LMFDB - Embedded newform 182.2.m.a.127.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [182,2,Mod(43,182)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(182, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("182.43");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 182 = 2 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	182.m (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:	$1.45327731679$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			127.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	182.127
Dual form			182.2.m.a.43.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.366025 - 0.633975i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-0.633975 - 0.366025i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(1.23205 - 2.13397i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.366025 - 0.633975i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-0.633975 - 0.366025i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(1.23205 - 2.13397i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.633975 - 0.366025i) q^{11} -0.732051 q^{12} +(2.59808 + 2.50000i) q^{13} -1.00000 q^{14} +(-0.633975 + 0.366025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.86603 + 4.96410i) q^{17} -2.46410i q^{18} +(-1.26795 - 0.732051i) q^{19} +(-0.866025 - 0.500000i) q^{20} +0.732051i q^{21} +(0.366025 - 0.633975i) q^{22} +(0.633975 + 1.09808i) q^{23} +(-0.633975 + 0.366025i) q^{24} +4.00000 q^{25} +(3.50000 + 0.866025i) q^{26} -4.00000 q^{27} +(-0.866025 + 0.500000i) q^{28} +(1.50000 + 2.59808i) q^{29} +(-0.366025 + 0.633975i) q^{30} +5.26795i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.464102 - 0.267949i) q^{33} +5.73205i q^{34} +(-0.500000 + 0.866025i) q^{35} +(-1.23205 - 2.13397i) q^{36} +(4.50000 - 2.59808i) q^{37} -1.46410 q^{38} +(0.633975 - 2.56218i) q^{39} -1.00000 q^{40} +(-2.13397 + 1.23205i) q^{41} +(0.366025 + 0.633975i) q^{42} +(-6.09808 + 10.5622i) q^{43} -0.732051i q^{44} +(-2.13397 - 1.23205i) q^{45} +(1.09808 + 0.633975i) q^{46} -2.92820i q^{47} +(-0.366025 + 0.633975i) q^{48} +(0.500000 + 0.866025i) q^{49} +(3.46410 - 2.00000i) q^{50} +4.19615 q^{51} +(3.46410 - 1.00000i) q^{52} +1.53590 q^{53} +(-3.46410 + 2.00000i) q^{54} +(-0.366025 - 0.633975i) q^{55} +(-0.500000 + 0.866025i) q^{56} +1.07180i q^{57} +(2.59808 + 1.50000i) q^{58} +(-9.29423 - 5.36603i) q^{59} +0.732051i q^{60} +(5.86603 - 10.1603i) q^{61} +(2.63397 + 4.56218i) q^{62} +(-2.13397 + 1.23205i) q^{63} -1.00000 q^{64} +(2.50000 - 2.59808i) q^{65} -0.535898 q^{66} +(10.0981 - 5.83013i) q^{67} +(2.86603 + 4.96410i) q^{68} +(0.464102 - 0.803848i) q^{69} +1.00000i q^{70} +(-12.0000 - 6.92820i) q^{71} +(-2.13397 - 1.23205i) q^{72} +11.3923i q^{73} +(2.59808 - 4.50000i) q^{74} +(-1.46410 - 2.53590i) q^{75} +(-1.26795 + 0.732051i) q^{76} -0.732051 q^{77} +(-0.732051 - 2.53590i) q^{78} -3.80385 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-2.23205 - 3.86603i) q^{81} +(-1.23205 + 2.13397i) q^{82} -3.80385i q^{83} +(0.633975 + 0.366025i) q^{84} +(4.96410 + 2.86603i) q^{85} +12.1962i q^{86} +(1.09808 - 1.90192i) q^{87} +(-0.366025 - 0.633975i) q^{88} +(2.19615 - 1.26795i) q^{89} -2.46410 q^{90} +(-1.00000 - 3.46410i) q^{91} +1.26795 q^{92} +(3.33975 - 1.92820i) q^{93} +(-1.46410 - 2.53590i) q^{94} +(-0.732051 + 1.26795i) q^{95} +0.732051i q^{96} +(-4.73205 - 2.73205i) q^{97} +(0.866025 + 0.500000i) q^{98} -1.80385i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 2 q^{4} - 6 q^{6} - 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^6 - 2 * q^9	$ 4 q + 2 q^{3} + 2 q^{4} - 6 q^{6} - 2 q^{9} - 2 q^{10} + 6 q^{11} + 4 q^{12} - 4 q^{14} - 6 q^{15} - 2 q^{16} - 8 q^{17} - 12 q^{19} - 2 q^{22} + 6 q^{23} - 6 q^{24} + 16 q^{25} + 14 q^{26} - 16 q^{27} + 6 q^{29} + 2 q^{30} + 12 q^{33} - 2 q^{35} + 2 q^{36} + 18 q^{37} + 8 q^{38} + 6 q^{39} - 4 q^{40} - 12 q^{41} - 2 q^{42} - 14 q^{43} - 12 q^{45} - 6 q^{46} + 2 q^{48} + 2 q^{49} - 4 q^{51} + 20 q^{53} + 2 q^{55} - 2 q^{56} - 6 q^{59} + 20 q^{61} + 14 q^{62} - 12 q^{63} - 4 q^{64} + 10 q^{65} - 16 q^{66} + 30 q^{67} + 8 q^{68} - 12 q^{69} - 48 q^{71} - 12 q^{72} + 8 q^{75} - 12 q^{76} + 4 q^{77} + 4 q^{78} - 36 q^{79} - 2 q^{81} + 2 q^{82} + 6 q^{84} + 6 q^{85} - 6 q^{87} + 2 q^{88} - 12 q^{89} + 4 q^{90} - 4 q^{91} + 12 q^{92} + 48 q^{93} + 8 q^{94} + 4 q^{95} - 12 q^{97}+O(q^{100}) $ 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^6 - 2 * q^9 - 2 * q^10 + 6 * q^11 + 4 * q^12 - 4 * q^14 - 6 * q^15 - 2 * q^16 - 8 * q^17 - 12 * q^19 - 2 * q^22 + 6 * q^23 - 6 * q^24 + 16 * q^25 + 14 * q^26 - 16 * q^27 + 6 * q^29 + 2 * q^30 + 12 * q^33 - 2 * q^35 + 2 * q^36 + 18 * q^37 + 8 * q^38 + 6 * q^39 - 4 * q^40 - 12 * q^41 - 2 * q^42 - 14 * q^43 - 12 * q^45 - 6 * q^46 + 2 * q^48 + 2 * q^49 - 4 * q^51 + 20 * q^53 + 2 * q^55 - 2 * q^56 - 6 * q^59 + 20 * q^61 + 14 * q^62 - 12 * q^63 - 4 * q^64 + 10 * q^65 - 16 * q^66 + 30 * q^67 + 8 * q^68 - 12 * q^69 - 48 * q^71 - 12 * q^72 + 8 * q^75 - 12 * q^76 + 4 * q^77 + 4 * q^78 - 36 * q^79 - 2 * q^81 + 2 * q^82 + 6 * q^84 + 6 * q^85 - 6 * q^87 + 2 * q^88 - 12 * q^89 + 4 * q^90 - 4 * q^91 + 12 * q^92 + 48 * q^93 + 8 * q^94 + 4 * q^95 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/182\mathbb{Z}\right)^\times$.

$n$	$15$	$157$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.366025	−	0.633975i	−0.211325	−	0.366025i	0.740805	−	0.671721i	$-0.234444\pi$
$3$	−0.366025	−	0.633975i	−0.211325	−	0.366025i	−0.952129	+	0.305695i	$0.901111\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		−	1.00000i		−	0.447214i	−0.974679	−	0.223607i	$-0.928217\pi$
$5$		−	1.00000i		−	0.447214i	0.974679	−	0.223607i	$-0.0717831\pi$
$6$	−0.633975	−	0.366025i	−0.258819	−	0.149429i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$		−	1.00000i		−	0.353553i
$9$	1.23205	−	2.13397i	0.410684	−	0.711325i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	0.633975	−	0.366025i	0.191151	−	0.110361i	−0.401371	−	0.915916i	$-0.631466\pi$
$11$	0.633975	−	0.366025i	0.191151	−	0.110361i	0.592521	+	0.805555i	$0.298133\pi$
$12$	−0.732051			−0.211325
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$13$	2.59808	+	2.50000i	0.720577	+	0.693375i
$14$	−1.00000			−0.267261
$15$	−0.633975	+	0.366025i	−0.163692	+	0.0945074i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.86603	+	4.96410i	−0.695113	+	1.20397i	0.275029	+	0.961436i	$0.411312\pi$
$17$	−2.86603	+	4.96410i	−0.695113	+	1.20397i	−0.970143	+	0.242536i	$0.922021\pi$
$18$		−	2.46410i		−	0.580794i
$19$	−1.26795	−	0.732051i	−0.290887	−	0.167944i	0.347455	−	0.937697i	$-0.387046\pi$
$19$	−1.26795	−	0.732051i	−0.290887	−	0.167944i	−0.638342	+	0.769753i	$0.720379\pi$
$20$	−0.866025	−	0.500000i	−0.193649	−	0.111803i
$21$			0.732051i			0.159747i
$22$	0.366025	−	0.633975i	0.0780369	−	0.135164i
$23$	0.633975	+	1.09808i	0.132193	+	0.228965i	0.924522	−	0.381130i	$-0.124465\pi$
$23$	0.633975	+	1.09808i	0.132193	+	0.228965i	−0.792329	+	0.610094i	$0.791132\pi$
$24$	−0.633975	+	0.366025i	−0.129410	+	0.0747146i
$25$	4.00000			0.800000
$26$	3.50000	+	0.866025i	0.686406	+	0.169842i
$27$	−4.00000			−0.769800
$28$	−0.866025	+	0.500000i	−0.163663	+	0.0944911i
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$	−0.366025	+	0.633975i	−0.0668268	+	0.115747i
$31$			5.26795i			0.946152i	0.881022	+	0.473076i	$0.156856\pi$
$31$			5.26795i			0.946152i	−0.881022	+	0.473076i	$0.843144\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−0.464102	−	0.267949i	−0.0807897	−	0.0466440i
$34$			5.73205i			0.983039i
$35$	−0.500000	+	0.866025i	−0.0845154	+	0.146385i
$36$	−1.23205	−	2.13397i	−0.205342	−	0.355662i
$37$	4.50000	−	2.59808i	0.739795	−	0.427121i	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	4.50000	−	2.59808i	0.739795	−	0.427121i	0.821995	+	0.569495i	$0.192861\pi$
$38$	−1.46410			−0.237509
$39$	0.633975	−	2.56218i	0.101517	−	0.410277i
$40$	−1.00000			−0.158114
$41$	−2.13397	+	1.23205i	−0.333271	+	0.192414i	−0.657292	−	0.753636i	$-0.728298\pi$
$41$	−2.13397	+	1.23205i	−0.333271	+	0.192414i	0.324021	+	0.946050i	$0.394965\pi$
$42$	0.366025	+	0.633975i	0.0564789	+	0.0978244i
$43$	−6.09808	+	10.5622i	−0.929948	+	1.61072i	−0.146544	+	0.989204i	$0.546815\pi$
$43$	−6.09808	+	10.5622i	−0.929948	+	1.61072i	−0.783404	+	0.621513i	$0.786518\pi$
$44$		−	0.732051i		−	0.110361i
$45$	−2.13397	−	1.23205i	−0.318114	−	0.183663i
$46$	1.09808	+	0.633975i	0.161903	+	0.0934745i
$47$		−	2.92820i		−	0.427122i	−0.976930	−	0.213561i	$-0.931494\pi$
$47$		−	2.92820i		−	0.427122i	0.976930	−	0.213561i	$-0.0685063\pi$
$48$	−0.366025	+	0.633975i	−0.0528312	+	0.0915064i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	3.46410	−	2.00000i	0.489898	−	0.282843i
$51$	4.19615			0.587579
$52$	3.46410	−	1.00000i	0.480384	−	0.138675i
$53$	1.53590			0.210972			0.105486	−	0.994421i	$-0.466360\pi$
$53$	1.53590			0.210972			0.105486	+	0.994421i	$0.466360\pi$
$54$	−3.46410	+	2.00000i	−0.471405	+	0.272166i
$55$	−0.366025	−	0.633975i	−0.0493549	−	0.0854851i
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$			1.07180i			0.141963i
