LMFDB - Embedded newform 37.2.f.b.12.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,2,Mod(7,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([16]))

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

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

chi := DirichletCharacter("37.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	37.f (of order $9$, degree $6$, 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:	$0.295446487479$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			12.1
Root			$0.939693 + 0.342020i$ of defining polynomial
Character	$\chi$	$=$	37.12
Dual form			37.2.f.b.34.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.673648 - 0.565258i) q^{2} +(-1.17365 - 0.984808i) q^{3} +(-0.213011 + 1.20805i) q^{4} +(0.826352 - 0.300767i) q^{5} -1.34730 q^{6} +(-3.53209 + 1.28558i) q^{7} +(1.41875 + 2.45734i) q^{8} +(-0.113341 - 0.642788i) q^{9} +O(q^{10})$	\(q+(0.673648 - 0.565258i) q^{2} +(-1.17365 - 0.984808i) q^{3} +(-0.213011 + 1.20805i) q^{4} +(0.826352 - 0.300767i) q^{5} -1.34730 q^{6} +(-3.53209 + 1.28558i) q^{7} +(1.41875 + 2.45734i) q^{8} +(-0.113341 - 0.642788i) q^{9} +(0.386659 - 0.669713i) q^{10} +(0.907604 + 1.57202i) q^{11} +(1.43969 - 1.20805i) q^{12} +(0.992726 - 5.63003i) q^{13} +(-1.65270 + 2.86257i) q^{14} +(-1.26604 - 0.460802i) q^{15} +(0.0393628 + 0.0143269i) q^{16} +(0.0812519 + 0.460802i) q^{17} +(-0.439693 - 0.368946i) q^{18} +(0.624485 + 0.524005i) q^{19} +(0.187319 + 1.06234i) q^{20} +(5.41147 + 1.96962i) q^{21} +(1.50000 + 0.545955i) q^{22} +(3.00000 - 5.19615i) q^{23} +(0.754900 - 4.28125i) q^{24} +(-3.23783 + 2.71686i) q^{25} +(-2.51367 - 4.35381i) q^{26} +(-2.79813 + 4.84651i) q^{27} +(-0.800660 - 4.54077i) q^{28} +(4.31908 + 7.48086i) q^{29} +(-1.11334 + 0.405223i) q^{30} +1.94356 q^{31} +(-5.29813 + 1.92836i) q^{32} +(0.482926 - 2.73881i) q^{33} +(0.315207 + 0.264490i) q^{34} +(-2.53209 + 2.12467i) q^{35} +0.800660 q^{36} +(-5.86097 + 1.62760i) q^{37} +0.716881 q^{38} +(-6.70961 + 5.63003i) q^{39} +(1.91147 + 1.60392i) q^{40} +(0.0996702 - 0.565258i) q^{41} +(4.75877 - 1.73205i) q^{42} -4.87939 q^{43} +(-2.09240 + 0.761570i) q^{44} +(-0.286989 - 0.497079i) q^{45} +(-0.916222 - 5.19615i) q^{46} +(6.02481 - 10.4353i) q^{47} +(-0.0320889 - 0.0555796i) q^{48} +(5.46064 - 4.58202i) q^{49} +(-0.645430 + 3.66041i) q^{50} +(0.358441 - 0.620838i) q^{51} +(6.58987 + 2.39852i) q^{52} +(8.79086 + 3.19961i) q^{53} +(0.854570 + 4.84651i) q^{54} +(1.22281 + 1.02606i) q^{55} +(-8.17024 - 6.85565i) q^{56} +(-0.216881 - 1.23000i) q^{57} +(7.13816 + 2.59808i) q^{58} +(0.286989 + 0.104455i) q^{59} +(0.826352 - 1.43128i) q^{60} +(-0.560307 + 3.17766i) q^{61} +(1.30928 - 1.09861i) q^{62} +(1.22668 + 2.12467i) q^{63} +(-2.52094 + 4.36640i) q^{64} +(-0.872989 - 4.95096i) q^{65} +(-1.22281 - 2.11797i) q^{66} +(3.13176 - 1.13987i) q^{67} -0.573978 q^{68} +(-8.63816 + 3.14403i) q^{69} +(-0.504748 + 2.86257i) q^{70} +(-10.7738 - 9.04028i) q^{71} +(1.41875 - 1.19047i) q^{72} -4.24897 q^{73} +(-3.02822 + 4.40938i) q^{74} +6.47565 q^{75} +(-0.766044 + 0.642788i) q^{76} +(-5.22668 - 4.38571i) q^{77} +(-1.33750 + 7.58532i) q^{78} +(3.01367 - 1.09689i) q^{79} +0.0368366 q^{80} +(6.21688 - 2.26276i) q^{81} +(-0.252374 - 0.437124i) q^{82} +(0.888003 + 5.03612i) q^{83} +(-3.53209 + 6.11776i) q^{84} +(0.205737 + 0.356347i) q^{85} +(-3.28699 + 2.75811i) q^{86} +(2.29813 - 13.0334i) q^{87} +(-2.57532 + 4.46059i) q^{88} +(-10.0569 - 3.66041i) q^{89} +(-0.474308 - 0.172634i) q^{90} +(3.73143 + 21.1620i) q^{91} +(5.63816 + 4.73097i) q^{92} +(-2.28106 - 1.91404i) q^{93} +(-1.84002 - 10.4353i) q^{94} +(0.673648 + 0.245188i) q^{95} +(8.11721 + 2.95442i) q^{96} +(-4.74510 + 8.21875i) q^{97} +(1.08853 - 6.17334i) q^{98} +(0.907604 - 0.761570i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 6 q^{3} - 9 q^{4} + 6 q^{5} - 6 q^{6} - 12 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 6 * q^3 - 9 * q^4 + 6 * q^5 - 6 * q^6 - 12 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 3 q^{2} - 6 q^{3} - 9 q^{4} + 6 q^{5} - 6 q^{6} - 12 q^{7} + 6 q^{8} + 6 q^{9} + 9 q^{10} + 9 q^{11} + 3 q^{12} - 12 q^{13} - 12 q^{14} - 3 q^{15} + 9 q^{16} + 3 q^{17} + 3 q^{18} - 9 q^{19} - 21 q^{20} + 12 q^{21} + 9 q^{22} + 18 q^{23} + 6 q^{24} + 6 q^{26} - 3 q^{27} + 24 q^{28} + 9 q^{29} - 18 q^{31} - 18 q^{32} - 18 q^{33} + 9 q^{34} - 6 q^{35} - 24 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} - 9 q^{40} + 15 q^{41} + 6 q^{42} - 18 q^{43} - 9 q^{44} + 6 q^{45} - 18 q^{46} + 9 q^{47} + 9 q^{48} + 24 q^{49} + 12 q^{50} - 6 q^{51} + 51 q^{52} + 21 q^{53} + 21 q^{54} + 18 q^{55} - 6 q^{56} + 15 q^{57} + 9 q^{58} - 6 q^{59} + 6 q^{60} - 9 q^{61} - 12 q^{62} - 6 q^{63} - 12 q^{64} - 33 q^{65} - 18 q^{66} + 24 q^{67} + 12 q^{68} - 18 q^{69} - 36 q^{70} - 12 q^{71} + 6 q^{72} - 33 q^{74} - 18 q^{77} - 3 q^{78} - 3 q^{79} + 24 q^{80} + 21 q^{81} - 18 q^{82} + 3 q^{83} - 12 q^{84} - 9 q^{85} - 12 q^{86} + 9 q^{88} - 24 q^{89} + 27 q^{90} + 42 q^{91} + 21 q^{93} + 9 q^{94} + 3 q^{95} + 18 q^{96} - 27 q^{97} + 27 q^{98} + 9 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 6 * q^3 - 9 * q^4 + 6 * q^5 - 6 * q^6 - 12 * q^7 + 6 * q^8 + 6 * q^9 + 9 * q^10 + 9 * q^11 + 3 * q^12 - 12 * q^13 - 12 * q^14 - 3 * q^15 + 9 * q^16 + 3 * q^17 + 3 * q^18 - 9 * q^19 - 21 * q^20 + 12 * q^21 + 9 * q^22 + 18 * q^23 + 6 * q^24 + 6 * q^26 - 3 * q^27 + 24 * q^28 + 9 * q^29 - 18 * q^31 - 18 * q^32 - 18 * q^33 + 9 * q^34 - 6 * q^35 - 24 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 - 9 * q^40 + 15 * q^41 + 6 * q^42 - 18 * q^43 - 9 * q^44 + 6 * q^45 - 18 * q^46 + 9 * q^47 + 9 * q^48 + 24 * q^49 + 12 * q^50 - 6 * q^51 + 51 * q^52 + 21 * q^53 + 21 * q^54 + 18 * q^55 - 6 * q^56 + 15 * q^57 + 9 * q^58 - 6 * q^59 + 6 * q^60 - 9 * q^61 - 12 * q^62 - 6 * q^63 - 12 * q^64 - 33 * q^65 - 18 * q^66 + 24 * q^67 + 12 * q^68 - 18 * q^69 - 36 * q^70 - 12 * q^71 + 6 * q^72 - 33 * q^74 - 18 * q^77 - 3 * q^78 - 3 * q^79 + 24 * q^80 + 21 * q^81 - 18 * q^82 + 3 * q^83 - 12 * q^84 - 9 * q^85 - 12 * q^86 + 9 * q^88 - 24 * q^89 + 27 * q^90 + 42 * q^91 + 21 * q^93 + 9 * q^94 + 3 * q^95 + 18 * q^96 - 27 * q^97 + 27 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

Coefficient data

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

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

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

$2$	0.673648	−	0.565258i	0.476341	−	0.399698i	−0.372760	−	0.927928i	$-0.621589\pi$
$2$	0.673648	−	0.565258i	0.476341	−	0.399698i	0.849101	+	0.528230i	$0.177144\pi$
$3$	−1.17365	−	0.984808i	−0.677606	−	0.568579i	0.237700	−	0.971339i	$-0.423607\pi$
$3$	−1.17365	−	0.984808i	−0.677606	−	0.568579i	−0.915306	+	0.402760i	$0.868051\pi$
$4$	−0.213011	+	1.20805i	−0.106506	+	0.604023i
$5$	0.826352	−	0.300767i	0.369556	−	0.134507i	−0.150565	−	0.988600i	$-0.548109\pi$
$5$	0.826352	−	0.300767i	0.369556	−	0.134507i	0.520121	+	0.854093i	$0.325887\pi$
$6$	−1.34730			−0.550031
$7$	−3.53209	+	1.28558i	−1.33500	+	0.485902i	−0.908236	−	0.418459i	$-0.862570\pi$
$7$	−3.53209	+	1.28558i	−1.33500	+	0.485902i	−0.426768	+	0.904361i	$0.640348\pi$
$8$	1.41875	+	2.45734i	0.501603	+	0.868802i
$9$	−0.113341	−	0.642788i	−0.0377803	−	0.214263i
$10$	0.386659	−	0.669713i	0.122272	−	0.211782i
$11$	0.907604	+	1.57202i	0.273653	+	0.473981i	0.969794	−	0.243924i	$-0.0784347\pi$
$11$	0.907604	+	1.57202i	0.273653	+	0.473981i	−0.696142	+	0.717905i	$0.745101\pi$
$12$	1.43969	−	1.20805i	0.415603	−	0.348733i
$13$	0.992726	−	5.63003i	0.275333	−	1.56149i	−0.462570	−	0.886583i	$-0.653073\pi$
$13$	0.992726	−	5.63003i	0.275333	−	1.56149i	0.737903	−	0.674907i	$-0.235816\pi$
$14$	−1.65270	+	2.86257i	−0.441704	+	0.765053i
$15$	−1.26604	−	0.460802i	−0.326891	−	0.118979i
$16$	0.0393628	+	0.0143269i	0.00984071	+	0.00358173i
$17$	0.0812519	+	0.460802i	0.0197065	+	0.111761i	0.993074	−	0.117488i	$-0.0374841\pi$
$17$	0.0812519	+	0.460802i	0.0197065	+	0.111761i	−0.973368	+	0.229249i	$0.926373\pi$
$18$	−0.439693	−	0.368946i	−0.103637	−	0.0869614i
$19$	0.624485	+	0.524005i	0.143267	+	0.120215i	0.711604	−	0.702580i	$-0.247969\pi$
$19$	0.624485	+	0.524005i	0.143267	+	0.120215i	−0.568338	+	0.822795i	$0.692413\pi$
$20$	0.187319	+	1.06234i	0.0418857	+	0.237546i
$21$	5.41147	+	1.96962i	1.18088	+	0.429805i
$22$	1.50000	+	0.545955i	0.319801	+	0.116398i
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$	0.754900	−	4.28125i	0.154093	−	0.873907i
$25$	−3.23783	+	2.71686i	−0.647565	+	0.543372i
$26$	−2.51367	−	4.35381i	−0.492971	−	0.853851i
$27$	−2.79813	+	4.84651i	−0.538501	+	0.932711i
$28$	−0.800660	−	4.54077i	−0.151310	−	0.858124i
$29$	4.31908	+	7.48086i	0.802033	+	1.38916i	0.918276	+	0.395941i	$0.129581\pi$
$29$	4.31908	+	7.48086i	0.802033	+	1.38916i	−0.116244	+	0.993221i	$0.537085\pi$
$30$	−1.11334	+	0.405223i	−0.203267	+	0.0739832i
$31$	1.94356			0.349074			0.174537	−	0.984651i	$-0.444157\pi$
$31$	1.94356			0.349074			0.174537	+	0.984651i	$0.444157\pi$
$32$	−5.29813	+	1.92836i	−0.936587	+	0.340890i
$33$	0.482926	−	2.73881i	0.0840666	−	0.476765i
$34$	0.315207	+	0.264490i	0.0540576	+	0.0453597i
$35$	−2.53209	+	2.12467i	−0.428001	+	0.359136i
$36$	0.800660			0.133443
$37$	−5.86097	+	1.62760i	−0.963537	+	0.267575i
$37$	−5.86097	+	1.62760i	−0.963537	+	0.267575i
$38$	0.716881			0.116294
$39$	−6.70961	+	5.63003i	−1.07440	+	0.901526i
$40$	1.91147	+	1.60392i	0.302231	+	0.253602i
$41$	0.0996702	−	0.565258i	0.0155659	−	0.0882785i	−0.976035	−	0.217613i	$-0.930173\pi$
$41$	0.0996702	−	0.565258i	0.0155659	−	0.0882785i	0.991601	+	0.129334i	$0.0412841\pi$
$42$	4.75877	−	1.73205i	0.734294	−	0.267261i
$43$	−4.87939			−0.744099			−0.372050	−	0.928213i	$-0.621345\pi$
$43$	−4.87939			−0.744099			−0.372050	+	0.928213i	$0.621345\pi$
$44$	−2.09240	+	0.761570i	−0.315441	+	0.114811i
$45$	−0.286989	−	0.497079i	−0.0427818	−	0.0741002i
$46$	−0.916222	−	5.19615i	−0.135090	−	0.766131i
