LMFDB - Embedded newform 220.3.h.a.199.20

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

$q$-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	$-0.972762\pi$
$13$		−	2.22215i		−	0.170935i	0.996341	−	0.0854675i	$-0.0272384\pi$
$14$	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	$0.193372\pi$
$17$			19.4076i			1.14163i	−0.821080	+	0.570813i	$0.806628\pi$
$18$	−10.6536	+	17.7472i	−0.591869	+	0.985956i
$19$			1.70493i			0.0897330i	0.998993	+	0.0448665i	$0.0142862\pi$
$19$			1.70493i			0.0897330i	−0.998993	+	0.0448665i	$0.985714\pi$
$20$	−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	$0.255892\pi$
$31$			44.6446i			1.44015i	−0.693898	+	0.720074i	$0.744108\pi$
$32$	−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	$0.0858629\pi$
$37$			19.7200i			0.532974i	−0.963839	+	0.266487i	$0.914137\pi$
$38$	−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	$0.202393\pi$
$53$			62.9482i			1.18770i	−0.804575	+	0.593850i	$0.797607\pi$
$54$	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	$0.102081\pi$
$59$			37.1968i			0.630454i	−0.949016	+	0.315227i	$0.897919\pi$
$60$	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	$0.115266\pi$
$71$			50.3046i			0.708515i	−0.935148	+	0.354258i	$0.884734\pi$
$72$	82.6893	+	4.23094i	1.14846	+	0.0587631i
$73$		−	27.2425i		−	0.373185i	−0.982437	−	0.186593i	$-0.940256\pi$
$73$		−	27.2425i		−	0.373185i	0.982437	−	0.186593i	$-0.0597445\pi$
$74$	−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	$0.0373354\pi$
$79$			18.4898i			0.234048i	−0.993129	+	0.117024i	$0.962665\pi$
$80$	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	$-0.648484\pi$
$97$		−	173.273i		−	1.78632i	0.449742	−	0.893159i	$-0.351516\pi$
$98$	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	$0.293677\pi$
$113$			180.163i			1.59437i	−0.603738	+	0.797183i	$0.706323\pi$
$114$	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	$-0.745295\pi$
$131$		−	187.980i		−	1.43496i	0.696579	−	0.717480i	$-0.254705\pi$
$132$	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	$0.182381\pi$
$137$			148.543i			1.08426i	−0.840295	+	0.542129i	$0.817619\pi$
$138$	32.6898	−	54.4558i	0.236882	−	0.394607i
$139$		−	129.371i		−	0.930724i	−0.885120	−	0.465362i	$-0.845924\pi$
$139$		−	129.371i		−	0.930724i	0.885120	−	0.465362i	$-0.154076\pi$
$140$	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	$0.250565\pi$
$151$			213.925i			1.41672i	−0.705851	+	0.708360i	$0.749435\pi$
$152$	−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	$0.176219\pi$
$157$			165.089i			1.05152i	−0.850633	+	0.525760i	$0.823781\pi$
$158$	−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	$0.188196\pi$
$173$			192.856i			1.11477i	−0.830253	+	0.557386i	$0.811804\pi$
$174$	−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	$0.0552074\pi$
$179$			61.7804i			0.345142i	−0.984997	+	0.172571i	$0.944793\pi$
$180$	−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	$-0.941210\pi$
$191$		−	70.1530i		−	0.367293i	0.982992	−	0.183646i	$-0.0587902\pi$
$192$	−280.055	−	28.7342i	−1.45862	−	0.149657i
$193$			336.346i			1.74273i	0.490638	+	0.871364i	$0.336764\pi$
$193$			336.346i			1.74273i	−0.490638	+	0.871364i	$0.663236\pi$
$194$	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	$-0.936692\pi$
$197$		−	77.8458i		−	0.395156i	0.980287	−	0.197578i	$-0.0633076\pi$
$198$	58.8608	+	35.3341i	0.297277	+	0.178455i
$199$			258.361i			1.29830i	0.760662	+	0.649148i	$0.224874\pi$
$199$			258.361i			1.29830i	−0.760662	+	0.649148i	$0.775126\pi$
$200$	−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	$0.0831242\pi$
$211$			108.954i			0.516369i	−0.966096	+	0.258184i	$0.916876\pi$
$212$	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	$0.00627525\pi$
$233$			9.18626i			0.0394260i	−0.999806	+	0.0197130i	$0.993725\pi$
$234$	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	$-0.981346\pi$
$239$		−	27.9965i		−	0.117140i	0.998283	−	0.0585701i	$-0.0186541\pi$
$240$	−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	$0.00538795\pi$
$251$			8.49681i			0.0338518i	−0.999857	+	0.0169259i	$0.994612\pi$
$252$	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	$-0.686740\pi$
$257$		−	428.056i		−	1.66559i	0.553582	−	0.832794i	$-0.313260\pi$
$258$	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	$-0.972019\pi$
$271$		−	47.5830i		−	0.175583i	0.996139	−	0.0877916i	$-0.0279809\pi$
$272$	−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	$0.0122781\pi$
$277$			21.3640i			0.0771264i	−0.999256	+	0.0385632i	$0.987722\pi$
$278$	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	$0.0490887\pi$
$293$			90.0131i			0.307212i	−0.988132	+	0.153606i	$0.950911\pi$
$294$	−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	$0.224528\pi$
$311$			403.255i			1.29664i	−0.761367	+	0.648321i	$0.775472\pi$
$312$	−3.99596	+	78.0968i	−0.0128076	+	0.250310i
$313$		−	233.203i		−	0.745058i	−0.928021	−	0.372529i	$-0.878491\pi$
$313$		−	233.203i		−	0.745058i	0.928021	−	0.372529i	$-0.121509\pi$
$314$	−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	$0.149150\pi$
$317$			286.321i			0.903222i	−0.892215	+	0.451611i	$0.850850\pi$
