LMFDB - Embedded newform 220.3.h.a.199.5

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			199.5
Character	$\chi$	$=$	220.199
Dual form			220.3.h.a.199.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.87504 - 0.695850i) q^{2} +2.63169 q^{3} +(3.03158 + 2.60950i) q^{4} +(1.21581 - 4.84993i) q^{5} +(-4.93453 - 1.83126i) q^{6} +12.3259 q^{7} +(-3.86853 - 7.00246i) q^{8} -2.07421 q^{9} +(-5.65453 + 8.24781i) q^{10} -3.31662i q^{11} +(7.97819 + 6.86740i) q^{12} +4.53354i q^{13} +(-23.1116 - 8.57698i) q^{14} +(3.19964 - 12.7635i) q^{15} +(2.38101 + 15.8218i) q^{16} -12.6318i q^{17} +(3.88924 + 1.44334i) q^{18} +16.3321i q^{19} +(16.3417 - 11.5303i) q^{20} +32.4379 q^{21} +(-2.30787 + 6.21882i) q^{22} +11.8230 q^{23} +(-10.1808 - 18.4283i) q^{24} +(-22.0436 - 11.7932i) q^{25} +(3.15467 - 8.50059i) q^{26} -29.1439 q^{27} +(37.3670 + 32.1644i) q^{28} +27.7124 q^{29} +(-14.8810 + 21.7057i) q^{30} -2.38101i q^{31} +(6.54514 - 31.3235i) q^{32} -8.72833i q^{33} +(-8.78983 + 23.6851i) q^{34} +(14.9860 - 59.7797i) q^{35} +(-6.28815 - 5.41266i) q^{36} -59.7221i q^{37} +(11.3647 - 30.6234i) q^{38} +11.9309i q^{39} +(-38.6648 + 10.2484i) q^{40} +16.4324 q^{41} +(-60.8225 - 22.5719i) q^{42} +48.6478 q^{43} +(8.65474 - 10.0546i) q^{44} +(-2.52185 + 10.0598i) q^{45} +(-22.1687 - 8.22706i) q^{46} -80.3163 q^{47} +(6.26608 + 41.6382i) q^{48} +102.928 q^{49} +(33.1264 + 37.4518i) q^{50} -33.2429i q^{51} +(-11.8303 + 13.7438i) q^{52} +66.9744i q^{53} +(54.6461 + 20.2798i) q^{54} +(-16.0854 - 4.03240i) q^{55} +(-47.6831 - 86.3116i) q^{56} +42.9810i q^{57} +(-51.9621 - 19.2837i) q^{58} -12.4898i q^{59} +(43.0064 - 30.3442i) q^{60} +2.82800 q^{61} +(-1.65683 + 4.46450i) q^{62} -25.5665 q^{63} +(-34.0689 + 54.1785i) q^{64} +(21.9873 + 5.51194i) q^{65} +(-6.07361 + 16.3660i) q^{66} -55.3752 q^{67} +(32.9626 - 38.2943i) q^{68} +31.1145 q^{69} +(-69.6971 + 101.662i) q^{70} +124.371i q^{71} +(8.02416 + 14.5246i) q^{72} +130.778i q^{73} +(-41.5576 + 111.982i) q^{74} +(-58.0119 - 31.0361i) q^{75} +(-42.6186 + 49.5121i) q^{76} -40.8804i q^{77} +(8.30210 - 22.3709i) q^{78} +74.9602i q^{79} +(79.6297 + 7.68868i) q^{80} -58.0297 q^{81} +(-30.8116 - 11.4345i) q^{82} -19.8604 q^{83} +(98.3383 + 84.6468i) q^{84} +(-61.2632 - 15.3579i) q^{85} +(-91.2168 - 33.8516i) q^{86} +72.9305 q^{87} +(-23.2245 + 12.8305i) q^{88} -92.5422 q^{89} +(11.7287 - 17.1077i) q^{90} +55.8799i q^{91} +(35.8425 + 30.8522i) q^{92} -6.26608i q^{93} +(150.597 + 55.8881i) q^{94} +(79.2095 + 19.8568i) q^{95} +(17.2248 - 82.4337i) q^{96} -7.08552i q^{97} +(-192.994 - 71.6222i) q^{98} +6.87938i 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 $

$2$	−1.87504	−	0.695850i	−0.937522	−	0.347925i
$2$	−1.87504	−	0.695850i	−0.937522	−	0.347925i
$3$	2.63169			0.877230			0.438615	−	0.898675i	$-0.355469\pi$
$3$	2.63169			0.877230			0.438615	+	0.898675i	$0.355469\pi$
$4$	3.03158	+	2.60950i	0.757896	+	0.652375i
$5$	1.21581	−	4.84993i	0.243163	−	0.969986i
$5$	1.21581	−	4.84993i	0.243163	−	0.969986i
$6$	−4.93453	−	1.83126i	−0.822422	−	0.305210i
$7$	12.3259			1.76084			0.880421	−	0.474193i	$-0.157260\pi$
$7$	12.3259			1.76084			0.880421	+	0.474193i	$0.157260\pi$
$8$	−3.86853	−	7.00246i	−0.483567	−	0.875307i
$9$	−2.07421			−0.230468
$10$	−5.65453	+	8.24781i	−0.565453	+	0.824781i
$11$		−	3.31662i		−	0.301511i
$11$		−	3.31662i		−	0.301511i
$12$	7.97819	+	6.86740i	0.664849	+	0.572283i
$13$			4.53354i			0.348734i	0.984681	+	0.174367i	$0.0557879\pi$
$13$			4.53354i			0.348734i	−0.984681	+	0.174367i	$0.944212\pi$
$14$	−23.1116	−	8.57698i	−1.65083	−	0.612641i
$15$	3.19964	−	12.7635i	0.213309	−	0.850900i
$16$	2.38101	+	15.8218i	0.148813	+	0.988865i
$17$		−	12.6318i		−	0.743046i	−0.928424	−	0.371523i	$-0.878836\pi$
$17$		−	12.6318i		−	0.743046i	0.928424	−	0.371523i	$-0.121164\pi$
$18$	3.88924	+	1.44334i	0.216069	+	0.0801856i
$19$			16.3321i			0.859584i	0.902928	+	0.429792i	$0.141413\pi$
$19$			16.3321i			0.859584i	−0.902928	+	0.429792i	$0.858587\pi$
$20$	16.3417	−	11.5303i	0.817087	−	0.576515i
$21$	32.4379			1.54466
$22$	−2.30787	+	6.21882i	−0.104903	+	0.282674i
$23$	11.8230			0.514045			0.257022	−	0.966405i	$-0.417259\pi$
$23$	11.8230			0.514045			0.257022	+	0.966405i	$0.417259\pi$
$24$	−10.1808	−	18.4283i	−0.424199	−	0.767846i
$25$	−22.0436	−	11.7932i	−0.881744	−	0.471728i
$26$	3.15467	−	8.50059i	0.121333	−	0.326946i
$27$	−29.1439			−1.07940
$28$	37.3670	+	32.1644i	1.33454	+	1.14873i
$29$	27.7124			0.955601			0.477801	−	0.878468i	$-0.341434\pi$
$29$	27.7124			0.955601			0.477801	+	0.878468i	$0.341434\pi$
$30$	−14.8810	+	21.7057i	−0.496032	+	0.723522i
$31$		−	2.38101i		−	0.0768068i	−0.999262	−	0.0384034i	$-0.987773\pi$
$31$		−	2.38101i		−	0.0768068i	0.999262	−	0.0384034i	$-0.0122272\pi$
$32$	6.54514	−	31.3235i	0.204536	−	0.978859i
$33$		−	8.72833i		−	0.264495i
$34$	−8.78983	+	23.6851i	−0.258524	+	0.696622i
$35$	14.9860	−	59.7797i	0.428171	−	1.70799i
$36$	−6.28815	−	5.41266i	−0.174671	−	0.150352i
$37$		−	59.7221i		−	1.61411i	−0.590476	−	0.807055i	$-0.701060\pi$
$37$		−	59.7221i		−	1.61411i	0.590476	−	0.807055i	$-0.298940\pi$
$38$	11.3647	−	30.6234i	0.299071	−	0.805879i
$39$			11.9309i			0.305920i
$40$	−38.6648	+	10.2484i	−0.966621	+	0.256211i
$41$	16.4324			0.400791			0.200396	−	0.979715i	$-0.435777\pi$
$41$	16.4324			0.400791			0.200396	+	0.979715i	$0.435777\pi$
$42$	−60.8225	−	22.5719i	−1.44816	−	0.537427i
$43$	48.6478			1.13134			0.565672	−	0.824630i	$-0.308617\pi$
$43$	48.6478			1.13134			0.565672	+	0.824630i	$0.308617\pi$
$44$	8.65474	−	10.0546i	0.196699	−	0.228514i
$45$	−2.52185	+	10.0598i	−0.0560412	+	0.223551i
$46$	−22.1687	−	8.22706i	−0.481929	−	0.178849i
$47$	−80.3163			−1.70886			−0.854429	−	0.519568i	$-0.826093\pi$
$47$	−80.3163			−1.70886			−0.854429	+	0.519568i	$0.826093\pi$
$48$	6.26608	+	41.6382i	0.130543	+	0.867462i
$49$	102.928			2.10056
$50$	33.1264	+	37.4518i	0.662528	+	0.749037i
$51$		−	33.2429i		−	0.651822i
$52$	−11.8303	+	13.7438i	−0.227505	+	0.264304i
$53$			66.9744i			1.26367i	0.775104	+	0.631834i	$0.217698\pi$
$53$			66.9744i			1.26367i	−0.775104	+	0.631834i	$0.782302\pi$
$54$	54.6461	+	20.2798i	1.01196	+	0.375552i
$55$	−16.0854	−	4.03240i	−0.292462	−	0.0733163i
$56$	−47.6831	−	86.3116i	−0.851485	−	1.54128i
