LMFDB - Embedded newform 637.2.bl.b.53.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [637,2,Mod(53,637)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(637, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([10, 0]))

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

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

chi := DirichletCharacter("637.53");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 637 = 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	637.bl (of order $21$, degree $12$, 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:	$5.08647060876$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$29$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			53.23
Character	$\chi$	$=$	637.53
Dual form			637.2.bl.b.625.23

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.47927 + 1.00855i) q^{2} +(1.63683 + 1.51876i) q^{3} +(0.440381 + 1.12207i) q^{4} +(1.13232 - 0.349275i) q^{5} +(0.889572 + 3.89747i) q^{6} +(0.173595 - 2.64005i) q^{7} +(0.316565 - 1.38696i) q^{8} +(0.148402 + 1.98029i) q^{9} +O(q^{10})$	\(q+(1.47927 + 1.00855i) q^{2} +(1.63683 + 1.51876i) q^{3} +(0.440381 + 1.12207i) q^{4} +(1.13232 - 0.349275i) q^{5} +(0.889572 + 3.89747i) q^{6} +(0.173595 - 2.64005i) q^{7} +(0.316565 - 1.38696i) q^{8} +(0.148402 + 1.98029i) q^{9} +(2.02727 + 0.625329i) q^{10} +(-0.460570 + 6.14588i) q^{11} +(-0.983326 + 2.50547i) q^{12} +(-0.900969 + 0.433884i) q^{13} +(2.91941 - 3.73026i) q^{14} +(2.38388 + 1.14802i) q^{15} +(3.63433 - 3.37217i) q^{16} +(-4.08464 + 0.615661i) q^{17} +(-1.77769 + 3.07905i) q^{18} +(2.80160 + 4.85252i) q^{19} +(0.890564 + 1.11673i) q^{20} +(4.29374 - 4.05767i) q^{21} +(-6.87971 + 8.62689i) q^{22} +(2.54869 + 0.384154i) q^{23} +(2.62462 - 1.78944i) q^{24} +(-2.97103 + 2.02562i) q^{25} +(-1.77037 - 0.266840i) q^{26} +(1.41190 - 1.77047i) q^{27} +(3.03877 - 0.967841i) q^{28} +(-5.42217 - 6.79919i) q^{29} +(2.36857 + 4.10248i) q^{30} +(3.62715 - 6.28241i) q^{31} +(5.96366 - 0.898877i) q^{32} +(-10.0880 + 9.36027i) q^{33} +(-6.66320 - 3.20883i) q^{34} +(-0.725538 - 3.05002i) q^{35} +(-2.15667 + 1.03860i) q^{36} +(-1.57219 + 4.00587i) q^{37} +(-0.749675 + 10.0037i) q^{38} +(-2.13370 - 0.658159i) q^{39} +(-0.125978 - 1.68105i) q^{40} +(1.67715 - 7.34806i) q^{41} +(10.4439 - 1.67193i) q^{42} +(-1.00823 - 4.41734i) q^{43} +(-7.09894 + 2.18973i) q^{44} +(0.859704 + 2.19049i) q^{45} +(3.38276 + 3.13874i) q^{46} +(-3.87665 - 2.64306i) q^{47} +11.0703 q^{48} +(-6.93973 - 0.916597i) q^{49} -6.43788 q^{50} +(-7.62091 - 5.19585i) q^{51} +(-0.883618 - 0.819878i) q^{52} +(-0.482978 - 1.23061i) q^{53} +(3.87418 - 1.19503i) q^{54} +(1.62509 + 7.11998i) q^{55} +(-3.60669 - 1.07652i) q^{56} +(-2.78405 + 12.1977i) q^{57} +(-1.16354 - 15.5263i) q^{58} +(-12.0110 - 3.70489i) q^{59} +(-0.238342 + 3.18045i) q^{60} +(-1.86939 + 4.76312i) q^{61} +(11.7016 - 5.63521i) q^{62} +(5.25382 - 0.0480214i) q^{63} +(0.794733 + 0.382723i) q^{64} +(-0.868642 + 0.805982i) q^{65} +(-24.3631 + 3.67214i) q^{66} +(-4.08655 + 7.07812i) q^{67} +(-2.48961 - 4.31214i) q^{68} +(3.58835 + 4.49964i) q^{69} +(2.00282 - 5.24353i) q^{70} +(5.72661 - 7.18094i) q^{71} +(2.79356 + 0.421062i) q^{72} +(1.03987 - 0.708969i) q^{73} +(-6.36579 + 4.34012i) q^{74} +(-7.93950 - 1.19669i) q^{75} +(-4.21110 + 5.28055i) q^{76} +(16.1455 + 2.28282i) q^{77} +(-2.49252 - 3.12553i) q^{78} +(3.83306 + 6.63906i) q^{79} +(2.93742 - 5.08776i) q^{80} +(10.8909 - 1.64155i) q^{81} +(9.89181 - 9.17826i) q^{82} +(-5.20613 - 2.50714i) q^{83} +(6.44388 + 3.03097i) q^{84} +(-4.41010 + 2.12379i) q^{85} +(2.96365 - 7.55126i) q^{86} +(1.45114 - 19.3641i) q^{87} +(8.37829 + 2.58436i) q^{88} +(-1.00095 - 13.3568i) q^{89} +(-0.937481 + 4.10737i) q^{90} +(0.989071 + 2.45392i) q^{91} +(0.691347 + 3.02899i) q^{92} +(15.4785 - 4.77449i) q^{93} +(-3.06895 - 7.81957i) q^{94} +(4.86718 + 4.51608i) q^{95} +(11.1267 + 7.58604i) q^{96} -5.42125 q^{97} +(-9.34128 - 8.35493i) q^{98} -12.2390 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) $ 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/637\mathbb{Z}\right)^\times$.

$n$	$197$	$248$
$\chi(n)$	$1$	$e\left(\frac{5}{21}\right)$

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 $

$2$	1.47927	+	1.00855i	1.04600	+	0.713150i	0.959100	−	0.283067i	$-0.0913518\pi$
$2$	1.47927	+	1.00855i	1.04600	+	0.713150i	0.0868992	+	0.996217i	$0.472304\pi$
$3$	1.63683	+	1.51876i	0.945025	+	0.876855i	0.992528	−	0.122016i	$-0.0389359\pi$
$3$	1.63683	+	1.51876i	0.945025	+	0.876855i	−0.0475031	+	0.998871i	$0.515126\pi$
$4$	0.440381	+	1.12207i	0.220190	+	0.561036i
$5$	1.13232	−	0.349275i	0.506390	−	0.156201i	−0.0310251	−	0.999519i	$-0.509877\pi$
$5$	1.13232	−	0.349275i	0.506390	−	0.156201i	0.537415	+	0.843318i	$0.319401\pi$
$6$	0.889572	+	3.89747i	0.363166	+	1.59113i
$7$	0.173595	−	2.64005i	0.0656126	−	0.997845i
$7$	0.173595	−	2.64005i	0.0656126	−	0.997845i
$8$	0.316565	−	1.38696i	0.111923	−	0.490365i
$9$	0.148402	+	1.98029i	0.0494674	+	0.660096i
$10$	2.02727	+	0.625329i	0.641078	+	0.197746i
$11$	−0.460570	+	6.14588i	−0.138867	+	1.85305i	0.299301	+	0.954159i	$0.403247\pi$
$11$	−0.460570	+	6.14588i	−0.138867	+	1.85305i	−0.438168	+	0.898893i	$0.644372\pi$
$12$	−0.983326	+	2.50547i	−0.283862	+	0.723268i
$13$	−0.900969	+	0.433884i	−0.249884	+	0.120338i
$13$	−0.900969	+	0.433884i	−0.249884	+	0.120338i
$14$	2.91941	−	3.73026i	0.780244	−	0.996954i
$15$	2.38388	+	1.14802i	0.615516	+	0.296417i
$16$	3.63433	−	3.37217i	0.908583	−	0.843042i
$17$	−4.08464	+	0.615661i	−0.990672	+	0.149320i	−0.624330	−	0.781161i	$-0.714628\pi$
$17$	−4.08464	+	0.615661i	−0.990672	+	0.149320i	−0.366342	+	0.930480i	$0.619390\pi$
$18$	−1.77769	+	3.07905i	−0.419005	+	0.725738i
$19$	2.80160	+	4.85252i	0.642732	+	1.11324i	0.984820	+	0.173576i	$0.0555323\pi$
$19$	2.80160	+	4.85252i	0.642732	+	1.11324i	−0.342089	+	0.939668i	$0.611134\pi$
$20$	0.890564	+	1.11673i	0.199136	+	0.249709i
$21$	4.29374	−	4.05767i	0.936971	−	0.885456i
$22$	−6.87971	+	8.62689i	−1.46676	+	1.83926i
$23$	2.54869	+	0.384154i	0.531439	+	0.0801016i	0.409280	−	0.912409i	$-0.365780\pi$
$23$	2.54869	+	0.384154i	0.531439	+	0.0801016i	0.122160	+	0.992510i	$0.461018\pi$
$24$	2.62462	−	1.78944i	0.535748	−	0.365267i
$25$	−2.97103	+	2.02562i	−0.594207	+	0.405123i
$26$	−1.77037	−	0.266840i	−0.347197	−	0.0523316i
$27$	1.41190	−	1.77047i	0.271721	−	0.340727i
$28$	3.03877	−	0.967841i	0.574274	−	0.182905i
$29$	−5.42217	−	6.79919i	−1.00687	−	1.26258i	−0.964668	−	0.263469i	$-0.915133\pi$
$29$	−5.42217	−	6.79919i	−1.00687	−	1.26258i	−0.0422047	−	0.999109i	$-0.513438\pi$
$30$	2.36857	+	4.10248i	0.432440	+	0.749007i
$31$	3.62715	−	6.28241i	0.651456	−	1.12835i	−0.331314	−	0.943521i	$-0.607492\pi$
$31$	3.62715	−	6.28241i	0.651456	−	1.12835i	0.982770	−	0.184834i	$-0.0591748\pi$
$32$	5.96366	−	0.898877i	1.05424	−	0.158901i
$33$	−10.0880	+	9.36027i	−1.75609	+	1.62941i
$34$	−6.66320	−	3.20883i	−1.14273	−	0.550309i
$35$	−0.725538	−	3.05002i	−0.122638	−	0.515547i
$36$	−2.15667	+	1.03860i	−0.359445	+	0.173100i
$37$	−1.57219	+	4.00587i	−0.258466	+	0.658561i	−0.999923	−	0.0124400i	$-0.996040\pi$
$37$	−1.57219	+	4.00587i	−0.258466	+	0.658561i	0.741457	+	0.671001i	$0.234135\pi$
$38$	−0.749675	+	10.0037i	−0.121613	+	1.62282i
$39$	−2.13370	−	0.658159i	−0.341665	−	0.105390i
$40$	−0.125978	−	1.68105i	−0.0199188	−	0.265798i
$41$	1.67715	−	7.34806i	0.261926	−	1.14757i	−0.657233	−	0.753688i	$-0.728273\pi$
$41$	1.67715	−	7.34806i	0.261926	−	1.14757i	0.919159	−	0.393886i	$-0.128870\pi$
$42$	10.4439	−	1.67193i	1.61153	−	0.257985i
$43$	−1.00823	−	4.41734i	−0.153753	−	0.673637i	−0.991774	−	0.127999i	$-0.959144\pi$
$43$	−1.00823	−	4.41734i	−0.153753	−	0.673637i	0.838021	−	0.545638i	$-0.183713\pi$
$44$	−7.09894	+	2.18973i	−1.07021	+	0.330115i
$45$	0.859704	+	2.19049i	0.128157	+	0.326539i
$46$	3.38276	+	3.13874i	0.498761	+	0.462782i
$47$	−3.87665	−	2.64306i	−0.565468	−	0.385529i	0.246578	−	0.969123i	$-0.420694\pi$
$47$	−3.87665	−	2.64306i	−0.565468	−	0.385529i	−0.812046	+	0.583594i	$0.801646\pi$
$48$	11.0703			1.59786
$49$	−6.93973	−	0.916597i	−0.991390	−	0.130942i
$50$	−6.43788			−0.910454
$51$	−7.62091	−	5.19585i	−1.06714	−	0.727565i
$52$	−0.883618	−	0.819878i	−0.122536	−	0.113697i
$53$	−0.482978	−	1.23061i	−0.0663422	−	0.169037i	0.893858	−	0.448351i	$-0.147988\pi$
$53$	−0.482978	−	1.23061i	−0.0663422	−	0.169037i	−0.960200	+	0.279313i	$0.909893\pi$
$54$	3.87418	−	1.19503i	0.527209	−	0.162622i
$55$	1.62509	+	7.11998i	0.219127	+	0.960058i
$56$	−3.60669	−	1.07652i	−0.481964	−	0.143855i
$57$	−2.78405	+	12.1977i	−0.368756	+	1.61563i
$58$	−1.16354	−	15.5263i	−0.152780	−	2.03871i
$59$	−12.0110	−	3.70489i	−1.56369	−	0.482336i	−0.612381	−	0.790563i	$-0.709788\pi$
$59$	−12.0110	−	3.70489i	−1.56369	−	0.482336i	−0.951313	+	0.308227i	$0.900264\pi$
$60$	−0.238342	+	3.18045i	−0.0307698	+	0.410595i
$61$	−1.86939	+	4.76312i	−0.239350	+	0.609854i	−0.999189	−	0.0402567i	$-0.987182\pi$
$61$	−1.86939	+	4.76312i	−0.239350	+	0.609854i	0.759839	+	0.650111i	$0.225278\pi$
$62$	11.7016	−	5.63521i	1.48611	−	0.715672i
$63$	5.25382	−	0.0480214i	0.661920	−	0.00605013i
$64$	0.794733	+	0.382723i	0.0993416	+	0.0478404i
$65$	−0.868642	+	0.805982i	−0.107742	+	0.0999697i
$66$	−24.3631	+	3.67214i	−2.99889	+	0.452010i
$67$	−4.08655	+	7.07812i	−0.499252	+	0.864730i	−1.00000		0.000863498i	$-0.999725\pi$
$67$	−4.08655	+	7.07812i	−0.499252	+	0.864730i	0.500748	+	0.865593i	$0.333058\pi$
$68$	−2.48961	−	4.31214i	−0.301910	−	0.522924i
$69$	3.58835	+	4.49964i	0.431986	+	0.541693i
$70$	2.00282	−	5.24353i	0.239383	−	0.626722i
$71$	5.72661	−	7.18094i	0.679624	−	0.852221i	−0.315696	−	0.948860i	$-0.602238\pi$
