LMFDB - Embedded newform 36.2.h.a.23.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,2,Mod(11,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("36.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$36 = 2^{2} \cdot 3^{2}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	36.h (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:	$0.287461447277$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.170772624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16$ x^8 - 3x^7 + 5x^6 - 6x^5 + 6x^4 - 12x^3 + 20x^2 - 24*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$1$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.4
Root			$0.335728 - 1.37379i$ of defining polynomial
Character	$\chi$	$=$	36.23
Dual form			36.2.h.a.11.4

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.02187 + 0.977642i) q^{2} +(-1.35760 - 1.07561i) q^{3} +(0.0884324 + 1.99804i) q^{4} +(-2.18614 - 1.26217i) q^{5} +(-0.335728 - 2.42637i) q^{6} +(1.10489 - 0.637910i) q^{7} +(-1.86301 + 2.12819i) q^{8} +(0.686141 + 2.92048i) q^{9} +(-1.00000 - 3.42703i) q^{10} +(0.252704 + 0.437696i) q^{11} +(2.02905 - 2.80766i) q^{12} +(1.18614 - 2.05446i) q^{13} +(1.75270 + 0.428329i) q^{14} +(1.61030 + 4.06494i) q^{15} +(-3.98436 + 0.353383i) q^{16} +0.792287i q^{17} +(-2.15404 + 3.65515i) q^{18} +4.70285i q^{19} +(2.32854 - 4.47962i) q^{20} +(-2.18614 - 0.322405i) q^{21} +(-0.169680 + 0.694322i) q^{22} +(1.61030 - 2.78912i) q^{23} +(4.81831 - 0.885370i) q^{24} +(0.686141 + 1.18843i) q^{25} +(3.22060 - 0.939764i) q^{26} +(2.20979 - 4.70285i) q^{27} +(1.37228 + 2.15121i) q^{28} +(2.18614 - 1.26217i) q^{29} +(-2.32854 + 5.72814i) q^{30} +(-7.04069 - 4.06494i) q^{31} +(-4.41698 - 3.53417i) q^{32} +(0.127719 - 0.866025i) q^{33} +(-0.774573 + 0.809613i) q^{34} -3.22060 q^{35} +(-5.77457 + 1.62920i) q^{36} -6.74456 q^{37} +(-4.59771 + 4.80570i) q^{38} +(-3.82009 + 1.51330i) q^{39} +(6.75893 - 2.30110i) q^{40} +(5.87228 + 3.39036i) q^{41} +(-1.91875 - 2.46672i) q^{42} +(6.69391 - 3.86473i) q^{43} +(-0.852189 + 0.543620i) q^{44} +(2.18614 - 7.25061i) q^{45} +(4.37228 - 1.27582i) q^{46} +(0.599485 + 1.03834i) q^{47} +(5.78926 + 3.80585i) q^{48} +(-2.68614 + 4.65253i) q^{49} +(-0.460714 + 1.88522i) q^{50} +(0.852189 - 1.07561i) q^{51} +(4.20979 + 2.18828i) q^{52} +1.87953i q^{53} +(6.85582 - 2.64532i) q^{54} -1.27582i q^{55} +(-0.700825 + 3.53986i) q^{56} +(5.05842 - 6.38458i) q^{57} +(3.46790 + 0.847492i) q^{58} +(-6.18850 + 10.7188i) q^{59} +(-7.97954 + 3.57693i) q^{60} +(1.18614 + 2.05446i) q^{61} +(-3.22060 - 11.0371i) q^{62} +(2.62112 + 2.78912i) q^{63} +(-1.05842 - 7.92967i) q^{64} +(-5.18614 + 2.99422i) q^{65} +(0.977175 - 0.760101i) q^{66} +(6.69391 + 3.86473i) q^{67} +(-1.58302 + 0.0700638i) q^{68} +(-5.18614 + 2.05446i) q^{69} +(-3.29103 - 3.14860i) q^{70} +11.8716 q^{71} +(-7.49364 - 3.98063i) q^{72} +3.37228 q^{73} +(-6.89206 - 6.59377i) q^{74} +(0.346781 - 2.35143i) q^{75} +(-9.39651 + 0.415885i) q^{76} +(0.558422 + 0.322405i) q^{77} +(-5.38310 - 2.18828i) q^{78} +(-8.55691 + 4.94034i) q^{79} +(9.15640 + 4.25639i) q^{80} +(-8.05842 + 4.00772i) q^{81} +(2.68614 + 9.20550i) q^{82} +(-3.82009 - 6.61659i) q^{83} +(0.450854 - 4.39652i) q^{84} +(1.00000 - 1.73205i) q^{85} +(10.6186 + 2.59500i) q^{86} +(-4.32550 - 0.637910i) q^{87} +(-1.40229 - 0.277627i) q^{88} -11.9769i q^{89} +(9.32245 - 5.27191i) q^{90} -3.02661i q^{91} +(5.71519 + 2.97080i) q^{92} +(5.18614 + 13.0916i) q^{93} +(-0.402528 + 1.64713i) q^{94} +(5.93580 - 10.2811i) q^{95} +(2.19510 + 9.54890i) q^{96} +(-5.24456 - 9.08385i) q^{97} +(-7.29339 + 2.12819i) q^{98} +(-1.10489 + 1.03834i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q - 3 q^{2} - q^{4} - 6 q^{5} - 3 q^{6} - 6 q^{9} - 8 q^{10} + 6 q^{12} - 2 q^{13} + 12 q^{14} - q^{16} + 18 q^{18} + 18 q^{20} - 6 q^{21} + 3 q^{22} + 3 q^{24} - 6 q^{25} - 12 q^{28} + 6 q^{29} - 18 q^{30}+ \cdots + 4 q^{97}+O(q^{100})$ 8 * q - 3 * q^2 - q^4 - 6 * q^5 - 3 * q^6 - 6 * q^9 - 8 * q^10 + 6 * q^12 - 2 * q^13 + 12 * q^14 - q^16 + 18 * q^18 + 18 * q^20 - 6 * q^21 + 3 * q^22 + 3 * q^24 - 6 * q^25 - 12 * q^28 + 6 * q^29 - 18 * q^30 - 33 * q^32 + 24 * q^33 + 7 * q^34 - 33 * q^36 - 8 * q^37 - 27 * q^38 + 10 * q^40 + 24 * q^41 - 18 * q^42 + 6 * q^45 + 12 * q^46 + 21 * q^48 - 10 * q^49 + 21 * q^50 + 16 * q^52 + 39 * q^54 + 18 * q^56 + 6 * q^57 + 4 * q^58 + 6 * q^60 - 2 * q^61 + 26 * q^64 - 30 * q^65 - 24 * q^66 - 15 * q^68 - 30 * q^69 - 6 * q^70 - 21 * q^72 + 4 * q^73 - 30 * q^74 - 3 * q^76 - 30 * q^77 - 12 * q^78 - 30 * q^81 + 10 * q^82 + 30 * q^84 + 8 * q^85 + 21 * q^86 - 21 * q^88 + 6 * q^90 + 24 * q^92 + 30 * q^93 - 18 * q^94 + 12 * q^96 + 4 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$ .

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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

)

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

$2$	1.02187	+	0.977642i	0.722570	+	0.691297i
$2$	1.02187	+	0.977642i	0.722570	+	0.691297i
$3$	−1.35760	−	1.07561i	−0.783809	−	0.621002i
$3$	−1.35760	−	1.07561i	−0.783809	−	0.621002i
$4$	0.0884324	+	1.99804i	0.0442162	+	0.999022i
$5$	−2.18614	−	1.26217i	−0.977672	−	0.564459i	−0.0761054	−	0.997100i	$-0.524249\pi$
$5$	−2.18614	−	1.26217i	−0.977672	−	0.564459i	−0.901566	+	0.432641i	$0.857582\pi$
$6$	−0.335728	−	2.42637i	−0.137061	−	0.990563i
$7$	1.10489	−	0.637910i	0.417610	−	0.241107i	−0.276444	−	0.961030i	$-0.589156\pi$
$7$	1.10489	−	0.637910i	0.417610	−	0.241107i	0.694054	+	0.719923i	$0.255823\pi$
$8$	−1.86301	+	2.12819i	−0.658672	+	0.752430i
$9$	0.686141	+	2.92048i	0.228714	+	0.973494i
$10$	−1.00000	−	3.42703i	−0.316228	−	1.08372i
$11$	0.252704	+	0.437696i	0.0761931	+	0.131970i	0.901605	−	0.432561i	$-0.142390\pi$
$11$	0.252704	+	0.437696i	0.0761931	+	0.131970i	−0.825411	+	0.564532i	$0.809057\pi$
$12$	2.02905	−	2.80766i	0.585737	−	0.810501i
$13$	1.18614	−	2.05446i	0.328976	−	0.569804i	−0.653333	−	0.757071i	$-0.726630\pi$
$13$	1.18614	−	2.05446i	0.328976	−	0.569804i	0.982309	+	0.187267i	$0.0599631\pi$
$14$	1.75270	+	0.428329i	0.468430	+	0.114476i
$15$	1.61030	+	4.06494i	0.415778	+	1.04956i
$16$	−3.98436	+	0.353383i	−0.996090	+	0.0883459i
$17$			0.792287i			0.192158i	0.995374	+	0.0960789i	$0.0306301\pi$
$17$			0.792287i			0.192158i	−0.995374	+	0.0960789i	$0.969370\pi$
$18$	−2.15404	+	3.65515i	−0.507712	+	0.861527i
$19$			4.70285i			1.07891i	0.842015	+	0.539454i	$0.181369\pi$
$19$			4.70285i			1.07891i	−0.842015	+	0.539454i	$0.818631\pi$
$20$	2.32854	−	4.47962i	0.520678	−	1.00167i
$21$	−2.18614	−	0.322405i	−0.477055	−	0.0703546i
$22$	−0.169680	+	0.694322i	−0.0361759	+	0.148030i
$23$	1.61030	−	2.78912i	0.335771	−	0.581572i	−0.647862	−	0.761758i	$-0.724336\pi$
$23$	1.61030	−	2.78912i	0.335771	−	0.581572i	0.983633	+	0.180186i	$0.0576698\pi$
$24$	4.81831	−	0.885370i	0.983534	−	0.180725i
$25$	0.686141	+	1.18843i	0.137228	+	0.237686i
$26$	3.22060	−	0.939764i	0.631612	−	0.184303i
$27$	2.20979	−	4.70285i	0.425274	−	0.905065i
$28$	1.37228	+	2.15121i	0.259337	+	0.406541i
$29$	2.18614	−	1.26217i	0.405956	−	0.234379i	−0.283095	−	0.959092i	$-0.591361\pi$
$29$	2.18614	−	1.26217i	0.405956	−	0.234379i	0.689051	+	0.724713i	$0.258028\pi$
$30$	−2.32854	+	5.72814i	−0.425132	+	1.04581i
$31$	−7.04069	−	4.06494i	−1.26455	−	0.730086i	−0.290595	−	0.956846i	$-0.593853\pi$
$31$	−7.04069	−	4.06494i	−1.26455	−	0.730086i	−0.973951	+	0.226761i	$0.927186\pi$
$32$	−4.41698	−	3.53417i	−0.780818	−	0.624758i
$33$	0.127719	−	0.866025i	0.0222330	−	0.150756i
$34$	−0.774573	+	0.809613i	−0.132838	+	0.138848i
$35$	−3.22060			−0.544381
$36$	−5.77457	+	1.62920i	−0.962429	+	0.271534i
$37$	−6.74456			−1.10880			−0.554400	−	0.832251i	$-0.687052\pi$
$37$	−6.74456			−1.10880			−0.554400	+	0.832251i	$0.687052\pi$
$38$	−4.59771	+	4.80570i	−0.745847	+	0.779588i
$39$	−3.82009	+	1.51330i	−0.611704	+	0.242322i
$40$	6.75893	−	2.30110i	1.06868	−	0.363837i
$41$	5.87228	+	3.39036i	0.917096	+	0.529486i	0.882708	−	0.469923i	$-0.155718\pi$
$41$	5.87228	+	3.39036i	0.917096	+	0.529486i	0.0343887	+	0.999409i	$0.489052\pi$
$42$	−1.91875	−	2.46672i	−0.296070	−	0.380623i
$43$	6.69391	−	3.86473i	1.02081	−	0.589366i	0.106473	−	0.994316i	$-0.466044\pi$
$43$	6.69391	−	3.86473i	1.02081	−	0.589366i	0.914339	+	0.404950i	$0.132711\pi$
$44$	−0.852189	+	0.543620i	−0.128472	+	0.0819538i
$45$	2.18614	−	7.25061i	0.325891	−	1.08086i
$46$	4.37228	−	1.27582i	0.644658	−	0.188110i
$47$	0.599485	+	1.03834i	0.0874439	+	0.151457i	0.906430	−	0.422356i	$-0.138797\pi$
$47$	0.599485	+	1.03834i	0.0874439	+	0.151457i	−0.818986	+	0.573813i	$0.805463\pi$
$48$	5.78926	+	3.80585i	0.835607	+	0.549327i
$49$	−2.68614	+	4.65253i	−0.383734	+	0.664647i
$50$	−0.460714	+	1.88522i	−0.0651548	+	0.266610i
$51$	0.852189	−	1.07561i	0.119330	−	0.150615i
$52$	4.20979	+	2.18828i	0.583792	+	0.303460i
$53$			1.87953i			0.258173i	0.991633	+	0.129086i	$0.0412045\pi$
$53$			1.87953i			0.258173i	−0.991633	+	0.129086i	$0.958796\pi$
$54$	6.85582	−	2.64532i	0.932959	−	0.359983i
$55$		−	1.27582i		−	0.172032i
$56$	−0.700825	+	3.53986i	−0.0936516	+	0.473033i
