LMFDB - Embedded newform 220.3.h.a.199.9

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			199.9
Character	$\chi$	$=$	220.199
Dual form			220.3.h.a.199.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.77475 - 0.922089i) q^{2} +5.34862 q^{3} +(2.29950 + 3.27296i) q^{4} +(3.88532 + 3.14711i) q^{5} +(-9.49248 - 4.93190i) q^{6} -2.03277 q^{7} +(-1.06309 - 7.92905i) q^{8} +19.6077 q^{9} +(-3.99357 - 9.16795i) q^{10} +3.31662i q^{11} +(12.2992 + 17.5058i) q^{12} -11.7832i q^{13} +(3.60766 + 1.87439i) q^{14} +(20.7811 + 16.8327i) q^{15} +(-5.42457 + 15.0524i) q^{16} -9.54644i q^{17} +(-34.7989 - 18.0801i) q^{18} +30.8261i q^{19} +(-1.36607 + 19.9533i) q^{20} -10.8725 q^{21} +(3.05822 - 5.88619i) q^{22} -30.3657 q^{23} +(-5.68605 - 42.4095i) q^{24} +(5.19142 + 24.4550i) q^{25} +(-10.8651 + 20.9123i) q^{26} +56.7367 q^{27} +(-4.67436 - 6.65318i) q^{28} +17.7331 q^{29} +(-21.3601 - 49.0359i) q^{30} -45.9125i q^{31} +(23.5069 - 21.7123i) q^{32} +17.7394i q^{33} +(-8.80267 + 16.9426i) q^{34} +(-7.89796 - 6.39734i) q^{35} +(45.0880 + 64.1754i) q^{36} -4.82884i q^{37} +(28.4244 - 54.7087i) q^{38} -63.0238i q^{39} +(20.8231 - 34.1525i) q^{40} +27.1140 q^{41} +(19.2960 + 10.0254i) q^{42} -30.4465 q^{43} +(-10.8552 + 7.62659i) q^{44} +(76.1823 + 61.7077i) q^{45} +(53.8917 + 27.9999i) q^{46} +53.3727 q^{47} +(-29.0140 + 80.5094i) q^{48} -44.8679 q^{49} +(13.3362 - 48.1886i) q^{50} -51.0603i q^{51} +(38.5659 - 27.0955i) q^{52} -29.7540i q^{53} +(-100.694 - 52.3163i) q^{54} +(-10.4378 + 12.8861i) q^{55} +(2.16101 + 16.1179i) q^{56} +164.877i q^{57} +(-31.4718 - 16.3515i) q^{58} -57.2759i q^{59} +(-7.30657 + 106.723i) q^{60} -84.0110 q^{61} +(-42.3354 + 81.4834i) q^{62} -39.8580 q^{63} +(-61.7397 + 16.8585i) q^{64} +(37.0830 - 45.7814i) q^{65} +(16.3573 - 31.4830i) q^{66} -99.3737 q^{67} +(31.2451 - 21.9521i) q^{68} -162.415 q^{69} +(8.11801 + 18.6363i) q^{70} -89.2609i q^{71} +(-20.8447 - 155.471i) q^{72} +25.3531i q^{73} +(-4.45262 + 8.57000i) q^{74} +(27.7669 + 130.801i) q^{75} +(-100.893 + 70.8846i) q^{76} -6.74193i q^{77} +(-58.1136 + 111.852i) q^{78} +72.2901i q^{79} +(-68.4477 + 41.4116i) q^{80} +126.994 q^{81} +(-48.1207 - 25.0015i) q^{82} +2.60402 q^{83} +(-25.0014 - 35.5853i) q^{84} +(30.0437 - 37.0910i) q^{85} +(54.0350 + 28.0744i) q^{86} +94.8474 q^{87} +(26.2977 - 3.52586i) q^{88} +130.436 q^{89} +(-78.3049 - 179.763i) q^{90} +23.9525i q^{91} +(-69.8261 - 99.3859i) q^{92} -245.569i q^{93} +(-94.7233 - 49.2144i) q^{94} +(-97.0130 + 119.769i) q^{95} +(125.730 - 116.131i) q^{96} +115.244i q^{97} +(79.6294 + 41.3722i) q^{98} +65.0315i 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 $

$2$	−1.77475	−	0.922089i	−0.887377	−	0.461045i
$2$	−1.77475	−	0.922089i	−0.887377	−	0.461045i
$3$	5.34862			1.78287			0.891437	−	0.453145i	$-0.149698\pi$
$3$	5.34862			1.78287			0.891437	+	0.453145i	$0.149698\pi$
$4$	2.29950	+	3.27296i	0.574876	+	0.818241i
$5$	3.88532	+	3.14711i	0.777064	+	0.629422i
$5$	3.88532	+	3.14711i	0.777064	+	0.629422i
$6$	−9.49248	−	4.93190i	−1.58208	−	0.821984i
$7$	−2.03277			−0.290396			−0.145198	−	0.989403i	$-0.546382\pi$
$7$	−2.03277			−0.290396			−0.145198	+	0.989403i	$0.546382\pi$
$8$	−1.06309	−	7.92905i	−0.132886	−	0.991131i
$9$	19.6077			2.17864
$10$	−3.99357	−	9.16795i	−0.399357	−	0.916795i
$11$			3.31662i			0.301511i
$11$			3.31662i			0.301511i
$12$	12.2992	+	17.5058i	1.02493	+	1.45882i
$13$		−	11.7832i		−	0.906399i	−0.891409	−	0.453199i	$-0.850283\pi$
$13$		−	11.7832i		−	0.906399i	0.891409	−	0.453199i	$-0.149717\pi$
$14$	3.60766	+	1.87439i	0.257690	+	0.133885i
$15$	20.7811	+	16.8327i	1.38541	+	1.12218i
$16$	−5.42457	+	15.0524i	−0.339036	+	0.940773i
$17$		−	9.54644i		−	0.561555i	−0.959773	−	0.280778i	$-0.909408\pi$
$17$		−	9.54644i		−	0.561555i	0.959773	−	0.280778i	$-0.0905923\pi$
$18$	−34.7989	−	18.0801i	−1.93327	−	1.00445i
$19$			30.8261i			1.62242i	0.584752	+	0.811212i	$0.301192\pi$
$19$			30.8261i			1.62242i	−0.584752	+	0.811212i	$0.698808\pi$
$20$	−1.36607	+	19.9533i	−0.0683033	+	0.997665i
$21$	−10.8725			−0.517738
$22$	3.05822	−	5.88619i	0.139010	−	0.267554i
$23$	−30.3657			−1.32025			−0.660125	−	0.751156i	$-0.729497\pi$
$23$	−30.3657			−1.32025			−0.660125	+	0.751156i	$0.729497\pi$
$24$	−5.68605	−	42.4095i	−0.236919	−	1.76706i
$25$	5.19142	+	24.4550i	0.207657	+	0.978202i
$26$	−10.8651	+	20.9123i	−0.417890	+	0.804317i
$27$	56.7367			2.10136
$28$	−4.67436	−	6.65318i	−0.166941	−	0.237613i
$29$	17.7331			0.611485			0.305742	−	0.952114i	$-0.401095\pi$
$29$	17.7331			0.611485			0.305742	+	0.952114i	$0.401095\pi$
$30$	−21.3601	−	49.0359i	−0.712003	−	1.63453i
$31$		−	45.9125i		−	1.48105i	−0.672029	−	0.740525i	$-0.734577\pi$
$31$		−	45.9125i		−	1.48105i	0.672029	−	0.740525i	$-0.265423\pi$
$32$	23.5069	−	21.7123i	0.734591	−	0.678510i
$33$			17.7394i			0.537557i
$34$	−8.80267	+	16.9426i	−0.258902	+	0.498311i
$35$	−7.89796	−	6.39734i	−0.225656	−	0.182781i
$36$	45.0880	+	64.1754i	1.25245	+	1.78265i
$37$		−	4.82884i		−	0.130509i	−0.997869	−	0.0652546i	$-0.979214\pi$
$37$		−	4.82884i		−	0.130509i	0.997869	−	0.0652546i	$-0.0207859\pi$
$38$	28.4244	−	54.7087i	0.748010	−	1.43970i
$39$		−	63.0238i		−	1.61599i
$40$	20.8231	−	34.1525i	0.520579	−	0.853814i
$41$	27.1140			0.661317			0.330659	−	0.943750i	$-0.392729\pi$
$41$	27.1140			0.661317			0.330659	+	0.943750i	$0.392729\pi$
$42$	19.2960	+	10.0254i	0.459429	+	0.238701i
$43$	−30.4465			−0.708058			−0.354029	−	0.935234i	$-0.615189\pi$
$43$	−30.4465			−0.708058			−0.354029	+	0.935234i	$0.615189\pi$
$44$	−10.8552	+	7.62659i	−0.246709	+	0.173332i
$45$	76.1823	+	61.7077i	1.69294	+	1.37128i
$46$	53.8917	+	27.9999i	1.17156	+	0.608694i
$47$	53.3727			1.13559			0.567794	−	0.823170i	$-0.307797\pi$
$47$	53.3727			1.13559			0.567794	+	0.823170i	$0.307797\pi$
$48$	−29.0140	+	80.5094i	−0.604458	+	1.67728i
$49$	−44.8679			−0.915670
$50$	13.3362	−	48.1886i	0.266725	−	0.963773i
$51$		−	51.0603i		−	1.00118i
$52$	38.5659	−	27.0955i	0.741653	−	0.521067i
$53$		−	29.7540i		−	0.561396i	−0.959796	−	0.280698i	$-0.909434\pi$
$53$		−	29.7540i		−	0.561396i	0.959796	−	0.280698i	$-0.0905659\pi$
$54$	−100.694	−	52.3163i	−1.86470	−	0.968821i
$55$	−10.4378	+	12.8861i	−0.189778	+	0.234294i