$47$	6.02481	−	10.4353i	0.878810	−	1.52214i	0.0261612	−	0.999658i	$-0.491672\pi$
$47$	6.02481	−	10.4353i	0.878810	−	1.52214i	0.852648	−	0.522485i	$-0.174995\pi$
$48$	−0.0320889	−	0.0555796i	−0.00463163	−	0.00802222i
$49$	5.46064	−	4.58202i	0.780091	−	0.654574i
$50$	−0.645430	+	3.66041i	−0.0912775	+	0.517661i
$51$	0.358441	−	0.620838i	0.0501917	−	0.0869346i
$52$	6.58987	+	2.39852i	0.913851	+	0.332614i
$53$	8.79086	+	3.19961i	1.20752	+	0.439500i	0.865842	−	0.500318i	$-0.166783\pi$
$53$	8.79086	+	3.19961i	1.20752	+	0.439500i	0.341675	+	0.939818i	$0.389006\pi$
$54$	0.854570	+	4.84651i	0.116292	+	0.659526i
$55$	1.22281	+	1.02606i	0.164884	+	0.138354i
$56$	−8.17024	−	6.85565i	−1.09179	−	0.916125i
$57$	−0.216881	−	1.23000i	−0.0287266	−	0.162917i
$58$	7.13816	+	2.59808i	0.937286	+	0.341144i
$59$	0.286989	+	0.104455i	0.0373628	+	0.0135989i	0.360634	−	0.932707i	$-0.382560\pi$
$59$	0.286989	+	0.104455i	0.0373628	+	0.0135989i	−0.323271	+	0.946306i	$0.604783\pi$
$60$	0.826352	−	1.43128i	0.106682	−	0.184778i
$61$	−0.560307	+	3.17766i	−0.0717400	+	0.406858i	0.927698	+	0.373332i	$0.121785\pi$
$61$	−0.560307	+	3.17766i	−0.0717400	+	0.406858i	−0.999438	+	0.0335259i	$0.989326\pi$
$62$	1.30928	−	1.09861i	0.166278	−	0.139524i
$63$	1.22668	+	2.12467i	0.154547	+	0.267684i
$64$	−2.52094	+	4.36640i	−0.315118	+	0.545801i
$65$	−0.872989	−	4.95096i	−0.108281	−	0.614092i
$66$	−1.22281	−	2.11797i	−0.150518	−	0.260704i
$67$	3.13176	−	1.13987i	0.382605	−	0.139257i	−0.143555	−	0.989642i	$-0.545853\pi$
$67$	3.13176	−	1.13987i	0.382605	−	0.139257i	0.526160	+	0.850385i	$0.323631\pi$
$68$	−0.573978			−0.0696051
$69$	−8.63816	+	3.14403i	−1.03991	+	0.378497i
$70$	−0.504748	+	2.86257i	−0.0603289	+	0.342142i
$71$	−10.7738	−	9.04028i	−1.27861	−	1.07288i	−0.993434	−	0.114410i	$-0.963502\pi$
$71$	−10.7738	−	9.04028i	−1.27861	−	1.07288i	−0.285179	−	0.958474i	$-0.592053\pi$
$72$	1.41875	−	1.19047i	0.167201	−	0.140298i
$73$	−4.24897			−0.497304			−0.248652	−	0.968593i	$-0.579988\pi$
$73$	−4.24897			−0.497304			−0.248652	+	0.968593i	$0.579988\pi$
$74$	−3.02822	+	4.40938i	−0.352023	+	0.512581i
$75$	6.47565			0.747744
$76$	−0.766044	+	0.642788i	−0.0878713	+	0.0737328i
$77$	−5.22668	−	4.38571i	−0.595636	−	0.499798i
$78$	−1.33750	+	7.58532i	−0.151442	+	0.858868i
$79$	3.01367	−	1.09689i	0.339064	−	0.123409i	−0.166876	−	0.985978i	$-0.553368\pi$
$79$	3.01367	−	1.09689i	0.339064	−	0.123409i	0.505940	+	0.862569i	$0.331146\pi$
$80$	0.0368366			0.00411846
$81$	6.21688	−	2.26276i	0.690765	−	0.251418i
$82$	−0.252374	−	0.437124i	−0.0278700	−	0.0482723i
$83$	0.888003	+	5.03612i	0.0974710	+	0.552786i	0.993962	+	0.109724i	$0.0349967\pi$
$83$	0.888003	+	5.03612i	0.0974710	+	0.552786i	−0.896491	+	0.443062i	$0.853892\pi$
$84$	−3.53209	+	6.11776i	−0.385382	+	0.667502i
$85$	0.205737	+	0.356347i	0.0223153	+	0.0386513i
$86$	−3.28699	+	2.75811i	−0.354445	+	0.297415i
$87$	2.29813	−	13.0334i	0.246386	−	1.39732i
$88$	−2.57532	+	4.46059i	−0.274530	+	0.475500i
$89$	−10.0569	−	3.66041i	−1.06603	−	0.388003i	−0.251339	−	0.967899i	$-0.580871\pi$
$89$	−10.0569	−	3.66041i	−1.06603	−	0.388003i	−0.814691	+	0.579896i	$0.803093\pi$
$90$	−0.474308	−	0.172634i	−0.0499964	−	0.0181972i
$91$	3.73143	+	21.1620i	0.391160	+	2.21838i
$92$	5.63816	+	4.73097i	0.587818	+	0.493238i
$93$	−2.28106	−	1.91404i	−0.236535	−	0.198476i
$94$	−1.84002	−	10.4353i	−0.189784	−	1.07632i
$95$	0.673648	+	0.245188i	0.0691148	+	0.0251557i
$96$	8.11721	+	2.95442i	0.828459	+	0.301535i
$97$	−4.74510	+	8.21875i	−0.481792	+	0.834488i	−0.999782	−	0.0208988i	$-0.993347\pi$
$97$	−4.74510	+	8.21875i	−0.481792	+	0.834488i	0.517990	+	0.855387i	$0.326681\pi$
$98$	1.08853	−	6.17334i	0.109958	−	0.623601i
$99$	0.907604	−	0.761570i	0.0912176	−	0.0765407i
$100$	−2.59240	−	4.49016i	−0.259240	−	0.449016i
$101$	6.20574	−	10.7487i	0.617494	−	1.06953i	−0.372448	−	0.928053i	$-0.621481\pi$
$101$	6.20574	−	10.7487i	0.617494	−	1.06953i	0.989941	−	0.141478i	$-0.0451853\pi$
$102$	−0.109470	−	0.620838i	−0.0108392	−	0.0614721i
$103$	−3.75624	−	6.50601i	−0.370114	−	0.641056i	0.619469	−	0.785021i	$-0.287348\pi$
$103$	−3.75624	−	6.50601i	−0.370114	−	0.641056i	−0.989583	+	0.143965i	$0.954015\pi$
$104$	15.2433	−	5.54812i	1.49473	−	0.544038i
$105$	5.06418			0.494213
$106$	7.73055	−	2.81369i	0.750858	−	0.273290i
$107$	−1.19459	+	6.77487i	−0.115486	+	0.654952i	0.871023	+	0.491242i	$0.163457\pi$
$107$	−1.19459	+	6.77487i	−0.115486	+	0.654952i	−0.986509	+	0.163709i	$0.947654\pi$
$108$	−5.25877	−	4.41263i	−0.506025	−	0.424606i
$109$	−0.532089	+	0.446476i	−0.0509649	+	0.0427646i	−0.667914	−	0.744238i	$-0.732813\pi$
$109$	−0.532089	+	0.446476i	−0.0509649	+	0.0427646i	0.616949	+	0.787003i	$0.288368\pi$
$110$	1.40373			0.133841
$111$	8.48158	+	3.86170i	0.805036	+	0.366536i
$112$	−0.157451			−0.0148778
$113$	−3.86437	+	3.24259i	−0.363529	+	0.305037i	−0.806196	−	0.591649i	$-0.798477\pi$
$113$	−3.86437	+	3.24259i	−0.363529	+	0.305037i	0.442666	+	0.896686i	$0.354033\pi$
$114$	−0.841367	−	0.705990i	−0.0788012	−	0.0661221i
$115$	0.916222	−	5.19615i	0.0854381	−	0.484544i
$116$	−9.95723	+	3.62414i	−0.924506	+	0.336493i
$117$	−3.73143			−0.344971
$118$	0.252374	−	0.0918566i	0.0232329	−	0.00845608i
$119$	−0.879385	−	1.52314i	−0.0806131	−	0.139626i
$120$	−0.663848	−	3.76487i	−0.0606008	−	0.343684i
$121$	3.85251	−	6.67274i	0.350228	−	0.606613i
$122$	1.41875	+	2.45734i	0.128447	+	0.222477i
$123$	−0.673648	+	0.565258i	−0.0607408	+	0.0509676i
$124$	−0.414000	+	2.34791i	−0.0371783	+	0.210849i
$125$	−4.05690	+	7.02676i	−0.362861	+	0.628493i
$126$	2.02734	+	0.737892i	0.180610	+	0.0657366i
$127$	2.44609	+	0.890304i	0.217055	+	0.0790017i	0.448259	−	0.893904i	$-0.352044\pi$
$127$	2.44609	+	0.890304i	0.217055	+	0.0790017i	−0.231204	+	0.972905i	$0.574266\pi$
$128$	−1.18820	−	6.73859i	−0.105023	−	0.595613i
$129$	5.72668	+	4.80526i	0.504206	+	0.423079i
$130$	−3.38666	−	2.84174i	−0.297030	−	0.249237i
$131$	0.648833	+	3.67972i	0.0566888	+	0.321498i	0.999944	−	0.0105701i	$-0.00336463\pi$
$131$	0.648833	+	3.67972i	0.0566888	+	0.321498i	−0.943255	+	0.332068i	$0.892254\pi$
$132$	3.20574	+	1.16679i	0.279024	+	0.101556i
$133$	−2.87939	−	1.04801i	−0.249674	−	0.0908740i
$134$	1.46538	−	2.53812i	0.126590	−	0.219260i
$135$	−0.854570	+	4.84651i	−0.0735497	+	0.417121i
$136$	−1.01707	+	0.853427i	−0.0872134	+	0.0731807i
$137$	3.72668	+	6.45480i	0.318392	+	0.551471i	0.980153	−	0.198244i	$-0.0635239\pi$
$137$	3.72668	+	6.45480i	0.318392	+	0.551471i	−0.661761	+	0.749715i	$0.730191\pi$
$138$	−4.04189	+	7.00076i	−0.344068	+	0.595944i
$139$	0.178396	+	1.01173i	0.0151313	+	0.0858141i	0.991438	−	0.130576i	$-0.0416827\pi$
$139$	0.178396	+	1.01173i	0.0151313	+	0.0858141i	−0.976307	+	0.216390i	$0.930572\pi$
$140$	−2.02734	−	3.51146i	−0.171342	−	0.296772i
$141$	−17.3478	+	6.31407i	−1.46095	+	0.531741i
$142$	−12.3678			−1.03789
$143$	9.75150	−	3.54925i	0.815461	−	0.296804i
$144$	0.00474774	−	0.0269258i	0.000395645	−	0.00224381i
$145$	5.81908	+	4.88279i	0.483248	+	0.405493i
$146$	−2.86231	+	2.40176i	−0.236887	+	0.198771i
$147$	−10.9213			−0.900772
$148$	−0.717759	−	7.42701i	−0.0589994	−	0.610497i
$149$	10.5030			0.860439			0.430219	−	0.902724i	$-0.358436\pi$
$149$	10.5030			0.860439			0.430219	+	0.902724i	$0.358436\pi$
$150$	4.36231	−	3.66041i	0.356181	−	0.298872i
$151$	3.26604	+	2.74054i	0.265787	+	0.223022i	0.765935	−	0.642918i	$-0.222277\pi$
$151$	3.26604	+	2.74054i	0.265787	+	0.223022i	−0.500148	+	0.865940i	$0.666721\pi$
$152$	−0.401674	+	2.27801i	−0.0325801	+	0.184771i
$153$	0.286989	−	0.104455i	0.0232017	−	0.00844472i
$154$	−6.00000			−0.483494
$155$	1.60607	−	0.584561i	0.129002	−	0.0469530i
$156$	−5.37211	−	9.30477i	−0.430113	−	0.744978i
$157$	−1.75490	−	9.95253i	−0.140056	−	0.794299i	−0.971204	−	0.238248i	$-0.923427\pi$
$157$	−1.75490	−	9.95253i	−0.140056	−	0.794299i	0.831148	−	0.556051i	$-0.187684\pi$
$158$	1.41013	−	2.44242i	0.112184	−	0.194308i
$159$	−7.16637	−	12.4125i	−0.568330	−	0.984377i
$160$	−3.79813	+	3.18701i	−0.300269	+	0.251955i
$161$	−3.91622	+	22.2100i	−0.308642	+	1.75039i
$162$	2.90895	−	5.03845i	0.228549	−	0.395858i
$163$	11.4893	+	4.18177i	0.899913	+	0.327542i	0.750218	−	0.661191i	$-0.229949\pi$
$163$	11.4893	+	4.18177i	0.899913	+	0.327542i	0.149695	+	0.988732i	$0.452171\pi$
$164$	0.661626	+	0.240812i	0.0516643	+	0.0188043i
$165$	−0.424678	−	2.40847i	−0.0330611	−	0.187499i
$166$	3.44491	+	2.89062i	0.267377	+	0.224356i
$167$	7.68732	+	6.45043i	0.594863	+	0.499149i	0.889790	−	0.456371i	$-0.150851\pi$
$167$	7.68732	+	6.45043i	0.594863	+	0.499149i	−0.294927	+	0.955520i	$0.595295\pi$
$168$	2.83750	+	16.0922i	0.218918	+	1.24154i
$169$	−18.4957	−	6.73189i	−1.42275	−	0.517838i
$170$	0.340022	+	0.123758i	0.0260785	+	0.00949181i
$171$	0.266044	−	0.460802i	0.0203449	−	0.0352384i
$172$	1.03936	−	5.89452i	0.0792507	−	0.449453i
$173$	−11.5437	+	9.68631i	−0.877651	+	0.736437i	−0.965695	−	0.259680i	$-0.916383\pi$
$173$	−11.5437	+	9.68631i	−0.877651	+	0.736437i	0.0880435	+	0.996117i	$0.471939\pi$
$174$	−5.81908	−	10.0789i	−0.441143	−	0.764082i
$175$	7.94356	−	13.7587i	0.600477	−	1.04006i
$176$	0.0132037	+	0.0748822i	0.000995270	+	0.00564446i
$177$	−0.233956	−	0.405223i	−0.0175852	−	0.0304584i
$178$	−8.84389	+	3.21891i	−0.662878	+	0.241268i
$179$	16.1411			1.20645			0.603223	−	0.797573i	$-0.293883\pi$
$179$	16.1411			1.20645			0.603223	+	0.797573i	$0.293883\pi$
$180$	0.661626	−	0.240812i	0.0493147	−	0.0179491i
$181$	3.36690	−	19.0946i	0.250259	−	1.41929i	−0.557694	−	0.830046i	$-0.688314\pi$
$181$	3.36690	−	19.0946i	0.250259	−	1.41929i	0.807954	−	0.589246i	$-0.200575\pi$
$182$	14.4757	+	12.1465i	1.07301	+	0.900360i
$183$	3.78699	−	3.17766i	0.279942	−	0.234899i
$184$	17.0250			1.25510
$185$	−4.35369	+	3.10775i	−0.320090	+	0.228487i
$186$	−2.61856			−0.192002
$187$	−0.650644	+	0.545955i	−0.0475798	+	0.0399242i
$188$	11.3229	+	9.50108i	0.825811	+	0.692938i
