LMFDB - Embedded newform 91.2.f.b.29.2

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			29.2
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	91.29
Dual form			91.2.f.b.22.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 1.50000i) q^{2} +(0.366025 + 0.633975i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.73205 q^{5} +(-0.633975 + 1.09808i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.73205 q^{8} +(1.23205 - 2.13397i) q^{9} +O(q^{10})$	\(q+(0.866025 + 1.50000i) q^{2} +(0.366025 + 0.633975i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.73205 q^{5} +(-0.633975 + 1.09808i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.73205 q^{8} +(1.23205 - 2.13397i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(-2.36603 - 4.09808i) q^{11} -0.732051 q^{12} +(-1.59808 + 3.23205i) q^{13} -1.73205 q^{14} +(-0.633975 - 1.09808i) q^{15} +(2.50000 + 4.33013i) q^{16} +(2.13397 - 3.69615i) q^{17} +4.26795 q^{18} +(-1.00000 + 1.73205i) q^{19} +(0.866025 - 1.50000i) q^{20} -0.732051 q^{21} +(4.09808 - 7.09808i) q^{22} +(-0.633975 - 1.09808i) q^{23} +(0.633975 + 1.09808i) q^{24} -2.00000 q^{25} +(-6.23205 + 0.401924i) q^{26} +4.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(1.50000 + 2.59808i) q^{29} +(1.09808 - 1.90192i) q^{30} -6.19615 q^{31} +(-2.59808 + 4.50000i) q^{32} +(1.73205 - 3.00000i) q^{33} +7.39230 q^{34} +(0.866025 - 1.50000i) q^{35} +(1.23205 + 2.13397i) q^{36} +(3.50000 + 6.06218i) q^{37} -3.46410 q^{38} +(-2.63397 + 0.169873i) q^{39} -3.00000 q^{40} +(-2.59808 - 4.50000i) q^{41} +(-0.633975 - 1.09808i) q^{42} +(-5.09808 + 8.83013i) q^{43} +4.73205 q^{44} +(-2.13397 + 3.69615i) q^{45} +(1.09808 - 1.90192i) q^{46} -0.928203 q^{47} +(-1.83013 + 3.16987i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-1.73205 - 3.00000i) q^{50} +3.12436 q^{51} +(-2.00000 - 3.00000i) q^{52} +3.92820 q^{53} +(3.46410 + 6.00000i) q^{54} +(4.09808 + 7.09808i) q^{55} +(-0.866025 + 1.50000i) q^{56} -1.46410 q^{57} +(-2.59808 + 4.50000i) q^{58} +(-5.36603 + 9.29423i) q^{59} +1.26795 q^{60} +(7.59808 - 13.1603i) q^{61} +(-5.36603 - 9.29423i) q^{62} +(1.23205 + 2.13397i) q^{63} +1.00000 q^{64} +(2.76795 - 5.59808i) q^{65} +6.00000 q^{66} +(-2.09808 - 3.63397i) q^{67} +(2.13397 + 3.69615i) q^{68} +(0.464102 - 0.803848i) q^{69} +3.00000 q^{70} +(-3.00000 + 5.19615i) q^{71} +(2.13397 - 3.69615i) q^{72} +7.19615 q^{73} +(-6.06218 + 10.5000i) q^{74} +(-0.732051 - 1.26795i) q^{75} +(-1.00000 - 1.73205i) q^{76} +4.73205 q^{77} +(-2.53590 - 3.80385i) q^{78} +5.80385 q^{79} +(-4.33013 - 7.50000i) q^{80} +(-2.23205 - 3.86603i) q^{81} +(4.50000 - 7.79423i) q^{82} +8.19615 q^{83} +(0.366025 - 0.633975i) q^{84} +(-3.69615 + 6.40192i) q^{85} -17.6603 q^{86} +(-1.09808 + 1.90192i) q^{87} +(-4.09808 - 7.09808i) q^{88} +(0.464102 + 0.803848i) q^{89} -7.39230 q^{90} +(-2.00000 - 3.00000i) q^{91} +1.26795 q^{92} +(-2.26795 - 3.92820i) q^{93} +(-0.803848 - 1.39230i) q^{94} +(1.73205 - 3.00000i) q^{95} -3.80385 q^{96} +(7.19615 - 12.4641i) q^{97} +(0.866025 - 1.50000i) q^{98} -11.6603 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	$0.0431180\pi$
$2$	0.866025	+	1.50000i	0.612372	+	1.06066i	−0.378467	+	0.925615i	$0.623549\pi$
$3$	0.366025	+	0.633975i	0.211325	+	0.366025i	0.952129	−	0.305695i	$-0.0988889\pi$
$3$	0.366025	+	0.633975i	0.211325	+	0.366025i	−0.740805	+	0.671721i	$0.765556\pi$
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−1.73205			−0.774597			−0.387298	−	0.921954i	$-0.626592\pi$
$5$	−1.73205			−0.774597			−0.387298	+	0.921954i	$0.626592\pi$
$6$	−0.633975	+	1.09808i	−0.258819	+	0.448288i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	1.73205			0.612372
$9$	1.23205	−	2.13397i	0.410684	−	0.711325i
$10$	−1.50000	−	2.59808i	−0.474342	−	0.821584i
$11$	−2.36603	−	4.09808i	−0.713384	−	1.23562i	−0.963580	−	0.267421i	$-0.913828\pi$
$11$	−2.36603	−	4.09808i	−0.713384	−	1.23562i	0.250196	−	0.968195i	$-0.419505\pi$
$12$	−0.732051			−0.211325
$13$	−1.59808	+	3.23205i	−0.443227	+	0.896410i
$13$	−1.59808	+	3.23205i	−0.443227	+	0.896410i
$14$	−1.73205			−0.462910
$15$	−0.633975	−	1.09808i	−0.163692	−	0.283522i
$16$	2.50000	+	4.33013i	0.625000	+	1.08253i
$17$	2.13397	−	3.69615i	0.517565	−	0.896449i	−0.482227	−	0.876046i	$-0.660172\pi$
$17$	2.13397	−	3.69615i	0.517565	−	0.896449i	0.999792	−	0.0204023i	$-0.00649471\pi$
$18$	4.26795			1.00597
$19$	−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
$21$	−0.732051			−0.159747
$22$	4.09808	−	7.09808i	0.873713	−	1.51331i
$23$	−0.633975	−	1.09808i	−0.132193	−	0.228965i	0.792329	−	0.610094i	$-0.208868\pi$
$23$	−0.633975	−	1.09808i	−0.132193	−	0.228965i	−0.924522	+	0.381130i	$0.875535\pi$
$24$	0.633975	+	1.09808i	0.129410	+	0.224144i
$25$	−2.00000			−0.400000
$26$	−6.23205	+	0.401924i	−1.22221	+	0.0788237i
$27$	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	$0.743482\pi$
$30$	1.09808	−	1.90192i	0.200480	−	0.347242i
$31$	−6.19615			−1.11286			−0.556431	−	0.830894i	$-0.687830\pi$
$31$	−6.19615			−1.11286			−0.556431	+	0.830894i	$0.687830\pi$
$32$	−2.59808	+	4.50000i	−0.459279	+	0.795495i
$33$	1.73205	−	3.00000i	0.301511	−	0.522233i
$34$	7.39230			1.26777
$35$	0.866025	−	1.50000i	0.146385	−	0.253546i
$36$	1.23205	+	2.13397i	0.205342	+	0.355662i
$37$	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
$39$	−2.63397	+	0.169873i	−0.421773	+	0.0272014i
$40$	−3.00000			−0.474342
$41$	−2.59808	−	4.50000i	−0.405751	−	0.702782i	0.588657	−	0.808383i	$-0.299657\pi$
$41$	−2.59808	−	4.50000i	−0.405751	−	0.702782i	−0.994409	+	0.105601i	$0.966323\pi$
$42$	−0.633975	−	1.09808i	−0.0978244	−	0.169437i
$43$	−5.09808	+	8.83013i	−0.777449	+	1.34658i	0.155958	+	0.987764i	$0.450153\pi$
$43$	−5.09808	+	8.83013i	−0.777449	+	1.34658i	−0.933408	+	0.358818i	$0.883180\pi$
$44$	4.73205			0.713384
$45$	−2.13397	+	3.69615i	−0.318114	+	0.550990i
$46$	1.09808	−	1.90192i	0.161903	−	0.280423i
$47$	−0.928203			−0.135392			−0.0676962	−	0.997706i	$-0.521565\pi$
$47$	−0.928203			−0.135392			−0.0676962	+	0.997706i	$0.521565\pi$
$48$	−1.83013	+	3.16987i	−0.264156	+	0.457532i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	−1.73205	−	3.00000i	−0.244949	−	0.424264i
$51$	3.12436			0.437497
$52$	−2.00000	−	3.00000i	−0.277350	−	0.416025i
$53$	3.92820			0.539580			0.269790	−	0.962919i	$-0.413046\pi$
$53$	3.92820			0.539580			0.269790	+	0.962919i	$0.413046\pi$
$54$	3.46410	+	6.00000i	0.471405	+	0.816497i
