LMFDB - Embedded newform 624.2.bj.a.181.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [624,2,Mod(181,624)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(624, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0, 2]))

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

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

chi := DirichletCharacter("624.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 624 = 2^{4} \cdot 3 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	624.bj (of order $4$, 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:	$4.98266508613$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$56$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			181.13
Character	$\chi$	$=$	624.181
Dual form			624.2.bj.a.493.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.08187 - 0.910804i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(0.340873 + 1.97074i) q^{4} +(-1.27636 + 1.27636i) q^{5} +(1.40903 - 0.120960i) q^{6} -0.0414407 q^{7} +(1.42618 - 2.44254i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.08187 - 0.910804i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(0.340873 + 1.97074i) q^{4} +(-1.27636 + 1.27636i) q^{5} +(1.40903 - 0.120960i) q^{6} -0.0414407 q^{7} +(1.42618 - 2.44254i) q^{8} -1.00000i q^{9} +(2.54336 - 0.218338i) q^{10} +(4.02885 - 4.02885i) q^{11} +(-1.63456 - 1.15249i) q^{12} +(-3.58400 + 0.393597i) q^{13} +(0.0448334 + 0.0377444i) q^{14} -1.80504i q^{15} +(-3.76761 + 1.34354i) q^{16} +6.77544 q^{17} +(-0.910804 + 1.08187i) q^{18} +(-0.288688 - 0.288688i) q^{19} +(-2.95044 - 2.08029i) q^{20} +(0.0293030 - 0.0293030i) q^{21} +(-8.02818 + 0.689189i) q^{22} +6.56592i q^{23} +(0.718680 + 2.73560i) q^{24} +1.74182i q^{25} +(4.23591 + 2.83850i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.0141260 - 0.0816688i) q^{28} +(0.181581 - 0.181581i) q^{29} +(-1.64404 + 1.95282i) q^{30} +10.1485i q^{31} +(5.29976 + 1.97802i) q^{32} +5.69766i q^{33} +(-7.33012 - 6.17109i) q^{34} +(0.0528933 - 0.0528933i) q^{35} +(1.97074 - 0.340873i) q^{36} +(-1.98436 + 1.98436i) q^{37} +(0.0493839 + 0.575260i) q^{38} +(2.25596 - 2.81259i) q^{39} +(1.29725 + 4.93788i) q^{40} -2.75174 q^{41} +(-0.0583913 + 0.00501267i) q^{42} +(5.03764 + 5.03764i) q^{43} +(9.31314 + 6.56649i) q^{44} +(1.27636 + 1.27636i) q^{45} +(5.98026 - 7.10345i) q^{46} +6.41756i q^{47} +(1.71408 - 3.61413i) q^{48} -6.99828 q^{49} +(1.58645 - 1.88441i) q^{50} +(-4.79096 + 4.79096i) q^{51} +(-1.99737 - 6.92896i) q^{52} +(-4.11670 - 4.11670i) q^{53} +(-0.120960 - 1.40903i) q^{54} +10.2845i q^{55} +(-0.0591018 + 0.101221i) q^{56} +0.408266 q^{57} +(-0.361832 + 0.0310619i) q^{58} +(0.765023 - 0.765023i) q^{59} +(3.55727 - 0.615290i) q^{60} +(8.06784 - 8.06784i) q^{61} +(9.24332 - 10.9794i) q^{62} +0.0414407i q^{63} +(-3.93204 - 6.96700i) q^{64} +(4.07210 - 5.07685i) q^{65} +(5.18945 - 6.16411i) q^{66} +(9.99051 + 9.99051i) q^{67} +(2.30956 + 13.3526i) q^{68} +(-4.64280 - 4.64280i) q^{69} +(-0.105399 + 0.00904809i) q^{70} +3.45439 q^{71} +(-2.44254 - 1.42618i) q^{72} -9.13881 q^{73} +(3.95417 - 0.339450i) q^{74} +(-1.23165 - 1.23165i) q^{75} +(0.470522 - 0.667334i) q^{76} +(-0.166959 + 0.166959i) q^{77} +(-5.00236 + 0.988112i) q^{78} +15.2695 q^{79} +(3.09398 - 6.52367i) q^{80} -1.00000 q^{81} +(2.97702 + 2.50629i) q^{82} +(-9.08115 - 9.08115i) q^{83} +(0.0677372 + 0.0477600i) q^{84} +(-8.64789 + 8.64789i) q^{85} +(-0.861754 - 10.0384i) q^{86} +0.256795i q^{87} +(-4.09480 - 15.5865i) q^{88} +7.16186 q^{89} +(-0.218338 - 2.54336i) q^{90} +(0.148524 - 0.0163110i) q^{91} +(-12.9397 + 2.23814i) q^{92} +(-7.17610 - 7.17610i) q^{93} +(5.84514 - 6.94295i) q^{94} +0.736939 q^{95} +(-5.14617 + 2.34882i) q^{96} +17.3099i q^{97} +(7.57121 + 6.37406i) q^{98} +(-4.02885 - 4.02885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q+O(q^{10}) $ 112 * q	$ 112 q - 8 q^{12} + 32 q^{14} + 32 q^{22} - 20 q^{26} + 8 q^{30} + 40 q^{38} - 80 q^{40} + 40 q^{42} + 16 q^{43} + 112 q^{49} - 64 q^{52} + 48 q^{62} + 16 q^{65} + 64 q^{68} + 40 q^{74} - 16 q^{75} - 36 q^{78} + 80 q^{79} - 112 q^{81} - 72 q^{88} + 8 q^{90} - 8 q^{91} - 96 q^{92} - 40 q^{94}+O(q^{100}) $ 112 * q - 8 * q^12 + 32 * q^14 + 32 * q^22 - 20 * q^26 + 8 * q^30 + 40 * q^38 - 80 * q^40 + 40 * q^42 + 16 * q^43 + 112 * q^49 - 64 * q^52 + 48 * q^62 + 16 * q^65 + 64 * q^68 + 40 * q^74 - 16 * q^75 - 36 * q^78 + 80 * q^79 - 112 * q^81 - 72 * q^88 + 8 * q^90 - 8 * q^91 - 96 * q^92 - 40 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/624\mathbb{Z}\right)^\times$.

$n$	$79$	$145$	$209$	$469$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.08187	−	0.910804i	−0.764996	−	0.644036i
$2$	−1.08187	−	0.910804i	−0.764996	−	0.644036i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	0.340873	+	1.97074i	0.170436	+	0.985369i
$5$	−1.27636	+	1.27636i	−0.570805	+	0.570805i	−0.932353	−	0.361548i	$-0.882248\pi$
$5$	−1.27636	+	1.27636i	−0.570805	+	0.570805i	0.361548	+	0.932353i	$0.382248\pi$
$6$	1.40903	−	0.120960i	0.575235	−	0.0493817i
$7$	−0.0414407			−0.0156631			−0.00783157	−	0.999969i	$-0.502493\pi$
$7$	−0.0414407			−0.0156631			−0.00783157	+	0.999969i	$0.502493\pi$
$8$	1.42618	−	2.44254i	0.504229	−	0.863570i
$9$		−	1.00000i		−	0.333333i
$10$	2.54336	−	0.218338i	0.804282	−	0.0690445i
$11$	4.02885	−	4.02885i	1.21475	−	1.21475i	0.245298	−	0.969448i	$-0.421114\pi$
$11$	4.02885	−	4.02885i	1.21475	−	1.21475i	0.969448	−	0.245298i	$-0.0788857\pi$
$12$	−1.63456	−	1.15249i	−0.471855	−	0.332695i
$13$	−3.58400	+	0.393597i	−0.994024	+	0.109164i
$13$	−3.58400	+	0.393597i	−0.994024	+	0.109164i
$14$	0.0448334	+	0.0377444i	0.0119822	+	0.0100876i
$15$		−	1.80504i		−	0.466060i
$16$	−3.76761	+	1.34354i	−0.941903	+	0.335885i
$17$	6.77544			1.64328			0.821642	−	0.570003i	$-0.193058\pi$
$17$	6.77544			1.64328			0.821642	+	0.570003i	$0.193058\pi$
$18$	−0.910804	+	1.08187i	−0.214679	+	0.254999i
$19$	−0.288688	−	0.288688i	−0.0662296	−	0.0662296i	0.673216	−	0.739446i	$-0.264912\pi$
$19$	−0.288688	−	0.288688i	−0.0662296	−	0.0662296i	−0.739446	+	0.673216i	$0.764912\pi$
$20$	−2.95044	−	2.08029i	−0.659739	−	0.465168i
$21$	0.0293030	−	0.0293030i	0.00639445	−	0.00639445i
$22$	−8.02818	+	0.689189i	−1.71161	+	0.146936i
$23$			6.56592i			1.36909i	0.728972	+	0.684544i	$0.239999\pi$
$23$			6.56592i			1.36909i	−0.728972	+	0.684544i	$0.760001\pi$
$24$	0.718680	+	2.73560i	0.146700	+	0.558402i
$25$			1.74182i			0.348363i
$26$	4.23591	+	2.83850i	0.830729	+	0.556676i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	−0.0141260	−	0.0816688i	−0.00266957	−	0.0154340i
$29$	0.181581	−	0.181581i	0.0337188	−	0.0337188i	−0.690046	−	0.723765i	$-0.742410\pi$
$29$	0.181581	−	0.181581i	0.0337188	−	0.0337188i	0.723765	+	0.690046i	$0.242410\pi$
$30$	−1.64404	+	1.95282i	−0.300159	+	0.356534i
$31$			10.1485i			1.82273i	0.411599	+	0.911365i	$0.364971\pi$
$31$			10.1485i			1.82273i	−0.411599	+	0.911365i	$0.635029\pi$
$32$	5.29976	+	1.97802i	0.936874	+	0.349668i
$33$			5.69766i			0.991835i
$34$	−7.33012	−	6.17109i	−1.25711	−	1.05833i
$35$	0.0528933	−	0.0528933i	0.00894059	−	0.00894059i
$36$	1.97074	−	0.340873i	0.328456	−	0.0568121i
$37$	−1.98436	+	1.98436i	−0.326226	+	0.326226i	−0.851150	−	0.524923i	$-0.824094\pi$
$37$	−1.98436	+	1.98436i	−0.326226	+	0.326226i	0.524923	+	0.851150i	$0.324094\pi$
$38$	0.0493839	+	0.575260i	0.00801112	+	0.0933195i
$39$	2.25596	−	2.81259i	0.361242	−	0.450375i
$40$	1.29725	+	4.93788i	0.205113	+	0.780747i
$41$	−2.75174			−0.429749			−0.214875	−	0.976642i	$-0.568934\pi$
$41$	−2.75174			−0.429749			−0.214875	+	0.976642i	$0.568934\pi$
$42$	−0.0583913	+	0.00501267i	−0.00900997	+	0.000773472i
$43$	5.03764	+	5.03764i	0.768233	+	0.768233i	0.977795	−	0.209563i	$-0.0672040\pi$
$43$	5.03764	+	5.03764i	0.768233	+	0.768233i	−0.209563	+	0.977795i	$0.567204\pi$
$44$	9.31314	+	6.56649i	1.40401	+	0.989935i
$45$	1.27636	+	1.27636i	0.190268	+	0.190268i
$46$	5.98026	−	7.10345i	0.881741	−	1.04735i
$47$			6.41756i			0.936098i	0.883703	+	0.468049i	$0.155043\pi$
$47$			6.41756i			0.936098i	−0.883703	+	0.468049i	$0.844957\pi$
$48$	1.71408	−	3.61413i	0.247406	−	0.521655i
$49$	−6.99828			−0.999755
$50$	1.58645	−	1.88441i	0.224358	−	0.266496i
$51$	−4.79096	+	4.79096i	−0.670868	+	0.670868i
$52$	−1.99737	−	6.92896i	−0.276985	−	0.960874i
$53$	−4.11670	−	4.11670i	−0.565472	−	0.565472i	0.365385	−	0.930857i	$-0.380937\pi$
$53$	−4.11670	−	4.11670i	−0.565472	−	0.565472i	−0.930857	+	0.365385i	$0.880937\pi$
$54$	−0.120960	−	1.40903i	−0.0164606	−	0.191745i
$55$			10.2845i			1.38677i
$56$	−0.0591018	+	0.101221i	−0.00789781	+	0.0135262i
$57$	0.408266			0.0540762
$58$	−0.361832	+	0.0310619i	−0.0475108	+	0.00407862i
$59$	0.765023	−	0.765023i	0.0995974	−	0.0995974i	−0.655552	−	0.755150i	$-0.727564\pi$
$59$	0.765023	−	0.765023i	0.0995974	−	0.0995974i	0.755150	+	0.655552i	$0.227564\pi$
$60$	3.55727	−	0.615290i	0.459241	−	0.0794336i
$61$	8.06784	−	8.06784i	1.03298	−	1.03298i	0.0335443	−	0.999437i	$-0.489321\pi$
