LMFDB - Embedded newform 220.3.w.a.7.8

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			7.8
Character	$\chi$	$=$	220.7
Dual form			220.3.w.a.63.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.89209 + 0.648077i) q^{2} +(-4.68739 + 2.38834i) q^{3} +(3.15999 - 2.45244i) q^{4} +(-2.84565 - 4.11124i) q^{5} +(7.32112 - 7.55674i) q^{6} +(0.358764 - 0.704115i) q^{7} +(-4.38962 + 6.68814i) q^{8} +(10.9773 - 15.1090i) q^{9} +(8.04862 + 5.93462i) q^{10} +(9.67047 + 5.24233i) q^{11} +(-8.95485 + 19.0427i) q^{12} +(-2.90025 - 18.3115i) q^{13} +(-0.222493 + 1.56475i) q^{14} +(23.1577 + 12.4746i) q^{15} +(3.97111 - 15.4994i) q^{16} +(-3.39896 + 21.4602i) q^{17} +(-10.9783 + 35.7017i) q^{18} +(-15.6275 - 5.07770i) q^{19} +(-19.0748 - 6.01269i) q^{20} +4.15731i q^{21} +(-21.6948 - 3.65174i) q^{22} +(2.41542 + 2.41542i) q^{23} +(4.60225 - 41.8338i) q^{24} +(-8.80451 + 23.3983i) q^{25} +(17.3548 + 32.7673i) q^{26} +(-7.96283 + 50.2753i) q^{27} +(-0.593104 - 3.10484i) q^{28} +(2.69421 + 8.29194i) q^{29} +(-51.9009 - 8.59497i) q^{30} +(-29.6349 + 40.7889i) q^{31} +(2.53109 + 31.8997i) q^{32} +(-57.8497 - 1.47642i) q^{33} +(-7.47673 - 42.8074i) q^{34} +(-3.91570 + 0.528702i) q^{35} +(-2.36558 - 74.6656i) q^{36} +(9.38918 - 18.4273i) q^{37} +(32.8594 - 0.520401i) q^{38} +(57.3287 + 78.9061i) q^{39} +(39.9879 - 0.985391i) q^{40} +(19.1830 + 6.23292i) q^{41} +(-2.69426 - 7.86599i) q^{42} +(1.87193 - 1.87193i) q^{43} +(43.4151 - 7.15050i) q^{44} +(-93.3544 - 2.13542i) q^{45} +(-6.13557 - 3.00481i) q^{46} +(31.2740 + 61.3786i) q^{47} +(18.4037 + 82.1359i) q^{48} +(28.4344 + 39.1366i) q^{49} +(1.49502 - 49.9776i) q^{50} +(-35.3221 - 108.710i) q^{51} +(-54.0725 - 50.7514i) 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} +(-10.4715 - 13.9430i) q^{58} +(3.43169 + 10.5617i) q^{59} +(103.771 - 17.3733i) q^{60} +(22.7745 + 31.3464i) q^{61} +(29.6374 - 96.3819i) q^{62} +(-6.70020 - 13.1499i) q^{63} +(-25.4625 - 58.7168i) q^{64} +(-67.0296 + 64.0317i) q^{65} +(110.414 - 34.6975i) q^{66} +(15.2404 - 15.2404i) q^{67} +(41.8891 + 76.1498i) q^{68} +(-17.0909 - 5.55316i) q^{69} +(7.06621 - 3.53802i) q^{70} +(-50.0607 - 68.9026i) q^{71} +(52.8649 + 139.741i) q^{72} +(-8.83037 + 17.3306i) q^{73} +(-5.82285 + 40.9510i) q^{74} +(-14.6130 - 130.705i) q^{75} +(-61.8356 + 22.2801i) q^{76} +(7.16062 - 4.92836i) q^{77} +(-159.608 - 112.144i) q^{78} +(-2.66749 + 3.67149i) q^{79} +(-75.0219 + 27.7797i) q^{80} +(-30.8097 - 94.8224i) q^{81} +(-40.3353 + 0.638797i) q^{82} +(-25.4037 + 160.393i) q^{83} +(10.1955 + 13.1371i) q^{84} +(97.9002 - 47.0944i) q^{85} +(-2.32871 + 4.75502i) q^{86} +(-32.4328 - 32.4328i) q^{87} +(-77.5111 + 41.6657i) q^{88} +126.526i q^{89} +(178.019 - 56.4604i) q^{90} +(-13.9339 - 4.52739i) q^{91} +(13.5564 + 1.70905i) q^{92} +(41.4922 - 261.972i) q^{93} +(-98.9511 - 95.8658i) q^{94} +(23.5950 + 78.6979i) q^{95} +(-88.0517 - 143.481i) q^{96} +(11.6378 + 73.4780i) q^{97} +(-79.1639 - 55.6222i) 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 $

$2$	−1.89209	+	0.648077i	−0.946044	+	0.324038i
$2$	−1.89209	+	0.648077i	−0.946044	+	0.324038i
$3$	−4.68739	+	2.38834i	−1.56246	+	0.796114i	−0.999538	−	0.0303947i	$-0.990324\pi$
$3$	−4.68739	+	2.38834i	−1.56246	+	0.796114i	−0.562924	+	0.826509i	$0.690324\pi$
$4$	3.15999	−	2.45244i	0.789998	−	0.613109i
$5$	−2.84565	−	4.11124i	−0.569131	−	0.822247i
$5$	−2.84565	−	4.11124i	−0.569131	−	0.822247i
$6$	7.32112	−	7.55674i	1.22019	−	1.25946i
$7$	0.358764	−	0.704115i	0.0512521	−	0.100588i	−0.863960	−	0.503561i	$-0.832023\pi$
$7$	0.358764	−	0.704115i	0.0512521	−	0.100588i	0.915212	+	0.402973i	$0.132023\pi$
$8$	−4.38962	+	6.68814i	−0.548702	+	0.836018i
$9$	10.9773	−	15.1090i	1.21970	−	1.67878i
$10$	8.04862	+	5.93462i	0.804862	+	0.593462i
$11$	9.67047	+	5.24233i	0.879134	+	0.476575i
$11$	9.67047	+	5.24233i	0.879134	+	0.476575i
$12$	−8.95485	+	19.0427i	−0.746237	+	1.58689i
$13$	−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	$-0.302694\pi$
$14$	−0.222493	+	1.56475i	−0.0158924	+	0.111768i
$15$	23.1577	+	12.4746i	1.54385	+	0.831637i
$16$	3.97111	−	15.4994i	0.248194	−	0.968710i
$17$	−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	$0.829328\pi$
$18$	−10.9783	+	35.7017i	−0.609905	+	1.98343i
$19$	−15.6275	−	5.07770i	−0.822502	−	0.267247i	−0.132618	−	0.991167i	$-0.542338\pi$
$19$	−15.6275	−	5.07770i	−0.822502	−	0.267247i	−0.689884	+	0.723920i	$0.742338\pi$
$20$	−19.0748	−	6.01269i	−0.953739	−	0.300634i
$21$			4.15731i			0.197967i
$22$	−21.6948	−	3.65174i	−0.986128	−	0.165988i
$23$	2.41542	+	2.41542i	0.105018	+	0.105018i	0.757664	−	0.652645i	$-0.226341\pi$
$23$	2.41542	+	2.41542i	0.105018	+	0.105018i	−0.652645	+	0.757664i	$0.726341\pi$
$24$	4.60225	−	41.8338i	0.191760	−	1.74308i
$25$	−8.80451	+	23.3983i	−0.352181	+	0.935932i
$26$	17.3548	+	32.7673i	0.667491	+	1.26028i
$27$	−7.96283	+	50.2753i	−0.294920	+	1.86205i
$28$	−0.593104	−	3.10484i	−0.0211823	−	0.110887i
$29$	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	$0.851969\pi$
$30$	−51.9009	−	8.59497i	−1.73003	−	0.286499i
$31$	−29.6349	+	40.7889i	−0.955964	+	1.31577i	−0.00713718	+	0.999975i	$0.502272\pi$
$31$	−29.6349	+	40.7889i	−0.955964	+	1.31577i	−0.948827	+	0.315797i	$0.897728\pi$
$32$	2.53109	+	31.8997i	0.0790966	+	0.996867i
$33$	−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
$36$	−2.36558	−	74.6656i	−0.0657105	−	2.07404i
$37$	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	$0.0598383\pi$
$38$	32.8594	−	0.520401i	0.864721	−	0.0136948i
$39$	57.3287	+	78.9061i	1.46997	+	2.02323i
$40$	39.9879	−	0.985391i	0.999697	−	0.0246348i
$41$	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	$0.520891\pi$
$42$	−2.69426	−	7.86599i	−0.0641489	−	0.187286i
$43$	1.87193	−	1.87193i	0.0435333	−	0.0435333i	−0.685005	−	0.728538i	$-0.740200\pi$
$43$	1.87193	−	1.87193i	0.0435333	−	0.0435333i	0.728538	+	0.685005i	$0.240200\pi$
$44$	43.4151	−	7.15050i	0.986707	−	0.162511i
$45$	−93.3544	−	2.13542i	−2.07454	−	0.0474537i
$46$	−6.13557	−	3.00481i	−0.133382	−	0.0653220i
$47$	31.2740	+	61.3786i	0.665403	+	1.30593i	0.938945	+	0.344068i	$0.111805\pi$
$47$	31.2740	+	61.3786i	0.665403	+	1.30593i	−0.273541	+	0.961860i	$0.588195\pi$
$48$	18.4037	+	82.1359i	0.383410	+	1.71116i
