LMFDB - Embedded newform 220.3.h.a.199.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(199,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("220.199");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.h (of order $2$, degree $1$, 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:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			199.13
Character	$\chi$	$=$	220.199
Dual form			220.3.h.a.199.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.58018 - 1.22598i) q^{2} +0.354051 q^{3} +(0.993967 + 3.87454i) q^{4} +(-4.79515 + 1.41652i) q^{5} +(-0.559466 - 0.434058i) q^{6} +6.53369 q^{7} +(3.17944 - 7.34106i) q^{8} -8.87465 q^{9} +(9.31385 + 3.64037i) q^{10} +3.31662i q^{11} +(0.351915 + 1.37178i) q^{12} -17.8331i q^{13} +(-10.3244 - 8.01014i) q^{14} +(-1.69773 + 0.501522i) q^{15} +(-14.0241 + 7.70232i) q^{16} -10.2601i q^{17} +(14.0236 + 10.8801i) q^{18} -24.2213i q^{19} +(-10.2546 - 17.1710i) q^{20} +2.31326 q^{21} +(4.06610 - 5.24088i) q^{22} -30.4450 q^{23} +(1.12568 - 2.59911i) q^{24} +(20.9869 - 13.5849i) q^{25} +(-21.8629 + 28.1796i) q^{26} -6.32853 q^{27} +(6.49427 + 25.3150i) q^{28} -22.6440 q^{29} +(3.29757 + 1.28887i) q^{30} -1.17131i q^{31} +(31.6035 + 5.02207i) q^{32} +1.17425i q^{33} +(-12.5787 + 16.2129i) q^{34} +(-31.3300 + 9.25513i) q^{35} +(-8.82111 - 34.3851i) q^{36} -20.5178i q^{37} +(-29.6947 + 38.2741i) q^{38} -6.31382i q^{39} +(-4.84707 + 39.7052i) q^{40} -39.0053 q^{41} +(-3.65537 - 2.83600i) q^{42} -35.0449 q^{43} +(-12.8504 + 3.29662i) q^{44} +(42.5553 - 12.5712i) q^{45} +(48.1087 + 37.3248i) q^{46} +18.3279 q^{47} +(-4.96523 + 2.72701i) q^{48} -6.31094 q^{49} +(-49.8180 - 4.26280i) q^{50} -3.63261i q^{51} +(69.0949 - 17.7255i) q^{52} -60.6114i q^{53} +(10.0003 + 7.75863i) q^{54} +(-4.69808 - 15.9037i) q^{55} +(20.7734 - 47.9642i) q^{56} -8.57557i q^{57} +(35.7817 + 27.7610i) q^{58} -24.8880i q^{59} +(-3.63065 - 6.07941i) q^{60} +99.4176 q^{61} +(-1.43600 + 1.85088i) q^{62} -57.9842 q^{63} +(-43.7824 - 46.6809i) q^{64} +(25.2610 + 85.5123i) q^{65} +(1.43961 - 1.85554i) q^{66} +66.1083 q^{67} +(39.7533 - 10.1982i) q^{68} -10.7791 q^{69} +(60.8538 + 23.7850i) q^{70} +73.5040i q^{71} +(-28.2164 + 65.1493i) q^{72} -11.7094i q^{73} +(-25.1543 + 32.4219i) q^{74} +(7.43043 - 4.80974i) q^{75} +(93.8463 - 24.0752i) q^{76} +21.6698i q^{77} +(-7.74059 + 9.97700i) q^{78} +91.6424i q^{79} +(56.3369 - 56.7992i) q^{80} +77.6312 q^{81} +(61.6356 + 47.8195i) q^{82} +123.435 q^{83} +(2.29930 + 8.96280i) q^{84} +(14.5337 + 49.1989i) q^{85} +(55.3774 + 42.9642i) q^{86} -8.01712 q^{87} +(24.3475 + 10.5450i) q^{88} -6.98478 q^{89} +(-82.6571 - 32.3070i) q^{90} -116.516i q^{91} +(-30.2613 - 117.960i) q^{92} -0.414703i q^{93} +(-28.9614 - 22.4695i) q^{94} +(34.3101 + 116.145i) q^{95} +(11.1892 + 1.77807i) q^{96} -113.558i q^{97} +(9.97246 + 7.73706i) q^{98} -29.4339i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 4 q^{4} + 4 q^{5} + 12 q^{6} + 180 q^{9} - 18 q^{10} - 56 q^{14} - 40 q^{16} + 84 q^{20} - 16 q^{21} + 104 q^{24} - 60 q^{25} + 28 q^{26} - 88 q^{29} - 166 q^{30} - 152 q^{34} - 248 q^{36} + 132 q^{40}+ \cdots + 216 q^{96}+O(q^{100}) $ 60 * q - 4 * q^4 + 4 * q^5 + 12 * q^6 + 180 * q^9 - 18 * q^10 - 56 * q^14 - 40 * q^16 + 84 * q^20 - 16 * q^21 + 104 * q^24 - 60 * q^25 + 28 * q^26 - 88 * q^29 - 166 * q^30 - 152 * q^34 - 248 * q^36 + 132 * q^40 - 200 * q^41 + 44 * q^44 + 84 * q^45 + 260 * q^46 + 420 * q^49 - 198 * q^50 - 116 * q^54 - 128 * q^56 - 4 * q^60 + 136 * q^61 + 116 * q^64 - 288 * q^65 - 544 * q^69 + 152 * q^70 + 436 * q^74 - 72 * q^76 - 176 * q^80 + 300 * q^81 - 136 * q^84 + 176 * q^85 - 348 * q^86 + 760 * q^89 + 40 * q^90 + 112 * q^94 + 216 * q^96

Character values

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

$n$	$101$	$111$	$177$
$\chi(n)$	$1$	$-1$	$-1$

Coefficient data

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

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

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

$2$	−1.58018	−	1.22598i	−0.790092	−	0.612988i
$2$	−1.58018	−	1.22598i	−0.790092	−	0.612988i
$3$	0.354051			0.118017			0.0590085	−	0.998257i	$-0.481206\pi$
$3$	0.354051			0.118017			0.0590085	+	0.998257i	$0.481206\pi$
$4$	0.993967	+	3.87454i	0.248492	+	0.968634i
$5$	−4.79515	+	1.41652i	−0.959030	+	0.283305i
$5$	−4.79515	+	1.41652i	−0.959030	+	0.283305i
$6$	−0.559466	−	0.434058i	−0.0932443	−	0.0723429i
$7$	6.53369			0.933384			0.466692	−	0.884420i	$-0.345446\pi$
$7$	6.53369			0.933384			0.466692	+	0.884420i	$0.345446\pi$
$8$	3.17944	−	7.34106i	0.397429	−	0.917633i
$9$	−8.87465			−0.986072
$10$	9.31385	+	3.64037i	0.931385	+	0.364037i
$11$			3.31662i			0.301511i
$11$			3.31662i			0.301511i
$12$	0.351915	+	1.37178i	0.0293262	+	0.114315i
$13$		−	17.8331i		−	1.37178i	−0.727707	−	0.685888i	$-0.759414\pi$
$13$		−	17.8331i		−	1.37178i	0.727707	−	0.685888i	$-0.240586\pi$
$14$	−10.3244	−	8.01014i	−0.737459	−	0.572153i
$15$	−1.69773	+	0.501522i	−0.113182	+	0.0334348i
$16$	−14.0241	+	7.70232i	−0.876504	+	0.481395i
$17$		−	10.2601i		−	0.603538i	−0.953381	−	0.301769i	$-0.902423\pi$
$17$		−	10.2601i		−	0.603538i	0.953381	−	0.301769i	$-0.0975771\pi$
$18$	14.0236	+	10.8801i	0.779088	+	0.604450i
$19$		−	24.2213i		−	1.27480i	−0.770531	−	0.637402i	$-0.780009\pi$
$19$		−	24.2213i		−	1.27480i	0.770531	−	0.637402i	$-0.219991\pi$
$20$	−10.2546	−	17.1710i	−0.512730	−	0.858550i
$21$	2.31326			0.110155
$22$	4.06610	−	5.24088i	0.184823	−	0.238222i
$23$	−30.4450			−1.32369			−0.661847	−	0.749639i	$-0.730227\pi$
$23$	−30.4450			−1.32369			−0.661847	+	0.749639i	$0.730227\pi$
$24$	1.12568	−	2.59911i	0.0469034	−	0.108296i
$25$	20.9869	−	13.5849i	0.839477	−	0.543396i
$26$	−21.8629	+	28.1796i	−0.840882	+	1.08383i
$27$	−6.32853			−0.234390
$28$	6.49427	+	25.3150i	0.231938	+	0.904107i
$29$	−22.6440			−0.780827			−0.390414	−	0.920640i	$-0.627668\pi$
$29$	−22.6440			−0.780827			−0.390414	+	0.920640i	$0.627668\pi$
$30$	3.29757	+	1.28887i	0.109919	+	0.0429625i
$31$		−	1.17131i		−	0.0377842i	−0.999822	−	0.0188921i	$-0.993986\pi$
$31$		−	1.17131i		−	0.0377842i	0.999822	−	0.0188921i	$-0.00601389\pi$
$32$	31.6035	+	5.02207i	0.987608	+	0.156940i
$33$			1.17425i			0.0355834i
$34$	−12.5787	+	16.2129i	−0.369961	+	0.476851i
$35$	−31.3300	+	9.25513i	−0.895143	+	0.264432i
$36$	−8.82111	−	34.3851i	−0.245031	−	0.955143i
$37$		−	20.5178i		−	0.554536i	−0.960793	−	0.277268i	$-0.910571\pi$
$37$		−	20.5178i		−	0.554536i	0.960793	−	0.277268i	$-0.0894289\pi$
$38$	−29.6947	+	38.2741i	−0.781440	+	1.00721i