$318$	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	$0.0118455\pi$
$331$			24.6298i			0.0744104i	−0.999308	+	0.0372052i	$0.988154\pi$
$332$	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	$0.0852592\pi$
$337$			178.380i			0.529317i	−0.964342	+	0.264658i	$0.914741\pi$
$338$	−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	$0.249956\pi$
$353$			499.148i			1.41402i	−0.707205	+	0.707009i	$0.750044\pi$
$354$	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	$0.225575\pi$
$359$			467.290i			1.30164i	−0.759231	+	0.650821i	$0.774425\pi$
$360$	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	$-0.690358\pi$
$373$		−	616.530i		−	1.65290i	0.563014	−	0.826448i	$-0.309642\pi$
$374$	−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	$0.364651\pi$
$379$			690.502i			1.82190i	−0.412513	+	0.910952i	$0.635349\pi$
$380$	−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	$-0.989031\pi$
$397$		−	27.3556i		−	0.0689057i	0.999406	−	0.0344528i	$-0.0109689\pi$
$398$	−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	$-0.917687\pi$
$419$		−	214.295i		−	0.511445i	0.966750	−	0.255722i	$-0.0823133\pi$
$420$	−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	$-0.835077\pi$
$431$		−	426.905i		−	0.990500i	0.868751	−	0.495250i	$-0.164923\pi$
$432$	52.9889	−	78.8396i	0.122659	−	0.182499i
$433$			27.7192i			0.0640167i	0.999488	+	0.0320084i	$0.0101903\pi$
$433$			27.7192i			0.0640167i	−0.999488	+	0.0320084i	$0.989810\pi$
$434$	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	$0.187370\pi$
$439$			487.493i			1.11046i	−0.831696	+	0.555231i	$0.812630\pi$
$440$	−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	$-0.887226\pi$
$457$		−	317.090i		−	0.693851i	0.937893	−	0.346925i	$-0.112774\pi$
$458$	−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	$0.0355764\pi$
$479$			106.849i			0.223068i	−0.993761	+	0.111534i	$0.964424\pi$
$480$	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	$-0.926198\pi$
$491$		−	225.649i		−	0.459570i	0.973241	−	0.229785i	$-0.0738022\pi$
$492$	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	$0.248618\pi$
$499$			702.622i			1.40806i	−0.710170	+	0.704031i	$0.751382\pi$
$500$	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	$-0.925835\pi$
$557$		−	257.215i		−	0.461786i	0.972979	−	0.230893i	$-0.0741647\pi$
$558$	−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	$-0.745360\pi$
$571$		−	819.200i		−	1.43468i	0.696725	−	0.717338i	$-0.254640\pi$
$572$	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	$-0.804351\pi$
$577$		−	665.479i		−	1.15334i	0.816976	−	0.576672i	$-0.195649\pi$
$578$	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	$0.230089\pi$
$593$			784.565i			1.32304i	−0.749926	+	0.661522i	$0.769911\pi$
$594$	−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	$-0.789899\pi$
$599$		−	734.563i		−	1.22631i	0.789961	−	0.613157i	$-0.210101\pi$
$600$	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	$0.144411\pi$
$613$			537.326i			0.876551i	−0.898841	+	0.438275i	$0.855589\pi$
$614$	−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	$0.0982213\pi$
$617$			374.763i			0.607395i	−0.952768	+	0.303698i	$0.901779\pi$
$618$	−401.877	+	669.461i	−0.650286	+	1.08327i
$619$		−	485.901i		−	0.784977i	−0.919757	−	0.392488i	$-0.871614\pi$
$619$		−	485.901i		−	0.784977i	0.919757	−	0.392488i	$-0.128386\pi$
$620$	−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	$-0.637871\pi$
$631$		−	1145.46i		−	1.81531i	0.419717	−	0.907655i	$-0.362129\pi$
$632$	−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	$-0.837299\pi$
$653$		−	638.860i		−	0.978346i	0.872187	−	0.489173i	$-0.162701\pi$
$654$	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	$-0.919582\pi$
$659$		−	329.450i		−	0.499924i	0.968256	−	0.249962i	$-0.0804182\pi$
$660$	−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	$0.209101\pi$
$673$			821.967i			1.22135i	−0.791882	+	0.610674i	$0.790899\pi$
$674$	−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	$0.0188464\pi$
$677$			80.1206i			0.118347i	−0.998248	+	0.0591733i	$0.981154\pi$
$678$	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	$0.109214\pi$
$691$			464.924i			0.672828i	−0.941714	+	0.336414i	$0.890786\pi$
$692$	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	$0.332493\pi$
$719$			1243.44i			1.72940i	−0.502285	+	0.864702i	$0.667507\pi$
$720$	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	$-0.870778\pi$
$733$		−	578.930i		−	0.789810i	0.918722	−	0.394905i	$-0.129222\pi$
$734$	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	$-0.935954\pi$
$739$		−	295.380i		−	0.399703i	0.979826	−	0.199851i	$-0.0640459\pi$
$740$	−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	$0.151970\pi$
$751$			690.163i			0.918992i	−0.888180	+	0.459496i	$0.848030\pi$
$752$	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	$0.120936\pi$
$757$			561.479i			0.741717i	−0.928689	+	0.370858i	$0.879064\pi$
$758$	−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	$-0.703526\pi$
$773$		−	1240.60i		−	1.60491i	0.596709	−	0.802457i	$-0.296474\pi$
$774$	−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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