LMFDB - Embedded newform 966.2.j.a.137.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(137,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("966.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			137.4
Character	$\chi$	$=$	966.137
Dual form			966.2.j.a.275.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-1.62530 + 0.598665i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.08784 + 1.88420i) q^{5} +(1.10822 - 1.33111i) q^{6} +(-2.11385 + 1.59112i) q^{7} +1.00000i q^{8} +(2.28320 - 1.94602i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.62530 + 0.598665i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.08784 + 1.88420i) q^{5} +(1.10822 - 1.33111i) q^{6} +(-2.11385 + 1.59112i) q^{7} +1.00000i q^{8} +(2.28320 - 1.94602i) q^{9} +(-1.88420 - 1.08784i) q^{10} +(2.08063 - 3.60376i) q^{11} +(-0.294191 + 1.70688i) q^{12} +2.86796 q^{13} +(1.03508 - 2.43487i) q^{14} +(-2.89608 - 2.41114i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.28849 - 3.96377i) q^{17} +(-1.00430 + 2.82690i) q^{18} +(-1.74210 + 1.00580i) q^{19} +2.17569 q^{20} +(2.48309 - 3.85153i) q^{21} +4.16126i q^{22} +(4.77029 + 0.494307i) q^{23} +(-0.598665 - 1.62530i) q^{24} +(0.133188 - 0.230689i) q^{25} +(-2.48373 + 1.43398i) q^{26} +(-2.54587 + 4.52974i) q^{27} +(0.321026 + 2.62620i) q^{28} -9.64344i q^{29} +(3.71365 + 0.640069i) q^{30} +(-3.25050 + 5.63003i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.22421 + 7.10279i) q^{33} +4.57697i q^{34} +(-5.29752 - 2.25202i) q^{35} +(-0.543702 - 2.95032i) q^{36} +(5.17325 - 2.98678i) q^{37} +(1.00580 - 1.74210i) q^{38} +(-4.66130 + 1.71695i) q^{39} +(-1.88420 + 1.08784i) q^{40} +0.0391655i q^{41} +(-0.224652 + 4.57707i) q^{42} +3.91238i q^{43} +(-2.08063 - 3.60376i) q^{44} +(6.15046 + 2.18505i) q^{45} +(-4.37835 + 1.95706i) q^{46} +(4.57081 - 2.63896i) q^{47} +(1.33111 + 1.10822i) q^{48} +(1.93669 - 6.72676i) q^{49} +0.266376i q^{50} +(-1.34651 + 7.81236i) q^{51} +(1.43398 - 2.48373i) q^{52} +(-5.37521 + 9.31013i) q^{53} +(-0.0600767 - 5.19581i) q^{54} +9.05361 q^{55} +(-1.59112 - 2.11385i) q^{56} +(2.22929 - 2.67766i) q^{57} +(4.82172 + 8.35146i) q^{58} +(9.30521 + 5.37237i) q^{59} +(-3.53615 + 1.30251i) q^{60} +(-1.03577 + 0.598005i) q^{61} -6.50100i q^{62} +(-1.72999 + 7.74643i) q^{63} -1.00000 q^{64} +(3.11990 + 5.40382i) q^{65} +(-2.49120 - 6.76330i) q^{66} +(7.71944 + 4.45682i) q^{67} +(-2.28849 - 3.96377i) q^{68} +(-8.04908 + 2.05241i) q^{69} +(5.71380 - 0.698453i) q^{70} -3.48931i q^{71} +(1.94602 + 2.28320i) q^{72} +(3.32966 - 5.76714i) q^{73} +(-2.98678 + 5.17325i) q^{74} +(-0.0783656 + 0.454673i) q^{75} +2.01160i q^{76} +(1.33587 + 10.9283i) q^{77} +(3.17833 - 3.81757i) q^{78} +(-3.16200 + 1.82558i) q^{79} +(1.08784 - 1.88420i) q^{80} +(1.42602 - 8.88631i) q^{81} +(-0.0195827 - 0.0339183i) q^{82} +2.89498 q^{83} +(-2.09398 - 4.07618i) q^{84} +9.95807 q^{85} +(-1.95619 - 3.38822i) q^{86} +(5.77318 + 15.6735i) q^{87} +(3.60376 + 2.08063i) q^{88} +(4.06645 + 7.04330i) q^{89} +(-6.41898 + 1.18293i) q^{90} +(-6.06243 + 4.56326i) q^{91} +(2.81323 - 3.88404i) q^{92} +(1.91254 - 11.0964i) q^{93} +(-2.63896 + 4.57081i) q^{94} +(-3.79026 - 2.18831i) q^{95} +(-1.70688 - 0.294191i) q^{96} +10.6238i q^{97} +(1.68616 + 6.79388i) q^{98} +(-2.26248 - 12.2771i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9}+O(q^{10}) $ 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9	$ 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9} - 64 q^{16} + 4 q^{24} - 72 q^{25} + 24 q^{27} - 8 q^{36} + 4 q^{39} + 12 q^{46} + 72 q^{49} + 4 q^{54} - 96 q^{55} - 128 q^{64} - 56 q^{69} + 32 q^{70} - 40 q^{73} - 40 q^{75} - 16 q^{78} + 36 q^{81} - 32 q^{82} - 64 q^{85} - 24 q^{87} + 32 q^{93} - 8 q^{94} - 4 q^{96}+O(q^{100}) $ 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9 - 64 * q^16 + 4 * q^24 - 72 * q^25 + 24 * q^27 - 8 * q^36 + 4 * q^39 + 12 * q^46 + 72 * q^49 + 4 * q^54 - 96 * q^55 - 128 * q^64 - 56 * q^69 + 32 * q^70 - 40 * q^73 - 40 * q^75 - 16 * q^78 + 36 * q^81 - 32 * q^82 - 64 * q^85 - 24 * q^87 + 32 * q^93 - 8 * q^94 - 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−1.62530	+	0.598665i	−0.938367	+	0.345639i
$3$	−1.62530	+	0.598665i	−0.938367	+	0.345639i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	1.08784	+	1.88420i	0.486499	+	0.842641i	0.999880	−	0.0155202i	$-0.00494042\pi$
$5$	1.08784	+	1.88420i	0.486499	+	0.842641i	−0.513381	+	0.858161i	$0.671607\pi$
$6$	1.10822	−	1.33111i	0.452428	−	0.543423i
$7$	−2.11385	+	1.59112i	−0.798959	+	0.601386i
$7$	−2.11385	+	1.59112i	−0.798959	+	0.601386i
$8$			1.00000i			0.353553i
$9$	2.28320	−	1.94602i	0.761067	−	0.648673i
$10$	−1.88420	−	1.08784i	−0.595837	−	0.344007i
$11$	2.08063	−	3.60376i	0.627334	−	1.08657i	−0.360751	−	0.932662i	$-0.617479\pi$
$11$	2.08063	−	3.60376i	0.627334	−	1.08657i	0.988085	−	0.153912i	$-0.0491872\pi$
$12$	−0.294191	+	1.70688i	−0.0849257	+	0.492735i
$13$	2.86796			0.795429			0.397715	−	0.917509i	$-0.369803\pi$
$13$	2.86796			0.795429			0.397715	+	0.917509i	$0.369803\pi$
$14$	1.03508	−	2.43487i	0.276638	−	0.650747i
$15$	−2.89608	−	2.41114i	−0.747764	−	0.622554i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.28849	−	3.96377i	0.555039	−	0.961357i	−0.442861	−	0.896590i	$-0.646036\pi$
$17$	2.28849	−	3.96377i	0.555039	−	0.961357i	0.997900	−	0.0647662i	$-0.0206302\pi$
$18$	−1.00430	+	2.82690i	−0.236716	+	0.666307i
$19$	−1.74210	+	1.00580i	−0.399664	+	0.230746i	−0.686339	−	0.727282i	$-0.740783\pi$
$19$	−1.74210	+	1.00580i	−0.399664	+	0.230746i	0.286675	+	0.958028i	$0.407450\pi$
$20$	2.17569			0.486499
$21$	2.48309	−	3.85153i	0.541854	−	0.840473i
$22$			4.16126i			0.887184i
$23$	4.77029	+	0.494307i	0.994674	+	0.103070i
$23$	4.77029	+	0.494307i	0.994674	+	0.103070i
$24$	−0.598665	−	1.62530i	−0.122202	−	0.331763i
$25$	0.133188	−	0.230689i	0.0266376	−	0.0461377i
$26$	−2.48373	+	1.43398i	−0.487099	+	0.281227i
$27$	−2.54587	+	4.52974i	−0.489954	+	0.871748i
$28$	0.321026	+	2.62620i	0.0606682	+	0.496306i
$29$		−	9.64344i		−	1.79074i	−0.445322	−	0.895371i	$-0.646911\pi$
$29$		−	9.64344i		−	1.79074i	0.445322	−	0.895371i	$-0.353089\pi$
$30$	3.71365	+	0.640069i	0.678016	+	0.116860i
$31$	−3.25050	+	5.63003i	−0.583807	+	1.01118i	0.411216	+	0.911538i	$0.365104\pi$
$31$	−3.25050	+	5.63003i	−0.583807	+	1.01118i	−0.995023	+	0.0996452i	$0.968229\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−1.22421	+	7.10279i	−0.213107	+	1.23644i
$34$			4.57697i			0.784944i
$35$	−5.29752	−	2.25202i	−0.895445	−	0.380661i
$36$	−0.543702	−	2.95032i	−0.0906169	−	0.491720i
$37$	5.17325	−	2.98678i	0.850477	−	0.491023i	−0.0103347	−	0.999947i	$-0.503290\pi$
$37$	5.17325	−	2.98678i	0.850477	−	0.491023i	0.860812	+	0.508923i	$0.169956\pi$
$38$	1.00580	−	1.74210i	0.163162	−	0.282605i
$39$	−4.66130	+	1.71695i	−0.746405	+	0.274931i
$40$	−1.88420	+	1.08784i	−0.297919	+	0.172003i
$41$			0.0391655i			0.00611662i	0.999995	+	0.00305831i	$0.000973492\pi$
$41$			0.0391655i			0.00611662i	−0.999995	+	0.00305831i	$0.999027\pi$
$42$	−0.224652	+	4.57707i	−0.0346646	+	0.706257i
$43$			3.91238i			0.596632i	0.954467	+	0.298316i	$0.0964250\pi$
$43$			3.91238i			0.596632i	−0.954467	+	0.298316i	$0.903575\pi$
$44$	−2.08063	−	3.60376i	−0.313667	−	0.543287i
$45$	6.15046	+	2.18505i	0.916857	+	0.325727i
$46$	−4.37835	+	1.95706i	−0.645552	+	0.288553i
$47$	4.57081	−	2.63896i	0.666721	−	0.384931i	−0.128112	−	0.991760i	$-0.540892\pi$
$47$	4.57081	−	2.63896i	0.666721	−	0.384931i	0.794833	+	0.606828i	$0.207558\pi$
$48$	1.33111	+	1.10822i	0.192129	+	0.159958i
$49$	1.93669	−	6.72676i	0.276669	−	0.960965i
$50$			0.266376i			0.0376713i
$51$	−1.34651	+	7.81236i	−0.188548	+	1.09395i
$52$	1.43398	−	2.48373i	0.198857	−	0.344431i
$53$	−5.37521	+	9.31013i	−0.738341	+	1.27884i	0.214900	+	0.976636i	$0.431057\pi$
$53$	−5.37521	+	9.31013i	−0.738341	+	1.27884i	−0.953242	+	0.302209i	$0.902276\pi$
$54$	−0.0600767	−	5.19581i	−0.00817540	−	0.707060i
$55$	9.05361			1.22079
$56$	−1.59112	−	2.11385i	−0.212622	−	0.282474i
$57$	2.22929	−	2.67766i	0.295277	−	0.354664i
$58$	4.82172	+	8.35146i	0.633123	+	1.09660i
$59$	9.30521	+	5.37237i	1.21144	+	0.699423i	0.963072	−	0.269244i	$-0.0867738\pi$
$59$	9.30521	+	5.37237i	1.21144	+	0.699423i	0.248364	+	0.968667i	$0.420107\pi$
$60$	−3.53615	+	1.30251i	−0.456515	+	0.168153i
$61$	−1.03577	+	0.598005i	−0.132617	+	0.0765666i	−0.564841	−	0.825200i	$-0.691062\pi$
$61$	−1.03577	+	0.598005i	−0.132617	+	0.0765666i	0.432224	+	0.901766i	$0.357729\pi$
$62$		−	6.50100i		−	0.825627i
$63$	−1.72999	+	7.74643i	−0.217958	+	0.975958i
$64$	−1.00000			−0.125000
$65$	3.11990	+	5.40382i	0.386975	+	0.670261i
$66$	−2.49120	−	6.76330i	−0.306646	−	0.832505i
$67$	7.71944	+	4.45682i	0.943080	+	0.544488i	0.890925	−	0.454151i	$-0.150057\pi$
$67$	7.71944	+	4.45682i	0.943080	+	0.544488i	0.0521557	+	0.998639i	$0.483391\pi$
$68$	−2.28849	−	3.96377i	−0.277520	−	0.480678i
$69$	−8.04908	+	2.05241i	−0.968995	+	0.247081i
$70$	5.71380	−	0.698453i	0.682930	−	0.0834811i