$57$			42.9810i			0.754053i
$58$	−51.9621	−	19.2837i	−0.895898	−	0.332478i
$59$		−	12.4898i		−	0.211691i	−0.994383	−	0.105845i	$-0.966245\pi$
$59$		−	12.4898i		−	0.211691i	0.994383	−	0.105845i	$-0.0337549\pi$
$60$	43.0064	−	30.3442i	0.716773	−	0.505736i
$61$	2.82800			0.0463606			0.0231803	−	0.999731i	$-0.492621\pi$
$61$	2.82800			0.0463606			0.0231803	+	0.999731i	$0.492621\pi$
$62$	−1.65683	+	4.46450i	−0.0267230	+	0.0720081i
$63$	−25.5665			−0.405818
$64$	−34.0689	+	54.1785i	−0.532326	+	0.846539i
$65$	21.9873	+	5.51194i	0.338267	+	0.0847991i
$66$	−6.07361	+	16.3660i	−0.0920244	+	0.247970i
$67$	−55.3752			−0.826496			−0.413248	−	0.910619i	$-0.635606\pi$
$67$	−55.3752			−0.826496			−0.413248	+	0.910619i	$0.635606\pi$
$68$	32.9626	−	38.2943i	0.484745	−	0.563152i
$69$	31.1145			0.450935
$70$	−69.6971	+	101.662i	−0.995673	+	1.45231i
$71$			124.371i			1.75170i	0.482584	+	0.875850i	$0.339698\pi$
$71$			124.371i			1.75170i	−0.482584	+	0.875850i	$0.660302\pi$
$72$	8.02416	+	14.5246i	0.111447	+	0.201730i
$73$			130.778i			1.79147i	0.444584	+	0.895737i	$0.353352\pi$
$73$			130.778i			1.79147i	−0.444584	+	0.895737i	$0.646648\pi$
$74$	−41.5576	+	111.982i	−0.561590	+	1.51326i
$75$	−58.0119	−	31.0361i	−0.773492	−	0.413814i
$76$	−42.6186	+	49.5121i	−0.560771	+	0.651475i
$77$		−	40.8804i		−	0.530914i
$78$	8.30210	−	22.3709i	0.106437	−	0.286807i
$79$			74.9602i			0.948863i	0.880292	+	0.474432i	$0.157346\pi$
$79$			74.9602i			0.948863i	−0.880292	+	0.474432i	$0.842654\pi$
$80$	79.6297	+	7.68868i	0.995371	+	0.0961085i
$81$	−58.0297			−0.716416
$82$	−30.8116	−	11.4345i	−0.375751	−	0.139445i
$83$	−19.8604			−0.239282			−0.119641	−	0.992817i	$-0.538174\pi$
$83$	−19.8604			−0.239282			−0.119641	+	0.992817i	$0.538174\pi$
$84$	98.3383	+	84.6468i	1.17069	+	1.00770i
$85$	−61.2632	−	15.3579i	−0.720744	−	0.180681i
$86$	−91.2168	−	33.8516i	−1.06066	−	0.393623i
$87$	72.9305			0.838282
$88$	−23.2245	+	12.8305i	−0.263915	+	0.145801i
$89$	−92.5422			−1.03980			−0.519900	−	0.854227i	$-0.674031\pi$
$89$	−92.5422			−1.03980			−0.519900	+	0.854227i	$0.674031\pi$
$90$	11.7287	−	17.1077i	0.130319	−	0.190086i
$91$			55.8799i			0.614065i
$92$	35.8425	+	30.8522i	0.389593	+	0.335350i
$93$		−	6.26608i		−	0.0673772i
$94$	150.597	+	55.8881i	1.60209	+	0.594555i
$95$	79.2095	+	19.8568i	0.833784	+	0.209019i
$96$	17.2248	−	82.4337i	0.179425	−	0.858684i
$97$		−	7.08552i		−	0.0730466i	−0.999333	−	0.0365233i	$-0.988372\pi$
$97$		−	7.08552i		−	0.0730466i	0.999333	−	0.0365233i	$-0.0116283\pi$
$98$	−192.994	−	71.6222i	−1.96933	−	0.730839i
$99$			6.87938i			0.0694887i
$100$	−36.0526	−	93.2749i	−0.360526	−	0.932749i
$101$	−21.3844			−0.211727			−0.105864	−	0.994381i	$-0.533761\pi$
$101$	−21.3844			−0.211727			−0.105864	+	0.994381i	$0.533761\pi$
$102$	−23.1321	+	62.3320i	−0.226785	+	0.611098i
$103$	0.914076			0.00887452			0.00443726	−	0.999990i	$-0.498588\pi$
$103$	0.914076			0.00887452			0.00443726	+	0.999990i	$0.498588\pi$
$104$	31.7459	−	17.5382i	0.305249	−	0.168636i
$105$	39.4384	−	157.322i	0.375604	−	1.49830i
$106$	46.6042	−	125.580i	0.439662	−	1.18472i
$107$	157.292			1.47002			0.735010	−	0.678056i	$-0.237177\pi$
$107$	157.292			1.47002			0.735010	+	0.678056i	$0.237177\pi$
$108$	−88.3521	−	76.0510i	−0.818075	−	0.704176i
$109$	−91.2074			−0.836765			−0.418383	−	0.908271i	$-0.637403\pi$
$109$	−91.2074			−0.836765			−0.418383	+	0.908271i	$0.637403\pi$
$110$	27.3549	+	18.7539i	0.248681	+	0.170490i
$111$		−	157.170i		−	1.41595i
$112$	29.3481	+	195.018i	0.262036	+	1.74124i
$113$		−	188.929i		−	1.67194i	−0.548778	−	0.835968i	$-0.684907\pi$
$113$		−	188.929i		−	1.67194i	0.548778	−	0.835968i	$-0.315093\pi$
$114$	29.9083	−	80.5913i	0.262354	−	0.706941i
$115$	14.3746	−	57.3409i	0.124996	−	0.498616i
$116$	84.0126	+	72.3156i	0.724247	+	0.623411i
$117$		−	9.40353i		−	0.0803720i
$118$	−8.69100	+	23.4188i	−0.0736525	+	0.198465i
$119$		−	155.698i		−	1.30839i
$120$	−101.754	+	26.9707i	−0.847949	+	0.224756i
$121$	−11.0000			−0.0909091
$122$	−5.30262	−	1.96786i	−0.0434641	−	0.0161300i
$123$	43.2451			0.351586
$124$	6.21325	−	7.21824i	0.0501069	−	0.0582116i
$125$	−83.9971	+	92.5715i	−0.671977	+	0.740572i
$126$	47.9384	+	17.7905i	0.380463	+	0.141194i
$127$	−159.673			−1.25727			−0.628635	−	0.777700i	$-0.716386\pi$
$127$	−159.673			−1.25727			−0.628635	+	0.777700i	$0.716386\pi$
$128$	101.581	−	77.8803i	0.793600	−	0.608440i
$129$	128.026			0.992449
$130$	−37.3918	−	25.6350i	−0.287629	−	0.197193i
$131$			54.1400i			0.413282i	0.978417	+	0.206641i	$0.0662532\pi$
$131$			54.1400i			0.413282i	−0.978417	+	0.206641i	$0.933747\pi$
$132$	22.7766	−	26.4607i	0.172550	−	0.200460i
$133$			201.308i			1.51359i
$134$	103.831	+	38.5329i	0.774858	+	0.287559i
$135$	−35.4335	+	141.346i	−0.262470	+	1.04701i
$136$	−88.4535	+	48.8665i	−0.650394	+	0.359312i
$137$			178.927i			1.30604i	0.757342	+	0.653018i	$0.226497\pi$
$137$			178.927i			1.30604i	−0.757342	+	0.653018i	$0.773503\pi$
$138$	−58.3412	−	21.6511i	−0.422762	−	0.156892i
$139$		−	26.3457i		−	0.189537i	−0.995499	−	0.0947687i	$-0.969789\pi$
$139$		−	26.3457i		−	0.189537i	0.995499	−	0.0947687i	$-0.0302111\pi$
$140$	201.426	−	142.121i	1.43876	−	1.01515i
$141$	−211.368			−1.49906
$142$	86.5434	−	233.201i	0.609460	−	1.64226i
$143$	15.0361			0.105147
$144$	−4.93872	−	32.8179i	−0.0342967	−	0.227902i
$145$	33.6931	−	134.403i	0.232367	−	0.926920i
$146$	91.0017	−	245.214i	0.623299	−	1.67955i
$147$	270.874			1.84268
$148$	155.845	−	181.053i	1.05301	−	1.22333i
$149$	−110.908			−0.744346			−0.372173	−	0.928163i	$-0.621387\pi$
$149$	−110.908			−0.744346			−0.372173	+	0.928163i	$0.621387\pi$
$150$	87.1784	+	98.5616i	0.581190	+	0.657077i
$151$			54.2134i			0.359029i	0.983755	+	0.179515i	$0.0574527\pi$
$151$			54.2134i			0.359029i	−0.983755	+	0.179515i	$0.942547\pi$
$152$	114.365	−	63.1813i	0.752400	−	0.415666i
$153$			26.2010i			0.171248i
$154$	−28.4466	+	76.6525i	−0.184718	+	0.497744i
$155$	−11.5477	−	2.89487i	−0.0745015	−	0.0186766i
$156$	−31.1336	+	36.1694i	−0.199574	+	0.231855i
$157$		−	118.752i		−	0.756383i	−0.925727	−	0.378191i	$-0.876546\pi$
$157$		−	118.752i		−	0.756383i	0.925727	−	0.378191i	$-0.123454\pi$
$158$	52.1611	−	140.554i	0.330133	−	0.889580i
$159$			176.256i			1.10853i
