i
$293$	−4.45871	−	6.67293i	−0.260481	−	0.389837i	0.678059	−	0.735007i	$-0.262821\pi$
$293$	−4.45871	−	6.67293i	−0.260481	−	0.389837i	−0.938540	+	0.345170i	$0.887821\pi$
$294$	−11.1308	+	6.77629i	−0.649159	+	0.395201i
$295$	−10.2585	−	4.24921i	−0.597273	−	0.247399i
$296$	9.06083	+	9.82099i	0.526650	+	0.570834i
$297$	16.3718	−	9.00169i	0.949987	−	0.522331i
$298$	0.347984	−	0.441123i	0.0201582	−	0.0255535i
$299$	16.7302	+	3.32784i	0.967532	+	0.192454i
$300$	1.56265	+	3.09162i	0.0902196	+	0.178495i
$301$	−9.30709	−	6.21880i	−0.536452	−	0.358446i
$302$	31.4546	+	2.48574i	1.81001	+	0.143038i
$303$	−9.75310	+	10.4960i	−0.560301	+	0.602979i
$304$	18.9892	+	24.1516i	1.08910	+	1.38519i
$305$	−1.95542	+	1.95542i	−0.111967	+	0.111967i
$306$	3.33301	+	3.37002i	0.190536	+	0.192651i
$307$	−16.4135	−	10.9672i	−0.936770	−	0.625929i	−0.00935169	−	0.999956i	$-0.502977\pi$
$307$	−16.4135	−	10.9672i	−0.936770	−	0.625929i	−0.927418	+	0.374027i	$0.877977\pi$
$308$	−0.359935	−	9.31403i	−0.0205092	−	0.530716i
$309$	1.18724	−	7.37190i	0.0675398	−	0.419373i
$310$	2.95493	−	0.348773i	0.167828	−	0.0198089i
$311$	13.1454	−	5.44500i	0.745407	−	0.308758i	0.0225410	−	0.999746i	$-0.492824\pi$
$311$	13.1454	−	5.44500i	0.745407	−	0.308758i	0.722866	+	0.690988i	$0.242824\pi$
$312$	−3.76073	+	18.5603i	−0.212909	+	1.05077i
$313$	18.7559	+	7.76897i	1.06015	+	0.439128i	0.843504	−	0.537123i	$-0.180489\pi$
$313$	18.7559	+	7.76897i	1.06015	+	0.439128i	0.216645	+	0.976251i	$0.430489\pi$
$314$	−1.62744	+	5.76337i	−0.0918420	+	0.325246i
$315$	2.39144	+	3.06617i	0.134742	+	0.172759i
$316$	30.5765	+	4.86306i	1.72006	+	0.273568i
$317$	3.27284	+	16.4537i	0.183821	+	0.924129i	0.957032	+	0.289981i	$0.0936491\pi$
$317$	3.27284	+	16.4537i	0.183821	+	0.924129i	−0.773212	+	0.634148i	$0.781351\pi$
$318$	0.346978	−	0.746907i	0.0194576	−	0.0418845i
$319$		−	27.6693i		−	1.54918i
$320$	4.96490	−	6.27294i	0.277546	−	0.350668i
$321$	1.02080	+	27.8242i	0.0569755	+	1.55300i
$322$	−7.20602	−	3.67458i	−0.401576	−	0.204776i
$323$	−8.41592	+	1.67403i	−0.468274	+	0.0931455i
$324$	17.9989	+	0.198720i	0.999939	+	0.0110400i
$325$	−2.14761	−	3.21413i	−0.119128	−	0.178288i
$326$	−15.6688	−	4.42450i	−0.867812	−	0.245050i
$327$	−0.345612	+	0.929377i	−0.0191124	+	0.0513947i
$328$	−2.06042	−	3.36961i	−0.113768	−	0.186055i
$329$	5.65434	+	13.6508i	0.311734	+	0.752592i
$330$	8.70295	−	1.35236i	0.479081	−	0.0744451i
$331$	3.53128	+	0.702415i	0.194097	+	0.0386082i	0.291181	−	0.956668i	$-0.405952\pi$
$331$	3.53128	+	0.702415i	0.194097	+	0.0386082i	−0.0970846	+	0.995276i	$0.530952\pi$
$332$	−1.18912	−	30.7708i	−0.0652614	−	1.68877i
$333$	−6.98933	+	12.3296i	−0.383013	+	0.675657i
$334$	5.49646	−	4.69136i	0.300753	−	0.256700i
$335$	−10.9509	−	10.9509i	−0.598309	−	0.598309i
$336$	4.10796	−	7.98541i	0.224107	−	0.435640i
$337$	−14.7361	+	14.7361i	−0.802727	+	0.802727i	−0.983521	−	0.180794i	$-0.942133\pi$
$337$	−14.7361	+	14.7361i	−0.802727	+	0.802727i	0.180794	+	0.983521i	$0.442133\pi$
$338$	0.216456	−	2.73905i	0.0117737	−	0.148985i
$339$	−24.5101	−	15.1075i	−1.33120	−	0.820529i
$340$	0.934135	+	2.02974i	0.0506606	+	0.110078i
$341$	1.47585	−	7.41962i	0.0799219	−	0.401795i
$342$	−18.2534	+	26.9943i	−0.987028	+	1.45968i
$343$	−14.7531	+	6.11095i	−0.796595	+	0.329961i
$344$	−24.4062	−	0.982566i	−1.31590	−	0.0529764i
$345$	2.66404	−	7.16382i	0.143427	−	0.385687i
$346$	−24.7900	+	13.8726i	−1.33272	+	0.745793i
$347$	−6.24124	+	4.17026i	−0.335047	+	0.223872i	−0.711701	−	0.702483i	$-0.752075\pi$
$347$	−6.24124	+	4.17026i	−0.335047	+	0.223872i	0.376653	+	0.926354i	$0.377075\pi$
$348$	13.1007	−	23.2160i	0.702271	−	1.24451i
$349$	−0.458337	−	2.30421i	−0.0245342	−	0.123342i	0.966577	−	0.256375i	$-0.0825282\pi$
$349$	−0.458337	−	2.30421i	−0.0245342	−	0.123342i	−0.991112	+	0.133033i	$0.957528\pi$
$350$	0.565883	+	1.74352i	0.0302477	+	0.0931951i
$351$	−19.9648	+	2.20529i	−1.06564	+	0.117710i
$352$	−11.2729	−	16.9301i	−0.600848	−	0.902378i
$353$	−9.10603			−0.484665			−0.242332	−	0.970193i	$-0.577912\pi$
$353$	−9.10603			−0.484665			−0.242332	+	0.970193i	$0.577912\pi$
$354$	−25.5447	+	9.33927i	−1.35769	+	0.496376i
$355$	−0.658453	+	0.130974i	−0.0349471	+	0.00695140i
$356$	1.18400	+	4.94577i	0.0627520	+	0.262125i
$357$	1.46895	+	2.03293i	0.0777453	+	0.107594i
$358$	10.6590	−	5.96480i	0.563344	−	0.315249i
$359$	10.0353	−	24.2274i	0.529644	−	1.27867i	−0.402112	−	0.915591i	$-0.631724\pi$
$359$	10.0353	−	24.2274i	0.529644	−	1.27867i	0.931756	−	0.363084i	$-0.118276\pi$
$360$	7.94256	+	2.98592i	0.418610	+	0.157372i
$361$	−15.3047	−	36.9489i	−0.805512	−	1.94468i
$362$	−1.89590	+	2.40334i	−0.0996463	+	0.126317i
$363$	0.531064	−	3.29752i	0.0278737	−	0.173075i
$364$	−3.47447	+	9.39928i	−0.182111	+	0.492656i
$365$	0.339658	−	0.508334i	0.0177785	−	0.0266074i
$366$	−0.285709	+	6.76776i	−0.0149343	+	0.353756i
$367$	−13.5394	−	13.5394i	−0.706751	−	0.706751i	0.259100	−	0.965851i	$-0.416574\pi$
$367$	−13.5394	−	13.5394i	−0.706751	−	0.706751i	−0.965851	+	0.259100i	$0.916574\pi$
$368$	−17.5984	+	1.36219i	−0.917381	+	0.0710092i
$369$	2.73720	−	3.17132i	0.142493	−	0.165092i
$370$	−5.08178	+	4.33742i	−0.264189	+	0.225491i
$371$	0.242116	−	0.362352i	0.0125700	−	0.0188124i
$372$	4.75133	−	5.52669i	0.246345	−	0.286545i
$373$	3.03848	−	15.2755i	0.157326	−	0.790934i	−0.818859	−	0.573995i	$-0.805393\pi$
$373$	3.03848	−	15.2755i	0.157326	−	0.790934i	0.976185	−	0.216939i	$-0.0696071\pi$
$374$	5.64169	−	0.665893i	0.291725	−	0.0344325i
$375$	−1.57483	+	0.721050i	−0.0813238	+	0.0372348i
$376$	26.0663	+	18.9768i	1.34427	+	0.978655i
$377$	−11.3837	+	27.4826i	−0.586288	+	1.41543i
$378$	9.39515	+	1.56634i	0.483234	+	0.0805639i
$379$	−10.4433	+	6.97800i	−0.536437	+	0.358436i	−0.794088	−	0.607802i	$-0.792051\pi$
$379$	−10.4433	+	6.97800i	−0.536437	+	0.358436i	0.257652	+	0.966238i	$0.417051\pi$
$380$	−12.4335	+	9.02119i	−0.637823	+	0.462777i
$381$	34.1392	−	8.10232i	1.74900	−	0.415094i
$382$	16.2563	+	8.28958i	0.831742	+	0.424132i
$383$	5.63992			0.288186			0.144093	−	0.989564i	$-0.453974\pi$
$383$	5.63992			0.288186			0.144093	+	0.989564i	$0.453974\pi$
$384$	−1.44260	−	19.5427i	−0.0736175	−	0.997287i
$385$	4.66049			0.237521
$386$	−25.3012	−	12.9019i	−1.28780	−	0.656687i