$71$		−	3.48931i		−	0.414105i	−0.978330	−	0.207053i	$-0.933613\pi$
$71$		−	3.48931i		−	0.414105i	0.978330	−	0.207053i	$-0.0663871\pi$
$72$	1.94602	+	2.28320i	0.229341	+	0.269078i
$73$	3.32966	−	5.76714i	0.389707	−	0.674993i	−0.602703	−	0.797966i	$-0.705910\pi$
$73$	3.32966	−	5.76714i	0.389707	−	0.674993i	0.992410	+	0.122973i	$0.0392429\pi$
$74$	−2.98678	+	5.17325i	−0.347206	+	0.601378i
$75$	−0.0783656	+	0.454673i	−0.00904888	+	0.0525011i
$76$			2.01160i			0.230746i
$77$	1.33587	+	10.9283i	0.152237	+	1.24540i
$78$	3.17833	−	3.81757i	0.359875	−	0.432254i
$79$	−3.16200	+	1.82558i	−0.355753	+	0.205394i	−0.667216	−	0.744864i	$-0.732514\pi$
$79$	−3.16200	+	1.82558i	−0.355753	+	0.205394i	0.311463	+	0.950258i	$0.399181\pi$
$80$	1.08784	−	1.88420i	0.121625	−	0.210660i
$81$	1.42602	−	8.88631i	0.158446	−	0.987368i
$82$	−0.0195827	−	0.0339183i	−0.00216255	−	0.00374565i
$83$	2.89498			0.317766			0.158883	−	0.987297i	$-0.449211\pi$
$83$	2.89498			0.317766			0.158883	+	0.987297i	$0.449211\pi$
$84$	−2.09398	−	4.07618i	−0.228472	−	0.444748i
$85$	9.95807			1.08010
$86$	−1.95619	−	3.38822i	−0.210941	−	0.365361i
$87$	5.77318	+	15.6735i	0.618950	+	1.68037i
$88$	3.60376	+	2.08063i	0.384162	+	0.221796i
$89$	4.06645	+	7.04330i	0.431043	+	0.746589i	0.996963	−	0.0778713i	$-0.0248123\pi$
$89$	4.06645	+	7.04330i	0.431043	+	0.746589i	−0.565920	+	0.824460i	$0.691479\pi$
$90$	−6.41898	+	1.18293i	−0.676620	+	0.124691i
$91$	−6.06243	+	4.56326i	−0.635515	+	0.478360i
$92$	2.81323	−	3.88404i	0.293299	−	0.404939i
$93$	1.91254	−	11.0964i	0.198321	−	1.15065i
$94$	−2.63896	+	4.57081i	−0.272188	+	0.471443i
$95$	−3.79026	−	2.18831i	−0.388872	−	0.224516i
$96$	−1.70688	−	0.294191i	−0.174208	−	0.0300258i
$97$			10.6238i			1.07868i	0.842088	+	0.539340i	$0.181326\pi$
$97$			10.6238i			1.07868i	−0.842088	+	0.539340i	$0.818674\pi$
$98$	1.68616	+	6.79388i	0.170328	+	0.686286i
$99$	−2.26248	−	12.2771i	−0.227388	−	1.23389i
$100$	−0.133188	−	0.230689i	−0.0133188	−	0.0230689i
$101$	−0.885376	−	0.511172i	−0.0880983	−	0.0508635i	0.455304	−	0.890336i	$-0.349531\pi$
$101$	−0.885376	−	0.511172i	−0.0880983	−	0.0508635i	−0.543402	+	0.839473i	$0.682864\pi$
$102$	−2.74007	−	7.43895i	−0.271308	−	0.736566i
$103$	−7.66765	+	4.42692i	−0.755516	+	0.436197i	−0.827684	−	0.561195i	$-0.810342\pi$
$103$	−7.66765	+	4.42692i	−0.755516	+	0.436197i	0.0721675	+	0.997393i	$0.477008\pi$
$104$			2.86796i			0.281227i
$105$	9.95827	+	0.488773i	0.971828	+	0.0476994i
$106$		−	10.7504i		−	1.04417i
$107$	−0.385350	−	0.667445i	−0.0372531	−	0.0645243i	0.846798	−	0.531915i	$-0.178527\pi$
$107$	−0.385350	−	0.667445i	−0.0372531	−	0.0645243i	−0.884051	+	0.467391i	$0.845194\pi$
$108$	2.64993	+	4.46966i	0.254990	+	0.430093i
$109$	11.6326	+	6.71606i	1.11420	+	0.643282i	0.939913	−	0.341414i	$-0.110906\pi$
$109$	11.6326	+	6.71606i	1.11420	+	0.643282i	0.174284	+	0.984695i	$0.444239\pi$
$110$	−7.84066	+	4.52681i	−0.747578	+	0.431614i
$111$	−6.62001	+	7.95145i	−0.628343	+	0.754718i
$112$	2.43487	+	1.03508i	0.230074	+	0.0978063i
$113$	2.67636			0.251771			0.125885	−	0.992045i	$-0.459823\pi$
$113$	2.67636			0.251771			0.125885	+	0.992045i	$0.459823\pi$
$114$	−0.591795	+	3.43357i	−0.0554267	+	0.321583i
$115$	4.25796	+	9.52592i	0.397057	+	0.888296i
$116$	−8.35146	−	4.82172i	−0.775414	−	0.447685i
$117$	6.54813	−	5.58111i	0.605375	−	0.515974i
$118$	−10.7447			−0.989133
$119$	1.46933	+	12.0201i	0.134693	+	1.10188i
$120$	2.41114	−	2.89608i	0.220106	−	0.264375i
$121$	−3.15805	−	5.46991i	−0.287096	−	0.497264i
$122$	0.598005	−	1.03577i	0.0541408	−	0.0937746i
$123$	−0.0234470	−	0.0636557i	−0.00211414	−	0.00573964i
$124$	3.25050	+	5.63003i	0.291903	+	0.505591i
$125$	11.4580			1.02483
$126$	−2.37500	−	7.57360i	−0.211582	−	0.674710i
$127$	19.7007			1.74815			0.874077	−	0.485788i	$-0.161467\pi$
$127$	19.7007			1.74815			0.874077	+	0.485788i	$0.161467\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	−2.34220	−	6.35879i	−0.206219	−	0.559860i
$130$	−5.40382	−	3.11990i	−0.473946	−	0.273633i
$131$	−10.3845	+	5.99548i	−0.907296	+	0.523828i	−0.879560	−	0.475788i	$-0.842163\pi$
$131$	−10.3845	+	5.99548i	−0.907296	+	0.523828i	−0.0277361	+	0.999615i	$0.508830\pi$
$132$	5.53909	+	4.61159i	0.482116	+	0.401387i
$133$	2.08218	−	4.89799i	0.180548	−	0.424709i
$134$	−8.91365			−0.770022
$135$	−11.3045	+	0.130708i	−0.972933	+	0.0112496i
$136$	3.96377	+	2.28849i	0.339891	+	0.196236i
$137$	−10.8353	+	18.7673i	−0.925720	+	1.60339i	−0.135322	+	0.990802i	$0.543207\pi$
$137$	−10.8353	+	18.7673i	−0.925720	+	1.60339i	−0.790398	+	0.612593i	$0.790126\pi$
$138$	5.94450	−	5.80197i	0.506030	−	0.493897i
$139$	−14.7043			−1.24720			−0.623601	−	0.781743i	$-0.714331\pi$
$139$	−14.7043			−1.24720			−0.623601	+	0.781743i	$0.714331\pi$
$140$	−4.59907	+	3.46178i	−0.388692	+	0.292574i
$141$	−5.84908	+	7.02548i	−0.492582	+	0.591652i
$142$	1.74466	+	3.02183i	0.146408	+	0.253587i
$143$	5.96717	−	10.3354i	0.499000	−	0.864293i
$144$	−2.82690	−	1.00430i	−0.235575	−	0.0836917i
$145$	18.1702	−	10.4906i	1.50895	−	0.871194i
$146$			6.65932i			0.551129i
$147$	0.879375	+	12.0924i	0.0725296	+	0.997366i
$148$		−	5.97355i		−	0.491023i
$149$	−7.78862	−	13.4903i	−0.638068	−	1.10517i	−0.985856	−	0.167594i	$-0.946400\pi$
$149$	−7.78862	−	13.4903i	−0.638068	−	1.10517i	0.347788	−	0.937573i	$-0.386933\pi$
$150$	−0.159470	−	0.432941i	−0.0130207	−	0.0353495i
$151$	6.93799	−	12.0170i	0.564606	−	0.977926i	−0.432480	−	0.901643i	$-0.642362\pi$
$151$	6.93799	−	12.0170i	0.564606	−	0.977926i	0.997086	−	0.0762826i	$-0.0243051\pi$
$152$	−1.00580	−	1.74210i	−0.0815811	−	0.141303i
$153$	−2.48851	−	13.5035i	−0.201184	−	1.09170i
$154$	−6.62106	−	8.79627i	−0.533540	−	0.708823i
$155$	−14.1441			−1.13609
$156$	−0.843729	+	4.89528i	−0.0675524	+	0.391936i
$157$	17.0996	+	9.87247i	1.36470	+	0.787909i	0.990245	−	0.139337i	$-0.0444972\pi$
$157$	17.0996	+	9.87247i	1.36470	+	0.787909i	0.374453	+	0.927246i	$0.377830\pi$
$158$	1.82558	−	3.16200i	0.145235	−	0.251555i
$159$	3.16268	−	18.3497i	0.250817	−	1.45523i
$160$			2.17569i			0.172003i
$161$	−10.8702	+	6.54521i	−0.856688	+	0.515834i
$162$	3.20819	+	8.40878i	0.252059	+	0.660656i
$163$	−10.1608	−	17.5989i	−0.795852	−	1.37846i	−0.922297	−	0.386482i	$-0.873690\pi$
$163$	−10.1608	−	17.5989i	−0.795852	−	1.37846i	0.126445	−	0.991974i	$-0.459643\pi$
$164$	0.0339183	+	0.0195827i	0.00264857	+	0.00152916i
$165$	−14.7148	+	5.42008i	−1.14555	+	0.421952i
$166$	−2.50713	+	1.44749i	−0.194591	+	0.112347i
$167$		−	12.4172i		−	0.960873i	−0.877030	−	0.480436i	$-0.840478\pi$
$167$		−	12.4172i		−	0.960873i	0.877030	−	0.480436i	$-0.159522\pi$
$168$	3.85153	+	2.48309i	0.297152	+	0.191574i
$169$	−4.77480			−0.367292
$170$	−8.62394	+	4.97903i	−0.661426	+	0.381875i
$171$	−2.02025	+	5.68660i	−0.154492	+	0.434865i
$172$	3.38822	+	1.95619i	0.258349	+	0.149158i
$173$	10.5275	−	6.07807i	0.800393	−	0.462107i	−0.0432155	−	0.999066i	$-0.513760\pi$
$173$	10.5275	−	6.07807i	0.800393	−	0.462107i	0.843609	+	0.536959i	$0.180427\pi$
$174$	−12.8365	−	10.6870i	−0.973130	−	0.810182i
$175$	0.0855137	+	0.699558i	0.00646423	+	0.0528816i
$176$	−4.16126			−0.313667
$177$	−18.3400	−	3.16101i	−1.37852	−	0.237596i
$178$	−7.04330	−	4.06645i	−0.527918	−	0.304794i
$179$	−5.46301	−	3.15407i	−0.408325	−	0.235746i	0.281745	−	0.959489i	$-0.409087\pi$
$179$	−5.46301	−	3.15407i	−0.408325	−	0.235746i	−0.690070	+	0.723743i	$0.742420\pi$
$180$	4.96754	−	4.23393i	0.370258	−	0.315579i
$181$		−	9.80813i		−	0.729033i	−0.931197	−	0.364516i	$-0.881234\pi$
$181$		−	9.80813i		−	0.729033i	0.931197	−	0.364516i	$-0.118766\pi$
$182$	2.96858	−	6.98312i	0.220046	−	0.517623i
$183$	1.32544	−	1.59202i	0.0979793	−	0.117685i
$184$	−0.494307	+	4.77029i	−0.0364408	+	0.351670i
$185$	11.2554	+	6.49830i	0.827512	+	0.477764i
$186$	3.89192	+	10.5661i	0.285369	+	0.774742i
$187$	−9.52299	−	16.4943i	−0.696390	−	1.20618i
$188$		−	5.27791i		−	0.384931i
$189$	−1.82576	−	13.6260i	−0.132805	−	0.991142i
$190$	4.37662			0.317513
$191$	−11.0861	−	19.2017i	−0.802160	−	1.38938i	−0.918191	−	0.396137i	$-0.870351\pi$
$191$	−11.0861	−	19.2017i	−0.802160	−	1.38938i	0.116031	−	0.993246i	$-0.462983\pi$
$192$	1.62530	−	0.598665i	0.117296	−	0.0432049i
$193$	−11.9601	+	20.7155i	−0.860905	+	1.49113i	0.0101511	+	0.999948i	$0.496769\pi$
$193$	−11.9601	+	20.7155i	−0.860905	+	1.49113i	−0.871056	+	0.491183i	$0.836565\pi$
$194$	−5.31188	−	9.20044i	−0.381371	−	0.660553i
$195$	−8.30584	−	6.91506i	−0.594794	−	0.495197i
$196$	−4.85720	−	5.04060i	−0.346943	−	0.360043i
$197$		−	22.2617i		−	1.58608i	−0.609170	−	0.793040i	$-0.708497\pi$
$197$		−	22.2617i		−	1.58608i	0.609170	−	0.793040i	$-0.291503\pi$
$198$	8.09790	+	9.50100i	0.575492	+	0.675207i
$199$	−14.6411	−	8.45302i	−1.03788	−	0.599219i	−0.118646	−	0.992937i	$-0.537855\pi$
$199$	−14.6411	−	8.45302i	−1.03788	−	0.599219i	−0.919231	+	0.393718i	$0.871189\pi$
$200$	0.230689	+	0.133188i	0.0163121	+	0.00941782i
$201$	−15.2146	−	2.62232i	−1.07315	−	0.184964i
$202$	1.02234			0.0719319
$203$	15.3438	+	20.3847i	1.07693	+	1.43073i
$204$	6.09245	+	5.07229i	0.426557	+	0.355131i
