LMFDB - Embedded newform 666.2.k.a.175.18

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(175,666)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("666.175"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.k (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			175.18
Character	$\chi$	$=$	666.175
Dual form			666.2.k.a.529.37

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +(1.61755 + 0.619290i) q^{3} -1.00000 q^{4} +1.59205i q^{5} +(0.619290 - 1.61755i) q^{6} +(1.63885 - 2.83857i) q^{7} +1.00000i q^{8} +(2.23296 + 2.00347i) q^{9} +1.59205 q^{10} +(0.527937 + 0.914413i) q^{11} +(-1.61755 - 0.619290i) q^{12} +1.20379i q^{13} +(-2.83857 - 1.63885i) q^{14} +(-0.985941 + 2.57523i) q^{15} +1.00000 q^{16} +(5.78971 + 3.34269i) q^{17} +(2.00347 - 2.23296i) q^{18} +(-0.277937 + 0.160467i) q^{19} -1.59205i q^{20} +(4.40882 - 3.57661i) q^{21} +(0.914413 - 0.527937i) q^{22} +(-7.78426 - 4.49424i) q^{23} +(-0.619290 + 1.61755i) q^{24} +2.46538 q^{25} +1.20379 q^{26} +(2.37120 + 4.62357i) q^{27} +(-1.63885 + 2.83857i) q^{28} +(-0.801755 + 0.462894i) q^{29} +(2.57523 + 0.985941i) q^{30} +(-3.25896 - 1.88156i) q^{31} -1.00000i q^{32} +(0.287678 + 1.80606i) q^{33} +(3.34269 - 5.78971i) q^{34} +(4.51914 + 2.60913i) q^{35} +(-2.23296 - 2.00347i) q^{36} +(-0.229501 - 6.07843i) q^{37} +(0.160467 + 0.277937i) q^{38} +(-0.745493 + 1.94719i) q^{39} -1.59205 q^{40} +10.1259 q^{41} +(-3.57661 - 4.40882i) q^{42} +(3.50132 - 2.02149i) q^{43} +(-0.527937 - 0.914413i) q^{44} +(-3.18963 + 3.55498i) q^{45} +(-4.49424 + 7.78426i) q^{46} +(6.23837 + 10.8052i) q^{47} +(1.61755 + 0.619290i) q^{48} +(-1.87163 - 3.24177i) q^{49} -2.46538i q^{50} +(7.29507 + 8.99249i) q^{51} -1.20379i q^{52} +(2.12291 - 3.67699i) q^{53} +(4.62357 - 2.37120i) q^{54} +(-1.45579 + 0.840502i) q^{55} +(2.83857 + 1.63885i) q^{56} +(-0.548953 + 0.0874402i) q^{57} +(0.462894 + 0.801755i) q^{58} +(-0.483876 + 0.279366i) q^{59} +(0.985941 - 2.57523i) q^{60} +(-4.69030 - 2.70794i) q^{61} +(-1.88156 + 3.25896i) q^{62} +(9.34646 - 3.05502i) q^{63} -1.00000 q^{64} -1.91649 q^{65} +(1.80606 - 0.287678i) q^{66} -16.1177 q^{67} +(-5.78971 - 3.34269i) q^{68} +(-9.80821 - 12.0904i) q^{69} +(2.60913 - 4.51914i) q^{70} +(-0.809770 - 1.40256i) q^{71} +(-2.00347 + 2.23296i) q^{72} -5.18397 q^{73} +(-6.07843 + 0.229501i) q^{74} +(3.98788 + 1.52678i) q^{75} +(0.277937 - 0.160467i) q^{76} +3.46083 q^{77} +(1.94719 + 0.745493i) q^{78} +(-6.99762 - 4.04008i) q^{79} +1.59205i q^{80} +(0.972209 + 8.94734i) q^{81} -10.1259i q^{82} -12.4651 q^{83} +(-4.40882 + 3.57661i) q^{84} +(-5.32173 + 9.21751i) q^{85} +(-2.02149 - 3.50132i) q^{86} +(-1.58355 + 0.252236i) q^{87} +(-0.914413 + 0.527937i) q^{88} +(-3.27507 - 1.89086i) q^{89} +(3.55498 + 3.18963i) q^{90} +(3.41702 + 1.97282i) q^{91} +(7.78426 + 4.49424i) q^{92} +(-4.10631 - 5.06177i) q^{93} +(10.8052 - 6.23837i) q^{94} +(-0.255471 - 0.442489i) q^{95} +(0.619290 - 1.61755i) q^{96} +(10.1206 - 5.84311i) q^{97} +(-3.24177 + 1.87163i) q^{98} +(-0.653139 + 3.09955i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) $ 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	1.61755	+	0.619290i	0.933895	+	0.357548i
$3$	1.61755	+	0.619290i	0.933895	+	0.357548i
$4$	−1.00000			−0.500000
$5$			1.59205i			0.711986i	0.934489	+	0.355993i	$0.115857\pi$
$5$			1.59205i			0.711986i	−0.934489	+	0.355993i	$0.884143\pi$
$6$	0.619290	−	1.61755i	0.252824	−	0.660363i
$7$	1.63885	−	2.83857i	0.619426	−	1.07288i	−0.370165	−	0.928966i	$-0.620699\pi$
$7$	1.63885	−	2.83857i	0.619426	−	1.07288i	0.989591	−	0.143911i	$-0.0459678\pi$
$8$			1.00000i			0.353553i
$9$	2.23296	+	2.00347i	0.744320	+	0.667824i
$10$	1.59205			0.503450
$11$	0.527937	+	0.914413i	0.159179	+	0.275706i	0.934573	−	0.355772i	$-0.115782\pi$
$11$	0.527937	+	0.914413i	0.159179	+	0.275706i	−0.775394	+	0.631478i	$0.782449\pi$
$12$	−1.61755	−	0.619290i	−0.466947	−	0.178774i
$13$			1.20379i			0.333870i	0.985968	+	0.166935i	$0.0533870\pi$
$13$			1.20379i			0.333870i	−0.985968	+	0.166935i	$0.946613\pi$
$14$	−2.83857	−	1.63885i	−0.758638	−	0.438000i
$15$	−0.985941	+	2.57523i	−0.254569	+	0.664920i
$16$	1.00000			0.250000
$17$	5.78971	+	3.34269i	1.40421	+	0.810721i	0.994821	−	0.101639i	$-0.0324085\pi$
$17$	5.78971	+	3.34269i	1.40421	+	0.810721i	0.409389	+	0.912360i	$0.365742\pi$
$18$	2.00347	−	2.23296i	0.472223	−	0.526313i
$19$	−0.277937	+	0.160467i	−0.0637631	+	0.0368136i	−0.531543	−	0.847032i	$-0.678387\pi$
$19$	−0.277937	+	0.160467i	−0.0637631	+	0.0368136i	0.467780	+	0.883845i	$0.345054\pi$
$20$		−	1.59205i		−	0.355993i
$21$	4.40882	−	3.57661i	0.962083	−	0.780480i
$22$	0.914413	−	0.527937i	0.194954	−	0.112556i
$23$	−7.78426	−	4.49424i	−1.62313	−	0.937114i	−0.986076	−	0.166295i	$-0.946820\pi$
$23$	−7.78426	−	4.49424i	−1.62313	−	0.937114i	−0.637053	−	0.770820i	$-0.719847\pi$
$24$	−0.619290	+	1.61755i	−0.126412	+	0.330182i
$25$	2.46538			0.493075
$26$	1.20379			0.236082
$27$	2.37120	+	4.62357i	0.456338	+	0.889807i
$28$	−1.63885	+	2.83857i	−0.309713	+	0.536438i
$29$	−0.801755	+	0.462894i	−0.148882	+	0.0859572i	−0.572591	−	0.819841i	$-0.694061\pi$
$29$	−0.801755	+	0.462894i	−0.148882	+	0.0859572i	0.423708	+	0.905799i	$0.360728\pi$
$30$	2.57523	+	0.985941i	0.470170	+	0.180007i
$31$	−3.25896	−	1.88156i	−0.585326	−	0.337938i	0.177921	−	0.984045i	$-0.443063\pi$
$31$	−3.25896	−	1.88156i	−0.585326	−	0.337938i	−0.763247	+	0.646107i	$0.776396\pi$
$32$		−	1.00000i		−	0.176777i
$33$	0.287678	+	1.80606i	0.0500784	+	0.314394i
$34$	3.34269	−	5.78971i	0.573267	−	0.992927i
$35$	4.51914	+	2.60913i	0.763874	+	0.441023i
$36$	−2.23296	−	2.00347i	−0.372160	−	0.333912i
$37$	−0.229501	−	6.07843i	−0.0377298	−	0.999288i
$37$	−0.229501	−	6.07843i	−0.0377298	−	0.999288i
$38$	0.160467	+	0.277937i	0.0260312	+	0.0450873i
$39$	−0.745493	+	1.94719i	−0.119374	+	0.311800i
$40$	−1.59205			−0.251725
$41$	10.1259			1.58140			0.790701	−	0.612203i	$-0.209716\pi$
$41$	10.1259			1.58140			0.790701	+	0.612203i	$0.209716\pi$
$42$	−3.57661	−	4.40882i	−0.551883	−	0.680295i
$43$	3.50132	−	2.02149i	0.533946	−	0.308274i	−0.208676	−	0.977985i	$-0.566915\pi$
$43$	3.50132	−	2.02149i	0.533946	−	0.308274i	0.742622	+	0.669711i	$0.233582\pi$
$44$	−0.527937	−	0.914413i	−0.0795894	−	0.137853i
$45$	−3.18963	+	3.55498i	−0.475481	+	0.529945i
$46$	−4.49424	+	7.78426i	−0.662640	+	1.14773i
$47$	6.23837	+	10.8052i	0.909959	+	1.57610i	0.814119	+	0.580699i	$0.197221\pi$
$47$	6.23837	+	10.8052i	0.909959	+	1.57610i	0.0958405	+	0.995397i	$0.469446\pi$
$48$	1.61755	+	0.619290i	0.233474	+	0.0893869i
$49$	−1.87163	−	3.24177i	−0.267376	−	0.463110i
$50$		−	2.46538i		−	0.348657i
$51$	7.29507	+	8.99249i	1.02151	+	1.25920i
$52$		−	1.20379i		−	0.166935i
$53$	2.12291	−	3.67699i	0.291604	−	0.505074i	−0.682585	−	0.730806i	$-0.739144\pi$
$53$	2.12291	−	3.67699i	0.291604	−	0.505074i	0.974189	+	0.225733i	$0.0724776\pi$
$54$	4.62357	−	2.37120i	0.629188	−	0.322679i
$55$	−1.45579	+	0.840502i	−0.196299	+	0.113333i
$56$	2.83857	+	1.63885i	0.379319	+	0.219000i
$57$	−0.548953	+	0.0874402i	−0.0727107	+	0.0115817i
$58$	0.462894	+	0.801755i	0.0607809	+	0.105276i
$59$	−0.483876	+	0.279366i	−0.0629953	+	0.0363704i	−0.531167	−	0.847267i	$-0.678246\pi$
$59$	−0.483876	+	0.279366i	−0.0629953	+	0.0363704i	0.468172	+	0.883638i	$0.344913\pi$
$60$	0.985941	−	2.57523i	0.127284	−	0.332460i
$61$	−4.69030	−	2.70794i	−0.600531	−	0.346717i	0.168719	−	0.985664i	$-0.446037\pi$
$61$	−4.69030	−	2.70794i	−0.600531	−	0.346717i	−0.769250	+	0.638947i	$0.779370\pi$
$62$	−1.88156	+	3.25896i	−0.238958	+	0.413888i
$63$	9.34646	−	3.05502i	1.17754	−	0.384896i
$64$	−1.00000			−0.125000
$65$	−1.91649			−0.237711
$66$	1.80606	−	0.287678i	0.222310	−	0.0354108i
$67$	−16.1177			−1.96909			−0.984543	−	0.175145i	$-0.943960\pi$
$67$	−16.1177			−1.96909			−0.984543	+	0.175145i	$0.943960\pi$
$68$	−5.78971	−	3.34269i	−0.702105	−	0.405361i
$69$	−9.80821	−	12.0904i	−1.18077	−	1.45551i
$70$	2.60913	−	4.51914i	0.311850	−	0.540140i
$71$	−0.809770	−	1.40256i	−0.0961020	−	0.166453i	0.813966	−	0.580912i	$-0.197304\pi$
$71$	−0.809770	−	1.40256i	−0.0961020	−	0.166453i	−0.910068	+	0.414459i	$0.863971\pi$
$72$	−2.00347	+	2.23296i	−0.236111	+	0.263157i
$73$	−5.18397			−0.606738			−0.303369	−	0.952873i	$-0.598111\pi$
$73$	−5.18397			−0.606738			−0.303369	+	0.952873i	$0.598111\pi$
$74$	−6.07843	+	0.229501i	−0.706603	+	0.0266790i
$75$	3.98788	+	1.52678i	0.460481	+	0.176298i
$76$	0.277937	−	0.160467i	0.0318816	−	0.0184068i
$77$	3.46083			0.394398
$78$	1.94719	+	0.745493i	0.220476	+	0.0844104i
$79$	−6.99762	−	4.04008i	−0.787293	−	0.454544i	0.0517154	−	0.998662i	$-0.483531\pi$
$79$	−6.99762	−	4.04008i	−0.787293	−	0.454544i	−0.839009	+	0.544118i	$0.816864\pi$