$387$	−6.90270	−	24.9712i	−0.350884	−	1.26936i
$388$	4.96535	−	3.60265i	0.252078	−	0.182897i
$389$	−21.2782	+	14.2176i	−1.07885	+	0.720863i	−0.962209	−	0.272311i	$-0.912212\pi$
$389$	−21.2782	+	14.2176i	−1.07885	+	0.720863i	−0.116639	+	0.993174i	$0.537212\pi$
$390$	−9.20062	−	2.23732i	−0.465892	−	0.113291i
$391$	1.88659	−	4.55462i	0.0954088	−	0.230337i
$392$	−8.85624	+	12.1648i	−0.447308	+	0.614416i
$393$	4.55193	+	9.94177i	0.229614	+	0.501496i
$394$	17.9937	−	2.12381i	0.906508	−	0.106996i
$395$	−3.02008	+	15.1830i	−0.151957	+	0.763938i
$396$	13.4549	−	16.8638i	0.676132	−	0.847438i
$397$	4.71661	−	7.05890i	0.236720	−	0.354276i	−0.694022	−	0.719954i	$-0.744163\pi$
$397$	4.71661	−	7.05890i	0.236720	−	0.354276i	0.930741	+	0.365678i	$0.119163\pi$
$398$	7.57536	−	6.46575i	0.379719	−	0.324099i
$399$	−11.7377	+	12.6317i	−0.587618	+	0.632377i
$400$	3.03827	+	2.60171i	0.151914	+	0.130086i
$401$	−15.5807	−	15.5807i	−0.778062	−	0.778062i	0.201439	−	0.979501i	$-0.435438\pi$
$401$	−15.5807	−	15.5807i	−0.778062	−	0.778062i	−0.979501	+	0.201439i	$0.935438\pi$
$402$	−37.9011	−	1.60004i	−1.89034	−	0.0798029i
$403$	−4.51847	+	6.76237i	−0.225081	+	0.336857i
$404$	−5.73632	+	15.5182i	−0.285393	+	0.772057i
$405$	−0.446804	+	8.98890i	−0.0222019	+	0.446662i
$406$	8.73645	−	11.0748i	0.433583	−	0.549633i
$407$	6.50050	+	15.6936i	0.322218	+	0.777903i
$408$	5.04897	+	2.11248i	0.249961	+	0.104583i
$409$	−5.40284	+	13.0436i	−0.267153	+	0.644965i	−0.999347	−	0.0361316i	$-0.988496\pi$
$409$	−5.40284	+	13.0436i	−0.267153	+	0.644965i	0.732194	+	0.681096i	$0.238496\pi$
$410$	1.72333	−	0.964381i	0.0851091	−	0.0476274i
$411$	24.2616	−	17.5309i	1.19673	−	0.864736i
$412$	−2.00737	−	8.38510i	−0.0988958	−	0.413104i
$413$	−14.1157	+	2.80779i	−0.694589	+	0.138162i
$414$	−7.06892	−	17.3359i	−0.347419	−	0.852015i
$415$	15.3969			0.755804
$416$	4.23149	+	21.4538i	0.207466	+	1.05186i
$417$	0.365123	+	9.95225i	0.0178802	+	0.487364i
$418$	12.0570	+	37.1483i	0.589726	+	1.81698i
$419$	4.93354	+	24.8026i	0.241019	+	1.21169i	0.891804	+	0.452423i	$0.149440\pi$
$419$	4.93354	+	24.8026i	0.241019	+	1.21169i	−0.650784	+	0.759263i	$0.725560\pi$
$420$	3.91041	+	2.20663i	0.190808	+	0.107672i
$421$	1.82362	−	1.21850i	0.0888778	−	0.0593863i	−0.510337	−	0.859974i	$-0.670479\pi$
$421$	1.82362	−	1.21850i	0.0888778	−	0.0593863i	0.599215	+	0.800588i	$0.295479\pi$
$422$	−17.5412	+	9.81612i	−0.853893	+	0.477841i
$423$	−10.7367	+	32.4691i	−0.522038	+	1.57870i
$424$	0.0382541	−	0.950205i	0.00185778	−	0.0461460i
$425$	−1.03215	+	0.427530i	−0.0500665	+	0.0207382i
$426$	−0.970479	+	1.32758i	−0.0470199	+	0.0643213i
$427$	−0.699281	+	3.51552i	−0.0338406	+	0.170128i
$428$	13.4412	+	29.2057i	0.649704	+	1.41171i
$429$	−12.6320	+	20.4937i	−0.609876	+	0.989446i
$430$	0.962146	−	12.1750i	0.0463988	−	0.587133i
$431$	20.3007	−	20.3007i	0.977850	−	0.977850i	−0.0219097	−	0.999760i	$-0.506975\pi$
$431$	20.3007	−	20.3007i	0.977850	−	0.977850i	0.999760	+	0.0219097i	$0.00697462\pi$
$432$	19.2740	−	7.77912i	0.927318	−	0.374273i
$433$	−12.3204	−	12.3204i	−0.592078	−	0.592078i	0.346114	−	0.938192i	$-0.387501\pi$
$433$	−12.3204	−	12.3204i	−0.592078	−	0.592078i	−0.938192	+	0.346114i	$0.887501\pi$
$434$	2.93343	−	2.50375i	0.140809	−	0.120184i
$435$	11.3464	+	6.99372i	0.544019	+	0.335323i
$436$	0.0442130	+	1.14410i	0.00211742	+	0.0547924i
$437$	33.2419	+	6.61222i	1.59017	+	0.316305i
$438$	−0.229945	−	1.47978i	−0.0109872	−	0.0707067i
$439$	−3.13414	−	7.56649i	−0.149584	−	0.361129i	0.831271	−	0.555868i	$-0.187614\pi$
$439$	−3.13414	−	7.56649i	−0.149584	−	0.361129i	−0.980855	+	0.194739i	$0.937614\pi$
$440$	8.67640	−	5.30537i	0.413631	−	0.252924i
$441$	−15.1529	−	5.01070i	−0.721567	−	0.238605i
$442$	−5.87759	−	1.65970i	−0.279568	−	0.0789437i
$443$	3.84105	+	5.74854i	0.182494	+	0.273121i	0.911425	−	0.411465i	$-0.134983\pi$
$443$	3.84105	+	5.74854i	0.182494	+	0.273121i	−0.728932	+	0.684586i	$0.759983\pi$
$444$	−1.97625	+	16.2456i	−0.0937887	+	0.770983i
$445$	−2.49390	+	0.496068i	−0.118222	+	0.0235159i
$446$	18.1780	+	9.26956i	0.860755	+	0.438926i
$447$	0.687667	−	0.0252288i	0.0325255	−	0.00119328i
$448$	0.833562	−	10.3358i	0.0393821	−	0.488319i
$449$		−	19.0736i		−	0.900141i	−0.892993	−	0.450071i	$-0.851399\pi$
$449$		−	19.0736i		−	0.900141i	0.892993	−	0.450071i	$-0.148601\pi$
$450$	−1.64520	+	3.91067i	−0.0775555	+	0.184351i
$451$	−0.979532	−	4.92444i	−0.0461244	−	0.231883i
$452$	−32.8335	−	5.22202i	−1.54436	−	0.245623i
$453$	22.6330	+	31.3226i	1.06339	+	1.47166i
$454$	8.48267	−	30.0402i	0.398111	−	1.40986i
$455$	−4.62905	−	1.91742i	−0.217013	−	0.0898899i
$456$	−7.47234	+	36.8782i	−0.349924	+	1.72698i
$457$	−9.17252	+	3.79938i	−0.429072	+	0.177728i	−0.586759	−	0.809762i	$-0.699596\pi$
$457$	−9.17252	+	3.79938i	−0.429072	+	0.177728i	0.157687	+	0.987489i	$0.449596\pi$
$458$	20.6268	−	2.43460i	0.963826	−	0.113761i
$459$	−0.500568	+	5.78346i	−0.0233645	+	0.269949i
$460$	−0.340802	−	8.81894i	−0.0158900	−	0.411185i
$461$	−27.3745	−	18.2911i	−1.27496	−	0.851900i	−0.280794	−	0.959768i	$-0.590598\pi$
$461$	−27.3745	−	18.2911i	−1.27496	−	0.851900i	−0.994165	+	0.107868i	$0.965598\pi$
$462$	8.40550	−	7.72455i	0.391059	−	0.359379i
$463$	4.58235	−	4.58235i	0.212960	−	0.212960i	−0.592564	−	0.805524i	$-0.701884\pi$
$463$	4.58235	−	4.58235i	0.212960	−	0.212960i	0.805524	+	0.592564i	$0.201884\pi$
$464$	3.65736	−	30.5632i	0.169789	−	1.41886i
$465$	2.66954	+	2.48060i	0.123797	+	0.115035i
$466$	14.8565	+	1.17405i	0.688216	+	0.0543870i
$467$	29.8830	+	19.9672i	1.38282	+	0.923971i	1.00000		0.000148569i	$4.72909e-5\pi$
$467$	29.8830	+	19.9672i	1.38282	+	0.923971i	0.382821	+	0.923823i	$0.374953\pi$
$468$	−20.3022	+	11.2145i	−0.938468	+	0.518388i
$469$	−19.6878	−	3.91615i	−0.909099	−	0.180831i
$470$	−9.98462	+	12.6570i	−0.460556	+	0.583825i
$471$	−6.66890	+	3.05341i	−0.307286	+	0.140694i
$472$	−23.0828	+	21.2961i	−1.06247	+	0.980235i
$473$	−28.6876	−	11.8828i	−1.31906	−	0.546372i
$474$	19.7182	+	32.3891i	0.905685	+	1.48768i
$475$	−4.26717	−	6.38627i	−0.195791	−	0.293022i
$476$	2.46837	+	1.51481i	0.113138	+	0.0694313i
$477$	0.972201	−	0.268742i	0.0445140	−	0.0123048i
$478$	−2.42043	+	0.785582i	−0.110708	+	0.0359317i
$479$		−	18.4346i		−	0.842298i	−0.906991	−	0.421149i	$-0.861627\pi$