$160$	−143.959	−	69.8269i	−0.899744	−	0.436418i
$161$	145.729			0.905152
$162$	108.808	+	40.3800i	0.671656	+	0.249259i
$163$	20.0363			0.122922			0.0614610	−	0.998109i	$-0.480424\pi$
$163$	20.0363			0.122922			0.0614610	+	0.998109i	$0.480424\pi$
$164$	49.8164	+	42.8805i	0.303758	+	0.261466i
$165$	−42.3317	−	10.6120i	−0.256556	−	0.0643152i
$166$	37.2391	+	13.8199i	0.224332	+	0.0832522i
$167$	−125.020			−0.748622			−0.374311	−	0.927303i	$-0.622121\pi$
$167$	−125.020			−0.748622			−0.374311	+	0.927303i	$0.622121\pi$
$168$	−125.487	−	227.145i	−0.746948	−	1.35205i
$169$	148.447			0.878385
$170$	104.184	+	71.4267i	0.612850	+	0.420157i
$171$		−	33.8762i		−	0.198107i
$172$	147.480	+	126.947i	0.857442	+	0.738061i
$173$			196.309i			1.13473i	0.823465	+	0.567367i	$0.192038\pi$
$173$			196.309i			1.13473i	−0.823465	+	0.567367i	$0.807962\pi$
$174$	−136.748	−	50.7487i	−0.785908	−	0.291659i
$175$	−271.707	−	145.362i	−1.55261	−	0.830639i
$176$	52.4751	−	7.89692i	0.298154	−	0.0448688i
$177$		−	32.8691i		−	0.185701i
$178$	173.521	+	64.3955i	0.974835	+	0.361772i
$179$			128.674i			0.718849i	0.933174	+	0.359425i	$0.117027\pi$
$179$			128.674i			0.718849i	−0.933174	+	0.359425i	$0.882973\pi$
$180$	−33.8962	+	23.9163i	−0.188312	+	0.132868i
$181$	−63.3884			−0.350212			−0.175106	−	0.984550i	$-0.556027\pi$
$181$	−63.3884			−0.350212			−0.175106	+	0.984550i	$0.556027\pi$
$182$	38.8841	−	104.777i	0.213649	−	0.575700i
$183$	7.44241			0.0406689
$184$	−45.7378	−	82.7903i	−0.248575	−	0.449947i
$185$	−289.648	−	72.6109i	−1.56566	−	0.392491i
$186$	−4.36026	+	11.7492i	−0.0234422	+	0.0631677i
$187$	−41.8949			−0.224037
$188$	−243.486	−	209.586i	−1.29514	−	1.11482i
$189$	−359.224			−1.90066
$190$	−134.704	−	92.3503i	−0.708968	−	0.486054i
$191$		−	37.9067i		−	0.198464i	−0.995064	−	0.0992322i	$-0.968361\pi$
$191$		−	37.9067i		−	0.198464i	0.995064	−	0.0992322i	$-0.0316387\pi$
$192$	−89.6587	+	142.581i	−0.466972	+	0.742609i
$193$			225.451i			1.16814i	0.811704	+	0.584069i	$0.198540\pi$
$193$			225.451i			1.16814i	−0.811704	+	0.584069i	$0.801460\pi$
$194$	−4.93046	+	13.2857i	−0.0254148	+	0.0684828i
$195$	57.8639	+	14.5057i	0.296738	+	0.0743883i
$196$	312.034	+	268.590i	1.59201	+	1.37036i
$197$		−	377.121i		−	1.91432i	−0.289563	−	0.957159i	$-0.593510\pi$
$197$		−	377.121i		−	1.91432i	0.289563	−	0.957159i	$-0.406490\pi$
$198$	4.78702	−	12.8992i	0.0241769	−	0.0651472i
$199$			296.936i			1.49214i	0.665867	+	0.746070i	$0.268062\pi$
$199$			296.936i			1.49214i	−0.665867	+	0.746070i	$0.731938\pi$
$200$	2.69493	+	199.982i	0.0134746	+	0.999909i
$201$	−145.730			−0.725026
$202$	40.0968	+	14.8804i	0.198499	+	0.0736652i
$203$	341.581			1.68266
$204$	86.7474	−	100.779i	0.425232	−	0.494013i
$205$	19.9788	−	79.6962i	0.0974575	−	0.388762i
$206$	−1.71393	−	0.636060i	−0.00832006	−	0.00308767i
$207$	−24.5235			−0.118471
$208$	−71.7290	+	10.7944i	−0.344851	+	0.0518962i
$209$	54.1674			0.259174
$210$	−183.421	+	267.542i	−0.873434	+	1.27401i
$211$		−	154.781i		−	0.733559i	−0.930308	−	0.366779i	$-0.880460\pi$
$211$		−	154.781i		−	0.733559i	0.930308	−	0.366779i	$-0.119540\pi$
$212$	−174.770	+	203.039i	−0.824386	+	0.957729i
$213$			327.305i			1.53664i
$214$	−294.930	−	109.452i	−1.37818	−	0.511457i
$215$	59.1467	−	235.938i	0.275101	−	1.09739i
$216$	112.744	+	204.079i	0.521963	+	0.944810i
$217$		−	29.3481i		−	0.135245i
$218$	171.018	+	63.4667i	0.784486	+	0.291132i
$219$			344.166i			1.57153i
$220$	−38.2417	−	54.1994i	−0.173826	−	0.246361i
$221$	57.2667			0.259125
$222$	−109.367	+	294.701i	−0.492643	+	1.32748i
$223$	−162.723			−0.729699			−0.364849	−	0.931067i	$-0.618880\pi$
$223$	−162.723			−0.729699			−0.364849	+	0.931067i	$0.618880\pi$
$224$	80.6747	−	386.090i	0.360155	−	1.72362i
$225$	45.7231	+	24.4616i	0.203214	+	0.108718i
$226$	−131.466	+	354.250i	−0.581709	+	1.56748i
$227$	171.179			0.754094			0.377047	−	0.926194i	$-0.376939\pi$
$227$	171.179			0.754094			0.377047	+	0.926194i	$0.376939\pi$
$228$	−112.159	+	130.301i	−0.491925	+	0.571494i
$229$	415.938			1.81632			0.908161	−	0.418621i	$-0.137487\pi$
$229$	415.938			1.81632			0.908161	+	0.418621i	$0.137487\pi$
$230$	−66.8537	+	97.5141i	−0.290668	+	0.423974i
$231$		−	107.584i		−	0.465733i
$232$	−107.207	−	194.055i	−0.462097	−	0.836445i
$233$		−	182.050i		−	0.781331i	−0.920533	−	0.390665i	$-0.872245\pi$
$233$		−	182.050i		−	0.781331i	0.920533	−	0.390665i	$-0.127755\pi$
$234$	−6.54345	+	17.6320i	−0.0279635	+	0.0753506i
$235$	−97.6496	+	389.528i	−0.415530	+	1.65757i
$236$	32.5920	−	37.8637i	0.138102	−	0.160440i
$237$			197.272i			0.832371i
$238$	−108.342	+	291.941i	−0.455220	+	1.22664i
$239$		−	27.7896i		−	0.116275i	−0.998309	−	0.0581373i	$-0.981484\pi$
$239$		−	27.7896i		−	0.116275i	0.998309	−	0.0581373i	$-0.0185161\pi$
$240$	209.561	+	20.2342i	0.873169	+	0.0843092i
$241$	276.374			1.14678			0.573390	−	0.819282i	$-0.305628\pi$
$241$	276.374			1.14678			0.573390	+	0.819282i	$0.305628\pi$
$242$	20.6255	+	7.65435i	0.0852293	+	0.0316296i
$243$	109.579			0.450941
$244$	8.57331	+	7.37966i	0.0351365	+	0.0302445i
$245$	125.141	−	499.192i	0.510779	−	2.03752i
$246$	−81.0865	−	30.0921i	−0.329620	−	0.122326i
$247$	−74.0422			−0.299766
$248$	−16.6729	+	9.21103i	−0.0672296	+	0.0371412i
$249$	−52.2664			−0.209905
$250$	221.914	−	115.126i	0.887657	−	0.460505i
$251$		−	145.061i		−	0.577931i	−0.957340	−	0.288965i	$-0.906689\pi$
$251$		−	145.061i		−	0.577931i	0.957340	−	0.288965i	$-0.0933113\pi$
$252$	−77.5071	−	66.7158i	−0.307568	−	0.264745i
$253$		−	39.2126i		−	0.154990i
$254$	299.395	+	111.109i	1.17872	+	0.437436i
$255$	−161.226	−	40.4172i	−0.632258	−	0.158499i
$256$	−244.662	+	75.3439i	−0.955709	+	0.294312i
$257$			218.884i			0.851688i	0.904797	+	0.425844i	$0.140023\pi$
$257$			218.884i			0.851688i	−0.904797	+	0.425844i	$0.859977\pi$
$258$	−240.054	−	89.0869i	−0.930443	−	0.345298i
$259$		−	736.128i		−	2.84219i
$260$	52.2731	+	74.0859i	0.201050	+	0.284946i
$261$	−57.4815			−0.220236
$262$	37.6733	−	101.515i	0.143791	−	0.387461i
$263$	−430.384			−1.63644			−0.818220	−	0.574905i	$-0.805039\pi$
$263$	−430.384			−1.63644			−0.818220	+	0.574905i	$0.805039\pi$
$264$	−61.1197	+	33.7658i	−0.231514	+	0.127901i
$265$	324.821	+	81.4283i	1.22574	+	0.307277i
$266$	140.080	−	377.461i	0.526617	−	1.41903i