$71$	5.72661	−	7.18094i	0.679624	−	0.852221i	0.995319	+	0.0966394i	$0.0308094\pi$
$72$	2.79356	+	0.421062i	0.329224	+	0.0496226i
$73$	1.03987	−	0.708969i	0.121707	−	0.0829785i	−0.500937	−	0.865484i	$-0.667011\pi$
$73$	1.03987	−	0.708969i	0.121707	−	0.0829785i	0.622644	+	0.782505i	$0.286059\pi$
$74$	−6.36579	+	4.34012i	−0.740008	+	0.504529i
$75$	−7.93950	−	1.19669i	−0.916775	−	0.138182i
$76$	−4.21110	+	5.28055i	−0.483046	+	0.605721i
$77$	16.1455	+	2.28282i	1.83995	+	0.260151i
$78$	−2.49252	−	3.12553i	−0.282223	−	0.353896i
$79$	3.83306	+	6.63906i	0.431253	+	0.746952i	0.996982	−	0.0776394i	$-0.0247383\pi$
$79$	3.83306	+	6.63906i	0.431253	+	0.746952i	−0.565728	+	0.824592i	$0.691405\pi$
$80$	2.93742	−	5.08776i	0.328414	−	0.568829i
$81$	10.8909	−	1.64155i	1.21010	−	0.182394i
$82$	9.89181	−	9.17826i	1.09237	−	1.01357i
$83$	−5.20613	−	2.50714i	−0.571447	−	0.275194i	0.125764	−	0.992060i	$-0.459862\pi$
$83$	−5.20613	−	2.50714i	−0.571447	−	0.275194i	−0.697211	+	0.716866i	$0.745576\pi$
$84$	6.44388	+	3.03097i	0.703084	+	0.330706i
$85$	−4.41010	+	2.12379i	−0.478342	+	0.230357i
$86$	2.96365	−	7.55126i	0.319579	−	0.814274i
$87$	1.45114	−	19.3641i	0.155578	−	2.07605i
$88$	8.37829	+	2.58436i	0.893129	+	0.275494i
$89$	−1.00095	−	13.3568i	−0.106101	−	1.41582i	−0.755391	−	0.655275i	$-0.772553\pi$
$89$	−1.00095	−	13.3568i	−0.106101	−	1.41582i	0.649290	−	0.760541i	$-0.275066\pi$
$90$	−0.937481	+	4.10737i	−0.0988192	+	0.432955i
$91$	0.989071	+	2.45392i	0.103683	+	0.257241i
$92$	0.691347	+	3.02899i	0.0720780	+	0.315794i
$93$	15.4785	−	4.77449i	1.60505	−	0.495091i
$94$	−3.06895	−	7.81957i	−0.316538	−	0.806527i
$95$	4.86718	+	4.51608i	0.499362	+	0.463340i
$96$	11.1267	+	7.58604i	1.13561	+	0.774247i
$97$	−5.42125			−0.550445			−0.275222	−	0.961381i	$-0.588751\pi$
$97$	−5.42125			−0.550445			−0.275222	+	0.961381i	$0.588751\pi$
$98$	−9.34128	−	8.35493i	−0.943612	−	0.843976i
$99$	−12.2390			−1.23006
$100$	−3.58127	−	2.44167i	−0.358127	−	0.244167i
$101$	7.79889	+	7.23631i	0.776018	+	0.720040i	0.965089	−	0.261924i	$-0.0843569\pi$
$101$	7.79889	+	7.23631i	0.776018	+	0.720040i	−0.189070	+	0.981964i	$0.560547\pi$
$102$	−6.03310	−	15.3721i	−0.597366	−	1.52206i
$103$	2.61632	−	0.807027i	0.257794	−	0.0795188i	−0.163165	−	0.986599i	$-0.552170\pi$
$103$	2.61632	−	0.807027i	0.257794	−	0.0795188i	0.420958	+	0.907080i	$0.361694\pi$
$104$	0.316565	+	1.38696i	0.0310417	+	0.136003i
$105$	3.44465	−	6.09428i	0.336164	−	0.594741i
$106$	0.526673	−	2.30750i	0.0511550	−	0.224125i
$107$	1.39753	+	18.6488i	0.135105	+	1.80285i	0.493991	+	0.869467i	$0.335537\pi$
$107$	1.39753	+	18.6488i	0.135105	+	1.80285i	−0.358886	+	0.933381i	$0.616843\pi$
$108$	2.60837	+	0.804574i	0.250990	+	0.0774202i
$109$	−1.02017	+	13.6133i	−0.0977148	+	1.30391i	0.705707	+	0.708504i	$0.250629\pi$
$109$	−1.02017	+	13.6133i	−0.0977148	+	1.30391i	−0.803422	+	0.595410i	$0.796990\pi$
$110$	−4.77689	+	12.1713i	−0.455459	+	1.16049i
$111$	−8.65735	+	4.16916i	−0.821719	+	0.395719i
$112$	−8.27179	−	10.1802i	−0.781611	−	0.961940i
$113$	13.4237	+	6.46450i	1.26279	+	0.608129i	0.940912	−	0.338651i	$-0.109971\pi$
$113$	13.4237	+	6.46450i	1.26279	+	0.608129i	0.321881	+	0.946780i	$0.395685\pi$
$114$	−16.4203	+	15.2358i	−1.53790	+	1.42697i
$115$	3.02012	−	0.455209i	0.281627	−	0.0424485i
$116$	5.24136	−	9.07830i	0.486648	−	0.842899i
$117$	−0.992921	−	1.71979i	−0.0917956	−	0.158995i
$118$	−14.0309	−	17.5941i	−1.29165	−	1.61967i
$119$	0.916303	+	10.8905i	0.0839974	+	0.998334i
$120$	2.34691	−	2.94293i	0.214242	−	0.268652i
$121$	−26.6826	−	4.02175i	−2.42569	−	0.365614i
$122$	−7.56914	+	5.16055i	−0.685278	+	0.467215i
$123$	13.9051	−	9.48035i	1.25378	−	0.854815i
$124$	8.64665	+	1.30327i	0.776492	+	0.117037i
$125$	−6.35074	+	7.96358i	−0.568028	+	0.712284i
$126$	7.82024	+	5.22769i	0.696682	+	0.465720i
$127$	1.06175	+	1.33139i	0.0942153	+	0.118142i	0.826704	−	0.562637i	$-0.190213\pi$
$127$	1.06175	+	1.33139i	0.0942153	+	0.118142i	−0.732489	+	0.680779i	$0.761642\pi$
$128$	−5.24139	−	9.07836i	−0.463278	−	0.802421i
$129$	5.05856	−	8.76169i	0.445382	−	0.771424i
$130$	−2.09782	+	0.316196i	−0.183991	+	0.0277322i
$131$	4.29469	−	3.98489i	0.375229	−	0.348162i	−0.469904	−	0.882717i	$-0.655712\pi$
$131$	4.29469	−	3.98489i	0.375229	−	0.348162i	0.845133	+	0.534556i	$0.179521\pi$
$132$	−14.9454	−	7.19735i	−1.30083	−	0.626449i
$133$	13.2972	−	6.55400i	1.15302	−	0.568304i
$134$	−13.1837	+	6.34894i	−1.13890	+	0.548465i
$135$	0.980346	−	2.49788i	0.0843748	−	0.214983i
$136$	−0.439156	+	5.86014i	−0.0376574	+	0.502502i
$137$	−0.664925	−	0.205102i	−0.0568083	−	0.0175231i	0.266221	−	0.963912i	$-0.414225\pi$
$137$	−0.664925	−	0.205102i	−0.0568083	−	0.0175231i	−0.323029	+	0.946389i	$0.604701\pi$
$138$	0.770019	+	10.2752i	0.0655484	+	0.874682i
$139$	−3.23037	+	14.1532i	−0.273996	+	1.20046i	0.631253	+	0.775577i	$0.282541\pi$
$139$	−3.23037	+	14.1532i	−0.273996	+	1.20046i	−0.905250	+	0.424880i	$0.860316\pi$
$140$	3.10283	−	2.15728i	0.262237	−	0.182323i
$141$	−2.33126	−	10.2139i	−0.196328	−	0.860168i
$142$	15.7135	−	4.84697i	1.31865	−	0.406749i
$143$	−2.25164	−	5.73708i	−0.188291	−	0.479759i
$144$	7.21721	+	6.69659i	0.601434	+	0.558049i
$145$	−8.51443	−	5.80504i	−0.707085	−	0.482083i
$146$	2.25327			0.186482
$147$	−9.96708	−	12.0401i	−0.822071	−	0.993049i
$148$	−5.18723			−0.426388
$149$	13.1727	+	8.98100i	1.07915	+	0.735752i	0.966186	−	0.257847i	$-0.0830131\pi$
$149$	13.1727	+	8.98100i	1.07915	+	0.735752i	0.112964	+	0.993599i	$0.463965\pi$
$150$	−10.5377	−	9.77758i	−0.860402	−	0.798336i
$151$	5.00428	+	12.7507i	0.407243	+	1.03764i	0.976508	+	0.215483i	$0.0691327\pi$
$151$	5.00428	+	12.7507i	0.407243	+	1.03764i	−0.569265	+	0.822154i	$0.692772\pi$
$152$	7.61714	−	2.34958i	0.617831	−	0.190576i
$153$	−1.82536	−	7.99741i	−0.147571	−	0.646552i
$154$	21.5811	+	19.6604i	1.73906	+	1.58428i
$155$	1.91281	−	8.38059i	0.153641	−	0.673145i
$156$	−0.201138	−	2.68400i	−0.0161039	−	0.214892i
$157$	4.21556	+	1.30033i	0.336439	+	0.103778i	0.458371	−	0.888761i	$-0.348433\pi$
$157$	4.21556	+	1.30033i	0.336439	+	0.103778i	−0.121933	+	0.992538i	$0.538909\pi$
$158$	−1.02568	+	13.6868i	−0.0815988	+	1.08886i
$159$	1.07844	−	2.74783i	0.0855260	−	0.217917i
$160$	6.43883	−	3.10078i	0.509034	−	0.245138i
$161$	1.45663	−	6.66199i	0.114798	−	0.525039i
$162$	17.7662	+	8.55574i	1.39584	+	0.672203i
$163$	−2.11764	+	1.96488i	−0.165866	+	0.153901i	−0.758739	−	0.651395i	$-0.774184\pi$
$163$	−2.11764	+	1.96488i	−0.165866	+	0.153901i	0.592873	+	0.805296i	$0.297994\pi$
$164$	8.98363	−	1.35406i	0.701504	−	0.105735i
$165$	−8.15352	+	14.1223i	−0.634751	+	1.09942i
$166$	−5.17268	−	8.95935i	−0.401478	−	0.695381i
$167$	−11.7847	−	14.7776i	−0.911929	−	1.14352i	−0.989209	−	0.146513i	$-0.953195\pi$
$167$	−11.7847	−	14.7776i	−0.911929	−	1.14352i	0.0772796	−	0.997009i	$-0.475377\pi$
$168$	−4.26858	−	7.23976i	−0.329328	−	0.558560i
$169$	0.623490	−	0.781831i	0.0479608	−	0.0601409i
$170$	−8.66565	−	1.30614i	−0.664625	−	0.100176i
$171$	−9.19362	+	6.26811i	−0.703054	+	0.479334i
$172$	4.51256	−	3.07661i	0.344080	−	0.234590i
$173$	−0.482689	−	0.0727537i	−0.0366982	−	0.00553136i	0.130668	−	0.991426i	$-0.458288\pi$
$173$	−0.482689	−	0.0727537i	−0.0366982	−	0.00553136i	−0.167366	+	0.985895i	$0.553526\pi$
$174$	21.6762	−	27.1811i	1.64327	−	2.06060i
$175$	4.83197	+	8.19532i	0.365263	+	0.619508i
$176$	19.0511	+	23.8893i	1.43603	+	1.80072i
$177$	−14.0331	−	24.3060i	−1.05479	−	1.82695i
$178$	11.9903	−	20.7677i	0.898708	−	1.55661i
$179$	7.18594	−	1.08311i	0.537102	−	0.0809551i	0.125111	−	0.992143i	$-0.460071\pi$
$179$	7.18594	−	1.08311i	0.537102	−	0.0809551i	0.411991	+	0.911188i	$0.364833\pi$
$180$	−2.07929	+	1.92930i	−0.154981	+	0.143802i
$181$	7.44386	+	3.58477i	0.553297	+	0.266454i	0.689572	−	0.724217i	$-0.257799\pi$
$181$	7.44386	+	3.58477i	0.553297	+	0.266454i	−0.136275	+	0.990671i	$0.543513\pi$
$182$	−1.01180	+	4.62753i	−0.0749993	+	0.343015i
$183$	−10.2939	+	4.95727i	−0.760946	+	0.366452i
$184$	1.33963	−	3.41333i	0.0987590	−	0.251634i
$185$	−0.381072	+	5.08506i	−0.0280170	+	0.373861i
$186$	27.7121	+	8.54806i	2.03195	+	0.626774i
$187$	−1.90251	−	25.3873i	−0.139126	−	1.85650i
$188$	1.25850	−	5.51383i	0.0917852	−	0.402137i
$189$	−4.42903	−	4.03483i	−0.322164	−	0.293491i
$190$	2.64517	+	11.5893i	0.191901	+	0.840774i
$191$	−1.42165	+	0.438519i	−0.102867	+	0.0317302i	−0.345761	−	0.938323i	$-0.612379\pi$
$191$	−1.42165	+	0.438519i	−0.102867	+	0.0317302i	0.242895	+	0.970053i	$0.421903\pi$
$192$	0.719580	+	1.83346i	0.0519312	+	0.132319i
$193$	19.1601	+	17.7779i	1.37917	+	1.27968i	0.920318	+	0.391172i	$0.127930\pi$
$193$	19.1601	+	17.7779i	1.37917	+	1.27968i	0.458854	+	0.888512i	$0.348260\pi$
$194$	−8.01947	−	5.46759i	−0.575765	−	0.392550i
$195$	−2.64591			−0.189478
$196$	−2.02763	−	8.19053i	−0.144831	−	0.585038i
$197$	−0.855369			−0.0609425			−0.0304713	−	0.999536i	$-0.509701\pi$
$197$	−0.855369			−0.0609425			−0.0304713	+	0.999536i	$0.509701\pi$
$198$	−18.1047	−	12.3436i	−1.28664	−	0.877219i
$199$	−9.09217	−	8.43630i	−0.644527	−	0.598034i	0.288657	−	0.957433i	$-0.406791\pi$
$199$	−9.09217	−	8.43630i	−0.644527	−	0.598034i	−0.933184	+	0.359399i	$0.882982\pi$
$200$	1.86893	+	4.76195i	0.132153	+	0.336720i
$201$	−17.4389	+	5.37920i	−1.23005	+	0.379420i
$202$	4.23848	+	18.5700i	0.298218	+	1.30658i
$203$	−18.8915	+	13.1345i	−1.32592	+	0.921862i
$204$	2.47401	−	10.8394i	0.173216	−	0.758907i
$205$	−0.667424	−	8.90615i	−0.0466149	−	0.622033i
$206$	4.68416	+	1.44487i	0.326361	+	0.100669i
$207$	−0.382504	+	5.10416i	−0.0265859	+	0.354764i
$208$	−1.81129	+	4.61510i	−0.125591	+	0.319999i
$209$	−31.1133	+	14.9834i	−2.15215	+	1.03642i