$56$	2.16101	+	16.1179i	0.0385895	+	0.287820i
$57$			164.877i			2.89258i
$58$	−31.4718	−	16.3515i	−0.542618	−	0.281922i
$59$		−	57.2759i		−	0.970778i	−0.874298	−	0.485389i	$-0.838678\pi$
$59$		−	57.2759i		−	0.970778i	0.874298	−	0.485389i	$-0.161322\pi$
$60$	−7.30657	+	106.723i	−0.121776	+	1.77871i
$61$	−84.0110			−1.37723			−0.688614	−	0.725128i	$-0.741781\pi$
$61$	−84.0110			−1.37723			−0.688614	+	0.725128i	$0.741781\pi$
$62$	−42.3354	+	81.4834i	−0.682830	+	1.31425i
$63$	−39.8580			−0.632667
$64$	−61.7397	+	16.8585i	−0.964683	+	0.263415i
$65$	37.0830	−	45.7814i	0.570507	−	0.704330i
$66$	16.3573	−	31.4830i	0.247838	−	0.477015i
$67$	−99.3737			−1.48319			−0.741595	−	0.670848i	$-0.765930\pi$
$67$	−99.3737			−1.48319			−0.741595	+	0.670848i	$0.765930\pi$
$68$	31.2451	−	21.9521i	0.459487	−	0.322824i
$69$	−162.415			−2.35384
$70$	8.11801	+	18.6363i	0.115972	+	0.266233i
$71$		−	89.2609i		−	1.25720i	−0.777730	−	0.628598i	$-0.783629\pi$
$71$		−	89.2609i		−	1.25720i	0.777730	−	0.628598i	$-0.216371\pi$
$72$	−20.8447	−	155.471i	−0.289510	−	2.15932i
$73$			25.3531i			0.347303i	0.984807	+	0.173652i	$0.0555567\pi$
$73$			25.3531i			0.347303i	−0.984807	+	0.173652i	$0.944443\pi$
$74$	−4.45262	+	8.57000i	−0.0601705	+	0.115811i
$75$	27.7669	+	130.801i	0.370226	+	1.74401i
$76$	−100.893	+	70.8846i	−1.32753	+	0.932692i
$77$		−	6.74193i		−	0.0875576i
$78$	−58.1136	+	111.852i	−0.745046	+	1.43400i
$79$			72.2901i			0.915064i	0.889193	+	0.457532i	$0.151267\pi$
$79$			72.2901i			0.915064i	−0.889193	+	0.457532i	$0.848733\pi$
$80$	−68.4477	+	41.4116i	−0.855596	+	0.517645i
$81$	126.994			1.56782
$82$	−48.1207	−	25.0015i	−0.586838	−	0.304897i
$83$	2.60402			0.0313737			0.0156868	−	0.999877i	$-0.495007\pi$
$83$	2.60402			0.0313737			0.0156868	+	0.999877i	$0.495007\pi$
$84$	−25.0014	−	35.5853i	−0.297635	−	0.423635i
$85$	30.0437	−	37.0910i	0.353455	−	0.436364i
$86$	54.0350	+	28.0744i	0.628314	+	0.326446i
$87$	94.8474			1.09020
$88$	26.2977	−	3.52586i	0.298837	−	0.0400666i
$89$	130.436			1.46557			0.732787	−	0.680458i	$-0.238219\pi$
$89$	130.436			1.46557			0.732787	+	0.680458i	$0.238219\pi$
$90$	−78.3049	−	179.763i	−0.870054	−	1.99736i
$91$			23.9525i			0.263214i
$92$	−69.8261	−	99.3859i	−0.758979	−	1.08028i
$93$		−	245.569i		−	2.64052i
$94$	−94.7233	−	49.2144i	−1.00770	−	0.523557i
$95$	−97.0130	+	119.769i	−1.02119	+	1.26073i
$96$	125.730	−	116.131i	1.30968	−	1.20970i
$97$			115.244i			1.18809i	0.804433	+	0.594043i	$0.202469\pi$
$97$			115.244i			1.18809i	−0.804433	+	0.594043i	$0.797531\pi$
$98$	79.6294	+	41.3722i	0.812545	+	0.422165i
$99$			65.0315i			0.656884i
$100$	−68.1028	+	73.2258i	−0.681028	+	0.732258i
$101$	−174.697			−1.72967			−0.864836	−	0.502054i	$-0.832578\pi$
$101$	−174.697			−1.72967			−0.864836	+	0.502054i	$0.832578\pi$
$102$	−47.0821	+	90.6194i	−0.461589	+	0.888425i
$103$	1.47775			0.0143471			0.00717354	−	0.999974i	$-0.497717\pi$
$103$	1.47775			0.0143471			0.00717354	+	0.999974i	$0.497717\pi$
$104$	−93.4295	+	12.5266i	−0.898360	+	0.120448i
$105$	−42.2432	−	34.2170i	−0.402316	−	0.325876i
$106$	−27.4358	+	52.8060i	−0.258829	+	0.498170i
$107$	62.9939			0.588728			0.294364	−	0.955693i	$-0.404892\pi$
$107$	62.9939			0.588728			0.294364	+	0.955693i	$0.404892\pi$
$108$	130.466	+	185.697i	1.20802	+	1.71942i
$109$	−30.8159			−0.282714			−0.141357	−	0.989959i	$-0.545147\pi$
$109$	−30.8159			−0.282714			−0.141357	+	0.989959i	$0.545147\pi$
$110$	30.4067	−	13.2452i	0.276424	−	0.120411i
$111$		−	25.8276i		−	0.232681i
$112$	11.0269	−	30.5980i	0.0984545	−	0.273196i
$113$			95.1112i			0.841692i	0.907132	+	0.420846i	$0.138267\pi$
$113$			95.1112i			0.841692i	−0.907132	+	0.420846i	$0.861733\pi$
$114$	152.031	−	292.616i	1.33361	−	2.56681i
$115$	−117.981	−	95.5642i	−1.02592	−	0.830993i
$116$	40.7772	+	58.0397i	0.351528	+	0.500342i
$117$		−	231.042i		−	1.97471i
$118$	−52.8135	+	101.651i	−0.447572	+	0.861446i
$119$			19.4057i			0.163073i
$120$	111.375	−	182.669i	0.928126	−	1.52224i
$121$	−11.0000			−0.0909091
$122$	149.099	+	77.4656i	1.22212	+	0.634964i
$123$	145.023			1.17904
$124$	150.270	−	105.576i	1.21185	−	0.851419i
$125$	−56.7924	+	111.354i	−0.454339	+	0.890829i
$126$	70.7381	+	36.7526i	0.561414	+	0.291688i
$127$	34.8579			0.274472			0.137236	−	0.990538i	$-0.456178\pi$
$127$	34.8579			0.274472			0.137236	+	0.990538i	$0.456178\pi$
$128$	125.118	+	27.0097i	0.977483	+	0.211014i
$129$	−162.847			−1.26238
$130$	−108.028	+	47.0570i	−0.830982	+	0.361977i
$131$			137.386i			1.04875i	0.851488	+	0.524374i	$0.175701\pi$
$131$			137.386i			1.04875i	−0.851488	+	0.524374i	$0.824299\pi$
$132$	−58.0603	+	40.7917i	−0.439851	+	0.309028i
$133$		−	62.6623i		−	0.471145i
$134$	176.364	+	91.6314i	1.31615	+	0.683816i
$135$	220.440	+	178.557i	1.63289	+	1.32264i
$136$	−75.6942	+	10.1487i	−0.556575	+	0.0746228i
$137$		−	186.735i		−	1.36303i	−0.731803	−	0.681516i	$-0.761321\pi$
$137$		−	186.735i		−	1.36303i	0.731803	−	0.681516i	$-0.238679\pi$
$138$	288.246	+	149.761i	2.08874	+	1.08522i
$139$		−	132.000i		−	0.949639i	−0.880083	−	0.474819i	$-0.842513\pi$
$139$		−	132.000i		−	0.949639i	0.880083	−	0.474819i	$-0.157487\pi$
$140$	2.77690	−	40.5604i	0.0198350	−	0.289717i
$141$	285.470			2.02461
$142$	−82.3065	+	158.416i	−0.579623	+	1.11561i
$143$	39.0804			0.273290
$144$	−106.364	+	295.143i	−0.738636	+	2.04960i
$145$	68.8986	+	55.8079i	0.475163	+	0.384882i
$146$	23.3779	−	44.9956i	0.160122	−	0.308189i
$147$	−239.981			−1.63252
$148$	15.8046	−	11.1039i	0.106788	−	0.0750265i
$149$	8.66913			0.0581821			0.0290910	−	0.999577i	$-0.490739\pi$
$149$	8.66913			0.0581821			0.0290910	+	0.999577i	$0.490739\pi$
$150$	71.3305	−	257.743i	0.475537	−	1.71828i
$151$		−	243.786i		−	1.61448i	−0.590224	−	0.807239i	$-0.700961\pi$
$151$		−	243.786i		−	1.61448i	0.590224	−	0.807239i	$-0.299039\pi$
$152$	244.421	−	32.7708i	1.60804	−	0.215597i
$153$		−	187.184i		−	1.22342i
$154$	−6.21666	+	11.9653i	−0.0403679	+	0.0776966i
$155$	144.492	−	178.385i	0.932204	−	1.15087i
$156$	206.275	−	144.923i	1.32227	−	0.928996i
$157$			193.037i			1.22953i	0.788709	+	0.614767i	$0.210750\pi$
$157$			193.037i			1.22953i	−0.788709	+	0.614767i	$0.789250\pi$
$158$	66.6579	−	128.297i	0.421886	−	0.812007i
$159$		−	159.143i		−	1.00090i