$479$		−	18.4346i		−	0.842298i	0.906991	−	0.421149i	$-0.138373\pi$
$480$	9.79194	−	0.343437i	0.446939	−	0.0156757i
$481$		−	18.2622i		−	0.832683i
$482$	1.78479	+	5.49906i	0.0812951	+	0.250475i
$483$	−2.28764	−	9.63901i	−0.104091	−	0.438590i
$484$	−0.897914	−	3.75073i	−0.0408143	−	0.170488i
$485$	1.70411	+	2.55038i	0.0773797	+	0.115807i
$486$	14.0929	+	16.9526i	0.639265	+	0.768987i
$487$	19.2003	+	7.95304i	0.870050	+	0.360387i	0.772630	−	0.634857i	$-0.218941\pi$
$487$	19.2003	+	7.95304i	0.870050	+	0.360387i	0.0974205	+	0.995243i	$0.468941\pi$
$488$	2.70012	+	7.34086i	0.122229	+	0.332305i
$489$	−8.30125	−	18.1306i	−0.375396	−	0.819894i
$490$	−5.90687	−	4.65969i	−0.266845	−	0.210503i
$491$	−5.98858	−	1.19120i	−0.270261	−	0.0537582i	0.0580994	−	0.998311i	$-0.481496\pi$
$491$	−5.98858	−	1.19120i	−0.270261	−	0.0537582i	−0.328360	+	0.944553i	$0.606496\pi$
$492$	1.50972	−	4.59566i	0.0680634	−	0.207188i
$493$	7.14823	+	4.77630i	0.321940	+	0.215114i
$494$	3.30789	−	41.8582i	0.148829	−	1.88329i
$495$	8.16583	+	7.04801i	0.367027	+	0.316784i
$496$	2.61095	−	8.00055i	0.117235	−	0.359235i
$497$	−0.615313	+	0.615313i	−0.0276006	+	0.0276006i
$498$	27.7693	−	25.5197i	1.24437	−	1.14356i
$499$	14.2646	+	9.53131i	0.638572	+	0.426680i	0.832262	−	0.554383i	$-0.187046\pi$
$499$	14.2646	+	9.53131i	0.638572	+	0.426680i	−0.193690	+	0.981063i	$0.562046\pi$
$500$	−1.35855	+	1.46777i	−0.0607561	+	0.0656406i
$501$	8.73783	+	1.40722i	0.390377	+	0.0628701i
$502$	−0.502276	−	4.25546i	−0.0224177	−	0.189930i
$503$	−28.3518	+	11.7437i	−1.26415	+	0.523626i	−0.911179	−	0.412010i	$-0.864827\pi$
$503$	−28.3518	+	11.7437i	−1.26415	+	0.523626i	−0.352966	+	0.935636i	$0.614827\pi$
$504$	10.7101	−	2.50153i	0.477064	−	0.111427i
$505$	−7.64253	−	3.16564i	−0.340088	−	0.140869i
$506$	−21.5943	−	6.09773i	−0.959982	−	0.271077i
$507$	2.72755	−	1.97087i	0.121135	−	0.0875295i
$508$	32.7931	−	23.7933i	1.45496	−	1.05566i
$509$	−6.05885	−	30.4599i	−0.268554	−	1.35011i	−0.845782	−	0.533528i	$-0.820866\pi$
$509$	−6.05885	−	30.4599i	−0.268554	−	1.35011i	0.577228	−	0.816583i	$-0.304134\pi$
$510$	−1.15294	+	2.48182i	−0.0510528	+	0.109897i
$511$		−	0.792434i		−	0.0350552i
$512$	−10.2141	−	20.1909i	−0.451403	−	0.892320i
$513$	−39.6688	+	4.38178i	−1.75142	+	0.193460i
$514$	2.31219	−	4.53432i	0.101986	−	0.200000i
$515$	4.22818	−	0.841037i	0.186316	−	0.0370605i
$516$	−18.4443	−	23.5532i	−0.811964	−	1.03687i
$517$	22.7716	+	34.0801i	1.00149	+	1.49884i
$518$	−2.35332	+	8.33397i	−0.103399	+	0.366173i
$519$	−32.6102	−	12.1269i	−1.43143	−	0.532312i
$520$	−10.8006	+	1.69994i	−0.473638	+	0.0745473i
$521$	−10.4188	−	25.1533i	−0.456457	−	1.10198i	−0.969822	−	0.243814i	$-0.921601\pi$
$521$	−10.4188	−	25.1533i	−0.456457	−	1.10198i	0.513365	−	0.858170i	$-0.328399\pi$
$522$	32.0558	−	6.19253i	1.40304	−	0.271040i
$523$	36.0659	+	7.17394i	1.57705	+	0.313695i	0.904538	−	0.426392i	$-0.140216\pi$
$523$	36.0659	+	7.17394i	1.57705	+	0.313695i	0.672511	+	0.740087i	$0.265216\pi$
$524$	9.26591	+	8.57640i	0.404783	+	0.374662i
$525$	−1.17799	+	1.91114i	−0.0514118	+	0.0834091i
$526$	−11.3002	−	13.2394i	−0.492710	−	0.577266i
$527$	1.66206	+	1.66206i	0.0724006	+	0.0724006i
$528$	6.85505	−	23.9493i	0.298328	−	1.04226i
$529$	2.49433	−	2.49433i	0.108449	−	0.108449i
$530$	0.474009	+	0.0374591i	0.0205897	+	0.00162712i
$531$	−28.9789	−	16.4274i	−1.25758	−	0.712888i
$532$	−6.90355	+	18.6758i	−0.299307	+	0.809698i
$533$	−1.05309	+	5.29422i	−0.0456142	+	0.229318i
$534$	−3.67571	+	5.02822i	−0.159063	+	0.217592i
$535$	−14.8515	+	6.15168i	−0.642085	+	0.265960i
$536$	−41.1107	+	15.1214i	−1.77571	+	0.653143i
$537$	14.0214	+	5.21422i	0.605069	+	0.225010i
$538$	−5.80607	−	10.3753i	−0.250317	−	0.447312i
$539$	−15.9047	+	10.6272i	−0.685065	+	0.457746i
$540$	3.51452	+	9.77999i	0.151241	+	0.420864i
$541$	−2.71208	−	13.6346i	−0.116602	−	0.586195i	−0.994267	−	0.106922i	$-0.965900\pi$
$541$	−2.71208	−	13.6346i	−0.116602	−	0.586195i	0.877666	−	0.479273i	$-0.159100\pi$
$542$	−29.3302	+	9.51951i	−1.25984	+	0.408898i
$543$	−3.74658	+	0.137453i	−0.160781	+	0.00589866i
$544$	6.31977	+	0.0101873i	0.270958	+	0.000436776i
$545$	−0.572477			−0.0245222
$546$	−11.5268	+	4.21426i	−0.493303	+	0.180353i
$547$	−19.5254	+	3.88384i	−0.834846	+	0.166061i	−0.593962	−	0.804493i	$-0.702437\pi$
$547$	−19.5254	+	3.88384i	−0.834846	+	0.166061i	−0.240884	+	0.970554i	$0.577437\pi$
$548$	18.0782	−	29.4582i	0.772261	−	1.25839i
$549$	−6.54172	+	5.10217i	−0.279194	+	0.217755i
$550$	2.48318	+	4.43740i	0.105883	+	0.189211i
$551$	−22.6186	+	54.6062i	−0.963586	+	2.32630i
$552$	−15.2317	−	15.3407i	−0.648302	−	0.652942i
$553$	7.67861	+	18.5378i	0.326528	+	0.788307i
$554$	−16.7816	−	13.2383i	−0.712982	−	0.562442i
$555$	−8.07860	−	1.30105i	−0.342917	−	0.0552267i
$556$	4.80768	+	10.4464i	0.203891	+	0.443025i
$557$	15.8638	−	23.7419i	0.672172	−	1.00598i	−0.325990	−	0.945373i	$-0.605697\pi$
$557$	15.8638	−	23.7419i	0.672172	−	1.00598i	0.998162	−	0.0606034i	$-0.0193025\pi$
$558$	8.92618	+	0.0492740i	0.377875	+	0.00208593i
$559$	23.6053	+	23.6053i	0.998397	+	0.998397i
$560$	5.14793	+	0.616030i	0.217540	+	0.0260320i
$561$	5.09682	+	4.73608i	0.215188	+	0.199957i
$562$	9.76853	+	11.4449i	0.412061	+	0.482776i
$563$	11.2835	−	16.8869i	0.475542	−	0.711699i	−0.513703	−	0.857968i	$-0.671727\pi$
$563$	11.2835	−	16.8869i	0.475542	−	0.711699i	0.989245	+	0.146269i	$0.0467266\pi$
$564$	2.97054	+	39.3768i	0.125082	+	1.65806i
$565$	3.24300	−	16.3037i	0.136434	−	0.685901i
$566$	−1.58248	−	13.4073i	−0.0665166	−	0.563553i
$567$	5.99147	+	10.0093i	0.251618	+	0.420350i
$568$	−0.445069	+	1.84598i	−0.0186747	+	0.0774555i
$569$	14.6124	−	35.2774i	0.612582	−	1.47890i	−0.247572	−	0.968870i	$-0.579633\pi$
$569$	14.6124	−	35.2774i	0.612582	−	1.47890i	0.860154	−	0.510035i	$-0.170367\pi$
$570$	−18.2811	−	4.44542i	−0.765709	−	0.186198i
$571$	−27.9452	+	18.6724i	−1.16947	+	0.781416i	−0.979711	−	0.200414i	$-0.935771\pi$
$571$	−27.9452	+	18.6724i	−1.16947	+	0.781416i	−0.189761	+	0.981830i	$0.560771\pi$
$572$	−4.36631	+	27.4532i	−0.182565	+	1.14788i
$573$	5.16076	+	21.7449i	0.215594	+	0.908407i
$574$	1.16281	−	2.28032i	0.0485347	−	0.0951788i
$575$	4.41276			0.184025
$576$	17.0912	−	16.8491i	0.712132	−	0.702046i