$210$	11.2419	−	5.54097i	0.775767	−	0.382363i
$211$	16.8158	+	8.09807i	1.15765	+	0.557494i	0.911323	−	0.411693i	$-0.135062\pi$
$211$	16.8158	+	8.09807i	1.15765	+	0.557494i	0.246326	+	0.969187i	$0.420777\pi$
$212$	1.16814	−	1.08387i	0.0802280	−	0.0744407i
$213$	20.2796	−	3.05666i	1.38954	−	0.209439i
$214$	−16.7409	+	28.9960i	−1.14438	+	1.98213i
$215$	−2.68450	−	4.64970i	−0.183082	−	0.317107i
$216$	−2.00861	−	2.51872i	−0.136669	−	0.171377i
$217$	−15.9562	−	10.6665i	−1.08318	−	0.724087i
$218$	−15.2387	+	19.1087i	−1.03210	+	1.29421i
$219$	2.77884	+	0.418842i	0.187776	+	0.0283028i
$220$	−7.27347	+	4.95897i	−0.490377	+	0.334333i
$221$	3.41301	−	2.32695i	0.229584	−	0.156528i
$222$	−17.0113	−	2.56404i	−1.14173	−	0.172087i
$223$	4.58496	−	5.74936i	0.307031	−	0.385005i	−0.604246	−	0.796798i	$-0.706526\pi$
$223$	4.58496	−	5.74936i	0.307031	−	0.385005i	0.911278	+	0.411792i	$0.135097\pi$
$224$	−1.33782	−	15.9004i	−0.0893869	−	1.06239i
$225$	−4.45221	−	5.58290i	−0.296814	−	0.372193i
$226$	13.3374	+	23.1011i	0.887194	+	1.53666i
$227$	3.67916	−	6.37249i	0.244194	−	0.422957i	−0.717711	−	0.696342i	$-0.754810\pi$
$227$	3.67916	−	6.37249i	0.244194	−	0.422957i	0.961905	+	0.273385i	$0.0881432\pi$
$228$	−14.9127	+	2.24773i	−0.987620	+	0.148860i
$229$	−1.40133	+	1.30024i	−0.0926024	+	0.0859225i	−0.725116	−	0.688627i	$-0.758214\pi$
$229$	−1.40133	+	1.30024i	−0.0926024	+	0.0859225i	0.632513	+	0.774549i	$0.282023\pi$
$230$	4.92666	+	2.37255i	0.324854	+	0.156442i
$231$	22.9604	+	28.2577i	1.51068	+	1.85922i
$232$	−11.1467	+	5.36796i	−0.731815	+	0.352424i
$233$	−5.39210	+	13.7389i	−0.353248	+	0.900062i	0.638237	+	0.769840i	$0.279664\pi$
$233$	−5.39210	+	13.7389i	−0.353248	+	0.900062i	−0.991485	+	0.130222i	$0.958431\pi$
$234$	0.265694	−	3.54543i	0.0173689	−	0.231772i
$235$	−5.31277	−	1.63877i	−0.346567	−	0.106902i
$236$	−1.13224	−	15.1087i	−0.0737027	−	0.983494i
$237$	−3.80904	+	16.6885i	−0.247424	+	1.08403i
$238$	−9.62816	+	17.0341i	−0.624101	+	1.10416i
$239$	−5.82929	−	25.5398i	−0.377066	−	1.65203i	−0.706395	−	0.707818i	$-0.749680\pi$
$239$	−5.82929	−	25.5398i	−0.377066	−	1.65203i	0.329330	−	0.944215i	$-0.393177\pi$
$240$	12.5351	−	3.86658i	0.809140	−	0.249587i
$241$	−6.13950	−	15.6432i	−0.395480	−	1.00767i	−0.980477	−	0.196632i	$-0.937000\pi$
$241$	−6.13950	−	15.6432i	−0.395480	−	1.00767i	0.584997	−	0.811035i	$-0.301096\pi$
$242$	−35.4145	−	32.8599i	−2.27653	−	2.11231i
$243$	14.7067	+	10.0268i	0.943432	+	0.643221i
$244$	−6.16780			−0.394853
$245$	−8.17815	+	1.38599i	−0.522483	+	0.0885477i
$246$	30.1308			1.92107
$247$	−4.62958	−	3.15640i	−0.294573	−	0.200837i
$248$	−7.56523	−	7.01951i	−0.480393	−	0.445739i
$249$	−4.71382	−	12.0106i	−0.298726	−	0.761142i
$250$	−17.4261	+	5.37523i	−1.10212	+	0.339960i
$251$	−2.42269	−	10.6145i	−0.152919	−	0.669982i	−0.992028	−	0.126019i	$-0.959780\pi$
$251$	−2.42269	−	10.6145i	−0.152919	−	0.669982i	0.839109	−	0.543964i	$-0.183077\pi$
$252$	2.36757	+	5.87402i	0.149143	+	0.370028i
$253$	−3.53481	+	15.4870i	−0.222232	+	0.973662i
$254$	0.227840	+	3.04031i	0.0142960	+	0.190766i
$255$	−10.4441	−	3.22158i	−0.654035	−	0.201743i
$256$	1.53437	−	20.4747i	0.0958981	−	1.27967i
$257$	−0.977266	+	2.49003i	−0.0609602	+	0.155324i	−0.958109	−	0.286405i	$-0.907540\pi$
$257$	−0.977266	+	2.49003i	−0.0609602	+	0.155324i	0.897148	+	0.441729i	$0.145635\pi$
$258$	16.3195	−	7.85907i	1.01601	−	0.489285i
$259$	10.3028	+	4.84605i	0.640183	+	0.301119i
$260$	−1.28690	−	0.619740i	−0.0798103	−	0.0384346i
$261$	12.6597	−	11.7465i	0.783616	−	0.727089i
$262$	10.3719	−	1.56332i	0.640781	−	0.0965822i
$263$	7.33508	−	12.7047i	0.452301	−	0.783408i	−0.546228	−	0.837637i	$-0.683937\pi$
$263$	7.33508	−	12.7047i	0.452301	−	0.783408i	0.998529	+	0.0542290i	$0.0172701\pi$
$264$	9.78883	+	16.9548i	0.602461	+	1.04349i
$265$	−0.976708	−	1.22475i	−0.0599987	−	0.0752360i
$266$	26.2802	+	3.71577i	1.61134	+	0.227829i
$267$	18.6473	−	23.3830i	1.14120	−	1.43102i
$268$	−9.74180	−	1.46834i	−0.595075	−	0.0896931i
$269$	−7.59262	+	5.17656i	−0.462930	+	0.315620i	−0.772229	−	0.635345i	$-0.780858\pi$
$269$	−7.59262	+	5.17656i	−0.462930	+	0.315620i	0.309299	+	0.950965i	$0.399906\pi$
$270$	3.96942	−	2.70631i	0.241571	−	0.164701i
$271$	−23.5654	−	3.55192i	−1.43150	−	0.215764i	−0.612913	−	0.790150i	$-0.710003\pi$
$271$	−23.5654	−	3.55192i	−1.43150	−	0.215764i	−0.818584	+	0.574386i	$0.805241\pi$
$272$	−12.7688	+	16.0116i	−0.774225	+	0.970847i
$273$	−2.10797	+	5.51882i	−0.127580	+	0.334014i
$274$	−0.776746	−	0.974008i	−0.0469249	−	0.0588420i
$275$	−11.0808	−	19.1926i	−0.668199	−	1.15735i
$276$	−3.46868	+	6.00794i	−0.208790	+	0.361635i
$277$	24.9368	−	3.75862i	1.49831	−	0.225834i	0.651874	−	0.758327i	$-0.273983\pi$
$277$	24.9368	−	3.75862i	1.49831	−	0.225834i	0.846434	+	0.532493i	$0.178745\pi$
$278$	−19.0527	+	17.6783i	−1.14271	+	1.06028i
$279$	12.9793	+	6.25049i	0.777049	+	0.374207i
$280$	−4.45993	+	0.0407650i	−0.266532	+	0.00243618i
$281$	−6.23067	+	3.00053i	−0.371691	+	0.178997i	−0.610398	−	0.792095i	$-0.708991\pi$
$281$	−6.23067	+	3.00053i	−0.371691	+	0.178997i	0.238708	+	0.971091i	$0.423276\pi$
$282$	6.85267	−	17.4603i	0.408070	−	1.03975i
$283$	−1.69550	+	22.6249i	−0.100787	+	1.34491i	0.685962	+	0.727637i	$0.259382\pi$
$283$	−1.69550	+	22.6249i	−0.100787	+	1.34491i	−0.786749	+	0.617273i	$0.788237\pi$
$284$	10.5794	+	3.26332i	0.627773	+	0.193642i
$285$	1.10792	+	14.7841i	0.0656274	+	0.875736i
$286$	2.45534	−	10.7576i	0.145187	−	0.636107i
$287$	−19.1081	−	5.70334i	−1.12792	−	0.336657i
$288$	2.66506	+	11.6764i	0.157040	+	0.688037i
$289$	0.0605396	−	0.0186740i	0.00356115	−	0.00109847i
$290$	−6.74046	−	17.1744i	−0.395813	−	1.00852i
$291$	−8.87367	−	8.23357i	−0.520184	−	0.482660i
$292$	1.25345	+	0.854588i	0.0733527	+	0.0500110i
$293$	26.7661			1.56369			0.781847	−	0.623470i	$-0.214278\pi$
$293$	26.7661			1.56369			0.781847	+	0.623470i	$0.214278\pi$
$294$	−2.60098	−	27.8628i	−0.151692	−	1.62499i
$295$	−14.8943			−0.867180
$296$	5.05828	+	3.44868i	0.294007	+	0.200450i
$297$	10.2308	+	9.49280i	0.593652	+	0.550828i
$298$	10.4282	+	26.5706i	0.604088	+	1.53919i
$299$	−2.46297	+	0.759726i	−0.142437	+	0.0439361i
$300$	−2.15363	−	9.43569i	−0.124340	−	0.544770i
$301$	−11.8370	+	1.89495i	−0.682274	+	0.109223i
$302$	−5.45702	+	23.9087i	−0.314016	+	1.37579i
$303$	1.77526	+	23.6892i	0.101986	+	1.36091i
$304$	26.5455	+	8.18819i	1.52249	+	0.469625i
$305$	−0.453108	+	6.04631i	−0.0259449	+	0.346211i
$306$	5.36557	−	13.6713i	0.306729	−	0.781534i
$307$	22.9247	−	11.0400i	1.30838	−	0.630084i	0.355856	−	0.934541i	$-0.384189\pi$
$307$	22.9247	−	11.0400i	1.30838	−	0.630084i	0.952526	+	0.304457i	$0.0984751\pi$
$308$	4.54867	+	19.1217i	0.259184	+	1.08956i
$309$	5.50815	+	2.65259i	0.313348	+	0.150900i
$310$	11.2818	−	10.4680i	0.640762	−	0.594540i
$311$	18.5117	−	2.79020i	1.04970	−	0.158217i	0.398538	−	0.917152i	$-0.369518\pi$
$311$	18.5117	−	2.79020i	1.04970	−	0.158217i	0.651167	+	0.758935i	$0.274280\pi$
$312$	−1.58829	+	2.75101i	−0.0899194	+	0.155745i
$313$	7.58611	+	13.1395i	0.428792	+	0.742690i	0.996766	−	0.0803567i	$-0.0256059\pi$
$313$	7.58611	+	13.1395i	0.428792	+	0.742690i	−0.567974	+	0.823046i	$0.692273\pi$
$314$	4.92450	+	6.17513i	0.277906	+	0.348483i
$315$	5.93225	−	1.88940i	0.334244	−	0.106456i
$316$	−5.76149	+	7.22468i	−0.324109	+	0.406420i
$317$	−17.0681	−	2.57260i	−0.958638	−	0.144491i	−0.348957	−	0.937139i	$-0.613464\pi$
$317$	−17.0681	−	2.57260i	−0.958638	−	0.144491i	−0.609680	+	0.792647i	$0.708702\pi$
$318$	4.36661	−	2.97711i	0.244868	−	0.166948i
$319$	44.2843	−	30.1925i	2.47944	−	1.69046i
$320$	1.03357	+	0.155786i	0.0577783	+	0.00870867i
$321$	−26.0355	+	32.6475i	−1.45316	+	1.82220i
$322$	8.87367	−	8.38579i	0.494510	−	0.467322i
$323$	−14.4311	−	18.0960i	−0.802965	−	1.00689i
$324$	6.63809	+	11.4975i	0.368783	+	0.638751i
$325$	1.79793	−	3.11410i	0.0997311	−	0.172739i
$326$	−5.11422	+	0.770845i	−0.283250	+	0.0426931i
$327$	−22.3451	+	20.7332i	−1.23569	+	1.14655i
$328$	−9.66054	−	4.65227i	−0.533414	−	0.256879i
$329$	−7.65076	+	9.77573i	−0.421800	+	0.538953i
$330$	−26.3043	+	12.6675i	−1.44800	+	0.697321i
$331$	−6.28922	+	16.0247i	−0.345687	+	0.880795i	0.647264	+	0.762266i	$0.275913\pi$
$331$	−6.28922	+	16.0247i	−0.345687	+	0.880795i	−0.992951	+	0.118529i	$0.962182\pi$
$332$	0.520512	−	6.94575i	0.0285668	−	0.381197i
$333$	−8.16609	−	2.51891i	−0.447499	−	0.138035i
$334$	−2.52887	−	33.7454i	−0.138374	−	1.84647i
$335$	−2.15508	+	9.44204i	−0.117745	+	0.515874i
$336$	1.92175	−	29.2261i	0.104840	−	1.59442i
$337$	3.97290	+	17.4064i	0.216417	+	0.948187i	0.960101	+	0.279655i	$0.0902199\pi$
$337$	3.97290	+	17.4064i	0.216417	+	0.948187i	−0.743683	+	0.668532i	$0.766923\pi$
$338$	1.71082	−	0.527718i	0.0930564	−	0.0287041i
$339$	12.1543	+	30.9686i	0.660130	+	1.68198i
$340$	−4.32517	−	4.01317i	−0.234565	−	0.217645i
$341$	36.9404	+	25.1855i	2.00043	+	1.36387i
$342$	−19.9215			−1.07723
$343$	−3.62456	+	18.1621i	−0.195708	+	0.980662i
$344$	−6.44584			−0.347536
$345$	5.63478	+	3.84172i	0.303366	+	0.206832i
$346$	−0.640650	−	0.594437i	−0.0344416	−	0.0319571i
$347$	0.621933	+	1.58466i	0.0333871	+	0.0850690i	0.946595	−	0.322425i	$-0.104498\pi$
$347$	0.621933	+	1.58466i	0.0333871	+	0.0850690i	−0.913208	+	0.407494i	$0.866403\pi$
$348$	22.3670	−	6.89929i	1.19899	−	0.369841i
$349$	−0.272143	−	1.19234i	−0.0145675	−	0.0638244i	0.967122	−	0.254314i	$-0.0818496\pi$
$349$	−0.272143	−	1.19234i	−0.0145675	−	0.0638244i	−0.981689	+	0.190489i	$0.938992\pi$
$350$	−1.11758	+	16.9963i	−0.0597373	+	0.908492i
$351$	−0.503902	+	2.20774i	−0.0268963	+	0.117840i
$352$	2.77771	+	37.0659i	0.148052	+	1.97562i
$353$	3.19441	+	0.985346i	0.170021	+	0.0524447i	0.378597	−	0.925562i	$-0.376407\pi$