$61$	8.06784	−	8.06784i	1.03298	−	1.03298i	0.999437	−	0.0335443i	$-0.0106795\pi$
$62$	9.24332	−	10.9794i	1.17390	−	1.39438i
$63$			0.0414407i			0.00522104i
$64$	−3.93204	−	6.96700i	−0.491505	−	0.870875i
$65$	4.07210	−	5.07685i	0.505082	−	0.629705i
$66$	5.18945	−	6.16411i	0.638777	−	0.758750i
$67$	9.99051	+	9.99051i	1.22054	+	1.22054i	0.967442	+	0.253094i	$0.0814481\pi$
$67$	9.99051	+	9.99051i	1.22054	+	1.22054i	0.253094	+	0.967442i	$0.418552\pi$
$68$	2.30956	+	13.3526i	0.280075	+	1.61924i
$69$	−4.64280	−	4.64280i	−0.558928	−	0.558928i
$70$	−0.105399	+	0.00904809i	−0.0125976	+	0.00108145i
$71$	3.45439			0.409961			0.204980	−	0.978766i	$-0.434287\pi$
$71$	3.45439			0.409961			0.204980	+	0.978766i	$0.434287\pi$
$72$	−2.44254	−	1.42618i	−0.287857	−	0.168076i
$73$	−9.13881			−1.06962			−0.534808	−	0.844974i	$-0.679616\pi$
$73$	−9.13881			−1.06962			−0.534808	+	0.844974i	$0.679616\pi$
$74$	3.95417	−	0.339450i	0.459663	−	0.0394603i
$75$	−1.23165	−	1.23165i	−0.142219	−	0.142219i
$76$	0.470522	−	0.667334i	0.0539726	−	0.0765485i
$77$	−0.166959	+	0.166959i	−0.0190267	+	0.0190267i
$78$	−5.00236	+	0.988112i	−0.566406	+	0.111882i
$79$	15.2695			1.71795			0.858976	−	0.512016i	$-0.171101\pi$
$79$	15.2695			1.71795			0.858976	+	0.512016i	$0.171101\pi$
$80$	3.09398	−	6.52367i	0.345918	−	0.729368i
$81$	−1.00000			−0.111111
$82$	2.97702	+	2.50629i	0.328756	+	0.276774i
$83$	−9.08115	−	9.08115i	−0.996786	−	0.996786i	0.00320923	−	0.999995i	$-0.498978\pi$
$83$	−9.08115	−	9.08115i	−0.996786	−	0.996786i	−0.999995	+	0.00320923i	$0.998978\pi$
$84$	0.0677372	+	0.0477600i	0.00739073	+	0.00521104i
$85$	−8.64789	+	8.64789i	−0.937995	+	0.937995i
$86$	−0.861754	−	10.0384i	−0.0929254	−	1.08246i
$87$			0.256795i			0.0275313i
$88$	−4.09480	−	15.5865i	−0.436507	−	1.66153i
$89$	7.16186			0.759156			0.379578	−	0.925160i	$-0.376069\pi$
$89$	7.16186			0.759156			0.379578	+	0.925160i	$0.376069\pi$
$90$	−0.218338	−	2.54336i	−0.0230148	−	0.268094i
$91$	0.148524	−	0.0163110i	0.0155695	−	0.00170985i
$92$	−12.9397	+	2.23814i	−1.34906	+	0.233342i
$93$	−7.17610	−	7.17610i	−0.744127	−	0.744127i
$94$	5.84514	−	6.94295i	0.602880	−	0.716110i
$95$	0.736939			0.0756083
$96$	−5.14617	+	2.34882i	−0.525229	+	0.239726i
$97$			17.3099i			1.75755i	0.477234	+	0.878776i	$0.341640\pi$
$97$			17.3099i			1.75755i	−0.477234	+	0.878776i	$0.658360\pi$
$98$	7.57121	+	6.37406i	0.764808	+	0.643878i
$99$	−4.02885	−	4.02885i	−0.404915	−	0.404915i
$100$	−3.43266	+	0.593737i	−0.343266	+	0.0593737i
$101$	7.34734	+	7.34734i	0.731088	+	0.731088i	0.970835	−	0.239748i	$-0.0770647\pi$
$101$	7.34734	+	7.34734i	0.731088	+	0.731088i	−0.239748	+	0.970835i	$0.577065\pi$
$102$	9.54680	−	0.819556i	0.945274	−	0.0811482i
$103$			2.43741i			0.240165i	0.992764	+	0.120083i	$0.0383160\pi$
$103$			2.43741i			0.240165i	−0.992764	+	0.120083i	$0.961684\pi$
$104$	−4.15004	+	9.31543i	−0.406945	+	0.913453i
$105$			0.0748024i			0.00729996i
$106$	0.704215	+	8.20322i	0.0683994	+	0.796767i
$107$	7.62597	+	7.62597i	0.737231	+	0.737231i	0.972041	−	0.234811i	$-0.0754470\pi$
$107$	7.62597	+	7.62597i	0.737231	+	0.737231i	−0.234811	+	0.972041i	$0.575447\pi$
$108$	−1.15249	+	1.63456i	−0.110898	+	0.157285i
$109$	−2.78908	−	2.78908i	−0.267145	−	0.267145i	0.560803	−	0.827949i	$-0.310492\pi$
$109$	−2.78908	−	2.78908i	−0.267145	−	0.267145i	−0.827949	+	0.560803i	$0.810492\pi$
$110$	9.36719	−	11.1265i	0.893126	−	1.06087i
$111$		−	2.80630i		−	0.266363i
$112$	0.156133	−	0.0556773i	0.0147531	−	0.00526101i
$113$	4.12521			0.388067			0.194034	−	0.980995i	$-0.437843\pi$
$113$	4.12521			0.388067			0.194034	+	0.980995i	$0.437843\pi$
$114$	−0.441690	−	0.371851i	−0.0413681	−	0.0348270i
$115$	−8.38047	−	8.38047i	−0.781482	−	0.781482i
$116$	0.419745	+	0.295953i	0.0389724	+	0.0274785i
$117$	0.393597	+	3.58400i	0.0363881	+	0.331341i
$118$	−1.52444	+	0.130867i	−0.140336	+	0.0120473i
$119$	−0.280779			−0.0257390
$120$	−4.40890	−	2.57431i	−0.402476	−	0.235001i
$121$		−	21.4633i		−	1.95121i
$122$	−16.0766	+	1.38011i	−1.45550	+	0.124949i
$123$	1.94577	−	1.94577i	0.175444	−	0.175444i
$124$	−20.0001	+	3.45936i	−1.79606	+	0.310659i
$125$	−8.60498	−	8.60498i	−0.769653	−	0.769653i
$126$	0.0377444	−	0.0448334i	0.00336254	−	0.00399407i
$127$	13.4545			1.19389			0.596946	−	0.802281i	$-0.296381\pi$
$127$	13.4545			1.19389			0.596946	+	0.802281i	$0.296381\pi$
$128$	−2.09162	+	11.1187i	−0.184875	+	0.982762i
$129$	−7.12430			−0.627259
$130$	−9.02949	+	1.78359i	−0.791938	+	0.156431i
$131$	−0.985572	+	0.985572i	−0.0861099	+	0.0861099i	−0.748850	−	0.662740i	$-0.769394\pi$
$131$	−0.985572	+	0.985572i	−0.0861099	+	0.0861099i	0.662740	+	0.748850i	$0.269394\pi$
$132$	−11.2286	+	1.94218i	−0.977324	+	0.169045i
$133$	0.0119634	+	0.0119634i	0.00103736	+	0.00103736i
$134$	−1.70901	−	19.9078i	−0.147636	−	1.71977i
$135$	−1.80504			−0.155353
$136$	9.66297	−	16.5493i	0.828593	−	1.41909i
$137$	0.516353			0.0441150			0.0220575	−	0.999757i	$-0.492978\pi$
$137$	0.516353			0.0441150			0.0220575	+	0.999757i	$0.492978\pi$
$138$	0.794213	+	9.25158i	0.0676079	+	0.787547i
$139$	−13.2662	−	13.2662i	−1.12523	−	1.12523i	−0.990943	−	0.134285i	$-0.957126\pi$
$139$	−13.2662	−	13.2662i	−1.12523	−	1.12523i	−0.134285	−	0.990943i	$-0.542874\pi$
$140$	0.122269	+	0.0862089i	0.0103336	+	0.00728598i
$141$	−4.53790	−	4.53790i	−0.382160	−	0.382160i
$142$	−3.73719	−	3.14627i	−0.313618	−	0.264029i
$143$	−12.8537	+	16.0252i	−1.07488	+	1.34009i
$144$	1.34354	+	3.76761i	0.111962	+	0.313968i
$145$			0.463526i			0.0384937i
$146$	9.88697	+	8.32366i	0.818252	+	0.688871i
$147$	4.94853	−	4.94853i	0.408148	−	0.408148i
$148$	−4.58706	−	3.23423i	−0.377054	−	0.265852i
$149$	1.78712	−	1.78712i	0.146406	−	0.146406i	−0.630104	−	0.776511i	$-0.716988\pi$
$149$	1.78712	−	1.78712i	0.146406	−	0.146406i	0.776511	+	0.630104i	$0.216988\pi$
$150$	0.210690	+	2.45427i	0.0172028	+	0.200391i
$151$	−10.2661			−0.835447			−0.417723	−	0.908574i	$-0.637172\pi$
$151$	−10.2661			−0.835447			−0.417723	+	0.908574i	$0.637172\pi$
$152$	−1.11685	+	0.293413i	−0.0905887	+	0.0237989i
$153$		−	6.77544i		−	0.547762i
$154$	0.332694	−	0.0285605i	0.0268092	−	0.00230147i
$155$	−12.9532	−	12.9532i	−1.04042	−	1.04042i
$156$	6.31187	+	3.48717i	0.505354	+	0.279197i
$157$	−2.08708	+	2.08708i	−0.166567	+	0.166567i	−0.785468	−	0.618902i	$-0.787578\pi$
$157$	−2.08708	+	2.08708i	−0.166567	+	0.166567i	0.618902	+	0.785468i	$0.287578\pi$
$158$	−16.5196	−	13.9075i	−1.31423	−	1.10642i
$159$	5.82189			0.461706
$160$	−9.28906	+	4.23973i	−0.734365	+	0.335180i
$161$		−	0.272096i		−	0.0214442i
$162$	1.08187	+	0.910804i	0.0849995	+	0.0715595i
$163$	3.39901	+	3.39901i	0.266231	+	0.266231i	0.827580	−	0.561348i	$-0.189717\pi$
$163$	3.39901	+	3.39901i	0.266231	+	0.266231i	−0.561348	+	0.827580i	$0.689717\pi$
$164$	−0.937992	−	5.42295i	−0.0732449	−	0.423462i
$165$	−7.27226	−	7.27226i	−0.566145	−	0.566145i
$166$	1.55345	+	18.0957i	0.120571	+	1.40450i
$167$	6.00539			0.464711			0.232355	−	0.972631i	$-0.425357\pi$
$167$	6.00539			0.464711			0.232355	+	0.972631i	$0.425357\pi$
$168$	−0.0297827	−	0.113365i	−0.00229778	−	0.00874632i
$169$	12.6902	−	2.82131i	0.976166	−	0.217024i
$170$	17.2324	−	1.47934i	1.32166	−	0.113460i
$171$	−0.288688	+	0.288688i	−0.0220765	+	0.0220765i
$172$	−8.21067	+	11.6451i	−0.626058	+	0.887927i
$173$	−12.8766	+	12.8766i	−0.978993	+	0.978993i	−0.999784	−	0.0207905i	$-0.993382\pi$
$173$	−12.8766	+	12.8766i	−0.978993	+	0.978993i	0.0207905	+	0.999784i	$0.493382\pi$
$174$	0.233890	−	0.277818i	0.0177311	−	0.0210613i
$175$		−	0.0721822i		−	0.00545646i
$176$	−9.76623	+	20.5921i	−0.736157	+	1.55219i
$177$			1.08191i			0.0813210i
$178$	−7.74818	−	6.52305i	−0.580751	−	0.488923i
$179$	−14.7238	+	14.7238i	−1.10051	+	1.10051i	−0.106162	+	0.994349i	$0.533856\pi$
$179$	−14.7238	+	14.7238i	−1.10051	+	1.10051i	−0.994349	+	0.106162i	$0.966144\pi$
$180$	−2.08029	+	2.95044i	−0.155056	+	0.219913i
$181$	−4.53235	−	4.53235i	−0.336887	−	0.336887i	0.518308	−	0.855194i	$-0.326562\pi$
$181$	−4.53235	−	4.53235i	−0.336887	−	0.336887i	−0.855194	+	0.518308i	$0.826562\pi$
$182$	−0.175539	−	0.117630i	−0.0130118	−	0.00871930i
$183$			11.4097i			0.843426i
$184$	16.0375	+	9.36415i	1.18230	+	0.690335i
$185$		−	5.06550i		−	0.372423i
$186$	1.22757	+	14.2996i	0.0900095	+	1.04850i
$187$	27.2972	−	27.2972i	1.99617	−	1.99617i
$188$	−12.6473	+	2.18757i	−0.922401	+	0.159545i
$189$	−0.0293030	−	0.0293030i	−0.00213148	−	0.00213148i
$190$	−0.797270	−	0.671207i	−0.0578400	−	0.0486945i
$191$	9.81257			0.710013			0.355006	−	0.934864i	$-0.384479\pi$
$191$	9.81257			0.710013			0.355006	+	0.934864i	$0.384479\pi$
$192$	7.70678	+	2.14604i	0.556189	+	0.154877i
$193$			0.145264i			0.0104564i	0.999986	+	0.00522818i	$0.00166419\pi$
$193$			0.145264i			0.0104564i	−0.999986	+	0.00522818i	$0.998336\pi$
$194$	15.7659	−	18.7270i	1.13193	−	1.34452i
$195$	0.710461	+	6.46928i	0.0508771	+	0.463275i
$196$	−2.38552	−	13.7918i	−0.170394	−	0.985127i