$49$	28.4344	+	39.1366i	0.580294	+	0.798706i
$50$	1.49502	−	49.9776i	0.0299003	−	0.999553i
$51$	−35.3221	−	108.710i	−0.692590	−	2.13157i
$52$	−54.0725	−	50.7514i	−1.03986	−	0.975989i
$53$	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
$58$	−10.4715	−	13.9430i	−0.180543	−	0.240397i
$59$	3.43169	+	10.5617i	0.0581642	+	0.179011i	0.975918	−	0.218140i	$-0.0699989\pi$
$59$	3.43169	+	10.5617i	0.0581642	+	0.179011i	−0.917753	+	0.397151i	$0.869999\pi$
$60$	103.771	−	17.3733i	1.72952	−	0.289555i
$61$	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	$0.697126\pi$
$62$	29.6374	−	96.3819i	0.478023	−	1.55455i
$63$	−6.70020	−	13.1499i	−0.106352	−	0.208728i
$64$	−25.4625	−	58.7168i	−0.397852	−	0.917450i
$65$	−67.0296	+	64.0317i	−1.03123	+	0.985103i
$66$	110.414	−	34.6975i	1.67293	−	0.525720i
$67$	15.2404	−	15.2404i	0.227469	−	0.227469i	−0.584166	−	0.811634i	$-0.698578\pi$
$67$	15.2404	−	15.2404i	0.227469	−	0.227469i	0.811634	+	0.584166i	$0.198578\pi$
$68$	41.8891	+	76.1498i	0.616016	+	1.11985i
$69$	−17.0909	−	5.55316i	−0.247694	−	0.0804806i
$70$	7.06621	−	3.53802i	0.100946	−	0.0505432i
$71$	−50.0607	−	68.9026i	−0.705080	−	0.970459i	−0.999889	−	0.0149028i	$-0.995256\pi$
$71$	−50.0607	−	68.9026i	−0.705080	−	0.970459i	0.294809	−	0.955556i	$-0.404744\pi$
$72$	52.8649	+	139.741i	0.734235	+	1.94084i
$73$	−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	$0.192533\pi$
$74$	−5.82285	+	40.9510i	−0.0786871	+	0.553392i
$75$	−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
$78$	−159.608	−	112.144i	−2.04626	−	1.43774i
$79$	−2.66749	+	3.67149i	−0.0337657	+	0.0464746i	−0.825566	−	0.564305i	$-0.809144\pi$
$79$	−2.66749	+	3.67149i	−0.0337657	+	0.0464746i	0.791800	+	0.610780i	$0.209144\pi$
$80$	−75.0219	+	27.7797i	−0.937774	+	0.347246i
$81$	−30.8097	−	94.8224i	−0.380366	−	1.17065i
$82$	−40.3353	+	0.638797i	−0.491893	+	0.00779021i
$83$	−25.4037	+	160.393i	−0.306069	+	1.93244i	0.0517703	+	0.998659i	$0.483514\pi$
$83$	−25.4037	+	160.393i	−0.306069	+	1.93244i	−0.357839	+	0.933783i	$0.616486\pi$
$84$	10.1955	+	13.1371i	0.121375	+	0.156394i
$85$	97.9002	−	47.0944i	1.15177	−	0.554051i
$86$	−2.32871	+	4.75502i	−0.0270780	+	0.0552909i
$87$	−32.4328	−	32.4328i	−0.372791	−	0.372791i
$88$	−77.5111	+	41.6657i	−0.880808	+	0.473474i
$89$			126.526i			1.42164i	0.703372	+	0.710822i	$0.251677\pi$
$89$			126.526i			1.42164i	−0.703372	+	0.710822i	$0.748323\pi$
$90$	178.019	−	56.4604i	1.97798	−	0.627338i
$91$	−13.9339	−	4.52739i	−0.153120	−	0.0497516i
$92$	13.5564	+	1.70905i	0.147352	+	0.0185766i
$93$	41.4922	−	261.972i	0.446153	−	2.81690i
$94$	−98.9511	−	95.8658i	−1.05267	−	1.01985i
$95$	23.5950	+	78.6979i	0.248368	+	0.828398i
$96$	−88.0517	−	143.481i	−0.917205	−	1.49460i
$97$	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	$0.824728\pi$
$98$	−79.1639	−	55.6222i	−0.807795	−	0.567574i
$99$	185.362	−	88.5644i	1.87235	−	0.894590i
$100$	29.5607	+	95.5310i	0.295607	+	0.955310i
$101$	−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	$0.319648\pi$
$102$	137.285	+	182.798i	1.34593	+	1.79213i
$103$	83.2419	−	163.371i	0.808174	−	1.58613i	−0.00204194	−	0.999998i	$-0.500650\pi$
$103$	83.2419	−	163.371i	0.808174	−	1.58613i	0.810216	−	0.586132i	$-0.199350\pi$
$104$	135.201	+	60.9830i	1.30001	+	0.586375i
$105$	17.0917	−	11.8303i	0.162778	−	0.112669i
$106$	−101.308	+	53.6566i	−0.955740	+	0.506195i
$107$	−106.976	+	54.5069i	−0.999774	+	0.509410i	−0.875696	−	0.482862i	$-0.839597\pi$
$107$	−106.976	+	54.5069i	−0.999774	+	0.509410i	−0.124078	+	0.992272i	$0.539597\pi$
$108$	98.1346	+	178.398i	0.908653	+	1.65183i
$109$	109.776			1.00712			0.503561	−	0.863960i	$-0.332023\pi$
$109$	109.776			1.00712			0.503561	+	0.863960i	$0.332023\pi$
$110$	46.7228	+	99.5841i	0.424752	+	0.905310i
$111$			108.800i			0.980184i
$112$	−9.48864	−	8.35674i	−0.0847200	−	0.0746137i
$113$	−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	$0.994101\pi$
$114$	−152.782	+	80.9188i	−1.34019	+	0.709814i
$115$	3.05691	−	16.8038i	0.0265819	−	0.146120i
$116$	28.8492	+	19.5951i	0.248700	+	0.168923i
$117$	−308.505	−	157.191i	−2.63680	−	1.34351i
$118$	−13.3378	−	17.7596i	−0.113032	−	0.150505i
$119$	13.8910	+	10.0924i	0.116731	+	0.0848102i
$120$	−185.085	+	100.124i	−1.54238	+	0.834363i
$121$	66.0360	+	101.392i	0.545752	+	0.837947i
$122$	−63.4062	−	44.5505i	−0.519723	−	0.365168i
$123$	−104.804	+	16.5994i	−0.852067	+	0.134954i
$124$	6.38622	+	201.570i	0.0515018	+	1.62557i
$125$	121.251	−	30.3860i	0.970004	−	0.243088i
$126$	21.1995	+	20.5385i	0.168250	+	0.163004i
$127$	92.1600	+	14.5967i	0.725670	+	0.114935i	0.508331	−	0.861162i	$-0.330263\pi$
$127$	92.1600	+	14.5967i	0.725670	+	0.114935i	0.217338	+	0.976096i	$0.430263\pi$
$128$	86.2303	+	94.5956i	0.673674	+	0.739028i
$129$	−4.30366	+	13.2453i	−0.0333617	+	0.102677i
$130$	85.3285	−	164.594i	0.656373	−	1.26611i
$131$	−109.250			−0.833972			−0.416986	−	0.908913i	$-0.636914\pi$
$131$	−109.250			−0.833972			−0.416986	+	0.908913i	$0.636914\pi$
$132$	−186.425	+	137.207i	−1.41231	+	1.03945i
$133$	−9.18188	+	9.18188i	−0.0690367	+	0.0690367i
$134$	−18.9592	+	38.7131i	−0.141487	+	0.288904i
$135$	229.353	−	110.329i	1.69891	−	0.817252i
$136$	−128.609	−	116.935i	−0.945653	−	0.859815i
$137$	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	$0.269019\pi$
$138$	35.9363	−	0.569130i	0.260408	−	0.00412413i
$139$	−86.0996	+	27.9755i	−0.619422	+	0.201262i	−0.601883	−	0.798584i	$-0.705583\pi$
$139$	−86.0996	+	27.9755i	−0.619422	+	0.201262i	−0.0175381	+	0.999846i	$0.505583\pi$
$140$	−11.0770	+	11.2737i	−0.0791213	+	0.0805264i
$141$	−293.186	−	213.012i	−2.07933	−	1.51073i
$142$	139.373	+	97.9266i	0.981502	+	0.689624i
$143$	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
$146$	5.47629	−	38.5137i	0.0375088	−	0.263793i
$147$	−226.755	−	115.537i	−1.54255	−	0.785968i
$148$	−15.5221	−	81.2565i	−0.104879	−	0.549031i
$149$	−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	$0.302739\pi$
$150$	112.356	+	237.835i	0.749040	+	1.58557i
$151$	−44.8767	+	138.116i	−0.297197	+	0.914677i	0.685278	+	0.728282i	$0.259681\pi$
$151$	−44.8767	+	138.116i	−0.297197	+	0.914677i	−0.982475	+	0.186396i	$0.940319\pi$
$152$	102.559	−	82.2301i	0.674732	−	0.540987i
$153$	286.931	+	286.931i	1.87537	+	1.87537i
$154$	−10.3546	+	13.9655i	−0.0672374	+	0.0906852i