$58$	2.59808	+	1.50000i	0.341144	+	0.196960i
$59$	−9.29423	−	5.36603i	−1.21001	−	0.698597i	−0.247245	−	0.968953i	$-0.579525\pi$
$59$	−9.29423	−	5.36603i	−1.21001	−	0.698597i	−0.962760	+	0.270356i	$0.912859\pi$
$60$			0.732051i			0.0945074i
$61$	5.86603	−	10.1603i	0.751068	−	1.30089i	−0.196238	−	0.980556i	$-0.562873\pi$
$61$	5.86603	−	10.1603i	0.751068	−	1.30089i	0.947306	−	0.320331i	$-0.103794\pi$
$62$	2.63397	+	4.56218i	0.334515	+	0.579397i
$63$	−2.13397	+	1.23205i	−0.268856	+	0.155224i
$64$	−1.00000			−0.125000
$65$	2.50000	−	2.59808i	0.310087	−	0.322252i
$66$	−0.535898			−0.0659645
$67$	10.0981	−	5.83013i	1.23368	−	0.712263i	0.265882	−	0.964006i	$-0.414337\pi$
$67$	10.0981	−	5.83013i	1.23368	−	0.712263i	0.967794	+	0.251742i	$0.0810035\pi$
$68$	2.86603	+	4.96410i	0.347557	+	0.601986i
$69$	0.464102	−	0.803848i	0.0558713	−	0.0967719i
$70$			1.00000i			0.119523i
$71$	−12.0000	−	6.92820i	−1.42414	−	0.822226i	−0.427489	−	0.904021i	$-0.640602\pi$
$71$	−12.0000	−	6.92820i	−1.42414	−	0.822226i	−0.996649	+	0.0817942i	$0.973935\pi$
$72$	−2.13397	−	1.23205i	−0.251491	−	0.145199i
$73$			11.3923i			1.33337i	0.745340	+	0.666684i	$0.232287\pi$
$73$			11.3923i			1.33337i	−0.745340	+	0.666684i	$0.767713\pi$
$74$	2.59808	−	4.50000i	0.302020	−	0.523114i
$75$	−1.46410	−	2.53590i	−0.169060	−	0.292820i
$76$	−1.26795	+	0.732051i	−0.145444	+	0.0839720i
$77$	−0.732051			−0.0834249
$78$	−0.732051	−	2.53590i	−0.0828884	−	0.287134i
$79$	−3.80385			−0.427966			−0.213983	−	0.976837i	$-0.568644\pi$
$79$	−3.80385			−0.427966			−0.213983	+	0.976837i	$0.568644\pi$
$80$	−0.866025	+	0.500000i	−0.0968246	+	0.0559017i
$81$	−2.23205	−	3.86603i	−0.248006	−	0.429558i
$82$	−1.23205	+	2.13397i	−0.136057	+	0.235658i
$83$		−	3.80385i		−	0.417527i	−0.977966	−	0.208763i	$-0.933056\pi$
$83$		−	3.80385i		−	0.417527i	0.977966	−	0.208763i	$-0.0669438\pi$
$84$	0.633975	+	0.366025i	0.0691723	+	0.0399366i
$85$	4.96410	+	2.86603i	0.538432	+	0.310864i
$86$			12.1962i			1.31514i
$87$	1.09808	−	1.90192i	0.117726	−	0.203908i
$88$	−0.366025	−	0.633975i	−0.0390184	−	0.0675819i
$89$	2.19615	−	1.26795i	0.232792	−	0.134402i	−0.379068	−	0.925369i	$-0.623755\pi$
$89$	2.19615	−	1.26795i	0.232792	−	0.134402i	0.611859	+	0.790967i	$0.290422\pi$
$90$	−2.46410			−0.259739
$91$	−1.00000	−	3.46410i	−0.104828	−	0.363137i
$92$	1.26795			0.132193
$93$	3.33975	−	1.92820i	0.346316	−	0.199945i
$94$	−1.46410	−	2.53590i	−0.151011	−	0.261558i
$95$	−0.732051	+	1.26795i	−0.0751068	+	0.130089i
$96$			0.732051i			0.0747146i
$97$	−4.73205	−	2.73205i	−0.480467	−	0.277398i	0.240144	−	0.970737i	$-0.422805\pi$
$97$	−4.73205	−	2.73205i	−0.480467	−	0.277398i	−0.720611	+	0.693340i	$0.756139\pi$
$98$	0.866025	+	0.500000i	0.0874818	+	0.0505076i
$99$		−	1.80385i		−	0.181294i
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	0.598076	+	1.03590i	0.0595108	+	0.103076i	0.894246	−	0.447576i	$-0.147713\pi$
$101$	0.598076	+	1.03590i	0.0595108	+	0.103076i	−0.834735	+	0.550652i	$0.814379\pi$
$102$	3.63397	−	2.09808i	0.359817	−	0.207741i
$103$	8.39230			0.826918			0.413459	−	0.910523i	$-0.364320\pi$
$103$	8.39230			0.826918			0.413459	+	0.910523i	$0.364320\pi$
$104$	2.50000	−	2.59808i	0.245145	−	0.254762i
$105$	0.732051			0.0714408
$106$	1.33013	−	0.767949i	0.129193	−	0.0745898i
$107$	−5.46410	−	9.46410i	−0.528235	−	0.914929i	−0.999458	−	0.0329154i	$-0.989521\pi$
$107$	−5.46410	−	9.46410i	−0.528235	−	0.914929i	0.471224	−	0.882014i	$-0.343813\pi$
$108$	−2.00000	+	3.46410i	−0.192450	+	0.333333i
$109$		−	10.0000i		−	0.957826i	−0.877862	−	0.478913i	$-0.841031\pi$
$109$		−	10.0000i		−	0.957826i	0.877862	−	0.478913i	$-0.158969\pi$
$110$	−0.633975	−	0.366025i	−0.0604471	−	0.0348992i
$111$	−3.29423	−	1.90192i	−0.312674	−	0.180523i
$112$			1.00000i			0.0944911i
$113$	−5.69615	+	9.86603i	−0.535849	+	0.928118i	0.463273	+	0.886216i	$0.346675\pi$
$113$	−5.69615	+	9.86603i	−0.535849	+	0.928118i	−0.999122	+	0.0419019i	$0.986658\pi$
$114$	0.535898	+	0.928203i	0.0501915	+	0.0869342i
$115$	1.09808	−	0.633975i	0.102396	−	0.0591184i
$116$	3.00000			0.278543
$117$	8.53590	−	2.46410i	0.789144	−	0.227806i
$118$	−10.7321			−0.987965
$119$	4.96410	−	2.86603i	0.455058	−	0.262728i
$120$	0.366025	+	0.633975i	0.0334134	+	0.0578737i
$121$	−5.23205	+	9.06218i	−0.475641	+	0.823834i
$122$		−	11.7321i		−	1.06217i
$123$	1.56218	+	0.901924i	0.140857	+	0.0813237i
$124$	4.56218	+	2.63397i	0.409696	+	0.236538i
$125$		−	9.00000i		−	0.804984i
$126$	−1.23205	+	2.13397i	−0.109760	+	0.190110i
$127$	4.92820	+	8.53590i	0.437307	+	0.757438i	0.997481	−	0.0709368i	$-0.0225989\pi$
$127$	4.92820	+	8.53590i	0.437307	+	0.757438i	−0.560173	+	0.828375i	$0.689266\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	8.92820			0.786084
$130$	0.866025	−	3.50000i	0.0759555	−	0.306970i
$131$	−5.07180			−0.443125			−0.221562	−	0.975146i	$-0.571116\pi$
$131$	−5.07180			−0.443125			−0.221562	+	0.975146i	$0.571116\pi$
$132$	−0.464102	+	0.267949i	−0.0403949	+	0.0233220i
$133$	0.732051	+	1.26795i	0.0634769	+	0.109945i
$134$	5.83013	−	10.0981i	0.503646	−	0.872341i
$135$			4.00000i			0.344265i
$136$	4.96410	+	2.86603i	0.425668	+	0.245760i
$137$	−5.30385	−	3.06218i	−0.453138	−	0.261620i	0.256016	−	0.966672i	$-0.417590\pi$
$137$	−5.30385	−	3.06218i	−0.453138	−	0.261620i	−0.709155	+	0.705053i	$0.750923\pi$
$138$		−	0.928203i		−	0.0790139i
$139$	0.169873	−	0.294229i	0.0144084	−	0.0249561i	−0.858731	−	0.512426i	$-0.828747\pi$
$139$	0.169873	−	0.294229i	0.0144084	−	0.0249561i	0.873140	+	0.487470i	$0.162080\pi$
$140$	0.500000	+	0.866025i	0.0422577	+	0.0731925i
$141$	−1.85641	+	1.07180i	−0.156338	+	0.0902616i
$142$	−13.8564			−1.16280
$143$	2.56218	+	0.633975i	0.214260	+	0.0530156i
$144$	−2.46410			−0.205342
$145$	2.59808	−	1.50000i	0.215758	−	0.124568i
$146$	5.69615	+	9.86603i	0.471417	+	0.816518i
$147$	0.366025	−	0.633975i	0.0301893	−	0.0522893i
$148$		−	5.19615i		−	0.427121i
$149$	−14.8923	−	8.59808i	−1.22003	−	0.704382i	−0.255102	−	0.966914i	$-0.582109\pi$
$149$	−14.8923	−	8.59808i	−1.22003	−	0.704382i	−0.964923	+	0.262532i	$0.915442\pi$
$150$	−2.53590	−	1.46410i	−0.207055	−	0.119543i
$151$			12.3923i			1.00847i	0.863566	+	0.504236i	$0.168226\pi$
$151$			12.3923i			1.00847i	−0.863566	+	0.504236i	$0.831774\pi$
$152$	−0.732051	+	1.26795i	−0.0593772	+	0.102844i
$153$	7.06218	+	12.2321i	0.570943	+	0.988903i
$154$	−0.633975	+	0.366025i	−0.0510871	+	0.0294952i
$155$	5.26795			0.423132
$156$	−1.90192	−	1.83013i	−0.152276	−	0.146527i
$157$	13.7321			1.09594			0.547968	−	0.836499i	$-0.315401\pi$
$157$	13.7321			1.09594			0.547968	+	0.836499i	$0.315401\pi$
$158$	−3.29423	+	1.90192i	−0.262075	+	0.151309i
$159$	−0.562178	−	0.973721i	−0.0445836	−	0.0772211i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$		−	1.26795i		−	0.0999284i
$162$	−3.86603	−	2.23205i	−0.303744	−	0.175366i
$163$	−0.633975	−	0.366025i	−0.0496567	−	0.0286693i	0.474966	−	0.880004i	$-0.342460\pi$
$163$	−0.633975	−	0.366025i	−0.0496567	−	0.0286693i	−0.524623	+	0.851335i	$0.675794\pi$
$164$			2.46410i			0.192414i
$165$	−0.267949	+	0.464102i	−0.0208598	+	0.0361303i
$166$	−1.90192	−	3.29423i	−0.147618	−	0.255682i
$167$	−4.56218	+	2.63397i	−0.353032	+	0.203823i	−0.666020	−	0.745934i	$-0.732003\pi$
$167$	−4.56218	+	2.63397i	−0.353032	+	0.203823i	0.312988	+	0.949757i	$0.398670\pi$
$168$	0.732051			0.0564789
$169$	0.500000	+	12.9904i	0.0384615	+	0.999260i
$170$	5.73205			0.439628
$171$	−3.12436	+	1.80385i	−0.238925	+	0.137944i
$172$	6.09808	+	10.5622i	0.464974	+	0.805359i
$173$	−10.4641	+	18.1244i	−0.795571	+	1.37797i	0.126905	+	0.991915i	$0.459496\pi$
$173$	−10.4641	+	18.1244i	−0.795571	+	1.37797i	−0.922476	+	0.386054i	$0.873838\pi$
$174$		−	2.19615i		−	0.166490i
$175$	−3.46410	−	2.00000i	−0.261861	−	0.151186i
$176$	−0.633975	−	0.366025i	−0.0477876	−	0.0275902i
$177$			7.85641i			0.590524i
$178$	1.26795	−	2.19615i	0.0950368	−	0.164609i
$179$	8.19615	+	14.1962i	0.612609	+	1.06107i	0.990799	+	0.135342i	$0.0432134\pi$
$179$	8.19615	+	14.1962i	0.612609	+	1.06107i	−0.378190	+	0.925728i	$0.623453\pi$
$180$	−2.13397	+	1.23205i	−0.159057	+	0.0918316i
$181$	3.19615			0.237568			0.118784	−	0.992920i	$-0.462100\pi$
$181$	3.19615			0.237568			0.118784	+	0.992920i	$0.462100\pi$
$182$	−2.59808	−	2.50000i	−0.192582	−	0.185312i
$183$	−8.58846			−0.634877
$184$	1.09808	−	0.633975i	0.0809513	−	0.0467372i
$185$	−2.59808	−	4.50000i	−0.191014	−	0.330847i
$186$	1.92820	−	3.33975i	0.141383	−	0.244882i
$187$			4.19615i			0.306853i
$188$	−2.53590	−	1.46410i	−0.184949	−	0.106781i
$189$	3.46410	+	2.00000i	0.251976	+	0.145479i
$190$			1.46410i			0.106217i
$191$	−3.56218	+	6.16987i	−0.257750	+	0.446436i	−0.965639	−	0.259888i	$-0.916314\pi$
$191$	−3.56218	+	6.16987i	−0.257750	+	0.446436i	0.707889	+	0.706324i	$0.249648\pi$
$192$	0.366025	+	0.633975i	0.0264156	+	0.0457532i
$193$	−20.0885	+	11.5981i	−1.44600	+	0.834848i	−0.998240	−	0.0593065i	$-0.981111\pi$
$193$	−20.0885	+	11.5981i	−1.44600	+	0.834848i	−0.447759	+	0.894154i	$0.647778\pi$
$194$	−5.46410			−0.392300
$195$	−2.56218	−	0.633975i	−0.183481	−	0.0453999i
$196$	1.00000			0.0714286