$55$	4.09808	+	7.09808i	0.552584	+	0.957104i
$56$	−0.866025	+	1.50000i	−0.115728	+	0.200446i
$57$	−1.46410			−0.193925
$58$	−2.59808	+	4.50000i	−0.341144	+	0.590879i
$59$	−5.36603	+	9.29423i	−0.698597	+	1.21001i	0.270356	+	0.962760i	$0.412859\pi$
$59$	−5.36603	+	9.29423i	−0.698597	+	1.21001i	−0.968953	+	0.247245i	$0.920475\pi$
$60$	1.26795			0.163692
$61$	7.59808	−	13.1603i	0.972834	−	1.68500i	0.285929	−	0.958251i	$-0.407698\pi$
$61$	7.59808	−	13.1603i	0.972834	−	1.68500i	0.686905	−	0.726747i	$-0.258969\pi$
$62$	−5.36603	−	9.29423i	−0.681486	−	1.18037i
$63$	1.23205	+	2.13397i	0.155224	+	0.268856i
$64$	1.00000			0.125000
$65$	2.76795	−	5.59808i	0.343322	−	0.694356i
$66$	6.00000			0.738549
$67$	−2.09808	−	3.63397i	−0.256321	−	0.443961i	0.708933	−	0.705276i	$-0.249177\pi$
$67$	−2.09808	−	3.63397i	−0.256321	−	0.443961i	−0.965253	+	0.261316i	$0.915844\pi$
$68$	2.13397	+	3.69615i	0.258782	+	0.448224i
$69$	0.464102	−	0.803848i	0.0558713	−	0.0967719i
$70$	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	$0.282538\pi$
$72$	2.13397	−	3.69615i	0.251491	−	0.435596i
$73$	7.19615			0.842246			0.421123	−	0.907004i	$-0.361636\pi$
$73$	7.19615			0.842246			0.421123	+	0.907004i	$0.361636\pi$
$74$	−6.06218	+	10.5000i	−0.704714	+	1.22060i
$75$	−0.732051	−	1.26795i	−0.0845299	−	0.146410i
$76$	−1.00000	−	1.73205i	−0.114708	−	0.198680i
$77$	4.73205			0.539267
$78$	−2.53590	−	3.80385i	−0.287134	−	0.430701i
$79$	5.80385			0.652984			0.326492	−	0.945200i	$-0.394133\pi$
$79$	5.80385			0.652984			0.326492	+	0.945200i	$0.394133\pi$
$80$	−4.33013	−	7.50000i	−0.484123	−	0.838525i
$81$	−2.23205	−	3.86603i	−0.248006	−	0.429558i
$82$	4.50000	−	7.79423i	0.496942	−	0.860729i
$83$	8.19615			0.899645			0.449822	−	0.893118i	$-0.351487\pi$
$83$	8.19615			0.899645			0.449822	+	0.893118i	$0.351487\pi$
$84$	0.366025	−	0.633975i	0.0399366	−	0.0691723i
$85$	−3.69615	+	6.40192i	−0.400904	+	0.694386i
$86$	−17.6603			−1.90435
$87$	−1.09808	+	1.90192i	−0.117726	+	0.203908i
$88$	−4.09808	−	7.09808i	−0.436856	−	0.756657i
$89$	0.464102	+	0.803848i	0.0491947	+	0.0852077i	0.889574	−	0.456791i	$-0.151001\pi$
$89$	0.464102	+	0.803848i	0.0491947	+	0.0852077i	−0.840379	+	0.541998i	$0.817668\pi$
$90$	−7.39230			−0.779217
$91$	−2.00000	−	3.00000i	−0.209657	−	0.314485i
$92$	1.26795			0.132193
$93$	−2.26795	−	3.92820i	−0.235175	−	0.407336i
$94$	−0.803848	−	1.39230i	−0.0829105	−	0.143605i
$95$	1.73205	−	3.00000i	0.177705	−	0.307794i
$96$	−3.80385			−0.388229
$97$	7.19615	−	12.4641i	0.730659	−	1.26554i	−0.225944	−	0.974140i	$-0.572546\pi$
$97$	7.19615	−	12.4641i	0.730659	−	1.26554i	0.956602	−	0.291397i	$-0.0941202\pi$
$98$	0.866025	−	1.50000i	0.0874818	−	0.151523i
$99$	−11.6603			−1.17190
$100$	1.00000	−	1.73205i	0.100000	−	0.173205i
$101$	2.13397	+	3.69615i	0.212338	+	0.367781i	0.952446	−	0.304708i	$-0.0985588\pi$
$101$	2.13397	+	3.69615i	0.212338	+	0.367781i	−0.740108	+	0.672489i	$0.765225\pi$
$102$	2.70577	+	4.68653i	0.267911	+	0.464036i
$103$	6.39230			0.629853			0.314926	−	0.949116i	$-0.398020\pi$
$103$	6.39230			0.629853			0.314926	+	0.949116i	$0.398020\pi$
$104$	−2.76795	+	5.59808i	−0.271420	+	0.548937i
$105$	1.26795			0.123739
$106$	3.40192	+	5.89230i	0.330424	+	0.572311i
$107$	−9.92820	−	17.1962i	−0.959796	−	1.66241i	−0.722991	−	0.690858i	$-0.757233\pi$
$107$	−9.92820	−	17.1962i	−0.959796	−	1.66241i	−0.236805	−	0.971557i	$-0.576100\pi$
$108$	−2.00000	+	3.46410i	−0.192450	+	0.333333i
$109$	12.3923			1.18697			0.593484	−	0.804846i	$-0.297752\pi$
$109$	12.3923			1.18697			0.593484	+	0.804846i	$0.297752\pi$
$110$	−7.09808	+	12.2942i	−0.676775	+	1.17221i
$111$	−2.56218	+	4.43782i	−0.243191	+	0.421219i
$112$	−5.00000			−0.472456
$113$	3.69615	−	6.40192i	0.347705	−	0.602242i	−0.638137	−	0.769923i	$-0.720294\pi$
$113$	3.69615	−	6.40192i	0.347705	−	0.602242i	0.985841	+	0.167681i	$0.0536278\pi$
$114$	−1.26795	−	2.19615i	−0.118754	−	0.205689i
$115$	1.09808	+	1.90192i	0.102396	+	0.177355i
$116$	−3.00000			−0.278543
$117$	4.92820	+	7.39230i	0.455613	+	0.683419i
$118$	−18.5885			−1.71121
$119$	2.13397	+	3.69615i	0.195621	+	0.338826i
$120$	−1.09808	−	1.90192i	−0.100240	−	0.173621i
$121$	−5.69615	+	9.86603i	−0.517832	+	0.896911i
$122$	26.3205			2.38295
$123$	1.90192	−	3.29423i	0.171491	−	0.297031i
$124$	3.09808	−	5.36603i	0.278215	−	0.481883i
$125$	12.1244			1.08444
$126$	−2.13397	+	3.69615i	−0.190110	+	0.329279i
$127$	1.19615	+	2.07180i	0.106141	+	0.183842i	0.914204	−	0.405254i	$-0.132817\pi$
$127$	1.19615	+	2.07180i	0.106141	+	0.183842i	−0.808063	+	0.589097i	$0.799484\pi$
$128$	6.06218	+	10.5000i	0.535826	+	0.928078i
$129$	−7.46410			−0.657178
$130$	10.7942	−	0.696152i	0.946716	−	0.0610566i
$131$	3.46410			0.302660			0.151330	−	0.988483i	$-0.451644\pi$
$131$	3.46410			0.302660			0.151330	+	0.988483i	$0.451644\pi$
$132$	1.73205	+	3.00000i	0.150756	+	0.261116i
$133$	−1.00000	−	1.73205i	−0.0867110	−	0.150188i
$134$	3.63397	−	6.29423i	0.313928	−	0.543739i
$135$	−6.92820			−0.596285
$136$	3.69615	−	6.40192i	0.316942	−	0.548960i
$137$	−10.9641	+	18.9904i	−0.936726	+	1.62246i	−0.165200	+	0.986260i	$0.552827\pi$
$137$	−10.9641	+	18.9904i	−0.936726	+	1.62246i	−0.771526	+	0.636198i	$0.780506\pi$
$138$	1.60770			0.136856
$139$	−10.2942	+	17.8301i	−0.873145	+	1.51233i	−0.0144194	+	0.999896i	$0.504590\pi$
$139$	−10.2942	+	17.8301i	−0.873145	+	1.51233i	−0.858726	+	0.512436i	$0.828743\pi$
$140$	0.866025	+	1.50000i	0.0731925	+	0.126773i
$141$	−0.339746	−	0.588457i	−0.0286118	−	0.0495570i
$142$	−10.3923			−0.872103
$143$	17.0263	−	1.09808i	1.42381	−	0.0918257i
$144$	12.3205			1.02671
$145$	−2.59808	−	4.50000i	−0.215758	−	0.373705i
$146$	6.23205	+	10.7942i	0.515768	+	0.893337i
$147$	0.366025	−	0.633975i	0.0301893	−	0.0522893i
$148$	−7.00000			−0.575396
$149$	−0.232051	+	0.401924i	−0.0190103	+	0.0329269i	−0.875374	−	0.483446i	$-0.839385\pi$
$149$	−0.232051	+	0.401924i	−0.0190103	+	0.0329269i	0.856364	+	0.516373i	$0.172718\pi$
$150$	1.26795	−	2.19615i	0.103528	−	0.179315i
$151$	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
$153$	−5.25833	−	9.10770i	−0.425111	−	0.736314i
$154$	4.09808	+	7.09808i	0.330232	+	0.571979i
$155$	10.7321			0.862019
$156$	1.16987	−	2.36603i	0.0936648	−	0.189434i
$157$	−9.19615			−0.733933			−0.366966	−	0.930234i	$-0.619604\pi$
$157$	−9.19615			−0.733933			−0.366966	+	0.930234i	$0.619604\pi$
$158$	5.02628	+	8.70577i	0.399869	+	0.692594i
$159$	1.43782	+	2.49038i	0.114027	+	0.197500i
$160$	4.50000	−	7.79423i	0.355756	−	0.616188i
