LMFDB - Embedded newform 220.3.w.a.7.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(7,220)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 5, 14]))

N = Newforms(chi, 3, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("220.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.w (of order $20$, degree $8$, 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:	$544$
Relative dimension:	$68$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.6
Character	$\chi$	$=$	220.7
Dual form			220.3.w.a.63.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.94429 - 0.468777i) q^{2} +(4.04592 - 2.06150i) q^{3} +(3.56050 + 1.82287i) q^{4} +(2.33189 + 4.42293i) q^{5} +(-8.83280 + 2.11151i) q^{6} +(3.03067 - 5.94803i) q^{7} +(-6.06810 - 5.21327i) q^{8} +(6.82960 - 9.40014i) q^{9} +(-2.46049 - 9.69257i) q^{10} +(2.74293 - 10.6525i) q^{11} +(18.1633 + 0.0352426i) q^{12} +(3.87209 + 24.4474i) q^{13} +(-8.68079 + 10.1440i) q^{14} +(18.5525 + 13.0876i) q^{15} +(9.35426 + 12.9807i) q^{16} +(2.85350 - 18.0163i) q^{17} +(-17.6853 + 15.0750i) q^{18} +(-10.7855 - 3.50442i) q^{19} +(0.240247 + 19.9986i) q^{20} -30.3129i q^{21} +(-10.3267 + 19.4257i) q^{22} +(20.8240 + 20.8240i) q^{23} +(-35.2982 - 8.58307i) q^{24} +(-14.1246 + 20.6276i) q^{25} +(3.93194 - 49.3479i) q^{26} +(1.86054 - 11.7470i) q^{27} +(21.6332 - 15.6534i) q^{28} +(-9.88305 - 30.4169i) q^{29} +(-29.9362 - 34.1430i) q^{30} +(8.80617 - 12.1207i) q^{31} +(-12.1023 - 29.6232i) q^{32} +(-10.8625 - 48.7538i) q^{33} +(-13.9936 + 33.6911i) q^{34} +(33.3749 - 0.465708i) q^{35} +(41.4520 - 21.0197i) q^{36} +(6.94136 - 13.6232i) q^{37} +(19.3273 + 11.8696i) q^{38} +(66.0644 + 90.9299i) q^{39} +(8.90776 - 38.9955i) q^{40} +(9.85319 + 3.20150i) q^{41} +(-14.2100 + 58.9370i) q^{42} +(-14.2190 + 14.2190i) q^{43} +(29.1844 - 32.9283i) q^{44} +(57.5020 + 8.28674i) q^{45} +(-30.7260 - 50.2496i) q^{46} +(-8.10427 - 15.9055i) q^{47} +(64.6062 + 33.2349i) q^{48} +(2.60743 + 3.58882i) q^{49} +(37.1319 - 33.4846i) q^{50} +(-25.5955 - 78.7748i) q^{51} +(-30.7780 + 94.1033i) q^{52} +(-69.7703 + 11.0505i) q^{53} +(-9.12414 + 21.9673i) q^{54} +(53.5116 - 12.7088i) q^{55} +(-49.3991 + 20.2935i) q^{56} +(-50.8615 + 8.05567i) q^{57} +(4.95673 + 63.7721i) q^{58} +(-24.7682 - 76.2288i) q^{59} +(42.1990 + 80.4172i) q^{60} +(-22.3830 - 30.8075i) q^{61} +(-22.8036 + 19.4379i) q^{62} +(-35.2140 - 69.1114i) q^{63} +(9.64368 + 63.2693i) q^{64} +(-99.0999 + 74.1347i) q^{65} +(-1.73484 + 99.8834i) q^{66} +(-15.3020 + 