$80$			1.59205i			0.177997i
$81$	0.972209	+	8.94734i	0.108023	+	0.994148i
$82$		−	10.1259i		−	1.11822i
$83$	−12.4651			−1.36822			−0.684112	−	0.729377i	$-0.739810\pi$
$83$	−12.4651			−1.36822			−0.684112	+	0.729377i	$0.739810\pi$
$84$	−4.40882	+	3.57661i	−0.481041	+	0.390240i
$85$	−5.32173	+	9.21751i	−0.577223	+	0.999779i
$86$	−2.02149	−	3.50132i	−0.217983	−	0.377557i
$87$	−1.58355	+	0.252236i	−0.169774	+	0.0270425i
$88$	−0.914413	+	0.527937i	−0.0974768	+	0.0562782i
$89$	−3.27507	−	1.89086i	−0.347157	−	0.200431i	0.316275	−	0.948667i	$-0.397568\pi$
$89$	−3.27507	−	1.89086i	−0.347157	−	0.200431i	−0.663432	+	0.748236i	$0.730901\pi$
$90$	3.55498	+	3.18963i	0.374728	+	0.336216i
$91$	3.41702	+	1.97282i	0.358201	+	0.206808i
$92$	7.78426	+	4.49424i	0.811565	+	0.468557i
$93$	−4.10631	−	5.06177i	−0.425804	−	0.524881i
$94$	10.8052	−	6.23837i	1.11447	−	0.643438i
$95$	−0.255471	−	0.442489i	−0.0262108	−	0.0453985i
$96$	0.619290	−	1.61755i	0.0632061	−	0.165091i
$97$	10.1206	−	5.84311i	1.02759	−	0.593278i	0.111295	−	0.993787i	$-0.464500\pi$
$97$	10.1206	−	5.84311i	1.02759	−	0.593278i	0.916292	+	0.400510i	$0.131167\pi$
$98$	−3.24177	+	1.87163i	−0.327468	+	0.189064i
$99$	−0.653139	+	3.09955i	−0.0656430	+	0.311517i
$100$	−2.46538			−0.246538
$101$	7.27190	+	12.5953i	0.723581	+	1.25328i	0.959555	+	0.281520i	$0.0908385\pi$
$101$	7.27190	+	12.5953i	0.723581	+	1.25328i	−0.235975	+	0.971759i	$0.575828\pi$
$102$	8.99249	−	7.29507i	0.890389	−	0.722319i
$103$	−13.1563	−	7.59578i	−1.29633	−	0.748434i	−0.316559	−	0.948573i	$-0.602527\pi$
$103$	−13.1563	−	7.59578i	−1.29633	−	0.748434i	−0.979768	+	0.200138i	$0.935861\pi$
$104$	−1.20379			−0.118041
$105$	5.69414	+	7.01906i	0.555691	+	0.684990i
$106$	−3.67699	−	2.12291i	−0.357141	−	0.206195i
$107$	−3.29759	−	5.71160i	−0.318790	−	0.552161i	0.661445	−	0.749993i	$-0.269943\pi$
$107$	−3.29759	−	5.71160i	−0.318790	−	0.552161i	−0.980236	+	0.197832i	$0.936610\pi$
$108$	−2.37120	−	4.62357i	−0.228169	−	0.444903i
$109$	−12.3722	−	7.14312i	−1.18505	−	0.684187i	−0.227870	−	0.973692i	$-0.573176\pi$
$109$	−12.3722	−	7.14312i	−1.18505	−	0.684187i	−0.957177	+	0.289505i	$0.906509\pi$
$110$	0.840502	+	1.45579i	0.0801387	+	0.138804i
$111$	3.39308	−	9.97432i	0.322057	−	0.946720i
$112$	1.63885	−	2.83857i	0.154856	−	0.268219i
$113$	−9.20127	+	5.31236i	−0.865583	+	0.499745i	−0.865878	−	0.500255i	$-0.833239\pi$
$113$	−9.20127	+	5.31236i	−0.865583	+	0.499745i	0.000294984		1.00000i	$0.499906\pi$
$114$	0.0874402	+	0.548953i	0.00818953	+	0.0514142i
$115$	7.15506	−	12.3929i	0.667213	−	1.15565i
$116$	0.801755	−	0.462894i	0.0744411	−	0.0429786i
$117$	−2.41175	+	2.68800i	−0.222966	+	0.248506i
$118$	0.279366	+	0.483876i	0.0257177	+	0.0445444i
$119$	18.9769	−	10.9563i	1.73961	−	1.00436i
$120$	−2.57523	−	0.985941i	−0.235085	−	0.0900037i
$121$	4.94257	−	8.56078i	0.449324	−	0.778252i
$122$	−2.70794	+	4.69030i	−0.245166	+	0.424640i
$123$	16.3792	+	6.27088i	1.47686	+	0.565426i
$124$	3.25896	+	1.88156i	0.292663	+	0.168969i
$125$			11.8853i			1.06305i
$126$	−3.05502	−	9.34646i	−0.272163	−	0.832649i
$127$	−0.859482	+	1.48867i	−0.0762667	+	0.132098i	−0.901636	−	0.432495i	$-0.857633\pi$
$127$	−0.859482	+	1.48867i	−0.0762667	+	0.132098i	0.825370	+	0.564593i	$0.190967\pi$
$128$			1.00000i			0.0883883i
$129$	6.91546	−	1.10153i	0.608872	−	0.0969843i
$130$			1.91649i			0.168087i
$131$	−15.9554	+	9.21188i	−1.39403	+	0.804846i	−0.993759	−	0.111549i	$-0.964419\pi$
$131$	−15.9554	+	9.21188i	−1.39403	+	0.804846i	−0.400275	+	0.916395i	$0.631085\pi$
$132$	−0.287678	−	1.80606i	−0.0250392	−	0.157197i
$133$			1.05192i			0.0912133i
$134$			16.1177i			1.39235i
$135$	−7.36096	+	3.77507i	−0.633530	+	0.324906i
$136$	−3.34269	+	5.78971i	−0.286633	+	0.496463i
$137$	−10.3412	−	17.9115i	−0.883511	−	1.53029i	−0.847410	−	0.530939i	$-0.821839\pi$
$137$	−10.3412	−	17.9115i	−0.883511	−	1.53029i	−0.0361012	−	0.999348i	$-0.511494\pi$
$138$	−12.0904	+	9.80821i	−1.02920	+	0.834930i
$139$	2.74214	+	4.74953i	0.232586	+	0.402850i	0.958568	−	0.284863i	$-0.0919481\pi$
$139$	2.74214	+	4.74953i	0.232586	+	0.402850i	−0.725983	+	0.687713i	$0.758615\pi$
$140$	−4.51914	−	2.60913i	−0.381937	−	0.220511i
$141$	3.39935	+	21.3413i	0.286277	+	1.79726i
$142$	−1.40256	+	0.809770i	−0.117700	+	0.0679544i
$143$	−1.10076	+	0.635522i	−0.0920499	+	0.0531451i
$144$	2.23296	+	2.00347i	0.186080	+	0.166956i
$145$	−0.736950	−	1.27643i	−0.0612004	−	0.106002i
$146$			5.18397i			0.429028i
$147$	−1.01987	−	6.40282i	−0.0841178	−	0.528095i
$148$	0.229501	+	6.07843i	0.0188649	+	0.499644i
$149$	−2.33940	+	4.05196i	−0.191651	+	0.331950i	−0.945798	−	0.324757i	$-0.894718\pi$
$149$	−2.33940	+	4.05196i	−0.191651	+	0.331950i	0.754146	+	0.656706i	$0.228051\pi$
$150$	1.52678	−	3.98788i	0.124661	−	0.325609i
$151$	−2.41779	+	4.18773i	−0.196757	+	0.340792i	−0.947475	−	0.319830i	$-0.896374\pi$
$151$	−2.41779	+	4.18773i	−0.196757	+	0.340792i	0.750718	+	0.660622i	$0.229708\pi$
$152$	−0.160467	−	0.277937i	−0.0130156	−	0.0225437i
$153$	6.23120	+	19.0636i	0.503763	+	1.54120i
$154$		−	3.46083i		−	0.278881i
$155$	2.99554	−	5.18842i	0.240607	−	0.416744i
$156$	0.745493	−	1.94719i	0.0596872	−	0.155900i
$157$	3.75659	+	6.50661i	0.299809	+	0.519284i	0.976092	−	0.217358i	$-0.0697438\pi$
$157$	3.75659	+	6.50661i	0.299809	+	0.519284i	−0.676283	+	0.736642i	$0.736410\pi$
$158$	−4.04008	+	6.99762i	−0.321411	+	0.556700i
$159$	5.71105	−	4.63303i	0.452916	−	0.367423i
$160$	1.59205			0.125863
$161$	−25.5144	+	14.7307i	−2.01082	+	1.16095i
$162$	8.94734	−	0.972209i	0.702969	−	0.0763840i
$163$	0.912588	+	0.526883i	0.0714794	+	0.0412686i	0.535314	−	0.844653i	$-0.320193\pi$
$163$	0.912588	+	0.526883i	0.0714794	+	0.0412686i	−0.463834	+	0.885922i	$0.653527\pi$
$164$	−10.1259			−0.790701
$165$	−2.87533	+	0.457999i	−0.223845	+	0.0356551i
$166$			12.4651i			0.967481i
$167$			8.40640i			0.650507i	0.945627	+	0.325253i	$0.105450\pi$
$167$			8.40640i			0.650507i	−0.945627	+	0.325253i	$0.894550\pi$
$168$	3.57661	+	4.40882i	0.275941	+	0.340148i
$169$	11.5509			0.888531
$170$	9.21751	+	5.32173i	0.706950	+	0.408158i
$171$	−0.942113	−	0.198522i	−0.0720451	−	0.0151814i
$172$	−3.50132	+	2.02149i	−0.266973	+	0.154137i
$173$	−20.3161			−1.54461			−0.772303	−	0.635255i	$-0.780895\pi$
$173$	−20.3161			−1.54461			−0.772303	+	0.635255i	$0.780895\pi$
$174$	0.252236	+	1.58355i	0.0191219	+	0.120048i
$175$	4.04037	−	6.99813i	0.305424	−	0.529009i
$176$	0.527937	+	0.914413i	0.0397947	+	0.0689265i
$177$	−0.955705	+	0.152230i	−0.0718352	+	0.0114423i
$178$	−1.89086	+	3.27507i	−0.141726	+	0.245477i
$179$		−	17.9888i		−	1.34455i	−0.740302	−	0.672274i	$-0.765318\pi$
$179$		−	17.9888i		−	1.34455i	0.740302	−	0.672274i	$-0.234682\pi$
$180$	3.18963	−	3.55498i	0.237741	−	0.264973i
$181$	4.04330	+	7.00320i	0.300536	+	0.520544i	0.976258	−	0.216613i	$-0.0695010\pi$
$181$	4.04330	+	7.00320i	0.300536	+	0.520544i	−0.675721	+	0.737157i	$0.736168\pi$
$182$	1.97282	−	3.41702i	0.146235	−	0.253287i
$183$	−5.90980	−	7.28490i	−0.436865	−	0.538515i
$184$	4.49424	−	7.78426i	0.331320	−	0.573863i
$185$	9.67717	−	0.365378i	0.711479	−	0.0268631i
$186$	−5.06177	+	4.10631i	−0.371147	+	0.301089i
$187$			7.05891i			0.516199i
$188$	−6.23837	−	10.8052i	−0.454980	−	0.788048i
$189$	17.0103	+	0.846518i	1.23732	+	0.0615751i
$190$	−0.442489	+	0.255471i	−0.0321016	+	0.0185338i
$191$	9.17993	−	5.30004i	0.664237	−	0.383497i	−0.129653	−	0.991559i	$-0.541386\pi$
$191$	9.17993	−	5.30004i	0.664237	−	0.383497i	0.793889	+	0.608062i	$0.208053\pi$
$192$	−1.61755	−	0.619290i	−0.116737	−	0.0446934i
$193$	−8.08156	−	4.66589i	−0.581724	−	0.335858i	0.180094	−	0.983649i	$-0.442360\pi$
$193$	−8.08156	−	4.66589i	−0.581724	−	0.335858i	−0.761818	+	0.647791i	$0.775693\pi$
$194$	−5.84311	−	10.1206i	−0.419511	−	0.726614i
$195$	−3.10002	−	1.18686i	−0.221997	−	0.0849929i
$196$	1.87163	+	3.24177i	0.133688	+	0.231555i
$197$	4.15550	−	7.19753i	0.296067	−	0.512803i	−0.679166	−	0.733985i	$-0.737658\pi$
$197$	4.15550	−	7.19753i	0.296067	−	0.512803i	0.975233	+	0.221182i	$0.0709915\pi$
$198$	3.09955	+	0.653139i	0.220276	+	0.0464166i
$199$			5.35120i			0.379336i	0.981848	+	0.189668i	$0.0607412\pi$
$199$			5.35120i			0.379336i	−0.981848	+	0.189668i	$0.939259\pi$
$200$			2.46538i			0.174328i
$201$	−26.0712	−	9.98151i	−1.83892	−	0.704041i
$202$	12.5953	−	7.27190i	0.886202	−	0.511649i
$203$			3.03445i			0.212976i
$204$	−7.29507	−	8.99249i	−0.510757	−	0.629600i
$205$			16.1210i			1.12594i
$206$	−7.59578	+	13.1563i	−0.529223	+	0.916641i
$207$	−8.37784	−	25.6310i	−0.582300	−	1.78148i
$208$			1.20379i			0.0834675i
$209$	−0.293466	−	0.169433i	−0.0202995	−	0.0117199i
$210$	7.01906	−	5.69414i	0.484361	−	0.392933i