$267$	−243.542			−0.912143
$268$	−167.875	−	144.502i	−0.626398	−	0.539185i
$269$	233.423			0.867742			0.433871	−	0.900975i	$-0.357147\pi$
$269$	233.423			0.867742			0.433871	+	0.900975i	$0.357147\pi$
$270$	164.795	−	240.373i	0.610351	−	0.890271i
$271$		−	314.298i		−	1.15977i	−0.814697	−	0.579886i	$-0.803097\pi$
$271$		−	314.298i		−	1.15977i	0.814697	−	0.579886i	$-0.196903\pi$
$272$	199.858	−	30.0764i	0.734772	−	0.110575i
$273$			147.059i			0.538676i
$274$	124.506	−	335.496i	0.454403	−	1.22444i
$275$	−39.1137	+	73.1103i	−0.142231	+	0.265856i
$276$	94.3264	+	81.1934i	0.341762	+	0.294179i
$277$			52.4195i			0.189240i	0.995513	+	0.0946200i	$0.0301636\pi$
$277$			52.4195i			0.189240i	−0.995513	+	0.0946200i	$0.969836\pi$
$278$	−18.3327	+	49.3994i	−0.0659448	+	0.177696i
$279$			4.93872i			0.0177015i
$280$	−476.579	+	126.321i	−1.70207	+	0.451147i
$281$	−428.059			−1.52334			−0.761671	−	0.647964i	$-0.775621\pi$
$281$	−428.059			−1.52334			−0.761671	+	0.647964i	$0.775621\pi$
$282$	396.324	+	147.080i	1.40540	+	0.521561i
$283$	245.145			0.866236			0.433118	−	0.901337i	$-0.357413\pi$
$283$	245.145			0.866236			0.433118	+	0.901337i	$0.357413\pi$
$284$	−324.545	+	377.040i	−1.14277	+	1.32761i
$285$	208.455	+	52.2569i	0.731420	+	0.183357i
$286$	−28.1933	−	10.4628i	−0.0985779	−	0.0365834i
$287$	202.545			0.705730
$288$	−13.5760	+	64.9716i	−0.0471389	+	0.225596i
$289$	129.438			0.447883
$290$	−156.701	+	228.567i	−0.540347	+	0.788162i
$291$		−	18.6469i		−	0.0640787i
$292$	−341.264	+	396.463i	−1.16871	+	1.35775i
$293$			388.800i			1.32696i	0.748192	+	0.663482i	$0.230922\pi$
$293$			388.800i			1.32696i	−0.748192	+	0.663482i	$0.769078\pi$
$294$	−507.900	−	188.487i	−1.72755	−	0.641114i
$295$	−60.5744	−	15.1852i	−0.205337	−	0.0514753i
$296$	−418.202	+	231.037i	−1.41284	+	0.780530i
$297$			96.6593i			0.325452i
$298$	207.957	+	77.1751i	0.697841	+	0.258977i
$299$			53.6002i			0.179265i
$300$	−94.8793	−	245.471i	−0.316264	−	0.818235i
$301$	599.628			1.99212
$302$	37.7244	−	101.653i	0.124915	−	0.336598i
$303$	−56.2772			−0.185733
$304$	−258.404	+	38.8869i	−0.850013	+	0.127917i
$305$	3.43831	−	13.7156i	0.0112732	−	0.0449691i
$306$	18.2320	−	49.1280i	0.0595816	−	0.160549i
$307$	−129.502			−0.421829			−0.210915	−	0.977504i	$-0.567644\pi$
$307$	−129.502			−0.421829			−0.210915	+	0.977504i	$0.567644\pi$
$308$	106.677	−	123.932i	0.346355	−	0.402378i
$309$	2.40556			0.00778499
$310$	19.6381	+	13.4635i	0.0633488	+	0.0434306i
$311$			431.813i			1.38847i	0.719750	+	0.694233i	$0.244256\pi$
$311$			431.813i			1.38847i	−0.719750	+	0.694233i	$0.755744\pi$
$312$	83.5455	−	46.1550i	0.267774	−	0.147933i
$313$		−	115.640i		−	0.369456i	−0.982790	−	0.184728i	$-0.940860\pi$
$313$		−	115.640i		−	0.369456i	0.982790	−	0.184728i	$-0.0591405\pi$
$314$	−82.6337	+	222.666i	−0.263165	+	0.709126i
$315$	−31.0841	+	123.996i	−0.0986797	+	0.393637i
$316$	−195.609	+	227.248i	−0.619015	+	0.719140i
$317$		−	513.271i		−	1.61915i	−0.587015	−	0.809576i	$-0.699697\pi$
$317$		−	513.271i		−	1.61915i	0.587015	−	0.809576i	$-0.300303\pi$
$318$	122.648	−	330.487i	0.385684	−	1.03927i
$319$		−	91.9118i		−	0.288125i
$320$	221.340	+	231.103i	0.691689	+	0.722196i
$321$	413.944			1.28955
$322$	−273.249	−	101.406i	−0.848600	−	0.314925i
$323$	206.303			0.638710
$324$	−175.922	−	151.429i	−0.542969	−	0.467372i
$325$	53.4650	−	99.9356i	0.164508	−	0.307494i
$326$	−37.5690	−	13.9423i	−0.115242	−	0.0427677i
$327$	−240.030			−0.734035
$328$	−63.5695	−	115.068i	−0.193809	−	0.350816i
$329$	−989.971			−3.00903
$330$	71.9895	+	49.3546i	0.218150	+	0.149559i
$331$		−	144.169i		−	0.435554i	−0.975999	−	0.217777i	$-0.930119\pi$
$331$		−	144.169i		−	0.435554i	0.975999	−	0.217777i	$-0.0698806\pi$
$332$	−60.2085	−	51.8257i	−0.181351	−	0.156102i
$333$			123.876i			0.372001i
$334$	234.418	+	86.9951i	0.701849	+	0.260464i
$335$	−67.3259	+	268.566i	−0.200973	+	0.801689i
$336$	77.2350	+	513.228i	0.229866	+	1.52746i
$337$			62.1121i			0.184309i	0.995745	+	0.0921545i	$0.0293754\pi$
$337$			62.1121i			0.184309i	−0.995745	+	0.0921545i	$0.970625\pi$
$338$	−278.345	−	103.297i	−0.823505	−	0.305612i
$339$		−	497.202i		−	1.46667i
$340$	−145.648	−	206.425i	−0.428377	−	0.607133i
$341$	−7.89692			−0.0231581
$342$	−23.5728	+	63.5195i	−0.0689263	+	0.185729i
$343$	664.706			1.93792
$344$	−188.196	−	340.654i	−0.547081	−	0.990275i
$345$	37.8295	−	150.903i	0.109651	−	0.437401i
$346$	136.602	−	368.088i	0.394802	−	1.06384i
$347$	202.503			0.583583			0.291792	−	0.956482i	$-0.405749\pi$
$347$	202.503			0.583583			0.291792	+	0.956482i	$0.405749\pi$
$348$	221.095	+	190.312i	0.635331	+	0.546874i
$349$	356.951			1.02278			0.511391	−	0.859348i	$-0.329130\pi$
$349$	356.951			1.02278			0.511391	+	0.859348i	$0.329130\pi$
$350$	408.313	+	461.627i	1.16661	+	1.31894i
$351$		−	132.125i		−	0.376425i
$352$	−103.888	−	21.7078i	−0.295137	−	0.0616698i
$353$		−	242.038i		−	0.685659i	−0.939398	−	0.342830i	$-0.888615\pi$
$353$		−	242.038i		−	0.685659i	0.939398	−	0.342830i	$-0.111385\pi$
$354$	−22.8720	+	61.6311i	−0.0646102	+	0.174099i
$355$	603.189	+	151.211i	1.69912	+	0.425948i
$356$	−280.549	−	241.489i	−0.788060	−	0.678339i
$357$		−	409.749i		−	1.14776i
$358$	89.5378	−	241.269i	0.250106	−	0.673937i
$359$		−	275.762i		−	0.768140i	−0.923304	−	0.384070i	$-0.874522\pi$
$359$		−	275.762i		−	0.768140i	0.923304	−	0.384070i	$-0.125478\pi$
$360$	80.1991	−	21.2574i	0.222775	−	0.0590484i
$361$	94.2626			0.261115
$362$	118.856	+	44.1089i	0.328332	+	0.121848i
$363$	−28.9486			−0.0797482
$364$	−145.819	+	169.405i	−0.400601	+	0.465398i
$365$	634.262	+	159.001i	1.73770	+	0.435620i
$366$	−13.9548	−	5.17880i	−0.0381280	−	0.0141497i
$367$	−378.758			−1.03204			−0.516019	−	0.856577i	$-0.672587\pi$
$367$	−378.758			−1.03204			−0.516019	+	0.856577i	$0.672587\pi$
$368$	28.1508	+	187.062i	0.0764966	+	0.508321i
$369$	−34.0844			−0.0923696
$370$	492.576	+	337.700i	1.33129	+	0.912703i
$371$			825.519i			2.22512i
$372$	16.3514	−	18.9962i	0.0439552	−	0.0510650i
$373$			151.017i			0.404872i	0.979296	+	0.202436i	$0.0648858\pi$
$373$			151.017i			0.404872i	−0.979296	+	0.202436i	$0.935114\pi$
$374$	78.5548	+	29.1526i	0.210039	+	0.0779480i
$375$	−221.054	+	243.619i	−0.589478	+	0.649652i
$376$	310.706	+	562.412i	0.826347	+	1.49578i
