LMFDB - Embedded newform 220.3.w.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(7,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 5, 14]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("220.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.w (of order $20$, degree $8$, 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:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$544$
Relative dimension:	$68$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.1
Character	$\chi$	$=$	220.7
Dual form			220.3.w.a.63.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.99975 - 0.0316704i) q^{2} +(4.68739 - 2.38834i) q^{3} +(3.99799 + 0.126666i) q^{4} +(-2.84565 - 4.11124i) q^{5} +(-9.44924 + 4.62763i) q^{6} +(-0.358764 + 0.704115i) q^{7} +(-7.99097 - 0.379918i) q^{8} +(10.9773 - 15.1090i) q^{9} +(5.56039 + 8.31156i) q^{10} +(-9.67047 - 5.24233i) q^{11} +(19.0427 - 8.95485i) q^{12} +(-2.90025 - 18.3115i) q^{13} +(0.739738 - 1.39669i) q^{14} +(-23.1577 - 12.4746i) q^{15} +(15.9679 + 1.01282i) q^{16} +(-3.39896 + 21.4602i) q^{17} +(-22.4304 + 29.8666i) q^{18} +(15.6275 + 5.07770i) q^{19} +(-10.8562 - 16.7971i) q^{20} +4.15731i q^{21} +(19.1725 + 10.7896i) q^{22} +(-2.41542 - 2.41542i) q^{23} +(-38.3641 + 17.3044i) q^{24} +(-8.80451 + 23.3983i) q^{25} +(5.21984 + 36.7102i) q^{26} +(7.96283 - 50.2753i) q^{27} +(-1.52353 + 2.76960i) q^{28} +(2.69421 + 8.29194i) q^{29} +(45.9145 + 25.6794i) q^{30} +(29.6349 - 40.7889i) q^{31} +(-31.8997 - 2.53109i) q^{32} +(-57.8497 - 1.47642i) q^{33} +(7.47673 - 42.8074i) q^{34} +(3.91570 - 0.528702i) q^{35} +(45.8011 - 59.0153i) q^{36} +(9.38918 - 18.4273i) q^{37} +(-31.0903 - 10.6490i) q^{38} +(-57.3287 - 78.9061i) q^{39} +(21.1776 + 33.9339i) q^{40} +(19.1830 + 6.23292i) q^{41} +(0.131664 - 8.31358i) q^{42} +(-1.87193 + 1.87193i) q^{43} +(-37.9985 - 22.1837i) q^{44} +(-93.3544 - 2.13542i) q^{45} +(4.75374 + 4.90673i) q^{46} +(-31.2740 - 61.3786i) q^{47} +(77.2667 - 33.3894i) q^{48} +(28.4344 + 39.1366i) q^{49} +(18.3479 - 46.5119i) q^{50} +(35.3221 + 108.710i) q^{51} +(-9.27575 - 73.5765i) q^{52} +(56.6145 - 8.96686i) q^{53} +(-17.5159 + 100.286i) q^{54} +(5.96636 + 54.6754i) q^{55} +(3.13438 - 5.49026i) q^{56} +(85.3796 - 13.5228i) q^{57} +(-5.12514 - 16.6671i) q^{58} +(-3.43169 - 10.5617i) q^{59} +(-91.0043 - 52.8065i) q^{60} +(22.7745 + 31.3464i) q^{61} +(-60.5541 + 80.6291i) q^{62} +(6.70020 + 13.1499i) q^{63} +(63.7113 + 6.07183i) q^{64} +(-67.0296 + 64.0317i) q^{65} +(115.638 + 4.78459i) q^{66} +(-15.2404 + 15.2404i) q^{67} +(-16.3073 + 85.3672i) q^{68} +(-17.0909 - 5.55316i) q^{69} +(-7.84716 + 0.933259i) q^{70} +(50.0607 + 68.9026i) q^{71} +(-93.4598 + 116.565i) q^{72} +(-8.83037 + 17.3306i) q^{73} +(-19.3596 + 36.5526i) q^{74} +(14.6130 + 130.705i) q^{75} +(61.8356 + 22.2801i) q^{76} +(7.16062 - 4.92836i) q^{77} +(112.144 + 159.608i) q^{78} +(2.66749 - 3.67149i) q^{79} +(-41.2752 - 68.5300i) q^{80} +(-30.8097 - 94.8224i) q^{81} +(-38.1637 - 13.0718i) q^{82} +(25.4037 - 160.393i) q^{83} +(-0.526589 + 16.6209i) q^{84} +(97.9002 - 47.0944i) q^{85} +(3.80268 - 3.68411i) q^{86} +(32.4328 + 32.4328i) q^{87} +(75.2848 + 45.5653i) q^{88} +126.526i q^{89} +(186.618 + 7.22687i) q^{90} +(13.9339 + 4.52739i) q^{91} +(-9.35089 - 9.96279i) q^{92} +(41.4922 - 261.972i) q^{93} +(60.5962 + 123.732i) q^{94} +(-23.5950 - 78.6979i) q^{95} +(-155.572 + 64.3233i) q^{96} +(11.6378 + 73.4780i) q^{97} +(-55.6222 - 79.1639i) q^{98} +(-185.362 + 88.5644i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) $ 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.99975	−	0.0316704i	−0.999875	−	0.0158352i
$2$	−1.99975	−	0.0316704i	−0.999875	−	0.0158352i
$3$	4.68739	−	2.38834i	1.56246	−	0.796114i	0.562924	−	0.826509i	$-0.309676\pi$
$3$	4.68739	−	2.38834i	1.56246	−	0.796114i	0.999538	+	0.0303947i	$0.00967643\pi$
$4$	3.99799	+	0.126666i	0.999498	+	0.0316664i
$5$	−2.84565	−	4.11124i	−0.569131	−	0.822247i
$5$	−2.84565	−	4.11124i	−0.569131	−	0.822247i
$6$	−9.44924	+	4.62763i	−1.57487	+	0.771272i
$7$	−0.358764	+	0.704115i	−0.0512521	+	0.100588i	−0.915212	−	0.402973i	$-0.867977\pi$
$7$	−0.358764	+	0.704115i	−0.0512521	+	0.100588i	0.863960	+	0.503561i	$0.167977\pi$
$8$	−7.99097	−	0.379918i	−0.998872	−	0.0474897i
$9$	10.9773	−	15.1090i	1.21970	−	1.67878i
$10$	5.56039	+	8.31156i	0.556039	+	0.831156i
$11$	−9.67047	−	5.24233i	−0.879134	−	0.476575i
$11$	−9.67047	−	5.24233i	−0.879134	−	0.476575i
$12$	19.0427	−	8.95485i	1.58689	−	0.746237i
$13$	−2.90025	−	18.3115i	−0.223096	−	1.40857i	−0.804013	−	0.594612i	$-0.797306\pi$
$13$	−2.90025	−	18.3115i	−0.223096	−	1.40857i	0.580917	−	0.813963i	$-0.302694\pi$
$14$	0.739738	−	1.39669i	0.0528385	−	0.0997636i
$15$	−23.1577	−	12.4746i	−1.54385	−	0.831637i
$16$	15.9679	+	1.01282i	0.997994	+	0.0633011i
$17$	−3.39896	+	21.4602i	−0.199939	+	1.26237i	0.659726	+	0.751506i	$0.270672\pi$
$17$	−3.39896	+	21.4602i	−0.199939	+	1.26237i	−0.859665	+	0.510859i	$0.829328\pi$
$18$	−22.4304	+	29.8666i	−1.24613	+	1.65925i
$19$	15.6275	+	5.07770i	0.822502	+	0.267247i	0.689884	−	0.723920i	$-0.257662\pi$
$19$	15.6275	+	5.07770i	0.822502	+	0.267247i	0.132618	+	0.991167i	$0.457662\pi$
$20$	−10.8562	−	16.7971i	−0.542808	−	0.839857i
$21$			4.15731i			0.197967i
$22$	19.1725	+	10.7896i	0.871477	+	0.490437i
$23$	−2.41542	−	2.41542i	−0.105018	−	0.105018i	0.652645	−	0.757664i	$-0.273659\pi$
$23$	−2.41542	−	2.41542i	−0.105018	−	0.105018i	−0.757664	+	0.652645i	$0.773659\pi$
$24$	−38.3641	+	17.3044i	−1.59851	+	0.721015i
$25$	−8.80451	+	23.3983i	−0.352181	+	0.935932i
$26$	5.21984	+	36.7102i	0.200763	+	1.41193i
$27$	7.96283	−	50.2753i	0.294920	−	1.86205i
$28$	−1.52353	+	2.76960i	−0.0544116	+	0.0989144i
$29$	2.69421	+	8.29194i	0.0929039	+	0.285929i	0.986702	−	0.162541i	$-0.0519690\pi$
$29$	2.69421	+	8.29194i	0.0929039	+	0.285929i	−0.893798	+	0.448470i	$0.851969\pi$
$30$	45.9145	+	25.6794i	1.53048	+	0.855980i
$31$	29.6349	−	40.7889i	0.955964	−	1.31577i	0.00713718	−	0.999975i	$-0.497728\pi$
$31$	29.6349	−	40.7889i	0.955964	−	1.31577i	0.948827	−	0.315797i	$-0.102272\pi$
$32$	−31.8997	−	2.53109i	−0.996867	−	0.0790966i
$33$	−57.8497	−	1.47642i	−1.75302	−	0.0447399i
$34$	7.47673	−	42.8074i	0.219904	−	1.25904i
$35$	3.91570	−	0.528702i	0.111877	−	0.0151058i
$36$	45.8011	−	59.0153i	1.27225	−	1.63931i
$37$	9.38918	−	18.4273i	0.253762	−	0.498035i	−0.728621	−	0.684917i	$-0.759838\pi$
$37$	9.38918	−	18.4273i	0.253762	−	0.498035i	0.982382	+	0.186882i	$0.0598383\pi$
$38$	−31.0903	−	10.6490i	−0.818167	−	0.280238i
$39$	−57.3287	−	78.9061i	−1.46997	−	2.02323i
$40$	21.1776	+	33.9339i	0.529440	+	0.848347i
$41$	19.1830	+	6.23292i	0.467877	+	0.152023i	0.533461	−	0.845825i	$-0.320891\pi$
$41$	19.1830	+	6.23292i	0.467877	+	0.152023i	−0.0655840	+	0.997847i	$0.520891\pi$
$42$	0.131664	−	8.31358i	0.00313485	−	0.197942i
$43$	−1.87193	+	1.87193i	−0.0435333	+	0.0435333i	−0.728538	−	0.685005i	$-0.759800\pi$
$43$	−1.87193	+	1.87193i	−0.0435333	+	0.0435333i	0.685005	+	0.728538i	$0.259800\pi$
$44$	−37.9985	−	22.1837i	−0.863601	−	0.504175i
$45$	−93.3544	−	2.13542i	−2.07454	−	0.0474537i
$46$	4.75374	+	4.90673i	0.103342	+	0.106668i
$47$	−31.2740	−	61.3786i	−0.665403	−	1.30593i	−0.938945	−	0.344068i	$-0.888195\pi$
$47$	−31.2740	−	61.3786i	−0.665403	−	1.30593i	0.273541	−	0.961860i	$-0.411805\pi$
$48$	77.2667	−	33.3894i	1.60972	−	0.695612i
