LMFDB - Embedded newform 546.2.q.j.251.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(251,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("546.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.q (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			251.2
Character	$\chi$	$=$	546.251
Dual form			546.2.q.j.335.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.63915 + 0.559644i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.94869i q^{5} +(-0.334907 + 1.69936i) q^{6} +(-1.08009 - 2.41524i) q^{7} -1.00000 q^{8} +(2.37360 - 1.83468i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.63915 + 0.559644i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.94869i q^{5} +(-0.334907 + 1.69936i) q^{6} +(-1.08009 - 2.41524i) q^{7} -1.00000 q^{8} +(2.37360 - 1.83468i) q^{9} +(-2.55364 - 1.47434i) q^{10} +(-1.48708 + 2.57570i) q^{11} +(1.30424 + 1.13972i) q^{12} +(-2.33135 + 2.75042i) q^{13} +(-2.63171 - 0.272231i) q^{14} +(1.65022 + 4.83333i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.27441 + 3.93940i) q^{17} +(-0.402078 - 2.97293i) q^{18} +(-3.30152 - 5.71840i) q^{19} +(-2.55364 + 1.47434i) q^{20} +(3.12211 + 3.35446i) q^{21} +(1.48708 + 2.57570i) q^{22} +(-1.82779 - 1.05528i) q^{23} +(1.63915 - 0.559644i) q^{24} -3.69475 q^{25} +(1.21626 + 3.39422i) q^{26} +(-2.86390 + 4.33567i) q^{27} +(-1.55161 + 2.14301i) q^{28} +(0.262375 + 0.151482i) q^{29} +(5.01089 + 0.987535i) q^{30} -7.31345 q^{31} +(0.500000 + 0.866025i) q^{32} +(0.996066 - 5.05418i) q^{33} +4.54883 q^{34} +(-7.12179 + 3.18486i) q^{35} +(-2.77567 - 1.13826i) q^{36} +(-5.19513 - 2.99941i) q^{37} -6.60304 q^{38} +(2.28216 - 5.81307i) q^{39} +2.94869i q^{40} +(4.22640 + 2.44011i) q^{41} +(4.46611 - 1.02659i) q^{42} +(-4.53030 - 7.84671i) q^{43} +2.97416 q^{44} +(-5.40989 - 6.99899i) q^{45} +(-1.82779 + 1.05528i) q^{46} +7.77801i q^{47} +(0.334907 - 1.69936i) q^{48} +(-4.66679 + 5.21738i) q^{49} +(-1.84738 + 3.19975i) q^{50} +(-5.93276 - 5.18439i) q^{51} +(3.54761 + 0.643796i) q^{52} -1.95097i q^{53} +(2.32285 + 4.64805i) q^{54} +(7.59492 + 4.38493i) q^{55} +(1.08009 + 2.41524i) q^{56} +(8.61195 + 7.52562i) q^{57} +(0.262375 - 0.151482i) q^{58} +(5.73006 - 3.30825i) q^{59} +(3.36068 - 3.84579i) q^{60} +(6.23017 - 3.59699i) q^{61} +(-3.65672 + 6.33363i) q^{62} +(-6.99490 - 3.75119i) q^{63} +1.00000 q^{64} +(8.11013 + 6.87441i) q^{65} +(-3.87901 - 3.38971i) q^{66} +(-6.91165 - 3.99044i) q^{67} +(2.27441 - 3.93940i) q^{68} +(3.58659 + 0.706838i) q^{69} +(-0.802725 + 7.76008i) q^{70} +(-4.69513 - 8.13220i) q^{71} +(-2.37360 + 1.83468i) q^{72} +9.10184 q^{73} +(-5.19513 + 2.99941i) q^{74} +(6.05624 - 2.06775i) q^{75} +(-3.30152 + 5.71840i) q^{76} +(7.82712 + 0.809659i) q^{77} +(-3.89318 - 4.88294i) q^{78} +11.3067 q^{79} +(2.55364 + 1.47434i) q^{80} +(2.26792 - 8.70956i) q^{81} +(4.22640 - 2.44011i) q^{82} -5.68231i q^{83} +(1.34400 - 4.38106i) q^{84} +(11.6161 - 6.70653i) q^{85} -9.06060 q^{86} +(-0.514846 - 0.101465i) q^{87} +(1.48708 - 2.57570i) q^{88} +(-12.8884 - 7.44115i) q^{89} +(-8.76625 + 1.18560i) q^{90} +(9.16101 + 2.66005i) q^{91} +2.11055i q^{92} +(11.9878 - 4.09293i) q^{93} +(6.73596 + 3.88901i) q^{94} +(-16.8618 + 9.73515i) q^{95} +(-1.30424 - 1.13972i) q^{96} +(-5.31270 - 9.20186i) q^{97} +(2.18499 + 6.65025i) q^{98} +(1.19584 + 8.84197i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9}+O(q^{10}) $ 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9	$ 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9} + 12 q^{15} - 12 q^{16} - 6 q^{18} + 12 q^{21} - 36 q^{23} - 12 q^{25} + 18 q^{28} + 6 q^{30} + 12 q^{32} - 36 q^{35} - 12 q^{36} + 36 q^{37} + 12 q^{39} - 12 q^{42} - 42 q^{43} - 36 q^{46} - 6 q^{50} + 12 q^{51} + 18 q^{56} - 36 q^{57} - 6 q^{60} + 66 q^{63} + 24 q^{64} + 66 q^{65} - 54 q^{67} + 48 q^{71} - 6 q^{72} + 36 q^{74} - 12 q^{78} - 48 q^{79} - 6 q^{81} - 24 q^{84} - 84 q^{86} + 36 q^{91} + 54 q^{93} - 36 q^{95} + 36 q^{99}+O(q^{100}) $ 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9 + 12 * q^15 - 12 * q^16 - 6 * q^18 + 12 * q^21 - 36 * q^23 - 12 * q^25 + 18 * q^28 + 6 * q^30 + 12 * q^32 - 36 * q^35 - 12 * q^36 + 36 * q^37 + 12 * q^39 - 12 * q^42 - 42 * q^43 - 36 * q^46 - 6 * q^50 + 12 * q^51 + 18 * q^56 - 36 * q^57 - 6 * q^60 + 66 * q^63 + 24 * q^64 + 66 * q^65 - 54 * q^67 + 48 * q^71 - 6 * q^72 + 36 * q^74 - 12 * q^78 - 48 * q^79 - 6 * q^81 - 24 * q^84 - 84 * q^86 + 36 * q^91 + 54 * q^93 - 36 * q^95 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.63915	+	0.559644i	−0.946361	+	0.323111i
$3$	−1.63915	+	0.559644i	−0.946361	+	0.323111i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		−	2.94869i		−	1.31869i	−0.751839	−	0.659346i	$-0.770833\pi$
$5$		−	2.94869i		−	1.31869i	0.751839	−	0.659346i	$-0.229167\pi$
$6$	−0.334907	+	1.69936i	−0.136725	+	0.693762i
$7$	−1.08009	−	2.41524i	−0.408238	−	0.912876i
$7$	−1.08009	−	2.41524i	−0.408238	−	0.912876i
$8$	−1.00000			−0.353553
$9$	2.37360	−	1.83468i	0.791199	−	0.611559i
$10$	−2.55364	−	1.47434i	−0.807531	−	0.466228i
$11$	−1.48708	+	2.57570i	−0.448371	+	0.776602i	−0.998280	−	0.0586229i	$-0.981329\pi$
$11$	−1.48708	+	2.57570i	−0.448371	+	0.776602i	0.549909	+	0.835225i	$0.314662\pi$
$12$	1.30424	+	1.13972i	0.376501	+	0.329009i
$13$	−2.33135	+	2.75042i	−0.646600	+	0.762830i
$13$	−2.33135	+	2.75042i	−0.646600	+	0.762830i
$14$	−2.63171	−	0.272231i	−0.703354	−	0.0727569i
$15$	1.65022	+	4.83333i	0.426084	+	1.24796i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.27441	+	3.93940i	0.551626	+	0.955445i	0.998157	+	0.0606766i	$0.0193258\pi$
$17$	2.27441	+	3.93940i	0.551626	+	0.955445i	−0.446531	+	0.894768i	$0.647341\pi$
$18$	−0.402078	−	2.97293i	−0.0947707	−	0.700727i
$19$	−3.30152	−	5.71840i	−0.757421	−	1.31189i	−0.944162	−	0.329483i	$-0.893126\pi$
$19$	−3.30152	−	5.71840i	−0.757421	−	1.31189i	0.186741	−	0.982409i	$-0.440208\pi$
$20$	−2.55364	+	1.47434i	−0.571011	+	0.329673i
$21$	3.12211	+	3.35446i	0.681300	+	0.732004i
$22$	1.48708	+	2.57570i	0.317046	+	0.549140i
$23$	−1.82779	−	1.05528i	−0.381121	−	0.220040i	0.297185	−	0.954820i	$-0.403952\pi$
$23$	−1.82779	−	1.05528i	−0.381121	−	0.220040i	−0.678306	+	0.734780i	$0.737285\pi$
$24$	1.63915	−	0.559644i	0.334589	−	0.114237i
$25$	−3.69475			−0.738950
$26$	1.21626	+	3.39422i	0.238528	+	0.665661i
$27$	−2.86390	+	4.33567i	−0.551159	+	0.834400i
$28$	−1.55161	+	2.14301i	−0.293227	+	0.404991i
$29$	0.262375	+	0.151482i	0.0487218	+	0.0281295i	0.524163	−	0.851618i	$-0.324378\pi$
$29$	0.262375	+	0.151482i	0.0487218	+	0.0281295i	−0.475441	+	0.879747i	$0.657712\pi$
$30$	5.01089	+	0.987535i	0.914859	+	0.180298i
$31$	−7.31345			−1.31353			−0.656767	−	0.754094i	$-0.728076\pi$
$31$	−7.31345			−1.31353			−0.656767	+	0.754094i	$0.728076\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	0.996066	−	5.05418i	0.173393	−	0.879819i
$34$	4.54883			0.780117
$35$	−7.12179	+	3.18486i	−1.20380	+	0.538340i
$36$	−2.77567	−	1.13826i	−0.462612	−	0.189709i
$37$	−5.19513	−	2.99941i	−0.854074	−	0.493100i	0.00794922	−	0.999968i	$-0.497470\pi$
$37$	−5.19513	−	2.99941i	−0.854074	−	0.493100i	−0.862023	+	0.506868i	$0.830803\pi$
$38$	−6.60304			−1.07116
$39$	2.28216	−	5.81307i	0.365438	−	0.930836i
$40$			2.94869i			0.466228i
$41$	4.22640	+	2.44011i	0.660053	+	0.381082i	0.792297	−	0.610135i	$-0.208885\pi$
$41$	4.22640	+	2.44011i	0.660053	+	0.381082i	−0.132244	+	0.991217i	$0.542218\pi$
$42$	4.46611	−	1.02659i	0.689135	−	0.158407i
$43$	−4.53030	−	7.84671i	−0.690864	−	1.19661i	−0.971555	−	0.236813i	$-0.923897\pi$
$43$	−4.53030	−	7.84671i	−0.690864	−	1.19661i	0.280691	−	0.959798i	$-0.409436\pi$
$44$	2.97416			0.448371
$45$	−5.40989	−	6.99899i	−0.806458	−	1.04335i
$46$	−1.82779	+	1.05528i	−0.269493	+	0.155592i
$47$			7.77801i			1.13454i	0.823532	+	0.567270i	$0.192000\pi$
$47$			7.77801i			1.13454i	−0.823532	+	0.567270i	$0.808000\pi$
$48$	0.334907	−	1.69936i	0.0483396	−	0.245282i
$49$	−4.66679	+	5.21738i	−0.666684	+	0.745340i
$50$	−1.84738	+	3.19975i	−0.261258	+	0.452513i
$51$	−5.93276	−	5.18439i	−0.830752	−	0.725959i
$52$	3.54761	+	0.643796i	0.491965	+	0.0892784i
$53$		−	1.95097i		−	0.267986i	−0.990982	−	0.133993i	$-0.957220\pi$
$53$		−	1.95097i		−	0.267986i	0.990982	−	0.133993i	$-0.0427800\pi$
$54$	2.32285	+	4.64805i	0.316100	+	0.632520i
$55$	7.59492	+	4.38493i	1.02410	+	0.591264i
$56$	1.08009	+	2.41524i	0.144334	+	0.322750i
$57$	8.61195	+	7.52562i	1.14068	+	0.996793i
$58$	0.262375	−	0.151482i	0.0344515	−	0.0198906i
$59$	5.73006	−	3.30825i	0.745990	−	0.430698i	−0.0782530	−	0.996934i	$-0.524934\pi$
$59$	5.73006	−	3.30825i	0.745990	−	0.430698i	0.824243	+	0.566236i	$0.191601\pi$
$60$	3.36068	−	3.84579i	0.433861	−	0.496490i
$61$	6.23017	−	3.59699i	0.797692	−	0.460548i	−0.0449714	−	0.998988i	$-0.514320\pi$
$61$	6.23017	−	3.59699i	0.797692	−	0.460548i	0.842664	+	0.538441i	$0.180986\pi$
$62$	−3.65672	+	6.33363i	−0.464404	+	0.804372i
$63$	−6.99490	−	3.75119i	−0.881274	−	0.472605i
$64$	1.00000			0.125000
$65$	8.11013	+	6.87441i	1.00594	+	0.852666i
$66$	−3.87901	−	3.38971i	−0.477473	−	0.417244i
$67$	−6.91165	−	3.99044i	−0.844392	−	0.487510i	0.0143627	−	0.999897i	$-0.495428\pi$