$577$	−19.5699			−0.814705			−0.407352	−	0.913271i	$-0.633548\pi$
$577$	−19.5699			−0.814705			−0.407352	+	0.913271i	$0.633548\pi$
$578$	10.1197	−	19.8453i	0.420925	−	0.825455i
$579$	−8.03218	−	33.8437i	−0.333806	−	1.40650i
$580$	15.1996	+	2.41742i	0.631128	+	0.100378i
$581$	16.5936	−	11.0875i	0.688418	−	0.459986i
$582$	7.30062	+	1.77530i	0.302620	+	0.0735884i
$583$	0.462632	−	1.11689i	0.0191602	−	0.0462569i
$584$	−0.902084	−	1.47527i	−0.0373285	−	0.0610470i
$585$	−5.21105	−	10.3600i	−0.215451	−	0.428335i
$586$	−1.33038	−	11.2715i	−0.0549576	−	0.465621i
$587$	−5.10802	+	25.6797i	−0.210830	+	1.05992i	0.719863	+	0.694116i	$0.244205\pi$
$587$	−5.10802	+	25.6797i	−0.210830	+	1.05992i	−0.930694	+	0.365800i	$0.880795\pi$
$588$	−18.3767	+	1.38631i	−0.757840	+	0.0571706i
$589$	−8.97792	+	13.4364i	−0.369929	+	0.553637i
$590$	−10.1945	−	11.9440i	−0.419699	−	0.491725i
$591$	16.2559	+	15.1053i	0.668677	+	0.621349i
$592$	5.10598	+	18.1942i	0.209855	+	0.747778i
$593$	−6.07330	−	6.07330i	−0.249401	−	0.249401i	0.571324	−	0.820725i	$-0.306430\pi$
$593$	−6.07330	−	6.07330i	−0.249401	−	0.249401i	−0.820725	+	0.571324i	$0.806430\pi$
$594$	26.4094	−	0.822942i	1.08359	−	0.0337657i
$595$	−0.804499	+	1.20402i	−0.0329813	+	0.0493599i
$596$	0.721810	−	0.332195i	0.0295665	−	0.0136072i
$597$	12.0427	+	1.93947i	0.492875	+	0.0793772i
$598$	18.9399	+	14.9409i	0.774508	+	0.610978i
$599$	14.3951	+	34.7529i	0.588169	+	1.41997i	0.885251	+	0.465114i	$0.153987\pi$
$599$	14.3951	+	34.7529i	0.588169	+	1.41997i	−0.297082	+	0.954852i	$0.596013\pi$
$600$	−0.0174699	+	4.89895i	−0.000713207	+	0.199999i
$601$	0.219555	−	0.530053i	0.00895584	−	0.0216213i	−0.919338	−	0.393468i	$-0.871275\pi$
$601$	0.219555	−	0.530053i	0.00895584	−	0.0216213i	0.928294	+	0.371847i	$0.121275\pi$
$602$	−7.73045	−	13.8142i	−0.315070	−	0.563023i
$603$	−28.5734	−	36.6353i	−1.16360	−	1.49190i
$604$	38.0317	+	23.3396i	1.54749	+	0.949674i
$605$	1.89130	−	0.376204i	0.0768924	−	0.0152949i
$606$	−19.0307	+	6.95771i	−0.773070	+	0.282638i
$607$	−41.8404			−1.69825			−0.849125	−	0.528192i	$-0.822870\pi$
$607$	−41.8404			−1.69825			−0.849125	+	0.528192i	$0.822870\pi$
$608$	8.40770	+	42.6274i	0.340977	+	1.72877i
$609$	17.2645	−	0.633392i	0.699594	−	0.0256663i
$610$	−3.71983	+	1.20732i	−0.150611	+	0.0488829i
$611$	−8.59676	−	43.2188i	−0.347788	−	1.74845i
$612$	2.03410	+	6.38705i	0.0822236	+	0.258181i
$613$	23.6404	−	15.7960i	0.954827	−	0.637995i	0.0225524	−	0.999746i	$-0.492821\pi$
$613$	23.6404	−	15.7960i	0.954827	−	0.637995i	0.932275	+	0.361750i	$0.117821\pi$
$614$	−13.6330	−	24.3620i	−0.550185	−	0.983169i
$615$	2.26697	+	0.843028i	0.0914130	+	0.0339942i
$616$	5.53029	−	11.9657i	0.222822	−	0.482111i
$617$	−5.26194	+	2.17957i	−0.211838	+	0.0877461i	−0.486079	−	0.873915i	$-0.661573\pi$
$617$	−5.26194	+	2.17957i	−0.211838	+	0.0877461i	0.274241	+	0.961661i	$0.411573\pi$
$618$	6.23181	−	8.52488i	0.250680	−	0.342921i
$619$	−3.70342	+	18.6184i	−0.148853	+	0.748335i	0.832182	+	0.554503i	$0.187092\pi$
$619$	−3.70342	+	18.6184i	−0.148853	+	0.748335i	−0.981035	+	0.193832i	$0.937908\pi$
$620$	3.94688	+	1.45897i	0.158510	+	0.0585937i
$621$	10.5687	−	20.3485i	0.424107	−	0.816555i
$622$	20.0596	+	1.58523i	0.804315	+	0.0635619i
$623$	−2.33051	+	2.33051i	−0.0933699	+	0.0933699i
$624$	−16.6620	+	20.9674i	−0.667014	+	0.839370i
$625$	−0.707107	−	0.707107i	−0.0282843	−	0.0282843i
$626$	18.6388	+	21.8375i	0.744958	+	0.872804i
$627$	−25.0989	+	40.7198i	−1.00235	+	1.62619i
$628$	−5.75301	+	6.21553i	−0.229570	+	0.248027i
$629$	−5.17650	−	1.02967i	−0.206401	−	0.0410556i
$630$	1.04304	+	5.39934i	0.0415559	+	0.215115i
$631$	−2.32149	−	5.60458i	−0.0924172	−	0.223115i	0.870911	−	0.491441i	$-0.163530\pi$
$631$	−2.32149	−	5.60458i	−0.0924172	−	0.223115i	−0.963328	+	0.268326i	$0.913530\pi$
$632$	35.3981	+	25.7706i	1.40806	+	1.02510i
$633$	−23.0747	−	8.58091i	−0.917138	−	0.341061i
$634$	−6.44725	+	22.8320i	−0.256053	+	0.906776i
$635$	11.2546	+	16.8437i	0.446626	+	0.668423i
$636$	0.916994	−	0.718089i	0.0363612	−	0.0284741i
$637$	20.1697	−	4.01200i	0.799151	−	0.158961i
$638$	17.7760	−	34.8596i	0.703758	−	1.38010i
$639$	−2.00864	+	0.147583i	−0.0794607	+	0.00583829i
$640$	10.2851	−	4.71340i	0.406555	−	0.186313i
$641$			24.4237i			0.964680i	0.875984	+	0.482340i	$0.160213\pi$
$641$			24.4237i			0.964680i	−0.875984	+	0.482340i	$0.839787\pi$
$642$	−16.5895	+	35.7106i	−0.654734	+	1.40938i
$643$	4.30232	+	21.6292i	0.169667	+	0.852974i	0.968037	+	0.250807i	$0.0806959\pi$
$643$	4.30232	+	21.6292i	0.169667	+	0.852974i	−0.798370	+	0.602167i	$0.794304\pi$
$644$	−6.71790	−	9.25895i	−0.264723	−	0.364854i
$645$	12.1239	−	8.76050i	0.477379	−	0.344944i
$646$	−11.6784	−	3.29772i	−0.459481	−	0.129747i
$647$	−30.4530	−	12.6140i	−1.19723	−	0.495909i	−0.307128	−	0.951668i	$-0.599368\pi$
$647$	−30.4530	−	12.6140i	−1.19723	−	0.495909i	−0.890103	+	0.455759i	$0.849368\pi$
$648$	22.5485	+	11.8137i	0.885791	+	0.464085i
$649$	−36.8855	+	15.2785i	−1.44788	+	0.599732i
$650$	−0.640801	−	5.42909i	−0.0251343	−	0.212947i
$651$	4.66333	+	0.751028i	0.182770	+	0.0294351i
$652$	−16.8980	−	15.6406i	−0.661778	−	0.612533i
$653$	−14.4081	−	9.62719i	−0.563833	−	0.376741i	0.240745	−	0.970588i	$-0.422608\pi$
$653$	−14.4081	−	9.62719i	−0.563833	−	0.376741i	−0.804578	+	0.593847i	$0.797608\pi$
$654$	−1.03250	+	0.948854i	−0.0403739	+	0.0371031i
$655$	−4.46391	+	4.46391i	−0.174419	+	0.174419i
$656$	−0.431061	−	5.56896i	−0.0168301	−	0.217431i
$657$	1.19839	−	1.38845i	0.0467536	−	0.0541688i
$658$	−1.64618	+	20.8308i	−0.0641746	+	0.812068i
$659$	−10.3756	−	6.93278i	−0.404178	−	0.270063i	0.336822	−	0.941568i	$-0.390648\pi$
$659$	−10.3756	−	6.93278i	−0.404178	−	0.270063i	−0.741000	+	0.671506i	$0.765648\pi$
$660$	11.8334	+	3.88737i	0.460613	+	0.151316i
$661$	−29.5506	−	5.87797i	−1.14938	−	0.228627i	−0.416601	−	0.909089i	$-0.636779\pi$
$661$	−29.5506	−	5.87797i	−1.14938	−	0.228627i	−0.732783	+	0.680463i	$0.761779\pi$
$662$	3.99768	+	3.15360i	0.155374	+	0.122568i
$663$	−3.11393	−	6.80106i	−0.120935	−	0.264131i
$664$	18.2705	−	39.5311i	0.709032	−	1.53410i
$665$	−9.19764	−	3.80979i	−0.356669	−	0.147737i
$666$	−16.7267	+	11.0434i	−0.648147	+	0.427922i
$667$	−18.8658	−	28.2347i	−0.730487	−	1.09325i
$668$	9.93876	−	2.37931i	0.384542	−	0.0920582i