$161$	1.26795			0.0999284
$162$	3.86603	−	6.69615i	0.303744	−	0.526099i
$163$	−2.90192	+	5.02628i	−0.227296	+	0.393689i	−0.957006	−	0.290069i	$-0.906322\pi$
$163$	−2.90192	+	5.02628i	−0.227296	+	0.393689i	0.729710	+	0.683757i	$0.239655\pi$
$164$	5.19615			0.405751
$165$	−3.00000	+	5.19615i	−0.233550	+	0.404520i
$166$	7.09808	+	12.2942i	0.550918	+	0.954217i
$167$	−12.2942	−	21.2942i	−0.951356	−	1.64780i	−0.742495	−	0.669852i	$-0.766358\pi$
$167$	−12.2942	−	21.2942i	−0.951356	−	1.64780i	−0.208861	−	0.977945i	$-0.566976\pi$
$168$	−1.26795			−0.0978244
$169$	−7.89230	−	10.3301i	−0.607100	−	0.794625i
$170$	−12.8038			−0.982010
$171$	2.46410	+	4.26795i	0.188435	+	0.326378i
$172$	−5.09808	−	8.83013i	−0.388725	−	0.673291i
$173$	−7.73205	+	13.3923i	−0.587857	+	1.01820i	0.406656	+	0.913581i	$0.366695\pi$
$173$	−7.73205	+	13.3923i	−0.587857	+	1.01820i	−0.994513	+	0.104617i	$0.966638\pi$
$174$	−3.80385			−0.288369
$175$	1.00000	−	1.73205i	0.0755929	−	0.130931i
$176$	11.8301	−	20.4904i	0.891729	−	1.54452i
$177$	−7.85641			−0.590524
$178$	−0.803848	+	1.39230i	−0.0602509	+	0.104358i
$179$	−3.46410	−	6.00000i	−0.258919	−	0.448461i	0.707034	−	0.707180i	$-0.250033\pi$
$179$	−3.46410	−	6.00000i	−0.258919	−	0.448461i	−0.965953	+	0.258719i	$0.916700\pi$
$180$	−2.13397	−	3.69615i	−0.159057	−	0.275495i
$181$	−25.5885			−1.90198			−0.950988	−	0.309229i	$-0.899929\pi$
$181$	−25.5885			−1.90198			−0.950988	+	0.309229i	$0.899929\pi$
$182$	2.76795	−	5.59808i	0.205174	−	0.414957i
$183$	11.1244			0.822336
$184$	−1.09808	−	1.90192i	−0.0809513	−	0.140212i
$185$	−6.06218	−	10.5000i	−0.445700	−	0.771975i
$186$	3.92820	−	6.80385i	0.288030	−	0.498882i
$187$	−20.1962			−1.47689
$188$	0.464102	−	0.803848i	0.0338481	−	0.0586266i
$189$	−2.00000	+	3.46410i	−0.145479	+	0.251976i
$190$	6.00000			0.435286
$191$	−0.633975	+	1.09808i	−0.0458728	+	0.0794540i	−0.888050	−	0.459747i	$-0.847940\pi$
$191$	−0.633975	+	1.09808i	−0.0458728	+	0.0794540i	0.842177	+	0.539201i	$0.181274\pi$
$192$	0.366025	+	0.633975i	0.0264156	+	0.0457532i
$193$	−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	$0.890928\pi$
$194$	24.9282			1.78974
$195$	4.56218	−	0.294229i	0.326704	−	0.0210702i
$196$	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	$0.973933\pi$
$198$	−10.0981	−	17.4904i	−0.717639	−	1.24299i
$199$	−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
$201$	1.53590	−	2.66025i	0.108334	−	0.187640i
$202$	−3.69615	+	6.40192i	−0.260060	+	0.450438i
$203$	−3.00000			−0.210559
$204$	−1.56218	+	2.70577i	−0.109374	+	0.189442i
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$	5.53590	+	9.58846i	0.385704	+	0.668059i
$207$	−3.12436			−0.217158
$208$	−17.9904	+	1.16025i	−1.24741	+	0.0804491i
$209$	9.46410			0.654646
$210$	1.09808	+	1.90192i	0.0757745	+	0.131245i
$211$	6.09808	+	10.5622i	0.419809	+	0.727130i	0.995920	−	0.0902411i	$-0.0287638\pi$
$211$	6.09808	+	10.5622i	0.419809	+	0.727130i	−0.576111	+	0.817371i	$0.695430\pi$
$212$	−1.96410	+	3.40192i	−0.134895	+	0.233645i
$213$	−4.39230			−0.300956
$214$	17.1962	−	29.7846i	1.17550	−	2.03603i
$215$	8.83013	−	15.2942i	0.602210	−	1.04306i
$216$	6.92820			0.471405
$217$	3.09808	−	5.36603i	0.210311	−	0.364270i
$218$	10.7321	+	18.5885i	0.726866	+	1.25897i
$219$	2.63397	+	4.56218i	0.177988	+	0.308283i
$220$	−8.19615			−0.552584
$221$	8.53590	+	12.8038i	0.574187	+	0.861280i
$222$	−8.87564			−0.595694
$223$	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
$225$	−2.46410	+	4.26795i	−0.164273	+	0.284530i
$226$	12.8038			0.851699
$227$	5.83013	−	10.0981i	0.386959	−	0.670233i	−0.605080	−	0.796165i	$-0.706859\pi$
$227$	5.83013	−	10.0981i	0.386959	−	0.670233i	0.992039	+	0.125932i	$0.0401921\pi$
$228$	0.732051	−	1.26795i	0.0484812	−	0.0839720i
$229$	6.39230			0.422415			0.211208	−	0.977441i	$-0.432260\pi$
$229$	6.39230			0.422415			0.211208	+	0.977441i	$0.432260\pi$
$230$	−1.90192	+	3.29423i	−0.125409	+	0.217215i
$231$	1.73205	+	3.00000i	0.113961	+	0.197386i
$232$	2.59808	+	4.50000i	0.170572	+	0.295439i
$233$	25.8564			1.69391			0.846955	−	0.531665i	$-0.178433\pi$
$233$	25.8564			1.69391			0.846955	+	0.531665i	$0.178433\pi$
$234$	−6.82051	+	13.7942i	−0.445871	+	0.901757i
$235$	1.60770			0.104874
$236$	−5.36603	−	9.29423i	−0.349299	−	0.605003i
$237$	2.12436	+	3.67949i	0.137992	+	0.239009i
$238$	−3.69615	+	6.40192i	−0.239586	+	0.414975i
$239$	−26.1962			−1.69449			−0.847244	−	0.531204i	$-0.821740\pi$
$239$	−26.1962			−1.69449			−0.847244	+	0.531204i	$0.821740\pi$
$240$	3.16987	−	5.49038i	0.204614	−	0.354403i
$241$	5.40192	−	9.35641i	0.347969	−	0.602699i	−0.637920	−	0.770103i	$-0.720205\pi$
$241$	5.40192	−	9.35641i	0.347969	−	0.602699i	0.985888	+	0.167404i	$0.0535383\pi$
$242$	−19.7321			−1.26842
$243$	7.63397	−	13.2224i	0.489720	−	0.848219i
$244$	7.59808	+	13.1603i	0.486417	+	0.842499i
$245$	0.866025	+	1.50000i	0.0553283	+	0.0958315i
$246$	6.58846			0.420065
$247$	−4.00000	−	6.00000i	−0.254514	−	0.381771i
$248$	−10.7321			−0.681486
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$	10.5000	+	18.1865i	0.664078	+	1.15022i
$251$	11.1962	−	19.3923i	0.706695	−	1.22403i	−0.259382	−	0.965775i	$-0.583519\pi$
$251$	11.1962	−	19.3923i	0.706695	−	1.22403i	0.966076	−	0.258256i	$-0.0831480\pi$
$252$	−2.46410			−0.155224
$253$	−3.00000	+	5.19615i	−0.188608	+	0.326679i
$254$	−2.07180	+	3.58846i	−0.129996	+	0.225160i
$255$	−5.41154			−0.338884
$256$	−9.50000	+	16.4545i	−0.593750	+	1.02841i
$257$	9.06218	+	15.6962i	0.565283	+	0.979099i	0.997023	+	0.0771011i	$0.0245664\pi$
$257$	9.06218	+	15.6962i	0.565283	+	0.979099i	−0.431740	+	0.901998i	$0.642100\pi$
$258$	−6.46410	−	11.1962i	−0.402437	−	0.697042i
$259$	−7.00000			−0.434959
$260$	3.46410	+	5.19615i	0.214834	+	0.322252i
$261$	7.39230			0.457572
$262$	3.00000	+	5.19615i	0.185341	+	0.321019i
$263$	−2.36603	−	4.09808i	−0.145895	−	0.252698i	0.783811	−	0.620999i	$-0.213273\pi$
$263$	−2.36603	−	4.09808i	−0.145895	−	0.252698i	−0.929707	+	0.368301i	$0.879940\pi$
$264$	3.00000	−	5.19615i	0.184637	−	0.319801i
$265$	−6.80385			−0.417957
$266$	1.73205	−	3.00000i	0.106199	−	0.183942i
$267$	−0.339746	+	0.588457i	−0.0207921	+	0.0360130i
$268$	4.19615			0.256321
$269$	−9.46410	+	16.3923i	−0.577036	+	0.999456i	0.418781	+	0.908087i	$0.362458\pi$
$269$	−9.46410	+	16.3923i	−0.577036	+	0.999456i	−0.995817	+	0.0913690i	$0.970876\pi$
$270$	−6.00000	−	10.3923i	−0.365148	−	0.632456i
$271$	−8.09808	−	14.0263i	−0.491923	−	0.852036i	0.508034	−	0.861337i	$-0.330373\pi$