$67$	−6.91165	−	3.99044i	−0.844392	−	0.487510i	−0.858755	+	0.512387i	$0.828761\pi$
$68$	2.27441	−	3.93940i	0.275813	−	0.477722i
$69$	3.58659	+	0.706838i	0.431775	+	0.0850932i
$70$	−0.802725	+	7.76008i	−0.0959440	+	0.927507i
$71$	−4.69513	−	8.13220i	−0.557209	−	0.965115i	−0.997728	−	0.0673716i	$-0.978539\pi$
$71$	−4.69513	−	8.13220i	−0.557209	−	0.965115i	0.440518	−	0.897744i	$-0.354795\pi$
$72$	−2.37360	+	1.83468i	−0.279731	+	0.216219i
$73$	9.10184			1.06529			0.532645	−	0.846339i	$-0.321198\pi$
$73$	9.10184			1.06529			0.532645	+	0.846339i	$0.321198\pi$
$74$	−5.19513	+	2.99941i	−0.603922	+	0.348674i
$75$	6.05624	−	2.06775i	0.699314	−	0.238763i
$76$	−3.30152	+	5.71840i	−0.378711	+	0.655946i
$77$	7.82712	+	0.809659i	0.891983	+	0.0922693i
$78$	−3.89318	−	4.88294i	−0.440816	−	0.552884i
$79$	11.3067			1.27210			0.636051	−	0.771647i	$-0.280567\pi$
$79$	11.3067			1.27210			0.636051	+	0.771647i	$0.280567\pi$
$80$	2.55364	+	1.47434i	0.285505	+	0.164837i
$81$	2.26792	−	8.70956i	0.251992	−	0.967729i
$82$	4.22640	−	2.44011i	0.466728	−	0.269466i
$83$		−	5.68231i		−	0.623714i	−0.950129	−	0.311857i	$-0.899049\pi$
$83$		−	5.68231i		−	0.623714i	0.950129	−	0.311857i	$-0.100951\pi$
$84$	1.34400	−	4.38106i	0.146642	−	0.478013i
$85$	11.6161	−	6.70653i	1.25994	−	0.727425i
$86$	−9.06060			−0.977029
$87$	−0.514846	−	0.101465i	−0.0551973	−	0.0108782i
$88$	1.48708	−	2.57570i	0.158523	−	0.274570i
$89$	−12.8884	−	7.44115i	−1.36617	−	0.788760i	−0.375736	−	0.926727i	$-0.622610\pi$
$89$	−12.8884	−	7.44115i	−1.36617	−	0.788760i	−0.990437	+	0.137967i	$0.955943\pi$
$90$	−8.76625	+	1.18560i	−0.924044	+	0.124973i
$91$	9.16101	+	2.66005i	0.960335	+	0.278849i
$92$			2.11055i			0.220040i
$93$	11.9878	−	4.09293i	1.24308	−	0.424417i
$94$	6.73596	+	3.88901i	0.694761	+	0.401120i
$95$	−16.8618	+	9.73515i	−1.72998	+	0.998806i
$96$	−1.30424	−	1.13972i	−0.133113	−	0.116322i
$97$	−5.31270	−	9.20186i	−0.539423	−	0.934307i	−0.998935	−	0.0461360i	$-0.985309\pi$
$97$	−5.31270	−	9.20186i	−0.539423	−	0.934307i	0.459513	−	0.888171i	$-0.348024\pi$
$98$	2.18499	+	6.65025i	0.220717	+	0.671777i
$99$	1.19584	+	8.84197i	0.120187	+	0.888652i
$100$	1.84738	+	3.19975i	0.184738	+	0.319975i
$101$	5.54280	−	9.60041i	0.551529	−	0.955276i	−0.446636	−	0.894716i	$-0.647378\pi$
$101$	5.54280	−	9.60041i	0.551529	−	0.955276i	0.998165	−	0.0605602i	$-0.0192887\pi$
$102$	−7.45619	+	2.54572i	−0.738273	+	0.252064i
$103$			11.2150i			1.10505i	0.833498	+	0.552523i	$0.186335\pi$
$103$			11.2150i			1.10505i	−0.833498	+	0.552523i	$0.813665\pi$
$104$	2.33135	−	2.75042i	0.228607	−	0.269701i
$105$	9.89127	−	9.20612i	0.965289	−	0.898425i
$106$	−1.68959	−	0.975484i	−0.164107	−	0.0947474i
$107$	12.3286	+	7.11791i	1.19185	+	0.688114i	0.958726	−	0.284333i	$-0.0917722\pi$
$107$	12.3286	+	7.11791i	1.19185	+	0.688114i	0.233123	+	0.972447i	$0.425106\pi$
$108$	5.18675	+	0.312379i	0.499096	+	0.0300586i
$109$		−	3.19314i		−	0.305847i	−0.988238	−	0.152924i	$-0.951131\pi$
$109$		−	3.19314i		−	0.305847i	0.988238	−	0.152924i	$-0.0488689\pi$
$110$	7.59492	−	4.38493i	0.724147	−	0.418087i
$111$	10.1942	+	2.00905i	0.967589	+	0.190690i
$112$	2.63171	+	0.272231i	0.248673	+	0.0257235i
$113$	−10.1785	+	5.87655i	−0.957511	+	0.552819i	−0.895406	−	0.445250i	$-0.853115\pi$
$113$	−10.1785	+	5.87655i	−0.957511	+	0.552819i	−0.0621050	+	0.998070i	$0.519781\pi$
$114$	10.8234	−	3.69536i	1.01370	−	0.346102i
$115$	−3.11168	+	5.38958i	−0.290165	+	0.502581i
$116$		−	0.302964i		−	0.0281295i
$117$	−0.487547	+	10.8057i	−0.0450737	+	0.998984i
$118$		−	6.61650i		−	0.609099i
$119$	7.05802	−	9.74818i	0.647008	−	0.893615i
$120$	−1.65022	−	4.83333i	−0.150643	−	0.441220i
$121$	1.07719	+	1.86575i	0.0979265	+	0.169614i
$122$		−	7.19399i		−	0.651313i
$123$	−8.29328	−	1.63442i	−0.747780	−	0.147371i
$124$	3.65672	+	6.33363i	0.328383	+	0.568777i
$125$		−	3.84877i		−	0.344244i
$126$	−6.74607	+	4.18217i	−0.600988	+	0.372577i
$127$	4.70251	−	8.14498i	0.417280	−	0.722750i	−0.578385	−	0.815764i	$-0.696317\pi$
$127$	4.70251	−	8.14498i	0.417280	−	0.722750i	0.995665	+	0.0930138i	$0.0296501\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	11.8172	+	10.3265i	1.04044	+	0.909201i
$130$	10.0085	−	3.58637i	0.877802	−	0.314546i
$131$	−16.3543			−1.42888			−0.714442	−	0.699694i	$-0.753320\pi$
$131$	−16.3543			−1.42888			−0.714442	+	0.699694i	$0.753320\pi$
$132$	−4.87508	+	1.66447i	−0.424321	+	0.144874i
$133$	−10.2454	+	14.1504i	−0.888387	+	1.22699i
$134$	−6.91165	+	3.99044i	−0.597075	+	0.344722i
$135$	12.7845	+	8.44476i	1.10032	+	0.726809i
$136$	−2.27441	−	3.93940i	−0.195029	−	0.337801i
$137$	−2.34996	−	4.07025i	−0.200771	−	0.347745i	0.748006	−	0.663692i	$-0.231011\pi$
$137$	−2.34996	−	4.07025i	−0.200771	−	0.347745i	−0.948777	+	0.315946i	$0.897678\pi$
$138$	2.40544	−	2.75266i	0.204764	−	0.234322i
$139$	−0.386606	+	0.223207i	−0.0327915	+	0.0189322i	−0.516306	−	0.856404i	$-0.672693\pi$
$139$	−0.386606	+	0.223207i	−0.0327915	+	0.0189322i	0.483515	+	0.875336i	$0.339360\pi$
$140$	6.31907	+	4.57522i	0.534059	+	0.386677i
$141$	−4.35292	−	12.7493i	−0.366582	−	1.07368i
$142$	−9.39026			−0.788013
$143$	−3.61735	−	10.0949i	−0.302498	−	0.844181i
$144$	0.402078	+	2.97293i	0.0335065	+	0.247744i
$145$	0.446673	−	0.773661i	0.0370942	−	0.0642490i
$146$	4.55092	−	7.88243i	0.376637	−	0.652354i
$147$	4.72967	−	11.1638i	0.390097	−	0.920774i
$148$			5.99882i			0.493100i
$149$	−6.44975	−	11.1713i	−0.528384	−	0.915189i	−0.999452	−	0.0330918i	$-0.989465\pi$
$149$	−6.44975	−	11.1713i	−0.528384	−	0.915189i	0.471068	−	0.882097i	$-0.343869\pi$
$150$	1.23740	−	6.27873i	0.101033	−	0.512656i
$151$		−	10.5573i		−	0.859142i	−0.903033	−	0.429571i	$-0.858665\pi$
$151$		−	10.5573i		−	0.859142i	0.903033	−	0.429571i	$-0.141335\pi$
$152$	3.30152	+	5.71840i	0.267789	+	0.463824i
$153$	12.6261	+	5.17773i	1.02076	+	0.418595i
$154$	4.61474	−	6.37365i	0.371867	−	0.513604i
$155$			21.5651i			1.73215i
$156$	−6.17534	+	0.930123i	−0.494423	+	0.0744695i
$157$			5.14640i			0.410727i	0.978686	+	0.205364i	$0.0658377\pi$
$157$			5.14640i			0.410727i	−0.978686	+	0.205364i	$0.934162\pi$
$158$	5.65335	−	9.79189i	0.449756	−	0.779001i
$159$	1.09185	+	3.19792i	0.0865891	+	0.253612i
$160$	2.55364	−	1.47434i	0.201883	−	0.116557i
$161$	−0.574558	+	5.55435i	−0.0452815	+	0.437744i
$162$	−6.40874	−	6.31886i	−0.503518	−	0.496457i
$163$	−19.6585	+	11.3498i	−1.53977	+	0.888989i	−0.540922	+	0.841073i	$0.681925\pi$
$163$	−19.6585	+	11.3498i	−1.53977	+	0.888989i	−0.998851	+	0.0479160i	$0.984742\pi$
$164$		−	4.88023i		−	0.381082i
$165$	−14.9032	−	2.93709i	−1.16021	−	0.228652i
$166$	−4.92102	−	2.84115i	−0.381946	−	0.220516i
$167$	15.7303	+	9.08191i	1.21725	+	0.702780i	0.964329	−	0.264707i	$-0.0852753\pi$
$167$	15.7303	+	9.08191i	1.21725	+	0.702780i	0.252921	+	0.967487i	$0.418609\pi$
$168$	−3.12211	−	3.35446i	−0.240876	−	0.258803i
$169$	−2.12963	−	12.8244i	−0.163818	−	0.986491i
$170$		−	13.4131i		−	1.02873i
$171$	−18.3279	−	7.51596i	−1.40157	−	0.574760i
$172$	−4.53030	+	7.84671i	−0.345432	+	0.598306i
$173$	−4.92782	−	8.53524i	−0.374656	−	0.648922i	0.615620	−	0.788043i	$-0.288906\pi$
$173$	−4.92782	−	8.53524i	−0.374656	−	0.648922i	−0.990275	+	0.139121i	$0.955572\pi$
$174$	−0.345294	+	0.395138i	−0.0261767	+	0.0299553i
$175$	3.99068	+	8.92372i	0.301667	+	0.674570i
$176$	−1.48708	−	2.57570i	−0.112093	−	0.194150i
$177$	−7.54096	+	8.62950i	−0.566813	+	0.648633i
$178$	−12.8884	+	7.44115i	−0.966030	+	0.557738i
$179$	−5.55478	−	3.20706i	−0.415184	−	0.239707i	0.277831	−	0.960630i	$-0.410385\pi$
$179$	−5.55478	−	3.20706i	−0.415184	−	0.239707i	−0.693015	+	0.720923i	$0.743718\pi$
$180$	−3.35636	+	8.18459i	−0.250168	+	0.610044i
$181$		−	9.31777i		−	0.692584i	−0.938127	−	0.346292i	$-0.887441\pi$
$181$		−	9.31777i		−	0.692584i	0.938127	−	0.346292i	$-0.112559\pi$
$182$	6.88418	−	6.60364i	0.510289	−	0.489494i
$183$	−8.19913	+	9.38268i	−0.606097	+	0.693587i
$184$	1.82779	+	1.05528i	0.134746	+	0.0777959i
$185$	−8.84432	+	15.3188i	−0.650247	+	1.12626i
$186$	2.44932	−	12.4282i	0.179593	−	0.911280i
$187$	−13.5289			−0.989333
$188$	6.73596	−	3.88901i	0.491270	−	0.283635i
$189$	13.5650	+	2.23409i	0.986708	+	0.162506i
$190$			19.4703i			1.41252i
$191$	19.2376	−	11.1068i	1.39198	−	0.803662i	0.398448	−	0.917191i	$-0.369549\pi$
$191$	19.2376	−	11.1068i	1.39198	−	0.803662i	0.993535	+	0.113529i	$0.0362154\pi$
$192$	−1.63915	+	0.559644i	−0.118295	+	0.0403888i
$193$	−14.0769	−	8.12729i	−1.01328	−	0.585015i	−0.101127	−	0.994874i	$-0.532245\pi$
$193$	−14.0769	−	8.12729i	−1.01328	−	0.585015i	−0.912149	+	0.409858i	$0.865578\pi$
$194$	−10.6254			−0.762859
$195$	−17.1409	−	6.72938i	−1.22749	−	0.481901i
$196$	6.85178	+	1.43287i	0.489413	+	0.102348i
$197$	−1.76094	+	3.05003i	−0.125462	+	0.217306i	−0.921913	−	0.387396i	$-0.873375\pi$
$197$	−1.76094	+	3.05003i	−0.125462	+	0.217306i	0.796452	+	0.604702i	$0.206708\pi$
$198$	8.25530	+	3.38536i	0.586678	+	0.240587i
$199$	7.32335	−	4.22814i	0.519139	−	0.299725i	−0.217443	−	0.976073i	$-0.569772\pi$
$199$	7.32335	−	4.22814i	0.519139	−	0.299725i	0.736582	+	0.676348i	$0.236438\pi$
