LMFDB - Embedded newform 220.3.h.a.199.19

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			199.19
Character	$\chi$	$=$	220.199
Dual form			220.3.h.a.199.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.02937 - 1.71476i) q^{2} -4.39883 q^{3} +(-1.88080 + 3.53024i) q^{4} +(0.646763 + 4.95799i) q^{5} +(4.52802 + 7.54293i) q^{6} -6.76347 q^{7} +(7.98955 - 0.408800i) q^{8} +10.3497 q^{9} +(7.83601 - 6.21265i) q^{10} +3.31662i q^{11} +(8.27331 - 15.5289i) q^{12} +2.22215i q^{13} +(6.96211 + 11.5977i) q^{14} +(-2.84500 - 21.8094i) q^{15} +(-8.92518 - 13.2793i) q^{16} -19.4076i q^{17} +(-10.6536 - 17.7472i) q^{18} -1.70493i q^{19} +(-18.7193 - 7.04176i) q^{20} +29.7513 q^{21} +(5.68721 - 3.41403i) q^{22} +7.21944 q^{23} +(-35.1446 + 1.79824i) q^{24} +(-24.1634 + 6.41330i) q^{25} +(3.81046 - 2.28742i) q^{26} -5.93701 q^{27} +(12.7207 - 23.8767i) q^{28} -31.6591 q^{29} +(-34.4692 + 27.3284i) q^{30} -44.6446i q^{31} +(-13.5836 + 28.9739i) q^{32} -14.5893i q^{33} +(-33.2794 + 19.9776i) q^{34} +(-4.37436 - 33.5332i) q^{35} +(-19.4657 + 36.5368i) q^{36} -19.7200i q^{37} +(-2.92354 + 1.75500i) q^{38} -9.77488i q^{39} +(7.19417 + 39.3477i) q^{40} +56.8872 q^{41} +(-30.6251 - 51.0164i) q^{42} +82.4889 q^{43} +(-11.7085 - 6.23791i) q^{44} +(6.69379 + 51.3136i) q^{45} +(-7.43147 - 12.3796i) q^{46} -13.5111 q^{47} +(39.2603 + 58.4136i) q^{48} -3.25546 q^{49} +(35.8703 + 34.8328i) q^{50} +85.3708i q^{51} +(-7.84474 - 4.17943i) q^{52} -62.9482i q^{53} +(6.11137 + 10.1805i) q^{54} +(-16.4438 + 2.14507i) q^{55} +(-54.0371 + 2.76490i) q^{56} +7.49968i q^{57} +(32.5889 + 54.2877i) q^{58} -37.1968i q^{59} +(82.3431 + 30.9755i) q^{60} +110.464 q^{61} +(-76.5547 + 45.9557i) q^{62} -69.9998 q^{63} +(63.6658 - 6.53225i) q^{64} +(-11.0174 + 1.43721i) q^{65} +(-25.0171 + 15.0177i) q^{66} +48.4315 q^{67} +(68.5136 + 36.5019i) q^{68} -31.7571 q^{69} +(-52.9986 + 42.0191i) q^{70} -50.3046i q^{71} +(82.6893 - 4.23094i) q^{72} +27.2425i q^{73} +(-33.8151 + 20.2992i) q^{74} +(106.291 - 28.2110i) q^{75} +(6.01880 + 3.20663i) q^{76} -22.4319i q^{77} +(-16.7616 + 10.0620i) q^{78} -18.4898i q^{79} +(60.0664 - 52.8396i) q^{80} -67.0313 q^{81} +(-58.5579 - 97.5479i) q^{82} -142.575 q^{83} +(-55.9563 + 105.029i) q^{84} +(96.2229 - 12.5521i) q^{85} +(-84.9115 - 141.449i) q^{86} +139.263 q^{87} +(1.35583 + 26.4983i) q^{88} -142.350 q^{89} +(81.1002 - 64.2989i) q^{90} -15.0295i q^{91} +(-13.5783 + 25.4864i) q^{92} +196.384i q^{93} +(13.9079 + 23.1682i) q^{94} +(8.45301 - 1.10268i) q^{95} +(59.7518 - 127.451i) q^{96} +173.273i q^{97} +(3.35107 + 5.58233i) q^{98} +34.3260i 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 $

$2$	−1.02937	−	1.71476i	−0.514684	−	0.857380i
$2$	−1.02937	−	1.71476i	−0.514684	−	0.857380i
$3$	−4.39883			−1.46628			−0.733138	−	0.680080i	$-0.761945\pi$
$3$	−4.39883			−1.46628			−0.733138	+	0.680080i	$0.761945\pi$
$4$	−1.88080	+	3.53024i	−0.470200	+	0.882560i
$5$	0.646763	+	4.95799i	0.129353	+	0.991599i
$5$	0.646763	+	4.95799i	0.129353	+	0.991599i
$6$	4.52802	+	7.54293i	0.754669	+	1.25716i
$7$	−6.76347			−0.966210			−0.483105	−	0.875562i	$-0.660491\pi$
$7$	−6.76347			−0.966210			−0.483105	+	0.875562i	$0.660491\pi$
$8$	7.98955	−	0.408800i	0.998694	−	0.0510999i
$9$	10.3497			1.14996
$10$	7.83601	−	6.21265i	0.783601	−	0.621265i
$11$			3.31662i			0.301511i
$11$			3.31662i			0.301511i
$12$	8.27331	−	15.5289i	0.689443	−	1.29408i
$13$			2.22215i			0.170935i	0.996341	+	0.0854675i	$0.0272384\pi$
$13$			2.22215i			0.170935i	−0.996341	+	0.0854675i	$0.972762\pi$
$14$	6.96211	+	11.5977i	0.497293	+	0.828409i
$15$	−2.84500	−	21.8094i	−0.189667	−	1.45396i
$16$	−8.92518	−	13.2793i	−0.557824	−	0.829959i
$17$		−	19.4076i		−	1.14163i	−0.821080	−	0.570813i	$-0.806628\pi$
$17$		−	19.4076i		−	1.14163i	0.821080	−	0.570813i	$-0.193372\pi$
$18$	−10.6536	−	17.7472i	−0.591869	−	0.985956i
$19$		−	1.70493i		−	0.0897330i	−0.998993	−	0.0448665i	$-0.985714\pi$
$19$		−	1.70493i		−	0.0897330i	0.998993	−	0.0448665i	$-0.0142862\pi$
$20$	−18.7193	−	7.04176i	−0.935967	−	0.352088i
$21$	29.7513			1.41673
$22$	5.68721	−	3.41403i	0.258510	−	0.155183i
$23$	7.21944			0.313889			0.156944	−	0.987607i	$-0.449836\pi$
$23$	7.21944			0.313889			0.156944	+	0.987607i	$0.449836\pi$
$24$	−35.1446	+	1.79824i	−1.46436	+	0.0749266i
$25$	−24.1634	+	6.41330i	−0.966536	+	0.256532i
$26$	3.81046	−	2.28742i	0.146556	−	0.0879776i
$27$	−5.93701			−0.219889
$28$	12.7207	−	23.8767i	0.454312	−	0.852738i
$29$	−31.6591			−1.09169			−0.545846	−	0.837885i	$-0.683792\pi$
$29$	−31.6591			−1.09169			−0.545846	+	0.837885i	$0.683792\pi$
$30$	−34.4692	+	27.3284i	−1.14897	+	0.910945i
$31$		−	44.6446i		−	1.44015i	−0.693898	−	0.720074i	$-0.744108\pi$
$31$		−	44.6446i		−	1.44015i	0.693898	−	0.720074i	$-0.255892\pi$
$32$	−13.5836	+	28.9739i	−0.424487	+	0.905434i
$33$		−	14.5893i		−	0.442099i
$34$	−33.2794	+	19.9776i	−0.978806	+	0.587577i
$35$	−4.37436	−	33.5332i	−0.124982	−	0.958093i
$36$	−19.4657	+	36.5368i	−0.540713	+	1.01491i
$37$		−	19.7200i		−	0.532974i	−0.963839	−	0.266487i	$-0.914137\pi$
$37$		−	19.7200i		−	0.532974i	0.963839	−	0.266487i	$-0.0858629\pi$
$38$	−2.92354	+	1.75500i	−0.0769352	+	0.0461842i
$39$		−	9.77488i		−	0.250638i
$40$	7.19417	+	39.3477i	0.179854	+	0.983693i
$41$	56.8872			1.38749			0.693747	−	0.720219i	$-0.255959\pi$
$41$	56.8872			1.38749			0.693747	+	0.720219i	$0.255959\pi$
$42$	−30.6251	−	51.0164i	−0.729169	−	1.21468i
$43$	82.4889			1.91835			0.959173	−	0.282820i	$-0.0912700\pi$
$43$	82.4889			1.91835			0.959173	+	0.282820i	$0.0912700\pi$
$44$	−11.7085	−	6.23791i	−0.266102	−	0.141771i
$45$	6.69379	+	51.3136i	0.148751	+	1.14030i
$46$	−7.43147	−	12.3796i	−0.161554	−	0.269122i
$47$	−13.5111			−0.287469			−0.143735	−	0.989616i	$-0.545911\pi$
$47$	−13.5111			−0.287469			−0.143735	+	0.989616i	$0.545911\pi$
$48$	39.2603	+	58.4136i	0.817924	+	1.21695i
$49$	−3.25546			−0.0664380
$50$	35.8703	+	34.8328i	0.717406	+	0.696655i
$51$			85.3708i			1.67394i
$52$	−7.84474	−	4.17943i	−0.150860	−	0.0803736i
$53$		−	62.9482i		−	1.18770i	−0.804575	−	0.593850i	$-0.797607\pi$
$53$		−	62.9482i		−	1.18770i	0.804575	−	0.593850i	$-0.202393\pi$
$54$	6.11137	+	10.1805i	0.113173	+	0.188528i
$55$	−16.4438	+	2.14507i	−0.298978	+	0.0390013i