$377$			125.636i			0.333251i
$378$	673.562	+	249.966i	1.78191	+	0.661287i
$379$		−	721.980i		−	1.90496i	−0.304599	−	0.952481i	$-0.598522\pi$
$379$		−	721.980i		−	1.90496i	0.304599	−	0.952481i	$-0.401478\pi$
$380$	188.314	+	266.895i	0.495563	+	0.702355i
$381$	−420.211			−1.10291
$382$	−26.3774	+	71.0767i	−0.0690508	+	0.186065i
$383$	−640.870			−1.67329			−0.836645	−	0.547746i	$-0.815486\pi$
$383$	−640.870			−1.67329			−0.836645	+	0.547746i	$0.815486\pi$
$384$	267.329	−	204.957i	0.696170	−	0.533741i
$385$	−198.267	−	49.7029i	−0.514979	−	0.129098i
$386$	156.880	−	422.730i	0.406424	−	1.09516i
$387$	−100.906			−0.260739
$388$	18.4897	−	21.4804i	0.0476538	−	0.0553617i
$389$	−103.555			−0.266209			−0.133104	−	0.991102i	$-0.542495\pi$
$389$	−103.555			−0.266209			−0.133104	+	0.991102i	$0.542495\pi$
$390$	−98.4035	−	67.4634i	−0.252317	−	0.172983i
$391$		−	149.346i		−	0.381959i
$392$	−398.179	−	720.747i	−1.01576	−	1.83864i
$393$			142.480i			0.362543i
$394$	−262.420	+	707.118i	−0.666039	+	1.79472i
$395$	363.552	+	91.1376i	0.920384	+	0.230728i
$396$	−17.9518	+	20.8554i	−0.0453327	+	0.0526652i
$397$		−	490.730i		−	1.23609i	−0.786141	−	0.618047i	$-0.787924\pi$
$397$		−	490.730i		−	1.23609i	0.786141	−	0.618047i	$-0.212076\pi$
$398$	206.623	−	556.768i	0.519153	−	1.39891i
$399$			529.779i			1.32777i
$400$	134.104	−	376.850i	0.335261	−	0.942125i
$401$	−505.365			−1.26026			−0.630131	−	0.776489i	$-0.716999\pi$
$401$	−505.365			−1.26026			−0.630131	+	0.776489i	$0.716999\pi$
$402$	273.251	+	101.406i	0.679728	+	0.252255i
$403$	10.7944			0.0267852
$404$	−64.8287	−	55.8027i	−0.160467	−	0.138126i
$405$	−70.5533	+	281.440i	−0.174206	+	0.694914i
$406$	−640.479	−	237.689i	−1.57753	−	0.585441i
$407$	−198.076			−0.486673
$408$	−232.782	+	128.601i	−0.570545	+	0.315199i
$409$	−145.058			−0.354666			−0.177333	−	0.984151i	$-0.556747\pi$
$409$	−145.058			−0.354666			−0.177333	+	0.984151i	$0.556747\pi$
$410$	−92.9177	+	135.532i	−0.226629	+	0.330565i
$411$			470.880i			1.14569i
$412$	2.77110	+	2.38528i	0.00672597	+	0.00578952i
$413$		−	153.947i		−	0.372754i
$414$	45.9826	+	17.0647i	0.111069	+	0.0412190i
$415$	−24.1465	+	96.3215i	−0.0581844	+	0.232100i
$416$	142.006	+	29.6726i	0.341361	+	0.0713285i
$417$		−	69.3337i		−	0.166268i
$418$	−101.566	−	37.6924i	−0.242982	−	0.0901733i
$419$		−	436.102i		−	1.04082i	−0.853918	−	0.520408i	$-0.825780\pi$
$419$		−	436.102i		−	1.04082i	0.853918	−	0.520408i	$-0.174220\pi$
$420$	530.092	−	374.019i	1.26212	−	0.890521i
$421$	426.638			1.01339			0.506696	−	0.862125i	$-0.330867\pi$
$421$	426.638			1.01339			0.506696	+	0.862125i	$0.330867\pi$
$422$	−107.704	+	290.221i	−0.255224	+	0.687728i
$423$	166.593			0.393837
$424$	468.986	−	259.093i	1.10610	−	0.611068i
$425$	−148.969	+	278.450i	−0.350516	+	0.655176i
$426$	227.755	−	613.711i	0.534637	−	1.44064i
$427$	34.8576			0.0816337
$428$	476.844	+	410.454i	1.11412	+	0.959005i
$429$	39.5702			0.0922383
$430$	−275.080	+	401.238i	−0.639722	+	0.933111i
$431$		−	19.1962i		−	0.0445387i	−0.999752	−	0.0222693i	$-0.992911\pi$
$431$		−	19.1962i		−	0.0445387i	0.999752	−	0.0222693i	$-0.00708914\pi$
$432$	−69.3919	−	461.110i	−0.160629	−	1.06738i
$433$		−	717.973i		−	1.65814i	−0.559148	−	0.829068i	$-0.688871\pi$
$433$		−	717.973i		−	1.65814i	0.559148	−	0.829068i	$-0.311129\pi$
$434$	−20.4219	+	55.0290i	−0.0470550	+	0.126795i
$435$	88.6699	−	353.708i	0.203839	−	0.813121i
$436$	−276.503	−	238.006i	−0.634181	−	0.545885i
$437$			193.095i			0.441865i
$438$	239.488	−	645.327i	0.546776	−	1.47335i
$439$		−	142.031i		−	0.323532i	−0.986829	−	0.161766i	$-0.948281\pi$
$439$		−	142.031i		−	0.323532i	0.986829	−	0.161766i	$-0.0517190\pi$
$440$	33.9902	+	128.237i	0.0772504	+	0.291447i
$441$	−213.494			−0.484113
$442$	−107.378	−	39.8490i	−0.242936	−	0.0901562i
$443$	−246.868			−0.557263			−0.278632	−	0.960398i	$-0.589881\pi$
$443$	−246.868			−0.557263			−0.278632	+	0.960398i	$0.589881\pi$
$444$	410.135	−	476.474i	0.923728	−	1.07314i
$445$	−112.514	+	448.823i	−0.252840	+	1.00859i
$446$	305.113	+	113.231i	0.684109	+	0.253881i
$447$	−291.874			−0.652962
$448$	−419.929	+	667.799i	−0.937343	+	1.49062i
$449$	−260.153			−0.579406			−0.289703	−	0.957117i	$-0.593557\pi$
$449$	−260.153			−0.579406			−0.289703	+	0.957117i	$0.593557\pi$
$450$	−68.7112	−	77.6831i	−0.152692	−	0.172629i
$451$		−	54.5003i		−	0.120843i
$452$	493.010	−	572.754i	1.09073	−	1.26715i
$453$			142.673i			0.314951i
$454$	−320.969	−	119.115i	−0.706980	−	0.262368i
$455$	271.014	+	67.9396i	0.595635	+	0.149318i
$456$	300.973	−	166.273i	0.660028	−	0.364635i
$457$		−	298.040i		−	0.652166i	−0.945341	−	0.326083i	$-0.894271\pi$
$457$		−	298.040i		−	0.652166i	0.945341	−	0.326083i	$-0.105729\pi$
$458$	−779.902	−	289.430i	−1.70284	−	0.631944i
$459$			368.139i			0.802046i
$460$	193.209	−	136.323i	0.420019	−	0.296355i
$461$	647.275			1.40407			0.702034	−	0.712144i	$-0.252276\pi$
$461$	647.275			1.40407			0.702034	+	0.712144i	$0.252276\pi$
$462$	−74.8626	+	201.726i	−0.162040	+	0.436635i
$463$	−130.560			−0.281987			−0.140993	−	0.990011i	$-0.545030\pi$
$463$	−130.560			−0.281987			−0.140993	+	0.990011i	$0.545030\pi$
$464$	65.9836	+	438.462i	0.142206	+	0.944961i
$465$	−30.3901	−	7.61839i	−0.0653550	−	0.0163836i
$466$	−126.680	+	341.352i	−0.271845	+	0.732515i
$467$	228.711			0.489746			0.244873	−	0.969555i	$-0.421254\pi$
$467$	228.711			0.489746			0.244873	+	0.969555i	$0.421254\pi$
$468$	24.5385	−	28.5076i	0.0524327	−	0.0609136i
$469$	−682.549			−1.45533
$470$	454.151	−	662.434i	0.966279	−	1.40943i
$471$		−	312.519i		−	0.663522i
$472$	−87.4590	+	48.3170i	−0.185294	+	0.102367i
$473$		−	161.347i		−	0.341113i
$474$	137.272	−	369.894i	0.289603	−	0.780366i
$475$	192.608	−	360.018i	0.405490	−	0.757933i
$476$	406.294	−	472.012i	0.853559	−	0.991621i
$477$		−	138.919i		−	0.291235i
$478$	−19.3374	+	52.1068i	−0.0404548	+	0.109010i
$479$		−	213.777i		−	0.446299i	−0.974784	−	0.223149i	$-0.928366\pi$
$479$		−	213.777i		−	0.446299i	0.974784	−	0.223149i	$-0.0716338\pi$
$480$	−378.855	−	183.763i	−0.789282	−	0.382839i
$481$	270.753			0.562895
$482$	−518.214	−	192.315i	−1.07513	−	0.398994i
$483$	383.515			0.794026
$484$	−33.3474	−	28.7045i	−0.0688996	−	0.0593068i
$485$	−34.3643	−	8.61467i	−0.0708542	−	0.0177622i