$271$	−8.09808	−	14.0263i	−0.491923	−	0.852036i	−0.999957	+	0.00930143i	$0.997039\pi$
$272$	21.3397			1.29391
$273$	1.16987	−	2.36603i	0.0708039	−	0.143198i
$274$	−37.9808			−2.29450
$275$	4.73205	+	8.19615i	0.285353	+	0.494247i
$276$	0.464102	+	0.803848i	0.0279356	+	0.0483859i
$277$	−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	$0.996047\pi$
$278$	−35.6603			−2.13876
$279$	−7.63397	+	13.2224i	−0.457034	+	0.791606i
$280$	1.50000	−	2.59808i	0.0896421	−	0.155265i
$281$	−7.39230			−0.440988			−0.220494	−	0.975388i	$-0.570767\pi$
$281$	−7.39230			−0.440988			−0.220494	+	0.975388i	$0.570767\pi$
$282$	0.588457	−	1.01924i	0.0350421	−	0.0606947i
$283$	0.0980762	+	0.169873i	0.00583003	+	0.0100979i	0.868926	−	0.494943i	$-0.164811\pi$
$283$	0.0980762	+	0.169873i	0.00583003	+	0.0100979i	−0.863096	+	0.505040i	$0.831478\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$	2.53590			0.150214
$286$	16.3923	+	24.5885i	0.969297	+	1.45395i
$287$	5.19615			0.306719
$288$	6.40192	+	11.0885i	0.377237	+	0.653394i
$289$	−0.607695	−	1.05256i	−0.0357468	−	0.0619152i
$290$	4.50000	−	7.79423i	0.264249	−	0.457693i
$291$	10.5359			0.617625
$292$	−3.59808	+	6.23205i	−0.210561	+	0.364703i
$293$	5.59808	−	9.69615i	0.327043	−	0.566455i	−0.654881	−	0.755732i	$-0.727281\pi$
$293$	5.59808	−	9.69615i	0.327043	−	0.566455i	0.981924	+	0.189277i	$0.0606144\pi$
$294$	1.26795			0.0739483
$295$	9.29423	−	16.0981i	0.541131	−	0.937266i
$296$	6.06218	+	10.5000i	0.352357	+	0.610300i
$297$	−9.46410	−	16.3923i	−0.549163	−	0.951178i
$298$	−0.803848			−0.0465656
$299$	4.56218	−	0.294229i	0.263838	−	0.0170157i
$300$	1.46410			0.0845299
$301$	−5.09808	−	8.83013i	−0.293848	−	0.508960i
$302$	1.73205	+	3.00000i	0.0996683	+	0.172631i
$303$	−1.56218	+	2.70577i	−0.0897448	+	0.155443i
$304$	−10.0000			−0.573539
$305$	−13.1603	+	22.7942i	−0.753554	+	1.30519i
$306$	9.10770	−	15.7750i	0.520652	−	0.901796i
$307$	26.5885			1.51748			0.758742	−	0.651392i	$-0.225814\pi$
$307$	26.5885			1.51748			0.758742	+	0.651392i	$0.225814\pi$
$308$	−2.36603	+	4.09808i	−0.134817	+	0.233510i
$309$	2.33975	+	4.05256i	0.133103	+	0.230542i
$310$	9.29423	+	16.0981i	0.527877	+	0.914309i
$311$	4.73205			0.268330			0.134165	−	0.990959i	$-0.457165\pi$
$311$	4.73205			0.268330			0.134165	+	0.990959i	$0.457165\pi$
$312$	−4.56218	+	0.294229i	−0.258282	+	0.0166574i
$313$	−12.7846			−0.722629			−0.361314	−	0.932444i	$-0.617672\pi$
$313$	−12.7846			−0.722629			−0.361314	+	0.932444i	$0.617672\pi$
$314$	−7.96410	−	13.7942i	−0.449440	−	0.778453i
$315$	−2.13397	−	3.69615i	−0.120236	−	0.208255i
$316$	−2.90192	+	5.02628i	−0.163246	+	0.282750i
$317$	0.464102			0.0260665			0.0130333	−	0.999915i	$-0.495851\pi$
$317$	0.464102			0.0260665			0.0130333	+	0.999915i	$0.495851\pi$
$318$	−2.49038	+	4.31347i	−0.139654	+	0.241887i
$319$	7.09808	−	12.2942i	0.397416	−	0.688345i
$320$	−1.73205			−0.0968246
$321$	7.26795	−	12.5885i	0.405657	−	0.702619i
$322$	1.09808	+	1.90192i	0.0611934	+	0.105990i
$323$	4.26795	+	7.39230i	0.237475	+	0.411319i
$324$	4.46410			0.248006
$325$	3.19615	−	6.46410i	0.177291	−	0.358564i
$326$	−10.0526			−0.556760
$327$	4.53590	+	7.85641i	0.250836	+	0.434460i
$328$	−4.50000	−	7.79423i	−0.248471	−	0.430364i
$329$	0.464102	−	0.803848i	0.0255868	−	0.0443176i
$330$	−10.3923			−0.572078
$331$	13.4904	−	23.3660i	0.741498	−	1.28431i	−0.210315	−	0.977634i	$-0.567449\pi$
$331$	13.4904	−	23.3660i	0.741498	−	1.28431i	0.951813	−	0.306679i	$-0.0992179\pi$
$332$	−4.09808	+	7.09808i	−0.224911	+	0.389558i
$333$	17.2487			0.945224
$334$	21.2942	−	36.8827i	1.16517	−	2.01813i
$335$	3.63397	+	6.29423i	0.198545	+	0.343890i
$336$	−1.83013	−	3.16987i	−0.0998416	−	0.172931i
$337$	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
$339$	5.41154			0.293915
$340$	−3.69615	−	6.40192i	−0.200452	−	0.347193i
$341$	14.6603	+	25.3923i	0.793897	+	1.37507i
$342$	−4.26795	+	7.39230i	−0.230784	+	0.399730i
$343$	1.00000			0.0539949
$344$	−8.83013	+	15.2942i	−0.476089	+	0.824610i
$345$	−0.803848	+	1.39230i	−0.0432777	+	0.0749592i
$346$	−26.7846			−1.43995
$347$	−5.36603	+	9.29423i	−0.288063	+	0.498940i	−0.973347	−	0.229336i	$-0.926345\pi$
$347$	−5.36603	+	9.29423i	−0.288063	+	0.498940i	0.685284	+	0.728276i	$0.259678\pi$
$348$	−1.09808	−	1.90192i	−0.0588631	−	0.101954i
$349$	−8.39230	−	14.5359i	−0.449230	−	0.778089i	0.549106	−	0.835753i	$-0.314968\pi$
$349$	−8.39230	−	14.5359i	−0.449230	−	0.778089i	−0.998336	+	0.0576637i	$0.981635\pi$
$350$	3.46410			0.185164
$351$	−6.39230	+	12.9282i	−0.341196	+	0.690056i
$352$	24.5885			1.31057
$353$	−1.66987	−	2.89230i	−0.0888784	−	0.153942i	0.818159	−	0.574992i	$-0.194995\pi$
$353$	−1.66987	−	2.89230i	−0.0888784	−	0.153942i	−0.907037	+	0.421050i	$0.861662\pi$
$354$	−6.80385	−	11.7846i	−0.361620	−	0.626345i
$355$	5.19615	−	9.00000i	0.275783	−	0.477670i
$356$	−0.928203			−0.0491947
$357$	−1.56218	+	2.70577i	−0.0826792	+	0.143205i
$358$	6.00000	−	10.3923i	0.317110	−	0.549250i
$359$	5.07180			0.267679			0.133840	−	0.991003i	$-0.457269\pi$
$359$	5.07180			0.267679			0.133840	+	0.991003i	$0.457269\pi$
$360$	−3.69615	+	6.40192i	−0.194804	+	0.337411i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−22.1603	−	38.3827i	−1.16472	−	2.01735i
$363$	−8.33975			−0.437723
$364$	3.59808	−	0.232051i	0.188590	−	0.0121628i
$365$	−12.4641			−0.652401
$366$	9.63397	+	16.6865i	0.503576	+	0.872219i
$367$	3.09808	+	5.36603i	0.161718	+	0.280104i	0.935485	−	0.353366i	$-0.114963\pi$
$367$	3.09808	+	5.36603i	0.161718	+	0.280104i	−0.773767	+	0.633471i	$0.781630\pi$
$368$	3.16987	−	5.49038i	0.165241	−	0.286206i
$369$	−12.8038			−0.666542
$370$	10.5000	−	18.1865i	0.545869	−	0.945473i
$371$	−1.96410	+	3.40192i	−0.101971	+	0.176619i
$372$	4.53590			0.235175
$373$	−4.69615	+	8.13397i	−0.243158	+	0.421161i	−0.961612	−	0.274413i	$-0.911517\pi$
$373$	−4.69615	+	8.13397i	−0.243158	+	0.421161i	0.718454	+	0.695574i	$0.244850\pi$
$374$	−17.4904	−	30.2942i	−0.904406	−	1.56648i
$375$	4.43782	+	7.68653i	0.229168	+	0.396931i
$376$	−1.60770			−0.0829105
$377$	−10.7942	+	0.696152i	−0.555931	+	0.0358537i
$378$	−6.92820			−0.356348
$379$	2.29423	+	3.97372i	0.117847	+	0.204116i	0.918914	−	0.394458i	$-0.129068\pi$
$379$	2.29423	+	3.97372i	0.117847	+	0.204116i	−0.801067	+	0.598574i	$0.795734\pi$
$380$	1.73205	+	3.00000i	0.0888523	+	0.153897i
$381$	−0.875644	+	1.51666i	−0.0448606	+	0.0777009i
$382$	−2.19615			−0.112365