$205$	−0.0737957	+	0.0426060i	−0.00515411	+	0.00297573i
$206$	4.42692	−	7.66765i	0.308438	−	0.534231i
$207$	11.8535	−	8.15447i	0.823873	−	0.566775i
$208$	−1.43398	−	2.48373i	−0.0994287	−	0.172215i
$209$			8.37079i			0.579020i
$210$	−8.86850	+	4.55585i	−0.611985	+	0.314383i
$211$	14.5437			1.00123			0.500616	−	0.865669i	$-0.333107\pi$
$211$	14.5437			1.00123			0.500616	+	0.865669i	$0.333107\pi$
$212$	5.37521	+	9.31013i	0.369171	+	0.639422i
$213$	2.08893	+	5.67118i	0.143131	+	0.388583i
$214$	0.667445	+	0.385350i	0.0456256	+	0.0263420i
$215$	−7.37171	+	4.25606i	−0.502747	+	0.290261i
$216$	−4.52974	−	2.54587i	−0.308210	−	0.173225i
$217$	−2.08699	−	17.0729i	−0.141674	−	1.15899i
$218$	−13.4321			−0.909738
$219$	−1.95911	+	11.3667i	−0.132385	+	0.768089i
$220$	4.52681	−	7.84066i	0.305197	−	0.528617i
$221$	6.56329	−	11.3679i	0.441495	−	0.764691i
$222$	1.75737	−	10.1962i	0.117947	−	0.684322i
$223$	5.18920			0.347495			0.173747	−	0.984790i	$-0.444412\pi$
$223$	5.18920			0.347495			0.173747	+	0.984790i	$0.444412\pi$
$224$	−2.62620	+	0.321026i	−0.175471	+	0.0214495i
$225$	−0.144829	−	0.785895i	−0.00965528	−	0.0523930i
$226$	−2.31779	+	1.33818i	−0.154177	+	0.0890143i
$227$	8.84808	−	15.3253i	0.587268	−	1.01718i	−0.407321	−	0.913285i	$-0.633537\pi$
$227$	8.84808	−	15.3253i	0.587268	−	1.01718i	0.994589	−	0.103892i	$-0.0331298\pi$
$228$	−1.20427	−	3.26945i	−0.0797550	−	0.216525i
$229$	14.0851	−	8.13205i	0.930771	−	0.537381i	0.0437157	−	0.999044i	$-0.486080\pi$
$229$	14.0851	−	8.13205i	0.930771	−	0.537381i	0.887055	+	0.461663i	$0.152747\pi$
$230$	−8.45046	−	6.12071i	−0.557207	−	0.403588i
$231$	−8.71359	−	16.9621i	−0.573312	−	1.11602i
$232$	9.64344			0.633123
$233$	5.98775	−	3.45703i	0.392271	−	0.226478i	−0.290873	−	0.956762i	$-0.593946\pi$
$233$	5.98775	−	3.45703i	0.392271	−	0.226478i	0.683144	+	0.730284i	$0.260612\pi$
$234$	−2.88029	+	8.10745i	−0.188291	+	0.530000i
$235$	9.94465	+	5.74155i	0.648718	+	0.374537i
$236$	9.30521	−	5.37237i	0.605718	−	0.349711i
$237$	4.04629	−	4.86009i	0.262834	−	0.315697i
$238$	−7.28250	−	9.67501i	−0.472055	−	0.627138i
$239$			4.25073i			0.274957i	0.990505	+	0.137478i	$0.0438998\pi$
$239$			4.25073i			0.274957i	−0.990505	+	0.137478i	$0.956100\pi$
$240$	−0.640069	+	3.71365i	−0.0413163	+	0.239715i
$241$	7.52283	+	4.34331i	0.484588	+	0.279777i	0.722327	−	0.691552i	$-0.243073\pi$
$241$	7.52283	+	4.34331i	0.484588	+	0.279777i	−0.237738	+	0.971329i	$0.576406\pi$
$242$	5.46991	+	3.15805i	0.351619	+	0.203007i
$243$	3.00221	+	15.2966i	0.192592	+	0.981279i
$244$			1.19601i			0.0765666i
$245$	14.7814	−	3.66856i	0.944348	−	0.234376i
$246$	0.0521335	+	0.0434039i	0.00332391	+	0.00276733i
$247$	−4.99626	+	2.88459i	−0.317905	+	0.183542i
$248$	−5.63003	−	3.25050i	−0.357507	−	0.206407i
$249$	−4.70521	+	1.73312i	−0.298181	+	0.109832i
$250$	−9.92292	+	5.72900i	−0.627580	+	0.362334i
$251$	3.01936			0.190580			0.0952901	−	0.995450i	$-0.469622\pi$
$251$	3.01936			0.190580			0.0952901	+	0.995450i	$0.469622\pi$
$252$	5.84361	+	5.37143i	0.368113	+	0.338368i
$253$	11.7066	−	16.1625i	0.735986	−	1.01613i
$254$	−17.0613	+	9.85035i	−1.07052	+	0.618066i
$255$	−16.1849	+	5.96154i	−1.01353	+	0.373326i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.57168	+	4.94886i	−0.534687	+	0.308702i	−0.742923	−	0.669377i	$-0.766561\pi$
$257$	−8.57168	+	4.94886i	−0.534687	+	0.308702i	0.208236	+	0.978079i	$0.433228\pi$
$258$	5.20780	+	4.33577i	0.324224	+	0.269933i
$259$	−6.18314	+	14.5448i	−0.384201	+	0.903772i
$260$	6.23979			0.386975
$261$	−18.7663	−	22.0179i	−1.16161	−	1.36287i
$262$	5.99548	−	10.3845i	0.370402	−	0.641555i
$263$	−4.54956	+	7.88007i	−0.280538	+	0.485906i	−0.971517	−	0.236968i	$-0.923846\pi$
$263$	−4.54956	+	7.88007i	−0.280538	+	0.485906i	0.690979	+	0.722874i	$0.257180\pi$
$264$	−7.10279	−	1.22421i	−0.437146	−	0.0753447i
$265$	−23.3896			−1.43681
$266$	0.645776	+	5.28287i	0.0395950	+	0.323913i
$267$	−10.8258	−	9.01304i	−0.662527	−	0.551589i
$268$	7.71944	−	4.45682i	0.471540	−	0.272244i
$269$	9.94734	+	5.74310i	0.606500	+	0.350163i	0.771594	−	0.636115i	$-0.219460\pi$
$269$	9.94734	+	5.74310i	0.606500	+	0.350163i	−0.165095	+	0.986278i	$0.552793\pi$
$270$	9.72459	−	5.76543i	0.591820	−	0.350873i
$271$	6.61519	+	11.4578i	0.401844	+	0.696014i	0.993949	−	0.109847i	$-0.0350361\pi$
$271$	6.61519	+	11.4578i	0.401844	+	0.696014i	−0.592105	+	0.805861i	$0.701703\pi$
$272$	−4.57697			−0.277520
$273$	7.12140	−	11.0460i	0.431007	−	0.668536i
$274$		−	21.6706i		−	1.30917i
$275$	−0.554231	−	0.959956i	−0.0334214	−	0.0578875i
$276$	−2.24710	+	7.99691i	−0.135260	+	0.481357i
$277$	−10.3706	+	17.9624i	−0.623108	+	1.07925i	0.365795	+	0.930695i	$0.380797\pi$
$277$	−10.3706	+	17.9624i	−0.623108	+	1.07925i	−0.988903	+	0.148559i	$0.952536\pi$
$278$	12.7343	−	7.35215i	0.763752	−	0.440953i
$279$	3.53460	+	19.1800i	0.211611	+	1.14828i
$280$	2.25202	−	5.29752i	0.134584	−	0.316588i
$281$	−12.0502			−0.718855			−0.359427	−	0.933173i	$-0.617028\pi$
$281$	−12.0502			−0.718855			−0.359427	+	0.933173i	$0.617028\pi$
$282$	1.55272	−	9.00878i	0.0924629	−	0.536465i
$283$	−12.6170	−	7.28445i	−0.750005	−	0.433016i	0.0756907	−	0.997131i	$-0.475884\pi$
$283$	−12.6170	−	7.28445i	−0.750005	−	0.433016i	−0.825696	+	0.564116i	$0.809217\pi$
$284$	−3.02183	−	1.74466i	−0.179313	−	0.103526i
$285$	7.47037	+	1.28756i	0.442507	+	0.0762686i
$286$			11.9343i			0.705692i
$287$	−0.0623169	−	0.0827898i	−0.00367845	−	0.00488693i
$288$	2.95032	−	0.543702i	0.173849	−	0.0320379i
$289$	−1.97434	−	3.41965i	−0.116138	−	0.201156i
$290$	−10.4906	+	18.1702i	−0.616027	+	1.06699i
$291$	−6.36007	−	17.2668i	−0.372834	−	1.01220i
$292$	−3.32966	−	5.76714i	−0.194854	−	0.337496i
$293$	8.98979			0.525189			0.262595	−	0.964906i	$-0.415422\pi$
$293$	8.98979			0.525189			0.262595	+	0.964906i	$0.415422\pi$
$294$	−6.80777	−	10.0327i	−0.397037	−	0.585117i
$295$			23.3772i			1.36107i
$296$	2.98678	+	5.17325i	0.173603	+	0.300689i
$297$	11.0271	+	18.5994i	0.639855	+	1.07925i
$298$	13.4903	+	7.78862i	0.781471	+	0.451183i
$299$	13.6810	+	1.41765i	0.791193	+	0.0819850i
$300$	0.354576	+	0.295203i	0.0204714	+	0.0170436i
$301$	−6.22506	−	8.27017i	−0.358806	−	0.476684i
$302$			13.8760i			0.798473i
$303$	1.74502	+	0.300765i	0.100249	+	0.0172785i
$304$	1.74210	+	1.00580i	0.0999161	+	0.0576866i
$305$	−2.25352	−	1.30107i	−0.129036	−	0.0744992i
$306$	8.90688	+	10.4501i	0.509172	+	0.597395i
$307$	8.96437			0.511623			0.255812	−	0.966727i	$-0.417657\pi$
$307$	8.96437			0.511623			0.255812	+	0.966727i	$0.417657\pi$
$308$	10.1321	+	4.30726i	0.577332	+	0.245429i
$309$	9.81199	−	11.7854i	0.558185	−	0.670449i
$310$	12.2492	−	7.07207i	0.695707	−	0.401667i
$311$	20.0945	+	11.6015i	1.13945	+	0.657863i	0.946295	−	0.323304i	$-0.104794\pi$
$311$	20.0945	+	11.6015i	1.13945	+	0.657863i	0.193158	+	0.981168i	$0.438127\pi$
$312$	−1.71695	−	4.66130i	−0.0972030	−	0.263894i
$313$	−11.8259	+	6.82766i	−0.668437	+	0.385922i	−0.795484	−	0.605975i	$-0.792783\pi$
$313$	−11.8259	+	6.82766i	−0.668437	+	0.385922i	0.127047	+	0.991897i	$0.459450\pi$
$314$	−19.7449			−1.11427
$315$	−16.4778	+	5.16726i	−0.928419	+	0.291142i
$316$			3.65116i			0.205394i
$317$	9.28047	−	5.35808i	0.521243	−	0.300940i	−0.216200	−	0.976349i	$-0.569366\pi$
$317$	9.28047	−	5.35808i	0.521243	−	0.300940i	0.737443	+	0.675409i	$0.236033\pi$
$318$	6.43589	+	17.4726i	0.360907	+	0.979817i
$319$	−34.7526	−	20.0644i	−1.94577	−	1.12339i
$320$	−1.08784	−	1.88420i	−0.0608124	−	0.105330i
$321$	1.02588	+	0.854103i	0.0572593	+	0.0476714i
$322$	6.14123	−	11.1034i	0.342237	−	0.618768i
$323$			9.20704i			0.512293i
$324$	−6.98276	−	5.67812i	−0.387931	−	0.315451i
$325$	0.381978	−	0.661606i	0.0211883	−	0.0366993i
$326$	17.5989	+	10.1608i	0.974716	+	0.562752i
$327$	−22.9271	−	3.95161i	−1.26787	−	0.218525i
$328$	−0.0391655			−0.00216255
$329$	−5.46309	+	12.8510i	−0.301190	+	0.708501i
$330$	10.0334	−	12.0513i	0.552320	−	0.663405i
$331$	0.221493	+	0.383637i	0.0121743	+	0.0210866i	0.872048	−	0.489420i	$-0.162791\pi$
$331$	0.221493	+	0.383637i	0.0121743	+	0.0210866i	−0.859874	+	0.510506i	$0.829458\pi$
$332$	1.44749	−	2.50713i	0.0794414	−	0.137597i
$333$	5.99924	−	16.8867i	0.328757	−	0.925383i
$334$	6.20861	+	10.7536i	0.339720	+	0.588412i
$335$			19.3933i			1.05957i
$336$	−4.57707	−	0.224652i	−0.249699	−	0.0122558i
$337$			0.617244i			0.0336234i	0.999859	+	0.0168117i	$0.00535158\pi$
$337$			0.617244i			0.0336234i	−0.999859	+	0.0168117i	$0.994648\pi$
$338$	4.13510	−	2.38740i	0.224920	−	0.129857i
$339$	−4.34988	+	1.60224i	−0.236253	+	0.0870218i
$340$	4.97903	−	8.62394i	0.270026	−	0.467699i
$341$	13.5262	+	23.4280i	0.732484	+	1.26870i
$342$	−1.09371	−	5.93486i	−0.0591410	−	0.320921i
$343$	6.60921	+	17.3008i	0.356864	+	0.934156i
$344$	−3.91238			−0.210941
$345$	−12.6233	−	12.9334i	−0.679615	−	0.696310i
$346$	−6.07807	+	10.5275i	−0.326759	+	0.565963i
$347$	6.81781	+	3.93626i	0.365999	+	0.211310i	0.671709	−	0.740815i	$-0.265560\pi$
$347$	6.81781	+	3.93626i	0.365999	+	0.211310i	−0.305710	+	0.952125i	$0.598894\pi$