$197$	11.2043	−	11.2043i	0.798276	−	0.798276i	−0.184548	−	0.982824i	$-0.559082\pi$
$197$	11.2043	−	11.2043i	0.798276	−	0.798276i	0.982824	+	0.184548i	$0.0590821\pi$
$198$	0.689189	+	8.02818i	0.0489785	+	0.570538i
$199$			3.57842i			0.253668i	0.991924	+	0.126834i	$0.0404815\pi$
$199$			3.57842i			0.253668i	−0.991924	+	0.126834i	$0.959519\pi$
$200$	4.25446	+	2.48414i	0.300836	+	0.175655i
$201$	−14.1287			−0.996563
$202$	−1.25686	−	14.6408i	−0.0884323	−	1.03013i
$203$	−0.00752487	+	0.00752487i	−0.000528142	+	0.000528142i
$204$	−11.0748	−	7.80861i	−0.775393	−	0.546712i
$205$	3.51221	−	3.51221i	0.245303	−	0.245303i
$206$	2.22000	−	2.63695i	0.154675	−	0.183725i
$207$	6.56592			0.456363
$208$	12.9743	−	6.29818i	0.899607	−	0.436700i
$209$	−2.32616			−0.160904
$210$	0.0681303	−	0.0809262i	0.00470144	−	0.00558444i
$211$	4.40701	−	4.40701i	0.303391	−	0.303391i	−0.538948	−	0.842339i	$-0.681178\pi$
$211$	4.40701	−	4.40701i	0.303391	−	0.303391i	0.842339	+	0.538948i	$0.181178\pi$
$212$	6.70966	−	9.51620i	0.460821	−	0.653575i
$213$	−2.44262	+	2.44262i	−0.167366	+	0.167366i
$214$	−1.30452	−	15.1961i	−0.0891754	−	1.03878i
$215$	−12.8597			−0.877022
$216$	2.73560	−	0.718680i	0.186134	−	0.0489000i
$217$		−	0.420563i		−	0.0285497i
$218$	0.477109	+	5.55772i	0.0323139	+	0.376416i
$219$	6.46211	−	6.46211i	0.436669	−	0.436669i
$220$	−20.2681	+	3.50571i	−1.36648	+	0.236355i
$221$	−24.2832	+	2.66679i	−1.63346	+	0.179388i
$222$	−2.55599	+	3.03605i	−0.171547	+	0.203766i
$223$			15.6143i			1.04561i	0.852452	+	0.522805i	$0.175114\pi$
$223$			15.6143i			1.04561i	−0.852452	+	0.522805i	$0.824886\pi$
$224$	−0.219626	−	0.0819707i	−0.0146744	−	0.00547690i
$225$	1.74182			0.116121
$226$	−4.46293	−	3.75726i	−0.296870	−	0.249929i
$227$	4.73928	+	4.73928i	0.314557	+	0.314557i	0.846672	−	0.532115i	$-0.178603\pi$
$227$	4.73928	+	4.73928i	0.314557	+	0.314557i	−0.532115	+	0.846672i	$0.678603\pi$
$228$	0.139167	+	0.804586i	0.00921655	+	0.0532850i
$229$	−12.3328	+	12.3328i	−0.814976	+	0.814976i	−0.985375	−	0.170399i	$-0.945494\pi$
$229$	−12.3328	+	12.3328i	−0.814976	+	0.814976i	0.170399	+	0.985375i	$0.445494\pi$
$230$	1.43359	+	16.6995i	0.0945281	+	1.10113i
$231$		−	0.236115i		−	0.0155352i
$232$	−0.184553	−	0.702487i	−0.0121165	−	0.0461206i
$233$		−	26.2262i		−	1.71814i	−0.511859	−	0.859069i	$-0.671043\pi$
$233$		−	26.2262i		−	1.71814i	0.511859	−	0.859069i	$-0.328957\pi$
$234$	2.83850	−	4.23591i	0.185559	−	0.276910i
$235$	−8.19111	−	8.19111i	−0.534329	−	0.534329i
$236$	1.76843	+	1.24688i	0.115115	+	0.0811652i
$237$	−10.7972	+	10.7972i	−0.701351	+	0.701351i
$238$	0.303766	+	0.255735i	0.0196902	+	0.0165768i
$239$		−	20.7444i		−	1.34184i	−0.741529	−	0.670921i	$-0.765899\pi$
$239$		−	20.7444i		−	1.34184i	0.741529	−	0.670921i	$-0.234101\pi$
$240$	2.42515	+	6.80071i	0.156543	+	0.438984i
$241$		−	16.9148i		−	1.08958i	−0.838573	−	0.544789i	$-0.816610\pi$
$241$		−	16.9148i		−	1.08958i	0.838573	−	0.544789i	$-0.183390\pi$
$242$	−19.5489	+	23.2205i	−1.25665	+	1.49267i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	18.6497	+	13.1495i	1.19393	+	0.841810i
$245$	8.93232	−	8.93232i	0.570665	−	0.570665i
$246$	−3.87729	+	0.332850i	−0.247207	+	0.0212218i
$247$	1.14829	+	0.921032i	0.0730637	+	0.0586039i
$248$	24.7882	+	14.4736i	1.57405	+	0.919074i
$249$	12.8427			0.813872
$250$	1.47199	+	17.1469i	0.0930971	+	1.08446i
$251$	11.7759	+	11.7759i	0.743290	+	0.743290i	0.973210	−	0.229920i	$-0.0738464\pi$
$251$	11.7759	+	11.7759i	0.743290	+	0.743290i	−0.229920	+	0.973210i	$0.573846\pi$
$252$	−0.0816688	+	0.0141260i	−0.00514465	+	0.000889855i
$253$	26.4531	+	26.4531i	1.66309	+	1.66309i
$254$	−14.5560	−	12.2544i	−0.913323	−	0.768909i
$255$		−	12.2300i		−	0.765870i
$256$	12.3898	−	10.1239i	0.774362	−	0.632743i
$257$	8.31306			0.518555			0.259277	−	0.965803i	$-0.416516\pi$
$257$	8.31306			0.518555			0.259277	+	0.965803i	$0.416516\pi$
$258$	7.70754	+	6.48884i	0.479851	+	0.403977i
$259$	0.0822332	−	0.0822332i	0.00510972	−	0.00510972i
$260$	11.3932	+	6.29449i	0.706576	+	0.390368i
$261$	−0.181581	−	0.181581i	−0.0112396	−	0.0112396i
$262$	1.96392	−	0.168595i	0.121331	−	0.0104158i
$263$		−	29.1351i		−	1.79655i	−0.439434	−	0.898275i	$-0.644821\pi$
$263$		−	29.1351i		−	1.79655i	0.439434	−	0.898275i	$-0.355179\pi$
$264$	13.9168	+	8.12587i	0.856519	+	0.500113i
$265$	10.5088			0.645548
$266$	−0.00204651	−	0.0238392i	−0.000125479	−	0.00146168i
$267$	−5.06420	+	5.06420i	−0.309924	+	0.309924i
$268$	−16.2832	+	23.0942i	−0.994654	+	1.41070i
$269$	1.09217	−	1.09217i	0.0665905	−	0.0665905i	−0.673027	−	0.739618i	$-0.735006\pi$
$269$	1.09217	−	1.09217i	0.0665905	−	0.0665905i	0.739618	+	0.673027i	$0.235006\pi$
$270$	1.95282	+	1.64404i	0.118845	+	0.100053i
$271$		−	7.65876i		−	0.465237i	−0.972568	−	0.232618i	$-0.925271\pi$
$271$		−	7.65876i		−	0.465237i	0.972568	−	0.232618i	$-0.0747293\pi$
$272$	−25.5272	+	9.10308i	−1.54781	+	0.551955i
$273$	−0.0934886	+	0.116556i	−0.00565819	+	0.00705428i
$274$	−0.558625	−	0.470296i	−0.0337478	−	0.0284116i
$275$	7.01752	+	7.01752i	0.423173	+	0.423173i
$276$	7.56714	−	10.7324i	0.455488	−	0.646012i
$277$	−0.413314	−	0.413314i	−0.0248336	−	0.0248336i	0.694581	−	0.719415i	$-0.255590\pi$
$277$	−0.413314	−	0.413314i	−0.0248336	−	0.0248336i	−0.719415	+	0.694581i	$0.755590\pi$
$278$	2.26937	+	26.4353i	0.136108	+	1.58548i
$279$	10.1485			0.607577
$280$	−0.0537590	−	0.204629i	−0.00321271	−	0.0122289i
$281$	13.9908			0.834624			0.417312	−	0.908763i	$-0.362972\pi$
$281$	13.9908			0.834624			0.417312	+	0.908763i	$0.362972\pi$
$282$	0.776268	+	9.04254i	0.0462261	+	0.538476i
$283$	6.39400	+	6.39400i	0.380084	+	0.380084i	0.871132	−	0.491049i	$-0.163386\pi$
$283$	6.39400	+	6.39400i	0.380084	+	0.380084i	−0.491049	+	0.871132i	$0.663386\pi$
$284$	1.17751	+	6.80770i	0.0698722	+	0.403962i
$285$	−0.521095	+	0.521095i	−0.0308670	+	0.0308670i
$286$	28.5018	−	5.62993i	1.68534	−	0.332905i
$287$	0.114034			0.00673122
$288$	1.97802	−	5.29976i	0.116556	−	0.312291i
$289$	28.9065			1.70038
$290$	0.422181	−	0.501473i	0.0247913	−	0.0294475i
$291$	−12.2399	−	12.2399i	−0.717518	−	0.717518i
$292$	−3.11517	−	18.0102i	−0.182301	−	1.05397i
$293$	−1.96179	+	1.96179i	−0.114609	+	0.114609i	−0.762085	−	0.647477i	$-0.775824\pi$
$293$	−1.96179	+	1.96179i	−0.114609	+	0.114609i	0.647477	+	0.762085i	$0.275824\pi$
$294$	−9.86080	+	0.846512i	−0.575093	+	0.0493696i
$295$			1.95289i			0.113701i
$296$	2.01684	+	7.67692i	0.117226	+	0.446212i
$297$	5.69766			0.330612
$298$	−3.56114	+	0.305710i	−0.206291	+	0.0177093i
$299$	−2.58433	−	23.5323i	−0.149456	−	1.36091i
$300$	2.00742	−	2.84709i	0.115899	−	0.164377i
$301$	−0.208763	−	0.208763i	−0.0120329	−	0.0120329i
$302$	11.1066	+	9.35044i	0.639113	+	0.538058i
$303$	−10.3907			−0.596931
$304$	1.47553	+	0.699800i	0.0846274	+	0.0401363i
$305$			20.5949i			1.17926i
$306$	−6.17109	+	7.33012i	−0.352778	+	0.419035i
$307$	17.2325	+	17.2325i	0.983509	+	0.983509i	0.999866	−	0.0163570i	$-0.00520683\pi$
$307$	17.2325	+	17.2325i	0.983509	+	0.983509i	−0.0163570	+	0.999866i	$0.505207\pi$
$308$	−0.385944	−	0.272120i	−0.0219912	−	0.0155055i
$309$	−1.72351	−	1.72351i	−0.0980471	−	0.0980471i
$310$	2.21581	+	25.8114i	0.125850	+	1.46599i
$311$		−	13.8567i		−	0.785741i	−0.919594	−	0.392871i	$-0.871482\pi$
$311$		−	13.8567i		−	0.785741i	0.919594	−	0.392871i	$-0.128518\pi$
$312$	−3.65248	−	9.52152i	−0.206781	−	0.539050i
$313$			28.3387i			1.60180i	0.598800	+	0.800899i	$0.295645\pi$
$313$			28.3387i			1.60180i	−0.598800	+	0.800899i	$0.704355\pi$
$314$	4.15886	−	0.357022i	0.234698	−	0.0201479i
$315$	−0.0528933	−	0.0528933i	−0.00298020	−	0.00298020i
$316$	5.20495	+	30.0922i	0.292801	+	1.69282i
$317$	−12.2981	−	12.2981i	−0.690731	−	0.690731i	0.271662	−	0.962393i	$-0.412427\pi$
$317$	−12.2981	−	12.2981i	−0.690731	−	0.690731i	−0.962393	+	0.271662i	$0.912427\pi$
$318$	−6.29851	−	5.30260i	−0.353203	−	0.297355i
$319$		−	1.46313i		−	0.0819195i
$320$	13.9111	+	3.87369i	0.777653	+	0.216546i
$321$	−10.7848			−0.601946
$322$	−0.247827	+	0.294372i	−0.0138108	+	0.0164047i
$323$	−1.95599	−	1.95599i	−0.108834	−	0.108834i
$324$	−0.340873	−	1.97074i	−0.0189374	−	0.109485i
$325$	−0.685574	−	6.24267i	−0.0380288	−	0.346281i
$326$	−0.581446	−	6.77311i	−0.0322033	−	0.375128i
$327$	3.94436			0.218123
$328$	−3.92447	+	6.72124i	−0.216692	+	0.371119i
$329$		−	0.265949i		−	0.0146622i
$330$	1.24402	+	14.4912i	0.0684808	+	0.797716i
$331$	4.25354	−	4.25354i	0.233796	−	0.233796i	−0.580479	−	0.814275i	$-0.697135\pi$
$331$	4.25354	−	4.25354i	0.233796	−	0.233796i	0.814275	+	0.580479i	$0.197135\pi$
$332$	14.8010	−	20.9921i	0.812313	−	1.15209i
$333$	1.98436	+	1.98436i	0.108742	+	0.108742i
$334$	−6.49703	−	5.46973i	−0.355502	−	0.299290i
$335$	−25.5030			−1.39338
$336$	−0.0710326	+	0.149772i	−0.00387515	+	0.00817075i
$337$	−29.0101			−1.58028			−0.790140	−	0.612926i	$-0.789992\pi$
$337$	−29.0101			−1.58028			−0.790140	+	0.612926i	$0.789992\pi$
$338$	−16.2987	−	8.50597i	−0.886534	−	0.462664i
$339$	−2.91696	+	2.91696i	−0.158428	+	0.158428i