$383$	−2.83013	+	4.90192i	−0.144613	+	0.250477i	−0.929228	−	0.369506i	$-0.879527\pi$
$383$	−2.83013	+	4.90192i	−0.144613	+	0.250477i	0.784616	+	0.619982i	$0.212860\pi$
$384$	−4.43782	+	7.68653i	−0.226467	+	0.392252i
$385$	−8.19615			−0.417715
$386$	4.33013	−	7.50000i	0.220398	−	0.381740i
$387$	12.5622	+	21.7583i	0.638571	+	1.10604i
$388$	7.19615	+	12.4641i	0.365329	+	0.632769i
$389$	−30.4641			−1.54459			−0.772296	−	0.635263i	$-0.780892\pi$
$389$	−30.4641			−1.54459			−0.772296	+	0.635263i	$0.780892\pi$
$390$	4.39230	+	6.58846i	0.222413	+	0.333620i
$391$	−5.41154			−0.273673
$392$	−0.866025	−	1.50000i	−0.0437409	−	0.0757614i
$393$	1.26795	+	2.19615i	0.0639596	+	0.110781i
$394$	10.3923	−	18.0000i	0.523557	−	0.906827i
$395$	−10.0526			−0.505799
$396$	5.83013	−	10.0981i	0.292975	−	0.507447i
$397$	−11.3923	+	19.7321i	−0.571763	+	0.990323i	0.424622	+	0.905371i	$0.360407\pi$
$397$	−11.3923	+	19.7321i	−0.571763	+	0.990323i	−0.996385	+	0.0849523i	$0.972926\pi$
$398$	−3.46410			−0.173640
$399$	0.732051	−	1.26795i	0.0366484	−	0.0634769i
$400$	−5.00000	−	8.66025i	−0.250000	−	0.433013i
$401$	−8.42820	−	14.5981i	−0.420884	−	0.728993i	0.575142	−	0.818054i	$-0.304947\pi$
$401$	−8.42820	−	14.5981i	−0.420884	−	0.728993i	−0.996026	+	0.0890606i	$0.971614\pi$
$402$	5.32051			0.265363
$403$	9.90192	−	20.0263i	0.493250	−	0.997580i
$404$	−4.26795			−0.212338
$405$	3.86603	+	6.69615i	0.192104	+	0.332734i
$406$	−2.59808	−	4.50000i	−0.128940	−	0.223331i
$407$	16.5622	−	28.6865i	0.820957	−	1.42194i
$408$	5.41154			0.267911
$409$	13.5981	−	23.5526i	0.672382	−	1.16460i	−0.304845	−	0.952402i	$-0.598605\pi$
$409$	13.5981	−	23.5526i	0.672382	−	1.16460i	0.977227	−	0.212197i	$-0.0680619\pi$
$410$	−7.79423	+	13.5000i	−0.384930	+	0.666717i
$411$	−16.0526			−0.791814
$412$	−3.19615	+	5.53590i	−0.157463	+	0.272734i
$413$	−5.36603	−	9.29423i	−0.264045	−	0.457339i
$414$	−2.70577	−	4.68653i	−0.132981	−	0.230331i
$415$	−14.1962			−0.696862
$416$	−10.3923	−	15.5885i	−0.509525	−	0.764287i
$417$	−15.0718			−0.738069
$418$	8.19615	+	14.1962i	0.400887	+	0.694357i
$419$	10.9019	+	18.8827i	0.532594	+	0.922480i	0.999276	+	0.0380543i	$0.0121160\pi$
$419$	10.9019	+	18.8827i	0.532594	+	0.922480i	−0.466682	+	0.884425i	$0.654551\pi$
$420$	−0.633975	+	1.09808i	−0.0309348	+	0.0535806i
$421$	30.1769			1.47073			0.735366	−	0.677670i	$-0.237010\pi$
$421$	30.1769			1.47073			0.735366	+	0.677670i	$0.237010\pi$
$422$	−10.5622	+	18.2942i	−0.514159	+	0.890549i
$423$	−1.14359	+	1.98076i	−0.0556034	+	0.0963079i
$424$	6.80385			0.330424
$425$	−4.26795	+	7.39230i	−0.207026	+	0.358579i
$426$	−3.80385	−	6.58846i	−0.184297	−	0.319212i
$427$	7.59808	+	13.1603i	0.367697	+	0.636869i
$428$	19.8564			0.959796
$429$	6.92820	+	10.3923i	0.334497	+	0.501745i
$430$	30.5885			1.47511
$431$	−17.6603	−	30.5885i	−0.850665	−	1.47339i	−0.880610	−	0.473843i	$-0.842867\pi$
$431$	−17.6603	−	30.5885i	−0.850665	−	1.47339i	0.0299451	−	0.999552i	$-0.490467\pi$
$432$	10.0000	+	17.3205i	0.481125	+	0.833333i
$433$	−8.79423	+	15.2321i	−0.422624	+	0.732006i	−0.996195	−	0.0871498i	$-0.972224\pi$
$433$	−8.79423	+	15.2321i	−0.422624	+	0.732006i	0.573572	+	0.819155i	$0.305557\pi$
$434$	10.7321			0.515155
$435$	1.90192	−	3.29423i	0.0911903	−	0.157946i
$436$	−6.19615	+	10.7321i	−0.296742	+	0.513972i
$437$	2.53590			0.121308
$438$	−4.56218	+	7.90192i	−0.217989	+	0.377569i
$439$	8.29423	+	14.3660i	0.395862	+	0.685653i	0.993211	−	0.116329i	$-0.0371125\pi$
$439$	8.29423	+	14.3660i	0.395862	+	0.685653i	−0.597349	+	0.801982i	$0.703779\pi$
$440$	7.09808	+	12.2942i	0.338388	+	0.586104i
$441$	−2.46410			−0.117338
$442$	−11.8135	+	23.8923i	−0.561909	+	1.13644i
$443$	−11.3205			−0.537854			−0.268927	−	0.963161i	$-0.586669\pi$
$443$	−11.3205			−0.537854			−0.268927	+	0.963161i	$0.586669\pi$
$444$	−2.56218	−	4.43782i	−0.121596	−	0.210610i
$445$	−0.803848	−	1.39230i	−0.0381060	−	0.0660016i
$446$	−8.66025	+	15.0000i	−0.410075	+	0.710271i
$447$	−0.339746			−0.0160694
$448$	−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	$0.0752847\pi$
$450$	−8.53590			−0.402386
$451$	−12.2942	+	21.2942i	−0.578913	+	1.00271i
$452$	3.69615	+	6.40192i	0.173852	+	0.301121i
$453$	0.732051	+	1.26795i	0.0343947	+	0.0595734i
$454$	20.1962			0.947852
$455$	3.46410	+	5.19615i	0.162400	+	0.243599i
$456$	−2.53590			−0.118754
$457$	−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	$0.916159\pi$
$458$	5.53590	+	9.58846i	0.258676	+	0.448039i
$459$	8.53590	−	14.7846i	0.398422	−	0.690086i
$460$	−2.19615			−0.102396
$461$	−7.79423	+	13.5000i	−0.363013	+	0.628758i	−0.988455	−	0.151513i	$-0.951585\pi$
$461$	−7.79423	+	13.5000i	−0.363013	+	0.628758i	0.625442	+	0.780271i	$0.284919\pi$
$462$	−3.00000	+	5.19615i	−0.139573	+	0.241747i
$463$	26.5885			1.23567			0.617835	−	0.786308i	$-0.288010\pi$
$463$	26.5885			1.23567			0.617835	+	0.786308i	$0.288010\pi$
$464$	−7.50000	+	12.9904i	−0.348179	+	0.603063i
$465$	3.92820	+	6.80385i	0.182166	+	0.315521i
$466$	22.3923	+	38.7846i	1.03730	+	1.79666i
$467$	−19.5167			−0.903123			−0.451562	−	0.892240i	$-0.649133\pi$
$467$	−19.5167			−0.903123			−0.451562	+	0.892240i	$0.649133\pi$
$468$	−8.86603	+	0.571797i	−0.409832	+	0.0264313i
$469$	4.19615			0.193760
$470$	1.39230	+	2.41154i	0.0642222	+	0.111236i
$471$	−3.36603	−	5.83013i	−0.155098	−	0.268638i
$472$	−9.29423	+	16.0981i	−0.427802	+	0.740974i
$473$	48.2487			2.21848
$474$	−3.67949	+	6.37307i	−0.169005	+	0.292725i
$475$	2.00000	−	3.46410i	0.0917663	−	0.158944i
$476$	−4.26795			−0.195621
$477$	4.83975	−	8.38269i	0.221597	−	0.383817i
$478$	−22.6865	−	39.2942i	−1.03766	−	1.79728i
$479$	−2.36603	−	4.09808i	−0.108106	−	0.187246i	0.806897	−	0.590693i	$-0.201145\pi$
$479$	−2.36603	−	4.09808i	−0.108106	−	0.187246i	−0.915003	+	0.403447i	$0.867812\pi$
$480$	6.58846			0.300721
$481$	−25.1865	+	1.62436i	−1.14841	+	0.0740642i
$482$	18.7128			0.852345
$483$	0.464102	+	0.803848i	0.0211174	+	0.0365763i
$484$	−5.69615	−	9.86603i	−0.258916	−	0.448456i
$485$	−12.4641	+	21.5885i	−0.565966	+	0.980281i
$486$	26.4449			1.19956
$487$	0.392305	−	0.679492i	0.0177770	−	0.0307907i	−0.857000	−	0.515316i	$-0.827674\pi$
$487$	0.392305	−	0.679492i	0.0177770	−	0.0307907i	0.874777	+	0.484526i	$0.161008\pi$
$488$	13.1603	−	22.7942i	0.595737	−	1.03185i
$489$	−4.24871			−0.192133
$490$	−1.50000	+	2.59808i	−0.0677631	+	0.117369i
$491$	−14.1962	−	24.5885i	−0.640663	−	1.10966i	−0.985285	−	0.170920i	$-0.945326\pi$
$491$	−14.1962	−	24.5885i	−0.640663	−	1.10966i	0.344622	−	0.938742i	$-0.388007\pi$