$200$	3.69475			0.261258
$201$	13.5624	+	2.67285i	0.956619	+	0.188528i
$202$	−5.54280	−	9.60041i	−0.389990	−	0.675482i
$203$	0.0824764	−	0.797313i	0.00578871	−	0.0559604i
$204$	−1.52343	+	7.73011i	−0.106662	+	0.541216i
$205$	7.19513	−	12.4623i	0.502530	−	0.870407i
$206$	9.71247	+	5.60750i	0.676700	+	0.390693i
$207$	−6.27453	+	0.848606i	−0.436110	+	0.0589822i
$208$	−1.21626	−	3.39422i	−0.0843325	−	0.235347i
$209$	19.6385			1.35842
$210$	−3.02710	−	13.1691i	−0.208890	−	0.908757i
$211$	1.64519	−	2.84956i	0.113260	−	0.196172i	−0.803823	−	0.594869i	$-0.797204\pi$
$211$	1.64519	−	2.84956i	0.113260	−	0.196172i	0.917083	+	0.398697i	$0.130537\pi$
$212$	−1.68959	+	0.975484i	−0.116041	+	0.0669965i
$213$	12.2471	+	10.7023i	0.839160	+	0.733307i
$214$	12.3286	−	7.11791i	0.842764	−	0.486570i
$215$	−23.1375	+	13.3584i	−1.57796	+	0.911037i
$216$	2.86390	−	4.33567i	0.194864	−	0.295005i
$217$	7.89922	+	17.6637i	0.536234	+	1.19909i
$218$	−2.76534	−	1.59657i	−0.187293	−	0.108133i
$219$	−14.9192	+	5.09379i	−1.00815	+	0.344207i
$220$		−	8.76986i		−	0.591264i
$221$	−16.1375	−	2.92852i	−1.08552	−	0.196993i
$222$	6.83697	−	7.82389i	0.458868	−	0.525105i
$223$	11.6151	−	20.1179i	0.777804	−	1.34720i	−0.155401	−	0.987852i	$-0.549667\pi$
$223$	11.6151	−	20.1179i	0.777804	−	1.34720i	0.933205	−	0.359345i	$-0.117000\pi$
$224$	1.55161	−	2.14301i	0.103672	−	0.143186i
$225$	−8.76985	+	6.77867i	−0.584657	+	0.451912i
$226$			11.7531i			0.781805i
$227$	−16.2928	+	9.40665i	−1.08139	+	0.624341i	−0.931271	−	0.364326i	$-0.881299\pi$
$227$	−16.2928	+	9.40665i	−1.08139	+	0.624341i	−0.150120	+	0.988668i	$0.547966\pi$
$228$	2.21140	−	11.2210i	0.146454	−	0.743127i
$229$	13.0413			0.861790			0.430895	−	0.902402i	$-0.358198\pi$
$229$	13.0413			0.861790			0.430895	+	0.902402i	$0.358198\pi$
$230$	3.11168	+	5.38958i	0.205178	+	0.355378i
$231$	−13.2829	+	3.05325i	−0.873951	+	0.200889i
$232$	−0.262375	−	0.151482i	−0.0172257	−	0.00994529i
$233$			15.0853i			0.988273i	0.869384	+	0.494137i	$0.164516\pi$
$233$			15.0853i			0.988273i	−0.869384	+	0.494137i	$0.835484\pi$
$234$	9.11420	+	5.82506i	0.595814	+	0.380796i
$235$	22.9349			1.49611
$236$	−5.73006	−	3.30825i	−0.372995	−	0.215349i
$237$	−18.5333	+	6.32773i	−1.20387	+	0.411030i
$238$	−4.91316	−	10.9865i	−0.318473	−	0.712150i
$239$	7.21221			0.466519			0.233260	−	0.972415i	$-0.425061\pi$
$239$	7.21221			0.466519			0.233260	+	0.972415i	$0.425061\pi$
$240$	−5.01089	−	0.987535i	−0.323452	−	0.0637451i
$241$	−1.89316	−	3.27906i	−0.121949	−	0.211223i	0.798587	−	0.601879i	$-0.205581\pi$
$241$	−1.89316	−	3.27906i	−0.121949	−	0.211223i	−0.920536	+	0.390657i	$0.872248\pi$
$242$	2.15438			0.138489
$243$	1.15680	+	15.5455i	0.0742087	+	0.997243i
$244$	−6.23017	−	3.59699i	−0.398846	−	0.230274i
$245$	15.3844	+	13.7609i	0.982875	+	0.879152i
$246$	−5.56209	+	6.36498i	−0.354626	+	0.405816i
$247$	23.4250	+	4.25101i	1.49050	+	0.270485i
$248$	7.31345			0.464404
$249$	3.18007	+	9.31413i	0.201529	+	0.590259i
$250$	−3.33313	−	1.92438i	−0.210806	−	0.121709i
$251$	−1.12841	−	1.95447i	−0.0712247	−	0.123365i	0.828214	−	0.560413i	$-0.189357\pi$
$251$	−1.12841	−	1.95447i	−0.0712247	−	0.123365i	−0.899438	+	0.437048i	$0.856024\pi$
$252$	0.248826	+	7.93335i	0.0156746	+	0.499754i
$253$	5.43614	−	3.13856i	0.341767	−	0.197319i
$254$	−4.70251	−	8.14498i	−0.295062	−	0.511062i
$255$	−15.2871	+	17.4938i	−0.957317	+	1.09551i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.72584	+	9.91745i	−0.357168	+	0.618634i	−0.987487	−	0.157703i	$-0.949591\pi$
$257$	−5.72584	+	9.91745i	−0.357168	+	0.618634i	0.630318	+	0.776337i	$0.282924\pi$
$258$	14.8516	−	5.07071i	0.924623	−	0.315689i
$259$	−1.63307	+	15.7871i	−0.101474	+	0.980966i
$260$	1.89835	−	10.4608i	0.117731	−	0.648750i
$261$	0.900692	−	0.121815i	0.0557515	−	0.00754018i
$262$	−8.17717	+	14.1633i	−0.505187	+	0.875010i
$263$	7.45900	+	4.30646i	0.459942	+	0.265547i	0.712020	−	0.702159i	$-0.247781\pi$
$263$	7.45900	+	4.30646i	0.459942	+	0.265547i	−0.252078	+	0.967707i	$0.581114\pi$
$264$	−0.996066	+	5.05418i	−0.0613036	+	0.311063i
$265$	−5.75279			−0.353391
$266$	7.13191	+	15.9480i	0.437286	+	0.977832i
$267$	25.2904	+	4.98418i	1.54775	+	0.305027i
$268$			7.98088i			0.487510i
$269$	0.400496	+	0.693680i	0.0244187	+	0.0422944i	0.877977	−	0.478704i	$-0.158893\pi$
$269$	0.400496	+	0.693680i	0.0244187	+	0.0422944i	−0.853558	+	0.520998i	$0.825560\pi$
$270$	13.7056	−	6.84935i	0.834099	−	0.416838i
$271$	−5.57461	+	9.65551i	−0.338634	+	0.586531i	−0.984176	−	0.177194i	$-0.943298\pi$
$271$	−5.57461	+	9.65551i	−0.338634	+	0.586531i	0.645542	+	0.763724i	$0.276631\pi$
$272$	−4.54883			−0.275813
$273$	−16.5049	+	0.766690i	−0.998923	+	0.0464022i
$274$	−4.69993			−0.283933
$275$	5.49439	−	9.51656i	0.331324	−	0.573870i
$276$	−1.18116	−	3.45950i	−0.0710973	−	0.208237i
$277$	−2.18140	−	3.77829i	−0.131068	−	0.227016i	0.793021	−	0.609195i	$-0.208507\pi$
$277$	−2.18140	−	3.77829i	−0.131068	−	0.227016i	−0.924088	+	0.382179i	$0.875174\pi$
$278$			0.446414i			0.0267741i
$279$	−17.3592	+	13.4178i	−1.03927	+	0.803303i
$280$	7.12179	−	3.18486i	0.425608	−	0.190332i
$281$	25.5114			1.52188			0.760940	−	0.648822i	$-0.224738\pi$
$281$	25.5114			1.52188			0.760940	+	0.648822i	$0.224738\pi$
$282$	−13.2177	−	2.60491i	−0.787101	−	0.155120i
$283$	22.5968	+	13.0463i	1.34324	+	0.775519i	0.987281	−	0.158983i	$-0.0508214\pi$
$283$	22.5968	+	13.0463i	1.34324	+	0.775519i	0.355958	+	0.934502i	$0.384155\pi$
$284$	−4.69513	+	8.13220i	−0.278605	+	0.482558i
$285$	22.1907	−	25.3939i	1.31446	−	1.50421i
$286$	−10.5511	−	1.91475i	−0.623903	−	0.113222i
$287$	1.32855	−	12.8433i	0.0784219	−	0.758118i
$288$	2.77567	+	1.13826i	0.163558	+	0.0670724i
$289$	−1.84591	+	3.19721i	−0.108583	+	0.188071i
$290$	−0.446673	−	0.773661i	−0.0262296	−	0.0454309i
$291$	13.8580	+	12.1100i	0.812373	+	0.709899i
$292$	−4.55092	−	7.88243i	−0.266322	−	0.461284i
$293$	−16.7126	+	9.64904i	−0.976362	+	0.563703i	−0.901170	−	0.433466i	$-0.857290\pi$
$293$	−16.7126	+	9.64904i	−0.976362	+	0.563703i	−0.0751922	+	0.997169i	$0.523957\pi$
$294$	−7.30329	−	9.67791i	−0.425937	−	0.564427i
$295$	−9.75500	−	16.8962i	−0.567958	−	0.983732i
$296$	5.19513	+	2.99941i	0.301961	+	0.174337i
$297$	−6.90852	−	13.8240i	−0.400873	−	0.802152i
$298$	−12.8995			−0.747248
$299$	7.16367	−	2.56698i	0.414286	−	0.148452i
$300$	−4.81884	−	4.21098i	−0.278216	−	0.243121i
$301$	−14.0585	+	19.4170i	−0.810321	+	1.11917i
$302$	−9.14291	−	5.27866i	−0.526115	−	0.303753i
$303$	−3.71264	+	18.8385i	−0.213286	+	1.08224i
$304$	6.60304			0.378711
$305$	−10.6064	−	18.3708i	−0.607321	−	1.05191i
$306$	10.7971	−	8.34562i	0.617228	−	0.477088i
$307$	−29.8634			−1.70439			−0.852196	−	0.523223i	$-0.824729\pi$
$307$	−29.8634			−1.70439			−0.852196	+	0.523223i	$0.824729\pi$
$308$	−3.21237	−	7.18331i	−0.183042	−	0.409307i
$309$	−6.27641	−	18.3830i	−0.357052	−	1.04577i
$310$	18.6759	+	10.7825i	1.06072	+	0.612407i
$311$	−13.7260			−0.778332			−0.389166	−	0.921168i	$-0.627237\pi$
$311$	−13.7260			−0.778332			−0.389166	+	0.921168i	$0.627237\pi$
$312$	−2.28216	+	5.81307i	−0.129202	+	0.329100i
$313$		−	2.42732i		−	0.137200i	−0.997644	−	0.0686002i	$-0.978147\pi$
$313$		−	2.42732i		−	0.137200i	0.997644	−	0.0686002i	$-0.0218533\pi$
$314$	4.45691	+	2.57320i	0.251518	+	0.145214i
$315$	−11.0611	+	20.6258i	−0.623221	+	1.16213i
$316$	−5.65335	−	9.79189i	−0.318026	−	0.550837i
$317$	29.9926			1.68455			0.842275	−	0.539048i	$-0.181216\pi$
$317$	29.9926			1.68455			0.842275	+	0.539048i	$0.181216\pi$
$318$	3.31540	+	0.653392i	0.185919	+	0.0366404i
$319$	−0.780344	+	0.450532i	−0.0436909	+	0.0252249i
$320$		−	2.94869i		−	0.164837i
$321$	−24.1918	−	4.76767i	−1.35026	−	0.266105i
$322$	4.52293	+	3.27476i	0.252053	+	0.182495i
$323$	15.0181	−	26.0120i	0.835627	−	1.44735i
$324$	−8.67667	+	2.39070i	−0.482037	+	0.132817i
$325$	8.61375	−	10.1621i	0.477805	−	0.563693i
$326$			22.6997i			1.25722i
$327$	1.78702	+	5.23402i	0.0988226	+	0.289442i
$328$	−4.22640	−	2.44011i	−0.233364	−	0.134733i
$329$	18.7858	−	8.40099i	1.03569	−	0.463162i
$330$	−9.99518	+	11.4380i	−0.550217	+	0.629641i
$331$	−7.70073	+	4.44602i	−0.423270	+	0.244375i	−0.696476	−	0.717580i	$-0.745250\pi$
$331$	−7.70073	+	4.44602i	−0.423270	+	0.244375i	0.273205	+	0.961956i	$0.411916\pi$
$332$	−4.92102	+	2.84115i	−0.270076	+	0.155929i
$333$	−17.8341	+	2.41199i	−0.977302	+	0.132176i
$334$	15.7303	−	9.08191i	0.860726	−	0.496940i
$335$	−11.7666	+	20.3803i	−0.642876	+	1.11349i
$336$	−4.46611	+	1.02659i	−0.243646	+	0.0560053i
$337$	−31.3592			−1.70825			−0.854123	−	0.520070i	$-0.825906\pi$
$337$	−31.3592			−1.70825			−0.854123	+	0.520070i	$0.825906\pi$
$338$	−12.1711	−	4.56787i	−0.662018	−	0.248459i
$339$	13.3952	−	15.3289i	0.727530	−	0.832549i
$340$	−11.6161	−	6.70653i	−0.629969	−	0.363713i
$341$	10.8757	−	18.8372i	0.588951	−	1.02009i
$342$	−15.6730	+	12.1145i	−0.847497	+	0.655074i
$343$	17.6418	+	5.63616i	0.952569	+	0.304324i
$344$	4.53030	+	7.84671i	0.244257	+	0.423066i
$345$	2.08424	−	10.5757i	0.112212	−	0.569379i
$346$	−9.85565			−0.529843
$347$	−17.1722	+	9.91440i	−0.921855	+	0.532233i	−0.884226	−	0.467059i	$-0.845314\pi$