$189$	3.65270	−	20.7155i	0.265695	−	1.50683i
$190$	0.592396	−	0.215615i	0.0429769	−	0.0156423i
$191$	11.5885			0.838516			0.419258	−	0.907867i	$-0.362290\pi$
$191$	11.5885			0.838516			0.419258	+	0.907867i	$0.362290\pi$
$192$	7.25877	−	2.64198i	0.523857	−	0.190668i
$193$	3.73396	+	6.46740i	0.268776	+	0.465534i	0.968546	−	0.248835i	$-0.0800475\pi$
$193$	3.73396	+	6.46740i	0.268776	+	0.465534i	−0.699770	+	0.714368i	$0.746714\pi$
$194$	1.44919	+	8.21875i	0.104046	+	0.590072i
$195$	−3.85117	+	6.67042i	−0.275788	+	0.477678i
$196$	4.37211	+	7.57272i	0.312294	+	0.540908i
$197$	7.49660	−	6.29039i	0.534110	−	0.448172i	−0.335408	−	0.942073i	$-0.608874\pi$
$197$	7.49660	−	6.29039i	0.534110	−	0.448172i	0.869518	+	0.493901i	$0.164430\pi$
$198$	0.180922	−	1.02606i	0.0128576	−	0.0729189i
$199$	−0.148833	+	0.257787i	−0.0105505	+	0.0182740i	−0.871252	−	0.490835i	$-0.836692\pi$
$199$	−0.148833	+	0.257787i	−0.0105505	+	0.0182740i	0.860702	+	0.509109i	$0.170025\pi$
$200$	−11.2699	−	4.10191i	−0.796903	−	0.290049i
$201$	−4.79813	−	1.74638i	−0.338434	−	0.123180i
$202$	−1.89528	−	10.7487i	−0.133351	−	0.756273i
$203$	−24.8726	−	20.8706i	−1.74571	−	1.46483i
$204$	0.673648	+	0.565258i	0.0471648	+	0.0395760i
$205$	−0.0876485	−	0.497079i	−0.00612164	−	0.0347175i
$206$	−6.20796	−	2.25951i	−0.432529	−	0.157428i
$207$	−3.68004	−	1.33943i	−0.255781	−	0.0930966i
$208$	0.119737	−	0.207391i	0.00830230	−	0.0143800i
$209$	−0.256959	+	1.45729i	−0.0177743	+	0.100803i
$210$	3.41147	−	2.86257i	0.235414	−	0.197536i
$211$	4.94356	+	8.56250i	0.340329	+	0.589467i	0.984494	−	0.175420i	$-0.0561283\pi$
$211$	4.94356	+	8.56250i	0.340329	+	0.589467i	−0.644165	+	0.764887i	$0.722795\pi$
$212$	−5.73783	+	9.93821i	−0.394076	+	0.682559i
$213$	3.74170	+	21.2202i	0.256377	+	1.45399i
$214$	3.02481	+	5.23913i	0.206772	+	0.358140i
$215$	−4.03209	+	1.46756i	−0.274986	+	0.100087i
$216$	−15.8794			−1.08046
$217$	−6.86484	+	2.49860i	−0.466016	+	0.169616i
$218$	−0.106067	+	0.601535i	−0.00718375	+	0.0407411i
$219$	4.98680	+	4.18442i	0.336976	+	0.282757i
$220$	−1.50000	+	1.25865i	−0.101130	+	0.0848581i
$221$	2.67499			0.179939
$222$	7.89646	−	2.19285i	0.529976	−	0.147175i
$223$	−27.3824			−1.83366			−0.916830	−	0.399278i	$-0.869261\pi$
$223$	−27.3824			−1.83366			−0.916830	+	0.399278i	$0.869261\pi$
$224$	16.2344	−	13.6223i	1.08471	−	0.910178i
$225$	2.11334	+	1.77330i	0.140889	+	0.118220i
$226$	−0.770325	+	4.36873i	−0.0512413	+	0.290604i
$227$	−16.2690	+	5.92145i	−1.07981	+	0.393020i	−0.819838	−	0.572595i	$-0.805937\pi$
$227$	−16.2690	+	5.92145i	−1.07981	+	0.393020i	−0.259976	+	0.965615i	$0.583715\pi$
$228$	1.53209			0.101465
$229$	−8.51501	+	3.09921i	−0.562688	+	0.204802i	−0.607675	−	0.794186i	$-0.707898\pi$
$229$	−8.51501	+	3.09921i	−0.562688	+	0.204802i	0.0449869	+	0.998988i	$0.485675\pi$
$230$	−2.31996	−	4.01828i	−0.152973	−	0.264958i
$231$	1.81521	+	10.2946i	0.119432	+	0.677332i
$232$	−12.2554	+	21.2269i	−0.804604	+	1.39362i
$233$	−1.31908	−	2.28471i	−0.0864157	−	0.149676i	0.819578	−	0.572968i	$-0.194208\pi$
$233$	−1.31908	−	2.28471i	−0.0864157	−	0.149676i	−0.905994	+	0.423291i	$0.860875\pi$
$234$	−2.51367	+	2.10922i	−0.164324	+	0.137884i
$235$	1.84002	−	10.4353i	0.120030	−	0.680723i
$236$	−0.187319	+	0.324446i	−0.0121934	+	0.0211196i
$237$	−4.61721	−	1.68053i	−0.299920	−	0.109162i
$238$	−1.45336	−	0.528981i	−0.0942075	−	0.0342887i
$239$	−3.43107	−	19.4586i	−0.221938	−	1.25867i	−0.868453	−	0.495771i	$-0.834886\pi$
$239$	−3.43107	−	19.4586i	−0.221938	−	1.25867i	0.646516	−	0.762901i	$-0.276226\pi$
$240$	−0.0432332	−	0.0362770i	−0.00279069	−	0.00234167i
$241$	15.0587	+	12.6358i	0.970017	+	0.813941i	0.982553	−	0.185980i	$-0.0595461\pi$
$241$	15.0587	+	12.6358i	0.970017	+	0.813941i	−0.0125364	+	0.999921i	$0.503991\pi$
$242$	−1.17658	−	6.67274i	−0.0756337	−	0.428940i
$243$	6.25150	+	2.27536i	0.401034	+	0.145964i
$244$	−3.71941	−	1.35375i	−0.238111	−	0.0866652i
$245$	3.13429	−	5.42874i	0.200242	−	0.346830i
$246$	−0.134285	+	0.761570i	−0.00856172	+	0.0485559i
$247$	3.57011	−	2.99568i	0.227161	−	0.190610i
$248$	2.75743	+	4.77600i	0.175097	+	0.303276i
$249$	3.91740	−	6.78514i	0.248255	−	0.429991i
$250$	1.23901	+	7.02676i	0.0783617	+	0.444412i
$251$	−5.98680	−	10.3694i	−0.377883	−	0.654513i	0.612871	−	0.790183i	$-0.290015\pi$
$251$	−5.98680	−	10.3694i	−0.377883	−	0.654513i	−0.990754	+	0.135670i	$0.956681\pi$
$252$	−2.82800	+	1.02931i	−0.178147	+	0.0648403i
$253$	10.8912			0.684727
$254$	2.15105	−	0.782920i	0.134969	−	0.0491248i
$255$	0.109470	−	0.620838i	0.00685530	−	0.0388784i
$256$	−12.3341	−	10.3495i	−0.770881	−	0.646846i
$257$	10.7023	−	8.98032i	0.667593	−	0.560177i	−0.244759	−	0.969584i	$-0.578709\pi$
$257$	10.7023	−	8.98032i	0.667593	−	0.560177i	0.912352	+	0.409407i	$0.134264\pi$
$258$	6.57398			0.409278
$259$	18.6091	−	13.2835i	1.15631	−	0.825398i
$260$	6.16695			0.382458
$261$	4.31908	−	3.62414i	0.267344	−	0.224328i
$262$	2.51707	+	2.11208i	0.155505	+	0.130484i
$263$	−3.48411	+	19.7594i	−0.214839	+	1.21841i	0.666346	+	0.745643i	$0.267857\pi$
$263$	−3.48411	+	19.7594i	−0.214839	+	1.21841i	−0.881185	+	0.472771i	$0.843254\pi$
$264$	7.41534	−	2.69896i	0.456383	−	0.166110i
$265$	8.22668			0.505361
$266$	−2.53209	+	0.921605i	−0.155252	+	0.0565072i
$267$	8.19846	+	14.2002i	0.501738	+	0.869035i
$268$	0.709912	+	4.02611i	0.0433648	+	0.245934i
$269$	−3.89440	+	6.74530i	−0.237446	+	0.411268i	−0.959981	−	0.280066i	$-0.909644\pi$
$269$	−3.89440	+	6.74530i	−0.237446	+	0.411268i	0.722535	+	0.691334i	$0.242977\pi$
$270$	2.16385	+	3.74789i	0.131688	+	0.228090i
$271$	−22.5273	+	18.9027i	−1.36844	+	1.14826i	−0.395164	+	0.918610i	$0.629312\pi$
$271$	−22.5273	+	18.9027i	−1.36844	+	1.14826i	−0.973274	+	0.229646i	$0.926243\pi$
$272$	−0.00340357	+	0.0193026i	−0.000206372	+	0.00117039i
$273$	16.4611	−	28.5115i	0.996271	−	1.72559i
$274$	6.15910	+	2.24173i	0.372085	+	0.135428i
$275$	−7.20961	−	2.62408i	−0.434756	−	0.158238i
$276$	−1.95811	−	11.1050i	−0.117864	−	0.668442i
$277$	−8.19459	−	6.87608i	−0.492365	−	0.413144i	0.362508	−	0.931981i	$-0.381921\pi$
$277$	−8.19459	−	6.87608i	−0.492365	−	0.413144i	−0.854873	+	0.518837i	$0.826365\pi$
$278$	0.692066	+	0.580713i	0.0415074	+	0.0348288i
$279$	−0.220285	−	1.24930i	−0.0131881	−	0.0747935i
$280$	−8.81345	−	3.20783i	−0.526705	−	0.191705i
$281$	−7.83022	−	2.84997i	−0.467112	−	0.170015i	0.0977317	−	0.995213i	$-0.468841\pi$
$281$	−7.83022	−	2.84997i	−0.467112	−	0.170015i	−0.564844	+	0.825198i	$0.691064\pi$
$282$	−8.11721	+	14.0594i	−0.483373	+	0.837226i
$283$	−3.90554	+	22.1494i	−0.232161	+	1.31665i	0.616351	+	0.787471i	$0.288610\pi$
$283$	−3.90554	+	22.1494i	−0.232161	+	1.31665i	−0.848512	+	0.529176i	$0.822501\pi$
$284$	13.2160	−	11.0895i	0.784226	−	0.658043i
$285$	−0.549163	−	0.951178i	−0.0325296	−	0.0563429i
$286$	4.56283	−	7.90306i	0.269806	−	0.467318i
$287$	0.374638	+	2.12467i	0.0221142	+	0.125416i
$288$	1.84002	+	3.18701i	0.108424	+	0.187796i
$289$	15.7690	−	5.73946i	0.927590	−	0.337615i
$290$	6.68004			0.392266
$291$	13.6630	−	4.97291i	0.800938	−	0.291517i
$292$	0.905078	−	5.13295i	0.0529657	−	0.300383i
$293$	16.8666	+	14.1528i	0.985360	+	0.826815i	0.984889	−	0.173185i	$-0.0554057\pi$
$293$	16.8666	+	14.1528i	0.985360	+	0.826815i	0.000470731		1.00000i	$0.499850\pi$
$294$	−7.35710	+	6.17334i	−0.429075	+	0.360036i
$295$	0.268571			0.0156368
$296$	−12.3148	−	12.0933i	−0.715783	−	0.702907i
$297$	−10.1584			−0.589449
$298$	7.07532	−	5.93690i	0.409862	−	0.343915i
$299$	−26.2763	−	22.0484i	−1.51960	−	1.27509i
$300$	−1.37939	+	7.82288i	−0.0796388	+	0.451654i
$301$	17.2344	−	6.27282i	0.993376	−	0.361559i
$302$	3.74928			0.215747
$303$	−17.8687	+	6.50368i	−1.02653	+	0.373627i
$304$	0.0170741	+	0.0295733i	0.000979269	+	0.00169614i
$305$	0.492726	+	2.79439i	0.0282134	+	0.160006i
$306$	0.134285	−	0.232589i	0.00767658	−	0.0132962i
$307$	2.59879	+	4.50124i	0.148321	+	0.256899i	0.930607	−	0.366020i	$-0.119280\pi$
$307$	2.59879	+	4.50124i	0.148321	+	0.256899i	−0.782286	+	0.622919i	$0.785946\pi$
$308$	6.41147	−	5.37987i	0.365328	−	0.306546i
$309$	−1.99866	+	11.3349i	−0.113700	+	0.644822i
$310$	0.751497	−	1.30163i	0.0426821	−	0.0739276i
$311$	−7.32547	−	2.66625i	−0.415390	−	0.151189i	0.125867	−	0.992047i	$-0.459829\pi$
$311$	−7.32547	−	2.66625i	−0.415390	−	0.151189i	−0.541256	+	0.840858i	$0.682051\pi$
$312$	−23.3542	−	8.50022i	−1.32217	−	0.481230i
$313$	−2.53983	−	14.4041i	−0.143560	−	0.814167i	−0.968512	−	0.248966i	$-0.919909\pi$
$313$	−2.53983	−	14.4041i	−0.143560	−	0.814167i	0.824953	−	0.565202i	$-0.191202\pi$
$314$	−6.80793	−	5.71253i	−0.384194	−	0.322377i
$315$	1.65270	+	1.38678i	0.0931193	+	0.0781364i
$316$	0.683144	+	3.87430i	0.0384298	+	0.217946i
$317$	−14.3922	−	5.23832i	−0.808345	−	0.294214i	−0.0954051	−	0.995439i	$-0.530415\pi$
$317$	−14.3922	−	5.23832i	−0.808345	−	0.294214i	−0.712940	+	0.701225i	$0.752637\pi$
$318$	−11.8439	−	4.31082i	−0.664173	−	0.241739i
$319$	−7.84002	+	13.5793i	−0.438957	+	0.760296i
$320$	−0.769915	+	4.36640i	−0.0430395	+	0.244089i
$321$	8.07398	−	6.77487i	0.450646	−	0.378136i
$322$	9.91622	+	17.1754i	0.552609	+	0.957148i
$323$	−0.190722	+	0.330341i	−0.0106121	+	0.0183807i
$324$	1.40925	+	7.99227i	0.0782918	+	0.444015i
$325$	12.0817	+	20.9262i	0.670173	+	1.16077i
$326$	10.1035	−	3.67739i	0.559583	−	0.203672i
$327$	1.06418			0.0588492
$328$	1.53044	−	0.557035i	0.0845044	−	0.0307571i
$329$	−7.86484	+	44.6037i	−0.433603	+	2.45908i
$330$	−1.64749	−	1.38241i	−0.0906913	−	0.0760990i
$331$	0.568048	−	0.476649i	0.0312228	−	0.0261990i	−0.627043	−	0.778985i	$-0.715735\pi$
$331$	0.568048	−	0.476649i	0.0312228	−	0.0261990i	0.658265	+	0.752786i	$0.271290\pi$
$332$	−6.27301			−0.344276
$333$	1.71048	+	3.58288i	0.0937340	+	0.196341i
$334$	8.82470			0.482866
$335$	2.24510	−	1.88386i	0.122663	−	0.102926i
$336$	0.184793	+	0.155059i	0.0100813	+	0.00845918i
$337$	3.31567	−	18.8041i	0.180616	−	1.02433i	−0.750843	−	0.660481i	$-0.770353\pi$