$211$	0.945591	−	1.63781i	0.0650972	−	0.112752i	−0.831640	−	0.555315i	$-0.812598\pi$
$211$	0.945591	−	1.63781i	0.0650972	−	0.112752i	0.896737	+	0.442564i	$0.145931\pi$
$212$	−2.12291	+	3.67699i	−0.145802	+	0.252537i
$213$	−0.441252	−	2.77020i	−0.0302341	−	0.189811i
$214$	−5.71160	+	3.29759i	−0.390437	+	0.225419i
$215$	3.21831	+	5.57427i	0.219487	+	0.380162i
$216$	−4.62357	+	2.37120i	−0.314594	+	0.161340i
$217$	−10.6819	+	6.16718i	−0.725132	+	0.418655i
$218$	−7.14312	+	12.3722i	−0.483793	+	0.837954i
$219$	−8.38535	−	3.21038i	−0.566629	−	0.216938i
$220$	1.45579	−	0.840502i	0.0981494	−	0.0566666i
$221$	−4.02388	+	6.96957i	−0.270676	+	0.468824i
$222$	−9.97432	−	3.39308i	−0.669432	−	0.227729i
$223$	−1.90080	−	3.29228i	−0.127287	−	0.220467i	0.795338	−	0.606167i	$-0.207294\pi$
$223$	−1.90080	−	3.29228i	−0.127287	−	0.220467i	−0.922625	+	0.385699i	$0.873960\pi$
$224$	−2.83857	−	1.63885i	−0.189660	−	0.109500i
$225$	5.50508	+	4.93931i	0.367006	+	0.329287i
$226$	5.31236	+	9.20127i	0.353373	+	0.612060i
$227$	8.54001	+	4.93058i	0.566821	+	0.327254i	0.755878	−	0.654712i	$-0.227210\pi$
$227$	8.54001	+	4.93058i	0.566821	+	0.327254i	−0.189058	+	0.981966i	$0.560543\pi$
$228$	0.548953	−	0.0874402i	0.0363553	−	0.00579087i
$229$	−6.96651			−0.460360			−0.230180	−	0.973148i	$-0.573931\pi$
$229$	−6.96651			−0.460360			−0.230180	+	0.973148i	$0.573931\pi$
$230$	−12.3929	−	7.15506i	−0.817165	−	0.471791i
$231$	5.59807	+	2.14326i	0.368326	+	0.141016i
$232$	−0.462894	−	0.801755i	−0.0303905	−	0.0526378i
$233$	26.0976			1.70971			0.854857	−	0.518864i	$-0.173645\pi$
$233$	26.0976			1.70971			0.854857	+	0.518864i	$0.173645\pi$
$234$	2.68800	+	2.41175i	0.175720	+	0.157661i
$235$	−17.2024	+	9.93179i	−1.12216	+	0.647878i
$236$	0.483876	−	0.279366i	0.0314977	−	0.0181852i
$237$	−8.81704	−	10.8686i	−0.572728	−	0.705991i
$238$	−10.9563	−	18.9769i	−0.710192	−	1.23009i
$239$	11.6637	−	6.73406i	0.754464	−	0.435590i	−0.0728404	−	0.997344i	$-0.523206\pi$
$239$	11.6637	−	6.73406i	0.754464	−	0.435590i	0.827305	+	0.561753i	$0.189873\pi$
$240$	−0.985941	+	2.57523i	−0.0636422	+	0.166230i
$241$	7.67592	+	4.43170i	0.494450	+	0.285471i	0.726419	−	0.687253i	$-0.241183\pi$
$241$	7.67592	+	4.43170i	0.494450	+	0.285471i	−0.231969	+	0.972723i	$0.574517\pi$
$242$	−8.56078	−	4.94257i	−0.550307	−	0.317720i
$243$	−3.96840	+	15.0749i	−0.254573	+	0.967054i
$244$	4.69030	+	2.70794i	0.300266	+	0.173358i
$245$	5.16105	−	2.97974i	0.329728	−	0.190368i
$246$	6.27088	−	16.3792i	0.399817	−	1.04430i
$247$	−0.193168	−	0.334576i	−0.0122910	−	0.0212886i
$248$	1.88156	−	3.25896i	0.119479	−	0.206944i
$249$	−20.1630	−	7.71953i	−1.27778	−	0.489205i
$250$	11.8853			0.751689
$251$			7.70689i			0.486454i	0.969969	+	0.243227i	$0.0782061\pi$
$251$			7.70689i			0.486454i	−0.969969	+	0.243227i	$0.921794\pi$
$252$	−9.34646	+	3.05502i	−0.588772	+	0.192448i
$253$		−	9.49070i		−	0.596675i
$254$	1.48867	+	0.859482i	0.0934072	+	0.0539287i
$255$	−14.3165	+	11.6141i	−0.896534	+	0.727304i
$256$	1.00000			0.0625000
$257$	3.46581	−	2.00099i	0.216191	−	0.124818i	−0.387994	−	0.921662i	$-0.626832\pi$
$257$	3.46581	−	2.00099i	0.216191	−	0.124818i	0.604186	+	0.796844i	$0.293499\pi$
$258$	−1.10153	−	6.91546i	−0.0685783	−	0.430538i
$259$	−17.6301	−	9.31016i	−1.09548	−	0.578505i
$260$	1.91649			0.118855
$261$	−2.71768	−	0.572671i	−0.168220	−	0.0354474i
$262$	9.21188	+	15.9554i	0.569112	+	0.985731i
$263$	−1.63109	+	2.82514i	−0.100578	+	0.174206i	−0.911923	−	0.410362i	$-0.865402\pi$
$263$	−1.63109	+	2.82514i	−0.100578	+	0.174206i	0.811345	+	0.584567i	$0.198736\pi$
$264$	−1.80606	+	0.287678i	−0.111155	+	0.0177054i
$265$	5.85396	+	3.37978i	0.359606	+	0.207618i
$266$	1.05192			0.0644975
$267$	−4.12661	−	5.08679i	−0.252544	−	0.311307i
$268$	16.1177			0.984543
$269$	0.959973			0.0585306			0.0292653	−	0.999572i	$-0.490683\pi$
$269$	0.959973			0.0585306			0.0292653	+	0.999572i	$0.490683\pi$
$270$	3.77507	+	7.36096i	0.229743	+	0.447974i
$271$	13.4485	−	23.2935i	0.816937	−	1.41498i	−0.0909914	−	0.995852i	$-0.529004\pi$
$271$	13.4485	−	23.2935i	0.816937	−	1.41498i	0.907929	−	0.419125i	$-0.137663\pi$
$272$	5.78971	+	3.34269i	0.351053	+	0.202680i
$273$	4.30547	+	5.30727i	0.260579	+	0.321211i
$274$	−17.9115	+	10.3412i	−1.08208	+	0.624737i
$275$	1.30156	+	2.25437i	0.0784872	+	0.135944i
$276$	9.80821	+	12.0904i	0.590385	+	0.727756i
$277$	20.4988	+	11.8350i	1.23166	+	0.711097i	0.967375	−	0.253349i	$-0.0815322\pi$
$277$	20.4988	+	11.8350i	1.23166	+	0.711097i	0.264281	+	0.964446i	$0.414865\pi$
$278$	4.74953	−	2.74214i	0.284858	−	0.164463i
$279$	−3.50747	−	10.7307i	−0.209987	−	0.642429i
$280$	−2.60913	+	4.51914i	−0.155925	+	0.270070i
$281$			9.02020i			0.538100i	0.963126	+	0.269050i	$0.0867097\pi$
$281$			9.02020i			0.538100i	−0.963126	+	0.269050i	$0.913290\pi$
$282$	21.3413	−	3.39935i	1.27086	−	0.202429i
$283$		−	9.63246i		−	0.572590i	−0.958141	−	0.286295i	$-0.907576\pi$
$283$		−	9.63246i		−	0.572590i	0.958141	−	0.286295i	$-0.0924238\pi$
$284$	0.809770	+	1.40256i	0.0480510	+	0.0832267i
$285$	−0.139209	−	0.873961i	−0.00824604	−	0.0517690i
$286$	0.635522	+	1.10076i	0.0375792	+	0.0650891i
$287$	16.5948	−	28.7431i	0.979561	−	1.69665i
$288$	2.00347	−	2.23296i	0.118056	−	0.131578i
$289$	13.8471	+	23.9840i	0.814538	+	1.41082i
$290$	−1.27643	+	0.736950i	−0.0749548	+	0.0432752i
$291$	19.9891	−	3.18397i	1.17178	−	0.186648i
$292$	5.18397			0.303369
$293$	−16.0288			−0.936413			−0.468207	−	0.883619i	$-0.655100\pi$
$293$	−16.0288			−0.936413			−0.468207	+	0.883619i	$0.655100\pi$
$294$	−6.40282	+	1.01987i	−0.373420	+	0.0594803i
$295$	−0.444765	−	0.770355i	−0.0258952	−	0.0448518i
$296$	6.07843	−	0.229501i	0.353302	−	0.0133395i
$297$	−2.97601	+	4.60921i	−0.172686	+	0.267453i
$298$	4.05196	+	2.33940i	0.234724	+	0.135518i
$299$	5.41010	−	9.37057i	0.312874	−	0.541914i
$300$	−3.98788	−	1.52678i	−0.230240	−	0.0881489i
$301$		−	13.2516i		−	0.763811i
$302$	4.18773	+	2.41779i	0.240977	+	0.139128i
$303$	3.96254	+	24.8770i	0.227642	+	1.42915i
$304$	−0.277937	+	0.160467i	−0.0159408	+	0.00920341i
$305$	4.31118	−	7.46719i	0.246858	−	0.427570i
$306$	19.0636	−	6.23120i	1.08979	−	0.356214i
$307$	−11.9587			−0.682518			−0.341259	−	0.939969i	$-0.610853\pi$
$307$	−11.9587			−0.682518			−0.341259	+	0.939969i	$0.610853\pi$
$308$	−3.46083			−0.197199
$309$	−16.5770	−	20.4341i	−0.943032	−	1.16246i
$310$	−5.18842	−	2.99554i	−0.294683	−	0.170135i
$311$	6.33578	−	3.65796i	0.359269	−	0.207424i	−0.309491	−	0.950902i	$-0.600159\pi$
$311$	6.33578	−	3.65796i	0.359269	−	0.207424i	0.668760	+	0.743478i	$0.266825\pi$
$312$	−1.94719	−	0.745493i	−0.110238	−	0.0422052i
$313$			13.3202i			0.752899i	0.926437	+	0.376450i	$0.122855\pi$
$313$			13.3202i			0.752899i	−0.926437	+	0.376450i	$0.877145\pi$
$314$	6.50661	−	3.75659i	0.367189	−	0.211997i
$315$	4.86374	+	14.8800i	0.274041	+	0.838395i
$316$	6.99762	+	4.04008i	0.393647	+	0.227272i
$317$	−12.8746			−0.723108			−0.361554	−	0.932351i	$-0.617754\pi$
$317$	−12.8746			−0.723108			−0.361554	+	0.932351i	$0.617754\pi$
$318$	−4.63303	−	5.71105i	−0.259808	−	0.320260i
$319$	−0.846552	−	0.488757i	−0.0473978	−	0.0273651i
$320$		−	1.59205i		−	0.0889983i
$321$	−1.79690	−	11.2810i	−0.100293	−	0.629643i
$322$	14.7307	+	25.5144i	0.820912	+	1.42186i
$323$	−2.14556			−0.119382
$324$	−0.972209	−	8.94734i	−0.0540116	−	0.497074i
$325$			2.96779i			0.164623i
$326$	0.526883	−	0.912588i	0.0291813	−	0.0505436i
$327$	−15.5891	−	19.2164i	−0.862079	−	1.06267i
$328$			10.1259i			0.559110i
$329$	40.8949			2.25461
$330$	0.457999	+	2.87533i	0.0252120	+	0.158282i
$331$		−	7.82927i		−	0.430336i	−0.976577	−	0.215168i	$-0.930970\pi$
$331$		−	7.82927i		−	0.430336i	0.976577	−	0.215168i	$-0.0690299\pi$
$332$	12.4651			0.684112
$333$	11.6655	−	14.0327i	0.639265	−	0.768986i
$334$	8.40640			0.459978
$335$		−	25.6601i		−	1.40196i
$336$	4.40882	−	3.57661i	0.240521	−	0.195120i
$337$	11.6839			0.636463			0.318232	−	0.948013i	$-0.396911\pi$
$337$	11.6839			0.636463			0.318232	+	0.948013i	$0.396911\pi$
$338$		−	11.5509i		−	0.628286i
$339$	−18.1734	+	2.89476i	−0.987046	+	0.157222i
$340$	5.32173	−	9.21751i	0.288611	−	0.499889i
$341$		−	3.97338i		−	0.215170i
$342$	−0.198522	+	0.942113i	−0.0107349	+	0.0509436i
$343$	10.6746			0.576372
$344$	2.02149	+	3.50132i	0.108991	+	0.188778i
$345$	19.2485	−	15.6152i	1.03630	−	0.840692i
$346$			20.3161i			1.09220i
$347$	−2.43982	−	1.40863i	−0.130976	−	0.0756193i	0.433080	−	0.901355i	$-0.357427\pi$
$347$	−2.43982	−	1.40863i	−0.130976	−	0.0756193i	−0.564057	+	0.825736i	$0.690760\pi$
$348$	1.58355	−	0.252236i	0.0848871	−	0.0135213i
$349$	15.7605			0.843639			0.421820	−	0.906680i	$-0.361392\pi$
$349$	15.7605			0.843639			0.421820	+	0.906680i	$0.361392\pi$
