LMFDB - Embedded newform 91.2.f.b.29.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,2,Mod(22,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("91.22");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	91.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.726638658394$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			29.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	91.29
Dual form			91.2.f.b.22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 1.50000i) q^{2} +(-1.36603 - 2.36603i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205 q^{5} +(-2.36603 + 4.09808i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.73205 q^{8} +(-2.23205 + 3.86603i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 1.50000i) q^{2} +(-1.36603 - 2.36603i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205 q^{5} +(-2.36603 + 4.09808i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.73205 q^{8} +(-2.23205 + 3.86603i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(-0.633975 - 1.09808i) q^{11} +2.73205 q^{12} +(3.59808 + 0.232051i) q^{13} +1.73205 q^{14} +(-2.36603 - 4.09808i) q^{15} +(2.50000 + 4.33013i) q^{16} +(3.86603 - 6.69615i) q^{17} +7.73205 q^{18} +(-1.00000 + 1.73205i) q^{19} +(-0.866025 + 1.50000i) q^{20} +2.73205 q^{21} +(-1.09808 + 1.90192i) q^{22} +(-2.36603 - 4.09808i) q^{23} +(2.36603 + 4.09808i) q^{24} -2.00000 q^{25} +(-2.76795 - 5.59808i) q^{26} +4.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(1.50000 + 2.59808i) q^{29} +(-4.09808 + 7.09808i) q^{30} +4.19615 q^{31} +(2.59808 - 4.50000i) q^{32} +(-1.73205 + 3.00000i) q^{33} -13.3923 q^{34} +(-0.866025 + 1.50000i) q^{35} +(-2.23205 - 3.86603i) q^{36} +(3.50000 + 6.06218i) q^{37} +3.46410 q^{38} +(-4.36603 - 8.83013i) q^{39} -3.00000 q^{40} +(2.59808 + 4.50000i) q^{41} +(-2.36603 - 4.09808i) q^{42} +(0.0980762 - 0.169873i) q^{43} +1.26795 q^{44} +(-3.86603 + 6.69615i) q^{45} +(-4.09808 + 7.09808i) q^{46} +12.9282 q^{47} +(6.83013 - 11.8301i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(1.73205 + 3.00000i) q^{50} -21.1244 q^{51} +(-2.00000 + 3.00000i) q^{52} -9.92820 q^{53} +(-3.46410 - 6.00000i) q^{54} +(-1.09808 - 1.90192i) q^{55} +(0.866025 - 1.50000i) q^{56} +5.46410 q^{57} +(2.59808 - 4.50000i) q^{58} +(-3.63397 + 6.29423i) q^{59} +4.73205 q^{60} +(2.40192 - 4.16025i) q^{61} +(-3.63397 - 6.29423i) q^{62} +(-2.23205 - 3.86603i) q^{63} +1.00000 q^{64} +(6.23205 + 0.401924i) q^{65} +6.00000 q^{66} +(3.09808 + 5.36603i) q^{67} +(3.86603 + 6.69615i) q^{68} +(-6.46410 + 11.1962i) q^{69} +3.00000 q^{70} +(-3.00000 + 5.19615i) q^{71} +(3.86603 - 6.69615i) q^{72} -3.19615 q^{73} +(6.06218 - 10.5000i) q^{74} +(2.73205 + 4.73205i) q^{75} +(-1.00000 - 1.73205i) q^{76} +1.26795 q^{77} +(-9.46410 + 14.1962i) q^{78} +16.1962 q^{79} +(4.33013 + 7.50000i) q^{80} +(1.23205 + 2.13397i) q^{81} +(4.50000 - 7.79423i) q^{82} -2.19615 q^{83} +(-1.36603 + 2.36603i) q^{84} +(6.69615 - 11.5981i) q^{85} -0.339746 q^{86} +(4.09808 - 7.09808i) q^{87} +(1.09808 + 1.90192i) q^{88} +(-6.46410 - 11.1962i) q^{89} +13.3923 q^{90} +(-2.00000 + 3.00000i) q^{91} +4.73205 q^{92} +(-5.73205 - 9.92820i) q^{93} +(-11.1962 - 19.3923i) q^{94} +(-1.73205 + 3.00000i) q^{95} -14.1962 q^{96} +(-3.19615 + 5.53590i) q^{97} +(-0.866025 + 1.50000i) q^{98} +5.66025 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 2 q^{4} - 6 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 2 * q^4 - 6 * q^6 - 2 * q^7 - 2 * q^9	$ 4 q - 2 q^{3} - 2 q^{4} - 6 q^{6} - 2 q^{7} - 2 q^{9} - 6 q^{10} - 6 q^{11} + 4 q^{12} + 4 q^{13} - 6 q^{15} + 10 q^{16} + 12 q^{17} + 24 q^{18} - 4 q^{19} + 4 q^{21} + 6 q^{22} - 6 q^{23} + 6 q^{24} - 8 q^{25} - 18 q^{26} + 16 q^{27} - 2 q^{28} + 6 q^{29} - 6 q^{30} - 4 q^{31} - 12 q^{34} - 2 q^{36} + 14 q^{37} - 14 q^{39} - 12 q^{40} - 6 q^{42} - 10 q^{43} + 12 q^{44} - 12 q^{45} - 6 q^{46} + 24 q^{47} + 10 q^{48} - 2 q^{49} - 36 q^{51} - 8 q^{52} - 12 q^{53} + 6 q^{55} + 8 q^{57} - 18 q^{59} + 12 q^{60} + 20 q^{61} - 18 q^{62} - 2 q^{63} + 4 q^{64} + 18 q^{65} + 24 q^{66} + 2 q^{67} + 12 q^{68} - 12 q^{69} + 12 q^{70} - 12 q^{71} + 12 q^{72} + 8 q^{73} + 4 q^{75} - 4 q^{76} + 12 q^{77} - 24 q^{78} + 44 q^{79} - 2 q^{81} + 18 q^{82} + 12 q^{83} - 2 q^{84} + 6 q^{85} - 36 q^{86} + 6 q^{87} - 6 q^{88} - 12 q^{89} + 12 q^{90} - 8 q^{91} + 12 q^{92} - 16 q^{93} - 24 q^{94} - 36 q^{96} + 8 q^{97} - 12 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 2 * q^4 - 6 * q^6 - 2 * q^7 - 2 * q^9 - 6 * q^10 - 6 * q^11 + 4 * q^12 + 4 * q^13 - 6 * q^15 + 10 * q^16 + 12 * q^17 + 24 * q^18 - 4 * q^19 + 4 * q^21 + 6 * q^22 - 6 * q^23 + 6 * q^24 - 8 * q^25 - 18 * q^26 + 16 * q^27 - 2 * q^28 + 6 * q^29 - 6 * q^30 - 4 * q^31 - 12 * q^34 - 2 * q^36 + 14 * q^37 - 14 * q^39 - 12 * q^40 - 6 * q^42 - 10 * q^43 + 12 * q^44 - 12 * q^45 - 6 * q^46 + 24 * q^47 + 10 * q^48 - 2 * q^49 - 36 * q^51 - 8 * q^52 - 12 * q^53 + 6 * q^55 + 8 * q^57 - 18 * q^59 + 12 * q^60 + 20 * q^61 - 18 * q^62 - 2 * q^63 + 4 * q^64 + 18 * q^65 + 24 * q^66 + 2 * q^67 + 12 * q^68 - 12 * q^69 + 12 * q^70 - 12 * q^71 + 12 * q^72 + 8 * q^73 + 4 * q^75 - 4 * q^76 + 12 * q^77 - 24 * q^78 + 44 * q^79 - 2 * q^81 + 18 * q^82 + 12 * q^83 - 2 * q^84 + 6 * q^85 - 36 * q^86 + 6 * q^87 - 6 * q^88 - 12 * q^89 + 12 * q^90 - 8 * q^91 + 12 * q^92 - 16 * q^93 - 24 * q^94 - 36 * q^96 + 8 * q^97 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/91\mathbb{Z}\right)^\times$.