$348$	16.4602	+	2.83702i	0.882361	+	0.152080i
$349$	−7.27743			−0.389552			−0.194776	−	0.980848i	$-0.562398\pi$
$349$	−7.27743			−0.389552			−0.194776	+	0.980848i	$0.562398\pi$
$350$	−0.423836	−	0.563078i	−0.0226550	−	0.0300978i
$351$	−7.30147	+	12.9911i	−0.389724	+	0.693414i
$352$	3.60376	−	2.08063i	0.192081	−	0.110898i
$353$	−4.12308	−	2.38046i	−0.219449	−	0.126699i	0.386246	−	0.922396i	$-0.373772\pi$
$353$	−4.12308	−	2.38046i	−0.219449	−	0.126699i	−0.605695	+	0.795697i	$0.707105\pi$
$354$	17.4634	−	6.43249i	0.928170	−	0.341883i
$355$	6.57457	−	3.79583i	0.348942	−	0.201462i
$356$	8.13291			0.431043
$357$	−9.58408	−	18.6566i	−0.507243	−	0.987410i
$358$	6.30814			0.333396
$359$	3.07587	+	5.32757i	0.162338	+	0.281178i	0.935707	−	0.352778i	$-0.114763\pi$
$359$	3.07587	+	5.32757i	0.162338	+	0.281178i	−0.773369	+	0.633957i	$0.781430\pi$
$360$	−2.18505	+	6.15046i	−0.115162	+	0.324158i
$361$	−7.47673	+	12.9501i	−0.393512	+	0.681583i
$362$	4.90407	+	8.49409i	0.257752	+	0.446439i
$363$	8.40742	+	6.99962i	0.441275	+	0.367385i
$364$	0.920690	+	7.53185i	0.0482573	+	0.394776i
$365$	14.4886			0.758368
$366$	−0.351856	+	2.04145i	−0.0183918	+	0.106708i
$367$	25.6286	+	14.7967i	1.33780	+	0.772382i	0.986481	−	0.163873i	$-0.0523987\pi$
$367$	25.6286	+	14.7967i	1.33780	+	0.772382i	0.351323	+	0.936254i	$0.385732\pi$
$368$	−1.95706	−	4.37835i	−0.102019	−	0.228237i
$369$	0.0762168	+	0.0894227i	0.00396769	+	0.00465516i
$370$	−12.9966			−0.675661
$371$	−3.45116	−	28.2328i	−0.179175	−	1.46577i
$372$	−8.65353	−	7.20453i	−0.448665	−	0.373537i
$373$	−24.2659	+	14.0099i	−1.25644	+	0.725408i	−0.972381	−	0.233398i	$-0.925015\pi$
$373$	−24.2659	+	14.0099i	−1.25644	+	0.725408i	−0.284062	+	0.958806i	$0.591682\pi$
$374$	16.4943	+	9.52299i	0.852900	+	0.492422i
$375$	−18.6227	+	6.85950i	−0.961671	+	0.354223i
$376$	2.63896	+	4.57081i	0.136094	+	0.235721i
$377$		−	27.6570i		−	1.42441i
$378$	8.39413	+	10.8875i	0.431748	+	0.559995i
$379$		−	26.3499i		−	1.35350i	−0.736212	−	0.676751i	$-0.763387\pi$
$379$		−	26.3499i		−	1.35350i	0.736212	−	0.676751i	$-0.236613\pi$
$380$	−3.79026	+	2.18831i	−0.194436	+	0.112258i
$381$	−32.0195	+	11.7941i	−1.64041	+	0.604230i
$382$	19.2017	+	11.0861i	0.982442	+	0.567213i
$383$	−12.6715	−	21.9476i	−0.647482	−	1.12147i	−0.983722	−	0.179696i	$-0.942489\pi$
$383$	−12.6715	−	21.9476i	−0.647482	−	1.12147i	0.336240	−	0.941776i	$-0.390845\pi$
$384$	−1.10822	+	1.33111i	−0.0565536	+	0.0679279i
$385$	−19.1379	+	14.4054i	−0.975360	+	0.734166i
$386$		−	23.9202i		−	1.21750i
$387$	7.61357	+	8.93275i	0.387019	+	0.454077i
$388$	9.20044	+	5.31188i	0.467082	+	0.269670i
$389$	4.63042	−	8.02012i	0.234772	−	0.406636i	−0.724435	−	0.689343i	$-0.757899\pi$
$389$	4.63042	−	8.02012i	0.234772	−	0.406636i	0.959206	+	0.282707i	$0.0912324\pi$
$390$	10.6506	+	1.83569i	0.539314	+	0.0929539i
$391$	12.8761	−	17.7771i	0.651170	−	0.899028i
$392$	6.72676	+	1.93669i	0.339752	+	0.0978174i
$393$	13.2886	−	15.9613i	0.670322	−	0.805140i
$394$	11.1308	+	19.2792i	0.560764	+	0.971271i
$395$	−6.87952	−	3.97190i	−0.346146	−	0.199848i
$396$	−11.7635	−	4.17916i	−0.591137	−	0.210011i
$397$	5.95046	+	10.3065i	0.298645	+	0.517268i	0.975826	−	0.218548i	$-0.0701321\pi$
$397$	5.95046	+	10.3065i	0.298645	+	0.517268i	−0.677181	+	0.735816i	$0.736799\pi$
$398$	16.9060			0.847423
$399$	−0.451910	+	9.20722i	−0.0226238	+	0.460938i
$400$	−0.266376			−0.0133188
$401$	15.6210	+	27.0564i	0.780078	+	1.35113i	0.931896	+	0.362726i	$0.118154\pi$
$401$	15.6210	+	27.0564i	0.780078	+	1.35113i	−0.151818	+	0.988408i	$0.548513\pi$
$402$	14.4874	−	5.33628i	0.722563	−	0.266150i
$403$	−9.32230	+	16.1467i	−0.464377	+	0.804324i
$404$	−0.885376	+	0.511172i	−0.0440491	+	0.0254318i
$405$	18.2949	−	6.98002i	0.909080	−	0.346840i
$406$	−23.4805	−	9.98177i	−1.16532	−	0.495387i
$407$		−	24.8575i		−	1.23214i
$408$	−7.81236	−	1.34651i	−0.386769	−	0.0666620i
$409$	17.1352	−	29.6790i	0.847281	−	1.46753i	−0.0363445	−	0.999339i	$-0.511571\pi$
$409$	17.1352	−	29.6790i	0.847281	−	1.46753i	0.883626	−	0.468194i	$-0.155095\pi$
$410$	0.0426060	−	0.0737957i	0.00210416	−	0.00364451i
$411$	6.37529	−	36.9891i	0.314470	−	1.82454i
$412$			8.85384i			0.436197i
$413$	−28.2179	+	3.44934i	−1.38851	+	0.169731i
$414$	−6.18816	+	12.9887i	−0.304132	+	0.638360i
$415$	3.14929	+	5.45473i	0.154593	+	0.267762i
$416$	2.48373	+	1.43398i	0.121775	+	0.0703067i
$417$	23.8989	−	8.80294i	1.17033	−	0.431082i
$418$	−4.18540	−	7.24932i	−0.204714	−	0.354576i
$419$	−22.2454			−1.08676			−0.543380	−	0.839487i	$-0.682856\pi$
$419$	−22.2454			−1.08676			−0.543380	+	0.839487i	$0.682856\pi$
$420$	5.40243	−	8.37973i	0.263611	−	0.408889i
$421$		−	11.6545i		−	0.568007i	−0.958823	−	0.284003i	$-0.908337\pi$
$421$		−	11.6545i		−	0.568007i	0.958823	−	0.284003i	$-0.0916627\pi$
$422$	−12.5953	+	7.27187i	−0.613127	+	0.353989i
$423$	5.30061	−	14.9201i	0.257725	−	0.725442i
$424$	−9.31013	−	5.37521i	−0.452140	−	0.261043i
$425$	−0.609598	−	1.05586i	−0.0295699	−	0.0512165i
$426$	−4.64466	−	3.86692i	−0.225034	−	0.187353i
$427$	1.23797	−	2.91213i	0.0599096	−	0.140928i
$428$	−0.770699			−0.0372531
$429$	−3.51098	+	20.3705i	−0.169512	+	0.983498i
$430$	4.25606	−	7.37171i	0.205245	−	0.355496i
$431$	13.8153	−	23.9289i	0.665461	−	1.15261i	−0.313699	−	0.949523i	$-0.601568\pi$
$431$	13.8153	−	23.9289i	0.665461	−	1.15261i	0.979160	−	0.203090i	$-0.0650985\pi$
$432$	5.19581	−	0.0600767i	0.249983	−	0.00289044i
$433$			23.8684i			1.14704i	0.819191	+	0.573521i	$0.194423\pi$
$433$			23.8684i			1.14704i	−0.819191	+	0.573521i	$0.805577\pi$
$434$	10.3439	+	13.7421i	0.496521	+	0.659642i
$435$	−23.2517	+	27.9282i	−1.11483	+	1.33905i
$436$	11.6326	−	6.71606i	0.557098	−	0.321641i
$437$	−8.80748	+	3.93683i	−0.421319	+	0.188324i
$438$	−3.98670	−	10.8234i	−0.190492	−	0.517162i
$439$	11.1108	+	19.2445i	0.530291	+	0.918491i	0.999375	+	0.0353377i	$0.0112507\pi$
$439$	11.1108	+	19.2445i	0.530291	+	0.918491i	−0.469084	+	0.883153i	$0.655416\pi$
$440$			9.05361i			0.431614i
$441$	−8.66855	−	19.1274i	−0.412788	−	0.910827i
$442$			13.1266i			0.624368i
$443$	−16.8557	+	9.73165i	−0.800839	+	0.462365i	−0.843765	−	0.536714i	$-0.819666\pi$
$443$	−16.8557	+	9.73165i	−0.800839	+	0.462365i	0.0429253	+	0.999078i	$0.486332\pi$
$444$	3.57616	+	9.70882i	0.169717	+	0.460760i
$445$	−8.84734	+	15.3240i	−0.419404	+	0.726429i
$446$	−4.49398	+	2.59460i	−0.212796	+	0.122858i
$447$	20.7350	+	17.2630i	0.980732	+	0.816511i
$448$	2.11385	−	1.59112i	0.0998698	−	0.0751733i
$449$			13.7320i			0.648053i	0.946048	+	0.324027i	$0.105037\pi$
$449$			13.7320i			0.648053i	−0.946048	+	0.324027i	$0.894963\pi$
$450$	0.518373	+	0.608191i	0.0244364	+	0.0286704i
$451$	0.141143	+	0.0814889i	0.00664616	+	0.00383716i
$452$	1.33818	−	2.31779i	0.0629426	−	0.109020i
$453$	−4.08219	+	23.6847i	−0.191798	+	1.11280i
$454$			17.6962i			0.830522i
$455$	−15.1931	−	6.45871i	−0.712263	−	0.302789i
$456$	2.67766	+	2.22929i	0.125393	+	0.104396i
$457$	−24.4212	+	14.0996i	−1.14238	+	0.659552i	−0.947018	−	0.321180i	$-0.895921\pi$
$457$	−24.4212	+	14.0996i	−1.14238	+	0.659552i	−0.195359	+	0.980732i	$0.562587\pi$
$458$	−8.13205	+	14.0851i	−0.379986	+	0.658155i
$459$	12.1287	+	20.4575i	0.566117	+	0.954875i
$460$	10.3787	+	1.07546i	0.483908	+	0.0501435i
$461$			2.62141i			0.122091i	0.998135	+	0.0610456i	$0.0194435\pi$
$461$			2.62141i			0.122091i	−0.998135	+	0.0610456i	$0.980556\pi$
$462$	16.0272	+	10.3328i	0.745654	+	0.480724i
$463$	−23.3142			−1.08350			−0.541751	−	0.840539i	$-0.682239\pi$
$463$	−23.3142			−1.08350			−0.541751	+	0.840539i	$0.682239\pi$
$464$	−8.35146	+	4.82172i	−0.387707	+	0.223843i
$465$	22.9885	−	8.46760i	1.06607	−	0.392676i
$466$	−3.45703	+	5.98775i	−0.160144	+	0.277377i
$467$	−9.04858	−	15.6726i	−0.418718	−	0.725241i	0.577093	−	0.816679i	$-0.304187\pi$
$467$	−9.04858	−	15.6726i	−0.418718	−	0.725241i	−0.995811	+	0.0914376i	$0.970854\pi$
$468$	−1.55931	−	8.46140i	−0.0720794	−	0.391128i
$469$	−23.4090	+	2.86151i	−1.08093	+	0.132132i
$470$	−11.4831			−0.529676
$471$	−33.7023	−	5.80879i	−1.55292	−	0.267655i
$472$	−5.37237	+	9.30521i	−0.247283	+	0.428307i
$473$	14.0993	+	8.14022i	0.648285	+	0.374288i
$474$	−1.07414	+	6.23211i	−0.0493369	+	0.286250i
$475$			0.535842i			0.0245861i
$476$	11.1443	+	4.73755i	0.510800	+	0.217145i
$477$	5.84502	+	31.7172i	0.267625	+	1.45223i
$478$	−2.12537	−	3.68124i	−0.0972120	−	0.168376i
$479$	−11.5695	+	20.0390i	−0.528624	+	0.915603i	0.470819	+	0.882230i	$0.343958\pi$
$479$	−11.5695	+	20.0390i	−0.528624	+	0.915603i	−0.999443	+	0.0333736i	$0.989375\pi$
$480$	−1.30251	−	3.53615i	−0.0594511	−	0.161402i
$481$	14.8367	−	8.56596i	0.676494	−	0.390574i
$482$	−8.68662			−0.395665
$483$	13.7489	−	17.1455i	0.625596	−	0.780147i
$484$	−6.31610			−0.287096
$485$	−20.0173	+	11.5570i	−0.908939	+	0.524776i
$486$	−10.2483	−	11.7462i	−0.464873	−	0.532817i
$487$	12.6837	−	21.9688i	0.574754	−	0.995503i	−0.421314	−	0.906915i	$-0.638431\pi$
$487$	12.6837	−	21.9688i	0.574754	−	0.995503i	0.996068	−	0.0885882i	$-0.0282355\pi$
$488$	−0.598005	−	1.03577i	−0.0270704	−	0.0468873i