$155$	252.023	+	5.76486i	1.62596	+	0.0371927i
$156$	374.670	+	108.748i	2.40173	+	0.697102i
$157$	−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	$0.382492\pi$
$158$	2.66773	−	8.67552i	0.0168843	−	0.0549084i
$159$	−243.958	+	177.246i	−1.53433	+	1.11475i
$160$	123.945	−	101.182i	0.774655	−	0.632385i
$161$	2.56730	−	0.834167i	0.0159460	−	0.00518116i
$162$	119.747	+	159.445i	0.739178	+	0.984230i
$163$	−9.57708	−	60.4673i	−0.0587551	−	0.370965i	−0.999493	−	0.0318313i	$-0.989866\pi$
$163$	−9.57708	−	60.4673i	−0.0587551	−	0.370965i	0.940738	−	0.339134i	$-0.110134\pi$
$164$	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	$-0.948343\pi$
$167$	−16.4044	−	103.573i	−0.0982299	−	0.620199i	0.888631	−	0.458624i	$-0.151657\pi$
$168$	−27.8047	−	18.2490i	−0.165504	−	0.108625i
$169$	−166.170	+	53.9919i	−0.983254	+	0.319479i
$170$	−154.715	+	152.554i	−0.910089	+	0.897374i
$171$	−248.268	+	180.377i	−1.45186	+	1.05484i
$172$	1.32450	−	10.5061i	0.00770057	−	0.0610819i
$173$	−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	$0.955117\pi$
$174$	82.3847	+	40.3468i	0.473475	+	0.231878i
$175$	13.3163	+	14.5939i	0.0760934	+	0.0833935i
$176$	119.655	−	129.068i	0.679859	−	0.733343i
$177$	−41.3105	−	41.3105i	−0.233393	−	0.233393i
$178$	−81.9988	−	239.399i	−0.460667	−	1.34494i
$179$	17.2452	−	53.0753i	0.0963420	−	0.296510i	−0.891259	−	0.453494i	$-0.850177\pi$
$179$	17.2452	−	53.0753i	0.0963420	−	0.296510i	0.987601	+	0.156984i	$0.0501772\pi$
$180$	−300.236	+	222.198i	−1.66798	+	1.23443i
$181$	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	$0.266110\pi$
$182$	29.2982	−	0.464002i	0.160979	−	0.00254946i
$183$	−181.619	−	92.5394i	−0.992452	−	0.505680i
$184$	−26.7575	+	5.55191i	−0.145421	+	0.0301734i
$185$	−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
$188$	249.353	+	117.259i	1.32634	+	0.623716i
$189$	32.5428	+	23.6437i	0.172184	+	0.125099i
$190$	−95.6460	−	133.612i	−0.503400	−	0.703221i
$191$	28.3963	−	9.22653i	0.148672	−	0.0483065i	−0.233736	−	0.972300i	$-0.575095\pi$
$191$	28.3963	−	9.22653i	0.148672	−	0.0483065i	0.382408	+	0.923994i	$0.375095\pi$
$192$	259.588	+	214.415i	1.35202	+	1.11674i
$193$	−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	$0.764100\pi$
$194$	−69.6391	−	131.485i	−0.358964	−	0.677756i
$195$	161.264	−	460.231i	0.826996	−	2.36016i
$196$	185.833	+	53.9378i	0.948125	+	0.275193i
$197$	−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	$0.363406\pi$
$198$	−293.325	+	287.701i	−1.48144	+	1.45303i
$199$	111.439			0.559994			0.279997	−	0.960001i	$-0.409667\pi$
$199$	111.439			0.559994			0.279997	+	0.960001i	$0.409667\pi$
$200$	−117.843	−	161.595i	−0.589214	−	0.807977i
$201$	−35.0383	+	107.837i	−0.174320	+	0.536502i
$202$	43.5900	−	141.756i	0.215792	−	0.701762i
$203$	6.80506	+	1.07782i	0.0335225	+	0.00530944i
$204$	−378.222	−	256.898i	−1.85403	−	1.25930i
$205$	−28.9631	−	96.6024i	−0.141283	−	0.471231i
$206$	−51.6237	+	363.060i	−0.250601	+	1.76243i
$207$	63.0095	−	9.97973i	0.304394	−	0.0482112i
$208$	−295.333	−	27.7648i	−1.41987	−	0.133485i
$209$	−124.507	−	131.028i	−0.595726	−	0.626930i
$210$	−24.6720	+	33.4606i	−0.117486	+	0.159336i
$211$	203.761	+	148.041i	0.965694	+	0.701618i	0.954466	−	0.298319i	$-0.0964260\pi$
$211$	203.761	+	148.041i	0.965694	+	0.701618i	0.0112277	+	0.999937i	$0.496426\pi$
$212$	156.911	−	167.179i	0.740145	−	0.788579i
$213$	399.217	+	203.411i	1.87426	+	0.954981i
$214$	167.083	−	172.460i	0.780762	−	0.805890i
$215$	−13.0228	−	2.36909i	−0.0605713	−	0.0110190i
$216$	−301.295	−	273.946i	−1.39488	−	1.26827i
$217$	18.0881	+	35.5000i	0.0833555	+	0.163594i
$218$	−207.706	+	71.1434i	−0.952781	+	0.326346i
$219$		−	102.325i		−	0.467238i
$220$	−152.942	−	158.142i	−0.695190	−	0.718826i
$221$	402.826			1.82274
$222$	−70.5111	−	205.860i	−0.317617	−	0.927297i
$223$	134.549	−	68.5564i	0.603361	−	0.307428i	−0.125496	−	0.992094i	$-0.540052\pi$
$223$	134.549	−	68.5564i	0.603361	−	0.307428i	0.728856	+	0.684667i	$0.240052\pi$
$224$	23.3691	+	9.66231i	0.104327	+	0.0431353i
$225$	256.875	+	389.879i	1.14167	+	1.73279i
$226$	141.995	+	137.567i	0.628295	+	0.608705i
$227$	143.699	−	282.024i	0.633034	−	1.24240i	−0.322235	−	0.946660i	$-0.604434\pi$
$227$	143.699	−	282.024i	0.633034	−	1.24240i	0.955269	−	0.295739i	$-0.0955658\pi$
$228$	236.635	−	252.120i	1.03787	−	1.10579i
$229$	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	$0.107853\pi$
$230$	5.10622	+	33.7754i	0.0222009	+	0.146850i
$231$	−21.7940	+	40.2031i	−0.0943462	+	0.174040i
$232$	−67.2842	−	18.3791i	−0.290018	−	0.0792204i
$233$	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	$0.945478\pi$
$234$	685.591	+	97.4846i	2.92988	+	0.416601i
$235$	163.347	−	303.237i	0.695094	−	1.29037i
$236$	36.7459	+	24.9588i	0.155703	+	0.105757i
$237$	3.73480	−	23.5806i	0.0157586	−	0.0994961i
$238$	−32.8237	−	10.0933i	−0.137915	−	0.0424088i
$239$	366.460	+	119.070i	1.53330	+	0.498201i	0.949519	−	0.313708i	$-0.101571\pi$
$239$	366.460	+	119.070i	1.53330	+	0.498201i	0.583784	+	0.811909i	$0.301571\pi$
$240$	285.309	−	309.392i	1.18879	−	1.28913i
$241$		−	233.938i		−	0.970695i	−0.874321	−	0.485348i	$-0.838693\pi$
$241$		−	233.938i		−	0.970695i	0.874321	−	0.485348i	$-0.161307\pi$
$242$	−190.655	−	149.045i	−0.787832	−	0.615890i
$243$	46.9468	+	46.9468i	0.193197	+	0.193197i
$244$	148.842	+	43.2014i	0.610009	+	0.177055i
$245$	79.9853	−	228.270i	0.326471	−	0.931713i
$246$	187.541	−	99.3287i	0.762363	−	0.403775i
$247$	−47.6563	+	300.890i	−0.192940	+	1.21818i
$248$	−142.716	−	377.250i	−0.575469	−	1.52117i
$249$	−263.996	−	812.495i	−1.06022	−	3.26303i
$250$	−209.724	+	136.073i	−0.838897	+	0.544291i
$251$	11.6241	−	15.9992i	0.0463111	−	0.0637417i	−0.785233	−	0.619200i	$-0.787457\pi$
$251$	11.6241	−	15.9992i	0.0463111	−	0.0637417i	0.831545	+	0.555458i	$0.187457\pi$
$252$	−53.4218	−	25.1217i	−0.211991	−	0.0996893i
$253$	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
$256$	−224.461	−	123.099i	−0.876799	−	0.480857i
$257$	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	$-0.108922\pi$
$258$	−0.441071	−	27.8504i	−0.00170958	−	0.107947i
$259$	−9.60643	−	13.2221i	−0.0370905	−	0.0510507i
$260$	−54.7795	+	366.726i	−0.210690	+	1.41048i
$261$	154.858	+	50.3165i	0.593327	+	0.192784i
$262$	206.711	−	70.8026i	0.788974	−	0.270239i