$353$	3.19441	+	0.985346i	0.170021	+	0.0524447i	−0.208576	+	0.978006i	$0.566883\pi$
$354$	3.75508	−	50.1081i	0.199580	−	2.66322i
$355$	3.97624	−	10.1313i	0.211037	−	0.537714i
$356$	14.5465	−	7.00521i	0.770961	−	0.371275i
$357$	−15.0403	+	19.2176i	−0.796015	+	1.01710i
$358$	11.7223	+	5.64515i	0.619542	+	0.298355i
$359$	−15.4690	+	14.3532i	−0.816424	+	0.757531i	−0.973165	−	0.230109i	$-0.926092\pi$
$359$	−15.4690	+	14.3532i	−0.816424	+	0.757531i	0.156741	+	0.987640i	$0.449901\pi$
$360$	3.31028	−	0.498944i	0.174467	−	0.0262966i
$361$	−6.19795	+	10.7352i	−0.326208	+	0.565009i
$362$	7.39604	+	12.8103i	0.388727	+	0.673295i
$363$	−37.5668	−	47.1073i	−1.97175	−	2.47249i
$364$	−2.31791	+	2.19047i	−0.121491	+	0.114812i
$365$	0.929838	−	1.16598i	0.0486700	−	0.0610302i
$366$	−20.2270	−	3.04874i	−1.05728	−	0.159360i
$367$	19.3828	−	13.2150i	1.01178	−	0.689817i	0.0605033	−	0.998168i	$-0.480729\pi$
$367$	19.3828	−	13.2150i	1.01178	−	0.689817i	0.951273	+	0.308351i	$0.0997771\pi$
$368$	10.5582	−	7.19848i	0.550386	−	0.375247i
$369$	14.8002	+	2.23077i	0.770466	+	0.116129i
$370$	−5.69223	+	7.13783i	−0.295925	+	0.371078i
$371$	−3.33271	+	1.06146i	−0.173026	+	0.0551082i
$372$	12.1737	+	15.2654i	0.631179	+	0.791474i
$373$	−1.36021	−	2.35596i	−0.0704291	−	0.121987i	0.828660	−	0.559752i	$-0.189104\pi$
$373$	−1.36021	−	2.35596i	−0.0704291	−	0.121987i	−0.899089	+	0.437765i	$0.855770\pi$
$374$	22.7899	−	39.4733i	1.17844	−	2.04112i
$375$	−22.4898	+	3.38980i	−1.16137	+	0.175048i
$376$	−4.89302	+	4.54006i	−0.252338	+	0.234136i
$377$	7.83527	+	3.77327i	0.403537	+	0.194333i
$378$	−2.48239	−	10.4355i	−0.127680	−	0.536743i
$379$	12.4586	−	5.99973i	0.639953	−	0.308185i	−0.0856224	−	0.996328i	$-0.527288\pi$
$379$	12.4586	−	5.99973i	0.639953	−	0.308185i	0.725576	+	0.688142i	$0.241574\pi$
$380$	−2.92396	+	7.45012i	−0.149996	+	0.382183i
$381$	−0.284157	+	3.79181i	−0.0145578	+	0.194260i
$382$	−2.54526	−	0.785109i	−0.130227	−	0.0401696i
$383$	0.767295	+	10.2388i	0.0392069	+	0.523180i	0.981885	+	0.189477i	$0.0606793\pi$
$383$	0.767295	+	10.2388i	0.0392069	+	0.523180i	−0.942678	+	0.333703i	$0.891702\pi$
$384$	5.20855	−	22.8202i	0.265798	−	1.16454i
$385$	19.0792	−	3.05432i	0.972366	−	0.155663i
$386$	10.4130	+	45.6221i	0.530005	+	2.32210i
$387$	8.59798	−	2.65213i	0.437060	−	0.134815i
$388$	−2.38741	−	6.08303i	−0.121203	−	0.308819i
$389$	−27.7764	−	25.7727i	−1.40832	−	1.30673i	−0.893236	−	0.449588i	$-0.851571\pi$
$389$	−27.7764	−	25.7727i	−1.40832	−	1.30673i	−0.515083	−	0.857140i	$-0.672239\pi$
$390$	−3.91401	−	2.66853i	−0.198194	−	0.135126i
$391$	−10.6470			−0.538443
$392$	−3.46816	+	9.33497i	−0.175168	+	0.471487i
$393$	13.0818			0.659888
$394$	−1.26532	−	0.862680i	−0.0637458	−	0.0434612i
$395$	6.65911	+	6.17875i	0.335056	+	0.310887i
$396$	−5.38980	−	13.7330i	−0.270848	−	0.690109i
$397$	−4.52315	+	1.39521i	−0.227010	+	0.0700235i	−0.406174	−	0.913796i	$-0.633137\pi$
$397$	−4.52315	+	1.39521i	−0.227010	+	0.0700235i	0.179163	+	0.983819i	$0.442661\pi$
$398$	−4.94134	−	21.6494i	−0.247687	−	1.08519i
$399$	31.7193	+	9.46748i	1.58795	+	0.473967i
$400$	−3.96701	+	17.3806i	−0.198350	+	0.869030i
$401$	−1.32096	−	17.6270i	−0.0659656	−	0.880249i	−0.927804	−	0.373067i	$-0.878306\pi$
$401$	−1.32096	−	17.6270i	−0.0659656	−	0.880249i	0.861839	−	0.507182i	$-0.169313\pi$
$402$	−31.2220	−	9.63072i	−1.55721	−	0.480337i
$403$	−0.542115	+	7.23402i	−0.0270047	+	0.360352i
$404$	−4.68518	+	11.9376i	−0.233096	+	0.593920i
$405$	11.7587	−	5.66269i	0.584294	−	0.281381i
$406$	−41.1923	+	0.376509i	−2.04434	+	0.0186858i
$407$	−23.8955	−	11.5075i	−1.18446	−	0.570404i
$408$	−9.61895	+	8.92508i	−0.476209	+	0.441857i
$409$	22.4781	−	3.38803i	1.11147	−	0.167527i	0.432458	−	0.901654i	$-0.357646\pi$
$409$	22.4781	−	3.38803i	1.11147	−	0.167527i	0.679013	+	0.734127i	$0.262408\pi$
$410$	7.99497	−	13.8477i	0.394844	−	0.683889i
$411$	−0.776869	−	1.34558i	−0.0383201	−	0.0663724i
$412$	2.05772	+	2.58030i	0.101377	+	0.127122i
$413$	−11.8661	+	31.0664i	−0.583894	+	1.52868i
$414$	−5.71361	+	7.16464i	−0.280809	+	0.352123i
$415$	−6.77069	−	1.02052i	−0.332360	−	0.0500953i
$416$	−4.98306	+	3.39740i	−0.244315	+	0.166571i
$417$	−26.7828	+	18.2602i	−1.31156	+	0.894206i
$418$	−61.1363	−	9.21482i	−2.99028	−	0.450712i
$419$	−18.9334	+	23.7417i	−0.924955	+	1.15986i	0.0618733	+	0.998084i	$0.480293\pi$
$419$	−18.9334	+	23.7417i	−0.924955	+	1.15986i	−0.986828	+	0.161773i	$0.948279\pi$
$420$	8.35518	+	1.18134i	0.407691	+	0.0576437i
$421$	4.85815	+	6.09193i	0.236772	+	0.296903i	0.885994	−	0.463696i	$-0.153477\pi$
$421$	4.85815	+	6.09193i	0.236772	+	0.296903i	−0.649222	+	0.760599i	$0.724906\pi$
$422$	16.7078	+	28.9387i	0.813323	+	1.40872i
$423$	4.65871	−	8.06912i	0.226514	−	0.392334i
$424$	−1.85970	+	0.280305i	−0.0903150	+	0.0136128i
$425$	10.8885	−	10.1031i	0.528171	−	0.490071i
$426$	33.0817	+	15.9313i	1.60281	+	0.771875i
$427$	12.2503	+	5.76212i	0.592836	+	0.278849i
$428$	−20.3098	+	9.78071i	−0.981714	+	0.472768i
$429$	5.02768	−	12.8103i	0.242739	−	0.618488i
$430$	0.718341	−	9.58559i	0.0346415	−	0.462258i
$431$	−23.0543	−	7.11131i	−1.11049	−	0.342540i	−0.315353	−	0.948974i	$-0.602123\pi$
$431$	−23.0543	−	7.11131i	−1.11049	−	0.342540i	−0.795133	+	0.606435i	$0.792599\pi$
$432$	−0.838997	−	11.1956i	−0.0403663	−	0.538651i
$433$	8.50818	−	37.2768i	0.408877	−	1.79141i	−0.180527	−	0.983570i	$-0.557780\pi$
$433$	8.50818	−	37.2768i	0.408877	−	1.79141i	0.589404	−	0.807838i	$-0.299362\pi$
$434$	−12.8459	−	31.8711i	−0.616623	−	1.52986i
$435$	−5.12024	−	22.4332i	−0.245497	−	1.07559i
$436$	−15.7243	+	4.85031i	−0.753058	+	0.232288i
$437$	5.27631	+	13.4438i	0.252400	+	0.643106i
$438$	3.68822	+	3.42217i	0.176230	+	0.163518i
$439$	17.6062	+	12.0037i	0.840298	+	0.572906i	0.905200	−	0.424986i	$-0.139721\pi$
$439$	17.6062	+	12.0037i	0.840298	+	0.572906i	−0.0649016	+	0.997892i	$0.520673\pi$
$440$	10.3896			0.495303
$441$	0.785257	−	13.8787i	0.0373932	−	0.660890i
$442$	7.39559			0.351773
$443$	32.9649	+	22.4751i	1.56621	+	1.06782i	0.962736	+	0.270442i	$0.0871700\pi$
$443$	32.9649	+	22.4751i	1.56621	+	1.06782i	0.603475	+	0.797382i	$0.293782\pi$
$444$	−8.49063	−	7.87815i	−0.402947	−	0.373880i
$445$	−5.79859	−	14.7746i	−0.274880	−	0.700382i
$446$	12.5809	−	3.88068i	0.595721	−	0.183756i
$447$	7.92154	+	34.7065i	0.374676	+	1.64156i
$448$	1.14837	−	2.03170i	0.0542554	−	0.0959886i
$449$	1.69735	−	7.43660i	0.0801031	−	0.350955i	−0.918954	−	0.394364i	$-0.870965\pi$
$449$	1.69735	−	7.43660i	0.0801031	−	0.350955i	0.999057	+	0.0434094i	$0.0138220\pi$
$450$	−0.955395	−	12.7489i	−0.0450378	−	0.600987i
$451$	44.3878	+	13.6918i	2.09014	+	0.644723i
$452$	−1.34211	+	17.9092i	−0.0631274	+	0.842376i
$453$	−11.1741	+	28.4710i	−0.525003	+	1.33769i
$454$	11.8694	−	5.71601i	0.557059	−	0.268265i
$455$	1.97704	+	2.43317i	0.0926851	+	0.114069i
$456$	16.0364	+	7.72273i	0.750974	+	0.361650i
$457$	−8.52377	+	7.90890i	−0.398725	+	0.369963i	−0.853898	−	0.520440i	$-0.825768\pi$
$457$	−8.52377	+	7.90890i	−0.398725	+	0.369963i	0.455173	+	0.890403i	$0.349577\pi$
$458$	−3.38429	+	0.510100i	−0.158138	+	0.0238354i
$459$	−4.67711	+	8.10099i	−0.218309	+	0.378122i
$460$	1.84078	+	3.18832i	0.0858267	+	0.148656i
$461$	9.84948	+	12.3509i	0.458736	+	0.575237i	0.956373	−	0.292149i	$-0.0943702\pi$
$461$	9.84948	+	12.3509i	0.458736	+	0.575237i	−0.497637	+	0.867385i	$0.665799\pi$
$462$	5.46534	+	64.9572i	0.254271	+	3.02208i
$463$	−2.70346	+	3.39003i	−0.125640	+	0.157548i	−0.840673	−	0.541543i	$-0.817840\pi$
$463$	−2.70346	+	3.39003i	−0.125640	+	0.157548i	0.715033	+	0.699091i	$0.246412\pi$
$464$	−42.6340	−	6.42604i	−1.97923	−	0.298322i
$465$	15.8590	−	10.8125i	0.735445	−	0.501418i
$466$	−21.8326	+	14.8852i	−1.01138	+	0.689545i
$467$	4.53330	+	0.683286i	0.209776	+	0.0316187i	0.253090	−	0.967443i	$-0.418553\pi$
$467$	4.53330	+	0.683286i	0.209776	+	0.0316187i	−0.0433133	+	0.999062i	$0.513791\pi$
$468$	1.49246	−	1.87149i	0.0689892	−	0.0865097i
$469$	17.9772	+	12.0174i	0.830109	+	0.554913i
$470$	−6.20622	−	7.78236i	−0.286272	−	0.358973i
$471$	4.92528	+	8.53084i	0.226945	+	0.393080i
$472$	−8.94078	+	15.4859i	−0.411533	+	0.712796i
$473$	27.6128	−	4.16196i	1.26964	−	0.191367i
$474$	−22.4657	+	20.8451i	−1.03189	+	0.957449i
$475$	−18.1530	−	8.74202i	−0.832917	−	0.401112i
$476$	−11.8164	+	5.82414i	−0.541606	+	0.266949i
$477$	2.36529	−	1.13906i	0.108299	−	0.0521540i
$478$	17.1350	−	43.6593i	0.783737	−	1.99693i
$479$	2.36456	−	31.5529i	0.108040	−	1.44169i	−0.635037	−	0.772481i	$-0.719015\pi$
$479$	2.36456	−	31.5529i	0.108040	−	1.44169i	0.743077	−	0.669206i	$-0.233366\pi$
$480$	15.2486	+	4.70357i	0.696000	+	0.214688i
$481$	−0.321589	−	4.29131i	−0.0146632	−	0.195667i
$482$	6.69494	−	29.3324i	0.304946	−	1.33606i
$483$	12.5022	−	8.69230i	0.568870	−	0.395513i
$484$	−7.23779	−	31.7108i	−0.328991	−	1.44140i
$485$	−6.13860	+	1.89351i	−0.278739	+	0.0859797i
$486$	11.6425	+	29.6647i	0.528116	+	1.34562i
$487$	−4.70108	−	4.36196i	−0.213026	−	0.197659i	0.566441	−	0.824102i	$-0.308320\pi$
$487$	−4.70108	−	4.36196i	−0.213026	−	0.197659i	−0.779468	+	0.626443i	$0.784510\pi$
$488$	6.01447	+	4.10060i	0.272262	+	0.185625i
$489$	−6.45039			−0.291697
$490$	−13.4955	−	6.19780i	−0.609665	−	0.279988i
$491$	−12.6749			−0.572012			−0.286006	−	0.958228i	$-0.592328\pi$
$491$	−12.6749			−0.572012			−0.286006	+	0.958228i	$0.592328\pi$
$492$	16.7612	+	11.4276i	0.755653	+	0.515195i
$493$	26.3336	+	24.4341i	1.18601	+	1.10045i
$494$	−3.66502	−	9.33831i	−0.164897	−	0.420150i
$495$	−13.8584	+	4.27476i	−0.622891	+	0.192136i
$496$	−8.00307	−	35.0638i	−0.359349	−	1.57441i
$497$	−17.9639	−	16.3651i	−0.805793	−	0.734076i
$498$	5.14027	−	22.5210i	0.230341	−	1.00919i