$337$	3.31567	−	18.8041i	0.180616	−	1.02433i	0.931459	−	0.363845i	$-0.118536\pi$
$338$	−16.2649	+	5.91993i	−0.884692	+	0.322002i
$339$	7.72874			0.419768
$340$	−0.474308	+	0.172634i	−0.0257229	+	0.00936239i
$341$	1.76399	+	3.05531i	0.0955251	+	0.165454i
$342$	−0.0812519	−	0.460802i	−0.00439360	−	0.0249173i
$343$	−0.241230	+	0.417822i	−0.0130252	+	0.0225603i
$344$	−6.92262	−	11.9903i	−0.373243	−	0.646475i
$345$	−6.19253	+	5.19615i	−0.333395	+	0.279751i
$346$	−2.30113	+	13.0503i	−0.123709	+	0.701590i
$347$	2.68479	−	4.65020i	0.144127	−	0.249636i	−0.784920	−	0.619597i	$-0.787296\pi$
$347$	2.68479	−	4.65020i	0.144127	−	0.249636i	0.929047	+	0.369962i	$0.120629\pi$
$348$	15.2554	+	5.55250i	0.817774	+	0.297645i
$349$	−21.9996	−	8.00720i	−1.17761	−	0.428615i	−0.322253	−	0.946653i	$-0.604440\pi$
$349$	−21.9996	−	8.00720i	−1.17761	−	0.428615i	−0.855358	+	0.518038i	$0.826663\pi$
$350$	−2.42602	−	13.7587i	−0.129676	−	0.735431i
$351$	24.5082	+	20.5648i	1.30815	+	1.09767i
$352$	−7.84002	−	6.57856i	−0.417875	−	0.350638i
$353$	−0.532966	−	3.02260i	−0.0283669	−	0.160877i	0.967334	−	0.253506i	$-0.0815839\pi$
$353$	−0.532966	−	3.02260i	−0.0283669	−	0.160877i	−0.995701	+	0.0926295i	$0.970473\pi$
$354$	−0.386659	−	0.140732i	−0.0205507	−	0.00747984i
$355$	−11.6220	−	4.23005i	−0.616830	−	0.224508i
$356$	6.56418	−	11.3695i	0.347901	−	0.602582i
$357$	−0.467911	+	2.65366i	−0.0247645	+	0.140446i
$358$	10.8735	−	9.12391i	0.574680	−	0.482214i
$359$	3.70187	+	6.41182i	0.195377	+	0.338403i	0.947024	−	0.321163i	$-0.104074\pi$
$359$	3.70187	+	6.41182i	0.195377	+	0.338403i	−0.751647	+	0.659566i	$0.770740\pi$
$360$	0.814330	−	1.41046i	0.0429190	−	0.0743378i
$361$	−3.18392	−	18.0569i	−0.167574	−	0.950362i
$362$	−8.52528	−	14.7662i	−0.448079	−	0.776095i
$363$	−11.0929	+	4.03747i	−0.582224	+	0.211912i
$364$	−26.3595			−1.38161
$365$	−3.51114	+	1.27795i	−0.183782	+	0.0668911i
$366$	0.754900	−	4.28125i	0.0394593	−	0.223785i
$367$	8.34524	+	7.00249i	0.435618	+	0.365527i	0.834067	−	0.551664i	$-0.186007\pi$
$367$	8.34524	+	7.00249i	0.435618	+	0.365527i	−0.398449	+	0.917191i	$0.630451\pi$
$368$	0.192533	−	0.161555i	0.0100365	−	0.00842162i
$369$	−0.374638			−0.0195028
$370$	−1.17617	+	4.55449i	−0.0611464	+	0.236777i
$371$	−35.1634			−1.82559
$372$	2.79813	−	2.34791i	0.145076	−	0.121734i
$373$	21.1930	+	17.7830i	1.09733	+	0.920771i	0.997243	−	0.0742076i	$-0.0236428\pi$
$373$	21.1930	+	17.7830i	1.09733	+	0.920771i	0.100089	+	0.994978i	$0.468087\pi$
$374$	−0.129700	+	0.735564i	−0.00670661	+	0.0380351i
$375$	11.6814	−	4.25168i	0.603224	−	0.219556i
$376$	34.1908			1.76325
$377$	46.4051	−	16.8901i	2.38999	−	0.869884i
$378$	−9.24897	−	16.0197i	−0.475716	−	0.823964i
$379$	−1.11468	−	6.32169i	−0.0572575	−	0.324724i	0.942703	−	0.333634i	$-0.108275\pi$
$379$	−1.11468	−	6.32169i	−0.0572575	−	0.324724i	−0.999960	+	0.00891019i	$0.997164\pi$
$380$	−0.439693	+	0.761570i	−0.0225558	+	0.0390677i
$381$	−1.99407	−	3.45383i	−0.102159	−	0.176945i
$382$	7.80659	−	6.55051i	0.399420	−	0.335153i
$383$	2.30154	−	13.0527i	0.117603	−	0.666960i	−0.867825	−	0.496869i	$-0.834483\pi$
$383$	2.30154	−	13.0527i	0.117603	−	0.666960i	0.985428	−	0.170091i	$-0.0544061\pi$
$384$	−5.24170	+	9.07888i	−0.267489	+	0.463305i
$385$	−5.63816	−	2.05212i	−0.287347	−	0.104586i
$386$	6.17112	+	2.24610i	0.314102	+	0.114324i
$387$	0.553033	+	3.13641i	0.0281123	+	0.159433i
$388$	−8.91787	−	7.48298i	−0.452736	−	0.379891i
$389$	24.1407	+	20.2564i	1.22398	+	1.02704i	0.998607	+	0.0527699i	$0.0168050\pi$
$389$	24.1407	+	20.2564i	1.22398	+	1.02704i	0.225374	+	0.974272i	$0.427639\pi$
$390$	1.17617	+	6.67042i	0.0595579	+	0.337770i
$391$	2.63816	+	0.960210i	0.133417	+	0.0485599i
$392$	19.0069	+	6.91793i	0.959992	+	0.349408i
$393$	2.86231	−	4.95767i	0.144384	−	0.250081i
$394$	1.49437	−	8.47502i	0.0752855	−	0.426965i
$395$	2.16044	−	1.81283i	0.108704	−	0.0912133i
$396$	0.726682	+	1.25865i	0.0365171	+	0.0632495i
$397$	−4.51455	+	7.81943i	−0.226579	+	0.392446i	−0.956792	−	0.290774i	$-0.906087\pi$
$397$	−4.51455	+	7.81943i	−0.226579	+	0.392446i	0.730213	+	0.683219i	$0.239421\pi$
$398$	0.0454548	+	0.257787i	0.00227844	+	0.0129217i
$399$	2.34730	+	4.06564i	0.117512	+	0.203536i
$400$	−0.166374	+	0.0605553i	−0.00831871	+	0.00302776i
$401$	−19.6955			−0.983548			−0.491774	−	0.870723i	$-0.663651\pi$
$401$	−19.6955			−0.983548			−0.491774	+	0.870723i	$0.663651\pi$
$402$	−4.21941	+	1.53574i	−0.210445	+	0.0765957i
$403$	1.92943	−	10.9423i	0.0961115	−	0.545076i
$404$	11.6630	+	9.78639i	0.580254	+	0.486891i
$405$	4.45677	−	3.73967i	0.221459	−	0.185826i
$406$	−28.5526			−1.41704
$407$	−7.87804	−	7.73632i	−0.390500	−	0.383475i
$408$	2.03415			0.100705
$409$	−25.7199	+	21.5815i	−1.27177	+	1.06714i	−0.277442	+	0.960742i	$0.589487\pi$
$409$	−25.7199	+	21.5815i	−1.27177	+	1.06714i	−0.994324	+	0.106396i	$0.966069\pi$
$410$	−0.340022	−	0.285313i	−0.0167925	−	0.0140906i
$411$	1.98293	−	11.2457i	0.0978105	−	0.554711i
$412$	8.65967	−	3.15186i	0.426631	−	0.155281i
$413$	−1.14796			−0.0564872
$414$	−3.23618	+	1.17787i	−0.159049	+	0.0578893i
$415$	2.24850	+	3.89452i	0.110375	+	0.191175i
$416$	5.59714	+	31.7430i	0.274423	+	1.55633i
$417$	0.786989	−	1.36310i	0.0385390	−	0.0667515i
$418$	0.650644	+	1.12695i	0.0318241	+	0.0551209i
$419$	7.99273	−	6.70669i	0.390470	−	0.327643i	−0.426326	−	0.904570i	$-0.640192\pi$
$419$	7.99273	−	6.70669i	0.390470	−	0.327643i	0.816796	+	0.576926i	$0.195748\pi$
$420$	−1.07873	+	6.11776i	−0.0526364	+	0.298516i
$421$	15.0535	−	26.0734i	0.733663	−	1.27074i	−0.221645	−	0.975127i	$-0.571143\pi$
$421$	15.0535	−	26.0734i	0.733663	−	1.27074i	0.955308	−	0.295614i	$-0.0955241\pi$
$422$	8.17024	+	2.97373i	0.397721	+	0.144759i
$423$	−7.39053	−	2.68993i	−0.359340	−	0.130789i
$424$	4.60947	+	26.1416i	0.223856	+	1.26955i
$425$	−1.51501	−	1.27125i	−0.0734890	−	0.0616646i
$426$	14.5155	+	12.1799i	0.703277	+	0.590120i
$427$	−2.10607	−	11.9441i	−0.101920	−	0.578015i
$428$	−7.92989	−	2.88624i	−0.383306	−	0.139512i
$429$	−14.9402	−	5.43777i	−0.721318	−	0.262538i
$430$	−1.88666	+	3.26779i	−0.0909828	+	0.157587i
$431$	−0.715699	+	4.05893i	−0.0344740	+	0.195512i	−0.997181	−	0.0750346i	$-0.976093\pi$
$431$	−0.715699	+	4.05893i	−0.0344740	+	0.195512i	0.962707	+	0.270547i	$0.0872044\pi$
$432$	−0.179578	+	0.150684i	−0.00863995	+	0.00724978i
$433$	−15.1172	−	26.1838i	−0.726487	−	1.25831i	−0.958359	−	0.285566i	$-0.907818\pi$
$433$	−15.1172	−	26.1838i	−0.726487	−	1.25831i	0.231872	−	0.972746i	$-0.425515\pi$
$434$	−3.21213	+	5.56358i	−0.154187	+	0.267060i
$435$	−2.02094	−	11.4613i	−0.0968969	−	0.549529i
$436$	−0.426022	−	0.737892i	−0.0204028	−	0.0353386i
$437$	4.59627	−	1.67290i	0.219869	−	0.0800259i
$438$	5.72462			0.273533
$439$	15.0881	−	5.49162i	0.720116	−	0.262101i	0.0441412	−	0.999025i	$-0.485945\pi$
$439$	15.0881	−	5.49162i	0.720116	−	0.262101i	0.675975	+	0.736924i	$0.263723\pi$
$440$	−0.786522	+	4.46059i	−0.0374960	+	0.212650i
$441$	−3.56418	−	2.99070i	−0.169723	−	0.142414i
$442$	1.80200	−	1.51206i	0.0857126	−	0.0719214i
$443$	3.34461			0.158907			0.0794536	−	0.996839i	$-0.474682\pi$
$443$	3.34461			0.158907			0.0794536	+	0.996839i	$0.474682\pi$
$444$	−6.47178	+	9.42355i	−0.307137	+	0.447222i
$445$	−9.41147			−0.446147
$446$	−18.4461	+	15.4781i	−0.873448	+	0.732910i
$447$	−12.3268	−	10.3434i	−0.583039	−	0.489227i
$448$	3.29086	−	18.6634i	0.155478	−	0.881762i
$449$	−34.3025	+	12.4851i	−1.61883	+	0.589207i	−0.983159	−	0.182750i	$-0.941500\pi$
$449$	−34.3025	+	12.4851i	−1.61883	+	0.589207i	−0.635674	+	0.771957i	$0.719278\pi$
$450$	2.42602			0.114364
$451$	0.979055	−	0.356347i	0.0461019	−	0.0167797i
$452$	−3.09405	−	5.35904i	−0.145532	−	0.252068i
$453$	−1.13429	−	6.43285i	−0.0532934	−	0.302242i
$454$	−7.61246	+	13.1852i	−0.357271	+	0.618811i
$455$	9.44831	+	16.3650i	0.442944	+	0.767201i
$456$	2.71482	−	2.27801i	0.127133	−	0.106677i
$457$	−4.68685	+	26.5805i	−0.219242	+	1.24338i	0.654151	+	0.756364i	$0.273026\pi$
$457$	−4.68685	+	26.5805i	−0.219242	+	1.24338i	−0.873392	+	0.487017i	$0.838085\pi$
$458$	−3.98427	+	6.90096i	−0.186173	+	0.322461i
$459$	−2.46064	−	0.895599i	−0.114853	−	0.0418030i
$460$	6.08202	+	2.21368i	0.283576	+	0.103213i
$461$	−1.04230	−	5.91117i	−0.0485447	−	0.275311i	0.950867	−	0.309599i	$-0.100195\pi$
$461$	−1.04230	−	5.91117i	−0.0485447	−	0.275311i	−0.999412	+	0.0342880i	$0.989084\pi$
$462$	7.04189	+	5.90885i	0.327618	+	0.274904i
$463$	−4.53596	−	3.80612i	−0.210804	−	0.176885i	0.531272	−	0.847201i	$-0.321714\pi$
$463$	−4.53596	−	3.80612i	−0.210804	−	0.176885i	−0.742076	+	0.670316i	$0.766159\pi$
$464$	0.0628336	+	0.356347i	0.00291698	+	0.0165430i
$465$	−2.46064	−	0.895599i	−0.114109	−	0.0415324i
$466$	−2.18004	−	0.793471i	−0.100989	−	0.0367569i
$467$	−3.25237	+	5.63328i	−0.150502	+	0.260677i	−0.931412	−	0.363966i	$-0.881422\pi$
$467$	−3.25237	+	5.63328i	−0.150502	+	0.260677i	0.780910	+	0.624643i	$0.214756\pi$
$468$	0.794836	−	4.50774i	0.0367413	−	0.208370i
$469$	−9.59627	+	8.05222i	−0.443114	+	0.371817i
$470$	−4.65910	−	8.06980i	−0.214908	−	0.372232i
$471$	−7.74170	+	13.4090i	−0.356719	+	0.617855i
$472$	0.150482	+	0.853427i	0.00692650	+	0.0392821i
$473$	−4.42855	−	7.67047i	−0.203625	−	0.352689i
$474$	−4.06031	+	1.47783i	−0.186496	+	0.0678790i
$475$	−3.44562			−0.158096
$476$	2.02734	−	0.737892i	0.0929230	−	0.0338212i
$477$	1.06031	−	6.01330i	0.0485481	−	0.275330i
$478$	−13.3105	−	11.1688i	−0.608806	−	0.510849i
$479$	12.0680	−	10.1263i	0.551403	−	0.462682i	−0.324013	−	0.946053i	$-0.605032\pi$
$479$	12.0680	−	10.1263i	0.551403	−	0.462682i	0.875416	+	0.483371i	$0.160588\pi$
$480$	7.59627			0.346721
$481$	3.34507	+	34.6132i	0.152522	+	1.57822i
$482$	17.2867			0.787389
$483$	26.4688	−	22.2100i	1.20437	−	1.01059i
$484$	7.24035	+	6.07538i	0.329107	+	0.276153i
$485$	−1.44919	+	8.21875i	−0.0658042	+	0.373194i
$486$	5.49747	−	2.00092i	0.249370	−	0.0907634i
$487$	−32.7452			−1.48382			−0.741912	−	0.670497i	$-0.766081\pi$