$n$	$15$	$66$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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	−	1.50000i	−0.612372	−	1.06066i	−0.990839	−	0.135045i	$-0.956882\pi$
$2$	−0.866025	−	1.50000i	−0.612372	−	1.06066i	0.378467	−	0.925615i	$-0.376451\pi$
$3$	−1.36603	−	2.36603i	−0.788675	−	1.36603i	−0.926779	−	0.375608i	$-0.877434\pi$
$3$	−1.36603	−	2.36603i	−0.788675	−	1.36603i	0.138104	−	0.990418i	$-0.455899\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	1.73205			0.774597			0.387298	−	0.921954i	$-0.373408\pi$
$5$	1.73205			0.774597			0.387298	+	0.921954i	$0.373408\pi$
$6$	−2.36603	+	4.09808i	−0.965926	+	1.67303i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	−1.73205			−0.612372
$9$	−2.23205	+	3.86603i	−0.744017	+	1.28868i
$10$	−1.50000	−	2.59808i	−0.474342	−	0.821584i
$11$	−0.633975	−	1.09808i	−0.191151	−	0.331082i	0.754481	−	0.656322i	$-0.227889\pi$
$11$	−0.633975	−	1.09808i	−0.191151	−	0.331082i	−0.945632	+	0.325239i	$0.894555\pi$
$12$	2.73205			0.788675
$13$	3.59808	+	0.232051i	0.997927	+	0.0643593i
$13$	3.59808	+	0.232051i	0.997927	+	0.0643593i
$14$	1.73205			0.462910
$15$	−2.36603	−	4.09808i	−0.610905	−	1.05812i
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	3.86603	−	6.69615i	0.937649	−	1.62406i	0.167808	−	0.985820i	$-0.446331\pi$
$17$	3.86603	−	6.69615i	0.937649	−	1.62406i	0.769841	−	0.638236i	$-0.220336\pi$
$18$	7.73205			1.82246
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$	−0.866025	+	1.50000i	−0.193649	+	0.335410i
$21$	2.73205			0.596182
$22$	−1.09808	+	1.90192i	−0.234111	+	0.405492i
$23$	−2.36603	−	4.09808i	−0.493350	−	0.854508i	0.506620	−	0.862169i	$-0.330895\pi$
$23$	−2.36603	−	4.09808i	−0.493350	−	0.854508i	−0.999971	+	0.00766135i	$0.997561\pi$
$24$	2.36603	+	4.09808i	0.482963	+	0.836516i
$25$	−2.00000			−0.400000
$26$	−2.76795	−	5.59808i	−0.542839	−	1.09787i
$27$	4.00000			0.769800
$28$	−0.500000	−	0.866025i	−0.0944911	−	0.163663i
$29$	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	$0.743482\pi$
$30$	−4.09808	+	7.09808i	−0.748203	+	1.29593i
$31$	4.19615			0.753651			0.376826	−	0.926284i	$-0.377016\pi$
$31$	4.19615			0.753651			0.376826	+	0.926284i	$0.377016\pi$
$32$	2.59808	−	4.50000i	0.459279	−	0.795495i
$33$	−1.73205	+	3.00000i	−0.301511	+	0.522233i
$34$	−13.3923			−2.29676
$35$	−0.866025	+	1.50000i	−0.146385	+	0.253546i
$36$	−2.23205	−	3.86603i	−0.372008	−	0.644338i
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	0.995998	+	0.0893706i	$0.0284856\pi$
$37$	3.50000	+	6.06218i	0.575396	+	0.996616i	−0.420602	+	0.907245i	$0.638181\pi$
$38$	3.46410			0.561951
$39$	−4.36603	−	8.83013i	−0.699124	−	1.41395i
$40$	−3.00000			−0.474342
$41$	2.59808	+	4.50000i	0.405751	+	0.702782i	0.994409	−	0.105601i	$-0.0336766\pi$
$41$	2.59808	+	4.50000i	0.405751	+	0.702782i	−0.588657	+	0.808383i	$0.700343\pi$
$42$	−2.36603	−	4.09808i	−0.365086	−	0.632347i
$43$	0.0980762	−	0.169873i	0.0149565	−	0.0259054i	−0.858450	−	0.512897i	$-0.828572\pi$
$43$	0.0980762	−	0.169873i	0.0149565	−	0.0259054i	0.873407	+	0.486991i	$0.161906\pi$
$44$	1.26795			0.191151
$45$	−3.86603	+	6.69615i	−0.576313	+	0.998203i
$46$	−4.09808	+	7.09808i	−0.604228	+	1.04655i
$47$	12.9282			1.88577			0.942886	−	0.333115i	$-0.108100\pi$
$47$	12.9282			1.88577			0.942886	+	0.333115i	$0.108100\pi$
$48$	6.83013	−	11.8301i	0.985844	−	1.70753i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	1.73205	+	3.00000i	0.244949	+	0.424264i
$51$	−21.1244			−2.95800
$52$	−2.00000	+	3.00000i	−0.277350	+	0.416025i
$53$	−9.92820			−1.36374			−0.681872	−	0.731472i	$-0.738834\pi$
$53$	−9.92820			−1.36374			−0.681872	+	0.731472i	$0.738834\pi$
$54$	−3.46410	−	6.00000i	−0.471405	−	0.816497i
$55$	−1.09808	−	1.90192i	−0.148065	−	0.256455i
$56$	0.866025	−	1.50000i	0.115728	−	0.200446i
$57$	5.46410			0.723738
$58$	2.59808	−	4.50000i	0.341144	−	0.590879i
$59$	−3.63397	+	6.29423i	−0.473103	+	0.819439i	−0.999526	−	0.0307841i	$-0.990200\pi$
$59$	−3.63397	+	6.29423i	−0.473103	+	0.819439i	0.526423	+	0.850223i	$0.323533\pi$
$60$	4.73205			0.610905
$61$	2.40192	−	4.16025i	0.307535	−	0.532666i	−0.670288	−	0.742101i	$-0.733829\pi$
$61$	2.40192	−	4.16025i	0.307535	−	0.532666i	0.977822	+	0.209435i	$0.0671626\pi$
$62$	−3.63397	−	6.29423i	−0.461515	−	0.799368i
$63$	−2.23205	−	3.86603i	−0.281212	−	0.487073i
$64$	1.00000			0.125000
$65$	6.23205	+	0.401924i	0.772991	+	0.0498525i
$66$	6.00000			0.738549
$67$	3.09808	+	5.36603i	0.378490	+	0.655564i	0.990843	−	0.135020i	$-0.0431100\pi$
$67$	3.09808	+	5.36603i	0.378490	+	0.655564i	−0.612353	+	0.790585i	$0.709777\pi$
$68$	3.86603	+	6.69615i	0.468824	+	0.812028i
$69$	−6.46410	+	11.1962i	−0.778186	+	1.34786i
$70$	3.00000			0.358569
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$	3.86603	−	6.69615i	0.455615	−	0.789149i
$73$	−3.19615			−0.374081			−0.187041	−	0.982352i	$-0.559890\pi$
$73$	−3.19615			−0.374081			−0.187041	+	0.982352i	$0.559890\pi$
$74$	6.06218	−	10.5000i	0.704714	−	1.22060i
$75$	2.73205	+	4.73205i	0.315470	+	0.546410i
$76$	−1.00000	−	1.73205i	−0.114708	−	0.198680i
$77$	1.26795			0.144496
$78$	−9.46410	+	14.1962i	−1.07160	+	1.60740i
$79$	16.1962			1.82221			0.911105	−	0.412175i	$-0.135231\pi$
$79$	16.1962			1.82221			0.911105	+	0.412175i	$0.135231\pi$
$80$	4.33013	+	7.50000i	0.484123	+	0.838525i
$81$	1.23205	+	2.13397i	0.136895	+	0.237108i
$82$	4.50000	−	7.79423i	0.496942	−	0.860729i
$83$	−2.19615			−0.241059			−0.120530	−	0.992710i	$-0.538459\pi$
$83$	−2.19615			−0.241059			−0.120530	+	0.992710i	$0.538459\pi$
$84$	−1.36603	+	2.36603i	−0.149046	+	0.258155i
$85$	6.69615	−	11.5981i	0.726300	−	1.25799i
$86$	−0.339746			−0.0366357
$87$	4.09808	−	7.09808i	0.439360	−	0.760994i
$88$	1.09808	+	1.90192i	0.117055	+	0.202746i
$89$	−6.46410	−	11.1962i	−0.685193	−	1.18679i	−0.973376	−	0.229214i	$-0.926384\pi$
$89$	−6.46410	−	11.1962i	−0.685193	−	1.18679i	0.288183	−	0.957575i	$-0.406949\pi$
$90$	13.3923			1.41167
$91$	−2.00000	+	3.00000i	−0.209657	+	0.314485i
$92$	4.73205			0.493350
$93$	−5.73205	−	9.92820i	−0.594386	−	1.02951i
$94$	−11.1962	−	19.3923i	−1.15479	−	2.00016i
$95$	−1.73205	+	3.00000i	−0.177705	+	0.307794i
$96$	−14.1962			−1.44889
$97$	−3.19615	+	5.53590i	−0.324520	+	0.562085i	−0.981415	−	0.191897i	$-0.938536\pi$
$97$	−3.19615	+	5.53590i	−0.324520	+	0.562085i	0.656895	+	0.753982i	$0.271869\pi$
$98$	−0.866025	+	1.50000i	−0.0874818	+	0.151523i
$99$	5.66025			0.568877
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$	3.86603	+	6.69615i	0.384684	+	0.666292i	0.991725	−	0.128378i	$-0.0409771\pi$
$101$	3.86603	+	6.69615i	0.384684	+	0.666292i	−0.607041	+	0.794670i	$0.707644\pi$
$102$	18.2942	+	31.6865i	1.81140	+	3.13743i
$103$	−14.3923			−1.41812			−0.709058	−	0.705150i	$-0.750880\pi$
$103$	−14.3923			−1.41812			−0.709058	+	0.705150i	$0.750880\pi$
$104$	−6.23205	−	0.401924i	−0.611103	−	0.0394119i
$105$	4.73205			0.461801
$106$	8.59808	+	14.8923i	0.835119	+	1.44647i
$107$	3.92820	+	6.80385i	0.379754	+	0.657753i	0.991026	−	0.133667i	$-0.0426754\pi$
$107$	3.92820	+	6.80385i	0.379754	+	0.657753i	−0.611273	+	0.791420i	$0.709342\pi$
$108$	−2.00000	+	3.46410i	−0.192450	+	0.333333i
$109$	−8.39230			−0.803837			−0.401919	−	0.915675i	$-0.631656\pi$
$109$	−8.39230			−0.803837			−0.401919	+	0.915675i	$0.631656\pi$
$110$	−1.90192	+	3.29423i	−0.181341	+	0.314092i
$111$	9.56218	−	16.5622i	0.907602	−	1.57201i
$112$	−5.00000			−0.472456