$347$	−17.1722	+	9.91440i	−0.921855	+	0.532233i	−0.0376284	+	0.999292i	$0.511980\pi$
$348$	0.169552	+	0.496602i	0.00908895	+	0.0266207i
$349$	7.68781	−	13.3157i	0.411519	−	0.712772i	−0.583537	−	0.812087i	$-0.698332\pi$
$349$	7.68781	−	13.3157i	0.411519	−	0.712772i	0.995056	+	0.0993146i	$0.0316650\pi$
$350$	9.72351	+	1.00583i	0.519743	+	0.0537637i
$351$	−5.24816	−	17.9849i	−0.280126	−	0.959963i
$352$	−2.97416			−0.158523
$353$	13.9267	+	8.04057i	0.741242	+	0.427956i	0.822521	−	0.568735i	$-0.192567\pi$
$353$	13.9267	+	8.04057i	0.741242	+	0.427956i	−0.0812785	+	0.996691i	$0.525900\pi$
$354$	3.70289	+	10.8454i	0.196806	+	0.576427i
$355$	−23.9793	+	13.8445i	−1.27269	+	0.734788i
$356$			14.8823i			0.788760i
$357$	−6.11361	+	19.9287i	−0.323567	+	1.05474i
$358$	−5.55478	+	3.20706i	−0.293579	+	0.169498i
$359$	−3.32956			−0.175727			−0.0878637	−	0.996133i	$-0.528004\pi$
$359$	−3.32956			−0.175727			−0.0878637	+	0.996133i	$0.528004\pi$
$360$	5.40989	+	6.99899i	0.285126	+	0.368879i
$361$	−12.3001	+	21.3044i	−0.647373	+	1.12128i
$362$	−8.06943	−	4.65888i	−0.424120	−	0.244866i
$363$	−2.80983	−	2.45539i	−0.147478	−	0.128875i
$364$	−2.27683	−	9.26369i	−0.119338	−	0.485550i
$365$		−	26.8385i		−	1.40479i
$366$	4.02607	+	11.7920i	0.210446	+	0.616377i
$367$	0.873061	+	0.504062i	0.0455734	+	0.0263118i	0.522614	−	0.852570i	$-0.324957\pi$
$367$	0.873061	+	0.504062i	0.0455734	+	0.0263118i	−0.477040	+	0.878881i	$0.658290\pi$
$368$	1.82779	−	1.05528i	0.0952802	−	0.0550100i
$369$	14.5086	−	1.96223i	0.755287	−	0.102150i
$370$	8.84432	+	15.3188i	0.459794	+	0.796387i
$371$	−4.71206	+	2.10723i	−0.244638	+	0.109402i
$372$	−9.53848	−	8.33528i	−0.494547	−	0.432164i
$373$	−7.20358	−	12.4770i	−0.372987	−	0.646033i	0.617036	−	0.786935i	$-0.288333\pi$
$373$	−7.20358	−	12.4770i	−0.372987	−	0.646033i	−0.990024	+	0.140902i	$0.955000\pi$
$374$	−6.76446	+	11.7164i	−0.349782	+	0.605840i
$375$	2.15394	+	6.30869i	0.111229	+	0.325780i
$376$		−	7.77801i		−	0.401120i
$377$	−1.02833	+	0.368483i	−0.0529615	+	0.0189779i
$378$	8.71727	−	10.6306i	0.448368	−	0.546778i
$379$	26.2238	+	15.1403i	1.34703	+	0.777707i	0.987827	−	0.155553i	$-0.0497161\pi$
$379$	26.2238	+	15.1403i	1.34703	+	0.777707i	0.359200	+	0.933260i	$0.383049\pi$
$380$	16.8618	+	9.73515i	0.864991	+	0.499403i
$381$	−3.14980	+	15.9825i	−0.161369	+	0.818811i
$382$		−	22.2137i		−	1.13655i
$383$	16.2735	−	9.39549i	0.831536	−	0.480087i	−0.0228425	−	0.999739i	$-0.507272\pi$
$383$	16.2735	−	9.39549i	0.831536	−	0.480087i	0.854378	+	0.519652i	$0.173938\pi$
$384$	−0.334907	+	1.69936i	−0.0170906	+	0.0867203i
$385$	2.38743	−	23.0797i	0.121675	−	1.17625i
$386$	−14.0769	+	8.12729i	−0.716494	+	0.413668i
$387$	−25.1493	−	10.3133i	−1.27841	−	0.524254i
$388$	−5.31270	+	9.20186i	−0.269711	+	0.467154i
$389$		−	12.2677i		−	0.621999i	−0.950410	−	0.310999i	$-0.899336\pi$
$389$		−	12.2677i		−	0.621999i	0.950410	−	0.310999i	$-0.100664\pi$
$390$	−14.3983	+	11.4798i	−0.729085	+	0.581301i
$391$		−	9.60053i		−	0.485520i
$392$	4.66679	−	5.21738i	0.235708	−	0.263518i
$393$	26.8071	−	9.15261i	1.35224	−	0.461688i
$394$	1.76094	+	3.05003i	0.0887147	+	0.153658i
$395$		−	33.3399i		−	1.67751i
$396$	7.05945	−	5.45662i	0.354751	−	0.274205i
$397$	−7.56662	−	13.1058i	−0.379758	−	0.657760i	0.611269	−	0.791423i	$-0.290659\pi$
$397$	−7.56662	−	13.1058i	−0.379758	−	0.657760i	−0.991027	+	0.133663i	$0.957326\pi$
$398$		−	8.45628i		−	0.423875i
$399$	8.87447	−	28.9283i	0.444279	−	1.44823i
$400$	1.84738	−	3.19975i	0.0923688	−	0.159987i
$401$	−12.9955	+	22.5089i	−0.648965	+	1.12404i	0.334406	+	0.942429i	$0.391464\pi$
$401$	−12.9955	+	22.5089i	−0.648965	+	1.12404i	−0.983371	+	0.181611i	$0.941869\pi$
$402$	9.09597	−	10.4090i	0.453666	−	0.519153i
$403$	17.0502	−	20.1151i	0.849330	−	1.00200i
$404$	−11.0856			−0.551529
$405$	−25.6818	−	6.68740i	−1.27614	−	0.332299i
$406$	−0.649256	−	0.470083i	−0.0322220	−	0.0233298i
$407$	15.4511	−	8.92072i	0.765885	−	0.442184i
$408$	5.93276	+	5.18439i	0.293715	+	0.256665i
$409$	−4.57187	−	7.91871i	−0.226064	−	0.391555i	0.730574	−	0.682834i	$-0.239253\pi$
$409$	−4.57187	−	7.91871i	−0.226064	−	0.391555i	−0.956638	+	0.291279i	$0.905919\pi$
$410$	−7.19513	−	12.4623i	−0.355342	−	0.615471i
$411$	6.12983	+	5.35660i	0.302362	+	0.264221i
$412$	9.71247	−	5.60750i	0.478499	−	0.276262i
$413$	−14.1792	−	10.2663i	−0.697715	−	0.505170i
$414$	−2.40235	+	5.85820i	−0.118069	+	0.287915i
$415$	−16.7553			−0.822488
$416$	−3.54761	−	0.643796i	−0.173936	−	0.0315647i
$417$	0.508787	−	0.582231i	0.0249154	−	0.0285120i
$418$	9.81925	−	17.0074i	0.480275	−	0.831861i
$419$	17.7086	−	30.6722i	0.865121	−	1.49843i	−0.00180635	−	0.999998i	$-0.500575\pi$
$419$	17.7086	−	30.6722i	0.865121	−	1.49843i	0.866927	−	0.498435i	$-0.166092\pi$
$420$	−12.9184	−	3.96303i	−0.630352	−	0.193376i
$421$			35.6470i			1.73733i	0.495401	+	0.868664i	$0.335021\pi$
$421$			35.6470i			1.73733i	−0.495401	+	0.868664i	$0.664979\pi$
$422$	−1.64519	−	2.84956i	−0.0800868	−	0.138714i
$423$	14.2701	+	18.4619i	0.693838	+	0.897647i
$424$			1.95097i			0.0947474i
$425$	−8.40339	−	14.5551i	−0.407624	−	0.706026i
$426$	15.3920	−	5.25520i	0.745745	−	0.254616i
$427$	−15.4168	−	11.1623i	−0.746071	−	0.540181i
$428$		−	14.2358i		−	0.688114i
$429$	11.5789	+	14.5226i	0.559036	+	0.701160i
$430$			26.7169i			1.28840i
$431$	−8.91682	+	15.4444i	−0.429508	+	0.743930i	−0.996830	−	0.0795668i	$-0.974646\pi$
$431$	−8.91682	+	15.4444i	−0.429508	+	0.743930i	0.567322	+	0.823496i	$0.307980\pi$
$432$	−2.32285	−	4.64805i	−0.111758	−	0.223629i
$433$	−1.25421	+	0.724116i	−0.0602733	+	0.0347988i	−0.529834	−	0.848101i	$-0.677746\pi$
$433$	−1.25421	+	0.724116i	−0.0602733	+	0.0347988i	0.469561	+	0.882900i	$0.344412\pi$
$434$	19.2469	+	1.99095i	0.923879	+	0.0955687i
$435$	−0.299188	+	1.51812i	−0.0143450	+	0.0727883i
$436$	−2.76534	+	1.59657i	−0.132436	+	0.0764619i
$437$			13.9361i			0.666652i
$438$	−3.04827	+	15.4673i	−0.145652	+	0.739058i
$439$	−18.8250	−	10.8686i	−0.898467	−	0.518730i	−0.0217642	−	0.999763i	$-0.506928\pi$
$439$	−18.8250	−	10.8686i	−0.898467	−	0.518730i	−0.876702	+	0.481033i	$0.840262\pi$
$440$	−7.59492	−	4.38493i	−0.362074	−	0.209043i
$441$	−1.50487	+	20.9460i	−0.0716605	+	0.997429i
$442$	−10.6049	+	12.5112i	−0.504423	+	0.595097i
$443$			27.6214i			1.31233i	0.754617	+	0.656166i	$0.227823\pi$
$443$			27.6214i			1.31233i	−0.754617	+	0.656166i	$0.772177\pi$
$444$	−3.35720	−	9.83294i	−0.159326	−	0.466651i
$445$	−21.9416	+	38.0040i	−1.04013	+	1.80156i
$446$	−11.6151	−	20.1179i	−0.549991	−	0.952612i
$447$	16.8240	+	14.7018i	0.795750	+	0.695372i
$448$	−1.08009	−	2.41524i	−0.0510297	−	0.114109i
$449$	17.4715	+	30.2615i	0.824530	+	1.42813i	0.902278	+	0.431155i	$0.141894\pi$
$449$	17.4715	+	30.2615i	0.824530	+	1.42813i	−0.0777474	+	0.996973i	$0.524773\pi$
$450$	1.48558	+	10.9842i	0.0700308	+	0.517802i
$451$	−12.5700	+	7.25728i	−0.591898	+	0.341732i
$452$	10.1785	+	5.87655i	0.478756	+	0.276410i
$453$	5.90834	+	17.3050i	0.277598	+	0.813059i
$454$			18.8133i			0.882952i
$455$	7.84366	−	27.0129i	0.367717	−	1.26639i
$456$	−8.61195	−	7.52562i	−0.403291	−	0.352419i
$457$	27.1028	+	15.6478i	1.26782	+	0.731974i	0.974574	−	0.224064i	$-0.0719324\pi$
$457$	27.1028	+	15.6478i	1.26782	+	0.731974i	0.293242	+	0.956038i	$0.405266\pi$
$458$	6.52063	−	11.2941i	0.304689	−	0.527737i
$459$	−23.5936	−	1.42096i	−1.10126	−	0.0663245i
$460$	6.22335			0.290165
$461$	9.34366	−	5.39456i	0.435178	−	0.251250i	−0.266372	−	0.963870i	$-0.585825\pi$
$461$	9.34366	−	5.39456i	0.435178	−	0.251250i	0.701550	+	0.712620i	$0.252492\pi$
$462$	−3.99726	+	13.0300i	−0.185969	+	0.606209i
$463$		−	9.84138i		−	0.457368i	−0.973501	−	0.228684i	$-0.926558\pi$
$463$		−	9.84138i		−	0.457368i	0.973501	−	0.228684i	$-0.0734422\pi$
$464$	−0.262375	+	0.151482i	−0.0121804	+	0.00703238i
$465$	−12.0688	−	35.3483i	−0.559675	−	1.63924i
$466$	13.0643	+	7.54267i	0.605191	+	0.349407i
$467$	4.09209			0.189359			0.0946797	−	0.995508i	$-0.469817\pi$
$467$	4.09209			0.189359			0.0946797	+	0.995508i	$0.469817\pi$
$468$	9.60175	−	4.98060i	0.443841	−	0.230228i
$469$	−2.17265	+	21.0034i	−0.100324	+	0.969845i
$470$	11.4675	−	19.8622i	0.528954	−	0.916176i
$471$	−2.88015	−	8.43570i	−0.132710	−	0.388697i
$472$	−5.73006	+	3.30825i	−0.263747	+	0.152275i
$473$	26.9476			1.23905
$474$	−3.78669	+	19.2142i	−0.173928	+	0.882537i
$475$	12.1983	+	21.1281i	0.559697	+	0.969423i
$476$	−11.9712	−	1.23833i	−0.548698	−	0.0567589i
$477$	−3.57939	−	4.63081i	−0.163889	−	0.212030i
$478$	3.60610	−	6.24596i	0.164939	−	0.285683i
$479$	−13.9551	−	8.05700i	−0.637626	−	0.368134i	0.146073	−	0.989274i	$-0.453336\pi$
$479$	−13.9551	−	8.05700i	−0.637626	−	0.368134i	−0.783700	+	0.621140i	$0.786670\pi$
$480$	−3.36068	+	3.84579i	−0.153393	+	0.175536i
$481$	20.3613	−	7.29613i	0.928395	−	0.332675i
$482$	−3.78633			−0.172463
$483$	−2.16668	−	9.42594i	−0.0985872	−	0.428895i
$484$	1.07719	−	1.86575i	0.0489633	−	0.0848069i
$485$	−27.1334	+	15.6655i	−1.23206	+	0.711332i
$486$	14.0412	+	6.77092i	0.636921	+	0.307135i
$487$	16.3782	−	9.45595i	0.742166	−	0.428490i	−0.0806900	−	0.996739i	$-0.525712\pi$