$489$	27.0501	+	22.5207i	1.22325	+	1.01842i
$490$	−10.9668	+	10.5678i	−0.495428	+	0.477403i
$491$		−	15.4798i		−	0.698594i	−0.937012	−	0.349297i	$-0.886420\pi$
$491$		−	15.4798i		−	0.698594i	0.937012	−	0.349297i	$-0.113580\pi$
$492$	−0.0668509	−	0.0115221i	−0.00301387	−	0.000519458i
$493$	−38.2244	−	22.0689i	−1.72154	−	0.993932i
$494$	2.88459	−	4.99626i	0.129784	−	0.224793i
$495$	20.6712	−	17.6185i	0.929102	−	0.791893i
$496$	6.50100			0.291903
$497$	5.55191	+	7.37587i	0.249037	+	0.330853i
$498$	3.20827	−	3.85354i	0.143766	−	0.172681i
$499$	0.671368	+	1.16284i	0.0300546	+	0.0520560i	0.880661	−	0.473746i	$-0.157099\pi$
$499$	0.671368	+	1.16284i	0.0300546	+	0.0520560i	−0.850607	+	0.525802i	$0.823765\pi$
$500$	5.72900	−	9.92292i	0.256209	−	0.443766i
$501$	7.43375	+	20.1817i	0.332115	+	0.901652i
$502$	−2.61484	+	1.50968i	−0.116706	+	0.0673803i
$503$	22.3915			0.998390			0.499195	−	0.866490i	$-0.333629\pi$
$503$	22.3915			0.998390			0.499195	+	0.866490i	$0.333629\pi$
$504$	−7.74643	−	1.72999i	−0.345053	−	0.0770598i
$505$		−	2.22430i		−	0.0989802i
$506$	−2.05694	+	19.8504i	−0.0914421	+	0.882459i
$507$	7.76048	−	2.85850i	0.344655	−	0.126951i
$508$	9.85035	−	17.0613i	0.437038	−	0.756973i
$509$	10.1671	−	5.86996i	0.450648	−	0.260182i	−0.257456	−	0.966290i	$-0.582884\pi$
$509$	10.1671	−	5.86996i	0.450648	−	0.260182i	0.708104	+	0.706108i	$0.249551\pi$
$510$	11.0357	−	13.2553i	0.488670	−	0.586953i
$511$	2.13781	+	17.4887i	0.0945713	+	0.773655i
$512$		−	1.00000i		−	0.0441942i
$513$	−0.120850	−	10.4519i	−0.00533567	−	0.461462i
$514$	4.94886	−	8.57168i	0.218285	−	0.378081i
$515$	−16.6824	−	9.63160i	−0.735115	−	0.424419i
$516$	−6.67798	−	1.15099i	−0.293981	−	0.0506694i
$517$		−	21.9628i		−	0.965922i
$518$	−1.91767	−	15.6878i	−0.0842574	−	0.689281i
$519$	−13.4717	+	16.1811i	−0.591341	+	0.710274i
$520$	−5.40382	+	3.11990i	−0.236973	+	0.136816i
$521$	20.5002	−	35.5073i	0.898128	−	1.55560i	0.0682441	−	0.997669i	$-0.478260\pi$
$521$	20.5002	−	35.5073i	0.898128	−	1.55560i	0.829884	−	0.557935i	$-0.188406\pi$
$522$	27.2611	+	9.68491i	1.19318	+	0.423897i
$523$	−26.8318	+	15.4914i	−1.17327	+	0.677390i	−0.954449	−	0.298375i	$-0.903556\pi$
$523$	−26.8318	+	15.4914i	−1.17327	+	0.677390i	−0.218824	+	0.975764i	$0.570222\pi$
$524$			11.9910i			0.523828i
$525$	−0.557786	−	1.08580i	−0.0243438	−	0.0473881i
$526$		−	9.09912i		−	0.396741i
$527$	14.8774	+	25.7685i	0.648072	+	1.12249i
$528$	6.76330	−	2.49120i	0.294335	−	0.108416i
$529$	22.5113	+	4.71597i	0.978753	+	0.205042i
$530$	20.2559	−	11.6948i	0.879862	−	0.507989i
$531$	31.7004	−	5.84193i	1.37568	−	0.253518i
$532$	−3.20069	−	4.25221i	−0.138768	−	0.184357i
$533$			0.112325i			0.00486534i
$534$	13.8819	+	2.39263i	0.600730	+	0.103539i
$535$	0.838401	−	1.45215i	0.0362472	−	0.0627820i
$536$	−4.45682	+	7.71944i	−0.192505	+	0.333429i
$537$	10.7673	+	1.85580i	0.464642	+	0.0800837i
$538$	−11.4862			−0.495205
$539$	−20.2121	−	20.9752i	−0.870596	−	0.903468i
$540$	−5.53903	+	9.85530i	−0.238362	+	0.424105i
$541$	−3.25399	−	5.63607i	−0.139900	−	0.242314i	0.787559	−	0.616240i	$-0.211345\pi$
$541$	−3.25399	−	5.63607i	−0.139900	−	0.242314i	−0.927459	+	0.373926i	$0.878011\pi$
$542$	−11.4578	−	6.61519i	−0.492156	−	0.284147i
$543$	5.87178	+	15.9412i	0.251982	+	0.684101i
$544$	3.96377	−	2.28849i	0.169945	−	0.0981180i
$545$			29.2241i			1.25182i
$546$	−0.644294	+	13.1268i	−0.0275732	+	0.561777i
$547$	21.6612			0.926166			0.463083	−	0.886315i	$-0.346743\pi$
$547$	21.6612			0.926166			0.463083	+	0.886315i	$0.346743\pi$
$548$	10.8353	+	18.7673i	0.462860	+	0.801697i
$549$	−1.20115	+	3.38100i	−0.0512639	+	0.144298i
$550$	0.959956	+	0.554231i	0.0409327	+	0.0236325i
$551$	9.69936	+	16.7998i	0.413207	+	0.715695i
$552$	−2.05241	−	8.04908i	−0.0873562	−	0.342591i
$553$	3.77926	−	8.89011i	0.160711	−	0.378046i
$554$		−	20.7412i		−	0.881208i
$555$	−22.1837	−	3.82349i	−0.941645	−	0.162298i
$556$	−7.35215	+	12.7343i	−0.311801	+	0.540054i
$557$	16.1230	−	27.9258i	0.683153	−	1.18326i	−0.290861	−	0.956765i	$-0.593942\pi$
$557$	16.1230	−	27.9258i	0.683153	−	1.18326i	0.974013	−	0.226490i	$-0.0727251\pi$
$558$	−12.6511	−	14.8431i	−0.535562	−	0.628358i
$559$			11.2205i			0.474579i
$560$	0.698453	+	5.71380i	0.0295150	+	0.241452i
$561$	25.3523	+	21.1071i	1.07037	+	0.891143i
$562$	10.4358	−	6.02510i	0.440207	−	0.254154i
$563$	−2.90147	+	5.02549i	−0.122282	+	0.211799i	−0.920667	−	0.390348i	$-0.872355\pi$
$563$	−2.90147	+	5.02549i	−0.122282	+	0.211799i	0.798385	+	0.602147i	$0.205688\pi$
$564$	3.15970	+	8.57819i	0.133047	+	0.361207i
$565$	2.91146	+	5.04280i	0.122486	+	0.212152i
$566$	14.5689			0.612376
$567$	11.1248	+	21.0532i	0.467197	+	0.884153i
$568$	3.48931			0.146408
$569$	−16.6912	−	28.9100i	−0.699731	−	1.21197i	−0.968560	−	0.248782i	$-0.919970\pi$
$569$	−16.6912	−	28.9100i	−0.699731	−	1.21197i	0.268828	−	0.963188i	$-0.413364\pi$
$570$	−7.11331	+	2.62012i	−0.297944	+	0.109745i
$571$	31.3200	+	18.0826i	1.31070	+	0.756735i	0.982213	−	0.187773i	$-0.0601268\pi$
$571$	31.3200	+	18.0826i	1.31070	+	0.756735i	0.328490	+	0.944507i	$0.393460\pi$
$572$	−5.96717	−	10.3354i	−0.249500	−	0.432146i
$573$	29.5136	+	24.5716i	1.23295	+	1.02649i
$574$	0.0953629	+	0.0405396i	0.00398037	+	0.00169209i
$575$	0.749377	−	1.03462i	0.0312512	−	0.0431465i
$576$	−2.28320	+	1.94602i	−0.0951334	+	0.0810841i
$577$	−15.6843	+	27.1660i	−0.652946	+	1.13094i	0.329458	+	0.944170i	$0.393134\pi$
$577$	−15.6843	+	27.1660i	−0.652946	+	1.13094i	−0.982404	+	0.186766i	$0.940199\pi$
$578$	3.41965	+	1.97434i	0.142239	+	0.0821217i
$579$	7.03710	−	40.8289i	0.292452	−	1.69679i
$580$		−	20.9811i		−	0.871194i
$581$	−6.11954	+	4.60626i	−0.253881	+	0.191100i
$582$	14.1414	+	11.7734i	0.586179	+	0.488025i
$583$	22.3676	+	38.7419i	0.926373	+	1.60453i
$584$	5.76714	+	3.32966i	0.238646	+	0.137782i
$585$	17.6393	+	6.26663i	0.729295	+	0.259093i
$586$	−7.78539	+	4.49490i	−0.321611	+	0.185682i
$587$		−	1.45529i		−	0.0600664i	−0.999549	−	0.0300332i	$-0.990439\pi$
$587$		−	1.45529i		−	0.0600664i	0.999549	−	0.0300332i	$-0.00956131\pi$
$588$	10.9120	+	5.28465i	0.450005	+	0.217935i
$589$		−	13.0774i		−	0.538845i
$590$	−11.6886	−	20.2453i	−0.481212	−	0.833484i
$591$	13.3273	+	36.1819i	0.548211	+	1.48833i
$592$	−5.17325	−	2.98678i	−0.212619	−	0.122756i
$593$	9.47194	−	5.46863i	0.388966	−	0.224570i	−0.292746	−	0.956190i	$-0.594569\pi$
$593$	9.47194	−	5.46863i	0.388966	−	0.224570i	0.681712	+	0.731621i	$0.261236\pi$
$594$	−18.8494	−	10.5941i	−0.773401	−	0.434679i
$595$	−21.0498	+	15.8445i	−0.862959	+	0.649560i
$596$	−15.5772			−0.638068
$597$	28.8566	+	4.97361i	1.18102	+	0.203556i
$598$	−12.5569	+	5.61278i	−0.513491	+	0.229524i
$599$	4.99124	+	2.88169i	0.203936	+	0.117743i	0.598490	−	0.801130i	$-0.295768\pi$
$599$	4.99124	+	2.88169i	0.203936	+	0.117743i	−0.394554	+	0.918873i	$0.629101\pi$
$600$	−0.454673	−	0.0783656i	−0.0185620	−	0.00319926i
$601$	41.2584			1.68296			0.841482	−	0.540286i	$-0.181684\pi$
$601$	41.2584			1.68296			0.841482	+	0.540286i	$0.181684\pi$
$602$	9.52614	+	4.04964i	0.388256	+	0.165051i
$603$	26.2981	−	4.84636i	1.07094	−	0.197359i
$604$	−6.93799	−	12.0170i	−0.282303	−	0.488963i
$605$	6.87094	−	11.9008i	0.279343	−	0.483837i
$606$	−1.66162	+	0.612042i	−0.0674986	+	0.0248625i
$607$	−5.72505	−	9.91607i	−0.232372	−	0.402481i	0.726133	−	0.687554i	$-0.241315\pi$
$607$	−5.72505	−	9.91607i	−0.232372	−	0.402481i	−0.958506	+	0.285073i	$0.907982\pi$
$608$	−2.01160			−0.0815811
$609$	−37.1420	−	23.9455i	−1.50507	−	0.970320i
$610$	2.60214			0.105358
$611$	13.1089	−	7.56842i	0.530329	−	0.306186i
$612$	−12.9387	−	4.59666i	−0.523014	−	0.185809i
$613$	−18.8621	−	10.8900i	−0.761832	−	0.439844i	0.0681212	−	0.997677i	$-0.478300\pi$
$613$	−18.8621	−	10.8900i	−0.761832	−	0.439844i	−0.829953	+	0.557833i	$0.811633\pi$
$614$	−7.76337	+	4.48218i	−0.313304	+	0.180886i
$615$	0.0944335	−	0.113426i	0.00380792	−	0.00457379i
$616$	−10.9283	+	1.33587i	−0.440315	+	0.0538239i
$617$	18.7690			0.755612			0.377806	−	0.925885i	$-0.376679\pi$
$617$	18.7690			0.755612			0.377806	+	0.925885i	$0.376679\pi$
$618$	−2.60472	+	15.1125i	−0.104777	+	0.607913i
$619$	−17.2410	−	9.95412i	−0.692976	−	0.400090i	0.111750	−	0.993736i	$-0.464354\pi$
$619$	−17.2410	−	9.95412i	−0.692976	−	0.400090i	−0.804726	+	0.593646i	$0.797688\pi$
$620$	−7.07207	+	12.2492i	−0.284021	+	0.491939i
$621$	−14.3836	+	20.3497i	−0.577196	+	0.816606i
$622$	−23.2031			−0.930359
$623$	−19.8026	−	8.41825i	−0.793374	−	0.337270i
$624$	3.81757	+	3.17833i	0.152825	+	0.127235i
$625$	11.7986	+	20.4357i	0.471943	+	0.817430i
$626$	6.82766	−	11.8259i	0.272888	−	0.472656i
$627$	−5.01130	−	13.6051i	−0.200132	−	0.543333i
$628$	17.0996	−	9.87247i	0.682349	−	0.393954i
$629$		−	27.3408i		−	1.09015i
$630$	11.6866	−	12.7139i	0.465604	−	0.506533i
$631$		−	19.6361i		−	0.781701i	−0.920454	−	0.390850i	$-0.872181\pi$
$631$		−	19.6361i		−	0.781701i	0.920454	−	0.390850i	$-0.127819\pi$
$632$	−1.82558	−	3.16200i	−0.0726177	−	0.125778i
$633$	−23.6380	+	8.70683i	−0.939524	+	0.346065i
$634$	−5.35808	+	9.28047i	−0.212797	+	0.368575i