$57$	5.05842	−	6.38458i	0.670004	−	0.845659i
$58$	3.46790	+	0.847492i	0.455357	+	0.111281i
$59$	−6.18850	+	10.7188i	−0.805674	+	1.39547i	0.110161	+	0.993914i	$0.464863\pi$
$59$	−6.18850	+	10.7188i	−0.805674	+	1.39547i	−0.915835	+	0.401555i	$0.868470\pi$
$60$	−7.97954	+	3.57693i	−1.03015	+	0.461779i
$61$	1.18614	+	2.05446i	0.151870	+	0.263046i	0.931915	−	0.362677i	$-0.118137\pi$
$61$	1.18614	+	2.05446i	0.151870	+	0.263046i	−0.780045	+	0.625723i	$0.784804\pi$
$62$	−3.22060	−	11.0371i	−0.409017	−	1.40172i
$63$	2.62112	+	2.78912i	0.330230	+	0.351397i
$64$	−1.05842	−	7.92967i	−0.132303	−	0.991209i
$65$	−5.18614	+	2.99422i	−0.643262	+	0.371387i
$66$	0.977175	−	0.760101i	0.120282	−	0.0935620i
$67$	6.69391	+	3.86473i	0.817791	+	0.472152i	0.849654	−	0.527340i	$-0.176811\pi$
$67$	6.69391	+	3.86473i	0.817791	+	0.472152i	−0.0318630	+	0.999492i	$0.510144\pi$
$68$	−1.58302	+	0.0700638i	−0.191970	+	0.00849648i
$69$	−5.18614	+	2.05446i	−0.624338	+	0.247327i
$70$	−3.29103	−	3.14860i	−0.393354	−	0.376329i
$71$	11.8716			1.40890			0.704450	−	0.709754i	$-0.251194\pi$
$71$	11.8716			1.40890			0.704450	+	0.709754i	$0.251194\pi$
$72$	−7.49364	−	3.98063i	−0.883133	−	0.469122i
$73$	3.37228			0.394696			0.197348	−	0.980334i	$-0.436767\pi$
$73$	3.37228			0.394696			0.197348	+	0.980334i	$0.436767\pi$
$74$	−6.89206	−	6.59377i	−0.801186	−	0.766510i
$75$	0.346781	−	2.35143i	0.0400428	−	0.271519i
$76$	−9.39651	+	0.415885i	−1.07785	+	0.0477052i
$77$	0.558422	+	0.322405i	0.0636381	+	0.0367415i
$78$	−5.38310	−	2.18828i	−0.609516	−	0.247774i
$79$	−8.55691	+	4.94034i	−0.962728	+	0.555831i	−0.897012	−	0.442007i	$-0.854267\pi$
$79$	−8.55691	+	4.94034i	−0.962728	+	0.555831i	−0.0657165	+	0.997838i	$0.520933\pi$
$80$	9.15640	+	4.25639i	1.02372	+	0.475879i
$81$	−8.05842	+	4.00772i	−0.895380	+	0.445302i
$82$	2.68614	+	9.20550i	0.296635	+	1.01658i
$83$	−3.82009	−	6.61659i	−0.419309	−	0.726265i	0.576561	−	0.817054i	$-0.304394\pi$
$83$	−3.82009	−	6.61659i	−0.419309	−	0.726265i	−0.995870	+	0.0907894i	$0.971061\pi$
$84$	0.450854	−	4.39652i	0.0491922	−	0.479699i
$85$	1.00000	−	1.73205i	0.108465	−	0.187867i
$86$	10.6186	+	2.59500i	1.14504	+	0.279826i
$87$	−4.32550	−	0.637910i	−0.463742	−	0.0683912i
$88$	−1.40229	−	0.277627i	−0.149485	−	0.0295952i
$89$		−	11.9769i		−	1.26955i	−0.772698	−	0.634773i	$-0.781093\pi$
$89$		−	11.9769i		−	1.26955i	0.772698	−	0.634773i	$-0.218907\pi$
$90$	9.32245	−	5.27191i	0.982672	−	0.555708i
$91$		−	3.02661i		−	0.317274i
$92$	5.71519	+	2.97080i	0.595850	+	0.309728i
$93$	5.18614	+	13.0916i	0.537778	+	1.35753i
$94$	−0.402528	+	1.64713i	−0.0415176	+	0.169888i
$95$	5.93580	−	10.2811i	0.609000	−	1.05482i
$96$	2.19510	+	9.54890i	0.224037	+	0.974581i
$97$	−5.24456	−	9.08385i	−0.532505	−	0.922325i	−0.999280	−	0.0379490i	$-0.987918\pi$
$97$	−5.24456	−	9.08385i	−0.532505	−	0.922325i	0.466775	−	0.884376i	$-0.345416\pi$
$98$	−7.29339	+	2.12819i	−0.736744	+	0.214980i
$99$	−1.10489	+	1.03834i	−0.111046	+	0.104357i
$100$	−2.31386	+	1.47603i	−0.231386	+	0.147603i
$101$	1.06930	−	0.617359i	0.106399	−	0.0614295i	−0.445856	−	0.895105i	$-0.647101\pi$
$101$	1.06930	−	0.617359i	0.106399	−	0.0614295i	0.552255	+	0.833675i	$0.313767\pi$
$102$	1.92238	−	0.265993i	0.190344	−	0.0263372i
$103$	−0.411331	−	0.237482i	−0.0405297	−	0.0233998i	0.479598	−	0.877488i	$-0.340782\pi$
$103$	−0.411331	−	0.237482i	−0.0405297	−	0.0233998i	−0.520128	+	0.854088i	$0.674116\pi$
$104$	2.16249	+	6.35180i	0.212050	+	0.622845i
$105$	4.37228	+	3.46410i	0.426691	+	0.338062i
$106$	−1.83751	+	1.92063i	−0.178474	+	0.186548i
$107$	−12.5652			−1.21472			−0.607360	−	0.794427i	$-0.707771\pi$
$107$	−12.5652			−1.21472			−0.607360	+	0.794427i	$0.707771\pi$
$108$	9.59193	+	3.99937i	0.922984	+	0.384839i
$109$	13.4891			1.29202			0.646012	−	0.763327i	$-0.276436\pi$
$109$	13.4891			1.29202			0.646012	+	0.763327i	$0.276436\pi$
$110$	1.24730	−	1.30372i	0.118925	−	0.124305i
$111$	9.15640	+	7.25450i	0.869087	+	0.688566i
$112$	−4.17686	+	2.93212i	−0.394677	+	0.277059i
$113$	−6.30298	−	3.63903i	−0.592935	−	0.342331i	0.173322	−	0.984865i	$-0.444550\pi$
$113$	−6.30298	−	3.63903i	−0.592935	−	0.342331i	−0.766257	+	0.642534i	$0.777883\pi$
$114$	11.4109	−	1.57888i	1.06873	−	0.147876i
$115$	−7.04069	+	4.06494i	−0.656548	+	0.379058i
$116$	2.71519	+	4.25639i	0.252099	+	0.395196i
$117$	6.81386	+	2.05446i	0.629942	+	0.189935i
$118$	−16.8030	+	4.90307i	−1.54684	+	0.451364i
$119$	0.505408	+	0.875393i	0.0463307	+	0.0802471i
$120$	−11.6510	−	4.14598i	−1.06359	−	0.378474i
$121$	5.37228	−	9.30506i	0.488389	−	0.845915i
$122$	−0.796442	+	3.25901i	−0.0721065	+	0.295057i
$123$	−4.32550	−	10.9190i	−0.390017	−	0.984534i
$124$	7.49931	−	14.4271i	0.673458	−	1.29559i
$125$			9.15759i			0.819080i
$126$	−0.0483257	+	5.41263i	−0.00430520	+	0.482196i
$127$		−	7.65492i		−	0.679265i	−0.940558	−	0.339632i	$-0.889697\pi$
$127$		−	7.65492i		−	0.679265i	0.940558	−	0.339632i	$-0.110303\pi$
$128$	6.67081	−	9.13785i	0.589622	−	0.807679i
$129$	−13.2446	−	1.95327i	−1.16612	−	0.171975i
$130$	−8.22683	−	2.01049i	−0.721541	−	0.176332i
$131$	3.82009	−	6.61659i	0.333763	−	0.578094i	−0.649484	−	0.760375i	$-0.725015\pi$
$131$	3.82009	−	6.61659i	0.333763	−	0.578094i	0.983246	+	0.182282i	$0.0583483\pi$
$132$	1.74165	+	0.178603i	0.151591	+	0.0155454i
$133$	3.00000	+	5.19615i	0.260133	+	0.450564i
$134$	3.06198	+	10.4935i	0.264514	+	0.906500i
$135$	−10.7667	+	7.49198i	−0.926650	+	0.644807i
$136$	−1.68614	−	1.47603i	−0.144585	−	0.126569i
$137$	−4.75544	+	2.74555i	−0.406284	+	0.234568i	−0.689192	−	0.724579i	$-0.742034\pi$
$137$	−4.75544	+	2.74555i	−0.406284	+	0.234568i	0.282908	+	0.959147i	$0.408701\pi$
$138$	−7.30808	−	2.97080i	−0.622105	−	0.252892i
$139$	13.3233	+	7.69219i	1.13006	+	0.652443i	0.943951	−	0.330085i	$-0.107077\pi$
$139$	13.3233	+	7.69219i	1.13006	+	0.652443i	0.186114	+	0.982528i	$0.440411\pi$
$140$	−0.284805	−	6.43491i	−0.0240705	−	0.543849i
$141$	0.302985	−	2.05446i	0.0255159	−	0.173016i
$142$	12.1312	+	11.6062i	1.01803	+	0.973968i
$143$	1.19897			0.100263
$144$	−3.76588	−	11.3938i	−0.313823	−	0.949481i
$145$	−6.37228			−0.529189
$146$	3.44603	+	3.29688i	0.285195	+	0.272852i
$147$	8.65099	−	3.42703i	0.713522	−	0.282657i
$148$	−0.596438	−	13.4759i	−0.0490269	−	1.10771i
$149$	−11.1861	−	6.45832i	−0.916404	−	0.529086i	−0.0339182	−	0.999425i	$-0.510799\pi$
$149$	−11.1861	−	6.45832i	−0.916404	−	0.529086i	−0.882486	+	0.470338i	$0.844132\pi$
$150$	2.65322	−	2.06382i	0.216634	−	0.168510i
$151$	2.62112	−	1.51330i	0.213304	−	0.123151i	−0.389542	−	0.921009i	$-0.627367\pi$
$151$	2.62112	−	1.51330i	0.213304	−	0.123151i	0.602846	+	0.797858i	$0.294033\pi$
$152$	−10.0086	−	8.76144i	−0.811804	−	0.710647i
$153$	−2.31386	+	0.543620i	−0.187064	+	0.0439491i
$154$	0.255437	+	0.875393i	0.0205837	+	0.0705411i
$155$	10.2613	+	17.7731i	0.824207	+	1.42757i
$156$	−3.36147	−	7.49888i	−0.269133	−	0.600391i
$157$	−5.93070	+	10.2723i	−0.473322	+	0.819817i	−0.999534	−	0.0305363i	$-0.990278\pi$
$157$	−5.93070	+	10.2723i	−0.473322	+	0.819817i	0.526212	+	0.850353i	$0.323612\pi$
$158$	−13.5739	−	3.31722i	−1.07988	−	0.263904i
$159$	2.02163	−	2.55164i	0.160326	−	0.202358i
$160$	5.19542	+	13.3012i	0.410734	+	1.05155i
$161$		−	4.10891i		−	0.323828i
$162$	−12.1528	−	3.78288i	−0.954812	−	0.297212i
$163$			1.75079i			0.137132i	0.997647	+	0.0685660i	$0.0218424\pi$
$163$			1.75079i			0.137132i	−0.997647	+	0.0685660i	$0.978158\pi$
$164$	−6.25480	+	12.0329i	−0.488417	+	0.939611i
$165$	−1.37228	+	1.73205i	−0.106832	+	0.134840i
$166$	2.56502	−	10.4960i	0.199084	−	0.814645i
$167$	−8.74507	+	15.1469i	−0.676714	+	1.17210i	0.299251	+	0.954174i	$0.403263\pi$
$167$	−8.74507	+	15.1469i	−0.676714	+	1.17210i	−0.975965	+	0.217928i	$0.930070\pi$
$168$	4.75893	−	4.05189i	0.367160	−	0.312610i
$169$	3.68614	+	6.38458i	0.283549	+	0.491122i
$170$	2.71519	−	0.792287i	0.208246	−	0.0607656i
$171$	−13.7346	+	3.22682i	−1.05031	+	0.246761i
$172$	8.31386	+	13.0330i	0.633926	+	0.993754i
$173$	15.3030	−	8.83518i	1.16346	−	0.671726i	0.211333	−	0.977414i	$-0.432220\pi$
$173$	15.3030	−	8.83518i	1.16346	−	0.671726i	0.952132	+	0.305688i	$0.0988864\pi$
$174$	−3.79644	−	4.88065i	−0.287808	−	0.370001i
$175$	1.51622	+	0.875393i	0.114616	+	0.0661735i
$176$	−1.16154	−	1.65464i	−0.0875543	−	0.124723i
$177$	19.9307	−	7.89542i	1.49808	−	0.593456i
$178$	11.7091	−	12.2388i	0.877634	−	0.917337i
$179$	8.83915			0.660669			0.330334	−	0.943864i	$-0.392838\pi$
$179$	8.83915			0.660669			0.330334	+	0.943864i	$0.392838\pi$
$180$	14.6804	+	3.72682i	1.09421	+	0.277781i
$181$	−4.00000			−0.297318			−0.148659	−	0.988889i	$-0.547496\pi$
$181$	−4.00000			−0.297318			−0.148659	+	0.988889i	$0.547496\pi$
$182$	2.95894	−	3.09279i	0.219331	−	0.229253i
$183$	0.599485	−	4.06494i	0.0443152	−	0.300489i
$184$	2.93580	+	8.62319i	0.216430	+	0.635710i
$185$	14.7446	+	8.51278i	1.08404	+	0.625872i
$186$	−7.49931	+	18.4481i	−0.549876	+	1.35268i
$187$	−0.346781	+	0.200214i	−0.0253591	+	0.0146411i
$188$	−2.02163	+	1.28962i	−0.147443	+	0.0940552i
$189$	−0.558422	−	6.60580i	−0.0406192	−	0.480501i