$113$	−6.69615	+	11.5981i	−0.629921	+	1.09106i	0.357646	+	0.933857i	$0.383579\pi$
$113$	−6.69615	+	11.5981i	−0.629921	+	1.09106i	−0.987567	+	0.157198i	$0.949754\pi$
$114$	−4.73205	−	8.19615i	−0.443197	−	0.767640i
$115$	−4.09808	−	7.09808i	−0.382148	−	0.661899i
$116$	−3.00000			−0.278543
$117$	−8.92820	+	13.3923i	−0.825413	+	1.23812i
$118$	12.5885			1.15886
$119$	3.86603	+	6.69615i	0.354398	+	0.613835i
$120$	4.09808	+	7.09808i	0.374101	+	0.647963i
$121$	4.69615	−	8.13397i	0.426923	−	0.739452i
$122$	−8.32051			−0.753303
$123$	7.09808	−	12.2942i	0.640012	−	1.10853i
$124$	−2.09808	+	3.63397i	−0.188413	+	0.326341i
$125$	−12.1244			−1.08444
$126$	−3.86603	+	6.69615i	−0.344413	+	0.596541i
$127$	−9.19615	−	15.9282i	−0.816027	−	1.41340i	−0.908588	−	0.417693i	$-0.862839\pi$
$127$	−9.19615	−	15.9282i	−0.816027	−	1.41340i	0.0925619	−	0.995707i	$-0.470494\pi$
$128$	−6.06218	−	10.5000i	−0.535826	−	0.928078i
$129$	−0.535898			−0.0471832
$130$	−4.79423	−	9.69615i	−0.420482	−	0.850409i
$131$	−3.46410			−0.302660			−0.151330	−	0.988483i	$-0.548356\pi$
$131$	−3.46410			−0.302660			−0.151330	+	0.988483i	$0.548356\pi$
$132$	−1.73205	−	3.00000i	−0.150756	−	0.261116i
$133$	−1.00000	−	1.73205i	−0.0867110	−	0.150188i
$134$	5.36603	−	9.29423i	0.463554	−	0.802899i
$135$	6.92820			0.596285
$136$	−6.69615	+	11.5981i	−0.574190	+	0.994527i
$137$	−4.03590	+	6.99038i	−0.344810	+	0.597229i	−0.985319	−	0.170722i	$-0.945390\pi$
$137$	−4.03590	+	6.99038i	−0.344810	+	0.597229i	0.640509	+	0.767951i	$0.278723\pi$
$138$	22.3923			1.90616
$139$	5.29423	−	9.16987i	0.449051	−	0.777778i	−0.549274	−	0.835642i	$-0.685096\pi$
$139$	5.29423	−	9.16987i	0.449051	−	0.777778i	0.998324	+	0.0578639i	$0.0184290\pi$
$140$	−0.866025	−	1.50000i	−0.0731925	−	0.126773i
$141$	−17.6603	−	30.5885i	−1.48726	−	2.57601i
$142$	10.3923			0.872103
$143$	−2.02628	−	4.09808i	−0.169446	−	0.342698i
$144$	−22.3205			−1.86004
$145$	2.59808	+	4.50000i	0.215758	+	0.373705i
$146$	2.76795	+	4.79423i	0.229077	+	0.396773i
$147$	−1.36603	+	2.36603i	−0.112668	+	0.195146i
$148$	−7.00000			−0.575396
$149$	3.23205	−	5.59808i	0.264780	−	0.458612i	−0.702726	−	0.711461i	$-0.748034\pi$
$149$	3.23205	−	5.59808i	0.264780	−	0.458612i	0.967506	+	0.252848i	$0.0813674\pi$
$150$	4.73205	−	8.19615i	0.386370	−	0.669213i
$151$	2.00000			0.162758			0.0813788	−	0.996683i	$-0.474068\pi$
$151$	2.00000			0.162758			0.0813788	+	0.996683i	$0.474068\pi$
$152$	1.73205	−	3.00000i	0.140488	−	0.243332i
$153$	17.2583	+	29.8923i	1.39525	+	2.41665i
$154$	−1.09808	−	1.90192i	−0.0884855	−	0.153261i
$155$	7.26795			0.583776
$156$	9.83013	+	0.633975i	0.787040	+	0.0507586i
$157$	1.19615			0.0954634			0.0477317	−	0.998860i	$-0.484801\pi$
$157$	1.19615			0.0954634			0.0477317	+	0.998860i	$0.484801\pi$
$158$	−14.0263	−	24.2942i	−1.11587	−	1.93275i
$159$	13.5622	+	23.4904i	1.07555	+	1.86291i
$160$	4.50000	−	7.79423i	0.355756	−	0.616188i
$161$	4.73205			0.372938
$162$	2.13397	−	3.69615i	0.167661	−	0.290397i
$163$	−8.09808	+	14.0263i	−0.634290	+	1.09862i	0.352375	+	0.935859i	$0.385374\pi$
$163$	−8.09808	+	14.0263i	−0.634290	+	1.09862i	−0.986665	+	0.162764i	$0.947959\pi$
$164$	−5.19615			−0.405751
$165$	−3.00000	+	5.19615i	−0.233550	+	0.404520i
$166$	1.90192	+	3.29423i	0.147618	+	0.255682i
$167$	3.29423	+	5.70577i	0.254915	+	0.441526i	0.964872	−	0.262719i	$-0.0846192\pi$
$167$	3.29423	+	5.70577i	0.254915	+	0.441526i	−0.709957	+	0.704245i	$0.751286\pi$
$168$	−4.73205			−0.365086
$169$	12.8923	+	1.66987i	0.991716	+	0.128452i
$170$	−23.1962			−1.77906
$171$	−4.46410	−	7.73205i	−0.341378	−	0.591285i
$172$	0.0980762	+	0.169873i	0.00747824	+	0.0129527i
$173$	−4.26795	+	7.39230i	−0.324486	+	0.562027i	−0.981408	−	0.191932i	$-0.938525\pi$
$173$	−4.26795	+	7.39230i	−0.324486	+	0.562027i	0.656922	+	0.753958i	$0.271858\pi$
$174$	−14.1962			−1.07621
$175$	1.00000	−	1.73205i	0.0755929	−	0.130931i
$176$	3.16987	−	5.49038i	0.238938	−	0.413853i
$177$	19.8564			1.49250
$178$	−11.1962	+	19.3923i	−0.839187	+	1.45351i
$179$	3.46410	+	6.00000i	0.258919	+	0.448461i	0.965953	−	0.258719i	$-0.0833004\pi$
$179$	3.46410	+	6.00000i	0.258919	+	0.448461i	−0.707034	+	0.707180i	$0.749967\pi$
$180$	−3.86603	−	6.69615i	−0.288157	−	0.499102i
$181$	5.58846			0.415387			0.207693	−	0.978194i	$-0.433404\pi$
$181$	5.58846			0.415387			0.207693	+	0.978194i	$0.433404\pi$
$182$	6.23205	+	0.401924i	0.461950	+	0.0297926i
$183$	−13.1244			−0.970180
$184$	4.09808	+	7.09808i	0.302114	+	0.523277i
$185$	6.06218	+	10.5000i	0.445700	+	0.771975i
$186$	−9.92820	+	17.1962i	−0.727971	+	1.26088i
$187$	−9.80385			−0.716928
$188$	−6.46410	+	11.1962i	−0.471443	+	0.816563i
$189$	−2.00000	+	3.46410i	−0.145479	+	0.251976i
$190$	6.00000			0.435286
$191$	−2.36603	+	4.09808i	−0.171200	+	0.296526i	−0.938840	−	0.344355i	$-0.888098\pi$
$191$	−2.36603	+	4.09808i	−0.171200	+	0.296526i	0.767640	+	0.640881i	$0.221431\pi$
$192$	−1.36603	−	2.36603i	−0.0985844	−	0.170753i
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	0.761911	−	0.647682i	$-0.224262\pi$
$193$	−2.50000	−	4.33013i	−0.179954	−	0.311689i	−0.941865	+	0.335993i	$0.890928\pi$
$194$	11.0718			0.794909
$195$	−7.56218	−	15.2942i	−0.541539	−	1.09524i
$196$	1.00000			0.0714286
$197$	−6.00000	−	10.3923i	−0.427482	−	0.740421i	0.569166	−	0.822222i	$-0.307266\pi$
$197$	−6.00000	−	10.3923i	−0.427482	−	0.740421i	−0.996649	+	0.0818013i	$0.973933\pi$
$198$	−4.90192	−	8.49038i	−0.348365	−	0.603385i
$199$	−1.00000	+	1.73205i	−0.0708881	+	0.122782i	−0.899291	−	0.437351i	$-0.855917\pi$
$199$	−1.00000	+	1.73205i	−0.0708881	+	0.122782i	0.828403	+	0.560133i	$0.189250\pi$
$200$	3.46410			0.244949
$201$	8.46410	−	14.6603i	0.597012	−	1.03405i
$202$	6.69615	−	11.5981i	0.471140	−	0.816038i
$203$	−3.00000			−0.210559
$204$	10.5622	−	18.2942i	0.739500	−	1.28085i
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$	12.4641	+	21.5885i	0.868415	+	1.50414i
$207$	21.1244			1.46824
$208$	7.99038	+	16.1603i	0.554033	+	1.12051i
$209$	2.53590			0.175412
$210$	−4.09808	−	7.09808i	−0.282794	−	0.489814i
$211$	0.901924	+	1.56218i	0.0620910	+	0.107545i	0.895400	−	0.445263i	$-0.146890\pi$
$211$	0.901924	+	1.56218i	0.0620910	+	0.107545i	−0.833309	+	0.552808i	$0.813556\pi$
$212$	4.96410	−	8.59808i	0.340936	−	0.590518i
$213$	16.3923			1.12318
$214$	6.80385	−	11.7846i	0.465101	−	0.805579i
$215$	0.169873	−	0.294229i	0.0115852	−	0.0200662i
$216$	−6.92820			−0.471405
$217$	−2.09808	+	3.63397i	−0.142427	+	0.246690i
$218$	7.26795	+	12.5885i	0.492248	+	0.852598i
$219$	4.36603	+	7.56218i	0.295029	+	0.511005i
$220$	2.19615			0.148065
$221$	15.4641	−	23.1962i	1.04023	−	1.56034i
$222$	−33.1244			−2.22316
$223$	5.00000	+	8.66025i	0.334825	+	0.579934i	0.983451	−	0.181173i	$-0.0579895\pi$
$223$	5.00000	+	8.66025i	0.334825	+	0.579934i	−0.648626	+	0.761107i	$0.724656\pi$
$224$	2.59808	+	4.50000i	0.173591	+	0.300669i
$225$	4.46410	−	7.73205i	0.297607	−	0.515470i
$226$	23.1962			1.54299
$227$	−2.83013	+	4.90192i	−0.187842	+	0.325352i	−0.944531	−	0.328424i	$-0.893483\pi$
$227$	−2.83013	+	4.90192i	−0.187842	+	0.325352i	0.756688	+	0.653776i	$0.226816\pi$
$228$	−2.73205	+	4.73205i	−0.180934	+	0.313388i
$229$	−14.3923			−0.951070			−0.475535	−	0.879697i	$-0.657746\pi$
$229$	−14.3923			−0.951070			−0.475535	+	0.879697i	$0.657746\pi$
$230$	−7.09808	+	12.2942i	−0.468033	+	0.810657i
$231$	−1.73205	−	3.00000i	−0.113961	−	0.197386i
$232$	−2.59808	−	4.50000i	−0.170572	−	0.295439i
$233$	−1.85641			−0.121617			−0.0608086	−	0.998149i	$-0.519368\pi$