$39$		−	6.31382i		−	0.161893i
$40$	−4.84707	+	39.7052i	−0.121177	+	0.992631i
$41$	−39.0053			−0.951349			−0.475674	−	0.879621i	$-0.657796\pi$
$41$	−39.0053			−0.951349			−0.475674	+	0.879621i	$0.657796\pi$
$42$	−3.65537	−	2.83600i	−0.0870327	−	0.0675237i
$43$	−35.0449			−0.814998			−0.407499	−	0.913206i	$-0.633599\pi$
$43$	−35.0449			−0.814998			−0.407499	+	0.913206i	$0.633599\pi$
$44$	−12.8504	+	3.29662i	−0.292054	+	0.0749231i
$45$	42.5553	−	12.5712i	0.945673	−	0.279359i
$46$	48.1087	+	37.3248i	1.04584	+	0.811409i
$47$	18.3279			0.389954			0.194977	−	0.980808i	$-0.437537\pi$
$47$	18.3279			0.389954			0.194977	+	0.980808i	$0.437537\pi$
$48$	−4.96523	+	2.72701i	−0.103442	+	0.0568128i
$49$	−6.31094			−0.128795
$50$	−49.8180	−	4.26280i	−0.996359	−	0.0852560i
$51$		−	3.63261i		−	0.0712277i
$52$	69.0949	−	17.7255i	1.32875	−	0.340875i
$53$		−	60.6114i		−	1.14361i	−0.820389	−	0.571806i	$-0.806243\pi$
$53$		−	60.6114i		−	1.14361i	0.820389	−	0.571806i	$-0.193757\pi$
$54$	10.0003	+	7.75863i	0.185190	+	0.143678i
$55$	−4.69808	−	15.9037i	−0.0854197	−	0.289158i
$56$	20.7734	−	47.9642i	0.370954	−	0.856503i
$57$		−	8.57557i		−	0.150449i
$58$	35.7817	+	27.7610i	0.616926	+	0.478638i
$59$		−	24.8880i		−	0.421830i	−0.977504	−	0.210915i	$-0.932356\pi$
$59$		−	24.8880i		−	0.421830i	0.977504	−	0.210915i	$-0.0676444\pi$
$60$	−3.63065	−	6.07941i	−0.0605108	−	0.101323i
$61$	99.4176			1.62980			0.814899	−	0.579604i	$-0.196793\pi$
$61$	99.4176			1.62980			0.814899	+	0.579604i	$0.196793\pi$
$62$	−1.43600	+	1.85088i	−0.0231612	+	0.0298530i
$63$	−57.9842			−0.920384
$64$	−43.7824	−	46.6809i	−0.684100	−	0.729389i
$65$	25.2610	+	85.5123i	0.388631	+	1.31557i
$66$	1.43961	−	1.85554i	0.0218122	−	0.0281142i
$67$	66.1083			0.986691			0.493346	−	0.869833i	$-0.335774\pi$
$67$	66.1083			0.986691			0.493346	+	0.869833i	$0.335774\pi$
$68$	39.7533	−	10.1982i	0.584607	−	0.149974i
$69$	−10.7791			−0.156218
$70$	60.8538	+	23.7850i	0.869339	+	0.339786i
$71$			73.5040i			1.03527i	0.855602	+	0.517634i	$0.173187\pi$
$71$			73.5040i			1.03527i	−0.855602	+	0.517634i	$0.826813\pi$
$72$	−28.2164	+	65.1493i	−0.391894	+	0.904852i
$73$		−	11.7094i		−	0.160403i	−0.996779	−	0.0802013i	$-0.974444\pi$
$73$		−	11.7094i		−	0.160403i	0.996779	−	0.0802013i	$-0.0255563\pi$
$74$	−25.1543	+	32.4219i	−0.339924	+	0.438134i
$75$	7.43043	−	4.80974i	0.0990724	−	0.0641299i
$76$	93.8463	−	24.0752i	1.23482	−	0.316778i
$77$			21.6698i			0.281426i
$78$	−7.74059	+	9.97700i	−0.0992383	+	0.127910i
$79$			91.6424i			1.16003i	0.814606	+	0.580015i	$0.196953\pi$
$79$			91.6424i			1.16003i	−0.814606	+	0.580015i	$0.803047\pi$
$80$	56.3369	−	56.7992i	0.704212	−	0.709990i
$81$	77.6312			0.958410
$82$	61.6356	+	47.8195i	0.751653	+	0.583165i
$83$	123.435			1.48717			0.743583	−	0.668643i	$-0.233125\pi$
$83$	123.435			1.48717			0.743583	+	0.668643i	$0.233125\pi$
$84$	2.29930	+	8.96280i	0.0273726	+	0.106700i
$85$	14.5337	+	49.1989i	0.170985	+	0.578811i
$86$	55.3774	+	42.9642i	0.643924	+	0.499584i
$87$	−8.01712			−0.0921508
$88$	24.3475	+	10.5450i	0.276677	+	0.119829i
$89$	−6.98478			−0.0784807			−0.0392403	−	0.999230i	$-0.512494\pi$
$89$	−6.98478			−0.0784807			−0.0392403	+	0.999230i	$0.512494\pi$
$90$	−82.6571	−	32.3070i	−0.918412	−	0.358966i
$91$		−	116.516i		−	1.28039i
$92$	−30.2613	−	117.960i	−0.328927	−	1.28218i
$93$		−	0.414703i		−	0.00445917i
$94$	−28.9614	−	22.4695i	−0.308100	−	0.239037i
$95$	34.3101	+	116.145i	0.361159	+	1.22258i
$96$	11.1892	+	1.77807i	0.116554	+	0.0185215i
$97$		−	113.558i		−	1.17070i	−0.810780	−	0.585352i	$-0.800956\pi$
$97$		−	113.558i		−	1.17070i	0.810780	−	0.585352i	$-0.199044\pi$
$98$	9.97246	+	7.73706i	0.101760	+	0.0789496i
$99$		−	29.4339i		−	0.297312i
$100$	73.4955	+	67.8116i	0.734955	+	0.678116i
$101$	−37.7496			−0.373758			−0.186879	−	0.982383i	$-0.559837\pi$
$101$	−37.7496			−0.373758			−0.186879	+	0.982383i	$0.559837\pi$
$102$	−4.45349	+	5.74020i	−0.0436617	+	0.0562764i
$103$	−172.276			−1.67259			−0.836293	−	0.548283i	$-0.815282\pi$
$103$	−172.276			−1.67259			−0.836293	+	0.548283i	$0.815282\pi$
$104$	−130.914	−	56.6991i	−1.25879	−	0.545184i
$105$	−11.0924	+	3.27679i	−0.105642	+	0.0312075i
$106$	−74.3081	+	95.7773i	−0.701020	+	0.903559i
$107$	−55.1292			−0.515226			−0.257613	−	0.966248i	$-0.582936\pi$
$107$	−55.1292			−0.515226			−0.257613	+	0.966248i	$0.582936\pi$
$108$	−6.29035	−	24.5201i	−0.0582440	−	0.227038i
$109$	−117.871			−1.08139			−0.540693	−	0.841220i	$-0.681838\pi$
$109$	−117.871			−1.08139			−0.540693	+	0.841220i	$0.681838\pi$
$110$	−12.0737	+	30.8905i	−0.109761	+	0.280823i
$111$		−	7.26435i		−	0.0654446i
$112$	−91.6288	+	50.3246i	−0.818114	+	0.449326i
$113$		−	14.9494i		−	0.132296i	−0.997810	−	0.0661478i	$-0.978929\pi$
$113$		−	14.9494i		−	0.132296i	0.997810	−	0.0661478i	$-0.0210709\pi$
$114$	−10.5134	+	13.5510i	−0.0922231	+	0.118868i
$115$	145.988	−	43.1261i	1.26946	−	0.375009i
$116$	−22.5074	−	87.7349i	−0.194029	−	0.756336i
$117$			158.262i			1.35267i
$118$	−30.5121	+	39.3276i	−0.258577	+	0.333285i
$119$		−	67.0366i		−	0.563332i
$120$	−1.71611	+	14.0577i	−0.0143009	+	0.117147i
$121$	−11.0000			−0.0909091
$122$	−157.098	−	121.884i	−1.28769	−	0.999046i
$123$	−13.8099			−0.112275
$124$	4.53828	−	1.16424i	0.0365990	−	0.00938905i
$125$	−81.3920	+	94.8701i	−0.651136	+	0.758961i
$126$	91.6257	+	71.0872i	0.727188	+	0.564184i
$127$	17.5623			0.138286			0.0691430	−	0.997607i	$-0.477974\pi$
$127$	17.5623			0.138286			0.0691430	+	0.997607i	$0.477974\pi$
$128$	11.9546	+	127.441i	0.0933955	+	0.995629i
$129$	−12.4077			−0.0961836
$130$	64.9189	−	166.095i	0.499376	−	1.27765i
$131$		−	249.534i		−	1.90484i	−0.304795	−	0.952418i	$-0.598588\pi$
$131$		−	249.534i		−	1.90484i	0.304795	−	0.952418i	$-0.401412\pi$
$132$	−4.54969	+	1.16717i	−0.0344673	+	0.00884219i
$133$		−	158.254i		−	1.18988i
$134$	−104.463	−	81.0472i	−0.779577	−	0.604830i
$135$	30.3463	−	8.96453i	0.224787	−	0.0664039i
$136$	−75.3203	−	32.6215i	−0.553826	−	0.239864i
$137$			174.228i			1.27174i	0.771797	+	0.635869i	$0.219358\pi$
$137$			174.228i			1.27174i	−0.771797	+	0.635869i	$0.780642\pi$
$138$	17.0329	+	13.2149i	0.123427	+	0.0957600i
$139$			184.565i			1.32781i	0.747819	+	0.663903i	$0.231101\pi$
$139$			184.565i			1.32781i	−0.747819	+	0.663903i	$0.768899\pi$
$140$	−67.0003	−	112.190i	−0.478574	−	0.801357i
$141$	6.48899			0.0460212
$142$	90.1141	−	116.150i	0.634606	−	0.817957i
$143$	59.1456			0.413606
$144$	124.459	−	68.3554i	0.864296	−	0.474690i
$145$	108.581	−	32.0758i	0.748837	−	0.221212i
$146$	−14.3554	+	18.5030i	−0.0983249	+	0.126733i