$190$	16.1168	−	4.70285i	1.16924	−	0.341181i
$191$	−7.54610	−	13.0702i	−0.546017	−	0.945728i	−0.998542	−	0.0539770i	$-0.982810\pi$
$191$	−7.54610	−	13.0702i	−0.546017	−	0.945728i	0.452526	−	0.891751i	$-0.350523\pi$
$192$	−7.09230	+	11.9038i	−0.511843	+	0.859079i
$193$	−3.87228	+	6.70699i	−0.278733	+	0.482780i	−0.971070	−	0.238795i	$-0.923248\pi$
$193$	−3.87228	+	6.70699i	−0.278733	+	0.482780i	0.692337	+	0.721574i	$0.256581\pi$
$194$	3.52150	−	14.4098i	0.252829	−	1.03456i
$195$	10.2613	+	1.51330i	0.734826	+	0.108370i
$196$	−9.53351	−	4.95559i	−0.680965	−	0.353971i
$197$			23.9538i			1.70663i	0.521392	+	0.853317i	$0.325413\pi$
$197$			23.9538i			1.70663i	−0.521392	+	0.853317i	$0.674587\pi$
$198$	−2.14418	−	0.0191439i	−0.152380	−	0.00136050i
$199$		−	12.9073i		−	0.914973i	−0.889217	−	0.457486i	$-0.848750\pi$
$199$		−	12.9073i		−	0.914973i	0.889217	−	0.457486i	$-0.151250\pi$
$200$	−3.80749	−	0.753812i	−0.269231	−	0.0533025i
$201$	−4.93070	−	12.4468i	−0.347785	−	0.877927i
$202$	1.69624	+	0.414530i	0.119347	+	0.0291662i
$203$	1.61030	−	2.78912i	0.113021	−	0.195758i
$204$	2.22447	+	1.60759i	0.155744	+	0.112554i
$205$	−8.55842	−	14.8236i	−0.597746	−	1.03533i
$206$	−0.188154	−	0.644810i	−0.0131093	−	0.0449261i
$207$	9.25048	+	2.78912i	0.642953	+	0.193857i
$208$	−4.00000	+	8.60485i	−0.277350	+	0.596639i
$209$	−2.05842	+	1.18843i	−0.142384	+	0.0822055i
$210$	1.08125	+	7.81438i	0.0746132	+	0.539244i
$211$	−15.1863	−	8.76780i	−1.04547	−	0.603600i	−0.124090	−	0.992271i	$-0.539601\pi$
$211$	−15.1863	−	8.76780i	−1.04547	−	0.603600i	−0.921377	+	0.388671i	$0.872934\pi$
$212$	−3.75538	+	0.166211i	−0.257920	+	0.0114154i
$213$	−16.1168	−	12.7692i	−1.10431	−	0.874929i
$214$	−12.8399	−	12.2842i	−0.877720	−	0.839732i
$215$	−19.5118			−1.33069
$216$	5.89174	+	13.4643i	0.400882	+	0.916129i
$217$	−10.3723			−0.704116
$218$	13.7841	+	13.1875i	0.933578	+	0.893173i
$219$	−4.57820	−	3.62725i	−0.309366	−	0.245107i
$220$	2.54915	−	0.112824i	0.171863	−	0.00760658i
$221$	1.62772	+	0.939764i	0.109492	+	0.0632154i
$222$	2.26434	+	16.3648i	0.151973	+	1.09834i
$223$	−7.04069	+	4.06494i	−0.471479	+	0.272209i	−0.716859	−	0.697218i	$-0.754421\pi$
$223$	−7.04069	+	4.06494i	−0.471479	+	0.272209i	0.245379	+	0.969427i	$0.421087\pi$
$224$	−7.13477	−	1.08724i	−0.476712	−	0.0726443i
$225$	−3.00000	+	2.81929i	−0.200000	+	0.187953i
$226$	−2.88316	−	9.88067i	−0.191785	−	0.657253i
$227$	−7.19932	−	12.4696i	−0.477835	−	0.827635i	0.521842	−	0.853042i	$-0.325245\pi$
$227$	−7.19932	−	12.4696i	−0.477835	−	0.827635i	−0.999677	+	0.0254070i	$0.991912\pi$
$228$	13.2040	+	9.54235i	0.874457	+	0.631957i
$229$	−1.81386	+	3.14170i	−0.119863	+	0.207609i	−0.919713	−	0.392591i	$-0.871579\pi$
$229$	−1.81386	+	3.14170i	−0.119863	+	0.207609i	0.799850	+	0.600200i	$0.204912\pi$
$230$	−11.1687	−	2.72943i	−0.736444	−	0.179974i
$231$	−0.411331	−	1.03834i	−0.0270636	−	0.0683177i
$232$	−1.38665	+	7.00396i	−0.0910381	+	0.459832i
$233$		−	4.84630i		−	0.317491i	−0.987320	−	0.158746i	$-0.949255\pi$
$233$		−	4.84630i		−	0.317491i	0.987320	−	0.158746i	$-0.0507450\pi$
$234$	4.95435	+	8.76090i	0.323876	+	0.572718i
$235$		−	3.02661i		−	0.197434i
$236$	−21.9639	−	11.4170i	−1.42973	−	0.743184i
$237$	16.9307	+	2.49689i	1.09977	+	0.162190i
$238$	−0.339360	+	1.38864i	−0.0219974	+	0.0900125i
$239$	6.02987	−	10.4440i	0.390040	−	0.675569i	−0.602414	−	0.798184i	$-0.705794\pi$
$239$	6.02987	−	10.4440i	0.390040	−	0.675569i	0.992454	+	0.122614i	$0.0391278\pi$
$240$	−7.85250	−	15.6271i	−0.506877	−	1.00873i
$241$	3.24456	+	5.61975i	0.209001	+	0.362000i	0.951400	−	0.307958i	$-0.0996456\pi$
$241$	3.24456	+	5.61975i	0.209001	+	0.362000i	−0.742399	+	0.669958i	$0.766312\pi$
$242$	14.5868	−	4.25639i	0.937674	−	0.273611i
$243$	15.2508	+	3.22682i	0.978341	+	0.207001i
$244$	−4.00000	+	2.55164i	−0.256074	+	0.163352i
$245$	11.7446	−	6.78073i	0.750333	−	0.433205i
$246$	6.25480	−	15.3866i	0.398791	−	0.981013i
$247$	9.66181	+	5.57825i	0.614766	+	0.354935i
$248$	21.7678	−	7.41094i	1.38226	−	0.470595i
$249$	−1.93070	+	13.0916i	−0.122353	+	0.829645i
$250$	−8.95284	+	9.35785i	−0.566227	+	0.591843i
$251$	11.1780			0.705551			0.352776	−	0.935708i	$-0.385238\pi$
$251$	11.1780			0.705551			0.352776	+	0.935708i	$0.385238\pi$
$252$	−5.34100	+	5.48376i	−0.336451	+	0.345444i
$253$	1.62772			0.102334
$254$	7.48378	−	7.82233i	0.469574	−	0.490817i
$255$	−3.22060	+	1.27582i	−0.201682	+	0.0798950i
$256$	15.7502	−	2.81601i	0.984390	−	0.176001i
$257$	12.9891	+	7.49927i	0.810239	+	0.467792i	0.847039	−	0.531531i	$-0.178383\pi$
$257$	12.9891	+	7.49927i	0.810239	+	0.467792i	−0.0367996	+	0.999323i	$0.511716\pi$
$258$	−11.6246	−	14.9444i	−0.723717	−	0.930399i
$259$	−7.45202	+	4.30243i	−0.463046	+	0.267340i
$260$	−6.44121	−	10.0974i	−0.399467	−	0.626211i
$261$	5.18614	+	5.51856i	0.321014	+	0.341590i
$262$	10.3723	−	3.02661i	0.640802	−	0.186984i
$263$	13.9873	+	24.2267i	0.862494	+	1.49388i	0.869514	+	0.493908i	$0.164432\pi$
$263$	13.9873	+	24.2267i	0.862494	+	1.49388i	−0.00701993	+	0.999975i	$0.502235\pi$
$264$	1.60513	+	1.88522i	0.0987889	+	0.116027i
$265$	2.37228	−	4.10891i	0.145728	−	0.252408i
$266$	−2.01437	+	8.24271i	−0.123509	+	0.505393i
$267$	−12.8824	+	16.2598i	−0.788391	+	0.995082i
$268$	−7.12994	+	13.7165i	−0.435531	+	0.837868i
$269$		−	21.4843i		−	1.30992i	−0.755663	−	0.654961i	$-0.772685\pi$
$269$		−	21.4843i		−	1.30992i	0.755663	−	0.654961i	$-0.227315\pi$
$270$	−18.3266	−	2.87016i	−1.11532	−	0.174672i
$271$			29.9679i			1.82042i	0.414146	+	0.910211i	$0.364080\pi$
$271$			29.9679i			1.82042i	−0.414146	+	0.910211i	$0.635920\pi$
$272$	−0.279981	−	3.15676i	−0.0169763	−	0.191406i
$273$	−3.25544	+	4.10891i	−0.197028	+	0.248683i
$274$	−7.54360	−	1.84352i	−0.455726	−	0.111371i
$275$	−0.346781	+	0.600642i	−0.0209117	+	0.0362201i
$276$	−4.56352	−	10.1805i	−0.274691	−	0.612791i
$277$	−3.18614	−	5.51856i	−0.191437	−	0.331578i	0.754290	−	0.656541i	$-0.227981\pi$
$277$	−3.18614	−	5.51856i	−0.191437	−	0.331578i	−0.945727	+	0.324963i	$0.894648\pi$
$278$	6.09442	+	20.8858i	0.365519	+	1.25265i
$279$	7.04069	−	23.3513i	0.421515	−	1.39801i
$280$	6.00000	−	6.85407i	0.358569	−	0.409609i
$281$	−19.9307	+	11.5070i	−1.18897	+	0.686450i	−0.958072	−	0.286529i	$-0.907499\pi$
$281$	−19.9307	+	11.5070i	−1.18897	+	0.686450i	−0.230894	+	0.972979i	$0.574165\pi$
$282$	2.31813	−	1.80317i	0.138043	−	0.107377i
$283$	−8.55691	−	4.94034i	−0.508656	−	0.293673i	0.223625	−	0.974675i	$-0.428211\pi$
$283$	−8.55691	−	4.94034i	−0.508656	−	0.293673i	−0.732281	+	0.681003i	$0.761544\pi$
$284$	1.04983	+	23.7200i	0.0622961	+	1.40752i
$285$	−19.1168	+	7.57301i	−1.13238	+	0.448587i
$286$	1.22519	+	1.17216i	0.0724470	+	0.0693115i
$287$	8.65099			0.510652
$288$	7.29080	−	15.3246i	0.429614	−	0.903012i
$289$	16.3723			0.963075
$290$	−6.51164	−	6.22981i	−0.382376	−	0.365827i
$291$	−2.65064	+	17.9733i	−0.155384	+	1.05361i
$292$	0.298219	+	6.73797i	0.0174519	+	0.394310i
$293$	−20.1861	−	11.6545i	−1.17929	−	0.680862i	−0.223437	−	0.974718i	$-0.571728\pi$
$293$	−20.1861	−	11.6545i	−1.17929	−	0.680862i	−0.955850	+	0.293857i	$0.905061\pi$
$294$	12.1906	+	4.95559i	0.710970	+	0.289016i
$295$	27.0579	−	15.6219i	1.57537	−	0.909540i
$296$	12.5652	−	14.3537i	0.730335	−	0.834294i
$297$	2.61684	−	0.221215i	0.151845	−	0.0128362i
$298$	−5.11684	−	17.5356i	−0.296411	−	1.01581i
$299$	−3.82009	−	6.61659i	−0.220921	−	0.382647i
$300$	4.72892	+	0.484942i	0.273024	+	0.0279981i
$301$	4.93070	−	8.54023i	0.284201	−	0.492251i
$302$	4.15791	+	1.01612i	0.239261	+	0.0584710i
$303$	−2.11571	−	0.312018i	−0.121544	−	0.0179250i
$304$	−1.66191	−	18.7379i	−0.0953171	−	1.07469i
$305$		−	5.98844i		−	0.342897i
$306$	−2.89593	−	1.70662i	−0.165549	−	0.0975608i
$307$		−	1.20128i		−	0.0685609i	−0.999412	−	0.0342805i	$-0.989086\pi$
$307$		−	1.20128i		−	0.0685609i	0.999412	−	0.0342805i	$-0.0109140\pi$
$308$	−0.594797	+	1.14426i	−0.0338917	+	0.0652004i
$309$	0.302985	+	0.764836i	0.0172362	+	0.0435100i
$310$	−6.89001	+	28.1936i	−0.391326	+	1.60129i
$311$	−9.56773	+	16.5718i	−0.542536	+	0.939700i	0.456221	+	0.889866i	$0.349203\pi$
$311$	−9.56773	+	16.5718i	−0.542536	+	0.939700i	−0.998758	+	0.0498340i	$0.984131\pi$
$312$	3.89624	−	10.9492i	0.220581	−	0.619875i
$313$	9.24456	+	16.0121i	0.522534	+	0.905055i	0.999656	+	0.0262180i	$0.00834640\pi$
$313$	9.24456	+	16.0121i	0.522534	+	0.905055i	−0.477123	+	0.878837i	$0.658320\pi$
$314$	−16.1030	+	4.69882i	−0.908746	+	0.265170i
$315$	−2.20979	−	9.40571i	−0.124507	−	0.529952i
$316$	−10.6277	−	16.6602i	−0.597856	−	0.937210i
$317$	−28.1644	+	16.2607i	−1.58187	+	0.913293i	−0.587283	+	0.809381i	$0.699803\pi$
$317$	−28.1644	+	16.2607i	−1.58187	+	0.913293i	−0.994587	+	0.103911i	$0.966864\pi$
$318$	4.56044	−	0.631011i	0.255737	−	0.0353853i
$319$	1.10489	+	0.637910i	0.0618621	+	0.0357161i
$320$	−7.69473	+	18.6713i	−0.430148	+	1.04376i
$321$	17.0584	+	13.5152i	0.952108	+	0.754343i
$322$	4.01704	−	4.19877i	0.223861	−	0.233988i
$323$	−3.72601			−0.207321
$324$	−8.72023	−	15.7467i	−0.484457	−	0.874815i
$325$	3.25544			0.180579