$499$	−2.40106	−	32.0399i	−0.107486	−	1.43430i	−0.746642	−	0.665227i	$-0.768335\pi$
$499$	−2.40106	−	32.0399i	−0.107486	−	1.43430i	0.639155	−	0.769078i	$-0.279284\pi$
$500$	−11.7324	−	3.61898i	−0.524691	−	0.161846i
$501$	3.15395	−	42.0865i	0.140908	−	1.88029i
$502$	7.12143	−	18.1451i	0.317845	−	0.809856i
$503$	−22.9745	+	11.0639i	−1.02438	+	0.493316i	−0.869143	−	0.494562i	$-0.835329\pi$
$503$	−22.9745	+	11.0639i	−1.02438	+	0.493316i	−0.155238	+	0.987877i	$0.549614\pi$
$504$	1.59657	−	7.30205i	0.0711169	−	0.325259i
$505$	11.3583	+	5.46987i	0.505438	+	0.243406i
$506$	−20.8483	+	19.3444i	−0.926821	+	0.859965i
$507$	2.20796	−	0.332796i	0.0980590	−	0.0147800i
$508$	−1.02635	+	1.77768i	−0.0455367	+	0.0788719i
$509$	−8.94995	−	15.5018i	−0.396700	−	0.687104i	0.596617	−	0.802526i	$-0.296511\pi$
$509$	−8.94995	−	15.5018i	−0.396700	−	0.687104i	−0.993317	+	0.115422i	$0.963178\pi$
$510$	−12.2005	−	15.2989i	−0.540247	−	0.677449i
$511$	−1.69120	−	2.86837i	−0.0748142	−	0.126889i
$512$	9.84766	−	12.3486i	0.435209	−	0.545735i
$513$	12.5468	+	1.89113i	0.553955	+	0.0834953i
$514$	−3.95695	+	2.69780i	−0.174534	+	0.118995i
$515$	2.68064	−	1.82763i	0.118123	−	0.0805350i
$516$	12.0589	+	1.81759i	0.530865	+	0.0800150i
$517$	18.0294	−	22.6081i	0.792931	−	0.994303i
$518$	10.3531	+	17.5594i	0.454888	+	0.771517i
$519$	−0.679586	−	0.852173i	−0.0298305	−	0.0374063i
$520$	0.842884	+	1.45992i	0.0369629	+	0.0640216i
$521$	18.6377	−	32.2814i	0.816531	−	1.41427i	−0.0916931	−	0.995787i	$-0.529228\pi$
$521$	18.6377	−	32.2814i	0.816531	−	1.41427i	0.908224	−	0.418485i	$-0.137439\pi$
$522$	30.5740	−	4.60828i	1.33819	−	0.201699i
$523$	−21.8149	+	20.2412i	−0.953898	+	0.885088i	−0.993466	−	0.114129i	$-0.963592\pi$
$523$	−21.8149	+	20.2412i	−0.953898	+	0.885088i	0.0395683	+	0.999217i	$0.487402\pi$
$524$	6.36263	+	3.06408i	0.277953	+	0.133855i
$525$	−4.53757	+	20.7529i	−0.198036	+	0.905733i
$526$	23.6639	−	11.3959i	1.03179	−	0.496886i
$527$	−10.9478	+	27.8945i	−0.476893	+	1.21510i
$528$	−5.09865	+	68.0367i	−0.221890	+	2.96092i
$529$	−15.6299	−	4.82119i	−0.679561	−	0.209617i
$530$	−0.209591	−	2.79679i	−0.00910403	−	0.121485i
$531$	5.55430	−	24.3350i	0.241036	−	1.05605i
$532$	13.2099	+	12.0342i	0.572722	+	0.521748i
$533$	1.67715	+	7.34806i	0.0726453	+	0.318280i
$534$	51.1672	−	15.7830i	2.21422	−	0.682997i
$535$	8.09602	+	20.6283i	0.350021	+	0.891840i
$536$	8.52341	+	7.90857i	0.368155	+	0.341598i
$537$	13.4071	+	9.14083i	0.578561	+	0.394456i
$538$	−16.4523			−0.709309
$539$	8.82953	−	42.2286i	0.380315	−	1.81891i
$540$	3.23453			0.139192
$541$	3.25841	+	2.22154i	0.140090	+	0.0955116i	0.631337	−	0.775509i	$-0.282506\pi$
$541$	3.25841	+	2.22154i	0.140090	+	0.0955116i	−0.491247	+	0.871020i	$0.663459\pi$
$542$	−31.2773	−	29.0211i	−1.34347	−	1.24656i
$543$	6.73994	+	17.1731i	0.289238	+	0.736967i
$544$	−23.8060	+	7.34319i	−1.02067	+	0.314837i
$545$	3.59961	+	15.7709i	0.154190	+	0.675551i
$546$	−8.68424	+	6.03781i	−0.371651	+	0.258395i
$547$	7.78063	−	34.0892i	0.332676	−	1.45755i	−0.481252	−	0.876582i	$-0.659818\pi$
$547$	7.78063	−	34.0892i	0.332676	−	1.45755i	0.813928	−	0.580966i	$-0.197325\pi$
$548$	−0.0626807	−	0.836416i	−0.00267759	−	0.0357299i
$549$	−9.70976	−	2.99507i	−0.414403	−	0.127826i
$550$	2.96509	−	39.5664i	0.126432	−	1.68712i
$551$	17.8024	−	45.3598i	0.758409	−	1.93239i
$552$	7.37677	−	3.55247i	0.313976	−	0.151203i
$553$	18.1928	−	8.96697i	0.773638	−	0.381314i
$554$	40.6790	+	19.5900i	1.72828	+	0.832297i
$555$	−8.34672	+	7.74463i	−0.354299	+	0.328741i
$556$	−17.3035	+	2.60808i	−0.733830	+	0.110607i
$557$	−12.8955	+	22.3356i	−0.546398	+	0.946389i	0.452119	+	0.891957i	$0.350668\pi$
$557$	−12.8955	+	22.3356i	−0.546398	+	0.946389i	−0.998517	+	0.0544319i	$0.982665\pi$
$558$	12.8959	+	22.3363i	0.545927	+	0.945573i
$559$	2.82499	+	3.54243i	0.119484	+	0.149829i
$560$	−12.9220	−	8.63815i	−0.546055	−	0.365028i
$561$	35.4430	−	44.4442i	1.49641	−	1.87643i
$562$	−12.2430	−	1.84534i	−0.516440	−	0.0778408i
$563$	−8.28793	+	5.65062i	−0.349295	+	0.238145i	−0.725239	−	0.688497i	$-0.758271\pi$
$563$	−8.28793	+	5.65062i	−0.349295	+	0.238145i	0.375944	+	0.926642i	$0.377318\pi$
$564$	10.4341	−	7.11386i	0.439355	−	0.299548i
$565$	17.4578	+	2.63134i	0.734456	+	0.110701i
$566$	−25.3264	+	31.7582i	−1.06455	+	1.33490i
$567$	−2.44315	−	29.0376i	−0.102603	−	1.21946i
$568$	−8.14684	−	10.2158i	−0.341834	−	0.428646i
$569$	−12.4507	−	21.5652i	−0.521960	−	0.904061i	−0.999674	−	0.0255458i	$-0.991868\pi$
$569$	−12.4507	−	21.5652i	−0.521960	−	0.904061i	0.477714	−	0.878516i	$-0.341466\pi$
$570$	−13.2716	+	22.9871i	−0.555885	+	0.962822i
$571$	−2.99912	+	0.452044i	−0.125509	+	0.0189175i	−0.211496	−	0.977379i	$-0.567834\pi$
$571$	−2.99912	+	0.452044i	−0.125509	+	0.0189175i	0.0859872	+	0.996296i	$0.472596\pi$
$572$	5.44584	−	5.05300i	0.227702	−	0.211276i
$573$	−2.99300	−	1.44135i	−0.125034	−	0.0602133i
$574$	−22.5139	−	27.7082i	−0.939712	−	1.15652i
$575$	−8.35041	+	4.02134i	−0.348236	+	0.167702i
$576$	−0.639963	+	1.63060i	−0.0266651	+	0.0679416i
$577$	0.0498136	−	0.664717i	0.00207377	−	0.0276725i	−0.996071	−	0.0885592i	$-0.971774\pi$
$577$	0.0498136	−	0.664717i	0.00207377	−	0.0276725i	0.998145	+	0.0608866i	$0.0193928\pi$
$578$	0.108388	+	0.0334332i	0.00450834	+	0.00139064i
$579$	4.36141	+	58.1990i	0.181254	+	2.41867i
$580$	2.76408	−	12.1102i	0.114772	−	0.502850i
$581$	−7.52273	+	13.3092i	−0.312095	+	0.552159i
$582$	−4.82259	−	21.1292i	−0.199903	−	0.875832i
$583$	7.78562	−	2.40154i	0.322447	−	0.0994618i
$584$	−0.654127	−	1.66669i	−0.0270680	−	0.0689681i
$585$	−1.72499	−	1.60055i	−0.0713194	−	0.0661747i
$586$	39.5943	+	26.9949i	1.63562	+	1.11515i
$587$	−21.5817			−0.890772			−0.445386	−	0.895339i	$-0.646934\pi$
$587$	−21.5817			−0.890772			−0.445386	+	0.895339i	$0.646934\pi$
$588$	9.12053	−	16.4860i	0.376124	−	0.679871i
$589$	40.6474			1.67485
$590$	−22.0326	−	15.0216i	−0.907069	−	0.618429i
$591$	−1.40009	−	1.29910i	−0.0575922	−	0.0534378i
$592$	7.79461	+	19.8603i	0.320357	+	0.816255i
$593$	20.0969	−	6.19908i	0.825282	−	0.254566i	0.146785	−	0.989168i	$-0.453108\pi$
$593$	20.0969	−	6.19908i	0.825282	−	0.254566i	0.678498	+	0.734603i	$0.262631\pi$
$594$	5.56015	+	24.3606i	0.228136	+	0.999529i
$595$	4.84134	+	12.0116i	0.198476	+	0.492426i
$596$	−4.27632	+	18.7358i	−0.175165	+	0.767447i
$597$	−2.06965	−	27.6176i	−0.0847053	−	1.13031i
$598$	−4.40961	−	1.36019i	−0.180322	−	0.0556221i
$599$	0.114767	−	1.53147i	0.00468927	−	0.0625740i	−0.994368	−	0.105980i	$-0.966202\pi$
$599$	0.114767	−	1.53147i	0.00468927	−	0.0625740i	0.999058	+	0.0434063i	$0.0138210\pi$
$600$	−4.17312	+	10.6329i	−0.170367	+	0.434088i
$601$	−9.86951	+	4.75291i	−0.402586	+	0.193875i	−0.624209	−	0.781257i	$-0.714579\pi$
$601$	−9.86951	+	4.75291i	−0.402586	+	0.193875i	0.221623	+	0.975132i	$0.428864\pi$
$602$	−19.4212	−	9.13505i	−0.791551	−	0.372317i
$603$	−14.6232	−	7.04215i	−0.595502	−	0.286778i
$604$	−12.1034	+	11.2303i	−0.492481	+	0.456956i
$605$	−31.6179	+	4.76564i	−1.28545	+	0.193751i
$606$	−21.2656	+	36.8331i	−0.863857	+	1.49624i
$607$	3.66462	+	6.34731i	0.148742	+	0.257629i	0.930763	−	0.365623i	$-0.119144\pi$
$607$	3.66462	+	6.34731i	0.148742	+	0.257629i	−0.782020	+	0.623253i	$0.785811\pi$
$608$	21.0696	+	26.4205i	0.854486	+	1.07149i
$609$	−50.8703	−	7.19258i	−2.06137	−	0.291458i
$610$	−6.76825	+	8.48712i	−0.274039	+	0.343633i
$611$	4.63952	+	0.699295i	0.187695	+	0.0282905i
$612$	8.16981	−	5.57008i	0.330245	−	0.225157i
$613$	−7.22624	+	4.92677i	−0.291865	+	0.198990i	−0.700396	−	0.713754i	$-0.746993\pi$
$613$	−7.22624	+	4.92677i	−0.291865	+	0.198990i	0.408531	+	0.912744i	$0.366041\pi$
$614$	45.0461	+	6.78960i	1.81791	+	0.274006i
$615$	12.4338	−	15.5915i	0.501380	−	0.628711i
$616$	8.27727	−	21.6705i	0.333501	−	0.873128i
$617$	−16.5802	−	20.7909i	−0.667494	−	0.837011i	0.326642	−	0.945148i	$-0.394083\pi$
$617$	−16.5802	−	20.7909i	−0.667494	−	0.837011i	−0.994136	+	0.108137i	$0.965512\pi$
$618$	5.47277	+	9.47911i	0.220147	+	0.381306i
$619$	5.17008	−	8.95485i	0.207803	−	0.359926i	−0.743219	−	0.669048i	$-0.766702\pi$
$619$	5.17008	−	8.95485i	0.207803	−	0.359926i	0.951022	+	0.309123i	$0.100035\pi$
$620$	10.2460	−	1.54433i	0.411489	−	0.0620219i
$621$	4.27864	−	3.97000i	0.171696	−	0.159310i
$622$	30.1978	+	14.5425i	1.21082	+	0.583102i
$623$	−35.4363	+	0.323898i	−1.41973	+	0.0129767i
$624$	−9.97399	+	4.80322i	−0.399279	+	0.192283i
$625$	2.15896	−	5.50094i	0.0863585	−	0.220038i
$626$	−2.02995	+	27.0878i	−0.0811331	+	1.08265i
$627$	−73.6834	−	22.7283i	−2.94263	−	0.907681i
$628$	0.397390	+	5.30280i	0.0158576	+	0.211605i
$629$	3.95557	−	17.3305i	0.157719	−	0.691012i
$630$	10.6809	+	3.18801i	0.425538	+	0.127014i
$631$	−9.68765	−	42.4444i	−0.385659	−	1.68968i	−0.679375	−	0.733791i	$-0.737749\pi$
$631$	−9.68765	−	42.4444i	−0.385659	−	1.68968i	0.293716	−	0.955893i	$-0.405108\pi$
$632$	10.4215	−	3.21461i	0.414546	−	0.127870i
$633$	15.2257	+	38.7943i	0.605165	+	1.54194i
$634$	−22.6536	−	21.0195i	−0.899690	−	0.834791i
$635$	1.66727	+	1.13672i	0.0661635	+	0.0451095i
$636$	3.55818			0.141091
$637$	6.65018	−	2.18521i	0.263490	−	0.0865812i
$638$	95.9589			3.79905
$639$	15.0702	+	10.2747i	0.596167	+	0.406460i
$640$	−9.10579	−	8.44894i	−0.359938	−	0.333974i
$641$	13.2389	+	33.7323i	0.522907	+	1.33235i	0.911638	+	0.410994i	$0.134818\pi$
$641$	13.2389	+	33.7323i	0.522907	+	1.33235i	−0.388731	+	0.921351i	$0.627087\pi$
$642$	−71.4399	+	22.0363i	−2.81951	+	0.869703i
$643$	−8.40773	−	36.8367i	−0.331569	−	1.45270i	−0.816094	−	0.577920i	$-0.803865\pi$
$643$	−8.40773	−	36.8367i	−0.331569	−	1.45270i	0.484525	−	0.874778i	$-0.338993\pi$
$644$	8.11670	−	1.29938i	0.319843	−	0.0512026i