15.3020i) q^{67} +(43.0012 - 58.9453i) q^{68} +(127.181 + 41.3235i) q^{69} +(-65.1086 - 14.7399i) q^{70} +(12.2736 + 16.8932i) q^{71} +(-90.4481 + 21.4365i) q^{72} +(-36.2433 + 71.1314i) q^{73} +(-19.8822 + 23.2334i) q^{74} +(-14.6232 + 112.575i) q^{75} +(-32.0136 - 32.1380i) q^{76} +(-55.0486 - 48.5993i) q^{77} +(-85.8223 - 207.763i) q^{78} +(-58.2496 + 80.1738i) q^{79} +(-35.5995 + 71.6427i) q^{80} +(15.6260 + 48.0919i) q^{81} +(-17.6566 - 10.8436i) q^{82} +(-16.4491 + 103.856i) q^{83} +(55.2567 - 107.929i) q^{84} +(86.3386 - 29.3911i) q^{85} +(34.3112 - 20.9802i) q^{86} +(-102.690 - 102.690i) q^{87} +(-72.1788 + 50.3410i) q^{88} -69.0839i q^{89} +(-107.916 - 43.0674i) q^{90} +(157.149 + 51.0608i) q^{91} +(36.1842 + 112.103i) q^{92} +(10.6423 - 67.1931i) q^{93} +(8.30087 + 34.7240i) q^{94} +(-9.65079 - 55.8753i) q^{95} +(-110.033 - 94.9041i) q^{96} +(22.7249 + 143.479i) q^{97} +(-3.38724 - 8.20000i) q^{98} +(-81.4022 - 98.5364i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) $ 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.94429	−	0.468777i	−0.972143	−	0.234389i
$2$	−1.94429	−	0.468777i	−0.972143	−	0.234389i
$3$	4.04592	−	2.06150i	1.34864	−	0.687166i	0.377573	−	0.925980i	$-0.376759\pi$
$3$	4.04592	−	2.06150i	1.34864	−	0.687166i	0.971065	+	0.238814i	$0.0767586\pi$
$4$	3.56050	+	1.82287i	0.890124	+	0.455718i
$5$	2.33189	+	4.42293i	0.466378	+	0.884586i
$5$	2.33189	+	4.42293i	0.466378	+	0.884586i
$6$	−8.83280	+	2.11151i	−1.47213	+	0.351918i
$7$	3.03067	−	5.94803i	0.432953	−	0.849718i	−0.566714	−	0.823914i	$-0.691786\pi$
$7$	3.03067	−	5.94803i	0.432953	−	0.849718i	0.999667	−	0.0258034i	$-0.00821440\pi$
$8$	−6.06810	−	5.21327i	−0.758513	−	0.651658i
$9$	6.82960	−	9.40014i	0.758845	−	1.04446i
$10$	−2.46049	−	9.69257i	−0.246049	−	0.969257i
$11$	2.74293	−	10.6525i	0.249357	−	0.968412i
$11$	2.74293	−	10.6525i	0.249357	−	0.968412i
$12$	18.1633	+	0.0352426i	1.51361	+	0.00293689i
$13$	3.87209	+	24.4474i	0.297853	+	1.88057i	0.451237	+	0.892404i	$0.350983\pi$
$13$	3.87209	+	24.4474i	0.297853	+	1.88057i	−0.153384	+	0.988167i	$0.549017\pi$
$14$	−8.68079	+	10.1440i	−0.620056	+	0.724568i
$15$	18.5525	+	13.0876i	1.23683	+	0.872507i
$16$	9.35426	+	12.9807i	0.584641	+	0.811292i
$17$	2.85350	−	18.0163i	0.167853	−	1.05978i	−0.749587	−	0.661906i	$-0.769748\pi$
$17$	2.85350	−	18.0163i	0.167853	−	1.05978i	0.917440	−	0.397874i	$-0.130252\pi$
$18$	−17.6853	+	15.0750i	−0.982515	+	0.837500i
$19$	−10.7855	−	3.50442i	−0.567657	−	0.184443i	0.0111065	−	0.999938i	$-0.496465\pi$