$326$	−1.71164	+	1.78907i	−0.0947990	+	0.0990876i
$327$	−18.3128	−	14.5090i	−1.01270	−	0.802349i
$328$	−18.1554	+	6.18109i	−1.00247	+	0.341294i
$329$	1.32473	+	0.764836i	0.0730350	+	0.0421667i
$330$	−3.09562	+	0.428329i	−0.170408	+	0.0235787i
$331$	24.0254	−	13.8711i	1.32056	−	0.762424i	0.336739	−	0.941598i	$-0.390676\pi$
$331$	24.0254	−	13.8711i	1.32056	−	0.762424i	0.983817	+	0.179174i	$0.0573426\pi$
$332$	12.8824	−	8.21782i	0.707014	−	0.451012i
$333$	−4.62772	−	19.6974i	−0.253597	−	1.07941i
$334$	−23.7446	+	6.92860i	−1.29924	+	0.379116i
$335$	−9.75588	−	16.8977i	−0.533021	−	0.923219i
$336$	8.82430	+	0.512032i	0.481405	+	0.0279336i
$337$	7.87228	−	13.6352i	0.428830	−	0.742756i	−0.567939	−	0.823071i	$-0.692259\pi$
$337$	7.87228	−	13.6352i	0.428830	−	0.742756i	0.996770	+	0.0803144i	$0.0255924\pi$
$338$	−2.47508	+	10.1279i	−0.134627	+	0.550887i
$339$	4.64275	+	11.7199i	0.252160	+	0.636536i
$340$	3.54915	+	1.84487i	0.192479	+	0.100052i
$341$		−	4.10891i		−	0.222510i
$342$	−17.1896	−	10.1301i	−0.929509	−	0.547775i
$343$			15.7848i			0.852300i
$344$	−4.24589	+	21.4460i	−0.228923	+	1.15629i
$345$	13.9307	+	2.05446i	0.750004	+	0.110608i
$346$	24.2753	+	5.93244i	1.30505	+	0.318930i
$347$	3.47331	−	6.01594i	0.186457	−	0.322953i	−0.757610	−	0.652708i	$-0.773633\pi$
$347$	3.47331	−	6.01594i	0.186457	−	0.322953i	0.944066	+	0.329755i	$0.106966\pi$
$348$	0.892059	−	8.69894i	0.0478194	−	0.466312i
$349$	2.81386	+	4.87375i	0.150622	+	0.260886i	0.931456	−	0.363853i	$-0.118539\pi$
$349$	2.81386	+	4.87375i	0.150622	+	0.260886i	−0.780834	+	0.624739i	$0.785206\pi$
$350$	0.693562	+	2.37686i	0.0370725	+	0.127049i
$351$	−7.04069	−	10.1182i	−0.375804	−	0.540067i
$352$	0.430703	−	2.82639i	0.0229566	−	0.150647i
$353$	7.24456	−	4.18265i	0.385589	−	0.222620i	−0.294658	−	0.955603i	$-0.595206\pi$
$353$	7.24456	−	4.18265i	0.385589	−	0.222620i	0.680247	+	0.732983i	$0.261872\pi$
$354$	28.0855	+	11.4170i	1.49273	+	0.606807i
$355$	−25.9530	−	14.9840i	−1.37744	−	0.795266i
$356$	23.9303	−	1.05914i	1.26830	−	0.0561345i
$357$	0.255437	−	1.73205i	0.0135192	−	0.0916698i
$358$	9.03245	+	8.64152i	0.477380	+	0.456719i
$359$	−1.38712			−0.0732096			−0.0366048	−	0.999330i	$-0.511654\pi$
$359$	−1.38712			−0.0732096			−0.0366048	+	0.999330i	$0.511654\pi$
$360$	11.3579	+	18.1605i	0.598614	+	0.957140i
$361$	−3.11684			−0.164044
$362$	−4.08748	−	3.91057i	−0.214833	−	0.205535i
$363$	−17.3020	+	6.85407i	−0.908119	+	0.359745i
$364$	6.04729	−	0.267650i	0.316964	−	0.0140287i
$365$	−7.37228	−	4.25639i	−0.385883	−	0.222790i
$366$	4.58666	−	3.56776i	0.239748	−	0.186490i
$367$	−5.52447	+	3.18955i	−0.288375	+	0.166493i	−0.637209	−	0.770691i	$-0.719911\pi$
$367$	−5.52447	+	3.18955i	−0.288375	+	0.166493i	0.348834	+	0.937185i	$0.386578\pi$
$368$	−5.43039	+	11.6819i	−0.283079	+	0.608962i
$369$	−5.87228	+	19.4762i	−0.305699	+	1.01389i
$370$	6.74456	+	23.1138i	0.350633	+	1.20163i
$371$	1.19897	+	2.07668i	0.0622474	+	0.107816i
$372$	−25.6989	+	11.5199i	−1.33243	+	0.597277i
$373$	9.93070	−	17.2005i	0.514192	−	0.890607i	−0.485672	−	0.874141i	$-0.661425\pi$
$373$	9.93070	−	17.2005i	0.514192	−	0.890607i	0.999864	−	0.0164662i	$-0.00524158\pi$
$374$	−0.550103	−	0.134435i	−0.0284451	−	0.00695147i
$375$	9.84996	−	12.4323i	0.508650	−	0.642002i
$376$	−3.32663	−	0.658610i	−0.171558	−	0.0339652i
$377$		−	5.98844i		−	0.308420i
$378$	5.88747	−	7.29620i	0.302819	−	0.375276i
$379$		−	6.45364i		−	0.331501i	−0.986168	−	0.165751i	$-0.946995\pi$
$379$		−	6.45364i		−	0.331501i	0.986168	−	0.165751i	$-0.0530047\pi$
$380$	21.0670	+	10.9508i	1.08071	+	0.561764i
$381$	−8.23369	+	10.3923i	−0.421825	+	0.532414i
$382$	5.06688	−	20.7334i	0.259244	−	1.06082i
$383$	−4.32550	+	7.49198i	−0.221023	+	0.382822i	−0.955119	−	0.296223i	$-0.904273\pi$
$383$	−4.32550	+	7.49198i	−0.221023	+	0.382822i	0.734096	+	0.679045i	$0.237606\pi$
$384$	−18.8850	+	5.23034i	−0.963722	+	0.266910i
$385$	−0.813859	−	1.40965i	−0.0414781	−	0.0718422i
$386$	−10.5140	+	3.06796i	−0.535148	+	0.156155i
$387$	15.8798	+	16.8977i	0.807217	+	0.858958i
$388$	17.6861	−	11.2822i	0.897878	−	0.572766i
$389$	27.3030	−	15.7634i	1.38432	−	0.799235i	0.391649	−	0.920115i	$-0.371905\pi$
$389$	27.3030	−	15.7634i	1.38432	−	0.799235i	0.992667	+	0.120879i	$0.0385714\pi$
$390$	9.00623	+	11.5783i	0.456048	+	0.586288i
$391$	2.20979	+	1.27582i	0.111754	+	0.0645210i
$392$	−4.89720	−	14.3843i	−0.247346	−	0.726518i
$393$	−12.3030	+	4.87375i	−0.620603	+	0.245848i
$394$	−23.4182	+	24.4776i	−1.17979	+	1.23316i
$395$	24.9422			1.25498
$396$	−2.17235	−	2.11580i	−0.109165	−	0.106323i
$397$	−18.7446			−0.940763			−0.470381	−	0.882463i	$-0.655884\pi$
$397$	−18.7446			−0.940763			−0.470381	+	0.882463i	$0.655884\pi$
$398$	12.6187	−	13.1895i	0.632518	−	0.661132i
$399$	1.51622	−	10.2811i	0.0759062	−	0.514699i
$400$	−3.15380	−	4.49266i	−0.157690	−	0.224633i
$401$	3.98913	+	2.30312i	0.199207	+	0.115012i	0.596286	−	0.802772i	$-0.296643\pi$
$401$	3.98913	+	2.30312i	0.199207	+	0.115012i	−0.397078	+	0.917785i	$0.629976\pi$
$402$	7.12994	−	17.5394i	0.355609	−	0.874787i
$403$	−16.7025	+	9.64319i	−0.832011	+	0.480362i
$404$	1.32807	+	2.08191i	0.0660740	+	0.103579i
$405$	22.6753	+	1.40965i	1.12674	+	0.0700459i
$406$	4.37228	−	1.27582i	0.216993	−	0.0633179i
$407$	−1.70438	−	2.95207i	−0.0844829	−	0.146329i
$408$	0.701467	+	3.81749i	0.0347278	+	0.188994i
$409$	−6.87228	+	11.9031i	−0.339812	+	0.588572i	−0.984397	−	0.175960i	$-0.943697\pi$
$409$	−6.87228	+	11.9031i	−0.339812	+	0.588572i	0.644585	+	0.764533i	$0.277030\pi$
$410$	5.74661	−	23.5149i	0.283805	−	1.16132i
$411$	9.40910	+	1.38762i	0.464117	+	0.0684465i
$412$	0.438125	−	0.842859i	0.0215849	−	0.0415247i
$413$			15.7908i			0.777016i
$414$	6.72601	+	11.8938i	0.330565	+	0.584547i
$415$			19.2864i			0.946731i
$416$	−12.4999	+	4.88246i	−0.612860	+	0.239383i
$417$	−9.81386	−	24.7735i	−0.480587	−	1.21316i
$418$	−3.26530	−	0.797979i	−0.159711	−	0.0390305i
$419$	13.4819	−	23.3513i	0.658634	−	1.14079i	−0.322336	−	0.946625i	$-0.604468\pi$
$419$	13.4819	−	23.3513i	0.658634	−	1.14079i	0.980970	−	0.194162i	$-0.0621986\pi$
$420$	−6.53478	+	9.04235i	−0.318864	+	0.441221i
$421$	5.30298	+	9.18504i	0.258452	+	0.447651i	0.965827	−	0.259186i	$-0.0834544\pi$
$421$	5.30298	+	9.18504i	0.258452	+	0.447651i	−0.707376	+	0.706838i	$0.750121\pi$
$422$	−6.94661	−	23.8063i	−0.338156	−	1.15887i
$423$	−2.62112	+	2.46323i	−0.127443	+	0.119766i
$424$	−4.00000	−	3.50157i	−0.194257	−	0.170051i
$425$	−0.941578	+	0.543620i	−0.0456732	+	0.0263695i
$426$	−3.98563	−	28.8049i	−0.193104	−	1.39560i
$427$	2.62112	+	1.51330i	0.126845	+	0.0732339i
$428$	−1.11117	−	25.1057i	−0.0537103	−	1.21353i
$429$	−1.62772	−	1.28962i	−0.0785870	−	0.0622635i
$430$	−19.9385	−	19.0755i	−0.961518	−	0.919904i
$431$	−31.1952			−1.50262			−0.751310	−	0.659949i	$-0.770578\pi$
$431$	−31.1952			−1.50262			−0.751310	+	0.659949i	$0.770578\pi$
$432$	−7.14267	+	19.5188i	−0.343652	+	0.939097i
$433$	−8.62772			−0.414622			−0.207311	−	0.978275i	$-0.566471\pi$
$433$	−8.62772			−0.414622			−0.207311	+	0.978275i	$0.566471\pi$
$434$	−10.5991	−	10.1404i	−0.508774	−	0.486754i
$435$	8.65099	+	6.85407i	0.414783	+	0.328627i
$436$	1.19288	+	26.9519i	0.0571284	+	1.29076i
$437$	13.1168	+	7.57301i	0.627464	+	0.362266i
$438$	−1.13217	−	8.18241i	−0.0540972	−	0.390971i
$439$	5.65357	−	3.26409i	0.269830	−	0.155786i	−0.358980	−	0.933345i	$-0.616876\pi$
$439$	5.65357	−	3.26409i	0.269830	−	0.155786i	0.628810	+	0.777559i	$0.283542\pi$
$440$	2.71519	+	2.37686i	0.129442	+	0.113312i
$441$	−15.4307	−	4.65253i	−0.734795	−	0.221549i
$442$	0.744563	+	2.55164i	0.0354152	+	0.121369i
$443$	6.18850	+	10.7188i	0.294025	+	0.509265i	0.974758	−	0.223266i	$-0.0716719\pi$
$443$	6.18850	+	10.7188i	0.294025	+	0.509265i	−0.680733	+	0.732532i	$0.738339\pi$
$444$	−13.6851	+	18.9364i	−0.649465	+	0.898683i
$445$	−15.1168	+	26.1831i	−0.716607	+	1.24120i
$446$	−11.1687	−	2.72943i	−0.528854	−	0.129242i
$447$	8.23966	+	20.7997i	0.389723	+	0.983791i
$448$	−6.22787	−	8.08627i	−0.294239	−	0.382040i
$449$			19.4024i			0.915657i	0.889041	+	0.457828i	$0.151373\pi$
$449$			19.4024i			0.915657i	−0.889041	+	0.457828i	$0.848627\pi$
$450$	−5.82186	−	0.0519795i	−0.274445	−	0.00245034i
$451$			3.42703i			0.161373i
$452$	6.71355	−	12.9154i	0.315779	−	0.607492i
$453$	−5.18614	−	0.764836i	−0.243666	−	0.0359351i
$454$	4.83403	−	19.7806i	0.226872	−	0.928351i
$455$	−3.82009	+	6.61659i	−0.179088	+	0.310190i
$456$	4.16377	+	22.6598i	0.194986	+	1.06114i
$457$	−19.9891	−	34.6222i	−0.935052	−	1.61956i	−0.774541	−	0.632523i	$-0.782019\pi$
$457$	−19.9891	−	34.6222i	−0.935052	−	1.61956i	−0.160510	−	0.987034i	$-0.551314\pi$
$458$	−4.92498	+	1.43710i	−0.230129	+	0.0671511i
$459$	3.72601	+	1.75079i	0.173915	+	0.0817196i
$460$	−8.74456	−	13.7081i	−0.407717	−	0.639145i
$461$	0.302985	−	0.174928i	0.0141114	−	0.00814722i	−0.492928	−	0.870070i	$-0.664073\pi$
$461$	0.302985	−	0.174928i	0.0141114	−	0.00814722i	0.507039	+	0.861923i	$0.330740\pi$
$462$	0.594797	−	1.46318i	0.0276725	−	0.0680733i
$463$	4.13734	+	2.38870i	0.192279	+	0.111012i	0.593049	−	0.805167i	$-0.297924\pi$