$197$	6.12436	−	3.53590i	0.436342	−	0.251922i	−0.265703	−	0.964055i	$-0.585604\pi$
$197$	6.12436	−	3.53590i	0.436342	−	0.251922i	0.702045	+	0.712133i	$0.252271\pi$
$198$	−0.901924	−	1.56218i	−0.0640969	−	0.111019i
$199$	−2.73205	+	4.73205i	−0.193670	+	0.335446i	−0.946464	−	0.322810i	$-0.895372\pi$
$199$	−2.73205	+	4.73205i	−0.193670	+	0.335446i	0.752794	+	0.658256i	$0.228706\pi$
$200$		−	4.00000i		−	0.282843i
$201$	−7.39230	−	4.26795i	−0.521413	−	0.301038i
$202$	1.03590	+	0.598076i	0.0728856	+	0.0420805i
$203$		−	3.00000i		−	0.210559i
$204$	2.09808	−	3.63397i	0.146895	−	0.254429i
$205$	1.23205	+	2.13397i	0.0860502	+	0.149043i
$206$	7.26795	−	4.19615i	0.506382	−	0.292360i
$207$	3.12436			0.217158
$208$	0.866025	−	3.50000i	0.0600481	−	0.242681i
$209$	−1.07180			−0.0741377
$210$	0.633975	−	0.366025i	0.0437484	−	0.0252582i
$211$	10.6340	+	18.4186i	0.732073	+	1.26799i	0.955996	+	0.293381i	$0.0947804\pi$
$211$	10.6340	+	18.4186i	0.732073	+	1.26799i	−0.223923	+	0.974607i	$0.571886\pi$
$212$	0.767949	−	1.33013i	0.0527430	−	0.0913535i
$213$			10.1436i			0.695028i
$214$	−9.46410	−	5.46410i	−0.646953	−	0.373518i
$215$	10.5622	+	6.09808i	0.720335	+	0.415885i
$216$			4.00000i			0.272166i
$217$	2.63397	−	4.56218i	0.178806	−	0.309701i
$218$	−5.00000	−	8.66025i	−0.338643	−	0.586546i
$219$	7.22243	−	4.16987i	0.488047	−	0.281774i
$220$	−0.732051			−0.0493549
$221$	−19.8564	+	5.73205i	−1.33569	+	0.385579i
$222$	−3.80385			−0.255298
$223$	10.7321	−	6.19615i	0.718671	−	0.414925i	−0.0955922	−	0.995421i	$-0.530474\pi$
$223$	10.7321	−	6.19615i	0.718671	−	0.414925i	0.814263	+	0.580496i	$0.197141\pi$
$224$	0.500000	+	0.866025i	0.0334077	+	0.0578638i
$225$	4.92820	−	8.53590i	0.328547	−	0.569060i
$226$			11.3923i			0.757805i
$227$	1.09808	+	0.633975i	0.0728819	+	0.0420784i	0.535998	−	0.844219i	$-0.319935\pi$
$227$	1.09808	+	0.633975i	0.0728819	+	0.0420784i	−0.463116	+	0.886298i	$0.653269\pi$
$228$	0.928203	+	0.535898i	0.0614718	+	0.0354907i
$229$		−	24.3923i		−	1.61189i	−0.591991	−	0.805944i	$-0.701658\pi$
$229$		−	24.3923i		−	1.61189i	0.591991	−	0.805944i	$-0.298342\pi$
$230$	0.633975	−	1.09808i	0.0418030	−	0.0724050i
$231$	0.267949	+	0.464102i	0.0176298	+	0.0305356i
$232$	2.59808	−	1.50000i	0.170572	−	0.0984798i
$233$	4.39230			0.287749			0.143875	−	0.989596i	$-0.454044\pi$
$233$	4.39230			0.287749			0.143875	+	0.989596i	$0.454044\pi$
$234$	6.16025	−	6.40192i	0.402708	−	0.418507i
$235$	−2.92820			−0.191015
$236$	−9.29423	+	5.36603i	−0.605003	+	0.349299i
$237$	1.39230	+	2.41154i	0.0904399	+	0.156647i
$238$	2.86603	−	4.96410i	0.185777	−	0.321775i
$239$		−	29.5167i		−	1.90927i	−0.297772	−	0.954637i	$-0.596244\pi$
$239$		−	29.5167i		−	1.90927i	0.297772	−	0.954637i	$-0.403756\pi$
$240$	0.633975	+	0.366025i	0.0409229	+	0.0236268i
$241$	−13.3301	−	7.69615i	−0.858669	−	0.495753i	0.00489737	−	0.999988i	$-0.498441\pi$
$241$	−13.3301	−	7.69615i	−0.858669	−	0.495753i	−0.863566	+	0.504235i	$0.831774\pi$
$242$			10.4641i			0.672658i
$243$	−7.63397	+	13.2224i	−0.489720	+	0.848219i
$244$	−5.86603	−	10.1603i	−0.375534	−	0.650444i
$245$	0.866025	−	0.500000i	0.0553283	−	0.0319438i
$246$	1.80385			0.115009
$247$	−1.46410	−	5.07180i	−0.0931586	−	0.322711i
$248$	5.26795			0.334515
$249$	−2.41154	+	1.39230i	−0.152825	+	0.0882337i
$250$	−4.50000	−	7.79423i	−0.284605	−	0.492950i
$251$	11.4641	−	19.8564i	0.723608	−	1.25333i	−0.235937	−	0.971768i	$-0.575816\pi$
$251$	11.4641	−	19.8564i	0.723608	−	1.25333i	0.959545	−	0.281557i	$-0.0908508\pi$
$252$			2.46410i			0.155224i
$253$	0.803848	+	0.464102i	0.0505375	+	0.0291778i
$254$	8.53590	+	4.92820i	0.535590	+	0.309223i
$255$		−	4.19615i		−	0.262773i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	0.669873	+	1.16025i	0.0417855	+	0.0723747i	0.886162	−	0.463376i	$-0.153362\pi$
$257$	0.669873	+	1.16025i	0.0417855	+	0.0723747i	−0.844376	+	0.535751i	$0.820029\pi$
$258$	7.73205	−	4.46410i	0.481376	−	0.277923i
$259$	−5.19615			−0.322873
$260$	−1.00000	−	3.46410i	−0.0620174	−	0.214834i
$261$	7.39230			0.457572
$262$	−4.39230	+	2.53590i	−0.271357	+	0.156668i
$263$	10.2942	+	17.8301i	0.634769	+	1.09945i	0.986564	+	0.163376i	$0.0522382\pi$
$263$	10.2942	+	17.8301i	0.634769	+	1.09945i	−0.351795	+	0.936077i	$0.614428\pi$
$264$	−0.267949	+	0.464102i	−0.0164911	+	0.0285635i
$265$		−	1.53590i		−	0.0943495i
$266$	1.26795	+	0.732051i	0.0777430	+	0.0448849i
$267$	−1.60770	−	0.928203i	−0.0983893	−	0.0568051i
$268$		−	11.6603i		−	0.712263i
$269$	14.3923	−	24.9282i	0.877514	−	1.51990i	0.0234543	−	0.999725i	$-0.492534\pi$
$269$	14.3923	−	24.9282i	0.877514	−	1.51990i	0.854060	−	0.520174i	$-0.174133\pi$
$270$	2.00000	+	3.46410i	0.121716	+	0.210819i
$271$	6.16987	−	3.56218i	0.374793	−	0.216387i	−0.300757	−	0.953701i	$-0.597239\pi$
$271$	6.16987	−	3.56218i	0.374793	−	0.216387i	0.675550	+	0.737314i	$0.263906\pi$
$272$	5.73205			0.347557
$273$	−1.83013	+	1.90192i	−0.110764	+	0.115110i
$274$	−6.12436			−0.369986
$275$	2.53590	−	1.46410i	0.152920	−	0.0882886i
$276$	−0.464102	−	0.803848i	−0.0279356	−	0.0483859i
$277$	4.69615	−	8.13397i	0.282164	−	0.488723i	−0.689753	−	0.724045i	$-0.742281\pi$
$277$	4.69615	−	8.13397i	0.282164	−	0.488723i	0.971918	+	0.235321i	$0.0756143\pi$
$278$		−	0.339746i		−	0.0203766i
$279$	11.2417	+	6.49038i	0.673021	+	0.388569i
$280$	0.866025	+	0.500000i	0.0517549	+	0.0298807i
$281$		−	16.6603i		−	0.993867i	−0.867789	−	0.496934i	$-0.834459\pi$
$281$		−	16.6603i		−	0.993867i	0.867789	−	0.496934i	$-0.165541\pi$
$282$	−1.07180	+	1.85641i	−0.0638246	+	0.110547i
$283$	−5.29423	−	9.16987i	−0.314709	−	0.545092i	0.664666	−	0.747140i	$-0.268574\pi$
$283$	−5.29423	−	9.16987i	−0.314709	−	0.545092i	−0.979376	+	0.202048i	$0.935240\pi$
$284$	−12.0000	+	6.92820i	−0.712069	+	0.411113i
$285$	1.07180			0.0634878
$286$	2.53590	−	0.732051i	0.149951	−	0.0432871i
$287$	2.46410			0.145451
$288$	−2.13397	+	1.23205i	−0.125746	+	0.0725993i
$289$	−7.92820	−	13.7321i	−0.466365	−	0.807768i
$290$	1.50000	−	2.59808i	0.0880830	−	0.152564i
$291$			4.00000i			0.234484i
$292$	9.86603	+	5.69615i	0.577365	+	0.333342i
$293$	15.0622	+	8.69615i	0.879942	+	0.508035i	0.870639	−	0.491922i	$-0.163706\pi$
$293$	15.0622	+	8.69615i	0.879942	+	0.508035i	0.00930260	+	0.999957i	$0.497039\pi$
$294$		−	0.732051i		−	0.0426941i
$295$	−5.36603	+	9.29423i	−0.312422	+	0.541131i
$296$	−2.59808	−	4.50000i	−0.151010	−	0.261557i
$297$	−2.53590	+	1.46410i	−0.147148	+	0.0849558i
$298$	−17.1962			−0.996146
$299$	−1.09808	+	4.43782i	−0.0635034	+	0.256646i
$300$	−2.92820			−0.169060
$301$	10.5622	−	6.09808i	0.608794	−	0.351487i
$302$	6.19615	+	10.7321i	0.356549	+	0.617560i
$303$	0.437822	−	0.758330i	0.0251522	−	0.0435649i
$304$			1.46410i			0.0839720i
$305$	−10.1603	−	5.86603i	−0.581774	−	0.335888i
$306$	12.2321	+	7.06218i	0.699260	+	0.403718i
$307$		−	23.5167i		−	1.34217i	−0.741382	−	0.671083i	$-0.765829\pi$
$307$		−	23.5167i		−	1.34217i	0.741382	−	0.671083i	$-0.234171\pi$
$308$	−0.366025	+	0.633975i	−0.0208562	+	0.0361241i
$309$	−3.07180	−	5.32051i	−0.174748	−	0.302673i
$310$	4.56218	−	2.63397i	0.259114	−	0.149600i
$311$	10.1962			0.578171			0.289085	−	0.957303i	$-0.406649\pi$
$311$	10.1962			0.578171			0.289085	+	0.957303i	$0.406649\pi$
$312$	−2.56218	−	0.633975i	−0.145055	−	0.0358917i
$313$	−32.0000			−1.80875			−0.904373	−	0.426742i	$-0.859661\pi$
$313$	−32.0000			−1.80875			−0.904373	+	0.426742i	$0.859661\pi$
$314$	11.8923	−	6.86603i	0.671122	−	0.387472i
$315$	1.23205	+	2.13397i	0.0694182	+	0.120236i
$316$	−1.90192	+	3.29423i	−0.106992	+	0.185315i
$317$			7.05256i			0.396111i	0.980191	+	0.198056i	$0.0634627\pi$
$317$			7.05256i			0.396111i	−0.980191	+	0.198056i	$0.936537\pi$
$318$	−0.973721	−	0.562178i	−0.0546035	−	0.0315254i
$319$	1.90192	+	1.09808i	0.106487	+	0.0614805i
$320$			1.00000i			0.0559017i
$321$	−4.00000	+	6.92820i	−0.223258	+	0.386695i
$322$	−0.633975	−	1.09808i	−0.0353300	−	0.0611934i
$323$	7.26795	−	4.19615i	0.404400	−	0.233480i
$324$	−4.46410			−0.248006
$325$	10.3923	+	10.0000i	0.576461	+	0.554700i
$326$	−0.732051			−0.0405445
$327$	−6.33975	+	3.66025i	−0.350589	+	0.202413i
$328$	1.23205	+	2.13397i	0.0680286	+	0.117829i
$329$	−1.46410	+	2.53590i	−0.0807185	+	0.139809i
$330$			0.535898i			0.0295002i
$331$	3.75833	+	2.16987i	0.206577	+	0.119267i	0.599719	−	0.800210i	$-0.295279\pi$
$331$	3.75833	+	2.16987i	0.206577	+	0.119267i	−0.393143	+	0.919477i	$0.628612\pi$
$332$	−3.29423	−	1.90192i	−0.180794	−	0.104382i
$333$		−	12.8038i		−	0.701647i
$334$	−2.63397	+	4.56218i	−0.144125	+	0.249631i
$335$	−5.83013	−	10.0981i	−0.318534	−	0.551717i
$336$	0.633975	−	0.366025i	0.0345861	−	0.0199683i
$337$	−6.32051			−0.344300			−0.172150	−	0.985071i	$-0.555071\pi$
$337$	−6.32051			−0.344300			−0.172150	+	0.985071i	$0.555071\pi$
$338$	6.92820	+	11.0000i	0.376845	+	0.598321i
$339$	8.33975			0.452953
$340$	4.96410	−	2.86603i	0.269216	−	0.155432i
$341$	1.92820	+	3.33975i	0.104418	+	0.180857i
$342$	−1.80385	+	3.12436i	−0.0975409	+	0.168946i
$343$		−	1.00000i		−	0.0539949i
$344$	10.5622	+	6.09808i	0.569474	+	0.328786i
$345$	−0.803848	−	0.464102i	−0.0432777	−	0.0249864i
$346$			20.9282i			1.12511i