$669$	5.77085	+	24.3155i	0.223114	+	0.940093i
$670$	−6.76129	−	20.8320i	−0.261211	−	0.804809i
$671$			9.94323i			0.383854i
$672$	10.3057	−	7.42141i	0.397550	−	0.286287i
$673$		−	3.00549i		−	0.115853i	−0.998321	−	0.0579267i	$-0.981551\pi$
$673$		−	3.00549i		−	0.115853i	0.998321	−	0.0579267i	$-0.0184490\pi$
$674$	−28.0327	+	9.09838i	−1.07978	+	0.350457i
$675$	−4.95420	+	1.56712i	−0.190687	+	0.0603185i
$676$	2.03240	−	3.31177i	0.0781691	−	0.127376i
$677$	−10.5539	−	15.7950i	−0.405618	−	0.607051i	0.571280	−	0.820755i	$-0.306447\pi$
$677$	−10.5539	−	15.7950i	−0.405618	−	0.607051i	−0.976898	+	0.213705i	$0.931447\pi$
$678$	−21.1736	−	34.7799i	−0.813168	−	1.33571i
$679$	3.67312	+	1.52145i	0.140961	+	0.0583881i
$680$	−0.127110	+	3.15733i	−0.00487446	+	0.121078i
$681$	34.7600	−	15.9152i	1.33201	−	0.609872i
$682$	6.62608	−	8.39957i	0.253726	−	0.321636i
$683$	−28.5316	−	5.67530i	−1.09173	−	0.217159i	−0.383784	−	0.923423i	$-0.625379\pi$
$683$	−28.5316	−	5.67530i	−1.09173	−	0.217159i	−0.707949	+	0.706264i	$0.750379\pi$
$684$	−40.3392	+	22.2824i	−1.54241	+	0.851990i
$685$	14.3691	+	9.60111i	0.549014	+	0.366840i
$686$	−22.5130	−	1.77911i	−0.859549	−	0.0679268i
$687$	18.6347	+	17.3157i	0.710957	+	0.660637i
$688$	−30.1173	−	16.9176i	−1.14821	−	0.644977i
$689$	−0.919021	+	0.919021i	−0.0350119	+	0.0350119i
$690$	7.95871	−	7.31395i	0.302983	−	0.278437i
$691$	29.5729	+	19.7600i	1.12501	+	0.751705i	0.971640	−	0.236464i	$-0.0759885\pi$
$691$	29.5729	+	19.7600i	1.12501	+	0.751705i	0.153366	+	0.988169i	$0.450989\pi$
$692$	−40.1444	+	1.55135i	−1.52606	+	0.0589737i
$693$	13.8758	+	1.71549i	0.527099	+	0.0651662i
$694$	−10.5423	+	1.24432i	−0.400180	+	0.0472336i
$695$	−5.31212	+	2.20035i	−0.201500	+	0.0834642i
$696$	31.4202	−	20.8326i	1.19098	−	0.789658i
$697$	1.44130	+	0.597004i	0.0545930	+	0.0226132i
$698$	0.902890	−	3.19746i	0.0341749	−	0.121026i
$699$	10.6900	+	14.7942i	0.404332	+	0.559567i
$700$	−0.407180	+	2.56015i	−0.0153900	+	0.0967646i
$701$	−0.650303	−	3.26929i	−0.0245616	−	0.123480i	0.966559	−	0.256443i	$-0.0825506\pi$
$701$	−0.650303	−	3.26929i	−0.0245616	−	0.123480i	−0.991121	+	0.132964i	$0.957551\pi$
$702$	−26.5698	−	10.0479i	−1.00281	−	0.379234i
$703$		−	36.2858i		−	1.36854i
$704$	−3.32568	−	28.5719i	−0.125341	−	1.07684i
$705$	−19.7311	+	0.723884i	−0.743115	+	0.0272630i
$706$	−11.4724	−	5.85013i	−0.431769	−	0.220172i
$707$	−10.5161	+	2.09179i	−0.395500	+	0.0786698i
$708$	−38.1829	−	4.64488i	−1.43500	−	0.174565i
$709$	23.7706	+	35.5752i	0.892722	+	1.33605i	0.941419	+	0.337240i	$0.109493\pi$
$709$	23.7706	+	35.5752i	0.892722	+	1.33605i	−0.0486963	+	0.998814i	$0.515507\pi$
$710$	−0.913707	−	0.258010i	−0.0342908	−	0.00968294i
$711$	−14.5805	+	44.0931i	−0.546812	+	1.65362i
$712$	−1.68571	+	6.99167i	−0.0631745	+	0.262024i
$713$	−3.55293	−	8.57752i	−0.133058	−	0.321231i
$714$	0.544638	+	3.50495i	0.0203826	+	0.131169i
$715$	−13.6321	−	2.71159i	−0.509811	−	0.101408i
$716$	17.2609	−	0.667038i	0.645072	−	0.0249284i
$717$	−2.65313	−	1.63534i	−0.0990828	−	0.0610728i
$718$	28.2080	−	24.0762i	1.05271	−	0.898515i
$719$	21.5809	+	21.5809i	0.804831	+	0.804831i	0.983846	−	0.179015i	$-0.0572911\pi$
$719$	21.5809	+	21.5809i	0.804831	+	0.804831i	−0.179015	+	0.983846i	$0.557291\pi$
$720$	8.08827	+	8.86453i	0.301432	+	0.330361i
$721$	3.95116	−	3.95116i	0.147149	−	0.147149i
$722$	4.45574	−	56.3831i	0.165825	−	2.09836i
$723$	−3.71539	+	6.02774i	−0.138177	+	0.224174i
$724$	−3.93260	+	1.80988i	−0.146154	+	0.0672636i
$725$	−1.50128	+	7.54744i	−0.0557561	+	0.280305i
$726$	2.78755	−	3.81326i	0.103456	−	0.141523i
$727$	15.2151	−	6.30231i	0.564298	−	0.233740i	−0.0822520	−	0.996612i	$-0.526211\pi$
$727$	15.2151	−	6.30231i	0.564298	−	0.233740i	0.646550	+	0.762872i	$0.276211\pi$
$728$	−10.4159	+	9.60969i	−0.386039	+	0.356159i
$729$	−4.63903	+	26.5985i	−0.171816	+	0.985129i
$730$	0.754501	−	0.422221i	0.0279253	−	0.0156271i
$731$	8.02196	−	5.36010i	0.296703	−	0.198250i
$732$	−4.70787	+	8.34292i	−0.174008	+	0.308363i
$733$	3.16166	+	15.8948i	0.116779	+	0.587086i	0.994216	+	0.107396i	$0.0342511\pi$
$733$	3.16166	+	15.8948i	0.116779	+	0.587086i	−0.877438	+	0.479691i	$0.840749\pi$
$734$	−8.35951	−	25.7562i	−0.308555	−	0.950678i
$735$	−0.337827	−	9.20824i	−0.0124609	−	0.339651i
$736$	−23.0468	−	9.58984i	−0.849516	−	0.353486i
$737$	−55.6846			−2.05117
$738$	5.48590	−	2.23694i	0.201939	−	0.0823428i
$739$	31.0064	−	6.16756i	1.14059	−	0.226877i	0.411575	−	0.911376i	$-0.364979\pi$
$739$	31.0064	−	6.16756i	1.14059	−	0.226877i	0.729014	+	0.684499i	$0.239979\pi$
$740$	−9.18891	+	2.19980i	−0.337791	+	0.0808662i
$741$	41.6825	−	30.1189i	1.53124	−	1.10645i
$742$	0.537825	−	0.300969i	0.0197442	−	0.0110489i
$743$	−6.07280	+	14.6610i	−0.222790	+	0.537861i	−0.995267	−	0.0971810i	$-0.969017\pi$
$743$	−6.07280	+	14.6610i	−0.222790	+	0.537861i	0.772477	+	0.635042i	$0.219017\pi$
$744$	9.53663	−	3.91042i	0.349630	−	0.143363i
$745$	0.152037	+	0.367050i	0.00557021	+	0.0134477i
$746$	13.6417	−	17.2930i	0.499459	−	0.633141i
$747$	45.8417	+	5.66748i	1.67726	+	0.207362i
$748$	7.53557	+	2.78554i	0.275528	+	0.101849i
$749$	−11.5759	+	17.3245i	−0.422973	+	0.633023i
$750$	−2.44731	−	0.103316i	−0.0893631	−	0.00377257i
$751$	30.9271	+	30.9271i	1.12855	+	1.12855i	0.990414	+	0.138133i	$0.0441102\pi$
$751$	30.9271	+	30.9271i	1.12855	+	1.12855i	0.138133	+	0.990414i	$0.455890\pi$
$752$	20.6485	+	40.6545i	0.752973	+	1.48252i
$753$	3.57237	−	3.84448i	0.130184	−	0.140100i
$754$	−31.9980	+	27.3110i	−1.16530	+	0.994608i
$755$	−12.3954	+	18.5510i	−0.451114	+	0.675140i
$756$	10.8303	+	8.00926i	0.393896	+	0.291294i
$757$	−5.17358	+	26.0094i	−0.188037	+	0.945326i	0.765359	+	0.643604i	$0.222562\pi$
$757$	−5.17358	+	26.0094i	−0.188037	+	0.945326i	−0.953396	+	0.301722i	$0.902438\pi$
$758$	−17.6402	+	2.08208i	−0.640719	+	0.0756247i
$759$	−11.4406	−	24.9871i	−0.415266	−	0.906974i
$760$	−21.4601	+	3.37768i	−0.778440	+	0.122521i
$761$	18.8972	−	45.6219i	0.685023	−	1.65379i	−0.0695527	−	0.997578i	$-0.522157\pi$
$761$	18.8972	−	45.6219i	0.685023	−	1.65379i	0.754576	−	0.656213i	$-0.227843\pi$
$762$	48.2161	+	11.7247i	1.74669	+	0.424743i
$763$	−0.616971	+	0.412247i	−0.0223358	+	0.0149243i
$764$	15.1551	+	20.8875i	0.548293	+	0.755684i
$765$	−3.23042	+	0.892972i	−0.116796	+	0.0322855i