$463$	4.13734	+	2.38870i	0.192279	+	0.111012i	−0.400770	+	0.916179i	$0.631257\pi$
$464$	−8.26434	+	5.80148i	−0.383662	+	0.269327i
$465$	5.18614	−	35.1658i	0.240502	−	1.63077i
$466$	4.73794	−	4.95228i	0.219481	−	0.229410i
$467$	5.11313			0.236608			0.118304	−	0.992977i	$-0.462254\pi$
$467$	5.11313			0.236608			0.118304	+	0.992977i	$0.462254\pi$
$468$	−3.50233	+	13.7961i	−0.161895	+	0.637724i
$469$	9.86141			0.455357
$470$	2.95894	−	3.09279i	0.136486	−	0.142660i
$471$	19.1004	−	7.56651i	0.880102	−	0.348647i
$472$	−11.2825	−	33.1395i	−0.519318	−	1.52537i
$473$	3.38316	+	1.95327i	0.155558	+	0.0898113i
$474$	14.8599	+	19.1037i	0.682538	+	0.877460i
$475$	−5.58902	+	3.22682i	−0.256442	+	0.148057i
$476$	−1.70438	+	1.08724i	−0.0781201	+	0.0498336i
$477$	−5.48913	+	1.28962i	−0.251330	+	0.0590477i
$478$	16.3723	−	4.77739i	0.748851	−	0.218513i
$479$	6.53528	+	11.3194i	0.298605	+	0.517198i	0.975817	−	0.218589i	$-0.0701455\pi$
$479$	6.53528	+	11.3194i	0.298605	+	0.517198i	−0.677212	+	0.735788i	$0.736812\pi$
$480$	7.25352	−	23.6458i	0.331077	−	1.07928i
$481$	−8.00000	+	13.8564i	−0.364769	+	0.631798i
$482$	−2.17858	+	8.91467i	−0.0992317	+	0.406052i
$483$	−4.41957	+	5.57825i	−0.201098	+	0.253819i
$484$	19.0670	+	9.91119i	0.866682	+	0.450508i
$485$			26.4781i			1.20231i
$486$	12.4297	+	18.2072i	0.563821	+	0.825897i
$487$		−	42.8752i		−	1.94286i	−0.237325	−	0.971430i	$-0.576271\pi$
$487$		−	42.8752i		−	1.94286i	0.237325	−	0.971430i	$-0.423729\pi$
$488$	−6.58207	−	1.30312i	−0.297956	−	0.0589897i
$489$	1.88316	−	2.37686i	0.0851593	−	0.107485i
$490$	18.6305	+	4.55296i	0.841641	+	0.205682i
$491$	−6.88206	+	11.9201i	−0.310583	+	0.537946i	−0.978489	−	0.206300i	$-0.933858\pi$
$491$	−6.88206	+	11.9201i	−0.310583	+	0.537946i	0.667906	+	0.744246i	$0.267191\pi$
$492$	21.4342	−	9.60812i	0.966326	−	0.433168i
$493$	1.00000	+	1.73205i	0.0450377	+	0.0780076i
$494$	4.41957	+	15.1460i	0.198846	+	0.681452i
$495$	3.72601	−	0.875393i	0.167472	−	0.0393460i
$496$	29.4891	+	13.7081i	1.32410	+	0.615513i
$497$	13.1168	−	7.57301i	0.588371	−	0.339696i
$498$	−14.7718	+	11.4903i	−0.661940	+	0.514894i
$499$	−2.96790	−	1.71352i	−0.132861	−	0.0767076i	0.432096	−	0.901828i	$-0.357774\pi$
$499$	−2.96790	−	1.71352i	−0.132861	−	0.0767076i	−0.564958	+	0.825120i	$0.691107\pi$
$500$	−18.2973	+	0.809827i	−0.818278	+	0.0362166i
$501$	28.1644	−	11.1571i	1.25829	−	0.498464i
$502$	11.4225	+	10.9281i	0.509810	+	0.487746i
$503$	−19.3236			−0.861597			−0.430799	−	0.902448i	$-0.641768\pi$
$503$	−19.3236			−0.861597			−0.430799	+	0.902448i	$0.641768\pi$
$504$	−10.8190	+	0.382095i	−0.481914	+	0.0170199i
$505$	−3.11684			−0.138698
$506$	1.66332	+	1.59133i	0.0739434	+	0.0707431i
$507$	1.86301	−	12.6325i	0.0827390	−	0.561030i
$508$	15.2949	−	0.676943i	0.678600	−	0.0300345i
$509$	12.8139	+	7.39809i	0.567964	+	0.327914i	0.756336	−	0.654183i	$-0.226988\pi$
$509$	12.8139	+	7.39809i	0.567964	+	0.327914i	−0.188372	+	0.982098i	$0.560321\pi$
$510$	−4.53833	−	1.84487i	−0.200961	−	0.0816924i
$511$	3.72601	−	2.15121i	0.164829	−	0.0951641i
$512$	18.8477	+	12.5205i	0.832960	+	0.553333i
$513$	22.1168	+	10.3923i	0.976483	+	0.458831i
$514$	5.94158	+	20.3620i	0.262072	+	0.898129i
$515$	0.599485	+	1.03834i	0.0264165	+	0.0457547i
$516$	2.73146	−	26.6360i	0.120246	−	1.17258i
$517$	−0.302985	+	0.524785i	−0.0133252	+	0.0230800i
$518$	−11.8212	−	2.88889i	−0.519395	−	0.126931i
$519$	−30.2785	−	4.46537i	−1.32908	−	0.196008i
$520$	3.28953	−	16.6154i	0.144255	−	0.728632i
$521$		−	26.0357i		−	1.14064i	−0.821421	−	0.570322i	$-0.806819\pi$
$521$		−	26.0357i		−	1.14064i	0.821421	−	0.570322i	$-0.193181\pi$
$522$	−0.0956173	+	10.7094i	−0.00418505	+	0.468739i
$523$		−	9.40571i		−	0.411283i	−0.978627	−	0.205641i	$-0.934072\pi$
$523$		−	9.40571i		−	0.411283i	0.978627	−	0.205641i	$-0.0659281\pi$
$524$	13.5580	+	7.04758i	0.592286	+	0.307875i
$525$	−1.11684	−	2.81929i	−0.0487431	−	0.123044i
$526$	−9.39187	+	38.4311i	−0.409505	+	1.67568i
$527$	3.22060	−	5.57825i	0.140292	−	0.242992i
$528$	−0.202838	+	3.49569i	−0.00882739	+	0.152130i
$529$	6.31386	+	10.9359i	0.274516	+	0.475475i
$530$	6.44121	−	1.87953i	0.279788	−	0.0816415i
$531$	−35.5502	−	10.7188i	−1.54275	−	0.465156i
$532$	−10.1168	+	6.45364i	−0.438621	+	0.279801i
$533$	13.9307	−	8.04290i	0.603406	−	0.348376i
$534$	−29.0604	+	4.02098i	−1.25757	+	0.174005i
$535$	27.4692	+	15.8593i	1.18760	+	0.685659i
$536$	−20.6957	+	7.04593i	−0.893917	+	0.304338i
$537$	−12.0000	−	9.50744i	−0.517838	−	0.410276i
$538$	21.0040	−	21.9542i	0.905546	−	0.946511i
$539$	−2.71519			−0.116952
$540$	−15.9214	−	20.8498i	−0.685149	−	0.897233i
$541$	−8.97825			−0.386005			−0.193003	−	0.981198i	$-0.561823\pi$
$541$	−8.97825			−0.386005			−0.193003	+	0.981198i	$0.561823\pi$
$542$	−29.2979	+	30.6233i	−1.25845	+	1.31538i
$543$	5.43039	+	4.30243i	0.233040	+	0.184635i
$544$	2.80007	−	3.49951i	0.120052	−	0.150040i
$545$	−29.4891	−	17.0256i	−1.26318	−	0.729295i
$546$	−7.34368	+	1.01612i	−0.314280	+	0.0434858i
$547$	−19.2591	+	11.1192i	−0.823458	+	0.475424i	−0.851608	−	0.524180i	$-0.824372\pi$
$547$	−19.2591	+	11.1192i	−0.823458	+	0.475424i	0.0281494	+	0.999604i	$0.491039\pi$
$548$	−5.90627	−	9.25878i	−0.252303	−	0.395515i
$549$	−5.18614	+	4.87375i	−0.221339	+	0.208006i
$550$	−0.941578	+	0.274750i	−0.0401490	+	0.0117154i
$551$	5.93580	+	10.2811i	0.252873	+	0.437990i
$552$	5.28953	−	14.8646i	0.225137	−	0.632678i
$553$	−6.30298	+	10.9171i	−0.268030	+	0.464242i
$554$	2.13936	−	8.75415i	0.0908925	−	0.371928i
$555$	−10.8608	−	27.4163i	−0.461014	−	1.16376i
$556$	−14.1911	+	27.3007i	−0.601838	+	1.15781i
$557$		−	7.22316i		−	0.306055i	−0.988222	−	0.153027i	$-0.951098\pi$
$557$		−	7.22316i		−	0.306055i	0.988222	−	0.153027i	$-0.0489023\pi$
$558$	30.0239	−	16.9787i	1.27101	−	0.718767i
$559$		−	18.3365i		−	0.775549i
$560$	12.8320	−	1.13811i	0.542253	−	0.0480938i
$561$	0.686141	+	0.101190i	0.0289689	+	0.00427224i
$562$	−31.6163	−	7.72645i	−1.33365	−	0.325921i
$563$	7.89288	−	13.6709i	0.332645	−	0.576158i	−0.650384	−	0.759605i	$-0.725392\pi$
$563$	7.89288	−	13.6709i	0.332645	−	0.576158i	0.983030	+	0.183447i	$0.0587255\pi$
$564$	4.13169	+	0.423696i	0.173975	+	0.0178408i
$565$	9.18614	+	15.9109i	0.386464	+	0.669375i
$566$	−3.91416	−	13.4140i	−0.164525	−	0.563831i
$567$	−6.34713	+	9.56866i	−0.266554	+	0.401846i
$568$	−22.1168	+	25.2651i	−0.928002	+	1.06010i
$569$	−21.9891	+	12.6954i	−0.921832	+	0.532220i	−0.884219	−	0.467072i	$-0.845309\pi$
$569$	−21.9891	+	12.6954i	−0.921832	+	0.532220i	−0.0376130	+	0.999292i	$0.511975\pi$
$570$	−26.9386	−	10.9508i	−1.12833	−	0.458679i
$571$	3.66146	+	2.11395i	0.153227	+	0.0884659i	0.574653	−	0.818397i	$-0.305137\pi$
$571$	3.66146	+	2.11395i	0.153227	+	0.0884659i	−0.421426	+	0.906863i	$0.638470\pi$
$572$	0.106028	+	2.39560i	0.00443324	+	0.100165i
$573$	−3.81386	+	25.8607i	−0.159326	+	1.08035i
$574$	8.84018	+	8.45757i	0.368982	+	0.353012i
$575$	4.41957			0.184309
$576$	22.4322	−	8.53197i	0.934677	−	0.355499i
$577$	31.8397			1.32550			0.662751	−	0.748840i	$-0.269389\pi$
$577$	31.8397			1.32550			0.662751	+	0.748840i	$0.269389\pi$
$578$	16.7303	+	16.0062i	0.695890	+	0.665771i
$579$	12.4711	−	4.94034i	0.518280	−	0.205313i
$580$	−0.563516	−	12.7321i	−0.0233987	−	0.528672i
$581$	−8.44158	−	4.87375i	−0.350216	−	0.202197i
$582$	−20.2801	+	15.7750i	−0.840635	+	0.653894i
$583$	−0.822662	+	0.474964i	−0.0340712	+	0.0196710i
$584$	−6.28258	+	7.17687i	−0.259975	+	0.296981i
$585$	−12.3030	−	13.0916i	−0.508666	−	0.541270i
$586$	−9.23369	−	31.6442i	−0.381440	−	1.30721i
$587$	−1.95708	−	3.38977i	−0.0807774	−	0.139911i	0.822807	−	0.568321i	$-0.192407\pi$
$587$	−1.95708	−	3.38977i	−0.0807774	−	0.139911i	−0.903584	+	0.428411i	$0.859074\pi$
$588$	7.61239	+	16.9820i	0.313930	+	0.700326i
$589$	19.1168	−	33.1113i	0.787696	−	1.36433i
$590$	42.9222	+	10.4894i	1.76708	+	0.431842i
$591$	25.7648	−	32.5196i	1.05982	−	1.33768i
$592$	26.8728	−	2.38342i	1.10446	−	0.0979578i
$593$			8.80773i			0.361690i	0.983512	+	0.180845i	$0.0578833\pi$
$593$			8.80773i			0.361690i	−0.983512	+	0.180845i	$0.942117\pi$
$594$	2.89034	+	2.33228i	0.118592	+	0.0956948i
$595$		−	2.55164i		−	0.104607i
$596$	11.9148	−	22.9215i	0.488049	−	0.938902i
$597$	−13.8832	+	17.5229i	−0.568200	+	0.717164i
$598$	2.56502	−	10.4960i	0.104892	−	0.429212i
$599$	0.0940770	−	0.162946i	0.00384388	−	0.00665780i	−0.864097	−	0.503325i	$-0.832110\pi$
$599$	0.0940770	−	0.162946i	0.00384388	−	0.00665780i	0.867941	+	0.496667i	$0.165443\pi$
$600$	4.35824	+	5.11874i	0.177924	+	0.208972i
$601$	−7.98913	−	13.8376i	−0.325883	−	0.564446i	0.655807	−	0.754928i	$-0.272328\pi$
$601$	−7.98913	−	13.8376i	−0.325883	−	0.564446i	−0.981691	+	0.190482i	$0.938995\pi$
$602$	13.3878	−	3.90653i	0.545647	−	0.159218i
$603$	−6.69391	+	22.2012i	−0.272597	+	0.904102i
$604$	3.25544	+	5.10328i	0.132462	+	0.207650i
$605$	−23.4891	+	13.5615i	−0.954969	+	0.551351i
$606$	−1.85694	−	2.38725i	−0.0754329	−	0.0969753i
$607$	−3.44378	−	1.98827i	−0.139779	−	0.0807013i	0.428480	−	0.903551i	$-0.359049\pi$