$49$	28.4344	+	39.1366i	0.580294	+	0.798706i
$50$	18.3479	−	46.5119i	0.366957	−	0.930238i
$51$	35.3221	+	108.710i	0.692590	+	2.13157i
$52$	−9.27575	−	73.5765i	−0.178380	−	1.41493i
$53$	56.6145	−	8.96686i	1.06820	−	0.169186i	0.402510	−	0.915416i	$-0.368138\pi$
$53$	56.6145	−	8.96686i	1.06820	−	0.169186i	0.665689	+	0.746230i	$0.268138\pi$
$54$	−17.5159	+	100.286i	−0.324368	+	1.85715i
$55$	5.96636	+	54.6754i	0.108479	+	0.994099i
$56$	3.13438	−	5.49026i	0.0559711	−	0.0980404i
$57$	85.3796	−	13.5228i	1.49789	−	0.237242i
$58$	−5.12514	−	16.6671i	−0.0883645	−	0.287364i
$59$	−3.43169	−	10.5617i	−0.0581642	−	0.179011i	0.917753	−	0.397151i	$-0.130001\pi$
$59$	−3.43169	−	10.5617i	−0.0581642	−	0.179011i	−0.975918	+	0.218140i	$0.930001\pi$
$60$	−91.0043	−	52.8065i	−1.51674	−	0.880108i
$61$	22.7745	+	31.3464i	0.373352	+	0.513875i	0.953808	−	0.300416i	$-0.0971256\pi$
$61$	22.7745	+	31.3464i	0.373352	+	0.513875i	−0.580456	+	0.814292i	$0.697126\pi$
$62$	−60.5541	+	80.6291i	−0.976680	+	1.30047i
$63$	6.70020	+	13.1499i	0.106352	+	0.208728i
$64$	63.7113	+	6.07183i	0.995489	+	0.0948723i
$65$	−67.0296	+	64.0317i	−1.03123	+	0.985103i
$66$	115.638	+	4.78459i	1.75209	+	0.0724937i
$67$	−15.2404	+	15.2404i	−0.227469	+	0.227469i	−0.811634	−	0.584166i	$-0.801422\pi$
$67$	−15.2404	+	15.2404i	−0.227469	+	0.227469i	0.584166	+	0.811634i	$0.301422\pi$
$68$	−16.3073	+	85.3672i	−0.239813	+	1.25540i
$69$	−17.0909	−	5.55316i	−0.247694	−	0.0804806i
$70$	−7.84716	+	0.933259i	−0.112102	+	0.0133323i
$71$	50.0607	+	68.9026i	0.705080	+	0.970459i	0.999889	+	0.0149028i	$0.00474388\pi$
$71$	50.0607	+	68.9026i	0.705080	+	0.970459i	−0.294809	+	0.955556i	$0.595256\pi$
$72$	−93.4598	+	116.565i	−1.29805	+	1.61896i
$73$	−8.83037	+	17.3306i	−0.120964	+	0.237405i	−0.943546	−	0.331241i	$-0.892533\pi$
$73$	−8.83037	+	17.3306i	−0.120964	+	0.237405i	0.822582	+	0.568646i	$0.192533\pi$
$74$	−19.3596	+	36.5526i	−0.261616	+	0.493954i
$75$	14.6130	+	130.705i	0.194840	+	1.74273i
$76$	61.8356	+	22.2801i	0.813627	+	0.293159i
$77$	7.16062	−	4.92836i	0.0929951	−	0.0640047i
$78$	112.144	+	159.608i	1.43774	+	2.04626i
$79$	2.66749	−	3.67149i	0.0337657	−	0.0464746i	−0.791800	−	0.610780i	$-0.790856\pi$
$79$	2.66749	−	3.67149i	0.0337657	−	0.0464746i	0.825566	+	0.564305i	$0.190856\pi$
$80$	−41.2752	−	68.5300i	−0.515940	−	0.856625i
$81$	−30.8097	−	94.8224i	−0.380366	−	1.17065i
$82$	−38.1637	−	13.0718i	−0.465411	−	0.159412i
$83$	25.4037	−	160.393i	0.306069	−	1.93244i	−0.0517703	−	0.998659i	$-0.516486\pi$
$83$	25.4037	−	160.393i	0.306069	−	1.93244i	0.357839	−	0.933783i	$-0.383514\pi$
$84$	−0.526589	+	16.6209i	−0.00626891	+	0.197868i
$85$	97.9002	−	47.0944i	1.15177	−	0.554051i
$86$	3.80268	−	3.68411i	0.0442172	−	0.0428385i
$87$	32.4328	+	32.4328i	0.372791	+	0.372791i
$88$	75.2848	+	45.5653i	0.855509	+	0.517787i
$89$			126.526i			1.42164i	0.703372	+	0.710822i	$0.251677\pi$
$89$			126.526i			1.42164i	−0.703372	+	0.710822i	$0.748323\pi$
$90$	186.618	+	7.22687i	2.07353	+	0.0802986i
$91$	13.9339	+	4.52739i	0.153120	+	0.0497516i
$92$	−9.35089	−	9.96279i	−0.101640	−	0.108291i
$93$	41.4922	−	261.972i	0.446153	−	2.81690i
$94$	60.5962	+	123.732i	0.644640	+	1.31630i
$95$	−23.5950	−	78.6979i	−0.248368	−	0.828398i
$96$	−155.572	+	64.3233i	−1.62054	+	0.670034i
$97$	11.6378	+	73.4780i	0.119977	+	0.757505i	0.972170	+	0.234277i	$0.0752724\pi$
$97$	11.6378	+	73.4780i	0.119977	+	0.757505i	−0.852193	+	0.523228i	$0.824728\pi$
$98$	−55.6222	−	79.1639i	−0.567574	−	0.807795i
$99$	−185.362	+	88.5644i	−1.87235	+	0.894590i
$100$	−38.1642	+	92.4310i	−0.381642	+	0.924310i
$101$	−43.5862	+	59.9913i	−0.431547	+	0.593973i	−0.968307	−	0.249762i	$-0.919648\pi$
$101$	−43.5862	+	59.9913i	−0.431547	+	0.593973i	0.536761	+	0.843734i	$0.319648\pi$
$102$	−67.1924	−	218.512i	−0.658749	−	2.14227i
$103$	−83.2419	+	163.371i	−0.808174	+	1.58613i	0.00204194	+	0.999998i	$0.499350\pi$
$103$	−83.2419	+	163.371i	−0.808174	+	1.58613i	−0.810216	+	0.586132i	$0.800650\pi$
$104$	16.2190	+	147.428i	0.155952	+	1.41758i
$105$	17.0917	−	11.8303i	0.162778	−	0.112669i
$106$	−113.499	+	16.1385i	−1.07074	+	0.152250i
$107$	106.976	−	54.5069i	0.999774	−	0.509410i	0.124078	−	0.992272i	$-0.460403\pi$
$107$	106.976	−	54.5069i	0.999774	−	0.509410i	0.875696	+	0.482862i	$0.160403\pi$
$108$	38.2035	−	199.992i	0.353736	−	1.85178i
$109$	109.776			1.00712			0.503561	−	0.863960i	$-0.332023\pi$
$109$	109.776			1.00712			0.503561	+	0.863960i	$0.332023\pi$
$110$	−10.1996	−	109.526i	−0.0927240	−	0.995692i
$111$		−	108.800i		−	0.980184i
$112$	−6.44186	+	10.8799i	−0.0575166	+	0.0971418i
$113$	−44.8781	−	88.0782i	−0.397151	−	0.779453i	0.602677	−	0.797985i	$-0.294101\pi$
$113$	−44.8781	−	88.0782i	−0.397151	−	0.779453i	−0.999828	+	0.0185320i	$0.994101\pi$
$114$	−171.166	+	24.3382i	−1.50146	+	0.213493i
$115$	−3.05691	+	16.8038i	−0.0265819	+	0.146120i
$116$	9.72115	+	33.4924i	0.0838030	+	0.288727i
$117$	−308.505	−	157.191i	−2.63680	−	1.34351i
$118$	6.52803	+	21.2293i	0.0553223	+	0.179910i
$119$	−13.8910	−	10.0924i	−0.116731	−	0.0848102i
$120$	180.313	+	108.482i	1.50261	+	0.904015i
$121$	66.0360	+	101.392i	0.545752	+	0.837947i
$122$	−44.5505	−	63.4062i	−0.365168	−	0.519723i
$123$	104.804	−	16.5994i	0.852067	−	0.134954i
$124$	123.647	−	159.320i	0.997150	−	1.28484i
$125$	121.251	−	30.3860i	0.970004	−	0.243088i
$126$	−12.9823	−	26.5087i	−0.103034	−	0.210386i
$127$	−92.1600	−	14.5967i	−0.725670	−	0.114935i	−0.217338	−	0.976096i	$-0.569737\pi$
$127$	−92.1600	−	14.5967i	−0.725670	−	0.114935i	−0.508331	+	0.861162i	$0.669737\pi$
$128$	−127.214	−	14.1599i	−0.993862	−	0.110624i
$129$	−4.30366	+	13.2453i	−0.0333617	+	0.102677i
$130$	136.070	−	125.925i	1.04670	−	0.968650i
$131$	109.250			0.833972			0.416986	−	0.908913i	$-0.363086\pi$
$131$	109.250			0.833972			0.416986	+	0.908913i	$0.363086\pi$
$132$	−231.096	−	13.2303i	−1.75073	−	0.100229i
$133$	−9.18188	+	9.18188i	−0.0690367	+	0.0690367i
$134$	30.9596	−	29.9943i	0.231042	−	0.223838i
$135$	−229.353	+	110.329i	−1.69891	+	0.817252i
$136$	35.3141	−	170.197i	0.259663	−	1.25145i
$137$	209.052	+	33.1106i	1.52593	+	0.241683i	0.862307	−	0.506386i	$-0.169019\pi$
$137$	209.052	+	33.1106i	1.52593	+	0.241683i	0.663621	+	0.748069i	$0.269019\pi$
$138$	34.0016	+	11.6462i	0.246388	+	0.0843927i
$139$	86.0996	−	27.9755i	0.619422	−	0.201262i	0.0175381	−	0.999846i	$-0.494417\pi$
$139$	86.0996	−	27.9755i	0.619422	−	0.201262i	0.601883	+	0.798584i	$0.294417\pi$
$140$	15.7219	−	1.61776i	0.112299	−	0.0115554i
$141$	−293.186	−	213.012i	−2.07933	−	1.51073i
$142$	−97.9266	−	139.373i	−0.689624	−	0.981502i
$143$	−67.9479	+	192.285i	−0.475160	+	1.34465i
$144$	190.588	−	230.141i	1.32353	−	1.59820i
$145$	26.4233	−	34.6725i	0.182230	−	0.239121i
$146$	18.2074	−	34.3771i	0.124708	−	0.235460i
$147$	226.755	+	115.537i	1.54255	+	0.785968i
$148$	39.8720	−	72.4830i	0.269405	−	0.489750i
$149$	−2.07443	+	1.50716i	−0.0139223	+	0.0101152i	−0.594725	−	0.803929i	$-0.702739\pi$
$149$	−2.07443	+	1.50716i	−0.0139223	+	0.0101152i	0.580802	+	0.814045i	$0.302739\pi$
$150$	−25.0829	−	261.840i	−0.167219	−	1.74560i
$151$	44.8767	−	138.116i	0.297197	−	0.914677i	−0.685278	−	0.728282i	$-0.740319\pi$
$151$	44.8767	−	138.116i	0.297197	−	0.914677i	0.982475	−	0.186396i	$-0.0596807\pi$
$152$	−122.950	−	46.5129i	−0.808883	−	0.306006i
$153$	286.931	+	286.931i	1.87537	+	1.87537i