$263$	−318.409	+	318.409i	−1.21068	+	1.21068i	−0.239878	+	0.970803i	$0.577107\pi$
$263$	−318.409	+	318.409i	−1.21068	+	1.21068i	−0.970803	+	0.239878i	$0.922893\pi$
$264$	263.812	−	380.426i	0.999290	−	1.44101i
$265$	−197.970	−	207.239i	−0.747057	−	0.782034i
$266$	11.4224	−	23.3235i	0.0429412	−	0.0876823i
$267$	−302.188	−	593.078i	−1.13179	−	2.22126i
$268$	10.7834	−	85.5356i	0.0402367	−	0.319163i
$269$	−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	$0.972028\pi$
$270$	−362.455	+	357.391i	−1.34242	+	1.32367i
$271$	−6.42649	−	19.7787i	−0.0237140	−	0.0729841i	0.938499	−	0.345281i	$-0.112217\pi$
$271$	−6.42649	−	19.7787i	−0.0237140	−	0.0729841i	−0.962213	+	0.272297i	$0.912217\pi$
$272$	319.122	+	137.903i	1.17324	+	0.506995i
$273$	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	$0.406112\pi$
$278$	144.778	−	108.731i	0.520783	−	0.391119i
$279$	290.968	+	895.507i	1.04290	+	3.20970i
$280$	13.6524	−	28.5096i	0.0487585	−	0.101820i
$281$	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	$0.717269\pi$
$282$	692.782	+	213.031i	2.45668	+	0.755428i
$283$	166.329	+	326.440i	0.587736	+	1.15350i	0.973025	+	0.230701i	$0.0741020\pi$
$283$	166.329	+	326.440i	0.587736	+	1.15350i	−0.385288	+	0.922796i	$0.625898\pi$
$284$	−327.171	−	94.9611i	−1.15201	−	0.334370i
$285$	−298.556	−	312.534i	−1.04757	−	1.09661i
$286$	−3.94823	+	407.855i	−0.0138050	+	1.42607i
$287$	11.2709	−	11.2709i	0.0392713	−	0.0392713i
$288$	509.758	+	311.932i	1.76999	+	1.08310i
$289$	−174.132	−	56.5790i	−0.602533	−	0.195775i
$290$	−27.5248	+	82.7278i	−0.0949130	+	0.285268i
$291$	−230.041	−	316.625i	−0.790520	−	1.08806i
$292$	14.5982	+	76.4204i	0.0499940	+	0.261714i
$293$	−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	$0.237254\pi$
$294$	503.917	+	71.6522i	1.71400	+	0.243715i
$295$	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
$298$	2.94824	−	4.19606i	0.00989342	−	0.0140807i
$299$	37.2246	−	51.2352i	0.124497	−	0.171355i
$300$	−366.723	−	377.190i	−1.22241	−	1.25730i
$301$	−0.646473	−	1.98964i	−0.00214775	−	0.00661010i
$302$	−4.59931	−	290.412i	−0.0152295	−	0.961628i
$303$	61.0257	−	385.301i	0.201405	−	1.27162i
$304$	−140.760	+	222.053i	−0.463025	+	0.730437i
$305$	64.0641	−	182.832i	0.210046	−	0.599450i
$306$	−728.852	−	356.945i	−2.38187	−	1.16649i
$307$	143.736	+	143.736i	0.468194	+	0.468194i	0.901329	−	0.433135i	$-0.142593\pi$
$307$	143.736	+	143.736i	0.468194	+	0.468194i	−0.433135	+	0.901329i	$0.642593\pi$
$308$	10.5410	−	33.1346i	0.0342241	−	0.107580i
$309$			964.595i			3.12167i
$310$	−480.587	+	152.423i	−1.55028	+	0.491687i
$311$	110.031	+	35.7514i	0.353799	+	0.114956i	0.480524	−	0.876982i	$-0.340447\pi$
$311$	110.031	+	35.7514i	0.353799	+	0.114956i	−0.126725	+	0.991938i	$0.540447\pi$
$312$	−779.386	+	37.0547i	−2.49803	+	0.118765i
$313$	−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	$0.721906\pi$
$314$	44.5279	−	45.9610i	0.141809	−	0.146373i
$315$	−34.9958	+	64.9661i	−0.111098	+	0.206242i
$316$	0.574836	+	18.1437i	0.00181910	+	0.0574169i
$317$	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	$0.800491\pi$
$318$	346.721	−	493.469i	1.09032	−	1.55179i
$319$	−17.4147	+	94.3109i	−0.0545917	+	0.295645i
$320$	−168.941	+	271.770i	−0.527940	+	0.849281i
$321$	371.256	−	510.990i	1.15656	−	1.59187i
$322$	−4.31695	+	3.24212i	−0.0134067	+	0.0100687i
$323$	162.086	−	318.111i	0.501814	−	0.984865i
$324$	−329.904	−	224.079i	−1.01822	−	0.691603i
$325$	453.993	+	93.3626i	1.39690	+	0.287270i
$326$	57.3081	+	108.203i	0.175792	+	0.331910i
$327$	−514.563	+	262.183i	−1.57359	+	0.801783i
$328$	−125.893	+	100.938i	−0.383819	+	0.307739i
$329$	54.4376			0.165464
$330$	−456.848	−	355.199i	−1.38439	−	1.07636i
$331$		−	133.022i		−	0.401878i	−0.979604	−	0.200939i	$-0.935601\pi$
$331$		−	133.022i		−	0.401878i	0.979604	−	0.200939i	$-0.0643992\pi$
$332$	313.077	+	569.141i	0.943004	+	1.71428i
$333$	−175.350	−	344.144i	−0.526577	−	1.03347i
$334$	98.1619	+	185.338i	0.293898	+	0.554905i
$335$	−106.026	−	19.2880i	−0.316495	−	0.0575760i
$336$	64.4356	+	16.5091i	0.191773	+	0.0491343i
$337$	−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	$0.672459\pi$
$338$	279.417	−	209.848i	0.826678	−	0.620853i
$339$	420.722	+	305.672i	1.24107	+	0.901688i
$340$	193.868	−	388.912i	0.570200	−	1.14386i
$341$	−500.412	+	239.092i	−1.46748	+	0.701150i
$342$	352.846	−	502.186i	1.03171	−	1.46838i
$343$	76.0033	−	12.0377i	0.221584	−	0.0350954i
$344$	4.30269	+	20.7368i	0.0125078	+	0.0602815i
$345$	25.8043	+	86.0669i	0.0747952	+	0.249469i
$346$	455.491	−	470.150i	1.31645	−	1.35882i
$347$	96.6434	+	15.3068i	0.278511	+	0.0441119i	0.294127	−	0.955766i	$-0.404971\pi$
$347$	96.6434	+	15.3068i	0.278511	+	0.0441119i	−0.0156162	+	0.999878i	$0.504971\pi$
$348$	−182.027	−	22.9480i	−0.523066	−	0.0659426i
$349$	−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	$0.893395\pi$
$350$	−34.6536	−	18.9829i	−0.0990104	−	0.0542367i
$351$	943.709			2.68863
$352$	−142.752	+	321.754i	−0.405546	+	0.914075i
$353$	−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	$0.341618\pi$
$354$	104.935	+	51.3907i	0.296428	+	0.145172i
$355$	−140.819	+	401.884i	−0.396675	+	1.13207i
$356$	310.298	+	399.822i	0.871623	+	1.12310i
$357$	−89.2167	−	14.1305i	−0.249907	−	0.0395813i
$358$	1.76742	+	111.599i	0.00493693	+	0.311730i
$359$	−311.869	+	101.332i	−0.868717	+	0.282263i	−0.709264	−	0.704943i	$-0.750973\pi$
$359$	−311.869	+	101.332i	−0.868717	+	0.282263i	−0.159452	+	0.987206i	$0.550973\pi$
$360$	424.072	−	614.994i	1.17798	−	1.70832i
$361$	−73.6181	−	53.4867i	−0.203928	−	0.148163i
$362$	−44.2318	+	62.9526i	−0.122187	+	0.173902i
$363$	−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
$366$	403.611	+	57.3897i	1.10276	+	0.156803i
$367$	−5.55342	−	2.82961i	−0.0151319	−	0.00771010i	0.446408	−	0.894829i	$-0.352703\pi$
$367$	−5.55342	−	2.82961i	−0.0151319	−	0.00771010i	−0.461540	+	0.887119i	$0.652703\pi$
$368$	47.0294	−	27.8456i	0.127797	−	0.0756674i
$369$	304.751	−	221.415i	0.825884	−	0.600040i
$370$	184.929	−	92.5932i	0.499808	−	0.250252i
$371$	13.9976	−	43.0801i	0.0377293	−	0.116119i
$372$	−511.354	−	929.585i	−1.37461	−	2.49889i
$373$	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	$0.718485\pi$
$374$	152.107	−	453.163i	0.406703	−	1.21167i