$607$	−3.44378	−	1.98827i	−0.139779	−	0.0807013i	−0.568259	+	0.822850i	$0.692383\pi$
$608$	16.6207	−	20.7724i	0.674057	−	0.842432i
$609$	−5.18614	+	2.05446i	−0.210153	+	0.0832508i
$610$	5.85455	−	6.11940i	0.237044	−	0.247767i
$611$	2.84429			0.115068
$612$	−1.29080	−	4.57512i	−0.0521774	−	0.184938i
$613$	4.23369			0.170997			0.0854985	−	0.996338i	$-0.472752\pi$
$613$	4.23369			0.170997			0.0854985	+	0.996338i	$0.472752\pi$
$614$	1.17443	−	1.22756i	0.0473960	−	0.0495401i
$615$	−4.32550	+	29.3300i	−0.174421	+	1.18270i
$616$	−1.72648	+	0.587788i	−0.0695620	+	0.0236827i
$617$	−4.24456	−	2.45060i	−0.170880	−	0.0986574i	0.412121	−	0.911129i	$-0.364788\pi$
$617$	−4.24456	−	2.45060i	−0.170880	−	0.0986574i	−0.583001	+	0.812472i	$0.698121\pi$
$618$	−0.438125	+	1.07777i	−0.0176240	+	0.0433544i
$619$	−8.08103	+	4.66559i	−0.324804	+	0.187526i	−0.653532	−	0.756899i	$-0.726713\pi$
$619$	−8.08103	+	4.66559i	−0.324804	+	0.187526i	0.328728	+	0.944425i	$0.393380\pi$
$620$	−34.6040	+	22.0742i	−1.38973	+	0.886522i
$621$	−9.55842	−	13.7364i	−0.383566	−	0.551222i
$622$	−25.9783	+	7.58039i	−1.04163	+	0.303946i
$623$	−7.64018	−	13.2332i	−0.306097	−	0.530176i
$624$	14.6858	−	7.37950i	0.587904	−	0.295416i
$625$	14.9891	−	25.9619i	0.599565	−	1.03848i
$626$	−6.20732	+	25.4001i	−0.248095	+	1.01519i
$627$	4.07279	+	0.600642i	0.162652	+	0.0239873i
$628$	−21.0489	−	10.9414i	−0.839944	−	0.436610i
$629$		−	5.34363i		−	0.213064i
$630$	6.93730	−	11.7718i	0.276389	−	0.468999i
$631$			42.8752i			1.70683i	0.521228	+	0.853417i	$0.325474\pi$
$631$			42.8752i			1.70683i	−0.521228	+	0.853417i	$0.674526\pi$
$632$	5.42758	−	27.4147i	0.215898	−	1.09050i
$633$	11.1861	+	28.2376i	0.444609	+	1.12234i
$634$	−44.6775	−	10.9184i	−1.77437	−	0.433624i
$635$	−9.66181	+	16.7347i	−0.383417	+	0.664098i
$636$	5.27707	+	3.81366i	0.209249	+	0.151222i
$637$	6.37228	+	11.0371i	0.252479	+	0.437306i
$638$	0.505408	+	1.73205i	0.0200093	+	0.0685725i
$639$	8.14558	+	34.6708i	0.322234	+	1.37155i
$640$	−26.1168	+	11.5569i	−1.03236	+	0.456827i
$641$	18.1277	−	10.4660i	0.716002	−	0.413384i	−0.0972775	−	0.995257i	$-0.531013\pi$
$641$	18.1277	−	10.4660i	0.716002	−	0.413384i	0.813279	+	0.581873i	$0.197680\pi$
$642$	4.21848	+	30.4878i	0.166490	+	1.20326i
$643$	31.1307	+	17.9733i	1.22767	+	0.708798i	0.966543	−	0.256506i	$-0.0825713\pi$
$643$	31.1307	+	17.9733i	1.22767	+	0.708798i	0.261131	+	0.965303i	$0.415905\pi$
$644$	8.20979	−	0.363361i	0.323511	−	0.0143184i
$645$	26.4891	+	20.9870i	1.04301	+	0.826362i
$646$	−3.80749	−	3.64270i	−0.149804	−	0.143320i
$647$	46.0993			1.81235			0.906174	−	0.422904i	$-0.138989\pi$
$647$	46.0993			1.81235			0.906174	+	0.422904i	$0.138989\pi$
$648$	6.48367	−	24.6163i	0.254703	−	0.967019i
$649$	−6.25544			−0.245547
$650$	3.32663	+	3.18265i	0.130481	+	0.124834i
$651$	14.0814	+	11.1565i	0.551893	+	0.437258i
$652$	−3.49815	+	0.154826i	−0.136998	+	0.00606346i
$653$	3.81386	+	2.20193i	0.149248	+	0.0861683i	0.572764	−	0.819720i	$-0.305871\pi$
$653$	3.81386	+	2.20193i	0.149248	+	0.0861683i	−0.423516	+	0.905888i	$0.639204\pi$
$654$	−4.52868	−	32.7297i	−0.177085	−	1.27983i
$655$	−16.7025	+	9.64319i	−0.652621	+	0.376791i
$656$	−24.5954	−	11.4333i	−0.960288	−	0.446394i
$657$	2.31386	+	9.84868i	0.0902723	+	0.384234i
$658$	0.605969	+	2.07668i	0.0236231	+	0.0809573i
$659$	−6.02987	−	10.4440i	−0.234891	−	0.406842i	0.724350	−	0.689432i	$-0.242140\pi$
$659$	−6.02987	−	10.4440i	−0.234891	−	0.406842i	−0.959241	+	0.282590i	$0.908807\pi$
$660$	−3.58207	−	2.58871i	−0.139432	−	0.100765i
$661$	−7.81386	+	13.5340i	−0.303924	+	0.526412i	−0.977021	−	0.213142i	$-0.931630\pi$
$661$	−7.81386	+	13.5340i	−0.303924	+	0.526412i	0.673097	+	0.739554i	$0.264964\pi$
$662$	38.1118	+	9.31383i	1.48126	+	0.361992i
$663$	−1.19897	−	3.02661i	−0.0465641	−	0.117544i
$664$	21.1982	+	4.19685i	0.822651	+	0.162869i
$665$		−	15.1460i		−	0.587338i
$666$	14.5281	−	24.6524i	0.562951	−	0.955260i
$667$		−	8.12989i		−	0.314791i
$668$	−31.0375	−	16.1336i	−1.20088	−	0.624226i
$669$	13.9307	+	2.05446i	0.538592	+	0.0794299i
$670$	6.55065	−	26.8050i	0.253074	−	1.03557i
$671$	−0.599485	+	1.03834i	−0.0231429	+	0.0400846i
$672$	8.51670	+	9.15024i	0.328539	+	0.352978i
$673$	−14.9307	−	25.8607i	−0.575536	−	0.996858i	−0.995983	−	0.0895410i	$-0.971460\pi$
$673$	−14.9307	−	25.8607i	−0.575536	−	0.996858i	0.420447	−	0.907317i	$-0.361873\pi$
$674$	21.3748	−	6.23711i	0.823326	−	0.240244i
$675$	7.10524	−	0.600642i	0.273481	−	0.0231187i
$676$	−12.4307	+	7.92967i	−0.478104	+	0.304987i
$677$	−3.04755	+	1.75950i	−0.117127	+	0.0676232i	−0.557419	−	0.830231i	$-0.688208\pi$
$677$	−3.04755	+	1.75950i	−0.117127	+	0.0676232i	0.440292	+	0.897855i	$0.354875\pi$
$678$	−6.71355	+	16.5151i	−0.257832	+	0.634259i
$679$	−11.5894	−	6.69112i	−0.444759	−	0.256782i
$680$	1.82314	+	5.35501i	0.0699140	+	0.205355i
$681$	−3.63859	+	24.6723i	−0.139431	+	0.945445i
$682$	4.01704	−	4.19877i	0.153821	−	0.160779i
$683$	−20.0172			−0.765936			−0.382968	−	0.923762i	$-0.625098\pi$
$683$	−20.0172			−0.765936			−0.382968	+	0.923762i	$0.625098\pi$
$684$	−7.66191	−	27.1570i	−0.292960	−	1.03837i
$685$	13.8614			0.529617
$686$	−15.4319	+	16.1300i	−0.589193	+	0.615847i
$687$	5.84172	−	2.31416i	0.222876	−	0.0882907i
$688$	−25.3052	+	17.7640i	−0.964752	+	0.677246i
$689$	3.86141	+	2.22938i	0.147108	+	0.0849328i
$690$	12.2268	+	15.7186i	0.465468	+	0.598398i
$691$	17.3961	−	10.0436i	0.661777	−	0.382077i	−0.131177	−	0.991359i	$-0.541875\pi$
$691$	17.3961	−	10.0436i	0.661777	−	0.382077i	0.792954	+	0.609282i	$0.208542\pi$
$692$	19.0064	+	29.7947i	0.722513	+	1.13263i
$693$	−0.558422	+	1.85208i	−0.0212127	+	0.0703546i
$694$	9.43070	−	2.75186i	0.357985	−	0.104459i
$695$	−19.4177	−	33.6324i	−0.736555	−	1.27575i
$696$	9.41602	−	8.01707i	0.356913	−	0.303886i
$697$	−2.68614	+	4.65253i	−0.101745	+	0.176227i
$698$	−1.88938	+	7.73128i	−0.0715143	+	0.292633i
$699$	−5.21271	+	6.57932i	−0.197163	+	0.248853i
$700$	−1.61499	+	3.10690i	−0.0610409	+	0.117430i
$701$		−	32.7615i		−	1.23738i	−0.785634	−	0.618692i	$-0.787663\pi$
$701$		−	32.7615i		−	1.23738i	0.785634	−	0.618692i	$-0.212337\pi$
$702$	2.69727	−	17.2227i	0.101802	−	0.650029i
$703$		−	31.7187i		−	1.19629i
$704$	3.20332	−	2.46713i	0.120730	−	0.0929834i
$705$	−3.25544	+	4.10891i	−0.122607	+	0.154751i
$706$	11.4921	+	2.80847i	0.432512	+	0.105698i
$707$	0.787639	−	1.36423i	0.0296222	−	0.0513072i
$708$	17.5379	+	39.1242i	0.659115	+	1.47038i
$709$	−11.9307	−	20.6646i	−0.448067	−	0.776075i	0.550193	−	0.835037i	$-0.314554\pi$
$709$	−11.9307	−	20.6646i	−0.448067	−	0.776075i	−0.998260	+	0.0589626i	$0.981221\pi$
$710$	−11.8716	−	40.6844i	−0.445533	−	1.52686i
$711$	−20.2994	−	21.6005i	−0.761287	−	0.810084i
$712$	25.4891	+	22.3130i	0.955245	+	0.836215i
$713$	−22.6753	+	13.0916i	−0.849195	+	0.490283i
$714$	1.95435	−	1.52020i	0.0731397	−	0.0568922i
$715$	−2.62112	−	1.51330i	−0.0980242	−	0.0565943i
$716$	0.781666	+	17.6610i	0.0292122	+	0.660023i
$717$	−19.4198	+	7.69304i	−0.725247	+	0.287302i
$718$	−1.41746	−	1.35611i	−0.0528991	−	0.0506096i
$719$	16.2912			0.607558			0.303779	−	0.952743i	$-0.401752\pi$
$719$	16.2912			0.607558			0.303779	+	0.952743i	$0.401752\pi$
$720$	−6.14813	+	29.6616i	−0.229127	+	1.10542i
$721$	−0.605969			−0.0225675
$722$	−3.18501	−	3.04716i	−0.118534	−	0.113403i
$723$	1.63983	−	11.1192i	0.0609859	−	0.413528i
$724$	−0.353729	−	7.99218i	−0.0131463	−	0.297027i
$725$	3.00000	+	1.73205i	0.111417	+	0.0643268i
$726$	−24.3812	−	9.91119i	−0.904871	−	0.367839i
$727$	−32.9937	+	19.0489i	−1.22367	+	0.706485i	−0.965698	−	0.259668i	$-0.916387\pi$
$727$	−32.9937	+	19.0489i	−1.22367	+	0.706485i	−0.257969	+	0.966153i	$0.583053\pi$
$728$	6.44121	+	5.63858i	0.238727	+	0.208980i
$729$	−17.2337	−	20.7846i	−0.638285	−	0.769800i
$730$	−3.37228	−	11.5569i	−0.124814	−	0.427741i
$731$	3.06198	+	5.30350i	0.113251	+	0.196157i
$732$	8.17495	+	0.838325i	0.302155	+	0.0309854i
$733$	−0.186141	+	0.322405i	−0.00687526	+	0.0119083i	−0.869443	−	0.494034i	$-0.835522\pi$
$733$	−0.186141	+	0.322405i	−0.00687526	+	0.0119083i	0.862567	+	0.505942i	$0.168855\pi$
$734$	−8.76352	−	2.14165i	−0.323467	−	0.0790496i
$735$	−23.2378	−	3.42703i	−0.857138	−	0.126408i
$736$	−16.9699	+	6.62842i	−0.625518	+	0.244327i
$737$			3.90653i			0.143899i
$738$	−25.0414	+	14.1611i	−0.921787	+	0.521277i
$739$			6.45364i			0.237401i	0.992930	+	0.118700i	$0.0378728\pi$
$739$			6.45364i			0.237401i	−0.992930	+	0.118700i	$0.962127\pi$
$740$	−15.7050	+	30.2131i	−0.577328	+	1.11066i
$741$	−7.11684	−	17.9653i	−0.261444	−	0.659972i
$742$	−0.805056	+	3.29426i	−0.0295546	+	0.120936i
$743$	10.5785	−	18.3226i	0.388089	−	0.672190i	−0.604103	−	0.796906i	$-0.706469\pi$
$743$	10.5785	−	18.3226i	0.388089	−	0.672190i	0.992193	+	0.124716i	$0.0398019\pi$
$744$	−37.5232	−	13.3526i	−1.37567	−	0.489528i
$745$	16.3030	+	28.2376i	0.597295	+	1.03455i
$746$	26.9638	−	7.86797i	0.987215	−	0.288067i
$747$	16.7025	−	15.6964i	0.611112	−	0.574301i
$748$	−0.430703	−	0.675178i	−0.0157481	−	0.0246870i
$749$	−13.8832	+	8.01544i	−0.507279	+	0.292878i
$750$	22.2197	−	3.07446i	0.811350	−	0.112263i