$154$	−14.4755	+	9.62871i	−0.0939969	+	0.0625241i
$155$	−252.023	−	5.76486i	−1.62596	−	0.0371927i
$156$	−219.205	−	322.728i	−1.40516	−	2.06877i
$157$	−28.5093	+	14.5262i	−0.181588	+	0.0925235i	−0.542421	−	0.840107i	$-0.682492\pi$
$157$	−28.5093	+	14.5262i	−0.181588	+	0.0925235i	0.360833	+	0.932630i	$0.382492\pi$
$158$	−5.45060	+	7.25758i	−0.0344974	+	0.0459341i
$159$	243.958	−	177.246i	1.53433	−	1.11475i
$160$	80.3697	+	138.350i	0.502311	+	0.864687i
$161$	2.56730	−	0.834167i	0.0159460	−	0.00518116i
$162$	58.6085	+	190.597i	0.361781	+	1.17652i
$163$	9.57708	+	60.4673i	0.0587551	+	0.370965i	0.999493	+	0.0318313i	$0.0101339\pi$
$163$	9.57708	+	60.4673i	0.0587551	+	0.370965i	−0.940738	+	0.339134i	$0.889866\pi$
$164$	75.9039	+	27.3490i	0.462829	+	0.166762i
$165$	158.550	+	242.035i	0.960911	+	1.46688i
$166$	−55.8808	+	319.941i	−0.336631	+	1.92735i
$167$	16.4044	+	103.573i	0.0982299	+	0.620199i	0.986860	+	0.161575i	$0.0516574\pi$
$167$	16.4044	+	103.573i	0.0982299	+	0.620199i	−0.888631	+	0.458624i	$0.848343\pi$
$168$	1.57944	−	33.2209i	0.00940141	−	0.197744i
$169$	−166.170	+	53.9919i	−0.983254	+	0.319479i
$170$	−197.267	+	91.0764i	−1.16040	+	0.535743i
$171$	248.268	−	180.377i	1.45186	−	1.05484i
$172$	−7.72109	+	7.24687i	−0.0448900	+	0.0421330i
$173$	−291.630	+	148.593i	−1.68572	+	0.858920i	−0.695650	+	0.718381i	$0.744883\pi$
$173$	−291.630	+	148.593i	−1.68572	+	0.858920i	−0.990075	+	0.140539i	$0.955117\pi$
$174$	−63.8303	−	65.8846i	−0.366841	−	0.378647i
$175$	−13.3163	−	14.5939i	−0.0760934	−	0.0833935i
$176$	−149.108	−	93.5034i	−0.847203	−	0.531270i
$177$	−41.3105	−	41.3105i	−0.233393	−	0.233393i
$178$	4.00714	−	253.021i	0.0225120	−	1.42147i
$179$	−17.2452	+	53.0753i	−0.0963420	+	0.296510i	−0.987601	−	0.156984i	$-0.949823\pi$
$179$	−17.2452	+	53.0753i	−0.0963420	+	0.296510i	0.891259	+	0.453494i	$0.149823\pi$
$180$	−372.960	−	20.3622i	−2.07200	−	0.113123i
$181$	31.1221	−	22.6115i	0.171945	−	0.124926i	−0.498484	−	0.866899i	$-0.666110\pi$
$181$	31.1221	−	22.6115i	0.171945	−	0.124926i	0.670430	+	0.741973i	$0.266110\pi$
$182$	−27.7209	−	9.49494i	−0.152313	−	0.0521700i
$183$	181.619	+	92.5394i	0.992452	+	0.505680i
$184$	18.3839	+	20.2192i	0.0999125	+	0.109887i
$185$	−102.477	+	13.8366i	−0.553932	+	0.0747924i
$186$	−91.2708	+	522.563i	−0.490703	+	2.80948i
$187$	145.371	−	189.712i	0.777385	−	1.01450i
$188$	−117.259	−	249.353i	−0.623716	−	1.32634i
$189$	32.5428	+	23.6437i	0.172184	+	0.125099i
$190$	44.6916	+	158.123i	0.235219	+	0.832228i
$191$	−28.3963	+	9.22653i	−0.148672	+	0.0483065i	−0.382408	−	0.923994i	$-0.624905\pi$
$191$	−28.3963	+	9.22653i	−0.148672	+	0.0483065i	0.233736	+	0.972300i	$0.424905\pi$
$192$	313.141	−	123.703i	1.63094	−	0.644289i
$193$	−237.530	−	37.6211i	−1.23073	−	0.194928i	−0.493001	−	0.870029i	$-0.664100\pi$
$193$	−237.530	−	37.6211i	−1.23073	−	0.194928i	−0.737725	+	0.675101i	$0.764100\pi$
$194$	−20.9455	−	147.306i	−0.107967	−	0.759310i
$195$	−161.264	+	460.231i	−0.826996	+	2.36016i
$196$	108.723	+	160.070i	0.554711	+	0.816682i
$197$	−97.1717	+	97.1717i	−0.493257	+	0.493257i	−0.909331	−	0.416073i	$-0.863406\pi$
$197$	−97.1717	+	97.1717i	−0.493257	+	0.493257i	0.416073	+	0.909331i	$0.363406\pi$
$198$	373.483	−	171.236i	1.88628	−	0.864829i
$199$	−111.439			−0.559994			−0.279997	−	0.960001i	$-0.590333\pi$
$199$	−111.439			−0.559994			−0.279997	+	0.960001i	$0.590333\pi$
$200$	79.2461	−	183.630i	0.396230	−	0.918151i
$201$	−35.0383	+	107.837i	−0.174320	+	0.536502i
$202$	89.0614	−	118.587i	0.440898	−	0.587065i
$203$	−6.80506	−	1.07782i	−0.0335225	−	0.00530944i
$204$	127.448	+	439.097i	0.624743	+	2.15243i
$205$	−28.9631	−	96.6024i	−0.141283	−	0.471231i
$206$	171.637	−	324.066i	0.833189	−	1.57313i
$207$	−63.0095	+	9.97973i	−0.304394	+	0.0482112i
$208$	−27.7648	−	295.333i	−0.133485	−	1.41987i
$209$	−124.507	−	131.028i	−0.595726	−	0.626930i
$210$	−34.5537	+	23.1163i	−0.164542	+	0.110077i
$211$	−203.761	−	148.041i	−0.965694	−	0.701618i	−0.0112277	−	0.999937i	$-0.503574\pi$
$211$	−203.761	−	148.041i	−0.965694	−	0.701618i	−0.954466	+	0.298319i	$0.903574\pi$
$212$	227.480	−	28.6783i	1.07302	−	0.135275i
$213$	399.217	+	203.411i	1.87426	+	0.954981i
$214$	−215.651	+	105.612i	−1.00772	+	0.493515i
$215$	13.0228	+	2.36909i	0.0605713	+	0.0110190i
$216$	−82.7312	+	398.724i	−0.383015	+	1.84594i
$217$	18.0881	+	35.5000i	0.0833555	+	0.163594i
$218$	−219.525	−	3.47666i	−1.00699	−	0.0159480i
$219$			102.325i			0.467238i
$220$	16.9280	+	219.348i	0.0769454	+	0.997035i
$221$	402.826			1.82274
$222$	−3.44576	+	217.574i	−0.0155214	+	0.980061i
$223$	−134.549	+	68.5564i	−0.603361	+	0.307428i	−0.728856	−	0.684667i	$-0.759948\pi$
$223$	−134.549	+	68.5564i	−0.603361	+	0.307428i	0.125496	+	0.992094i	$0.459948\pi$
$224$	13.2267	−	21.5530i	0.0590476	−	0.0962188i
$225$	256.875	+	389.879i	1.14167	+	1.73279i
$226$	86.9555	+	177.556i	0.384759	+	0.785645i
$227$	−143.699	+	282.024i	−0.633034	+	1.24240i	0.322235	+	0.946660i	$0.395566\pi$
$227$	−143.699	+	282.024i	−0.633034	+	1.24240i	−0.955269	+	0.295739i	$0.904434\pi$
$228$	343.060	−	43.2494i	1.50465	−	0.189690i
$229$	76.8476	−	105.772i	0.335579	−	0.461885i	−0.607565	−	0.794270i	$-0.707853\pi$
$229$	76.8476	−	105.772i	0.335579	−	0.461885i	0.943144	+	0.332385i	$0.107853\pi$
$230$	6.64525	−	33.5066i	0.0288924	−	0.145681i
$231$	21.7940	−	40.2031i	0.0943462	−	0.174040i
$232$	−18.3791	−	67.2842i	−0.0792204	−	0.290018i
$233$	1.03568	+	6.53904i	0.00444499	+	0.0280646i	0.989811	−	0.142386i	$-0.0454776\pi$
$233$	1.03568	+	6.53904i	0.00444499	+	0.0280646i	−0.985366	+	0.170451i	$0.945478\pi$
$234$	611.955	+	324.114i	2.61519	+	1.38510i
$235$	−163.347	+	303.237i	−0.695094	+	1.29037i
$236$	−12.3821	−	42.6601i	−0.0524664	−	0.180763i
$237$	3.73480	−	23.5806i	0.0157586	−	0.0994961i
$238$	27.4589	+	20.6222i	0.115374	+	0.0866481i
$239$	−366.460	−	119.070i	−1.53330	−	0.498201i	−0.583784	−	0.811909i	$-0.698429\pi$
$239$	−366.460	−	119.070i	−1.53330	−	0.498201i	−0.949519	+	0.313708i	$0.898429\pi$
$240$	−357.146	−	222.647i	−1.48811	−	0.927696i
$241$		−	233.938i		−	0.970695i	−0.874321	−	0.485348i	$-0.838693\pi$
$241$		−	233.938i		−	0.970695i	0.874321	−	0.485348i	$-0.161307\pi$
$242$	−128.844	−	204.849i	−0.532415	−	0.846484i
$243$	−46.9468	−	46.9468i	−0.193197	−	0.193197i
$244$	87.0818	+	128.207i	0.356892	+	0.525440i
$245$	79.9853	−	228.270i	0.326471	−	0.931713i
$246$	−210.108	+	29.8754i	−0.854098	+	0.121445i
$247$	47.6563	−	300.890i	0.192940	−	1.21818i
$248$	−252.308	+	314.684i	−1.01737	+	1.26889i
$249$	−263.996	−	812.495i	−1.06022	−	3.26303i
$250$	−243.433	+	56.9244i	−0.973732	+	0.227697i
$251$	−11.6241	+	15.9992i	−0.0463111	+	0.0637417i	−0.831545	−	0.555458i	$-0.812543\pi$
$251$	−11.6241	+	15.9992i	−0.0463111	+	0.0637417i	0.785233	+	0.619200i	$0.212543\pi$
$252$	25.1217	+	53.4218i	0.0996893	+	0.211991i
$253$	10.6958	+	36.0207i	0.0422760	+	0.142374i
$254$	183.835	+	32.1085i	0.723759	+	0.126412i
$255$	346.419	−	454.569i	1.35850	−	1.78262i
$256$	253.948	+	32.3452i	0.991986	+	0.126348i
$257$	169.564	−	332.788i	0.659782	−	1.29489i	−0.282240	−	0.959344i	$-0.591078\pi$
$257$	169.564	−	332.788i	0.659782	−	1.29489i	0.942022	−	0.335551i	$-0.108922\pi$
$258$	9.02572	−	26.3510i	0.0349834	−	0.102136i
$259$	9.60643	+	13.2221i	0.0370905	+	0.0510507i
$260$	−276.095	+	247.508i	−1.06190	+	0.951954i
$261$	154.858	+	50.3165i	0.593327	+	0.192784i