$492$	1.90192	+	3.29423i	0.0857453	+	0.148515i
$493$	12.8038			0.576656
$494$	5.53590	−	11.1962i	0.249072	−	0.503739i
$495$	20.1962			0.907750
$496$	−15.4904	−	26.8301i	−0.695539	−	1.20471i
$497$	−3.00000	−	5.19615i	−0.134568	−	0.233079i
$498$	−5.19615	+	9.00000i	−0.232845	+	0.403300i
$499$	12.9808			0.581099			0.290549	−	0.956860i	$-0.406162\pi$
$499$	12.9808			0.581099			0.290549	+	0.956860i	$0.406162\pi$
$500$	−6.06218	+	10.5000i	−0.271109	+	0.469574i
$501$	9.00000	−	15.5885i	0.402090	−	0.696441i
$502$	38.7846			1.73104
$503$	−6.29423	+	10.9019i	−0.280646	+	0.486093i	−0.971544	−	0.236859i	$-0.923882\pi$
$503$	−6.29423	+	10.9019i	−0.280646	+	0.486093i	0.690898	+	0.722952i	$0.257215\pi$
$504$	2.13397	+	3.69615i	0.0950548	+	0.164640i
$505$	−3.69615	−	6.40192i	−0.164477	−	0.284882i
$506$	−10.3923			−0.461994
$507$	3.66025	−	8.78461i	0.162558	−	0.390138i
$508$	−2.39230			−0.106141
$509$	−5.13397	−	8.89230i	−0.227559	−	0.394144i	0.729525	−	0.683954i	$-0.239741\pi$
$509$	−5.13397	−	8.89230i	−0.227559	−	0.394144i	−0.957084	+	0.289810i	$0.906408\pi$
$510$	−4.68653	−	8.11731i	−0.207523	−	0.359441i
$511$	−3.59808	+	6.23205i	−0.159170	+	0.275690i
$512$	−8.66025			−0.382733
$513$	−4.00000	+	6.92820i	−0.176604	+	0.305888i
$514$	−15.6962	+	27.1865i	−0.692328	+	1.19915i
$515$	−11.0718			−0.487882
$516$	3.73205	−	6.46410i	0.164294	−	0.284566i
$517$	2.19615	+	3.80385i	0.0965867	+	0.167293i
$518$	−6.06218	−	10.5000i	−0.266357	−	0.461344i
$519$	−11.3205			−0.496915
$520$	4.79423	−	9.69615i	0.210241	−	0.425204i
$521$	0.124356			0.00544812			0.00272406	−	0.999996i	$-0.499133\pi$
$521$	0.124356			0.00544812			0.00272406	+	0.999996i	$0.499133\pi$
$522$	6.40192	+	11.0885i	0.280205	+	0.485329i
$523$	−16.5885	−	28.7321i	−0.725363	−	1.25636i	−0.958825	−	0.283999i	$-0.908339\pi$
$523$	−16.5885	−	28.7321i	−0.725363	−	1.25636i	0.233462	−	0.972366i	$-0.424995\pi$
$524$	−1.73205	+	3.00000i	−0.0756650	+	0.131056i
$525$	1.46410			0.0638986
$526$	4.09808	−	7.09808i	0.178685	−	0.309491i
$527$	−13.2224	+	22.9019i	−0.575978	+	0.997623i
$528$	17.3205			0.753778
$529$	10.6962	−	18.5263i	0.465050	−	0.805490i
$530$	−5.89230	−	10.2058i	−0.255945	−	0.443310i
$531$	13.2224	+	22.9019i	0.573805	+	0.993859i
$532$	2.00000			0.0867110
$533$	18.6962	−	1.20577i	0.809820	−	0.0522278i
$534$	−1.17691			−0.0509301
$535$	17.1962	+	29.7846i	0.743455	+	1.28770i
$536$	−3.63397	−	6.29423i	−0.156964	−	0.271869i
$537$	2.53590	−	4.39230i	0.109432	−	0.189542i
$538$	−32.7846			−1.41344
$539$	−2.36603	+	4.09808i	−0.101912	+	0.176517i
$540$	3.46410	−	6.00000i	0.149071	−	0.258199i
$541$	−35.3923			−1.52163			−0.760817	−	0.648966i	$-0.775202\pi$
$541$	−35.3923			−1.52163			−0.760817	+	0.648966i	$0.775202\pi$
$542$	14.0263	−	24.2942i	0.602480	−	1.04353i
$543$	−9.36603	−	16.2224i	−0.401935	−	0.696171i
$544$	11.0885	+	19.2058i	0.475414	+	0.823441i
$545$	−21.4641			−0.919421
$546$	4.56218	−	0.294229i	0.195243	−	0.0125918i
$547$	28.1962			1.20558			0.602790	−	0.797900i	$-0.294056\pi$
$547$	28.1962			1.20558			0.602790	+	0.797900i	$0.294056\pi$
$548$	−10.9641	−	18.9904i	−0.468363	−	0.811229i
$549$	−18.7224	−	32.4282i	−0.799054	−	1.38400i
$550$	−8.19615	+	14.1962i	−0.349485	+	0.605326i
$551$	−6.00000			−0.255609
$552$	0.803848	−	1.39230i	0.0342140	−	0.0592604i
$553$	−2.90192	+	5.02628i	−0.123402	+	0.213739i
$554$	−29.4449			−1.25099
$555$	4.43782	−	7.68653i	0.188375	−	0.326275i
$556$	−10.2942	−	17.8301i	−0.436573	−	0.756166i
$557$	12.8205	+	22.2058i	0.543222	+	0.940889i	0.998716	+	0.0506499i	$0.0161293\pi$
$557$	12.8205	+	22.2058i	0.543222	+	0.940889i	−0.455494	+	0.890239i	$0.650537\pi$
$558$	−26.4449			−1.11950
$559$	−20.3923	−	30.5885i	−0.862503	−	1.29375i
$560$	8.66025			0.365963
$561$	−7.39230	−	12.8038i	−0.312103	−	0.540579i
$562$	−6.40192	−	11.0885i	−0.270049	−	0.467738i
$563$	5.02628	−	8.70577i	0.211832	−	0.366905i	−0.740456	−	0.672105i	$-0.765390\pi$
$563$	5.02628	−	8.70577i	0.211832	−	0.366905i	0.952288	+	0.305201i	$0.0987236\pi$
$564$	0.679492			0.0286118
$565$	−6.40192	+	11.0885i	−0.269331	+	0.466495i
$566$	−0.169873	+	0.294229i	−0.00714029	+	0.0123674i
$567$	4.46410			0.187475
$568$	−5.19615	+	9.00000i	−0.218026	+	0.377632i
$569$	−14.5359	−	25.1769i	−0.609377	−	1.05547i	−0.991343	−	0.131295i	$-0.958086\pi$
$569$	−14.5359	−	25.1769i	−0.609377	−	1.05547i	0.381967	−	0.924176i	$-0.375247\pi$
$570$	2.19615	+	3.80385i	0.0919867	+	0.159326i
$571$	−24.7846			−1.03720			−0.518602	−	0.855016i	$-0.673547\pi$
$571$	−24.7846			−1.03720			−0.518602	+	0.855016i	$0.673547\pi$
$572$	−7.56218	+	15.2942i	−0.316191	+	0.639484i
$573$	−0.928203			−0.0387762
$574$	4.50000	+	7.79423i	0.187826	+	0.325325i
$575$	1.26795	+	2.19615i	0.0528771	+	0.0915859i
$576$	1.23205	−	2.13397i	0.0513355	−	0.0889156i
$577$	32.8038			1.36564			0.682821	−	0.730586i	$-0.260753\pi$
$577$	32.8038			1.36564			0.682821	+	0.730586i	$0.260753\pi$
$578$	1.05256	−	1.82309i	0.0437807	−	0.0758304i
$579$	1.83013	−	3.16987i	0.0760575	−	0.131735i
$580$	5.19615			0.215758
$581$	−4.09808	+	7.09808i	−0.170017	+	0.294478i
$582$	9.12436	+	15.8038i	0.378217	+	0.655091i
$583$	−9.29423	−	16.0981i	−0.384928	−	0.666714i
$584$	12.4641			0.515768
$585$	−8.53590	−	12.8038i	−0.352916	−	0.529374i
$586$	19.3923			0.801089
$587$	2.19615	+	3.80385i	0.0906449	+	0.157002i	0.907783	−	0.419441i	$-0.137774\pi$
$587$	2.19615	+	3.80385i	0.0906449	+	0.157002i	−0.817138	+	0.576442i	$0.804441\pi$
$588$	0.366025	+	0.633975i	0.0150946	+	0.0261447i
$589$	6.19615	−	10.7321i	0.255308	−	0.442206i
$590$	32.1962			1.32549
$591$	4.39230	−	7.60770i	0.180675	−	0.312939i
$592$	−17.5000	+	30.3109i	−0.719246	+	1.24577i
$593$	41.4449			1.70194			0.850968	−	0.525217i	$-0.176016\pi$
$593$	41.4449			1.70194			0.850968	+	0.525217i	$0.176016\pi$
$594$	16.3923	−	28.3923i	0.672584	−	1.16495i
$595$	−3.69615	−	6.40192i	−0.151527	−	0.262453i
$596$	−0.232051	−	0.401924i	−0.00950517	−	0.0164634i
$597$	−1.46410			−0.0599217
$598$	4.39230	+	6.58846i	0.179615	+	0.269422i
$599$	16.1436			0.659609			0.329805	−	0.944049i	$-0.393017\pi$
$599$	16.1436			0.659609			0.329805	+	0.944049i	$0.393017\pi$
$600$	−1.26795	−	2.19615i	−0.0517638	−	0.0896575i
$601$	−10.9904	−	19.0359i	−0.448307	−	0.776490i	0.549969	−	0.835185i	$-0.314640\pi$
$601$	−10.9904	−	19.0359i	−0.448307	−	0.776490i	−0.998276	+	0.0586946i	$0.981306\pi$
$602$	8.83013	−	15.2942i	0.359889	−	0.623346i
$603$	−10.3397			−0.421067