$766$	7.10554	+	3.62334i	0.256734	+	0.130917i
$767$	42.9225			1.54984
$768$	10.7377	−	25.5480i	0.387462	−	0.921886i
$769$	22.4653			0.810119			0.405060	−	0.914290i	$-0.367251\pi$
$769$	22.4653			0.810119			0.405060	+	0.914290i	$0.367251\pi$
$770$	5.87160	+	2.99411i	0.211598	+	0.107900i
$771$	6.06525	−	1.43948i	0.218435	−	0.0518415i
$772$	−23.5873	−	32.5092i	−0.848927	−	1.17003i
$773$	3.57840	−	2.39101i	0.128706	−	0.0859988i	−0.489551	−	0.871975i	$-0.662839\pi$
$773$	3.57840	−	2.39101i	0.128706	−	0.0859988i	0.618257	+	0.785976i	$0.287839\pi$
$774$	7.34617	−	35.8950i	0.264053	−	1.29022i
$775$	−0.805148	+	1.94380i	−0.0289218	+	0.0698233i
$776$	8.57019	−	1.34889i	0.307652	−	0.0484223i
$777$	−9.64338	+	4.41531i	−0.345954	+	0.158398i
$778$	−35.9418	+	4.24224i	−1.28857	+	0.152092i
$779$	−2.09242	+	10.5193i	−0.0749686	+	0.376892i
$780$	−10.1542	−	8.72962i	−0.363579	−	0.312571i
$781$	−1.34110	+	2.00710i	−0.0479884	+	0.0718197i
$782$	5.30295	−	4.52619i	0.189633	−	0.161856i
$783$	31.2077	+	24.9991i	1.11527	+	0.893397i
$784$	−18.9729	+	9.63638i	−0.677604	+	0.344156i
$785$	−2.99437	−	2.99437i	−0.106874	−	0.106874i
$786$	−0.652226	+	15.4497i	−0.0232641	+	0.551071i
$787$	−3.12702	+	4.67991i	−0.111466	+	0.166821i	−0.883008	−	0.469357i	$-0.844486\pi$
$787$	−3.12702	+	4.67991i	−0.111466	+	0.166821i	0.771542	+	0.636178i	$0.219486\pi$
$788$	24.0340	+	8.88424i	0.856178	+	0.316488i
$789$	3.38960	−	21.0469i	0.120673	−	0.749291i
$790$	−13.5591	+	17.1883i	−0.482412	+	0.611531i
$791$	−8.24539	−	19.9061i	−0.293172	−	0.707781i
$792$	27.7854	−	12.6021i	0.987311	−	0.447797i
$793$	4.09084	−	9.87615i	0.145270	−	0.350712i
$794$	10.4773	−	5.86311i	0.371824	−	0.208074i
$795$	0.341072	+	0.472020i	0.0120966	+	0.0167408i
$796$	13.6978	−	3.27922i	0.485507	−	0.116229i
$797$	24.3071	−	4.83499i	0.861002	−	0.171264i	0.255209	−	0.966886i	$-0.417856\pi$
$797$	24.3071	−	4.83499i	0.861002	−	0.171264i	0.605793	+	0.795622i	$0.292856\pi$
$798$	−22.9031	+	8.37346i	−0.810760	+	0.296417i
$799$	−12.7353			−0.450542
$800$	2.15636	+	5.22973i	0.0762387	+	0.184899i
$801$	−7.60778	+	0.558973i	−0.268808	+	0.0197503i
$802$	−9.61983	−	29.6393i	−0.339688	−	1.04660i
$803$	−0.428855	−	2.15600i	−0.0151340	−	0.0760835i
$804$	−46.7224	−	26.3653i	−1.64777	−	0.929831i
$805$	4.75573	−	3.17768i	0.167617	−	0.111998i
$806$	−10.0371	+	5.61681i	−0.353543	+	0.197844i
$807$	5.07546	−	13.6483i	0.178665	−	0.480443i
$808$	−17.1966	+	15.8655i	−0.604973	+	0.558147i
$809$	16.6911	−	6.91369i	0.586828	−	0.243072i	−0.0694571	−	0.997585i	$-0.522127\pi$
$809$	16.6911	−	6.91369i	0.586828	−	0.243072i	0.656285	+	0.754513i	$0.272127\pi$
$810$	−6.33780	+	11.0378i	−0.222687	+	0.387828i
$811$	−2.99171	+	15.0403i	−0.105053	+	0.528137i	0.892041	+	0.451955i	$0.149273\pi$
$811$	−2.99171	+	15.0403i	−0.105053	+	0.528137i	−0.997094	+	0.0761826i	$0.975727\pi$
$812$	18.1217	−	8.34006i	0.635947	−	0.292679i
$813$	−32.1500	−	19.8167i	−1.12755	−	0.695001i
$814$	−1.89252	+	23.9481i	−0.0663329	+	0.839379i
$815$	8.14073	−	8.14073i	0.285157	−	0.285157i
$816$	5.00388	+	5.90513i	0.175171	+	0.206721i
$817$	46.9022	+	46.9022i	1.64090	+	1.64090i
$818$	−15.1867	+	12.9622i	−0.530989	+	0.453212i
$819$	−13.0764	−	7.41270i	−0.456928	−	0.259021i
$820$	2.79073	−	0.107846i	0.0974564	−	0.00376614i
$821$	−9.46848	−	1.88340i	−0.330452	−	0.0657310i	0.0270760	−	0.999633i	$-0.491380\pi$
$821$	−9.46848	−	1.88340i	−0.330452	−	0.0657310i	−0.357528	+	0.933902i	$0.616380\pi$
$822$	41.8290	−	6.49986i	1.45895	−	0.226709i
$823$	−16.5902	−	40.0522i	−0.578297	−	1.39613i	−0.894340	−	0.447388i	$-0.852354\pi$
$823$	−16.5902	−	40.0522i	−0.578297	−	1.39613i	0.316043	−	0.948745i	$-0.397646\pi$
$824$	2.85796	−	11.8537i	0.0995616	−	0.412944i
$825$	−2.17071	+	5.83721i	−0.0755745	+	0.203226i
$826$	−19.5878	−	5.53114i	−0.681545	−	0.192453i
$827$	7.58598	+	11.3532i	0.263790	+	0.394790i	0.939594	−	0.342292i	$-0.111203\pi$
$827$	7.58598	+	11.3532i	0.263790	+	0.394790i	−0.675803	+	0.737082i	$0.736203\pi$
$828$	2.23150	−	26.3824i	0.0775502	−	0.916851i
$829$	−9.31345	+	1.85256i	−0.323470	+	0.0643421i	−0.354154	−	0.935187i	$-0.615231\pi$
$829$	−9.31345	+	1.85256i	−0.323470	+	0.0643421i	0.0306847	+	0.999529i	$0.490231\pi$
$830$	19.3980	+	9.89168i	0.673316	+	0.343345i
$831$	−0.959777	−	26.1609i	−0.0332943	−	0.907511i
$832$	−8.45179	+	29.7474i	−0.293013	+	1.03131i
$833$		−	5.94340i		−	0.205926i
$834$	−5.93377	+	12.7731i	−0.205470	+	0.442296i
$835$	0.996871	+	5.01161i	0.0344982	+	0.173434i
$836$	−8.67560	+	54.5479i	−0.300052	+	1.88658i
$837$	7.03503	+	8.36821i	0.243166	+	0.289248i
$838$	−9.71871	+	34.4175i	−0.335727	+	1.18893i
$839$	40.7010	+	16.8589i	1.40515	+	0.582034i	0.951084	−	0.308933i	$-0.0999718\pi$
$839$	40.7010	+	16.8589i	1.40515	+	0.582034i	0.454069	+	0.890966i	$0.349972\pi$
$840$	3.50896	+	5.29228i	0.121070	+	0.182601i
$841$	27.9175	−	11.5638i	0.962673	−	0.398752i
$842$	3.08034	−	0.363576i	0.106156	−	0.0125296i
$843$	−2.93018	+	18.1942i	−0.100921	+	0.626643i
$844$	−28.4059	+	1.09773i	−0.977772	+	0.0377853i
$845$	1.61541	+	1.07938i	0.0555718	+	0.0371319i
$846$	−34.3865	+	34.0089i	−1.18223	+	1.16925i
$847$	1.76739	−	1.76739i	0.0607283	−	0.0607283i
$848$	0.658650	−	1.17256i	0.0226181	−	0.0402657i
$849$	11.2552	−	12.1125i	0.386277	−	0.415699i
$850$	−1.57503	−	0.124469i	−0.0540232	−	0.00426924i
$851$	17.3338	+	11.5820i	0.594193	+	0.397027i
$852$	−2.07557	+	1.04909i	−0.0711078	+	0.0359412i
$853$	−12.6737	−	2.52095i	−0.433939	−	0.0863158i	−0.0267128	−	0.999643i	$-0.508504\pi$
$853$	−12.6737	−	2.52095i	−0.433939	−	0.0863158i	−0.407226	+	0.913327i	$0.633504\pi$
$854$	−3.13953	+	3.97984i	−0.107433	+	0.136187i
$855$	−10.3540	−	20.5848i	−0.354101	−	0.703984i
$856$	−1.82898	+	45.4305i	−0.0625132	+	1.55278i
$857$	−42.2689	−	17.5084i	−1.44388	−	0.598074i	−0.483143	−	0.875541i	$-0.660505\pi$
$857$	−42.2689	−	17.5084i	−1.44388	−	0.598074i	−0.960735	+	0.277467i	$0.910505\pi$
$858$	−29.0807	+	17.7040i	−0.992798	+	0.604405i
$859$	−11.0229	−	16.4969i	−0.376097	−	0.562868i	0.594343	−	0.804211i	$-0.297412\pi$
$859$	−11.0229	−	16.4969i	−0.376097	−	0.562868i	−0.970440	+	0.241343i	$0.922412\pi$
$860$	9.03398	−	14.7208i	0.308056	−	0.501975i
$861$	3.05023	−	0.723917i	0.103952	−	0.0246710i