$262$	−218.473	−	3.46000i	−0.833867	−	0.0132061i
$263$	318.409	−	318.409i	1.21068	−	1.21068i	0.239878	−	0.970803i	$-0.422893\pi$
$263$	318.409	−	318.409i	1.21068	−	1.21068i	0.970803	−	0.239878i	$-0.0771073\pi$
$264$	461.714	+	33.7761i	1.74892	+	0.127940i
$265$	−197.970	−	207.239i	−0.747057	−	0.782034i
$266$	18.6523	−	18.0707i	0.0701213	−	0.0679349i
$267$	302.188	+	593.078i	1.13179	+	2.22126i
$268$	−62.8614	+	59.0006i	−0.234558	+	0.220151i
$269$	−162.704	−	223.943i	−0.604847	−	0.832501i	0.391294	−	0.920266i	$-0.372028\pi$
$269$	−162.704	−	223.943i	−0.604847	−	0.832501i	−0.996141	+	0.0877651i	$0.972028\pi$
$270$	462.143	−	213.367i	1.71164	−	0.790247i
$271$	6.42649	+	19.7787i	0.0237140	+	0.0729841i	0.962213	−	0.272297i	$-0.0877834\pi$
$271$	6.42649	+	19.7787i	0.0237140	+	0.0729841i	−0.938499	+	0.345281i	$0.887783\pi$
$272$	−76.0096	+	339.232i	−0.279447	+	1.24718i
$273$	76.1264	−	12.0572i	0.278851	−	0.0441657i
$274$	−417.003	−	72.8336i	−1.52191	−	0.265816i
$275$	207.805	−	180.116i	0.755656	−	0.654969i
$276$	−67.6258	−	24.3663i	−0.245021	−	0.0882838i
$277$	75.2055	−	11.9114i	0.271500	−	0.0430014i	−0.0191999	−	0.999816i	$-0.506112\pi$
$277$	75.2055	−	11.9114i	0.271500	−	0.0430014i	0.290700	+	0.956814i	$0.406112\pi$
$278$	−173.064	+	53.2171i	−0.622531	+	0.191428i
$279$	−290.968	−	895.507i	−1.04290	−	3.20970i
$280$	−31.4911	+	2.73720i	−0.112468	+	0.00977570i
$281$	84.8934	+	116.846i	0.302112	+	0.415821i	0.932901	−	0.360133i	$-0.117269\pi$
$281$	84.8934	+	116.846i	0.302112	+	0.415821i	−0.630789	+	0.775954i	$0.717269\pi$
$282$	579.553	+	435.256i	2.05515	+	1.54346i
$283$	−166.329	−	326.440i	−0.587736	−	1.15350i	−0.973025	−	0.230701i	$-0.925898\pi$
$283$	−166.329	−	326.440i	−0.587736	−	1.15350i	0.385288	−	0.922796i	$-0.374102\pi$
$284$	191.415	+	281.813i	0.673995	+	0.992300i
$285$	−298.556	−	312.534i	−1.04757	−	1.09661i
$286$	141.969	−	382.369i	0.496393	−	1.33695i
$287$	−11.2709	+	11.2709i	−0.0392713	+	0.0392713i
$288$	−388.417	+	454.189i	−1.34867	+	1.57704i
$289$	−174.132	−	56.5790i	−0.602533	−	0.195775i
$290$	−53.9381	+	68.4995i	−0.185993	+	0.236205i
$291$	230.041	+	316.625i	0.790520	+	1.08806i
$292$	−37.4989	+	68.1690i	−0.128421	+	0.233456i
$293$	−72.0153	+	141.338i	−0.245786	+	0.482382i	−0.980634	−	0.195850i	$-0.937254\pi$
$293$	−72.0153	+	141.338i	−0.245786	+	0.482382i	0.734848	+	0.678232i	$0.237254\pi$
$294$	−449.793	−	238.227i	−1.52991	−	0.810296i
$295$	−33.6560	+	44.1633i	−0.114088	+	0.149706i
$296$	−82.0296	+	143.685i	−0.277127	+	0.485422i
$297$	−340.564	+	444.442i	−1.14668	+	1.49644i
$298$	4.19606	−	2.94824i	0.0140807	−	0.00989342i
$299$	−37.2246	+	51.2352i	−0.124497	+	0.171355i
$300$	41.8668	+	524.409i	0.139556	+	1.74803i
$301$	−0.646473	−	1.98964i	−0.00214775	−	0.00661010i
$302$	−94.1163	+	274.777i	−0.311644	+	0.909856i
$303$	−61.0257	+	385.301i	−0.201405	+	1.27162i
$304$	244.396	+	96.9080i	0.803935	+	0.318776i
$305$	64.0641	−	182.832i	0.210046	−	0.599450i
$306$	−564.703	−	582.877i	−1.84543	−	1.90483i
$307$	−143.736	−	143.736i	−0.468194	−	0.468194i	0.433135	−	0.901329i	$-0.357407\pi$
$307$	−143.736	−	143.736i	−0.468194	−	0.468194i	−0.901329	+	0.433135i	$0.857407\pi$
$308$	29.2524	−	18.7966i	0.0949752	−	0.0610278i
$309$			964.595i			3.12167i
$310$	503.801	+	19.5100i	1.62516	+	0.0629354i
$311$	−110.031	−	35.7514i	−0.353799	−	0.114956i	0.126725	−	0.991938i	$-0.459553\pi$
$311$	−110.031	−	35.7514i	−0.353799	−	0.114956i	−0.480524	+	0.876982i	$0.659553\pi$
$312$	428.134	+	652.317i	1.37222	+	2.09076i
$313$	−83.9908	+	530.297i	−0.268341	+	1.69424i	0.373684	+	0.927556i	$0.378094\pi$
$313$	−83.9908	+	530.297i	−0.268341	+	1.69424i	−0.642026	+	0.766683i	$0.721906\pi$
$314$	57.4714	−	28.1458i	0.183030	−	0.0896365i
$315$	34.9958	−	64.9661i	0.111098	−	0.206242i
$316$	11.1297	−	14.3407i	0.0352205	−	0.0453820i
$317$	44.8903	+	283.426i	0.141610	+	0.894089i	0.951532	+	0.307551i	$0.0995095\pi$
$317$	44.8903	+	283.426i	0.141610	+	0.894089i	−0.809922	+	0.586538i	$0.800491\pi$
$318$	−493.469	+	346.721i	−1.55179	+	1.09032i
$319$	17.4147	−	94.3109i	0.0545917	−	0.295645i
$320$	−156.338	−	279.211i	−0.488555	−	0.872533i
$321$	371.256	−	510.990i	1.15656	−	1.59187i
$322$	−5.16038	+	1.58682i	−0.0160260	+	0.00492800i
$323$	−162.086	+	318.111i	−0.501814	+	0.984865i
$324$	−111.166	−	383.002i	−0.343105	−	1.18210i
$325$	453.993	+	93.3626i	1.39690	+	0.287270i
$326$	−17.2367	−	121.223i	−0.0528734	−	0.371849i
$327$	514.563	−	262.183i	1.57359	−	0.801783i
$328$	−150.923	−	57.0951i	−0.460130	−	0.174070i
$329$	54.4376			0.165464
$330$	−309.395	−	489.031i	−0.937562	−	1.48191i
$331$			133.022i			0.401878i	0.979604	+	0.200939i	$0.0643992\pi$
$331$			133.022i			0.401878i	−0.979604	+	0.200939i	$0.935601\pi$
$332$	121.880	−	638.031i	0.367109	−	1.92178i
$333$	−175.350	−	344.144i	−0.526577	−	1.03347i
$334$	−29.5245	−	207.640i	−0.0883966	−	0.621677i
$335$	106.026	+	19.2880i	0.316495	+	0.0575760i
$336$	−4.21060	+	66.3835i	−0.0125315	+	0.197570i
$337$	−42.3373	−	21.5719i	−0.125630	−	0.0640117i	0.390046	−	0.920795i	$-0.372459\pi$
$337$	−42.3373	−	21.5719i	−0.125630	−	0.0640117i	−0.515676	+	0.856784i	$0.672459\pi$
$338$	334.008	−	102.708i	0.988189	−	0.303868i
$339$	−420.722	−	305.672i	−1.24107	−	0.901688i
$340$	397.370	−	175.882i	1.16873	−	0.517301i
$341$	−500.412	+	239.092i	−1.46748	+	0.701150i
$342$	−502.186	+	352.846i	−1.46838	+	1.03171i
$343$	−76.0033	+	12.0377i	−0.221584	+	0.0350954i
$344$	15.6698	−	14.2474i	0.0455516	−	0.0414168i
$345$	25.8043	+	86.0669i	0.0747952	+	0.249469i
$346$	587.894	−	287.913i	1.69911	−	0.832118i
$347$	−96.6434	−	15.3068i	−0.278511	−	0.0441119i	0.0156162	−	0.999878i	$-0.495029\pi$
$347$	−96.6434	−	15.3068i	−0.278511	−	0.0441119i	−0.294127	+	0.955766i	$0.595029\pi$
$348$	125.558	+	133.774i	0.360799	+	0.384409i
$349$	−130.375	+	401.254i	−0.373568	+	1.14972i	0.570871	+	0.821039i	$0.306605\pi$
$349$	−130.375	+	401.254i	−0.373568	+	1.14972i	−0.944440	+	0.328685i	$0.893395\pi$
$350$	26.1672	+	29.6058i	0.0747633	+	0.0845880i
$351$	−943.709			−2.68863
$352$	295.217	+	191.706i	0.838684	+	0.544619i
$353$	−141.712	+	141.712i	−0.401449	+	0.401449i	−0.878744	−	0.477294i	$-0.841618\pi$
$353$	−141.712	+	141.712i	−0.401449	+	0.401449i	0.477294	+	0.878744i	$0.341618\pi$
$354$	81.3023	+	83.9190i	0.229668	+	0.237059i
$355$	140.819	−	401.884i	0.396675	−	1.13207i
$356$	−16.0266	+	505.851i	−0.0450184	+	1.42093i
$357$	−89.2167	−	14.1305i	−0.249907	−	0.0395813i
$358$	36.1670	−	105.591i	0.101025	−	0.294947i
$359$	311.869	−	101.332i	0.868717	−	0.282263i	0.159452	−	0.987206i	$-0.449027\pi$
$359$	311.869	−	101.332i	0.868717	−	0.282263i	0.709264	+	0.704943i	$0.249027\pi$
$360$	745.181	+	52.5311i	2.06995	+	0.145920i
$361$	−73.6181	−	53.4867i	−0.203928	−	0.148163i
$362$	−62.9526	+	44.2318i	−0.173902	+	0.122187i
$363$	551.694	+	317.545i	1.51982	+	0.874779i
$364$	55.1341	+	19.8654i	0.151467	+	0.0545754i
$365$	96.3782	−	13.0131i	0.264050	−	0.0356523i
$366$	−360.261	−	190.807i	−0.984320	−	0.521332i
$367$	5.55342	+	2.82961i	0.0151319	+	0.00771010i	0.461540	−	0.887119i	$-0.347297\pi$
$367$	5.55342	+	2.82961i	0.0151319	+	0.00771010i	−0.446408	+	0.894829i	$0.647297\pi$
$368$	−36.1229	−	41.0156i	−0.0981599	−	0.111455i
$369$	304.751	−	221.415i	0.825884	−	0.600040i
$370$	205.367	−	24.4242i	0.555046	−	0.0660114i
$371$	−13.9976	+	43.0801i	−0.0377293	+	0.116119i