$350$	−6.99813	−	4.04037i	−0.374066	−	0.215967i
$351$	−5.56579	+	2.85442i	−0.297080	+	0.152357i
$352$	0.914413	−	0.527937i	0.0487384	−	0.0281391i
$353$		−	12.3966i		−	0.659806i	−0.944015	−	0.329903i	$-0.892984\pi$
$353$		−	12.3966i		−	0.659806i	0.944015	−	0.329903i	$-0.107016\pi$
$354$	0.152230	+	0.955705i	0.00809092	+	0.0507951i
$355$	2.23295	−	1.28919i	0.118513	−	0.0684233i
$356$	3.27507	+	1.89086i	0.173578	+	0.100216i
$357$	37.4813	−	5.97021i	1.98372	−	0.315977i
$358$	−17.9888			−0.950739
$359$	−8.17129			−0.431264			−0.215632	−	0.976475i	$-0.569181\pi$
$359$	−8.17129			−0.431264			−0.215632	+	0.976475i	$0.569181\pi$
$360$	−3.55498	−	3.18963i	−0.187364	−	0.168108i
$361$	−9.44850	+	16.3653i	−0.497290	+	0.861331i
$362$	7.00320	−	4.04330i	0.368080	−	0.212511i
$363$	13.2965	−	10.7866i	0.697884	−	0.566151i
$364$	−3.41702	−	1.97282i	−0.179101	−	0.103404i
$365$		−	8.25314i		−	0.431989i
$366$	−7.28490	+	5.90980i	−0.380788	+	0.308910i
$367$	5.55405	−	9.61990i	0.289919	−	0.502155i	−0.683871	−	0.729603i	$-0.739705\pi$
$367$	5.55405	−	9.61990i	0.289919	−	0.502155i	0.973790	+	0.227448i	$0.0730383\pi$
$368$	−7.78426	−	4.49424i	−0.405782	−	0.234279i
$369$	22.6107	+	20.2870i	1.17707	+	1.05610i
$370$	−0.365378	−	9.67717i	−0.0189951	−	0.503092i
$371$	−6.95825	−	12.0521i	−0.361255	−	0.625711i
$372$	4.10631	+	5.06177i	0.212902	+	0.262440i
$373$	−6.62523			−0.343041			−0.171521	−	0.985181i	$-0.554868\pi$
$373$	−6.62523			−0.343041			−0.171521	+	0.985181i	$0.554868\pi$
$374$	7.05891			0.365008
$375$	−7.36042	+	19.2250i	−0.380091	+	0.992776i
$376$	−10.8052	+	6.23837i	−0.557234	+	0.321719i
$377$	−0.557225	−	0.965141i	−0.0286985	−	0.0497073i
$378$	0.846518	−	17.0103i	0.0435402	−	0.874918i
$379$	10.8446	−	18.7833i	0.557048	−	0.964835i	−0.440693	−	0.897658i	$-0.645267\pi$
$379$	10.8446	−	18.7833i	0.557048	−	0.964835i	0.997741	−	0.0671772i	$-0.0213993\pi$
$380$	0.255471	+	0.442489i	0.0131054	+	0.0226992i
$381$	−2.31217	+	1.87573i	−0.118456	+	0.0960965i
$382$	−5.30004	−	9.17993i	−0.271173	−	0.469686i
$383$		−	1.74725i		−	0.0892804i	−0.999003	−	0.0446402i	$-0.985786\pi$
$383$		−	1.74725i		−	0.0892804i	0.999003	−	0.0446402i	$-0.0142141\pi$
$384$	−0.619290	+	1.61755i	−0.0316030	+	0.0825454i
$385$			5.50981i			0.280806i
$386$	−4.66589	+	8.08156i	−0.237488	+	0.411341i
$387$	11.8683	+	2.50089i	0.603299	+	0.127127i
$388$	−10.1206	+	5.84311i	−0.513793	+	0.296639i
$389$	−14.8999	−	8.60248i	−0.755456	−	0.436163i	0.0722058	−	0.997390i	$-0.476996\pi$
$389$	−14.8999	−	8.60248i	−0.755456	−	0.436163i	−0.827662	+	0.561227i	$0.810329\pi$
$390$	−1.18686	+	3.10002i	−0.0600991	+	0.156976i
$391$	−30.0457	−	52.0407i	−1.51948	−	2.63181i
$392$	3.24177	−	1.87163i	0.163734	−	0.0945318i
$393$	−31.5136	+	5.01966i	−1.58965	+	0.253208i
$394$	−7.19753	−	4.15550i	−0.362607	−	0.209351i
$395$	6.43200	−	11.1406i	0.323629	−	0.560542i
$396$	0.653139	−	3.09955i	0.0328215	−	0.155758i
$397$	27.7036			1.39040			0.695201	−	0.718816i	$-0.255315\pi$
$397$	27.7036			1.39040			0.695201	+	0.718816i	$0.255315\pi$
$398$	5.35120			0.268231
$399$	−0.651446	+	1.70154i	−0.0326131	+	0.0851836i
$400$	2.46538			0.123269
$401$	19.4612	+	11.2359i	0.971848	+	0.561096i	0.899799	−	0.436305i	$-0.143713\pi$
$401$	19.4612	+	11.2359i	0.971848	+	0.561096i	0.0720486	+	0.997401i	$0.477046\pi$
$402$	−9.98151	+	26.0712i	−0.497833	+	1.30031i
$403$	2.26499	−	3.92309i	0.112827	−	0.195423i
$404$	−7.27190	−	12.5953i	−0.361790	−	0.626639i
$405$	−14.2446	+	1.54781i	−0.707820	+	0.0769111i
$406$	3.03445			0.150597
$407$	5.43704	−	3.41889i	0.269504	−	0.169468i
$408$	−8.99249	+	7.29507i	−0.445195	+	0.361160i
$409$	11.0857	−	6.40032i	0.548151	−	0.316475i	−0.200225	−	0.979750i	$-0.564167\pi$
$409$	11.0857	−	6.40032i	0.548151	−	0.316475i	0.748376	+	0.663275i	$0.230834\pi$
$410$	16.1210			0.796157
$411$	−5.63505	−	35.3771i	−0.277957	−	1.74502i
$412$	13.1563	+	7.59578i	0.648163	+	0.374217i
$413$			1.83135i			0.0901150i
$414$	−25.6310	+	8.37784i	−1.25969	+	0.411748i
$415$		−	19.8451i		−	0.974157i
$416$	1.20379			0.0590204
$417$	1.49422	+	9.38080i	0.0731725	+	0.459380i
$418$	−0.169433	+	0.293466i	−0.00828723	+	0.0143539i
$419$	5.11690	+	8.86273i	0.249977	+	0.432973i	0.963519	−	0.267639i	$-0.0862436\pi$
$419$	5.11690	+	8.86273i	0.249977	+	0.432973i	−0.713542	+	0.700612i	$0.752910\pi$
$420$	−5.69414	−	7.01906i	−0.277846	−	0.342495i
$421$	−5.80736	+	3.35288i	−0.283033	+	0.163409i	−0.634796	−	0.772680i	$-0.718916\pi$
$421$	−5.80736	+	3.35288i	−0.283033	+	0.163409i	0.351763	+	0.936089i	$0.385582\pi$
$422$	−1.63781	−	0.945591i	−0.0797274	−	0.0460306i
$423$	−7.71782	+	36.6259i	−0.375253	+	1.78081i
$424$	3.67699	+	2.12291i	0.178571	+	0.103098i
$425$	14.2738	+	8.24099i	0.692382	+	0.399747i
$426$	−2.77020	+	0.441252i	−0.134217	+	0.0213787i
$427$	−15.3734	+	8.87581i	−0.743969	+	0.429531i
$428$	3.29759	+	5.71160i	0.159395	+	0.276081i
$429$	−2.17411	+	0.346303i	−0.104967	+	0.0167197i
$430$	5.57427	−	3.21831i	0.268815	−	0.155201i
$431$	7.89713	−	4.55941i	0.380391	−	0.219619i	−0.297597	−	0.954692i	$-0.596185\pi$
$431$	7.89713	−	4.55941i	0.380391	−	0.219619i	0.677989	+	0.735072i	$0.262852\pi$
$432$	2.37120	+	4.62357i	0.114084	+	0.222452i
$433$	35.7362			1.71737			0.858686	−	0.512503i	$-0.171282\pi$
$433$	35.7362			1.71737			0.858686	+	0.512503i	$0.171282\pi$
$434$	6.16718	+	10.6819i	0.296034	+	0.512746i
$435$	−0.401572	−	2.52109i	−0.0192539	−	0.120877i
$436$	12.3722	+	7.14312i	0.592523	+	0.342093i
$437$	2.88471			0.137994
$438$	−3.21038	+	8.38535i	−0.153398	+	0.400668i
$439$	−6.06816	−	3.50345i	−0.289617	−	0.167211i	0.348152	−	0.937438i	$-0.386809\pi$
$439$	−6.06816	−	3.50345i	−0.289617	−	0.167211i	−0.637769	+	0.770227i	$0.720143\pi$
$440$	−0.840502	−	1.45579i	−0.0400693	−	0.0694021i
$441$	2.31550	−	10.9885i	0.110262	−	0.523262i
$442$	6.96957	+	4.02388i	0.331509	+	0.191397i
$443$	−11.9101	−	20.6289i	−0.565865	−	0.980107i	−0.996969	−	0.0778044i	$-0.975209\pi$
$443$	−11.9101	−	20.6289i	−0.565865	−	0.980107i	0.431104	−	0.902302i	$-0.358124\pi$
$444$	−3.39308	+	9.97432i	−0.161029	+	0.473360i
$445$	3.01035	−	5.21408i	0.142704	−	0.247171i
$446$	−3.29228	+	1.90080i	−0.155894	+	0.0900055i
$447$	−6.29345	+	5.10549i	−0.297670	+	0.241482i
$448$	−1.63885	+	2.83857i	−0.0774282	+	0.134110i
$449$	−14.4942	+	8.36825i	−0.684025	+	0.394922i	−0.801370	−	0.598169i	$-0.795895\pi$
$449$	−14.4942	+	8.36825i	−0.684025	+	0.394922i	0.117345	+	0.993091i	$0.462562\pi$
$450$	4.93931	−	5.50508i	0.232841	−	0.259512i
$451$	5.34584	+	9.25927i	0.251726	+	0.436002i
$452$	9.20127	−	5.31236i	0.432791	−	0.249872i
$453$	−6.50432	+	5.27656i	−0.305600	+	0.247915i
$454$	4.93058	−	8.54001i	0.231404	−	0.400803i
$455$	−3.14083	+	5.44007i	−0.147244	+	0.255035i
$456$	−0.0874402	−	0.548953i	−0.00409476	−	0.0257071i
$457$	−28.7644	−	16.6072i	−1.34554	−	0.776850i	−0.357929	−	0.933749i	$-0.616517\pi$
$457$	−28.7644	−	16.6072i	−1.34554	−	0.776850i	−0.987615	+	0.156899i	$0.949850\pi$
$458$			6.96651i			0.325524i
$459$	−1.72661	+	34.6953i	−0.0805912	+	1.61944i
$460$	−7.15506	+	12.3929i	−0.333606	+	0.577823i
$461$		−	34.3608i		−	1.60034i	−0.599771	−	0.800171i	$-0.704742\pi$
$461$		−	34.3608i		−	1.60034i	0.599771	−	0.800171i	$-0.295258\pi$
$462$	2.14326	−	5.59807i	0.0997134	−	0.260446i
$463$		−	20.5700i		−	0.955971i	−0.878368	−	0.477986i	$-0.841367\pi$
$463$		−	20.5700i		−	0.955971i	0.878368	−	0.477986i	$-0.158633\pi$
$464$	−0.801755	+	0.462894i	−0.0372206	+	0.0214893i
$465$	8.05858	−	6.53744i	0.373708	−	0.303167i
$466$		−	26.0976i		−	1.20895i
$467$			19.7693i			0.914816i	0.889257	+	0.457408i	$0.151222\pi$
$467$			19.7693i			0.914816i	−0.889257	+	0.457408i	$0.848778\pi$
$468$	2.41175	−	2.68800i	0.111483	−	0.124253i
$469$	−26.4144	+	45.7510i	−1.21970	+	2.11259i
$470$	9.93179	+	17.2024i	0.458119	+	0.793486i
$471$	2.04701	+	12.8512i	0.0943212	+	0.592153i
$472$	−0.279366	−	0.483876i	−0.0128589	−	0.0222722i
$473$	3.69695	+	2.13443i	0.169986	+	0.0981414i
$474$	−10.8686	+	8.81704i	−0.499211	+	0.404980i
$475$	−0.685219	+	0.395612i	−0.0314400	+	0.0181519i
$476$	−18.9769	+	10.9563i	−0.869804	+	0.502182i
$477$	12.1071	−	3.95738i	0.554347	−	0.181196i
$478$	−6.73406	−	11.6637i	−0.308009	−	0.533487i
$479$			28.2153i			1.28919i	0.764524	+	0.644596i	$0.222974\pi$
$479$			28.2153i			1.28919i	−0.764524	+	0.644596i	$0.777026\pi$
$480$	2.57523	+	0.985941i	0.117542	+	0.0450019i
$481$	7.31713	−	0.276270i	0.333632	−	0.0125968i
$482$	4.43170	−	7.67592i	0.201858	−	0.349629i
$483$	−50.3935	+	8.02694i	−2.29298	+	0.365239i
$484$	−4.94257	+	8.56078i	−0.224662	+	0.389126i
$485$	9.30252	+	16.1124i	0.422406	+	0.731628i
$486$	15.0749	+	3.96840i	0.683810	+	0.180010i
$487$			26.8052i			1.21466i	0.794451	+	0.607329i	$0.207759\pi$