$233$	−1.85641			−0.121617			−0.0608086	+	0.998149i	$0.519368\pi$
$234$	27.8205	+	1.79423i	1.81868	+	0.117292i
$235$	22.3923			1.46071
$236$	−3.63397	−	6.29423i	−0.236552	−	0.409719i
$237$	−22.1244	−	38.3205i	−1.43713	−	2.48918i
$238$	6.69615	−	11.5981i	0.434047	−	0.751792i
$239$	−15.8038			−1.02227			−0.511133	−	0.859502i	$-0.670774\pi$
$239$	−15.8038			−1.02227			−0.511133	+	0.859502i	$0.670774\pi$
$240$	11.8301	−	20.4904i	0.763631	−	1.32265i
$241$	10.5981	−	18.3564i	0.682682	−	1.18244i	−0.291477	−	0.956578i	$-0.594147\pi$
$241$	10.5981	−	18.3564i	0.682682	−	1.18244i	0.974159	−	0.225862i	$-0.0725199\pi$
$242$	−16.2679			−1.04574
$243$	9.36603	−	16.2224i	0.600831	−	1.04067i
$244$	2.40192	+	4.16025i	0.153767	+	0.266333i
$245$	−0.866025	−	1.50000i	−0.0553283	−	0.0958315i
$246$	−24.5885			−1.56770
$247$	−4.00000	+	6.00000i	−0.254514	+	0.381771i
$248$	−7.26795			−0.461515
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$	10.5000	+	18.1865i	0.664078	+	1.15022i
$251$	0.803848	−	1.39230i	0.0507384	−	0.0878815i	−0.839541	−	0.543297i	$-0.817176\pi$
$251$	0.803848	−	1.39230i	0.0507384	−	0.0878815i	0.890279	+	0.455415i	$0.150509\pi$
$252$	4.46410			0.281212
$253$	−3.00000	+	5.19615i	−0.188608	+	0.326679i
$254$	−15.9282	+	27.5885i	−0.999424	+	1.73105i
$255$	−36.5885			−2.29126
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	−3.06218	−	5.30385i	−0.191013	−	0.330845i	0.754573	−	0.656216i	$-0.227844\pi$
$257$	−3.06218	−	5.30385i	−0.191013	−	0.330845i	−0.945586	+	0.325371i	$0.894511\pi$
$258$	0.464102	+	0.803848i	0.0288937	+	0.0500454i
$259$	−7.00000			−0.434959
$260$	−3.46410	+	5.19615i	−0.214834	+	0.322252i
$261$	−13.3923			−0.828963
$262$	3.00000	+	5.19615i	0.185341	+	0.321019i
$263$	−0.633975	−	1.09808i	−0.0390925	−	0.0677103i	0.845817	−	0.533473i	$-0.179113\pi$
$263$	−0.633975	−	1.09808i	−0.0390925	−	0.0677103i	−0.884910	+	0.465763i	$0.845780\pi$
$264$	3.00000	−	5.19615i	0.184637	−	0.319801i
$265$	−17.1962			−1.05635
$266$	−1.73205	+	3.00000i	−0.106199	+	0.183942i
$267$	−17.6603	+	30.5885i	−1.08079	+	1.87198i
$268$	−6.19615			−0.378490
$269$	−2.53590	+	4.39230i	−0.154616	+	0.267804i	−0.932919	−	0.360086i	$-0.882748\pi$
$269$	−2.53590	+	4.39230i	−0.154616	+	0.267804i	0.778303	+	0.627889i	$0.216081\pi$
$270$	−6.00000	−	10.3923i	−0.365148	−	0.632456i
$271$	−2.90192	−	5.02628i	−0.176279	−	0.305325i	0.764324	−	0.644832i	$-0.223073\pi$
$271$	−2.90192	−	5.02628i	−0.176279	−	0.305325i	−0.940603	+	0.339508i	$0.889740\pi$
$272$	38.6603			2.34412
$273$	9.83013	+	0.633975i	0.594946	+	0.0383699i
$274$	13.9808			0.844609
$275$	1.26795	+	2.19615i	0.0764602	+	0.132433i
$276$	−6.46410	−	11.1962i	−0.389093	−	0.673929i
$277$	−8.50000	+	14.7224i	−0.510716	+	0.884585i	0.489207	+	0.872167i	$0.337286\pi$
$277$	−8.50000	+	14.7224i	−0.510716	+	0.884585i	−0.999923	+	0.0124177i	$0.996047\pi$
$278$	−18.3397			−1.09994
$279$	−9.36603	+	16.2224i	−0.560729	+	0.971212i
$280$	1.50000	−	2.59808i	0.0896421	−	0.155265i
$281$	13.3923			0.798918			0.399459	−	0.916751i	$-0.369198\pi$
$281$	13.3923			0.798918			0.399459	+	0.916751i	$0.369198\pi$
$282$	−30.5885	+	52.9808i	−1.82152	+	3.15496i
$283$	−5.09808	−	8.83013i	−0.303049	−	0.524897i	0.673776	−	0.738936i	$-0.264671\pi$
$283$	−5.09808	−	8.83013i	−0.303049	−	0.524897i	−0.976825	+	0.214039i	$0.931338\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$	9.46410			0.560605
$286$	−4.39230	+	6.58846i	−0.259722	+	0.389584i
$287$	−5.19615			−0.306719
$288$	11.5981	+	20.0885i	0.683423	+	1.18372i
$289$	−21.3923	−	37.0526i	−1.25837	−	2.17956i
$290$	4.50000	−	7.79423i	0.264249	−	0.457693i
$291$	17.4641			1.02376
$292$	1.59808	−	2.76795i	0.0935203	−	0.161982i
$293$	0.401924	−	0.696152i	0.0234806	−	0.0406697i	−0.854046	−	0.520197i	$-0.825859\pi$
$293$	0.401924	−	0.696152i	0.0234806	−	0.0406697i	0.877527	+	0.479527i	$0.159192\pi$
$294$	4.73205			0.275979
$295$	−6.29423	+	10.9019i	−0.366464	+	0.634735i
$296$	−6.06218	−	10.5000i	−0.352357	−	0.610300i
$297$	−2.53590	−	4.39230i	−0.147148	−	0.254867i
$298$	−11.1962			−0.648576
$299$	−7.56218	−	15.2942i	−0.437332	−	0.884488i
$300$	−5.46410			−0.315470
$301$	0.0980762	+	0.169873i	0.00565302	+	0.00979132i
$302$	−1.73205	−	3.00000i	−0.0996683	−	0.172631i
$303$	10.5622	−	18.2942i	0.606781	−	1.05098i
$304$	−10.0000			−0.573539
$305$	4.16025	−	7.20577i	0.238215	−	0.412601i
$306$	29.8923	−	51.7750i	1.70883	−	2.95978i
$307$	−4.58846			−0.261877			−0.130939	−	0.991390i	$-0.541799\pi$
$307$	−4.58846			−0.261877			−0.130939	+	0.991390i	$0.541799\pi$
$308$	−0.633975	+	1.09808i	−0.0361241	+	0.0625687i
$309$	19.6603	+	34.0526i	1.11843	+	1.93718i
$310$	−6.29423	−	10.9019i	−0.357488	−	0.619188i
$311$	1.26795			0.0718988			0.0359494	−	0.999354i	$-0.488554\pi$
$311$	1.26795			0.0718988			0.0359494	+	0.999354i	$0.488554\pi$
$312$	7.56218	+	15.2942i	0.428124	+	0.865865i
$313$	28.7846			1.62700			0.813501	−	0.581563i	$-0.197559\pi$
$313$	28.7846			1.62700			0.813501	+	0.581563i	$0.197559\pi$
$314$	−1.03590	−	1.79423i	−0.0584591	−	0.101254i
$315$	−3.86603	−	6.69615i	−0.217826	−	0.377285i
$316$	−8.09808	+	14.0263i	−0.455552	+	0.789040i
$317$	−6.46410			−0.363060			−0.181530	−	0.983385i	$-0.558105\pi$
$317$	−6.46410			−0.363060			−0.181530	+	0.983385i	$0.558105\pi$
$318$	23.4904	−	40.6865i	1.31728	−	2.28159i
$319$	1.90192	−	3.29423i	0.106487	−	0.184441i
$320$	1.73205			0.0968246
$321$	10.7321	−	18.5885i	0.599005	−	1.03751i
$322$	−4.09808	−	7.09808i	−0.228377	−	0.395560i
$323$	7.73205	+	13.3923i	0.430223	+	0.745168i
$324$	−2.46410			−0.136895
$325$	−7.19615	−	0.464102i	−0.399171	−	0.0257437i
$326$	28.0526			1.55369
$327$	11.4641	+	19.8564i	0.633966	+	1.09806i
$328$	−4.50000	−	7.79423i	−0.248471	−	0.430364i
$329$	−6.46410	+	11.1962i	−0.356377	+	0.617264i
$330$	10.3923			0.572078
$331$	−12.4904	+	21.6340i	−0.686533	+	1.18911i	0.286419	+	0.958105i	$0.407535\pi$
$331$	−12.4904	+	21.6340i	−0.686533	+	1.18911i	−0.972952	+	0.231006i	$0.925798\pi$
$332$	1.09808	−	1.90192i	0.0602648	−	0.104382i
$333$	−31.2487			−1.71242
$334$	5.70577	−	9.88269i	0.312206	−	0.540757i
$335$	5.36603	+	9.29423i	0.293177	+	0.507798i
$336$	6.83013	+	11.8301i	0.372614	+	0.645386i
$337$	11.0000			0.599208			0.299604	−	0.954064i	$-0.403145\pi$
$337$	11.0000			0.599208			0.299604	+	0.954064i	$0.403145\pi$
$338$	−8.66025	−	20.7846i	−0.471056	−	1.13053i
$339$	36.5885			1.98721
$340$	6.69615	+	11.5981i	0.363150	+	0.628994i
$341$	−2.66025	−	4.60770i	−0.144061	−	0.249521i
$342$	−7.73205	+	13.3923i	−0.418101	+	0.724173i
$343$	1.00000			0.0539949
$344$	−0.169873	+	0.294229i	−0.00915894	+	0.0158637i
$345$	−11.1962	+	19.3923i	−0.602781	+	1.04405i
$346$	14.7846			0.794826
$347$	−3.63397	+	6.29423i	−0.195082	+	0.337892i	−0.946927	−	0.321448i	$-0.895831\pi$
$347$	−3.63397	+	6.29423i	−0.195082	+	0.337892i	0.751845	+	0.659339i	$0.229164\pi$
$348$	4.09808	+	7.09808i	0.219680	+	0.380497i
$349$	12.3923	+	21.4641i	0.663345	+	1.14895i	0.979731	+	0.200317i	$0.0641971\pi$
$349$	12.3923	+	21.4641i	0.663345	+	1.14895i	−0.316386	+	0.948630i	$0.602470\pi$
$350$	−3.46410			−0.185164
$351$	14.3923	+	0.928203i	0.768204	+	0.0495438i
$352$	−6.58846			−0.351166
$353$	−10.3301	−	17.8923i	−0.549817	−	0.952311i	−0.998287	−	0.0585131i	$-0.981364\pi$
$353$	−10.3301	−	17.8923i	−0.549817	−	0.952311i	0.448469	−	0.893798i	$-0.351969\pi$
$354$	−17.1962	−	29.7846i	−0.913965	−	1.58303i
$355$	−5.19615	+	9.00000i	−0.275783	+	0.477670i