$372$	199.069	−	1042.11i	0.535130	−	2.80136i
$373$	52.1408	+	52.1408i	0.139788	+	0.139788i	0.773538	−	0.633750i	$-0.218485\pi$
$373$	52.1408	+	52.1408i	0.139788	+	0.139788i	−0.633750	+	0.773538i	$0.718485\pi$
$374$	−296.714	+	374.772i	−0.793352	+	1.00206i
$375$	495.776	−	432.019i	1.32207	−	1.15205i
$376$	226.591	+	502.356i	0.602635	+	1.33605i
$377$	144.024	−	73.3837i	0.382026	−	0.194652i
$378$	−64.3287	−	48.3122i	−0.170182	−	0.127810i
$379$	−29.5446	+	21.4654i	−0.0779541	+	0.0566370i	−0.626080	−	0.779759i	$-0.715342\pi$
$379$	−29.5446	+	21.4654i	−0.0779541	+	0.0566370i	0.548126	+	0.836396i	$0.315342\pi$
$380$	−84.3642	−	317.622i	−0.222011	−	0.835848i
$381$	−466.852	+	151.689i	−1.22533	+	0.398135i
$382$	57.0778	−	17.5514i	0.149418	−	0.0459461i
$383$	25.2604	+	159.488i	0.0659542	+	0.416418i	0.998470	+	0.0552900i	$0.0176083\pi$
$383$	25.2604	+	159.488i	0.0659542	+	0.416418i	−0.932516	+	0.361128i	$0.882392\pi$
$384$	−630.121	+	237.459i	−1.64094	+	0.618382i
$385$	−40.6383	−	15.4146i	−0.105554	−	0.0400379i
$386$	473.809	+	82.7554i	1.22749	+	0.214392i
$387$	7.73421	+	48.8319i	0.0199850	+	0.126181i
$388$	37.2206	+	295.239i	0.0959294	+	0.760925i
$389$	462.733	−	150.351i	1.18955	−	0.386507i	0.353641	−	0.935381i	$-0.384943\pi$
$389$	462.733	−	150.351i	1.18955	−	0.386507i	0.835905	+	0.548874i	$0.184943\pi$
$390$	337.064	−	915.239i	0.864266	−	2.34677i
$391$	60.0454	−	43.6255i	0.153569	−	0.111574i
$392$	−212.350	−	323.542i	−0.541709	−	0.825363i
$393$	512.098	−	260.927i	1.30305	−	0.663937i
$394$	197.397	−	191.242i	0.501006	−	0.485385i
$395$	−22.6851	−	0.518907i	−0.0574307	−	0.00131369i
$396$	−752.296	+	330.601i	−1.89974	+	0.834851i
$397$	−213.142	−	213.142i	−0.536882	−	0.536882i	0.385730	−	0.922612i	$-0.373950\pi$
$397$	−213.142	−	213.142i	−0.536882	−	0.536882i	−0.922612	+	0.385730i	$0.873950\pi$
$398$	222.850	+	3.52931i	0.559924	+	0.00886762i
$399$	−21.1095	+	64.9685i	−0.0529061	+	0.162828i
$400$	−164.288	+	364.705i	−0.410720	+	0.911762i
$401$	−471.582	+	342.624i	−1.17602	+	0.854425i	−0.991717	−	0.128445i	$-0.959001\pi$
$401$	−471.582	+	342.624i	−1.17602	+	0.854425i	−0.184299	+	0.982870i	$0.559001\pi$
$402$	73.4831	−	214.537i	0.182794	−	0.533674i
$403$	−832.854	−	424.360i	−2.06663	−	1.05300i
$404$	−181.856	+	234.324i	−0.450139	+	0.580009i
$405$	−302.164	+	396.498i	−0.746083	+	0.979006i
$406$	13.5743	+	2.37088i	0.0334342	+	0.00583961i
$407$	−187.400	+	128.980i	−0.460442	+	0.316903i
$408$	−240.957	−	882.119i	−0.590580	−	2.16206i
$409$	−198.527	−	144.238i	−0.485395	−	0.352660i	0.318015	−	0.948086i	$-0.396984\pi$
$409$	−198.527	−	144.238i	−0.485395	−	0.352660i	−0.803411	+	0.595425i	$0.796984\pi$
$410$	54.8594	+	194.098i	0.133803	+	0.473409i
$411$	1058.99	−	344.086i	2.57661	−	0.837192i
$412$	−353.494	+	642.614i	−0.857995	+	1.55974i
$413$	8.66778	+	1.37284i	0.0209874	+	0.00332407i
$414$	126.319	−	17.9614i	0.305119	−	0.0433851i
$415$	−731.702	+	351.981i	−1.76314	+	0.848148i
$416$	46.1693	+	591.472i	0.110984	+	1.42181i
$417$	336.767	−	336.767i	0.807595	−	0.807595i
$418$	244.832	+	265.967i	0.585724	+	0.636285i
$419$	649.531			1.55019			0.775097	−	0.631842i	$-0.217701\pi$
$419$	649.531			1.55019			0.775097	+	0.631842i	$0.217701\pi$
$420$	69.8309	−	45.1324i	0.166264	−	0.107458i
$421$	−130.256	+	400.888i	−0.309398	+	0.952228i	0.668602	+	0.743621i	$0.266893\pi$
$421$	−130.256	+	400.888i	−0.309398	+	0.952228i	−0.977999	+	0.208608i	$0.933107\pi$
$422$	402.783	+	302.499i	0.954462	+	0.716822i
$423$	−1270.67	−	201.255i	−3.00396	−	0.475780i
$424$	−455.812	+	50.1451i	−1.07503	+	0.118267i
$425$	−472.206	−	268.477i	−1.11107	−	0.631710i
$426$	−791.891	−	419.414i	−1.85890	−	0.984541i
$427$	−30.2421	+	4.78988i	−0.0708247	+	0.0112175i
$428$	434.593	−	204.368i	1.01540	−	0.477496i
$429$	140.743	+	1063.59i	0.328073	+	2.47924i
$430$	−25.9674	−	5.15001i	−0.0603892	−	0.0119768i
$431$	−348.025	−	252.855i	−0.807482	−	0.586670i	0.105618	−	0.994407i	$-0.466318\pi$
$431$	−348.025	−	252.855i	−0.807482	−	0.586670i	−0.913099	+	0.407737i	$0.866318\pi$
$432$	178.069	−	794.727i	0.412198	−	1.83965i
$433$	−64.6673	−	32.9496i	−0.149347	−	0.0760961i	0.377720	−	0.925920i	$-0.376708\pi$
$433$	−64.6673	−	32.9496i	−0.149347	−	0.0760961i	−0.527067	+	0.849824i	$0.676708\pi$
$434$	−35.0474	−	71.5639i	−0.0807545	−	0.164894i
$435$	41.0464	−	225.631i	0.0943595	−	0.518693i
$436$	438.885	+	13.9049i	1.00662	+	0.0318919i
$437$	−25.4823	−	50.0119i	−0.0583119	−	0.114444i
$438$	3.24068	−	204.624i	0.00739880	−	0.467179i
$439$			314.540i			0.716492i	0.933627	+	0.358246i	$0.116625\pi$
$439$			314.540i			0.716492i	−0.933627	+	0.358246i	$0.883375\pi$
$440$	−26.9049	−	439.177i	−0.0611475	−	0.998129i
$441$	903.449			2.04864
$442$	−805.550	−	12.7577i	−1.82251	−	0.0288635i
$443$	641.753	−	326.989i	1.44865	−	0.738125i	0.459939	−	0.887950i	$-0.347871\pi$
$443$	641.753	−	326.989i	1.44865	−	0.738125i	0.988712	+	0.149825i	$0.0478711\pi$
$444$	13.7813	−	434.984i	0.0310389	−	0.979693i
$445$	520.179	−	360.050i	1.16894	−	0.809101i
$446$	271.236	−	132.834i	0.608153	−	0.297835i
$447$	−6.12402	+	12.0191i	−0.0137003	+	0.0268883i
$448$	−27.1326	+	42.6817i	−0.0605639	+	0.0952717i
$449$	−18.3218	+	25.2178i	−0.0408057	+	0.0561643i	−0.828932	−	0.559349i	$-0.811051\pi$
$449$	−18.3218	+	25.2178i	−0.0408057	+	0.0561643i	0.788127	+	0.615513i	$0.211051\pi$
$450$	−501.338	−	787.795i	−1.11408	−	1.75065i
$451$	−152.833	−	160.839i	−0.338876	−	0.356627i
$452$	−168.266	−	357.821i	−0.372270	−	0.791639i
$453$	−119.515	−	754.585i	−0.263829	−	1.66575i
$454$	296.293	−	559.427i	0.652628	−	1.23222i
$455$	−21.0378	−	70.1689i	−0.0462370	−	0.154217i
$456$	−687.403	+	75.6231i	−1.50746	+	0.165840i
$457$	51.6064	−	325.830i	0.112924	−	0.712975i	−0.864649	−	0.502377i	$-0.832459\pi$
$457$	51.6064	−	325.830i	0.112924	−	0.712975i	0.977573	−	0.210598i	$-0.0675411\pi$
$458$	−157.026	+	209.083i	−0.342851	+	0.456513i
$459$	1051.85	+	341.768i	2.29162	+	0.744592i
$460$	−14.3500	+	66.7944i	−0.0311956	+	0.145205i
$461$		−	336.365i		−	0.729642i	−0.931078	−	0.364821i	$-0.881130\pi$
$461$		−	336.365i		−	0.729642i	0.931078	−	0.364821i	$-0.118870\pi$
$462$	−44.8557	+	79.7060i	−0.0970903	+	0.172524i
$463$	227.276	+	227.276i	0.490878	+	0.490878i	0.908583	−	0.417705i	$-0.137165\pi$
$463$	227.276	+	227.276i	0.490878	+	0.490878i	−0.417705	+	0.908583i	$0.637165\pi$
$464$	34.6227	+	135.134i	0.0746180	+	0.291236i
$465$	−1195.10	+	574.896i	−2.57011	+	1.23634i
$466$	−1.86401	−	13.1092i	−0.00400002	−	0.0281314i
$467$	−88.5767	+	559.251i	−0.189672	+	1.19754i	0.690659	+	0.723180i	$0.257320\pi$
$467$	−88.5767	+	559.251i	−0.189672	+	1.19754i	−0.880331	+	0.474360i	$0.842680\pi$
$468$	−1213.49	−	667.527i	−2.59293	−	1.42634i
$469$	−5.26328	−	16.1987i	−0.0112223	−	0.0345388i
$470$	336.257	−	601.224i	0.715440	−	1.27920i
$471$	−98.9404	+	136.180i	−0.210065	+	0.289129i
$472$	23.4100	+	85.7017i	0.0495974	+	0.181571i
$473$	27.9158	−	8.28919i	0.0590185	−	0.0175247i
$474$	−8.21546	+	47.0370i	−0.0173322	+	0.0992341i
$475$	−256.402	+	320.951i	−0.539794	+	0.675687i
$476$	−54.2579	−	42.1089i	−0.113987	−	0.0884642i
$477$	485.996	−	953.821i	1.01886	−	1.99963i
$478$	729.056	+	249.716i	1.52522	+	0.522418i
$479$	380.114	+	523.183i	0.793558	+	1.09224i	0.993656	+	0.112463i	$0.0358741\pi$
$479$	380.114	+	523.183i	0.793558	+	1.09224i	−0.200098	+	0.979776i	$0.564126\pi$
$480$	707.151	+	456.549i	1.47323	+	0.951144i