$375$	−495.776	+	432.019i	−1.32207	+	1.15205i
$376$	−547.790	−	60.2638i	−1.45689	−	0.160276i
$377$	144.024	−	73.3837i	0.382026	−	0.194652i
$378$	−76.8968	−	23.6458i	−0.203431	−	0.0625550i
$379$	29.5446	−	21.4654i	0.0779541	−	0.0566370i	−0.548126	−	0.836396i	$-0.684658\pi$
$379$	29.5446	−	21.4654i	0.0779541	−	0.0566370i	0.626080	+	0.779759i	$0.284658\pi$
$380$	267.561	+	190.820i	0.704109	+	0.502157i
$381$	−466.852	+	151.689i	−1.22533	+	0.398135i
$382$	−47.7489	+	35.8604i	−0.124997	+	0.0938755i
$383$	−25.2604	−	159.488i	−0.0659542	−	0.416418i	−0.998470	−	0.0552900i	$-0.982392\pi$
$383$	−25.2604	−	159.488i	−0.0659542	−	0.416418i	0.932516	−	0.361128i	$-0.117608\pi$
$384$	−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
$388$	216.975	+	203.649i	0.559215	+	0.524869i
$389$	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	$0.184943\pi$
$390$	−6.86089	+	975.309i	−0.0175920	+	2.50079i
$391$	−60.0454	+	43.6255i	−0.153569	+	0.111574i
$392$	−386.567	+	18.3787i	−0.986141	+	0.0468845i
$393$	512.098	−	260.927i	1.30305	−	0.663937i
$394$	120.883	−	246.832i	0.306809	−	0.626478i
$395$	22.6851	+	0.518907i	0.0574307	+	0.00131369i
$396$	368.545	−	734.452i	0.930670	−	1.85468i
$397$	−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	$0.873950\pi$
$398$	−210.852	+	72.2209i	−0.529779	+	0.181460i
$399$	21.1095	−	64.9685i	0.0529061	−	0.162828i
$400$	327.695	+	229.382i	0.819238	+	0.573454i
$401$	−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	$0.559001\pi$
$402$	−3.59099	−	226.744i	−0.00893282	−	0.564041i
$403$	832.854	+	424.360i	2.06663	+	1.05300i
$404$	9.39268	+	296.464i	0.0232492	+	0.733823i
$405$	−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
$408$	882.119	+	240.957i	2.16206	+	0.590580i
$409$	−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	$0.796984\pi$
$410$	117.406	+	164.010i	0.286357	+	0.400024i
$411$	−1058.99	+	344.086i	−2.57661	+	0.837192i
$412$	−137.614	−	720.398i	−0.334015	−	1.74854i
$413$	8.66778	+	1.37284i	0.0209874	+	0.00332407i
$414$	−112.752	+	59.7175i	−0.272348	+	0.144245i
$415$	731.702	−	351.981i	1.76314	−	0.848148i
$416$	576.790	−	138.865i	1.38652	−	0.333811i
$417$	336.767	−	336.767i	0.807595	−	0.807595i
$418$	320.494	+	167.227i	0.766732	+	0.400065i
$419$	−649.531			−1.55019			−0.775097	−	0.631842i	$-0.782299\pi$
$419$	−649.531			−1.55019			−0.775097	+	0.631842i	$0.782299\pi$
$420$	24.9966	−	79.2998i	0.0595157	−	0.188809i
$421$	−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	$0.933107\pi$
$422$	−481.477	−	148.054i	−1.14094	−	0.350839i
$423$	1270.67	+	201.255i	3.00396	+	0.475780i
$424$	−188.544	+	418.007i	−0.444680	+	0.985866i
$425$	−472.206	−	268.477i	−1.11107	−	0.631710i
$426$	−887.179	−	126.148i	−2.08258	−	0.296123i
$427$	30.2421	−	4.78988i	0.0708247	−	0.0112175i
$428$	−204.368	+	434.593i	−0.477496	+	1.01540i
$429$	140.743	+	1063.59i	0.328073	+	2.47924i
$430$	26.1757	−	3.95728i	0.0608737	−	0.00920297i
$431$	348.025	+	252.855i	0.807482	+	0.586670i	0.913099	−	0.407737i	$-0.133682\pi$
$431$	348.025	+	252.855i	0.807482	+	0.586670i	−0.105618	+	0.994407i	$0.533682\pi$
$432$	747.614	+	323.068i	1.73059	+	0.747841i
$433$	−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	$0.676708\pi$
$434$	−57.2311	−	55.4466i	−0.131869	−	0.127757i
$435$	−41.0464	+	225.631i	−0.0943595	+	0.518693i
$436$	346.892	−	269.219i	0.795624	−	0.617475i
$437$	−25.4823	−	50.0119i	−0.0583119	−	0.114444i
$438$	66.3145	+	193.608i	0.151403	+	0.442027i
$439$		−	314.540i		−	0.716492i	−0.933627	−	0.358246i	$-0.883375\pi$
$439$		−	314.540i		−	0.716492i	0.933627	−	0.358246i	$-0.116625\pi$
$440$	391.867	+	200.100i	0.890607	+	0.454773i
$441$	903.449			2.04864
$442$	−762.182	+	261.062i	−1.72439	+	0.590638i
$443$	−641.753	+	326.989i	−1.44865	+	0.738125i	−0.988712	−	0.149825i	$-0.952129\pi$
$443$	−641.753	+	326.989i	−1.44865	+	0.738125i	−0.459939	+	0.887950i	$0.652129\pi$
$444$	266.826	+	343.809i	0.600960	+	0.774344i
$445$	520.179	−	360.050i	1.16894	−	0.809101i
$446$	−210.150	+	216.913i	−0.471187	+	0.486352i
$447$	6.12402	−	12.0191i	0.0137003	−	0.0268883i
$448$	−50.4784	−	3.13694i	−0.112675	−	0.00700210i
$449$	−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	$0.211051\pi$
$450$	−738.701	−	571.210i	−1.64156	−	1.26935i
$451$	152.833	+	160.839i	0.338876	+	0.356627i
$452$	−357.821	−	168.266i	−0.791639	−	0.372270i
$453$	−119.515	−	754.585i	−0.263829	−	1.66575i
$454$	−89.1169	+	626.743i	−0.196293	+	1.38049i
$455$	21.0378	+	70.1689i	0.0462370	+	0.154217i
$456$	−284.341	+	630.391i	−0.623555	+	1.38244i
$457$	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	$-0.0675411\pi$
$458$	−76.8543	+	249.933i	−0.167804	+	0.545704i
$459$	−1051.85	−	341.768i	−2.29162	−	0.744592i
$460$	−31.5505	−	60.5968i	−0.0685880	−	0.131732i
$461$		−	336.365i		−	0.729642i	−0.931078	−	0.364821i	$-0.881130\pi$
$461$		−	336.365i		−	0.729642i	0.931078	−	0.364821i	$-0.118870\pi$
$462$	15.1814	−	90.1920i	0.0328602	−	0.195221i
$463$	−227.276	−	227.276i	−0.490878	−	0.490878i	0.417705	−	0.908583i	$-0.362835\pi$
$463$	−227.276	−	227.276i	−0.490878	−	0.490878i	−0.908583	+	0.417705i	$0.862835\pi$
$464$	139.219	−	8.83042i	0.300040	−	0.0190311i
$465$	−1195.10	+	574.896i	−2.57011	+	1.23634i
$466$	−6.19740	−	11.7012i	−0.0132992	−	0.0251100i
$467$	88.5767	−	559.251i	0.189672	−	1.19754i	−0.690659	−	0.723180i	$-0.742680\pi$
$467$	88.5767	−	559.251i	0.189672	−	1.19754i	0.880331	−	0.474360i	$-0.157320\pi$
$468$	−1360.38	+	259.866i	−2.90679	+	0.555270i
$469$	−5.26328	−	16.1987i	−0.0112223	−	0.0345388i
$470$	−112.546	+	679.612i	−0.239460	+	1.44598i
$471$	98.9404	−	136.180i	0.210065	−	0.289129i
$472$	−85.7017	−	23.4100i	−0.181571	−	0.0495974i
$473$	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
$476$	68.6465	−	2.17488i	0.144215	−	0.00456908i
$477$	485.996	−	953.821i	1.01886	−	1.99963i
$478$	−770.540	+	12.2032i	−1.61201	+	0.0255297i
$479$	−380.114	−	523.183i	−0.793558	−	1.09224i	−0.993656	−	0.112463i	$-0.964126\pi$
$479$	−380.114	−	523.183i	−0.793558	−	1.09224i	0.200098	−	0.979776i	$-0.435874\pi$
$480$	−339.321	+	770.299i	−0.706918	+	1.60479i
$481$	−364.662	−	118.486i	−0.758133	−	0.246332i
$482$	151.610	+	442.630i	0.314543	+	0.918320i
$483$	−10.0417	+	10.0417i	−0.0207902	+	0.0207902i
$484$	457.330	+	158.447i	0.944896	+	0.327371i