$356$	12.9282			0.685193
$357$	10.5622	−	18.2942i	0.559010	−	0.968233i
$358$	6.00000	−	10.3923i	0.317110	−	0.549250i
$359$	18.9282			0.998992			0.499496	−	0.866316i	$-0.333518\pi$
$359$	18.9282			0.998992			0.499496	+	0.866316i	$0.333518\pi$
$360$	6.69615	−	11.5981i	0.352918	−	0.611272i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−4.83975	−	8.38269i	−0.254371	−	0.440584i
$363$	−25.6603			−1.34681
$364$	−1.59808	−	3.23205i	−0.0837620	−	0.169405i
$365$	−5.53590			−0.289762
$366$	11.3660	+	19.6865i	0.594112	+	1.02903i
$367$	−2.09808	−	3.63397i	−0.109519	−	0.189692i	0.806057	−	0.591838i	$-0.201598\pi$
$367$	−2.09808	−	3.63397i	−0.109519	−	0.189692i	−0.915575	+	0.402146i	$0.868264\pi$
$368$	11.8301	−	20.4904i	0.616688	−	1.06813i
$369$	−23.1962			−1.20754
$370$	10.5000	−	18.1865i	0.545869	−	0.945473i
$371$	4.96410	−	8.59808i	0.257723	−	0.446390i
$372$	11.4641			0.594386
$373$	5.69615	−	9.86603i	0.294936	−	0.510843i	−0.680034	−	0.733180i	$-0.738035\pi$
$373$	5.69615	−	9.86603i	0.294936	−	0.510843i	0.974970	+	0.222337i	$0.0713685\pi$
$374$	8.49038	+	14.7058i	0.439027	+	0.760417i
$375$	16.5622	+	28.6865i	0.855267	+	1.48137i
$376$	−22.3923			−1.15479
$377$	4.79423	+	9.69615i	0.246915	+	0.499377i
$378$	6.92820			0.356348
$379$	−13.2942	−	23.0263i	−0.682879	−	1.18278i	−0.974098	−	0.226124i	$-0.927394\pi$
$379$	−13.2942	−	23.0263i	−0.682879	−	1.18278i	0.291220	−	0.956656i	$-0.405939\pi$
$380$	−1.73205	−	3.00000i	−0.0888523	−	0.153897i
$381$	−25.1244	+	43.5167i	−1.28716	+	2.22943i
$382$	8.19615			0.419352
$383$	5.83013	−	10.0981i	0.297906	−	0.515988i	−0.677751	−	0.735291i	$-0.737045\pi$
$383$	5.83013	−	10.0981i	0.297906	−	0.515988i	0.975657	+	0.219304i	$0.0703786\pi$
$384$	−16.5622	+	28.6865i	−0.845185	+	1.46390i
$385$	2.19615			0.111926
$386$	−4.33013	+	7.50000i	−0.220398	+	0.381740i
$387$	0.437822	+	0.758330i	0.0222558	+	0.0385481i
$388$	−3.19615	−	5.53590i	−0.162260	−	0.281043i
$389$	−23.5359			−1.19332			−0.596659	−	0.802495i	$-0.703505\pi$
$389$	−23.5359			−1.19332			−0.596659	+	0.802495i	$0.703505\pi$
$390$	−16.3923	+	24.5885i	−0.830057	+	1.24508i
$391$	−36.5885			−1.85036
$392$	0.866025	+	1.50000i	0.0437409	+	0.0757614i
$393$	4.73205	+	8.19615i	0.238700	+	0.413441i
$394$	−10.3923	+	18.0000i	−0.523557	+	0.906827i
$395$	28.0526			1.41148
$396$	−2.83013	+	4.90192i	−0.142219	+	0.246331i
$397$	9.39230	−	16.2679i	0.471386	−	0.816465i	−0.528078	−	0.849196i	$-0.677087\pi$
$397$	9.39230	−	16.2679i	0.471386	−	0.816465i	0.999464	+	0.0327309i	$0.0104204\pi$
$398$	3.46410			0.173640
$399$	−2.73205	+	4.73205i	−0.136774	+	0.236899i
$400$	−5.00000	−	8.66025i	−0.250000	−	0.433013i
$401$	5.42820	+	9.40192i	0.271072	+	0.469510i	0.969136	−	0.246525i	$-0.0792887\pi$
$401$	5.42820	+	9.40192i	0.271072	+	0.469510i	−0.698065	+	0.716034i	$0.745955\pi$
$402$	−29.3205			−1.46237
$403$	15.0981	+	0.973721i	0.752089	+	0.0485045i
$404$	−7.73205			−0.384684
$405$	2.13397	+	3.69615i	0.106038	+	0.183663i
$406$	2.59808	+	4.50000i	0.128940	+	0.223331i
$407$	4.43782	−	7.68653i	0.219975	−	0.381007i
$408$	36.5885			1.81140
$409$	8.40192	−	14.5526i	0.415448	−	0.719578i	−0.580027	−	0.814597i	$-0.696958\pi$
$409$	8.40192	−	14.5526i	0.415448	−	0.719578i	0.995475	+	0.0950195i	$0.0302913\pi$
$410$	7.79423	−	13.5000i	0.384930	−	0.666717i
$411$	22.0526			1.08777
$412$	7.19615	−	12.4641i	0.354529	−	0.614062i
$413$	−3.63397	−	6.29423i	−0.178816	−	0.309719i
$414$	−18.2942	−	31.6865i	−0.899112	−	1.55731i
$415$	−3.80385			−0.186724
$416$	10.3923	−	15.5885i	0.509525	−	0.764287i
$417$	−28.9282			−1.41662
$418$	−2.19615	−	3.80385i	−0.107417	−	0.186052i
$419$	16.0981	+	27.8827i	0.786442	+	1.36216i	0.928134	+	0.372247i	$0.121413\pi$
$419$	16.0981	+	27.8827i	0.786442	+	1.36216i	−0.141691	+	0.989911i	$0.545254\pi$
$420$	−2.36603	+	4.09808i	−0.115450	+	0.199966i
$421$	−32.1769			−1.56821			−0.784103	−	0.620630i	$-0.786877\pi$
$421$	−32.1769			−1.56821			−0.784103	+	0.620630i	$0.786877\pi$
$422$	1.56218	−	2.70577i	0.0760456	−	0.131715i
$423$	−28.8564	+	49.9808i	−1.40305	+	2.43015i
$424$	17.1962			0.835119
$425$	−7.73205	+	13.3923i	−0.375060	+	0.649622i
$426$	−14.1962	−	24.5885i	−0.687806	−	1.19131i
$427$	2.40192	+	4.16025i	0.116237	+	0.201329i
$428$	−7.85641			−0.379754
$429$	−6.92820	+	10.3923i	−0.334497	+	0.501745i
$430$	−0.588457			−0.0283779
$431$	−0.339746	−	0.588457i	−0.0163650	−	0.0283450i	0.857727	−	0.514106i	$-0.171876\pi$
$431$	−0.339746	−	0.588457i	−0.0163650	−	0.0283450i	−0.874092	+	0.485761i	$0.838543\pi$
$432$	10.0000	+	17.3205i	0.481125	+	0.833333i
$433$	6.79423	−	11.7679i	0.326510	−	0.565532i	−0.655307	−	0.755363i	$-0.727461\pi$
$433$	6.79423	−	11.7679i	0.326510	−	0.565532i	0.981817	+	0.189831i	$0.0607941\pi$
$434$	7.26795			0.348873
$435$	7.09808	−	12.2942i	0.340327	−	0.589463i
$436$	4.19615	−	7.26795i	0.200959	−	0.348072i
$437$	9.46410			0.452729
$438$	7.56218	−	13.0981i	0.361335	−	0.625850i
$439$	−7.29423	−	12.6340i	−0.348135	−	0.602987i	0.637784	−	0.770216i	$-0.279851\pi$
$439$	−7.29423	−	12.6340i	−0.348135	−	0.602987i	−0.985918	+	0.167229i	$0.946518\pi$
$440$	1.90192	+	3.29423i	0.0906707	+	0.157046i
$441$	4.46410			0.212576
$442$	−48.1865	−	3.10770i	−2.29200	−	0.147818i
$443$	23.3205			1.10799			0.553995	−	0.832520i	$-0.313103\pi$
$443$	23.3205			1.10799			0.553995	+	0.832520i	$0.313103\pi$
$444$	9.56218	+	16.5622i	0.453801	+	0.786006i
$445$	−11.1962	−	19.3923i	−0.530749	−	0.919283i
$446$	8.66025	−	15.0000i	0.410075	−	0.710271i
$447$	−17.6603			−0.835301
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	6.00000	−	10.3923i	0.283158	−	0.490443i	−0.689003	−	0.724758i	$-0.741951\pi$
$449$	6.00000	−	10.3923i	0.283158	−	0.490443i	0.972161	+	0.234315i	$0.0752847\pi$
$450$	−15.4641			−0.728985
$451$	3.29423	−	5.70577i	0.155119	−	0.268674i
$452$	−6.69615	−	11.5981i	−0.314961	−	0.545528i
$453$	−2.73205	−	4.73205i	−0.128363	−	0.222331i
$454$	9.80385			0.460117
$455$	−3.46410	+	5.19615i	−0.162400	+	0.243599i
$456$	−9.46410			−0.443197
$457$	−5.50000	−	9.52628i	−0.257279	−	0.445621i	0.708233	−	0.705979i	$-0.249493\pi$
$457$	−5.50000	−	9.52628i	−0.257279	−	0.445621i	−0.965512	+	0.260358i	$0.916159\pi$
$458$	12.4641	+	21.5885i	0.582409	+	1.00876i
$459$	15.4641	−	26.7846i	0.721802	−	1.25020i
$460$	8.19615			0.382148
$461$	7.79423	−	13.5000i	0.363013	−	0.628758i	−0.625442	−	0.780271i	$-0.715081\pi$
$461$	7.79423	−	13.5000i	0.363013	−	0.628758i	0.988455	+	0.151513i	$0.0484146\pi$
$462$	−3.00000	+	5.19615i	−0.139573	+	0.241747i
$463$	−4.58846			−0.213244			−0.106622	−	0.994300i	$-0.534003\pi$
$463$	−4.58846			−0.213244			−0.106622	+	0.994300i	$0.534003\pi$
$464$	−7.50000	+	12.9904i	−0.348179	+	0.603063i
$465$	−9.92820	−	17.1962i	−0.460409	−	0.797452i
$466$	1.60770	+	2.78461i	0.0744750	+	0.128995i
$467$	25.5167			1.18077			0.590385	−	0.807122i	$-0.298976\pi$
$467$	25.5167			1.18077			0.590385	+	0.807122i	$0.298976\pi$
$468$	−7.13397	−	14.4282i	−0.329768	−	0.666944i
$469$	−6.19615			−0.286112
$470$	−19.3923	−	33.5885i	−0.894500	−	1.54932i
$471$	−1.63397	−	2.83013i	−0.0752896	−	0.130405i
$472$	6.29423	−	10.9019i	0.289715	−	0.501802i
$473$	−0.248711			−0.0114358
$474$	−38.3205	+	66.3731i	−1.76012	+	3.04862i
$475$	2.00000	−	3.46410i	0.0917663	−	0.158944i
$476$	−7.73205			−0.354398
$477$	22.1603	−	38.3827i	1.01465	−	1.75742i
$478$	13.6865	+	23.7058i	0.626007	+	1.08428i
$479$	−0.633975	−	1.09808i	−0.0289670	−	0.0501724i	0.851178	−	0.524876i	$-0.175888\pi$