$481$	−364.662	−	118.486i	−0.758133	−	0.246332i
$482$	−7.40890	+	467.816i	−0.0153712	+	0.970574i
$483$	10.0417	−	10.0417i	0.0207902	−	0.0207902i
$484$	251.169	+	413.727i	0.518944	+	0.854808i
$485$	268.968	−	256.939i	0.554574	−	0.529770i
$486$	92.3950	+	95.3686i	0.190113	+	0.196232i
$487$	−334.673	−	656.833i	−0.687213	−	1.34873i	−0.925949	−	0.377648i	$-0.876733\pi$
$487$	−334.673	−	656.833i	−0.687213	−	1.34873i	0.238736	−	0.971085i	$-0.423267\pi$
$488$	−170.081	−	259.141i	−0.348527	−	0.531026i
$489$	189.308	+	260.560i	0.387133	+	0.532843i
$490$	−167.180	+	453.949i	−0.341184	+	0.926427i
$491$	123.991	+	381.604i	0.252527	+	0.777198i	0.994307	+	0.106554i	$0.0339818\pi$
$491$	123.991	+	381.604i	0.252527	+	0.777198i	−0.741780	+	0.670643i	$0.766018\pi$
$492$	421.110	−	53.0891i	0.855914	−	0.107905i
$493$	−187.104	+	29.6344i	−0.379522	+	0.0601103i
$494$	−104.830	+	600.195i	−0.212206	+	1.21497i
$495$	891.586	+	510.045i	1.80118	+	1.03039i
$496$	514.519	−	621.299i	1.03734	−	1.25262i
$497$	−66.4753	+	10.5287i	−0.133753	+	0.0211844i
$498$	502.193	+	1633.15i	1.00842	+	3.27941i
$499$	−79.3671	−	244.267i	−0.159052	−	0.489512i	0.839497	−	0.543365i	$-0.182850\pi$
$499$	−79.3671	−	244.267i	−0.159052	−	0.489512i	−0.998549	+	0.0538524i	$0.982850\pi$
$500$	488.608	−	106.125i	0.977215	−	0.212250i
$501$	324.262	+	446.308i	0.647229	+	0.890835i
$502$	23.7520	−	31.6262i	0.0473146	−	0.0630004i
$503$	−165.908	−	325.614i	−0.329838	−	0.647343i	0.665219	−	0.746648i	$-0.268338\pi$
$503$	−165.908	−	325.614i	−0.329838	−	0.647343i	−0.995057	+	0.0993049i	$0.968338\pi$
$504$	−48.5452	−	107.626i	−0.0963199	−	0.213543i
$505$	370.669	+	8.47881i	0.733999	+	0.0167897i
$506$	−20.2482	−	72.3711i	−0.0400162	−	0.143026i
$507$	−649.951	+	649.951i	−1.28196	+	1.28196i
$508$	−366.606	−	70.0311i	−0.721666	−	0.137857i
$509$	−407.684	−	132.465i	−0.800951	−	0.260245i	−0.120191	−	0.992751i	$-0.538351\pi$
$509$	−407.684	−	132.465i	−0.800951	−	0.260245i	−0.680760	+	0.732506i	$0.738351\pi$
$510$	−707.147	+	898.052i	−1.38656	+	1.76089i
$511$	−9.03469	−	12.4352i	−0.0176804	−	0.0243350i
$512$	−506.809	−	72.7249i	−0.989861	−	0.142041i
$513$	379.722	−	745.247i	0.740199	−	1.45272i
$514$	−349.625	+	660.122i	−0.680204	+	1.28428i
$515$	908.536	−	122.671i	1.76415	−	0.238197i
$516$	−18.8837	+	52.4095i	−0.0365963	+	0.101569i
$517$	−19.3328	+	757.508i	−0.0373942	+	1.46520i
$518$	−18.7917	−	26.7452i	−0.0362774	−	0.0516316i
$519$	−1012.09	+	1393.03i	−1.95008	+	2.68406i
$520$	559.959	−	486.210i	1.07684	−	0.935019i
$521$	24.6239	+	75.7846i	0.0472628	+	0.145460i	0.971903	−	0.235382i	$-0.0756342\pi$
$521$	24.6239	+	75.7846i	0.0472628	+	0.145460i	−0.924640	+	0.380842i	$0.875634\pi$
$522$	−308.084	−	105.525i	−0.590199	−	0.202155i
$523$	−119.392	+	753.810i	−0.228283	+	1.44132i	0.561268	+	0.827634i	$0.310314\pi$
$523$	−119.392	+	753.810i	−0.228283	+	1.44132i	−0.789550	+	0.613686i	$0.789686\pi$
$524$	436.782	+	13.8383i	0.833554	+	0.0264089i
$525$	−97.2740	−	36.6031i	−0.185284	−	0.0697202i
$526$	−646.822	+	626.654i	−1.22970	+	1.19136i
$527$	774.611	+	774.611i	1.46985	+	1.46985i
$528$	−922.243	−	82.1665i	−1.74667	−	0.155618i
$529$		−	517.331i		−	0.977942i
$530$	389.327	+	420.696i	0.734580	+	0.793766i
$531$	−197.247	−	64.0894i	−0.371463	−	0.120696i
$532$	−37.8721	+	35.5461i	−0.0711883	+	0.0668160i
$533$	58.4985	−	369.345i	0.109753	−	0.692956i
$534$	−585.517	−	1195.58i	−1.09647	−	2.23891i
$535$	−528.507	−	284.695i	−0.987864	−	0.532140i
$536$	127.576	−	115.995i	0.238014	−	0.216410i
$537$	45.9270	+	289.972i	0.0855252	+	0.539985i
$538$	318.275	+	452.982i	0.591588	+	0.841974i
$539$	−69.8072	−	527.532i	−0.129512	−	0.978723i
$540$	−930.927	+	412.044i	−1.72394	+	0.763044i
$541$	−460.547	+	633.888i	−0.851288	+	1.17170i	0.132290	+	0.991211i	$0.457767\pi$
$541$	−460.547	+	633.888i	−0.851288	+	1.17170i	−0.983578	+	0.180486i	$0.942233\pi$
$542$	−12.2250	−	39.7560i	−0.0225553	−	0.0733505i
$543$	91.8773	−	180.319i	0.169203	−	0.332080i
$544$	162.744	−	675.972i	0.299161	−	1.24260i
$545$	−312.385	−	451.316i	−0.573183	−	0.828102i
$546$	−152.616	+	21.7005i	−0.279516	+	0.0397445i
$547$	951.671	−	484.901i	1.73980	−	0.886473i	0.771673	−	0.636020i	$-0.219420\pi$
$547$	951.671	−	484.901i	1.73980	−	0.886473i	0.968129	−	0.250453i	$-0.0805797\pi$
$548$	831.595	+	158.856i	1.51751	+	0.289883i
$549$	723.616			1.31806
$550$	−421.263	+	353.606i	−0.765933	+	0.642921i
$551$			143.263i			0.260005i
$552$	134.463	+	50.8683i	0.243592	+	0.0921527i
$553$	1.62815	+	3.19542i	0.00294421	+	0.00577834i
$554$	−150.769	+	21.4380i	−0.272147	+	0.0386967i
$555$	−447.304	+	309.608i	−0.805954	+	0.557853i
$556$	347.769	−	100.940i	0.625484	−	0.181546i
$557$	535.225	+	272.711i	0.960907	+	0.489607i	0.862787	−	0.505568i	$-0.168717\pi$
$557$	535.225	+	272.711i	0.960907	+	0.489607i	0.0981203	+	0.995175i	$0.468717\pi$
$558$	553.502	+	1800.01i	0.991939	+	3.22582i
$559$	39.7069	+	28.8488i	0.0710321	+	0.0516078i
$560$	63.0610	−	4.47637i	0.112609	−	0.00799352i
$561$	228.313	−	1236.45i	0.406975	−	2.20401i
$562$	−166.065	−	236.351i	−0.295489	−	0.420553i
$563$	1018.76	−	161.356i	1.80952	−	0.286600i	0.842016	−	0.539453i	$-0.181369\pi$
$563$	1018.76	−	161.356i	1.80952	−	0.286600i	0.967505	+	0.252853i	$0.0813689\pi$
$564$	−1145.18	−	888.758i	−2.03045	−	1.57581i
$565$	−234.403	+	435.145i	−0.414872	+	0.770167i
$566$	322.279	+	658.066i	0.569397	+	1.16266i
$567$	77.8193	+	12.3254i	0.137247	+	0.0217379i
$568$	−373.856	−	569.618i	−0.658197	−	1.00285i
$569$	18.9365	−	58.2805i	0.0332803	−	0.102426i	−0.933037	−	0.359782i	$-0.882851\pi$
$569$	18.9365	−	58.2805i	0.0332803	−	0.102426i	0.966317	+	0.257356i	$0.0828512\pi$
$570$	587.139	+	634.446i	1.03007	+	1.11306i
$571$	790.541			1.38448			0.692242	−	0.721665i	$-0.256623\pi$
$571$	790.541			1.38448			0.692242	+	0.721665i	$0.256623\pi$
$572$	−296.011	+	760.146i	−0.517502	+	1.32893i
$573$	−111.069	+	111.069i	−0.193837	+	0.193837i
$574$	22.8958	−	22.1819i	0.0398882	−	0.0386445i
$575$	77.7834	−	35.2501i	0.135275	−	0.0613046i
$576$	791.120	−	895.962i	1.37347	−	1.55549i
$577$	342.424	+	54.2347i	0.593457	+	0.0939943i	0.445936	−	0.895065i	$-0.352871\pi$
$577$	342.424	+	54.2347i	0.593457	+	0.0939943i	0.147520	+	0.989059i	$0.452871\pi$
$578$	346.429	+	118.659i	0.599358	+	0.205292i
$579$	−1203.25	+	390.959i	−2.07815	+	0.675231i
$580$	110.032	−	135.274i	0.189710	−	0.233230i
$581$	103.821	+	75.4303i	0.178693	+	0.129828i
$582$	−449.997	−	640.456i	−0.773191	−	1.10044i
$583$	−594.496	−	210.078i	−1.01972	−	0.360340i
$584$	77.1474	−	135.133i	0.132102	−	0.231393i
$585$	231.649	+	1715.65i	0.395980	+	2.93273i
$586$	148.489	−	280.360i	0.253394	−	0.478430i
$587$	−656.105	−	334.302i	−1.11773	−	0.569509i	−0.205278	−	0.978704i	$-0.565810\pi$
$587$	−656.105	−	334.302i	−1.11773	−	0.569509i	−0.912447	+	0.409194i	$0.865810\pi$
$588$	891.929	+	490.639i	1.51689	+	0.834421i
$589$	670.234	−	486.954i	1.13792	−	0.826746i
$590$	68.7023	−	87.2496i	0.116445	−	0.147881i
$591$	−223.402	+	687.561i	−0.378007	+	1.16339i
$592$	168.589	−	284.736i	0.284779	−	0.480973i
$593$	−186.148	−	186.148i	−0.313909	−	0.313909i	0.532513	−	0.846422i	$-0.321248\pi$
$593$	−186.148	−	186.148i	−0.313909	−	0.313909i	−0.846422	+	0.532513i	$0.821248\pi$
$594$	695.118	−	877.987i	1.17023	−	1.47809i
$595$	−1.96327	+	85.8288i	−0.00329962	+	0.144250i