$160$	159.663	−	10.3805i	0.997893	−	0.0648780i
$161$	61.7265			0.383394
$162$	−225.382	−	117.099i	−1.39125	−	0.722836i
$163$	−56.9654			−0.349481			−0.174740	−	0.984615i	$-0.555909\pi$
$163$	−56.9654			−0.349481			−0.174740	+	0.984615i	$0.555909\pi$
$164$	62.3487	+	88.7431i	0.380175	+	0.541117i
$165$	−55.8277	+	68.9231i	−0.338350	+	0.417716i
$166$	−4.62149	−	2.40113i	−0.0278403	−	0.0144647i
$167$	−223.464			−1.33811			−0.669053	−	0.743214i	$-0.733300\pi$
$167$	−223.464			−1.33811			−0.669053	+	0.743214i	$0.733300\pi$
$168$	11.5584	+	86.2087i	0.0688001	+	0.513147i
$169$	30.1565			0.178441
$170$	−87.5213	+	38.1244i	−0.514831	+	0.224261i
$171$			604.429i			3.53467i
$172$	−70.0118	−	99.6502i	−0.407045	−	0.579362i
$173$		−	106.144i		−	0.613547i	−0.951782	−	0.306774i	$-0.900751\pi$
$173$		−	106.144i		−	0.613547i	0.951782	−	0.306774i	$-0.0992495\pi$
$174$	−168.331	−	87.4578i	−0.967418	−	0.502631i
$175$	−10.5530	−	49.7115i	−0.0603026	−	0.284065i
$176$	−49.9231	−	17.9913i	−0.283654	−	0.102223i
$177$		−	306.347i		−	1.73077i
$178$	−231.492	−	120.274i	−1.30052	−	0.675695i
$179$		−	21.5882i		−	0.120604i	−0.998180	−	0.0603022i	$-0.980794\pi$
$179$		−	21.5882i		−	0.120604i	0.998180	−	0.0603022i	$-0.0192064\pi$
$180$	−26.7855	+	391.239i	−0.148808	+	2.17355i
$181$	−48.5900			−0.268453			−0.134226	−	0.990951i	$-0.542855\pi$
$181$	−48.5900			−0.268453			−0.134226	+	0.990951i	$0.542855\pi$
$182$	22.0863	−	42.5098i	0.121353	−	0.233570i
$183$	−449.343			−2.45542
$184$	32.2814	+	240.771i	0.175443	+	1.30854i
$185$	15.1969	−	18.7616i	0.0821453	−	0.101414i
$186$	−226.436	+	435.824i	−1.21740	+	2.34314i
$187$	31.6619			0.169315
$188$	122.731	+	174.687i	0.652822	+	0.929185i
$189$	−115.333			−0.610226
$190$	282.612	−	123.106i	1.48743	−	0.647927i
$191$			85.7501i			0.448954i	0.974479	+	0.224477i	$0.0720673\pi$
$191$			85.7501i			0.448954i	−0.974479	+	0.224477i	$0.927933\pi$
$192$	−330.222	+	90.1700i	−1.71991	+	0.469635i
$193$			299.543i			1.55204i	0.630711	+	0.776018i	$0.282763\pi$
$193$			299.543i			1.55204i	−0.630711	+	0.776018i	$0.717237\pi$
$194$	106.266	−	204.530i	0.547761	−	1.05428i
$195$	198.343	−	244.868i	1.01714	−	1.25573i
$196$	−103.174	−	146.851i	−0.526397	−	0.749239i
$197$		−	36.1064i		−	0.183281i	−0.995792	−	0.0916406i	$-0.970789\pi$
$197$		−	36.1064i		−	0.183281i	0.995792	−	0.0916406i	$-0.0292111\pi$
$198$	59.9648	−	115.415i	0.302853	−	0.582904i
$199$			58.2599i			0.292763i	0.989228	+	0.146382i	$0.0467628\pi$
$199$			58.2599i			0.292763i	−0.989228	+	0.146382i	$0.953237\pi$
$200$	188.386	−	67.1609i	0.941932	−	0.335804i
$201$	−531.512			−2.64434
$202$	310.044	+	161.086i	1.53487	+	0.797456i
$203$	−36.0472			−0.177572
$204$	167.118	−	117.413i	0.819208	−	0.575555i
$205$	105.347	+	85.3307i	0.513886	+	0.416247i
$206$	−2.62264	−	1.36262i	−0.0127313	−	0.00661464i
$207$	−595.403			−2.87634
$208$	177.365	+	63.9188i	0.852716	+	0.307302i
$209$	−102.238			−0.489179
$210$	43.4201	+	99.6787i	0.206763	+	0.474660i
$211$		−	13.7636i		−	0.0652303i	−0.999468	−	0.0326151i	$-0.989616\pi$
$211$		−	13.7636i		−	0.0652303i	0.999468	−	0.0326151i	$-0.0103836\pi$
$212$	97.3837	−	68.4194i	0.459357	−	0.322733i
$213$		−	477.423i		−	2.24142i
$214$	−111.799	−	58.0860i	−0.522423	−	0.271430i
$215$	−118.294	−	95.8184i	−0.550206	−	0.445667i
$216$	−60.3161	−	449.868i	−0.279241	−	2.08272i
$217$			93.3296i			0.430090i
$218$	54.6906	+	28.4150i	0.250874	+	0.130344i
$219$			135.604i			0.619198i
$220$	−66.1776	−	4.53073i	−0.300807	−	0.0205942i
$221$	−112.487			−0.508993
$222$	−23.8154	+	45.8377i	−0.107276	+	0.206476i
$223$	22.2087			0.0995906			0.0497953	−	0.998759i	$-0.484143\pi$
$223$	22.2087			0.0995906			0.0497953	+	0.998759i	$0.484143\pi$
$224$	−47.7841	+	44.1361i	−0.213322	+	0.197036i
$225$	101.792	+	479.508i	0.452409	+	2.13115i
$226$	87.7010	−	168.799i	0.388057	−	0.746898i
$227$	384.449			1.69361			0.846804	−	0.531905i	$-0.178524\pi$
$227$	384.449			1.69361			0.846804	+	0.531905i	$0.178524\pi$
$228$	−539.636	+	379.135i	−2.36682	+	1.66287i
$229$	−34.4507			−0.150440			−0.0752199	−	0.997167i	$-0.523966\pi$
$229$	−34.4507			−0.150440			−0.0752199	+	0.997167i	$0.523966\pi$
$230$	121.268	+	278.392i	0.527251	+	1.21040i
$231$		−	36.0600i		−	0.156104i
$232$	−18.8518	−	140.606i	−0.0812577	−	0.606062i
$233$		−	381.682i		−	1.63812i	−0.573707	−	0.819060i	$-0.694495\pi$
$233$		−	381.682i		−	1.63812i	0.573707	−	0.819060i	$-0.305505\pi$
$234$	−213.041	+	410.042i	−0.910431	+	1.75232i
$235$	207.370	+	167.970i	0.882425	+	0.714764i
$236$	187.462	−	131.706i	0.794330	−	0.558077i
$237$			386.652i			1.63144i
$238$	17.8938	−	34.4403i	0.0751840	−	0.144707i
$239$			99.0654i			0.414499i	0.978288	+	0.207250i	$0.0664513\pi$
$239$			99.0654i			0.414499i	−0.978288	+	0.207250i	$0.933549\pi$
$240$	−366.101	+	221.495i	−1.52542	+	0.922895i
$241$	377.488			1.56634			0.783170	−	0.621807i	$-0.213601\pi$
$241$	377.488			1.56634			0.783170	+	0.621807i	$0.213601\pi$
$242$	19.5223	+	10.1430i	0.0806706	+	0.0419131i
$243$	168.610			0.693868
$244$	−193.183	−	274.965i	−0.791735	−	1.12690i
$245$	−174.326	−	141.204i	−0.711534	−	0.576343i
$246$	−257.379	−	133.724i	−1.04626	−	0.543592i
$247$	363.229			1.47056
$248$	−364.043	+	48.8090i	−1.46791	+	0.196811i
$249$	13.9279			0.0559353
$250$	203.470	−	145.258i	0.813882	−	0.581031i
$251$			133.640i			0.532429i	0.963914	+	0.266215i	$0.0857730\pi$
$251$			133.640i			0.532429i	−0.963914	+	0.266215i	$0.914227\pi$
$252$	−91.6536	−	130.454i	−0.363705	−	0.517674i
$253$		−	100.712i		−	0.398070i
$254$	−61.8642	−	32.1421i	−0.243560	−	0.126544i
$255$	160.692	−	198.385i	0.630165	−	0.777982i
$256$	−197.148	−	163.305i	−0.770109	−	0.637912i
$257$			339.153i			1.31966i	0.751414	+	0.659831i	$0.229372\pi$
$257$			339.153i			1.31966i	−0.751414	+	0.659831i	$0.770628\pi$
$258$	289.013	+	150.159i	1.12020	+	0.582012i
$259$			9.81591i			0.0378993i
$260$	235.113	+	16.0966i	0.904282	+	0.0619100i
$261$	347.705			1.33220
$262$	126.682	−	243.826i	0.483520	−	0.930635i
$263$	38.3128			0.145676			0.0728380	−	0.997344i	$-0.476794\pi$
$263$	38.3128			0.145676			0.0728380	+	0.997344i	$0.476794\pi$
$264$	140.656	−	18.8585i	0.532789	−	0.0714337i
$265$	93.6390	−	115.604i	0.353355	−	0.436241i
$266$	−57.7802	+	111.210i	−0.217219	+	0.418083i