$486$	−205.465	−	76.2504i	−0.422768	−	0.156894i
$487$	925.573			1.90056			0.950280	−	0.311396i	$-0.100797\pi$
$487$	925.573			1.90056			0.950280	+	0.311396i	$0.100797\pi$
$488$	−10.9402	−	19.8029i	−0.0224184	−	0.0405798i
$489$	52.7293			0.107831
$490$	−582.007	+	848.927i	−1.18777	+	1.73250i
$491$		−	643.261i		−	1.31010i	−0.755583	−	0.655052i	$-0.772647\pi$
$491$		−	643.261i		−	1.31010i	0.755583	−	0.655052i	$-0.227353\pi$
$492$	131.101	+	112.848i	0.266466	+	0.229366i
$493$		−	350.057i		−	0.710056i
$494$	138.833	+	51.5223i	0.281037	+	0.104296i
$495$	33.3645	+	8.36404i	0.0674031	+	0.0168971i
$496$	37.6720	−	5.66921i	0.0759516	−	0.0114299i
$497$			1532.98i			3.08447i
$498$	98.0018	+	36.3696i	0.196791	+	0.0730313i
$499$			224.200i			0.449298i	0.974440	+	0.224649i	$0.0721235\pi$
$499$			224.200i			0.449298i	−0.974440	+	0.224649i	$0.927876\pi$
$500$	−496.210	+	61.4478i	−0.992420	+	0.122896i
$501$	−329.013			−0.656713
$502$	−100.940	+	271.995i	−0.201077	+	0.541823i
$503$	53.0447			0.105457			0.0527283	−	0.998609i	$-0.483208\pi$
$503$	53.0447			0.105457			0.0527283	+	0.998609i	$0.483208\pi$
$504$	98.9049	+	179.029i	0.196240	+	0.355215i
$505$	−25.9995	+	103.713i	−0.0514841	+	0.205372i
$506$	−27.2861	+	73.5253i	−0.0539251	+	0.145307i
$507$	390.666			0.770545
$508$	−484.063	−	416.668i	−0.952880	−	0.820212i
$509$	82.5528			0.162186			0.0810931	−	0.996707i	$-0.474159\pi$
$509$	82.5528			0.162186			0.0810931	+	0.996707i	$0.474159\pi$
$510$	274.181	+	187.973i	0.537610	+	0.368574i
$511$			1611.95i			3.15450i
$512$	511.179	+	28.9746i	0.998397	+	0.0565910i
$513$		−	475.981i		−	0.927838i
$514$	152.310	−	410.417i	0.296324	−	0.798477i
$515$	1.11135	−	4.43320i	0.00215795	−	0.00860816i
$516$	388.122	+	334.084i	0.752174	+	0.647449i
$517$			266.379i			0.515240i
$518$	−512.235	+	1380.27i	−0.988871	+	2.66462i
$519$			516.624i			0.995422i
$520$	−46.4617	−	175.289i	−0.0893494	−	0.337094i
$521$	−28.9162			−0.0555013			−0.0277507	−	0.999615i	$-0.508834\pi$
$521$	−28.9162			−0.0555013			−0.0277507	+	0.999615i	$0.508834\pi$
$522$	107.780	+	39.9985i	0.206476	+	0.0766255i
$523$	−682.051			−1.30411			−0.652056	−	0.758171i	$-0.726093\pi$
$523$	−682.051			−1.30411			−0.652056	+	0.758171i	$0.726093\pi$
$524$	−141.278	+	164.130i	−0.269615	+	0.313225i
$525$	−715.048	−	382.547i	−1.36200	−	0.728661i
$526$	806.989	+	299.483i	1.53420	+	0.569359i
$527$	−30.0764			−0.0570710
$528$	138.098	−	20.7822i	0.261550	−	0.0393603i
$529$	−389.216			−0.735758
$530$	−552.392	−	378.709i	−1.04225	−	0.714544i
$531$			25.9064i			0.0487879i
$532$	−525.313	+	610.281i	−0.987430	+	1.14715i
$533$			74.4972i			0.139770i
$534$	456.652	+	169.469i	0.855154	+	0.317358i
$535$	191.238	−	762.856i	0.357454	−	1.42590i
$536$	214.221	+	387.763i	0.399666	+	0.723438i
$537$			338.630i			0.630596i
$538$	−437.678	−	162.427i	−0.813528	−	0.301909i
$539$		−	341.372i		−	0.633344i
$540$	−476.262	+	336.038i	−0.881966	+	0.622292i
$541$	−291.343			−0.538527			−0.269264	−	0.963066i	$-0.586780\pi$
$541$	−291.343			−0.538527			−0.269264	+	0.963066i	$0.586780\pi$
$542$	−218.705	+	589.324i	−0.403514	+	1.08731i
$543$	−166.819			−0.307217
$544$	−395.671	−	82.6767i	−0.727337	−	0.151979i
$545$	−110.891	+	442.349i	−0.203470	+	0.811650i
$546$	102.331	−	275.742i	0.187419	−	0.505021i
$547$	62.2215			0.113750			0.0568752	−	0.998381i	$-0.481886\pi$
$547$	62.2215			0.113750			0.0568752	+	0.998381i	$0.481886\pi$
$548$	−466.910	+	542.432i	−0.852025	+	0.989839i
$549$	−5.86586			−0.0106846
$550$	124.214	−	109.868i	0.225843	−	0.199760i
$551$			452.602i			0.821420i
$552$	−120.368	−	217.878i	−0.218057	−	0.394707i
$553$			923.951i			1.67080i
$554$	36.4761	−	98.2888i	0.0658413	−	0.177417i
$555$	−762.263	−	191.089i	−1.37345	−	0.344305i
$556$	68.7491	−	79.8692i	0.123649	−	0.143650i
$557$			476.464i			0.855412i	0.903918	+	0.427706i	$0.140678\pi$
$557$			476.464i			0.855412i	−0.903918	+	0.427706i	$0.859322\pi$
$558$	3.43661	−	9.26033i	0.00615880	−	0.0165956i
$559$			220.547i			0.394538i
$560$	981.507	+	94.7698i	1.75269	+	0.169232i
$561$	−110.254			−0.196532
$562$	802.630	+	297.865i	1.42817	+	0.530009i
$563$	214.796			0.381521			0.190761	−	0.981637i	$-0.438905\pi$
$563$	214.796			0.381521			0.190761	+	0.981637i	$0.438905\pi$
$564$	−640.779	−	551.564i	−1.13613	−	0.977950i
$565$	−916.291	−	229.702i	−1.62175	−	0.406552i
$566$	−459.657	−	170.584i	−0.812115	−	0.301385i
$567$	−715.268			−1.26150
$568$	870.901	−	481.132i	1.53328	−	0.847064i
$569$	692.867			1.21769			0.608846	−	0.793288i	$-0.291633\pi$
$569$	692.867			1.21769			0.608846	+	0.793288i	$0.291633\pi$
$570$	−354.499	−	243.037i	−0.621928	−	0.426381i
$571$			405.570i			0.710281i	0.934813	+	0.355141i	$0.115567\pi$
$571$			405.570i			0.710281i	−0.934813	+	0.355141i	$0.884433\pi$
$572$	45.5831	+	39.2366i	0.0796907	+	0.0685955i
$573$		−	99.7586i		−	0.174099i
$574$	−379.780	−	140.941i	−0.661638	−	0.245541i
$575$	−260.622	−	139.432i	−0.453256	−	0.242490i
$576$	70.6661	−	112.378i	0.122684	−	0.195100i
$577$		−	885.493i		−	1.53465i	−0.641259	−	0.767325i	$-0.721587\pi$
$577$		−	885.493i		−	1.53465i	0.641259	−	0.767325i	$-0.278413\pi$
$578$	−242.702	−	90.0696i	−0.419900	−	0.155830i
$579$			593.316i			1.02473i
$580$	452.869	−	319.533i	0.780809	−	0.550919i
$581$	−244.797			−0.421338
$582$	−12.9754	+	34.9638i	−0.0222946	+	0.0600752i
$583$	222.129			0.381010
$584$	915.765	−	505.918i	1.56809	−	0.866298i
$585$	−45.6064	−	11.4329i	−0.0779597	−	0.0195435i
$586$	270.547	−	729.018i	0.461684	−	1.24406i
$587$	47.6840			0.0812334			0.0406167	−	0.999175i	$-0.487068\pi$
$587$	47.6840			0.0812334			0.0406167	+	0.999175i	$0.487068\pi$
$588$	821.176	+	706.845i	1.39656	+	1.20212i
$589$	38.8869			0.0660219
$590$	103.013	+	70.6236i	0.174598	+	0.119701i
$591$		−	992.464i		−	1.67930i
$592$	944.914	−	142.199i	1.59614	−	0.240201i
$593$		−	283.001i		−	0.477236i	−0.971113	−	0.238618i	$-0.923306\pi$
$593$		−	283.001i		−	0.477236i	0.971113	−	0.238618i	$-0.0766944\pi$
$594$	67.2604	−	181.241i	0.113233	−	0.305119i
$595$	−755.124	−	189.300i	−1.26912	−	0.318151i
$596$	−336.226	−	289.413i	−0.564137	−	0.485593i
$597$			781.443i			1.30895i
$598$	37.2977	−	100.503i	0.0623708	−	0.168065i
$599$			1057.36i			1.76521i	0.470120	+	0.882603i	$0.344211\pi$
$599$			1057.36i			1.76521i	−0.470120	+	0.882603i	$0.655789\pi$