$487$	−32.7452			−1.48382			−0.741912	+	0.670497i	$0.766081\pi$
$488$	−8.60354	+	3.13143i	−0.389464	+	0.141753i
$489$	−9.36618	−	16.2227i	−0.423553	−	0.733616i
$490$	−0.957234	−	5.42874i	−0.0432434	−	0.245246i
$491$	14.1552	−	24.5176i	0.638817	−	1.10646i	−0.346876	−	0.937911i	$-0.612758\pi$
$491$	14.1552	−	24.5176i	0.638817	−	1.10646i	0.985693	−	0.168552i	$-0.0539091\pi$
$492$	−0.539363	−	0.934204i	−0.0243164	−	0.0421172i
$493$	−3.09627	+	2.59808i	−0.139449	+	0.117011i
$494$	0.711667	−	4.03606i	0.0320194	−	0.181591i
$495$	0.520945	−	0.902302i	0.0234147	−	0.0405555i
$496$	0.0765042	+	0.0278452i	0.00343514	+	0.00125029i
$497$	49.6759	+	18.0806i	2.22827	+	0.811024i
$498$	−1.19640	−	6.78514i	−0.0536121	−	0.304050i
$499$	12.5576	+	10.5371i	0.562156	+	0.471705i	0.879033	−	0.476762i	$-0.158190\pi$
$499$	12.5576	+	10.5371i	0.562156	+	0.471705i	−0.316876	+	0.948467i	$0.602634\pi$
$500$	−7.62449	−	6.39770i	−0.340977	−	0.286114i
$501$	−2.66978	−	15.1411i	−0.119277	−	0.676453i
$502$	−9.89440	−	3.60127i	−0.441609	−	0.160732i
$503$	29.5805	+	10.7664i	1.31893	+	0.480052i	0.903116	−	0.429397i	$-0.141274\pi$
$503$	29.5805	+	10.7664i	1.31893	+	0.480052i	0.415815	+	0.909449i	$0.363496\pi$
$504$	−3.48070	+	6.02876i	−0.155043	+	0.268542i
$505$	1.89528	−	10.7487i	0.0843387	−	0.478309i
$506$	7.33687	−	6.15636i	0.326164	−	0.273684i
$507$	15.0778	+	26.1156i	0.669631	+	1.15983i
$508$	−1.59657	+	2.76534i	−0.0708364	+	0.122692i
$509$	1.05731	+	5.99633i	0.0468646	+	0.265783i	0.999233	−	0.0391686i	$-0.0124710\pi$
$509$	1.05731	+	5.99633i	0.0468646	+	0.265783i	−0.952368	+	0.304951i	$0.901360\pi$
$510$	−0.277189	−	0.480105i	−0.0122741	−	0.0212594i
$511$	15.0077	−	5.46237i	0.663903	−	0.241641i
$512$	−0.473897			−0.0209435
$513$	−4.28699	+	1.56034i	−0.189275	+	0.0688905i
$514$	2.13341	−	12.0992i	0.0941006	−	0.533671i
$515$	−5.06077	−	4.24649i	−0.223004	−	0.187123i
$516$	−7.02481	+	5.89452i	−0.309250	+	0.259492i
$517$	21.8726			0.961955
$518$	5.02734	−	19.4673i	0.220889	−	0.855346i
$519$	23.0874			1.01342
$520$	10.9277	−	9.16940i	0.479210	−	0.402105i
$521$	−19.7854	−	16.6019i	−0.866814	−	0.727343i	0.0966108	−	0.995322i	$-0.469200\pi$
$521$	−19.7854	−	16.6019i	−0.866814	−	0.727343i	−0.963425	+	0.267979i	$0.913644\pi$
$522$	0.860967	−	4.88279i	0.0376835	−	0.213714i
$523$	24.4586	−	8.90219i	1.06950	−	0.389266i	0.253510	−	0.967333i	$-0.418415\pi$
$523$	24.4586	−	8.90219i	1.06950	−	0.389266i	0.815989	+	0.578067i	$0.196193\pi$
$524$	−4.58347			−0.200230
$525$	−22.8726	+	8.32494i	−0.998241	+	0.363330i
$526$	8.82207	+	15.2803i	0.384661	+	0.666252i
$527$	0.157918	+	0.895599i	0.00687903	+	0.0390129i
$528$	0.0582480	−	0.100888i	0.00253492	−	0.00439061i
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	5.54189	−	4.65020i	0.240724	−	0.201992i
$531$	0.0346151	−	0.196312i	0.00150217	−	0.00851922i
$532$	1.87939	−	3.25519i	0.0814817	−	0.141130i
$533$	−3.08347	−	1.12229i	−0.133560	−	0.0486119i
$534$	13.5496	+	4.93166i	0.586350	+	0.213414i
$535$	1.05051	+	5.95772i	0.0454174	+	0.257575i
$536$	7.24422	+	6.07862i	0.312903	+	0.262557i
$537$	−18.9440	−	15.8959i	−0.817495	−	0.685960i
$538$	1.18938	+	6.74530i	0.0512777	+	0.290810i
$539$	12.1591	+	4.42555i	0.523730	+	0.190622i
$540$	−5.67277	−	2.06472i	−0.244117	−	0.0888514i
$541$	2.31861	−	4.01595i	0.0996849	−	0.172659i	−0.811869	−	0.583839i	$-0.801550\pi$
$541$	2.31861	−	4.01595i	0.0996849	−	0.172659i	0.911554	+	0.411180i	$0.134883\pi$
$542$	−4.49061	+	25.4675i	−0.192888	+	1.09392i
$543$	−22.7561	+	19.0946i	−0.976557	+	0.819429i
$544$	−1.31908	−	2.28471i	−0.0565550	−	0.0979561i
$545$	−0.305407	+	0.528981i	−0.0130822	+	0.0226591i
$546$	−5.02734	−	28.5115i	−0.215150	−	1.22018i
$547$	−14.1013	−	24.4242i	−0.602929	−	1.04430i	−0.992375	−	0.123254i	$-0.960667\pi$
$547$	−14.1013	−	24.4242i	−0.602929	−	1.04430i	0.389446	−	0.921049i	$-0.372666\pi$
$548$	−8.59152	+	3.12706i	−0.367011	+	0.133581i
$549$	2.10607			0.0898847
$550$	−6.34002	+	2.30758i	−0.270339	+	0.0983955i
$551$	−1.22281	+	6.93491i	−0.0520935	+	0.295437i
$552$	−19.9813	−	16.7663i	−0.850462	−	0.713622i
$553$	−9.23442	+	7.74860i	−0.392688	+	0.329504i
$554$	−9.40703			−0.399666
$555$	8.17024	+	0.640140i	0.346808	+	0.0271724i
$556$	−1.26022			−0.0534453
$557$	−9.77972	+	8.20616i	−0.414380	+	0.347706i	−0.826020	−	0.563640i	$-0.809400\pi$
$557$	−9.77972	+	8.20616i	−0.414380	+	0.347706i	0.411640	+	0.911346i	$0.364956\pi$
$558$	−0.854570	−	0.717070i	−0.0361768	−	0.0303560i
$559$	−4.84389	+	27.4711i	−0.204875	+	1.16190i
$560$	−0.130110	+	0.0473563i	−0.00549816	+	0.00200117i
$561$	1.30129			0.0549404
$562$	−6.88578	+	2.50622i	−0.290459	+	0.105718i
$563$	17.6878	+	30.6361i	0.745451	+	1.29116i	0.949984	+	0.312300i	$0.101099\pi$
$563$	17.6878	+	30.6361i	0.745451	+	1.29116i	−0.204532	+	0.978860i	$0.565567\pi$
$564$	−3.93242	−	22.3019i	−0.165585	−	0.939077i
$565$	−2.21806	+	3.84180i	−0.0933146	+	0.161626i
$566$	9.88919	+	17.1286i	0.415673	+	0.719968i
$567$	−19.0496	+	15.9845i	−0.800009	+	0.671287i
$568$	6.92979	−	39.3008i	0.290767	−	1.64902i
$569$	−19.0449	+	32.9867i	−0.798403	+	1.38287i	0.122253	+	0.992499i	$0.460988\pi$
$569$	−19.0449	+	32.9867i	−0.798403	+	1.38287i	−0.920656	+	0.390376i	$0.872345\pi$
$570$	−0.907604	−	0.330341i	−0.0380153	−	0.0138365i
$571$	−21.1951	−	7.71437i	−0.886986	−	0.322836i	−0.141960	−	0.989872i	$-0.545340\pi$
$571$	−21.1951	−	7.71437i	−0.886986	−	0.322836i	−0.745025	+	0.667036i	$0.767563\pi$
$572$	2.21048	+	12.5363i	0.0924250	+	0.524168i
$573$	−13.6009	−	11.4125i	−0.568184	−	0.476763i
$574$	1.45336	+	1.21952i	0.0606622	+	0.0509016i
$575$	4.40373	+	24.9748i	0.183648	+	1.04152i
$576$	3.09240	+	1.12554i	0.128850	+	0.0468975i
$577$	22.7875	+	8.29396i	0.948654	+	0.345282i	0.769578	−	0.638553i	$-0.220467\pi$
$577$	22.7875	+	8.29396i	0.948654	+	0.345282i	0.179077	+	0.983835i	$0.442689\pi$
$578$	7.37851	−	12.7800i	0.306905	−	0.531576i
$579$	1.98680	−	11.2677i	0.0825684	−	0.468269i
$580$	−7.13816	+	5.98962i	−0.296396	+	0.248706i
$581$	−9.61081	−	16.6464i	−0.398724	−	0.690610i
$582$	6.39306	−	11.0731i	0.265001	−	0.458995i
$583$	2.94878	+	16.7233i	0.122126	+	0.692610i
$584$	−6.02822	−	10.4412i	−0.249449	−	0.432059i
$585$	−3.08347	+	1.12229i	−0.127486	+	0.0464011i
$586$	19.3622			0.799844
$587$	5.04354	−	1.83570i	0.208169	−	0.0757674i	−0.235831	−	0.971794i	$-0.575781\pi$
$587$	5.04354	−	1.83570i	0.208169	−	0.0757674i	0.444000	+	0.896027i	$0.353559\pi$
$588$	2.32635	−	13.1934i	0.0959371	−	0.544087i
$589$	1.21373	+	1.01844i	0.0500107	+	0.0419640i
$590$	0.180922	−	0.151812i	0.00744845	−	0.00624999i
$591$	−14.9932			−0.616738
$592$	−0.254023	−	0.0199027i	−0.0104403	−	0.000817997i
$593$	8.44562			0.346820			0.173410	−	0.984850i	$-0.444521\pi$
$593$	8.44562			0.346820			0.173410	+	0.984850i	$0.444521\pi$
$594$	−6.84318	+	5.74211i	−0.280779	+	0.235602i
$595$	−1.18479	−	0.994159i	−0.0485718	−	0.0407565i
$596$	−2.23725	+	12.6881i	−0.0916415	+	0.519725i
$597$	0.428548	−	0.155979i	0.0175393	−	0.00638379i
$598$	−30.1640			−1.23350
$599$	12.8760	−	4.68647i	0.526098	−	0.191484i	−0.0652970	−	0.997866i	$-0.520799\pi$
$599$	12.8760	−	4.68647i	0.526098	−	0.191484i	0.591395	+	0.806382i	$0.298577\pi$
$600$	9.18732	+	15.9129i	0.375071	+	0.649642i
$601$	−0.515892	−	2.92577i	−0.0210437	−	0.119345i	0.972476	−	0.233001i	$-0.0748547\pi$
$601$	−0.515892	−	2.92577i	−0.0210437	−	0.119345i	−0.993520	+	0.113657i	$0.963744\pi$
$602$	8.06418	−	13.9676i	0.328671	−	0.569275i
$603$	−1.08765	−	1.88386i	−0.0442925	−	0.0767168i
$604$	−4.00640	+	3.36177i	−0.163018	+	0.136788i
$605$	1.17658	−	6.67274i	0.0478350	−	0.271286i
$606$	−8.36097	+	14.4816i	−0.339641	+	0.588276i
$607$	−11.5842	−	4.21632i	−0.470190	−	0.171135i	0.0960484	−	0.995377i	$-0.469380\pi$
$607$	−11.5842	−	4.21632i	−0.470190	−	0.171135i	−0.566238	+	0.824241i	$0.691602\pi$
$608$	−4.31908	−	1.57202i	−0.175162	−	0.0637537i
$609$	8.63816	+	48.9894i	0.350036	+	1.98515i
$610$	1.91147	+	1.60392i	0.0773933	+	0.0649407i
$611$	−52.7700	−	44.2793i	−2.13484	−	1.79135i
$612$	0.0650551	+	0.368946i	0.00262970	+	0.0149138i
$613$	28.4666	+	10.3610i	1.14976	+	0.418477i	0.845428	−	0.534090i	$-0.179346\pi$
$613$	28.4666	+	10.3610i	1.14976	+	0.418477i	0.304329	+	0.952567i	$0.401568\pi$
$614$	4.29503	+	1.56326i	0.173333	+	0.0630882i
$615$	−0.386659	+	0.669713i	−0.0155916	+	0.0270055i
$616$	3.36184	−	19.0660i	0.135453	−	0.768190i
$617$	−3.03983	+	2.55072i	−0.122379	+	0.102688i	−0.701923	−	0.712253i	$-0.747675\pi$
$617$	−3.03983	+	2.55072i	−0.122379	+	0.102688i	0.579544	+	0.814941i	$0.303231\pi$
$618$	5.06077	+	8.76552i	0.203574	+	0.352601i
$619$	12.2028	−	21.1359i	0.490472	−	0.849522i	−0.509468	−	0.860490i	$-0.670158\pi$
$619$	12.2028	−	21.1359i	0.490472	−	0.849522i	0.999940	+	0.0109673i	$0.00349107\pi$
$620$	0.364066	+	2.06472i	0.0146212	+	0.0829211i
$621$	16.7888	+	29.0791i	0.673711	+	1.16690i
$622$	−6.44191	+	2.34466i	−0.258297	+	0.0940125i
$623$	40.2276			1.61169
$624$	−0.344770	+	0.125486i	−0.0138019	+	0.00502346i
$625$	2.43077	−	13.7856i	0.0972308	−	0.551423i
$626$	−9.85298	−	8.26763i	−0.393804	−	0.330441i
$627$	1.73673	−	1.45729i	0.0693583	−	0.0581985i
$628$	12.3969			0.494691
$629$	−1.22621	−	2.56850i	−0.0488924	−	0.102413i
$630$	1.89723			0.0755875
$631$	7.45084	−	6.25199i	0.296613	−	0.248888i	−0.482320	−	0.875995i	$-0.660206\pi$
$631$	7.45084	−	6.25199i	0.296613	−	0.248888i	0.778933	+	0.627107i	$0.215761\pi$
$632$	6.97107	+	5.84942i	0.277294	+	0.232677i
$633$	2.63041	−	14.9178i	0.104550	−	0.592930i
$634$	−12.6563	+	4.60651i	−0.502645	+	0.182948i
$635$	2.28910			0.0908403
$636$	16.5214	−	6.01330i	0.655117	−	0.238443i
$637$	−20.3760	−	35.2922i	−0.807326	−	1.39833i
$638$	2.39440	+	13.5793i	0.0947952	+	0.537610i
$639$	−4.58987	+	7.94989i	−0.181572	+	0.314493i
$640$	−3.00862	−	5.21108i	−0.118926	−	0.205986i
$641$	18.0416	−	15.1387i	0.712602	−	0.597944i	−0.212726	−	0.977112i	$-0.568234\pi$