$487$	16.3782	−	9.45595i	0.742166	−	0.428490i	0.822856	+	0.568249i	$0.192379\pi$
$488$	−6.23017	+	3.59699i	−0.282027	+	0.162828i
$489$	25.8713	−	29.6058i	1.16994	−	1.33882i
$490$	19.6095	−	6.44285i	0.885867	−	0.291058i
$491$	−9.88961	−	5.70977i	−0.446312	−	0.257678i	0.259959	−	0.965620i	$-0.416291\pi$
$491$	−9.88961	−	5.70977i	−0.446312	−	0.257678i	−0.706271	+	0.707941i	$0.749624\pi$
$492$	2.73119	+	7.99940i	0.123132	+	0.360641i
$493$			1.37813i			0.0620679i
$494$	15.3940	−	18.1612i	0.692608	−	0.817109i
$495$	26.0722	−	3.52617i	1.17186	−	0.158489i
$496$	3.65672	−	6.33363i	0.164192	−	0.284388i
$497$	−14.5701	+	20.1234i	−0.653556	+	0.902659i
$498$	9.65631	+	1.90304i	0.432710	+	0.0852774i
$499$		−	13.0772i		−	0.585417i	−0.956202	−	0.292709i	$-0.905443\pi$
$499$		−	13.0772i		−	0.585417i	0.956202	−	0.292709i	$-0.0945566\pi$
$500$	−3.33313	+	1.92438i	−0.149062	+	0.0860611i
$501$	−30.8670	−	6.08319i	−1.37903	−	0.271777i
$502$	−2.25682			−0.100727
$503$	14.9730	+	25.9339i	0.667611	+	1.15634i	0.978570	+	0.205913i	$0.0660165\pi$
$503$	14.9730	+	25.9339i	0.667611	+	1.15634i	−0.310959	+	0.950423i	$0.600650\pi$
$504$	6.99490	+	3.75119i	0.311578	+	0.167091i
$505$	−28.3086	−	16.3440i	−1.25972	−	0.727297i
$506$		−	6.27711i		−	0.279052i
$507$	10.6679	+	19.8292i	0.473777	+	0.880645i
$508$	−9.40502			−0.417280
$509$	22.5334	+	13.0097i	0.998776	+	0.576643i	0.907886	−	0.419218i	$-0.137696\pi$
$509$	22.5334	+	13.0097i	0.998776	+	0.576643i	0.0908898	+	0.995861i	$0.471029\pi$
$510$	7.50654	+	21.9860i	0.332395	+	0.973555i
$511$	−9.83085	−	21.9832i	−0.434891	−	0.972477i
$512$	−1.00000			−0.0441942
$513$	34.2484	+	2.06265i	1.51210	+	0.0910682i
$514$	5.72584	+	9.91745i	0.252556	+	0.437440i
$515$	33.0695			1.45722
$516$	3.03446	−	15.3973i	0.133584	−	0.677826i
$517$	−20.0338	−	11.5665i	−0.881085	−	0.508695i
$518$	12.8555	+	9.30785i	0.564840	+	0.408964i
$519$	12.8541	+	11.2327i	0.564233	+	0.493060i
$520$	−8.11013	−	6.87441i	−0.355653	−	0.301463i
$521$	7.99767			0.350384			0.175192	−	0.984534i	$-0.443945\pi$
$521$	7.99767			0.350384			0.175192	+	0.984534i	$0.443945\pi$
$522$	0.344851	−	0.840930i	0.0150937	−	0.0368065i
$523$	−15.3715	−	8.87474i	−0.672149	−	0.388065i	0.124741	−	0.992189i	$-0.460190\pi$
$523$	−15.3715	−	8.87474i	−0.672149	−	0.388065i	−0.796890	+	0.604124i	$0.793523\pi$
$524$	8.17717	+	14.1633i	0.357221	+	0.618725i
$525$	−11.5354	−	12.3939i	−0.503447	−	0.540915i
$526$	7.45900	−	4.30646i	0.325228	−	0.187770i
$527$	−16.6338	−	28.8106i	−0.724580	−	1.25501i
$528$	3.87901	+	3.38971i	0.168812	+	0.147518i
$529$	−9.27279	−	16.0609i	−0.403165	−	0.698302i
$530$	−2.87640	+	4.98206i	−0.124943	+	0.216407i
$531$	7.53128	−	18.3653i	0.326830	−	0.796985i
$532$	17.3773	+	1.79756i	0.753401	+	0.0779340i
$533$	−16.5646	+	5.93563i	−0.717490	+	0.257101i
$534$	16.9616	−	19.4101i	0.734002	−	0.839956i
$535$	20.9885	−	36.3531i	0.907411	−	1.57168i
$536$	6.91165	+	3.99044i	0.298538	+	0.172361i
$537$	10.8999	+	2.14813i	0.470366	+	0.0926986i
$538$	0.800992			0.0345332
$539$	−6.49851	−	19.7789i	−0.279910	−	0.851937i
$540$	0.921106	−	15.2941i	0.0396381	−	0.658154i
$541$			23.8308i			1.02457i	0.858817	+	0.512283i	$0.171200\pi$
$541$			23.8308i			1.02457i	−0.858817	+	0.512283i	$0.828800\pi$
$542$	5.57461	+	9.65551i	0.239450	+	0.414740i
$543$	5.21464	+	15.2732i	0.223781	+	0.655435i
$544$	−2.27441	+	3.93940i	−0.0975147	+	0.168900i
$545$	−9.41557			−0.403319
$546$	−7.58848	+	14.6770i	−0.324757	+	0.628118i
$547$	10.2018			0.436199			0.218099	−	0.975927i	$-0.430014\pi$
$547$	10.2018			0.436199			0.218099	+	0.975927i	$0.430014\pi$
$548$	−2.34996	+	4.07025i	−0.100385	+	0.173873i
$549$	8.18860	−	19.9682i	0.349481	−	0.852221i
$550$	−5.49439	−	9.51656i	−0.234281	−	0.405787i
$551$		−	2.00049i		−	0.0852236i
$552$	−3.58659	−	0.706838i	−0.152656	−	0.0300850i
$553$	−12.2123	−	27.3084i	−0.519320	−	1.16127i
$554$	−4.36280			−0.185358
$555$	5.92404	−	30.0594i	0.251462	−	1.27595i
$556$	0.386606	+	0.223207i	0.0163957	+	0.00946609i
$557$	17.2494	−	29.8768i	0.730880	−	1.26592i	−0.225627	−	0.974214i	$-0.572443\pi$
$557$	17.2494	−	29.8768i	0.730880	−	1.26592i	0.956507	−	0.291708i	$-0.0942235\pi$
$558$	2.94058	+	21.7424i	0.124485	+	0.920429i
$559$	32.1435	+	5.83317i	1.35952	+	0.246717i
$560$	0.802725	−	7.76008i	0.0339213	−	0.327923i
$561$	22.1759	−	7.57139i	0.936267	−	0.319664i
$562$	12.7557	−	22.0935i	0.538066	−	0.931957i
$563$	−14.5978	−	25.2842i	−0.615225	−	1.06560i	−0.990345	−	0.138624i	$-0.955732\pi$
$563$	−14.5978	−	25.2842i	−0.615225	−	1.06560i	0.375120	−	0.926976i	$-0.377601\pi$
$564$	−8.86475	+	10.1444i	−0.373273	+	0.427156i
$565$	17.3281	+	30.0132i	0.728999	+	1.26266i
$566$	22.5968	−	13.0463i	0.949813	−	0.548375i
$567$	−23.4853	+	3.92957i	−0.986289	+	0.165026i
$568$	4.69513	+	8.13220i	0.197003	+	0.341220i
$569$	−0.384044	−	0.221728i	−0.0161000	−	0.00929532i	0.491928	−	0.870636i	$-0.336292\pi$
$569$	−0.384044	−	0.221728i	−0.0161000	−	0.00929532i	−0.508028	+	0.861340i	$0.669625\pi$
$570$	−10.8964	−	31.9147i	−0.456402	−	1.33676i
$571$	25.1817			1.05382			0.526910	−	0.849921i	$-0.323350\pi$
$571$	25.1817			1.05382			0.526910	+	0.849921i	$0.323350\pi$
$572$	−6.93380	+	8.18019i	−0.289917	+	0.342031i
$573$	−25.3173	+	28.9719i	−1.05765	+	1.21032i
$574$	−10.4584	−	7.57223i	−0.436524	−	0.316059i
$575$	6.75323	+	3.89898i	0.281629	+	0.162599i
$576$	2.37360	−	1.83468i	0.0988999	−	0.0764449i
$577$	14.3244			0.596334			0.298167	−	0.954514i	$-0.403625\pi$
$577$	14.3244			0.596334			0.298167	+	0.954514i	$0.403625\pi$
$578$	1.84591	+	3.19721i	0.0767797	+	0.132986i
$579$	27.6225	+	5.44377i	1.14795	+	0.226235i
$580$	−0.893346			−0.0370942
$581$	−13.7242	+	6.13743i	−0.569374	+	0.254624i
$582$	17.4166	−	5.94644i	0.721940	−	0.246488i
$583$	5.02510	+	2.90124i	0.208118	+	0.120157i
$584$	−9.10184			−0.376637
$585$	31.8625	+	1.43762i	1.31735	+	0.0594384i
$586$			19.2981i			0.797196i
$587$	20.7228	+	11.9643i	0.855321	+	0.493820i	0.862443	−	0.506155i	$-0.168934\pi$
$587$	20.7228	+	11.9643i	0.855321	+	0.493820i	−0.00712184	+	0.999975i	$0.502267\pi$
$588$	−12.0330	+	1.48588i	−0.496231	+	0.0612766i
$589$	24.1455	+	41.8212i	0.994898	+	1.72321i
$590$	−19.5100			−0.803214
$591$	1.17950	−	5.98494i	0.0485181	−	0.246188i
$592$	5.19513	−	2.99941i	0.213519	−	0.123275i
$593$		−	32.2797i		−	1.32557i	−0.748811	−	0.662783i	$-0.769375\pi$
$593$		−	32.2797i		−	1.32557i	0.748811	−	0.662783i	$-0.230625\pi$
$594$	−15.4262	−	0.929063i	−0.632946	−	0.0381199i
$595$	−28.7443	−	20.8119i	−1.17840	−	0.853204i
$596$	−6.44975	+	11.1713i	−0.264192	+	0.457594i
$597$	−9.63779	+	11.0290i	−0.394448	+	0.451387i
$598$	1.35876	−	7.48741i	0.0555640	−	0.306183i
$599$			8.21378i			0.335606i	0.985821	+	0.167803i	$0.0536673\pi$
$599$			8.21378i			0.335606i	−0.985821	+	0.167803i	$0.946333\pi$
$600$	−6.05624	+	2.06775i	−0.247245	+	0.0844154i
$601$	32.8675	+	18.9761i	1.34069	+	0.774051i	0.986909	−	0.161276i	$-0.0515609\pi$
$601$	32.8675	+	18.9761i	1.34069	+	0.774051i	0.353786	+	0.935327i	$0.384894\pi$
$602$	9.78630	+	21.8835i	0.398860	+	0.891906i
$603$	−23.7266	+	3.20894i	−0.966223	+	0.130678i
$604$	−9.14291	+	5.27866i	−0.372020	+	0.214786i
$605$	5.50151	−	3.17630i	0.223668	−	0.129135i
$606$	14.4583	+	12.6345i	0.587327	+	0.513240i
$607$	34.8288	−	20.1084i	1.41366	−	0.816175i	0.417926	−	0.908481i	$-0.362757\pi$
$607$	34.8288	−	20.1084i	1.41366	−	0.816175i	0.995731	+	0.0923059i	$0.0294238\pi$
$608$	3.30152	−	5.71840i	0.133894	−	0.231912i
$609$	0.311021	+	1.35307i	0.0126032	+	0.0548292i
$610$	−21.2128			−0.858881
$611$	−21.3928	−	18.1333i	−0.865460	−	0.733593i
$612$	−1.82898	−	13.5234i	−0.0739323	−	0.546649i
$613$	−9.81926	−	5.66915i	−0.396596	−	0.228975i	0.288418	−	0.957505i	$-0.406871\pi$
$613$	−9.81926	−	5.66915i	−0.396596	−	0.228975i	−0.685014	+	0.728530i	$0.740204\pi$
$614$	−14.9317	+	25.8624i	−0.602593	+	1.04372i
$615$	−4.81940	+	24.4543i	−0.194337	+	0.986092i
$616$	−7.82712	−	0.809659i	−0.315364	−	0.0326221i
$617$	−5.77858	−	10.0088i	−0.232637	−	0.402939i	0.725946	−	0.687751i	$-0.241402\pi$
$617$	−5.77858	−	10.0088i	−0.232637	−	0.402939i	−0.958583	+	0.284812i	$0.908069\pi$
$618$	−19.0584	−	3.75598i	−0.766639	−	0.151088i
$619$	−9.50860			−0.382183			−0.191091	−	0.981572i	$-0.561203\pi$
$619$	−9.50860			−0.382183			−0.191091	+	0.981572i	$0.561203\pi$
$620$	18.6759	−	10.7825i	0.750042	−	0.433037i
$621$	9.80994	−	4.90249i	0.393659	−	0.196730i
$622$	−6.86302	+	11.8871i	−0.275182	+	0.476629i
$623$	−4.05143	+	39.1659i	−0.162317	+	1.56915i
$624$	3.89318	+	4.88294i	0.155852	+	0.195474i
$625$	−29.8226			−1.19290
$626$	−2.10212	−	1.21366i	−0.0840178	−	0.0485077i
$627$	−32.1904	+	10.9906i	−1.28556	+	0.438921i
$628$	4.45691	−	2.57320i	0.177850	−	0.102682i
$629$		−	27.2876i		−	1.08803i
$630$	12.3319	+	19.8921i	0.491315	+	0.792518i
$631$	31.8644	−	18.3969i	1.26850	−	0.732369i	0.293797	−	0.955868i	$-0.405081\pi$
$631$	31.8644	−	18.3969i	1.26850	−	0.732369i	0.974704	+	0.223499i	$0.0717478\pi$
$632$	−11.3067			−0.449756
$633$	−1.10197	+	5.59157i	−0.0437995	+	0.222245i
$634$	14.9963	−	25.9743i	0.595579	−	1.03157i
$635$	−24.0170	−	13.8662i	−0.953086	−	0.550264i