$147$	−2.23439			−0.0152000
$148$	79.4970	−	20.3940i	0.537142	−	0.137798i
$149$	−153.906			−1.03293			−0.516465	−	0.856308i	$-0.672752\pi$
$149$	−153.906			−1.03293			−0.516465	+	0.856308i	$0.672752\pi$
$150$	−17.6381	−	1.50925i	−0.117587	−	0.0100617i
$151$			257.202i			1.70333i	0.524090	+	0.851663i	$0.324405\pi$
$151$			257.202i			1.70333i	−0.524090	+	0.851663i	$0.675595\pi$
$152$	−177.810	−	77.0100i	−1.16980	−	0.506645i
$153$			91.0552i			0.595132i
$154$	26.5666	−	34.2423i	0.172511	−	0.222352i
$155$	1.65919	+	5.61660i	0.0107044	+	0.0362361i
$156$	24.4631	−	6.27572i	0.156815	−	0.0402290i
$157$			291.323i			1.85556i	0.373128	+	0.927780i	$0.378285\pi$
$157$			291.323i			1.85556i	−0.373128	+	0.927780i	$0.621715\pi$
$158$	112.351	−	144.812i	0.711085	−	0.916531i
$159$		−	21.4595i		−	0.134966i
$160$	−158.657	+	20.6855i	−0.991608	+	0.129285i
$161$	−198.918			−1.23551
$162$	−122.672	−	95.1740i	−0.757232	−	0.587494i
$163$	47.0391			0.288583			0.144292	−	0.989535i	$-0.453910\pi$
$163$	47.0391			0.288583			0.144292	+	0.989535i	$0.453910\pi$
$164$	−38.7700	−	151.127i	−0.236402	−	0.921509i
$165$	−1.66336	−	5.63072i	−0.0100810	−	0.0341256i
$166$	−195.050	−	151.328i	−1.17500	−	0.911615i
$167$	110.048			0.658968			0.329484	−	0.944161i	$-0.393125\pi$
$167$	110.048			0.658968			0.329484	+	0.944161i	$0.393125\pi$
$168$	7.35485	−	16.9818i	0.0437789	−	0.101082i
$169$	−149.019			−0.881768
$170$	37.3507	−	95.5614i	0.219710	−	0.562126i
$171$			214.955i			1.25705i
$172$	−34.8335	−	135.783i	−0.202520	−	0.789435i
$173$			7.40275i			0.0427904i	0.999771	+	0.0213952i	$0.00681083\pi$
$173$			7.40275i			0.0427904i	−0.999771	+	0.0213952i	$0.993189\pi$
$174$	12.6685	+	9.82880i	0.0728077	+	0.0564873i
$175$	137.122	−	88.7595i	0.783554	−	0.507197i
$176$	−25.5457	−	46.5125i	−0.145146	−	0.264276i
$177$		−	8.81161i		−	0.0497831i
$178$	11.0372	+	8.56317i	0.0620070	+	0.0481077i
$179$		−	295.467i		−	1.65065i	−0.564654	−	0.825327i	$-0.690991\pi$
$179$		−	295.467i		−	1.65065i	0.564654	−	0.825327i	$-0.309009\pi$
$180$	91.0059	+	152.387i	0.505589	+	0.846592i
$181$	40.6345			0.224500			0.112250	−	0.993680i	$-0.464194\pi$
$181$	40.6345			0.224500			0.112250	+	0.993680i	$0.464194\pi$
$182$	−142.845	+	184.116i	−0.784865	+	1.01163i
$183$	35.1989			0.192344
$184$	−96.7978	+	223.498i	−0.526075	+	1.21467i
$185$	29.0640	+	98.3860i	0.157103	+	0.531816i
$186$	−0.508416	+	0.655307i	−0.00273342	+	0.00352316i
$187$	34.0290			0.181974
$188$	18.2173	+	71.0119i	0.0969005	+	0.377723i
$189$	−41.3486			−0.218776
$190$	88.1743	−	225.593i	0.464075	−	1.18733i
$191$			264.076i			1.38260i	0.722570	+	0.691298i	$0.242961\pi$
$191$			264.076i			1.38260i	−0.722570	+	0.691298i	$0.757039\pi$
$192$	−15.5012	−	16.5274i	−0.0807353	−	0.0860802i
$193$		−	304.864i		−	1.57961i	−0.613361	−	0.789803i	$-0.710183\pi$
$193$		−	304.864i		−	1.57961i	0.613361	−	0.789803i	$-0.289817\pi$
$194$	−139.220	+	179.443i	−0.717627	+	0.924964i
$195$	8.94368	+	30.2757i	0.0458650	+	0.155260i
$196$	−6.27287	−	24.4520i	−0.0320044	−	0.124755i
$197$		−	129.546i		−	0.657592i	−0.944401	−	0.328796i	$-0.893357\pi$
$197$		−	129.546i		−	0.657592i	0.944401	−	0.328796i	$-0.106643\pi$
$198$	−36.0852	+	46.5110i	−0.182249	+	0.234904i
$199$			24.7630i			0.124437i	0.998063	+	0.0622187i	$0.0198176\pi$
$199$			24.7630i			0.124437i	−0.998063	+	0.0622187i	$0.980182\pi$
$200$	−33.0010	−	197.259i	−0.165005	−	0.986293i
$201$	23.4057			0.116446
$202$	59.6513	+	46.2801i	0.295304	+	0.229109i
$203$	−147.949			−0.728811
$204$	14.0747	−	3.61070i	0.0689936	−	0.0176995i
$205$	187.036	−	55.2520i	0.912372	−	0.269522i
$206$	272.229	+	211.207i	1.32150	+	1.02528i
$207$	270.188			1.30526
$208$	137.356	+	250.092i	0.660366	+	1.20237i
$209$	80.3329			0.384368
$210$	21.5453	+	8.42110i	0.102597	+	0.0401005i
$211$		−	236.345i		−	1.12012i	−0.828453	−	0.560059i	$-0.810779\pi$
$211$		−	236.345i		−	1.12012i	0.828453	−	0.560059i	$-0.189221\pi$
$212$	234.841	−	60.2458i	1.10774	−	0.284178i
$213$			26.0241i			0.122179i
$214$	87.1142	+	67.5870i	0.407076	+	0.315827i
$215$	168.046	−	49.6420i	0.781608	−	0.230893i
$216$	−20.1212	+	46.4582i	−0.0931535	+	0.215084i
$217$		−	7.65296i		−	0.0352671i
$218$	186.258	+	144.507i	0.854394	+	0.662876i
$219$		−	4.14572i		−	0.0189302i
$220$	56.9498	−	34.0107i	0.258863	−	0.154594i
$221$	−182.970			−0.827918
$222$	−8.90592	+	11.4790i	−0.0401167	+	0.0517073i
$223$	−429.110			−1.92426			−0.962129	−	0.272594i	$-0.912118\pi$
$223$	−429.110			−1.92426			−0.962129	+	0.272594i	$0.912118\pi$
$224$	206.487	+	32.8126i	0.921817	+	0.146485i
$225$	−186.251	+	120.561i	−0.827784	+	0.535827i
$226$	−18.3276	+	23.6228i	−0.0810956	+	0.104526i
$227$	−105.352			−0.464106			−0.232053	−	0.972703i	$-0.574544\pi$
$227$	−105.352			−0.464106			−0.232053	+	0.972703i	$0.574544\pi$
$228$	33.2263	−	8.52383i	0.145730	−	0.0373852i
$229$	412.612			1.80180			0.900900	−	0.434026i	$-0.142907\pi$
$229$	412.612			1.80180			0.900900	+	0.434026i	$0.142907\pi$
$230$	−283.560	−	110.831i	−1.23287	−	0.481873i
$231$			7.67220i			0.0332130i
$232$	−71.9951	+	166.231i	−0.310324	+	0.716513i
$233$		−	294.910i		−	1.26571i	−0.774272	−	0.632854i	$-0.781884\pi$
$233$		−	294.910i		−	1.26571i	0.774272	−	0.632854i	$-0.218116\pi$
$234$	194.026	−	250.084i	0.829170	−	1.06873i
$235$	−87.8848	+	25.9619i	−0.373978	+	0.110476i
$236$	96.4294	−	24.7378i	0.408599	−	0.104821i
$237$			32.4461i			0.136903i
$238$	−82.1852	+	105.930i	−0.345316	+	0.445085i
$239$		−	27.8481i		−	0.116519i	−0.998301	−	0.0582596i	$-0.981445\pi$
$239$		−	27.8481i		−	0.116519i	0.998301	−	0.0582596i	$-0.0185551\pi$
$240$	19.9461	−	20.1098i	0.0831089	−	0.0837909i
$241$	247.367			1.02642			0.513210	−	0.858263i	$-0.328456\pi$
$241$	247.367			1.02642			0.513210	+	0.858263i	$0.328456\pi$
$242$	17.3820	+	13.4857i	0.0718266	+	0.0557262i
$243$	84.4422			0.347499
$244$	98.8178	+	385.197i	0.404991	+	1.57868i
$245$	30.2619	−	8.93961i	0.123518	−	0.0364882i
$246$	21.8221	+	16.9305i	0.0887078	+	0.0688234i
$247$	−431.940			−1.74875
$248$	−8.59865	−	3.72410i	−0.0346720	−	0.0150165i
$249$	43.7022			0.175511
$250$	244.923	−	50.1276i	0.979692	−	0.200510i
$251$		−	68.7817i		−	0.274031i	−0.990569	−	0.137015i	$-0.956249\pi$
$251$		−	68.7817i		−	0.274031i	0.990569	−	0.137015i	$-0.0437509\pi$
$252$	−57.6343	−	224.662i	−0.228708	−	0.891515i
$253$		−	100.975i		−	0.399109i
$254$	−27.7517	−	21.5310i	−0.109259	−	0.0847677i
$255$	5.14569	+	17.4189i	0.0201792	+	0.0683095i
$256$	137.348	−	216.036i	0.536517	−	0.843889i
$257$		−	91.7718i		−	0.357089i	−0.983932	−	0.178544i	$-0.942861\pi$