$641$	18.0416	−	15.1387i	0.712602	−	0.597944i	0.925328	+	0.379168i	$0.123790\pi$
$642$	1.60947	−	9.12776i	0.0635207	−	0.360244i
$643$	−24.0205	+	41.6048i	−0.947277	+	1.64073i	−0.196151	+	0.980574i	$0.562844\pi$
$643$	−24.0205	+	41.6048i	−0.947277	+	1.64073i	−0.751126	+	0.660159i	$0.770489\pi$
$644$	−25.9965	−	9.46195i	−1.02441	−	0.372853i
$645$	6.17752	+	2.24843i	0.243240	+	0.0885320i
$646$	0.0582480	+	0.330341i	0.00229174	+	0.0129971i
$647$	−18.5804	−	15.5908i	−0.730470	−	0.612937i	0.199790	−	0.979839i	$-0.435974\pi$
$647$	−18.5804	−	15.5908i	−0.730470	−	0.612937i	−0.930260	+	0.366902i	$0.880419\pi$
$648$	14.3806	+	12.0667i	0.564922	+	0.474026i
$649$	0.0962667	+	0.545955i	0.00377880	+	0.0214306i
$650$	19.9675	+	7.26758i	0.783190	+	0.285058i
$651$	10.5175	+	3.82807i	0.412215	+	0.150034i
$652$	−7.49912	+	12.9889i	−0.293688	+	0.508683i
$653$	6.85117	−	38.8549i	0.268107	−	1.52051i	−0.491933	−	0.870633i	$-0.663709\pi$
$653$	6.85117	−	38.8549i	0.268107	−	1.52051i	0.760040	−	0.649877i	$-0.225179\pi$
$654$	0.716881	−	0.601535i	0.0280323	−	0.0235219i
$655$	1.64290	+	2.84559i	0.0641936	+	0.111186i
$656$	0.0120217	−	0.0208222i	0.000469369	−	0.000812970i
$657$	0.481582	+	2.73119i	0.0187883	+	0.106554i
$658$	19.9145	+	34.4929i	0.776347	+	1.34467i
$659$	−8.49747	+	3.09283i	−0.331015	+	0.120479i	−0.502181	−	0.864763i	$-0.667469\pi$
$659$	−8.49747	+	3.09283i	−0.331015	+	0.120479i	0.171166	+	0.985242i	$0.445247\pi$
$660$	3.00000			0.116775
$661$	−24.3323	+	8.85625i	−0.946418	+	0.344468i	−0.768697	−	0.639613i	$-0.779095\pi$
$661$	−24.3323	+	8.85625i	−0.946418	+	0.344468i	−0.177721	+	0.984081i	$0.556872\pi$
$662$	0.113235	−	0.642187i	0.00440100	−	0.0249593i
$663$	−3.13950	−	2.63435i	−0.121928	−	0.102310i
$664$	−11.1156	+	9.32711i	−0.431370	+	0.361962i
$665$	−2.69459			−0.104492
$666$	3.17752	+	1.44674i	0.123126	+	0.0560600i
$667$	51.8289			2.00682
$668$	−9.42989	+	7.91262i	−0.364853	+	0.306148i
$669$	32.1373	+	26.9664i	1.24250	+	1.04258i
$670$	0.447539	−	2.53812i	0.0172899	−	0.0980562i
$671$	−5.50387	+	2.00324i	−0.212475	+	0.0773344i
$672$	−32.4688			−1.25251
$673$	−18.5223	+	6.74156i	−0.713982	+	0.259868i	−0.673369	−	0.739307i	$-0.735153\pi$
$673$	−18.5223	+	6.74156i	−0.713982	+	0.259868i	−0.0406131	+	0.999175i	$0.512931\pi$
$674$	−8.39558	−	14.5416i	−0.323386	−	0.560121i
$675$	−4.10741	−	23.2943i	−0.158094	−	0.896597i
$676$	12.0722	−	20.9097i	0.464316	−	0.804219i
$677$	−16.7260	−	28.9702i	−0.642831	−	1.11342i	−0.984798	−	0.173704i	$-0.944426\pi$
$677$	−16.7260	−	28.9702i	−0.642831	−	1.11342i	0.341967	−	0.939712i	$-0.388907\pi$
$678$	5.20645	−	4.36873i	0.199953	−	0.167780i
$679$	6.19429	−	35.1296i	0.237715	−	1.34815i
$680$	−0.583778	+	1.01113i	−0.0223869	+	0.0387752i
$681$	24.9256	+	9.07218i	0.955152	+	0.347647i
$682$	2.91534	+	1.06110i	0.111634	+	0.0406316i
$683$	−1.42737	−	8.09500i	−0.0546167	−	0.309746i	0.945245	−	0.326361i	$-0.105822\pi$
$683$	−1.42737	−	8.09500i	−0.0546167	−	0.309746i	−0.999862	+	0.0166142i	$0.994711\pi$
$684$	0.500000	+	0.419550i	0.0191180	+	0.0160419i
$685$	5.02094	+	4.21307i	0.191840	+	0.160973i
$686$	0.0736733	+	0.417822i	0.00281286	+	0.0159525i
$687$	13.0458	+	4.74827i	0.497727	+	0.181158i
$688$	−0.192066	−	0.0699065i	−0.00732247	−	0.00266516i
$689$	26.7408	−	46.3165i	1.01874	−	1.76452i
$690$	−1.23442	+	7.00076i	−0.0469937	+	0.266514i
$691$	7.58512	−	6.36467i	0.288552	−	0.242124i	−0.487009	−	0.873397i	$-0.661912\pi$
$691$	7.58512	−	6.36467i	0.288552	−	0.242124i	0.775560	+	0.631274i	$0.217468\pi$
$692$	−9.24257	−	16.0086i	−0.351350	−	0.608556i
$693$	−2.22668	+	3.85673i	−0.0845846	+	0.146505i
$694$	−0.819955	−	4.65020i	−0.0311251	−	0.176519i
$695$	0.451714	+	0.782392i	0.0171345	+	0.0296778i
$696$	35.2879	−	12.8438i	1.33759	−	0.486841i
$697$	0.268571			0.0101728
$698$	−19.3461	+	7.04141i	−0.732261	+	0.266521i
$699$	−0.701867	+	3.98048i	−0.0265470	+	0.150556i
$700$	14.9290	+	12.5269i	0.564264	+	0.473473i
$701$	−24.8161	+	20.8232i	−0.937293	+	0.786482i	−0.977112	−	0.212725i	$-0.931766\pi$
$701$	−24.8161	+	20.8232i	−0.937293	+	0.786482i	0.0398194	+	0.999207i	$0.487322\pi$
$702$	28.1343			1.06186
$703$	−4.51296	−	2.05477i	−0.170209	−	0.0774971i
$704$	−9.15207			−0.344932
$705$	−12.4363	+	10.4353i	−0.468378	+	0.393016i
$706$	−2.06758	−	1.73491i	−0.0778145	−	0.0652941i
$707$	−8.10101	+	45.9431i	−0.304670	+	1.72787i
$708$	0.539363	−	0.196312i	0.0202705	−	0.00737786i
$709$	−8.32325			−0.312586			−0.156293	−	0.987711i	$-0.549954\pi$
$709$	−8.32325			−0.312586			−0.156293	+	0.987711i	$0.549954\pi$
$710$	−10.2202	+	3.71984i	−0.383556	+	0.139603i
$711$	−1.04664	−	1.81283i	−0.0392519	−	0.0679864i
$712$	−5.27332	−	29.9065i	−0.197626	−	1.12079i
$713$	5.83069	−	10.0990i	0.218361	−	0.378212i
$714$	1.18479	+	2.05212i	0.0443397	+	0.0767987i
$715$	6.99067	−	5.86587i	0.261436	−	0.219371i
$716$	−3.43824	+	19.4992i	−0.128493	+	0.728721i
$717$	−15.1361	+	26.2165i	−0.565268	+	0.979073i
$718$	6.11809	+	2.22680i	0.228325	+	0.0831035i
$719$	25.3901	+	9.24125i	0.946892	+	0.344640i	0.768884	−	0.639389i	$-0.220812\pi$
$719$	25.3901	+	9.24125i	0.946892	+	0.344640i	0.178008	+	0.984029i	$0.443035\pi$
$720$	−0.00417509	−	0.0236781i	−0.000155597	−	0.000882432i
$721$	21.6313	+	18.1509i	0.805594	+	0.675973i
$722$	−12.3516	−	10.3643i	−0.459680	−	0.385717i
$723$	−5.22984	−	29.6599i	−0.194500	−	1.10306i
$724$	22.3500	+	8.13473i	0.830631	+	0.302325i
$725$	−34.3089	−	12.4874i	−1.27420	−	0.463771i
$726$	−5.19047	+	8.99016i	−0.192637	+	0.333656i
$727$	−0.526464	+	2.98572i	−0.0195255	+	0.110734i	−0.993013	−	0.118006i	$-0.962350\pi$
$727$	−0.526464	+	2.98572i	−0.0195255	+	0.110734i	0.973487	+	0.228741i	$0.0734608\pi$
$728$	−46.7083	+	39.1929i	−1.73113	+	1.45259i
$729$	−15.0201	−	26.0155i	−0.556299	−	0.963538i
$730$	−1.64290	+	2.84559i	−0.0608066	+	0.105320i
$731$	−0.396459	−	2.24843i	−0.0146636	−	0.0831613i
$732$	3.03209	+	5.25173i	0.112069	+	0.194110i
$733$	−49.0925	+	17.8682i	−1.81327	+	0.659977i	−0.816716	+	0.577039i	$0.804208\pi$
$733$	−49.0925	+	17.8682i	−1.81327	+	0.659977i	−0.996555	+	0.0829374i	$0.973570\pi$
$734$	9.57996			0.353603
$735$	−9.02481	+	3.28476i	−0.332885	+	0.121160i
$736$	−5.87433	+	33.3150i	−0.216531	+	1.22801i
$737$	4.63429	+	3.88863i	0.170706	+	0.143239i
$738$	−0.252374	+	0.211767i	−0.00929001	+	0.00779524i
$739$	−6.93313			−0.255039			−0.127520	−	0.991836i	$-0.540702\pi$
$739$	−6.93313			−0.255039			−0.127520	+	0.991836i	$0.540702\pi$
$740$	−2.82692	−	5.92145i	−0.103920	−	0.217677i
$741$	−7.14022			−0.262302
$742$	−23.6878	+	19.8764i	−0.869606	+	0.729686i
$743$	11.3892	+	9.55666i	0.417829	+	0.350600i	0.827336	−	0.561707i	$-0.189855\pi$
$743$	11.3892	+	9.55666i	0.417829	+	0.350600i	−0.409508	+	0.912307i	$0.634300\pi$
$744$	1.46720	−	8.32088i	0.0537900	−	0.305058i
$745$	8.67917	−	3.15896i	0.317980	−	0.115735i
$746$	24.3286			0.890734
$747$	3.13651	−	1.14160i	0.114759	−	0.0417688i
$748$	−0.520945	−	0.902302i	−0.0190476	−	0.0329914i
$749$	−4.49020	−	25.4652i	−0.164068	−	0.930478i
$750$	5.46585	−	9.46713i	0.199585	−	0.345691i
$751$	4.75103	+	8.22902i	0.173368	+	0.300281i	0.939595	−	0.342288i	$-0.111202\pi$
$751$	4.75103	+	8.22902i	0.173368	+	0.300281i	−0.766228	+	0.642569i	$0.777868\pi$
$752$	0.386659	−	0.324446i	0.0141000	−	0.0118313i
$753$	−3.18551	+	18.0659i	−0.116086	+	0.658358i
$754$	21.7135	−	37.6088i	0.790758	−	1.36963i
$755$	3.52317	+	1.28233i	0.128221	+	0.0466687i
$756$	24.2472	+	8.82526i	0.881863	+	0.320972i
$757$	6.95171	+	39.4251i	0.252664	+	1.43293i	0.801998	+	0.597327i	$0.203771\pi$
$757$	6.95171	+	39.4251i	0.252664	+	1.43293i	−0.549333	+	0.835603i	$0.685118\pi$
$758$	−4.32429	−	3.62851i	−0.157065	−	0.131793i
$759$	−12.7825	−	10.7258i	−0.463975	−	0.389321i
$760$	0.353226	+	2.00324i	0.0128129	+	0.0726653i
$761$	5.88413	+	2.14165i	0.213300	+	0.0776347i	0.446460	−	0.894804i	$-0.352684\pi$
$761$	5.88413	+	2.14165i	0.213300	+	0.0776347i	−0.233160	+	0.972438i	$0.574907\pi$
$762$	−3.29561	−	1.19950i	−0.119387	−	0.0434534i
$763$	1.30541	−	2.26103i	0.0472589	−	0.0818548i
$764$	−2.46848	+	13.9995i	−0.0893066	+	0.506483i
$765$	0.205737	−	0.172634i	0.00743844	−	0.00624159i
$766$	−5.82770	−	10.0939i	−0.210563	−	0.364706i
$767$	0.872989	−	1.51206i	0.0315218	−	0.0545973i
$768$	4.28359	+	24.2934i	0.154571	+	0.876613i
$769$	−9.79086	−	16.9583i	−0.353067	−	0.611531i	0.633718	−	0.773564i	$-0.281528\pi$
$769$	−9.79086	−	16.9583i	−0.353067	−	0.611531i	−0.986785	+	0.162034i	$0.948195\pi$
$770$	−4.95811	+	1.80460i	−0.178678	+	0.0650334i
$771$	−21.4047			−0.770870
$772$	−8.60829	+	3.13316i	−0.309819	+	0.112765i
$773$	5.93898	−	33.6816i	0.213610	−	1.21144i	−0.669692	−	0.742639i	$-0.733574\pi$
$773$	5.93898	−	33.6816i	0.213610	−	1.21144i	0.883302	−	0.468804i	$-0.155315\pi$
$774$	2.14543	+	1.80023i	0.0771159	+	0.0647079i
$775$	−6.29292	+	5.28039i	−0.226048	+	0.189677i
$776$	−26.9284			−0.966673
$777$	−34.9222	−	2.73616i	−1.25283	−	0.0981592i
$778$	27.7124			0.993539
$779$	0.358441	−	0.300767i	0.0128425	−	0.0107761i
$780$	−7.23783	−	6.07326i	−0.259156	−	0.217457i
$781$	4.43313	−	25.1416i	0.158630	−	0.899635i
$782$	2.31996	−	0.844395i	0.0829614	−	0.0301955i
$783$	−48.3414			−1.72758
$784$	0.280592	−	0.102127i	0.0100212	−	0.00364740i
$785$	−4.44356	−	7.69648i	−0.158598	−	0.274699i
$786$	−0.874171	−	4.95767i	−0.0311806	−	0.176834i
$787$	4.76723	−	8.25708i	0.169933	−	0.294333i	−0.768463	−	0.639894i	$-0.778978\pi$
$787$	4.76723	−	8.25708i	0.169933	−	0.294333i	0.938396	+	0.345561i	$0.112311\pi$
$788$	6.00222	+	10.3962i	0.213820	+	0.370348i
$789$	23.5483	−	19.7594i	0.838341	−	0.703452i
$790$	0.430664	−	2.44242i	0.0153223	−	0.0868973i
$791$	9.48070	−	16.4211i	0.337095	−	0.583866i
$792$	3.15910	+	1.14982i	0.112254	+	0.0408570i
$793$	17.3341	+	6.30909i	0.615552	+	0.224042i
$794$	1.37878	+	7.81943i	0.0489309	+	0.277501i
$795$	−9.65523	−	8.10170i	−0.342436	−	0.287338i
$796$	−0.279715	−	0.234709i	−0.00991424	−	0.00831903i