$636$	2.22356	−	2.54453i	0.0881697	−	0.100897i
$637$	−3.47009	−	24.9992i	−0.137490	−	0.990503i
$638$			0.901063i			0.0356734i
$639$	−26.0643	−	10.6885i	−1.03109	−	0.422832i
$640$	−2.55364	−	1.47434i	−0.100941	−	0.0582785i
$641$	−0.705356	+	0.407237i	−0.0278599	+	0.0160849i	−0.513865	−	0.857871i	$-0.671787\pi$
$641$	−0.705356	+	0.407237i	−0.0278599	+	0.0160849i	0.486005	+	0.873956i	$0.338454\pi$
$642$	−16.2248	+	18.5669i	−0.640343	+	0.732777i
$643$	12.1386	+	21.0247i	0.478699	+	0.829132i	0.999702	−	0.0244235i	$-0.00777502\pi$
$643$	12.1386	+	21.0247i	0.478699	+	0.829132i	−0.521002	+	0.853555i	$0.674442\pi$
$644$	5.09749	−	2.27959i	0.200869	−	0.0898286i
$645$	30.4497	−	34.8452i	1.19896	−	1.37203i
$646$	−15.0181	−	26.0120i	−0.590877	−	1.02343i
$647$	−18.8943	+	32.7258i	−0.742810	+	1.28659i	0.208400	+	0.978044i	$0.433174\pi$
$647$	−18.8943	+	32.7258i	−0.742810	+	1.28659i	−0.951211	+	0.308542i	$0.900159\pi$
$648$	−2.26792	+	8.70956i	−0.0890925	+	0.342144i
$649$			19.6785i			0.772450i
$650$	−4.49378	−	12.5408i	−0.176261	−	0.491890i
$651$	−22.8334	−	24.5327i	−0.894911	−	0.961512i
$652$	19.6585	+	11.3498i	0.769887	+	0.444494i
$653$	−0.550580	−	0.317878i	−0.0215459	−	0.0124395i	0.489188	−	0.872178i	$-0.337293\pi$
$653$	−0.550580	−	0.317878i	−0.0215459	−	0.0124395i	−0.510734	+	0.859739i	$0.670626\pi$
$654$	5.42631	+	1.06940i	0.212185	+	0.0418170i
$655$			48.2238i			1.88426i
$656$	−4.22640	+	2.44011i	−0.165013	+	0.0952704i
$657$	21.6041	−	16.6989i	0.842856	−	0.651487i
$658$	2.11742	−	20.4695i	0.0825456	−	0.797983i
$659$	17.8316	−	10.2951i	0.694619	−	0.401038i	−0.110721	−	0.993851i	$-0.535316\pi$
$659$	17.8316	−	10.2951i	0.694619	−	0.401038i	0.805340	+	0.592813i	$0.201983\pi$
$660$	4.90800	+	14.3751i	0.191044	+	0.559549i
$661$	12.1923	−	21.1177i	0.474226	−	0.821383i	−0.525339	−	0.850893i	$-0.676061\pi$
$661$	12.1923	−	21.1177i	0.474226	−	0.821383i	0.999564	+	0.0295104i	$0.00939480\pi$
$662$			8.89204i			0.345599i
$663$	28.0906	−	4.23097i	1.09095	−	0.164317i
$664$			5.68231i			0.220516i
$665$	41.7251	+	30.2104i	1.61803	+	1.17151i
$666$	−6.82820	+	16.6508i	−0.264587	+	0.645204i
$667$	−0.319711	−	0.553755i	−0.0123792	−	0.0214415i
$668$		−	18.1638i		−	0.702780i
$669$	−7.77995	+	39.4765i	−0.300790	+	1.52625i
$670$	11.7666	+	20.3803i	0.454582	+	0.787359i
$671$			21.3961i			0.825985i
$672$	−1.34400	+	4.38106i	−0.0518458	+	0.169003i
$673$	−10.0414	+	17.3922i	−0.387068	+	0.670422i	−0.992054	−	0.125815i	$-0.959846\pi$
$673$	−10.0414	+	17.3922i	−0.387068	+	0.670422i	0.604985	+	0.796236i	$0.293179\pi$
$674$	−15.6796	+	27.1579i	−0.603956	+	1.04608i
$675$	10.5814	−	16.0192i	0.407279	−	0.616580i
$676$	−10.0414	+	8.25651i	−0.386208	+	0.317558i
$677$	−46.1229			−1.77265			−0.886324	−	0.463066i	$-0.846749\pi$
$677$	−46.1229			−1.77265			−0.886324	+	0.463066i	$0.846749\pi$
$678$	−6.57755	−	19.2650i	−0.252609	−	0.739870i
$679$	−16.4865	+	22.7703i	−0.632694	+	0.873845i
$680$	−11.6161	+	6.70653i	−0.445455	+	0.257184i
$681$	21.4419	−	24.5370i	0.821655	−	0.940262i
$682$	−10.8757	−	18.8372i	−0.416451	−	0.721314i
$683$	7.53356	+	13.0485i	0.288264	+	0.499287i	0.973395	−	0.229132i	$-0.0735887\pi$
$683$	7.53356	+	13.0485i	0.288264	+	0.499287i	−0.685132	+	0.728419i	$0.740255\pi$
$684$	2.65494	+	19.6304i	0.101514	+	0.750588i
$685$	−12.0019	+	6.92930i	−0.458569	+	0.264755i
$686$	13.7020	−	12.4602i	0.523144	−	0.475732i
$687$	−21.3765	+	7.29846i	−0.815565	+	0.278454i
$688$	9.06060			0.345432
$689$	5.36598	+	4.54838i	0.204428	+	0.173280i
$690$	−8.11674	−	7.09288i	−0.308999	−	0.270021i
$691$	−9.91201	+	17.1681i	−0.377071	+	0.653105i	−0.990635	−	0.136540i	$-0.956402\pi$
$691$	−9.91201	+	17.1681i	−0.377071	+	0.653105i	0.613564	+	0.789645i	$0.289735\pi$
$692$	−4.92782	+	8.53524i	−0.187328	+	0.324461i
$693$	20.0639	−	12.4384i	0.762164	−	0.472497i
$694$			19.8288i			0.752691i
$695$	0.658168	+	1.13998i	0.0249657	+	0.0432419i
$696$	0.514846	+	0.101465i	0.0195152	+	0.00384601i
$697$			22.1993i			0.840859i
$698$	−7.68781	−	13.3157i	−0.290988	−	0.504006i
$699$	−8.44242	−	24.7271i	−0.319322	−	0.935263i
$700$	5.73283	−	7.91789i	0.216680	−	0.299268i
$701$			20.9647i			0.791826i	0.918288	+	0.395913i	$0.129572\pi$
$701$			20.9647i			0.791826i	−0.918288	+	0.395913i	$0.870428\pi$
$702$	−18.1995	−	4.44741i	−0.686895	−	0.167857i
$703$			39.6105i			1.49394i
$704$	−1.48708	+	2.57570i	−0.0560464	+	0.0970752i
$705$	−37.5937	+	12.8354i	−1.41586	+	0.483409i
$706$	13.9267	−	8.04057i	0.524138	−	0.302611i
$707$	−29.1741	−	3.01785i	−1.09720	−	0.113498i
$708$	11.2438	+	2.21591i	0.422570	+	0.0832791i
$709$	17.8618	−	10.3125i	0.670813	−	0.387294i	−0.125572	−	0.992085i	$-0.540077\pi$
$709$	17.8618	−	10.3125i	0.670813	−	0.387294i	0.796384	+	0.604791i	$0.206743\pi$
$710$			27.6889i			1.03915i
$711$	26.8375	−	20.7441i	1.00649	−	0.777966i
$712$	12.8884	+	7.44115i	0.483015	+	0.278869i
$713$	13.3674	+	7.71770i	0.500615	+	0.289030i
$714$	14.2019	+	15.2589i	0.531494	+	0.571049i
$715$	−29.7668	+	10.6664i	−1.11322	+	0.398902i
$716$			6.41411i			0.239707i
$717$	−11.8219	+	4.03627i	−0.441495	+	0.150737i
$718$	−1.66478	+	2.88348i	−0.0621290	+	0.107611i
$719$	5.40916	+	9.36895i	0.201728	+	0.349403i	0.949085	−	0.315019i	$-0.102011\pi$
$719$	5.40916	+	9.36895i	0.201728	+	0.349403i	−0.747357	+	0.664422i	$0.768678\pi$
$720$	8.76625	−	1.18560i	0.326699	−	0.0441848i
$721$	27.0869	−	12.1133i	1.00877	−	0.451121i
$722$	12.3001	+	21.3044i	0.457762	+	0.792867i
$723$	4.93828	+	4.31535i	0.183657	+	0.160490i
$724$	−8.06943	+	4.65888i	−0.299898	+	0.173146i
$725$	−0.969409	−	0.559689i	−0.0360030	−	0.0207863i
$726$	−3.53135	+	1.20569i	−0.131061	+	0.0447473i
$727$		−	29.3823i		−	1.08973i	−0.838524	−	0.544864i	$-0.816581\pi$
$727$		−	29.3823i		−	1.08973i	0.838524	−	0.544864i	$-0.183419\pi$
$728$	−9.16101	−	2.66005i	−0.339530	−	0.0985882i
$729$	−10.5961	−	24.8339i	−0.392448	−	0.919774i
$730$	−23.2428	−	13.4192i	−0.860255	−	0.496668i
$731$	20.6075	−	35.6933i	0.762197	−	1.32016i
$732$	12.2252	+	2.40931i	0.451856	+	0.0890508i
$733$	−29.5041			−1.08976			−0.544880	−	0.838514i	$-0.683425\pi$
$733$	−29.5041			−1.08976			−0.544880	+	0.838514i	$0.683425\pi$
$734$	0.873061	−	0.504062i	0.0322253	−	0.0186053i
$735$	−32.9185	−	13.9463i	−1.21422	−	0.514418i
$736$		−	2.11055i		−	0.0777959i
$737$	20.5563	−	11.8682i	0.757202	−	0.437171i
$738$	5.55495	−	13.5459i	0.204481	−	0.498632i
$739$	16.1935	+	9.34935i	0.595689	+	0.343921i	0.767344	−	0.641236i	$-0.221578\pi$
$739$	16.1935	+	9.34935i	0.595689	+	0.343921i	−0.171655	+	0.985157i	$0.554911\pi$
$740$	17.6886			0.650247
$741$	−40.7761	+	6.14164i	−1.49795	+	0.225619i
$742$	−0.531115	+	5.13438i	−0.0194978	+	0.188489i
$743$	−9.61724	+	16.6575i	−0.352822	+	0.611106i	−0.986743	−	0.162292i	$-0.948111\pi$
$743$	−9.61724	+	16.6575i	−0.352822	+	0.611106i	0.633921	+	0.773398i	$0.281445\pi$
$744$	−11.9878	+	4.09293i	−0.439494	+	0.150054i
$745$	−32.9407	+	19.0183i	−1.20685	+	0.696777i
$746$	−14.4072			−0.527484
$747$	−10.4252	−	13.4875i	−0.381438	−	0.493482i
$748$	6.76446	+	11.7164i	0.247333	+	0.428394i
$749$	3.87544	−	37.4645i	0.141605	−	1.36892i
$750$	6.54046	+	1.28898i	0.238824	+	0.0470668i
$751$	−3.33075	+	5.76902i	−0.121541	+	0.210515i	−0.920375	−	0.391036i	$-0.872117\pi$
$751$	−3.33075	+	5.76902i	−0.121541	+	0.210515i	0.798835	+	0.601551i	$0.205450\pi$
$752$	−6.73596	−	3.88901i	−0.245635	−	0.141817i
$753$	2.94344	+	2.57214i	0.107265	+	0.0937342i
$754$	−0.195047	+	1.07480i	−0.00710320	+	0.0391418i
$755$	−31.1302			−1.13294
$756$	−4.84772	−	12.8647i	−0.176310	−	0.467883i
$757$	16.3979	−	28.4019i	0.595990	−	1.03229i	−0.397416	−	0.917638i	$-0.630093\pi$
$757$	16.3979	−	28.4019i	0.595990	−	1.03229i	0.993406	−	0.114647i	$-0.0365736\pi$
$758$	26.2238	−	15.1403i	0.952493	−	0.549922i
$759$	−7.15415	+	8.18685i	−0.259679	+	0.297164i
$760$	16.8618	−	9.73515i	0.611641	−	0.353131i
$761$	−35.2854	+	20.3721i	−1.27910	+	0.738486i	−0.976682	−	0.214690i	$-0.931126\pi$
$761$	−35.2854	+	20.3721i	−1.27910	+	0.738486i	−0.302414	+	0.953177i	$0.597792\pi$
$762$	12.2664	+	10.7191i	0.444364	+	0.388311i
$763$	−7.71221	+	3.44890i	−0.279201	+	0.124858i
$764$	−19.2376	−	11.1068i	−0.695992	−	0.401831i
$765$	15.2675	−	37.2303i	0.551998	−	1.34606i
$766$		−	18.7910i		−	0.678946i
$767$	−4.25968	+	23.4728i	−0.153808	+	0.847552i
$768$	1.30424	+	1.13972i	0.0470627	+	0.0411261i
$769$	3.08568	−	5.34455i	0.111272	−	0.192729i	−0.805011	−	0.593260i	$-0.797841\pi$
$769$	3.08568	−	5.34455i	0.111272	−	0.192729i	0.916284	+	0.400530i	$0.131174\pi$
$770$	−18.7939	−	13.6074i	−0.677285	−	0.490378i
$771$	3.83525	−	19.4606i	0.138123	−	0.700856i
$772$			16.2546i			0.585015i
$773$	9.47547	−	5.47067i	0.340809	−	0.196766i	−0.319821	−	0.947478i	$-0.603623\pi$
$773$	9.47547	−	5.47067i	0.340809	−	0.196766i	0.660630	+	0.750712i	$0.270289\pi$
$774$	−21.5062	+	16.6233i	−0.773025	+	0.597511i
$775$	27.0214			0.970636
$776$	5.31270	+	9.20186i	0.190715	+	0.330327i
$777$	−6.15835	−	26.7914i	−0.220930	−	0.961135i
$778$	−10.6242	−	6.13387i	−0.380895	−	0.219910i
$779$		−	32.2244i		−	1.15456i
$780$	2.74264	+	18.2092i	0.0982023	+	0.651992i
$781$	27.9281			0.999347