$267$	697.653			2.61293
$268$	−228.510	−	325.246i	−0.852649	−	1.21361i
$269$	421.371			1.56644			0.783218	−	0.621747i	$-0.213577\pi$
$269$	421.371			1.56644			0.783218	+	0.621747i	$0.213577\pi$
$270$	−226.582	−	520.160i	−0.839193	−	1.92652i
$271$		−	328.909i		−	1.21369i	−0.794822	−	0.606843i	$-0.792436\pi$
$271$		−	328.909i		−	1.21369i	0.794822	−	0.606843i	$-0.207564\pi$
$272$	143.697	+	51.7854i	0.528296	+	0.190387i
$273$			128.113i			0.469278i
$274$	−172.187	+	331.409i	−0.628419	+	1.20952i
$275$	−81.1082	+	17.2180i	−0.294939	+	0.0626109i
$276$	−373.473	−	531.577i	−1.35316	−	1.92601i
$277$			474.088i			1.71151i	0.517383	+	0.855754i	$0.326906\pi$
$277$			474.088i			1.71151i	−0.517383	+	0.855754i	$0.673094\pi$
$278$	−121.716	+	234.267i	−0.437826	+	0.842688i
$279$		−	900.241i		−	3.22667i
$280$	−42.3286	+	69.4242i	−0.151174	+	0.247944i
$281$	307.011			1.09257			0.546284	−	0.837600i	$-0.316042\pi$
$281$	307.011			1.09257			0.546284	+	0.837600i	$0.316042\pi$
$282$	−506.639	−	263.229i	−1.79659	−	0.933436i
$283$	−140.232			−0.495519			−0.247759	−	0.968822i	$-0.579694\pi$
$283$	−140.232			−0.495519			−0.247759	+	0.968822i	$0.579694\pi$
$284$	292.148	−	205.256i	1.02869	−	0.722731i
$285$	−518.885	+	640.599i	−1.82065	+	2.24772i
$286$	−69.3581	−	36.0356i	−0.242511	−	0.125999i
$287$	−55.1165			−0.192044
$288$	460.917	−	425.729i	1.60041	−	1.47823i
$289$	197.866			0.684656
$290$	−70.8182	−	162.576i	−0.244201	−	0.560607i
$291$			616.398i			2.11821i
$292$	−82.9799	+	58.2996i	−0.284178	+	0.199656i
$293$			11.6922i			0.0399051i	0.999801	+	0.0199526i	$0.00635152\pi$
$293$			11.6922i			0.0399051i	−0.999801	+	0.0199526i	$0.993648\pi$
$294$	425.907	+	221.284i	1.44866	+	0.752667i
$295$	180.253	−	222.535i	0.611029	−	0.754357i
$296$	−38.2881	+	5.13348i	−0.129352	+	0.0173428i
$297$			188.174i			0.633584i
$298$	−15.3856	−	7.99371i	−0.0516294	−	0.0268245i
$299$			357.805i			1.19667i
$300$	−364.256	+	391.657i	−1.21419	+	1.30552i
$301$	61.8907			0.205617
$302$	−224.793	+	432.661i	−0.744347	+	1.43265i
$303$	−934.387			−3.08379
$304$	−464.005	−	167.218i	−1.52633	−	0.550060i
$305$	−326.409	−	264.392i	−1.07019	−	0.866858i
$306$	−172.600	+	332.206i	−0.564053	+	1.08564i
$307$	357.934			1.16591			0.582955	−	0.812505i	$-0.301896\pi$
$307$	357.934			1.16591			0.582955	+	0.812505i	$0.301896\pi$
$308$	22.0661	−	15.5031i	0.0716432	−	0.0503347i
$309$	7.90392			0.0255790
$310$	−420.924	+	183.355i	−1.35782	+	0.591468i
$311$			237.747i			0.764459i	0.924067	+	0.382230i	$0.124844\pi$
$311$			237.747i			0.764459i	−0.924067	+	0.382230i	$0.875156\pi$
$312$	−499.719	+	66.9998i	−1.60166	+	0.214743i
$313$		−	224.140i		−	0.716103i	−0.933702	−	0.358052i	$-0.883441\pi$
$313$		−	224.140i		−	0.716103i	0.933702	−	0.358052i	$-0.116559\pi$
$314$	177.997	−	342.593i	0.566870	−	1.09106i
$315$	−154.861	−	125.437i	−0.491622	−	0.398214i
$316$	−236.603	+	166.231i	−0.748743	+	0.526048i
$317$		−	54.9016i		−	0.173191i	−0.996244	−	0.0865956i	$-0.972401\pi$
$317$		−	54.9016i		−	0.173191i	0.996244	−	0.0865956i	$-0.0275988\pi$
$318$	−146.744	+	282.439i	−0.461459	+	0.888174i
$319$			58.8139i			0.184370i
$320$	−292.934	−	128.801i	−0.915419	−	0.402502i
$321$	336.930			1.04963
$322$	−109.549	−	56.9174i	−0.340215	−	0.176762i
$323$	294.279			0.911081
$324$	292.022	+	415.645i	0.901303	+	1.28286i
$325$	288.158	−	61.1714i	0.886641	−	0.188220i
$326$	101.100	+	52.5272i	0.310121	+	0.161126i
$327$	−164.822			−0.504044
$328$	−28.8246	−	214.988i	−0.0878797	−	0.655452i
$329$	−108.494			−0.329770
$330$	162.634	−	70.8434i	0.492829	−	0.214677i
$331$		−	256.380i		−	0.774561i	−0.921962	−	0.387280i	$-0.873415\pi$
$331$		−	256.380i		−	0.774561i	0.921962	−	0.387280i	$-0.126585\pi$
$332$	5.98794	+	8.52285i	0.0180360	+	0.0256712i
$333$		−	94.6826i		−	0.284332i
$334$	396.593	+	206.054i	1.18740	+	0.616927i
$335$	−386.099	−	312.740i	−1.15253	−	0.933552i
$336$	58.9787	−	163.657i	0.175532	−	0.487075i
$337$		−	216.614i		−	0.642771i	−0.946948	−	0.321386i	$-0.895851\pi$
$337$		−	216.614i		−	0.642771i	0.946948	−	0.321386i	$-0.104149\pi$
$338$	−53.5204	−	27.8070i	−0.158344	−	0.0822693i
$339$			508.714i			1.50063i
$340$	190.483	+	13.0411i	0.560244	+	0.0383561i
$341$	152.275			0.446553
$342$	557.338	−	1072.71i	1.62964	−	3.13659i
$343$	190.812			0.556302
$344$	32.3673	+	241.412i	0.0940909	+	0.701778i
$345$	−631.033	−	511.137i	−1.82908	−	1.48156i
$346$	−97.8740	+	188.379i	−0.282873	+	0.544448i
$347$	−374.740			−1.07994			−0.539971	−	0.841684i	$-0.681565\pi$
$347$	−374.740			−1.07994			−0.539971	+	0.841684i	$0.681565\pi$
$348$	218.102	+	310.432i	0.626730	+	0.892046i
$349$	220.920			0.633008			0.316504	−	0.948591i	$-0.397491\pi$
$349$	220.920			0.633008			0.316504	+	0.948591i	$0.397491\pi$
$350$	−27.1095	+	97.9564i	−0.0774557	+	0.279875i
$351$		−	668.540i		−	1.90467i
$352$	72.0116	+	77.9636i	0.204578	+	0.221488i
$353$		−	30.0188i		−	0.0850392i	−0.999096	−	0.0425196i	$-0.986462\pi$
$353$		−	30.0188i		−	0.0850392i	0.999096	−	0.0425196i	$-0.0135385\pi$
$354$	−282.479	+	543.691i	−0.797964	+	1.53585i
$355$	280.914	−	346.807i	0.791306	−	0.976922i
$356$	299.938	+	426.912i	0.842523	+	1.19919i
$357$			103.794i			0.290739i
$358$	−19.9062	+	38.3137i	−0.0556040	+	0.107021i
$359$			305.430i			0.850779i	0.905010	+	0.425390i	$0.139863\pi$
$359$			305.430i			0.850779i	−0.905010	+	0.425390i	$0.860137\pi$
$360$	408.295	−	669.654i	1.13415	−	1.86015i
$361$	−589.246			−1.63226
$362$	86.2353	+	44.8043i	0.238219	+	0.123769i
$363$	−58.8348			−0.162079
$364$	−78.3956	+	55.0788i	−0.215373	+	0.151315i
$365$	−79.7891	+	98.5051i	−0.218600	+	0.269877i
$366$	797.473	+	414.334i	2.17889	+	1.13206i
$367$	556.329			1.51588			0.757941	−	0.652323i	$-0.226205\pi$
$367$	556.329			1.51588			0.757941	+	0.652323i	$0.226205\pi$
$368$	164.721	−	457.076i	0.447612	−	1.24206i
$369$	531.644			1.44077
$370$	−44.2706	+	19.2843i	−0.119650	+	0.0521198i
$371$			60.4830i			0.163027i
$372$	803.737	−	564.686i	2.16058	−	1.51797i
$373$			617.259i			1.65485i	0.561577	+	0.827425i	$0.310195\pi$
$373$			617.259i			1.65485i	−0.561577	+	0.827425i	$0.689805\pi$
$374$	−56.1922	−	29.1951i	−0.150246	−	0.0780619i
$375$	−303.761	+	595.588i	−0.810029	+	1.58824i
$376$	−56.7398	−	423.195i	−0.150904	−	1.12552i