$487$			26.8052i			1.21466i	−0.794451	+	0.607329i	$0.792241\pi$
$488$	2.70794	−	4.69030i	0.122583	−	0.212320i
$489$	1.14987	+	1.41742i	0.0519987	+	0.0640978i
$490$	−2.97974	−	5.16105i	−0.134611	−	0.233153i
$491$	4.17889	−	7.23804i	0.188590	−	0.326648i	−0.756190	−	0.654352i	$-0.772941\pi$
$491$	4.17889	−	7.23804i	0.188590	−	0.326648i	0.944781	+	0.327704i	$0.106275\pi$
$492$	−16.3792	−	6.27088i	−0.738432	−	0.282713i
$493$	−6.18924			−0.278749
$494$	−0.334576	+	0.193168i	−0.0150533	+	0.00869103i
$495$	−4.93464	−	1.03983i	−0.221796	−	0.0467369i
$496$	−3.25896	−	1.88156i	−0.146332	−	0.0844845i
$497$	−5.30835			−0.238112
$498$	−7.71953	+	20.1630i	−0.345920	+	0.903526i
$499$			36.9379i			1.65357i	0.562521	+	0.826783i	$0.309832\pi$
$499$			36.9379i			1.65357i	−0.562521	+	0.826783i	$0.690168\pi$
$500$		−	11.8853i		−	0.531525i
$501$	−5.20600	+	13.5978i	−0.232587	+	0.607505i
$502$	7.70689			0.343975
$503$	20.9129	+	12.0741i	0.932460	+	0.538356i	0.887589	−	0.460637i	$-0.152379\pi$
$503$	20.9129	+	12.0741i	0.932460	+	0.538356i	0.0448714	+	0.998993i	$0.485712\pi$
$504$	3.05502	+	9.34646i	0.136081	+	0.416324i
$505$	−20.0523	+	11.5772i	−0.892317	+	0.515180i
$506$	−9.49070			−0.421913
$507$	18.6842	+	7.15336i	0.829794	+	0.317692i
$508$	0.859482	−	1.48867i	0.0381333	−	0.0660489i
$509$	2.34465	+	4.06106i	0.103925	+	0.180003i	0.913298	−	0.407291i	$-0.133526\pi$
$509$	2.34465	+	4.06106i	0.103925	+	0.180003i	−0.809374	+	0.587294i	$0.800193\pi$
$510$	11.6141	+	14.3165i	0.514282	+	0.633945i
$511$	−8.49573	+	14.7150i	−0.375829	+	0.650955i
$512$		−	1.00000i		−	0.0441942i
$513$	−1.40097	−	0.904562i	−0.0618545	−	0.0399374i
$514$	−2.00099	−	3.46581i	−0.0882598	−	0.152870i
$515$	12.0929	−	20.9455i	0.532875	−	0.922967i
$516$	−6.91546	+	1.10153i	−0.304436	+	0.0484922i
$517$	−6.58692	+	11.4089i	−0.289693	+	0.501762i
$518$	−9.31016	+	17.6301i	−0.409065	+	0.774624i
$519$	−32.8624	−	12.5816i	−1.44250	−	0.552270i
$520$		−	1.91649i		−	0.0840435i
$521$	8.26993	+	14.3239i	0.362312	+	0.627543i	0.988341	−	0.152257i	$-0.0486541\pi$
$521$	8.26993	+	14.3239i	0.362312	+	0.627543i	−0.626029	+	0.779800i	$0.715321\pi$
$522$	−0.572671	+	2.71768i	−0.0250651	+	0.118950i
$523$	−31.9640	+	18.4544i	−1.39769	+	0.806955i	−0.994150	−	0.108008i	$-0.965553\pi$
$523$	−31.9640	+	18.4544i	−1.39769	+	0.806955i	−0.403538	+	0.914963i	$0.632220\pi$
$524$	15.9554	−	9.21188i	0.697017	−	0.402423i
$525$	10.8694	−	8.81769i	0.474379	−	0.384836i
$526$	2.82514	+	1.63109i	0.123182	+	0.0711191i
$527$	−12.5789	−	21.7874i	−0.547947	−	0.949073i
$528$	0.287678	+	1.80606i	0.0125196	+	0.0785986i
$529$	28.8964	+	50.0501i	1.25637	+	2.17609i
$530$	3.37978	−	5.85396i	0.146808	−	0.254280i
$531$	−1.64018	−	0.345619i	−0.0711777	−	0.0149986i
$532$		−	1.05192i		−	0.0456066i
$533$			12.1894i			0.527983i
$534$	−5.08679	+	4.12661i	−0.220127	+	0.178576i
$535$	9.09315	−	5.24993i	0.393131	−	0.226974i
$536$		−	16.1177i		−	0.696177i
$537$	11.1403	−	29.0979i	0.480740	−	1.25567i
$538$		−	0.959973i		−	0.0413874i
$539$	1.97621	−	3.42289i	0.0851214	−	0.147435i
$540$	7.36096	−	3.77507i	0.316765	−	0.162453i
$541$		−	7.26554i		−	0.312370i	−0.987728	−	0.156185i	$-0.950080\pi$
$541$		−	7.26554i		−	0.312370i	0.987728	−	0.156185i	$-0.0499196\pi$
$542$	−23.2935	−	13.4485i	−1.00054	−	0.577662i
$543$	2.20324	+	13.8320i	0.0945500	+	0.593589i
$544$	3.34269	−	5.78971i	0.143317	−	0.248232i
$545$	11.3722	−	19.6972i	0.487132	−	0.843737i
$546$	5.30727	−	4.30547i	0.227130	−	0.184257i
$547$	25.1586	−	14.5253i	1.07570	−	0.621057i	0.145968	−	0.989289i	$-0.453370\pi$
$547$	25.1586	−	14.5253i	1.07570	−	0.621057i	0.929734	+	0.368232i	$0.120037\pi$
$548$	10.3412	+	17.9115i	0.441756	+	0.765143i
$549$	−5.04795	−	15.4436i	−0.215441	−	0.659117i
$550$	2.25437	−	1.30156i	0.0961268	−	0.0554988i
$551$	0.148558	−	0.257310i	0.00632880	−	0.0109618i
$552$	12.0904	−	9.80821i	0.514601	−	0.417465i
$553$	−22.9360	+	13.2421i	−0.975340	+	0.563113i
$554$	11.8350	−	20.4988i	0.502821	−	0.870912i
$555$	15.8796	+	5.40196i	0.674052	+	0.229300i
$556$	−2.74214	−	4.74953i	−0.116293	−	0.201425i
$557$	−36.7383	−	21.2109i	−1.55665	−	0.898734i	−0.997574	−	0.0696198i	$-0.977821\pi$
$557$	−36.7383	−	21.2109i	−1.55665	−	0.898734i	−0.559079	−	0.829114i	$-0.688845\pi$
$558$	−10.7307	+	3.50747i	−0.454266	+	0.148483i
$559$	2.43344	+	4.21484i	0.102923	+	0.178269i
$560$	4.51914	+	2.60913i	0.190968	+	0.110256i
$561$	−4.37152	+	11.4182i	−0.184566	+	0.482076i
$562$	9.02020			0.380494
$563$	1.78548	+	1.03085i	0.0752490	+	0.0434450i	0.537152	−	0.843485i	$-0.319500\pi$
$563$	1.78548	+	1.03085i	0.0752490	+	0.0434450i	−0.461903	+	0.886930i	$0.652833\pi$
$564$	−3.39935	−	21.3413i	−0.143139	−	0.898631i
$565$	−8.45754	−	14.6489i	−0.355811	−	0.616283i
$566$	−9.63246			−0.404882
$567$	26.9909	+	11.9036i	1.13351	+	0.499905i
$568$	1.40256	−	0.809770i	0.0588502	−	0.0339772i
$569$	−38.9160	+	22.4681i	−1.63144	+	0.941914i	−0.647794	+	0.761816i	$0.724308\pi$
$569$	−38.9160	+	22.4681i	−1.63144	+	0.941914i	−0.983649	+	0.180098i	$0.942358\pi$
$570$	−0.873961	+	0.139209i	−0.0366062	+	0.00583083i
$571$	22.4150	+	38.8240i	0.938041	+	1.62473i	0.769120	+	0.639104i	$0.220695\pi$
$571$	22.4150	+	38.8240i	0.938041	+	1.62473i	0.168921	+	0.985630i	$0.445972\pi$
$572$	1.10076	−	0.635522i	0.0460250	−	0.0265725i
$573$	18.1313	−	2.88805i	0.757446	−	0.120650i
$574$	−28.7431	−	16.5948i	−1.19971	−	0.692654i
$575$	−19.1911	−	11.0800i	−0.800325	−	0.462068i
$576$	−2.23296	−	2.00347i	−0.0930399	−	0.0834780i
$577$	−11.4499	−	6.61060i	−0.476665	−	0.275203i	0.242360	−	0.970186i	$-0.422078\pi$
$577$	−11.4499	−	6.61060i	−0.476665	−	0.275203i	−0.719026	+	0.694983i	$0.755412\pi$
$578$	23.9840	−	13.8471i	0.997601	−	0.575965i
$579$	−10.1828	−	12.5522i	−0.423184	−	0.521650i
$580$	0.736950	+	1.27643i	0.0306002	+	0.0530011i
$581$	−20.4284	+	35.3831i	−0.847514	+	1.46794i
$582$	−3.18397	−	19.9891i	−0.131980	−	0.828576i
$583$	4.48305			0.185669
$584$		−	5.18397i		−	0.214514i
$585$	−4.27944	−	3.83963i	−0.176933	−	0.158749i
$586$			16.0288i			0.662144i
$587$	14.3270	+	8.27173i	0.591341	+	0.341411i	0.765627	−	0.643284i	$-0.222429\pi$
$587$	14.3270	+	8.27173i	0.591341	+	0.341411i	−0.174287	+	0.984695i	$0.555762\pi$
$588$	1.01987	+	6.40282i	0.0420589	+	0.264048i
$589$	1.20771			0.0497629
$590$	−0.770355	+	0.444765i	−0.0317150	+	0.0183107i
$591$	11.1791	−	9.06894i	0.459847	−	0.373046i
$592$	−0.229501	−	6.07843i	−0.00943245	−	0.249822i
$593$	−23.9123			−0.981962			−0.490981	−	0.871170i	$-0.663361\pi$
$593$	−23.9123			−0.981962			−0.490981	+	0.871170i	$0.663361\pi$
$594$	4.60921	+	2.97601i	0.189118	+	0.122107i
$595$	17.4430	+	30.2121i	0.715093	+	1.23858i
$596$	2.33940	−	4.05196i	0.0958256	−	0.165975i
$597$	−3.31395	+	8.65585i	−0.135631	+	0.354260i
$598$	−9.37057	−	5.41010i	−0.383191	−	0.221236i
$599$	−4.60380			−0.188106			−0.0940530	−	0.995567i	$-0.529982\pi$
$599$	−4.60380			−0.188106			−0.0940530	+	0.995567i	$0.529982\pi$
$600$	−1.52678	+	3.98788i	−0.0623307	+	0.162804i
$601$	−16.3267			−0.665980			−0.332990	−	0.942930i	$-0.608057\pi$
$601$	−16.3267			−0.665980			−0.332990	+	0.942930i	$0.608057\pi$
$602$	−13.2516			−0.540096
$603$	−35.9901	−	32.2913i	−1.46563	−	1.31500i
$604$	2.41779	−	4.18773i	0.0983783	−	0.170396i
$605$	13.6292	+	7.86881i	0.554105	+	0.319913i
$606$	24.8770	−	3.96254i	1.01056	−	0.160967i
$607$	−22.7738	+	13.1485i	−0.924362	+	0.533680i	−0.885024	−	0.465546i	$-0.845858\pi$
$607$	−22.7738	+	13.1485i	−0.924362	+	0.533680i	−0.0393376	+	0.999226i	$0.512525\pi$
$608$	0.160467	+	0.277937i	0.00650779	+	0.0112718i
$609$	−1.87920	+	4.90838i	−0.0761492	+	0.198898i
$610$	−7.46719	−	4.31118i	−0.302338	−	0.174555i
$611$	−13.0071	+	7.50965i	−0.526211	+	0.303808i
$612$	−6.23120	−	19.0636i	−0.251881	−	0.770600i
$613$	17.3918	−	30.1236i	0.702450	−	1.21668i	−0.265154	−	0.964206i	$-0.585423\pi$
$613$	17.3918	−	30.1236i	0.702450	−	1.21668i	0.967604	−	0.252473i	$-0.0812439\pi$
$614$			11.9587i			0.482613i
$615$	−9.98356	+	26.0765i	−0.402576	+	1.05151i
$616$			3.46083i			0.139441i
$617$	−5.41738	−	9.38318i	−0.218096	−	0.377753i	0.736130	−	0.676840i	$-0.236651\pi$
$617$	−5.41738	−	9.38318i	−0.218096	−	0.377753i	−0.954226	+	0.299087i	$0.903318\pi$
$618$	−20.4341	+	16.5770i	−0.821982	+	0.666824i
$619$	5.91122	+	10.2385i	0.237592	+	0.411522i	0.960023	−	0.279922i	$-0.0903085\pi$
$619$	5.91122	+	10.2385i	0.237592	+	0.411522i	−0.722431	+	0.691443i	$0.756975\pi$
$620$	−2.99554	+	5.18842i	−0.120304	+	0.208372i
$621$	2.32142	−	46.6478i	0.0931555	−	1.87191i
$622$	−3.65796	−	6.33578i	−0.146671	−	0.254041i
$623$	−10.7347	+	6.19767i	−0.430076	+	0.248304i
$624$	−0.745493	+	1.94719i	−0.0298436	+	0.0779499i
$625$	−6.59503			−0.263801
$626$	13.3202			0.532380