$751$	−18.7832	−	10.8445i	−0.685408	−	0.395721i	0.116481	−	0.993193i	$-0.462838\pi$
$751$	−18.7832	−	10.8445i	−0.685408	−	0.395721i	−0.801890	+	0.597472i	$0.796172\pi$
$752$	−2.75550	−	3.92527i	−0.100483	−	0.143140i
$753$	−15.1753	−	12.0232i	−0.553017	−	0.438149i
$754$	5.85455	−	6.11940i	0.213210	−	0.222855i
$755$	−7.64018			−0.278054
$756$	13.1493	−	1.69992i	0.478235	−	0.0618254i
$757$	14.0000			0.508839			0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$	6.30935	−	6.59477i	0.229166	−	0.239533i
$759$	−2.20979	−	1.75079i	−0.0802102	−	0.0635495i
$760$	10.8218	+	31.7863i	0.392547	+	1.15301i
$761$	15.0475	+	8.68771i	0.545473	+	0.314929i	0.747294	−	0.664493i	$-0.231353\pi$
$761$	15.0475	+	8.68771i	0.545473	+	0.314929i	−0.201821	+	0.979422i	$0.564686\pi$
$762$	−18.5737	+	2.56997i	−0.672854	+	0.0931004i
$763$	14.9040	−	8.60485i	0.539563	−	0.311517i
$764$	25.4476	−	16.2333i	0.920661	−	0.587299i
$765$	5.74456	+	1.73205i	0.207695	+	0.0626224i
$766$	−11.7446	+	3.42703i	−0.424348	+	0.123824i
$767$	14.6809	+	25.4280i	0.530095	+	0.918152i
$768$	−24.4114	−	13.1181i	−0.880871	−	0.473357i
$769$	−4.04755	+	7.01056i	−0.145958	+	0.252807i	−0.929730	−	0.368242i	$-0.879960\pi$
$769$	−4.04755	+	7.01056i	−0.145958	+	0.252807i	0.783772	+	0.621049i	$0.213293\pi$
$770$	0.546471	−	2.23614i	0.0196935	−	0.0805848i
$771$	−9.56773	−	24.1522i	−0.344573	−	0.869820i
$772$	−13.7433	−	7.14387i	−0.494632	−	0.257114i
$773$		−	0.699713i		−	0.0251669i	−0.999921	−	0.0125835i	$-0.995994\pi$
$773$		−	0.699713i		−	0.0251669i	0.999921	−	0.0125835i	$-0.00400555\pi$
$774$	−0.292778	+	32.7920i	−0.0105237	+	1.17868i
$775$		−	11.1565i		−	0.400753i
$776$	29.1028	+	5.76181i	1.04473	+	0.206837i
$777$	14.7446	+	2.17448i	0.528958	+	0.0780091i
$778$	43.3110	+	10.5844i	1.55278	+	0.379470i
$779$	−15.9444	+	27.6165i	−0.571267	+	0.989463i
$780$	−2.11622	+	20.6363i	−0.0757727	+	0.738899i
$781$	3.00000	+	5.19615i	0.107348	+	0.185933i
$782$	1.01082	+	3.46410i	0.0361467	+	0.123876i
$783$	−1.10489	−	13.0702i	−0.0394857	−	0.467092i
$784$	9.05842	−	19.4866i	0.323515	−	0.695950i
$785$	25.9307	−	14.9711i	0.925506	−	0.534341i
$786$	−17.3368	−	7.04758i	−0.618384	−	0.251379i
$787$	30.0903	+	17.3727i	1.07260	+	0.619268i	0.928892	−	0.370351i	$-0.120763\pi$
$787$	30.0903	+	17.3727i	1.07260	+	0.619268i	0.143712	+	0.989620i	$0.454096\pi$
$788$	−47.8607	+	2.11829i	−1.70497	+	0.0754609i
$789$	7.06930	−	47.9350i	0.251674	−	1.70653i
$790$	25.4876	+	24.3845i	0.906809	+	0.867562i
$791$	−9.28550			−0.330154
$792$	−0.151364	−	4.28586i	−0.00537850	−	0.152291i
$793$	5.62772			0.199846
$794$	−19.1545	−	18.3255i	−0.679767	−	0.650347i
$795$	−7.64018	+	3.02661i	−0.270969	+	0.107343i
$796$	25.7893	−	1.14142i	0.914078	−	0.0404566i
$797$	20.6970	+	11.9494i	0.733126	+	0.423270i	0.819565	−	0.572987i	$-0.194215\pi$
$797$	20.6970	+	11.9494i	0.733126	+	0.423270i	−0.0864387	+	0.996257i	$0.527549\pi$
$798$	11.6006	−	9.02361i	0.410657	−	0.319433i
$799$	−0.822662	+	0.474964i	−0.0291037	+	0.0168030i
$800$	1.16944	−	7.67420i	0.0413461	−	0.271324i
$801$	34.9783	−	8.21782i	1.23590	−	0.290363i
$802$	1.82473	+	6.25343i	0.0644336	+	0.220816i
$803$	0.852189	+	1.47603i	0.0300731	+	0.0520881i
$804$	24.4331	−	10.9525i	0.861690	−	0.386263i
$805$	−5.18614	+	8.98266i	−0.182787	+	0.316597i
$806$	−26.4954	−	6.47498i	−0.933259	−	0.228072i
$807$	−23.1087	+	29.1671i	−0.813464	+	1.02673i
$808$	−0.678246	+	3.42581i	−0.0238606	+	0.120520i
$809$			35.8381i			1.26000i	0.776595	+	0.630000i	$0.216945\pi$
$809$			35.8381i			1.26000i	−0.776595	+	0.630000i	$0.783055\pi$
$810$	21.7930	+	23.6088i	0.765729	+	0.829527i
$811$			1.20128i			0.0421828i	0.999778	+	0.0210914i	$0.00671410\pi$
$811$			1.20128i			0.0421828i	−0.999778	+	0.0210914i	$0.993286\pi$
$812$	5.71519	+	2.97080i	0.200564	+	0.104255i
$813$	32.2337	−	40.6844i	1.13048	−	1.42686i
$814$	1.14442	−	4.68290i	0.0401118	−	0.164136i
$815$	2.20979	−	3.82746i	0.0774054	−	0.134070i
$816$	−3.01533	+	4.58675i	−0.105558	+	0.160568i
$817$	18.1753	+	31.4805i	0.635872	+	1.10136i
$818$	−18.6596	+	5.44482i	−0.652417	+	0.190374i
$819$	8.83915	−	2.07668i	0.308865	−	0.0725650i
$820$	28.8614	−	18.4110i	1.00788	−	0.642940i
$821$	−15.8139	+	9.13014i	−0.551907	+	0.318644i	−0.749891	−	0.661561i	$-0.769894\pi$
$821$	−15.8139	+	9.13014i	−0.551907	+	0.318644i	0.197983	+	0.980205i	$0.436561\pi$
$822$	8.25827	+	10.6167i	0.288040	+	0.370300i
$823$	−12.1538	−	7.01701i	−0.423656	−	0.244598i	0.272984	−	0.962018i	$-0.411989\pi$
$823$	−12.1538	−	7.01701i	−0.423656	−	0.244598i	−0.696640	+	0.717421i	$0.745323\pi$
$824$	1.27172	−	0.432962i	0.0443025	−	0.0150829i
$825$	1.11684	−	0.442430i	0.0388835	−	0.0154035i
$826$	−15.4378	+	16.1362i	−0.537149	+	0.561449i
$827$	−47.4864			−1.65126			−0.825632	−	0.564210i	$-0.809181\pi$
$827$	−47.4864			−1.65126			−0.825632	+	0.564210i	$0.809181\pi$
$828$	−4.75475	+	18.7295i	−0.165239	+	0.650895i
$829$	−48.2337			−1.67523			−0.837613	−	0.546265i	$-0.816049\pi$
$829$	−48.2337			−1.67523			−0.837613	+	0.546265i	$0.816049\pi$
$830$	−18.8552	+	19.7082i	−0.654473	+	0.684080i
$831$	−1.61030	+	10.9190i	−0.0558607	+	0.378776i
$832$	−17.5466	−	7.23123i	−0.608319	−	0.250698i
$833$	−3.68614	−	2.12819i	−0.127717	−	0.0737376i
$834$	14.1911	−	34.9097i	0.491399	−	1.20882i
$835$	38.2359	−	22.0755i	1.32321	−	0.763954i
$836$	−2.55657	−	4.00772i	−0.0884207	−	0.138610i
$837$	−34.6753	+	24.1287i	−1.19855	+	0.834009i
$838$	36.6060	−	10.6815i	1.26453	−	0.368987i
$839$	21.3102	+	36.9104i	0.735711	+	1.27429i	0.954411	+	0.298496i	$0.0964850\pi$
$839$	21.3102	+	36.9104i	0.735711	+	1.27429i	−0.218700	+	0.975792i	$0.570182\pi$
$840$	−15.5179	+	2.85142i	−0.535417	+	0.0983835i
$841$	−11.3139	+	19.5962i	−0.390133	+	0.675730i
$842$	−3.56072	+	14.5703i	−0.122711	+	0.502127i
$843$	39.4349	+	5.81573i	1.35821	+	0.200304i
$844$	16.1755	−	31.1182i	0.556783	−	1.07113i
$845$		−	18.6101i		−	0.640208i
$846$	−5.08660	−	0.0454148i	−0.174881	−	0.00156139i
$847$		−	13.7081i		−	0.471017i
$848$	−0.664194	−	7.48871i	−0.0228085	−	0.257163i
$849$	6.30298	+	15.9109i	0.216318	+	0.546059i
$850$	−1.49364	−	0.365017i	−0.0512313	−	0.0125200i
$851$	−10.8608	+	18.8114i	−0.372303	+	0.644847i
$852$	24.0881	−	33.3314i	0.825245	−	1.14191i
$853$	−22.3030	−	38.6299i	−0.763640	−	1.32266i	−0.940963	−	0.338510i	$-0.890077\pi$
$853$	−22.3030	−	38.6299i	−0.763640	−	1.32266i	0.177323	−	0.984153i	$-0.443256\pi$
$854$	1.19897	+	4.10891i	0.0410279	+	0.140604i
$855$	34.0986	+	10.2811i	1.16615	+	0.351606i
$856$	23.4090	−	26.7411i	0.800102	−	0.913992i
$857$	32.5367	−	18.7851i	1.11143	−	0.641685i	0.172232	−	0.985056i	$-0.444902\pi$
$857$	32.5367	−	18.7851i	1.11143	−	0.641685i	0.939200	+	0.343371i	$0.111569\pi$
$858$	−0.402528	−	2.90915i	−0.0137421	−	0.0993167i
$859$	1.58077	+	0.912661i	0.0539353	+	0.0311396i	0.526725	−	0.850036i	$-0.323420\pi$
$859$	1.58077	+	0.912661i	0.0539353	+	0.0311396i	−0.472790	+	0.881175i	$0.656753\pi$
$860$	−1.72547	−	38.9854i	−0.0588381	−	1.32939i
$861$	−11.7446	−	9.30506i	−0.400254	−	0.317116i
$862$	−31.8774	−	30.4977i	−1.08575	−	1.03876i
$863$	40.0344			1.36279			0.681393	−	0.731918i	$-0.261375\pi$
$863$	40.0344			1.36279			0.681393	+	0.731918i	$0.261375\pi$
$864$	−26.3812	+	12.9626i	−0.897508	+	0.440998i
$865$	−44.6060			−1.51665
$866$	−8.81640	−	8.43482i	−0.299593	−	0.286627i
$867$	−22.2270	−	17.6101i	−0.754867	−	0.598072i
$868$	−0.917245	−	20.7243i	−0.0311333	−	0.703428i
$869$	−4.32473	−	2.49689i	−0.146707	−	0.0847011i
$870$	2.13936	+	15.4615i	0.0725309	+	0.524195i
$871$	15.8798	−	9.16823i	0.538068	−	0.310654i
$872$	−25.1303	+	28.7075i	−0.851020	+	0.972158i
$873$	22.9307	−	21.5494i	0.776087	−	0.729338i
$874$	6.00000	+	20.5622i	0.202953	+	0.695527i
$875$	5.84172	+	10.1182i	0.197486	+	0.342056i
$876$	6.84254	−	9.46821i	0.231188	−	0.319901i
$877$	−10.8139	+	18.7302i	−0.365158	+	0.632472i	−0.988802	−	0.149237i	$-0.952318\pi$
$877$	−10.8139	+	18.7302i	−0.365158	+	0.632472i	0.623643	+	0.781709i	$0.285652\pi$
$878$	8.96831	+	2.19169i	0.302666	+	0.0739661i
$879$	14.8690	+	37.5344i	0.501520	+	1.26600i
$880$	0.450854	+	5.08333i	0.0151983	+	0.171359i
$881$			52.9562i			1.78414i	0.451898	+	0.892070i	$0.350747\pi$
$881$			52.9562i			1.78414i	−0.451898	+	0.892070i	$0.649253\pi$
$882$	−11.2196	−	19.8400i	−0.377785	−	0.668047i
$883$			20.0127i			0.673481i	0.941597	+	0.336741i	$0.109325\pi$
$883$			20.0127i			0.673481i	−0.941597	+	0.336741i	$0.890675\pi$
$884$	−1.73375	+	3.33536i	−0.0583122	+	0.112180i
$885$	−53.5367	−	7.89542i	−1.79962	−	0.265402i
$886$	−4.15531	+	17.0033i	−0.139600	+	0.571239i
$887$	9.75588	−	16.8977i	0.327571	−	0.567369i	−0.654459	−	0.756098i	$-0.727103\pi$
$887$	9.75588	−	16.8977i	0.327571	−	0.567369i	0.982029	+	0.188729i	$0.0604368\pi$
$888$	−32.4974	+	5.97143i	−1.09054	+	0.200388i
$889$	−4.88316	−	8.45787i	−0.163776	−	0.283668i
$890$	−41.0452	+	11.9769i	−1.37584	+	0.401466i
$891$	−3.79056	−	2.51437i	−0.126989	−	0.0842347i
$892$	−8.74456	−	13.7081i	−0.292790	−	0.458982i
$893$	−4.88316	+	2.81929i	−0.163409	+	0.0943440i
$894$	−11.9148	+	29.3100i	−0.398490	+	0.980273i