$377$		−	208.952i		−	0.554249i
$378$	204.687	+	106.347i	0.541500	+	0.281341i
$379$		−	81.9364i		−	0.216191i	−0.994141	−	0.108096i	$-0.965525\pi$
$379$		−	81.9364i		−	0.216191i	0.994141	−	0.108096i	$-0.0344753\pi$
$380$	−615.081	−	42.1104i	−1.61864	−	0.110817i
$381$	186.442			0.489348
$382$	79.0693	−	152.185i	0.206988	−	0.398391i
$383$	244.150			0.637468			0.318734	−	0.947844i	$-0.396742\pi$
$383$	244.150			0.637468			0.318734	+	0.947844i	$0.396742\pi$
$384$	669.208	+	144.465i	1.74273	+	0.376210i
$385$	21.2176	−	26.1946i	0.0551106	−	0.0680378i
$386$	276.205	−	531.615i	0.715558	−	1.37724i
$387$	−596.987			−1.54260
$388$	−377.191	+	265.005i	−0.972140	+	0.683002i
$389$	30.6854			0.0788827			0.0394413	−	0.999222i	$-0.487442\pi$
$389$	30.6854			0.0788827			0.0394413	+	0.999222i	$0.487442\pi$
$390$	−577.799	+	251.690i	−1.48154	+	0.645359i
$391$			289.885i			0.741393i
$392$	47.6984	+	355.759i	0.121680	+	0.907550i
$393$			734.825i			1.86978i
$394$	−33.2933	+	64.0800i	−0.0845009	+	0.162640i
$395$	−227.505	+	280.870i	−0.575961	+	0.711064i
$396$	−212.846	+	149.540i	−0.537489	+	0.377627i
$397$			546.758i			1.37723i	0.725129	+	0.688613i	$0.241780\pi$
$397$			546.758i			1.37723i	−0.725129	+	0.688613i	$0.758220\pi$
$398$	53.7209	−	103.397i	0.134977	−	0.259792i
$399$		−	335.157i		−	0.839992i
$400$	−396.268	−	54.5150i	−0.990669	−	0.136288i
$401$	−747.604			−1.86435			−0.932175	−	0.362009i	$-0.882091\pi$
$401$	−747.604			−1.86435			−0.932175	+	0.362009i	$0.882091\pi$
$402$	943.303	+	490.102i	2.34653	+	1.21916i
$403$	−540.996			−1.34242
$404$	−401.716	−	571.777i	−0.994347	−	1.41529i
$405$	493.411	+	399.663i	1.21830	+	0.986822i
$406$	63.9749	+	33.2388i	0.157574	+	0.0818688i
$407$	16.0154			0.0393500
$408$	−404.859	+	54.2815i	−0.992302	+	0.133043i
$409$	193.274			0.472553			0.236276	−	0.971686i	$-0.424073\pi$
$409$	193.274			0.472553			0.236276	+	0.971686i	$0.424073\pi$
$410$	−108.282	−	248.580i	−0.264102	−	0.606293i
$411$		−	998.777i		−	2.43011i
$412$	3.39809	+	4.83662i	0.00824779	+	0.0117394i
$413$			116.429i			0.281910i
$414$	1056.69	+	549.015i	2.55240	+	1.32612i
$415$	10.1174	+	8.19512i	0.0243794	+	0.0197473i
$416$	−255.840	−	276.986i	−0.615001	−	0.665833i
$417$		−	706.017i		−	1.69309i
$418$	181.448	+	94.2730i	0.434087	+	0.225534i
$419$			377.567i			0.901113i	0.892748	+	0.450557i	$0.148774\pi$
$419$			377.567i			0.901113i	−0.892748	+	0.450557i	$0.851226\pi$
$420$	14.8526	−	216.942i	0.0353632	−	0.516529i
$421$	−157.158			−0.373296			−0.186648	−	0.982427i	$-0.559762\pi$
$421$	−157.158			−0.373296			−0.186648	+	0.982427i	$0.559762\pi$
$422$	−12.6913	+	24.4270i	−0.0300741	+	0.0578839i
$423$	1046.52			2.47404
$424$	−235.921	+	31.6311i	−0.556417	+	0.0746016i
$425$	233.459	−	49.5595i	0.549314	−	0.116611i
$426$	−440.226	+	847.308i	−1.03340	+	1.98899i
$427$	170.775			0.399941
$428$	144.855	+	206.177i	0.338445	+	0.481721i
$429$	209.026			0.487241
$430$	121.590	+	279.132i	0.282768	+	0.649144i
$431$		−	537.566i		−	1.24725i	−0.781722	−	0.623627i	$-0.785659\pi$
$431$		−	537.566i		−	1.24725i	0.781722	−	0.623627i	$-0.214341\pi$
$432$	−307.773	+	854.023i	−0.712437	+	1.97690i
$433$			94.9800i			0.219353i	0.993967	+	0.109677i	$0.0349815\pi$
$433$			94.9800i			0.219353i	−0.993967	+	0.109677i	$0.965018\pi$
$434$	86.0582	−	165.637i	0.198291	−	0.381652i
$435$	368.513	+	298.495i	0.847155	+	0.686196i
$436$	−70.8612	−	100.859i	−0.162526	−	0.231329i
$437$		−	936.056i		−	2.14200i
$438$	125.039	−	240.664i	0.285478	−	0.549462i
$439$			317.809i			0.723939i	0.932190	+	0.361969i	$0.117896\pi$
$439$			317.809i			0.723939i	−0.932190	+	0.361969i	$0.882104\pi$
$440$	113.271	+	69.0626i	0.257435	+	0.156960i
$441$	−879.757			−1.99491
$442$	199.638	+	103.723i	0.451669	+	0.234668i
$443$	259.822			0.586505			0.293253	−	0.956035i	$-0.405262\pi$
$443$	259.822			0.586505			0.293253	+	0.956035i	$0.405262\pi$
$444$	84.5328	−	59.3907i	0.190389	−	0.133763i
$445$	506.786	+	410.496i	1.13884	+	0.922464i
$446$	−39.4150	−	20.4784i	−0.0883744	−	0.0459157i
$447$	46.3679			0.103731
$448$	125.503	−	34.2695i	0.280140	−	0.0764945i
$449$	−384.329			−0.855967			−0.427983	−	0.903787i	$-0.640776\pi$
$449$	−384.329			−0.855967			−0.427983	+	0.903787i	$0.640776\pi$
$450$	261.494	−	944.870i	0.581097	−	2.09971i
$451$			89.9270i			0.199395i
$452$	−311.295	+	218.708i	−0.688707	+	0.483868i
$453$		−	1303.92i		−	2.87841i
$454$	−682.303	−	354.496i	−1.50287	−	0.780829i
$455$	−75.3811	+	93.0631i	−0.165673	+	0.204534i
$456$	1307.32	−	175.279i	2.86692	−	0.384383i
$457$		−	310.420i		−	0.679257i	−0.940560	−	0.339628i	$-0.889699\pi$
$457$		−	310.420i		−	0.679257i	0.940560	−	0.339628i	$-0.110301\pi$
$458$	61.1416	+	31.7666i	0.133497	+	0.0693595i
$459$		−	541.634i		−	1.18003i
$460$	41.4816	−	605.896i	0.0901774	−	1.31717i
$461$	683.902			1.48352			0.741760	−	0.670666i	$-0.233992\pi$
$461$	683.902			1.48352			0.741760	+	0.670666i	$0.233992\pi$
$462$	−33.2506	+	63.9977i	−0.0719709	+	0.138523i
$463$	−33.0667			−0.0714184			−0.0357092	−	0.999362i	$-0.511369\pi$
$463$	−33.0667			−0.0714184			−0.0357092	+	0.999362i	$0.511369\pi$
$464$	−96.1943	+	266.925i	−0.207315	+	0.575269i
$465$	772.831	−	954.113i	1.66200	−	2.05186i
$466$	−351.945	+	677.392i	−0.755247	+	1.45363i
$467$	−75.6470			−0.161985			−0.0809925	−	0.996715i	$-0.525809\pi$
$467$	−75.6470			−0.161985			−0.0809925	+	0.996715i	$0.525809\pi$
$468$	756.191	−	531.281i	1.61579	−	1.13522i
$469$	202.004			0.430712
$470$	−213.148	−	489.318i	−0.453505	−	1.04110i
$471$			1032.48i			2.19210i
$472$	−454.143	+	60.8893i	−0.962168	+	0.129003i
$473$		−	100.980i		−	0.213487i
$474$	356.528	−	686.213i	0.752169	−	1.44771i
$475$	−753.853	+	160.031i	−1.58706	+	0.336907i
$476$	−63.5141	+	44.6235i	−0.133433	+	0.0937468i
$477$		−	583.408i		−	1.22308i
$478$	91.3471	−	175.817i	0.191103	−	0.367817i
$479$			404.091i			0.843613i	0.906686	+	0.421807i	$0.138604\pi$
$479$			404.091i			0.843613i	−0.906686	+	0.421807i	$0.861396\pi$
$480$	853.976	−	55.5213i	1.77912	−	0.115669i
$481$	−56.8991			−0.118293
$482$	−669.948	−	348.078i	−1.38993	−	0.722153i
$483$	330.152			0.683544
$484$	−25.2945	−	36.0026i	−0.0522614	−	0.0743855i
$485$	−362.686	+	447.761i	−0.747807	+	0.923219i
$486$	−299.241	−	155.474i	−0.615723	−	0.319904i