$257$		−	91.7718i		−	0.357089i	0.983932	−	0.178544i	$-0.0571388\pi$
$258$	19.6064	+	15.2115i	0.0759939	+	0.0589594i
$259$		−	134.057i		−	0.517595i
$260$	−306.212	+	182.871i	−1.17774	+	0.703350i
$261$	200.957			0.769952
$262$	−305.922	+	394.309i	−1.16764	+	1.50500i
$263$	175.553			0.667502			0.333751	−	0.942661i	$-0.391685\pi$
$263$	175.553			0.667502			0.333751	+	0.942661i	$0.391685\pi$
$264$	8.62027	+	3.73346i	0.0326525	+	0.0141419i
$265$	85.8576	+	290.641i	0.323991	+	1.09676i
$266$	−194.016	+	250.071i	−0.729383	+	0.940117i
$267$	−2.47297			−0.00926205
$268$	65.7095	+	256.139i	0.245185	+	0.955743i
$269$	38.7131			0.143915			0.0719575	−	0.997408i	$-0.477075\pi$
$269$	38.7131			0.143915			0.0719575	+	0.997408i	$0.477075\pi$
$270$	−58.9430	−	23.0382i	−0.218307	−	0.0853266i
$271$			74.0663i			0.273307i	0.990619	+	0.136654i	$0.0436347\pi$
$271$			74.0663i			0.273307i	−0.990619	+	0.136654i	$0.956365\pi$
$272$	79.0269	+	143.889i	0.290540	+	0.529003i
$273$		−	41.2525i		−	0.151108i
$274$	213.599	−	275.313i	0.779560	−	1.00479i
$275$	45.0560	+	69.6057i	0.163840	+	0.253112i
$276$	−10.7140	−	41.7639i	−0.0388190	−	0.151318i
$277$			330.409i			1.19281i	0.802682	+	0.596407i	$0.203406\pi$
$277$			330.409i			1.19281i	−0.802682	+	0.596407i	$0.796594\pi$
$278$	226.272	−	291.647i	0.813929	−	1.04909i
$279$			10.3950i			0.0372579i
$280$	−31.6693	+	259.422i	−0.113104	+	0.926506i
$281$	247.162			0.879580			0.439790	−	0.898101i	$-0.355053\pi$
$281$	247.162			0.879580			0.439790	+	0.898101i	$0.355053\pi$
$282$	−10.2538	−	7.95535i	−0.0363610	−	0.0282105i
$283$	−280.371			−0.990712			−0.495356	−	0.868690i	$-0.664962\pi$
$283$	−280.371			−0.990712			−0.495356	+	0.868690i	$0.664962\pi$
$284$	−284.794	+	73.0605i	−1.00279	+	0.257255i
$285$	12.1475	+	41.1211i	0.0426228	+	0.144285i
$286$	−93.4610	−	72.5111i	−0.326787	−	0.253535i
$287$	−254.848			−0.887973
$288$	−280.470	−	44.5691i	−0.973853	−	0.154754i
$289$	183.729			0.635742
$290$	−210.903	−	82.4324i	−0.727250	−	0.284250i
$291$		−	40.2054i		−	0.138163i
$292$	45.3685	−	11.6388i	0.155371	−	0.0398587i
$293$		−	297.344i		−	1.01482i	−0.861703	−	0.507412i	$-0.830602\pi$
$293$		−	297.344i		−	1.01482i	0.861703	−	0.507412i	$-0.169398\pi$
$294$	3.53076	+	2.73931i	0.0120094	+	0.00931739i
$295$	35.2545	+	119.342i	0.119507	+	0.404548i
$296$	−150.623	−	65.2351i	−0.508860	−	0.220389i
$297$		−	20.9894i		−	0.0706713i
$298$	243.201	+	188.686i	0.816110	+	0.633173i
$299$			542.928i			1.81581i
$300$	26.0211	+	24.0088i	0.0867371	+	0.0800292i
$301$	−228.973			−0.760706
$302$	315.324	−	406.427i	1.04412	−	1.34578i
$303$	−13.3653			−0.0441098
$304$	186.560	+	339.681i	0.613685	+	1.11737i
$305$	−476.722	+	140.828i	−1.56302	+	0.461730i
$306$	111.631	−	143.884i	0.364809	−	0.470209i
$307$	−129.766			−0.422689			−0.211344	−	0.977412i	$-0.567784\pi$
$307$	−129.766			−0.422689			−0.211344	+	0.977412i	$0.567784\pi$
$308$	−83.9604	+	21.5391i	−0.272599	+	0.0699320i
$309$	−60.9946			−0.197393
$310$	4.26399	−	10.9094i	0.0137548	−	0.0351916i
$311$		−	334.287i		−	1.07488i	−0.843302	−	0.537440i	$-0.819392\pi$
$311$		−	334.287i		−	1.07488i	0.843302	−	0.537440i	$-0.180608\pi$
$312$	−46.3501	−	20.0744i	−0.148558	−	0.0643409i
$313$		−	111.216i		−	0.355323i	−0.984092	−	0.177662i	$-0.943147\pi$
$313$		−	111.216i		−	0.355323i	0.984092	−	0.177662i	$-0.0568533\pi$
$314$	357.155	−	460.344i	1.13744	−	1.46606i
$315$	278.043	−	82.1360i	0.882675	−	0.260749i
$316$	−355.072	+	91.0895i	−1.12364	+	0.288258i
$317$		−	491.831i		−	1.55152i	−0.631030	−	0.775759i	$-0.717367\pi$
$317$		−	491.831i		−	1.55152i	0.631030	−	0.775759i	$-0.282633\pi$
$318$	−26.3089	+	33.9100i	−0.0827323	+	0.106635i
$319$		−	75.1016i		−	0.235428i
$320$	276.068	+	161.823i	0.862711	+	0.505697i
$321$	−19.5185			−0.0608054
$322$	314.327	+	243.869i	0.976171	+	0.757356i
$323$	−248.514			−0.769393
$324$	77.1629	+	300.785i	0.238157	+	0.928349i
$325$	−242.261	−	374.261i	−0.745417	−	1.15157i
$326$	−74.3304	−	57.6688i	−0.228007	−	0.176898i
$327$	−41.7323			−0.127622
$328$	−124.015	+	286.340i	−0.378094	+	0.872989i
$329$	119.748			0.363977
$330$	−4.27471	+	10.9368i	−0.0129537	+	0.0331419i
$331$		−	305.401i		−	0.922662i	−0.887228	−	0.461331i	$-0.847372\pi$
$331$		−	305.401i		−	0.922662i	0.887228	−	0.461331i	$-0.152628\pi$
$332$	122.690	+	478.253i	0.369549	+	1.44052i
$333$			182.088i			0.546812i
$334$	−173.896	−	134.916i	−0.520646	−	0.403940i
$335$	−316.999	+	93.6441i	−0.946266	+	0.279534i
$336$	−32.4412	+	17.8174i	−0.0965513	+	0.0530281i
$337$		−	525.976i		−	1.56076i	−0.625306	−	0.780379i	$-0.715026\pi$
$337$		−	525.976i		−	1.56076i	0.625306	−	0.780379i	$-0.284974\pi$
$338$	235.477	+	182.693i	0.696678	+	0.540513i
$339$		−	5.29285i		−	0.0156131i
$340$	−176.177	+	105.214i	−0.518167	+	0.309452i
$341$	3.88479			0.0113924
$342$	263.530	−	339.669i	0.770556	−	0.993185i
$343$	−361.384			−1.05360
$344$	−111.423	+	257.267i	−0.323904	+	0.747869i
$345$	51.6872	−	15.2688i	0.149818	−	0.0442574i
$346$	9.07559	−	11.6977i	0.0262300	−	0.0338084i
$347$	663.664			1.91258			0.956288	−	0.292426i	$-0.0944625\pi$
$347$	663.664			1.91258			0.956288	+	0.292426i	$0.0944625\pi$
$348$	−7.96875	−	31.0626i	−0.0228987	−	0.0892604i
$349$	161.733			0.463419			0.231709	−	0.972785i	$-0.425568\pi$
$349$	161.733			0.463419			0.231709	+	0.972785i	$0.425568\pi$
$350$	−325.495	−	27.8518i	−0.929985	−	0.0795766i
$351$			112.857i			0.321531i
$352$	−16.6563	+	104.817i	−0.0473191	+	0.297775i
$353$			452.336i			1.28141i	0.767789	+	0.640703i	$0.221357\pi$
$353$			452.336i			1.28141i	−0.767789	+	0.640703i	$0.778643\pi$
$354$	−10.8028	+	13.9240i	−0.0305164	+	0.0393333i
$355$	−104.120	−	352.462i	−0.293296	−	0.992852i
$356$	−6.94264	−	27.0628i	−0.0195018	−	0.0760190i
$357$		−	23.7343i		−	0.0664828i
$358$	−362.236	+	466.893i	−1.01183	+	1.30417i
$359$			409.040i			1.13939i	0.821858	+	0.569693i	$0.192938\pi$
$359$			409.040i			1.13939i	−0.821858	+	0.569693i	$0.807062\pi$
$360$	43.0161	−	352.370i	0.119489	−	0.978806i
$361$	−225.671			−0.625127
$362$	−64.2101	−	49.8169i	−0.177376	−	0.137616i
$363$	−3.89456			−0.0107288
$364$	451.444	−	115.813i	1.24023	−	0.318167i
$365$	16.5867	+	56.1483i	0.0454429	+	0.153831i
$366$	−55.6207	−	43.1530i	−0.151969	−	0.117904i
$367$	183.633			0.500361			0.250181	−	0.968199i	$-0.419510\pi$
$367$	183.633			0.500361			0.250181	+	0.968199i	$0.419510\pi$
$368$	426.962	−	234.497i	1.16022	−	0.637220i
$369$	346.158			0.938098
$370$	74.6924	−	191.100i	0.201871	−	0.516486i
$371$		−	396.016i		−	1.06743i
$372$	1.60678	−	0.412201i	0.00431930	−	0.00110807i