$479$	−0.633975	−	1.09808i	−0.0289670	−	0.0501724i	−0.880146	+	0.474704i	$0.842555\pi$
$480$	−24.5885			−1.12230
$481$	11.1865	+	22.6244i	0.510062	+	1.03158i
$482$	−36.7128			−1.67222
$483$	−6.46410	−	11.1962i	−0.294127	−	0.509443i
$484$	4.69615	+	8.13397i	0.213461	+	0.369726i
$485$	−5.53590	+	9.58846i	−0.251372	+	0.435389i
$486$	−32.4449			−1.47173
$487$	−20.3923	+	35.3205i	−0.924064	+	1.60052i	−0.131003	+	0.991382i	$0.541820\pi$
$487$	−20.3923	+	35.3205i	−0.924064	+	1.60052i	−0.793060	+	0.609143i	$0.791514\pi$
$488$	−4.16025	+	7.20577i	−0.188326	+	0.326190i
$489$	44.2487			2.00100
$490$	−1.50000	+	2.59808i	−0.0677631	+	0.117369i
$491$	−3.80385	−	6.58846i	−0.171665	−	0.297333i	0.767337	−	0.641244i	$-0.221581\pi$
$491$	−3.80385	−	6.58846i	−0.171665	−	0.297333i	−0.939002	+	0.343911i	$0.888248\pi$
$492$	7.09808	+	12.2942i	0.320006	+	0.554267i
$493$	23.1962			1.04470
$494$	12.4641	+	0.803848i	0.560786	+	0.0361668i
$495$	9.80385			0.440650
$496$	10.4904	+	18.1699i	0.471032	+	0.815851i
$497$	−3.00000	−	5.19615i	−0.134568	−	0.233079i
$498$	5.19615	−	9.00000i	0.232845	−	0.403300i
$499$	−38.9808			−1.74502			−0.872509	−	0.488598i	$-0.837509\pi$
$499$	−38.9808			−1.74502			−0.872509	+	0.488598i	$0.837509\pi$
$500$	6.06218	−	10.5000i	0.271109	−	0.469574i
$501$	9.00000	−	15.5885i	0.402090	−	0.696441i
$502$	−2.78461			−0.124283
$503$	9.29423	−	16.0981i	0.414409	−	0.717778i	−0.580957	−	0.813934i	$-0.697322\pi$
$503$	9.29423	−	16.0981i	0.414409	−	0.717778i	0.995366	+	0.0961565i	$0.0306549\pi$
$504$	3.86603	+	6.69615i	0.172206	+	0.298270i
$505$	6.69615	+	11.5981i	0.297975	+	0.516108i
$506$	10.3923			0.461994
$507$	−13.6603	−	32.7846i	−0.606673	−	1.45602i
$508$	18.3923			0.816027
$509$	−6.86603	−	11.8923i	−0.304331	−	0.527117i	0.672781	−	0.739842i	$-0.265100\pi$
$509$	−6.86603	−	11.8923i	−0.304331	−	0.527117i	−0.977112	+	0.212725i	$0.931766\pi$
$510$	31.6865	+	54.8827i	1.40310	+	2.43025i
$511$	1.59808	−	2.76795i	0.0706947	−	0.122447i
$512$	8.66025			0.382733
$513$	−4.00000	+	6.92820i	−0.176604	+	0.305888i
$514$	−5.30385	+	9.18653i	−0.233943	+	0.405201i
$515$	−24.9282			−1.09847
$516$	0.267949	−	0.464102i	0.0117958	−	0.0204309i
$517$	−8.19615	−	14.1962i	−0.360466	−	0.624346i
$518$	6.06218	+	10.5000i	0.266357	+	0.461344i
$519$	23.3205			1.02366
$520$	−10.7942	−	0.696152i	−0.473358	−	0.0305283i
$521$	−24.1244			−1.05691			−0.528454	−	0.848962i	$-0.677228\pi$
$521$	−24.1244			−1.05691			−0.528454	+	0.848962i	$0.677228\pi$
$522$	11.5981	+	20.0885i	0.507634	+	0.879248i
$523$	14.5885	+	25.2679i	0.637909	+	1.10489i	0.985891	+	0.167389i	$0.0535336\pi$
$523$	14.5885	+	25.2679i	0.637909	+	1.10489i	−0.347982	+	0.937501i	$0.613133\pi$
$524$	1.73205	−	3.00000i	0.0756650	−	0.131056i
$525$	−5.46410			−0.238473
$526$	−1.09808	+	1.90192i	−0.0478784	+	0.0829278i
$527$	16.2224	−	28.0981i	0.706660	−	1.22397i
$528$	−17.3205			−0.753778
$529$	0.303848	−	0.526279i	0.0132108	−	0.0228817i
$530$	14.8923	+	25.7942i	0.646880	+	1.12043i
$531$	−16.2224	−	28.0981i	−0.703994	−	1.21935i
$532$	2.00000			0.0867110
$533$	8.30385	+	16.7942i	0.359680	+	0.727439i
$534$	61.1769			2.64738
$535$	6.80385	+	11.7846i	0.294156	+	0.509493i
$536$	−5.36603	−	9.29423i	−0.231777	−	0.401450i
$537$	9.46410	−	16.3923i	0.408406	−	0.707380i
$538$	8.78461			0.378731
$539$	−0.633975	+	1.09808i	−0.0273072	+	0.0472975i
$540$	−3.46410	+	6.00000i	−0.149071	+	0.258199i
$541$	−14.6077			−0.628034			−0.314017	−	0.949417i	$-0.601675\pi$
$541$	−14.6077			−0.628034			−0.314017	+	0.949417i	$0.601675\pi$
$542$	−5.02628	+	8.70577i	−0.215897	+	0.373945i
$543$	−7.63397	−	13.2224i	−0.327605	−	0.567429i
$544$	−20.0885	−	34.7942i	−0.861285	−	1.49179i
$545$	−14.5359			−0.622649
$546$	−7.56218	−	15.2942i	−0.323631	−	0.654533i
$547$	17.8038			0.761238			0.380619	−	0.924732i	$-0.375711\pi$
$547$	17.8038			0.761238			0.380619	+	0.924732i	$0.375711\pi$
$548$	−4.03590	−	6.99038i	−0.172405	−	0.298614i
$549$	10.7224	+	18.5718i	0.457622	+	0.792625i
$550$	2.19615	−	3.80385i	0.0936443	−	0.162197i
$551$	−6.00000			−0.255609
$552$	11.1962	−	19.3923i	0.476540	−	0.825391i
$553$	−8.09808	+	14.0263i	−0.344365	+	0.596458i
$554$	29.4449			1.25099
$555$	16.5622	−	28.6865i	0.703025	−	1.21768i
$556$	5.29423	+	9.16987i	0.224525	+	0.388889i
$557$	−21.8205	−	37.7942i	−0.924565	−	1.60139i	−0.792260	−	0.610184i	$-0.791096\pi$
$557$	−21.8205	−	37.7942i	−0.924565	−	1.60139i	−0.132305	−	0.991209i	$-0.542238\pi$
$558$	32.4449			1.37350
$559$	0.392305	−	0.588457i	0.0165927	−	0.0248891i
$560$	−8.66025			−0.365963
$561$	13.3923	+	23.1962i	0.565424	+	0.979342i
$562$	−11.5981	−	20.0885i	−0.489235	−	0.847380i
$563$	−14.0263	+	24.2942i	−0.591137	+	1.02388i	0.402942	+	0.915225i	$0.367987\pi$
$563$	−14.0263	+	24.2942i	−0.591137	+	1.02388i	−0.994080	+	0.108654i	$0.965346\pi$
$564$	35.3205			1.48726
$565$	−11.5981	+	20.0885i	−0.487935	+	0.845128i
$566$	−8.83013	+	15.2942i	−0.371158	+	0.642864i
$567$	−2.46410			−0.103483
$568$	5.19615	−	9.00000i	0.218026	−	0.377632i
$569$	−21.4641	−	37.1769i	−0.899822	−	1.55854i	−0.827721	−	0.561140i	$-0.810363\pi$
$569$	−21.4641	−	37.1769i	−0.899822	−	1.55854i	−0.0721010	−	0.997397i	$-0.522970\pi$
$570$	−8.19615	−	14.1962i	−0.343299	−	0.594611i
$571$	16.7846			0.702414			0.351207	−	0.936298i	$-0.385771\pi$
$571$	16.7846			0.702414			0.351207	+	0.936298i	$0.385771\pi$
$572$	4.56218	+	0.294229i	0.190754	+	0.0123023i
$573$	12.9282			0.540083
$574$	4.50000	+	7.79423i	0.187826	+	0.325325i
$575$	4.73205	+	8.19615i	0.197340	+	0.341803i
$576$	−2.23205	+	3.86603i	−0.0930021	+	0.161084i
$577$	43.1962			1.79828			0.899140	−	0.437662i	$-0.144193\pi$
$577$	43.1962			1.79828			0.899140	+	0.437662i	$0.144193\pi$
$578$	−37.0526	+	64.1769i	−1.54118	+	2.66941i
$579$	−6.83013	+	11.8301i	−0.283850	+	0.491643i
$580$	−5.19615			−0.215758
$581$	1.09808	−	1.90192i	0.0455559	−	0.0789051i
$582$	−15.1244	−	26.1962i	−0.626925	−	1.08587i
$583$	6.29423	+	10.9019i	0.260680	+	0.451512i
$584$	5.53590			0.229077
$585$	−15.4641	+	23.1962i	−0.639362	+	0.959043i
$586$	−1.39230			−0.0575156
$587$	−8.19615	−	14.1962i	−0.338291	−	0.585938i	0.645820	−	0.763490i	$-0.276516\pi$
$587$	−8.19615	−	14.1962i	−0.338291	−	0.585938i	−0.984111	+	0.177552i	$0.943182\pi$
$588$	−1.36603	−	2.36603i	−0.0563339	−	0.0975732i
$589$	−4.19615	+	7.26795i	−0.172899	+	0.299471i
$590$	21.8038			0.897650
$591$	−16.3923	+	28.3923i	−0.674289	+	1.16790i
$592$	−17.5000	+	30.3109i	−0.719246	+	1.24577i
$593$	−17.4449			−0.716375			−0.358187	−	0.933650i	$-0.616605\pi$
$593$	−17.4449			−0.716375			−0.358187	+	0.933650i	$0.616605\pi$
$594$	−4.39230	+	7.60770i	−0.180218	+	0.312148i
$595$	6.69615	+	11.5981i	0.274515	+	0.475475i
$596$	3.23205	+	5.59808i	0.132390	+	0.229306i
$597$	5.46410			0.223631
$598$	−16.3923	+	24.5885i	−0.670331	+	1.00550i
$599$	43.8564			1.79192			0.895962	−	0.444131i	$-0.146487\pi$
$599$	43.8564			1.79192			0.895962	+	0.444131i	$0.146487\pi$
$600$	−4.73205	−	8.19615i	−0.193185	−	0.334607i
$601$	14.9904	+	25.9641i	0.611470	+	1.05910i	0.990993	+	0.133915i	$0.0427550\pi$
$601$	14.9904	+	25.9641i	0.611470	+	1.05910i	−0.379522	+	0.925183i	$0.623912\pi$
$602$	0.169873	−	0.294229i	0.00692351	−	0.0119919i
$603$	−27.6603			−1.12641
$604$	−1.00000	+	1.73205i	−0.0406894	+	0.0704761i
$605$	8.13397	−	14.0885i	0.330693	−	0.572777i
$606$	−36.5885			−1.48630
$607$	7.19615	−	12.4641i	0.292083	−	0.505902i	−0.682219	−	0.731148i	$-0.738985\pi$