$487$	−627.374			−1.28824			−0.644121	−	0.764924i	$-0.722777\pi$
$487$	−627.374			−1.28824			−0.644121	+	0.764924i	$0.722777\pi$
$488$	89.3110	+	666.127i	0.183014	+	1.36501i
$489$	−304.686			−0.623080
$490$	179.183	+	411.346i	0.365680	+	0.839482i
$491$		−	38.9169i		−	0.0792605i	−0.999214	−	0.0396303i	$-0.987382\pi$
$491$		−	38.9169i		−	0.0792605i	0.999214	−	0.0396303i	$-0.0126180\pi$
$492$	333.480	+	474.653i	0.677804	+	0.964742i
$493$		−	169.288i		−	0.343382i
$494$	−644.643	−	334.930i	−1.30494	−	0.677996i
$495$	−204.661	+	252.668i	−0.413457	+	0.510441i
$496$	691.093	+	249.056i	1.39333	+	0.502129i
$497$			181.447i			0.365084i
$498$	−24.7186	−	12.8428i	−0.0496357	−	0.0257887i
$499$			938.302i			1.88037i	0.340671	+	0.940183i	$0.389346\pi$
$499$			938.302i			1.88037i	−0.340671	+	0.940183i	$0.610654\pi$
$500$	−495.050	+	70.1787i	−0.990101	+	0.140357i
$501$	−1195.22			−2.38567
$502$	123.228	−	237.178i	0.245474	−	0.472465i
$503$	389.029			0.773417			0.386708	−	0.922202i	$-0.373612\pi$
$503$	389.029			0.773417			0.386708	+	0.922202i	$0.373612\pi$
$504$	42.3725	+	316.036i	0.0840725	+	0.627056i
$505$	−678.753	−	549.790i	−1.34407	−	1.08869i
$506$	−92.8652	+	178.739i	−0.183528	+	0.353238i
$507$	161.296			0.318138
$508$	80.1558	+	114.089i	0.157787	+	0.224584i
$509$	228.649			0.449212			0.224606	−	0.974450i	$-0.427891\pi$
$509$	228.649			0.449212			0.224606	+	0.974450i	$0.427891\pi$
$510$	−468.118	+	203.913i	−0.917879	+	0.399829i
$511$		−	51.5371i		−	0.100855i
$512$	199.307	+	471.615i	0.389271	+	0.921123i
$513$			1748.97i			3.40930i
$514$	312.730	−	601.914i	0.608423	−	1.17104i
$515$	5.74153	+	4.65064i	0.0111486	+	0.00903036i
$516$	−374.466	−	532.991i	−0.725710	−	1.03293i
$517$			177.017i			0.342393i
$518$	9.05115	−	17.4208i	0.0174733	−	0.0336309i
$519$		−	567.722i		−	1.09388i
$520$	−402.426	−	245.363i	−0.773896	−	0.471852i
$521$	305.011			0.585433			0.292717	−	0.956199i	$-0.405441\pi$
$521$	305.011			0.585433			0.292717	+	0.956199i	$0.405441\pi$
$522$	−617.091	−	320.615i	−1.18217	−	0.614205i
$523$	83.9819			0.160577			0.0802886	−	0.996772i	$-0.474416\pi$
$523$	83.9819			0.160577			0.0802886	+	0.996772i	$0.474416\pi$
$524$	−449.659	+	315.919i	−0.858128	+	0.602900i
$525$	−56.4437	−	265.888i	−0.107512	−	0.506453i
$526$	−67.9958	−	35.3278i	−0.129269	−	0.0671631i
$527$	−438.301			−0.831691
$528$	−267.020	−	96.2285i	−0.505719	−	0.182251i
$529$	393.078			0.743058
$530$	−272.783	+	118.825i	−0.514685	+	0.224198i
$531$		−	1123.05i		−	2.11497i
$532$	205.091	−	144.092i	0.385510	−	0.270850i
$533$		−	319.489i		−	0.599417i
$534$	−1238.16	−	643.298i	−2.31866	−	1.20468i
$535$	244.751	+	198.249i	0.457479	+	0.370558i
$536$	105.643	+	787.939i	0.197095	+	1.47004i
$537$		−	115.467i		−	0.215022i
$538$	−747.831	−	388.542i	−1.39002	−	0.722197i
$539$		−	148.810i		−	0.276085i
$540$	−77.5061	+	1132.08i	−0.143530	+	2.09645i
$541$	288.261			0.532829			0.266415	−	0.963859i	$-0.414161\pi$
$541$	288.261			0.532829			0.266415	+	0.963859i	$0.414161\pi$
$542$	−303.283	+	583.732i	−0.559563	+	1.07700i
$543$	−259.889			−0.478618
$544$	−207.275	−	224.407i	−0.381021	−	0.412513i
$545$	−119.730	−	96.9809i	−0.219687	−	0.177947i
$546$	118.131	−	227.369i	0.216358	−	0.416426i
$547$	864.578			1.58058			0.790291	−	0.612732i	$-0.209929\pi$
$547$	864.578			1.58058			0.790291	+	0.612732i	$0.209929\pi$
$548$	611.178	−	429.399i	1.11529	−	0.783574i
$549$	−1647.26			−3.00048
$550$	159.824	+	44.2313i	0.290588	+	0.0804206i
$551$			546.641i			0.992088i
$552$	172.661	+	1287.79i	0.312792	+	2.33296i
$553$		−	146.949i		−	0.265731i
$554$	437.151	−	841.389i	0.789081	−	1.51875i
$555$	81.2823	−	100.349i	0.146455	−	0.180808i
$556$	432.030	−	303.534i	0.777033	−	0.545924i
$557$			773.354i			1.38843i	0.719769	+	0.694213i	$0.244248\pi$
$557$			773.354i			1.38843i	−0.719769	+	0.694213i	$0.755752\pi$
$558$	−830.102	+	1597.71i	−1.48764	+	2.86327i
$559$			358.757i			0.641783i
$560$	139.138	−	84.1801i	0.248461	−	0.150322i
$561$	169.348			0.301868
$562$	−544.870	−	283.092i	−0.969519	−	0.503722i
$563$	99.7068			0.177099			0.0885496	−	0.996072i	$-0.471777\pi$
$563$	99.7068			0.177099			0.0885496	+	0.996072i	$0.471777\pi$
$564$	656.439	+	934.333i	1.16390	+	1.65662i
$565$	−299.325	+	369.537i	−0.529779	+	0.654048i
$566$	248.877	+	129.306i	0.439712	+	0.228456i
$567$	−258.149			−0.455289
$568$	−707.754	+	94.8921i	−1.24605	+	0.167064i
$569$	−792.233			−1.39233			−0.696163	−	0.717884i	$-0.745111\pi$
$569$	−792.233			−1.39233			−0.696163	+	0.717884i	$0.745111\pi$
$570$	1511.58	−	658.448i	2.65190	−	1.15517i
$571$		−	576.323i		−	1.00932i	−0.863317	−	0.504661i	$-0.831617\pi$
$571$		−	576.323i		−	1.00932i	0.863317	−	0.504661i	$-0.168383\pi$
$572$	89.8655	+	127.909i	0.157108	+	0.223617i
$573$			458.645i			0.800427i
$574$	97.8182	+	50.8223i	0.170415	+	0.0885407i
$575$	−157.641	−	742.595i	−0.274159	−	1.29147i
$576$	−1210.58	+	330.558i	−2.10169	+	0.573885i
$577$		−	323.574i		−	0.560787i	−0.959885	−	0.280393i	$-0.909535\pi$
$577$		−	323.574i		−	0.560787i	0.959885	−	0.280393i	$-0.0904649\pi$
$578$	−351.163	−	182.450i	−0.607548	−	0.315657i
$579$			1602.14i			2.76708i
$580$	−24.2245	+	353.833i	−0.0417664	+	0.610057i
$581$	−5.29336			−0.00911078
$582$	568.374	−	1093.96i	0.976588	−	1.87965i
$583$	98.6828			0.169267
$584$	201.026	−	26.9526i	0.344223	−	0.0461517i
$585$	727.113	−	897.670i	1.24293	−	1.53448i
$586$	10.7812	−	20.7508i	0.0183980	−	0.0354109i
$587$	−719.163			−1.22515			−0.612575	−	0.790412i	$-0.709866\pi$
$587$	−719.163			−1.22515			−0.612575	+	0.790412i	$0.709866\pi$
$588$	−551.837	−	785.449i	−0.938499	−	1.33580i
$589$	1415.30			2.40289
$590$	−525.103	+	228.735i	−0.890005	+	0.387687i
$591$		−	193.119i		−	0.326767i
$592$	72.6855	+	26.1944i	0.122780	+	0.0442473i
$593$			333.756i			0.562826i	0.959587	+	0.281413i	$0.0908030\pi$
$593$			333.756i			0.562826i	−0.959587	+	0.281413i	$0.909197\pi$
$594$	173.514	−	333.963i	0.292111	−	0.562228i
$595$	−61.0718	+	75.3973i	−0.102642	+	0.126718i
$596$	19.9347	+	28.3737i	0.0334475	+	0.0476070i
$597$			311.610i			0.521960i
$598$	329.928	−	635.016i	0.551719	−	1.06190i
$599$		−	997.885i		−	1.66592i	−0.553334	−	0.832959i	$-0.686645\pi$
$599$		−	997.885i		−	1.66592i	0.553334	−	0.832959i	$-0.313355\pi$