$19$	−10.7855	−	3.50442i	−0.567657	−	0.184443i	−0.578764	+	0.815495i	$0.696465\pi$
$20$	0.240247	+	19.9986i	0.0120123	+	0.999928i
$21$		−	30.3129i		−	1.44347i
$22$	−10.3267	+	19.4257i	−0.469395	+	0.882988i
$23$	20.8240	+	20.8240i	0.905390	+	0.905390i	0.995896	−	0.0905057i	$-0.0288483\pi$
$23$	20.8240	+	20.8240i	0.905390	+	0.905390i	−0.0905057	+	0.995896i	$0.528848\pi$
$24$	−35.2982	−	8.58307i	−1.47076	−	0.357628i
$25$	−14.1246	+	20.6276i	−0.564983	+	0.825103i
$26$	3.93194	−	49.3479i	0.151228	−	1.89800i
$27$	1.86054	−	11.7470i	0.0689089	−	0.435073i
$28$	21.6332	−	15.6534i	0.772614	−	0.559050i
$29$	−9.88305	−	30.4169i	−0.340795	−	1.04886i	−0.963797	−	0.266638i	$-0.914087\pi$
$29$	−9.88305	−	30.4169i	−0.340795	−	1.04886i	0.623002	−	0.782220i	$-0.285913\pi$
$30$	−29.9362	−	34.1430i	−0.997872	−	1.13810i
$31$	8.80617	−	12.1207i	0.284070	−	0.390989i	−0.643007	−	0.765861i	$-0.722313\pi$
$31$	8.80617	−	12.1207i	0.284070	−	0.390989i	0.927077	+	0.374872i	$0.122313\pi$
$32$	−12.1023	−	29.6232i	−0.378197	−	0.925725i
$33$	−10.8625	−	48.7538i	−0.329167	−	1.47739i
$34$	−13.9936	+	33.6911i	−0.411577	+	0.990915i
$35$	33.3749	−	0.465708i	0.953568	−	0.0133059i
$36$	41.4520	−	21.0197i	1.15145	−	0.583879i
$37$	6.94136	−	13.6232i	0.187604	−	0.368194i	−0.777978	−	0.628291i	$-0.783755\pi$
$37$	6.94136	−	13.6232i	0.187604	−	0.368194i	0.965582	+	0.260097i	$0.0837545\pi$
$38$	19.3273	+	11.8696i	0.508613	+	0.312357i
$39$	66.0644	+	90.9299i	1.69396	+	2.33154i
$40$	8.90776	−	38.9955i	0.222694	−	0.974888i
$41$	9.85319	+	3.20150i	0.240322	+	0.0780853i	0.426702	−	0.904392i	$-0.359675\pi$
$41$	9.85319	+	3.20150i	0.240322	+	0.0780853i	−0.186380	+	0.982478i	$0.559675\pi$
$42$	−14.2100	+	58.9370i	−0.338334	+	1.40326i
$43$	−14.2190	+	14.2190i	−0.330673	+	0.330673i	−0.852842	−	0.522169i	$-0.825123\pi$
$43$	−14.2190	+	14.2190i	−0.330673	+	0.330673i	0.522169	+	0.852842i	$0.325123\pi$
$44$	29.1844	−	32.9283i	0.663282	−	0.748370i
$45$	57.5020	+	8.28674i	1.27782	+	0.184150i
$46$	−30.7260	−	50.2496i	−0.667956	−	1.09238i
$47$	−8.10427	−	15.9055i	−0.172431	−	0.338415i	0.788577	−	0.614937i	$-0.210818\pi$
$47$	−8.10427	−	15.9055i	−0.172431	−	0.338415i	−0.961008	+	0.276521i	$0.910818\pi$
$48$	64.6062	+	33.2349i	1.34596	+	0.692394i
$49$	2.60743	+	3.58882i	0.0532129	+	0.0732413i
$50$	37.1319	−	33.4846i	0.742639	−	0.669692i
$51$	−25.5955	−	78.7748i	−0.501872	−	1.54460i
$52$	−30.7780	+	94.1033i	−0.591885	+	1.80968i
$53$	−69.7703	+	11.0505i	−1.31642	+	0.208501i	−0.774845	−	0.632151i	$-0.782172\pi$