$340$	−19.9905	−	14.0949i	−1.08414	−	0.764403i
$341$	40.8870	+	40.8870i	2.21415	+	2.21415i
$342$	0.575260	−	0.0493839i	0.0311065	−	0.00267037i
$343$	0.580099			0.0313224
$344$	19.4892	−	5.12009i	1.05079	−	0.276057i
$345$	11.8518			0.638078
$346$	25.6589	−	2.20272i	1.37943	−	0.118419i
$347$	−23.5912	−	23.5912i	−1.26644	−	1.26644i	−0.947914	−	0.318525i	$-0.896812\pi$
$347$	−23.5912	−	23.5912i	−1.26644	−	1.26644i	−0.318525	−	0.947914i	$-0.603188\pi$
$348$	−0.506075	+	0.0875343i	−0.0271285	+	0.00469233i
$349$	−3.28788	−	3.28788i	−0.175996	−	0.175996i	0.613612	−	0.789608i	$-0.289716\pi$
$349$	−3.28788	−	3.28788i	−0.175996	−	0.175996i	−0.789608	+	0.613612i	$0.789716\pi$
$350$	−0.0657438	+	0.0780915i	−0.00351415	+	0.00417417i
$351$	−2.81259	−	2.25596i	−0.150125	−	0.120414i
$352$	29.3211	−	13.3828i	1.56282	−	0.713305i
$353$			2.98003i			0.158611i	0.996850	+	0.0793054i	$0.0252702\pi$
$353$			2.98003i			0.158611i	−0.996850	+	0.0793054i	$0.974730\pi$
$354$	0.985403	−	1.17048i	0.0523736	−	0.0622102i
$355$	−4.40904	+	4.40904i	−0.234008	+	0.234008i
$356$	2.44128	+	14.1141i	0.129388	+	0.748048i
$357$	0.198541	−	0.198541i	0.0105079	−	0.0105079i
$358$	29.3397	−	2.51871i	1.55065	−	0.133118i
$359$	−21.0369			−1.11029			−0.555144	−	0.831754i	$-0.687337\pi$
$359$	−21.0369			−1.11029			−0.555144	+	0.831754i	$0.687337\pi$
$360$	4.93788	−	1.29725i	0.260249	−	0.0683711i
$361$		−	18.8333i		−	0.991227i
$362$	0.775317	+	9.03147i	0.0407498	+	0.474684i
$363$	15.1769	+	15.1769i	0.796579	+	0.796579i
$364$	0.0827723	+	0.287141i	0.00433845	+	0.0150503i
$365$	11.6644	−	11.6644i	0.610542	−	0.610542i
$366$	10.3920	−	12.3437i	0.543196	−	0.645217i
$367$	2.64061			0.137839			0.0689195	−	0.997622i	$-0.478045\pi$
$367$	2.64061			0.137839			0.0689195	+	0.997622i	$0.478045\pi$
$368$	−8.82158	−	24.7378i	−0.459856	−	1.28955i
$369$			2.75174i			0.143250i
$370$	−4.61368	+	5.48020i	−0.239854	+	0.284902i
$371$	0.170599	+	0.170599i	0.00885706	+	0.00885706i
$372$	11.6961	−	16.5883i	0.606413	−	0.860065i
$373$	11.0013	+	11.0013i	0.569625	+	0.569625i	0.932023	−	0.362398i	$-0.118042\pi$
$373$	11.0013	+	11.0013i	0.569625	+	0.569625i	−0.362398	+	0.932023i	$0.618042\pi$
$374$	−54.3944	+	4.66955i	−2.81267	+	0.241457i
$375$	12.1693			0.628419
$376$	15.6752	+	9.15257i	0.808385	+	0.472008i
$377$	−0.579318	+	0.722258i	−0.0298364	+	0.0371982i
$378$	0.00501267	+	0.0583913i	0.000257824	+	0.00300332i
$379$	6.79808	−	6.79808i	0.349194	−	0.349194i	−0.510615	−	0.859809i	$-0.670582\pi$
$379$	6.79808	−	6.79808i	0.349194	−	0.349194i	0.859809	+	0.510615i	$0.170582\pi$
$380$	0.251202	+	1.45231i	0.0128864	+	0.0745021i
$381$	−9.51376	+	9.51376i	−0.487405	+	0.487405i
$382$	−10.6159	−	8.93733i	−0.543157	−	0.457273i
$383$			19.4618i			0.994453i	0.867621	+	0.497227i	$0.165648\pi$
$383$			19.4618i			0.994453i	−0.867621	+	0.497227i	$0.834352\pi$
$384$	−6.38310	−	9.34110i	−0.325736	−	0.476686i
$385$		−	0.426199i		−	0.0217211i
$386$	0.132307	−	0.157157i	0.00673427	−	0.00799907i
$387$	5.03764	−	5.03764i	0.256078	−	0.256078i
$388$	−34.1132	+	5.90047i	−1.73184	+	0.299551i
$389$	−13.4442	−	13.4442i	−0.681647	−	0.681647i	0.278724	−	0.960371i	$-0.410088\pi$
$389$	−13.4442	−	13.4442i	−0.681647	−	0.681647i	−0.960371	+	0.278724i	$0.910088\pi$
$390$	5.12363	−	7.64600i	0.259445	−	0.387170i
$391$			44.4869i			2.24980i
$392$	−9.98079	+	17.0936i	−0.504106	+	0.863358i
$393$		−	1.39381i		−	0.0703084i
$394$	−22.3265	+	1.91665i	−1.12480	+	0.0965594i
$395$	−19.4894	+	19.4894i	−0.980616	+	0.980616i
$396$	6.56649	−	9.31314i	0.329978	−	0.468003i
$397$	−20.4893	−	20.4893i	−1.02833	−	1.02833i	−0.999587	−	0.0287424i	$-0.990850\pi$
$397$	−20.4893	−	20.4893i	−1.02833	−	1.02833i	−0.0287424	−	0.999587i	$-0.509150\pi$
$398$	3.25924	−	3.87138i	0.163371	−	0.194055i
$399$	−0.0169189			−0.000847003
$400$	−2.34020	−	6.56249i	−0.117010	−	0.328124i
$401$		−	17.7438i		−	0.886085i	−0.896501	−	0.443043i	$-0.853899\pi$
$401$		−	17.7438i		−	0.886085i	0.896501	−	0.443043i	$-0.146101\pi$
$402$	15.2854	+	12.8685i	0.762366	+	0.641822i
$403$	−3.99444	−	36.3724i	−0.198977	−	1.81184i
$404$	−11.9752	+	16.9842i	−0.595787	+	0.844995i
$405$	1.27636	−	1.27636i	0.0634228	−	0.0634228i
$406$	0.0149946	−	0.00128723i	0.000744169	−	6.38840e-5i
$407$			15.9894i			0.792563i
$408$	4.86937	+	18.5349i	0.241070	+	0.917613i
$409$	23.6125			1.16756			0.583782	−	0.811911i	$-0.301572\pi$
$409$	23.6125			1.16756			0.583782	+	0.811911i	$0.301572\pi$
$410$	−6.99867	+	0.600809i	−0.345640	+	0.0296719i
$411$	−0.365116	+	0.365116i	−0.0180099	+	0.0180099i
$412$	−4.80350	+	0.830847i	−0.236651	+	0.0409329i
$413$	−0.0317031	+	0.0317031i	−0.00156001	+	0.00156001i
$414$	−7.10345	−	5.98026i	−0.349115	−	0.293914i
$415$	23.1816			1.13794
$416$	−19.7729	−	5.00327i	−0.969446	−	0.245305i
$417$	18.7613			0.918745
$418$	2.51660	+	2.11868i	0.123091	+	0.103628i
$419$	−2.59479	+	2.59479i	−0.126764	+	0.126764i	−0.767642	−	0.640879i	$-0.778570\pi$
$419$	−2.59479	+	2.59479i	−0.126764	+	0.126764i	0.640879	+	0.767642i	$0.278570\pi$
$420$	−0.147416	+	0.0254981i	−0.00719316	+	0.00124418i
$421$	−4.81789	+	4.81789i	−0.234810	+	0.234810i	−0.814697	−	0.579887i	$-0.803097\pi$
$421$	−4.81789	+	4.81789i	−0.234810	+	0.234810i	0.579887	+	0.814697i	$0.303097\pi$
$422$	−8.78172	+	0.753877i	−0.427487	+	0.0366982i
$423$	6.41756			0.312033
$424$	−15.9263	+	4.18408i	−0.773452	+	0.203197i
$425$			11.8016i			0.572460i
$426$	4.86734	−	0.417843i	0.235824	−	0.0202445i
$427$	−0.334337	+	0.334337i	−0.0161797	+	0.0161797i
$428$	−12.4293	+	17.6283i	−0.600793	+	0.852095i
$429$	−2.24258	−	20.4204i	−0.108273	−	0.985908i
$430$	13.9125	+	11.7126i	0.670918	+	0.564833i
$431$			6.72110i			0.323744i	0.986812	+	0.161872i	$0.0517531\pi$
$431$			6.72110i			0.323744i	−0.986812	+	0.161872i	$0.948247\pi$
$432$	−3.61413	−	1.71408i	−0.173885	−	0.0824686i
$433$	−25.2547			−1.21367			−0.606833	−	0.794830i	$-0.707560\pi$
$433$	−25.2547			−1.21367			−0.606833	+	0.794830i	$0.707560\pi$
$434$	−0.383050	+	0.454993i	−0.0183870	+	0.0218404i
$435$	−0.327762	−	0.327762i	−0.0157150	−	0.0157150i
$436$	4.54582	−	6.44727i	0.217705	−	0.308768i
$437$	1.89550	−	1.89550i	0.0906741	−	0.0906741i
$438$	−12.8769	+	1.10543i	−0.615280	+	0.0528195i
$439$		−	10.3475i		−	0.493862i	−0.969033	−	0.246931i	$-0.920578\pi$
$439$		−	10.3475i		−	0.493862i	0.969033	−	0.246931i	$-0.0794220\pi$
$440$	25.1204	+	14.6676i	1.19757	+	0.699248i
$441$			6.99828i			0.333252i
$442$	28.7001	+	19.2321i	1.36512	+	0.914778i
$443$	−6.29246	−	6.29246i	−0.298964	−	0.298964i	0.541644	−	0.840608i	$-0.317802\pi$
$443$	−6.29246	−	6.29246i	−0.298964	−	0.298964i	−0.840608	+	0.541644i	$0.817802\pi$
$444$	5.53049	−	0.956592i	0.262465	−	0.0453978i
$445$	−9.14111	+	9.14111i	−0.433330	+	0.433330i
$446$	14.2216	−	16.8926i	0.673410	−	0.799887i
$447$			2.52737i			0.119540i
$448$	0.162947	+	0.288718i	0.00769851	+	0.0136406i
$449$		−	7.98751i		−	0.376954i	−0.982078	−	0.188477i	$-0.939645\pi$
$449$		−	7.98751i		−	0.376954i	0.982078	−	0.188477i	$-0.0603551\pi$
$450$	−1.88441	−	1.58645i	−0.0888321	−	0.0747861i
$451$	−11.0864	+	11.0864i	−0.522036	+	0.522036i
$452$	1.40617	+	8.12971i	0.0661407	+	0.382389i
$453$	7.25926	−	7.25926i	0.341070	−	0.341070i
$454$	−0.810717	−	9.44383i	−0.0380488	−	0.443221i
$455$	−0.168751	+	0.210388i	−0.00791117	+	0.00986316i
$456$	0.582260	−	0.997209i	0.0272668	−	0.0466986i
$457$	−14.7308			−0.689079			−0.344540	−	0.938772i	$-0.611965\pi$
$457$	−14.7308			−0.689079			−0.344540	+	0.938772i	$0.611965\pi$
$458$	24.5753	−	2.10969i	1.14833	−	0.0985794i
$459$	4.79096	+	4.79096i	0.223623	+	0.223623i
$460$	13.6590	−	19.3724i	0.636855	−	0.903241i
$461$	−23.4273	−	23.4273i	−1.09112	−	1.09112i	−0.995409	−	0.0957091i	$-0.969488\pi$
$461$	−23.4273	−	23.4273i	−1.09112	−	1.09112i	−0.0957091	−	0.995409i	$-0.530512\pi$
$462$	−0.215055	+	0.255445i	−0.0100053	+	0.0118844i
$463$			10.3506i			0.481033i	0.970645	+	0.240517i	$0.0773168\pi$
$463$			10.3506i			0.481033i	−0.970645	+	0.240517i	$0.922683\pi$
$464$	−0.440166	+	0.928090i	−0.0204342	+	0.0430855i
$465$	18.3185			0.849502
$466$	−23.8870	+	28.3733i	−1.10654	+	1.31437i
$467$	1.75481	−	1.75481i	0.0812028	−	0.0812028i	−0.665339	−	0.746542i	$-0.731713\pi$
$467$	1.75481	−	1.75481i	0.0812028	−	0.0812028i	0.746542	+	0.665339i	$0.231713\pi$
$468$	−6.92896	+	1.99737i	−0.320291	+	0.0923283i
$469$	−0.414014	−	0.414014i	−0.0191174	−	0.0191174i
$470$	1.40120	+	16.3222i	0.0646324	+	0.752886i
$471$		−	2.95157i		−	0.136001i
$472$	−0.777544	−	2.95966i	−0.0357894	−	0.136229i
$473$	40.5918			1.86641
$474$	21.5152	−	1.84700i	0.988226	−	0.0848354i
$475$	0.502841	−	0.502841i	0.0230719	−	0.0230719i
$476$	−0.0957099	−	0.553342i	−0.00438686	−	0.0253624i
$477$	−4.11670	+	4.11670i	−0.188491	+	0.188491i
$478$	−18.8940	+	22.4426i	−0.864193	+	1.02650i
$479$		−	18.3396i		−	0.837960i	−0.907996	−	0.418980i	$-0.862388\pi$
$479$		−	18.3396i		−	0.837960i	0.907996	−	0.418980i	$-0.137612\pi$
$480$	3.57042	−	9.56630i	0.162967	−	0.436640i
$481$	6.33090	−	7.89298i	0.288664	−	0.359889i
