LMFDB - Embedded newform 220.3.h.a.199.6

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

$q$-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	$-0.944212\pi$
$13$		−	4.53354i		−	0.348734i	0.984681	−	0.174367i	$-0.0557879\pi$
$14$	−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	$0.121164\pi$
$17$			12.6318i			0.743046i	−0.928424	+	0.371523i	$0.878836\pi$
$18$	3.88924	−	1.44334i	0.216069	−	0.0801856i
$19$		−	16.3321i		−	0.859584i	−0.902928	−	0.429792i	$-0.858587\pi$
$19$		−	16.3321i		−	0.859584i	0.902928	−	0.429792i	$-0.141413\pi$
$20$	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	$0.0122272\pi$
$31$			2.38101i			0.0768068i	−0.999262	+	0.0384034i	$0.987773\pi$
$32$	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	$0.298940\pi$
$37$			59.7221i			1.61411i	−0.590476	+	0.807055i	$0.701060\pi$
$38$	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	$-0.782302\pi$
$53$		−	66.9744i		−	1.26367i	0.775104	−	0.631834i	$-0.217698\pi$
$54$	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	$0.0337549\pi$
$59$			12.4898i			0.211691i	−0.994383	+	0.105845i	$0.966245\pi$
$60$	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	$-0.660302\pi$
$71$		−	124.371i		−	1.75170i	0.482584	−	0.875850i	$-0.339698\pi$
$72$	8.02416	−	14.5246i	0.111447	−	0.201730i
$73$		−	130.778i		−	1.79147i	−0.444584	−	0.895737i	$-0.646648\pi$
$73$		−	130.778i		−	1.79147i	0.444584	−	0.895737i	$-0.353352\pi$
$74$	−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	$-0.842654\pi$
$79$		−	74.9602i		−	0.948863i	0.880292	−	0.474432i	$-0.157346\pi$
$80$	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	$0.0116283\pi$
$97$			7.08552i			0.0730466i	−0.999333	+	0.0365233i	$0.988372\pi$
$98$	−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	$0.315093\pi$
$113$			188.929i			1.67194i	−0.548778	+	0.835968i	$0.684907\pi$
$114$	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	$-0.933747\pi$
$131$		−	54.1400i		−	0.413282i	0.978417	−	0.206641i	$-0.0662532\pi$
$132$	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	$-0.773503\pi$
$137$		−	178.927i		−	1.30604i	0.757342	−	0.653018i	$-0.226497\pi$
$138$	−58.3412	+	21.6511i	−0.422762	+	0.156892i
$139$			26.3457i			0.189537i	0.995499	+	0.0947687i	$0.0302111\pi$
$139$			26.3457i			0.189537i	−0.995499	+	0.0947687i	$0.969789\pi$
$140$	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	$-0.942547\pi$
$151$		−	54.2134i		−	0.359029i	0.983755	−	0.179515i	$-0.0574527\pi$
$152$	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	$0.123454\pi$
$157$			118.752i			0.756383i	−0.925727	+	0.378191i	$0.876546\pi$
$158$	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	$-0.807962\pi$
$173$		−	196.309i		−	1.13473i	0.823465	−	0.567367i	$-0.192038\pi$
$174$	−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	$-0.882973\pi$
$179$		−	128.674i		−	0.718849i	0.933174	−	0.359425i	$-0.117027\pi$
$180$	−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	$0.0316387\pi$
$191$			37.9067i			0.198464i	−0.995064	+	0.0992322i	$0.968361\pi$
$192$	−89.6587	−	142.581i	−0.466972	−	0.742609i
$193$		−	225.451i		−	1.16814i	−0.811704	−	0.584069i	$-0.801460\pi$
$193$		−	225.451i		−	1.16814i	0.811704	−	0.584069i	$-0.198540\pi$
$194$	−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	$0.406490\pi$
$197$			377.121i			1.91432i	−0.289563	+	0.957159i	$0.593510\pi$
$198$	4.78702	+	12.8992i	0.0241769	+	0.0651472i
$199$		−	296.936i		−	1.49214i	−0.665867	−	0.746070i	$-0.731938\pi$
$199$		−	296.936i		−	1.49214i	0.665867	−	0.746070i	$-0.268062\pi$
$200$	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	$0.119540\pi$
$211$			154.781i			0.733559i	−0.930308	+	0.366779i	$0.880460\pi$
$212$	−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	$0.127755\pi$
$233$			182.050i			0.781331i	−0.920533	+	0.390665i	$0.872245\pi$
$234$	−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	$0.0185161\pi$
$239$			27.7896i			0.116275i	−0.998309	+	0.0581373i	$0.981484\pi$
$240$	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	$0.0933113\pi$
$251$			145.061i			0.577931i	−0.957340	+	0.288965i	$0.906689\pi$
$252$	−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	$-0.859977\pi$
$257$		−	218.884i		−	0.851688i	0.904797	−	0.425844i	$-0.140023\pi$
$258$	−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	$0.196903\pi$
$271$			314.298i			1.15977i	−0.814697	+	0.579886i	$0.803097\pi$
$272$	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	$-0.969836\pi$
$277$		−	52.4195i		−	0.189240i	0.995513	−	0.0946200i	$-0.0301636\pi$
$278$	−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	$-0.769078\pi$
$293$		−	388.800i		−	1.32696i	0.748192	−	0.663482i	$-0.230922\pi$
$294$	−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	$-0.755744\pi$
$311$		−	431.813i		−	1.38847i	0.719750	−	0.694233i	$-0.244256\pi$
$312$	83.5455	+	46.1550i	0.267774	+	0.147933i
$313$			115.640i			0.369456i	0.982790	+	0.184728i	$0.0591405\pi$
$313$			115.640i			0.369456i	−0.982790	+	0.184728i	$0.940860\pi$
$314$	−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	$0.300303\pi$
$317$			513.271i			1.61915i	−0.587015	+	0.809576i	$0.699697\pi$
$318$	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	$0.0698806\pi$