$347$	−14.4904	+	25.0981i	−0.777884	+	1.34734i	0.155275	+	0.987871i	$0.450374\pi$
$347$	−14.4904	+	25.0981i	−0.777884	+	1.34734i	−0.933159	+	0.359464i	$0.882960\pi$
$348$	−1.09808	−	1.90192i	−0.0588631	−	0.101954i
$349$	−1.73205	+	1.00000i	−0.0927146	+	0.0535288i	−0.545640	−	0.838019i	$-0.683714\pi$
$349$	−1.73205	+	1.00000i	−0.0927146	+	0.0535288i	0.452926	+	0.891548i	$0.350380\pi$
$350$	−4.00000			−0.213809
$351$	−10.3923	−	10.0000i	−0.554700	−	0.533761i
$352$	−0.732051			−0.0390184
$353$	−31.3301	+	18.0885i	−1.66753	+	0.962751i	−0.698573	+	0.715539i	$0.746181\pi$
$353$	−31.3301	+	18.0885i	−1.66753	+	0.962751i	−0.968961	+	0.247213i	$0.920485\pi$
$354$	3.92820	+	6.80385i	0.208782	+	0.361620i
$355$	−6.92820	+	12.0000i	−0.367711	+	0.636894i
$356$		−	2.53590i		−	0.134402i
$357$	−3.63397	−	2.09808i	−0.192330	−	0.111042i
$358$	14.1962	+	8.19615i	0.750290	+	0.433180i
$359$			16.3923i			0.865153i	0.901597	+	0.432576i	$0.142395\pi$
$359$			16.3923i			0.865153i	−0.901597	+	0.432576i	$0.857605\pi$
$360$	−1.23205	+	2.13397i	−0.0649348	+	0.112470i
$361$	−8.42820	−	14.5981i	−0.443590	−	0.768320i
$362$	2.76795	−	1.59808i	0.145480	−	0.0839930i
$363$	7.66025			0.402059
$364$	−3.50000	−	0.866025i	−0.183450	−	0.0453921i
$365$	11.3923			0.596300
$366$	−7.43782	+	4.29423i	−0.388781	+	0.224463i
$367$	−16.9545	−	29.3660i	−0.885017	−	1.53289i	−0.845694	−	0.533667i	$-0.820813\pi$
$367$	−16.9545	−	29.3660i	−0.885017	−	1.53289i	−0.0393224	−	0.999227i	$-0.512520\pi$
$368$	0.633975	−	1.09808i	0.0330482	−	0.0572412i
$369$			6.07180i			0.316085i
$370$	−4.50000	−	2.59808i	−0.233944	−	0.135068i
$371$	−1.33013	−	0.767949i	−0.0690568	−	0.0398699i
$372$		−	3.85641i		−	0.199945i
$373$	16.2321	−	28.1147i	0.840464	−	1.45573i	−0.0490394	−	0.998797i	$-0.515616\pi$
$373$	16.2321	−	28.1147i	0.840464	−	1.45573i	0.889503	−	0.456929i	$-0.151051\pi$
$374$	2.09808	+	3.63397i	0.108489	+	0.187908i
$375$	−5.70577	+	3.29423i	−0.294645	+	0.170113i
$376$	−2.92820			−0.151011
$377$	−2.59808	+	10.5000i	−0.133808	+	0.540778i
$378$	4.00000			0.205738
$379$	19.2224	−	11.0981i	0.987390	−	0.570070i	0.0828969	−	0.996558i	$-0.473583\pi$
$379$	19.2224	−	11.0981i	0.987390	−	0.570070i	0.904493	+	0.426488i	$0.140249\pi$
$380$	0.732051	+	1.26795i	0.0375534	+	0.0650444i
$381$	3.60770	−	6.24871i	0.184828	−	0.320131i
$382$			7.12436i			0.364514i
$383$	28.2224	+	16.2942i	1.44210	+	0.832596i	0.997990	−	0.0633765i	$-0.0201869\pi$
$383$	28.2224	+	16.2942i	1.44210	+	0.832596i	0.444109	+	0.895973i	$0.353520\pi$
$384$	0.633975	+	0.366025i	0.0323524	+	0.0186787i
$385$			0.732051i			0.0373088i
$386$	−11.5981	+	20.0885i	−0.590327	+	1.02248i
$387$	15.0263	+	26.0263i	0.763829	+	1.32299i
$388$	−4.73205	+	2.73205i	−0.240233	+	0.138699i
$389$	−24.3205			−1.23310			−0.616549	−	0.787316i	$-0.711470\pi$
$389$	−24.3205			−1.23310			−0.616549	+	0.787316i	$0.711470\pi$
$390$	−2.53590	+	0.732051i	−0.128410	+	0.0370688i
$391$	−7.26795			−0.367556
$392$	0.866025	−	0.500000i	0.0437409	−	0.0252538i
$393$	1.85641	+	3.21539i	0.0936433	+	0.162195i
$394$	3.53590	−	6.12436i	0.178136	−	0.308541i
$395$			3.80385i			0.191392i
$396$	−1.56218	−	0.901924i	−0.0785024	−	0.0453234i
$397$	−25.5167	−	14.7321i	−1.28064	−	0.739380i	−0.303678	−	0.952775i	$-0.598215\pi$
$397$	−25.5167	−	14.7321i	−1.28064	−	0.739380i	−0.976966	+	0.213394i	$0.931548\pi$
$398$			5.46410i			0.273891i
$399$	0.535898	−	0.928203i	0.0268285	−	0.0464683i
$400$	−2.00000	−	3.46410i	−0.100000	−	0.173205i
$401$	−28.6244	+	16.5263i	−1.42943	+	0.825283i	−0.997076	−	0.0764198i	$-0.975651\pi$
$401$	−28.6244	+	16.5263i	−1.42943	+	0.825283i	−0.432356	+	0.901703i	$0.642318\pi$
$402$	−8.53590			−0.425732
$403$	−13.1699	+	13.6865i	−0.656038	+	0.681775i
$404$	1.19615			0.0595108
$405$	−3.86603	+	2.23205i	−0.192104	+	0.110911i
$406$	−1.50000	−	2.59808i	−0.0744438	−	0.128940i
$407$	1.90192	−	3.29423i	0.0942749	−	0.163289i
$408$		−	4.19615i		−	0.207741i
$409$	22.7942	+	13.1603i	1.12710	+	0.650733i	0.943204	−	0.332213i	$-0.107795\pi$
$409$	22.7942	+	13.1603i	1.12710	+	0.650733i	0.183898	+	0.982945i	$0.441129\pi$
$410$	2.13397	+	1.23205i	0.105389	+	0.0608467i
$411$			4.48334i			0.221147i
$412$	4.19615	−	7.26795i	0.206730	−	0.358066i
$413$	5.36603	+	9.29423i	0.264045	+	0.457339i
$414$	2.70577	−	1.56218i	0.132981	−	0.0767769i
$415$	−3.80385			−0.186724
$416$	−1.00000	−	3.46410i	−0.0490290	−	0.169842i
$417$	−0.248711			−0.0121794
$418$	−0.928203	+	0.535898i	−0.0453999	+	0.0262116i
$419$	−2.56218	−	4.43782i	−0.125171	−	0.216802i	0.796629	−	0.604469i	$-0.206614\pi$
$419$	−2.56218	−	4.43782i	−0.125171	−	0.216802i	−0.921800	+	0.387667i	$0.873281\pi$
$420$	0.366025	−	0.633975i	0.0178602	−	0.0309348i
$421$			14.1244i			0.688379i	0.938900	+	0.344189i	$0.111846\pi$
$421$			14.1244i			0.688379i	−0.938900	+	0.344189i	$0.888154\pi$
$422$	18.4186	+	10.6340i	0.896603	+	0.517654i
$423$	−6.24871	−	3.60770i	−0.303823	−	0.175412i
$424$		−	1.53590i		−	0.0745898i
$425$	−11.4641	+	19.8564i	−0.556091	+	0.963177i
$426$	5.07180	+	8.78461i	0.245729	+	0.425616i
$427$	−10.1603	+	5.86603i	−0.491689	+	0.283877i
$428$	−10.9282			−0.528235
$429$	−0.535898	−	1.85641i	−0.0258734	−	0.0896281i
$430$	12.1962			0.588151
$431$	22.9808	−	13.2679i	1.10694	−	0.639095i	0.168908	−	0.985632i	$-0.445976\pi$
$431$	22.9808	−	13.2679i	1.10694	−	0.639095i	0.938036	+	0.346537i	$0.112643\pi$
$432$	2.00000	+	3.46410i	0.0962250	+	0.166667i
$433$	10.8660	−	18.8205i	0.522188	−	0.904456i	−0.477479	−	0.878643i	$-0.658449\pi$
$433$	10.8660	−	18.8205i	0.522188	−	0.904456i	0.999667	−	0.0258127i	$-0.00821735\pi$
$434$		−	5.26795i		−	0.252870i
$435$	−1.90192	−	1.09808i	−0.0911903	−	0.0526487i
$436$	−8.66025	−	5.00000i	−0.414751	−	0.239457i
$437$		−	1.85641i		−	0.0888040i
$438$	4.16987	−	7.22243i	0.199244	−	0.345101i
$439$	−9.63397	−	16.6865i	−0.459805	−	0.796405i	0.539146	−	0.842212i	$-0.318747\pi$
$439$	−9.63397	−	16.6865i	−0.459805	−	0.796405i	−0.998950	+	0.0458077i	$0.985414\pi$
$440$	−0.633975	+	0.366025i	−0.0302236	+	0.0174496i
$441$	2.46410			0.117338
$442$	−14.3301	+	14.8923i	−0.681615	+	0.708355i
$443$	35.3205			1.67813			0.839064	−	0.544033i	$-0.183103\pi$
$443$	35.3205			1.67813			0.839064	+	0.544033i	$0.183103\pi$
$444$	−3.29423	+	1.90192i	−0.156337	+	0.0902613i
$445$	−1.26795	−	2.19615i	−0.0601066	−	0.104108i
$446$	6.19615	−	10.7321i	0.293396	−	0.508177i
$447$			12.5885i			0.595414i
$448$	0.866025	+	0.500000i	0.0409159	+	0.0236228i
$449$	15.5885	+	9.00000i	0.735665	+	0.424736i	0.820491	−	0.571660i	$-0.193700\pi$
$449$	15.5885	+	9.00000i	0.735665	+	0.424736i	−0.0848262	+	0.996396i	$0.527033\pi$
$450$		−	9.85641i		−	0.464635i
$451$	−0.901924	+	1.56218i	−0.0424699	+	0.0735601i
$452$	5.69615	+	9.86603i	0.267924	+	0.464059i
$453$	7.85641	−	4.53590i	0.369126	−	0.213115i
$454$	1.26795			0.0595078
$455$	−3.46410	+	1.00000i	−0.162400	+	0.0468807i
$456$	1.07180			0.0501915
$457$	−12.3564	+	7.13397i	−0.578008	+	0.333713i	−0.760341	−	0.649524i	$-0.774968\pi$
$457$	−12.3564	+	7.13397i	−0.578008	+	0.333713i	0.182333	+	0.983237i	$0.441635\pi$
$458$	−12.1962	−	21.1244i	−0.569889	−	0.987076i
$459$	11.4641	−	19.8564i	0.535098	−	0.926818i
$460$		−	1.26795i		−	0.0591184i
$461$	7.20577	+	4.16025i	0.335606	+	0.193762i	0.658327	−	0.752732i	$-0.271264\pi$
$461$	7.20577	+	4.16025i	0.335606	+	0.193762i	−0.322721	+	0.946494i	$0.604598\pi$
$462$	0.464102	+	0.267949i	0.0215920	+	0.0124661i
$463$		−	3.94744i		−	0.183453i	−0.995784	−	0.0917266i	$-0.970761\pi$
$463$		−	3.94744i		−	0.183453i	0.995784	−	0.0917266i	$-0.0292386\pi$
$464$	1.50000	−	2.59808i	0.0696358	−	0.120613i
$465$	−1.92820	−	3.33975i	−0.0894183	−	0.154877i
$466$	3.80385	−	2.19615i	0.176210	−	0.101735i
$467$	24.7321			1.14446			0.572231	−	0.820092i	$-0.306078\pi$
$467$	24.7321			1.14446			0.572231	+	0.820092i	$0.306078\pi$
$468$	2.13397	−	8.62436i	0.0986430	−	0.398661i
$469$	−11.6603			−0.538421
$470$	−2.53590	+	1.46410i	−0.116972	+	0.0675340i
$471$	−5.02628	−	8.70577i	−0.231599	−	0.401141i
$472$	−5.36603	+	9.29423i	−0.246991	+	0.427802i
$473$			8.92820i			0.410519i
$474$	2.41154	+	1.39230i	0.110766	+	0.0639507i
$475$	−5.07180	−	2.92820i	−0.232710	−	0.134355i
$476$		−	5.73205i		−	0.262728i
$477$	1.89230	−	3.27757i	0.0866427	−	0.150070i
$478$	−14.7583	−	25.5622i	−0.675030	−	1.16919i
$479$	27.8827	−	16.0981i	1.27399	−	0.735540i	0.298256	−	0.954486i	$-0.403595\pi$
$479$	27.8827	−	16.0981i	1.27399	−	0.735540i	0.975737	+	0.218946i	$0.0702619\pi$
$480$	0.732051			0.0334134
$481$	18.1865	+	4.50000i	0.829235	+	0.205182i
$482$	−15.3923			−0.701100
$483$	−0.803848	+	0.464102i	−0.0365763	+	0.0211174i
$484$	5.23205	+	9.06218i	0.237820	+	0.411917i
$485$	−2.73205	+	4.73205i	−0.124056	+	0.214871i
$486$			15.2679i			0.692568i
$487$	27.1244	+	15.6603i	1.22912	+	0.709634i	0.966846	−	0.255359i	$-0.0821937\pi$
$487$	27.1244	+	15.6603i	1.22912	+	0.709634i	0.262276	+	0.964993i	$0.415527\pi$
$488$	−10.1603	−	5.86603i	−0.459933	−	0.265542i
$489$			0.535898i			0.0242342i
$490$	0.500000	−	0.866025i	0.0225877	−	0.0391230i
$491$	−13.8564	−	24.0000i	−0.625331	−	1.08310i	−0.988477	−	0.151373i	$-0.951631\pi$