$596$	−8.48445	+	5.76285i	−0.0142356	+	0.00966921i
$597$	−522.357	+	266.154i	−0.874969	+	0.445819i
$598$	76.0625	−	101.279i	0.127195	−	0.169362i
$599$	500.128	−	363.364i	0.834938	−	0.606618i	−0.0860143	−	0.996294i	$-0.527413\pi$
$599$	500.128	−	363.364i	0.834938	−	0.606618i	0.920952	+	0.389676i	$0.127413\pi$
$600$	−67.1149	−	1050.01i	−0.111858	−	1.75002i
$601$	58.1760	−	18.9025i	0.0967987	−	0.0314518i	−0.260217	−	0.965550i	$-0.583794\pi$
$601$	58.1760	−	18.9025i	0.0967987	−	0.0314518i	0.357016	+	0.934098i	$0.383794\pi$
$602$	1.22977	+	3.99925i	0.00204281	+	0.00664328i
$603$	62.9683	+	397.566i	0.104425	+	0.659314i
$604$	196.911	−	546.504i	0.326012	−	0.904807i
$605$	228.929	−	560.015i	0.378395	−	0.925644i
$606$	134.239	−	768.573i	0.221516	−	1.26827i
$607$	30.2481	+	190.979i	0.0498321	+	0.314628i	0.999996	+	0.00287634i	$0.000915568\pi$
$607$	30.2481	+	190.979i	0.0498321	+	0.314628i	−0.950164	+	0.311751i	$0.899084\pi$
$608$	−485.662	−	201.532i	−0.798787	−	0.331467i
$609$	−34.4722	+	11.2007i	−0.0566045	+	0.0183919i
$610$	−133.903	+	363.590i	−0.219512	+	0.596049i
$611$	−1033.23	+	750.686i	−1.69105	+	1.22862i
$612$	1110.80	+	1183.49i	1.81504	+	1.93381i
$613$	−157.985	+	80.4974i	−0.257724	+	0.131317i	−0.578080	−	0.815980i	$-0.696198\pi$
$613$	−157.985	+	80.4974i	−0.257724	+	0.131317i	0.320355	+	0.947297i	$0.396198\pi$
$614$	282.883	+	291.988i	0.460722	+	0.475550i
$615$	−366.481	−	383.639i	−0.595903	−	0.623803i
$616$	−59.0927	+	36.6620i	−0.0959297	+	0.0595162i
$617$	346.005	+	346.005i	0.560787	+	0.560787i	0.929531	−	0.368744i	$-0.120212\pi$
$617$	346.005	+	346.005i	0.560787	+	0.560787i	−0.368744	+	0.929531i	$0.620212\pi$
$618$	30.5491	−	1928.95i	0.0494322	−	3.12127i
$619$	−227.677	+	700.717i	−0.367814	+	1.13201i	0.580386	+	0.814341i	$0.302902\pi$
$619$	−227.677	+	700.717i	−0.367814	+	1.13201i	−0.948200	+	0.317674i	$0.897098\pi$
$620$	−1006.86	−	54.9706i	−1.62396	−	0.0886623i
$621$	−140.670	+	102.202i	−0.226521	+	0.164577i
$622$	218.903	+	74.9785i	0.351934	+	0.120544i
$623$	−89.0890	−	45.3931i	−0.143000	−	0.0728622i
$624$	−835.501	−	1318.03i	−1.33894	−	2.11223i
$625$	−469.961	−	412.021i	−0.751938	−	0.659234i
$626$	184.755	−	1057.80i	0.295136	−	1.68978i
$627$	−896.552	−	316.816i	−1.42991	−	0.505288i
$628$	−115.820	+	54.4645i	−0.184426	+	0.0867269i
$629$	363.540	+	264.127i	0.577965	+	0.419916i
$630$	−72.0403	+	128.808i	−0.114350	+	0.204456i
$631$	−628.775	+	204.301i	−0.996474	+	0.323774i	−0.761456	−	0.648217i	$-0.775515\pi$
$631$	−628.775	+	204.301i	−0.996474	+	0.323774i	−0.235018	+	0.971991i	$0.575515\pi$
$632$	−22.7107	+	28.3254i	−0.0359347	+	0.0448186i
$633$	−1308.68	−	207.275i	−2.06743	−	0.327448i
$634$	−80.7931	−	568.203i	−0.127434	−	0.896219i
$635$	202.245	+	420.429i	0.318496	+	0.662093i
$636$	997.794	−	677.727i	1.56886	−	1.06561i
$637$	634.182	−	634.182i	0.995576	−	0.995576i
$638$	−37.8120	+	188.047i	−0.0592664	+	0.294744i
$639$	1590.58			2.48917
$640$	303.793	+	563.302i	0.474677	+	0.880160i
$641$	61.0175	−	187.793i	0.0951911	−	0.292968i	−0.892112	−	0.451814i	$-0.850777\pi$
$641$	61.0175	−	187.793i	0.0951911	−	0.292968i	0.987303	+	0.158845i	$0.0507772\pi$
$642$	−758.602	+	1010.09i	−1.18162	+	1.57335i
$643$	−779.047	−	123.389i	−1.21158	−	0.191896i	−0.482236	−	0.876041i	$-0.660175\pi$
$643$	−779.047	−	123.389i	−1.21158	−	0.191896i	−0.729346	+	0.684145i	$0.760175\pi$
$644$	10.3697	−	3.00980i	0.0161020	−	0.00467361i
$645$	66.7012	−	19.9982i	0.103413	−	0.0310049i
$646$	334.206	−	631.010i	0.517346	−	0.976795i
$647$	136.397	−	21.6032i	0.210815	−	0.0333898i	−0.0501336	−	0.998743i	$-0.515965\pi$
$647$	136.397	−	21.6032i	0.210815	−	0.0333898i	0.260949	+	0.965353i	$0.415965\pi$
$648$	210.175	+	769.429i	0.324343	+	1.18739i
$649$	−22.1816	+	120.126i	−0.0341781	+	0.185094i
$650$	−904.914	−	201.080i	−1.39218	−	0.309354i
$651$	169.572	+	123.201i	0.260479	+	0.189249i
$652$	30.6300	+	242.961i	0.0469785	+	0.372640i
$653$	535.462	+	272.832i	0.820004	+	0.417813i	0.813072	−	0.582163i	$-0.197794\pi$
$653$	535.462	+	272.832i	0.820004	+	0.417813i	0.00693167	+	0.999976i	$0.497794\pi$
$654$	−1037.30	+	508.004i	−1.58609	+	0.776765i
$655$	−310.889	−	449.154i	−0.474639	−	0.685731i
$656$	299.999	+	118.956i	0.457316	+	0.181335i
$657$	164.914	+	323.662i	0.251010	+	0.492636i
$658$	−108.861	−	1.72406i	−0.165443	−	0.00262015i
$659$			468.411i			0.710790i	0.934716	+	0.355395i	$0.115654\pi$
$659$			468.411i			0.710790i	−0.934716	+	0.355395i	$0.884346\pi$
$660$	603.226	+	987.738i	0.913978	+	1.49657i
$661$	−512.822			−0.775828			−0.387914	−	0.921696i	$-0.626804\pi$
$661$	−512.822			−0.775828			−0.387914	+	0.921696i	$0.626804\pi$
$662$	4.21285	−	266.010i	0.00636382	−	0.401827i
$663$	1888.20	−	962.086i	2.84796	−	1.45111i
$664$	−263.936	+	1272.04i	−0.397495	+	1.91573i
$665$	63.8773	+	11.6204i	0.0960562	+	0.0174743i
$666$	339.757	+	693.755i	0.510146	+	1.04167i
$667$	13.5209	−	26.5362i	0.0202712	−	0.0397844i
$668$	52.4655	+	416.163i	0.0785411	+	0.622998i
$669$	−466.949	+	642.700i	−0.697981	+	0.960688i
$670$	−211.414	−	41.9290i	−0.315543	−	0.0625806i
$671$	−55.9120	−	422.526i	−0.0833263	−	0.629696i
$672$	10.5225	−	132.617i	0.0156585	−	0.197347i
$673$	155.797	+	983.663i	0.231496	+	1.46161i	0.780168	+	0.625571i	$0.215134\pi$
$673$	155.797	+	983.663i	0.231496	+	1.46161i	−0.548671	+	0.836038i	$0.684866\pi$
$674$	83.9808	+	44.4793i	0.124601	+	0.0659930i
$675$	1106.25	+	628.966i	1.63889	+	0.931802i
$676$	−671.185	+	194.811i	−0.992877	+	0.288182i
$677$	−106.068	+	669.689i	−0.156674	+	0.989201i	0.776589	+	0.630007i	$0.216948\pi$
$677$	−106.068	+	669.689i	−0.156674	+	0.989201i	−0.933263	+	0.359193i	$0.883052\pi$
$678$	831.657	+	624.592i	1.22663	+	0.921228i
$679$	−55.9122	−	18.1670i	−0.0823449	−	0.0267555i
$680$	−800.210	+	339.136i	−1.17678	+	0.498729i
$681$			1665.16i			2.44517i
$682$	1008.27	−	462.276i	1.47840	−	0.677825i
$683$	534.510	+	534.510i	0.782591	+	0.782591i	0.980267	−	0.197676i	$-0.0633394\pi$
$683$	534.510	+	534.510i	0.782591	+	0.782591i	−0.197676	+	0.980267i	$0.563339\pi$
$684$	1015.42	−	689.699i	1.48453	−	1.00833i
$685$	−458.764	−	953.683i	−0.669729	−	1.39224i
$686$	152.369	−	21.6654i	0.222112	−	0.0315822i
$687$	107.595	−	679.331i	0.156616	−	0.988837i
$688$	−31.7868	+	27.9949i	−0.0462017	+	0.0406903i
$689$	−328.393	−	1010.69i	−0.476622	−	1.46689i
$690$	−48.8764	−	172.930i	−0.0708354	−	0.250622i
$691$	475.213	−	654.075i	0.687718	−	0.946563i	−0.312276	−	0.949992i	$-0.601091\pi$
$691$	475.213	−	654.075i	0.687718	−	0.946563i	0.999994	+	0.00342825i	$0.00109125\pi$
$692$	−1184.76	+	557.135i	−1.71208	+	0.805108i
$693$	4.14190	−	162.290i	0.00597677	−	0.234185i
$694$	192.778	+	33.6705i	0.277778	+	0.0485166i
$695$	−360.023	−	274.367i	−0.518019	−	0.394773i
$696$	−246.848	−	271.492i	−0.354667	−	0.390074i
$697$	−198.962	+	390.485i	−0.285455	+	0.560237i
$698$	273.426	−	798.278i	0.391727	−	1.14366i
$699$	20.4721	+	28.1775i	0.0292877	+	0.0403111i
$700$	−51.3901	−	60.0329i	−0.0734145	−	0.0857613i
$701$	425.140	+	138.137i	0.606477	+	0.197056i	0.596127	−	0.802890i	$-0.296705\pi$
$701$	425.140	+	138.137i	0.606477	+	0.197056i	0.0103500	+	0.999946i	$0.496705\pi$
$702$	1887.18	+	29.8877i	2.68829	+	0.0425750i
$703$	240.298	−	240.298i	0.341818	−	0.341818i
$704$	−584.288	−	392.713i	−0.829955	−	0.557831i
$705$	−41.4372	+	1811.52i	−0.0587762	+	2.56953i
$706$	287.876	−	278.900i	0.407756	−	0.395042i