$627$	−0.369769	−	0.455807i	−0.0147672	−	0.0182032i
$628$	−3.75659	−	6.50661i	−0.149904	−	0.259642i
$629$	18.9896	−	35.9595i	0.757164	−	1.43380i
$630$	14.8800	−	4.86374i	0.592835	−	0.193776i
$631$	−15.9266	−	9.19521i	−0.634027	−	0.366055i	0.148283	−	0.988945i	$-0.452625\pi$
$631$	−15.9266	−	9.19521i	−0.634027	−	0.366055i	−0.782310	+	0.622890i	$0.785959\pi$
$632$	4.04008	−	6.99762i	0.160706	−	0.278350i
$633$	2.54382	−	2.06365i	0.101108	−	0.0820228i
$634$			12.8746i			0.511315i
$635$	−2.37003	−	1.36834i	−0.0940518	−	0.0543008i
$636$	−5.71105	+	4.63303i	−0.226458	+	0.183712i
$637$	3.90239	−	2.25305i	0.154618	−	0.0892690i
$638$	−0.488757	+	0.846552i	−0.0193501	+	0.0335153i
$639$	1.00181	−	4.75421i	0.0396310	−	0.188074i
$640$	−1.59205			−0.0629313
$641$	−16.7623			−0.662071			−0.331035	−	0.943618i	$-0.607398\pi$
$641$	−16.7623			−0.662071			−0.331035	+	0.943618i	$0.607398\pi$
$642$	−11.2810	+	1.79690i	−0.445225	+	0.0709178i
$643$	−9.42584	−	5.44201i	−0.371719	−	0.214612i	0.302490	−	0.953152i	$-0.402182\pi$
$643$	−9.42584	−	5.44201i	−0.371719	−	0.214612i	−0.674209	+	0.738541i	$0.735515\pi$
$644$	25.5144	−	14.7307i	1.00541	−	0.580473i
$645$	1.75369	+	11.0098i	0.0690515	+	0.433509i
$646$			2.14556i			0.0844161i
$647$	33.5311	−	19.3592i	1.31824	−	0.761089i	0.334798	−	0.942290i	$-0.391332\pi$
$647$	33.5311	−	19.3592i	1.31824	−	0.761089i	0.983446	+	0.181201i	$0.0579986\pi$
$648$	−8.94734	+	0.972209i	−0.351485	+	0.0381920i
$649$	−0.510912	−	0.294975i	−0.0200551	−	0.0115788i
$650$	2.96779			0.116406
$651$	−21.0978	+	3.36056i	−0.826886	+	0.131711i
$652$	−0.912588	−	0.526883i	−0.0357397	−	0.0206343i
$653$			44.1097i			1.72614i	0.505081	+	0.863072i	$0.331463\pi$
$653$			44.1097i			1.72614i	−0.505081	+	0.863072i	$0.668537\pi$
$654$	−19.2164	+	15.5891i	−0.751420	+	0.609582i
$655$	−14.6658	−	25.4019i	−0.573039	−	0.992533i
$656$	10.1259			0.395350
$657$	−11.5756	−	10.3859i	−0.451607	−	0.405194i
$658$		−	40.8949i		−	1.59425i
$659$	−14.1531	+	24.5138i	−0.551325	+	0.954924i	0.446854	+	0.894607i	$0.352544\pi$
$659$	−14.1531	+	24.5138i	−0.551325	+	0.954924i	−0.998179	+	0.0603167i	$0.980789\pi$
$660$	2.87533	−	0.457999i	0.111922	−	0.0178276i
$661$			33.6989i			1.31074i	0.755310	+	0.655368i	$0.227486\pi$
$661$			33.6989i			1.31074i	−0.755310	+	0.655368i	$0.772514\pi$
$662$	−7.82927			−0.304293
$663$	−10.8250	+	8.78170i	−0.420409	+	0.341053i
$664$		−	12.4651i		−	0.483740i
$665$	−1.67471			−0.0649426
$666$	−14.0327	−	11.6655i	−0.543756	−	0.452029i
$667$	8.32142			0.322207
$668$		−	8.40640i		−	0.325253i
$669$	−1.03577	−	6.50259i	−0.0400451	−	0.251405i
$670$	−25.6601			−0.991337
$671$		−	5.71849i		−	0.220760i
$672$	−3.57661	−	4.40882i	−0.137971	−	0.170074i
$673$	7.08424	−	12.2703i	0.273077	−	0.472984i	−0.696571	−	0.717488i	$-0.745292\pi$
$673$	7.08424	−	12.2703i	0.273077	−	0.472984i	0.969648	+	0.244504i	$0.0786251\pi$
$674$		−	11.6839i		−	0.450047i
$675$	5.84590	+	11.3988i	0.225009	+	0.438742i
$676$	−11.5509			−0.444265
$677$	−5.47275	−	9.47909i	−0.210335	−	0.364311i	0.741484	−	0.670970i	$-0.234122\pi$
$677$	−5.47275	−	9.47909i	−0.210335	−	0.364311i	−0.951819	+	0.306659i	$0.900789\pi$
$678$	2.89476	+	18.1734i	0.111173	+	0.697947i
$679$		−	38.3038i		−	1.46997i
$680$	−9.21751	−	5.32173i	−0.353475	−	0.204079i
$681$	10.7605	+	13.2642i	0.412342	+	0.508286i
$682$	−3.97338			−0.152149
$683$	38.5858	+	22.2775i	1.47645	+	0.852427i	0.999647	−	0.0265855i	$-0.00846342\pi$
$683$	38.5858	+	22.2775i	1.47645	+	0.852427i	0.476800	+	0.879012i	$0.341797\pi$
$684$	0.942113	+	0.198522i	0.0360226	+	0.00759069i
$685$	28.5161	−	16.4638i	1.08954	−	0.629048i
$686$		−	10.6746i		−	0.407557i
$687$	−11.2687	−	4.31429i	−0.429928	−	0.164600i
$688$	3.50132	−	2.02149i	0.133486	−	0.0770685i
$689$	4.42631	+	2.55553i	0.168629	+	0.0973580i
$690$	−15.6152	−	19.2485i	−0.594459	−	0.732778i
$691$	−0.403606			−0.0153539			−0.00767694	−	0.999971i	$-0.502444\pi$
$691$	−0.403606			−0.0153539			−0.00767694	+	0.999971i	$0.502444\pi$
$692$	20.3161			0.772303
$693$	7.72789	+	6.93367i	0.293558	+	0.263388i
$694$	−1.40863	+	2.43982i	−0.0534709	+	0.0926143i
$695$	−7.56149	+	4.36563i	−0.286824	+	0.165598i
$696$	−0.252236	−	1.58355i	−0.00956097	−	0.0600242i
$697$	58.6261	+	33.8478i	2.22062	+	1.28208i
$698$		−	15.7605i		−	0.596543i
$699$	42.2143	+	16.1620i	1.59669	+	0.611304i
$700$	−4.04037	+	6.99813i	−0.152712	+	0.264505i
$701$	−29.8771	−	17.2495i	−1.12844	−	0.651506i	−0.184900	−	0.982757i	$-0.559196\pi$
$701$	−29.8771	−	17.2495i	−1.12844	−	0.651506i	−0.943543	+	0.331251i	$0.892529\pi$
$702$	2.85442	+	5.56579i	0.107733	+	0.210067i
$703$	1.03917	+	1.65259i	0.0391932	+	0.0623287i
$704$	−0.527937	−	0.914413i	−0.0198974	−	0.0344632i
$705$	−33.9764	+	5.41194i	−1.27963	+	0.203825i
$706$	−12.3966			−0.466554
$707$	47.6701			1.79282
$708$	0.955705	−	0.152230i	0.0359176	−	0.00572114i
$709$	42.7092	−	24.6582i	1.60398	−	0.926057i	0.613296	−	0.789853i	$-0.289843\pi$
$709$	42.7092	−	24.6582i	1.60398	−	0.926057i	0.990681	−	0.136203i	$-0.0434901\pi$
$710$	−1.28919	−	2.23295i	−0.0483826	−	0.0838011i
$711$	−7.53121	−	23.0408i	−0.282443	−	0.864099i
$712$	1.89086	−	3.27507i	0.0708631	−	0.122738i
$713$	16.9124	+	29.2931i	0.633373	+	1.09703i
$714$	−5.97021	−	37.4813i	−0.223430	−	1.40270i
$715$	−1.01178	−	1.75246i	−0.0378386	−	0.0655383i
$716$			17.9888i			0.672274i
$717$	23.0371	−	3.66946i	0.860335	−	0.137039i
$718$			8.17129i			0.304950i
$719$	11.7975	−	20.4339i	0.439973	−	0.762056i	−0.557714	−	0.830033i	$-0.688321\pi$
$719$	11.7975	−	20.4339i	0.439973	−	0.762056i	0.997687	+	0.0679774i	$0.0216546\pi$
$720$	−3.18963	+	3.55498i	−0.118870	+	0.132486i
$721$	−43.1222	+	24.8966i	−1.60596	+	0.927199i
$722$	16.3653	+	9.44850i	0.609053	+	0.351637i
$723$	9.67171	+	11.9221i	0.359695	+	0.443389i
$724$	−4.04330	−	7.00320i	−0.150268	−	0.260272i
$725$	−1.97663	+	1.14121i	−0.0734102	+	0.0423834i
$726$	−10.7866	−	13.2965i	−0.400329	−	0.493478i
$727$	36.7510	+	21.2182i	1.36302	+	0.786940i	0.990025	−	0.140893i	$-0.0449974\pi$
$727$	36.7510	+	21.2182i	1.36302	+	0.786940i	0.372995	+	0.927833i	$0.378331\pi$
$728$	−1.97282	+	3.41702i	−0.0731176	+	0.126643i
$729$	−15.7548	+	21.9268i	−0.583512	+	0.812105i
$730$	−8.25314			−0.305462
$731$	27.0288			0.999697
$732$	5.90980	+	7.28490i	0.218433	+	0.269258i
$733$	47.0163			1.73658			0.868292	−	0.496053i	$-0.165218\pi$
$733$	47.0163			1.73658			0.868292	+	0.496053i	$0.165218\pi$
$734$	−9.61990	−	5.55405i	−0.355077	−	0.205004i
$735$	10.1936	−	1.62369i	0.375997	−	0.0598907i
$736$	−4.49424	+	7.78426i	−0.165660	+	0.286931i
$737$	−8.50910	−	14.7382i	−0.313437	−	0.542888i
$738$	20.2870	−	22.6107i	0.746774	−	0.832313i
$739$	−35.0041			−1.28765			−0.643823	−	0.765174i	$-0.722653\pi$
$739$	−35.0041			−1.28765			−0.643823	+	0.765174i	$0.722653\pi$
$740$	−9.67717	+	0.365378i	−0.355740	+	0.0134315i
$741$	−0.105259	−	0.660822i	−0.00386680	−	0.0242759i
$742$	−12.0521	+	6.95825i	−0.442445	+	0.255446i
$743$	22.3444			0.819737			0.409868	−	0.912145i	$-0.365575\pi$
$743$	22.3444			0.819737			0.409868	+	0.912145i	$0.365575\pi$
$744$	5.06177	−	4.10631i	0.185573	−	0.150544i
$745$	−6.45092	−	3.72444i	−0.236344	−	0.136453i
$746$			6.62523i			0.242567i
$747$	−27.8341	−	24.9735i	−1.01840	−	0.913733i
$748$		−	7.05891i		−	0.258099i
$749$	−21.6170			−0.789868
$750$	19.2250	+	7.36042i	0.701999	+	0.268765i
$751$	23.0064	−	39.8483i	0.839517	−	1.45409i	−0.0507822	−	0.998710i	$-0.516171\pi$
$751$	23.0064	−	39.8483i	0.839517	−	1.45409i	0.890299	−	0.455376i	$-0.150495\pi$
$752$	6.23837	+	10.8052i	0.227490	+	0.394024i
$753$	−4.77280	+	12.4663i	−0.173931	+	0.454297i
$754$	−0.965141	+	0.557225i	−0.0351484	+	0.0202929i
$755$	−6.66707	−	3.84924i	−0.242640	−	0.140088i
$756$	−17.0103	−	0.846518i	−0.618660	−	0.0307876i
$757$	3.30989	+	1.91097i	0.120300	+	0.0694553i	0.558943	−	0.829206i	$-0.311207\pi$
$757$	3.30989	+	1.91097i	0.120300	+	0.0694553i	−0.438643	+	0.898662i	$0.644541\pi$
$758$	−18.7833	−	10.8446i	−0.682241	−	0.393892i
$759$	5.87750	−	15.3517i	0.213340	−	0.557232i
$760$	0.442489	−	0.255471i	0.0160508	−	0.00926692i
$761$	−20.1594	−	34.9171i	−0.730778	−	1.26574i	−0.956551	−	0.291564i	$-0.905824\pi$
$761$	−20.1594	−	34.9171i	−0.730778	−	1.26574i	0.225774	−	0.974180i	$-0.427509\pi$
$762$	1.87573	+	2.31217i	0.0679505	+	0.0837612i
$763$	−40.5524	+	23.4129i	−1.46810	+	0.847606i
$764$	−9.17993	+	5.30004i	−0.332118	+	0.191749i
$765$	−30.3502	+	9.92038i	−1.09731	+	0.358672i
$766$	−1.74725			−0.0631308
$767$	−0.336297	−	0.582483i	−0.0121430	−	0.0210323i
$768$	1.61755	+	0.619290i	0.0583684	+	0.0223467i
$769$	−12.3114	−	7.10799i	−0.443960	−	0.256321i	0.261316	−	0.965253i	$-0.415844\pi$