$482$	−15.4061	+	18.2996i	−0.701727	+	0.833522i
$483$	0.192401	+	0.192401i	0.00875456	+	0.00875456i
$484$	42.2986	−	7.31627i	1.92266	−	0.332558i
$485$	−22.0936	−	22.0936i	−1.00322	−	1.00322i
$486$	−1.40903	+	0.120960i	−0.0639149	+	0.00548685i
$487$	−25.9626			−1.17648			−0.588240	−	0.808686i	$-0.700179\pi$
$487$	−25.9626			−1.17648			−0.588240	+	0.808686i	$0.700179\pi$
$488$	−8.19989	−	31.2122i	−0.371192	−	1.41291i
$489$	−4.80693			−0.217377
$490$	−17.7992	+	1.52799i	−0.804085	+	0.0690276i
$491$	−7.28151	−	7.28151i	−0.328610	−	0.328610i	0.523448	−	0.852058i	$-0.324645\pi$
$491$	−7.28151	−	7.28151i	−0.328610	−	0.328610i	−0.852058	+	0.523448i	$0.824645\pi$
$492$	4.49787	+	3.17135i	0.202780	+	0.142975i
$493$	1.23029	−	1.23029i	0.0554096	−	0.0554096i
$494$	−0.403413	−	2.04230i	−0.0181504	−	0.0918873i
$495$	10.2845			0.462255
$496$	−13.6350	−	38.2357i	−0.612228	−	1.71684i
$497$	−0.143153			−0.00642127
$498$	−13.8941	−	11.6972i	−0.622608	−	0.524163i
$499$	0.102696	+	0.102696i	0.00459732	+	0.00459732i	0.709402	−	0.704804i	$-0.248965\pi$
$499$	0.102696	+	0.102696i	0.00459732	+	0.00459732i	−0.704804	+	0.709402i	$0.748965\pi$
$500$	14.0249	−	19.8914i	0.627215	−	0.889568i
$501$	−4.24645	+	4.24645i	−0.189717	+	0.189717i
$502$	−2.01443	−	23.4655i	−0.0899083	−	1.04732i
$503$			7.12744i			0.317797i	0.987295	+	0.158898i	$0.0507942\pi$
$503$			7.12744i			0.317797i	−0.987295	+	0.158898i	$0.949206\pi$
$504$	0.101221	+	0.0591018i	0.00450873	+	0.00263260i
$505$	−18.7557			−0.834617
$506$	−4.52515	−	52.7124i	−0.201168	−	2.34335i
$507$	−6.97833	+	10.9683i	−0.309919	+	0.487118i
$508$	4.58627	+	26.5153i	0.203483	+	1.17642i
$509$	21.6328	+	21.6328i	0.958858	+	0.958858i	0.999186	−	0.0403283i	$-0.0128404\pi$
$509$	21.6328	+	21.6328i	0.958858	+	0.958858i	−0.0403283	+	0.999186i	$0.512840\pi$
$510$	−11.1391	+	13.2312i	−0.493247	+	0.585887i
$511$	0.378719			0.0167535
$512$	−22.6250	−	0.331982i	−0.999892	−	0.0146717i
$513$		−	0.408266i		−	0.0180254i
$514$	−8.99363	−	7.57157i	−0.396692	−	0.333968i
$515$	−3.11101	−	3.11101i	−0.137088	−	0.137088i
$516$	−2.42848	−	14.0401i	−0.106908	−	0.618082i
$517$	25.8554	+	25.8554i	1.13712	+	1.13712i
$518$	−0.163864	+	0.0140671i	−0.00719976	+	0.000618072i
$519$		−	18.2103i		−	0.799345i
$520$	−6.59288	−	17.1868i	−0.289117	−	0.753690i
$521$			19.9403i			0.873600i	0.899559	+	0.436800i	$0.143888\pi$
$521$			19.9403i			0.873600i	−0.899559	+	0.436800i	$0.856112\pi$
$522$	0.0310619	+	0.361832i	0.00135954	+	0.0158369i
$523$	−18.3043	−	18.3043i	−0.800393	−	0.800393i	0.182764	−	0.983157i	$-0.441496\pi$
$523$	−18.3043	−	18.3043i	−0.800393	−	0.800393i	−0.983157	+	0.182764i	$0.941496\pi$
$524$	−2.27826	−	1.60635i	−0.0995262	−	0.0701737i
$525$	0.0510405	+	0.0510405i	0.00222759	+	0.00222759i
$526$	−26.5364	+	31.5204i	−1.15704	+	1.37435i
$527$			68.7607i			2.99526i
$528$	−7.65504	−	21.4666i	−0.333143	−	0.934213i
$529$	−20.1112			−0.874402
$530$	−11.3691	−	9.57142i	−0.493842	−	0.415756i
$531$	−0.765023	−	0.765023i	−0.0331991	−	0.0331991i
$532$	−0.0194988	+	0.0276548i	−0.000845380	+	0.00119899i
$533$	9.86224	−	1.08308i	0.427181	−	0.0469133i
$534$	10.0913	−	0.866298i	0.436693	−	0.0374884i
$535$	−19.4670			−0.841630
$536$	38.6505	−	10.1540i	1.66945	−	0.438587i
$537$		−	20.8226i		−	0.898563i
$538$	−2.17633	+	0.186829i	−0.0938281	+	0.00805478i
$539$	−28.1951	+	28.1951i	−1.21445	+	1.21445i
$540$	−0.615290	−	3.55727i	−0.0264779	−	0.153080i
$541$	23.2162	+	23.2162i	0.998144	+	0.998144i	0.999998	−	0.00185427i	$-0.000590232\pi$
$541$	23.2162	+	23.2162i	0.998144	+	0.998144i	−0.00185427	+	0.999998i	$0.500590\pi$
$542$	−6.97563	+	8.28576i	−0.299629	+	0.355904i
$543$	6.40970			0.275067
$544$	35.9082	+	13.4020i	1.53955	+	0.574605i
$545$	7.11974			0.304976
$546$	0.207302	−	0.0409481i	0.00887169	−	0.00175242i
$547$	25.0199	−	25.0199i	1.06977	−	1.06977i	0.0723965	−	0.997376i	$-0.476935\pi$
$547$	25.0199	−	25.0199i	1.06977	−	1.06977i	0.997376	−	0.0723965i	$-0.0230647\pi$
$548$	0.176010	+	1.01760i	0.00751879	+	0.0434695i
$549$	−8.06784	−	8.06784i	−0.344327	−	0.344327i
$550$	−1.20044	−	13.9836i	−0.0511869	−	0.596263i
$551$	−0.104841			−0.00446636
$552$	−17.9617	+	4.71879i	−0.764501	+	0.200845i
$553$	−0.632779			−0.0269085
$554$	0.0707028	+	0.823598i	0.00300387	+	0.0349913i
$555$	3.58185	+	3.58185i	0.152041	+	0.152041i
$556$	21.6222	−	30.6664i	0.916985	−	1.30054i
$557$	−9.59909	−	9.59909i	−0.406726	−	0.406726i	0.473869	−	0.880595i	$-0.342857\pi$
$557$	−9.59909	−	9.59909i	−0.406726	−	0.406726i	−0.880595	+	0.473869i	$0.842857\pi$
$558$	−10.9794	−	9.24332i	−0.464794	−	0.391301i
$559$	−20.0377	−	16.0721i	−0.847505	−	0.679778i
$560$	−0.128217	+	0.270346i	−0.00541816	+	0.0114242i
$561$			38.6041i			1.62987i
$562$	−15.1362	−	12.7429i	−0.638484	−	0.537528i
$563$	9.87534	−	9.87534i	0.416196	−	0.416196i	−0.467694	−	0.883890i	$-0.654915\pi$
$563$	9.87534	−	9.87534i	0.416196	−	0.416196i	0.883890	+	0.467694i	$0.154915\pi$
$564$	7.39617	−	10.4899i	0.311435	−	0.441703i
$565$	−5.26525	+	5.26525i	−0.221511	+	0.221511i
$566$	−1.09378	−	12.7411i	−0.0459749	−	0.535550i
$567$	0.0414407			0.00174035
$568$	4.92657	−	8.43750i	0.206714	−	0.354030i
$569$			27.8281i			1.16662i	0.812251	+	0.583308i	$0.198242\pi$
$569$			27.8281i			1.16662i	−0.812251	+	0.583308i	$0.801758\pi$
$570$	1.03837	−	0.0891401i	0.0434925	−	0.00373367i
$571$	8.84947	+	8.84947i	0.370339	+	0.370339i	0.867601	−	0.497262i	$-0.165661\pi$
$571$	8.84947	+	8.84947i	0.370339	+	0.370339i	−0.497262	+	0.867601i	$0.665661\pi$
$572$	−35.9629	−	19.8687i	−1.50368	−	0.830752i
$573$	−6.93854	+	6.93854i	−0.289861	+	0.289861i
$574$	−0.123370	−	0.103863i	−0.00514935	−	0.00433515i
$575$	−11.4366			−0.476940
$576$	−6.96700	+	3.93204i	−0.290292	+	0.163835i
$577$		−	40.7787i		−	1.69764i	−0.528681	−	0.848821i	$-0.677313\pi$
$577$		−	40.7787i		−	1.69764i	0.528681	−	0.848821i	$-0.322687\pi$
$578$	−31.2730	−	26.3282i	−1.30079	−	1.09511i
$579$	−0.102718	−	0.102718i	−0.00426879	−	0.00426879i
$580$	−0.913488	+	0.158003i	−0.0379305	+	0.00656073i
$581$	0.376330	+	0.376330i	0.0156128	+	0.0156128i
$582$	2.09380	+	24.3902i	0.0867909	+	1.01101i
$583$	−33.1711			−1.37381
$584$	−13.0335	+	22.3219i	−0.539332	+	0.923688i
$585$	−5.07685	−	4.07210i	−0.209902	−	0.168361i
$586$	3.90920	−	0.335590i	0.161488	−	0.0138631i
$587$	−20.0869	+	20.0869i	−0.829074	+	0.829074i	−0.987389	−	0.158315i	$-0.949394\pi$
$587$	−20.0869	+	20.0869i	−0.829074	+	0.829074i	0.158315	+	0.987389i	$0.449394\pi$
$588$	11.4391	+	8.06544i	0.471740	+	0.332613i
$589$	2.92976	−	2.92976i	0.120719	−	0.120719i
$590$	1.77870	−	2.11276i	0.0732278	−	0.0869811i
$591$			15.8453i			0.651789i
$592$	4.81022	−	10.1423i	0.197699	−	0.416848i
$593$			13.8757i			0.569806i	0.958556	+	0.284903i	$0.0919614\pi$
$593$			13.8757i			0.569806i	−0.958556	+	0.284903i	$0.908039\pi$
$594$	−6.16411	−	5.18945i	−0.252917	−	0.212926i
$595$	0.358375	−	0.358375i	0.0146919	−	0.0146919i
$596$	4.13112	+	2.91276i	0.169217	+	0.119311i
$597$	−2.53033	−	2.53033i	−0.103559	−	0.103559i
$598$	−18.6374	+	27.8126i	−0.762139	+	1.13734i
$599$		−	20.7417i		−	0.847484i	−0.905783	−	0.423742i	$-0.860716\pi$
$599$		−	20.7417i		−	0.847484i	0.905783	−	0.423742i	$-0.139284\pi$
$600$	−4.76491	+	1.25181i	−0.194527	+	0.0511049i
$601$			21.0537i			0.858799i	0.903115	+	0.429400i	$0.141275\pi$
$601$			21.0537i			0.858799i	−0.903115	+	0.429400i	$0.858725\pi$
$602$	0.0357117	+	0.415997i	0.00145550	+	0.0169548i
$603$	9.99051	−	9.99051i	0.406845	−	0.406845i
$604$	−3.49945	−	20.2319i	−0.142390	−	0.823223i
$605$	27.3949	+	27.3949i	1.11376	+	1.11376i
$606$	11.2414	+	9.46390i	0.456649	+	0.384445i
$607$	−35.9523			−1.45926			−0.729630	−	0.683842i	$-0.760308\pi$
$607$	−35.9523			−1.45926			−0.729630	+	0.683842i	$0.760308\pi$
$608$	−0.958945	−	2.10101i	−0.0388903	−	0.0852071i
$609$		−	0.0106418i		−	0.000431226i
$610$	18.7579	−	22.2810i	0.759487	−	0.902130i
$611$	−2.52594	−	23.0006i	−0.102188	−	0.930503i
$612$	13.3526	−	2.30956i	0.539747	−	0.0933585i
$613$	−20.7659	+	20.7659i	−0.838726	+	0.838726i	−0.988691	−	0.149965i	$-0.952084\pi$
$613$	−20.7659	+	20.7659i	−0.838726	+	0.838726i	0.149965	+	0.988691i	$0.452084\pi$
$614$	−2.94784	−	34.3386i	−0.118965	−	1.38580i
$615$			4.96701i			0.200289i
$616$	0.169691	+	0.645917i	0.00683706	+	0.0260247i
$617$	25.7452			1.03646			0.518232	−	0.855240i	$-0.326590\pi$
$617$	25.7452			1.03646			0.518232	+	0.855240i	$0.326590\pi$
$618$	0.294829	+	3.43439i	0.0118598	+	0.138151i
$619$	6.61127	−	6.61127i	0.265729	−	0.265729i	−0.561647	−	0.827377i	$-0.689832\pi$
$619$	6.61127	−	6.61127i	0.265729	−	0.265729i	0.827377	+	0.561647i	$0.189832\pi$
$620$	21.1119	−	29.9427i	0.847875	−	1.20253i
$621$	−4.64280	+	4.64280i	−0.186309	+	0.186309i
$622$	−12.6207	+	14.9911i	−0.506045	+	0.601089i
$623$	−0.296793			−0.0118908
$624$	−4.72075	+	13.6277i	−0.188981	+	0.545545i
$625$	13.2570			0.530280
$626$	25.8110	−	30.6587i	1.03161	−	1.22537i
$627$	1.64485	−	1.64485i	0.0656888	−	0.0656888i