$491$	−13.8564	−	24.0000i	−0.625331	−	1.08310i	0.363146	−	0.931732i	$-0.381703\pi$
$492$	1.56218	−	0.901924i	0.0704284	−	0.0406619i
$493$	−17.1962			−0.774476
$494$	−3.80385	−	3.66025i	−0.171143	−	0.164683i
$495$	−1.80385			−0.0810769
$496$	4.56218	−	2.63397i	0.204848	−	0.118269i
$497$	6.92820	+	12.0000i	0.310772	+	0.538274i
$498$	−1.39230	+	2.41154i	−0.0623907	+	0.108064i
$499$			11.2679i			0.504423i	0.967672	+	0.252211i	$0.0811578\pi$
$499$			11.2679i			0.504423i	−0.967672	+	0.252211i	$0.918842\pi$
$500$	−7.79423	−	4.50000i	−0.348569	−	0.201246i
$501$	3.33975	+	1.92820i	0.149209	+	0.0861458i
$502$		−	22.9282i		−	1.02334i
$503$	−10.3660	+	17.9545i	−0.462198	+	0.800551i	−0.999070	−	0.0431129i	$-0.986272\pi$
$503$	−10.3660	+	17.9545i	−0.462198	+	0.800551i	0.536872	+	0.843664i	$0.319606\pi$
$504$	1.23205	+	2.13397i	0.0548799	+	0.0950548i
$505$	1.03590	−	0.598076i	0.0460969	−	0.0266140i
$506$	0.928203			0.0412637
$507$	8.05256	−	5.07180i	0.357627	−	0.225246i
$508$	9.85641			0.437307
$509$	−23.7224	+	13.6962i	−1.05148	+	0.607071i	−0.923063	−	0.384649i	$-0.874322\pi$
$509$	−23.7224	+	13.6962i	−1.05148	+	0.607071i	−0.128415	+	0.991720i	$0.540989\pi$
$510$	−2.09808	−	3.63397i	−0.0929044	−	0.160915i
$511$	5.69615	−	9.86603i	0.251983	−	0.436447i
$512$			1.00000i			0.0441942i
$513$	5.07180	+	2.92820i	0.223925	+	0.129283i
$514$	1.16025	+	0.669873i	0.0511766	+	0.0295468i
$515$		−	8.39230i		−	0.369809i
$516$	4.46410	−	7.73205i	0.196521	−	0.340385i
$517$	−1.07180	−	1.85641i	−0.0471376	−	0.0816447i
$518$	−4.50000	+	2.59808i	−0.197719	+	0.114153i
$519$	15.3205			0.672496
$520$	−2.59808	−	2.50000i	−0.113933	−	0.109632i
$521$	44.3731			1.94402			0.972010	−	0.234941i	$-0.0754896\pi$
$521$	44.3731			1.94402			0.972010	+	0.234941i	$0.0754896\pi$
$522$	6.40192	−	3.69615i	0.280205	−	0.161776i
$523$	−10.7321	−	18.5885i	−0.469280	−	0.812816i	0.530103	−	0.847933i	$-0.322153\pi$
$523$	−10.7321	−	18.5885i	−0.469280	−	0.812816i	−0.999383	+	0.0351165i	$0.988820\pi$
$524$	−2.53590	+	4.39230i	−0.110781	+	0.191879i
$525$			2.92820i			0.127797i
$526$	17.8301	+	10.2942i	0.777430	+	0.448850i
$527$	−26.1506	−	15.0981i	−1.13914	−	0.657683i
$528$			0.535898i			0.0233220i
$529$	10.6962	−	18.5263i	0.465050	−	0.805490i
$530$	−0.767949	−	1.33013i	−0.0333576	−	0.0577770i
$531$	−22.9019	+	13.2224i	−0.993859	+	0.573805i
$532$	1.46410			0.0634769
$533$	−8.62436	−	2.13397i	−0.373562	−	0.0924327i
$534$	−1.85641			−0.0803346
$535$	−9.46410	+	5.46410i	−0.409169	+	0.236234i
$536$	−5.83013	−	10.0981i	−0.251823	−	0.436170i
$537$	6.00000	−	10.3923i	0.258919	−	0.448461i
$538$		−	28.7846i		−	1.24099i
$539$	0.633975	+	0.366025i	0.0273072	+	0.0157658i
$540$	3.46410	+	2.00000i	0.149071	+	0.0860663i
$541$			8.26795i			0.355467i	0.984079	+	0.177733i	$0.0568765\pi$
$541$			8.26795i			0.355467i	−0.984079	+	0.177733i	$0.943124\pi$
$542$	3.56218	−	6.16987i	0.153009	−	0.265019i
$543$	−1.16987	−	2.02628i	−0.0502041	−	0.0869560i
$544$	4.96410	−	2.86603i	0.212834	−	0.122880i
$545$	−10.0000			−0.428353
$546$	−0.633975	+	2.56218i	−0.0271316	+	0.109651i
$547$	−30.4449			−1.30173			−0.650864	−	0.759194i	$-0.725593\pi$
$547$	−30.4449			−1.30173			−0.650864	+	0.759194i	$0.725593\pi$
$548$	−5.30385	+	3.06218i	−0.226569	+	0.130810i
$549$	−14.4545	−	25.0359i	−0.616902	−	1.06851i
$550$	1.46410	−	2.53590i	0.0624295	−	0.108131i
$551$		−	4.39230i		−	0.187118i
$552$	−0.803848	−	0.464102i	−0.0342140	−	0.0197535i
$553$	3.29423	+	1.90192i	0.140085	+	0.0808780i
$554$		−	9.39230i		−	0.399041i
$555$	−1.90192	+	3.29423i	−0.0807322	+	0.139832i
$556$	−0.169873	−	0.294229i	−0.00720422	−	0.0124781i
$557$	22.6244	−	13.0622i	0.958625	−	0.553462i	0.0628752	−	0.998021i	$-0.479973\pi$
$557$	22.6244	−	13.0622i	0.958625	−	0.553462i	0.895749	+	0.444559i	$0.146640\pi$
$558$	12.9808			0.549519
$559$	−42.2487	+	12.1962i	−1.78693	+	0.515842i
$560$	1.00000			0.0422577
$561$	2.66025	−	1.53590i	0.112316	−	0.0648457i
$562$	−8.33013	−	14.4282i	−0.351385	−	0.608617i
$563$	−14.2224	+	24.6340i	−0.599404	+	1.03820i	0.393505	+	0.919322i	$0.371262\pi$
$563$	−14.2224	+	24.6340i	−0.599404	+	1.03820i	−0.992909	+	0.118876i	$0.962071\pi$
$564$			2.14359i			0.0902616i
$565$	9.86603	+	5.69615i	0.415067	+	0.239639i
$566$	−9.16987	−	5.29423i	−0.385439	−	0.222533i
$567$			4.46410i			0.187475i
$568$	−6.92820	+	12.0000i	−0.290701	+	0.503509i
$569$	−5.66025	−	9.80385i	−0.237290	−	0.410999i	0.722646	−	0.691219i	$-0.242926\pi$
$569$	−5.66025	−	9.80385i	−0.237290	−	0.410999i	−0.959936	+	0.280220i	$0.909593\pi$
$570$	0.928203	−	0.535898i	0.0388782	−	0.0224463i
$571$	5.46410			0.228666			0.114333	−	0.993443i	$-0.463527\pi$
$571$	5.46410			0.228666			0.114333	+	0.993443i	$0.463527\pi$
$572$	1.83013	−	1.90192i	0.0765215	−	0.0795234i
$573$	5.21539			0.217876
$574$	2.13397	−	1.23205i	0.0890704	−	0.0514248i
$575$	2.53590	+	4.39230i	0.105754	+	0.183172i
$576$	−1.23205	+	2.13397i	−0.0513355	+	0.0889156i
$577$			34.1769i			1.42280i	0.702786	+	0.711402i	$0.251939\pi$
$577$			34.1769i			1.42280i	−0.702786	+	0.711402i	$0.748061\pi$
$578$	−13.7321	−	7.92820i	−0.571178	−	0.329770i
$579$	14.7058	+	8.49038i	0.611151	+	0.352848i
$580$		−	3.00000i		−	0.124568i
$581$	−1.90192	+	3.29423i	−0.0789051	+	0.136668i
$582$	2.00000	+	3.46410i	0.0829027	+	0.143592i
$583$	0.973721	−	0.562178i	0.0403274	−	0.0232830i
$584$	11.3923			0.471417
$585$	−2.46410	−	8.53590i	−0.101878	−	0.352916i
$586$	17.3923			0.718469
$587$	−24.9282	+	14.3923i	−1.02890	+	0.594034i	−0.916668	−	0.399648i	$-0.869132\pi$
$587$	−24.9282	+	14.3923i	−1.02890	+	0.594034i	−0.112229	+	0.993682i	$0.535799\pi$
$588$	−0.366025	−	0.633975i	−0.0150946	−	0.0261447i
$589$	3.85641	−	6.67949i	0.158900	−	0.275224i
$590$			10.7321i			0.441832i
$591$	−4.48334	−	2.58846i	−0.184420	−	0.106475i
$592$	−4.50000	−	2.59808i	−0.184949	−	0.106780i
$593$		−	3.14359i		−	0.129092i	−0.997915	−	0.0645460i	$-0.979440\pi$
$593$		−	3.14359i		−	0.129092i	0.997915	−	0.0645460i	$-0.0205599\pi$
$594$	−1.46410	+	2.53590i	−0.0600728	+	0.104049i
$595$	−2.86603	−	4.96410i	−0.117496	−	0.203508i
$596$	−14.8923	+	8.59808i	−0.610013	+	0.352191i
$597$	4.00000			0.163709
$598$	1.26795	+	4.39230i	0.0518503	+	0.179615i
$599$	30.9282			1.26369			0.631846	−	0.775094i	$-0.282297\pi$
$599$	30.9282			1.26369			0.631846	+	0.775094i	$0.282297\pi$
$600$	−2.53590	+	1.46410i	−0.103528	+	0.0597717i
$601$	11.5263	+	19.9641i	0.470167	+	0.814353i	0.999418	−	0.0341125i	$-0.0108604\pi$
$601$	11.5263	+	19.9641i	0.470167	+	0.814353i	−0.529251	+	0.848465i	$0.677527\pi$
$602$	6.09808	−	10.5622i	0.248539	−	0.430482i
$603$		−	28.7321i		−	1.17006i
$604$	10.7321	+	6.19615i	0.436681	+	0.252118i
$605$	9.06218	+	5.23205i	0.368430	+	0.212713i
$606$		−	0.875644i		−	0.0355706i
$607$	4.92820	−	8.53590i	0.200030	−	0.346461i	−0.748508	−	0.663126i	$-0.769230\pi$
$607$	4.92820	−	8.53590i	0.200030	−	0.346461i	0.948538	+	0.316664i	$0.102563\pi$
$608$	0.732051	+	1.26795i	0.0296886	+	0.0514221i
$609$	−1.90192	+	1.09808i	−0.0770698	+	0.0444963i
$610$	−11.7321			−0.475017
$611$	7.32051	−	7.60770i	0.296156	−	0.307774i
$612$	14.1244			0.570943
$613$	13.8397	−	7.99038i	0.558982	−	0.322728i	−0.193755	−	0.981050i	$-0.562067\pi$
$613$	13.8397	−	7.99038i	0.558982	−	0.322728i	0.752737	+	0.658322i	$0.228733\pi$
$614$	−11.7583	−	20.3660i	−0.474528	−	0.821906i
$615$	0.901924	−	1.56218i	0.0363691	−	0.0629931i
$616$			0.732051i			0.0294952i
$617$	−28.7487	−	16.5981i	−1.15738	−	0.668213i	−0.206705	−	0.978403i	$-0.566274\pi$
$617$	−28.7487	−	16.5981i	−1.15738	−	0.668213i	−0.950675	+	0.310190i	$0.899607\pi$
$618$	−5.32051	−	3.07180i	−0.214022	−	0.123566i
$619$			34.0526i			1.36869i	0.729159	+	0.684344i	$0.239911\pi$
$619$			34.0526i			1.36869i	−0.729159	+	0.684344i	$0.760089\pi$
$620$	2.63397	−	4.56218i	0.105783	−	0.183221i
$621$	−2.53590	−	4.39230i	−0.101762	−	0.176257i
$622$	8.83013	−	5.09808i	0.354056	−	0.204414i
$623$	−2.53590			−0.101599
$624$	−2.53590	+	0.732051i	−0.101517	+	0.0293055i
$625$	11.0000			0.440000
$626$	−27.7128	+	16.0000i	−1.10763	+	0.639489i
$627$	0.392305	+	0.679492i	0.0156671	+	0.0271363i
$628$	6.86603	−	11.8923i	0.273984	−	0.474555i
$629$			29.7846i			1.18759i
$630$	2.13397	+	1.23205i	0.0850196	+	0.0490861i
$631$	9.12436	+	5.26795i	0.363235	+	0.209714i	0.670499	−	0.741911i	$-0.266080\pi$
$631$	9.12436	+	5.26795i	0.363235	+	0.209714i	−0.307264	+	0.951624i	$0.599413\pi$
$632$			3.80385i			0.151309i
$633$	7.78461	−	13.4833i	0.309410	−	0.535915i
$634$	3.52628	+	6.10770i	0.140046	+	0.242568i
$635$	8.53590	−	4.92820i	0.338737	−	0.195570i
$636$	−1.12436			−0.0445836
$637$	−0.866025	+	3.50000i	−0.0343132	+	0.138675i
$638$	2.19615			0.0869465
$639$	−29.5692	+	17.0718i	−1.16974	+	0.675350i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	22.2321	−	38.5070i	0.878113	−	1.52094i	0.0247042	−	0.999695i	$-0.492136\pi$
$641$	22.2321	−	38.5070i	0.878113	−	1.52094i	0.853409	−	0.521242i	$-0.174531\pi$
$642$			8.00000i			0.315735i
$643$	30.9282	+	17.8564i	1.21969	+	0.704188i	0.964851	−	0.262796i	$-0.0846446\pi$
$643$	30.9282	+	17.8564i	1.21969	+	0.704188i	0.254838	+	0.966984i	$0.417978\pi$