$485$	268.968	−	256.939i	0.554574	−	0.529770i
$486$	−119.253	−	58.4023i	−0.245376	−	0.120169i
$487$	334.673	+	656.833i	0.687213	+	1.34873i	0.925949	+	0.377648i	$0.123267\pi$
$487$	334.673	+	656.833i	0.687213	+	1.34873i	−0.238736	+	0.971085i	$0.576733\pi$
$488$	−309.621	+	14.7204i	−0.634468	+	0.0301648i
$489$	189.308	+	260.560i	0.387133	+	0.532843i
$490$	−3.40293	+	483.743i	−0.00694475	+	0.987231i
$491$	−123.991	−	381.604i	−0.252527	−	0.777198i	−0.994307	−	0.106554i	$-0.966018\pi$
$491$	−123.991	−	381.604i	−0.252527	−	0.777198i	0.741780	−	0.670643i	$-0.233982\pi$
$492$	−290.472	+	309.480i	−0.590390	+	0.629024i
$493$	−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
$498$	1026.06	+	1366.22i	2.06037	+	2.74342i
$499$	79.3671	+	244.267i	0.159052	+	0.489512i	0.998549	−	0.0538524i	$-0.0171500\pi$
$499$	79.3671	+	244.267i	0.159052	+	0.489512i	−0.839497	+	0.543365i	$0.817150\pi$
$500$	308.631	−	393.379i	0.617262	−	0.786758i
$501$	324.262	+	446.308i	0.647229	+	0.890835i
$502$	−11.6251	+	37.8051i	−0.0231575	+	0.0753091i
$503$	165.908	+	325.614i	0.329838	+	0.647343i	0.995057	−	0.0993049i	$-0.0316619\pi$
$503$	165.908	+	325.614i	0.329838	+	0.647343i	−0.665219	+	0.746648i	$0.731662\pi$
$504$	117.360	+	12.9110i	0.232856	+	0.0256171i
$505$	370.669	+	8.47881i	0.733999	+	0.0167897i
$506$	−43.5816	−	61.2226i	−0.0861297	−	0.120993i
$507$	649.951	−	649.951i	1.28196	−	1.28196i
$508$	327.023	−	179.891i	0.643745	−	0.354116i
$509$	−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	$0.738351\pi$
$510$	360.859	−	1084.59i	0.707567	−	2.12665i
$511$	9.03469	+	12.4352i	0.0176804	+	0.0243350i
$512$	504.477	+	87.4470i	0.985307	+	0.170795i
$513$	379.722	−	745.247i	0.740199	−	1.45272i
$514$	−105.158	+	739.554i	−0.204587	+	1.43882i
$515$	−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
$518$	26.7452	+	18.7917i	0.0516316	+	0.0362774i
$519$	1012.09	−	1393.03i	1.95008	−	2.68406i
$520$	−134.019	−	729.379i	−0.257729	−	1.40265i
$521$	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	$0.875634\pi$
$522$	−325.614	+	5.15682i	−0.623782	+	0.00987896i
$523$	119.392	−	753.810i	0.228283	−	1.44132i	−0.561268	−	0.827634i	$-0.689686\pi$
$523$	119.392	−	753.810i	0.228283	−	1.44132i	0.789550	−	0.613686i	$-0.210314\pi$
$524$	−345.230	+	267.929i	−0.658836	+	0.511316i
$525$	−97.2740	−	36.6031i	−0.185284	−	0.0697202i
$526$	396.104	−	808.811i	0.753050	−	1.53766i
$527$	−774.611	−	774.611i	−1.46985	−	1.46985i
$528$	−252.611	+	890.770i	−0.478430	+	1.68707i
$529$		−	517.331i		−	0.977942i
$530$	508.884	+	263.815i	0.960158	+	0.497763i
$531$	197.247	+	64.0894i	0.371463	+	0.120696i
$532$	−6.49670	+	51.5327i	−0.0122118	+	0.0968659i
$533$	58.4985	−	369.345i	0.109753	−	0.692956i
$534$	956.126	+	926.314i	1.79050	+	1.73467i
$535$	528.507	+	284.695i	0.987864	+	0.532140i
$536$	35.0305	+	168.829i	0.0653553	+	0.314980i
$537$	45.9270	+	289.972i	0.0855252	+	0.539985i
$538$	452.982	+	318.275i	0.841974	+	0.591588i
$539$	69.8072	+	527.532i	0.129512	+	0.978723i
$540$	454.179	−	911.113i	0.841072	−	1.68725i
$541$	−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	$0.942233\pi$
$542$	24.9776	+	33.2582i	0.0460841	+	0.0613620i
$543$	−91.8773	+	180.319i	−0.169203	+	0.332080i
$544$	−693.178	−	54.1083i	−1.27422	−	0.0994637i
$545$	−312.385	−	451.316i	−0.573183	−	0.828102i
$546$	−136.224	+	72.1491i	−0.249494	+	0.132141i
$547$	−951.671	+	484.901i	−1.73980	+	0.886473i	−0.771673	+	0.636020i	$0.780580\pi$
$547$	−951.671	+	484.901i	−1.73980	+	0.886473i	−0.968129	+	0.250453i	$0.919420\pi$
$548$	741.805	−	408.058i	1.35366	−	0.744631i
$549$	723.616			1.31806
$550$	276.457	−	475.470i	0.502649	−	0.864491i
$551$		−	143.263i		−	0.260005i
$552$	112.163	−	89.9299i	0.203193	−	0.162917i
$553$	1.62815	+	3.19542i	0.00294421	+	0.00577834i
$554$	−134.576	+	71.2763i	−0.242917	+	0.128658i
$555$	447.304	−	309.608i	0.805954	−	0.557853i
$556$	−203.466	+	299.556i	−0.365946	+	0.538770i
$557$	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	$0.468717\pi$
$558$	−1130.89	−	1505.81i	−2.02669	−	2.69858i
$559$	−39.7069	−	28.8488i	−0.0710321	−	0.0516078i
$560$	−7.35513	+	62.7904i	−0.0131342	+	0.112126i
$561$	228.313	−	1236.45i	0.406975	−	2.20401i
$562$	−236.351	−	166.065i	−0.420553	−	0.295489i
$563$	−1018.76	+	161.356i	−1.80952	+	0.286600i	−0.967505	−	0.252853i	$-0.918631\pi$
$563$	−1018.76	+	161.356i	−1.80952	+	0.286600i	−0.842016	+	0.539453i	$0.818631\pi$
$564$	−1448.87	+	45.9034i	−2.56891	+	0.0813891i
$565$	−234.403	+	435.145i	−0.414872	+	0.770167i
$566$	−526.268	−	509.859i	−0.929802	−	0.900810i
$567$	−77.8193	−	12.3254i	−0.137247	−	0.0217379i
$568$	680.577	−	32.3570i	1.19820	−	0.0569665i
$569$	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	$0.0828512\pi$
$570$	767.441	+	397.855i	1.34639	+	0.697992i
$571$	−790.541			−1.38448			−0.692242	−	0.721665i	$-0.743377\pi$
$571$	−790.541			−1.38448			−0.692242	+	0.721665i	$0.743377\pi$
$572$	−256.851	−	774.256i	−0.449040	−	1.35359i
$573$	−111.069	+	111.069i	−0.193837	+	0.193837i
$574$	−14.0211	+	28.6298i	−0.0244270	+	0.0498778i
$575$	−77.7834	+	35.2501i	−0.135275	+	0.0613046i
$576$	−1166.66	−	259.840i	−2.02546	−	0.451111i
$577$	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	$0.452871\pi$
$578$	366.141	−	5.79864i	0.633462	−	0.0100323i
$579$	1203.25	−	390.959i	2.07815	−	0.675231i
$580$	−1.53471	−	174.366i	−0.00264605	−	0.300632i
$581$	103.821	+	75.4303i	0.178693	+	0.129828i
$582$	640.456	+	449.997i	1.10044	+	0.773191i
$583$	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
$586$	44.6614	−	314.095i	0.0762140	−	0.535999i
$587$	656.105	+	334.302i	1.11773	+	0.569509i	0.912447	−	0.409194i	$-0.134190\pi$
$587$	656.105	+	334.302i	1.11773	+	0.569509i	0.205278	+	0.978704i	$0.434190\pi$
$588$	−999.891	+	191.005i	−1.70049	+	0.324838i
$589$	670.234	−	486.954i	1.13792	−	0.826746i
$590$	−35.0590	+	105.373i	−0.0594220	+	0.178598i
$591$	223.402	−	687.561i	0.378007	−	1.16339i
$592$	−248.326	−	218.703i	−0.419470	−	0.369431i
$593$	−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	$0.821248\pi$
$594$	356.344	−	1061.64i	0.599906	−	1.78726i
$595$	1.96327	−	85.8288i	0.00329962	−	0.144250i
$596$	−2.85896	+	9.85001i	−0.00479691	+	0.0165269i
$597$	−522.357	+	266.154i	−0.874969	+	0.445819i
$598$	−37.2278	+	121.066i	−0.0622539	+	0.202451i