$628$	−4.82451	−	3.40165i	−0.192519	−	0.135741i
$629$	−13.4449	+	13.4449i	−0.536082	+	0.536082i
$630$	0.00904809	+	0.105399i	0.000360485	+	0.00419919i
$631$	4.58315			0.182452			0.0912261	−	0.995830i	$-0.470921\pi$
$631$	4.58315			0.182452			0.0912261	+	0.995830i	$0.470921\pi$
$632$	21.7770	−	37.2964i	0.866242	−	1.48357i
$633$			6.23245i			0.247718i
$634$	2.10376	+	24.5061i	0.0835508	+	0.973262i
$635$	−17.1728	+	17.1728i	−0.681480	+	0.681480i
$636$	1.98452	+	11.4734i	0.0786914	+	0.454950i
$637$	25.0819	−	2.75451i	0.993780	−	0.109137i
$638$	−1.33262	+	1.58291i	−0.0527591	+	0.0626681i
$639$		−	3.45439i		−	0.136654i
$640$	−11.5218	−	16.8611i	−0.455438	−	0.666493i
$641$	12.6104			0.498082			0.249041	−	0.968493i	$-0.419885\pi$
$641$	12.6104			0.498082			0.249041	+	0.968493i	$0.419885\pi$
$642$	11.6677	+	9.82280i	0.460486	+	0.387675i
$643$	−1.99949	−	1.99949i	−0.0788523	−	0.0788523i	0.666581	−	0.745433i	$-0.267757\pi$
$643$	−1.99949	−	1.99949i	−0.0788523	−	0.0788523i	−0.745433	+	0.666581i	$0.767757\pi$
$644$	0.536231	−	0.0927502i	0.0211304	−	0.00365487i
$645$	9.09316	−	9.09316i	0.358043	−	0.358043i
$646$	0.334597	+	3.89764i	0.0131646	+	0.153351i
$647$		−	45.5615i		−	1.79121i	−0.444852	−	0.895604i	$-0.646744\pi$
$647$		−	45.5615i		−	1.79121i	0.444852	−	0.895604i	$-0.353256\pi$
$648$	−1.42618	+	2.44254i	−0.0560255	+	0.0959522i
$649$		−	6.16433i		−	0.241971i
$650$	−4.94415	+	7.37817i	−0.193926	+	0.289396i
$651$	0.297383	+	0.297383i	0.0116554	+	0.0116554i
$652$	−5.53993	+	7.85719i	−0.216960	+	0.307711i
$653$	16.3520	−	16.3520i	0.639901	−	0.639901i	−0.310630	−	0.950531i	$-0.600540\pi$
$653$	16.3520	−	16.3520i	0.639901	−	0.639901i	0.950531	+	0.310630i	$0.100540\pi$
$654$	−4.26727	−	3.59253i	−0.166863	−	0.140479i
$655$		−	2.51589i		−	0.0983039i
$656$	10.3675	−	3.69707i	0.404782	−	0.144346i
$657$			9.13881i			0.356539i
$658$	−0.242227	+	0.287721i	−0.00944299	+	0.0112165i
$659$	4.62742	−	4.62742i	0.180259	−	0.180259i	−0.611210	−	0.791469i	$-0.709317\pi$
$659$	4.62742	−	4.62742i	0.180259	−	0.180259i	0.791469	+	0.611210i	$0.209317\pi$
$660$	11.8528	−	16.8106i	0.461370	−	0.654353i
$661$	20.9747	−	20.9747i	0.815822	−	0.815822i	−0.169677	−	0.985500i	$-0.554273\pi$
$661$	20.9747	−	20.9747i	0.815822	−	0.815822i	0.985500	+	0.169677i	$0.0542726\pi$
$662$	−8.47591	+	0.727624i	−0.329425	+	0.0282799i
$663$	15.2851	−	19.0565i	0.593624	−	0.740094i
$664$	−35.1324	+	9.22979i	−1.36340	+	0.358185i
$665$	−0.0305393			−0.00118426
$666$	−0.339450	−	3.95417i	−0.0131534	−	0.153221i
$667$	1.19225	+	1.19225i	0.0461640	+	0.0461640i
$668$	2.04707	+	11.8350i	0.0792036	+	0.457912i
$669$	−11.0410	−	11.0410i	−0.426869	−	0.426869i
$670$	27.5908	+	23.2282i	1.06593	+	0.897383i
$671$		−	65.0083i		−	2.50962i
$672$	0.213261	−	0.0973369i	0.00822672	−	0.00375485i
$673$	−13.1618			−0.507351			−0.253676	−	0.967289i	$-0.581640\pi$
$673$	−13.1618			−0.507351			−0.253676	+	0.967289i	$0.581640\pi$
$674$	31.3851	+	26.4225i	1.20891	+	1.01776i
$675$	−1.23165	+	1.23165i	−0.0474062	+	0.0474062i
$676$	9.88579	+	24.0473i	0.380223	+	0.924895i
$677$	−0.489813	−	0.489813i	−0.0188250	−	0.0188250i	0.697632	−	0.716457i	$-0.254237\pi$
$677$	−0.489813	−	0.489813i	−0.0188250	−	0.0188250i	−0.716457	+	0.697632i	$0.754237\pi$
$678$	5.81255	−	0.498985i	0.223230	−	0.0191634i
$679$		−	0.717335i		−	0.0275288i
$680$	8.78943	+	33.4563i	0.337059	+	1.28299i
$681$	−6.70236			−0.256835
$682$	−6.99425	−	81.4743i	−0.267824	−	3.11981i
$683$	2.09670	−	2.09670i	0.0802282	−	0.0802282i	−0.665854	−	0.746082i	$-0.731933\pi$
$683$	2.09670	−	2.09670i	0.0802282	−	0.0802282i	0.746082	+	0.665854i	$0.231933\pi$
$684$	−0.667334	−	0.470522i	−0.0255162	−	0.0179909i
$685$	−0.659051	+	0.659051i	−0.0251811	+	0.0251811i
$686$	−0.627590	−	0.528357i	−0.0239615	−	0.0201728i
$687$		−	17.4412i		−	0.665425i
$688$	−25.7481	−	12.2116i	−0.981638	−	0.465563i
$689$	16.3746	+	13.1339i	0.623822	+	0.500363i
$690$	−12.8220	−	10.7946i	−0.488127	−	0.410945i
$691$	−13.4451	−	13.4451i	−0.511476	−	0.511476i	0.403503	−	0.914979i	$-0.367793\pi$
$691$	−13.4451	−	13.4451i	−0.511476	−	0.511476i	−0.914979	+	0.403503i	$0.867793\pi$
$692$	−29.7658	−	20.9872i	−1.13153	−	0.797813i
$693$	0.166959	+	0.166959i	0.00634224	+	0.00634224i
$694$	4.03558	+	47.0094i	0.153188	+	1.78445i
$695$	33.8650			1.28457
$696$	0.627232	+	0.366235i	0.0237752	+	0.0138821i
$697$	−18.6442			−0.706201
$698$	0.562434	+	6.55165i	0.0212885	+	0.247984i
$699$	18.5448	+	18.5448i	0.701427	+	0.701427i
$700$	0.142252	−	0.0246049i	0.00537662	−	0.000929979i
$701$	−23.7952	+	23.7952i	−0.898732	+	0.898732i	−0.995324	−	0.0965925i	$-0.969206\pi$
$701$	−23.7952	+	23.7952i	−0.898732	+	0.898732i	0.0965925	+	0.995324i	$0.469206\pi$
$702$	0.988112	+	5.00236i	0.0372939	+	0.188802i
$703$	1.14572			0.0432116
$704$	−43.9106	−	12.2274i	−1.65494	−	0.460837i
$705$	11.5840			0.436278
$706$	2.71422	−	3.22399i	0.102151	−	0.121337i
$707$	−0.304479	−	0.304479i	−0.0114511	−	0.0114511i
$708$	−2.13215	+	0.368792i	−0.0801311	+	0.0138600i
$709$	−1.92154	+	1.92154i	−0.0721648	+	0.0721648i	−0.742268	−	0.670103i	$-0.766250\pi$
$709$	−1.92154	+	1.92154i	−0.0721648	+	0.0721648i	0.670103	+	0.742268i	$0.266250\pi$
$710$	8.78577	−	0.754225i	0.329724	−	0.0283055i
$711$		−	15.2695i		−	0.572651i
$712$	10.2141	−	17.4932i	0.382789	−	0.655584i
$713$	−66.6344			−2.49548
$714$	−0.395627	+	0.0339630i	−0.0148060	+	0.00127103i
$715$	−4.04796	−	36.8598i	−0.151385	−	1.37848i
$716$	−34.0358	−	23.9979i	−1.27198	−	0.896842i
$717$	14.6685	+	14.6685i	0.547804	+	0.547804i
$718$	22.7592	+	19.1605i	0.849365	+	0.715065i
$719$	34.2315			1.27662			0.638309	−	0.769780i	$-0.279634\pi$
$719$	34.2315			1.27662			0.638309	+	0.769780i	$0.279634\pi$
$720$	−6.52367	−	3.09398i	−0.243123	−	0.115306i
$721$		−	0.101008i		−	0.00376174i
$722$	−17.1535	+	20.3751i	−0.638386	+	0.758284i
$723$	11.9606	+	11.9606i	0.444818	+	0.444818i
$724$	7.38711	−	10.4770i	0.274540	−	0.389375i
$725$	0.316281	+	0.316281i	0.0117464	+	0.0117464i
$726$	−2.59620	−	30.2425i	−0.0963542	−	1.12241i
$727$		−	15.1513i		−	0.561932i	−0.959718	−	0.280966i	$-0.909345\pi$
$727$		−	15.1513i		−	0.561932i	0.959718	−	0.280966i	$-0.0906548\pi$
$728$	0.171981	−	0.386038i	0.00637403	−	0.0143075i
$729$			1.00000i			0.0370370i
$730$	−23.2433	+	1.99535i	−0.860273	+	0.0738512i
$731$	34.1322	+	34.1322i	1.26242	+	1.26242i
$732$	−22.4854	+	3.88924i	−0.831085	+	0.143750i
$733$	16.2817	+	16.2817i	0.601377	+	0.601377i	0.940678	−	0.339301i	$-0.110190\pi$
$733$	16.2817	+	16.2817i	0.601377	+	0.601377i	−0.339301	+	0.940678i	$0.610190\pi$
$734$	−2.85679	−	2.40508i	−0.105446	−	0.0887732i
$735$			12.6322i			0.465946i
$736$	−12.9875	+	34.7978i	−0.478727	+	1.28266i
$737$	80.5006			2.96528
$738$	2.50629	−	2.97702i	0.0922580	−	0.109585i
$739$	21.0071	+	21.0071i	0.772759	+	0.772759i	0.978588	−	0.205829i	$-0.0659892\pi$
$739$	21.0071	+	21.0071i	0.772759	+	0.772759i	−0.205829	+	0.978588i	$0.565989\pi$
$740$	9.98277	−	1.72669i	0.366974	−	0.0634744i
$741$	−1.46323	+	0.160693i	−0.0537530	+	0.00590319i
$742$	−0.0291832	−	0.339948i	−0.00107135	−	0.0124799i
$743$	11.9154			0.437132			0.218566	−	0.975822i	$-0.429862\pi$
$743$	11.9154			0.437132			0.218566	+	0.975822i	$0.429862\pi$
$744$	−27.7623	+	7.29355i	−1.01782	+	0.267395i
$745$			4.56201i			0.167139i
$746$	−1.88191	−	21.9219i	−0.0689018	−	0.802619i
$747$	−9.08115	+	9.08115i	−0.332262	+	0.332262i
$748$	63.1006	+	44.4908i	2.30719	+	1.62675i
$749$	−0.316026	−	0.316026i	−0.0115473	−	0.0115473i
$750$	−13.1655	−	11.0838i	−0.480737	−	0.404724i
$751$	12.1999			0.445180			0.222590	−	0.974912i	$-0.428549\pi$
$751$	12.1999			0.445180			0.222590	+	0.974912i	$0.428549\pi$
$752$	−8.62226	−	24.1789i	−0.314421	−	0.881713i
$753$	−16.6537			−0.606894
$754$	1.28458	−	0.253742i	0.0467817	−	0.00924074i
$755$	13.1033	−	13.1033i	0.476877	−	0.476877i
$756$	0.0477600	−	0.0677372i	0.00173701	−	0.00246358i
$757$	3.30627	+	3.30627i	0.120168	+	0.120168i	0.764634	−	0.644465i	$-0.222920\pi$
$757$	3.30627	+	3.30627i	0.120168	+	0.120168i	−0.644465	+	0.764634i	$0.722920\pi$
$758$	−13.5463	+	1.16290i	−0.492025	+	0.0422385i
$759$	−37.4104			−1.35791
$760$	1.05100	−	1.80001i	0.0381240	−	0.0652931i
$761$	13.1153			0.475429			0.237715	−	0.971335i	$-0.423602\pi$
$761$	13.1153			0.475429			0.237715	+	0.971335i	$0.423602\pi$
$762$	18.9578	−	1.62745i	0.686768	−	0.0589564i
$763$	0.115582	+	0.115582i	0.00418433	+	0.00418433i
$764$	3.34484	+	19.3380i	0.121012	+	0.699624i
$765$	8.64789	+	8.64789i	0.312665	+	0.312665i
$766$	17.7259	−	21.0551i	0.640463	−	0.760752i
$767$	−2.44073	+	3.04295i	−0.0881297	+	0.109875i
$768$	−1.60224	+	15.9196i	−0.0578160	+	0.574448i
$769$		−	7.27124i		−	0.262208i	−0.991369	−	0.131104i	$-0.958148\pi$
$769$		−	7.27124i		−	0.262208i	0.991369	−	0.131104i	$-0.0418521\pi$
$770$	−0.388183	+	0.461090i	−0.0139892	+	0.0166165i
$771$	−5.87822	+	5.87822i	−0.211699	+	0.211699i
$772$	−0.286278	+	0.0495167i	−0.0103034	+	0.00178214i
$773$	−28.3845	+	28.3845i	−1.02092	+	1.02092i	−0.0211413	+	0.999776i	$0.506730\pi$