$56$	−54.0371	+	2.76490i	−0.964948	+	0.0493733i
$57$			7.49968i			0.131573i
$58$	32.5889	+	54.2877i	0.561877	+	0.935995i
$59$		−	37.1968i		−	0.630454i	−0.949016	−	0.315227i	$-0.897919\pi$
$59$		−	37.1968i		−	0.630454i	0.949016	−	0.315227i	$-0.102081\pi$
$60$	82.3431	+	30.9755i	1.37239	+	0.516258i
$61$	110.464			1.81089			0.905444	−	0.424465i	$-0.139538\pi$
$61$	110.464			1.81089			0.905444	+	0.424465i	$0.139538\pi$
$62$	−76.5547	+	45.9557i	−1.23475	+	0.741221i
$63$	−69.9998			−1.11111
$64$	63.6658	−	6.53225i	0.994778	−	0.102066i
$65$	−11.0174	+	1.43721i	−0.169499	+	0.0221109i
$66$	−25.0171	+	15.0177i	−0.379046	+	0.227541i
$67$	48.4315			0.722858			0.361429	−	0.932400i	$-0.382289\pi$
$67$	48.4315			0.722858			0.361429	+	0.932400i	$0.382289\pi$
$68$	68.5136	+	36.5019i	1.00755	+	0.536792i
$69$	−31.7571			−0.460248
$70$	−52.9986	+	42.0191i	−0.757123	+	0.600272i
$71$		−	50.3046i		−	0.708515i	−0.935148	−	0.354258i	$-0.884734\pi$
$71$		−	50.3046i		−	0.708515i	0.935148	−	0.354258i	$-0.115266\pi$
$72$	82.6893	−	4.23094i	1.14846	−	0.0587631i
$73$			27.2425i			0.373185i	0.982437	+	0.186593i	$0.0597445\pi$
$73$			27.2425i			0.373185i	−0.982437	+	0.186593i	$0.940256\pi$
$74$	−33.8151	+	20.2992i	−0.456961	+	0.274313i
$75$	106.291	−	28.2110i	1.41721	−	0.376146i
$76$	6.01880	+	3.20663i	0.0791947	+	0.0421924i
$77$		−	22.4319i		−	0.291323i
$78$	−16.7616	+	10.0620i	−0.214892	+	0.128999i
$79$		−	18.4898i		−	0.234048i	−0.993129	−	0.117024i	$-0.962665\pi$
$79$		−	18.4898i		−	0.234048i	0.993129	−	0.117024i	$-0.0373354\pi$
$80$	60.0664	−	52.8396i	0.750830	−	0.660495i
$81$	−67.0313			−0.827546
$82$	−58.5579	−	97.5479i	−0.714121	−	1.18961i
$83$	−142.575			−1.71777			−0.858887	−	0.512165i	$-0.828844\pi$
$83$	−142.575			−1.71777			−0.858887	+	0.512165i	$0.828844\pi$
$84$	−55.9563	+	105.029i	−0.666147	+	1.25035i
$85$	96.2229	−	12.5521i	1.13203	−	0.147672i
$86$	−84.9115	−	141.449i	−0.987343	−	1.64475i
$87$	139.263			1.60072
$88$	1.35583	+	26.4983i	0.0154072	+	0.301117i
$89$	−142.350			−1.59944			−0.799719	−	0.600374i	$-0.795018\pi$
$89$	−142.350			−1.59944			−0.799719	+	0.600374i	$0.795018\pi$
$90$	81.1002	−	64.2989i	0.901113	−	0.714432i
$91$		−	15.0295i		−	0.165159i
$92$	−13.5783	+	25.4864i	−0.147591	+	0.277026i
$93$			196.384i			2.11165i
$94$	13.9079	+	23.1682i	0.147956	+	0.246470i
$95$	8.45301	−	1.10268i	0.0889791	−	0.0116072i
$96$	59.7518	−	127.451i	0.622415	−	1.32762i
$97$			173.273i			1.78632i	0.449742	+	0.893159i	$0.351516\pi$
$97$			173.273i			1.78632i	−0.449742	+	0.893159i	$0.648484\pi$
$98$	3.35107	+	5.58233i	0.0341946	+	0.0569626i
$99$			34.3260i			0.346727i
$100$	22.8060	−	97.3647i	0.228060	−	0.973647i
$101$	34.7297			0.343859			0.171929	−	0.985109i	$-0.445000\pi$
$101$	34.7297			0.343859			0.171929	+	0.985109i	$0.445000\pi$
$102$	146.390	−	87.8780i	1.43520	−	0.861549i
$103$	−88.7535			−0.861684			−0.430842	−	0.902427i	$-0.641783\pi$
$103$	−88.7535			−0.861684			−0.430842	+	0.902427i	$0.641783\pi$
$104$	0.908416	+	17.7540i	0.00873477	+	0.170712i
$105$	19.2421	+	147.507i	0.183258	+	1.40483i
$106$	−107.941	+	64.7969i	−1.01831	+	0.611291i
$107$	−3.82436			−0.0357417			−0.0178708	−	0.999840i	$-0.505689\pi$
$107$	−3.82436			−0.0357417			−0.0178708	+	0.999840i	$0.505689\pi$
$108$	11.1663	−	20.9591i	0.103392	−	0.194065i
$109$	16.4510			0.150926			0.0754632	−	0.997149i	$-0.475956\pi$
$109$	16.4510			0.150926			0.0754632	+	0.997149i	$0.475956\pi$
$110$	20.6050	+	25.9891i	0.187318	+	0.236265i
$111$			86.7450i			0.781486i
$112$	60.3652	+	89.8145i	0.538975	+	0.801915i
$113$		−	180.163i		−	1.59437i	−0.603738	−	0.797183i	$-0.706323\pi$
$113$		−	180.163i		−	1.59437i	0.603738	−	0.797183i	$-0.293677\pi$
$114$	12.8601	−	7.71993i	0.112808	−	0.0677187i
$115$	4.66927	+	35.7940i	0.0406024	+	0.311252i
$116$	59.5444	−	111.764i	0.513314	−	0.963484i
$117$			22.9986i			0.196569i
$118$	−63.7836	+	38.2892i	−0.540539	+	0.324485i
$119$			131.263i			1.10305i
$120$	−31.6459	−	173.084i	−0.263716	−	1.44237i
$121$	−11.0000			−0.0909091
$122$	−113.708	−	189.420i	−0.932036	−	1.55262i
$123$	−250.237			−2.03445
$124$	157.606	+	83.9675i	1.27102	+	0.677157i
$125$	−47.4251	−	115.654i	−0.379401	−	0.925232i
$126$	72.0556	+	120.033i	0.571870	+	0.952641i
$127$	13.2800			0.104567			0.0522837	−	0.998632i	$-0.483350\pi$
$127$	13.2800			0.104567			0.0522837	+	0.998632i	$0.483350\pi$
$128$	−76.7368	−	102.447i	−0.599506	−	0.800370i
$129$	−362.854			−2.81282
$130$	13.8055	+	17.4128i	0.106196	+	0.133945i
$131$			187.980i			1.43496i	0.696579	+	0.717480i	$0.254705\pi$
$131$			187.980i			1.43496i	−0.696579	+	0.717480i	$0.745295\pi$
$132$	51.5036	+	27.4395i	0.390179	+	0.207875i
$133$			11.5312i			0.0867009i
$134$	−49.8539	−	83.0484i	−0.372044	−	0.619764i
$135$	−3.83984	−	29.4356i	−0.0284432	−	0.218042i
$136$	−7.93383	−	155.058i	−0.0583370	−	1.14013i
$137$		−	148.543i		−	1.08426i	−0.840295	−	0.542129i	$-0.817619\pi$
$137$		−	148.543i		−	1.08426i	0.840295	−	0.542129i	$-0.182381\pi$
$138$	32.6898	+	54.4558i	0.236882	+	0.394607i
$139$			129.371i			0.930724i	0.885120	+	0.465362i	$0.154076\pi$
$139$			129.371i			0.930724i	−0.885120	+	0.465362i	$0.845924\pi$
$140$	126.608	+	47.6268i	0.904341	+	0.340191i
$141$	59.4328			0.421509
$142$	−86.2603	+	51.7820i	−0.607467	+	0.364662i
$143$	−7.37005			−0.0515388
$144$	−92.3728	−	137.437i	−0.641478	−	0.954424i
$145$	−20.4759	−	156.966i	−0.141213	−	1.08252i
$146$	46.7144	−	28.0426i	0.319962	−	0.192073i
$147$	14.3202			0.0974164
$148$	69.6164	+	37.0894i	0.470381	+	0.250604i
$149$	32.3173			0.216895			0.108447	−	0.994102i	$-0.465412\pi$
$149$	32.3173			0.216895			0.108447	+	0.994102i	$0.465412\pi$
$150$	−157.787	−	153.223i	−1.05192	−	1.02149i
$151$		−	213.925i		−	1.41672i	−0.705851	−	0.708360i	$-0.749435\pi$
$151$		−	213.925i		−	1.41672i	0.705851	−	0.708360i	$-0.250565\pi$
$152$	−0.696973	−	13.6216i	−0.00458535	−	0.0896157i
$153$		−	200.863i		−	1.31283i
$154$	−38.4653	+	23.0907i	−0.249775	+	0.149940i
$155$	221.347	−	28.8745i	1.42805	−	0.186287i
$156$	34.5077	+	18.3846i	0.221203	+	0.117850i
$157$		−	165.089i		−	1.05152i	−0.850633	−	0.525760i	$-0.823781\pi$
$157$		−	165.089i		−	1.05152i	0.850633	−	0.525760i	$-0.176219\pi$
$158$	−31.7055	+	19.0328i	−0.200668	+	0.120461i
$159$			276.898i			1.74150i