$635$	21.4313	+	37.1201i	0.850475	+	1.47307i
$636$	−14.3100	−	11.9138i	−0.567427	−	0.472413i
$637$	5.55434	−	19.2921i	0.220071	−	0.764380i
$638$	40.1289			1.58872
$639$	−6.79027	−	7.96681i	−0.268619	−	0.315162i
$640$	1.88420	+	1.08784i	0.0744796	+	0.0430008i
$641$	−24.1188	+	41.7750i	−0.952636	+	1.65001i	−0.212950	+	0.977063i	$0.568307\pi$
$641$	−24.1188	+	41.7750i	−0.952636	+	1.65001i	−0.739687	+	0.672952i	$0.765026\pi$
$642$	−1.31549	−	0.226733i	−0.0519184	−	0.00894844i
$643$		−	37.6629i		−	1.48528i	−0.669691	−	0.742640i	$-0.733573\pi$
$643$		−	37.6629i		−	1.48528i	0.669691	−	0.742640i	$-0.266427\pi$
$644$	0.233237	+	12.6864i	0.00919082	+	0.499916i
$645$	9.43329	−	11.3306i	0.371436	−	0.446140i
$646$	−4.60352	−	7.97353i	−0.181123	−	0.313714i
$647$	−17.8203	−	10.2885i	−0.700588	−	0.404484i	0.106979	−	0.994261i	$-0.465882\pi$
$647$	−17.8203	−	10.2885i	−0.700588	−	0.404484i	−0.807566	+	0.589777i	$0.799216\pi$
$648$	8.88631	+	1.42602i	0.349087	+	0.0560192i
$649$	38.7214	−	22.3558i	1.51995	−	0.877543i
$650$			0.763957i			0.0299648i
$651$	13.6129	+	26.4992i	0.533533	+	1.03859i
$652$	−20.3215			−0.795852
$653$	35.5826	−	20.5436i	1.39246	−	0.803935i	0.398869	−	0.917008i	$-0.369403\pi$
$653$	35.5826	−	20.5436i	1.39246	−	0.803935i	0.993587	+	0.113073i	$0.0360694\pi$
$654$	21.8312	−	8.04134i	0.853669	−	0.314441i
$655$	−22.5934	−	13.0443i	−0.882797	−	0.509683i
$656$	0.0339183	−	0.0195827i	0.00132429	−	0.000764578i
$657$	−3.62068	−	19.6471i	−0.141256	−	0.766507i
$658$	−1.69435	−	13.8609i	−0.0660525	−	0.540353i
$659$	24.4698			0.953208			0.476604	−	0.879118i	$-0.341868\pi$
$659$	24.4698			0.953208			0.476604	+	0.879118i	$0.341868\pi$
$660$	−2.66349	+	15.4535i	−0.103676	+	0.601525i
$661$	−38.0891	−	21.9908i	−1.48150	−	0.855342i	−0.481716	−	0.876327i	$-0.659986\pi$
$661$	−38.0891	−	21.9908i	−1.48150	−	0.855342i	−0.999780	+	0.0209852i	$0.993320\pi$
$662$	−0.383637	−	0.221493i	−0.0149105	−	0.00860856i
$663$	−3.86173	+	22.4055i	−0.149977	+	0.870159i
$664$			2.89498i			0.112347i
$665$	11.4939	−	1.40501i	0.445714	−	0.0544838i
$666$	3.24783	+	17.6239i	0.125851	+	0.682912i
$667$	4.76682	−	46.0020i	0.184572	−	1.78120i
$668$	−10.7536	−	6.20861i	−0.416070	−	0.240218i
$669$	−8.43402	+	3.10659i	−0.326078	+	0.120108i
$670$	−9.69666	−	16.7951i	−0.374615	−	0.648852i
$671$			4.97691i			0.192131i
$672$	4.07618	−	2.09398i	0.157242	−	0.0807770i
$673$	16.0428			0.618404			0.309202	−	0.950996i	$-0.399938\pi$
$673$	16.0428			0.618404			0.309202	+	0.950996i	$0.399938\pi$
$674$	−0.308622	−	0.534549i	−0.0118877	−	0.0205900i
$675$	0.705879	+	1.19061i	0.0271693	+	0.0458267i
$676$	−2.38740	+	4.13510i	−0.0918231	+	0.159042i
$677$	1.74465	+	3.02183i	0.0670525	+	0.116138i	0.897603	−	0.440806i	$-0.145307\pi$
$677$	1.74465	+	3.02183i	0.0670525	+	0.116138i	−0.830550	+	0.556944i	$0.811974\pi$
$678$	2.96599	−	3.56252i	0.113908	−	0.136818i
$679$	−16.9037	−	22.4570i	−0.648703	−	0.861820i
$680$			9.95807i			0.381875i
$681$	−5.20606	+	30.2053i	−0.199497	+	1.15747i
$682$	−23.4280	−	13.5262i	−0.897105	−	0.517944i
$683$	−21.4107	−	12.3615i	−0.819258	−	0.472999i	0.0309028	−	0.999522i	$-0.490162\pi$
$683$	−21.4107	−	12.3615i	−0.819258	−	0.472999i	−0.850160	+	0.526524i	$0.823495\pi$
$684$	3.91461	+	4.59289i	0.149679	+	0.175613i
$685$	−47.1484			−1.80145
$686$	−14.3742	−	11.6783i	−0.548808	−	0.445881i
$687$	−18.0242	+	21.6493i	−0.687665	+	0.825972i
$688$	3.38822	−	1.95619i	0.129175	−	0.0745790i
$689$	−15.4159	+	26.7011i	−0.587298	+	1.01723i
$690$	17.3988	+	4.88900i	0.662360	+	0.186121i
$691$	6.24465	+	10.8160i	0.237558	+	0.411462i	0.960013	−	0.279956i	$-0.0903198\pi$
$691$	6.24465	+	10.8160i	0.237558	+	0.411462i	−0.722455	+	0.691418i	$0.756987\pi$
$692$		−	12.1561i		−	0.462107i
$693$	24.3168	+	22.3519i	0.923718	+	0.849079i
$694$	−7.87253			−0.298837
$695$	−15.9960	−	27.7059i	−0.606762	−	1.05094i
$696$	−15.6735	+	5.77318i	−0.594102	+	0.218832i
$697$	0.155243	+	0.0896297i	0.00588025	+	0.00339497i
$698$	6.30244	−	3.63871i	0.238551	−	0.137727i
$699$	−7.66229	+	9.20337i	−0.289815	+	0.348103i
$700$	0.648592	+	0.275722i	0.0245145	+	0.0104213i
$701$	0.721810			0.0272624			0.0136312	−	0.999907i	$-0.495661\pi$
$701$	0.721810			0.0272624			0.0136312	+	0.999907i	$0.495661\pi$
$702$	−0.172298	−	14.9014i	−0.00650295	−	0.562416i
$703$	−6.00820	+	10.4065i	−0.226604	+	0.392489i
$704$	−2.08063	+	3.60376i	−0.0784167	+	0.135822i
$705$	−19.6003	−	3.37823i	−0.738190	−	0.127231i
$706$	4.76092			0.179180
$707$	2.68488	−	0.328199i	0.100975	−	0.0123432i
$708$	−11.9075	+	14.3024i	−0.447512	+	0.537518i
$709$	−2.76380	+	1.59568i	−0.103797	+	0.0599270i	−0.551000	−	0.834505i	$-0.685753\pi$
$709$	−2.76380	+	1.59568i	−0.103797	+	0.0599270i	0.447203	+	0.894432i	$0.352420\pi$
$710$	−3.79583	+	6.57457i	−0.142455	+	0.246739i
$711$	−3.66686	+	10.3215i	−0.137518	+	0.387086i
$712$	−7.04330	+	4.06645i	−0.263959	+	0.152397i
$713$	−18.2888	+	25.2501i	−0.684920	+	0.945624i
$714$	17.6283	+	11.3650i	0.659724	+	0.425325i
$715$	25.9654			0.971051
$716$	−5.46301	+	3.15407i	−0.204162	+	0.117873i
$717$	−2.54476	−	6.90872i	−0.0950359	−	0.258011i
$718$	−5.32757	−	3.07587i	−0.198823	−	0.114791i
$719$	−20.0086	+	11.5520i	−0.746196	+	0.430817i	−0.824318	−	0.566127i	$-0.808441\pi$
$719$	−20.0086	+	11.5520i	−0.746196	+	0.430817i	0.0781216	+	0.996944i	$0.475108\pi$
$720$	−1.18293	−	6.41898i	−0.0440850	−	0.239221i
$721$	9.16448	−	21.5580i	0.341303	−	0.802861i
$722$		−	14.9535i		−	0.556510i
$723$	−14.8270	−	2.55553i	−0.551424	−	0.0950411i
$724$	−8.49409	−	4.90407i	−0.315680	−	0.182258i
$725$	−2.22463	−	1.28439i	−0.0826207	−	0.0477011i
$726$	−10.7809	−	1.85814i	−0.400115	−	0.0689621i
$727$			44.9539i			1.66725i	0.552333	+	0.833624i	$0.313738\pi$
$727$			44.9539i			1.66725i	−0.552333	+	0.833624i	$0.686262\pi$
$728$	−4.56326	−	6.06243i	−0.169126	−	0.224688i
$729$	−14.0370	−	23.0643i	−0.519891	−	0.854233i
$730$	−12.5475	+	7.24430i	−0.464404	+	0.268124i
$731$	15.5078	+	8.95343i	0.573576	+	0.331154i
$732$	−0.716008	−	1.94387i	−0.0264644	−	0.0718476i
$733$	10.3529	−	5.97726i	0.382394	−	0.220775i	−0.296465	−	0.955044i	$-0.595808\pi$
$733$	10.3529	−	5.97726i	0.382394	−	0.220775i	0.678859	+	0.734268i	$0.262475\pi$
$734$	−29.5934			−1.09231
$735$	−21.8279	+	14.8116i	−0.805136	+	0.546334i
$736$	3.88404	+	2.81323i	0.143168	+	0.103697i
$737$	32.1226	−	18.5460i	1.18325	−	0.683151i
$738$	−0.110717	−	0.0393339i	−0.00407555	−	0.00144790i
$739$	−13.5567	+	23.4808i	−0.498690	+	0.863756i	−0.999999	−	0.00151219i	$-0.999519\pi$
$739$	−13.5567	+	23.4808i	−0.498690	+	0.863756i	0.501309	+	0.865268i	$0.332852\pi$
$740$	11.2554	−	6.49830i	0.413756	−	0.238882i
$741$	6.39352	−	7.67942i	0.234872	−	0.282110i
$742$	17.1052	+	22.7247i	0.627951	+	0.834250i
$743$	−42.6061			−1.56307			−0.781533	−	0.623864i	$-0.785562\pi$
$743$	−42.6061			−1.56307			−0.781533	+	0.623864i	$0.785562\pi$
$744$	11.0964	+	1.91254i	0.406815	+	0.0701170i
$745$	16.9456	−	29.3507i	0.620839	−	1.07532i
$746$	14.0099	−	24.2659i	0.512941	−	0.888439i
$747$	6.60983	−	5.63369i	0.241841	−	0.206126i
$748$	−19.0460			−0.696390
$749$	1.87655	+	0.797739i	0.0685678	+	0.0291487i
$750$	12.6980	−	15.2518i	0.463664	−	0.556919i
$751$	29.0074	−	16.7474i	1.05849	−	0.611122i	0.133479	−	0.991052i	$-0.457385\pi$
$751$	29.0074	−	16.7474i	1.05849	−	0.611122i	0.925015	+	0.379929i	$0.124052\pi$
$752$	−4.57081	−	2.63896i	−0.166680	−	0.0962328i
$753$	−4.90736	+	1.80758i	−0.178834	+	0.0658720i
$754$	13.8285	+	23.9517i	0.503604	+	0.872268i
$755$	30.1898			1.09872
$756$	−12.7133	−	5.23182i	−0.462378	−	0.190279i
$757$		−	4.66121i		−	0.169415i	−0.996406	−	0.0847073i	$-0.973004\pi$
$757$		−	4.66121i		−	0.169415i	0.996406	−	0.0847073i	$-0.0269955\pi$
$758$	13.1749	+	22.8197i	0.478535	+	0.828848i
$759$	−9.35078	+	33.2772i	−0.339412	+	1.20789i
$760$	2.18831	−	3.79026i	0.0793783	−	0.137487i
$761$	−38.1246	+	22.0113i	−1.38202	+	0.797908i	−0.992398	−	0.123069i	$-0.960726\pi$
$761$	−38.1246	+	22.0113i	−1.38202	+	0.797908i	−0.389618	+	0.920976i	$0.627393\pi$
$762$	21.8327	−	26.2238i	0.790915	−	0.949987i
$763$	−35.2755	+	4.31206i	−1.27706	+	0.156107i
$764$	−22.1722			−0.802160
$765$	22.7363	−	19.3786i	0.822032	−	0.700635i
$766$	21.9476	+	12.6715i	0.793000	+	0.457839i
$767$	26.6870	+	15.4077i	0.963611	+	0.556341i
$768$	0.294191	−	1.70688i	0.0106157	−	0.0615919i
$769$			21.0033i			0.757397i	0.925520	+	0.378699i	$0.123628\pi$
$769$			21.0033i			0.757397i	−0.925520	+	0.378699i	$0.876372\pi$
$770$	9.37126	−	22.0444i	0.337717	−	0.794424i
$771$	10.9688	−	13.1750i	0.395033	−	0.474484i
$772$	11.9601	+	20.7155i	0.430453	+	0.745566i
$773$	−5.95221	+	10.3095i	−0.214086	+	0.370808i	−0.952989	−	0.303003i	$-0.902011\pi$
$773$	−5.95221	+	10.3095i	−0.214086	+	0.370808i	0.738903	+	0.673811i	$0.235344\pi$
$774$	−11.0599	−	3.92920i	−0.397540	−	0.141232i
$775$	0.865856	+	1.49971i	0.0311025	+	0.0538710i
$776$	−10.6238			−0.381371
$777$	1.34197	−	27.3414i	0.0481430	−	0.980866i
$778$			9.26084i			0.332017i
$779$	−0.0393926	−	0.0682300i	−0.00141139	−	0.00244459i