$782$	−8.31430	−	4.80026i	−0.297319	−	0.171657i
$783$	−1.40819	+	0.703740i	−0.0503247	+	0.0251496i
$784$	−2.18499	−	6.65025i	−0.0780354	−	0.237509i
$785$	15.1751			0.541623
$786$	5.47718	−	27.7920i	0.195364	−	0.991306i
$787$	−23.8089	−	41.2382i	−0.848696	−	1.46998i	−0.882373	−	0.470551i	$-0.844055\pi$
$787$	−23.8089	−	41.2382i	−0.848696	−	1.46998i	0.0336771	−	0.999433i	$-0.489278\pi$
$788$	3.52187			0.125462
$789$	−14.6365	−	2.88452i	−0.521072	−	0.102692i
$790$	−28.8732	−	16.6700i	−1.02726	−	0.593090i
$791$	25.1870	+	18.2363i	0.895547	+	0.648407i
$792$	−1.19584	−	8.84197i	−0.0424925	−	0.314186i
$793$	−4.63146	+	25.5214i	−0.164468	+	0.906293i
$794$	−15.1332			−0.537059
$795$	9.42966	−	3.21952i	0.334436	−	0.114184i
$796$	−7.32335	−	4.22814i	−0.259569	−	0.149862i
$797$	1.06444	+	1.84366i	0.0377043	+	0.0653057i	0.884262	−	0.466992i	$-0.154662\pi$
$797$	1.06444	+	1.84366i	0.0377043	+	0.0653057i	−0.846557	+	0.532297i	$0.821329\pi$
$798$	−20.6154	−	22.1497i	−0.729778	−	0.784090i
$799$	−30.6407	+	17.6904i	−1.08399	+	0.625842i
$800$	−1.84738	−	3.19975i	−0.0653146	−	0.113128i
$801$	−44.2441	+	5.98384i	−1.56329	+	0.211429i
$802$	12.9955	+	22.5089i	0.458887	+	0.794816i
$803$	−13.5352	+	23.4436i	−0.477645	+	0.827306i
$804$	−4.46645	−	13.0818i	−0.157520	−	0.461360i
$805$	16.3780	+	1.69419i	0.577250	+	0.0597124i
$806$	−8.89506	−	24.8234i	−0.313315	−	0.874368i
$807$	−1.04469	−	0.912907i	−0.0367747	−	0.0321358i
$808$	−5.54280	+	9.60041i	−0.194995	+	0.337741i
$809$	−46.1292	−	26.6327i	−1.62182	−	0.936357i	−0.986434	−	0.164161i	$-0.947508\pi$
$809$	−46.1292	−	26.6327i	−1.62182	−	0.936357i	−0.635384	−	0.772196i	$-0.719158\pi$
$810$	−18.6323	+	18.8974i	−0.654674	+	0.663986i
$811$	−50.4687			−1.77220			−0.886098	−	0.463498i	$-0.846594\pi$
$811$	−50.4687			−1.77220			−0.886098	+	0.463498i	$0.846594\pi$
$812$	−0.731732	+	0.327230i	−0.0256788	+	0.0114835i
$813$	3.73395	−	18.9466i	0.130955	−	0.664486i
$814$		−	17.8414i		−	0.625342i
$815$	33.4671	+	57.9668i	1.17230	+	2.03049i
$816$	7.45619	−	2.54572i	0.261019	−	0.0891182i
$817$	−29.9138	+	51.8122i	−1.04655	+	1.81268i
$818$	−9.14373			−0.319703
$819$	26.6249	−	10.4936i	0.930349	−	0.366676i
$820$	−14.3903			−0.502530
$821$	−8.71741	+	15.0990i	−0.304240	+	0.526958i	−0.977092	−	0.212819i	$-0.931736\pi$
$821$	−8.71741	+	15.0990i	−0.304240	+	0.526958i	0.672852	+	0.739777i	$0.265069\pi$
$822$	7.70386	−	2.63029i	0.268703	−	0.0917418i
$823$	5.37142	+	9.30357i	0.187236	+	0.324302i	0.944328	−	0.329006i	$-0.106714\pi$
$823$	5.37142	+	9.30357i	0.187236	+	0.324302i	−0.757092	+	0.653308i	$0.773380\pi$
$824$		−	11.2150i		−	0.390693i
$825$	−3.68021	+	18.6739i	−0.128129	+	0.650143i
$826$	−15.9805	+	7.14645i	−0.556031	+	0.248657i
$827$	−5.26465			−0.183070			−0.0915349	−	0.995802i	$-0.529177\pi$
$827$	−5.26465			−0.183070			−0.0915349	+	0.995802i	$0.529177\pi$
$828$	3.87218	+	5.00960i	0.134567	+	0.174095i
$829$	27.2373	+	15.7255i	0.945991	+	0.546168i	0.891833	−	0.452364i	$-0.149419\pi$
$829$	27.2373	+	15.7255i	0.945991	+	0.546168i	0.0541581	+	0.998532i	$0.482753\pi$
$830$	−8.37767	+	14.5106i	−0.290793	+	0.503669i
$831$	5.69013	+	4.97237i	0.197388	+	0.172489i
$832$	−2.33135	+	2.75042i	−0.0808249	+	0.0953537i
$833$	−31.1676	−	6.51787i	−1.07989	−	0.225831i
$834$	−0.249833	−	0.731738i	−0.00865101	−	0.0253380i
$835$	26.7797	−	46.3838i	0.926750	−	1.60518i
$836$	−9.81925	−	17.0074i	−0.339606	−	0.588215i
$837$	20.9450	−	31.7087i	0.723966	−	1.09601i
$838$	−17.7086	−	30.6722i	−0.611733	−	1.05955i
$839$	31.9843	−	18.4661i	1.10422	−	0.637521i	0.166893	−	0.985975i	$-0.446627\pi$
$839$	31.9843	−	18.4661i	1.10422	−	0.637521i	0.937326	+	0.348454i	$0.113293\pi$
$840$	−9.89127	+	9.20612i	−0.341281	+	0.317641i
$841$	−14.4541	−	25.0352i	−0.498417	−	0.863284i
$842$	30.8712	+	17.8235i	1.06389	+	0.614238i
$843$	−41.8168	+	14.2773i	−1.44025	+	0.491736i
$844$	−3.29039			−0.113260
$845$	−37.8151	+	6.27962i	−1.30088	+	0.216026i
$846$	23.1235	−	3.12737i	0.795003	−	0.107521i
$847$	3.34277	−	4.61687i	0.114859	−	0.158637i
$848$	1.68959	+	0.975484i	0.0580207	+	0.0334982i
$849$	−44.3407	−	8.73856i	−1.52177	−	0.299907i
$850$	−16.8068			−0.576468
$851$	6.33041	+	10.9646i	0.217004	+	0.375861i
$852$	3.14486	−	15.9575i	0.107741	−	0.546694i
$853$	3.68591			0.126203			0.0631015	−	0.998007i	$-0.479901\pi$
$853$	3.68591			0.126203			0.0631015	+	0.998007i	$0.479901\pi$
$854$	−17.3752	+	7.77019i	−0.594568	+	0.265890i
$855$	−22.1622	+	54.0432i	−0.757932	+	1.84824i
$856$	−12.3286	−	7.11791i	−0.421382	−	0.243285i
$857$	−39.8059			−1.35974			−0.679872	−	0.733331i	$-0.737965\pi$
$857$	−39.8059			−1.35974			−0.679872	+	0.733331i	$0.737965\pi$
$858$	18.3664	−	2.76633i	0.627020	−	0.0944411i
$859$		−	45.4217i		−	1.54977i	−0.632104	−	0.774883i	$-0.717809\pi$
$859$		−	45.4217i		−	1.54977i	0.632104	−	0.774883i	$-0.282191\pi$
$860$	23.1375	+	13.3584i	0.788981	+	0.455519i
$861$	5.01001	+	21.7956i	0.170741	+	0.742793i
$862$	8.91682	+	15.4444i	0.303708	+	0.526038i
$863$	−44.9563			−1.53033			−0.765165	−	0.643835i	$-0.777342\pi$
$863$	−44.9563			−1.53033			−0.765165	+	0.643835i	$0.777342\pi$
$864$	−5.18675	−	0.312379i	−0.176457	−	0.0106273i
$865$	−25.1678	+	14.5306i	−0.855729	+	0.494056i
$866$			1.44823i			0.0492129i
$867$	1.23642	−	6.27374i	0.0419909	−	0.213068i
$868$	11.3476	−	15.6728i	0.385164	−	0.531969i
$869$	−16.8140	+	29.1226i	−0.570374	+	0.987917i
$870$	1.16514	+	1.01816i	0.0395018	+	0.0345190i
$871$	27.0888	−	9.70683i	0.917871	−	0.328903i
$872$			3.19314i			0.108133i
$873$	−29.4926	−	12.0944i	−0.998174	−	0.409334i
$874$	12.0690	+	6.96803i	0.408239	+	0.235697i
$875$	−9.29571	+	4.15704i	−0.314252	+	0.140533i
$876$	11.8710	+	10.3735i	0.401083	+	0.350490i
$877$	−16.0955	+	9.29272i	−0.543505	+	0.313793i	−0.746498	−	0.665387i	$-0.768266\pi$
$877$	−16.0955	+	9.29272i	−0.543505	+	0.313793i	0.202993	+	0.979180i	$0.434933\pi$
$878$	−18.8250	+	10.8686i	−0.635312	+	0.366797i
$879$	21.9944	−	25.1693i	0.741853	−	0.848940i
$880$	−7.59492	+	4.38493i	−0.256025	+	0.147816i
$881$	−2.12649	+	3.68320i	−0.0716434	+	0.124090i	−0.899622	−	0.436670i	$-0.856158\pi$
$881$	−2.12649	+	3.68320i	−0.0716434	+	0.124090i	0.827978	+	0.560760i	$0.189491\pi$
$882$	17.3873	+	11.7763i	0.585462	+	0.396527i
$883$	43.2033			1.45391			0.726954	−	0.686687i	$-0.240936\pi$
$883$	43.2033			1.45391			0.726954	+	0.686687i	$0.240936\pi$
$884$	5.53256	+	15.4397i	0.186080	+	0.519293i
$885$	25.4457	+	22.2359i	0.855348	+	0.747452i
$886$	23.9208	+	13.8107i	0.803636	+	0.463979i
$887$	20.6564	−	35.7780i	0.693575	−	1.20131i	−0.277084	−	0.960846i	$-0.589368\pi$
$887$	20.6564	−	35.7780i	0.693575	−	1.20131i	0.970659	−	0.240461i	$-0.0772987\pi$
$888$	−10.1942	−	2.00905i	−0.342094	−	0.0674191i
$889$	−24.7513	−	2.56034i	−0.830131	−	0.0858711i
$890$	21.9416	+	38.0040i	0.735484	+	1.27390i
$891$	19.0606	+	18.7933i	0.638555	+	0.629599i
$892$	−23.2302			−0.777804
$893$	44.4778	−	25.6793i	1.48839	−	0.859324i
$894$	21.1442	−	7.21913i	0.707167	−	0.241444i
$895$	−9.45660	+	16.3793i	−0.316099	+	0.547500i
$896$	−2.63171	−	0.272231i	−0.0879192	−	0.00909462i
$897$	−10.3057	+	8.21676i	−0.344097	+	0.274350i
$898$	34.9430			1.16606
$899$	−1.91886	−	1.10786i	−0.0639977	−	0.0369491i
$900$	10.2554	+	4.20558i	0.341848	+	0.140186i
$901$	7.68564	−	4.43731i	0.256046	−	0.147828i
$902$			14.5146i			0.483282i
$903$	12.1774	−	39.6950i	0.405239	−	1.32097i
$904$	10.1785	−	5.87655i	0.338531	−	0.195451i
$905$	−27.4752			−0.913306
$906$	17.9407	+	3.53572i	0.596041	+	0.117466i
$907$	−17.1308	+	29.6714i	−0.568820	+	0.985224i	0.427864	+	0.903843i	$0.359266\pi$
$907$	−17.1308	+	29.6714i	−0.568820	+	0.985224i	−0.996683	+	0.0813810i	$0.974067\pi$
$908$	16.2928	+	9.40665i	0.540696	+	0.312171i
$909$	−4.45727	−	32.9567i	−0.147838	−	1.09311i
$910$	−19.4721	−	20.2993i	−0.645493	−	0.672915i
$911$			10.9073i			0.361374i	0.983541	+	0.180687i	$0.0578321\pi$
$911$			10.9073i			0.361374i	−0.983541	+	0.180687i	$0.942168\pi$
$912$	−10.8234	+	3.69536i	−0.358397	+	0.122365i
$913$	14.6359	+	8.45004i	0.484378	+	0.279656i
$914$	27.1028	−	15.6478i	0.896482	−	0.517584i
$915$	27.6666	+	24.1767i	0.914629	+	0.799256i
$916$	−6.52063	−	11.2941i	−0.215448	−	0.373166i
$917$	17.6642	+	39.4997i	0.583324	+	1.30439i
$918$	−13.0274	+	19.7222i	−0.429968	+	0.650930i
$919$	−17.1083	−	29.6324i	−0.564350	−	0.977483i	−0.997110	−	0.0759734i	$-0.975794\pi$
$919$	−17.1083	−	29.6324i	−0.564350	−	0.977483i	0.432760	−	0.901509i	$-0.357540\pi$
$920$	3.11168	−	5.38958i	0.102589	−	0.177689i
$921$	48.9504	−	16.7128i	1.61297	−	0.550707i
$922$		−	10.7891i		−	0.355321i
$923$	33.3130	+	6.04541i	1.09651	+	0.198987i
$924$	9.28565	+	9.97671i	0.305475	+	0.328210i
$925$	19.1947	+	11.0821i	0.631118	+	0.364376i
$926$	−8.52289	−	4.92069i	−0.280079	−	0.161704i
$927$	20.5759	+	26.6199i	0.675801	+	0.874311i
$928$			0.302964i			0.00994529i
$929$	43.2772	−	24.9861i	1.41988	−	0.819767i	0.423591	−	0.905854i	$-0.360769\pi$
$929$	43.2772	−	24.9861i	1.41988	−	0.819767i	0.996288	+	0.0860866i	$0.0274362\pi$
$930$	−36.6469	−	7.22228i	−1.20170	−	0.236828i
$931$	45.2426	+	9.46129i	1.48277	+	0.310081i