$797$	5.69001	+	32.2696i	0.201550	+	1.14305i	0.902776	+	0.430110i	$0.141525\pi$
$797$	5.69001	+	32.2696i	0.201550	+	1.14305i	−0.701226	+	0.712939i	$0.747364\pi$
$798$	3.87939	+	1.41198i	0.137329	+	0.0499836i
$799$	5.29813	+	1.92836i	0.187434	+	0.0682206i
$800$	11.9153	−	20.6380i	0.421271	−	0.729663i
$801$	−1.21301	+	6.87933i	−0.0428596	+	0.243069i
$802$	−13.2679	+	11.1331i	−0.468504	+	0.393122i
$803$	−3.85638	−	6.67945i	−0.136089	−	0.235713i
$804$	3.13176	−	5.42437i	0.110449	−	0.191303i
$805$	3.44387	+	19.5311i	0.121380	+	0.688382i
$806$	−4.88548	−	8.46189i	−0.172084	−	0.298058i
$807$	11.2135	−	4.08137i	0.394733	−	0.143671i
$808$	35.2175			1.23895
$809$	4.74257	−	1.72616i	0.166740	−	0.0606884i	−0.257301	−	0.966331i	$-0.582833\pi$
$809$	4.74257	−	1.72616i	0.166740	−	0.0606884i	0.424041	+	0.905643i	$0.360611\pi$
$810$	0.888414	−	5.03845i	0.0312157	−	0.177033i
$811$	−36.3560	−	30.5063i	−1.27663	−	1.07122i	−0.993699	−	0.112080i	$-0.964249\pi$
$811$	−36.3560	−	30.5063i	−1.27663	−	1.07122i	−0.282932	−	0.959140i	$-0.591307\pi$
$812$	30.5107	−	25.6015i	1.07072	−	0.898438i
$813$	45.0547			1.58014
$814$	−9.68004	−	0.758433i	−0.339285	−	0.0265831i
$815$	10.7520			0.376625
$816$	0.0230039	−	0.0193026i	0.000805298	−	0.000675726i
$817$	−3.04710	−	2.55682i	−0.106605	−	0.0894519i
$818$	−5.12701	+	29.0767i	−0.179262	+	1.01664i
$819$	13.1797	−	4.79703i	0.460537	−	0.167622i
$820$	0.619165			0.0216222
$821$	−4.21941	+	1.53574i	−0.147258	+	0.0535977i	−0.414598	−	0.910005i	$-0.636078\pi$
$821$	−4.21941	+	1.53574i	−0.147258	+	0.0535977i	0.267339	+	0.963602i	$0.413856\pi$
$822$	−5.02094	−	8.69653i	−0.175126	−	0.303326i
$823$	1.33733	+	7.58440i	0.0466165	+	0.264376i	0.999204	−	0.0398890i	$-0.0127004\pi$
$823$	1.33733	+	7.58440i	0.0466165	+	0.264376i	−0.952588	+	0.304265i	$0.901589\pi$
$824$	10.6583	−	18.4608i	0.371300	−	0.643111i
$825$	5.87733	+	10.1798i	0.204622	+	0.354416i
$826$	−0.773318	+	0.648891i	−0.0269072	+	0.0225778i
$827$	0.499533	−	2.83299i	0.0173705	−	0.0985128i	−0.974890	−	0.222687i	$-0.928517\pi$
$827$	0.499533	−	2.83299i	0.0173705	−	0.0985128i	0.992260	+	0.124174i	$0.0396282\pi$
$828$	2.40198	−	4.16035i	0.0834745	−	0.144582i
$829$	32.5702	+	11.8546i	1.13121	+	0.411726i	0.838731	−	0.544546i	$-0.183298\pi$
$829$	32.5702	+	11.8546i	1.13121	+	0.411726i	0.292478	+	0.956272i	$0.405520\pi$
$830$	3.71611	+	1.35255i	0.128988	+	0.0469478i
$831$	2.84595	+	16.1402i	0.0987250	+	0.559897i
$832$	22.0804	+	18.5276i	0.765499	+	0.642330i
$833$	2.55509	+	2.14398i	0.0885287	+	0.0742844i
$834$	−0.240352	−	1.36310i	−0.00832271	−	0.0472005i
$835$	8.29251	+	3.01823i	0.286974	+	0.104450i
$836$	−1.70574	−	0.620838i	−0.0589941	−	0.0214721i
$837$	−5.43835	+	9.41950i	−0.187977	+	0.325585i
$838$	1.59327	−	9.03590i	0.0550387	−	0.312140i
$839$	24.7527	−	20.7700i	0.854557	−	0.717059i	−0.106231	−	0.994341i	$-0.533878\pi$
$839$	24.7527	−	20.7700i	0.854557	−	0.717059i	0.960788	+	0.277283i	$0.0894339\pi$
$840$	7.18479	+	12.4444i	0.247899	+	0.429373i
$841$	−22.8089	+	39.5061i	−0.786513	+	1.36228i
$842$	−4.59745	−	26.0734i	−0.158439	−	0.898550i
$843$	6.38326	+	11.0561i	0.219851	+	0.380793i
$844$	−11.3969	+	4.14814i	−0.392298	+	0.142785i
$845$	−17.3087			−0.595438
$846$	−6.49912	+	2.36549i	−0.223444	+	0.0813271i
$847$	−5.02910	+	28.5214i	−0.172802	+	0.980008i
$848$	0.300193	+	0.251892i	0.0103087	+	0.00864999i
$849$	26.3967	−	22.1494i	0.905932	−	0.760167i
$850$	−1.73917			−0.0596530
$851$	−9.12567	+	35.3373i	−0.312824	+	1.21135i
$852$	−26.4320			−0.905546
$853$	37.5087	−	31.4735i	1.28427	−	1.07763i	0.291633	−	0.956530i	$-0.405802\pi$
$853$	37.5087	−	31.4735i	1.28427	−	1.07763i	0.992640	−	0.121102i	$-0.0386429\pi$
$854$	−8.17024	−	6.85565i	−0.279580	−	0.234595i
$855$	0.0812519	−	0.460802i	0.00277876	−	0.0157591i
$856$	−18.3430	+	6.67631i	−0.626951	+	0.228192i
$857$	42.5948			1.45501			0.727506	−	0.686101i	$-0.240679\pi$
$857$	42.5948			1.45501			0.727506	+	0.686101i	$0.240679\pi$
$858$	−13.1382	+	4.78190i	−0.448529	+	0.163251i
$859$	10.9978	+	19.0487i	0.375239	+	0.649934i	0.990363	−	0.138497i	$-0.0442272\pi$
$859$	10.9978	+	19.0487i	0.375239	+	0.649934i	−0.615123	+	0.788431i	$0.710894\pi$
$860$	−0.914000	−	5.18355i	−0.0311672	−	0.176758i
$861$	1.65270	−	2.86257i	0.0563240	−	0.0975560i
$862$	1.81221	+	3.13885i	0.0617243	+	0.106910i
$863$	−9.12907	+	7.66020i	−0.310757	+	0.260756i	−0.784805	−	0.619743i	$-0.787237\pi$
$863$	−9.12907	+	7.66020i	−0.310757	+	0.260756i	0.474048	+	0.880499i	$0.342792\pi$
$864$	5.47906	−	31.0733i	0.186401	−	1.05713i
$865$	−6.62583	+	11.4763i	−0.225285	+	0.390205i
$866$	−24.9843	−	9.09353i	−0.849000	−	0.309011i
$867$	−24.1596	−	8.79336i	−0.820502	−	0.298638i
$868$	−1.55613	−	8.82526i	−0.0528186	−	0.299549i
$869$	4.45954	+	3.74200i	0.151280	+	0.126939i
$870$	−7.84002	−	6.57856i	−0.265802	−	0.223034i
$871$	−3.30851	−	18.7635i	−0.112104	−	0.635776i
$872$	−1.85204	−	0.674089i	−0.0627181	−	0.0228275i
$873$	5.82073	+	2.11857i	0.197002	+	0.0717028i
$874$	2.15064	−	3.72503i	0.0727466	−	0.126001i
$875$	5.29591	−	30.0346i	0.179034	−	1.01536i
$876$	−6.11721	+	5.13295i	−0.206681	+	0.173426i
$877$	−11.3451	−	19.6502i	−0.383096	−	0.663542i	0.608407	−	0.793625i	$-0.291809\pi$
$877$	−11.3451	−	19.6502i	−0.383096	−	0.663542i	−0.991503	+	0.130083i	$0.958475\pi$
$878$	7.05990	−	12.2281i	0.238260	−	0.412678i
$879$	−5.85773	−	33.2208i	−0.197576	−	1.12051i
$880$	0.0334331	+	0.0579078i	0.00112703	+	0.00195207i
$881$	50.5001	−	18.3805i	1.70139	−	0.619255i	0.705407	−	0.708802i	$-0.250764\pi$
$881$	50.5001	−	18.3805i	1.70139	−	0.619255i	0.995983	+	0.0895466i	$0.0285418\pi$
$882$	−4.09152			−0.137769
$883$	−44.7139	+	16.2745i	−1.50474	+	0.547682i	−0.957284	−	0.289150i	$-0.906627\pi$
$883$	−44.7139	+	16.2745i	−1.50474	+	0.547682i	−0.547460	+	0.836832i	$0.684405\pi$
$884$	−0.569803	+	3.23151i	−0.0191645	+	0.108688i
$885$	−0.315207	−	0.264490i	−0.0105956	−	0.00889075i
$886$	2.25309	−	1.89057i	0.0756940	−	0.0635148i
$887$	−35.5449			−1.19348			−0.596740	−	0.802435i	$-0.703538\pi$
$887$	−35.5449			−1.19348			−0.596740	+	0.802435i	$0.703538\pi$
$888$	2.54370	+	26.3209i	0.0853610	+	0.883273i
$889$	−9.78436			−0.328157
$890$	−6.34002	+	5.31991i	−0.212518	+	0.178324i
$891$	9.19956	+	7.71935i	0.308197	+	0.258608i
$892$	5.83275	−	33.0792i	0.195295	−	1.10757i
$893$	9.23055	−	3.35965i	0.308889	−	0.112426i
$894$	−14.1506			−0.473268
$895$	13.3383	−	4.85473i	0.445849	−	0.162276i
$896$	12.8598	+	22.2738i	0.429615	+	0.744115i
$897$	9.12567	+	51.7542i	0.304697	+	1.72802i
$898$	−16.0505	+	27.8003i	−0.535612	+	0.927708i
$899$	8.39440	+	14.5395i	0.279969	+	0.484920i
$900$	−2.59240	+	2.17528i	−0.0864132	+	0.0725093i
$901$	−0.760115	+	4.31082i	−0.0253231	+	0.143614i
$902$	0.458111	−	0.793471i	0.0152534	−	0.0264197i
$903$	−26.4047	−	9.61051i	−0.878692	−	0.319818i
$904$	−13.4507	−	4.89567i	−0.447365	−	0.162827i
$905$	−2.96080	−	16.7915i	−0.0984203	−	0.558169i
$906$	−4.40033	−	3.69232i	−0.146191	−	0.122669i
$907$	18.2310	+	15.2976i	0.605351	+	0.507950i	0.893161	−	0.449738i	$-0.148483\pi$
$907$	18.2310	+	15.2976i	0.605351	+	0.507950i	−0.287810	+	0.957688i	$0.592927\pi$
$908$	−3.68789	−	20.9151i	−0.122387	−	0.694091i
$909$	−7.61246	−	2.77071i	−0.252489	−	0.0918987i
$910$	15.6153	+	5.68349i	0.517641	+	0.188406i
$911$	−25.8603	+	44.7913i	−0.856788	+	1.48400i	0.0181876	+	0.999835i	$0.494210\pi$
$911$	−25.8603	+	44.7913i	−0.856788	+	1.48400i	−0.874976	+	0.484166i	$0.839123\pi$
$912$	0.00908496	−	0.0515234i	0.000300833	−	0.00170611i
$913$	−7.11090	+	5.96675i	−0.235336	+	0.197471i
$914$	11.8675	+	20.5552i	0.392543	+	0.679904i
$915$	2.17365	−	3.76487i	0.0718586	−	0.124463i
$916$	−1.93020	−	10.9467i	−0.0637755	−	0.361689i
$917$	−7.02229	−	12.1630i	−0.231896	−	0.401656i
$918$	−2.16385	+	0.787576i	−0.0714176	+	0.0259939i
$919$	−49.1557			−1.62150			−0.810748	−	0.585395i	$-0.800940\pi$
$919$	−49.1557			−1.62150			−0.810748	+	0.585395i	$0.800940\pi$
$920$	14.0686	−	5.12056i	0.463829	−	0.168820i
$921$	1.38279	−	7.84219i	0.0455644	−	0.258409i
$922$	−4.04348	−	3.39288i	−0.133165	−	0.111739i
$923$	−61.5925	+	51.6822i	−2.02734	+	1.70114i
$924$	−12.8229			−0.421844
$925$	14.5548	−	21.1933i	0.478560	−	0.696831i
$926$	−5.20708			−0.171115
$927$	−3.75624	+	3.15186i	−0.123371	+	0.103521i
$928$	−37.3089	−	31.3059i	−1.22472	−	1.02767i
$929$	−6.14512	+	34.8507i	−0.201615	+	1.14342i	0.701063	+	0.713099i	$0.252709\pi$
$929$	−6.14512	+	34.8507i	−0.201615	+	1.14342i	−0.902678	+	0.430316i	$0.858402\pi$
$930$	−2.16385	+	0.787576i	−0.0709554	+	0.0258256i
$931$	5.81109			0.190451
$932$	3.04101	−	1.10684i	0.0996117	−	0.0362557i
$933$	5.97178	+	10.3434i	0.195507	+	0.338629i
$934$	0.993299	+	5.63328i	0.0325017	+	0.184326i
$935$	−0.373455	+	0.646844i	−0.0122133	+	0.0211541i
$936$	−5.29396	−	9.16940i	−0.173038	−	0.299711i
$937$	27.7449	−	23.2808i	0.906388	−	0.760550i	−0.0650407	−	0.997883i	$-0.520718\pi$
$937$	27.7449	−	23.2808i	0.906388	−	0.760550i	0.971428	+	0.237333i	$0.0762733\pi$
$938$	−1.91292	+	10.8487i	−0.0624592	+	0.354224i
$939$	−11.2044	+	19.4066i	−0.365642	+	0.633310i
$940$	12.2144	+	4.44566i	0.398388	+	0.145001i
$941$	18.0376	+	6.56515i	0.588009	+	0.214018i	0.618854	−	0.785506i	$-0.287597\pi$
$941$	18.0376	+	6.56515i	0.588009	+	0.214018i	−0.0308444	+	0.999524i	$0.509820\pi$
$942$	2.36437	+	13.4090i	0.0770354	+	0.436889i
$943$	−2.63816	−	2.21368i	−0.0859102	−	0.0720872i
$944$	0.00980018	+	0.00822333i	0.000318969	+	0.000267647i
$945$	−3.21213	−	18.2169i	−0.104491	−	0.592596i
$946$	−7.31908	−	2.66393i	−0.237964	−	0.0866117i
$947$	48.7217	+	17.7332i	1.58324	+	0.576253i	0.975906	−	0.218192i	$-0.0700159\pi$
$947$	48.7217	+	17.7332i	1.58324	+	0.576253i	0.607336	+	0.794445i	$0.292238\pi$
$948$	3.01367	−	5.21983i	0.0978795	−	0.169532i
$949$	−4.21806	+	23.9218i	−0.136924	+	0.776535i
$950$	−2.32114	+	1.94767i	−0.0753076	+	0.0631906i
$951$	11.7326	+	20.3215i	0.380456	+	0.658969i
$952$	2.49525	−	4.32190i	0.0808716	−	0.140074i