$645$	2.66768	−	11.6879i	0.105040	−	0.460210i
$646$	−3.09674	−	41.3232i	−0.121840	−	1.62584i
$647$	−27.3723	−	8.44322i	−1.07611	−	0.331937i	−0.294469	−	0.955661i	$-0.595143\pi$
$647$	−27.3723	−	8.44322i	−1.07611	−	0.331937i	−0.781645	+	0.623724i	$0.785619\pi$
$648$	1.17093	−	15.6250i	0.0459984	−	0.613806i
$649$	28.3017	−	72.1116i	1.11094	−	2.83063i
$650$	5.80033	−	2.79329i	0.227508	−	0.109562i
$651$	−9.91790	−	41.6928i	−0.388713	−	1.63407i
$652$	−3.13730	−	1.51084i	−0.122866	−	0.0591692i
$653$	−8.61912	+	7.99737i	−0.337292	+	0.312961i	−0.830574	−	0.556908i	$-0.811988\pi$
$653$	−8.61912	+	7.99737i	−0.337292	+	0.312961i	0.493282	+	0.869869i	$0.335797\pi$
$654$	−53.9647	+	8.13388i	−2.11019	+	0.318060i
$655$	3.47115	−	6.01221i	0.135629	−	0.234916i
$656$	−18.6836	−	32.3609i	−0.729471	−	1.26348i
$657$	1.55828	+	1.95402i	0.0607944	+	0.0762337i
$658$	−21.1768	+	6.74476i	−0.825558	+	0.262938i
$659$	6.78970	−	8.51402i	0.264489	−	0.331659i	−0.631798	−	0.775133i	$-0.717683\pi$
$659$	6.78970	−	8.51402i	0.264489	−	0.331659i	0.896287	+	0.443474i	$0.146254\pi$
$660$	−19.4369	−	2.92964i	−0.756581	−	0.114036i
$661$	−10.2214	+	6.96881i	−0.397565	+	0.271055i	−0.745557	−	0.666442i	$-0.767816\pi$
$661$	−10.2214	+	6.96881i	−0.397565	+	0.271055i	0.347991	+	0.937498i	$0.386864\pi$
$662$	−25.4651	+	17.3618i	−0.989728	+	0.674785i
$663$	9.12060	+	1.37471i	0.354215	+	0.0533893i
$664$	−5.12538	+	6.42702i	−0.198903	+	0.249417i
$665$	12.7676	−	12.0656i	0.495106	−	0.467885i
$666$	−9.53939	−	11.9620i	−0.369644	−	0.463519i
$667$	−11.2075	−	19.4120i	−0.433957	−	0.751636i
$668$	11.3917	−	19.7311i	0.440759	−	0.763418i
$669$	16.2367	−	2.44729i	0.627746	−	0.0946175i
$670$	−12.7107	+	11.7938i	−0.491056	+	0.455634i
$671$	−28.4125	−	13.6828i	−1.09685	−	0.528217i
$672$	21.9591	−	28.0581i	0.847090	−	1.08236i
$673$	−29.5518	+	14.2314i	−1.13914	+	0.548581i	−0.905754	−	0.423804i	$-0.860695\pi$
$673$	−29.5518	+	14.2314i	−1.13914	+	0.548581i	−0.233385	+	0.972384i	$0.574980\pi$
$674$	−11.6782	+	29.7555i	−0.449827	+	1.14614i
$675$	−0.608517	+	8.12009i	−0.0234218	+	0.312543i
$676$	1.15184	+	0.355297i	0.0443017	+	0.0136653i
$677$	−0.232781	−	3.10624i	−0.00894649	−	0.119383i	0.990942	−	0.134287i	$-0.0428745\pi$
$677$	−0.232781	−	3.10624i	−0.00894649	−	0.119383i	−0.999889	+	0.0149048i	$0.995255\pi$
$678$	−13.2539	+	58.0690i	−0.509012	+	2.23013i
$679$	−0.941100	+	14.3124i	−0.0361161	+	0.549259i
$680$	1.54953	+	6.78895i	0.0594219	+	0.260344i
$681$	15.7004	−	4.84294i	0.601642	−	0.185582i
$682$	29.2439	+	74.5122i	1.11981	+	2.85322i
$683$	−7.26396	−	6.73997i	−0.277948	−	0.257898i	0.528864	−	0.848707i	$-0.322618\pi$
$683$	−7.26396	−	6.73997i	−0.277948	−	0.257898i	−0.806812	+	0.590809i	$0.798809\pi$
$684$	−11.0820	−	7.55555i	−0.423729	−	0.288894i
$685$	−0.824546			−0.0315043
$686$	−23.6790	+	23.2111i	−0.904070	+	0.886203i
$687$	−4.26849			−0.162853
$688$	−18.5602	−	12.6542i	−0.707603	−	0.482435i
$689$	0.969090	+	0.899184i	0.0369194	+	0.0342562i
$690$	4.46078	+	11.3659i	0.169819	+	0.432691i
$691$	−12.4999	+	3.85570i	−0.475517	+	0.146678i	−0.523244	−	0.852183i	$-0.675278\pi$
$691$	−12.4999	+	3.85570i	−0.475517	+	0.146678i	0.0477270	+	0.998860i	$0.484802\pi$
$692$	−0.130932	−	0.573651i	−0.00497729	−	0.0218069i
$693$	−2.12462	+	32.3115i	−0.0807076	+	1.22741i
$694$	−0.678199	+	2.97138i	−0.0257441	+	0.112792i
$695$	1.28553	+	17.1542i	0.0487630	+	0.650697i
$696$	−26.3979	−	8.14266i	−1.00061	−	0.308647i
$697$	−2.32663	+	31.0468i	−0.0881275	+	1.17598i
$698$	0.799956	−	2.03826i	0.0302788	−	0.0771491i
$699$	−29.6919	+	14.2989i	−1.12305	+	0.540834i
$700$	−7.06782	+	9.03088i	−0.267139	+	0.341335i
$701$	30.1408	+	14.5150i	1.13840	+	0.548225i	0.905530	−	0.424283i	$-0.139474\pi$
$701$	30.1408	+	14.5150i	1.13840	+	0.548225i	0.232871	+	0.972508i	$0.425188\pi$
$702$	−2.97201	+	2.75762i	−0.112171	+	0.104080i
$703$	−23.8432	+	3.59378i	−0.899263	+	0.135542i
$704$	−2.71820	+	4.70806i	−0.102446	+	0.177442i
$705$	−6.20721	−	10.7512i	−0.233777	−	0.404914i
$706$	3.73162	+	4.67930i	0.140441	+	0.176108i
$707$	20.4581	−	19.3333i	0.769405	−	0.727102i
$708$	21.0932	−	26.4500i	0.792731	−	0.994053i
$709$	7.10497	+	1.07090i	0.266833	+	0.0402186i	0.281096	−	0.959680i	$-0.409302\pi$
$709$	7.10497	+	1.07090i	0.266833	+	0.0402186i	−0.0142631	+	0.999898i	$0.504540\pi$
$710$	16.0998	−	10.9767i	0.604215	−	0.411947i
$711$	−12.5784	+	8.57582i	−0.471727	+	0.321618i
$712$	−18.8422	−	2.84000i	−0.706141	−	0.106434i
$713$	11.6579	−	14.6186i	0.436592	−	0.547470i
$714$	−41.6304	+	13.2592i	−1.55798	+	0.496212i
$715$	−4.55340	−	5.70978i	−0.170287	−	0.213534i
$716$	4.37987	+	7.58615i	0.163683	+	0.283508i
$717$	29.2472	−	50.6576i	1.09226	−	1.89184i
$718$	−37.3587	+	5.63091i	−1.39421	+	0.210144i
$719$	−22.1727	+	20.5732i	−0.826902	+	0.767253i	−0.975114	−	0.221703i	$-0.928839\pi$
$719$	−22.1727	+	20.5732i	−0.826902	+	0.767253i	0.148213	+	0.988956i	$0.452648\pi$
$720$	10.5112	+	5.06191i	0.391728	+	0.188646i
$721$	−1.67641	−	7.04731i	−0.0624329	−	0.262455i
$722$	−19.9953	+	9.62925i	−0.744149	+	0.358363i
$723$	13.7089	−	34.9297i	0.509839	−	1.29905i
$724$	−0.744241	+	9.93120i	−0.0276595	+	0.369090i
$725$	29.8820	+	9.21738i	1.10979	+	0.342325i
$726$	−8.06141	−	107.572i	−0.299187	−	3.99237i
$727$	4.53247	−	19.8581i	0.168100	−	0.736495i	−0.818656	−	0.574284i	$-0.805280\pi$
$727$	4.53247	−	19.8581i	0.168100	−	0.736495i	0.986756	−	0.162211i	$-0.0518624\pi$
$728$	3.71660	−	0.594978i	0.137746	−	0.0220513i
$729$	1.49149	+	6.53463i	0.0552402	+	0.242023i
$730$	2.55142	−	0.787010i	0.0944325	−	0.0291286i
$731$	6.83783	+	17.4225i	0.252906	+	0.644395i
$732$	−10.0956	−	9.36739i	−0.373146	−	0.346229i
$733$	−4.24637	−	2.89512i	−0.156843	−	0.106934i	0.482355	−	0.875976i	$-0.339781\pi$
$733$	−4.24637	−	2.89512i	−0.156843	−	0.106934i	−0.639199	+	0.769042i	$0.720734\pi$
$734$	42.0003			1.55026
$735$	−15.4912	−	10.1520i	−0.571403	−	0.374462i
$736$	15.5449			0.572991
$737$	−41.6191	−	28.3754i	−1.53306	−	1.04522i
$738$	19.6436	+	18.2266i	0.723090	+	0.670929i
$739$	3.31620	+	8.44953i	0.121988	+	0.310821i	0.978803	−	0.204803i	$-0.0656554\pi$
$739$	3.31620	+	8.44953i	0.121988	+	0.310821i	−0.856815	+	0.515624i	$0.827560\pi$
$740$	−5.87362	+	1.81177i	−0.215918	+	0.0666020i
$741$	−2.78405	−	12.1977i	−0.102275	−	0.448094i
$742$	−6.00050	−	1.79101i	−0.220285	−	0.0657502i
$743$	6.47969	−	28.3894i	0.237717	−	1.04151i	−0.705339	−	0.708870i	$-0.749205\pi$
$743$	6.47969	−	28.3894i	0.237717	−	1.04151i	0.943056	−	0.332635i	$-0.107938\pi$
$744$	−1.72208	−	22.9795i	−0.0631344	−	0.842469i
$745$	18.0526	+	5.56848i	0.661395	+	0.204013i
$746$	0.363976	−	4.85693i	0.0133261	−	0.177825i
$747$	4.19226	−	10.6817i	0.153387	−	0.390823i
$748$	27.6485	−	13.3148i	1.01093	−	0.486838i
$749$	49.4764	−	0.452228i	1.80783	−	0.0165240i
$750$	−36.6872	−	17.6676i	−1.33963	−	0.645131i
$751$	31.5108	−	29.2377i	1.14984	−	1.06690i	0.152943	−	0.988235i	$-0.451125\pi$
$751$	31.5108	−	29.2377i	1.14984	−	1.06690i	0.996901	−	0.0786648i	$-0.0250657\pi$
$752$	−23.0019	+	3.46697i	−0.838792	+	0.126428i
$753$	12.1553	−	21.0537i	0.442965	−	0.767238i
$754$	7.78494	+	13.4839i	0.283511	+	0.491055i
$755$	10.1200	+	12.6900i	0.368303	+	0.461837i
$756$	2.57692	−	6.74655i	0.0937215	−	0.245370i
$757$	−3.53671	+	4.43490i	−0.128544	+	0.161189i	−0.841938	−	0.539574i	$-0.818585\pi$
$757$	−3.53671	+	4.43490i	−0.128544	+	0.161189i	0.713394	+	0.700763i	$0.247157\pi$
$758$	24.4805	+	3.68985i	0.889173	+	0.134021i
$759$	−29.3069	+	19.9811i	−1.06377	+	0.725269i
$760$	7.80440	−	5.32095i	0.283095	−	0.193011i
$761$	36.9158	+	5.56416i	1.33820	+	0.201701i	0.778838	−	0.627225i	$-0.215809\pi$
$761$	36.9158	+	5.56416i	1.33820	+	0.201701i	0.559359	+	0.828926i	$0.311047\pi$
$762$	−4.24456	+	5.32252i	−0.153764	+	0.192814i
$763$	35.7626	+	5.05650i	1.29469	+	0.183057i
$764$	−1.11812	−	1.40207i	−0.0404520	−	0.0507252i
$765$	−4.86019	−	8.41809i	−0.175720	−	0.304357i
$766$	−9.19132	+	15.9198i	−0.332096	+	0.575207i
$767$	12.4290	−	1.87337i	0.448785	−	0.0676435i
$768$	33.6077	−	31.1834i	1.21271	−	1.12523i
$769$	11.4903	+	5.53344i	0.414351	+	0.199541i	0.629432	−	0.777055i	$-0.283287\pi$
$769$	11.4903	+	5.53344i	0.414351	+	0.199541i	−0.215081	+	0.976596i	$0.569002\pi$
$770$	31.3037	+	14.7241i	1.12811	+	0.530620i
$771$	−5.38138	+	2.59153i	−0.193806	+	0.0933318i
$772$	−11.5104	+	29.3280i	−0.414268	+	1.05554i
$773$	−3.71861	+	49.6214i	−0.133749	+	1.78476i	0.378180	+	0.925732i	$0.376550\pi$
$773$	−3.71861	+	49.6214i	−0.133749	+	1.78476i	−0.511930	+	0.859027i	$0.671069\pi$
$774$	15.3935	+	4.74826i	0.553308	+	0.170673i
$775$	1.94937	+	26.0125i	0.0700233	+	0.934396i
$776$	−1.71618	+	7.51906i	−0.0616071	+	0.269919i
$777$	9.50392	+	23.5796i	0.340951	+	0.845913i
$778$	−15.0957	−	66.1385i	−0.541206	−	2.37118i
$779$	40.3553	−	12.4480i	1.44588	−	0.445994i
$780$	−1.16521	−	2.96890i	−0.0417211	−	0.106304i
$781$	41.4957	+	38.5024i	1.48483	+	1.37772i
$782$	−15.7498	−	10.7380i	−0.563211	−	0.383991i
$783$	−19.6933			−0.703782
$784$	−28.3122	+	20.0707i	−1.01115	+	0.716811i
$785$	5.22755			0.186579
$786$	19.3514	+	13.1936i	0.690243	+	0.470599i
$787$	−18.3632	−	17.0386i	−0.654577	−	0.607359i	0.281328	−	0.959612i	$-0.409225\pi$
$787$	−18.3632	−	17.0386i	−0.654577	−	0.607359i	−0.935905	+	0.352253i	$0.885416\pi$
$788$	−0.376688	−	0.959785i	−0.0134190	−	0.0341909i
$789$	31.3017	−	9.65530i	1.11437	−	0.343738i
$790$	3.61904	+	15.8561i	0.128760	+	0.564133i
$791$	19.3969	−	34.3170i	0.689674	−	1.22017i
$792$	−3.87442	+	16.9750i	−0.137672	+	0.603179i
$793$	−0.382381	−	5.10251i	−0.0135787	−	0.181196i
$794$	−8.09808	−	2.49793i	−0.287390	−	0.0886481i
$795$	0.261397	−	3.48810i	0.00927078	−	0.123710i