$780$	−10.1415	+	3.73554i	−0.363125	+	0.133754i
$781$	−12.5746	−	7.25997i	−0.449956	−	0.259782i
$782$	−2.26243	+	21.8335i	−0.0809043	+	0.780764i
$783$	43.6822	+	24.5510i	1.56108	+	0.877380i
$784$	−6.79388	+	1.68616i	−0.242639	+	0.0602200i
$785$			42.9588i			1.53327i
$786$	−3.52764	+	20.4672i	−0.125827	+	0.730040i
$787$	−19.4773	−	11.2452i	−0.694289	−	0.400848i	0.110928	−	0.993828i	$-0.464618\pi$
$787$	−19.4773	−	11.2452i	−0.694289	−	0.400848i	−0.805217	+	0.592980i	$0.797951\pi$
$788$	−19.2792	−	11.1308i	−0.686793	−	0.396520i
$789$	2.67688	−	15.5311i	0.0952995	−	0.552923i
$790$	7.94379			0.282627
$791$	−5.65741	+	4.25840i	−0.201154	+	0.151411i
$792$	12.2771	−	2.26248i	0.436246	−	0.0803939i
$793$	−2.97056	+	1.71505i	−0.105488	+	0.0609033i
$794$	−10.3065	−	5.95046i	−0.365764	−	0.211174i
$795$	38.0150	−	14.0025i	1.34825	−	0.496617i
$796$	−14.6411	+	8.45302i	−0.518939	+	0.299609i
$797$	−35.3416			−1.25186			−0.625932	−	0.779878i	$-0.715281\pi$
$797$	−35.3416			−1.25186			−0.625932	+	0.779878i	$0.715281\pi$
$798$	−4.21225	−	8.19964i	−0.149112	−	0.290264i
$799$		−	24.1569i		−	0.854608i
$800$	0.230689	−	0.133188i	0.00815607	−	0.00470891i
$801$	22.9909	+	8.16788i	0.812345	+	0.288598i
$802$	−27.0564	−	15.6210i	−0.955396	−	0.551598i
$803$	−13.8556	−	23.9986i	−0.488953	−	0.846891i
$804$	−9.87827	+	11.8650i	−0.348380	+	0.418447i
$805$	−24.1575	−	13.3614i	−0.851441	−	0.470928i
$806$		−	18.6446i		−	0.656728i
$807$	−19.6056	−	3.37914i	−0.690150	−	0.118951i
$808$	0.511172	−	0.885376i	0.0179830	−	0.0311474i
$809$	1.62867	+	0.940312i	0.0572609	+	0.0330596i	0.528357	−	0.849022i	$-0.322808\pi$
$809$	1.62867	+	0.940312i	0.0572609	+	0.0330596i	−0.471096	+	0.882082i	$0.656142\pi$
$810$	−12.3538	+	15.1923i	−0.434069	+	0.533804i
$811$	−31.2212			−1.09633			−0.548163	−	0.836372i	$-0.684673\pi$
$811$	−31.2212			−1.09633			−0.548163	+	0.836372i	$0.684673\pi$
$812$	25.3256	−	3.09579i	0.888755	−	0.108641i
$813$	−17.6111	−	14.6622i	−0.617647	−	0.514224i
$814$	12.4288	+	21.5272i	0.435628	+	0.754530i
$815$	22.1066	−	38.2898i	0.774362	−	1.34123i
$816$	7.43895	−	2.74007i	0.260415	−	0.0959217i
$817$	−3.93507	−	6.81574i	−0.137671	−	0.238453i
$818$			34.2704i			1.19824i
$819$	−4.96154	+	22.2165i	−0.173370	+	0.776306i
$820$			0.0852119i			0.00297573i
$821$	43.3045	−	25.0019i	1.51134	−	0.872572i	0.511426	−	0.859327i	$-0.329117\pi$
$821$	43.3045	−	25.0019i	1.51134	−	0.872572i	0.999912	−	0.0132444i	$-0.00421594\pi$
$822$	12.9734	+	35.2212i	0.452499	+	1.22848i
$823$	−8.91052	+	15.4335i	−0.310601	+	0.537977i	−0.978493	−	0.206282i	$-0.933864\pi$
$823$	−8.91052	+	15.4335i	−0.310601	+	0.537977i	0.667891	+	0.744259i	$0.267197\pi$
$824$	−4.42692	−	7.66765i	−0.154219	−	0.267115i
$825$	1.47548	+	1.22842i	0.0513697	+	0.0427680i
$826$	22.7127	−	17.0961i	0.790276	−	0.594851i
$827$	22.7207			0.790076			0.395038	−	0.918665i	$-0.370731\pi$
$827$	22.7207			0.790076			0.395038	+	0.918665i	$0.370731\pi$
$828$	−1.13525	−	14.3426i	−0.0394527	−	0.498441i
$829$	−4.64397	+	8.04359i	−0.161292	+	0.279365i	−0.935332	−	0.353771i	$-0.884899\pi$
$829$	−4.64397	+	8.04359i	−0.161292	+	0.279365i	0.774041	+	0.633136i	$0.218233\pi$
$830$	−5.45473	−	3.14929i	−0.189336	−	0.109313i
$831$	6.10187	−	35.4028i	0.211672	−	1.22811i
$832$	−2.86796			−0.0994287
$833$	−22.2313	−	23.0707i	−0.770268	−	0.799352i
$834$	−16.2956	+	19.5730i	−0.564270	+	0.677758i
$835$	23.3965	−	13.5080i	0.809671	−	0.467464i
$836$	7.24932	+	4.18540i	0.250723	+	0.144755i
$837$	−17.2272	−	29.0573i	−0.595459	−	1.00437i
$838$	19.2651	−	11.1227i	0.665502	−	0.384228i
$839$	27.5372			0.950690			0.475345	−	0.879800i	$-0.342323\pi$
$839$	27.5372			0.950690			0.475345	+	0.879800i	$0.342323\pi$
$840$	−0.488773	+	9.95827i	−0.0168643	+	0.343593i
$841$	−63.9959			−2.20675
$842$	5.82726	+	10.0931i	0.200821	+	0.347832i
$843$	19.5852	−	7.21403i	0.674550	−	0.248464i
$844$	7.27187	−	12.5953i	0.250308	−	0.433547i
$845$	−5.19424	−	8.99669i	−0.178687	−	0.309496i
$846$	2.86961	+	15.5715i	0.0986592	+	0.535360i
$847$	15.3789	+	6.53770i	0.528425	+	0.224638i
$848$	10.7504			0.369171
$849$	24.8674	+	4.28604i	0.853447	+	0.147097i
$850$	1.05586	+	0.609598i	0.0362155	+	0.0209091i
$851$	26.1543	−	11.6906i	0.896557	−	0.400749i
$852$	5.95585	+	1.02653i	0.204044	+	0.0351682i
$853$	−25.3052			−0.866434			−0.433217	−	0.901290i	$-0.642622\pi$
$853$	−25.3052			−0.866434			−0.433217	+	0.901290i	$0.642622\pi$
$854$	0.383950	+	3.14096i	0.0131385	+	0.107482i
$855$	−12.9124	+	2.37957i	−0.441595	+	0.0813797i
$856$	0.667445	−	0.385350i	0.0228128	−	0.0131710i
$857$	−11.8011	−	6.81335i	−0.403117	−	0.232740i	0.284711	−	0.958613i	$-0.408102\pi$
$857$	−11.8011	−	6.81335i	−0.403117	−	0.232740i	−0.687828	+	0.725874i	$0.741436\pi$
$858$	−7.14466	−	19.3969i	−0.243915	−	0.662199i
$859$	−10.4473	−	18.0952i	−0.356457	−	0.617402i	0.630909	−	0.775857i	$-0.282682\pi$
$859$	−10.4473	−	18.0952i	−0.356457	−	0.617402i	−0.987366	+	0.158455i	$0.949349\pi$
$860$			8.51212i			0.290261i
$861$	0.150847	+	0.0972513i	0.00514085	+	0.00331432i
$862$			27.6307i			0.941104i
$863$	−31.6450	+	18.2703i	−1.07721	+	0.621927i	−0.930142	−	0.367200i	$-0.880316\pi$
$863$	−31.6450	+	18.2703i	−1.07721	+	0.621927i	−0.147067	+	0.989127i	$0.546983\pi$
$864$	−4.46966	+	2.64993i	−0.152061	+	0.0901525i
$865$	22.9046	+	13.2240i	0.778781	+	0.449629i
$866$	−11.9342	−	20.6706i	−0.405540	−	0.702417i
$867$	5.25612	+	4.37600i	0.178507	+	0.148617i
$868$	−15.8291	−	6.72908i	−0.537274	−	0.228400i
$869$			15.1934i			0.515402i
$870$	6.17246	−	35.8123i	0.209266	−	1.21415i
$871$	22.1391	+	12.7820i	0.750154	+	0.433101i
$872$	−6.71606	+	11.6326i	−0.227434	+	0.393928i
$873$	20.6740	+	24.2562i	0.699710	+	0.820947i
$874$	5.65909	−	7.81313i	0.191421	−	0.264283i
$875$	−24.2204	+	18.2310i	−0.818800	+	0.616321i
$876$	8.86428	+	7.37998i	0.299496	+	0.249346i
$877$	11.2827	+	19.5422i	0.380989	+	0.659892i	0.991204	−	0.132344i	$-0.0422503\pi$
$877$	11.2827	+	19.5422i	0.380989	+	0.659892i	−0.610215	+	0.792236i	$0.708917\pi$
$878$	−19.2445	−	11.1108i	−0.649471	−	0.374972i
$879$	−14.6111	+	5.38187i	−0.492821	+	0.181526i
$880$	−4.52681	−	7.84066i	−0.152599	−	0.264309i
$881$	14.4371			0.486399			0.243199	−	0.969976i	$-0.421803\pi$
$881$	14.4371			0.486399			0.243199	+	0.969976i	$0.421803\pi$
$882$	17.0709	+	12.2305i	0.574806	+	0.411823i
$883$	−44.6551			−1.50276			−0.751382	−	0.659867i	$-0.770612\pi$
$883$	−44.6551			−1.50276			−0.751382	+	0.659867i	$0.770612\pi$
$884$	−6.56329	−	11.3679i	−0.220747	−	0.382346i
$885$	−13.9951	−	37.9950i	−0.470440	−	1.27719i
$886$	9.73165	−	16.8557i	0.326941	−	0.566279i
$887$	−45.8168	+	26.4523i	−1.53838	+	0.888182i	−0.539443	+	0.842022i	$0.681365\pi$
$887$	−45.8168	+	26.4523i	−1.53838	+	0.888182i	−0.998934	+	0.0461598i	$0.985302\pi$
$888$	−7.95145	−	6.62001i	−0.266833	−	0.222153i
$889$	−41.6442	+	31.3461i	−1.39670	+	1.05132i
$890$		−	17.6947i		−	0.593127i
$891$	−29.0571	−	23.6281i	−0.973449	−	0.791573i
$892$	2.59460	−	4.49398i	0.0868737	−	0.150470i
$893$	−5.30852	+	9.19463i	−0.177643	+	0.307687i
$894$	−26.5885	−	4.58269i	−0.889253	−	0.153268i
$895$		−	13.7246i		−	0.458761i
$896$	−1.03508	+	2.43487i	−0.0345798	+	0.0813433i
$897$	−23.0844	+	5.88622i	−0.770767	+	0.196535i
$898$	−6.86600	−	11.8923i	−0.229121	−	0.396850i
$899$	54.2928	+	31.3460i	1.81077	+	1.04545i
$900$	−0.753020	−	0.267522i	−0.0251007	−	0.00891740i
$901$	24.6022	+	42.6122i	0.819617	+	1.41962i
$902$	−0.162978			−0.00542657
$903$	15.0686	+	9.71478i	0.501453	+	0.323288i
$904$			2.67636i			0.0890143i
$905$	18.4805	−	10.6697i	0.614313	−	0.354674i
$906$	−8.30706	−	22.5526i	−0.275984	−	0.749261i
$907$	−8.58561	−	4.95691i	−0.285081	−	0.164591i	0.350641	−	0.936510i	$-0.385964\pi$
$907$	−8.58561	−	4.95691i	−0.285081	−	0.164591i	−0.635721	+	0.771919i	$0.719297\pi$
$908$	−8.84808	−	15.3253i	−0.293634	−	0.508589i
$909$	−3.01624	+	0.555850i	−0.100043	+	0.0184364i
$910$	16.3870	−	2.00314i	0.543222	−	0.0664033i
$911$	−37.5002			−1.24244			−0.621218	−	0.783638i	$-0.713362\pi$
$911$	−37.5002			−1.24244			−0.621218	+	0.783638i	$0.713362\pi$
$912$	−3.43357	−	0.591795i	−0.113697	−	0.0195963i
$913$	6.02339	−	10.4328i	0.199345	−	0.345276i
$914$	14.0996	−	24.4212i	0.466374	−	0.807783i
$915$	4.44156	+	0.765528i	0.146833	+	0.0253076i
$916$		−	16.2641i		−	0.537381i
$917$	12.4117	−	29.1965i	0.409869	−	0.964152i
$918$	−20.7325	−	11.6524i	−0.684274	−	0.384586i
$919$	45.2323	−	26.1149i	1.49207	−	0.861450i	0.492116	−	0.870530i	$-0.336224\pi$
$919$	45.2323	−	26.1149i	1.49207	−	0.861450i	0.999959	+	0.00907961i	$0.00289017\pi$
$920$	−9.52592	+	4.25796i	−0.314060	+	0.140381i
$921$	−14.5698	+	5.36665i	−0.480091	+	0.176837i
$922$	−1.31070	−	2.27021i	−0.0431657	−	0.0747653i
$923$		−	10.0072i		−	0.329391i
$924$	−19.0464	−	0.934837i	−0.626580	−	0.0307539i
$925$		−	1.59121i		−	0.0523188i
$926$	20.1907	−	11.6571i	0.663507	−	0.383076i
$927$	−8.89192	+	25.0289i	−0.292049	+	0.822058i
$928$	4.82172	−	8.35146i	0.158281	−	0.274150i
$929$	−44.7236	+	25.8212i	−1.46733	+	0.847166i	−0.999331	−	0.0365608i	$-0.988360\pi$