$600$	1007.61	−	359.218i	1.67934	−	0.598697i
$601$	−32.8441			−0.0546491			−0.0273245	−	0.999627i	$-0.508699\pi$
$601$	−32.8441			−0.0546491			−0.0273245	+	0.999627i	$0.508699\pi$
$602$	−109.841	−	57.0687i	−0.182460	−	0.0947985i
$603$	−1948.49			−3.23133
$604$	797.904	−	560.587i	1.32103	−	0.928125i
$605$	−42.7385	−	34.6182i	−0.0706422	−	0.0572202i
$606$	1658.31	+	861.589i	2.73648	+	1.42176i
$607$	211.332			0.348157			0.174079	−	0.984732i	$-0.444305\pi$
$607$	211.332			0.348157			0.174079	+	0.984732i	$0.444305\pi$
$608$	669.305	+	724.626i	1.10083	+	1.19182i
$609$	−192.803			−0.316589
$610$	335.504	+	770.209i	0.550006	+	1.26264i
$611$		−	628.900i		−	1.02930i
$612$	612.646	−	430.430i	1.00106	−	0.703317i
$613$		−	798.912i		−	1.30328i	−0.758527	−	0.651641i	$-0.774081\pi$
$613$		−	798.912i		−	1.30328i	0.758527	−	0.651641i	$-0.225919\pi$
$614$	−635.245	−	330.047i	−1.03460	−	0.537536i
$615$	563.459	+	456.402i	0.916193	+	0.742116i
$616$	−53.4571	+	7.16726i	−0.0867810	+	0.0116352i
$617$		−	336.733i		−	0.545758i	−0.962048	−	0.272879i	$-0.912024\pi$
$617$		−	336.733i		−	0.545758i	0.962048	−	0.272879i	$-0.0879759\pi$
$618$	−14.0275	−	7.28812i	−0.0226982	−	0.0117931i
$619$			282.352i			0.456143i	0.973644	+	0.228071i	$0.0732419\pi$
$619$			282.352i			0.456143i	−0.973644	+	0.228071i	$0.926758\pi$
$620$	916.106	+	62.7195i	1.47759	+	0.101161i
$621$	−1722.85			−2.77432
$622$	219.224	−	421.942i	0.352450	−	0.678363i
$623$	−265.146			−0.425596
$624$	948.658	+	341.877i	1.52028	+	0.547880i
$625$	−571.098	+	253.913i	−0.913757	+	0.406260i
$626$	−206.677	+	397.794i	−0.330156	+	0.635454i
$627$	−546.835			−0.872145
$628$	−631.802	+	443.889i	−1.00605	+	0.706829i
$629$	−46.0982			−0.0732881
$630$	159.176	+	365.416i	0.252660	+	0.580026i
$631$		−	97.5847i		−	0.154651i	−0.997006	−	0.0773254i	$-0.975362\pi$
$631$		−	97.5847i		−	0.154651i	0.997006	−	0.0773254i	$-0.0246380\pi$
$632$	573.192	−	76.8507i	0.906949	−	0.121599i
$633$		−	73.6162i		−	0.116297i
$634$	−50.6242	+	97.4369i	−0.0798489	+	0.153686i
$635$	135.434	+	109.702i	0.213282	+	0.172758i
$636$	520.868	−	365.949i	0.818976	−	0.575392i
$637$			528.686i			0.829963i
$638$	54.2317	−	104.380i	0.0850026	−	0.163605i
$639$		−	1750.20i		−	2.73897i
$640$	401.120	+	498.701i	0.626750	+	0.779220i
$641$	230.322			0.359316			0.179658	−	0.983729i	$-0.442501\pi$
$641$	230.322			0.359316			0.179658	+	0.983729i	$0.442501\pi$
$642$	−597.968	−	310.680i	−0.931415	−	0.483925i
$643$	313.342			0.487312			0.243656	−	0.969862i	$-0.421653\pi$
$643$	313.342			0.487312			0.243656	+	0.969862i	$0.421653\pi$
$644$	141.940	+	202.029i	0.220404	+	0.313709i
$645$	−632.711	−	512.496i	−0.980948	−	0.794568i
$646$	−522.273	−	271.352i	−0.808472	−	0.420049i
$647$	156.535			0.241939			0.120970	−	0.992656i	$-0.461400\pi$
$647$	156.535			0.241939			0.120970	+	0.992656i	$0.461400\pi$
$648$	−135.005	−	1006.94i	−0.208342	−	1.55392i
$649$	189.963			0.292701
$650$	−567.816	−	157.143i	−0.873563	−	0.241759i
$651$			499.184i			0.766796i
$652$	−130.992	−	186.446i	−0.200908	−	0.285959i
$653$			297.130i			0.455023i	0.973775	+	0.227511i	$0.0730589\pi$
$653$			297.130i			0.455023i	−0.973775	+	0.227511i	$0.926941\pi$
$654$	292.519	+	151.981i	0.447277	+	0.232387i
$655$	−432.369	+	533.788i	−0.660105	+	0.814944i
$656$	−147.082	+	408.130i	−0.224210	+	0.622150i
$657$			497.118i			0.756648i
$658$	192.551	+	100.041i	0.292630	+	0.152039i
$659$			485.210i			0.736281i	0.929770	+	0.368141i	$0.120006\pi$
$659$			485.210i			0.736281i	−0.929770	+	0.368141i	$0.879994\pi$
$660$	−353.959	−	24.2331i	−0.536301	−	0.0367169i
$661$	−555.193			−0.839928			−0.419964	−	0.907541i	$-0.637957\pi$
$661$	−555.193			−0.839928			−0.419964	+	0.907541i	$0.637957\pi$
$662$	−236.405	+	455.011i	−0.357107	+	0.687327i
$663$	−601.653			−0.907470
$664$	−2.76830	−	20.6474i	−0.00416912	−	0.0310954i
$665$	197.205	−	243.463i	0.296549	−	0.366110i
$666$	−87.3058	+	168.038i	−0.131090	+	0.252310i
$667$	−538.477			−0.807312
$668$	−513.856	−	731.389i	−0.769245	−	1.09489i
$669$	118.786			0.177557
$670$	396.856	+	911.053i	0.592322	+	1.35978i
$671$		−	278.633i		−	0.415250i
$672$	−255.579	+	236.067i	−0.380326	+	0.351291i
$673$			389.279i			0.578423i	0.957265	+	0.289211i	$0.0933931\pi$
$673$			389.279i			0.578423i	−0.957265	+	0.289211i	$0.906607\pi$
$674$	−199.737	+	384.436i	−0.296346	+	0.570380i
$675$	294.544	+	1387.50i	0.436362	+	2.05555i
$676$	69.3450	+	98.7012i	0.102581	+	0.146008i
$677$		−	110.415i		−	0.163095i	−0.996669	−	0.0815475i	$-0.974014\pi$
$677$		−	110.415i		−	0.163095i	0.996669	−	0.0815475i	$-0.0259862\pi$
$678$	469.079	−	902.841i	0.691857	−	1.33162i
$679$		−	234.265i		−	0.345015i
$680$	−326.035	−	198.787i	−0.479463	−	0.292334i
$681$	2056.27			3.01949
$682$	−270.250	−	140.411i	−0.396261	−	0.205881i
$683$	725.394			1.06207			0.531035	−	0.847350i	$-0.321803\pi$
$683$	725.394			1.06207			0.531035	+	0.847350i	$0.321803\pi$
$684$	−1978.27	+	1389.89i	−2.89221	+	2.03200i
$685$	587.677	−	725.527i	0.857922	−	1.05916i
$686$	−338.644	−	175.945i	−0.493650	−	0.256480i
$687$	−184.264			−0.268215
$688$	165.159	−	458.292i	0.240057	−	0.666122i
$689$	−350.597			−0.508849
$690$	648.615	+	1489.01i	0.940022	+	2.15799i
$691$		−	1160.43i		−	1.67935i	−0.543093	−	0.839673i	$-0.682747\pi$
$691$		−	1160.43i		−	1.67935i	0.543093	−	0.839673i	$-0.317253\pi$
$692$	347.404	−	244.078i	0.502030	−	0.352714i
$693$		−	132.194i		−	0.190756i
$694$	665.071	+	345.543i	0.958315	+	0.497901i
$695$	415.418	−	512.861i	0.597723	−	0.737930i
$696$	−100.831	−	752.050i	−0.144872	−	1.08053i
$697$		−	258.842i		−	0.371366i
$698$	−392.078	−	203.708i	−0.561717	−	0.291845i
$699$		−	2041.47i		−	2.92056i
$700$	138.437	−	148.851i	0.197767	−	0.212644i
$701$	−338.309			−0.482610			−0.241305	−	0.970449i	$-0.577575\pi$
$701$	−338.309			−0.482610			−0.241305	+	0.970449i	$0.577575\pi$
$702$	−616.453	+	1186.49i	−0.878138	+	1.69016i
$703$	148.854			0.211741
$704$	−55.9135	−	204.767i	−0.0794225	−	0.290863i
$705$	1109.14	+	898.405i	1.57325	+	1.27433i
$706$	−27.6800	+	53.2760i	−0.0392068	+	0.0754618i
$707$	355.118			0.502289
$708$	1002.66	−	704.446i	1.41619	−	0.994980i
$709$	−320.852			−0.452542			−0.226271	−	0.974064i	$-0.572654\pi$
$709$	−320.852			−0.452542			−0.226271	+	0.974064i	$0.572654\pi$