$707$	−26.6036	−	52.2124i	−0.0376288	−	0.0738507i
$708$	−159.926	−	170.392i	−0.225885	−	0.240666i
$709$	−126.263	−	173.786i	−0.178086	−	0.245114i	0.710637	−	0.703559i	$-0.248407\pi$
$709$	−126.263	−	173.786i	−0.178086	−	0.245114i	−0.888723	+	0.458445i	$0.848407\pi$
$710$	−294.331	+	799.207i	−0.414551	+	1.12564i
$711$	−26.1906	−	80.6064i	−0.0368363	−	0.113370i
$712$	48.0696	−	1011.07i	0.0675135	−	1.42004i
$713$	−170.103	+	26.9417i	−0.238574	+	0.0377864i
$714$	177.964	+	31.0831i	0.249249	+	0.0435337i
$715$	983.883	−	267.825i	1.37606	−	0.374581i
$716$	−75.6691	+	210.010i	−0.105683	+	0.293311i
$717$	−2002.12	+	317.104i	−2.79235	+	0.442265i
$718$	−626.870	+	192.762i	−0.873077	+	0.268471i
$719$	−218.676	−	673.017i	−0.304140	−	0.936046i	−0.979997	−	0.199013i	$-0.936226\pi$
$719$	−218.676	−	673.017i	−0.304140	−	0.936046i	0.675857	−	0.737033i	$-0.263774\pi$
$720$	−1488.51	−	128.649i	−2.06738	−	0.178679i
$721$	−85.1680	−	117.224i	−0.118125	−	0.162585i
$722$	145.524	+	109.292i	0.201557	+	0.151373i
$723$	−558.723	−	1096.56i	−0.772784	−	1.51667i
$724$	127.290	−	86.4587i	0.175815	−	0.119418i
$725$	−217.739	−	9.96645i	−0.300329	−	0.0137468i
$726$	−1093.19	−	652.482i	−1.50578	−	0.898736i
$727$	−237.357	+	237.357i	−0.326489	+	0.326489i	−0.851250	−	0.524761i	$-0.824155\pi$
$727$	−237.357	+	237.357i	−0.326489	+	0.326489i	0.524761	+	0.851250i	$0.324155\pi$
$728$	−109.625	−	41.4720i	−0.150584	−	0.0569670i
$729$	521.219	+	169.354i	0.714978	+	0.232310i
$730$	−193.144	+	22.9706i	−0.264581	+	0.0314665i
$731$	−33.8094	−	46.5347i	−0.0462509	−	0.0636590i
$732$	714.389	+	392.977i	0.975941	+	0.536853i
$733$	185.121	−	363.320i	0.252552	−	0.495661i	−0.729570	−	0.683906i	$-0.760280\pi$
$733$	185.121	−	363.320i	0.252552	−	0.495661i	0.982122	+	0.188245i	$0.0602798\pi$
$734$	−11.0158	−	5.83438i	−0.0150079	−	0.00794875i
$735$	−170.264	−	1261.02i	−0.231652	−	1.71567i
$736$	70.9377	+	83.1650i	0.0963827	+	0.112996i
$737$	227.277	−	67.4867i	0.308381	−	0.0915694i
$738$	−616.438	+	433.122i	−0.835282	+	0.586886i
$739$	109.430	−	150.617i	0.148078	−	0.203812i	−0.728534	−	0.685009i	$-0.759798\pi$
$739$	109.430	−	150.617i	0.148078	−	0.203812i	0.876612	+	0.481198i	$0.159798\pi$
$740$	−411.456	+	42.3382i	−0.556022	+	0.0572138i
$741$	−495.245	−	1524.21i	−0.668346	−	2.05696i
$742$	29.3560	−	85.7061i	0.0395633	−	0.115507i
$743$	−27.0739	+	170.938i	−0.0364386	+	0.230064i	−0.999186	−	0.0403376i	$-0.987157\pi$
$743$	−27.0739	+	170.938i	−0.0364386	+	0.230064i	0.962747	+	0.270402i	$0.0871566\pi$
$744$	−431.091	+	2077.64i	−0.579423	+	2.79253i
$745$	12.0994	+	4.23960i	0.0162408	+	0.00569074i
$746$	−102.617	−	105.920i	−0.137557	−	0.141984i
$747$	−2144.51	−	2144.51i	−2.87083	−	2.87083i
$748$	605.222	−	740.053i	0.809121	−	0.989376i
$749$			94.8784i			0.126673i
$750$	−1005.11	+	848.228i	−1.34015	+	1.13097i
$751$	−50.5888	−	16.4373i	−0.0673619	−	0.0218872i	0.275142	−	0.961404i	$-0.411275\pi$
$751$	−50.5888	−	16.4373i	−0.0673619	−	0.0218872i	−0.342504	+	0.939516i	$0.611275\pi$
$752$	−437.215	−	1011.76i	−0.581402	−	1.34543i
$753$	−16.2750	+	102.757i	−0.0216136	+	0.136463i
$754$	−290.335	+	142.188i	−0.385060	+	0.188578i
$755$	−695.532	+	208.532i	−0.921235	+	0.276202i
$756$	127.111	+	98.6496i	0.168136	+	0.130489i
$757$	38.4006	+	242.452i	0.0507274	+	0.320280i	0.999983	+	0.00577539i	$0.00183837\pi$
$757$	38.4006	+	242.452i	0.0507274	+	0.320280i	−0.949256	+	0.314505i	$0.898162\pi$
$758$	59.7616	−	41.9897i	0.0788412	−	0.0553954i
$759$	136.165	+	143.298i	0.179401	+	0.188798i
$760$	158.648	+	637.837i	0.208747	+	0.839259i
$761$	425.109	−	585.112i	0.558618	−	0.768872i	−0.432532	−	0.901619i	$-0.642380\pi$
$761$	425.109	−	585.112i	0.558618	−	0.768872i	0.991150	+	0.132747i	$0.0423796\pi$
$762$	938.390	−	288.555i	1.23148	−	0.378681i
$763$	−39.3838	+	77.2950i	−0.0516170	+	0.101304i
$764$	−114.697	+	33.2908i	−0.150127	+	0.0435743i
$765$	363.135	−	1996.15i	0.474686	−	2.60934i
$766$	−45.4635	−	319.736i	−0.0593518	−	0.417410i
$767$	−183.447	+	93.4707i	−0.239174	+	0.121865i
$768$	1267.61	−	454.901i	1.65053	−	0.592319i
$769$	−356.119			−0.463093			−0.231547	−	0.972824i	$-0.574379\pi$
$769$	−356.119			−0.463093			−0.231547	+

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.99975 - 0.0316704i) q^{2} +(4.68739 - 2.38834i) q^{3} +(3.99799 + 0.126666i) q^{4} +(-2.84565 - 4.11124i) q^{5} +(-9.44924 + 4.62763i) q^{6} +(-0.358764 + 0.704115i) q^{7} +(-7.99097 - 0.379918i) q^{8} +(10.9773 - 15.1090i) q^{9} +(5.56039 + 8.31156i) q^{10} +(-9.67047 - 5.24233i) q^{11} +(19.0427 - 8.95485i) q^{12} +(-2.90025 - 18.3115i) q^{13} +(0.739738 - 1.39669i) q^{14} +(-23.1577 - 12.4746i) q^{15} +(15.9679 + 1.01282i) q^{16} +(-3.39896 + 21.4602i) q^{17} +(-22.4304 + 29.8666i) q^{18} +(15.6275 + 5.07770i) q^{19} +(-10.8562 - 16.7971i) q^{20} +4.15731i q^{21} +(19.1725 + 10.7896i) q^{22} +(-2.41542 - 2.41542i) q^{23} +(-38.3641 + 17.3044i) q^{24} +(-8.80451 + 23.3983i) q^{25} +(5.21984 + 36.7102i) q^{26} +(7.96283 - 50.2753i) q^{27} +(-1.52353 + 2.76960i) q^{28} +(2.69421 + 8.29194i) q^{29} +(45.9145 + 25.6794i) q^{30} +(29.6349 - 40.7889i) q^{31} +(-31.8997 - 2.53109i) q^{32} +(-57.8497 - 1.47642i) q^{33} +(7.47673 - 42.8074i) q^{34} +(3.91570 - 0.528702i) q^{35} +(45.8011 - 59.0153i) q^{36} +(9.38918 - 18.4273i) q^{37} +(-31.0903 - 10.6490i) q^{38} +(-57.3287 - 78.9061i) q^{39} +(21.1776 + 33.9339i) q^{40} +(19.1830 + 6.23292i) q^{41} +(0.131664 - 8.31358i) q^{42} +(-1.87193 + 1.87193i) q^{43} +(-37.9985 - 22.1837i) q^{44} +(-93.3544 - 2.13542i) q^{45} +(4.75374 + 4.90673i) q^{46} +(-31.2740 - 61.3786i) q^{47} +(77.2667 - 33.3894i) q^{48} +(28.4344 + 39.1366i) q^{49} +(18.3479 - 46.5119i) q^{50} +(35.3221 + 108.710i) q^{51} +(-9.27575 - 73.5765i) q^{52} +(56.6145 - 8.96686i) q^{53} +(-17.5159 + 100.286i) q^{54} +(5.96636 + 54.6754i) q^{55} +(3.13438 - 5.49026i) q^{56} +(85.3796 - 13.5228i) q^{57} +(-5.12514 - 16.6671i) q^{58} +(-3.43169 - 10.5617i) q^{59} +(-91.0043 - 52.8065i) q^{60} +(22.7745 + 31.3464i) q^{61} +(-60.5541 + 80.6291i) q^{62} +(6.70020 + 13.1499i) q^{63} +(63.7113 + 6.07183i) q^{64} +(-67.0296 + 64.0317i) q^{65} +(115.638 + 4.78459i) q^{66} +(-15.2404 + 15.2404i) q^{67} +(-16.3073 + 85.3672i) q^{68} +(-17.0909 - 5.55316i) q^{69} +(-7.84716 + 0.933259i) q^{70} +(50.0607 + 68.9026i) q^{71} +(-93.4598 + 116.565i) q^{72} +(-8.83037 + 17.3306i) q^{73} +(-19.3596 + 36.5526i) q^{74} +(14.6130 + 130.705i) q^{75} +(61.8356 + 22.2801i) q^{76} +(7.16062 - 4.92836i) q^{77} +(112.144 + 159.608i) q^{78} +(2.66749 - 3.67149i) q^{79} +(-41.2752 - 68.5300i) q^{80} +(-30.8097 - 94.8224i) q^{81} +(-38.1637 - 13.0718i) q^{82} +(25.4037 - 160.393i) q^{83} +(-0.526589 + 16.6209i) q^{84} +(97.9002 - 47.0944i) q^{85} +(3.80268 - 3.68411i) q^{86} +(32.4328 + 32.4328i) q^{87} +(75.2848 + 45.5653i) q^{88} +126.526i q^{89} +(186.618 + 7.22687i) q^{90} +(13.9339 + 4.52739i) q^{91} +(-9.35089 - 9.96279i) q^{92} +(41.4922 - 261.972i) q^{93} +(60.5962 + 123.732i) q^{94} +(-23.5950 - 78.6979i) q^{95} +(-155.572 + 64.3233i) q^{96} +(11.6378 + 73.4780i) q^{97} +(-55.6222 - 79.1639i) q^{98} +(-185.362 + 88.5644i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) \) 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Introduction

L-functions

Modular forms

Varieties

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