$862$	38.6183	−	12.5341i	1.31534	−	0.426912i
$863$		−	25.0975i		−	0.854327i	−0.904174	−	0.427164i	$-0.859513\pi$
$863$		−	25.0975i		−	0.854327i	0.904174	−	0.427164i	$-0.140487\pi$
$864$	29.2803	+	2.58181i	0.996135	+	0.0878350i
$865$		−	20.0872i		−	0.682985i
$866$	−7.60684	−	23.4372i	−0.258491	−	0.796427i
$867$	26.5457	−	6.30014i	0.901539	−	0.213964i
$868$	5.30426	−	1.26982i	0.180038	−	0.0431006i
$869$	30.9238	+	46.2808i	1.04902	+	1.56997i
$870$	9.80188	+	16.1006i	0.332315	+	0.545862i
$871$	55.3089	+	22.9097i	1.87407	+	0.776266i
$872$	−0.679320	+	1.46982i	−0.0230047	+	0.0497743i
$873$	4.13493	+	8.22061i	0.139946	+	0.278225i
$874$	37.6323	+	29.6866i	1.27293	+	1.00416i
$875$	−1.27126	−	0.252869i	−0.0429764	−	0.00854854i
$876$	0.660979	−	2.01205i	0.0223324	−	0.0679810i
$877$	−25.4038	−	16.9743i	−0.857825	−	0.573180i	0.0470335	−	0.998893i	$-0.485023\pi$
$877$	−25.4038	−	16.9743i	−0.857825	−	0.573180i	−0.904858	+	0.425713i	$0.860023\pi$
$878$	0.912458	−	11.5463i	0.0307940	−	0.389668i
$879$	9.46218	−	10.1829i	0.319151	−	0.343461i
$880$	14.3395	−	1.10994i	0.483385	−	0.0374161i
$881$	23.7159	−	23.7159i	0.799009	−	0.799009i	−0.183931	−	0.982939i	$-0.558882\pi$
$881$	23.7159	−	23.7159i	0.799009	−	0.799009i	0.982939	+	0.183931i	$0.0588822\pi$
$882$	−15.8715	−	16.0477i	−0.534422	−	0.540355i
$883$	13.9215	+	9.30206i	0.468496	+	0.313039i	0.767315	−	0.641271i	$-0.221593\pi$
$883$	13.9215	+	9.30206i	0.468496	+	0.313039i	−0.298818	+	0.954310i	$0.596593\pi$
$884$	−6.33871	−	5.86703i	−0.213194	−	0.197330i
$885$	3.05794	−	18.9875i	0.102791	−	0.638259i
$886$	1.14609	+	9.71005i	0.0385035	+	0.326216i
$887$	−20.5521	+	8.51294i	−0.690071	+	0.285837i	−0.700030	−	0.714114i	$-0.746830\pi$
$887$	−20.5521	+	8.51294i	−0.690071	+	0.285837i	0.00995903	+	0.999950i	$0.496830\pi$
$888$	−12.9267	+	19.1977i	−0.433793	+	0.644232i
$889$	24.2587	+	10.0483i	0.813610	+	0.337008i
$890$	−3.46068	−	0.977218i	−0.116002	−	0.0327564i
$891$	21.7181	+	23.9900i	0.727583	+	0.803697i
$892$	16.9467	+	23.3568i	0.567418	+	0.782044i
$893$	−17.0812	−	85.8731i	−0.571601	−	2.87363i
$894$	0.882577	+	0.410004i	0.0295178	+	0.0137126i
$895$			8.63691i			0.288700i
$896$	7.69034	−	12.4862i	0.256916	−	0.417133i
$897$	1.08321	+	29.5254i	0.0361674	+	0.985824i
$898$	12.2538	−	24.0302i	0.408914	−	0.801900i
$899$	15.8795	−	3.15862i	0.529609	−	0.105346i
$900$	−4.58512	+	3.86997i	−0.152837	+	0.128999i
$901$	0.208684	+	0.312318i	0.00695228	+	0.0104048i
$902$	1.92961	−	6.83343i	0.0642489	−	0.227528i
$903$	6.75769	−	18.1720i	0.224882	−	0.604725i
$904$	−38.0109	−	27.6728i	−1.26423	−	0.920383i
$905$	−0.828335	−	1.99978i	−0.0275348	−	0.0664748i
$906$	8.39155	+	54.0027i	0.278791	+	1.79412i
$907$	55.4221	+	11.0241i	1.84026	+	0.366051i	0.987673	−	0.156534i	$-0.0500320\pi$
$907$	55.4221	+	11.0241i	1.84026	+	0.366051i	0.852588	+	0.522584i	$0.175032\pi$
$908$	29.9862	−	32.3970i	0.995128	−	1.07513i
$909$	−21.5891	−	12.2383i	−0.716066	−	0.405920i
$910$	−4.60015	−	5.38960i	−0.152494	−	0.178664i
$911$	−22.8657	−	22.8657i	−0.757575	−	0.757575i	0.218305	−	0.975881i	$-0.429947\pi$
$911$	−22.8657	−	22.8657i	−0.757575	−	0.757575i	−0.975881	+	0.218305i	$0.929947\pi$
$912$	−33.1064	+	41.6610i	−1.09626	+	1.37953i
$913$	39.1462	−	39.1462i	1.29555	−	1.29555i
$914$	−13.9970	−	1.10613i	−0.462981	−	0.0365876i
$915$	−4.07745	−	2.51326i	−0.134796	−	0.0830859i
$916$	27.5511	+	10.1843i	0.910313	+	0.336499i
$917$	−1.59634	+	8.02535i	−0.0527159	+	0.265021i
$918$	−4.34621	+	6.96480i	−0.143446	+	0.229873i
$919$	−34.9020	+	14.4569i	−1.15131	+	0.476889i	−0.874973	−	0.484172i	$-0.839121\pi$
$919$	−34.9020	+	14.4569i	−1.15131	+	0.476889i	−0.276338	+	0.961061i	$0.589121\pi$
$920$	5.23633	−	11.3296i	0.172637	−	0.373527i
$921$	11.9175	−	32.0472i	0.392696	−	1.05599i
$922$	−22.7372	−	40.6310i	−0.748811	−	1.33811i
$923$	2.15781	−	1.44180i	0.0710253	−	0.0474576i
$924$	15.5524	−	4.33183i	0.511637	−	0.142507i
$925$	−0.921661	−	4.63350i	−0.0303040	−	0.152349i
$926$	8.71705	−	2.82924i	0.286460	−	0.0929745i
$927$	12.8983	−	0.947686i	0.423635	−	0.0311261i
$928$	24.2430	−	36.1558i	0.795814	−	1.18687i
$929$	40.2469			1.32046			0.660229	−	0.751065i	$-0.270459\pi$
$929$	40.2469			1.32046			0.660229	+	0.751065i	$0.270459\pi$
$930$	1.76962	+	4.84026i	0.0580281	+	0.158718i
$931$	40.0759	−	7.97159i	1.31343	−	0.261258i
$932$	17.9630	+	11.0237i	0.588397	+	0.361092i
$933$	14.4338	+	19.9754i	0.472541	+	0.653964i
$934$	24.8208	+	44.3542i	0.812160	+	1.45131i
$935$	−1.53723	+	3.71119i	−0.0502727	+	0.121369i
$936$	−32.7827	+	1.08567i	−1.07154	+	0.0354862i
$937$	−14.9019	−	35.9763i	−0.486823	−	1.17529i	−0.956310	−	0.292355i	$-0.905561\pi$
$937$	−14.9019	−	35.9763i	−0.486823	−	1.17529i	0.469487	−	0.882940i	$-0.344439\pi$
$938$	−22.2881	−	17.5822i	−0.727732	−	0.574078i
$939$	−5.59092	+	34.7155i	−0.182453	+	1.13290i
$940$	−20.7107	+	9.53159i	−0.675510	+	0.310886i
$941$	−6.80861	+	10.1898i	−0.221954	+	0.332178i	−0.925689	−	0.378284i	$-0.876514\pi$
$941$	−6.80861	+	10.1898i	−0.221954	+	0.332178i	0.703735	+	0.710462i	$0.251514\pi$
$942$	−10.3636	−	0.437511i	−0.337663	−	0.0142549i
$943$	−4.35719	−	4.35719i	−0.141890	−	0.141890i
$944$	−42.7629	+	12.0009i	−1.39181	+	0.390595i
$945$	−4.21075	+	5.25649i	−0.136976	+	0.170994i
$946$	−28.5085	−	33.4010i	−0.926892	−	1.08596i
$947$	29.8223	−	44.6322i	0.969095	−	1.45035i	0.0777790	−	0.996971i	$-0.475217\pi$
$947$	29.8223	−	44.6322i	0.969095	−	1.45035i	0.891316	−	0.453383i	$-0.149783\pi$
$948$	4.03400	+	53.4738i	0.131018	+	1.73675i
$949$	−0.461058	+	2.31789i	−0.0149666	+	0.0752420i
$950$	−1.27323	−	10.7873i	−0.0413091	−	0.349985i
$951$	−26.4193	+	12.0963i	−0.856706	+	0.392250i
$952$	2.13664	+	3.49426i	0.0692488	+	0.113249i
$953$	0.400336	−	0.966498i	0.0129682	−	0.0313079i	−0.917263	−	0.398282i	$-0.869606\pi$
$953$	0.400336	−	0.966498i	0.0129682	−	0.0313079i	0.930231	+	0.366975i	$0.119606\pi$
$954$	1.39750	+	0.286008i	0.0452456	+	0.00925984i
$955$	−10.7286	+	7.16861i	−0.347169	+	0.231971i
$956$	−3.55411	−	0.565265i	−0.114948	−	0.0182820i
$957$	46.6293	−	11.0666i	1.50731	−	0.357733i
$958$	11.8432	−	23.2251i	0.382637	−	0.750370i
$959$	22.3997			0.723325
$960$	12.5572	+	5.85810i	0.405281	+	0.189069i
$961$	−26.5734			−0.857206
$962$	11.7324	−	23.0079i	0.378269	−	0.741804i