$932$	13.0643	−	7.54267i	0.427935	−	0.247068i
$933$	22.4990	−	7.68170i	0.736584	−	0.251488i
$934$	2.04605	−	3.54386i	0.0669487	−	0.115958i
$935$			39.8926i			1.30463i
$936$	0.487547	−	10.8057i	0.0159360	−	0.353194i
$937$			8.38154i			0.273813i	0.990584	+	0.136906i	$0.0437160\pi$
$937$			8.38154i			0.273813i	−0.990584	+	0.136906i	$0.956284\pi$
$938$	17.1031	+	12.3832i	0.558437	+	0.404327i
$939$	1.35844	+	3.97874i	0.0443309	+	0.129841i
$940$	−11.4675	−	19.8622i	−0.374027	−	0.647834i
$941$			28.7655i			0.937727i	0.883271	+	0.468864i	$0.155336\pi$
$941$			28.7655i			0.937727i	−0.883271	+	0.468864i	$0.844664\pi$
$942$	−8.74561	−	1.72356i	−0.284947	−	0.0561568i
$943$	−5.14998	−	8.92003i	−0.167707	−	0.290476i
$944$			6.61650i			0.215349i
$945$	6.58762	−	39.9989i	0.214295	−	1.30116i
$946$	13.4738	−	23.3373i	0.438072	−	0.758763i
$947$	−7.05513	+	12.2199i	−0.229261	+	0.397092i	−0.957589	−	0.288137i	$-0.906964\pi$
$947$	−7.05513	+	12.2199i	−0.229261	+	0.397092i	0.728328	+	0.685228i	$0.240298\pi$
$948$	14.7466	+	12.8865i	0.478948	+	0.418533i
$949$	−21.2196	+	25.0339i	−0.688816	+	0.812635i
$950$	24.3966			0.791530
$951$	−49.1622	+	16.7852i	−1.59419	+	0.544296i
$952$	−7.05802	+	9.74818i	−0.228752	+	0.315940i
$953$	−15.3943	+	8.88791i	−0.498671	+	0.287908i	−0.728164	−	0.685402i	$-0.759626\pi$
$953$	−15.3943	+	8.88791i	−0.498671	+	0.287908i	0.229494	+	0.973310i	$0.426293\pi$
$954$	−5.80010	+	0.784441i	−0.187785	+	0.0253972i
$955$	−32.7506	−	56.7256i	−1.05978	−	1.83560i
$956$	−3.60610	−	6.24596i	−0.116630	−	0.202009i
$957$	1.02696	−	1.17520i	0.0331969	−	0.0379889i
$958$	−13.9551	+	8.05700i	−0.450870	+	0.260310i
$959$	−7.29247	+	10.0720i	−0.235486	+	0.325242i
$960$	1.65022	+	4.83333i	0.0532605	+	0.155995i
$961$	22.4865			0.725371
$962$	3.86202	−	21.2815i	0.124516	−	0.686142i
$963$	42.3221	−	5.72391i	1.36381	−	0.184450i
$964$	−1.89316	+	3.27906i	−0.0609747	+	0.105611i
$965$	−23.9648	+	41.5083i	−0.771455	+	1.33620i
$966$	−9.24644	−	2.83657i	−0.297499	−	0.0912653i
$967$		−	6.66040i		−	0.214184i	−0.994249	−	0.107092i	$-0.965846\pi$
$967$		−	6.66040i		−	0.214184i	0.994249	−	0.107092i	$-0.0341539\pi$
$968$	−1.07719	−	1.86575i	−0.0346223	−	0.0599675i
$969$	−10.0593	+	51.0423i	−0.323151	+	1.63971i
$970$			31.3309i			1.00598i
$971$	7.85459	+	13.6046i	0.252066	+	0.436591i	0.964094	−	0.265560i	$-0.0855567\pi$
$971$	7.85459	+	13.6046i	0.252066	+	0.436591i	−0.712029	+	0.702151i	$0.752223\pi$
$972$	12.8844	−	8.77456i	0.413267	−	0.281444i
$973$	0.956670	+	0.692662i	0.0306694	+	0.0222057i
$974$		−	18.9119i		−	0.605976i
$975$	−8.43202	+	21.4778i	−0.270041	+	0.687841i
$976$			7.19399i			0.230274i
$977$	3.04501	−	5.27412i	0.0974186	−	0.168734i	−0.813197	−	0.581989i	$-0.802275\pi$
$977$	3.04501	−	5.27412i	0.0974186	−	0.168734i	0.910615	+	0.413255i	$0.135608\pi$
$978$	−12.7038	−	37.2081i	−0.406221	−	1.18978i
$979$	38.3323	−	22.1312i	1.22510	−	0.707315i
$980$	4.22508	−	20.2038i	0.134965	−	0.645385i
$981$	−5.85838	−	7.57923i	−0.187044	−	0.241986i
$982$	−9.88961	+	5.70977i	−0.315590	+	0.182206i
$983$			31.8439i			1.01566i	0.861456	+	0.507832i	$0.169553\pi$
$983$			31.8439i			1.01566i	−0.861456	+	0.507832i	$0.830447\pi$
$984$	8.29328	+	1.63442i	0.264380	+	0.0521034i
$985$	8.99359	+	5.19245i	0.286560	+	0.165445i
$986$	1.19350	+	0.689066i	0.0380087	+	0.0219443i
$987$	−26.0911	+	24.2838i	−0.830488	+	0.772962i
$988$	−8.03102	−	22.4122i	−0.255501	−	0.713026i
$989$			19.1228i			0.608071i
$990$	9.98235	−	24.3423i	0.317260	−	0.773648i
$991$	7.69665	−	13.3310i	0.244492	−	0.423473i	−0.717497	−	0.696562i	$-0.754712\pi$
$991$	7.69665	−	13.3310i	0.244492	−	0.423473i	0.961989	+	0.273089i	$0.0880454\pi$
$992$	−3.65672	−	6.33363i	−0.116101	−	0.201093i
$993$	10.1344	−	11.5973i	0.321606	−	0.368030i
$994$	10.1424	+	22.6798i	0.321697	+	0.719358i
$995$	−12.4675	−	21.5943i	−0.395245	−	0.684584i
$996$	6.47624	−	7.41109i	0.205208	−	0.234829i
$997$	−25.1310	+	14.5094i	−0.795907	+	0.459517i	−0.842038	−	0.539418i	$-0.818644\pi$
$997$	−25.1310	+	14.5094i	−0.795907	+	0.459517i	0.0461311	+	0.998935i	$0.485311\pi$
$998$	−11.3252	−	6.53861i	−0.358493	−	0.206976i
$999$	27.8828	−	13.9344i	0.882173	−	0.440864i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.q.j.251.2	yes	24
3.2	odd	2		546.2.q.i.251.5	✓	24
7.6	odd	2	inner	546.2.q.j.251.11	yes	24
13.10	even	6		546.2.q.i.335.8	yes	24
21.20	even	2		546.2.q.i.251.8	yes	24
39.23	odd	6	inner	546.2.q.j.335.11	yes	24
91.62	odd	6		546.2.q.i.335.5	yes	24
273.62	even	6	inner	546.2.q.j.335.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.q.i.251.5	✓	24	3.2	odd	2
546.2.q.i.251.8	yes	24	21.20	even	2
546.2.q.i.335.5	yes	24	91.62	odd	6
546.2.q.i.335.8	yes	24	13.10	even	6
546.2.q.j.251.2	yes	24	1.1	even	1	trivial
546.2.q.j.251.11	yes	24	7.6	odd	2	inner
546.2.q.j.335.2	yes	24	273.62	even	6	inner
546.2.q.j.335.11	yes	24	39.23	odd	6	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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.63915 + 0.559644i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.94869i q^{5} +(-0.334907 + 1.69936i) q^{6} +(-1.08009 - 2.41524i) q^{7} -1.00000 q^{8} +(2.37360 - 1.83468i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.63915 + 0.559644i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.94869i q^{5} +(-0.334907 + 1.69936i) q^{6} +(-1.08009 - 2.41524i) q^{7} -1.00000 q^{8} +(2.37360 - 1.83468i) q^{9} +(-2.55364 - 1.47434i) q^{10} +(-1.48708 + 2.57570i) q^{11} +(1.30424 + 1.13972i) q^{12} +(-2.33135 + 2.75042i) q^{13} +(-2.63171 - 0.272231i) q^{14} +(1.65022 + 4.83333i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.27441 + 3.93940i) q^{17} +(-0.402078 - 2.97293i) q^{18} +(-3.30152 - 5.71840i) q^{19} +(-2.55364 + 1.47434i) q^{20} +(3.12211 + 3.35446i) q^{21} +(1.48708 + 2.57570i) q^{22} +(-1.82779 - 1.05528i) q^{23} +(1.63915 - 0.559644i) q^{24} -3.69475 q^{25} +(1.21626 + 3.39422i) q^{26} +(-2.86390 + 4.33567i) q^{27} +(-1.55161 + 2.14301i) q^{28} +(0.262375 + 0.151482i) q^{29} +(5.01089 + 0.987535i) q^{30} -7.31345 q^{31} +(0.500000 + 0.866025i) q^{32} +(0.996066 - 5.05418i) q^{33} +4.54883 q^{34} +(-7.12179 + 3.18486i) q^{35} +(-2.77567 - 1.13826i) q^{36} +(-5.19513 - 2.99941i) q^{37} -6.60304 q^{38} +(2.28216 - 5.81307i) q^{39} +2.94869i q^{40} +(4.22640 + 2.44011i) q^{41} +(4.46611 - 1.02659i) q^{42} +(-4.53030 - 7.84671i) q^{43} +2.97416 q^{44} +(-5.40989 - 6.99899i) q^{45} +(-1.82779 + 1.05528i) q^{46} +7.77801i q^{47} +(0.334907 - 1.69936i) q^{48} +(-4.66679 + 5.21738i) q^{49} +(-1.84738 + 3.19975i) q^{50} +(-5.93276 - 5.18439i) q^{51} +(3.54761 + 0.643796i) q^{52} -1.95097i q^{53} +(2.32285 + 4.64805i) q^{54} +(7.59492 + 4.38493i) q^{55} +(1.08009 + 2.41524i) q^{56} +(8.61195 + 7.52562i) q^{57} +(0.262375 - 0.151482i) q^{58} +(5.73006 - 3.30825i) q^{59} +(3.36068 - 3.84579i) q^{60} +(6.23017 - 3.59699i) q^{61} +(-3.65672 + 6.33363i) q^{62} +(-6.99490 - 3.75119i) q^{63} +1.00000 q^{64} +(8.11013 + 6.87441i) q^{65} +(-3.87901 - 3.38971i) q^{66} +(-6.91165 - 3.99044i) q^{67} +(2.27441 - 3.93940i) q^{68} +(3.58659 + 0.706838i) q^{69} +(-0.802725 + 7.76008i) q^{70} +(-4.69513 - 8.13220i) q^{71} +(-2.37360 + 1.83468i) q^{72} +9.10184 q^{73} +(-5.19513 + 2.99941i) q^{74} +(6.05624 - 2.06775i) q^{75} +(-3.30152 + 5.71840i) q^{76} +(7.82712 + 0.809659i) q^{77} +(-3.89318 - 4.88294i) q^{78} +11.3067 q^{79} +(2.55364 + 1.47434i) q^{80} +(2.26792 - 8.70956i) q^{81} +(4.22640 - 2.44011i) q^{82} -5.68231i q^{83} +(1.34400 - 4.38106i) q^{84} +(11.6161 - 6.70653i) q^{85} -9.06060 q^{86} +(-0.514846 - 0.101465i) q^{87} +(1.48708 - 2.57570i) q^{88} +(-12.8884 - 7.44115i) q^{89} +(-8.76625 + 1.18560i) q^{90} +(9.16101 + 2.66005i) q^{91} +2.11055i q^{92} +(11.9878 - 4.09293i) q^{93} +(6.73596 + 3.88901i) q^{94} +(-16.8618 + 9.73515i) q^{95} +(-1.30424 - 1.13972i) q^{96} +(-5.31270 - 9.20186i) q^{97} +(2.18499 + 6.65025i) q^{98} +(1.19584 + 8.84197i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9}+O(q^{10}) \) 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9	\( 24 q + 12 q^{2} - 12 q^{4} - 18 q^{7} - 24 q^{8} + 6 q^{9} + 12 q^{15} - 12 q^{16} - 6 q^{18} + 12 q^{21} - 36 q^{23} - 12 q^{25} + 18 q^{28} + 6 q^{30} + 12 q^{32} - 36 q^{35} - 12 q^{36} + 36 q^{37} + 12 q^{39} - 12 q^{42} - 42 q^{43} - 36 q^{46} - 6 q^{50} + 12 q^{51} + 18 q^{56} - 36 q^{57} - 6 q^{60} + 66 q^{63} + 24 q^{64} + 66 q^{65} - 54 q^{67} + 48 q^{71} - 6 q^{72} + 36 q^{74} - 12 q^{78} - 48 q^{79} - 6 q^{81} - 24 q^{84} - 84 q^{86} + 36 q^{91} + 54 q^{93} - 36 q^{95} + 36 q^{99}+O(q^{100}) \) 24 * q + 12 * q^2 - 12 * q^4 - 18 * q^7 - 24 * q^8 + 6 * q^9 + 12 * q^15 - 12 * q^16 - 6 * q^18 + 12 * q^21 - 36 * q^23 - 12 * q^25 + 18 * q^28 + 6 * q^30 + 12 * q^32 - 36 * q^35 - 12 * q^36 + 36 * q^37 + 12 * q^39 - 12 * q^42 - 42 * q^43 - 36 * q^46 - 6 * q^50 + 12 * q^51 + 18 * q^56 - 36 * q^57 - 6 * q^60 + 66 * q^63 + 24 * q^64 + 66 * q^65 - 54 * q^67 + 48 * q^71 - 6 * q^72 + 36 * q^74 - 12 * q^78 - 48 * q^79 - 6 * q^81 - 24 * q^84 - 84 * q^86 + 36 * q^91 + 54 * q^93 - 36 * q^95 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more