$600$	7.09221	+	526.290i	0.0118204	+	0.877150i
$601$	711.377			1.18366			0.591828	−	0.806064i	$-0.298406\pi$
$601$	711.377			1.18366			0.591828	+	0.806064i	$0.298406\pi$
$602$	−1124.33	−	417.251i	−1.86766	−	0.693108i
$603$	114.860			0.190481
$604$	−141.470	+	164.353i	−0.234222	+	0.272107i
$605$	−13.3739	+	53.3492i	−0.0221057	+	0.0881805i
$606$	105.522	+	39.1605i	0.174129	+	0.0646213i
$607$	−418.046			−0.688709			−0.344355	−	0.938840i	$-0.611902\pi$
$607$	−418.046			−0.688709			−0.344355	+	0.938840i	$0.611902\pi$
$608$	511.578	+	106.896i	0.841412	+	0.175815i
$609$	898.934			1.47608
$610$	−15.9910	+	23.3248i	−0.0262147	+	0.0382373i
$611$		−	364.117i		−	0.595937i
$612$	−68.3715	+	79.4305i	−0.111718	+	0.129788i
$613$		−	540.562i		−	0.881831i	−0.897549	−	0.440916i	$-0.854654\pi$
$613$		−	540.562i		−	0.881831i	0.897549	−	0.440916i	$-0.145346\pi$
$614$	242.821	+	90.1137i	0.395474	+	0.146765i
$615$	52.5779	−	209.736i	0.0854926	−	0.341033i
$616$	−286.263	+	158.147i	−0.464713	+	0.256732i
$617$		−	610.765i		−	0.989895i	−0.868923	−	0.494948i	$-0.835187\pi$
$617$		−	610.765i		−	0.989895i	0.868923	−	0.494948i	$-0.164813\pi$
$618$	−4.51054	−	1.67391i	−0.00729861	−	0.00270860i
$619$			217.837i			0.351918i	0.984397	+	0.175959i	$0.0563026\pi$
$619$			217.837i			0.351918i	−0.984397	+	0.175959i	$0.943697\pi$
$620$	−27.4538	−	38.9099i	−0.0442803	−	0.0627578i
$621$	−344.569			−0.554862
$622$	300.477	−	809.669i	0.483083	−	1.30172i
$623$	−1140.66			−1.83092
$624$	−188.768	+	28.4075i	−0.302513	+	0.0455249i
$625$	346.840	+	519.930i	0.554945	+	0.831887i
$626$	−80.4680	+	216.830i	−0.128543	+	0.346373i
$627$	142.552			0.227355
$628$	309.884	−	360.007i	0.493445	−	0.573260i
$629$	−754.396			−1.19936
$630$	144.567	−	210.868i	0.229471	−	0.334711i
$631$			302.659i			0.479650i	0.970816	+	0.239825i	$0.0770901\pi$
$631$			302.659i			0.479650i	−0.970816	+	0.239825i	$0.922910\pi$
$632$	524.906	−	289.986i	0.830547	−	0.458839i
$633$		−	407.335i		−	0.643500i
$634$	−357.160	+	962.406i	−0.563344	+	1.51799i
$635$	−194.133	+	774.404i	−0.305721	+	1.21953i
$636$	−459.940	+	534.334i	−0.723176	+	0.840148i
$637$			466.627i			0.732538i
$638$	−63.9568	+	172.339i	−0.100246	+	0.270123i
$639$		−	257.971i		−	0.403711i
$640$	−254.210	−	587.347i	−0.397204	−	0.917730i
$641$	−790.165			−1.23271			−0.616353	−	0.787470i	$-0.711391\pi$
$641$	−790.165			−1.23271			−0.616353	+	0.787470i	$0.711391\pi$
$642$	−776.164	−	288.043i	−1.20898	−	0.448665i
$643$	−610.520			−0.949486			−0.474743	−	0.880124i	$-0.657459\pi$
$643$	−610.520			−0.949486			−0.474743	+	0.880124i	$0.657459\pi$
$644$	441.791	+	380.281i	0.686011	+	0.590499i
$645$	155.656	−	620.917i	0.241327	−	0.962661i
$646$	−386.828	−	143.556i	−0.598805	−	0.222223i
$647$	471.930			0.729413			0.364706	−	0.931123i	$-0.381169\pi$
$647$	471.930			0.729413			0.364706	+	0.931123i	$0.381169\pi$
$648$	224.490	+	406.351i	0.346435	+	0.627085i
$649$	−41.4238			−0.0638272
$650$	−169.789	+	150.180i	−0.261215	+	0.231046i
$651$		−	77.2351i		−	0.118641i
$652$	60.7417	+	52.2847i	0.0931622	+	0.0801913i
$653$			384.236i			0.588417i	0.955741	+	0.294209i	$0.0950560\pi$
$653$			384.236i			0.588417i	−0.955741	+	0.294209i	$0.904944\pi$
$654$	450.066	+	167.025i	0.688175	+	0.255389i
$655$	262.575	+	65.8241i	0.400878	+	0.100495i
$656$	39.1258	+	259.992i	0.0596430	+	0.396329i
$657$		−	271.261i		−	0.412878i
$658$	1856.24	+	688.871i	2.82103	+	1.04692i
$659$			624.328i			0.947388i	0.880690	+	0.473694i	$0.157080\pi$
$659$			624.328i			0.947388i	−0.880690	+	0.473694i	$0.842920\pi$
$660$	−100.640	−	142.636i	−0.152485	−	0.216115i
$661$	−761.714			−1.15237			−0.576183	−	0.817321i	$-0.695458\pi$
$661$	−761.714			−1.15237			−0.576183	+	0.817321i	$0.695458\pi$
$662$	−100.320	+	270.322i	−0.151540	+	0.408342i
$663$	150.708			0.227312
$664$	76.8306	+	139.072i	0.115709	+	0.209445i
$665$	976.328	+	244.752i	1.46816	+	0.368049i
$666$	86.1994	−	232.274i	0.129428	−	0.348759i
$667$	327.645			0.491222
$668$	−379.008	−	326.239i	−0.567377	−	0.488382i
$669$	−428.236			−0.640113
$670$	313.121	−	456.724i	0.467344	−	0.681678i
$671$		−	9.37940i		−	0.0139782i
$672$	212.311	−	1016.07i	0.315938	−	1.51201i
$673$		−	1053.59i		−	1.56552i	−0.622325	−	0.782759i	$-0.713812\pi$
$673$		−	1053.59i		−	1.56552i	0.622325	−	0.782759i	$-0.286188\pi$
$674$	43.2208	−	116.463i	0.0641257	−	0.172794i
$675$	642.436	+	343.700i	0.951757	+	0.509185i
$676$	450.030	+	387.373i	0.665724	+	0.573036i
$677$			897.006i			1.32497i	0.749075	+	0.662486i	$0.230498\pi$
$677$			897.006i			1.32497i	−0.749075	+	0.662486i	$0.769502\pi$
$678$	−345.978	+	932.276i	−0.510292	+	1.37504i
$679$		−	87.3354i		−	0.128624i
$680$	129.456	+	488.406i	0.190376	+	0.718244i
$681$	450.491			0.661514
$682$	14.8071	+	5.49508i	0.0217113	+	0.00805730i
$683$	−116.784			−0.170987			−0.0854937	−	0.996339i	$-0.527247\pi$
$683$	−116.784			−0.170987			−0.0854937	+	0.996339i	$0.527247\pi$
$684$	88.4001	−	102.699i	0.129240	−	0.150144i
$685$	867.783	+	217.542i	1.26684	+	0.317579i
$686$	−1246.35	−	462.536i	−1.81684	−	0.674251i
$687$	1094.62			1.59333
$688$	115.831	+	769.698i	0.168359	+	1.11875i
$689$	−303.631			−0.440684
$690$	−175.938	+	256.627i	−0.254983	+	0.371923i
$691$		−	603.974i		−	0.874059i	−0.899447	−	0.437029i	$-0.856031\pi$
$691$		−	603.974i		−	0.874059i	0.899447	−	0.437029i	$-0.143969\pi$
$692$	−512.268	+	595.127i	−0.740272	+	0.860010i
$693$			84.7945i			0.122359i
$694$	−379.703	−	140.912i	−0.547122	−	0.203043i
$695$	−127.775	−	32.0314i	−0.183849	−	0.0460884i
$696$	−282.134	−	510.693i	−0.405365	−	0.733755i
$697$		−	207.571i		−	0.297806i
$698$	−669.299	−	248.385i	−0.958882	−	0.355852i
$699$		−	479.099i		−	0.685407i
$700$	−444.381	−	1149.70i	−0.634830	−	1.64242i
$701$	624.447			0.890795			0.445398	−	0.895333i	$-0.353062\pi$
$701$	624.447			0.890795			0.445398	+	0.895333i	$0.353062\pi$
$702$	−91.9392	+	247.740i	−0.130968	+	0.352906i
$703$	975.387			1.38746
$704$	179.690	+	112.994i	0.255241	+	0.160502i
$705$	−256.984	+	1025.12i	−0.364516	+	1.45407i
$706$	−168.422	+	453.832i	−0.238558	+	0.642821i
$707$	−263.582			−0.372818
$708$	85.7721	−	99.6456i	0.121147	−	0.140742i
$709$	935.347			1.31925			0.659624	−	0.751596i	$-0.270715\pi$
$709$	935.347			1.31925			0.659624	+	0.751596i	$0.270715\pi$