$929$	−44.7236	+	25.8212i	−1.46733	+	0.847166i	−0.468003	+	0.883727i	$0.655026\pi$
$930$	−15.6748	+	18.8274i	−0.513997	+	0.617375i
$931$	3.39188	+	13.6666i	0.111164	+	0.447904i
$932$		−	6.91406i		−	0.226478i
$933$	−39.6050	−	6.82615i	−1.29661	−	0.223478i
$934$	15.6726	+	9.04858i	0.512823	+	0.296078i
$935$	20.7191	−	35.8865i	0.677586	−	1.17361i
$936$	5.58111	+	6.54813i	0.182424	+	0.214032i
$937$		−	47.6042i		−	1.55516i	−0.628783	−	0.777581i	$-0.716447\pi$
$937$		−	47.6042i		−	1.55516i	0.628783	−	0.777581i	$-0.283553\pi$
$938$	18.8421	−	14.1827i	0.615215	−	0.463080i
$939$	15.1331	−	18.1767i	0.493849	−	0.593175i
$940$	9.94465	−	5.74155i	0.324359	−	0.187269i
$941$	−1.37681	+	2.38471i	−0.0448828	+	0.0777393i	−0.887594	−	0.460626i	$-0.847625\pi$
$941$	−1.37681	+	2.38471i	−0.0448828	+	0.0777393i	0.842711	+	0.538366i	$0.180958\pi$
$942$	32.0915	−	11.8206i	1.04560	−	0.385136i
$943$	−0.0193598	+	0.186831i	−0.000630441	+	0.00608404i
$944$		−	10.7447i		−	0.349711i
$945$	23.6879	−	18.2630i	0.770568	−	0.594096i
$946$	−16.2804			−0.529323
$947$	−8.26782	+	4.77343i	−0.268668	+	0.155116i	−0.628282	−	0.777986i	$-0.716242\pi$
$947$	−8.26782	+	4.77343i	−0.268668	+	0.155116i	0.359614	+	0.933101i	$0.382908\pi$
$948$	−2.18582	−	5.93423i	−0.0709922	−	0.192735i
$949$	9.54933	−	16.5399i	0.309984	−	0.536909i
$950$	−0.267921	−	0.464053i	−0.00869251	−	0.0150559i
$951$	−11.8759	+	14.2644i	−0.385101	+	0.462554i
$952$	−12.0201	+	1.46933i	−0.389572	+	0.0476212i
$953$	−42.1950			−1.36683			−0.683416	−	0.730029i	$-0.739506\pi$
$953$	−42.1950			−1.36683			−0.683416	+	0.730029i	$0.739506\pi$
$954$	−20.9205	−	24.5454i	−0.677327	−	0.794685i
$955$	24.1199	−	41.7768i	0.780500	−	1.35187i
$956$	3.68124	+	2.12537i	0.119060	+	0.0687392i
$957$	68.4953	+	11.8056i	2.21414	+	0.381620i
$958$		−	23.1390i		−	0.747587i
$959$	−6.95681	−	56.9113i	−0.224647	−	1.83776i
$960$	2.89608	+	2.41114i	0.0934706	+	0.0778192i
$961$	−5.63148	−	9.75401i	−0.181661	−	0.314646i
$962$	−8.56596	+	14.8367i	−0.276178	+	0.478354i
$963$	−2.17869	−	0.774014i	−0.0702073	−	0.0249422i
$964$	7.52283	−	4.34331i	0.242294	−	0.139889i
$965$	−52.0428			−1.67532
$966$	−3.33413	+	21.7229i	−0.107274	+	0.698922i
$967$	0.0753660			0.00242361			0.00121180	−	0.999999i	$-0.499614\pi$
$967$	0.0753660			0.00242361			0.00121180	+	0.999999i	$0.499614\pi$
$968$	5.46991	−	3.15805i	0.175809	−	0.101504i
$969$	−5.51193	−	14.9642i	−0.177069	−	0.480719i
$970$	11.5570	−	20.0173i	0.371073	−	0.642717i
$971$	−6.81415	−	11.8025i	−0.218677	−	0.378759i	0.735727	−	0.677278i	$-0.236841\pi$
$971$	−6.81415	−	11.8025i	−0.218677	−	0.378759i	−0.954404	+	0.298519i	$0.903507\pi$
$972$	14.7484	+	5.04832i	0.473054	+	0.161925i
$973$	31.0826	−	23.3963i	0.996463	−	0.750050i
$974$			25.3674i			0.812825i
$975$	−0.224749	+	1.30399i	−0.00719774	+	0.0417609i
$976$	1.03577	+	0.598005i	0.0331543	+	0.0191417i
$977$	−9.95048	+	17.2347i	−0.318344	+	0.551388i	−0.980143	−	0.198294i	$-0.936460\pi$
$977$	−9.95048	+	17.2347i	−0.318344	+	0.551388i	0.661799	+	0.749682i	$0.269793\pi$
$978$	−34.6865	−	5.97841i	−1.10915	−	0.191169i
$979$	33.8432			1.08163
$980$	4.21363	−	14.6353i	0.134599	−	0.467508i
$981$	39.6291	−	7.30306i	1.26526	−	0.233169i
$982$	7.73991	+	13.4059i	0.246990	+	0.427800i
$983$	12.4582	−	21.5782i	0.397353	−	0.688236i	−0.596045	−	0.802951i	$-0.703262\pi$
$983$	12.4582	−	21.5782i	0.397353	−	0.688236i	0.993398	+	0.114715i	$0.0365954\pi$
$984$	0.0636557	−	0.0234470i	0.00202927	−	0.000747463i
$985$	41.9455	−	24.2173i	1.33650	−	0.771626i
$986$	44.1377			1.40563
$987$	1.18569	−	24.1574i	0.0377411	−	0.768937i
$988$			5.76919i			0.183542i
$989$	−1.93392	+	18.6632i	−0.0614949	+	0.593455i
$990$	−9.09255	+	25.5937i	−0.288980	+	0.813421i
$991$	−9.77185	+	16.9253i	−0.310413	+	0.537651i	−0.978452	−	0.206475i	$-0.933801\pi$
$991$	−9.77185	+	16.9253i	−0.310413	+	0.537651i	0.668039	+	0.744126i	$0.267134\pi$
$992$	−5.63003	+	3.25050i	−0.178754	+	0.103203i
$993$	−0.589662	−	0.490925i	−0.0187124	−	0.0155790i
$994$	−8.49603	−	3.61174i	−0.269478	−	0.114557i
$995$		−	36.7823i		−	1.16608i
$996$	−0.851679	+	4.94140i	−0.0269865	+	0.156574i
$997$	20.9512	−	36.2885i	0.663530	−	1.14927i	−0.316152	−	0.948709i	$-0.602391\pi$
$997$	20.9512	−	36.2885i	0.663530	−	1.14927i	0.979682	−	0.200559i	$-0.0642757\pi$
$998$	−1.16284	−	0.671368i	−0.0368092	−	0.0212518i
$999$	0.358871	+	31.0374i	0.0113542	+	0.981981i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.j.a.137.4	yes	128
3.2	odd	2	inner	966.2.j.a.137.49	yes	128
7.2	even	3	inner	966.2.j.a.275.50	yes	128
21.2	odd	6	inner	966.2.j.a.275.3	yes	128
23.22	odd	2	inner	966.2.j.a.137.3	✓	128
69.68	even	2	inner	966.2.j.a.137.50	yes	128
161.114	odd	6	inner	966.2.j.a.275.49	yes	128
483.275	even	6	inner	966.2.j.a.275.4	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.j.a.137.3	✓	128	23.22	odd	2	inner
966.2.j.a.137.4	yes	128	1.1	even	1	trivial
966.2.j.a.137.49	yes	128	3.2	odd	2	inner
966.2.j.a.137.50	yes	128	69.68	even	2	inner
966.2.j.a.275.3	yes	128	21.2	odd	6	inner
966.2.j.a.275.4	yes	128	483.275	even	6	inner
966.2.j.a.275.49	yes	128	161.114	odd	6	inner
966.2.j.a.275.50	yes	128	7.2	even	3	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.62530 + 0.598665i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.08784 + 1.88420i) q^{5} +(1.10822 - 1.33111i) q^{6} +(-2.11385 + 1.59112i) q^{7} +1.00000i q^{8} +(2.28320 - 1.94602i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-1.62530 + 0.598665i) q^{3} +(0.500000 - 0.866025i) q^{4} +(1.08784 + 1.88420i) q^{5} +(1.10822 - 1.33111i) q^{6} +(-2.11385 + 1.59112i) q^{7} +1.00000i q^{8} +(2.28320 - 1.94602i) q^{9} +(-1.88420 - 1.08784i) q^{10} +(2.08063 - 3.60376i) q^{11} +(-0.294191 + 1.70688i) q^{12} +2.86796 q^{13} +(1.03508 - 2.43487i) q^{14} +(-2.89608 - 2.41114i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.28849 - 3.96377i) q^{17} +(-1.00430 + 2.82690i) q^{18} +(-1.74210 + 1.00580i) q^{19} +2.17569 q^{20} +(2.48309 - 3.85153i) q^{21} +4.16126i q^{22} +(4.77029 + 0.494307i) q^{23} +(-0.598665 - 1.62530i) q^{24} +(0.133188 - 0.230689i) q^{25} +(-2.48373 + 1.43398i) q^{26} +(-2.54587 + 4.52974i) q^{27} +(0.321026 + 2.62620i) q^{28} -9.64344i q^{29} +(3.71365 + 0.640069i) q^{30} +(-3.25050 + 5.63003i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.22421 + 7.10279i) q^{33} +4.57697i q^{34} +(-5.29752 - 2.25202i) q^{35} +(-0.543702 - 2.95032i) q^{36} +(5.17325 - 2.98678i) q^{37} +(1.00580 - 1.74210i) q^{38} +(-4.66130 + 1.71695i) q^{39} +(-1.88420 + 1.08784i) q^{40} +0.0391655i q^{41} +(-0.224652 + 4.57707i) q^{42} +3.91238i q^{43} +(-2.08063 - 3.60376i) q^{44} +(6.15046 + 2.18505i) q^{45} +(-4.37835 + 1.95706i) q^{46} +(4.57081 - 2.63896i) q^{47} +(1.33111 + 1.10822i) q^{48} +(1.93669 - 6.72676i) q^{49} +0.266376i q^{50} +(-1.34651 + 7.81236i) q^{51} +(1.43398 - 2.48373i) q^{52} +(-5.37521 + 9.31013i) q^{53} +(-0.0600767 - 5.19581i) q^{54} +9.05361 q^{55} +(-1.59112 - 2.11385i) q^{56} +(2.22929 - 2.67766i) q^{57} +(4.82172 + 8.35146i) q^{58} +(9.30521 + 5.37237i) q^{59} +(-3.53615 + 1.30251i) q^{60} +(-1.03577 + 0.598005i) q^{61} -6.50100i q^{62} +(-1.72999 + 7.74643i) q^{63} -1.00000 q^{64} +(3.11990 + 5.40382i) q^{65} +(-2.49120 - 6.76330i) q^{66} +(7.71944 + 4.45682i) q^{67} +(-2.28849 - 3.96377i) q^{68} +(-8.04908 + 2.05241i) q^{69} +(5.71380 - 0.698453i) q^{70} -3.48931i q^{71} +(1.94602 + 2.28320i) q^{72} +(3.32966 - 5.76714i) q^{73} +(-2.98678 + 5.17325i) q^{74} +(-0.0783656 + 0.454673i) q^{75} +2.01160i q^{76} +(1.33587 + 10.9283i) q^{77} +(3.17833 - 3.81757i) q^{78} +(-3.16200 + 1.82558i) q^{79} +(1.08784 - 1.88420i) q^{80} +(1.42602 - 8.88631i) q^{81} +(-0.0195827 - 0.0339183i) q^{82} +2.89498 q^{83} +(-2.09398 - 4.07618i) q^{84} +9.95807 q^{85} +(-1.95619 - 3.38822i) q^{86} +(5.77318 + 15.6735i) q^{87} +(3.60376 + 2.08063i) q^{88} +(4.06645 + 7.04330i) q^{89} +(-6.41898 + 1.18293i) q^{90} +(-6.06243 + 4.56326i) q^{91} +(2.81323 - 3.88404i) q^{92} +(1.91254 - 11.0964i) q^{93} +(-2.63896 + 4.57081i) q^{94} +(-3.79026 - 2.18831i) q^{95} +(-1.70688 - 0.294191i) q^{96} +10.6238i q^{97} +(1.68616 + 6.79388i) q^{98} +(-2.26248 - 12.2771i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9}+O(q^{10}) \) 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9	\( 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9} - 64 q^{16} + 4 q^{24} - 72 q^{25} + 24 q^{27} - 8 q^{36} + 4 q^{39} + 12 q^{46} + 72 q^{49} + 4 q^{54} - 96 q^{55} - 128 q^{64} - 56 q^{69} + 32 q^{70} - 40 q^{73} - 40 q^{75} - 16 q^{78} + 36 q^{81} - 32 q^{82} - 64 q^{85} - 24 q^{87} + 32 q^{93} - 8 q^{94} - 4 q^{96}+O(q^{100}) \) 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9 - 64 * q^16 + 4 * q^24 - 72 * q^25 + 24 * q^27 - 8 * q^36 + 4 * q^39 + 12 * q^46 + 72 * q^49 + 4 * q^54 - 96 * q^55 - 128 * q^64 - 56 * q^69 + 32 * q^70 - 40 * q^73 - 40 * q^75 - 16 * q^78 + 36 * q^81 - 32 * q^82 - 64 * q^85 - 24 * q^87 + 32 * q^93 - 8 * q^94 - 4 * q^96

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