$769$	−12.3114	−	7.10799i	−0.443960	−	0.256321i	−0.705276	+	0.708933i	$0.749177\pi$
$770$	5.50981			0.198560
$771$	6.84533	−	1.09036i	0.246528	−	0.0392684i
$772$	8.08156	+	4.66589i	0.290862	+	0.167929i
$773$	−3.48847	−	6.04220i	−0.125471	−	0.217323i	0.796446	−	0.604710i	$-0.206711\pi$
$773$	−3.48847	−	6.04220i	−0.125471	−	0.217323i	−0.921917	+	0.387387i	$0.873378\pi$
$774$	2.50089	−	11.8683i	0.0898927	−	0.426597i
$775$	−8.03456	−	4.63875i	−0.288610	−	0.166629i
$776$	5.84311	+	10.1206i	0.209755	+	0.363307i
$777$	−22.7520	−	25.9779i	−0.816224	−	0.931951i
$778$	−8.60248	+	14.8999i	−0.308414	+	0.534188i
$779$	−2.81436	+	1.62487i	−0.100835	+	0.0582172i
$780$	3.10002	+	1.18686i	0.110999	+	0.0424965i
$781$	0.855014	−	1.48093i	0.0305948	−	0.0529918i
$782$	−52.0407	+	30.0457i	−1.86097	+	1.07443i
$783$	−4.04134	−	2.60936i	−0.144426	−	0.0932509i
$784$	−1.87163	−	3.24177i	−0.0668441	−	0.115777i
$785$	−10.3589	+	5.98069i	−0.369723	+	0.213460i
$786$	5.01966	+	31.5136i	0.179045	+	1.12405i
$787$	13.4970	−	23.3775i	0.481117	−	0.833319i	−0.518648	−	0.854988i	$-0.673565\pi$
$787$	13.4970	−	23.3775i	0.481117	−	0.833319i	0.999765	+	0.0216685i	$0.00689785\pi$
$788$	−4.15550	+	7.19753i	−0.148034	+	0.256402i
$789$	−4.38796	+	3.55969i	−0.156216	+	0.126728i
$790$	−11.1406	−	6.43200i	−0.396363	−	0.228840i
$791$			34.8245i			1.23822i
$792$	−3.09955	−	0.653139i	−0.110138	−	0.0232083i
$793$	3.25978	−	5.64611i	0.115758	−	0.200499i
$794$		−	27.7036i		−	0.983162i
$795$	7.37602	+	9.09228i	0.261600	+	0.322470i
$796$		−	5.35120i		−	0.189668i
$797$	−26.3416	+	15.2083i	−0.933066	+	0.538706i	−0.887780	−	0.460268i	$-0.847753\pi$
$797$	−26.3416	+	15.2083i	−0.933066	+	0.538706i	−0.0452861	+	0.998974i	$0.514420\pi$
$798$	1.70154	+	0.651446i	0.0602339	+	0.0230609i
$799$			83.4117i			2.95089i
$800$		−	2.46538i		−	0.0871642i
$801$	−3.52481	−	10.7837i	−0.124543	−	0.381024i
$802$	11.2359	−	19.4612i	0.396755	−	0.687200i
$803$	−2.73681	−	4.74029i	−0.0965799	−	0.167281i
$804$	26.0712	+	9.98151i	0.919459	+	0.352021i
$805$	−23.4521	−	40.6202i	−0.826577	−	1.43167i
$806$	−3.92309	−	2.26499i	−0.138185	−	0.0797810i
$807$	1.55281	+	0.594502i	0.0546614	+	0.0209275i
$808$	−12.5953	+	7.27190i	−0.443101	+	0.255824i
$809$	−20.9790	+	12.1123i	−0.737584	+	0.425844i	−0.821190	−	0.570655i	$-0.806690\pi$
$809$	−20.9790	+	12.1123i	−0.737584	+	0.425844i	0.0836063	+	0.996499i	$0.473356\pi$
$810$	1.54781	+	14.2446i	0.0543843	+	0.500504i
$811$	22.4166	+	38.8267i	0.787154	+	1.36339i	0.927704	+	0.373317i	$0.121780\pi$
$811$	22.4166	+	38.8267i	0.787154	+	1.36339i	−0.140550	+	0.990074i	$0.544887\pi$
$812$		−	3.03445i		−	0.106488i
$813$	36.1791	−	29.3499i	1.26885	−	1.02935i
$814$	−3.41889	−	5.43704i	−0.119832	−	0.190568i
$815$	−0.838824	+	1.45289i	−0.0293827	+	0.0508923i
$816$	7.29507	+	8.99249i	0.255378	+	0.314800i
$817$	−0.648764	+	1.12369i	−0.0226974	+	0.0393130i
$818$	−6.40032	−	11.0857i	−0.223782	−	0.387602i
$819$	3.67759	+	11.2511i	0.128505	+	0.393146i
$820$		−	16.1210i		−	0.562968i
$821$	−27.0806	+	46.9050i	−0.945121	+	1.63700i	−0.189612	+	0.981859i	$0.560723\pi$
$821$	−27.0806	+	46.9050i	−0.945121	+	1.63700i	−0.755509	+	0.655138i	$0.772610\pi$
$822$	−35.3771	+	5.63505i	−1.23392	+	0.196545i
$823$	11.0239	+	19.0939i	0.384268	+	0.665571i	0.991667	−	0.128825i	$-0.0411207\pi$
$823$	11.0239	+	19.0939i	0.384268	+	0.665571i	−0.607400	+	0.794396i	$0.707787\pi$
$824$	7.59578	−	13.1563i	0.264612	−	0.458321i
$825$	0.709236	+	4.45261i	0.0246924	+	0.155020i
$826$	1.83135			0.0637209
$827$	33.0751	−	19.0959i	1.15013	−	0.664030i	0.201213	−	0.979547i	$-0.435512\pi$
$827$	33.0751	−	19.0959i	1.15013	−	0.664030i	0.948920	+	0.315518i	$0.102178\pi$
$828$	8.37784	+	25.6310i	0.291150	+	0.890738i
$829$	13.8487	+	7.99553i	0.480984	+	0.277696i	0.720827	−	0.693115i	$-0.243762\pi$
$829$	13.8487	+	7.99553i	0.480984	+	0.277696i	−0.239842	+	0.970812i	$0.577096\pi$
$830$	−19.8451			−0.688833
$831$	25.8287	+	31.8385i	0.895986	+	1.10446i
$832$		−	1.20379i		−	0.0417338i
$833$		−	25.0252i		−	0.867071i
$834$	9.38080	−	1.49422i	0.324831	−	0.0517407i
$835$	−13.3834			−0.463152
$836$	0.293466	+	0.169433i	0.0101497	+	0.00585995i
$837$	0.971887	−	19.5296i	0.0335933	−	0.675041i
$838$	8.86273	−	5.11690i	0.306158	−	0.176760i
$839$	−49.4209			−1.70620			−0.853099	−	0.521749i	$-0.825280\pi$
$839$	−49.4209			−1.70620			−0.853099	+	0.521749i	$0.825280\pi$
$840$	−7.01906	+	5.69414i	−0.242181	+	0.196467i
$841$	−14.0715	+	24.3725i	−0.485223	+	0.840430i
$842$	3.35288	+	5.80736i	0.115548	+	0.200135i
$843$	−5.58613	+	14.5907i	−0.192396	+	0.502529i
$844$	−0.945591	+	1.63781i	−0.0325486	+	0.0563758i
$845$			18.3896i			0.632622i
$846$	36.6259	+	7.71782i	1.25922	+	0.265344i
$847$	−16.2002	−	28.0596i	−0.556646	−	0.964139i
$848$	2.12291	−	3.67699i	0.0729011	−	0.126268i
$849$	5.96529	−	15.5810i	0.204728	−	0.534739i
$850$	8.24099	−	14.2738i	0.282664	−	0.489588i
$851$	−25.5314	+	48.3475i	−0.875207	+	1.65733i
$852$	0.441252	+	2.77020i	0.0151171	+	0.0949056i
$853$		−	12.7134i		−	0.435300i	−0.976027	−	0.217650i	$-0.930161\pi$
$853$		−	12.7134i		−	0.435300i	0.976027	−	0.217650i	$-0.0698391\pi$
$854$	8.87581	+	15.3734i	0.303724	+	0.526065i
$855$	0.316058	−	1.49989i	0.0108089	−	0.0512952i
$856$	5.71160	−	3.29759i	0.195219	−	0.112709i
$857$	5.27254	−	3.04410i	0.180107	−	0.103985i	−0.407236	−	0.913323i	$-0.633507\pi$
$857$	5.27254	−	3.04410i	0.180107	−	0.103985i	0.587343	+	0.809338i	$0.300174\pi$
$858$	0.346303	+	2.17411i	0.0118226	+	0.0742228i
$859$	−3.07198	−	1.77361i	−0.104815	−	0.0605148i	0.446676	−	0.894696i	$-0.352608\pi$
$859$	−3.07198	−	1.77361i	−0.104815	−	0.0605148i	−0.551491	+	0.834181i	$0.685941\pi$
$860$	−3.21831	−	5.57427i	−0.109743	−	0.190081i
$861$	44.6433	−	36.2164i	1.52144	−	1.23425i
$862$	−4.55941	−	7.89713i	−0.155294	−	0.268977i
$863$	22.4327	−	38.8546i	0.763619	−	1.32263i	−0.177354	−	0.984147i	$-0.556754\pi$
$863$	22.4327	−	38.8546i	0.763619	−	1.32263i	0.940973	−	0.338481i	$-0.109913\pi$
$864$	4.62357	−	2.37120i	0.157297	−	0.0806699i
$865$		−	32.3443i		−	1.09974i
$866$		−	35.7362i		−	1.21436i
$867$	7.54546	+	47.3708i	0.256257	+	1.60880i
$868$	10.6819	−	6.16718i	0.362566	−	0.209328i
$869$		−	8.53162i		−	0.289415i
$870$	−2.52109	+	0.401572i	−0.0854729	+	0.0136146i
$871$		−	19.4022i		−	0.657419i
$872$	7.14312	−	12.3722i	0.241897	−	0.418977i
$873$	34.3053	+	7.22883i	1.16106	+	0.244659i
$874$		−	2.88471i		−	0.0975767i
$875$	33.7371	+	19.4781i	1.14052	+	0.658480i
$876$	8.38535	+	3.21038i	0.283315	+	0.108469i
$877$	−16.4264	+	28.4514i	−0.554681	+	0.960736i	0.443247	+	0.896400i	$0.353826\pi$
$877$	−16.4264	+	28.4514i	−0.554681	+	0.960736i	−0.997928	+	0.0643367i	$0.979507\pi$
$878$	−3.50345	+	6.06816i	−0.118236	+	0.204790i
$879$	−25.9275	−	9.92649i	−0.874512	−	0.334812i
$880$	−1.45579	+	0.840502i	−0.0490747	+	0.0283333i
$881$	−14.3862	−	24.9176i	−0.484683	−	0.839496i	0.515162	−	0.857093i	$-0.327732\pi$
$881$	−14.3862	−	24.9176i	−0.484683	−	0.839496i	−0.999845	+	0.0175966i	$0.994399\pi$
$882$	−10.9885	−	2.31550i	−0.370002	−	0.0779670i
$883$	7.28817	−	4.20783i	0.245267	−	0.141605i	−0.372328	−	0.928101i	$-0.621440\pi$
$883$	7.28817	−	4.20783i	0.245267	−	0.141605i	0.617595	+	0.786496i	$0.288107\pi$
$884$	4.02388	−	6.96957i	0.135338	−	0.234412i
$885$	−0.242357	−	1.52153i	−0.00814675	−	0.0511457i
$886$	−20.6289	+	11.9101i	−0.693040	+	0.400127i
$887$	4.50221	−	7.79806i	0.151169	−	0.261833i	−0.780488	−	0.625170i	$-0.785029\pi$
$887$	4.50221	−	7.79806i	0.151169	−	0.261833i	0.931658	+	0.363337i	$0.118363\pi$
$888$	9.97432	+	3.39308i	0.334716	+	0.113864i
$889$	2.81712	+	4.87939i	0.0944831	+	0.163649i
$890$	−5.21408	−	3.01035i	−0.174776	−	0.100907i
$891$	−7.66830	+	5.61263i	−0.256898	+	0.188030i
$892$	1.90080	+	3.29228i	0.0636435	+	0.110234i
$893$	−3.46774	−	2.00210i	−0.116044	−	0.0669978i
$894$	5.10549	+	6.29345i	0.170753	+	0.210484i
$895$	28.6391			0.957300
$896$	2.83857	+	1.63885i	0.0948298	+	0.0547500i
$897$	14.5542	−	11.8070i	0.485952	−	0.394224i
$898$	8.36825	+	14.4942i	0.279252	+	0.483679i
$899$	3.48385			0.116193
$900$	−5.50508	−	4.93931i	−0.183503	−	0.164644i
$901$	24.5821	−	14.1925i	0.818948	−	0.472820i
$902$	9.25927	−	5.34584i	0.308300	−	0.177997i
$903$	8.20661	−	21.4352i	0.273099	−	0.713319i
$904$	−5.31236	−	9.20127i	−0.176686	−	0.306030i
$905$	−11.1494	+	6.43714i	−0.370620	+	0.213978i
$906$	5.27656	+	6.50432i	0.175302	+	0.216091i
$907$	27.4904	+	15.8716i	0.912803	+	0.527007i	0.881332	−	0.472498i	$-0.156647\pi$
$907$	27.4904	+	15.8716i	0.912803	+	0.527007i	0.0314711	+	0.999505i	$0.489981\pi$
$908$	−8.54001	−	4.93058i	−0.283410	−	0.163627i
$909$	−8.99646	+	42.6938i	−0.298394	+	1.41606i
$910$	5.44007	+	3.14083i	0.180337	+	0.104117i