$160$	−152.438	−	48.6080i	−0.952736	−	0.303800i
$161$	−48.8285			−0.303283
$162$	68.9999	+	114.942i	0.425925	+	0.709521i
$163$	175.402			1.07608			0.538042	−	0.842918i	$-0.319164\pi$
$163$	175.402			1.07608			0.538042	+	0.842918i	$0.319164\pi$
$164$	−106.993	+	200.826i	−0.652399	+	1.22455i
$165$	72.3334	−	9.43580i	0.438385	−	0.0571867i
$166$	146.763	+	244.482i	0.884112	+	1.47278i
$167$	−265.308			−1.58867			−0.794336	−	0.607479i	$-0.792181\pi$
$167$	−265.308			−1.58867			−0.794336	+	0.607479i	$0.792181\pi$
$168$	237.700	−	12.1623i	1.41488	−	0.0723948i
$169$	164.062			0.970781
$170$	−120.573	−	152.078i	−0.709251	−	0.894578i
$171$		−	17.6454i		−	0.103190i
$172$	−155.145	+	291.205i	−0.902006	+	1.69306i
$173$		−	192.856i		−	1.11477i	−0.830253	−	0.557386i	$-0.811804\pi$
$173$		−	192.856i		−	1.11477i	0.830253	−	0.557386i	$-0.188196\pi$
$174$	−143.353	−	238.802i	−0.823867	−	1.37243i
$175$	163.428	−	43.3761i	0.933877	−	0.247864i
$176$	44.0426	−	29.6015i	0.250242	−	0.168190i
$177$			163.622i			0.924420i
$178$	146.531	+	244.096i	0.823206	+	1.37133i
$179$		−	61.7804i		−	0.345142i	−0.984997	−	0.172571i	$-0.944793\pi$
$179$		−	61.7804i		−	0.345142i	0.984997	−	0.172571i	$-0.0552074\pi$
$180$	−193.739	−	72.8800i	−1.07633	−	0.404889i
$181$	−44.5899			−0.246353			−0.123176	−	0.992385i	$-0.539308\pi$
$181$	−44.5899			−0.246353			−0.123176	+	0.992385i	$0.539308\pi$
$182$	−25.7719	+	15.4709i	−0.141604	+	0.0850048i
$183$	−485.913			−2.65526
$184$	57.6801	−	2.95131i	0.313479	−	0.0160397i
$185$	97.7718	−	12.7542i	0.528496	−	0.0689416i
$186$	336.751	−	202.151i	1.81049	−	1.08683i
$187$	64.3678			0.344213
$188$	25.4116	−	47.6973i	0.135168	−	0.253709i
$189$	40.1548			0.212459
$190$	−10.5921	−	13.3598i	−0.0557479	−	0.0703148i
$191$			70.1530i			0.367293i	0.982992	+	0.183646i	$0.0587902\pi$
$191$			70.1530i			0.367293i	−0.982992	+	0.183646i	$0.941210\pi$
$192$	−280.055	+	28.7342i	−1.45862	+	0.149657i
$193$		−	336.346i		−	1.74273i	−0.490638	−	0.871364i	$-0.663236\pi$
$193$		−	336.346i		−	1.74273i	0.490638	−	0.871364i	$-0.336764\pi$
$194$	297.121	−	178.362i	1.53155	−	0.919390i
$195$	48.4638	−	6.32203i	0.248532	−	0.0324207i
$196$	6.12287	−	11.4926i	0.0312391	−	0.0586355i
$197$			77.8458i			0.395156i	0.980287	+	0.197578i	$0.0633076\pi$
$197$			77.8458i			0.395156i	−0.980287	+	0.197578i	$0.936692\pi$
$198$	58.8608	−	35.3341i	0.297277	−	0.178455i
$199$		−	258.361i		−	1.29830i	−0.760662	−	0.649148i	$-0.775126\pi$
$199$		−	258.361i		−	1.29830i	0.760662	−	0.649148i	$-0.224874\pi$
$200$	−190.433	+	61.1173i	−0.952164	+	0.305587i
$201$	−213.042			−1.05991
$202$	−35.7497	−	59.5531i	−0.176979	−	0.294817i
$203$	214.125			1.05480
$204$	−301.379	−	160.565i	−1.47735	−	0.787085i
$205$	36.7926	+	282.046i	0.179476	+	1.37584i
$206$	91.3600	+	152.191i	0.443495	+	0.738790i
$207$	74.7189			0.360961
$208$	29.5088	−	19.8331i	0.141869	−	0.0953516i
$209$	5.65460			0.0270555
$210$	233.132	−	184.835i	1.11015	−	0.880165i
$211$		−	108.954i		−	0.516369i	−0.966096	−	0.258184i	$-0.916876\pi$
$211$		−	108.954i		−	0.516369i	0.966096	−	0.258184i	$-0.0831242\pi$
$212$	222.222	+	118.393i	1.04822	+	0.558457i
$213$			221.281i			1.03888i
$214$	3.93668	+	6.55786i	0.0183957	+	0.0306442i
$215$	53.3508	+	408.979i	0.248143	+	1.90223i
$216$	−47.4340	+	2.42705i	−0.219602	+	0.0112363i
$217$			301.952i			1.39148i
$218$	−16.9341	−	28.2095i	−0.0776794	−	0.129401i
$219$		−	119.835i		−	0.547193i
$220$	23.3549	−	62.0850i	0.106159	−	0.282205i
$221$	43.1268			0.195144
$222$	148.747	−	89.2926i	0.670031	−	0.402219i
$223$	−116.380			−0.521883			−0.260941	−	0.965355i	$-0.584033\pi$
$223$	−116.380			−0.521883			−0.260941	+	0.965355i	$0.584033\pi$
$224$	91.8722	−	195.964i	0.410144	−	0.874840i
$225$	−250.083	+	66.3756i	−1.11148	+	0.295002i
$226$	−308.937	+	185.454i	−1.36698	+	0.820595i
$227$	85.6133			0.377151			0.188576	−	0.982059i	$-0.439613\pi$
$227$	85.6133			0.377151			0.188576	+	0.982059i	$0.439613\pi$
$228$	−26.4757	−	14.1054i	−0.116121	−	0.0618657i
$229$	286.685			1.25190			0.625950	−	0.779863i	$-0.284711\pi$
$229$	286.685			1.25190			0.625950	+	0.779863i	$0.284711\pi$
$230$	56.5716	−	44.8519i	0.245964	−	0.195008i
$231$			98.6740i			0.427160i
$232$	−252.942	+	12.9422i	−1.09027	+	0.0557854i
$233$		−	9.18626i		−	0.0394260i	−0.999806	−	0.0197130i	$-0.993725\pi$
$233$		−	9.18626i		−	0.0394260i	0.999806	−	0.0197130i	$-0.00627525\pi$
$234$	39.4370	−	23.6740i	0.168534	−	0.101171i
$235$	−8.73846	−	66.9878i	−0.0371849	−	0.285054i
$236$	131.314	+	69.9597i	0.556414	+	0.296440i
$237$			81.3333i			0.343179i
$238$	225.084	−	135.118i	0.945733	−	0.567723i
$239$			27.9965i			0.117140i	0.998283	+	0.0585701i	$0.0186541\pi$
$239$			27.9965i			0.117140i	−0.998283	+	0.0585701i	$0.981346\pi$
$240$	−264.222	+	232.432i	−1.10092	+	0.968468i
$241$	−258.214			−1.07143			−0.535714	−	0.844400i	$-0.679957\pi$
$241$	−258.214			−1.07143			−0.535714	+	0.844400i	$0.679957\pi$
$242$	11.3231	+	18.8624i	0.0467895	+	0.0779436i
$243$	348.292			1.43330
$244$	−207.761	+	389.965i	−0.851480	+	1.59822i
$245$	−2.10551	−	16.1405i	−0.00859393	−	0.0658798i
$246$	257.586	+	429.096i	1.04710	+	1.74429i
$247$	3.78861			0.0153385
$248$	−18.2507	−	356.690i	−0.0735914	−	1.43827i
$249$	627.164			2.51873
$250$	−149.501	+	200.373i	−0.598004	+	0.801493i
$251$		−	8.49681i		−	0.0338518i	−0.999857	−	0.0169259i	$-0.994612\pi$
$251$		−	8.49681i		−	0.0338518i	0.999857	−	0.0169259i	$-0.00538795\pi$
$252$	131.656	−	247.116i	0.522443	−	0.980619i
$253$			23.9442i			0.0946411i
$254$	−13.6701	−	22.7721i	−0.0538192	−	0.0896539i
$255$	−423.268	+	55.2147i	−1.65987	+	0.216528i
$256$	−96.6822	+	237.041i	−0.377665	+	0.925942i
$257$			428.056i			1.66559i	0.553582	+	0.832794i	$0.313260\pi$
$257$			428.056i			1.66559i	−0.553582	+	0.832794i	$0.686740\pi$
$258$	373.511	+	622.208i	1.44772	+	2.41166i
$259$			133.376i			0.514965i
$260$	15.6479	−	41.5973i	0.0601842	−	0.159989i
$261$	−327.661			−1.25541
$262$	322.340	−	193.500i	1.23031	−	0.738552i
$263$	−56.6652			−0.215457			−0.107729	−	0.994180i	$-0.534358\pi$
$263$	−56.6652			−0.215457			−0.107729	+	0.994180i	$0.534358\pi$
$264$	−5.96408	−	116.562i	−0.0225912	−	0.441521i
$265$	312.097	−	40.7126i	1.17772	−	0.153632i
$266$	19.7733	−	11.8699i	0.0743356	−	0.0446236i
$267$	626.173			2.34522