$644$	−1.09808	−	0.633975i	−0.0432703	−	0.0249821i
$645$		−	8.92820i		−	0.351548i
$646$	4.19615	−	7.26795i	0.165095	−	0.285954i
$647$	−6.92820	−	12.0000i	−0.272376	−	0.471769i	0.697094	−	0.716980i	$-0.254476\pi$
$647$	−6.92820	−	12.0000i	−0.272376	−	0.471769i	−0.969470	+	0.245211i	$0.921143\pi$
$648$	−3.86603	+	2.23205i	−0.151872	+	0.0876832i
$649$	−7.85641			−0.308391
$650$	14.0000	+	3.46410i	0.549125	+	0.135873i
$651$	−3.85641			−0.151144
$652$	−0.633975	+	0.366025i	−0.0248284	+	0.0143347i
$653$	−6.19615	−	10.7321i	−0.242474	−	0.419978i	0.718944	−	0.695068i	$-0.244626\pi$
$653$	−6.19615	−	10.7321i	−0.242474	−	0.419978i	−0.961418	+	0.275090i	$0.911292\pi$
$654$	−3.66025	+	6.33975i	−0.143127	+	0.247904i
$655$			5.07180i			0.198171i
$656$	2.13397	+	1.23205i	0.0833177	+	0.0481035i
$657$	24.3109	+	14.0359i	0.948458	+	0.547593i
$658$			2.92820i			0.114153i
$659$	−4.39230	+	7.60770i	−0.171100	+	0.296354i	−0.938805	−	0.344450i	$-0.888065\pi$
$659$	−4.39230	+	7.60770i	−0.171100	+	0.296354i	0.767705	+	0.640804i	$0.221399\pi$
$660$	0.267949	+	0.464102i	0.0104299	+	0.0180651i
$661$	1.66987	−	0.964102i	0.0649505	−	0.0374992i	−0.467173	−	0.884166i	$-0.654727\pi$
$661$	1.66987	−	0.964102i	0.0649505	−	0.0374992i	0.532124	+	0.846667i	$0.321394\pi$
$662$	4.33975			0.168669
$663$	10.9019	+	10.4904i	0.423396	+	0.407413i
$664$	−3.80385			−0.147618
$665$	1.26795	−	0.732051i	0.0491690	−	0.0283877i
$666$	−6.40192	−	11.0885i	−0.248070	−	0.429669i
$667$	−1.90192	+	3.29423i	−0.0736428	+	0.127553i
$668$			5.26795i			0.203823i
$669$	−7.85641	−	4.53590i	−0.303746	−	0.175368i
$670$	−10.0981	−	5.83013i	−0.390123	−	0.225237i
$671$		−	8.58846i		−	0.331554i
$672$	0.366025	−	0.633975i	0.0141197	−	0.0244561i
$673$	10.8923	+	18.8660i	0.419867	+	0.727232i	0.995926	−	0.0901768i	$-0.0287432\pi$
$673$	10.8923	+	18.8660i	0.419867	+	0.727232i	−0.576058	+	0.817409i	$0.695410\pi$
$674$	−5.47372	+	3.16025i	−0.210840	+	0.121728i
$675$	−16.0000			−0.615840
$676$	11.5000	+	6.06218i	0.442308	+	0.233161i
$677$	27.8564			1.07061			0.535304	−	0.844659i	$-0.320197\pi$
$677$	27.8564			1.07061			0.535304	+	0.844659i	$0.320197\pi$
$678$	7.22243	−	4.16987i	0.277376	−	0.160143i
$679$	2.73205	+	4.73205i	0.104846	+	0.181599i
$680$	2.86603	−	4.96410i	0.109907	−	0.190365i
$681$		−	0.928203i		−	0.0355688i
$682$	3.33975	+	1.92820i	0.127885	+	0.0738347i
$683$	5.66025	+	3.26795i	0.216584	+	0.125045i	0.604367	−	0.796706i	$-0.293426\pi$
$683$	5.66025	+	3.26795i	0.216584	+	0.125045i	−0.387784	+	0.921750i	$0.626759\pi$
$684$			3.60770i			0.137944i
$685$	−3.06218	+	5.30385i	−0.117000	+	0.202650i
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$	−15.4641	+	8.92820i	−0.589992	+	0.340632i
$688$	12.1962			0.464974
$689$	3.99038	+	3.83975i	0.152021	+	0.146283i
$690$	−0.928203			−0.0353361
$691$	5.07180	−	2.92820i	0.192940	−	0.111394i	−0.400418	−	0.916333i	$-0.631135\pi$
$691$	5.07180	−	2.92820i	0.192940	−	0.111394i	0.593358	+	0.804938i	$0.297802\pi$
$692$	10.4641	+	18.1244i	0.397785	+	0.688985i
$693$	−0.901924	+	1.56218i	−0.0342613	+	0.0593422i
$694$			28.9808i			1.10009i
$695$	−0.294229	−	0.169873i	−0.0111607	−	0.00644365i
$696$	−1.90192	−	1.09808i	−0.0720922	−	0.0416225i
$697$		−	14.1244i		−	0.534998i
$698$	−1.00000	+	1.73205i	−0.0378506	+	0.0655591i
$699$	−1.60770	−	2.78461i	−0.0608086	−	0.105324i
$700$	−3.46410	+	2.00000i	−0.130931	+	0.0755929i
$701$	−14.5359			−0.549013			−0.274507	−	0.961585i	$-0.588515\pi$
$701$	−14.5359			−0.549013			−0.274507	+	0.961585i	$0.588515\pi$
$702$	−14.0000	−	3.46410i	−0.528396	−	0.130744i
$703$	−7.60770			−0.286930
$704$	−0.633975	+	0.366025i	−0.0238938	+	0.0137951i
$705$	1.07180	+	1.85641i	0.0403662	+	0.0699163i
$706$	−18.0885	+	31.3301i	−0.680768	+	1.17912i
$707$		−	1.19615i		−	0.0449859i
$708$	6.80385	+	3.92820i	0.255704	+	0.147631i
$709$	−5.64359	−	3.25833i	−0.211950	−	0.122369i	0.390268	−	0.920702i	$-0.372383\pi$
$709$	−5.64359	−	3.25833i	−0.211950	−	0.122369i	−0.602217	+	0.798332i	$0.705716\pi$
$710$			13.8564i			0.520022i
$711$	−4.68653	+	8.11731i	−0.175759	+	0.304423i
$712$	−1.26795	−	2.19615i	−0.0475184	−	0.0823043i
$713$	−5.78461	+	3.33975i	−0.216635	+	0.125074i
$714$	−4.19615			−0.157037
$715$	0.633975	−	2.56218i	0.0237093	−	0.0958200i
$716$	16.3923			0.612609
$717$	−18.7128	+	10.8038i	−0.698843	+	0.403477i
$718$	8.19615	+	14.1962i	0.305878	+	0.529796i
$719$	−3.09808	+	5.36603i	−0.115539	+	0.200119i	−0.917995	−	0.396592i	$-0.870193\pi$
$719$	−3.09808	+	5.36603i	−0.115539	+	0.200119i	0.802456	+	0.596711i	$0.203526\pi$
$720$			2.46410i			0.0918316i
$721$	−7.26795	−	4.19615i	−0.270673	−	0.156273i
$722$	−14.5981	−	8.42820i	−0.543284	−	0.313665i
$723$			11.2679i			0.419060i
$724$	1.59808	−	2.76795i	0.0593920	−	0.102870i
$725$	6.00000	+	10.3923i	0.222834	+	0.385961i
$726$	6.63397	−	3.83013i	0.246210	−	0.142149i
$727$	−53.8564			−1.99742			−0.998712	−	0.0507424i	$-0.983841\pi$
$727$	−53.8564			−1.99742			−0.998712	+	0.0507424i	$0.983841\pi$
$728$	−3.46410	+	1.00000i	−0.128388	+	0.0370625i
$729$	−2.21539			−0.0820515
$730$	9.86603	−	5.69615i	0.365158	−	0.210824i
$731$	−34.9545	−	60.5429i	−1.29284	−	2.23926i
$732$	−4.29423	+	7.43782i	−0.158719	+	0.274910i
$733$		−	2.46410i		−	0.0910137i	−0.998964	−	0.0455068i	$-0.985510\pi$
$733$		−	2.46410i		−	0.0910137i	0.998964	−	0.0455068i	$-0.0144903\pi$
$734$	−29.3660	−	16.9545i	−1.08392	−	0.625801i
$735$	−0.633975	−	0.366025i	−0.0233845	−	0.0135011i
$736$		−	1.26795i		−	0.0467372i
$737$	4.26795	−	7.39230i	0.157212	−	0.272299i
$738$	3.03590	+	5.25833i	0.111753	+	0.193562i
$739$	5.66025	−	3.26795i	0.208216	−	0.120213i	−0.392266	−	0.919852i	$-0.628309\pi$
$739$	5.66025	−	3.26795i	0.208216	−	0.120213i	0.600482	+	0.799638i	$0.294975\pi$
$740$	−5.19615			−0.191014
$741$	−2.67949	+	2.78461i	−0.0984336	+	0.102295i
$742$	−1.53590			−0.0563846
$743$	−4.39230	+	2.53590i	−0.161138	+	0.0930331i	−0.578401	−	0.815753i	$-0.696323\pi$
$743$	−4.39230	+	2.53590i	−0.161138	+	0.0930331i	0.417262	+	0.908786i	$0.362990\pi$
$744$	−1.92820	−	3.33975i	−0.0706914	−	0.122441i
$745$	−8.59808	+	14.8923i	−0.315009	+	0.545612i
$746$		−	32.4641i		−	1.18860i
$747$	−8.11731	−	4.68653i	−0.296997	−	0.171471i
$748$	3.63397	+	2.09808i	0.132871	+	0.0767133i
$749$			10.9282i			0.399308i
$750$	−3.29423	+	5.70577i	−0.120288	+	0.208345i
$751$	3.22243	+	5.58142i	0.117588	+	0.203669i	0.918811	−	0.394697i	$-0.129150\pi$
$751$	3.22243	+	5.58142i	0.117588	+	0.203669i	−0.801223	+	0.598366i	$0.795817\pi$
$752$	−2.53590	+	1.46410i	−0.0924747	+	0.0533903i
$753$	−16.7846			−0.611665
$754$	3.00000	+	10.3923i	0.109254	+	0.378465i
$755$	12.3923			0.451002
$756$	3.46410	−	2.00000i	0.125988	−	0.0727393i
$757$	22.1962	+	38.4449i	0.806733	+	1.39730i	0.915115	+	0.403193i	$0.132100\pi$
$757$	22.1962	+	38.4449i	0.806733	+	1.39730i	−0.108382	+	0.994109i	$0.534567\pi$
$758$	11.0981	−	19.2224i	0.403100	−	0.698190i
$759$		−	0.679492i		−	0.0246640i
$760$	1.26795	+	0.732051i	0.0459934	+	0.0265543i
$761$	15.8038	+	9.12436i	0.572889	+	0.330758i	0.758302	−	0.651903i	$-0.226029\pi$
$761$	15.8038	+	9.12436i	0.572889	+	0.330758i	−0.185413	+	0.982661i	$0.559362\pi$
$762$		−	7.21539i		−	0.261386i
$763$	−5.00000	+	8.66025i	−0.181012	+	0.313522i
$764$	3.56218	+	6.16987i	0.128875	+	0.223218i
$765$	12.2321	−	7.06218i	0.442251	−	0.255334i
$766$	32.5885			1.17747
$767$	−10.7321	−	37.1769i	−0.387512	−	1.34238i
$768$	0.732051			0.0264156
$769$	0.339746	−	0.196152i	0.0122516	−	0.00707344i	−0.493862	−	0.869540i	$-0.664415\pi$
$769$	0.339746	−	0.196152i	0.0122516	−	0.00707344i	0.506113	+	0.862467i	$0.331082\pi$
$770$	0.366025	+	0.633975i	0.0131906	+	0.0228469i
$771$	0.490381	−	0.849365i	0.0176606	−	0.0305891i
$772$			23.1962i			0.834848i
$773$	40.0526	+	23.1244i	1.44059	+	0.831725i	0.997889	−	0.0649438i	$-0.0206868\pi$
$773$	40.0526	+	23.1244i	1.44059	+	0.831725i	0.442701	+	0.896669i	$0.354020\pi$
$774$	26.0263	+	15.0263i	0.935495	+	0.540108i
$775$			21.0718i			0.756921i
$776$	−2.73205	+	4.73205i	−0.0980749	+	0.169871i
$777$	1.90192	+	3.29423i	0.0682311	+	0.118180i
$778$	−21.0622	+	12.1603i	−0.755116	+	0.435966i
$779$	3.60770			0.129259
$780$	−1.83013	+	1.90192i	−0.0655291	+	0.0680998i
$781$	−10.1436			−0.362966
$782$	−6.29423	+	3.63397i	−0.225081	+	0.129951i
$783$	−6.00000	−	10.3923i	−0.214423	−	0.371391i
$784$	0.500000	−	0.866025i	0.0178571	−	0.0309295i
$785$		−	13.7321i		−	0.490118i
$786$	3.21539	+	1.85641i	0.114689	+	0.0662158i
$787$	−38.9545	−	22.4904i	−1.38858	−	0.801696i	−0.395422	−	0.918499i	$-0.629402\pi$
$787$	−38.9545	−	22.4904i	−1.38858	−	0.801696i	−0.993155	+	0.116804i	$0.962735\pi$
$788$		−	7.07180i		−	0.251922i
$789$	7.53590	−	13.0526i	0.268285	−	0.464683i
$790$	1.90192	+	3.29423i	0.0676674	+	0.117203i
$791$	9.86603	−	5.69615i	0.350795	−	0.202532i
$792$	−1.80385			−0.0640969
$793$	40.6410	−	11.7321i	1.44320	−	0.416617i
$794$	−29.4641			−1.04564
$795$	−0.973721	+	0.562178i	−0.0345343	+	0.0199384i
$796$	2.73205	+	4.73205i	0.0968350	+	0.167723i
$797$	−4.46410	+	7.73205i	−0.158127	+	0.273883i	−0.934193	−	0.356768i	$-0.883879\pi$