$796$	5.46212	−	13.9173i	0.193600	−	0.493284i
$797$	−9.03198	+	4.34957i	−0.319929	+	0.154070i	−0.586955	−	0.809620i	$-0.699673\pi$
$797$	−9.03198	+	4.34957i	−0.319929	+	0.154070i	0.267026	+	0.963689i	$0.413959\pi$
$798$	37.3728	+	45.9953i	1.32298	+	1.62822i
$799$	17.4620	+	8.40924i	0.617760	+	0.297497i
$800$	−15.8975	+	14.7507i	−0.562060	+	0.521516i
$801$	26.3017	−	3.96435i	0.929326	−	0.140073i
$802$	15.8236	−	27.4072i	0.558750	−	0.967784i
$803$	3.87831	+	6.71742i	0.136862	+	0.237053i
$804$	−13.7156	−	17.1988i	−0.483713	−	0.606557i
$805$	−0.677499	−	8.05228i	−0.0238787	−	0.283806i
$806$	−8.09778	+	10.1543i	−0.285232	+	0.357670i
$807$	−20.2898	−	3.05819i	−0.714234	−	0.107653i
$808$	12.5053	−	8.52599i	0.439936	−	0.299943i
$809$	−7.85158	+	5.35312i	−0.276047	+	0.188206i	−0.693428	−	0.720526i	$-0.743900\pi$
$809$	−7.85158	+	5.35312i	−0.276047	+	0.188206i	0.417381	+	0.908732i	$0.362948\pi$
$810$	23.1053	+	3.48257i	0.811839	+	0.122365i
$811$	−4.89726	+	6.14097i	−0.171966	+	0.215639i	−0.860344	−	0.509713i	$-0.829751\pi$
$811$	−4.89726	+	6.14097i	−0.171966	+	0.215639i	0.688378	+	0.725352i	$0.258323\pi$
$812$	−23.0573	−	15.4134i	−0.809152	−	0.540904i
$813$	−33.1781	−	41.6041i	−1.16361	−	1.45912i
$814$	−23.7420	−	41.1223i	−0.832156	−	1.44134i
$815$	−1.71156	+	2.96451i	−0.0599534	+	0.103842i
$816$	−45.2182	+	6.81555i	−1.58295	+	0.238592i
$817$	18.6105	−	17.2681i	0.651101	−	0.604133i
$818$	36.6681	+	17.6584i	1.28207	+	0.617412i
$819$	−4.71270	+	2.32281i	−0.164675	+	0.0811657i
$820$	9.69942	−	4.67099i	0.338718	−	0.163118i
$821$	1.69002	−	4.30611i	0.0589822	−	0.150284i	−0.898345	−	0.439291i	$-0.855230\pi$
$821$	1.69002	−	4.30611i	0.0589822	−	0.150284i	0.957327	+	0.289007i	$0.0933250\pi$
$822$	0.207881	−	2.77398i	0.00725067	−	0.0967535i
$823$	1.63821	+	0.505322i	0.0571046	+	0.0176144i	0.323176	−	0.946339i	$-0.395249\pi$
$823$	1.63821	+	0.505322i	0.0571046	+	0.0176144i	−0.266071	+	0.963953i	$0.585726\pi$
$824$	−0.291081	−	3.88421i	−0.0101403	−	0.135313i
$825$	11.0114	−	48.2441i	0.383368	−	1.67964i
$826$	−48.8851	+	33.9879i	−1.70093	+	1.18259i
$827$	0.668241	+	2.92775i	0.0232370	+	0.101808i	0.985217	−	0.171313i	$-0.0548011\pi$
$827$	0.668241	+	2.92775i	0.0232370	+	0.101808i	−0.961980	+	0.273121i	$0.911944\pi$
$828$	−5.89568	+	1.81858i	−0.204889	+	0.0631999i
$829$	−10.3076	−	26.2634i	−0.357998	−	0.912165i	−0.990488	−	0.137596i	$-0.956062\pi$
$829$	−10.3076	−	26.2634i	−0.357998	−	0.912165i	0.632490	−	0.774568i	$-0.282033\pi$
$830$	−8.98642	−	8.33818i	−0.311923	−	0.289422i
$831$	46.5258	+	31.7208i	1.61396	+	1.10038i
$832$	−0.882087			−0.0305809
$833$	28.9106	−	0.528547i	1.00169	−	0.0183131i
$834$	−58.0352			−2.00959
$835$	−18.5055	−	12.6169i	−0.640410	−	0.436624i
$836$	−30.5141	−	28.3130i	−1.05535	−	0.979225i
$837$	−6.00163	−	15.2919i	−0.207447	−	0.528566i
$838$	−51.9521	+	16.0251i	−1.79465	+	0.553577i
$839$	−1.59020	−	6.96714i	−0.0549000	−	0.240532i	0.940032	−	0.341088i	$-0.110795\pi$
$839$	−1.59020	−	6.96714i	−0.0549000	−	0.240532i	−0.994931	+	0.100555i	$0.967938\pi$
$840$	−7.36207	−	6.70683i	−0.254016	−	0.231408i
$841$	−10.3759	+	45.4599i	−0.357791	+	1.56758i
$842$	1.04251	+	13.9113i	0.0359271	+	0.479414i
$843$	−14.7556	−	4.55151i	−0.508211	−	0.156762i
$844$	−1.68125	+	22.4348i	−0.0578712	+	0.772237i
$845$	0.432917	−	1.10305i	0.0148928	−	0.0379462i
$846$	15.0296	−	7.23785i	0.516727	−	0.248843i
$847$	−15.2496	+	69.7451i	−0.523981	+	2.39647i
$848$	−5.90512	−	2.84376i	−0.202783	−	0.0976551i
$849$	−37.1370	+	34.4581i	−1.27454	+	1.18260i
$850$	26.2965	−	3.96355i	0.901961	−	0.135949i
$851$	−5.54590	+	9.60577i	−0.190111	+	0.329282i
$852$	12.3605	+	21.4091i	0.423465	+	0.733463i
$853$	7.50736	+	9.41393i	0.257047	+	0.322327i	0.893564	−	0.448936i	$-0.148197\pi$
$853$	7.50736	+	9.41393i	0.257047	+	0.322327i	−0.636517	+	0.771263i	$0.719625\pi$
$854$	12.3102	+	20.8788i	0.421245	+	0.714457i
$855$	−8.22085	+	10.3086i	−0.281147	+	0.352547i
$856$	26.3076	+	3.96523i	0.899174	+	0.135529i
$857$	−10.1144	+	6.89590i	−0.345502	+	0.235560i	−0.723621	−	0.690198i	$-0.757524\pi$
$857$	−10.1144	+	6.89590i	−0.345502	+	0.235560i	0.378118	+	0.925757i	$0.376571\pi$
$858$	20.3571	−	13.8792i	0.694980	−	0.473829i
$859$	−31.0192	−	4.67539i	−1.05836	−	0.159522i	−0.403277	−	0.915078i	$-0.632129\pi$
$859$	−31.0192	−	4.67539i	−1.05836	−	0.159522i	−0.655084	+	0.755556i	$0.727367\pi$
$860$	4.03509	−	5.05984i	0.137595	−	0.172539i
$861$	−22.6148	−	38.3560i	−0.770709	−	1.30717i
$862$	−26.9314	−	33.7709i	−0.917286	−	1.15024i
$863$	10.0300	+	17.3724i	0.341425	+	0.591365i	0.984698	−	0.174272i	$-0.0557572\pi$
$863$	10.0300	+	17.3724i	0.341425	+	0.591365i	−0.643273	+	0.765637i	$0.722424\pi$
$864$	6.82867	−	11.8276i	0.232316	−	0.402383i
$865$	−0.571970	+	0.0862107i	−0.0194476	+	0.00293125i
$866$	50.1813	−	46.5614i	1.70523	−	1.58222i
$867$	0.127454	+	0.0613788i	0.00432858	+	0.00208453i
$868$	4.94172	−	22.6013i	0.167733	−	0.767139i
$869$	−42.5682	+	20.4998i	−1.44403	+	0.695407i
$870$	15.0508	−	38.3487i	0.510269	−	1.30014i
$871$	0.610777	−	8.15025i	0.0206954	−	0.276161i
$872$	18.5581	+	5.72441i	0.628456	+	0.193853i
$873$	−0.804525	−	10.7356i	−0.0272291	−	0.363346i
$874$	−5.75366	+	25.2084i	−0.194620	+	0.852687i
$875$	19.9218	+	18.1487i	0.673479	+	0.613538i
$876$	0.753775	+	3.30251i	0.0254677	+	0.111581i
$877$	−17.3013	+	5.33674i	−0.584223	+	0.180209i	−0.572757	−	0.819725i	$-0.694126\pi$
$877$	−17.3013	+	5.33674i	−0.584223	+	0.180209i	−0.0114664	+	0.999934i	$0.503650\pi$
$878$	13.9380	+	35.5134i	0.470384	+	1.19852i
$879$	43.8117	+	40.6513i	1.47773	+	1.37113i
$880$	29.9159	+	20.3963i	1.00846	+	0.687559i
$881$	−30.1842			−1.01693			−0.508466	−	0.861082i	$-0.669787\pi$
$881$	−30.1842			−1.01693			−0.508466	+	0.861082i	$0.669787\pi$
$882$	15.1589	−	19.7383i	0.510427	−	0.664624i
$883$	3.41283			0.114851			0.0574254	−	0.998350i	$-0.481711\pi$
$883$	3.41283			0.114851			0.0574254	+	0.998350i	$0.481711\pi$
$884$	4.11403	+	2.80490i	0.138370	+	0.0943390i
$885$	−24.3795	−	22.6208i	−0.819506	−	0.760391i
$886$	26.0967	+	66.4933i	0.876736	+	2.23389i
$887$	−8.97652	+	2.76889i	−0.301402	+	0.0929702i	−0.441768	−	0.897130i	$-0.645648\pi$
$887$	−8.97652	+	2.76889i	−0.301402	+	0.0929702i	0.140366	+	0.990100i	$0.455172\pi$
$888$	3.04185	+	13.3272i	0.102078	+	0.447232i
$889$	3.69926	−	2.57196i	0.124069	−	0.0862606i
$890$	6.32318	−	27.7037i	0.211954	−	0.928629i
$891$	5.07270	+	67.6905i	0.169942	+	2.26772i
$892$	8.47032	+	2.61275i	0.283607	+	0.0874812i
$893$	1.96464	−	26.2163i	0.0657442	−	0.877295i
$894$	−23.2851	+	59.3294i	−0.778770	+	1.98427i
$895$	7.75849	−	3.73629i	0.259338	−	0.124890i
$896$	−24.8772	+	12.2616i	−0.831089	+	0.409631i
$897$	−5.18531	−	2.49711i	−0.173132	−	0.0833762i
$898$	10.0110	−	9.28885i	0.334071	−	0.309973i
$899$	−62.3824	+	9.40263i	−2.08057	+	0.313595i
$900$	4.30374	−	7.45430i	0.143458	−	0.248477i
$901$	2.73043	+	4.72925i	0.0909639	+	0.157554i
$902$	51.8526	+	65.0211i	1.72650	+	2.16497i
$903$	−22.2532	−	14.8758i	−0.740539	−	0.495037i
$904$	13.2155	−	16.5717i	0.439540	−	0.551166i
$905$	9.68091	+	1.45916i	0.321804	+	0.0485042i
$906$	−45.2438	+	30.8467i	−1.50312	+	1.02481i
$907$	−8.38598	+	5.71746i	−0.278452	+	0.189845i	−0.694491	−	0.719502i	$-0.744370\pi$
$907$	−8.38598	+	5.71746i	−0.278452	+	0.189845i	0.416039	+	0.909347i	$0.363418\pi$
$908$	8.77062	+	1.32196i	0.291063	+	0.0438707i
$909$	−13.1726	+	16.5179i	−0.436908	+	0.547865i
$910$	0.470602	+	5.59325i	0.0156003	+	0.185414i
$911$	21.2075	+	26.5934i	0.702637	+	0.881078i	0.997217	−	0.0745482i	$-0.0237514\pi$
$911$	21.2075	+	26.5934i	0.702637	+	0.881078i	−0.294581	+	0.955627i	$0.595180\pi$
$912$	31.0146	+	53.7188i	1.02700	+	1.77881i
$913$	17.8064	−	30.8415i	0.589305	−	1.02071i
$914$	−20.5854	+	3.10275i	−0.680905	+	0.102630i
$915$	−9.92454	+	9.20863i	−0.328095	+	0.304428i
$916$	−2.07608	−	0.999789i	−0.0685957	−	0.0330340i
$917$	−9.77478	−	12.0300i	−0.322792	−	0.397264i
$918$	−15.0889	+	7.26644i	−0.498008	+	0.239828i
$919$	−1.35021	+	3.44028i	−0.0445393	+	0.113484i	−0.951412	−	0.307920i	$-0.900367\pi$
$919$	−1.35021	+	3.44028i	−0.0445393	+	0.113484i	0.906873	+	0.421404i	$0.138462\pi$
$920$	0.324705	−	4.33289i	0.0107052	−	0.142851i
$921$	54.2909	+	16.7465i	1.78895	+	0.551817i
$922$	2.11359	+	28.2039i	0.0696073	+	0.928845i
$923$	−2.04380	+	8.95449i	−0.0672726	+	0.294741i
$924$	−21.5958	+	38.2073i	−0.710450	+	1.25693i
$925$	−3.44333	−	15.0862i	−0.113216	−	0.496032i
$926$	−7.41815	+	2.28819i	−0.243775	+	0.0751947i
$927$	1.98641	+	5.06130i	0.0652424	+	0.166235i
$928$	−38.4476	−	35.6742i	−1.26211	−	1.17106i
$929$	−24.6286	−	16.7915i	−0.808039	−	0.550912i	0.0873597	−	0.996177i	$-0.472157\pi$
$929$	−24.6286	−	16.7915i	−0.808039	−	0.550912i	−0.895399	+	0.445265i	$0.853109\pi$
$930$	34.3647			1.12686
$931$	−14.9946	−	36.2431i	−0.491427	−	1.18782i
$932$	−17.7906			−0.582749
$933$	34.5382	+	23.5478i	1.13073	+	0.770919i
$934$	6.01684	+	5.58281i	0.196877	+	0.182675i
$935$	−11.0214	−	28.0821i	−0.360438	−	0.918382i
$936$	−2.69960	+	0.832717i	−0.0882393	+	0.0272182i
$937$	8.10984	+	35.5315i	0.264937	+	1.16076i	0.915821	+	0.401587i	$0.131541\pi$
$937$	8.10984	+	35.5315i	0.264937	+	1.16076i	−0.650884	+	0.759177i	$0.725602\pi$
$938$	14.4729	+	35.9078i	0.472557	+	1.17243i
$939$	−7.53857	+	33.0286i	−0.246012	+	1.07785i
$940$	−0.500821	−	6.68299i	−0.0163350	−	0.217975i
$941$	−23.7523	−	7.32663i	−0.774304	−	0.238841i	−0.117672	−	0.993052i	$-0.537543\pi$
$941$	−23.7523	−	7.32663i	−0.774304	−	0.238841i	−0.656632	+	0.754211i	$0.728019\pi$
$942$	−1.31795	+	17.5868i	−0.0429410	+	0.573008i
$943$	7.09732	−	18.0837i	0.231120	−	0.588885i
$944$	−56.1454	+	27.0382i	−1.82738	+	0.880018i