$268$	−91.0900	+	170.975i	−0.339888	+	0.637966i
$269$	−354.085			−1.31630			−0.658151	−	0.752886i	$-0.728661\pi$
$269$	−354.085			−1.31630			−0.658151	+	0.752886i	$0.728661\pi$
$270$	−46.5224	+	36.8845i	−0.172305	+	0.136609i
$271$			47.5830i			0.175583i	0.996139	+	0.0877916i	$0.0279809\pi$
$271$			47.5830i			0.175583i	−0.996139	+	0.0877916i	$0.972019\pi$
$272$	−257.721	+	173.217i	−0.947502	+	0.636826i
$273$			66.1121i			0.242169i
$274$	−254.716	+	152.906i	−0.929620	+	0.558050i
$275$	−21.2705	−	80.1409i	−0.0773473	−	0.291422i
$276$	59.7287	−	112.110i	0.216408	−	0.406196i
$277$		−	21.3640i		−	0.0771264i	−0.999256	−	0.0385632i	$-0.987722\pi$
$277$		−	21.3640i		−	0.0771264i	0.999256	−	0.0385632i	$-0.0122781\pi$
$278$	221.840	−	133.170i	0.797984	−	0.479029i
$279$		−	462.057i		−	1.65612i
$280$	−48.6576	−	266.127i	−0.173777	−	0.950454i
$281$	315.774			1.12375			0.561876	−	0.827222i	$-0.310080\pi$
$281$	315.774			1.12375			0.561876	+	0.827222i	$0.310080\pi$
$282$	−61.1783	−	101.913i	−0.216944	−	0.361394i
$283$	−399.142			−1.41039			−0.705197	−	0.709011i	$-0.749142\pi$
$283$	−399.142			−1.41039			−0.705197	+	0.709011i	$0.749142\pi$
$284$	177.587	+	94.6129i	0.625307	+	0.333144i
$285$	−37.1833	+	4.85052i	−0.130468	+	0.0170194i
$286$	7.58650	+	12.6379i	0.0265262	+	0.0441884i
$287$	−384.755			−1.34061
$288$	−140.586	+	299.870i	−0.488145	+	1.04122i
$289$	−87.6560			−0.303308
$290$	−248.081	+	196.687i	−0.855451	+	0.678230i
$291$		−	762.197i		−	2.61923i
$292$	−96.1727	−	51.2377i	−0.329358	−	0.175472i
$293$		−	90.0131i		−	0.307212i	−0.988132	−	0.153606i	$-0.950911\pi$
$293$		−	90.0131i		−	0.307212i	0.988132	−	0.153606i	$-0.0490887\pi$
$294$	−14.7408	−	24.5557i	−0.0501387	−	0.0835228i
$295$	184.422	−	24.0575i	0.625158	−	0.0815509i
$296$	−8.06154	−	157.554i	−0.0272349	−	0.532277i
$297$		−	19.6908i		−	0.0662991i
$298$	−33.2664	−	55.4164i	−0.111632	−	0.185961i
$299$			16.0427i			0.0536546i
$300$	−100.320	+	428.290i	−0.334399	+	1.42763i
$301$	−557.911			−1.85353
$302$	−366.830	+	220.208i	−1.21467	+	0.729164i
$303$	−152.770			−0.504191
$304$	−22.6403	+	15.2168i	−0.0744747	+	0.0500552i
$305$	71.4442	+	547.681i	0.234243	+	1.79567i
$306$	−344.431	+	206.762i	−1.12559	+	0.675692i
$307$	27.1789			0.0885305			0.0442653	−	0.999020i	$-0.485905\pi$
$307$	27.1789			0.0885305			0.0442653	+	0.999020i	$0.485905\pi$
$308$	79.1900	+	42.1899i	0.257110	+	0.136980i
$309$	390.411			1.26347
$310$	−277.361	−	349.835i	−0.894713	−	1.12850i
$311$		−	403.255i		−	1.29664i	−0.761367	−	0.648321i	$-0.775472\pi$
$311$		−	403.255i		−	1.29664i	0.761367	−	0.648321i	$-0.224528\pi$
$312$	−3.99596	−	78.0968i	−0.0128076	−	0.250310i
$313$			233.203i			0.745058i	0.928021	+	0.372529i	$0.121509\pi$
$313$			233.203i			0.745058i	−0.928021	+	0.372529i	$0.878491\pi$
$314$	−283.087	+	169.937i	−0.901552	+	0.541201i
$315$	−45.2733	−	347.058i	−0.143725	−	1.10177i
$316$	65.2733	+	34.7756i	0.206561	+	0.110049i
$317$		−	286.321i		−	0.903222i	−0.892215	−	0.451611i	$-0.850850\pi$
$317$		−	286.321i		−	0.903222i	0.892215	−	0.451611i	$-0.149150\pi$
$318$	474.814	−	285.030i	1.49312	−	0.896321i
$319$		−	105.001i		−	0.329158i
$320$	73.5635	+	311.430i	0.229886	+	0.973218i
$321$	16.8227			0.0524072
$322$	50.2625	+	83.7291i	0.156095	+	0.260028i
$323$	−33.0886			−0.102441
$324$	126.072	−	236.636i	0.389112	−	0.730359i
$325$	−14.2513	−	53.6948i	−0.0438503	−	0.165215i
$326$	−180.553	−	300.772i	−0.553843	−	0.922612i
$327$	−72.3650			−0.221300
$328$	454.503	−	23.2555i	1.38568	−	0.0709008i
$329$	91.3817			0.277756
$330$	−90.6379	−	114.322i	−0.274660	−	0.346429i
$331$		−	24.6298i		−	0.0744104i	−0.999308	−	0.0372052i	$-0.988154\pi$
$331$		−	24.6298i		−	0.0744104i	0.999308	−	0.0372052i	$-0.0118455\pi$
$332$	268.156	−	503.325i	0.807697	−	1.51604i
$333$		−	204.096i		−	0.612901i
$334$	273.100	+	454.940i	0.817664	+	1.36209i
$335$	31.3237	+	240.123i	0.0935037	+	0.716785i
$336$	−265.536	−	395.078i	−0.790286	−	1.17583i
$337$		−	178.380i		−	0.529317i	−0.964342	−	0.264658i	$-0.914741\pi$
$337$		−	178.380i		−	0.529317i	0.964342	−	0.264658i	$-0.0852592\pi$
$338$	−168.880	−	281.327i	−0.499646	−	0.832328i
$339$			792.507i			2.33778i
$340$	−136.664	+	363.298i	−0.401953	+	1.06852i
$341$	148.069			0.434221
$342$	−30.2577	+	18.1637i	−0.0884728	+	0.0531101i
$343$	353.428			1.03040
$344$	659.049	−	33.7214i	1.91584	−	0.0980274i
$345$	−20.5393	−	157.451i	−0.0595343	−	0.456381i
$346$	−330.701	+	198.520i	−0.955783	+	0.573756i
$347$	257.701			0.742653			0.371326	−	0.928502i	$-0.378903\pi$
$347$	257.701			0.742653			0.371326	+	0.928502i	$0.378903\pi$
$348$	−261.926	+	491.631i	−0.752660	+	1.41273i
$349$	−46.4966			−0.133228			−0.0666141	−	0.997779i	$-0.521220\pi$
$349$	−46.4966			−0.133228			−0.0666141	+	0.997779i	$0.521220\pi$
$350$	−242.608	−	235.590i	−0.693165	−	0.673115i
$351$		−	13.1929i		−	0.0375867i
$352$	−96.0955	−	45.0516i	−0.272999	−	0.127988i
$353$		−	499.148i		−	1.41402i	−0.707205	−	0.707009i	$-0.750044\pi$
$353$		−	499.148i		−	1.41402i	0.707205	−	0.707009i	$-0.249956\pi$
$354$	280.573	−	168.428i	0.792579	−	0.475784i
$355$	249.410	−	32.5352i	0.702563	−	0.0916484i
$356$	267.732	−	502.530i	0.752056	−	1.41160i
$357$		−	577.403i		−	1.61738i
$358$	−105.939	+	63.5948i	−0.295918	+	0.177639i
$359$		−	467.290i		−	1.30164i	−0.759231	−	0.650821i	$-0.774425\pi$
$359$		−	467.290i		−	1.30164i	0.759231	−	0.650821i	$-0.225575\pi$
$360$	74.4574	+	407.236i	0.206826	+	1.13121i
$361$	358.093			0.991948
$362$	45.8994	+	76.4609i	0.126794	+	0.211218i
$363$	48.3871			0.133298
$364$	53.0577	+	28.2674i	0.145763	+	0.0776578i
$365$	−135.068	+	17.6195i	−0.370050	+	0.0482725i
$366$	500.184	+	833.224i	1.36662	+	2.27657i
$367$	−512.944			−1.39767			−0.698833	−	0.715285i	$-0.746297\pi$
$367$	−512.944			−1.39767			−0.698833	+	0.715285i	$0.746297\pi$
$368$	−64.4349	−	95.8695i	−0.175095	−	0.260515i
$369$	588.764			1.59557
$370$	−122.514	−	154.526i	−0.331118	−	0.417639i
$371$			425.748i			1.14757i
$372$	−693.282	−	369.358i	−1.86366	−	0.992899i
$373$			616.530i			1.65290i	0.563014	+	0.826448i	$0.309642\pi$
$373$			616.530i			1.65290i	−0.563014	+	0.826448i	$0.690358\pi$
$374$	−66.2582	−	110.375i	−0.177161	−	0.295121i
$375$	208.615	+	508.742i	0.556306	+	1.35665i
$376$	−107.947	+	5.52332i	−0.287094	+	0.0146897i