$953$	−4.13593	−	23.4560i	−0.133976	−	0.759816i	−0.975567	−	0.219701i	$-0.929492\pi$
$953$	−4.13593	−	23.4560i	−0.133976	−	0.759816i	0.841591	−	0.540115i	$-0.181619\pi$
$954$	−2.68479	−	4.65020i	−0.0869234	−	0.150556i
$955$	9.57620	−	3.48545i	0.309879	−	0.112787i
$956$	24.2377			0.783904
$957$	22.5744	−	8.21643i	0.729728	−	0.265599i
$958$	2.40565	−	13.6431i	0.0777230	−	0.440789i
$959$	−21.4611	−	18.0080i	−0.693015	−	0.581509i
$960$	5.20368	−	4.36640i	0.167948	−	0.140925i
$961$	−27.2226			−0.878147
$962$	21.8188	+	21.4263i	0.703465	+	0.690811i
$963$	4.49020			0.144695
$964$	−18.4722	+	15.5001i	−0.594951	+	0.499223i
$965$	5.03074	+	4.22130i	0.161945	+	0.135888i
$966$	5.27631	−	29.9234i	0.169763	−	0.962771i
$967$	24.5082	−	8.92026i	0.788131	−	0.286856i	0.0835720	−	0.996502i	$-0.473367\pi$
$967$	24.5082	−	8.92026i	0.788131	−	0.286856i	0.704559	+	0.709646i	$0.251145\pi$
$968$	21.8630			0.702702
$969$	0.549163	−	0.199879i	0.0176417	−	0.00642104i
$970$	3.66947	+	6.35571i	0.117820	+	0.204070i
$971$	6.41370	+	36.3739i	0.205825	+	1.16729i	0.896136	+	0.443780i	$0.146363\pi$
$971$	6.41370	+	36.3739i	0.205825	+	1.16729i	−0.690310	+	0.723513i	$0.742526\pi$
$972$	−4.08037	+	7.06742i	−0.130878	+	0.226687i
$973$	−1.93077	−	3.34419i	−0.0618976	−	0.107210i
$974$	−22.0587	+	18.5095i	−0.706807	+	0.593081i
$975$	6.42855	−	36.4581i	0.205878	−	1.16759i
$976$	−0.0675813	+	0.117054i	−0.00216323	+	0.00374682i
$977$	−9.08647	−	3.30720i	−0.290702	−	0.105807i	0.192553	−	0.981287i	$-0.438323\pi$
$977$	−9.08647	−	3.30720i	−0.290702	−	0.105807i	−0.483255	+	0.875480i	$0.660546\pi$
$978$	−15.4795	−	5.63409i	−0.494981	−	0.180158i
$979$	−3.37346	−	19.1318i	−0.107816	−	0.611456i
$980$	5.89053	+	4.94274i	0.188166	+	0.157890i
$981$	0.347296	+	0.291416i	0.0110883	+	0.00930420i
$982$	−4.32311	−	24.5176i	−0.137956	−	0.782387i
$983$	−6.06923	−	2.20902i	−0.193578	−	0.0704568i	0.243412	−	0.969923i	$-0.421733\pi$
$983$	−6.06923	−	2.20902i	−0.193578	−	0.0704568i	−0.436990	+	0.899466i	$0.643956\pi$
$984$	−2.34477	−	0.853427i	−0.0747485	−	0.0272062i
$985$	4.30288	−	7.45281i	0.137101	−	0.237466i
$986$	−0.617211	+	3.50038i	−0.0196560	+	0.111475i
$987$	53.1566	−	44.6037i	1.69199	−	1.41975i
$988$	2.85844	+	4.95096i	0.0909391	+	0.157511i
$989$	−14.6382	+	25.3540i	−0.465466	+	0.806211i
$990$	−0.159100	−	0.902302i	−0.00505654	−	0.0286771i
$991$	−3.55350	−	6.15484i	−0.112881	−	0.195515i	0.804050	−	0.594562i	$-0.202674\pi$
$991$	−3.55350	−	6.15484i	−0.112881	−	0.195515i	−0.916931	+	0.399047i	$0.869341\pi$
$992$	−10.2973	+	3.74789i	−0.326938	+	0.118996i
$993$	−1.13610			−0.0360529
$994$	43.6843	−	15.8998i	1.38558	−	0.504310i
$995$	−0.0454548	+	0.257787i	−0.00144101	+	0.00817239i
$996$	7.36231	+	6.17771i	0.233284	+	0.195748i
$997$	14.6393	−	12.2838i	0.463630	−	0.389032i	−0.380835	−	0.924643i	$-0.624363\pi$
$997$	14.6393	−	12.2838i	0.463630	−	0.389032i	0.844464	+	0.535612i	$0.179919\pi$
$998$	14.4156			0.456318
$999$	8.51161	−	32.9595i	0.269295	−	1.04279i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.2.f.b.12.1	✓	6
3.2	odd	2		333.2.x.a.271.1		6
4.3	odd	2		592.2.bc.c.49.1		6
5.2	odd	4		925.2.bc.b.49.2		12
5.3	odd	4		925.2.bc.b.49.1		12
5.4	even	2		925.2.p.a.826.1		6
37.15	odd	36		1369.2.b.e.1368.4		6
37.16	even	9		1369.2.a.i.1.3		3
37.21	even	18		1369.2.a.l.1.1		3
37.22	odd	36		1369.2.b.e.1368.3		6
37.34	even	9	inner	37.2.f.b.34.1	yes	6
111.71	odd	18		333.2.x.a.145.1		6
148.71	odd	18		592.2.bc.c.145.1		6
185.34	even	18		925.2.p.a.626.1		6
185.108	odd	36		925.2.bc.b.774.2		12
185.182	odd	36		925.2.bc.b.774.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.2.f.b.12.1	✓	6	1.1	even	1	trivial
37.2.f.b.34.1	yes	6	37.34	even	9	inner
333.2.x.a.145.1		6	111.71	odd	18
333.2.x.a.271.1		6	3.2	odd	2
592.2.bc.c.49.1		6	4.3	odd	2
592.2.bc.c.145.1		6	148.71	odd	18
925.2.p.a.626.1		6	185.34	even	18
925.2.p.a.826.1		6	5.4	even	2
925.2.bc.b.49.1		12	5.3	odd	4
925.2.bc.b.49.2		12	5.2	odd	4
925.2.bc.b.774.1		12	185.182	odd	36
925.2.bc.b.774.2		12	185.108	odd	36
1369.2.a.i.1.3		3	37.16	even	9
1369.2.a.l.1.1		3	37.21	even	18
1369.2.b.e.1368.3		6	37.22	odd	36
1369.2.b.e.1368.4		6	37.15	odd	36

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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	37.f (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.673648 - 0.565258i) q^{2} +(-1.17365 - 0.984808i) q^{3} +(-0.213011 + 1.20805i) q^{4} +(0.826352 - 0.300767i) q^{5} -1.34730 q^{6} +(-3.53209 + 1.28558i) q^{7} +(1.41875 + 2.45734i) q^{8} +(-0.113341 - 0.642788i) q^{9} +O(q^{10})\)	\(q+(0.673648 - 0.565258i) q^{2} +(-1.17365 - 0.984808i) q^{3} +(-0.213011 + 1.20805i) q^{4} +(0.826352 - 0.300767i) q^{5} -1.34730 q^{6} +(-3.53209 + 1.28558i) q^{7} +(1.41875 + 2.45734i) q^{8} +(-0.113341 - 0.642788i) q^{9} +(0.386659 - 0.669713i) q^{10} +(0.907604 + 1.57202i) q^{11} +(1.43969 - 1.20805i) q^{12} +(0.992726 - 5.63003i) q^{13} +(-1.65270 + 2.86257i) q^{14} +(-1.26604 - 0.460802i) q^{15} +(0.0393628 + 0.0143269i) q^{16} +(0.0812519 + 0.460802i) q^{17} +(-0.439693 - 0.368946i) q^{18} +(0.624485 + 0.524005i) q^{19} +(0.187319 + 1.06234i) q^{20} +(5.41147 + 1.96962i) q^{21} +(1.50000 + 0.545955i) q^{22} +(3.00000 - 5.19615i) q^{23} +(0.754900 - 4.28125i) q^{24} +(-3.23783 + 2.71686i) q^{25} +(-2.51367 - 4.35381i) q^{26} +(-2.79813 + 4.84651i) q^{27} +(-0.800660 - 4.54077i) q^{28} +(4.31908 + 7.48086i) q^{29} +(-1.11334 + 0.405223i) q^{30} +1.94356 q^{31} +(-5.29813 + 1.92836i) q^{32} +(0.482926 - 2.73881i) q^{33} +(0.315207 + 0.264490i) q^{34} +(-2.53209 + 2.12467i) q^{35} +0.800660 q^{36} +(-5.86097 + 1.62760i) q^{37} +0.716881 q^{38} +(-6.70961 + 5.63003i) q^{39} +(1.91147 + 1.60392i) q^{40} +(0.0996702 - 0.565258i) q^{41} +(4.75877 - 1.73205i) q^{42} -4.87939 q^{43} +(-2.09240 + 0.761570i) q^{44} +(-0.286989 - 0.497079i) q^{45} +(-0.916222 - 5.19615i) q^{46} +(6.02481 - 10.4353i) q^{47} +(-0.0320889 - 0.0555796i) q^{48} +(5.46064 - 4.58202i) q^{49} +(-0.645430 + 3.66041i) q^{50} +(0.358441 - 0.620838i) q^{51} +(6.58987 + 2.39852i) q^{52} +(8.79086 + 3.19961i) q^{53} +(0.854570 + 4.84651i) q^{54} +(1.22281 + 1.02606i) q^{55} +(-8.17024 - 6.85565i) q^{56} +(-0.216881 - 1.23000i) q^{57} +(7.13816 + 2.59808i) q^{58} +(0.286989 + 0.104455i) q^{59} +(0.826352 - 1.43128i) q^{60} +(-0.560307 + 3.17766i) q^{61} +(1.30928 - 1.09861i) q^{62} +(1.22668 + 2.12467i) q^{63} +(-2.52094 + 4.36640i) q^{64} +(-0.872989 - 4.95096i) q^{65} +(-1.22281 - 2.11797i) q^{66} +(3.13176 - 1.13987i) q^{67} -0.573978 q^{68} +(-8.63816 + 3.14403i) q^{69} +(-0.504748 + 2.86257i) q^{70} +(-10.7738 - 9.04028i) q^{71} +(1.41875 - 1.19047i) q^{72} -4.24897 q^{73} +(-3.02822 + 4.40938i) q^{74} +6.47565 q^{75} +(-0.766044 + 0.642788i) q^{76} +(-5.22668 - 4.38571i) q^{77} +(-1.33750 + 7.58532i) q^{78} +(3.01367 - 1.09689i) q^{79} +0.0368366 q^{80} +(6.21688 - 2.26276i) q^{81} +(-0.252374 - 0.437124i) q^{82} +(0.888003 + 5.03612i) q^{83} +(-3.53209 + 6.11776i) q^{84} +(0.205737 + 0.356347i) q^{85} +(-3.28699 + 2.75811i) q^{86} +(2.29813 - 13.0334i) q^{87} +(-2.57532 + 4.46059i) q^{88} +(-10.0569 - 3.66041i) q^{89} +(-0.474308 - 0.172634i) q^{90} +(3.73143 + 21.1620i) q^{91} +(5.63816 + 4.73097i) q^{92} +(-2.28106 - 1.91404i) q^{93} +(-1.84002 - 10.4353i) q^{94} +(0.673648 + 0.245188i) q^{95} +(8.11721 + 2.95442i) q^{96} +(-4.74510 + 8.21875i) q^{97} +(1.08853 - 6.17334i) q^{98} +(0.907604 - 0.761570i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 6 q^{3} - 9 q^{4} + 6 q^{5} - 6 q^{6} - 12 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 6 * q^3 - 9 * q^4 + 6 * q^5 - 6 * q^6 - 12 * q^7 + 6 * q^8 + 6 * q^9	\( 6 q + 3 q^{2} - 6 q^{3} - 9 q^{4} + 6 q^{5} - 6 q^{6} - 12 q^{7} + 6 q^{8} + 6 q^{9} + 9 q^{10} + 9 q^{11} + 3 q^{12} - 12 q^{13} - 12 q^{14} - 3 q^{15} + 9 q^{16} + 3 q^{17} + 3 q^{18} - 9 q^{19} - 21 q^{20} + 12 q^{21} + 9 q^{22} + 18 q^{23} + 6 q^{24} + 6 q^{26} - 3 q^{27} + 24 q^{28} + 9 q^{29} - 18 q^{31} - 18 q^{32} - 18 q^{33} + 9 q^{34} - 6 q^{35} - 24 q^{36} - 12 q^{37} - 12 q^{38} - 6 q^{39} - 9 q^{40} + 15 q^{41} + 6 q^{42} - 18 q^{43} - 9 q^{44} + 6 q^{45} - 18 q^{46} + 9 q^{47} + 9 q^{48} + 24 q^{49} + 12 q^{50} - 6 q^{51} + 51 q^{52} + 21 q^{53} + 21 q^{54} + 18 q^{55} - 6 q^{56} + 15 q^{57} + 9 q^{58} - 6 q^{59} + 6 q^{60} - 9 q^{61} - 12 q^{62} - 6 q^{63} - 12 q^{64} - 33 q^{65} - 18 q^{66} + 24 q^{67} + 12 q^{68} - 18 q^{69} - 36 q^{70} - 12 q^{71} + 6 q^{72} - 33 q^{74} - 18 q^{77} - 3 q^{78} - 3 q^{79} + 24 q^{80} + 21 q^{81} - 18 q^{82} + 3 q^{83} - 12 q^{84} - 9 q^{85} - 12 q^{86} + 9 q^{88} - 24 q^{89} + 27 q^{90} + 42 q^{91} + 21 q^{93} + 9 q^{94} + 3 q^{95} + 18 q^{96} - 27 q^{97} + 27 q^{98} + 9 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 6 * q^3 - 9 * q^4 + 6 * q^5 - 6 * q^6 - 12 * q^7 + 6 * q^8 + 6 * q^9 + 9 * q^10 + 9 * q^11 + 3 * q^12 - 12 * q^13 - 12 * q^14 - 3 * q^15 + 9 * q^16 + 3 * q^17 + 3 * q^18 - 9 * q^19 - 21 * q^20 + 12 * q^21 + 9 * q^22 + 18 * q^23 + 6 * q^24 + 6 * q^26 - 3 * q^27 + 24 * q^28 + 9 * q^29 - 18 * q^31 - 18 * q^32 - 18 * q^33 + 9 * q^34 - 6 * q^35 - 24 * q^36 - 12 * q^37 - 12 * q^38 - 6 * q^39 - 9 * q^40 + 15 * q^41 + 6 * q^42 - 18 * q^43 - 9 * q^44 + 6 * q^45 - 18 * q^46 + 9 * q^47 + 9 * q^48 + 24 * q^49 + 12 * q^50 - 6 * q^51 + 51 * q^52 + 21 * q^53 + 21 * q^54 + 18 * q^55 - 6 * q^56 + 15 * q^57 + 9 * q^58 - 6 * q^59 + 6 * q^60 - 9 * q^61 - 12 * q^62 - 6 * q^63 - 12 * q^64 - 33 * q^65 - 18 * q^66 + 24 * q^67 + 12 * q^68 - 18 * q^69 - 36 * q^70 - 12 * q^71 + 6 * q^72 - 33 * q^74 - 18 * q^77 - 3 * q^78 - 3 * q^79 + 24 * q^80 + 21 * q^81 - 18 * q^82 + 3 * q^83 - 12 * q^84 - 9 * q^85 - 12 * q^86 + 9 * q^88 - 24 * q^89 + 27 * q^90 + 42 * q^91 + 21 * q^93 + 9 * q^94 + 3 * q^95 + 18 * q^96 - 27 * q^97 + 27 * q^98 + 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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