$373$		−	444.907i		−	1.19278i	−0.802695	−	0.596390i	$-0.796601\pi$
$373$		−	444.907i		−	1.19278i	0.802695	−	0.596390i	$-0.203399\pi$
$374$	−53.7722	−	41.7188i	−0.143776	−	0.111548i
$375$	−28.8169	+	33.5888i	−0.0768451	+	0.0895702i
$376$	58.2723	−	134.546i	0.154979	−	0.357835i
$377$			403.812i			1.07112i
$378$	65.3385	+	50.6924i	0.172853	+	0.134107i
$379$		−	282.809i		−	0.746199i	−0.927791	−	0.373100i	$-0.878295\pi$
$379$		−	282.809i		−	0.746199i	0.927791	−	0.373100i	$-0.121705\pi$
$380$	−415.904	+	248.380i	−1.09448	+	0.653630i
$381$	6.21796			0.0163201
$382$	323.751	−	417.289i	0.847515	−	1.09238i
$383$	395.624			1.03296			0.516480	−	0.856299i	$-0.327242\pi$
$383$	395.624			1.03296			0.516480	+	0.856299i	$0.327242\pi$
$384$	4.23254	+	45.1204i	0.0110222	+	0.117501i
$385$	−30.6958	−	103.910i	−0.0797293	−	0.269896i
$386$	−373.756	+	481.741i	−0.968279	+	1.24803i
$387$	311.011			0.803647
$388$	439.985	−	112.873i	1.13398	−	0.290910i
$389$	408.322			1.04967			0.524836	−	0.851204i	$-0.324127\pi$
$389$	408.322			1.04967			0.524836	+	0.851204i	$0.324127\pi$
$390$	22.9846	−	58.8059i	0.0589349	−	0.150784i
$391$			312.370i			0.798900i
$392$	−20.0652	+	46.3290i	−0.0511868	+	0.118186i
$393$		−	88.3475i		−	0.224803i
$394$	−158.820	+	204.706i	−0.403096	+	0.519559i
$395$	−129.814	−	439.439i	−0.328642	−	1.11250i
$396$	114.043	−	29.2563i	0.287986	−	0.0738796i
$397$		−	632.825i		−	1.59402i	−0.603968	−	0.797009i	$-0.706414\pi$
$397$		−	632.825i		−	1.59402i	0.603968	−	0.797009i	$-0.293586\pi$
$398$	30.3589	−	39.1302i	0.0762786	−	0.0983170i
$399$		−	56.0301i		−	0.140426i
$400$	−189.686	+	352.163i	−0.474216	+	0.880408i
$401$	−147.429			−0.367654			−0.183827	−	0.982959i	$-0.558849\pi$
$401$	−147.429			−0.367654			−0.183827	+	0.982959i	$0.558849\pi$
$402$	−36.9853	−	28.6948i	−0.0920033	−	0.0713801i
$403$	−20.8880			−0.0518314
$404$	−37.5218	−	146.262i	−0.0928759	−	0.362035i
$405$	−372.253	+	109.967i	−0.919144	+	0.271522i
$406$	233.786	+	181.382i	0.575828	+	0.446753i
$407$	68.0499			0.167199
$408$	−26.6672	−	11.5497i	−0.0653609	−	0.0283080i
$409$	−301.796			−0.737887			−0.368944	−	0.929452i	$-0.620280\pi$
$409$	−301.796			−0.737887			−0.368944	+	0.929452i	$0.620280\pi$
$410$	−363.289	−	141.994i	−0.886071	−	0.346326i
$411$			61.6856i			0.150087i
$412$	−171.237	−	667.491i	−0.415624	−	1.62012i
$413$		−	162.610i		−	0.393730i
$414$	−426.948	−	331.244i	−1.03127	−	0.800107i
$415$	−591.888	+	174.849i	−1.42624	+	0.421322i
$416$	89.5589	−	563.587i	0.215286	−	1.35478i
$417$			65.3454i			0.156704i
$418$	−126.941	−	98.4862i	−0.303686	−	0.235613i
$419$			12.4944i			0.0298197i	0.999889	+	0.0149098i	$0.00474612\pi$
$419$			12.4944i			0.0298197i	−0.999889	+	0.0149098i	$0.995254\pi$
$420$	−23.7215	−	39.7209i	−0.0564798	−	0.0945736i
$421$	−763.149			−1.81270			−0.906352	−	0.422523i	$-0.861145\pi$
$421$	−763.149			−1.81270			−0.906352	+	0.422523i	$0.861145\pi$
$422$	−289.753	+	373.468i	−0.686618	+	0.884996i
$423$	−162.653			−0.384523
$424$	−444.952	−	192.710i	−1.04942	−	0.454505i
$425$	−139.383	−	215.329i	−0.327960	−	0.506656i
$426$	31.9050	−	41.1229i	0.0748943	−	0.0965327i
$427$	649.564			1.52123
$428$	−54.7966	−	213.600i	−0.128029	−	0.499065i
$429$	20.9406			0.0488125
$430$	−326.403	−	127.576i	−0.759077	−	0.296689i
$431$			437.127i			1.01421i	0.861883	+	0.507107i	$0.169285\pi$
$431$			437.127i			1.01421i	−0.861883	+	0.507107i	$0.830715\pi$
$432$	88.7517	−	48.7444i	0.205444	−	0.112834i
$433$			454.224i			1.04902i	0.851406	+	0.524508i	$0.175751\pi$
$433$			454.224i			1.04902i	−0.851406	+	0.524508i	$0.824249\pi$
$434$	−9.38235	+	12.0931i	−0.0216183	+	0.0278643i
$435$	38.4433	−	11.3565i	0.0883754	−	0.0261068i
$436$	−117.160	−	456.695i	−0.268715	−	1.04747i
$437$			737.416i			1.68745i
$438$	−5.08255	+	6.55100i	−0.0116040	+	0.0149566i
$439$			348.609i			0.794098i	0.917797	+	0.397049i	$0.129966\pi$
$439$			348.609i			0.794098i	−0.917797	+	0.397049i	$0.870034\pi$
$440$	−131.687	−	16.0759i	−0.299289	−	0.0365362i
$441$	56.0074			0.127001
$442$	289.126	+	224.317i	0.654132	+	0.507504i
$443$	−166.492			−0.375828			−0.187914	−	0.982185i	$-0.560173\pi$
$443$	−166.492			−0.375828			−0.187914	+	0.982185i	$0.560173\pi$
$444$	28.1460	−	7.22052i	0.0633919	−	0.0162624i
$445$	33.4931	−	9.89411i	0.0752653	−	0.0222340i
$446$	678.072	+	526.078i	1.52034	+	1.17955i
$447$	−54.4907			−0.121903
$448$	−286.060	−	304.998i	−0.638527	−	0.680799i
$449$	−266.939			−0.594519			−0.297259	−	0.954797i	$-0.596073\pi$
$449$	−266.939			−0.594519			−0.297259	+	0.954797i	$0.596073\pi$
$450$	442.117	+	37.8309i	0.982482	+	0.0840686i
$451$		−	129.366i		−	0.286842i
$452$	57.9220	−	14.8592i	0.128146	−	0.0328744i
$453$			91.0626i			0.201021i
$454$	166.476	+	129.159i	0.366687	+	0.284492i
$455$	165.047	+	558.710i	0.362742	+	1.22794i
$456$	−62.9538	−	27.2655i	−0.138056	−	0.0597927i
$457$		−	103.640i		−	0.226784i	−0.993550	−	0.113392i	$-0.963828\pi$
$457$		−	103.640i		−	0.226784i	0.993550	−	0.113392i	$-0.0361716\pi$
$458$	−652.004	−	505.853i	−1.42359	−	1.10448i
$459$			64.9317i			0.141463i
$460$	312.201	+	522.771i	0.678698	+	1.13646i
$461$	149.998			0.325376			0.162688	−	0.986678i	$-0.447984\pi$
$461$	149.998			0.325376			0.162688	+	0.986678i	$0.447984\pi$
$462$	9.40594	−	12.1235i	0.0203592	−	0.0262413i
$463$	297.906			0.643426			0.321713	−	0.946837i	$-0.395741\pi$
$463$	297.906			0.643426			0.321713	+	0.946837i	$0.395741\pi$
$464$	317.561	−	174.411i	0.684398	−	0.375886i
$465$	0.587437	+	1.98856i	0.00126331	+	0.00427648i
$466$	−361.552	+	466.012i	−0.775863	+	1.00003i
$467$	−189.087			−0.404896			−0.202448	−	0.979293i	$-0.564890\pi$
$467$	−189.087			−0.404896			−0.202448	+	0.979293i	$0.564890\pi$
$468$	−613.193	+	157.308i	−1.31024	+	0.336127i
$469$	431.931			0.920961
$470$	170.703	+	66.7201i	0.363198	+	0.141958i
$471$			103.143i			0.218987i
$472$	−182.704	−	79.1298i	−0.387085	−	0.167648i
$473$		−	116.231i		−	0.245731i
$474$	39.7781	−	51.2708i	0.0839200	−	0.108166i
$475$	−329.044	−	508.330i	−0.692724	−	1.07017i
$476$	259.736	−	66.6321i	0.545663	−	0.139983i
$477$			537.905i			1.12768i
$478$	−34.1411	+	44.0051i	−0.0714248	+	0.0920609i
$479$		−	45.7640i		−	0.0955408i	−0.998858	−	0.0477704i	$-0.984788\pi$
$479$		−	45.7640i		−	0.0955408i	0.998858	−	0.0477704i	$-0.0152116\pi$
$480$	−56.1727	+	7.32373i	−0.117026	+	0.0152578i
$481$	−365.896			−0.760698
$482$	−390.886	−	303.266i	−0.810967	−	0.629183i
$483$	−70.4270			−0.145812
$484$	−10.9336	−	42.6199i	−0.0225902	−	0.0880576i
$485$	160.858	+	544.529i	0.331666	+	1.12274i
$486$	−133.434	−	103.524i	−0.274556	−	0.213012i