$710$	−818.340	+	356.470i	−1.15259	+	0.502070i
$711$			1417.44i			1.99359i
$712$	−138.665	−	1034.23i	−0.194754	−	1.45258i
$713$			1394.17i			1.95535i
$714$	95.7071	−	184.208i	0.134044	−	0.257995i
$715$	151.840	+	122.990i	0.212363	+	0.172014i
$716$	70.6573	−	49.6421i	0.0986834	−	0.0693325i
$717$			529.863i			0.739000i
$718$	281.634	−	542.063i	0.392247	−	0.754962i
$719$			202.700i			0.281919i	0.990015	+	0.140959i	$0.0450187\pi$
$719$			202.700i			0.281919i	−0.990015	+	0.140959i	$0.954981\pi$
$720$	−1342.10	+	811.987i	−1.86403	+	1.12776i
$721$	−3.00392			−0.00416633
$722$	1045.77	+	543.338i	1.44843	+	0.752545i
$723$	2019.04			2.79259
$724$	−111.733	−	159.033i	−0.154327	−	0.219659i
$725$	92.0597	+	433.663i	0.126979	+	0.598156i
$726$	104.417	+	54.2510i	0.143826	+	0.0747258i
$727$	231.020			0.317772			0.158886	−	0.987297i	$-0.449210\pi$
$727$	231.020			0.317772			0.158886	+	0.987297i	$0.449210\pi$
$728$	189.921	−	25.4636i	0.260880	−	0.0349775i
$729$	−241.112			−0.330743
$730$	232.437	−	101.250i	0.318406	−	0.138698i
$731$			290.655i			0.397613i
$732$	−1033.26	−	1470.68i	−1.41156	−	2.00913i
$733$		−	1059.05i		−	1.44482i	−0.691466	−	0.722409i	$-0.743035\pi$
$733$		−	1059.05i		−	1.44482i	0.691466	−	0.722409i	$-0.256965\pi$
$734$	−987.347	−	512.985i	−1.34516	−	0.698890i
$735$	−932.403	−	755.246i	−1.26858	−	1.02755i
$736$	−713.805	+	659.310i	−0.969843	+	0.895802i
$737$		−	329.585i		−	0.447198i
$738$	−943.538	−	490.223i	−1.27851	−	0.664259i
$739$			1024.26i			1.38601i	0.720935	+	0.693003i	$0.243713\pi$
$739$			1024.26i			1.38601i	−0.720935	+	0.693003i	$0.756287\pi$
$740$	96.3512	+	6.59651i	0.130204	+	0.00891420i
$741$	1942.78			2.62183
$742$	55.7707	−	107.342i	0.0751627	−	0.144666i
$743$	−476.832			−0.641766			−0.320883	−	0.947119i	$-0.603980\pi$
$743$	−476.832			−0.641766			−0.320883	+	0.947119i	$0.603980\pi$
$744$	−1947.13	+	261.061i	−2.61711	+	0.350888i
$745$	33.6823	+	27.2827i	0.0452112	+	0.0366211i
$746$	569.168	−	1095.48i	0.762959	−	1.46848i
$747$	51.0588			0.0683519
$748$	72.8067	+	103.628i	0.0973352	+	0.138541i
$749$	−128.052			−0.170964
$750$	1088.29	−	776.928i	1.45105	−	1.03590i
$751$			381.504i			0.507995i	0.967205	+	0.253998i	$0.0817455\pi$
$751$			381.504i			0.507995i	−0.967205	+	0.253998i	$0.918254\pi$
$752$	−289.524	+	803.385i	−0.385005	+	1.06833i
$753$			714.788i			0.949254i
$754$	−192.672	+	370.838i	−0.255534	+	0.491828i
$755$	767.222	−	947.188i	1.01619	−	1.25455i
$756$	−265.208	−	377.480i	−0.350804	−	0.499312i
$757$		−	149.082i		−	0.196938i	−0.995140	−	0.0984689i	$-0.968606\pi$
$757$		−	149.082i		−	0.196938i	0.995140	−	0.0984689i	$-0.0313945\pi$
$758$	−75.5527	+	145.417i	−0.0996738	+	0.191843i
$759$		−	538.669i		−	0.709709i
$760$	1052.79	+	641.896i	1.38525	+	0.844600i
$761$	−32.8053			−0.0431082			−0.0215541	−	0.999768i	$-0.506861\pi$
$761$	−32.8053			−0.0431082			−0.0215541	+	0.999768i	$0.506861\pi$
$762$	−330.888	−	171.916i	−0.434236	−	0.225611i
$763$	62.6416			0.0820990
$764$	−280.657	+	197.183i	−0.367352	+	0.258092i
$765$	589.088	−	727.270i	0.770050	−	0.950679i
$766$	−433.306	−	225.128i	−0.565674	−	0.293901i
$767$	−674.893			−0.879912
$768$	−1054.47	−	873.459i	−1.37301	−	1.13732i
$769$	463.563			0.602812			0.301406	−	0.953496i	$-0.402544\pi$
$769$	463.563			0.602812			0.301406	+	0.953496i	$0.402544\pi$
$770$	−61.8097	+	26.9244i	−0.0802724	+	0.0349667i
$771$			1814.00i			2.35279i
$772$	−980.393	+	688.800i	−1.26994	+	0.892228i
$773$			775.141i			1.00277i	0.865224	+	0.501385i	$0.167176\pi$
$773$			775.141i			1.00277i	−0.865224	+	0.501385i	$0.832824\pi$
$774$	1059.50	+	550.475i	1.36887	+	0.711208i
$775$	1122.79	−	238.351i	1.44876

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+(-1.77475 - 0.922089i) q^{2} +5.34862 q^{3} +(2.29950 + 3.27296i) q^{4} +(3.88532 + 3.14711i) q^{5} +(-9.49248 - 4.93190i) q^{6} -2.03277 q^{7} +(-1.06309 - 7.92905i) q^{8} +19.6077 q^{9} +(-3.99357 - 9.16795i) q^{10} +3.31662i q^{11} +(12.2992 + 17.5058i) q^{12} -11.7832i q^{13} +(3.60766 + 1.87439i) q^{14} +(20.7811 + 16.8327i) q^{15} +(-5.42457 + 15.0524i) q^{16} -9.54644i q^{17} +(-34.7989 - 18.0801i) q^{18} +30.8261i q^{19} +(-1.36607 + 19.9533i) q^{20} -10.8725 q^{21} +(3.05822 - 5.88619i) q^{22} -30.3657 q^{23} +(-5.68605 - 42.4095i) q^{24} +(5.19142 + 24.4550i) q^{25} +(-10.8651 + 20.9123i) q^{26} +56.7367 q^{27} +(-4.67436 - 6.65318i) q^{28} +17.7331 q^{29} +(-21.3601 - 49.0359i) q^{30} -45.9125i q^{31} +(23.5069 - 21.7123i) q^{32} +17.7394i q^{33} +(-8.80267 + 16.9426i) q^{34} +(-7.89796 - 6.39734i) q^{35} +(45.0880 + 64.1754i) q^{36} -4.82884i q^{37} +(28.4244 - 54.7087i) q^{38} -63.0238i q^{39} +(20.8231 - 34.1525i) q^{40} +27.1140 q^{41} +(19.2960 + 10.0254i) q^{42} -30.4465 q^{43} +(-10.8552 + 7.62659i) q^{44} +(76.1823 + 61.7077i) q^{45} +(53.8917 + 27.9999i) q^{46} +53.3727 q^{47} +(-29.0140 + 80.5094i) q^{48} -44.8679 q^{49} +(13.3362 - 48.1886i) q^{50} -51.0603i q^{51} +(38.5659 - 27.0955i) q^{52} -29.7540i q^{53} +(-100.694 - 52.3163i) q^{54} +(-10.4378 + 12.8861i) q^{55} +(2.16101 + 16.1179i) q^{56} +164.877i q^{57} +(-31.4718 - 16.3515i) q^{58} -57.2759i q^{59} +(-7.30657 + 106.723i) q^{60} -84.0110 q^{61} +(-42.3354 + 81.4834i) q^{62} -39.8580 q^{63} +(-61.7397 + 16.8585i) q^{64} +(37.0830 - 45.7814i) q^{65} +(16.3573 - 31.4830i) q^{66} -99.3737 q^{67} +(31.2451 - 21.9521i) q^{68} -162.415 q^{69} +(8.11801 + 18.6363i) q^{70} -89.2609i q^{71} +(-20.8447 - 155.471i) q^{72} +25.3531i q^{73} +(-4.45262 + 8.57000i) q^{74} +(27.7669 + 130.801i) q^{75} +(-100.893 + 70.8846i) q^{76} -6.74193i q^{77} +(-58.1136 + 111.852i) q^{78} +72.2901i q^{79} +(-68.4477 + 41.4116i) q^{80} +126.994 q^{81} +(-48.1207 - 25.0015i) q^{82} +2.60402 q^{83} +(-25.0014 - 35.5853i) q^{84} +(30.0437 - 37.0910i) q^{85} +(54.0350 + 28.0744i) q^{86} +94.8474 q^{87} +(26.2977 - 3.52586i) q^{88} +130.436 q^{89} +(-78.3049 - 179.763i) q^{90} +23.9525i q^{91} +(-69.8261 - 99.3859i) q^{92} -245.569i q^{93} +(-94.7233 - 49.2144i) q^{94} +(-97.0130 + 119.769i) q^{95} +(125.730 - 116.131i) q^{96} +115.244i q^{97} +(79.6294 + 41.3722i) q^{98} +65.0315i 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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