$377$		−	70.3514i		−	0.186608i
$378$	−41.3341	−	68.8558i	−0.109349	−	0.182158i
$379$		−	690.502i		−	1.82190i	−0.412513	−	0.910952i	$-0.635349\pi$
$379$		−	690.502i		−	1.82190i	0.412513	−	0.910952i	$-0.364651\pi$
$380$	−12.0057	+	31.9151i	−0.0315939	+	0.0839871i
$381$	−58.4166			−0.153324
$382$	120.295	−	72.2133i	0.314910	−	0.189040i
$383$	−385.778			−1.00725			−0.503626	−	0.863922i	$-0.668001\pi$
$383$	−385.778			−1.00725			−0.503626	+	0.863922i	$0.668001\pi$
$384$	337.552	+	450.648i	0.879041	+	1.17356i
$385$	111.217	−	14.5081i	0.288876	−	0.0376834i
$386$	−576.753	+	346.225i	−1.49418	+	0.896955i
$387$	853.733			2.20603
$388$	−611.694	−	325.891i	−1.57653	−	0.839926i
$389$	−514.438			−1.32246			−0.661231	−	0.750182i	$-0.729966\pi$
$389$	−514.438			−1.32246			−0.661231	+	0.750182i	$0.729966\pi$
$390$	−60.7278	−	76.5960i	−0.155712	−	0.196400i
$391$		−	140.112i		−	0.358343i
$392$	−26.0097	+	1.33083i	−0.0663512	+	0.00339498i
$393$		−	826.890i		−	2.10405i
$394$	133.487	−	80.1321i	0.338799	−	0.203381i
$395$	91.6722	−	11.9585i	0.232081	−	0.0302747i
$396$	−121.179	−	64.5603i	−0.306008	−	0.163031i
$397$			27.3556i			0.0689057i	0.999406	+	0.0344528i	$0.0109689\pi$
$397$			27.3556i			0.0689057i	−0.999406	+	0.0344528i	$0.989031\pi$
$398$	−443.027	+	265.949i	−1.11313	+	0.668213i
$399$		−	50.7238i		−	0.127127i
$400$	300.827	+	263.634i	0.752068	+	0.659086i
$401$	510.105			1.27208			0.636041	−	0.771655i	$-0.280571\pi$
$401$	510.105			1.27208			0.636041	+	0.771655i	$0.280571\pi$
$402$	219.299	+	365.316i	0.545519	+	0.908745i
$403$	99.2071			0.246172
$404$	−65.3196	+	122.604i	−0.161682	+	0.303476i
$405$	−43.3534	−	332.340i	−0.107045	−	0.820594i
$406$	−220.414	−	367.173i	−0.542891	−	0.904368i
$407$	65.4039			0.160698
$408$	34.8995	+	682.074i	0.0855381	+	1.67175i
$409$	471.021			1.15164			0.575820	−	0.817577i	$-0.304683\pi$
$409$	471.021			1.15164			0.575820	+	0.817577i	$0.304683\pi$
$410$	445.769	−	353.420i	1.08724	−	0.862000i
$411$			653.416i			1.58982i
$412$	166.927	−	313.321i	0.405164	−	0.760488i
$413$			251.580i			0.609151i
$414$	−76.9133	−	128.125i	−0.185781	−	0.309481i
$415$	−92.2125	−	706.887i	−0.222199	−	1.70334i
$416$	−64.3845	−	30.1848i	−0.154770	−	0.0725597i
$417$		−	569.079i		−	1.36470i
$418$	−5.82067	−	9.69628i	−0.0139250	−	0.0231968i
$419$			214.295i			0.511445i	0.966750	+	0.255722i	$0.0823133\pi$
$419$			214.295i			0.511445i	−0.966750	+	0.255722i	$0.917687\pi$
$420$	−556.925	−	209.502i	−1.32601	−	0.498814i
$421$	−93.6045			−0.222338			−0.111169	−	0.993801i	$-0.535460\pi$
$421$	−93.6045			−0.222338			−0.111169	+	0.993801i	$0.535460\pi$
$422$	−186.830	+	112.154i	−0.442724	+	0.265767i
$423$	−139.835			−0.330580
$424$	−25.7332	−	502.927i	−0.0606915	−	1.18615i
$425$	124.467	+	468.954i	0.292863	+	1.10342i
$426$	379.444	−	227.780i	0.890714	−	0.534695i
$427$	−747.121			−1.74970
$428$	7.19286	−	13.5009i	0.0168057	−	0.0315442i
$429$	32.4196			0.0755701
$430$	646.383	−	512.474i	1.50322	−	1.19180i
$431$			426.905i			0.990500i	0.868751	+	0.495250i	$0.164923\pi$
$431$			426.905i			0.990500i	−0.868751	+	0.495250i	$0.835077\pi$
$432$	52.9889	+	78.8396i	0.122659	+	0.182499i
$433$		−	27.7192i		−	0.0640167i	−0.999488	−	0.0320084i	$-0.989810\pi$
$433$		−	27.7192i		−	0.0640167i	0.999488	−	0.0320084i	$-0.0101903\pi$
$434$	517.775	−	310.820i	1.19303	−	0.716175i
$435$	90.0701	+	690.464i	0.207058	+	1.58727i
$436$	−30.9410	+	58.0759i	−0.0709656	+	0.133202i
$437$		−	12.3086i		−	0.0281662i
$438$	−205.488	+	123.355i	−0.469152	+	0.281631i
$439$		−	487.493i		−	1.11046i	−0.831696	−	0.555231i	$-0.812630\pi$
$439$		−	487.493i		−	1.11046i	0.831696	−	0.555231i	$-0.187370\pi$
$440$	−130.502	+	23.8604i	−0.296595	+	0.0542281i
$441$	−33.6930			−0.0764013
$442$	−44.3933	−	73.9520i	−0.100437	−	0.167312i
$443$	−223.850			−0.505304			−0.252652	−	0.967557i	$-0.581303\pi$
$443$	−223.850			−0.505304			−0.252652	+	0.967557i	$0.581303\pi$
$444$	−306.231	−	163.150i	−0.689709	−	0.367455i
$445$	−92.0668	−	705.770i	−0.206892	−	1.58600i
$446$	119.798	+	199.563i	0.268605	+	0.447452i
$447$	−142.158			−0.318027
$448$	−430.602	+	44.1807i	−0.961164	+	0.0986176i
$449$	23.8039			0.0530155			0.0265077	−	0.999649i	$-0.491561\pi$
$449$	23.8039			0.0530155			0.0265077	+	0.999649i	$0.491561\pi$
$450$	371.246	+	360.508i	0.824991	+	0.801129i
$451$			188.674i			0.418345i
$452$	636.020	+	338.851i	1.40712	+	0.749671i
$453$			941.018i			2.07730i
$454$	−88.1277	−	146.806i	−0.194114	−	0.323362i
$455$	74.5161	−	9.72052i	0.163772	−	0.0213638i
$456$	3.06586	+	59.9190i	0.00672339	+	0.131401i
$457$			317.090i			0.693851i	0.937893	+	0.346925i	$0.112774\pi$
$457$			317.090i			0.693851i	−0.937893	+	0.346925i	$0.887226\pi$
$458$	−295.105	−	491.596i	−0.644333	−	1.07335i
$459$			115.223i			0.251031i
$460$	−135.143	−	50.8376i	−0.293790	−	0.110517i
$461$	−548.166			−1.18908			−0.594540	−	0.804066i	$-0.702666\pi$
$461$	−548.166			−1.18908			−0.594540	+	0.804066i	$0.702666\pi$
$462$	169.202	−	101.572i	0.366239	−	0.219853i
$463$	−527.246			−1.13876			−0.569380	−	0.822074i	$-0.692817\pi$
$463$	−527.246			−1.13876			−0.569380	+	0.822074i	$0.692817\pi$
$464$	282.563	+	420.412i	0.608972	+	0.906060i
$465$	−973.669	+	127.014i	−2.09391	+	0.273148i
$466$	−15.7522	+	9.45605i	−0.0338031	+	0.0202920i
$467$	−345.096			−0.738964			−0.369482	−	0.929238i	$-0.620465\pi$
$467$	−345.096			−0.738964			−0.369482	+	0.929238i	$0.620465\pi$
$468$	−81.1905	−	43.2557i	−0.173484	−	0.0924268i
$469$	−327.565			−0.698433
$470$	−105.873	+	83.9395i	−0.225261	+	0.178595i
$471$			726.197i			1.54182i
$472$	−15.2060	−	297.186i	−0.0322162	−	0.629631i
$473$			273.585i			0.578403i
$474$	139.467	−	83.7220i	0.294234	−	0.176629i
$475$	10.9342	+	41.1968i	0.0230194	+	0.0867301i
$476$	−463.390	−	246.879i	−0.973508	−	0.518654i
$477$		−	651.493i		−	1.36581i
$478$	48.0073	−	28.8187i	0.100434	−	0.0602902i
$479$		−	106.849i		−	0.223068i	−0.993761	−	0.111534i	$-0.964424\pi$
$479$		−	106.849i		−	0.223068i	0.993761	−	0.111534i	$-0.0355764\pi$
$480$	670.547	+	213.818i	1.39697	+	0.445455i
$481$	43.8210			0.0911039
$482$	265.797	+	442.775i	0.551447	+	0.918620i
$483$	214.788			0.444696
$484$	20.6888	−	38.8326i	0.0427454	−	0.0802327i
$485$	−859.085	+	112.066i	−1.77131	+	0.231065i