$487$	−448.388			−0.920715			−0.460357	−	0.887734i	$-0.652279\pi$
$487$	−448.388			−0.920715			−0.460357	+	0.887734i	$0.652279\pi$
$488$	316.092	−	729.831i	0.647729	−	1.49556i
$489$	16.6542			0.0340577
$490$	−58.7792	−	22.9741i	−0.119957	−	0.0468860i
$491$		−	11.8893i		−	0.0242145i	−0.999927	−	0.0121072i	$-0.996146\pi$
$491$		−	11.8893i		−	0.0242145i	0.999927	−	0.0121072i	$-0.00385394\pi$
$492$	−13.7265	−	53.5068i	−0.0278995	−	0.108754i
$493$			232.331i			0.471259i
$494$	682.545	+	529.548i	1.38167	+	1.07196i
$495$	41.6938	+	141.140i	0.0842299	+	0.285131i
$496$	9.02180	+	16.4265i	0.0181891	+	0.0331180i
$497$			480.252i			0.966301i
$498$	−69.0575	−	53.5778i	−0.138670	−	0.107586i
$499$		−	857.568i		−	1.71857i	−0.511495	−	0.859286i	$-0.670908\pi$
$499$		−	857.568i		−	1.71857i	0.511495	−	0.859286i	$-0.329092\pi$
$500$	−448.479	−	221.059i	−0.896957	−	0.442117i
$501$	38.9625			0.0777694
$502$	−84.3247	+	108.688i	−0.167977	+	0.216509i
$503$	737.996			1.46719			0.733595	−	0.679587i	$-0.237841\pi$
$503$	737.996			1.46719			0.733595	+	0.679587i	$0.237841\pi$
$504$	−184.357	+	425.665i	−0.365788	+	0.844574i
$505$	181.015	−	53.4732i	0.358445	−	0.105888i
$506$	−123.792	+	159.558i	−0.244649	+	0.315333i
$507$	−52.7602			−0.104064
$508$	17.4564	+	68.0459i	0.0343629	+	0.133949i
$509$	−130.675			−0.256729			−0.128365	−	0.991727i	$-0.540973\pi$
$509$	−130.675			−0.256729			−0.128365	+	0.991727i	$0.540973\pi$
$510$	13.2240	−	33.8336i	0.0259295	−	0.0663404i
$511$		−	76.5055i		−	0.149717i
$512$	−481.890	+	172.990i	−0.941192	+	0.337872i
$513$			153.285i			0.298802i
$514$	−112.510	+	145.016i	−0.218891	+	0.282133i
$515$	826.091	−	244.034i	1.60406	−	0.473852i
$516$	−12.3328	−	48.0740i	−0.0239008	−	0.0931667i
$517$			60.7866i			0.117576i
$518$	−164.351	+	211.835i	−0.317279	+	0.408948i
$519$			2.62095i			0.00505000i
$520$	708.067	+	86.4382i	1.36167	+	0.166227i
$521$	−136.275			−0.261565			−0.130782	−	0.991411i	$-0.541749\pi$
$521$	−136.275			−0.261565			−0.130782	+	0.991411i	$0.541749\pi$
$522$	−317.550	−	246.369i	−0.608333	−	0.471971i
$523$	370.734			0.708861			0.354431	−	0.935082i	$-0.384675\pi$
$523$	370.734			0.708861			0.354431	+	0.935082i	$0.384675\pi$
$524$	966.827	−	248.028i	1.84509	−	0.473336i
$525$	48.5481	−	31.4254i	0.0924726	−	0.0598578i
$526$	−277.406	−	215.224i	−0.527389	−	0.409171i
$527$	−12.0178			−0.0228042
$528$	−9.04448	−	16.4678i	−0.0171297	−	0.0311890i
$529$	397.896			0.752167
$530$	220.648	−	564.526i	0.416317	−	1.06514i
$531$			220.872i			0.415955i
$532$	613.162	−	157.300i	1.15256	−	0.295676i
$533$			695.585i			1.30504i
$534$	3.90774	+	3.03180i	0.00731787	+	0.00567752i
$535$	264.353	−	78.0918i	0.494117	−	0.145966i
$536$	210.187	−	485.305i	0.392140	−	0.905420i
$537$		−	104.610i		−	0.194805i
$538$	−61.1739	−	47.4614i	−0.113706	−	0.0882182i
$539$		−	20.9310i		−	0.0388331i
$540$	64.8966	+	108.667i	0.120179	+	0.201236i
$541$	441.525			0.816127			0.408064	−	0.912953i	$-0.366204\pi$
$541$	441.525			0.816127			0.408064	+	0.912953i	$0.366204\pi$
$542$	90.8034	−	117.038i	0.167534	−	0.215938i
$543$	14.3867			0.0264948
$544$	51.5271	−	324.256i	0.0947190	−	0.596059i
$545$	565.209	−	166.967i	1.03708	−	0.306362i
$546$	−50.5746	+	65.1866i	−0.0926274	+	0.119389i
$547$	−588.923			−1.07664			−0.538321	−	0.842740i	$-0.680941\pi$
$547$	−588.923			−1.07664			−0.538321	+	0.842740i	$0.680941\pi$
$548$	−675.053	+	173.177i	−1.23185	+	0.316016i
$549$	−882.296			−1.60710
$550$	14.1381	−	165.227i	0.0257057	−	0.300414i
$551$			548.467i			0.995402i
$552$	−34.2713	+	79.1298i	−0.0620858	+	0.143351i
$553$			598.763i			1.08275i
$554$	405.074	−	522.108i	0.731180	−	0.942433i
$555$	10.2901	+	34.8336i	0.0185408	+	0.0627633i
$556$	−715.104	+	183.451i	−1.28616	+	0.329949i
$557$		−	234.944i		−	0.421802i	−0.977507	−	0.210901i	$-0.932360\pi$
$557$		−	234.944i		−	0.421802i	0.977507	−	0.210901i	$-0.0676398\pi$
$558$	12.7440	−	16.4259i	0.0228386	−	0.0294372i
$559$			624.959i			1.11799i
$560$	368.088	−	371.108i	0.657300	−	0.662693i
$561$	12.0480			0.0214760
$562$	−390.562	−	303.015i	−0.694950	−	0.539172i
$563$	1089.05			1.93437			0.967185	−	0.254075i	$-0.0817710\pi$
$563$	1089.05			1.93437			0.967185	+	0.254075i	$0.0817710\pi$
$564$	6.44984	+	25.1418i	0.0114359	+	0.0445777i
$565$	21.1762	+	71.6846i	0.0374800	+	0.126875i
$566$	443.039	+	343.729i	0.782754	+	0.607294i
$567$	507.218			0.894564
$568$	539.597	+	233.701i	0.949995	+	0.411446i
$569$	8.71234			0.0153117			0.00765583	−	0.999971i	$-0.497563\pi$
$569$	8.71234			0.0153117			0.00765583	+	0.999971i	$0.497563\pi$
$570$	31.2182	−	79.8715i	0.0547688	−	0.140125i
$571$			158.034i			0.276768i	0.990379	+	0.138384i	$0.0441907\pi$
$571$			158.034i			0.276768i	−0.990379	+	0.138384i	$0.955809\pi$
$572$	58.7888	+	229.162i	0.102778	+	0.400633i
$573$			93.4963i			0.163170i
$574$	402.707	+	312.438i	0.701581	+	0.544317i
$575$	−638.946	+	413.592i	−1.11121	+	0.719290i
$576$	388.553	+	414.276i	0.674571	+	0.719230i
$577$		−	515.203i		−	0.892900i	−0.894809	−	0.446450i	$-0.852688\pi$
$577$		−	515.203i		−	0.892900i	0.894809	−	0.446450i	$-0.147312\pi$
$578$	−290.326	−	225.248i	−0.502295	−	0.389702i
$579$		−	107.937i		−	0.186420i
$580$	232.205	+	388.820i	0.400353	+	0.670379i
$581$	806.484			1.38810
$582$	−49.2908	+	63.5319i	−0.0846921	+	0.109161i
$583$	201.025			0.344812
$584$	−85.9594	−	37.2293i	−0.147191	−	0.0637488i
$585$	−224.183	−	758.891i	−0.383218	−	1.29725i
$586$	−364.536	+	469.858i	−0.622075	+	0.801805i
$587$	−853.172			−1.45345			−0.726723	−	0.686931i	$-0.758957\pi$
$587$	−853.172			−1.45345			−0.726723	+	0.686931i	$0.758957\pi$
$588$	−2.22091	−	8.65724i	−0.00377707	−	0.0147232i
$589$	−28.3706			−0.0481674
$590$	90.6014	−	231.803i	0.153562	−	0.392886i
$591$		−	45.8658i		−	0.0776070i
$592$	158.035	+	287.743i	0.266951	+	0.486053i
$593$			907.797i			1.53086i	0.643522	+	0.765428i	$0.277472\pi$
$593$			907.797i			1.53086i	−0.643522	+	0.765428i	$0.722528\pi$
$594$	−25.7325	+	33.1671i	−0.0433206	+	0.0558368i
$595$	94.9590	+	321.450i	0.159595	+	0.540253i
$596$	−152.978	−	596.316i	−0.256674	−	1.00053i
$597$			8.76737i			0.0146857i
$598$	665.616	−	857.926i	1.11307	−	1.43466i
$599$		−	519.661i		−	0.867548i	−0.901022	−	0.433774i	$-0.857182\pi$
$599$		−	519.661i		−	0.867548i	0.901022	−	0.433774i	$-0.142818\pi$
$600$	−11.6840	−	69.8395i	−0.0194734	−	0.116399i
$601$	138.114			0.229807			0.114904	−	0.993377i	$-0.463344\pi$
$601$	138.114			0.229807			0.114904	+	0.993377i	$0.463344\pi$
$602$	361.819	+	280.715i	0.601028	+	0.466304i
$603$	−586.688			−0.972948