$604$	−1.00000	+	1.73205i	−0.0406894	+	0.0704761i
$605$	9.86603	−	17.0885i	0.401111	−	0.694745i
$606$	−5.41154			−0.219829
$607$	−3.19615	+	5.53590i	−0.129728	+	0.224695i	−0.923571	−	0.383427i	$-0.874744\pi$
$607$	−3.19615	+	5.53590i	−0.129728	+	0.224695i	0.793843	+	0.608122i	$0.208077\pi$
$608$	−5.19615	−	9.00000i	−0.210732	−	0.364998i
$609$	−1.09808	−	1.90192i	−0.0444963	−	0.0770698i
$610$	−45.5885			−1.84582
$611$	1.48334	−	3.00000i	0.0600095	−	0.121367i
$612$	10.5167			0.425111
$613$	8.69615	+	15.0622i	0.351234	+	0.608356i	0.986466	−	0.163966i	$-0.0524287\pi$
$613$	8.69615	+	15.0622i	0.351234	+	0.608356i	−0.635232	+	0.772322i	$0.719095\pi$
$614$	23.0263	+	39.8827i	0.929265	+	1.60953i
$615$	−3.29423	+	5.70577i	−0.132836	+	0.230079i
$616$	8.19615			0.330232
$617$	−14.3038	+	24.7750i	−0.575851	+	0.997404i	0.420097	+	0.907479i	$0.361996\pi$
$617$	−14.3038	+	24.7750i	−0.575851	+	0.997404i	−0.995949	+	0.0899245i	$0.971337\pi$
$618$	−4.05256	+	7.01924i	−0.163018	+	0.282355i
$619$	−37.3731			−1.50215			−0.751075	−	0.660217i	$-0.770464\pi$
$619$	−37.3731			−1.50215			−0.751075	+	0.660217i	$0.770464\pi$
$620$	−5.36603	+	9.29423i	−0.215505	+	0.373265i
$621$	−2.53590	−	4.39230i	−0.101762	−	0.176257i
$622$	4.09808	+	7.09808i	0.164318	+	0.284607i
$623$	−0.928203			−0.0371877
$624$	−7.32051	−	10.9808i	−0.293055	−	0.439582i
$625$	−11.0000			−0.440000
$626$	−11.0718	−	19.1769i	−0.442518	−	0.766464i
$627$	3.46410	+	6.00000i	0.138343	+	0.239617i
$628$	4.59808	−	7.96410i	0.183483	−	0.317802i
$629$	29.8756			1.19122
$630$	3.69615	−	6.40192i	0.147258	−	0.255059i
$631$	−14.3923	+	24.9282i	−0.572949	+	0.992376i	0.423313	+	0.905984i	$0.360867\pi$
$631$	−14.3923	+	24.9282i	−0.572949	+	0.992376i	−0.996261	+	0.0863924i	$0.972466\pi$
$632$	10.0526			0.399869
$633$	−4.46410	+	7.73205i	−0.177432	+	0.307321i
$634$	0.401924	+	0.696152i	0.0159624	+	0.0276477i
$635$	−2.07180	−	3.58846i	−0.0822167	−	0.142404i
$636$	−2.87564			−0.114027
$637$	3.59808	−	0.232051i	0.142561	−	0.00919419i
$638$	24.5885			0.973466
$639$	7.39230	+	12.8038i	0.292435	+	0.506512i
$640$	−10.5000	−	18.1865i	−0.415049	−	0.718886i
$641$	−0.571797	+	0.990381i	−0.0225846	+	0.0391177i	−0.877097	−	0.480314i	$-0.840523\pi$
$641$	−0.571797	+	0.990381i	−0.0225846	+	0.0391177i	0.854512	+	0.519431i	$0.173856\pi$
$642$	25.1769			0.993654
$643$	−20.3923	+	35.3205i	−0.804194	+	1.39290i	0.112640	+	0.993636i	$0.464069\pi$
$643$	−20.3923	+	35.3205i	−0.804194	+	1.39290i	−0.916834	+	0.399269i	$0.869264\pi$
$644$	−0.633975	+	1.09808i	−0.0249821	+	0.0432703i
$645$	12.9282			0.509048
$646$	−7.39230	+	12.8038i	−0.290846	+	0.503761i
$647$	22.5167	+	39.0000i	0.885221	+	1.53325i	0.845460	+	0.534039i	$0.179326\pi$
$647$	22.5167	+	39.0000i	0.885221	+	1.53325i	0.0397614	+	0.999209i	$0.487340\pi$
$648$	−3.86603	−	6.69615i	−0.151872	−	0.263050i
$649$	50.7846			1.99347
$650$	12.4641	−	0.803848i	0.488882	−	0.0315295i
$651$	4.53590			0.177776
$652$	−2.90192	−	5.02628i	−0.113648	−	0.196844i
$653$	5.07180	+	8.78461i	0.198475	+	0.343768i	0.948034	−	0.318169i	$-0.103068\pi$
$653$	5.07180	+	8.78461i	0.198475	+	0.343768i	−0.749559	+	0.661937i	$0.769735\pi$
$654$	−7.85641	+	13.6077i	−0.307210	+	0.532103i
$655$	−6.00000			−0.234439
$656$	12.9904	−	22.5000i	0.507189	−	0.878477i
$657$	8.86603	−	15.3564i	0.345897	−	0.599110i
$658$	1.60770			0.0626745
$659$	−3.80385	+	6.58846i	−0.148177	+	0.256650i	−0.930554	−	0.366156i	$-0.880674\pi$
$659$	−3.80385	+	6.58846i	−0.148177	+	0.256650i	0.782377	+	0.622805i	$0.214007\pi$
$660$	−3.00000	−	5.19615i	−0.116775	−	0.202260i
$661$	11.4019	+	19.7487i	0.443483	+	0.768136i	0.997945	−	0.0640734i	$-0.0204092\pi$
$661$	11.4019	+	19.7487i	0.443483	+	0.768136i	−0.554462	+	0.832209i	$0.687076\pi$
$662$	46.7321			1.81629
$663$	−4.99296	+	10.0981i	−0.193910	+	0.392177i
$664$	14.1962			0.550918
$665$	1.73205	+	3.00000i	0.0671660	+	0.116335i
$666$	14.9378	+	25.8731i	0.578829	+	1.00256i
$667$	1.90192	−	3.29423i	0.0736428	−	0.127553i
$668$	24.5885			0.951356
$669$	−3.66025	+	6.33975i	−0.141514	+	0.245109i
$670$	−6.29423	+	10.9019i	−0.243167	+	0.421178i
$671$	−71.9090			−2.77601
$672$	1.90192	−	3.29423i	0.0733683	−	0.127078i
$673$	−9.08846	−	15.7417i	−0.350334	−	0.606797i	0.635974	−	0.771711i	$-0.280599\pi$
$673$	−9.08846	−	15.7417i	−0.350334	−	0.606797i	−0.986308	+	0.164914i	$0.947265\pi$
$674$	9.52628	+	16.5000i	0.366939	+	0.635556i
$675$	−8.00000			−0.307920
$676$	12.8923	−	1.66987i	0.495858	−	0.0642259i
$677$	−36.9282			−1.41927			−0.709633	−	0.704571i	$-0.751139\pi$
$677$	−36.9282			−1.41927			−0.709633	+	0.704571i	$0.751139\pi$
$678$	4.68653	+	8.11731i	0.179985	+	0.311744i
$679$	7.19615	+	12.4641i	0.276163	+	0.478328i
$680$	−6.40192	+	11.0885i	−0.245503	+	0.425223i
$681$	8.53590			0.327096
$682$	−25.3923	+	43.9808i	−0.972322	+	1.68411i
$683$	−4.26795	+	7.39230i	−0.163309	+	0.282859i	−0.936053	−	0.351858i	$-0.885550\pi$
$683$	−4.26795	+	7.39230i	−0.163309	+	0.282859i	0.772745	+	0.634717i	$0.218883\pi$
$684$	−4.92820			−0.188435
$685$	18.9904	−	32.8923i	0.725585	−	1.25675i
$686$	0.866025	+	1.50000i	0.0330650	+	0.0572703i
$687$	2.33975	+	4.05256i	0.0892669	+	0.154615i
$688$	−50.9808			−1.94362
$689$	−6.27757	+	12.6962i	−0.239156	+	0.483685i
$690$	−2.78461			−0.106008
$691$	10.1962	+	17.6603i	0.387880	+	0.671828i	0.992164	−	0.124941i	$-0.0398742\pi$
$691$	10.1962	+	17.6603i	0.387880	+	0.671828i	−0.604284	+	0.796769i	$0.706541\pi$
$692$	−7.73205	−	13.3923i	−0.293928	−	0.509099i
$693$	5.83013	−	10.0981i	0.221468	−	0.383594i
$694$	−18.5885			−0.705608
$695$	17.8301	−	30.8827i	0.676335	−	1.17145i
$696$	−1.90192	+	3.29423i	−0.0720922	+	0.124867i
$697$	−22.1769			−0.840011
$698$	14.5359	−	25.1769i	0.550192	−	0.952960i
$699$	9.46410	+	16.3923i	0.357965	+	0.620014i
$700$	1.00000	+	1.73205i	0.0377964	+	0.0654654i
$701$	−20.7846			−0.785024			−0.392512	−	0.919747i	$-0.628394\pi$
$701$	−20.7846			−0.785024			−0.392512	+	0.919747i	$0.628394\pi$
$702$	−24.9282	+	1.60770i	−0.940854	+	0.0606785i
$703$	−14.0000			−0.528020
$704$	−2.36603	−	4.09808i	−0.0891729	−	0.154452i
$705$	0.588457	+	1.01924i	0.0221626	+	0.0383867i
$706$	2.89230	−	5.00962i	0.108853	−	0.188539i
$707$	−4.26795			−0.160513
$708$	3.92820	−	6.80385i	0.147631	−	0.255704i
$709$	16.0885	−	27.8660i	0.604215	−	1.04653i	−0.387960	−	0.921676i	$-0.626820\pi$
$709$	16.0885	−	27.8660i	0.604215	−	1.04653i	0.992175	−	0.124854i	$-0.0398464\pi$
$710$	18.0000			0.675528
$711$	7.15064	−	12.3853i	0.268170	−	0.464484i