$773$	−28.3845	+	28.3845i	−1.02092	+	1.02092i	−0.999776	+	0.0211413i	$0.993270\pi$
$774$	−10.0384	+	0.861754i	−0.360821	+	0.0309751i
$775$	−17.6769			−0.634972
$776$	42.2802	+	24.6870i	1.51777	+	0.886210i
$777$			0.116295i			0.00417207i
$778$	2.29980	+	26.7898i	0.0824519	+	0.960461i
$779$	0.794394	+	0.794394i	0.0284621	+	0.0284621i
$780$	−12.5071	+	3.60533i	−0.447825	+	0.129092i
$781$	13.9172	−	13.9172i	0.497998	−	0.497998i
$782$	40.5189	−	48.1290i	1.44895	−	1.72109i
$783$	0.256795			0.00917710
$784$	26.3668	−	9.40248i	0.941672	−	0.335803i
$785$		−	5.32772i		−	0.190154i
$786$	−1.26949	+	1.50792i	−0.0452811	+	0.0537856i
$787$	15.9425	+	15.9425i	0.568289	+	0.568289i	0.931649	−	0.363360i	$-0.118370\pi$
$787$	15.9425	+	15.9425i	0.568289	+	0.568289i	−0.363360	+	0.931649i	$0.618370\pi$
$788$	25.9000	+	18.2615i	0.922651	+	0.650541i
$789$	20.6017	+	20.6017i	0.733439	+	0.733439i
$790$	38.8359	−	3.33391i	1.38172	−	0.118615i
$791$	−0.170952			−0.00607835
$792$	−15.5865	+	4.09480i	−0.553843	+	0.145502i
$793$	−25.7397	+	32.0907i	−0.914043	+	1.13957i
$794$	3.50497	+	40.8285i	0.124387	+	1.44895i
$795$	−7.43082	+	7.43082i	−0.263544	+	0.263544i
$796$	−7.05213	+	1.21979i	−0.249956	+	0.0432342i
$797$	23.2381	−	23.2381i	0.823134	−	0.823134i	−0.163422	−	0.986556i	$-0.552253\pi$
$797$	23.2381	−	23.2381i	0.823134	−	0.823134i	0.986556	+	0.163422i	$0.0522532\pi$
$798$	0.0183040	+	0.0154098i	0.000647953	+	0.000545500i
$799$			43.4818i			1.53827i
$800$	−3.44535	+	9.23120i	−0.121812	+	0.326372i
$801$		−	7.16186i		−	0.253052i
$802$	−16.1612	+	19.1965i	−0.570670	+	0.677851i
$803$	−36.8189	+	36.8189i	−1.29931	+	1.29931i
$804$	−4.81609	−	27.8440i	−0.169851	−	0.981982i
$805$	0.347293	+	0.347293i	0.0122405	+	0.0122405i
$806$	−28.8067	+	42.9882i	−1.01467	+	1.51420i
$807$			1.54456i			0.0543709i
$808$	28.4248	−	7.46760i	0.999981	−	0.262709i
$809$			36.6381i			1.28813i	0.764972	+	0.644064i	$0.222753\pi$
$809$			36.6381i			1.28813i	−0.764972	+	0.644064i	$0.777247\pi$
$810$	−2.54336	+	0.218338i	−0.0893647	+	0.00767162i
$811$	7.45503	−	7.45503i	0.261781	−	0.261781i	−0.563996	−	0.825777i	$-0.690737\pi$
$811$	7.45503	−	7.45503i	0.261781	−	0.261781i	0.825777	+	0.563996i	$0.190737\pi$
$812$	−0.0173946	−	0.0122645i	−0.000610429	−	0.000430400i
$813$	5.41556	+	5.41556i	0.189932	+	0.189932i
$814$	14.5632	−	17.2984i	0.510439	−	0.606307i
$815$	−8.67672			−0.303932
$816$	11.6136	−	24.4873i	0.406558	−	0.857227i
$817$		−	2.90861i		−	0.101759i
$818$	−25.5456	−	21.5064i	−0.893181	−	0.751952i
$819$	−0.0163110	−	0.148524i	−0.000569951	−	0.00518984i
$820$	8.11885	+	5.72442i	0.283523	+	0.199905i
$821$	−1.21484	+	1.21484i	−0.0423981	+	0.0423981i	−0.727988	−	0.685590i	$-0.759544\pi$
$821$	−1.21484	+	1.21484i	−0.0423981	+	0.0423981i	0.685590	+	0.727988i	$0.259544\pi$
$822$	0.727557	−	0.0624580i	0.0253765	−	0.00217847i
$823$			36.6740i			1.27838i	0.769051	+	0.639188i	$0.220729\pi$
$823$			36.6740i			1.27838i	−0.769051	+	0.639188i	$0.779271\pi$
$824$	5.95348	+	3.47618i	0.207399	+	0.121098i
$825$	−9.92428			−0.345519
$826$	0.0631739	−	0.00542323i	0.00219810	−	0.000188698i
$827$	−1.90648	+	1.90648i	−0.0662946	+	0.0662946i	−0.739477	−	0.673182i	$-0.764927\pi$
$827$	−1.90648	+	1.90648i	−0.0662946	+	0.0662946i	0.673182	+	0.739477i	$0.264927\pi$
$828$	2.23814	+	12.9397i	0.0777808	+	0.449686i
$829$	−5.11543	+	5.11543i	−0.177666	+	0.177666i	−0.790338	−	0.612672i	$-0.790095\pi$
$829$	−5.11543	+	5.11543i	−0.177666	+	0.177666i	0.612672	+	0.790338i	$0.290095\pi$
$830$	−25.0794	−	21.1139i	−0.870519	−	0.732874i
$831$	0.584514			0.0202766
$832$	16.8346	+	23.4221i	0.583636	+	0.812015i
$833$	−47.4164			−1.64288
$834$	−20.2972	−	17.0879i	−0.702836	−	0.591704i
$835$	−7.66503	+	7.66503i	−0.265259	+	0.265259i
$836$	−0.792926	−	4.58426i	−0.0274239	−	0.158550i
$837$	−7.17610	+	7.17610i	−0.248042	+	0.248042i
$838$	5.17056	−	0.443873i	0.178614	−	0.0153333i
$839$	23.4179			0.808475			0.404237	−	0.914654i	$-0.367537\pi$
$839$	23.4179			0.808475			0.404237	+	0.914654i	$0.367537\pi$
$840$	0.182708	+	0.106681i	0.00630403	+	0.00368086i
$841$			28.9341i			0.997726i
$842$	9.60047	−	0.824164i	0.330854	−	0.0284026i
$843$	−9.89302	+	9.89302i	−0.340734	+	0.340734i
$844$	10.1873	+	7.18283i	0.350661	+	0.247243i
$845$	−12.5962	+	19.7982i	−0.433322	+	0.681079i
$846$	−6.94295	−	5.84514i	−0.238703	−	0.200960i
$847$			0.889457i			0.0305621i
$848$	21.0411	+	9.97916i	0.722553	+	0.342686i
$849$	−9.04247			−0.310337
$850$	10.7489	−	12.7677i	0.368685	−	0.437929i
$851$	−13.0291	−	13.0291i	−0.446632	−	0.446632i
$852$	−5.64639	−	3.98114i	−0.193442	−	0.136392i
$853$	25.0651	−	25.0651i	0.858211	−	0.858211i	−0.132916	−	0.991127i	$-0.542434\pi$
$853$	25.0651	−	25.0651i	0.858211	−	0.858211i	0.991127	+	0.132916i	$0.0424341\pi$
$854$	0.666225	−	0.0571928i	0.0227977	−	0.00195710i
$855$		−	0.736939i		−	0.0252028i
$856$	29.5028	−	7.75079i	1.00838	−	0.264917i
$857$			7.52172i			0.256937i	0.991714	+	0.128469i	$0.0410062\pi$
$857$			7.52172i			0.256937i	−0.991714	+	0.128469i	$0.958994\pi$
$858$	−16.1728	+	24.1348i	−0.552131	+	0.823947i
$859$	15.7151	+	15.7151i	0.536192	+	0.536192i	0.922408	−	0.386216i	$-0.126218\pi$
$859$	15.7151	+	15.7151i	0.536192	+	0.536192i	−0.386216	+	0.922408i	$0.626218\pi$
$860$	−4.38351	−	25.3430i	−0.149476	−	0.864190i
$861$	−0.0806343	+	0.0806343i	−0.00274801	+	0.00274801i
$862$	6.12160	−	7.27133i	0.208503	−	0.247663i
$863$		−	12.5967i		−	0.428796i	−0.976746	−	0.214398i	$-0.931221\pi$
$863$		−	12.5967i		−	0.428796i	0.976746	−	0.214398i	$-0.0687790\pi$
$864$	2.34882	+	5.14617i	0.0799085	+	0.175076i
$865$		−	32.8704i		−	1.11763i
$866$	27.3223	+	23.0021i	0.928449	+	0.781644i
$867$	−20.4400	+	20.4400i	−0.694179	+	0.694179i
$868$	0.828819	−	0.143358i	0.0281319	−	0.00486590i
$869$	61.5186	−	61.5186i	2.08687	−	2.08687i
$870$	0.0560681	+	0.653122i	0.00190089	+	0.0221429i
$871$	−39.7383	−	31.8738i	−1.34648	−	1.08000i
$872$	−10.7902	+	2.83473i	−0.365401	+	0.0959961i
$873$	17.3099			0.585851
$874$	−3.77711	+	0.324250i	−0.127763	+	0.0109679i
$875$	0.356597	+	0.356597i	0.0120552	+	0.0120552i
$876$	14.9379	+	10.5324i	0.504704	+	0.355856i
$877$	22.9613	+	22.9613i	0.775349	+	0.775349i	0.979036	−	0.203687i	$-0.0652925\pi$
$877$	22.9613	+	22.9613i	0.775349	+	0.775349i	−0.203687	+	0.979036i	$0.565292\pi$
$878$	−9.42459	+	11.1947i	−0.318064	+	0.377802i
$879$		−	2.77439i		−	0.0935778i
$880$	−13.8177	−	38.7481i	−0.465794	−	1.30620i
$881$	−16.9541			−0.571197			−0.285599	−	0.958349i	$-0.592192\pi$
$881$	−16.9541			−0.571197			−0.285599	+	0.958349i	$0.592192\pi$
$882$	6.37406	−	7.57121i	0.214626	−	0.254936i
$883$	−3.42569	+	3.42569i	−0.115284	+	0.115284i	−0.762395	−	0.647112i	$-0.775977\pi$
$883$	−3.42569	+	3.42569i	−0.115284	+	0.115284i	0.647112	+	0.762395i	$0.275977\pi$
$884$	−13.5330	−	46.9467i	−0.455165	−	1.57899i
$885$	−1.38090	−	1.38090i	−0.0464184	−	0.0464184i
$886$	1.07641	+	12.5388i	0.0361627	+	0.421250i
$887$			13.0603i			0.438521i	0.975666	+	0.219261i	$0.0703645\pi$
$887$			13.0603i			0.438521i	−0.975666	+	0.219261i	$0.929635\pi$
$888$	−6.85452	−	4.00228i	−0.230023	−	0.134308i
$889$	−0.557564			−0.0187001
$890$	18.2152	−	1.56371i	0.610575	−	0.0524156i
$891$	−4.02885	+	4.02885i	−0.134972	+	0.134972i
$892$	−30.7717	+	5.32248i	−1.03031	+	0.178210i
$893$	1.85267	−	1.85267i	0.0619973	−	0.0619973i
$894$	2.30194	−	2.73428i	0.0769883	−	0.0914478i
$895$		−	37.5858i		−	1.25635i
$896$	0.0866784	−	0.460767i	0.00289572	−	0.0153931i
$897$	18.4672	+	14.8124i	0.616603	+	0.494573i
$898$	−7.27506	+	8.64143i	−0.242772	+	0.288368i
$899$	1.84278	+	1.84278i	0.0614603	+	0.0614603i
$900$	0.593737	+	3.43266i	0.0197912	+	0.114422i
$901$	−27.8924	−	27.8924i	−0.929231	−	0.929231i
$902$	22.0915	−	1.89647i	0.735565	−	0.0631455i
$903$	0.295236			0.00982484
$904$	5.88328	−	10.0760i	0.195675	−	0.335123i
$905$	11.5698			0.384593
$906$	−14.4653	+	1.24179i	−0.480578	+	0.0412558i
$907$	−17.7435	−	17.7435i	−0.589164	−	0.589164i	0.348241	−	0.937405i	$-0.386779\pi$
$907$	−17.7435	−	17.7435i	−0.589164	−	0.589164i	−0.937405	+	0.348241i	$0.886779\pi$
$908$	−7.72439	+	10.9554i	−0.256343	+	0.363567i
$909$	7.34734	−	7.34734i	0.243696	−	0.243696i
$910$	0.374189	−	0.0739131i	0.0124042	−	0.00245020i
$911$	3.60225			0.119348			0.0596740	−	0.998218i	$-0.480994\pi$
$911$	3.60225			0.119348			0.0596740	+	0.998218i	$0.480994\pi$
$912$	−1.53819	+	0.548523i	−0.0509345	+	0.0181634i
$913$	−73.1733			−2.42168
$914$	15.9368	+	13.4169i	0.527143	+	0.443792i
$915$	−14.5628	−	14.5628i	−0.481432	−	0.481432i
$916$	−28.5087	−	20.1008i	−0.941953	−	0.664150i
$917$	0.0408429	−	0.0408429i	0.00134875	−	0.00134875i
$918$	−0.819556	−	9.54680i	−0.0270494	−	0.315091i
$919$		−	16.8166i		−	0.554729i	−0.960765	−	0.277365i	$-0.910539\pi$
$919$		−	16.8166i		−	0.554729i	0.960765	−	0.277365i	$-0.0894610\pi$
$920$	−32.4217	+	8.51763i	−1.06891	+	0.280818i
$921$	−24.3704			−0.803032
$922$	4.00755	+	46.6829i	0.131982	+	1.53742i