$963$	−46.4822	+	12.8489i	−1.49787	+	0.414050i
$964$	−1.28425	+	8.07472i	−0.0413628	+	0.260069i
$965$	16.6979	−	11.1572i	0.537525	−	0.359163i
$966$	3.31041	−	13.6136i	0.106511	−	0.438009i
$967$	19.5230	−	47.1327i	0.627818	−	1.51569i	−0.214511	−	0.976722i	$-0.568816\pi$
$967$	19.5230	−	47.1327i	0.627818	−	1.51569i	0.842329	−	0.538964i	$-0.181184\pi$
$968$	1.27839	−	5.30228i	0.0410890	−	0.170422i
$969$	−6.18718	−	13.5133i	−0.198761	−	0.434109i
$970$	0.508470	+	4.30794i	0.0163260	+	0.138320i
$971$	−4.55240	+	22.8864i	−0.146093	+	0.734461i	0.836394	+	0.548129i	$0.184660\pi$
$971$	−4.55240	+	22.8864i	−0.146093	+	0.734461i	−0.982487	+	0.186331i	$0.940340\pi$
$972$	6.86397	+	30.4119i	0.220162	+	0.975463i
$973$	−4.14049	+	6.19668i	−0.132738	+	0.198657i
$974$	19.0805	+	22.3549i	0.611378	+	0.716299i
$975$	4.55761	−	4.90476i	0.145960	−	0.157078i
$976$	−1.31431	+	10.9832i	−0.0420700	+	0.351563i
$977$	42.2669	+	42.2669i	1.35224	+	1.35224i	0.883153	+	0.469085i	$0.155416\pi$
$977$	42.2669	+	42.2669i	1.35224	+	1.35224i	0.469085	+	0.883153i	$0.344584\pi$
$978$	1.18945	−	28.1752i	0.0380345	−	0.900945i
$979$	−5.07944	+	7.60193i	−0.162340	+	0.242959i
$980$	−4.44827	−	9.66544i	−0.142095	−	0.308751i
$981$	−1.70445	−	0.210724i	−0.0544190	−	0.00672791i
$982$	−6.77952	−	5.34809i	−0.216343	−	0.170664i
$983$	18.1396	+	43.7929i	0.578563	+	1.39678i	0.894102	+	0.447863i	$0.147815\pi$
$983$	18.1396	+	43.7929i	0.578563	+	1.39678i	−0.315539	+	0.948913i	$0.602185\pi$
$984$	4.85451	−	4.82001i	0.154756	−	0.153656i
$985$	−4.90285	+	11.8365i	−0.156218	+	0.377143i
$986$	5.93731	+	10.6098i	0.189082	+	0.337886i
$987$	−20.7433	+	14.9887i	−0.660268	+	0.477096i
$988$	31.0591	−	50.6106i	0.988122	−	1.61014i
$989$	−37.3759	+	7.43453i	−1.18849	+	0.236404i
$990$	5.75989	+	14.1257i	0.183061	+	0.448943i
$991$	−29.0528			−0.922892			−0.461446	−	0.887168i	$-0.652669\pi$
$991$	−29.0528			−0.922892			−0.461446	+	0.887168i	$0.652669\pi$
$992$	8.42936	−	8.40223i	0.267633	−	0.266771i
$993$	0.228636	+	6.23199i	0.00725555	+	0.197766i
$994$	−1.17052	+	0.379907i	−0.0371266	+	0.0120499i
$995$	1.37391	+	6.90712i	0.0435559	+	0.218971i
$996$	51.3806	−	14.3111i	1.62806	−	0.453464i
$997$	−22.3300	+	14.9204i	−0.707198	+	0.472534i	−0.856427	−	0.516268i	$-0.827321\pi$
$997$	−22.3300	+	14.9204i	−0.707198	+	0.472534i	0.149229	+	0.988803i	$0.452321\pi$
$998$	11.8482	+	21.1724i	0.375047	+	0.670201i
$999$	−23.5738	−	6.84734i	−0.745841	−	0.216640i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.cn.a.11.108	yes	1024
3.2	odd	2	inner	960.2.cn.a.11.21	✓	1024
64.35	odd	16	inner	960.2.cn.a.611.21	yes	1024
192.35	even	16	inner	960.2.cn.a.611.108	yes	1024

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
960.2.cn.a.11.21	✓	1024	3.2	odd	2	inner
960.2.cn.a.11.108	yes	1024	1.1	even	1	trivial
960.2.cn.a.611.21	yes	1024	64.35	odd	16	inner
960.2.cn.a.611.108	yes	1024	192.35	even	16	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)

\(f(q)\)	\(=\)	\(q+(1.25987 + 0.642446i) q^{2} +(0.399961 + 1.68524i) q^{3} +(1.17453 + 1.61879i) q^{4} +(-0.831470 + 0.555570i) q^{5} +(-0.578777 + 2.38013i) q^{6} +(-0.496021 + 1.19750i) q^{7} +(0.439761 + 2.79403i) q^{8} +(-2.68006 + 1.34806i) q^{9} +O(q^{10})\)	\(q+(1.25987 + 0.642446i) q^{2} +(0.399961 + 1.68524i) q^{3} +(1.17453 + 1.61879i) q^{4} +(-0.831470 + 0.555570i) q^{5} +(-0.578777 + 2.38013i) q^{6} +(-0.496021 + 1.19750i) q^{7} +(0.439761 + 2.79403i) q^{8} +(-2.68006 + 1.34806i) q^{9} +(-1.40446 + 0.165770i) q^{10} +(-0.701467 + 3.52651i) q^{11} +(-2.25829 + 2.62681i) q^{12} +(2.14761 - 3.21413i) q^{13} +(-1.39425 + 1.19002i) q^{14} +(-1.26882 - 1.17902i) q^{15} +(-1.24097 + 3.80263i) q^{16} +(-0.789972 - 0.789972i) q^{17} +(-4.24258 - 0.0234197i) q^{18} +(4.26717 - 6.38627i) q^{19} +(-1.87594 - 0.693444i) q^{20} +(-2.21646 - 0.356960i) q^{21} +(-3.14935 + 3.99228i) q^{22} +(1.68869 + 4.07686i) q^{23} +(-4.53272 + 1.85861i) q^{24} +(0.382683 - 0.923880i) q^{25} +(4.77060 - 2.66965i) q^{26} +(-3.34372 - 3.97738i) q^{27} +(-2.52109 + 0.603542i) q^{28} +(-7.54744 + 1.50128i) q^{29} +(-0.841093 - 2.30056i) q^{30} -2.10395 q^{31} +(-4.00644 + 3.99355i) q^{32} +(-6.22358 + 0.228328i) q^{33} +(-0.487745 - 1.50277i) q^{34} +(-0.252869 - 1.27126i) q^{35} +(-5.33003 - 2.75513i) q^{36} +(3.92809 - 2.62467i) q^{37} +(9.47889 - 5.30442i) q^{38} +(6.27553 + 2.33371i) q^{39} +(-1.91793 - 2.07883i) q^{40} +(-1.29011 + 0.534381i) q^{41} +(-2.56312 - 1.87368i) q^{42} +(-1.68478 + 8.46996i) q^{43} +(-6.53258 + 3.00646i) q^{44} +(1.47945 - 2.60983i) q^{45} +(-0.491637 + 6.22119i) q^{46} +(8.06060 - 8.06060i) q^{47} +(-6.90468 - 0.570433i) q^{48} +(3.76178 + 3.76178i) q^{49} +(1.07567 - 0.918111i) q^{50} +(1.01533 - 1.64725i) q^{51} +(7.72543 - 0.298544i) q^{52} +(-0.329760 - 0.0655933i) q^{53} +(-1.65740 - 7.15912i) q^{54} +(-1.37598 - 3.32190i) q^{55} +(-3.56398 - 0.859283i) q^{56} +(12.4691 + 4.63694i) q^{57} +(-10.4733 - 2.95741i) q^{58} +(6.16890 + 9.23241i) q^{59} +(0.418318 - 3.43875i) q^{60} +(2.71225 - 0.539500i) q^{61} +(-2.65070 - 1.35167i) q^{62} +(-0.284935 - 3.87804i) q^{63} +(-7.61322 + 2.45741i) q^{64} +3.86560i q^{65} +(-7.98757 - 3.71065i) q^{66} +(3.02134 + 15.1893i) q^{67} +(0.350957 - 2.20664i) q^{68} +(-6.19508 + 4.47643i) q^{69} +(0.498134 - 1.76407i) q^{70} +(0.620249 + 0.256916i) q^{71} +(-4.94511 - 6.89535i) q^{72} +(-0.564831 + 0.233961i) q^{73} +(6.63508 - 0.783145i) q^{74} +(1.71002 + 0.275397i) q^{75} +(15.3499 - 0.593188i) q^{76} +(-3.87506 - 2.58923i) q^{77} +(6.40705 + 6.97185i) q^{78} +(10.9463 - 10.9463i) q^{79} +(-1.08080 - 3.85122i) q^{80} +(5.36547 - 7.22577i) q^{81} +(-1.96868 - 0.155577i) q^{82} +(-12.8021 - 8.55406i) q^{83} +(-2.02545 - 4.00725i) q^{84} +(1.09572 + 0.217953i) q^{85} +(-7.56409 + 9.58864i) q^{86} +(-5.54870 - 12.1188i) q^{87} +(-10.1617 - 0.409097i) q^{88} +(2.34921 + 0.973073i) q^{89} +(3.54058 - 2.33758i) q^{90} +(2.78366 + 4.16604i) q^{91} +(-4.61618 + 7.52202i) q^{92} +(-0.841498 - 3.54566i) q^{93} +(15.3338 - 4.97678i) q^{94} +7.68070i q^{95} +(-8.33250 - 5.15455i) q^{96} -3.06732i q^{97} +(2.32260 + 7.15608i) q^{98} +(-2.87397 - 10.3969i) 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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