$797$	−4.46410	+	7.73205i	−0.158127	+	0.273883i	0.776067	+	0.630651i	$0.217212\pi$
$798$		−	1.07180i		−	0.0379412i
$799$	14.5359	+	8.39230i	0.514243	+	0.296898i
$800$	−3.46410	−	2.00000i	−0.122474	−	0.0707107i
$801$		−	6.24871i		−	0.220787i
$802$	−16.5263	+	28.6244i	−0.583563	+	1.01076i
$803$	4.16987	+	7.22243i	0.147152	+	0.254874i
$804$	−7.39230	+	4.26795i	−0.260706	+	0.150519i
$805$	−1.26795			−0.0446893
$806$	−4.56218	+	18.4378i	−0.160696	+	0.649445i
$807$	−21.0718			−0.741762
$808$	1.03590	−	0.598076i	0.0364428	−	0.0210402i
$809$	3.62436	+	6.27757i	0.127426	+	0.220708i	0.922678	−	0.385570i	$-0.125995\pi$
$809$	3.62436	+	6.27757i	0.127426	+	0.220708i	−0.795253	+	0.606278i	$0.792662\pi$
$810$	−2.23205	+	3.86603i	−0.0784263	+	0.135838i
$811$		−	20.8756i		−	0.733043i	−0.930410	−	0.366522i	$-0.880549\pi$
$811$		−	20.8756i		−	0.733043i	0.930410	−	0.366522i	$-0.119451\pi$
$812$	−2.59808	−	1.50000i	−0.0911746	−	0.0526397i
$813$	−4.51666	−	2.60770i	−0.158406	−	0.0914559i
$814$		−	3.80385i		−	0.133325i
$815$	−0.366025	+	0.633975i	−0.0128213	+	0.0222072i
$816$	−2.09808	−	3.63397i	−0.0734474	−	0.127215i
$817$	15.4641	−	8.92820i	0.541020	−	0.312358i
$818$	26.3205			0.920275
$819$	−8.62436	−	2.13397i	−0.301359	−	0.0745671i
$820$	2.46410			0.0860502
$821$	−26.7846	+	15.4641i	−0.934789	+	0.539701i	−0.888323	−	0.459219i	$-0.848129\pi$
$821$	−26.7846	+	15.4641i	−0.934789	+	0.539701i	−0.0464662	+	0.998920i	$0.514796\pi$
$822$	2.24167	+	3.88269i	0.0781872	+	0.135424i
$823$	1.12436	−	1.94744i	0.0391926	−	0.0678835i	−0.845764	−	0.533558i	$-0.820855\pi$
$823$	1.12436	−	1.94744i	0.0391926	−	0.0678835i	0.884956	+	0.465674i	$0.154188\pi$
$824$		−	8.39230i		−	0.292360i
$825$	−1.85641	−	1.07180i	−0.0646318	−	0.0373152i
$826$	9.29423	+	5.36603i	0.323388	+	0.186708i
$827$		−	20.4449i		−	0.710938i	−0.934688	−	0.355469i	$-0.884321\pi$
$827$		−	20.4449i		−	0.710938i	0.934688	−	0.355469i	$-0.115679\pi$
$828$	1.56218	−	2.70577i	0.0542894	−	0.0940321i
$829$	−3.20577	−	5.55256i	−0.111341	−	0.192848i	0.804970	−	0.593315i	$-0.202181\pi$
$829$	−3.20577	−	5.55256i	−0.111341	−	0.192848i	−0.916311	+	0.400467i	$0.868848\pi$
$830$	−3.29423	+	1.90192i	−0.114344	+	0.0660167i
$831$	−6.87564			−0.238513
$832$	−2.59808	−	2.50000i	−0.0900721	−	0.0866719i
$833$	−5.73205			−0.198604
$834$	−0.215390	+	0.124356i	−0.00745836	+	0.00430608i
$835$	2.63397	+	4.56218i	0.0911524	+	0.157881i
$836$	−0.535898	+	0.928203i	−0.0185344	+	0.0321026i
$837$		−	21.0718i		−	0.728348i
$838$	−4.43782	−	2.56218i	−0.153302	−	0.0885090i
$839$	27.4641	+	15.8564i	0.948166	+	0.547424i	0.892511	−	0.451026i	$-0.148942\pi$
$839$	27.4641	+	15.8564i	0.948166	+	0.547424i	0.0556553	+	0.998450i	$0.482275\pi$
$840$		−	0.732051i		−	0.0252582i
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	7.06218	+	12.2321i	0.243379	+	0.421544i
$843$	−10.5622	+	6.09808i	−0.363781	+	0.210029i
$844$	21.2679			0.732073
$845$	12.9904	−	0.500000i	0.446883	−	0.0172005i
$846$	−7.21539			−0.248070
$847$	9.06218	−	5.23205i	0.311380	−	0.179775i
$848$	−0.767949	−	1.33013i	−0.0263715	−	0.0456767i
$849$	−3.87564	+	6.71281i	−0.133012	+	0.230383i
$850$			22.9282i			0.786431i
$851$	5.70577	+	3.29423i	0.195591	+	0.112925i
$852$	8.78461	+	5.07180i	0.300956	+	0.173757i
$853$		−	19.0000i		−	0.650548i	−0.945620	−	0.325274i	$-0.894544\pi$
$853$		−	19.0000i		−	0.650548i	0.945620	−	0.325274i	$-0.105456\pi$
$854$	−5.86603	+	10.1603i	−0.200731	+	0.347677i
$855$	1.80385	+	3.12436i	0.0616903	+	0.106851i
$856$	−9.46410	+	5.46410i	−0.323476	+	0.186759i
$857$	0.947441			0.0323640			0.0161820	−	0.999869i	$-0.494849\pi$
$857$	0.947441			0.0323640			0.0161820	+	0.999869i	$0.494849\pi$
$858$	−1.39230	−	1.33975i	−0.0475325	−	0.0457382i
$859$	−32.8372			−1.12039			−0.560195	−	0.828361i	$-0.689274\pi$
$859$	−32.8372			−1.12039			−0.560195	+	0.828361i	$0.689274\pi$
$860$	10.5622	−	6.09808i	0.360167	−	0.207943i
$861$	−0.901924	−	1.56218i	−0.0307375	−	0.0532389i
$862$	13.2679	−	22.9808i	0.451908	−	0.782728i
$863$		−	44.4449i		−	1.51292i	−0.654040	−	0.756460i	$-0.726927\pi$
$863$		−	44.4449i		−	1.51292i	0.654040	−	0.756460i	$-0.273073\pi$
$864$	3.46410	+	2.00000i	0.117851	+	0.0680414i
$865$	18.1244	+	10.4641i	0.616247	+	0.355790i
$866$		−	21.7321i		−	0.738485i
$867$	−5.80385	+	10.0526i	−0.197109	+	0.341403i
$868$	−2.63397	−	4.56218i	−0.0894029	−	0.154850i
$869$	−2.41154	+	1.39230i	−0.0818060	+	0.0472307i
$870$	−2.19615			−0.0744565
$871$	40.8109	+	10.0981i	1.38282	+	0.342160i
$872$	−10.0000			−0.338643
$873$	−11.6603	+	6.73205i	−0.394640	+	0.227845i
$874$	−0.928203	−	1.60770i	−0.0313969	−	0.0543811i
$875$	−4.50000	+	7.79423i	−0.152128	+	0.263493i
$876$		−	8.33975i		−	0.281774i
$877$	1.62436	+	0.937822i	0.0548506	+	0.0316680i	0.527175	−	0.849757i	$-0.323251\pi$
$877$	1.62436	+	0.937822i	0.0548506	+	0.0316680i	−0.472324	+	0.881425i	$0.656585\pi$
$878$	−16.6865	−	9.63397i	−0.563143	−	0.325131i
$879$		−	12.7321i		−	0.429441i
$880$	−0.366025	+	0.633975i	−0.0123387	+	0.0213713i
$881$	−17.1865	−	29.7679i	−0.579029	−	1.00291i	−0.995591	−	0.0938004i	$-0.970098\pi$
$881$	−17.1865	−	29.7679i	−0.579029	−	1.00291i	0.416562	−	0.909107i	$-0.363235\pi$
$882$	2.13397	−	1.23205i	0.0718547	−	0.0414853i
$883$	23.5167			0.791399			0.395699	−	0.918380i	$-0.370502\pi$
$883$	23.5167			0.791399			0.395699	+	0.918380i	$0.370502\pi$
$884$	−4.96410	+	20.0622i	−0.166961	+	0.674764i
$885$	7.85641			0.264090
$886$	30.5885	−	17.6603i	1.02764	−	0.593308i
$887$	−1.46410	−	2.53590i	−0.0491597	−	0.0851471i	0.840398	−	0.541969i	$-0.182321\pi$
$887$	−1.46410	−	2.53590i	−0.0491597	−	0.0851471i	−0.889558	+	0.456822i	$0.848988\pi$
$888$	−1.90192	+	3.29423i	−0.0638244	+	0.110547i
$889$		−	9.85641i		−	0.330573i
$890$	−2.19615	−	1.26795i	−0.0736152	−	0.0425018i
$891$	−2.83013	−	1.63397i	−0.0948128	−	0.0547402i
$892$		−	12.3923i		−	0.414925i
$893$	−2.14359	+	3.71281i	−0.0717326	+	0.124245i
$894$	6.29423	+	10.9019i	0.210510	+	0.364615i
$895$	14.1962	−	8.19615i	0.474525	−	0.273967i
$896$	1.00000			0.0334077
$897$	3.21539	−	0.928203i	0.107359	−	0.0309918i
$898$	18.0000			0.600668
$899$	−13.6865	+	7.90192i	−0.456471	+	0.263544i
$900$	−4.92820	−	8.53590i	−0.164273	−	0.284530i
$901$	−4.40192	+	7.62436i	−0.146649	+	0.254004i
$902$			1.80385i			0.0600616i
$903$	−7.73205	−	4.46410i	−0.257307	−	0.148556i
$904$	9.86603	+	5.69615i	0.328139	+	0.189451i
$905$		−	3.19615i		−	0.106244i
$906$	4.53590	−	7.85641i	0.150695	−	0.261012i
$907$	−11.0263	−	19.0981i	−0.366122	−	0.634141i	0.622834	−	0.782354i	$-0.285981\pi$
$907$	−11.0263	−	19.0981i	−0.366122	−	0.634141i	−0.988955	+	0.148213i	$0.952648\pi$
$908$	1.09808	−	0.633975i	0.0364409	−	0.0210392i
$909$	2.94744			0.0977605
$910$	−2.50000	+	2.59808i	−0.0828742	+	0.0861254i
$911$	−40.1051			−1.32874			−0.664371	−	0.747403i	$-0.731300\pi$
$911$	−40.1051			−1.32874			−0.664371	+	0.747403i	$0.731300\pi$
$912$	0.928203	−	0.535898i	0.0307359	−	0.0177454i
$913$	−1.39230	−	2.41154i	−0.0460786	−	0.0798104i
$914$	−7.13397	+	12.3564i	−0.235971	+	0.408714i
$915$			8.58846i			0.283926i
$916$	−21.1244	−	12.1962i	−0.697968	−	0.402972i
$917$	4.39230	+	2.53590i	0.145047	+	0.0837427i
$918$		−	22.9282i		−	0.756743i
$919$	−0.392305	+	0.679492i	−0.0129409	+	0.0224144i	−0.872423	−	0.488751i	$-0.837453\pi$
$919$	−0.392305	+	0.679492i	−0.0129409	+	0.0224144i	0.859482	+	0.511165i	$0.170786\pi$
$920$	−0.633975	−	1.09808i	−0.0209015	−	0.0362025i
$921$	−14.9090	+	8.60770i	−0.491267	+	0.283633i
$922$	8.32051			0.274021
$923$	−13.8564	−	48.0000i	−0.456089	−	1.57994i
$924$	0.535898			0.0176298
$925$	18.0000	−	10.3923i	0.591836	−	0.341697i
$926$	−1.97372	−	3.41858i	−0.0648605	−	0.112342i
$927$	10.3397	−	17.9090i	0.339602	−	0.588208i
$928$		−	3.00000i		−	0.0984798i
$929$	−47.7224	−	27.5526i	−1.56572	−	0.903970i	−0.996659	−	0.0816764i	$-0.973973\pi$
$929$	−47.7224	−	27.5526i	−1.56572	−	0.903970i	−0.569063	−	0.822294i	$-0.692694\pi$
$930$	−3.33975	−	1.92820i	−0.109515	−	0.0632283i
$931$		−	1.46410i		−	0.0479840i
$932$	2.19615	−	3.80385i	0.0719374	−	0.124599i
$933$	−3.73205	−	6.46410i	−0.122182	−	0.211625i
$934$	21.4186	−	12.3660i	0.700837	−	0.404629i
$935$	4.19615			0.137229
$936$	−2.46410	−	8.53590i	−0.0805417	−	0.279005i
$937$	55.5885			1.81600			0.907998	−	0.418975i	$-0.137610\pi$
$937$	55.5885			1.81600			0.907998	+	0.418975i	$0.137610\pi$
$938$	−10.0981	+	5.83013i	−0.329714	+	0.190360i
$939$	11.7128	+	20.2872i	0.382233	+	0.662047i
$940$	−1.46410	+	2.53590i	−0.0477537	+	0.0827119i
$941$		−	11.3205i		−	0.369038i	−0.982829	−	0.184519i	$-0.940927\pi$
$941$		−	11.3205i		−	0.369038i	0.982829	−	0.184519i	$-0.0590727\pi$
$942$	−8.70577	−	5.02628i	−0.283649	−	0.163765i
$943$	−2.70577	−	1.56218i	−0.0881120	−	0.0508715i
$944$			10.7321i			0.349299i
$945$	2.00000	−	3.46410i	0.0650600	−	0.112687i
$946$	4.46410	+	7.73205i	0.145140	+	0.251391i
$947$	46.0070	−	26.5622i	1.49503	−	0.863155i	0.495044	−	0.868868i	$-0.335152\pi$
$947$	46.0070	−	26.5622i	1.49503	−	0.863155i	0.999984	+	0.00571294i	$0.00181850\pi$
$948$	2.78461			0.0904399
$949$	−28.4808	+	29.5981i	−0.924525	+	0.960794i
$950$	−5.85641			−0.190007
$951$	4.47114	−	2.58142i	0.144987	−	0.0837081i