$923$	−12.3805	+	1.35964i	−0.407511	+	0.0447531i
$924$	0.465321	−	0.0804853i	0.0153079	−	0.00264777i
$925$	−3.45638	−	3.45638i	−0.113645	−	0.113645i
$926$	9.42736	−	11.1980i	0.309802	−	0.367988i
$927$	2.43741			0.0800551
$928$	1.32151	−	0.603165i	0.0433807	−	0.0197999i
$929$			31.0829i			1.01980i	0.860234	+	0.509899i	$0.170317\pi$
$929$			31.0829i			1.01980i	−0.860234	+	0.509899i	$0.829683\pi$
$930$	−19.8182	−	16.6846i	−0.649866	−	0.547110i
$931$	2.02032	+	2.02032i	0.0662133	+	0.0662133i
$932$	51.6850	−	8.93981i	1.69300	−	0.292833i
$933$	9.79817	+	9.79817i	0.320778	+	0.320778i
$934$	−3.49675	+	0.300183i	−0.114417	+	0.00982228i
$935$			69.6822i			2.27885i
$936$	9.31543	+	4.15004i	0.304484	+	0.135648i
$937$		−	61.0051i		−	1.99295i	−0.0838849	−	0.996475i	$-0.526733\pi$
$937$		−	61.0051i		−	1.99295i	0.0838849	−	0.996475i	$-0.473267\pi$
$938$	0.0708226	+	0.824994i	0.00231244	+	0.0269370i
$939$	−20.0385	−	20.0385i	−0.653931	−	0.653931i
$940$	13.3504	−	18.9347i	0.435442	−	0.617580i
$941$	−17.0952	−	17.0952i	−0.557287	−	0.557287i	0.371247	−	0.928534i	$-0.378930\pi$
$941$	−17.0952	−	17.0952i	−0.557287	−	0.557287i	−0.928534	+	0.371247i	$0.878930\pi$
$942$	−2.68830	+	3.19321i	−0.0875896	+	0.104040i
$943$		−	18.0677i		−	0.588365i
$944$	−1.85447	+	3.91015i	−0.0603578	+	0.127264i
$945$	0.0748024			0.00243332
$946$	−43.9150	−	36.9712i	−1.42780	−	1.20204i
$947$	0.934010	+	0.934010i	0.0303512	+	0.0303512i	0.722120	−	0.691768i	$-0.243168\pi$
$947$	0.934010	+	0.934010i	0.0303512	+	0.0303512i	−0.691768	+	0.722120i	$0.743168\pi$
$948$	−24.9588	−	17.5979i	−0.810625	−	0.571554i
$949$	32.7535	−	3.59701i	1.06322	−	0.116764i
$950$	−1.00200	+	0.0860176i	−0.0325091	+	0.00279078i
$951$	17.3922			0.563980
$952$	−0.400441	+	0.685815i	−0.0129784	+	0.0222274i
$953$			14.6734i			0.475318i	0.971349	+	0.237659i	$0.0763800\pi$
$953$			14.6734i			0.475318i	−0.971349	+	0.237659i	$0.923620\pi$
$954$	8.20322	−	0.704215i	0.265589	−	0.0227998i
$955$	−12.5244	+	12.5244i	−0.405279	+	0.405279i
$956$	40.8817	−	7.07118i	1.32221	−	0.228698i
$957$	1.03459	+	1.03459i	0.0334435	+	0.0334435i
$958$	−16.7038	+	19.8411i	−0.539676	+	0.641035i
$959$	−0.0213980			−0.000690979
$960$	−12.5757	+	7.09751i	−0.405880	+	0.229071i
$961$	−71.9927			−2.32235
$962$	−14.0381	+	2.77294i	−0.452608	+	0.0894032i
$963$	7.62597	−	7.62597i	0.245744	−	0.245744i
$964$	33.3346	−	5.76579i	1.07364	−	0.185704i
$965$	−0.185410	−	0.185410i	−0.00596855	−	0.00596855i
$966$	−0.0329128	−	0.383392i	−0.00105895	−	0.0123354i
$967$	57.6820			1.85493			0.927465	−	0.373911i	$-0.121983\pi$
$967$	57.6820			1.85493			0.927465	+	0.373911i	$0.121983\pi$
$968$	−52.4252	−	30.6105i	−1.68501	−	0.983859i
$969$	2.76618			0.0888626
$970$	3.77941	+	44.0253i	0.121349	+	1.41357i
$971$	10.1119	+	10.1119i	0.324507	+	0.324507i	0.850493	−	0.525986i	$-0.176304\pi$
$971$	10.1119	+	10.1119i	0.324507	+	0.324507i	−0.525986	+	0.850493i	$0.676304\pi$
$972$	1.63456	+	1.15249i	0.0524284	+	0.0369661i
$973$	0.549763	+	0.549763i	0.0176246	+	0.0176246i
$974$	28.0881	+	23.6469i	0.900002	+	0.757695i
$975$	4.89901	+	3.92946i	0.156894	+	0.125844i
$976$	−19.5570	+	41.2360i	−0.626005	+	1.31993i
$977$			36.6457i			1.17240i	0.810167	+	0.586199i	$0.199376\pi$
$977$			36.6457i			1.17240i	−0.810167	+	0.586199i	$0.800624\pi$
$978$	5.20046	+	4.37817i	0.166292	+	0.139998i
$979$	28.8541	−	28.8541i	0.922181	−	0.922181i
$980$	20.6480	+	14.5585i	0.659577	+	0.465053i
$981$	−2.78908	+	2.78908i	−0.0890485	+	0.0890485i
$982$	1.24560	+	14.5097i	0.0397486	+	0.463022i
$983$	21.3641			0.681408			0.340704	−	0.940171i	$-0.389335\pi$
$983$	21.3641			0.681408			0.340704	+	0.940171i	$0.389335\pi$
$984$	−1.97762	−	7.52765i	−0.0630442	−	0.239973i
$985$			28.6015i			0.911319i
$986$	−2.45157	+	0.210458i	−0.0780738	+	0.00670234i
$987$	0.188054	+	0.188054i	0.00598583	+	0.00598583i
$988$	−1.42369	+	2.57692i	−0.0452937	+	0.0819829i
$989$	−33.0767	+	33.0767i	−1.05178	+	1.05178i
$990$	−11.1265	−	9.36719i	−0.353623	−	0.297709i
$991$	17.0466			0.541503			0.270752	−	0.962649i	$-0.412728\pi$
$991$	17.0466			0.541503			0.270752	+	0.962649i	$0.412728\pi$
$992$	−20.0740	+	53.7848i	−0.637351	+	1.70767i
$993$			6.01541i			0.190893i
$994$	0.154872	+	0.130384i	0.00491224	+	0.00413552i
$995$	−4.56735	−	4.56735i	−0.144795	−	0.144795i
$996$	4.37772	+	25.3096i	0.138713	+	0.801964i
$997$	−7.05541	−	7.05541i	−0.223447	−	0.223447i	0.586501	−	0.809948i	$-0.300505\pi$
$997$	−7.05541	−	7.05541i	−0.223447	−	0.223447i	−0.809948	+	0.586501i	$0.800505\pi$
$998$	−0.0175676	−	0.204640i	−0.000556091	−	0.00647777i
$999$	−2.80630			−0.0887875

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	624.2.bj.a.181.13	✓	112
13.12	even	2	inner	624.2.bj.a.181.44	yes	112
16.13	even	4	inner	624.2.bj.a.493.44	yes	112
208.77	even	4	inner	624.2.bj.a.493.13	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
624.2.bj.a.181.13	✓	112	1.1	even	1	trivial
624.2.bj.a.181.44	yes	112	13.12	even	2	inner
624.2.bj.a.493.13	yes	112	208.77	even	4	inner
624.2.bj.a.493.44	yes	112	16.13	even	4	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:	\( N \)	\(=\)	\( 624 = 2^{4} \cdot 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	624.bj (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.08187 - 0.910804i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(0.340873 + 1.97074i) q^{4} +(-1.27636 + 1.27636i) q^{5} +(1.40903 - 0.120960i) q^{6} -0.0414407 q^{7} +(1.42618 - 2.44254i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.08187 - 0.910804i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(0.340873 + 1.97074i) q^{4} +(-1.27636 + 1.27636i) q^{5} +(1.40903 - 0.120960i) q^{6} -0.0414407 q^{7} +(1.42618 - 2.44254i) q^{8} -1.00000i q^{9} +(2.54336 - 0.218338i) q^{10} +(4.02885 - 4.02885i) q^{11} +(-1.63456 - 1.15249i) q^{12} +(-3.58400 + 0.393597i) q^{13} +(0.0448334 + 0.0377444i) q^{14} -1.80504i q^{15} +(-3.76761 + 1.34354i) q^{16} +6.77544 q^{17} +(-0.910804 + 1.08187i) q^{18} +(-0.288688 - 0.288688i) q^{19} +(-2.95044 - 2.08029i) q^{20} +(0.0293030 - 0.0293030i) q^{21} +(-8.02818 + 0.689189i) q^{22} +6.56592i q^{23} +(0.718680 + 2.73560i) q^{24} +1.74182i q^{25} +(4.23591 + 2.83850i) q^{26} +(0.707107 + 0.707107i) q^{27} +(-0.0141260 - 0.0816688i) q^{28} +(0.181581 - 0.181581i) q^{29} +(-1.64404 + 1.95282i) q^{30} +10.1485i q^{31} +(5.29976 + 1.97802i) q^{32} +5.69766i q^{33} +(-7.33012 - 6.17109i) q^{34} +(0.0528933 - 0.0528933i) q^{35} +(1.97074 - 0.340873i) q^{36} +(-1.98436 + 1.98436i) q^{37} +(0.0493839 + 0.575260i) q^{38} +(2.25596 - 2.81259i) q^{39} +(1.29725 + 4.93788i) q^{40} -2.75174 q^{41} +(-0.0583913 + 0.00501267i) q^{42} +(5.03764 + 5.03764i) q^{43} +(9.31314 + 6.56649i) q^{44} +(1.27636 + 1.27636i) q^{45} +(5.98026 - 7.10345i) q^{46} +6.41756i q^{47} +(1.71408 - 3.61413i) q^{48} -6.99828 q^{49} +(1.58645 - 1.88441i) q^{50} +(-4.79096 + 4.79096i) q^{51} +(-1.99737 - 6.92896i) q^{52} +(-4.11670 - 4.11670i) q^{53} +(-0.120960 - 1.40903i) q^{54} +10.2845i q^{55} +(-0.0591018 + 0.101221i) q^{56} +0.408266 q^{57} +(-0.361832 + 0.0310619i) q^{58} +(0.765023 - 0.765023i) q^{59} +(3.55727 - 0.615290i) q^{60} +(8.06784 - 8.06784i) q^{61} +(9.24332 - 10.9794i) q^{62} +0.0414407i q^{63} +(-3.93204 - 6.96700i) q^{64} +(4.07210 - 5.07685i) q^{65} +(5.18945 - 6.16411i) q^{66} +(9.99051 + 9.99051i) q^{67} +(2.30956 + 13.3526i) q^{68} +(-4.64280 - 4.64280i) q^{69} +(-0.105399 + 0.00904809i) q^{70} +3.45439 q^{71} +(-2.44254 - 1.42618i) q^{72} -9.13881 q^{73} +(3.95417 - 0.339450i) q^{74} +(-1.23165 - 1.23165i) q^{75} +(0.470522 - 0.667334i) q^{76} +(-0.166959 + 0.166959i) q^{77} +(-5.00236 + 0.988112i) q^{78} +15.2695 q^{79} +(3.09398 - 6.52367i) q^{80} -1.00000 q^{81} +(2.97702 + 2.50629i) q^{82} +(-9.08115 - 9.08115i) q^{83} +(0.0677372 + 0.0477600i) q^{84} +(-8.64789 + 8.64789i) q^{85} +(-0.861754 - 10.0384i) q^{86} +0.256795i q^{87} +(-4.09480 - 15.5865i) q^{88} +7.16186 q^{89} +(-0.218338 - 2.54336i) q^{90} +(0.148524 - 0.0163110i) q^{91} +(-12.9397 + 2.23814i) q^{92} +(-7.17610 - 7.17610i) q^{93} +(5.84514 - 6.94295i) q^{94} +0.736939 q^{95} +(-5.14617 + 2.34882i) q^{96} +17.3099i q^{97} +(7.57121 + 6.37406i) q^{98} +(-4.02885 - 4.02885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q+O(q^{10}) \) 112 * q	\( 112 q - 8 q^{12} + 32 q^{14} + 32 q^{22} - 20 q^{26} + 8 q^{30} + 40 q^{38} - 80 q^{40} + 40 q^{42} + 16 q^{43} + 112 q^{49} - 64 q^{52} + 48 q^{62} + 16 q^{65} + 64 q^{68} + 40 q^{74} - 16 q^{75} - 36 q^{78} + 80 q^{79} - 112 q^{81} - 72 q^{88} + 8 q^{90} - 8 q^{91} - 96 q^{92} - 40 q^{94}+O(q^{100}) \) 112 * q - 8 * q^12 + 32 * q^14 + 32 * q^22 - 20 * q^26 + 8 * q^30 + 40 * q^38 - 80 * q^40 + 40 * q^42 + 16 * q^43 + 112 * q^49 - 64 * q^52 + 48 * q^62 + 16 * q^65 + 64 * q^68 + 40 * q^74 - 16 * q^75 - 36 * q^78 + 80 * q^79 - 112 * q^81 - 72 * q^88 + 8 * q^90 - 8 * q^91 - 96 * q^92 - 40 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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