$486$	−358.521	−	597.237i	−0.737697	−	1.22888i
$487$	697.116			1.43145			0.715725	−	0.698382i	$-0.246096\pi$
$487$	697.116			1.43145			0.715725	+	0.698382i	$0.246096\pi$
$488$	882.559	−	45.1577i	1.80852	−	0.0925363i
$489$	−771.561			−1.57783
$490$	−25.5098	+	20.2250i	−0.0520608	+	0.0412756i
$491$			225.649i			0.459570i	0.973241	+	0.229785i	$0.0738022\pi$
$491$			225.649i			0.459570i	−0.973241	+	0.229785i	$0.926198\pi$
$492$	470.646	−	883.397i	0.956597	−	1.79552i
$493$			614.428i			1.24630i
$494$	−3.89988	−	6.49656i	−0.00789449	−	0.0131509i
$495$	−170.188	+	22.2008i	−0.343814	+	0.0448501i
$496$	−592.851	+	398.461i	−1.19526	+	0.803349i
$497$			340.234i			0.684575i
$498$	−645.583	−	1075.44i	−1.29635	−	2.15951i
$499$		−	702.622i		−	1.40806i	−0.710170	−	0.704031i	$-0.751382\pi$
$499$		−	702.622i		−	1.40806i	0.710170	−	0.704031i	$-0.248618\pi$
$500$	497.484	+	50.1002i	0.994967	+	0.100200i
$501$	1167.04			2.32943
$502$	−14.5700	+	8.74635i	−0.0290239	+	0.0174230i
$503$	453.682			0.901952			0.450976	−	0.892536i	$-0.351076\pi$
$503$	453.682			0.901952			0.450976	+	0.892536i	$0.351076\pi$
$504$	−559.266	+	28.6159i	−1.10966	+	0.0567775i
$505$	22.4619	+	172.190i	0.0444790	+	0.340970i
$506$	41.0585	−	24.6474i	0.0811433	−	0.0487103i
$507$	−721.680			−1.42343
$508$	−24.9771	+	46.8818i	−0.0491675	+	0.0922869i
$509$	−607.445			−1.19341			−0.596704	−	0.802461i	$-0.703523\pi$
$509$	−607.445			−1.19341			−0.596704	+	0.802461i	$0.703523\pi$
$510$	530.379	+	668.966i	1.03996	+	1.31170i
$511$		−	184.254i		−	0.360575i
$512$	505.990	−	78.2162i	0.988262	−	0.152766i
$513$			10.1222i			0.0197313i
$514$	734.014	−	440.628i	1.42804	−	0.857253i
$515$	−57.4025	−	440.039i	−0.111461	−	0.854445i
$516$	682.456	−	1280.96i	1.32259	−	2.48249i
$517$		−	44.8111i		−	0.0866753i
$518$	228.707	−	137.293i	0.441520	−	0.265044i
$519$			848.339i			1.63456i
$520$	−87.4368	+	15.9866i	−0.168148	+	0.0307434i
$521$	97.5728			0.187280			0.0936399	−	0.995606i	$-0.470150\pi$
$521$	97.5728			0.187280			0.0936399	+	0.995606i	$0.470150\pi$
$522$	337.284	+	561.861i	0.646139	+	1.07636i
$523$	−10.0320			−0.0191816			−0.00959080	−	0.999954i	$-0.503053\pi$
$523$	−10.0320			−0.0191816			−0.00959080	+	0.999954i	$0.503053\pi$
$524$	−663.614	−	353.552i	−1.26644	−	0.674718i
$525$	−718.893	+	190.804i	−1.36932	+	0.363436i
$526$	58.3294	+	97.1672i	0.110892	+	0.184729i
$527$	−866.445			−1.64411
$528$	−193.736	+	130.212i	−0.366924	+	0.246613i
$529$	−476.880			−0.901474
$530$	−391.075	−	493.262i	−0.737877	−	0.930683i
$531$		−	384.975i		−	0.725000i
$532$	−40.7080	−	21.6879i	−0.0765187	−	0.0407668i
$533$			126.412i			0.237171i
$534$	−644.563	−	1073.74i	−1.20705	−	2.01074i
$535$	−2.47346	−	18.9612i	−0.00462328	−	0.0354414i
$536$	386.946	−	19.7988i	0.721914	−	0.0369380i
$537$			271.761i			0.506073i
$538$	364.484	+	607.171i	0.677480	+	1.12857i
$539$		−	10.7971i		−	0.0200318i
$540$	111.137	+	41.8070i	0.205809	+	0.0774203i
$541$	−212.444			−0.392687			−0.196344	−	0.980535i	$-0.562907\pi$
$541$	−212.444			−0.392687			−0.196344	+	0.980535i	$0.562907\pi$
$542$	81.5934	−	48.9805i	0.150541	−	0.0903699i
$543$	196.143			0.361221
$544$	562.315	+	263.625i	1.03367	+	0.484605i
$545$	10.6399	+	81.5638i	0.0195227	+	0.149658i
$546$	113.366	−	68.0537i	0.207631	−	0.124641i
$547$	392.581			0.717699			0.358850	−	0.933395i	$-0.383169\pi$
$547$	392.581			0.717699			0.358850	+	0.933395i	$0.383169\pi$
$548$	524.393	+	279.380i	0.956922	+	0.509818i
$549$	1143.27			2.08246
$550$	−115.527	+	118.968i	−0.210049	+	0.216306i
$551$			53.9764i			0.0979608i
$552$	−253.725	+	12.9823i	−0.459646	+	0.0235186i
$553$			125.055i			0.226139i
$554$	−36.6341	+	21.9914i	−0.0661266	+	0.0396957i
$555$	−430.081	+	56.1035i	−0.774921	+	0.101087i
$556$	−456.709	−	243.320i	−0.821420	−	0.437626i
$557$			257.215i			0.461786i	0.972979	+	0.230893i	$0.0741647\pi$
$557$			257.215i			0.461786i	−0.972979	+	0.230893i	$0.925835\pi$
$558$	−792.316	+	475.627i	−1.41992	+	0.852378i
$559$			183.303i			0.327912i
$560$	−406.258	+	357.379i	−0.725460	+	0.638177i
$561$	−283.143			−0.504711
$562$	−325.048	−	541.477i	−0.578378	−	0.963482i
$563$	556.118			0.987776			0.493888	−	0.869526i	$-0.335575\pi$
$563$	556.118			0.987776			0.493888	+	0.869526i	$0.335575\pi$
$564$	−111.781	+	209.812i	−0.198194	+	0.372007i
$565$	893.248	−	116.523i	1.58097	−	0.206235i
$566$	410.864	+	684.432i	0.725908	+	1.20924i
$567$	453.364			0.799584
$568$	−20.5645	−	401.911i	−0.0362051	−	0.707590i
$569$	398.335			0.700062			0.350031	−	0.936738i	$-0.386171\pi$
$569$	398.335			0.700062			0.350031	+	0.936738i	$0.386171\pi$
$570$	46.5928	+	58.7675i	0.0817418	+	0.103101i
$571$			819.200i			1.43468i	0.696725	+	0.717338i	$0.254640\pi$
$571$			819.200i			1.43468i	−0.696725	+	0.717338i	$0.745360\pi$
$572$	13.8616	−	26.0181i	0.0242336	−	0.0454861i
$573$		−	308.591i		−	0.538553i
$574$	396.055	+	659.762i	0.689991	+	1.14941i
$575$	−174.446	+	46.3004i	−0.303385	+	0.0805225i
$576$	658.920	−	67.6067i	1.14396	−	0.117373i
$577$			665.479i			1.15334i	0.816976	+	0.576672i	$0.195649\pi$
$577$			665.479i			1.15334i	−0.816976	+	0.576672i	$0.804351\pi$
$578$	90.2304	+	150.309i	0.156108	+	0.260050i
$579$			1479.53i			2.55532i
$580$	592.637	+	222.936i	1.02179	+	0.384372i
$581$	964.304			1.65973
$582$	−1306.98	+	784.582i	−2.24568	+	1.34808i
$583$	208.775			0.358105
$584$	11.1367	+	217.655i	0.0190697	+	0.372698i
$585$	−114.027	+	14.8746i	−0.194918	+	0.0254267i
$586$	−154.351	+	92.6567i	−0.263397	+	0.158117i
$587$	536.375			0.913756			0.456878	−	0.889529i	$-0.348968\pi$
$587$	536.375			0.913756			0.456878	+	0.889529i	$0.348968\pi$
$588$	−26.9334	+	50.5538i	−0.0458052	+	0.0859758i
$589$	−76.1157			−0.129229
$590$	−231.091	−	291.474i	−0.391679	−	0.494024i
$591$		−	342.430i		−	0.579408i
$592$	−261.869	+	176.005i	−0.442347	+	0.297306i
$593$		−	784.565i		−	1.32304i	−0.749926	−	0.661522i	$-0.769911\pi$
$593$		−	784.565i		−	1.32304i	0.749926	−	0.661522i	$-0.230089\pi$
$594$	−33.7650	+	20.2691i	−0.0568435	+	0.0341231i
$595$	−650.801	+	84.8960i	−1.09378	+	0.142682i
$596$	−60.7824	+	114.088i	−0.101984	+	0.191423i
$597$			1136.48i			1.90366i
$598$	27.5094	−	16.5139i	0.0460024	−	0.0276152i
$599$			734.563i			1.22631i	0.789961	+	0.613157i	$0.210101\pi$