$952$	−2.86603	−	4.96410i	−0.0928884	−	0.160887i
$953$	18.5885	−	32.1962i	0.602139	−	1.04294i	−0.390357	−	0.920663i	$-0.627649\pi$
$953$	18.5885	−	32.1962i	0.602139	−	1.04294i	0.992497	−	0.122272i	$-0.0390181\pi$
$954$		−	3.78461i		−	0.122531i
$955$	6.16987	+	3.56218i	0.199652	+	0.115269i
$956$	−25.5622	−	14.7583i	−0.826740	−	0.477319i
$957$		−	1.60770i		−	0.0519694i
$958$	16.0981	−	27.8827i	0.520105	−	0.900849i
$959$	3.06218	+	5.30385i	0.0988829	+	0.171270i
$960$	0.633975	−	0.366025i	0.0204614	−	0.0118134i
$961$	3.24871			0.104797
$962$	18.0000	−	5.19615i	0.580343	−	0.167531i
$963$	−26.9282			−0.867749
$964$	−13.3301	+	7.69615i	−0.429334	+	0.247876i
$965$	11.5981	+	20.0885i	0.373355	+	0.646670i
$966$	−0.464102	+	0.803848i	−0.0149322	+	0.0258634i
$967$			13.5167i			0.434666i	0.976097	+	0.217333i	$0.0697358\pi$
$967$			13.5167i			0.434666i	−0.976097	+	0.217333i	$0.930264\pi$
$968$	9.06218	+	5.23205i	0.291269	+	0.168164i
$969$	−5.32051	−	3.07180i	−0.170919	−	0.0986803i
$970$			5.46410i			0.175442i
$971$	10.1962	−	17.6603i	0.327210	−	0.566745i	−0.654747	−	0.755848i	$-0.727225\pi$
$971$	10.1962	−	17.6603i	0.327210	−	0.566745i	0.981957	+	0.189104i	$0.0605582\pi$
$972$	7.63397	+	13.2224i	0.244860	+	0.424110i
$973$	−0.294229	+	0.169873i	−0.00943254	+	0.00544588i
$974$	31.3205			1.00357
$975$	2.53590	−	10.2487i	0.0812137	−	0.328221i
$976$	−11.7321			−0.375534
$977$	20.8923	−	12.0622i	0.668404	−	0.385903i	−0.127068	−	0.991894i	$-0.540557\pi$
$977$	20.8923	−	12.0622i	0.668404	−	0.385903i	0.795472	+	0.605991i	$0.207223\pi$
$978$	0.267949	+	0.464102i	0.00856807	+	0.0148403i
$979$	0.928203	−	1.60770i	0.0296655	−	0.0513822i
$980$		−	1.00000i		−	0.0319438i
$981$	−21.3397	−	12.3205i	−0.681326	−	0.393364i
$982$	−24.0000	−	13.8564i	−0.765871	−	0.442176i
$983$			44.1051i			1.40673i	0.710826	+	0.703367i	$0.248321\pi$
$983$			44.1051i			1.40673i	−0.710826	+	0.703367i	$0.751679\pi$
$984$	0.901924	−	1.56218i	0.0287523	−	0.0498004i
$985$	−3.53590	−	6.12436i	−0.112663	−	0.195138i
$986$	−14.8923	+	8.59808i	−0.474268	+	0.273819i
$987$	2.14359			0.0682313
$988$	−5.12436	−	1.26795i	−0.163027	−	0.0403388i
$989$	−15.4641			−0.491730
$990$	−1.56218	+	0.901924i	−0.0496493	+	0.0286650i
$991$	22.6865	+	39.2942i	0.720661	+	1.24822i	0.960735	+	0.277468i	$0.0894951\pi$
$991$	22.6865	+	39.2942i	0.720661	+	1.24822i	−0.240074	+	0.970755i	$0.577172\pi$
$992$	2.63397	−	4.56218i	0.0836288	−	0.144849i
$993$		−	3.17691i		−	0.100816i
$994$	12.0000	+	6.92820i	0.380617	+	0.219749i
$995$	4.73205	+	2.73205i	0.150016	+	0.0866118i
$996$			2.78461i			0.0882337i
$997$	10.9904	−	19.0359i	0.348069	−	0.602873i	−0.637838	−	0.770171i	$-0.720171\pi$
$997$	10.9904	−	19.0359i	0.348069	−	0.602873i	0.985906	+	0.167298i	$0.0535042\pi$
$998$	5.63397	+	9.75833i	0.178340	+	0.308895i
$999$	−18.0000	+	10.3923i	−0.569495	+	0.328798i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	182.2.m.a.127.2	yes	4
3.2	odd	2		1638.2.bj.c.127.1		4
4.3	odd	2		1456.2.cc.b.673.2		4
7.2	even	3		1274.2.v.a.361.1		4
7.3	odd	6		1274.2.o.a.569.2		4
7.4	even	3		1274.2.o.b.569.2		4
7.5	odd	6		1274.2.v.b.361.1		4
7.6	odd	2		1274.2.m.a.491.2		4
13.2	odd	12		2366.2.a.s.1.2		2
13.3	even	3		2366.2.d.k.337.4		4
13.4	even	6	inner	182.2.m.a.43.2	✓	4
13.10	even	6		2366.2.d.k.337.2		4
13.11	odd	12		2366.2.a.q.1.2		2
39.17	odd	6		1638.2.bj.c.1135.1		4
52.43	odd	6		1456.2.cc.b.225.2		4
91.4	even	6		1274.2.v.a.667.1		4
91.17	odd	6		1274.2.v.b.667.1		4
91.30	even	6		1274.2.o.b.459.1		4
91.69	odd	6		1274.2.m.a.589.2		4
91.82	odd	6		1274.2.o.a.459.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.m.a.43.2	✓	4	13.4	even	6	inner
182.2.m.a.127.2	yes	4	1.1	even	1	trivial
1274.2.m.a.491.2		4	7.6	odd	2
1274.2.m.a.589.2		4	91.69	odd	6
1274.2.o.a.459.1		4	91.82	odd	6
1274.2.o.a.569.2		4	7.3	odd	6
1274.2.o.b.459.1		4	91.30	even	6
1274.2.o.b.569.2		4	7.4	even	3
1274.2.v.a.361.1		4	7.2	even	3
1274.2.v.a.667.1		4	91.4	even	6
1274.2.v.b.361.1		4	7.5	odd	6
1274.2.v.b.667.1		4	91.17	odd	6
1456.2.cc.b.225.2		4	52.43	odd	6
1456.2.cc.b.673.2		4	4.3	odd	2
1638.2.bj.c.127.1		4	3.2	odd	2
1638.2.bj.c.1135.1		4	39.17	odd	6
2366.2.a.q.1.2		2	13.11	odd	12
2366.2.a.s.1.2		2	13.2	odd	12
2366.2.d.k.337.2		4	13.10	even	6
2366.2.d.k.337.4		4	13.3	even	3

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:	\( N \)	\(=\)	\( 182 = 2 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	182.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.366025 - 0.633975i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-0.633975 - 0.366025i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(1.23205 - 2.13397i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.366025 - 0.633975i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000i q^{5} +(-0.633975 - 0.366025i) q^{6} +(-0.866025 - 0.500000i) q^{7} -1.00000i q^{8} +(1.23205 - 2.13397i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.633975 - 0.366025i) q^{11} -0.732051 q^{12} +(2.59808 + 2.50000i) q^{13} -1.00000 q^{14} +(-0.633975 + 0.366025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.86603 + 4.96410i) q^{17} -2.46410i q^{18} +(-1.26795 - 0.732051i) q^{19} +(-0.866025 - 0.500000i) q^{20} +0.732051i q^{21} +(0.366025 - 0.633975i) q^{22} +(0.633975 + 1.09808i) q^{23} +(-0.633975 + 0.366025i) q^{24} +4.00000 q^{25} +(3.50000 + 0.866025i) q^{26} -4.00000 q^{27} +(-0.866025 + 0.500000i) q^{28} +(1.50000 + 2.59808i) q^{29} +(-0.366025 + 0.633975i) q^{30} +5.26795i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.464102 - 0.267949i) q^{33} +5.73205i q^{34} +(-0.500000 + 0.866025i) q^{35} +(-1.23205 - 2.13397i) q^{36} +(4.50000 - 2.59808i) q^{37} -1.46410 q^{38} +(0.633975 - 2.56218i) q^{39} -1.00000 q^{40} +(-2.13397 + 1.23205i) q^{41} +(0.366025 + 0.633975i) q^{42} +(-6.09808 + 10.5622i) q^{43} -0.732051i q^{44} +(-2.13397 - 1.23205i) q^{45} +(1.09808 + 0.633975i) q^{46} -2.92820i q^{47} +(-0.366025 + 0.633975i) q^{48} +(0.500000 + 0.866025i) q^{49} +(3.46410 - 2.00000i) q^{50} +4.19615 q^{51} +(3.46410 - 1.00000i) q^{52} +1.53590 q^{53} +(-3.46410 + 2.00000i) q^{54} +(-0.366025 - 0.633975i) q^{55} +(-0.500000 + 0.866025i) q^{56} +1.07180i q^{57} +(2.59808 + 1.50000i) q^{58} +(-9.29423 - 5.36603i) q^{59} +0.732051i q^{60} +(5.86603 - 10.1603i) q^{61} +(2.63397 + 4.56218i) q^{62} +(-2.13397 + 1.23205i) q^{63} -1.00000 q^{64} +(2.50000 - 2.59808i) q^{65} -0.535898 q^{66} +(10.0981 - 5.83013i) q^{67} +(2.86603 + 4.96410i) q^{68} +(0.464102 - 0.803848i) q^{69} +1.00000i q^{70} +(-12.0000 - 6.92820i) q^{71} +(-2.13397 - 1.23205i) q^{72} +11.3923i q^{73} +(2.59808 - 4.50000i) q^{74} +(-1.46410 - 2.53590i) q^{75} +(-1.26795 + 0.732051i) q^{76} -0.732051 q^{77} +(-0.732051 - 2.53590i) q^{78} -3.80385 q^{79} +(-0.866025 + 0.500000i) q^{80} +(-2.23205 - 3.86603i) q^{81} +(-1.23205 + 2.13397i) q^{82} -3.80385i q^{83} +(0.633975 + 0.366025i) q^{84} +(4.96410 + 2.86603i) q^{85} +12.1962i q^{86} +(1.09808 - 1.90192i) q^{87} +(-0.366025 - 0.633975i) q^{88} +(2.19615 - 1.26795i) q^{89} -2.46410 q^{90} +(-1.00000 - 3.46410i) q^{91} +1.26795 q^{92} +(3.33975 - 1.92820i) q^{93} +(-1.46410 - 2.53590i) q^{94} +(-0.732051 + 1.26795i) q^{95} +0.732051i q^{96} +(-4.73205 - 2.73205i) q^{97} +(0.866025 + 0.500000i) q^{98} -1.80385i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 2 q^{4} - 6 q^{6} - 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^6 - 2 * q^9	\( 4 q + 2 q^{3} + 2 q^{4} - 6 q^{6} - 2 q^{9} - 2 q^{10} + 6 q^{11} + 4 q^{12} - 4 q^{14} - 6 q^{15} - 2 q^{16} - 8 q^{17} - 12 q^{19} - 2 q^{22} + 6 q^{23} - 6 q^{24} + 16 q^{25} + 14 q^{26} - 16 q^{27} + 6 q^{29} + 2 q^{30} + 12 q^{33} - 2 q^{35} + 2 q^{36} + 18 q^{37} + 8 q^{38} + 6 q^{39} - 4 q^{40} - 12 q^{41} - 2 q^{42} - 14 q^{43} - 12 q^{45} - 6 q^{46} + 2 q^{48} + 2 q^{49} - 4 q^{51} + 20 q^{53} + 2 q^{55} - 2 q^{56} - 6 q^{59} + 20 q^{61} + 14 q^{62} - 12 q^{63} - 4 q^{64} + 10 q^{65} - 16 q^{66} + 30 q^{67} + 8 q^{68} - 12 q^{69} - 48 q^{71} - 12 q^{72} + 8 q^{75} - 12 q^{76} + 4 q^{77} + 4 q^{78} - 36 q^{79} - 2 q^{81} + 2 q^{82} + 6 q^{84} + 6 q^{85} - 6 q^{87} + 2 q^{88} - 12 q^{89} + 4 q^{90} - 4 q^{91} + 12 q^{92} + 48 q^{93} + 8 q^{94} + 4 q^{95} - 12 q^{97}+O(q^{100}) \) 4 * q + 2 * q^3 + 2 * q^4 - 6 * q^6 - 2 * q^9 - 2 * q^10 + 6 * q^11 + 4 * q^12 - 4 * q^14 - 6 * q^15 - 2 * q^16 - 8 * q^17 - 12 * q^19 - 2 * q^22 + 6 * q^23 - 6 * q^24 + 16 * q^25 + 14 * q^26 - 16 * q^27 + 6 * q^29 + 2 * q^30 + 12 * q^33 - 2 * q^35 + 2 * q^36 + 18 * q^37 + 8 * q^38 + 6 * q^39 - 4 * q^40 - 12 * q^41 - 2 * q^42 - 14 * q^43 - 12 * q^45 - 6 * q^46 + 2 * q^48 + 2 * q^49 - 4 * q^51 + 20 * q^53 + 2 * q^55 - 2 * q^56 - 6 * q^59 + 20 * q^61 + 14 * q^62 - 12 * q^63 - 4 * q^64 + 10 * q^65 - 16 * q^66 + 30 * q^67 + 8 * q^68 - 12 * q^69 - 48 * q^71 - 12 * q^72 + 8 * q^75 - 12 * q^76 + 4 * q^77 + 4 * q^78 - 36 * q^79 - 2 * q^81 + 2 * q^82 + 6 * q^84 + 6 * q^85 - 6 * q^87 + 2 * q^88 - 12 * q^89 + 4 * q^90 - 4 * q^91 + 12 * q^92 + 48 * q^93 + 8 * q^94 + 4 * q^95 - 12 * q^97

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