$607$	7.19615	−	12.4641i	0.292083	−	0.505902i	0.974302	+	0.225245i	$0.0723184\pi$
$608$	5.19615	+	9.00000i	0.210732	+	0.364998i
$609$	4.09808	+	7.09808i	0.166062	+	0.287629i
$610$	−14.4115			−0.583506
$611$	46.5167	+	3.00000i	1.88186	+	0.121367i
$612$	−34.5167			−1.39525
$613$	−1.69615	−	2.93782i	−0.0685070	−	0.118658i	0.829737	−	0.558154i	$-0.188490\pi$
$613$	−1.69615	−	2.93782i	−0.0685070	−	0.118658i	−0.898244	+	0.439497i	$0.855157\pi$
$614$	3.97372	+	6.88269i	0.160366	+	0.277763i
$615$	12.2942	−	21.2942i	0.495751	−	0.858666i
$616$	−2.19615			−0.0884855
$617$	−24.6962	+	42.7750i	−0.994230	+	1.72206i	−0.404214	+	0.914664i	$0.632455\pi$
$617$	−24.6962	+	42.7750i	−0.994230	+	1.72206i	−0.590016	+	0.807392i	$0.700878\pi$
$618$	34.0526	−	58.9808i	1.36979	−	2.37255i
$619$	35.3731			1.42176			0.710882	−	0.703311i	$-0.248296\pi$
$619$	35.3731			1.42176			0.710882	+	0.703311i	$0.248296\pi$
$620$	−3.63397	+	6.29423i	−0.145944	+	0.252782i
$621$	−9.46410	−	16.3923i	−0.379781	−	0.657801i
$622$	−1.09808	−	1.90192i	−0.0440288	−	0.0762602i
$623$	12.9282			0.517958
$624$	27.3205	−	40.9808i	1.09370	−	1.64054i
$625$	−11.0000			−0.440000
$626$	−24.9282	−	43.1769i	−0.996331	−	1.72570i
$627$	−3.46410	−	6.00000i	−0.138343	−	0.239617i
$628$	−0.598076	+	1.03590i	−0.0238658	+	0.0413368i
$629$	54.1244			2.15808
$630$	−6.69615	+	11.5981i	−0.266781	+	0.462078i
$631$	6.39230	−	11.0718i	0.254474	−	0.440761i	−0.710279	−	0.703920i	$-0.751431\pi$
$631$	6.39230	−	11.0718i	0.254474	−	0.440761i	0.964752	+	0.263159i	$0.0847645\pi$
$632$	−28.0526			−1.11587
$633$	2.46410	−	4.26795i	0.0979392	−	0.169636i
$634$	5.59808	+	9.69615i	0.222328	+	0.385083i
$635$	−15.9282	−	27.5885i	−0.632091	−	1.09481i
$636$	−27.1244			−1.07555
$637$	−1.59808	−	3.23205i	−0.0633181	−	0.128059i
$638$	−6.58846			−0.260840
$639$	−13.3923	−	23.1962i	−0.529791	−	0.917626i
$640$	−10.5000	−	18.1865i	−0.415049	−	0.718886i
$641$	−14.4282	+	24.9904i	−0.569880	+	0.987061i	0.426698	+	0.904394i	$0.359677\pi$
$641$	−14.4282	+	24.9904i	−0.569880	+	0.987061i	−0.996577	+	0.0826663i	$0.973656\pi$
$642$	−37.1769			−1.46726
$643$	0.392305	−	0.679492i	0.0154710	−	0.0267965i	−0.858186	−	0.513338i	$-0.828409\pi$
$643$	0.392305	−	0.679492i	0.0154710	−	0.0267965i	0.873657	+	0.486542i	$0.161742\pi$
$644$	−2.36603	+	4.09808i	−0.0932345	+	0.161487i
$645$	−0.928203			−0.0365480
$646$	13.3923	−	23.1962i	0.526913	−	0.912640i
$647$	−22.5167	−	39.0000i	−0.885221	−	1.53325i	−0.845460	−	0.534039i	$-0.820674\pi$
$647$	−22.5167	−	39.0000i	−0.885221	−	1.53325i	−0.0397614	−	0.999209i	$-0.512660\pi$
$648$	−2.13397	−	3.69615i	−0.0838304	−	0.145199i
$649$	9.21539			0.361736
$650$	5.53590	+	11.1962i	0.217136	+	0.439149i
$651$	11.4641			0.449314
$652$	−8.09808	−	14.0263i	−0.317145	−	0.549311i
$653$	18.9282	+	32.7846i	0.740718	+	1.28296i	0.952169	+	0.305572i	$0.0988478\pi$
$653$	18.9282	+	32.7846i	0.740718	+	1.28296i	−0.211451	+	0.977389i	$0.567819\pi$
$654$	19.8564	−	34.3923i	0.776447	−	1.34485i
$655$	−6.00000			−0.234439
$656$	−12.9904	+	22.5000i	−0.507189	+	0.878477i
$657$	7.13397	−	12.3564i	0.278323	−	0.482069i
$658$	22.3923			0.872943
$659$	−14.1962	+	24.5885i	−0.553004	+	0.957830i	0.445052	+	0.895505i	$0.353185\pi$
$659$	−14.1962	+	24.5885i	−0.553004	+	0.957830i	−0.998056	+	0.0623257i	$0.980148\pi$
$660$	−3.00000	−	5.19615i	−0.116775	−	0.202260i
$661$	16.5981	+	28.7487i	0.645590	+	1.11820i	0.984165	+	0.177256i	$0.0567220\pi$
$661$	16.5981	+	28.7487i	0.645590	+	1.11820i	−0.338574	+	0.940940i	$0.609945\pi$
$662$	43.2679			1.68166
$663$	−76.0070	−	4.90192i	−2.95187	−	0.190375i
$664$	3.80385			0.147618
$665$	−1.73205	−	3.00000i	−0.0671660	−	0.116335i
$666$	27.0622	+	46.8731i	1.04864	+	1.81629i
$667$	7.09808	−	12.2942i	0.274839	−	0.476034i
$668$	−6.58846			−0.254915
$669$	13.6603	−	23.6603i	0.528136	−	0.914758i
$670$	9.29423	−	16.0981i	0.359067	−	0.621923i
$671$	−6.09103			−0.235142
$672$	7.09808	−	12.2942i	0.273814	−	0.474260i
$673$	22.0885	+	38.2583i	0.851447	+	1.47475i	0.879902	+	0.475155i	$0.157608\pi$
$673$	22.0885	+	38.2583i	0.851447	+	1.47475i	−0.0284546	+	0.999595i	$0.509059\pi$
$674$	−9.52628	−	16.5000i	−0.366939	−	0.635556i
$675$	−8.00000			−0.307920
$676$	−7.89230	+	10.3301i	−0.303550	+	0.397313i
$677$	−23.0718			−0.886721			−0.443361	−	0.896343i	$-0.646214\pi$
$677$	−23.0718			−0.886721			−0.443361	+	0.896343i	$0.646214\pi$
$678$	−31.6865	−	54.8827i	−1.21691	−	2.10776i
$679$	−3.19615	−	5.53590i	−0.122657	−	0.212448i
$680$	−11.5981	+	20.0885i	−0.444766	+	0.770357i
$681$	15.4641			0.592586
$682$	−4.60770	+	7.98076i	−0.176438	+	0.305599i
$683$	−7.73205	+	13.3923i	−0.295859	+	0.512442i	−0.975184	−	0.221395i	$-0.928939\pi$
$683$	−7.73205	+	13.3923i	−0.295859	+	0.512442i	0.679326	+	0.733837i	$0.262272\pi$
$684$	8.92820			0.341378
$685$	−6.99038	+	12.1077i	−0.267089	+	0.462611i
$686$	−0.866025	−	1.50000i	−0.0330650	−	0.0572703i
$687$	19.6603	+	34.0526i	0.750085	+	1.29919i
$688$	0.980762			0.0373912
$689$	−35.7224	−	2.30385i	−1.36092	−	0.0877696i
$690$	38.7846			1.47650
$691$	−0.196152	−	0.339746i	−0.00746199	−	0.0129245i	0.862270	−	0.506448i	$-0.169042\pi$
$691$	−0.196152	−	0.339746i	−0.00746199	−	0.0129245i	−0.869732	+	0.493524i	$0.835709\pi$
$692$	−4.26795	−	7.39230i	−0.162243	−	0.281013i
$693$	−2.83013	+	4.90192i	−0.107508	+	0.186209i
$694$	12.5885			0.477851
$695$	9.16987	−	15.8827i	0.347833	−	0.602465i
$696$	−7.09808	+	12.2942i	−0.269052	+	0.466012i
$697$	40.1769			1.52181
$698$	21.4641	−	37.1769i	0.812428	−	1.40717i
$699$	2.53590	+	4.39230i	0.0959165	+	0.166132i
$700$	1.00000	+	1.73205i	0.0377964	+	0.0654654i
$701$	20.7846			0.785024			0.392512	−	0.919747i	$-0.371606\pi$
$701$	20.7846			0.785024			0.392512	+	0.919747i	$0.371606\pi$
$702$	−11.0718	−	22.3923i	−0.417878	−	0.845143i
$703$	−14.0000			−0.528020
$704$	−0.633975	−	1.09808i	−0.0238938	−	0.0413853i
$705$	−30.5885	−	52.9808i	−1.15203	−	1.99537i
$706$	−17.8923	+	30.9904i	−0.673386	+	1.16634i
$707$	−7.73205			−0.290794
$708$	−9.92820	+	17.1962i	−0.373125	+	0.646271i
$709$	−15.0885	+	26.1340i	−0.566659	+	0.981482i	0.430234	+	0.902717i	$0.358431\pi$
$709$	−15.0885	+	26.1340i	−0.566659	+	0.981482i	−0.996893	+	0.0787648i	$0.974902\pi$
$710$	18.0000			0.675528
$711$	−36.1506	+	62.6147i	−1.35575	+	2.34824i
$712$	11.1962	+	19.3923i	0.419594	+	0.726757i
$713$	−9.92820	−	17.1962i	−0.371814	−	0.644001i
$714$	−36.5885			−1.36929
$715$	−3.50962	−	7.09808i	−0.131252	−	0.265453i
$716$	−6.92820			−0.258919
$717$	21.5885	+	37.3923i	0.806236	+	1.39644i
$718$	−16.3923	−	28.3923i	−0.611755	−	1.05959i
$719$	3.63397	−	6.29423i	0.135524	−	0.234735i	−0.790273	−	0.612755i	$-0.790061\pi$
$719$	3.63397	−	6.29423i	0.135524	−	0.234735i	0.925798	+	0.378019i	$0.123395\pi$
$720$	−38.6603			−1.44078
$721$	7.19615	−	12.4641i	0.267999	−	0.464187i
$722$	12.9904	−	22.5000i	0.483452	−	0.837363i
$723$	−57.9090			−2.15366
$724$	−2.79423	+	4.83975i	−0.103847	+	0.179868i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$	22.2224	+	38.4904i	0.824752	+	1.42851i
$727$	−41.1769			−1.52717			−0.763584	−	0.645709i	$-0.776562\pi$
$727$	−41.1769			−1.52717			−0.763584	+	0.645709i	$0.776562\pi$
$728$	3.46410	−	5.19615i	0.128388	−	0.192582i
$729$	−43.7846			−1.62165
$730$	4.79423	+	8.30385i	0.177442	+	0.307339i
$731$	−0.758330	−	1.31347i	−0.0280479	−	0.0485803i
$732$	6.56218	−	11.3660i	0.242545	−	0.420100i
$733$	23.5885			0.871260			0.435630	−	0.900126i	$-0.356526\pi$
$733$	23.5885			0.871260			0.435630	+	0.900126i	$0.356526\pi$