$599$			734.563i			1.22631i	−0.789961	+	0.613157i	$0.789899\pi$
$600$	837.681	−	268.845i	1.39614	−	0.448074i
$601$	195.844			0.325864			0.162932	−	0.986637i	$-0.447905\pi$
$601$	195.844			0.325864			0.162932	+	0.986637i	$0.447905\pi$
$602$	574.296	+	956.683i	0.953980	+	1.58917i
$603$	501.251			0.831261
$604$	755.206	+	402.350i	1.25034	+	0.666142i
$605$	−7.11440	−	54.5379i	−0.0117593	−	0.0901453i
$606$	157.257	+	261.964i	0.259499	+	0.432283i
$607$	1195.06			1.96879			0.984395	−	0.175972i	$-0.0563067\pi$
$607$	1195.06			1.96879			0.984395	+	0.175972i	$0.0563067\pi$
$608$	49.3984	+	23.1590i	0.0812473	+	0.0380905i
$609$	−941.900			−1.54663
$610$	865.598	−	686.275i	1.41901	−	1.12504i
$611$		−	30.0237i		−	0.0491386i
$612$	709.094	+	377.783i	1.15865	+	0.617292i
$613$		−	537.326i		−	0.876551i	−0.898841	−	0.438275i	$-0.855589\pi$
$613$		−	537.326i		−	0.876551i	0.898841	−	0.438275i	$-0.144411\pi$
$614$	−27.9771	−	46.6052i	−0.0455653	−	0.0759043i
$615$	−161.844	−	1240.67i	−0.263161	−	2.01736i
$616$	−9.17015	−	179.221i	−0.0148866	−	0.290943i
$617$		−	374.763i		−	0.607395i	−0.952768	−	0.303698i	$-0.901779\pi$
$617$		−	374.763i		−	0.607395i	0.952768	−	0.303698i	$-0.0982213\pi$
$618$	−401.877	−	669.461i	−0.650286	−	1.08327i
$619$			485.901i			0.784977i	0.919757	+	0.392488i	$0.128386\pi$
$619$			485.901i			0.784977i	−0.919757	+	0.392488i	$0.871614\pi$
$620$	−314.376	+	835.717i	−0.507059	+	1.34793i
$621$	−42.8619			−0.0690207
$622$	−691.486	+	415.099i	−1.11171	+	0.667361i
$623$	962.780			1.54539
$624$	−129.804	+	87.2426i	−0.208019	+	0.139812i
$625$	542.739	−	309.934i	0.868383	−	0.495894i
$626$	399.887	−	240.052i	0.638797	−	0.383470i
$627$	−24.8736			−0.0396708
$628$	582.803	+	310.499i	0.928030	+	0.494425i
$629$	−382.719			−0.608456
$630$	−548.519	+	434.884i	−0.870664	+	0.690292i
$631$			1145.46i			1.81531i	0.419717	+	0.907655i	$0.362129\pi$
$631$			1145.46i			1.81531i	−0.419717	+	0.907655i	$0.637871\pi$
$632$	−7.55861	−	147.725i	−0.0119598	−	0.233742i
$633$			479.269i			0.757139i
$634$	−490.972	+	294.730i	−0.774404	+	0.464874i
$635$	8.58905	+	65.8424i	0.0135261	+	0.103689i
$636$	−977.516	−	520.790i	−1.53698	−	0.818852i
$637$		−	7.23414i		−	0.0113566i
$638$	−180.052	+	108.085i	−0.282213	+	0.169412i
$639$		−	520.636i		−	0.814767i
$640$	458.303	−	446.720i	0.716098	−	0.697999i
$641$	−493.176			−0.769385			−0.384692	−	0.923045i	$-0.625692\pi$
$641$	−493.176			−0.769385			−0.384692	+	0.923045i	$0.625692\pi$
$642$	−17.3168	−	28.8469i	−0.0269732	−	0.0449329i
$643$	831.666			1.29342			0.646708	−	0.762738i	$-0.276145\pi$
$643$	831.666			1.29342			0.646708	+	0.762738i	$0.276145\pi$
$644$	91.8366	−	172.376i	0.142603	−	0.267665i
$645$	−234.681	−	1799.03i	−0.363846	−	2.78919i
$646$	34.0604	+	56.7390i	0.0527250	+	0.0878312i
$647$	−570.901			−0.882382			−0.441191	−	0.897413i	$-0.645444\pi$
$647$	−570.901			−0.882382			−0.441191	+	0.897413i	$0.645444\pi$
$648$	−535.549	+	27.4023i	−0.826465	+	0.0422876i
$649$	123.368			0.190089
$650$	−77.4038	+	79.7094i	−0.119083	+	0.122630i
$651$		−	1328.24i		−	2.04030i
$652$	−329.895	+	619.210i	−0.505974	+	0.949708i
$653$			638.860i			0.978346i	0.872187	+	0.489173i	$0.162701\pi$
$653$			638.860i			0.978346i	−0.872187	+	0.489173i	$0.837299\pi$
$654$	74.4903	+	124.089i	0.113899	+	0.189738i
$655$	−932.002	+	121.578i	−1.42290	+	0.185616i
$656$	−507.729	−	755.425i	−0.773977	−	1.15156i
$657$			281.951i			0.429150i
$658$	−94.0655	−	156.698i	−0.142957	−	0.238142i
$659$			329.450i			0.499924i	0.968256	+	0.249962i	$0.0804182\pi$
$659$			329.450i			0.499924i	−0.968256	+	0.249962i	$0.919582\pi$
$660$	−102.734	+	273.101i	−0.155658	+	0.413790i
$661$	220.511			0.333602			0.166801	−	0.985991i	$-0.446656\pi$
$661$	220.511			0.333602			0.166801	+	0.985991i	$0.446656\pi$
$662$	−42.2343	+	25.3532i	−0.0637980	+	0.0382979i
$663$	−189.707			−0.286134
$664$	−1139.11	+	58.2847i	−1.71553	+	0.0877782i
$665$	−57.1717	+	7.45797i	−0.0859725	+	0.0112150i
$666$	−349.976	+	210.090i	−0.525489	+	0.315451i
$667$	−228.561			−0.342670
$668$	498.991	−	936.601i	0.746993	−	1.40210i
$669$	511.935			0.765224
$670$	379.510	−	300.888i	0.566432	−	0.449086i
$671$			366.368i			0.546003i
$672$	−404.130	+	862.012i	−0.601383	+	1.28276i
$673$		−	821.967i		−	1.22135i	−0.791882	−	0.610674i	$-0.790899\pi$
$673$		−	821.967i		−	1.22135i	0.791882	−	0.610674i	$-0.209101\pi$
$674$	−305.878	+	183.618i	−0.453825	+	0.272431i
$675$	143.458	−	38.0758i	0.212531	−	0.0564086i
$676$	−308.568	+	579.178i	−0.456461	+	0.856773i
$677$		−	80.1206i		−	0.118347i	−0.998248	−	0.0591733i	$-0.981154\pi$
$677$		−	80.1206i		−	0.118347i	0.998248	−	0.0591733i	$-0.0188464\pi$
$678$	1358.96	−	815.782i	2.00436	−	1.20322i
$679$		−	1171.93i		−	1.72596i
$680$	763.646	−	139.622i	1.12301	−	0.205326i
$681$	−376.598			−0.553008
$682$	−152.418	−	253.903i	−0.223487	−	0.372292i
$683$	240.382			0.351951			0.175975	−	0.984395i	$-0.443692\pi$
$683$	240.382			0.351951			0.175975	+	0.984395i	$0.443692\pi$
$684$	62.2926	+	33.1875i	0.0910711	+	0.0485198i
$685$	736.477	−	96.0723i	1.07515	−	0.140252i
$686$	−363.808	−	606.044i	−0.530332	−	0.883447i
$687$	−1261.08			−1.83563
$688$	−736.228	−	1095.40i	−1.07010	−	1.59215i
$689$	139.881			0.203020
$690$	−248.849	+	197.296i	−0.360650	+	0.285936i
$691$		−	464.924i		−	0.672828i	−0.941714	−	0.336414i	$-0.890786\pi$
$691$		−	464.924i		−	0.672828i	0.941714	−	0.336414i	$-0.109214\pi$
$692$	680.827	+	362.723i	0.983854	+	0.524166i
$693$		−	232.163i		−	0.335011i
$694$	−265.269	−	441.894i	−0.382232	−	0.636736i
$695$	−641.419	+	83.6722i	−0.922905	+	0.120392i
$696$	1112.65	−	56.9306i	1.59863	−	0.0817968i
$697$		−	1104.05i		−	1.58400i
$698$	47.8622	+	79.7305i	0.0685704	+	0.114227i
$699$			40.4088i			0.0578094i
$700$	−154.248	+	658.523i	−0.220354	+	0.940748i
$701$	−1056.49			−1.50711			−0.753557	−	0.657383i	$-0.771663\pi$
$701$	−1056.49			−1.50711			−0.753557	+	0.657383i	$0.771663\pi$
$702$	−22.6227	+	13.5804i	−0.0322261	+	0.0193453i
$703$	−33.6212			−0.0478253
$704$	21.6650	+	211.155i	0.0307742	+	0.299937i
$705$	38.4390	+	294.668i	0.0545234	+	0.417968i
$706$	−855.919	+	513.807i	−1.21235	+	0.727773i
$707$	−234.893			−0.332240
$708$	−577.626	−	307.741i	−0.815856	−	0.434662i
$709$	465.322			0.656308			0.328154	−	0.944624i	$-0.393574\pi$