$331$			144.169i			0.435554i	−0.975999	+	0.217777i	$0.930119\pi$
$332$	−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	$-0.970625\pi$
$337$		−	62.1121i		−	0.184309i	0.995745	−	0.0921545i	$-0.0293754\pi$
$338$	−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	$0.111385\pi$
$353$			242.038i			0.685659i	−0.939398	+	0.342830i	$0.888615\pi$
$354$	−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	$0.125478\pi$
$359$			275.762i			0.768140i	−0.923304	+	0.384070i	$0.874522\pi$
$360$	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	$-0.935114\pi$
$373$		−	151.017i		−	0.404872i	0.979296	−	0.202436i	$-0.0648858\pi$
$374$	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	$0.401478\pi$
$379$			721.980i			1.90496i	−0.304599	+	0.952481i	$0.598522\pi$
$380$	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	$0.212076\pi$
$397$			490.730i			1.23609i	−0.786141	+	0.618047i	$0.787924\pi$
$398$	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	$0.174220\pi$
$419$			436.102i			1.04082i	−0.853918	+	0.520408i	$0.825780\pi$
$420$	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	$0.00708914\pi$
$431$			19.1962i			0.0445387i	−0.999752	+	0.0222693i	$0.992911\pi$
$432$	−69.3919	+	461.110i	−0.160629	+	1.06738i
$433$			717.973i			1.65814i	0.559148	+	0.829068i	$0.311129\pi$
$433$			717.973i			1.65814i	−0.559148	+	0.829068i	$0.688871\pi$
$434$	−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	$0.0517190\pi$
$439$			142.031i			0.323532i	−0.986829	+	0.161766i	$0.948281\pi$
$440$	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	$0.105729\pi$
$457$			298.040i			0.652166i	−0.945341	+	0.326083i	$0.894271\pi$
$458$	−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	$0.0716338\pi$
$479$			213.777i			0.446299i	−0.974784	+	0.223149i	$0.928366\pi$
$480$	−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	$0.227353\pi$
$491$			643.261i			1.31010i	−0.755583	+	0.655052i	$0.772647\pi$
$492$	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	$-0.927876\pi$
$499$		−	224.200i		−	0.449298i	0.974440	−	0.224649i	$-0.0721235\pi$
$500$	−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	$-0.859322\pi$
$557$		−	476.464i		−	0.855412i	0.903918	−	0.427706i	$-0.140678\pi$
$558$	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	$-0.884433\pi$
$571$		−	405.570i		−	0.710281i	0.934813	−	0.355141i	$-0.115567\pi$
$572$	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	$0.278413\pi$
$577$			885.493i			1.53465i	−0.641259	+	0.767325i	$0.721587\pi$
$578$	−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	$0.0766944\pi$
$593$			283.001i			0.477236i	−0.971113	+	0.238618i	$0.923306\pi$
$594$	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	$-0.655789\pi$
$599$		−	1057.36i		−	1.76521i	0.470120	−	0.882603i	$-0.344211\pi$
$600$	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	$0.145346\pi$
$613$			540.562i			0.881831i	−0.897549	+	0.440916i	$0.854654\pi$
$614$	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	$0.164813\pi$
$617$			610.765i			0.989895i	−0.868923	+	0.494948i	$0.835187\pi$
$618$	−4.51054	+	1.67391i	−0.00729861	+	0.00270860i
$619$		−	217.837i		−	0.351918i	−0.984397	−	0.175959i	$-0.943697\pi$
$619$		−	217.837i		−	0.351918i	0.984397	−	0.175959i	$-0.0563026\pi$
$620$	−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	$-0.922910\pi$
$631$		−	302.659i		−	0.479650i	0.970816	−	0.239825i	$-0.0770901\pi$
$632$	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	$-0.904944\pi$
$653$		−	384.236i		−	0.588417i	0.955741	−	0.294209i	$-0.0950560\pi$
$654$	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	$-0.842920\pi$
$659$		−	624.328i		−	0.947388i	0.880690	−	0.473694i	$-0.157080\pi$
$660$	−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	$0.286188\pi$
$673$			1053.59i			1.56552i	−0.622325	+	0.782759i	$0.713812\pi$
$674$	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	$-0.769502\pi$
$677$		−	897.006i		−	1.32497i	0.749075	−	0.662486i	$-0.230498\pi$
$678$	−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	$0.143969\pi$
$691$			603.974i			0.874059i	−0.899447	+	0.437029i	$0.856031\pi$
$692$	−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	$0.170046\pi$
$719$			732.181i			1.01833i	−0.860668	+	0.509166i	$0.829954\pi$
$720$	−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	$0.0850638\pi$
$733$			387.121i			0.528133i	−0.964504	+	0.264066i	$0.914936\pi$
$734$	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	$0.173268\pi$
$739$			765.385i			1.03570i	−0.855470	+	0.517852i	$0.826732\pi$
$740$	−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	$-0.930596\pi$
$751$		−	324.908i		−	0.432634i	0.976323	−	0.216317i	$-0.0694044\pi$
$752$	−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	$0.0848499\pi$
$757$			398.815i			0.526836i	−0.964682	+	0.263418i	$0.915150\pi$
$758$	−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	$0.201833\pi$
$773$			915.903i			1.18487i	−0.805619	+	0.592434i	$0.798167\pi$
$774$	189.203	−	70.2154i	0.244448	−	0.0907176i
$775$	−28.0798	−	52.4861i

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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