$604$	−996.539	+	255.650i	−1.64990	+	0.423262i
$605$	52.7466	−	15.5818i	0.0871845	−	0.0257550i
$606$	21.1196	+	16.3855i	0.0348508	+	0.0270388i
$607$	177.510			0.292438			0.146219	−	0.989252i	$-0.453290\pi$
$607$	177.510			0.292438			0.146219	+	0.989252i	$0.453290\pi$
$608$	121.641	−	765.477i	0.200067	−	1.25901i
$609$	−52.3814			−0.0860121
$610$	925.960	+	361.917i	1.51797	+	0.593306i
$611$		−	326.842i		−	0.534930i
$612$	−352.797	+	90.5058i	−0.576465	+	0.147885i
$613$		−	13.7473i		−	0.0224263i	−0.999937	−	0.0112132i	$-0.996431\pi$
$613$		−	13.7473i		−	0.0224263i	0.999937	−	0.0112132i	$-0.00356934\pi$
$614$	205.053	+	159.089i	0.333963	+	0.259103i
$615$	66.2203	−	19.5620i	0.107675	−	0.0318081i
$616$	159.079	+	68.8977i	0.258246	+	0.111847i
$617$		−	434.502i		−	0.704216i	−0.935959	−	0.352108i	$-0.885465\pi$
$617$		−	434.502i		−	0.704216i	0.935959	−	0.352108i	$-0.114535\pi$
$618$	96.3827	+	74.7779i	0.155959	+	0.121000i
$619$			1108.67i			1.79106i	0.445000	+	0.895530i	$0.353204\pi$
$619$			1108.67i			1.79106i	−0.445000	+	0.895530i	$0.646796\pi$
$620$	−20.1125	+	12.0113i	−0.0324396	+	0.0193731i
$621$	192.672			0.310261
$622$	−409.828	+	528.236i	−0.658888	+	0.849254i
$623$	−45.6364			−0.0732526
$624$	48.6310	+	88.5453i	0.0779344	+	0.141900i
$625$	255.901	−	570.210i	0.409442	−	0.912336i
$626$	−136.348	+	175.742i	−0.217809	+	0.280738i
$627$	28.4419			0.0453619
$628$	−1128.74	+	289.565i	−1.79736	+	0.461091i
$629$	−210.516			−0.334683
$630$	−540.056	−	211.084i	−0.857231	−	0.335053i
$631$		−	1095.05i		−	1.73543i	−0.497066	−	0.867713i	$-0.665589\pi$
$631$		−	1095.05i		−	1.73543i	0.497066	−	0.867713i	$-0.334411\pi$
$632$	672.753	+	291.371i	1.06448	+	0.461030i
$633$		−	83.6781i		−	0.132193i
$634$	−602.973	+	777.184i	−0.951061	+	1.22584i
$635$	−84.2140	+	24.8775i	−0.132620	+	0.0391771i
$636$	83.1457	−	21.3301i	0.130732	−	0.0335378i
$637$			112.544i			0.176678i
$638$	−92.0728	+	118.674i	−0.144315	+	0.186010i
$639$		−	652.322i		−	1.02085i
$640$	−237.847	−	594.162i	−0.371636	−	0.928379i
$641$	999.847			1.55982			0.779912	−	0.625889i	$-0.215264\pi$
$641$	999.847			1.55982			0.779912	+	0.625889i	$0.215264\pi$
$642$	30.8429	+	23.9292i	0.0480418	+	0.0372729i
$643$	527.808			0.820853			0.410426	−	0.911894i	$-0.365380\pi$
$643$	527.808			0.820853			0.410426	+	0.911894i	$0.365380\pi$
$644$	−197.718	−	770.715i	−0.307015	−	1.19676i
$645$	59.4967	−	17.5758i	0.0922429	−	0.0272493i
$646$	392.698	+	304.672i	0.607891	+	0.471628i
$647$	−952.327			−1.47191			−0.735956	−	0.677029i	$-0.763267\pi$
$647$	−952.327			−1.47191			−0.735956	+	0.677029i	$0.763267\pi$
$648$	246.823	−	569.896i	0.380900	−	0.879468i
$649$	82.5441			0.127187
$650$	−76.0189	+	888.408i	−0.116952	+	1.36678i
$651$		−	2.70954i		−	0.00416212i
$652$	46.7553	+	182.255i	0.0717106	+	0.279532i
$653$			201.502i			0.308578i	0.988026	+	0.154289i	$0.0493088\pi$
$653$			201.502i			0.308578i	−0.988026	+	0.154289i	$0.950691\pi$
$654$	65.9448	+	51.1628i	0.100833	+	0.0782306i
$655$	353.470	+	1196.55i	0.539650	+	1.82679i
$656$	547.013	−	300.431i	0.833861	−	0.457975i
$657$			103.917i			0.158169i
$658$	−189.225	−	146.809i	−0.287576	−	0.223114i
$659$			651.891i			0.989212i	0.869117	+	0.494606i	$0.164688\pi$
$659$			651.891i			0.989212i	−0.869117	+	0.494606i	$0.835312\pi$
$660$	20.1631	−	12.0415i	0.0305502	−	0.0182447i
$661$	−558.690			−0.845220			−0.422610	−	0.906312i	$-0.638886\pi$
$661$	−558.690			−0.845220			−0.422610	+	0.906312i	$0.638886\pi$
$662$	−374.414	+	482.590i	−0.565581	+	0.728988i
$663$	−64.7807			−0.0977084
$664$	392.453	−	906.143i	0.591044	−	1.36467i
$665$	224.171	+	758.853i	0.337099	+	1.14113i
$666$	223.236	−	287.733i	0.335189	−	0.432032i
$667$	689.396			1.03358
$668$	109.384	+	426.384i	0.163748	+	0.638299i
$669$	−151.927			−0.227095
$670$	615.723	+	240.658i	0.918989	+	0.359192i
$671$			329.731i			0.491402i
$672$	73.1069	+	11.6173i	0.108790	+	0.0172877i
$673$		−	455.656i		−	0.677052i	−0.940957	−	0.338526i	$-0.890072\pi$
$673$		−	455.656i		−	0.677052i	0.940957	−	0.338526i	$-0.109928\pi$
$674$	−644.833	+	831.139i	−0.956726	+	1.23314i
$675$	−132.816	+	85.9725i	−0.196765	+	0.127367i
$676$	−148.120	−	577.379i	−0.219112	−	0.854110i
$677$		−	751.415i		−	1.10992i	−0.831877	−	0.554959i	$-0.812734\pi$
$677$		−	751.415i		−	1.10992i	0.831877	−	0.554959i	$-0.187266\pi$
$678$	−6.48890	+	8.36367i	−0.00957065	+	0.0123358i
$679$		−	741.954i		−	1.09272i
$680$	407.381	+	49.7317i	0.599090	+	0.0731348i
$681$	−37.3000			−0.0547724
$682$	−6.13869	−	4.76266i	−0.00900101	−	0.00698337i
$683$	792.308			1.16004			0.580020	−	0.814602i	$-0.303045\pi$
$683$	792.308			1.16004			0.580020	+	0.814602i	$0.303045\pi$
$684$	−832.852	+	213.659i	−1.21762	+	0.312366i
$685$	−246.798	−	835.450i	−0.360290	−	1.21963i
$686$	571.054	+	443.048i	0.832440	+	0.645843i
$687$	146.086			0.212643
$688$	491.472	−	269.927i	0.714349	−	0.392336i
$689$	−1080.89			−1.56878
$690$	−100.395	−	39.2397i	−0.145499	−	0.0568692i
$691$			306.154i			0.443059i	0.975154	+	0.221530i	$0.0711050\pi$
$691$			306.154i			0.443059i	−0.975154	+	0.221530i	$0.928895\pi$
$692$	−28.6822	+	7.35809i	−0.0414483	+	0.0106331i
$693$		−	192.312i		−	0.277506i
$694$	−1048.71	−	813.636i	−1.51111	−	1.17239i
$695$	−261.441	−	885.017i	−0.376174	−	1.27341i
$696$	−25.4899	+	58.8542i	−0.0366235	+	0.0845606i
$697$			400.200i			0.574175i
$698$	−255.568	−	198.281i	−0.366144	−	0.284070i
$699$		−	104.413i		−	0.149375i
$700$	480.196	+	443.060i	0.685995	+	0.632943i
$701$	58.5372			0.0835053			0.0417526	−	0.999128i	$-0.486706\pi$
$701$	58.5372			0.0835053			0.0417526	+	0.999128i	$0.486706\pi$
$702$	138.360	−	178.335i	0.197094	−	0.254039i
$703$	−496.968			−0.706925
$704$	154.823	−	145.210i	0.219919	−	0.206264i
$705$	−31.1157	+	9.19182i	−0.0441357	+	0.0130380i
$706$	554.553	−	714.775i	0.785486	−	1.01243i
$707$	−246.644			−0.348860
$708$	34.1409	−	8.75845i	0.0482216	−	0.0123707i
$709$	47.3009			0.0667150			0.0333575	−	0.999443i	$-0.489380\pi$
$709$	47.3009			0.0667150			0.0333575	+	0.999443i	$0.489380\pi$
$710$	−267.581	+	684.605i	−0.376875	+	0.964232i
$711$		−	813.294i		−	1.14387i
$712$	−22.2077	+	51.2757i	−0.0311905	+	0.0720164i
$713$			35.6605i			0.0500147i
$714$	−29.0977	+	37.5046i	−0.0407531	+	0.0525275i
$715$	−283.612	+	83.7813i	−0.396660	+	0.117177i
$716$	1144.80	−	293.685i	1.59888	−	0.410174i
$717$		−	9.85964i		−	0.0137512i
$718$	501.473	−	646.358i	0.698430	−	0.900220i
$719$		−	1129.40i		−	1.57079i	−0.618994	−	0.785396i	$-0.712459\pi$
$719$		−	1129.40i		−	1.57079i	0.618994	−	0.785396i	$-0.287541\pi$