$734$	−3.63397	+	6.29423i	−0.134132	+	0.232324i
$735$	−2.36603	+	4.09808i	−0.0872722	+	0.151160i
$736$	−24.5885			−0.906343
$737$	3.92820	−	6.80385i	0.144697	−	0.250623i
$738$	20.0885	+	34.7942i	0.739466	+	1.28079i
$739$	−20.3923	−	35.3205i	−0.750143	−	1.29929i	−0.947753	−	0.319005i	$-0.896651\pi$
$739$	−20.3923	−	35.3205i	−0.750143	−	1.29929i	0.197610	−	0.980281i	$-0.436682\pi$
$740$	−12.1244			−0.445700
$741$	19.6603	+	1.26795i	0.722237	+	0.0465793i
$742$	−17.1962			−0.631291
$743$	3.80385	+	6.58846i	0.139550	+	0.241707i	0.927326	−	0.374254i	$-0.122101\pi$
$743$	3.80385	+	6.58846i	0.139550	+	0.241707i	−0.787777	+	0.615961i	$0.788768\pi$
$744$	9.92820	+	17.1962i	0.363986	+	0.630442i
$745$	5.59808	−	9.69615i	0.205098	−	0.355240i
$746$	−19.7321			−0.722442
$747$	4.90192	−	8.49038i	0.179352	−	0.310647i
$748$	4.90192	−	8.49038i	0.179232	−	0.310439i
$749$	−7.85641			−0.287067
$750$	28.6865	−	49.6865i	1.04748	−	1.81430i
$751$	−17.9019	−	31.0070i	−0.653250	−	1.13146i	−0.982329	−	0.187161i	$-0.940072\pi$
$751$	−17.9019	−	31.0070i	−0.653250	−	1.13146i	0.329079	−	0.944302i	$-0.393262\pi$
$752$	32.3205	+	55.9808i	1.17861	+	2.04141i
$753$	−4.39230			−0.160064
$754$	10.3923	−	15.5885i	0.378465	−	0.567698i
$755$	3.46410			0.126072
$756$	−2.00000	−	3.46410i	−0.0727393	−	0.125988i
$757$	8.00000	+	13.8564i	0.290765	+	0.503620i	0.973991	−	0.226587i	$-0.0727569\pi$
$757$	8.00000	+	13.8564i	0.290765	+	0.503620i	−0.683226	+	0.730207i	$0.739424\pi$
$758$	−23.0263	+	39.8827i	−0.836352	+	1.44860i
$759$	16.3923			0.595003
$760$	3.00000	−	5.19615i	0.108821	−	0.188484i
$761$	−20.6603	+	35.7846i	−0.748934	+	1.29719i	0.199401	+	0.979918i	$0.436100\pi$
$761$	−20.6603	+	35.7846i	−0.748934	+	1.29719i	−0.948334	+	0.317273i	$0.897233\pi$
$762$	87.0333			3.15288
$763$	4.19615	−	7.26795i	0.151911	−	0.263117i
$764$	−2.36603	−	4.09808i	−0.0855998	−	0.148263i
$765$	29.8923	+	51.7750i	1.08076	+	1.87193i
$766$	−20.1962			−0.729717
$767$	−14.5359	+	21.8038i	−0.524861	+	0.787291i
$768$	51.9090			1.87310
$769$	−7.58846	−	13.1436i	−0.273647	−	0.473970i	0.696146	−	0.717900i	$-0.254897\pi$
$769$	−7.58846	−	13.1436i	−0.273647	−	0.473970i	−0.969793	+	0.243930i	$0.921563\pi$
$770$	−1.90192	−	3.29423i	−0.0685406	−	0.118716i
$771$	−8.36603	+	14.4904i	−0.301295	+	0.521858i

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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	91.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 1.50000i) q^{2} +(-1.36603 - 2.36603i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205 q^{5} +(-2.36603 + 4.09808i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.73205 q^{8} +(-2.23205 + 3.86603i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 1.50000i) q^{2} +(-1.36603 - 2.36603i) q^{3} +(-0.500000 + 0.866025i) q^{4} +1.73205 q^{5} +(-2.36603 + 4.09808i) q^{6} +(-0.500000 + 0.866025i) q^{7} -1.73205 q^{8} +(-2.23205 + 3.86603i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(-0.633975 - 1.09808i) q^{11} +2.73205 q^{12} +(3.59808 + 0.232051i) q^{13} +1.73205 q^{14} +(-2.36603 - 4.09808i) q^{15} +(2.50000 + 4.33013i) q^{16} +(3.86603 - 6.69615i) q^{17} +7.73205 q^{18} +(-1.00000 + 1.73205i) q^{19} +(-0.866025 + 1.50000i) q^{20} +2.73205 q^{21} +(-1.09808 + 1.90192i) q^{22} +(-2.36603 - 4.09808i) q^{23} +(2.36603 + 4.09808i) q^{24} -2.00000 q^{25} +(-2.76795 - 5.59808i) q^{26} +4.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(1.50000 + 2.59808i) q^{29} +(-4.09808 + 7.09808i) q^{30} +4.19615 q^{31} +(2.59808 - 4.50000i) q^{32} +(-1.73205 + 3.00000i) q^{33} -13.3923 q^{34} +(-0.866025 + 1.50000i) q^{35} +(-2.23205 - 3.86603i) q^{36} +(3.50000 + 6.06218i) q^{37} +3.46410 q^{38} +(-4.36603 - 8.83013i) q^{39} -3.00000 q^{40} +(2.59808 + 4.50000i) q^{41} +(-2.36603 - 4.09808i) q^{42} +(0.0980762 - 0.169873i) q^{43} +1.26795 q^{44} +(-3.86603 + 6.69615i) q^{45} +(-4.09808 + 7.09808i) q^{46} +12.9282 q^{47} +(6.83013 - 11.8301i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(1.73205 + 3.00000i) q^{50} -21.1244 q^{51} +(-2.00000 + 3.00000i) q^{52} -9.92820 q^{53} +(-3.46410 - 6.00000i) q^{54} +(-1.09808 - 1.90192i) q^{55} +(0.866025 - 1.50000i) q^{56} +5.46410 q^{57} +(2.59808 - 4.50000i) q^{58} +(-3.63397 + 6.29423i) q^{59} +4.73205 q^{60} +(2.40192 - 4.16025i) q^{61} +(-3.63397 - 6.29423i) q^{62} +(-2.23205 - 3.86603i) q^{63} +1.00000 q^{64} +(6.23205 + 0.401924i) q^{65} +6.00000 q^{66} +(3.09808 + 5.36603i) q^{67} +(3.86603 + 6.69615i) q^{68} +(-6.46410 + 11.1962i) q^{69} +3.00000 q^{70} +(-3.00000 + 5.19615i) q^{71} +(3.86603 - 6.69615i) q^{72} -3.19615 q^{73} +(6.06218 - 10.5000i) q^{74} +(2.73205 + 4.73205i) q^{75} +(-1.00000 - 1.73205i) q^{76} +1.26795 q^{77} +(-9.46410 + 14.1962i) q^{78} +16.1962 q^{79} +(4.33013 + 7.50000i) q^{80} +(1.23205 + 2.13397i) q^{81} +(4.50000 - 7.79423i) q^{82} -2.19615 q^{83} +(-1.36603 + 2.36603i) q^{84} +(6.69615 - 11.5981i) q^{85} -0.339746 q^{86} +(4.09808 - 7.09808i) q^{87} +(1.09808 + 1.90192i) q^{88} +(-6.46410 - 11.1962i) q^{89} +13.3923 q^{90} +(-2.00000 + 3.00000i) q^{91} +4.73205 q^{92} +(-5.73205 - 9.92820i) q^{93} +(-11.1962 - 19.3923i) q^{94} +(-1.73205 + 3.00000i) q^{95} -14.1962 q^{96} +(-3.19615 + 5.53590i) q^{97} +(-0.866025 + 1.50000i) q^{98} +5.66025 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{4} - 6 q^{6} - 2 q^{7} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 2 * q^4 - 6 * q^6 - 2 * q^7 - 2 * q^9	\( 4 q - 2 q^{3} - 2 q^{4} - 6 q^{6} - 2 q^{7} - 2 q^{9} - 6 q^{10} - 6 q^{11} + 4 q^{12} + 4 q^{13} - 6 q^{15} + 10 q^{16} + 12 q^{17} + 24 q^{18} - 4 q^{19} + 4 q^{21} + 6 q^{22} - 6 q^{23} + 6 q^{24} - 8 q^{25} - 18 q^{26} + 16 q^{27} - 2 q^{28} + 6 q^{29} - 6 q^{30} - 4 q^{31} - 12 q^{34} - 2 q^{36} + 14 q^{37} - 14 q^{39} - 12 q^{40} - 6 q^{42} - 10 q^{43} + 12 q^{44} - 12 q^{45} - 6 q^{46} + 24 q^{47} + 10 q^{48} - 2 q^{49} - 36 q^{51} - 8 q^{52} - 12 q^{53} + 6 q^{55} + 8 q^{57} - 18 q^{59} + 12 q^{60} + 20 q^{61} - 18 q^{62} - 2 q^{63} + 4 q^{64} + 18 q^{65} + 24 q^{66} + 2 q^{67} + 12 q^{68} - 12 q^{69} + 12 q^{70} - 12 q^{71} + 12 q^{72} + 8 q^{73} + 4 q^{75} - 4 q^{76} + 12 q^{77} - 24 q^{78} + 44 q^{79} - 2 q^{81} + 18 q^{82} + 12 q^{83} - 2 q^{84} + 6 q^{85} - 36 q^{86} + 6 q^{87} - 6 q^{88} - 12 q^{89} + 12 q^{90} - 8 q^{91} + 12 q^{92} - 16 q^{93} - 24 q^{94} - 36 q^{96} + 8 q^{97} - 12 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 2 * q^4 - 6 * q^6 - 2 * q^7 - 2 * q^9 - 6 * q^10 - 6 * q^11 + 4 * q^12 + 4 * q^13 - 6 * q^15 + 10 * q^16 + 12 * q^17 + 24 * q^18 - 4 * q^19 + 4 * q^21 + 6 * q^22 - 6 * q^23 + 6 * q^24 - 8 * q^25 - 18 * q^26 + 16 * q^27 - 2 * q^28 + 6 * q^29 - 6 * q^30 - 4 * q^31 - 12 * q^34 - 2 * q^36 + 14 * q^37 - 14 * q^39 - 12 * q^40 - 6 * q^42 - 10 * q^43 + 12 * q^44 - 12 * q^45 - 6 * q^46 + 24 * q^47 + 10 * q^48 - 2 * q^49 - 36 * q^51 - 8 * q^52 - 12 * q^53 + 6 * q^55 + 8 * q^57 - 18 * q^59 + 12 * q^60 + 20 * q^61 - 18 * q^62 - 2 * q^63 + 4 * q^64 + 18 * q^65 + 24 * q^66 + 2 * q^67 + 12 * q^68 - 12 * q^69 + 12 * q^70 - 12 * q^71 + 12 * q^72 + 8 * q^73 + 4 * q^75 - 4 * q^76 + 12 * q^77 - 24 * q^78 + 44 * q^79 - 2 * q^81 + 18 * q^82 + 12 * q^83 - 2 * q^84 + 6 * q^85 - 36 * q^86 + 6 * q^87 - 6 * q^88 - 12 * q^89 + 12 * q^90 - 8 * q^91 + 12 * q^92 - 16 * q^93 - 24 * q^94 - 36 * q^96 + 8 * q^97 - 12 * q^99

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