$709$	465.322			0.656308			0.328154	+	0.944624i	$0.393574\pi$
$710$	−312.525	−	394.187i	−0.440176	−	0.555193i
$711$		−	191.363i		−	0.269147i
$712$	−1137.31	+	58.1926i	−1.59735	+	0.0817312i
$713$		−	322.309i		−	0.452046i
$714$	−990.107	+	594.361i	−1.38670	+	0.832438i
$715$	−4.76668	−	36.5407i	−0.00666669	−	0.0511058i
$716$	218.100	+	116.197i	0.304608	+	0.162286i
$717$		−	123.152i		−	0.171760i
$718$	−801.289	+	481.013i	−1.11600	+	0.669935i
$719$		−	1243.44i		−	1.72940i	−0.502285	−	0.864702i	$-0.667507\pi$
$719$		−	1243.44i		−	1.72940i	0.502285	−	0.864702i	$-0.332493\pi$
$720$	621.668	−	546.873i	0.863428	−	0.759546i
$721$	600.281			0.832568
$722$	−368.610	−	614.044i	−0.510540	−	0.850476i
$723$	1135.84			1.57101
$724$	83.8646	−	157.413i	0.115835	−	0.217421i
$725$	764.991	−	203.039i	1.05516	−	0.280054i
$726$	−49.8082	−	82.9722i	−0.0686063	−	0.114287i
$727$	−556.549			−0.765542			−0.382771	−	0.923843i	$-0.625030\pi$
$727$	−556.549			−0.765542			−0.382771	+	0.923843i	$0.625030\pi$
$728$	−6.14404	−	120.079i	−0.00843962	−	0.164943i
$729$	−928.795			−1.27407
$730$	169.248	+	213.473i	0.231847	+	0.292428i
$731$		−	1600.91i		−	2.19003i
$732$	913.905	−	1715.39i	1.24850	−	2.34343i
$733$			578.930i			0.789810i	0.918722	+	0.394905i	$0.129222\pi$
$733$			578.930i			0.789810i	−0.918722	+	0.394905i	$0.870778\pi$
$734$	528.008	+	879.575i	0.719357	+	1.19833i
$735$	9.26178	+	70.9995i	0.0126011	+	0.0965979i
$736$	−98.0659	+	209.175i	−0.133242	+	0.284206i
$737$			160.629i			0.217950i
$738$	−606.056	−	1009.59i	−0.821214	−	1.36801i
$739$			295.380i			0.399703i	0.979826	+	0.199851i	$0.0640459\pi$
$739$			295.380i			0.399703i	−0.979826	+	0.199851i	$0.935954\pi$
$740$	−138.864	+	369.146i	−0.187654	+	0.498846i
$741$	−16.6654			−0.0224905
$742$	730.055	−	438.252i	0.983902	−	0.590636i
$743$	306.154			0.412051			0.206026	−	0.978547i	$-0.433947\pi$
$743$	306.154			0.412051			0.206026	+	0.978547i	$0.433947\pi$
$744$	80.2816	+	1569.02i	0.107905	+	2.10889i
$745$	20.9016	+	160.229i	0.0280559	+	0.215072i
$746$	1057.20	−	634.637i	1.41716	−	0.850719i
$747$	−1475.61			−1.97538
$748$	−121.063	+	227.234i	−0.161849	+	0.303789i
$749$	25.8660			0.0345340
$750$	657.629	−	881.407i	0.876839	−	1.17521i
$751$		−	690.163i		−	0.918992i	−0.888180	−	0.459496i	$-0.848030\pi$
$751$		−	690.163i		−	0.918992i	0.888180	−	0.459496i	$-0.151970\pi$
$752$	120.589	+	179.418i	0.160357	+	0.238588i
$753$			37.3760i			0.0496361i
$754$	−120.636	+	72.4175i	−0.159994	+	0.0960445i
$755$	1060.64	−	138.359i	1.40482	−	0.183257i
$756$	−75.5231	+	141.756i	−0.0998982	+	0.187508i
$757$		−	561.479i		−	0.741717i	−0.928689	−	0.370858i	$-0.879064\pi$
$757$		−	561.479i		−	0.741717i	0.928689	−	0.370858i	$-0.120936\pi$
$758$	−1184.04	+	710.781i	−1.56206	+	0.937705i
$759$		−	105.326i		−	0.138770i
$760$	67.0850	−	12.2655i	0.0882697	−	0.0161389i
$761$	1.53264			0.00201398			0.00100699	−	0.999999i	$-0.499679\pi$
$761$	1.53264			0.00201398			0.00100699	+	0.999999i	$0.499679\pi$
$762$	60.1323	+	100.170i	0.0789137	+	0.131457i
$763$	−111.266			−0.145827
$764$	−247.657	−	131.944i	−0.324158	−	0.172701i
$765$	995.876	−	129.911i	1.30180	−	0.169818i
$766$	397.107	+	661.516i	0.518417	+	0.863598i
$767$	82.6571			0.107767
$768$	425.288	−	1042.70i	0.553761	−	1.35769i
$769$	−912.045			−1.18601			−0.593007	−	0.805197i	$-0.702059\pi$
$769$	−912.045			−1.18601			−0.593007	+	0.805197i	$0.702059\pi$
$770$	−139.361	−	175.777i	−0.180989	−	0.228281i
$771$		−	1882.95i		−	2.44221i
$772$	1187.38	+	632.600i	1.53806	+	0.819430i
$773$			1240.60i			1.60491i	0.596709	+	0.802457i	$0.296474\pi$
$773$			1240.60i			1.60491i	−0.596709	+	0.802457i	$0.703526\pi$
$774$	−878.806	−	1463.95i	−1.13541	−	1.89140i
$775$

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+(-1.02937 - 1.71476i) q^{2} -4.39883 q^{3} +(-1.88080 + 3.53024i) q^{4} +(0.646763 + 4.95799i) q^{5} +(4.52802 + 7.54293i) q^{6} -6.76347 q^{7} +(7.98955 - 0.408800i) q^{8} +10.3497 q^{9} +(7.83601 - 6.21265i) q^{10} +3.31662i q^{11} +(8.27331 - 15.5289i) q^{12} +2.22215i q^{13} +(6.96211 + 11.5977i) q^{14} +(-2.84500 - 21.8094i) q^{15} +(-8.92518 - 13.2793i) q^{16} -19.4076i q^{17} +(-10.6536 - 17.7472i) q^{18} -1.70493i q^{19} +(-18.7193 - 7.04176i) q^{20} +29.7513 q^{21} +(5.68721 - 3.41403i) q^{22} +7.21944 q^{23} +(-35.1446 + 1.79824i) q^{24} +(-24.1634 + 6.41330i) q^{25} +(3.81046 - 2.28742i) q^{26} -5.93701 q^{27} +(12.7207 - 23.8767i) q^{28} -31.6591 q^{29} +(-34.4692 + 27.3284i) q^{30} -44.6446i q^{31} +(-13.5836 + 28.9739i) q^{32} -14.5893i q^{33} +(-33.2794 + 19.9776i) q^{34} +(-4.37436 - 33.5332i) q^{35} +(-19.4657 + 36.5368i) q^{36} -19.7200i q^{37} +(-2.92354 + 1.75500i) q^{38} -9.77488i q^{39} +(7.19417 + 39.3477i) q^{40} +56.8872 q^{41} +(-30.6251 - 51.0164i) q^{42} +82.4889 q^{43} +(-11.7085 - 6.23791i) q^{44} +(6.69379 + 51.3136i) q^{45} +(-7.43147 - 12.3796i) q^{46} -13.5111 q^{47} +(39.2603 + 58.4136i) q^{48} -3.25546 q^{49} +(35.8703 + 34.8328i) q^{50} +85.3708i q^{51} +(-7.84474 - 4.17943i) q^{52} -62.9482i q^{53} +(6.11137 + 10.1805i) q^{54} +(-16.4438 + 2.14507i) q^{55} +(-54.0371 + 2.76490i) q^{56} +7.49968i q^{57} +(32.5889 + 54.2877i) q^{58} -37.1968i q^{59} +(82.3431 + 30.9755i) q^{60} +110.464 q^{61} +(-76.5547 + 45.9557i) q^{62} -69.9998 q^{63} +(63.6658 - 6.53225i) q^{64} +(-11.0174 + 1.43721i) q^{65} +(-25.0171 + 15.0177i) q^{66} +48.4315 q^{67} +(68.5136 + 36.5019i) q^{68} -31.7571 q^{69} +(-52.9986 + 42.0191i) q^{70} -50.3046i q^{71} +(82.6893 - 4.23094i) q^{72} +27.2425i q^{73} +(-33.8151 + 20.2992i) q^{74} +(106.291 - 28.2110i) q^{75} +(6.01880 + 3.20663i) q^{76} -22.4319i q^{77} +(-16.7616 + 10.0620i) q^{78} -18.4898i q^{79} +(60.0664 - 52.8396i) q^{80} -67.0313 q^{81} +(-58.5579 - 97.5479i) q^{82} -142.575 q^{83} +(-55.9563 + 105.029i) q^{84} +(96.2229 - 12.5521i) q^{85} +(-84.9115 - 141.449i) q^{86} +139.263 q^{87} +(1.35583 + 26.4983i) q^{88} -142.350 q^{89} +(81.1002 - 64.2989i) q^{90} -15.0295i q^{91} +(-13.5783 + 25.4864i) q^{92} +196.384i q^{93} +(13.9079 + 23.1682i) q^{94} +(8.45301 - 1.10268i) q^{95} +(59.7518 - 127.451i) q^{96} +173.273i q^{97} +(3.35107 + 5.58233i) q^{98} +34.3260i 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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