$720$	−499.970	+	504.073i	−0.694403	+	0.700101i
$721$	−1125.60			−1.56116
$722$	356.601	+	276.667i	0.493908	+	0.383195i
$723$	87.5806			0.121135
$724$	40.3894	+	157.440i	0.0557864	+	0.217458i
$725$	−475.227	+	307.616i	−0.655486	+	0.424298i
$726$	6.15412	+	4.77463i	0.00847675	+	0.00657663i
$727$	−310.672			−0.427335			−0.213667	−	0.976906i	$-0.568541\pi$
$727$	−310.672			−0.427335			−0.213667	+	0.976906i	$0.568541\pi$
$728$	−855.349	−	370.454i	−1.17493	−	0.508866i
$729$	−668.784			−0.917399
$730$	42.6265	−	109.060i	0.0583924	−	0.149397i
$731$			359.566i			0.491882i
$732$	34.9865	+	136.379i	0.0477958	+	0.186311i
$733$			1164.11i			1.58815i	0.607823	+	0.794073i	$0.292043\pi$
$733$			1164.11i			1.58815i	−0.607823	+	0.794073i	$0.707957\pi$
$734$	−290.173	−	225.129i	−0.395332	−	0.306715i
$735$	10.7143	−	3.16508i	0.0145772	−	0.00430623i
$736$	−962.167	−	152.897i	−1.30729	−	0.207740i
$737$			219.256i			0.297499i
$738$	−546.994	−	424.382i	−0.741184	−	0.575043i
$739$		−	52.7151i		−	0.0713330i	−0.999364	−	0.0356665i	$-0.988645\pi$
$739$		−	52.7151i		−	0.0713330i	0.999364	−	0.0356665i	$-0.0113554\pi$
$740$	−352.311	+	210.402i	−0.476097	+	0.284327i
$741$	−152.929			−0.206382
$742$	−485.506	+	625.779i	−0.654321	+	0.843367i
$743$	208.365			0.280437			0.140219	−	0.990121i	$-0.455219\pi$
$743$	208.365			0.280437			0.140219	+	0.990121i	$0.455219\pi$
$744$	−3.04436	−	1.31852i	−0.00409188	−	0.00177221i
$745$	738.005	−	218.012i	0.990610	−	0.292634i
$746$	−545.445	+	703.035i	−0.731159	+	0.942406i
$747$	−1095.44			−1.46645
$748$	33.8237	+	131.847i	0.0452189	+	0.176266i
$749$	−360.197			−0.480903
$750$	86.7151	−	17.7477i	0.115620	−	0.0236636i
$751$			534.169i			0.711277i	0.934624	+	0.355639i	$0.115737\pi$
$751$			534.169i			0.711277i	−0.934624	+	0.355639i	$0.884263\pi$
$752$	−257.031	+	141.167i	−0.341797	+	0.187722i
$753$		−	24.3522i		−	0.0323402i
$754$	495.064	−	638.098i	0.656583	−	0.846283i
$755$	−364.333	−	1233.32i	−0.482561	−	1.63354i
$756$	−41.0992	−	160.207i	−0.0543640	−	0.211914i
$757$		−	708.766i		−	0.936283i	−0.883654	−	0.468141i	$-0.844924\pi$
$757$		−	708.766i		−	0.936283i	0.883654	−	0.468141i	$-0.155076\pi$
$758$	−346.718	+	446.891i	−0.457411	+	0.589566i
$759$		−	35.7501i		−	0.0471016i
$760$	961.712	+	117.402i	1.26541	+	0.154477i
$761$	−118.261			−0.155402			−0.0777009	−	0.996977i	$-0.524758\pi$
$761$	−118.261			−0.155402			−0.0777009	+	0.996977i	$0.524758\pi$
$762$	−9.82552	−	7.62306i	−0.0128944	−	0.0100040i
$763$	−770.132			−1.00935
$764$	−1023.17	+	262.483i	−1.33923	+	0.343564i
$765$	−128.982	−	436.623i	−0.168604	−	0.570749i
$766$	−625.158	−	485.025i	−0.816134	−	0.633192i
$767$	−443.829			−0.578656
$768$	48.6283	−	76.4876i	0.0633181	−	0.0995932i
$769$	145.212			0.188832			0.0944158	−	0.995533i	$-0.469902\pi$
$769$	145.212			0.188832			0.0944158	+	0.995533i	$0.469902\pi$
$770$	−78.8859	+	201.829i	−0.102449	+	0.262116i
$771$		−	32.4919i		−	0.0421425i
$772$	1181.21	−	303.025i	1.53006	−	0.392519i
$773$		−	31.4250i		−	0.0406533i	−0.999793	−	0.0203266i	$-0.993529\pi$
$773$		−	31.4250i		−	0.0406533i	0.999793	−	0.0203266i	$-0.00647062\pi$
$774$	−491.455	−	381.292i	−0.634955	−	0.492626i

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.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.58018 - 1.22598i) q^{2} +0.354051 q^{3} +(0.993967 + 3.87454i) q^{4} +(-4.79515 + 1.41652i) q^{5} +(-0.559466 - 0.434058i) q^{6} +6.53369 q^{7} +(3.17944 - 7.34106i) q^{8} -8.87465 q^{9} +(9.31385 + 3.64037i) q^{10} +3.31662i q^{11} +(0.351915 + 1.37178i) q^{12} -17.8331i q^{13} +(-10.3244 - 8.01014i) q^{14} +(-1.69773 + 0.501522i) q^{15} +(-14.0241 + 7.70232i) q^{16} -10.2601i q^{17} +(14.0236 + 10.8801i) q^{18} -24.2213i q^{19} +(-10.2546 - 17.1710i) q^{20} +2.31326 q^{21} +(4.06610 - 5.24088i) q^{22} -30.4450 q^{23} +(1.12568 - 2.59911i) q^{24} +(20.9869 - 13.5849i) q^{25} +(-21.8629 + 28.1796i) q^{26} -6.32853 q^{27} +(6.49427 + 25.3150i) q^{28} -22.6440 q^{29} +(3.29757 + 1.28887i) q^{30} -1.17131i q^{31} +(31.6035 + 5.02207i) q^{32} +1.17425i q^{33} +(-12.5787 + 16.2129i) q^{34} +(-31.3300 + 9.25513i) q^{35} +(-8.82111 - 34.3851i) q^{36} -20.5178i q^{37} +(-29.6947 + 38.2741i) q^{38} -6.31382i q^{39} +(-4.84707 + 39.7052i) q^{40} -39.0053 q^{41} +(-3.65537 - 2.83600i) q^{42} -35.0449 q^{43} +(-12.8504 + 3.29662i) q^{44} +(42.5553 - 12.5712i) q^{45} +(48.1087 + 37.3248i) q^{46} +18.3279 q^{47} +(-4.96523 + 2.72701i) q^{48} -6.31094 q^{49} +(-49.8180 - 4.26280i) q^{50} -3.63261i q^{51} +(69.0949 - 17.7255i) q^{52} -60.6114i q^{53} +(10.0003 + 7.75863i) q^{54} +(-4.69808 - 15.9037i) q^{55} +(20.7734 - 47.9642i) q^{56} -8.57557i q^{57} +(35.7817 + 27.7610i) q^{58} -24.8880i q^{59} +(-3.63065 - 6.07941i) q^{60} +99.4176 q^{61} +(-1.43600 + 1.85088i) q^{62} -57.9842 q^{63} +(-43.7824 - 46.6809i) q^{64} +(25.2610 + 85.5123i) q^{65} +(1.43961 - 1.85554i) q^{66} +66.1083 q^{67} +(39.7533 - 10.1982i) q^{68} -10.7791 q^{69} +(60.8538 + 23.7850i) q^{70} +73.5040i q^{71} +(-28.2164 + 65.1493i) q^{72} -11.7094i q^{73} +(-25.1543 + 32.4219i) q^{74} +(7.43043 - 4.80974i) q^{75} +(93.8463 - 24.0752i) q^{76} +21.6698i q^{77} +(-7.74059 + 9.97700i) q^{78} +91.6424i q^{79} +(56.3369 - 56.7992i) q^{80} +77.6312 q^{81} +(61.6356 + 47.8195i) q^{82} +123.435 q^{83} +(2.29930 + 8.96280i) q^{84} +(14.5337 + 49.1989i) q^{85} +(55.3774 + 42.9642i) q^{86} -8.01712 q^{87} +(24.3475 + 10.5450i) q^{88} -6.98478 q^{89} +(-82.6571 - 32.3070i) q^{90} -116.516i q^{91} +(-30.2613 - 117.960i) q^{92} -0.414703i q^{93} +(-28.9614 - 22.4695i) q^{94} +(34.3101 + 116.145i) q^{95} +(11.1892 + 1.77807i) q^{96} -113.558i q^{97} +(9.97246 + 7.73706i) q^{98} -29.4339i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 4 q^{4} + 4 q^{5} + 12 q^{6} + 180 q^{9} - 18 q^{10} - 56 q^{14} - 40 q^{16} + 84 q^{20} - 16 q^{21} + 104 q^{24} - 60 q^{25} + 28 q^{26} - 88 q^{29} - 166 q^{30} - 152 q^{34} - 248 q^{36} + 132 q^{40}+ \cdots + 216 q^{96}+O(q^{100}) \) 60 * q - 4 * q^4 + 4 * q^5 + 12 * q^6 + 180 * q^9 - 18 * q^10 - 56 * q^14 - 40 * q^16 + 84 * q^20 - 16 * q^21 + 104 * q^24 - 60 * q^25 + 28 * q^26 - 88 * q^29 - 166 * q^30 - 152 * q^34 - 248 * q^36 + 132 * q^40 - 200 * q^41 + 44 * q^44 + 84 * q^45 + 260 * q^46 + 420 * q^49 - 198 * q^50 - 116 * q^54 - 128 * q^56 - 4 * q^60 + 136 * q^61 + 116 * q^64 - 288 * q^65 - 544 * q^69 + 152 * q^70 + 436 * q^74 - 72 * q^76 - 176 * q^80 + 300 * q^81 - 136 * q^84 + 176 * q^85 - 348 * q^86 + 760 * q^89 + 40 * q^90 + 112 * q^94 + 216 * q^96

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