$710$	−1025.79	−	703.257i	−1.44477	−	0.990503i
$711$		−	155.483i		−	0.218683i
$712$	358.002	+	648.023i	0.502812	+	0.910144i
$713$		−	28.1508i		−	0.0394822i
$714$	−285.124	+	768.297i	−0.399333	+	1.07605i
$715$	18.2810	−	72.9238i	0.0255679	−	0.101991i
$716$	−335.775	+	390.086i	−0.468959	+	0.544813i
$717$		−	73.1336i		−	0.101999i
$718$	−191.889	+	517.066i	−0.267255	+	0.720148i
$719$		−	732.181i		−	1.01833i	−0.860668	−	0.509166i	$-0.829954\pi$
$719$		−	732.181i		−	1.01833i	0.860668	−	0.509166i	$-0.170046\pi$
$720$	−165.169	−	15.9480i	−0.229401	−	0.0221499i
$721$	11.2668			0.0156266
$722$	−176.747	−	65.5927i	−0.244801	−	0.0908486i
$723$	727.331			1.00599
$724$	−192.167	−	165.412i	−0.265425	−	0.228470i
$725$	−610.882	−	326.819i	−0.842596	−	0.450784i
$726$	54.2799	+	20.1439i	0.0747657	+	0.0277464i
$727$	−697.591			−0.959547			−0.479773	−	0.877392i	$-0.659281\pi$
$727$	−697.591			−0.959547			−0.479773	+	0.877392i	$0.659281\pi$
$728$	391.297	−	216.173i	0.537496	−	0.296942i
$729$	810.645			1.11200
$730$	−1078.63	−	739.486i	−1.47757	−	1.01299i
$731$		−	614.509i		−	0.840641i
$732$	22.5623	+	19.4210i	0.0308228	+	0.0265314i
$733$		−	387.121i		−	0.528133i	−0.964504	−	0.264066i	$-0.914936\pi$
$733$		−	387.121i		−	0.528133i	0.964504	−	0.264066i	$-0.0850638\pi$
$734$	710.189	+	263.559i	0.967559	+	0.359072i
$735$	329.332	−	1313.72i	0.448070	−	1.78737i
$736$	77.3834	−	370.339i	0.105140	−	0.503178i
$737$			183.659i			0.249198i
$738$	63.9097	+	23.7176i	0.0865986	+	0.0321377i
$739$		−	765.385i		−	1.03570i	−0.855470	−	0.517852i	$-0.826732\pi$
$739$		−	765.385i		−	1.03570i	0.855470	−	0.517852i	$-0.173268\pi$
$740$	−688.614	−	975.962i	−0.930559	−	1.31887i
$741$	−194.856			−0.262964
$742$	574.438	−	1547.89i	0.774175	−	2.08610i
$743$	212.800			0.286406			0.143203	−	0.989693i	$-0.454260\pi$
$743$	212.800			0.286406			0.143203	+	0.989693i	$0.454260\pi$
$744$	−43.8780	+	24.2406i	−0.0589758	+	0.0325814i
$745$	−134.843	+	537.894i	−0.180997	+	0.722005i
$746$	105.085	−	283.164i	0.140865	−	0.379576i
$747$	41.1947			0.0551468
$748$	−127.008	−	109.325i	−0.169797	−	0.146156i
$749$	1938.77			2.58847
$750$	584.009	−	302.977i	0.778679	−	0.403969i
$751$			324.908i			0.432634i	0.976323	+	0.216317i	$0.0694044\pi$
$751$			324.908i			0.432634i	−0.976323	+	0.216317i	$0.930596\pi$
$752$	−191.234	−	1270.75i	−0.254301	−	1.68983i
$753$		−	381.754i		−	0.506978i
$754$	87.4235	−	235.572i	0.115946	−	0.312430i
$755$	262.931	+	65.9134i	0.348253	+	0.0873025i
$756$	−1089.02	−	937.396i	−1.44050	−	1.23994i
$757$		−	398.815i		−	0.526836i	−0.964682	−	0.263418i	$-0.915150\pi$
$757$		−	398.815i		−	0.526836i	0.964682	−	0.263418i	$-0.0848499\pi$
$758$	−502.390	+	1353.75i	−0.662784	+	1.78594i
$759$		−	103.195i		−	0.135962i
$760$	−167.378	−	631.478i	−0.220235	−	0.830892i
$761$	−54.4148			−0.0715044			−0.0357522	−	0.999361i	$-0.511383\pi$
$761$	−54.4148			−0.0715044			−0.0357522	+	0.999361i	$0.511383\pi$
$762$	787.913	+	292.404i	1.03401	+	0.383732i
$763$	−1124.21			−1.47341
$764$	98.9176	−	114.917i	0.129473	−	0.150415i
$765$	127.073	+	31.8555i	0.166108	+	0.0416412i
$766$	1201.66	+	445.950i	1.56875	+	0.582180i
$767$	56.6228			0.0738237
$768$	−643.873	+	198.282i	−0.838377	+	0.258179i
$769$	74.6904			0.0971267			0.0485633	−	0.998820i	$-0.484536\pi$
$769$	74.6904			0.0971267			0.0485633	+	0.998820i	$0.484536\pi$
$770$	337.173	+	231.159i	0.437887	+	0.300207i
$771$			576.034i			0.747126i
$772$	−588.313	+	683.472i	−0.762064	+	0.885327i
$773$		−	915.903i		−	1.18487i	−0.805619	−	0.592434i	$-0.798167\pi$
$773$		−	915.903i		−	1.18487i	0.805619	−	0.592434i	$-0.201833\pi$
$774$	189.203	+	70.2154i	0.244448	+	0.0907176i
$775$

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+(-1.87504 - 0.695850i) q^{2} +2.63169 q^{3} +(3.03158 + 2.60950i) q^{4} +(1.21581 - 4.84993i) q^{5} +(-4.93453 - 1.83126i) q^{6} +12.3259 q^{7} +(-3.86853 - 7.00246i) q^{8} -2.07421 q^{9} +(-5.65453 + 8.24781i) q^{10} -3.31662i q^{11} +(7.97819 + 6.86740i) q^{12} +4.53354i q^{13} +(-23.1116 - 8.57698i) q^{14} +(3.19964 - 12.7635i) q^{15} +(2.38101 + 15.8218i) q^{16} -12.6318i q^{17} +(3.88924 + 1.44334i) q^{18} +16.3321i q^{19} +(16.3417 - 11.5303i) q^{20} +32.4379 q^{21} +(-2.30787 + 6.21882i) q^{22} +11.8230 q^{23} +(-10.1808 - 18.4283i) q^{24} +(-22.0436 - 11.7932i) q^{25} +(3.15467 - 8.50059i) q^{26} -29.1439 q^{27} +(37.3670 + 32.1644i) q^{28} +27.7124 q^{29} +(-14.8810 + 21.7057i) q^{30} -2.38101i q^{31} +(6.54514 - 31.3235i) q^{32} -8.72833i q^{33} +(-8.78983 + 23.6851i) q^{34} +(14.9860 - 59.7797i) q^{35} +(-6.28815 - 5.41266i) q^{36} -59.7221i q^{37} +(11.3647 - 30.6234i) q^{38} +11.9309i q^{39} +(-38.6648 + 10.2484i) q^{40} +16.4324 q^{41} +(-60.8225 - 22.5719i) q^{42} +48.6478 q^{43} +(8.65474 - 10.0546i) q^{44} +(-2.52185 + 10.0598i) q^{45} +(-22.1687 - 8.22706i) q^{46} -80.3163 q^{47} +(6.26608 + 41.6382i) q^{48} +102.928 q^{49} +(33.1264 + 37.4518i) q^{50} -33.2429i q^{51} +(-11.8303 + 13.7438i) q^{52} +66.9744i q^{53} +(54.6461 + 20.2798i) q^{54} +(-16.0854 - 4.03240i) q^{55} +(-47.6831 - 86.3116i) q^{56} +42.9810i q^{57} +(-51.9621 - 19.2837i) q^{58} -12.4898i q^{59} +(43.0064 - 30.3442i) q^{60} +2.82800 q^{61} +(-1.65683 + 4.46450i) q^{62} -25.5665 q^{63} +(-34.0689 + 54.1785i) q^{64} +(21.9873 + 5.51194i) q^{65} +(-6.07361 + 16.3660i) q^{66} -55.3752 q^{67} +(32.9626 - 38.2943i) q^{68} +31.1145 q^{69} +(-69.6971 + 101.662i) q^{70} +124.371i q^{71} +(8.02416 + 14.5246i) q^{72} +130.778i q^{73} +(-41.5576 + 111.982i) q^{74} +(-58.0119 - 31.0361i) q^{75} +(-42.6186 + 49.5121i) q^{76} -40.8804i q^{77} +(8.30210 - 22.3709i) q^{78} +74.9602i q^{79} +(79.6297 + 7.68868i) q^{80} -58.0297 q^{81} +(-30.8116 - 11.4345i) q^{82} -19.8604 q^{83} +(98.3383 + 84.6468i) q^{84} +(-61.2632 - 15.3579i) q^{85} +(-91.2168 - 33.8516i) q^{86} +72.9305 q^{87} +(-23.2245 + 12.8305i) q^{88} -92.5422 q^{89} +(11.7287 - 17.1077i) q^{90} +55.8799i q^{91} +(35.8425 + 30.8522i) q^{92} -6.26608i q^{93} +(150.597 + 55.8881i) q^{94} +(79.2095 + 19.8568i) q^{95} +(17.2248 - 82.4337i) q^{96} -7.08552i q^{97} +(-192.994 - 71.6222i) q^{98} +6.87938i 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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