$945$	−6.42435	−	3.02178i	−0.208984	−	0.0982986i
$946$	45.0442	+	21.6921i	1.46451	+	0.705272i
$947$	−30.8695	+	28.6427i	−1.00312	+	0.930762i	−0.997601	−	0.0692226i	$-0.977948\pi$
$947$	−30.8695	+	28.6427i	−1.00312	+	0.930762i	−0.00552177	+	0.999985i	$0.501758\pi$
$948$	−20.4031	+	3.07528i	−0.662663	+	0.0998803i
$949$	−0.629277	+	1.08994i	−0.0204272	+	0.0353810i
$950$	−18.0364	−	31.2399i	−0.585178	−	1.01356i
$951$	−24.0304	−	30.1331i	−0.779239	−	0.977134i
$952$	15.3948	+	2.17668i	0.498949	+	0.0705467i
$953$	−1.21910	+	1.52871i	−0.0394906	+	0.0495196i	−0.801185	−	0.598417i	$-0.795797\pi$
$953$	−1.21910	+	1.52871i	−0.0394906	+	0.0495196i	0.761694	+	0.647937i	$0.224368\pi$
$954$	4.64768	+	0.700526i	0.150474	+	0.0226804i
$955$	−1.45660	+	0.993090i	−0.0471343	+	0.0321356i
$956$	26.0904	−	17.7881i	0.843823	−	0.575309i
$957$	118.341	+	17.8370i	3.82542	+	0.576590i
$958$	35.3204	−	44.2903i	1.14115	−	1.43096i
$959$	−0.656907	+	1.71983i	−0.0212126	+	0.0555362i
$960$	1.45518	+	1.82474i	0.0469657	+	0.0588931i
$961$	−10.8125	−	18.7278i	−0.348790	−	0.604122i
$962$	3.85227	−	6.67233i	0.124202	−	0.215125i
$963$	−36.7226	+	5.53504i	−1.18337	+	0.178364i
$964$	14.8491	−	13.7779i	0.478256	−	0.443757i
$965$	27.9047	+	13.4382i	0.898285	+	0.432591i
$966$	27.2607	−	0.249170i	0.877098	−	0.00801692i
$967$	−5.68945	+	2.73990i	−0.182960	+	0.0881091i	−0.523122	−	0.852258i	$-0.675233\pi$
$967$	−5.68945	+	2.73990i	−0.182960	+	0.0881091i	0.340161	+	0.940367i	$0.389518\pi$
$968$	−14.0248	+	35.7345i	−0.450773	+	1.14855i
$969$	3.86219	−	51.5373i	0.124071	−	1.65562i
$970$	−10.9903	−	3.39006i	−0.352878	−	0.108848i
$971$	−0.774389	−	10.3335i	−0.0248513	−	0.331618i	−0.995748	−	0.0921190i	$-0.970636\pi$
$971$	−0.774389	−	10.3335i	−0.0248513	−	0.331618i	0.970897	−	0.239499i	$-0.0769831\pi$
$972$	−4.77429	+	20.9175i	−0.153135	+	0.670930i
$973$	36.8043	+	10.9853i	1.17989	+	0.352171i
$974$	−2.55490	−	11.1938i	−0.0818644	−	0.358671i
$975$	7.67247	−	2.36664i	0.245716	−	0.0757932i
$976$	9.26806	+	23.6146i	0.296663	+	0.755886i
$977$	−16.5248	−	15.3328i	−0.528675	−	0.490538i	0.370074	−	0.929002i	$-0.379332\pi$
$977$	−16.5248	−	15.3328i	−0.528675	−	0.490538i	−0.898749	+	0.438464i	$0.855523\pi$
$978$	−9.54184	−	6.50552i	−0.305114	−	0.208023i
$979$	82.5502			2.63831
$980$	−5.15668	−	8.56611i	−0.164724	−	0.273634i
$981$	−27.1096			−0.865542
$982$	−18.7496	−	12.7833i	−0.598324	−	0.407930i
$983$	7.92062	+	7.34926i	0.252629	+	0.234405i	0.796313	−	0.604885i	$-0.206781\pi$
$983$	7.92062	+	7.34926i	0.252629	+	0.234405i	−0.543685	+	0.839290i	$0.682971\pi$
$984$	−8.74700	−	22.2870i	−0.278844	−	0.710484i
$985$	−0.968553	+	0.298759i	−0.0308607	+	0.00951925i
$986$	14.3116	+	62.7032i	0.455774	+	1.99688i
$987$	−27.3700	+	4.38157i	−0.871196	+	0.139467i
$988$	1.50292	−	6.58474i	0.0478144	−	0.209489i
$989$	−0.872729	−	11.6458i	−0.0277512	−	0.370313i
$990$	−24.8116	−	7.65338i	−0.788566	−	0.243240i
$991$	1.16630	−	15.5632i	0.0370489	−	0.494383i	−0.947556	−	0.319589i	$-0.896455\pi$
$991$	1.16630	−	15.5632i	0.0370489	−	0.494383i	0.984605	−	0.174794i	$-0.0559258\pi$
$992$	15.9840	−	40.7265i	0.507492	−	1.29307i
$993$	−34.6320	+	16.6779i	−1.09901	+	0.529257i
$994$	−10.0685	−	42.3258i	−0.319352	−	1.34249i
$995$	−13.2419	−	6.37694i	−0.419795	−	0.202163i
$996$	11.4009	−	10.5785i	0.361251	−	0.335192i
$997$	12.1297	−	1.82825i	0.384151	−	0.0579014i	0.0458719	−	0.998947i	$-0.485393\pi$
$997$	12.1297	−	1.82825i	0.384151	−	0.0579014i	0.338279	+	0.941046i	$0.390155\pi$
$998$	28.7620	−	49.8172i	0.910444	−	1.57694i
$999$	4.87249	+	8.43940i	0.154159	+	0.267011i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	637.2.bl.b.53.23	✓	348
49.37	even	21	inner	637.2.bl.b.625.23	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
637.2.bl.b.53.23	✓	348	1.1	even	1	trivial
637.2.bl.b.625.23	yes	348	49.37	even	21	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 637 = 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	637.bl (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(1.47927 + 1.00855i) q^{2} +(1.63683 + 1.51876i) q^{3} +(0.440381 + 1.12207i) q^{4} +(1.13232 - 0.349275i) q^{5} +(0.889572 + 3.89747i) q^{6} +(0.173595 - 2.64005i) q^{7} +(0.316565 - 1.38696i) q^{8} +(0.148402 + 1.98029i) q^{9} +O(q^{10})\)	\(q+(1.47927 + 1.00855i) q^{2} +(1.63683 + 1.51876i) q^{3} +(0.440381 + 1.12207i) q^{4} +(1.13232 - 0.349275i) q^{5} +(0.889572 + 3.89747i) q^{6} +(0.173595 - 2.64005i) q^{7} +(0.316565 - 1.38696i) q^{8} +(0.148402 + 1.98029i) q^{9} +(2.02727 + 0.625329i) q^{10} +(-0.460570 + 6.14588i) q^{11} +(-0.983326 + 2.50547i) q^{12} +(-0.900969 + 0.433884i) q^{13} +(2.91941 - 3.73026i) q^{14} +(2.38388 + 1.14802i) q^{15} +(3.63433 - 3.37217i) q^{16} +(-4.08464 + 0.615661i) q^{17} +(-1.77769 + 3.07905i) q^{18} +(2.80160 + 4.85252i) q^{19} +(0.890564 + 1.11673i) q^{20} +(4.29374 - 4.05767i) q^{21} +(-6.87971 + 8.62689i) q^{22} +(2.54869 + 0.384154i) q^{23} +(2.62462 - 1.78944i) q^{24} +(-2.97103 + 2.02562i) q^{25} +(-1.77037 - 0.266840i) q^{26} +(1.41190 - 1.77047i) q^{27} +(3.03877 - 0.967841i) q^{28} +(-5.42217 - 6.79919i) q^{29} +(2.36857 + 4.10248i) q^{30} +(3.62715 - 6.28241i) q^{31} +(5.96366 - 0.898877i) q^{32} +(-10.0880 + 9.36027i) q^{33} +(-6.66320 - 3.20883i) q^{34} +(-0.725538 - 3.05002i) q^{35} +(-2.15667 + 1.03860i) q^{36} +(-1.57219 + 4.00587i) q^{37} +(-0.749675 + 10.0037i) q^{38} +(-2.13370 - 0.658159i) q^{39} +(-0.125978 - 1.68105i) q^{40} +(1.67715 - 7.34806i) q^{41} +(10.4439 - 1.67193i) q^{42} +(-1.00823 - 4.41734i) q^{43} +(-7.09894 + 2.18973i) q^{44} +(0.859704 + 2.19049i) q^{45} +(3.38276 + 3.13874i) q^{46} +(-3.87665 - 2.64306i) q^{47} +11.0703 q^{48} +(-6.93973 - 0.916597i) q^{49} -6.43788 q^{50} +(-7.62091 - 5.19585i) q^{51} +(-0.883618 - 0.819878i) q^{52} +(-0.482978 - 1.23061i) q^{53} +(3.87418 - 1.19503i) q^{54} +(1.62509 + 7.11998i) q^{55} +(-3.60669 - 1.07652i) q^{56} +(-2.78405 + 12.1977i) q^{57} +(-1.16354 - 15.5263i) q^{58} +(-12.0110 - 3.70489i) q^{59} +(-0.238342 + 3.18045i) q^{60} +(-1.86939 + 4.76312i) q^{61} +(11.7016 - 5.63521i) q^{62} +(5.25382 - 0.0480214i) q^{63} +(0.794733 + 0.382723i) q^{64} +(-0.868642 + 0.805982i) q^{65} +(-24.3631 + 3.67214i) q^{66} +(-4.08655 + 7.07812i) q^{67} +(-2.48961 - 4.31214i) q^{68} +(3.58835 + 4.49964i) q^{69} +(2.00282 - 5.24353i) q^{70} +(5.72661 - 7.18094i) q^{71} +(2.79356 + 0.421062i) q^{72} +(1.03987 - 0.708969i) q^{73} +(-6.36579 + 4.34012i) q^{74} +(-7.93950 - 1.19669i) q^{75} +(-4.21110 + 5.28055i) q^{76} +(16.1455 + 2.28282i) q^{77} +(-2.49252 - 3.12553i) q^{78} +(3.83306 + 6.63906i) q^{79} +(2.93742 - 5.08776i) q^{80} +(10.8909 - 1.64155i) q^{81} +(9.89181 - 9.17826i) q^{82} +(-5.20613 - 2.50714i) q^{83} +(6.44388 + 3.03097i) q^{84} +(-4.41010 + 2.12379i) q^{85} +(2.96365 - 7.55126i) q^{86} +(1.45114 - 19.3641i) q^{87} +(8.37829 + 2.58436i) q^{88} +(-1.00095 - 13.3568i) q^{89} +(-0.937481 + 4.10737i) q^{90} +(0.989071 + 2.45392i) q^{91} +(0.691347 + 3.02899i) q^{92} +(15.4785 - 4.77449i) q^{93} +(-3.06895 - 7.81957i) q^{94} +(4.86718 + 4.51608i) q^{95} +(11.1267 + 7.58604i) q^{96} -5.42125 q^{97} +(-9.34128 - 8.35493i) q^{98} -12.2390 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9}+O(q^{10}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9	\( 348 q + 3 q^{2} + 31 q^{4} + q^{5} - 4 q^{6} + 27 q^{7} - 12 q^{8} + 13 q^{9} - 5 q^{10} + 2 q^{11} - 40 q^{12} - 58 q^{13} - 45 q^{14} - 14 q^{15} + 27 q^{16} - 12 q^{17} - 59 q^{18} - 24 q^{19} - 99 q^{20} - 2 q^{21} - 10 q^{22} - 14 q^{23} + 28 q^{25} + 3 q^{26} - 9 q^{27} - 37 q^{28} - 26 q^{29} - 83 q^{30} - 49 q^{31} + 33 q^{32} + 2 q^{33} - 130 q^{34} - 38 q^{35} - 74 q^{36} - 4 q^{37} + 92 q^{38} + 24 q^{40} + 20 q^{41} - 52 q^{42} + 2 q^{43} + 226 q^{44} - 23 q^{45} + 71 q^{46} + 24 q^{47} + 86 q^{48} + 25 q^{49} + 114 q^{50} - 54 q^{51} + 31 q^{52} + 36 q^{53} + 75 q^{54} + 38 q^{55} + 126 q^{56} + 27 q^{57} - 33 q^{58} + q^{59} - 179 q^{60} - 15 q^{61} + 158 q^{62} - 5 q^{63} - 24 q^{64} + q^{65} - 150 q^{66} - 151 q^{67} + 140 q^{68} - 98 q^{69} - 126 q^{70} - 31 q^{71} - 149 q^{72} - 9 q^{73} + 39 q^{74} + 85 q^{75} - 81 q^{76} + 46 q^{77} - 25 q^{78} - 69 q^{79} - 64 q^{80} + 71 q^{81} - 52 q^{82} - q^{83} - 47 q^{84} + 62 q^{85} + 97 q^{86} + 150 q^{87} - 12 q^{88} + 23 q^{89} + 107 q^{90} - q^{91} - 43 q^{92} + 316 q^{93} - 86 q^{94} - 29 q^{95} + 177 q^{96} + 114 q^{97} - 336 q^{98} + 102 q^{99}+O(q^{100}) \) 348 * q + 3 * q^2 + 31 * q^4 + q^5 - 4 * q^6 + 27 * q^7 - 12 * q^8 + 13 * q^9 - 5 * q^10 + 2 * q^11 - 40 * q^12 - 58 * q^13 - 45 * q^14 - 14 * q^15 + 27 * q^16 - 12 * q^17 - 59 * q^18 - 24 * q^19 - 99 * q^20 - 2 * q^21 - 10 * q^22 - 14 * q^23 + 28 * q^25 + 3 * q^26 - 9 * q^27 - 37 * q^28 - 26 * q^29 - 83 * q^30 - 49 * q^31 + 33 * q^32 + 2 * q^33 - 130 * q^34 - 38 * q^35 - 74 * q^36 - 4 * q^37 + 92 * q^38 + 24 * q^40 + 20 * q^41 - 52 * q^42 + 2 * q^43 + 226 * q^44 - 23 * q^45 + 71 * q^46 + 24 * q^47 + 86 * q^48 + 25 * q^49 + 114 * q^50 - 54 * q^51 + 31 * q^52 + 36 * q^53 + 75 * q^54 + 38 * q^55 + 126 * q^56 + 27 * q^57 - 33 * q^58 + q^59 - 179 * q^60 - 15 * q^61 + 158 * q^62 - 5 * q^63 - 24 * q^64 + q^65 - 150 * q^66 - 151 * q^67 + 140 * q^68 - 98 * q^69 - 126 * q^70 - 31 * q^71 - 149 * q^72 - 9 * q^73 + 39 * q^74 + 85 * q^75 - 81 * q^76 + 46 * q^77 - 25 * q^78 - 69 * q^79 - 64 * q^80 + 71 * q^81 - 52 * q^82 - q^83 - 47 * q^84 + 62 * q^85 + 97 * q^86 + 150 * q^87 - 12 * q^88 + 23 * q^89 + 107 * q^90 - q^91 - 43 * q^92 + 316 * q^93 - 86 * q^94 - 29 * q^95 + 177 * q^96 + 114 * q^97 - 336 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

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