$712$	0.803848	+	1.39230i	0.0301255	+	0.0521788i
$713$	3.92820	+	6.80385i	0.147112	+	0.254806i
$714$	−5.41154			−0.202522
$715$	−29.4904	+	1.90192i	−1.10288	+	0.0711279i
$716$	6.92820			0.258919
$717$	−9.58846	−	16.6077i	−0.358087	−	0.620226i
$718$	4.39230	+	7.60770i	0.163919	+	0.283917i
$719$	5.36603	−	9.29423i	0.200119	−	0.346616i	−0.748448	−	0.663194i	$-0.769200\pi$
$719$	5.36603	−	9.29423i	0.200119	−	0.346616i	0.948567	+	0.316578i	$0.102534\pi$
$720$	−21.3397			−0.795285
$721$	−3.19615	+	5.53590i	−0.119031	+	0.206168i
$722$	−12.9904	+	22.5000i	−0.483452	+	0.837363i
$723$	7.90897			0.294138
$724$	12.7942	−	22.1603i	0.475494	−	0.823579i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$	−7.22243	−	12.5096i	−0.268050	−	0.464276i
$727$	21.1769			0.785408			0.392704	−	0.919665i	$-0.371540\pi$
$727$	21.1769			0.785408			0.392704	+	0.919665i	$0.371540\pi$
$728$	−3.46410	−	5.19615i	−0.128388	−	0.192582i
$729$	−2.21539			−0.0820515
$730$	−10.7942	−	18.6962i	−0.399512	−	0.691976i
$731$	21.7583	+	37.6865i	0.804761	+	1.39389i
$732$	−5.56218	+	9.63397i	−0.205584	+	0.356082i
$733$	−7.58846			−0.280286			−0.140143	−	0.990131i	$-0.544756\pi$
$733$	−7.58846			−0.280286			−0.140143	+	0.990131i	$0.544756\pi$
$734$	−5.36603	+	9.29423i	−0.198064	+	0.343056i
$735$	−0.633975	+	1.09808i	−0.0233845	+	0.0405032i
$736$	6.58846			0.242854
$737$	−9.92820	+	17.1962i	−0.365710	+	0.633428i
$738$	−11.0885	−	19.2058i	−0.408172	−	0.706974i
$739$	0.392305	+	0.679492i	0.0144312	+	0.0249955i	0.873151	−	0.487450i	$-0.162073\pi$
$739$	0.392305	+	0.679492i	0.0144312	+	0.0249955i	−0.858720	+	0.512446i	$0.828740\pi$
$740$	12.1244			0.445700
$741$	2.33975	−	4.73205i	0.0859527	−	0.173836i
$742$	−6.80385			−0.249777
$743$	14.1962	+	24.5885i	0.520806	+	0.902063i	0.999707	+	0.0241941i	$0.00770196\pi$
$743$	14.1962	+	24.5885i	0.520806	+	0.902063i	−0.478901	+	0.877869i	$0.658965\pi$
$744$	−3.92820	−	6.80385i	−0.144015	−	0.249441i
$745$	0.401924	−	0.696152i	0.0147253	−	0.0255051i
$746$	−16.2679			−0.595612
$747$	10.0981	−	17.4904i	0.369469	−	0.639940i
$748$	10.0981	−	17.4904i	0.369222	−	0.639512i
$749$	19.8564			0.725537
$750$	−7.68653	+	13.3135i	−0.280673	+	0.486139i
$751$	−23.0981	−	40.0070i	−0.842861	−	1.45988i	−0.887466	−	0.460873i	$-0.847536\pi$
$751$	−23.0981	−	40.0070i	−0.842861	−	1.45988i	0.0446053	−	0.999005i	$-0.485797\pi$
$752$	−2.32051	−	4.01924i	−0.0846202	−	0.146567i
$753$	16.3923			0.597369
$754$	−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	$0.739424\pi$
$758$	−3.97372	+	6.88269i	−0.144332	+	0.249990i
$759$	−4.39230			−0.159431
$760$	3.00000	−	5.19615i	0.108821	−	0.188484i
$761$	−3.33975	+	5.78461i	−0.121066	+	0.209692i	−0.920188	−	0.391476i	$-0.871965\pi$
$761$	−3.33975	+	5.78461i	−0.121066	+	0.209692i	0.799123	+	0.601168i	$0.205298\pi$
$762$	−3.03332			−0.109886
$763$	−6.19615	+	10.7321i	−0.224316	+	0.388526i
$764$	−0.633975	−	1.09808i	−0.0229364	−	0.0397270i
$765$	9.10770	+	15.7750i	0.329289	+	0.570346i
$766$	−9.80385			−0.354227
$767$	−21.4641	−	32.1962i	−0.775024	−	1.16254i
$768$	−13.9090			−0.501897
$769$	23.5885	+	40.8564i	0.850622	+	1.47332i	0.880648	+	0.473771i	$0.157107\pi$
$769$	23.5885	+	40.8564i	0.850622	+	1.47332i	−0.0300268	+	0.999549i	$0.509559\pi$
$770$	−7.09808	−	12.2942i	−0.255797	−	0.443053i
$771$	−6.63397	+	11.4904i	−0.238917	+	0.413816i

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)

\(f(q)\)	\(=\)	\(q+(0.866025 + 1.50000i) q^{2} +(0.366025 + 0.633975i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.73205 q^{5} +(-0.633975 + 1.09808i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.73205 q^{8} +(1.23205 - 2.13397i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 1.50000i) q^{2} +(0.366025 + 0.633975i) q^{3} +(-0.500000 + 0.866025i) q^{4} -1.73205 q^{5} +(-0.633975 + 1.09808i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.73205 q^{8} +(1.23205 - 2.13397i) q^{9} +(-1.50000 - 2.59808i) q^{10} +(-2.36603 - 4.09808i) q^{11} -0.732051 q^{12} +(-1.59808 + 3.23205i) q^{13} -1.73205 q^{14} +(-0.633975 - 1.09808i) q^{15} +(2.50000 + 4.33013i) q^{16} +(2.13397 - 3.69615i) q^{17} +4.26795 q^{18} +(-1.00000 + 1.73205i) q^{19} +(0.866025 - 1.50000i) q^{20} -0.732051 q^{21} +(4.09808 - 7.09808i) q^{22} +(-0.633975 - 1.09808i) q^{23} +(0.633975 + 1.09808i) q^{24} -2.00000 q^{25} +(-6.23205 + 0.401924i) q^{26} +4.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(1.50000 + 2.59808i) q^{29} +(1.09808 - 1.90192i) q^{30} -6.19615 q^{31} +(-2.59808 + 4.50000i) q^{32} +(1.73205 - 3.00000i) q^{33} +7.39230 q^{34} +(0.866025 - 1.50000i) q^{35} +(1.23205 + 2.13397i) q^{36} +(3.50000 + 6.06218i) q^{37} -3.46410 q^{38} +(-2.63397 + 0.169873i) q^{39} -3.00000 q^{40} +(-2.59808 - 4.50000i) q^{41} +(-0.633975 - 1.09808i) q^{42} +(-5.09808 + 8.83013i) q^{43} +4.73205 q^{44} +(-2.13397 + 3.69615i) q^{45} +(1.09808 - 1.90192i) q^{46} -0.928203 q^{47} +(-1.83013 + 3.16987i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-1.73205 - 3.00000i) q^{50} +3.12436 q^{51} +(-2.00000 - 3.00000i) q^{52} +3.92820 q^{53} +(3.46410 + 6.00000i) q^{54} +(4.09808 + 7.09808i) q^{55} +(-0.866025 + 1.50000i) q^{56} -1.46410 q^{57} +(-2.59808 + 4.50000i) q^{58} +(-5.36603 + 9.29423i) q^{59} +1.26795 q^{60} +(7.59808 - 13.1603i) q^{61} +(-5.36603 - 9.29423i) q^{62} +(1.23205 + 2.13397i) q^{63} +1.00000 q^{64} +(2.76795 - 5.59808i) q^{65} +6.00000 q^{66} +(-2.09808 - 3.63397i) q^{67} +(2.13397 + 3.69615i) q^{68} +(0.464102 - 0.803848i) q^{69} +3.00000 q^{70} +(-3.00000 + 5.19615i) q^{71} +(2.13397 - 3.69615i) q^{72} +7.19615 q^{73} +(-6.06218 + 10.5000i) q^{74} +(-0.732051 - 1.26795i) q^{75} +(-1.00000 - 1.73205i) q^{76} +4.73205 q^{77} +(-2.53590 - 3.80385i) q^{78} +5.80385 q^{79} +(-4.33013 - 7.50000i) q^{80} +(-2.23205 - 3.86603i) q^{81} +(4.50000 - 7.79423i) q^{82} +8.19615 q^{83} +(0.366025 - 0.633975i) q^{84} +(-3.69615 + 6.40192i) q^{85} -17.6603 q^{86} +(-1.09808 + 1.90192i) q^{87} +(-4.09808 - 7.09808i) q^{88} +(0.464102 + 0.803848i) q^{89} -7.39230 q^{90} +(-2.00000 - 3.00000i) q^{91} +1.26795 q^{92} +(-2.26795 - 3.92820i) q^{93} +(-0.803848 - 1.39230i) q^{94} +(1.73205 - 3.00000i) q^{95} -3.80385 q^{96} +(7.19615 - 12.4641i) q^{97} +(0.866025 - 1.50000i) q^{98} -11.6603 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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L-functions

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