$599$	−500.128	+	363.364i	−0.834938	+	0.606618i	−0.920952	−	0.389676i	$-0.872587\pi$
$599$	−500.128	+	363.364i	−0.834938	+	0.606618i	0.0860143	+	0.996294i	$0.472587\pi$
$600$	938.320	+	476.011i	1.56387	+	0.793352i
$601$	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	$0.383794\pi$
$602$	2.51262	+	3.34561i	0.00417379	+	0.00555749i
$603$	−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	$-0.999084\pi$
$607$	−30.2481	−	190.979i	−0.0498321	−	0.314628i	0.950164	−	0.311751i	$-0.100916\pi$
$608$	122.422	−	511.367i	0.201353	−	0.841063i
$609$	−34.4722	+	11.2007i	−0.0566045	+	0.0183919i
$610$	−2.72557	+	387.453i	−0.00446815	+	0.635169i
$611$	1033.23	−	750.686i	1.69105	−	1.22862i
$612$	1610.38	+	203.020i	2.63134	+	0.331732i
$613$	−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	$0.396198\pi$
$614$	−365.112	−	178.809i	−0.594645	−	0.291220i
$615$	366.481	+	383.639i	0.595903	+	0.623803i
$616$	1.52921	+	69.5249i	0.00248248	+	0.112865i
$617$	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	$0.620212\pi$
$618$	−625.132	−	1825.10i	−1.01154	−	2.95323i
$619$	227.677	−	700.717i	0.367814	−	1.13201i	−0.580386	−	0.814341i	$-0.697098\pi$
$619$	227.677	−	700.717i	0.367814	−	1.13201i	0.948200	−	0.317674i	$-0.102902\pi$
$620$	810.530	−	599.855i	1.30731	−	0.967507i
$621$	−140.670	+	102.202i	−0.226521	+	0.164577i
$622$	−231.359	+	3.66407i	−0.371960	+	0.00589079i
$623$	89.0890	+	45.3931i	0.143000	+	0.0728622i
$624$	1450.65	−	575.213i	2.32476	−	0.921815i
$625$	−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
$628$	−54.4645	+	115.820i	−0.0867269	+	0.184426i
$629$	363.540	+	264.127i	0.577965	+	0.419916i
$630$	24.1121	−	145.602i	0.0382732	−	0.231114i
$631$	628.775	−	204.301i	0.996474	−	0.323774i	0.235018	−	0.971991i	$-0.424485\pi$
$631$	628.775	−	204.301i	0.996474	−	0.323774i	0.761456	+	0.648217i	$0.224485\pi$
$632$	−12.8462	−	33.9570i	−0.0203262	−	0.0537295i
$633$	−1308.68	−	207.275i	−2.06743	−	0.327448i
$634$	−268.618	−	507.175i	−0.423688	−	0.799960i
$635$	−202.245	−	420.429i	−0.318496	−	0.662093i
$636$	−336.221	+	1158.39i	−0.528650	+	1.82136i
$637$	634.182	−	634.182i	0.995576	−	0.995576i
$638$	−28.1705	−	189.731i	−0.0441544	−	0.297383i
$639$	−1590.58			−2.48917
$640$	143.523	−	623.700i	0.224255	−	0.974530i
$641$	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	$0.0507772\pi$
$642$	−371.288	+	1207.44i	−0.578330	+	1.88075i
$643$	779.047	+	123.389i	1.21158	+	0.191896i	0.729346	−	0.684145i	$-0.239825\pi$
$643$	779.047	+	123.389i	1.21158	+	0.191896i	0.482236	+	0.876041i	$0.339825\pi$
$644$	6.06691	−	8.93210i	0.00942067	−	0.0138697i
$645$	66.7012	−	19.9982i	0.103413	−	0.0310049i
$646$	−100.520	+	706.939i	−0.155604	+	1.09433i
$647$	−136.397	+	21.6032i	−0.210815	+	0.0333898i	−0.260949	−	0.965353i	$-0.584035\pi$
$647$	−136.397	+	21.6032i	−0.210815	+	0.0333898i	0.0501336	+	0.998743i	$0.484035\pi$
$648$	769.429	+	210.175i	1.18739	+	0.324343i
$649$	−22.1816	+	120.126i	−0.0341781	+	0.185094i
$650$	−919.500	+	117.572i	−1.41462	+	0.180880i
$651$	−169.572	−	123.201i	−0.260479	−	0.189249i
$652$	−178.556	−	167.589i	−0.273858	−	0.257038i
$653$	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	$0.497794\pi$
$654$	803.684	−	829.550i	1.22887	−	1.26843i
$655$	310.889	+	449.154i	0.474639	+	0.685731i
$656$	172.784	−	272.572i	0.263390	−	0.415506i
$657$	164.914	+	323.662i	0.251010	+	0.492636i
$658$	−103.001	+	35.2797i	−0.156536	+	0.0536166i
$659$		−	468.411i		−	0.710790i	−0.934716	−	0.355395i	$-0.884346\pi$
$659$		−	468.411i		−	0.710790i	0.934716	−	0.355395i	$-0.115654\pi$
$660$	1094.59	+	375.995i	1.65847	+	0.569689i
$661$	−512.822			−0.775828			−0.387914	−	0.921696i	$-0.626804\pi$
$661$	−512.822			−0.775828			−0.387914	+	0.921696i	$0.626804\pi$
$662$	86.2082	+	251.688i	0.130224	+	0.380194i
$663$	−1888.20	+	962.086i	−2.84796	+	1.45111i
$664$	−961.217	−	873.966i	−1.44762	−	1.31621i
$665$	63.8773	+	11.6204i	0.0960562	+	0.0174743i
$666$	554.809	+	537.510i	0.833047	+	0.807072i
$667$	−13.5209	+	26.5362i	−0.0202712	+	0.0397844i
$668$	−305.845	−	287.060i	−0.457851	−	0.429730i
$669$	−466.949	+	642.700i	−0.697981	+	0.960688i
$670$	213.110	−	32.2183i	0.318075	−	0.0480870i
$671$	55.9120	+	422.526i	0.0833263	+	0.629696i
$672$	−132.617	+	10.5225i	−0.197347	+	0.0156585i
$673$	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	$0.684866\pi$
$674$	94.0862	+	13.3782i	0.139594	+	0.0198489i
$675$	−1106.25	−	628.966i	−1.63889	−	0.931802i
$676$	−392.684	+	578.135i	−0.580893	+	0.855229i
$677$	−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	$0.883052\pi$
$678$	−994.142	−	305.699i	−1.46629	−	0.450883i
$679$	55.9122	+	18.1670i	0.0823449	+	0.0267555i
$680$	−114.771	+	861.497i	−0.168780	+	1.26691i
$681$			1665.16i			2.44517i
$682$	791.874	−	776.689i	1.16110	−	1.13884i
$683$	−534.510	−	534.510i	−0.782591	−	0.782591i	0.197676	−	0.980267i	$-0.436661\pi$
$683$	−534.510	−	534.510i	−0.782591	−	0.782591i	−0.980267	+	0.197676i	$0.936661\pi$
$684$	−342.161	+	1178.85i	−0.500235	+	1.72347i
$685$	−458.764	−	953.683i	−0.669729	−	1.39224i
$686$	−136.003	+	72.0324i	−0.198256	+	0.105004i
$687$	−107.595	+	679.331i	−0.156616	+	0.988837i
$688$	−21.5801	−	36.4474i	−0.0313665	−	0.0529759i
$689$	−328.393	−	1010.69i	−0.476622	−	1.46689i
$690$	−104.602	−	146.123i	−0.151597	−	0.211772i
$691$	−475.213	+	654.075i	−0.687718	+	0.946563i	−0.999994	−	0.00342825i	$-0.998909\pi$
$691$	−475.213	+	654.075i	−0.687718	+	0.946563i	0.312276	+	0.949992i	$0.398909\pi$
$692$	−557.135	+	1184.76i	−0.805108	+	1.71208i
$693$	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
$696$	359.283	−	74.5477i	0.516211	−	0.107109i
$697$	−198.962	+	390.485i	−0.285455	+	0.560237i
$698$	−13.3619	−	843.701i	−0.0191431	−	1.20874i
$699$	−20.4721	−	28.1775i	−0.0292877	−	0.0403111i
$700$	77.8701	+	13.4590i	0.111243	+	0.0192272i
$701$	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	$0.496705\pi$
$702$	−1785.58	+	611.596i	−2.54356	+	0.871219i
$703$	−240.298	+	240.298i	−0.341818	+	0.341818i
$704$	61.5779	−	701.302i	0.0874685	−	0.996167i
$705$	−41.4372	+	1811.52i	−0.0587762	+	2.56953i
$706$	176.291	−	359.971i	0.249704	−	0.509874i
$707$	26.6036	+	52.2124i	0.0376288	+	0.0738507i
$708$	−231.852	−	29.2295i	−0.327475	−	0.0412846i