$911$	−45.2266	+	26.1116i	−1.49842	+	0.865115i	−0.999998	−	0.00181810i	$-0.999421\pi$
$911$	−45.2266	+	26.1116i	−1.49842	+	0.865115i	−0.498425	+	0.866933i	$0.666088\pi$
$912$	−0.548953	+	0.0874402i	−0.0181777	+	0.00289543i
$913$	−6.58079	−	11.3983i	−0.217792	−	0.377228i
$914$	−16.6072	+	28.7644i	−0.549316	+	0.951443i
$915$	11.5979	−	9.40870i	0.383416	−	0.311042i
$916$	6.96651			0.230180
$917$			60.3874i			1.99417i
$918$	34.6953	+	1.72661i	1.14512	+	0.0569866i
$919$			21.7083i			0.716091i	0.933704	+	0.358045i	$0.116557\pi$
$919$			21.7083i			0.716091i	−0.933704	+	0.358045i	$0.883443\pi$
$920$	12.3929	+	7.15506i	0.408583	+	0.235895i
$921$	−19.3438	−	7.40589i	−0.637400	−	0.244032i
$922$	−34.3608			−1.13161
$923$	1.68838	−	0.974789i	0.0555738	−	0.0320856i
$924$	−5.59807	−	2.14326i	−0.184163	−	0.0705080i
$925$	−0.565807	−	14.9856i	−0.0186036	−	0.492724i
$926$	−20.5700			−0.675974
$927$	−14.1595	−	43.3193i	−0.465059	−	1.42279i
$928$	0.462894	+	0.801755i	0.0151952	+	0.0263189i
$929$	−18.2624	+	31.6315i	−0.599171	+	1.03779i	0.393772	+	0.919208i	$0.371170\pi$
$929$	−18.2624	+	31.6315i	−0.599171	+	1.03779i	−0.992944	+	0.118587i	$0.962164\pi$
$930$	−6.53744	−	8.05858i	−0.214371	−	0.264251i
$931$	1.04039	+	0.600671i	0.0340975	+	0.0196862i
$932$	−26.0976			−0.854857
$933$	12.5138	−	1.99326i	0.409683	−	0.0652565i
$934$	19.7693			0.646873
$935$	−11.2381			−0.367527
$936$	−2.68800	−	2.41175i	−0.0878601	−	0.0788305i
$937$	25.7523	−	44.6044i	0.841292	−	1.45716i	−0.0475106	−	0.998871i	$-0.515129\pi$
$937$	25.7523	−	44.6044i	0.841292	−	1.45716i	0.888803	−	0.458290i	$-0.151538\pi$
$938$	45.7510	+	26.4144i	1.49382	+	0.862460i
$939$	−8.24904	+	21.5461i	−0.269197	+	0.703129i
$940$	17.2024	−	9.93179i	0.561079	−	0.323939i
$941$	21.6200	+	37.4470i	0.704793	+	1.22074i	0.966766	+	0.255662i	$0.0822935\pi$
$941$	21.6200	+	37.4470i	0.704793	+	1.22074i	−0.261973	+	0.965075i	$0.584373\pi$
$942$	12.8512	−	2.04701i	0.418715	−	0.0666952i
$943$	−78.8227	−	45.5083i	−2.56682	−	1.48195i
$944$	−0.483876	+	0.279366i	−0.0157488	+	0.00909259i
$945$	−1.34770	+	27.0813i	−0.0438406	+	0.880955i
$946$	2.13443	−	3.69695i	0.0693964	−	0.120198i
$947$			6.24672i			0.202991i	0.994836	+	0.101495i	$0.0323627\pi$
$947$			6.24672i			0.202991i	−0.994836	+	0.101495i	$0.967637\pi$
$948$	8.81704	+	10.8686i	0.286364	+	0.352996i
$949$		−	6.24039i		−	0.202572i
$950$	0.395612	+	0.685219i	0.0128353	+	0.0222314i
$951$	−20.8253	−	7.97310i	−0.675307	−	0.258546i
$952$	10.9563	+	18.9769i	0.355096	+	0.615044i
$953$	10.2294	−	17.7179i	0.331363	−	0.573938i	−0.651416	−	0.758721i	$-0.725825\pi$
$953$	10.2294	−	17.7179i	0.331363	−	0.573938i	0.982779	+	0.184782i	$0.0591580\pi$
$954$	−3.95738	−	12.1071i	−0.128125	−	0.391983i
$955$	8.43792	+	14.6149i	0.273045	+	0.472927i
$956$	−11.6637	+	6.73406i	−0.377232	+	0.217795i
$957$	−1.06666	−	1.31485i	−0.0344802	−	0.0425031i
$958$	28.2153			0.911596
$959$	−67.7908			−2.18908
$960$	0.985941	−	2.57523i	0.0318211	−	0.0831151i
$961$	−8.41946	−	14.5829i	−0.271596	−	0.470417i
$962$	−0.276270	−	7.31713i	−0.00890732	−	0.235914i
$963$	4.07963	−	19.3604i	0.131464	−	0.623880i
$964$	−7.67592	−	4.43170i	−0.247225	−	0.142735i
$965$	7.42833	−	12.8663i	0.239127	−	0.414179i
$966$	8.02694	+	50.3935i	0.258263	+	1.62138i
$967$			42.9985i			1.38274i	0.722501	+	0.691370i	$0.242992\pi$
$967$			42.9985i			1.38274i	−0.722501	+	0.691370i	$0.757008\pi$
$968$	8.56078	+	4.94257i	0.275154	+	0.158860i
$969$	−3.47057	−	1.32873i	−0.111491	−	0.0426849i
$970$	16.1124	−	9.30252i	0.517339	−	0.298686i
$971$	22.9910	−	39.8215i	0.737815	−	1.27793i	−0.215662	−	0.976468i	$-0.569191\pi$
$971$	22.9910	−	39.8215i	0.737815	−	1.27793i	0.953477	−	0.301465i	$-0.0974758\pi$
$972$	3.96840	−	15.0749i	0.127286	−	0.483527i
$973$	17.9758			0.576278
$974$	26.8052			0.858893
$975$	−1.83792	+	4.80055i	−0.0588606	+	0.153741i
$976$	−4.69030	−	2.70794i	−0.150133	−	0.0866792i
$977$	42.1726	−	24.3483i	1.34922	−	0.778972i	0.361081	−	0.932535i	$-0.382408\pi$
$977$	42.1726	−	24.3483i	1.34922	−	0.778972i	0.988139	+	0.153562i	$0.0490746\pi$
$978$	1.41742	−	1.14987i	0.0453240	−	0.0367687i
$979$		−	3.99302i		−	0.127618i
$980$	−5.16105	+	2.97974i	−0.164864	+	0.0951842i
$981$	−13.3157	−	40.7377i	−0.425137	−	1.30066i
$982$	−7.23804	−	4.17889i	−0.230975	−	0.133354i
$983$	36.4072			1.16121			0.580605	−	0.814186i	$-0.302816\pi$
$983$	36.4072			1.16121			0.580605	+	0.814186i	$0.302816\pi$
$984$	−6.27088	+	16.3792i	−0.199908	+	0.522150i
$985$	11.4588	+	6.61576i	0.365109	+	0.210796i
$986$			6.18924i			0.197106i
$987$	66.1497	+	25.3258i	2.10557	+	0.806130i
$988$	0.193168	+	0.334576i	0.00614549	+	0.0106443i
$989$	−36.3402			−1.15555
$990$	−1.03983	+	4.93464i	−0.0330480	+	0.156833i
$991$		−	12.4744i		−	0.396263i	−0.980175	−	0.198132i	$-0.936513\pi$
$991$		−	12.4744i		−	0.396263i	0.980175	−	0.198132i	$-0.0634874\pi$
$992$	−1.88156	+	3.25896i	−0.0597396	+	0.103472i
$993$	4.84859	−	12.6643i	0.153865	−	0.401888i
$994$			5.30835i			0.168371i
$995$	−8.51938			−0.270082
$996$	20.1630	+	7.71953i	0.638889	+	0.244603i
$997$		−	4.30710i		−	0.136407i	−0.997671	−	0.0682036i	$-0.978273\pi$
$997$		−	4.30710i		−	0.136407i	0.997671	−	0.0682036i	$-0.0217267\pi$
$998$	36.9379			1.16925
$999$	27.5599	−	15.4743i	0.871956	−	0.489585i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.k.a.175.18	✓	76
3.2	odd	2		1998.2.k.a.1063.27		76
9.2	odd	6		1998.2.t.a.397.26		76
9.7	even	3		666.2.t.a.619.9	yes	76
37.11	even	6		666.2.t.a.85.9	yes	76
111.11	odd	6		1998.2.t.a.307.26		76
333.11	odd	6		1998.2.k.a.1639.12		76
333.196	even	6	inner	666.2.k.a.529.37	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.18	✓	76	1.1	even	1	trivial
666.2.k.a.529.37	yes	76	333.196	even	6	inner
666.2.t.a.85.9	yes	76	37.11	even	6
666.2.t.a.619.9	yes	76	9.7	even	3
1998.2.k.a.1063.27		76	3.2	odd	2
1998.2.k.a.1639.12		76	333.11	odd	6
1998.2.t.a.307.26		76	111.11	odd	6
1998.2.t.a.397.26		76	9.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.61755 + 0.619290i) q^{3} -1.00000 q^{4} +1.59205i q^{5} +(0.619290 - 1.61755i) q^{6} +(1.63885 - 2.83857i) q^{7} +1.00000i q^{8} +(2.23296 + 2.00347i) q^{9} +1.59205 q^{10} +(0.527937 + 0.914413i) q^{11} +(-1.61755 - 0.619290i) q^{12} +1.20379i q^{13} +(-2.83857 - 1.63885i) q^{14} +(-0.985941 + 2.57523i) q^{15} +1.00000 q^{16} +(5.78971 + 3.34269i) q^{17} +(2.00347 - 2.23296i) q^{18} +(-0.277937 + 0.160467i) q^{19} -1.59205i q^{20} +(4.40882 - 3.57661i) q^{21} +(0.914413 - 0.527937i) q^{22} +(-7.78426 - 4.49424i) q^{23} +(-0.619290 + 1.61755i) q^{24} +2.46538 q^{25} +1.20379 q^{26} +(2.37120 + 4.62357i) q^{27} +(-1.63885 + 2.83857i) q^{28} +(-0.801755 + 0.462894i) q^{29} +(2.57523 + 0.985941i) q^{30} +(-3.25896 - 1.88156i) q^{31} -1.00000i q^{32} +(0.287678 + 1.80606i) q^{33} +(3.34269 - 5.78971i) q^{34} +(4.51914 + 2.60913i) q^{35} +(-2.23296 - 2.00347i) q^{36} +(-0.229501 - 6.07843i) q^{37} +(0.160467 + 0.277937i) q^{38} +(-0.745493 + 1.94719i) q^{39} -1.59205 q^{40} +10.1259 q^{41} +(-3.57661 - 4.40882i) q^{42} +(3.50132 - 2.02149i) q^{43} +(-0.527937 - 0.914413i) q^{44} +(-3.18963 + 3.55498i) q^{45} +(-4.49424 + 7.78426i) q^{46} +(6.23837 + 10.8052i) q^{47} +(1.61755 + 0.619290i) q^{48} +(-1.87163 - 3.24177i) q^{49} -2.46538i q^{50} +(7.29507 + 8.99249i) q^{51} -1.20379i q^{52} +(2.12291 - 3.67699i) q^{53} +(4.62357 - 2.37120i) q^{54} +(-1.45579 + 0.840502i) q^{55} +(2.83857 + 1.63885i) q^{56} +(-0.548953 + 0.0874402i) q^{57} +(0.462894 + 0.801755i) q^{58} +(-0.483876 + 0.279366i) q^{59} +(0.985941 - 2.57523i) q^{60} +(-4.69030 - 2.70794i) q^{61} +(-1.88156 + 3.25896i) q^{62} +(9.34646 - 3.05502i) q^{63} -1.00000 q^{64} -1.91649 q^{65} +(1.80606 - 0.287678i) q^{66} -16.1177 q^{67} +(-5.78971 - 3.34269i) q^{68} +(-9.80821 - 12.0904i) q^{69} +(2.60913 - 4.51914i) q^{70} +(-0.809770 - 1.40256i) q^{71} +(-2.00347 + 2.23296i) q^{72} -5.18397 q^{73} +(-6.07843 + 0.229501i) q^{74} +(3.98788 + 1.52678i) q^{75} +(0.277937 - 0.160467i) q^{76} +3.46083 q^{77} +(1.94719 + 0.745493i) q^{78} +(-6.99762 - 4.04008i) q^{79} +1.59205i q^{80} +(0.972209 + 8.94734i) q^{81} -10.1259i q^{82} -12.4651 q^{83} +(-4.40882 + 3.57661i) q^{84} +(-5.32173 + 9.21751i) q^{85} +(-2.02149 - 3.50132i) q^{86} +(-1.58355 + 0.252236i) q^{87} +(-0.914413 + 0.527937i) q^{88} +(-3.27507 - 1.89086i) q^{89} +(3.55498 + 3.18963i) q^{90} +(3.41702 + 1.97282i) q^{91} +(7.78426 + 4.49424i) q^{92} +(-4.10631 - 5.06177i) q^{93} +(10.8052 - 6.23837i) q^{94} +(-0.255471 - 0.442489i) q^{95} +(0.619290 - 1.61755i) q^{96} +(10.1206 - 5.84311i) q^{97} +(-3.24177 + 1.87163i) q^{98} +(-0.653139 + 3.09955i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) \) 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more