$895$	−19.3236	−	11.1565i	−0.645917	−	0.372920i
$896$	1.54141	−	14.3517i	0.0514949	−	0.479458i
$897$	−1.93070	+	13.0916i	−0.0644643	+	0.437115i
$898$	−18.9686	+	19.8267i	−0.632991	+	0.661626i
$899$	−20.5226			−0.684467
$900$	−5.89837	−	5.74482i	−0.196612	−	0.191494i
$901$	−1.48913			−0.0496100
$902$	−3.35041	+	3.50198i	−0.111557	+	0.116603i
$903$	−15.8798	+	6.29069i	−0.528448	+	0.209341i
$904$	19.4871	−	6.63444i	0.648130	−	0.220658i
$905$	8.74456	+	5.04868i	0.290679	+	0.167824i
$906$	−4.55182	−	5.85175i	−0.151224	−	0.194411i
$907$	−25.8884	+	14.9467i	−0.859611	+	0.496297i	−0.863882	−	0.503694i	$-0.831974\pi$
$907$	−25.8884	+	14.9467i	−0.859611	+	0.496297i	0.00427097	+	0.999991i	$0.498641\pi$
$908$	24.2781	−	15.4873i	0.805698	−	0.513963i
$909$	2.53667	+	2.69927i	0.0841361	+	0.0895290i
$910$	−10.3723	+	3.02661i	−0.343838	+	0.100331i
$911$	−17.9015	−	31.0063i	−0.593102	−	1.02728i	−0.993812	−	0.111078i	$-0.964570\pi$
$911$	−17.9015	−	31.0063i	−0.593102	−	1.02728i	0.400710	−	0.916205i	$-0.368764\pi$
$912$	−17.8984	+	27.2260i	−0.592674	+	0.901544i
$913$	1.93070	−	3.34408i	0.0638970	−	0.110673i
$914$	13.4218	−	54.9215i	0.443955	−	1.81664i
$915$	−6.44121	+	8.12989i	−0.212940	+	0.268766i
$916$	−6.43765	−	3.34634i	−0.212706	−	0.110566i
$917$		−	9.74749i		−	0.321891i
$918$	2.09585	+	5.43178i	0.0691735	+	0.179275i
$919$			36.9711i			1.21956i	0.792570	+	0.609781i	$0.208743\pi$
$919$			36.9711i			1.21956i	−0.792570	+	0.609781i	$0.791257\pi$
$920$	4.46585	−	22.5570i	0.147235	−	0.743681i
$921$	−1.29211	+	1.63086i	−0.0425765	+	0.0537387i
$922$	0.480628	+	0.117457i	0.0158286	+	0.00386823i
$923$	14.0814	−	24.3897i	0.463494	−	0.802796i
$924$	2.03827	−	0.913680i	0.0670542	−	0.0300579i
$925$	−4.62772	−	8.01544i	−0.152158	−	0.263546i
$926$	1.89253	+	6.48577i	0.0621925	+	0.213136i
$927$	0.411331	−	1.36423i	0.0135099	−	0.0448072i
$928$	−14.1168	−	2.15121i	−0.463408	−	0.0706170i
$929$	16.0693	−	9.27761i	0.527217	−	0.304389i	−0.212666	−	0.977125i	$-0.568215\pi$
$929$	16.0693	−	9.27761i	0.527217	−	0.304389i	0.739882	+	0.672736i	$0.234881\pi$
$930$	39.6791	−	30.8647i	1.30113	−	1.01209i
$931$	−21.8802	−	12.6325i	−0.717094	−	0.414014i
$932$	9.68311	−	0.428569i	0.317181	−	0.0140383i
$933$	30.8139	−	12.2067i	1.00880	−	0.399630i
$934$	5.22495	+	4.99882i	0.170966	+	0.163566i
$935$	1.01082			0.0330572
$936$	−17.0665	+	10.6738i	−0.557837	+	0.348883i
$937$	45.7228			1.49370			0.746850	−	0.664993i	$-0.231565\pi$
$937$	45.7228			1.49370			0.746850	+	0.664993i	$0.231565\pi$
$938$	10.0771	+	9.64092i	0.329028	+	0.314787i
$939$	4.67228	−	31.6814i	0.152474	−	1.03388i
$940$	6.04729	−	0.267650i	0.197241	−	0.00872978i
$941$	11.6970	+	6.75327i	0.381312	+	0.220150i	0.678389	−	0.734703i	$-0.262678\pi$
$941$	11.6970	+	6.75327i	0.381312	+	0.220150i	−0.297077	+	0.954854i	$0.596012\pi$
$942$	26.9155	+	10.9414i	0.876954	+	0.356490i
$943$	18.9123	−	10.9190i	0.615869	−	0.355572i
$944$	20.8694	−	44.8945i	0.679240	−	1.46119i
$945$	−7.11684	+	15.1460i	−0.231511	+	0.492700i
$946$	1.54755	+	5.30350i	0.0503151	+	0.172432i
$947$	3.28515	+	5.69005i	0.106753	+	0.184902i	0.914453	−	0.404692i	$-0.132621\pi$
$947$	3.28515	+	5.69005i	0.106753	+	0.184902i	−0.807700	+	0.589594i	$0.799288\pi$
$948$	−3.49167	+	34.0491i	−0.113404	+	1.10586i
$949$	4.00000	−	6.92820i	0.129845	−	0.224899i
$950$	−8.86592	−	2.16667i	−0.287648	−	0.0702960i
$951$	55.7260	+	8.21830i	1.80704	+	0.266497i
$952$	−2.80458	−	0.555254i	−0.0908971	−	0.0179959i
$953$			10.2997i			0.333641i	0.985987	+	0.166821i	$0.0533500\pi$
$953$			10.2997i			0.333641i	−0.985987	+	0.166821i	$0.946650\pi$
$954$	−6.86995	−	4.04858i	−0.222423	−	0.131077i
$955$			38.0978i			1.23282i
$956$	21.4009	+	11.1244i	0.692155	+	0.359788i
$957$	−0.813859	−	2.05446i	−0.0263083	−	0.0664111i
$958$	−4.38816	+	17.9562i	−0.141775	+	0.580137i
$959$	−3.50283	+	6.06709i	−0.113112	+	0.195916i
$960$	30.5293	−	17.0716i	0.985329	−	0.550983i
$961$	17.5475	+	30.3932i	0.566050	+	0.980427i
$962$	−21.7216	+	6.33830i	−0.700331	+	0.204355i
$963$	−8.62146	−	36.6963i	−0.277823	−	1.18252i
$964$	−10.9416	+	6.97975i	−0.352404	+	0.224802i
$965$	16.9307	−	9.77495i	0.545019	−	0.314667i
$966$	−9.96975	+	1.37948i	−0.320772	+	0.0443840i
$967$	−40.5748	−	23.4259i	−1.30480	−	0.753325i	−0.323574	−	0.946203i	$-0.604885\pi$
$967$	−40.5748	−	23.4259i	−1.30480	−	0.753325i	−0.981223	+	0.192878i	$0.938218\pi$
$968$	9.79440	+	28.7686i	0.314804	+	0.924659i
$969$	5.05842	+	4.00772i	0.162500	+	0.128747i
$970$	−25.8861	+	27.0571i	−0.831152	+	0.868753i
$971$	37.0019			1.18745			0.593724	−	0.804669i	$-0.297657\pi$
$971$	37.0019			1.18745			0.593724	+	0.804669i	$0.297657\pi$
$972$	−5.09866	+	30.7572i	−0.163540	+	0.986537i
$973$	19.6277			0.629236
$974$	41.9166	−	43.8128i	1.34309	−	1.40385i
$975$	−4.41957	−	3.50157i	−0.141540	−	0.112140i
$976$	−5.45202	−	7.76653i	−0.174515	−	0.248601i
$977$	−47.3614	−	27.3441i	−1.51523	−	0.874816i	−0.999841	−	0.0178572i	$-0.994316\pi$
$977$	−47.3614	−	27.3441i	−1.51523	−	0.874816i	−0.515385	−	0.856959i	$-0.672351\pi$
$978$	4.24806	−	0.587788i	0.135838	−	0.0187954i
$979$	5.24224	−	3.02661i	0.167543	−	0.0967307i
$980$	14.5868	+	22.8665i	0.465958	+	0.730444i
$981$	9.25544	+	39.3947i	0.295503	+	1.25778i
$982$	−18.6861	+	5.45257i	−0.596299	+	0.173998i
$983$	−17.2079	−	29.8050i	−0.548847	−	0.950631i	−0.998354	−	0.0573540i	$-0.981734\pi$
$983$	−17.2079	−	29.8050i	−0.548847	−	0.950631i	0.449507	−	0.893277i	$-0.351600\pi$
$984$	31.2962	+	11.1367i	0.997686	+	0.355025i
$985$	30.2337	−	52.3663i	0.963325	−	1.66853i
$986$	−0.671457	+	2.74757i	−0.0213835	+	0.0875005i
$987$	−0.975793	−	2.46323i	−0.0310598	−	0.0784055i
$988$	−10.2912	+	19.7980i	−0.327406	+	0.629859i
$989$		−	24.8935i		−	0.791568i
$990$	4.66332	+	2.74817i	0.148210	+	0.0873425i
$991$			7.65492i			0.243167i	0.992581	+	0.121583i	$0.0387972\pi$
$991$			7.65492i			0.243167i	−0.992581	+	0.121583i	$0.961203\pi$
$992$	16.7324	+	42.8377i	0.531253	+	1.36010i
$993$	−47.5367	−	7.01056i	−1.50853	−	0.222473i
$994$	20.8074	+	5.08495i	0.659970	+	0.161285i
$995$	−16.2912	+	28.2171i	−0.516465	+	0.894543i
$996$	−26.3283	−	2.69991i	−0.834243	−	0.0855500i
$997$	12.0693	+	20.9046i	0.382238	+	0.662056i	0.991382	−	0.131004i	$-0.0418200\pi$
$997$	12.0693	+	20.9046i	0.382238	+	0.662056i	−0.609143	+	0.793060i	$0.708487\pi$
$998$	−1.35760	−	4.65253i	−0.0429740	−	0.147273i
$999$	−14.9040	+	31.7187i	−0.471543	+	1.00354i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.2.h.a.23.4	yes	8
3.2	odd	2		108.2.h.a.71.1		8
4.3	odd	2	inner	36.2.h.a.23.3	yes	8
5.2	odd	4		900.2.o.a.599.3		16
5.3	odd	4		900.2.o.a.599.6		16
5.4	even	2		900.2.r.c.851.1		8
8.3	odd	2		576.2.s.f.383.1		8
8.5	even	2		576.2.s.f.383.4		8
9.2	odd	6	inner	36.2.h.a.11.3	✓	8
9.4	even	3		324.2.b.b.323.2		8
9.5	odd	6		324.2.b.b.323.7		8
9.7	even	3		108.2.h.a.35.2		8
12.11	even	2		108.2.h.a.71.2		8
20.3	even	4		900.2.o.a.599.1		16
20.7	even	4		900.2.o.a.599.8		16
20.19	odd	2		900.2.r.c.851.2		8
24.5	odd	2		1728.2.s.f.1151.2		8
24.11	even	2		1728.2.s.f.1151.1		8
36.7	odd	6		108.2.h.a.35.1		8
36.11	even	6	inner	36.2.h.a.11.4	yes	8
36.23	even	6		324.2.b.b.323.1		8
36.31	odd	6		324.2.b.b.323.8		8
45.2	even	12		900.2.o.a.299.1		16
45.29	odd	6		900.2.r.c.551.2		8
45.38	even	12		900.2.o.a.299.8		16
72.5	odd	6		5184.2.c.j.5183.8		8
72.11	even	6		576.2.s.f.191.4		8
72.13	even	6		5184.2.c.j.5183.2		8
72.29	odd	6		576.2.s.f.191.1		8
72.43	odd	6		1728.2.s.f.575.2		8
72.59	even	6		5184.2.c.j.5183.7		8
72.61	even	6		1728.2.s.f.575.1		8
72.67	odd	6		5184.2.c.j.5183.1		8
180.47	odd	12		900.2.o.a.299.6		16
180.83	odd	12		900.2.o.a.299.3		16
180.119	even	6		900.2.r.c.551.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.2.h.a.11.3	✓	8	9.2	odd	6	inner
36.2.h.a.11.4	yes	8	36.11	even	6	inner
36.2.h.a.23.3	yes	8	4.3	odd	2	inner
36.2.h.a.23.4	yes	8	1.1	even	1	trivial
108.2.h.a.35.1		8	36.7	odd	6
108.2.h.a.35.2		8	9.7	even	3
108.2.h.a.71.1		8	3.2	odd	2
108.2.h.a.71.2		8	12.11	even	2
324.2.b.b.323.1		8	36.23	even	6
324.2.b.b.323.2		8	9.4	even	3
324.2.b.b.323.7		8	9.5	odd	6
324.2.b.b.323.8		8	36.31	odd	6
576.2.s.f.191.1		8	72.29	odd	6
576.2.s.f.191.4		8	72.11	even	6
576.2.s.f.383.1		8	8.3	odd	2
576.2.s.f.383.4		8	8.5	even	2
900.2.o.a.299.1		16	45.2	even	12
900.2.o.a.299.3		16	180.83	odd	12
900.2.o.a.299.6		16	180.47	odd	12
900.2.o.a.299.8		16	45.38	even	12
900.2.o.a.599.1		16	20.3	even	4
900.2.o.a.599.3		16	5.2	odd	4
900.2.o.a.599.6		16	5.3	odd	4
900.2.o.a.599.8		16	20.7	even	4
900.2.r.c.551.1		8	180.119	even	6
900.2.r.c.551.2		8	45.29	odd	6
900.2.r.c.851.1		8	5.4	even	2
900.2.r.c.851.2		8	20.19	odd	2
1728.2.s.f.575.1		8	72.61	even	6
1728.2.s.f.575.2		8	72.43	odd	6
1728.2.s.f.1151.1		8	24.11	even	2
1728.2.s.f.1151.2		8	24.5	odd	2
5184.2.c.j.5183.1		8	72.67	odd	6
5184.2.c.j.5183.2		8	72.13	even	6
5184.2.c.j.5183.7		8	72.59	even	6
5184.2.c.j.5183.8		8	72.5	odd	6

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	36.2.h.a.23.4

Level	$36$
Weight	$2$
Character	36.23
Analytic conductor	$0.287$
Analytic rank	$0$
Dimension	$8$
Inner twists	$4$