$709$	−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	$0.848407\pi$
$710$	5.99108	−	851.662i	0.00843814	−	1.19952i
$711$	26.1906	+	80.6064i	0.0368363	+	0.113370i
$712$	−846.226	−	555.402i	−1.18852	−	0.780059i
$713$	−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
$718$	524.413	−	393.845i	0.730380	−	0.548531i
$719$	218.676	+	673.017i	0.304140	+	0.936046i	0.979997	+	0.199013i	$0.0637736\pi$
$719$	218.676	+	673.017i	0.304140	+	0.936046i	−0.675857	+	0.737033i	$0.736226\pi$
$720$	−403.818	+	1438.45i	−0.560858	+	1.99785i
$721$	−85.1680	−	117.224i	−0.118125	−	0.162585i
$722$	173.955	+	53.4913i	0.240936	+	0.0740877i
$723$	558.723	+	1096.56i	0.772784	+	1.51667i
$724$	42.8923	−	147.777i	0.0592435	−	0.204112i
$725$	−217.739	−	9.96645i	−0.300329	−	0.0137468i
$726$	1249.65	+	243.282i	1.72128	+	0.335100i
$727$	237.357	−	237.357i	0.326489	−	0.326489i	−0.524761	−	0.851250i	$-0.675845\pi$
$727$	237.357	−	237.357i	0.326489	−	0.326489i	0.851250	+	0.524761i	$0.175845\pi$
$728$	91.4443	−	73.3183i	0.125610	−	0.100712i
$729$	521.219	+	169.354i	0.714978	+	0.232310i
$730$	−173.923	+	87.0824i	−0.238250	+	0.119291i
$731$	33.8094	+	46.5347i	0.0462509	+	0.0636590i
$732$	−800.861	+	152.985i	−1.09407	+	0.208996i
$733$	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	$0.0602798\pi$
$734$	12.3414	+	1.75482i	0.0168138	+	0.00239077i
$735$	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
$738$	−433.122	+	616.438i	−0.586886	+	0.835282i
$739$	−109.430	+	150.617i	−0.148078	+	0.203812i	−0.876612	−	0.481198i	$-0.840202\pi$
$739$	−109.430	+	150.617i	−0.148078	+	0.203812i	0.728534	+	0.685009i	$0.240202\pi$
$740$	−289.894	+	295.043i	−0.391749	+	0.398706i
$741$	−495.245	−	1524.21i	−0.668346	−	2.05696i
$742$	1.43458	+	90.5828i	0.00193339	+	0.122079i
$743$	27.0739	−	170.938i	0.0364386	−	0.230064i	−0.962747	−	0.270402i	$-0.912843\pi$
$743$	27.0739	−	170.938i	0.0364386	−	0.230064i	0.999186	+	0.0403376i	$0.0128434\pi$
$744$	1569.97	+	1427.46i	2.11017	+	1.91863i
$745$	12.0994	+	4.23960i	0.0162408	+	0.00569074i
$746$	−132.446	−	64.8638i	−0.177542	−	0.0869487i
$747$	2144.51	+	2144.51i	2.87083	+	2.87083i
$748$	5.88492	+	956.001i	0.00786754	+	1.27808i
$749$			94.8784i			0.126673i
$750$	658.070	−	1138.72i	0.877426	−	1.51829i
$751$	50.5888	+	16.4373i	0.0673619	+	0.0218872i	0.342504	−	0.939516i	$-0.388725\pi$
$751$	50.5888	+	16.4373i	0.0673619	+	0.0218872i	−0.275142	+	0.961404i	$0.588725\pi$
$752$	1075.52	−	240.985i	1.43022	−	0.320459i
$753$	−16.2750	+	102.757i	−0.0216136	+	0.136463i
$754$	−224.947	+	232.187i	−0.298338	+	0.307940i
$755$	695.532	−	208.532i	0.921235	−	0.276202i
$756$	160.820	−	5.09515i	0.212725	−	0.00673961i
$757$	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	$0.898162\pi$
$758$	−41.9897	+	59.7616i	−0.0553954	+	0.0788412i
$759$	−136.165	−	143.298i	−0.179401	−	0.188798i
$760$	−629.915	−	187.647i	−0.828836	−	0.246904i
$761$	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	$0.0423796\pi$
$762$	785.018	−	589.565i	1.03021	−	0.773708i
$763$	39.3838	−	77.2950i	0.0516170	−	0.101304i
$764$	67.1048	−	98.7960i	0.0878335	−	0.129314i
$765$	363.135	−	1996.15i	0.474686	−	2.60934i
$766$	151.156	+	285.395i	0.197331	+	0.372578i
$767$	183.447	−	93.4707i	0.239174	−	0.121865i
$768$	1346.14	+	40.9253i	1.75278	+	0.0532882i
$769$	−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+(-1.89209 + 0.648077i) q^{2} +(-4.68739 + 2.38834i) q^{3} +(3.15999 - 2.45244i) q^{4} +(-2.84565 - 4.11124i) q^{5} +(7.32112 - 7.55674i) q^{6} +(0.358764 - 0.704115i) q^{7} +(-4.38962 + 6.68814i) q^{8} +(10.9773 - 15.1090i) q^{9} +(8.04862 + 5.93462i) q^{10} +(9.67047 + 5.24233i) q^{11} +(-8.95485 + 19.0427i) q^{12} +(-2.90025 - 18.3115i) q^{13} +(-0.222493 + 1.56475i) q^{14} +(23.1577 + 12.4746i) q^{15} +(3.97111 - 15.4994i) q^{16} +(-3.39896 + 21.4602i) q^{17} +(-10.9783 + 35.7017i) q^{18} +(-15.6275 - 5.07770i) q^{19} +(-19.0748 - 6.01269i) q^{20} +4.15731i q^{21} +(-21.6948 - 3.65174i) q^{22} +(2.41542 + 2.41542i) q^{23} +(4.60225 - 41.8338i) q^{24} +(-8.80451 + 23.3983i) q^{25} +(17.3548 + 32.7673i) q^{26} +(-7.96283 + 50.2753i) q^{27} +(-0.593104 - 3.10484i) q^{28} +(2.69421 + 8.29194i) q^{29} +(-51.9009 - 8.59497i) q^{30} +(-29.6349 + 40.7889i) q^{31} +(2.53109 + 31.8997i) q^{32} +(-57.8497 - 1.47642i) q^{33} +(-7.47673 - 42.8074i) q^{34} +(-3.91570 + 0.528702i) q^{35} +(-2.36558 - 74.6656i) q^{36} +(9.38918 - 18.4273i) q^{37} +(32.8594 - 0.520401i) q^{38} +(57.3287 + 78.9061i) q^{39} +(39.9879 - 0.985391i) q^{40} +(19.1830 + 6.23292i) q^{41} +(-2.69426 - 7.86599i) q^{42} +(1.87193 - 1.87193i) q^{43} +(43.4151 - 7.15050i) q^{44} +(-93.3544 - 2.13542i) q^{45} +(-6.13557 - 3.00481i) q^{46} +(31.2740 + 61.3786i) q^{47} +(18.4037 + 82.1359i) q^{48} +(28.4344 + 39.1366i) q^{49} +(1.49502 - 49.9776i) q^{50} +(-35.3221 - 108.710i) q^{51} +(-54.0725 - 50.7514i) 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} +(-10.4715 - 13.9430i) q^{58} +(3.43169 + 10.5617i) q^{59} +(103.771 - 17.3733i) q^{60} +(22.7745 + 31.3464i) q^{61} +(29.6374 - 96.3819i) q^{62} +(-6.70020 - 13.1499i) q^{63} +(-25.4625 - 58.7168i) q^{64} +(-67.0296 + 64.0317i) q^{65} +(110.414 - 34.6975i) q^{66} +(15.2404 - 15.2404i) q^{67} +(41.8891 + 76.1498i) q^{68} +(-17.0909 - 5.55316i) q^{69} +(7.06621 - 3.53802i) q^{70} +(-50.0607 - 68.9026i) q^{71} +(52.8649 + 139.741i) q^{72} +(-8.83037 + 17.3306i) q^{73} +(-5.82285 + 40.9510i) q^{74} +(-14.6130 - 130.705i) q^{75} +(-61.8356 + 22.2801i) q^{76} +(7.16062 - 4.92836i) q^{77} +(-159.608 - 112.144i) q^{78} +(-2.66749 + 3.67149i) q^{79} +(-75.0219 + 27.7797i) q^{80} +(-30.8097 - 94.8224i) q^{81} +(-40.3353 + 0.638797i) q^{82} +(-25.4037 + 160.393i) q^{83} +(10.1955 + 13.1371i) q^{84} +(97.9002 - 47.0944i) q^{85} +(-2.32871 + 4.75502i) q^{86} +(-32.4328 - 32.4328i) q^{87} +(-77.5111 + 41.6657i) q^{88} +126.526i q^{89} +(178.019 - 56.4604i) q^{90} +(-13.9339 - 4.52739i) q^{91} +(13.5564 + 1.70905i) q^{92} +(41.4922 - 261.972i) q^{93} +(-98.9511 - 95.8658i) q^{94} +(23.5950 + 78.6979i) q^{95} +(-88.0517 - 143.481i) q^{96} +(11.6378 + 73.4780i) q^{97} +(-79.1639 - 55.6222i) 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

Fields

Representations

Groups

Database

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