$53$	−69.7703	+	11.0505i	−1.31642	+	0.208501i	−0.541576	+	0.840652i	$0.682172\pi$
$54$	−9.12414	+	21.9673i	−0.168966	+	0.406802i
$55$	53.5116	−	12.7088i	0.972938	−	0.231068i
$56$	−49.3991	+	20.2935i	−0.882126	+	0.362384i
$57$	−50.8615	+	8.05567i	−0.892307	+	0.141328i
$58$	4.95673	+	63.7721i	0.0854608	+	1.09952i
$59$	−24.7682	−	76.2288i	−0.419801	−	1.29201i	−0.907886	−	0.419218i	$-0.862304\pi$
$59$	−24.7682	−	76.2288i	−0.419801	−	1.29201i	0.488085	−	0.872796i	$-0.337696\pi$
$60$	42.1990	+	80.4172i	0.703316	+	1.34029i
$61$	−22.3830	−	30.8075i	−0.366934	−	0.505042i	0.585130	−	0.810939i	$-0.301043\pi$
$61$	−22.3830	−	30.8075i	−0.366934	−	0.505042i	−0.952064	+	0.305898i	$0.901043\pi$
$62$	−22.8036	+	19.4379i	−0.367800	+	0.313514i
$63$	−35.2140	−	69.1114i	−0.558952	−	1.09701i
$64$	9.64368	+	63.2693i	0.150683	+	0.988582i
$65$	−99.0999	+	74.1347i	−1.52461	+	1.14053i
$66$	−1.73484	+	99.8834i	−0.0262854	+	1.51338i
$67$	−15.3020	+	15.3020i	−0.228388	+	0.228388i	−0.812019	−	0.583631i	$-0.801631\pi$
$67$	−15.3020	+	15.3020i	−0.228388	+	0.228388i	0.583631	+	0.812019i	$0.301631\pi$
$68$	43.0012	−	58.9453i	0.632371	−	0.866842i
$69$	127.181	+	41.3235i	1.84320	+	0.598891i
$70$	−65.1086	−	14.7399i	−0.930123	−	0.210570i
$71$	12.2736	+	16.8932i	0.172868	+	0.237932i	0.886656	−	0.462429i	$-0.153022\pi$
$71$	12.2736	+	16.8932i	0.172868	+	0.237932i	−0.713788	+	0.700362i	$0.753022\pi$
$72$	−90.4481	+	21.4365i	−1.25622	+	0.297728i
$73$	−36.2433	+	71.1314i	−0.496483	+	0.974403i	0.497766	+	0.867311i	$0.334154\pi$
$73$	−36.2433	+	71.1314i	−0.496483	+	0.974403i	−0.994249	+	0.107092i	$0.965846\pi$
$74$	−19.8822	+	23.2334i	−0.268679	+	0.313965i
$75$	−14.6232	+	112.575i	−0.194976	+	1.50100i
$76$	−32.0136	−	32.1380i	−0.421231	−	0.422869i
$77$	−55.0486	−	48.5993i	−0.714917	−	0.631160i
$78$	−85.8223	−	207.763i	−1.10029	−	2.66363i
$79$	−58.2496	+	80.1738i	−0.737337	+	1.01486i	0.261430	+	0.965222i	$0.415806\pi$
$79$	−58.2496	+	80.1738i	−0.737337	+	1.01486i	−0.998767	+	0.0496354i	$0.984194\pi$
$80$	−35.5995	+	71.6427i	−0.444993	+	0.895534i
$81$	15.6260	+	48.0919i	0.192914	+	0.593727i
$82$	−17.6566	−	10.8436i	−0.215325	−	0.132239i
$83$	−16.4491	+	103.856i	−0.198182	+	1.25127i	0.665179	+	0.746684i	$0.268355\pi$
$83$	−16.4491	+	103.856i	−0.198182	+	1.25127i	−0.863361	+	0.504587i	$0.831645\pi$
$84$	55.2567	−	107.929i	0.657817	−	1.28487i
$85$	86.3386	−	29.3911i	1.01575	−	0.345778i
$86$	34.3112	−	20.9802i	0.398968	−	0.243956i
$87$	−102.690	−	102.690i	−1.18035	−	1.18035i
$88$	−72.1788	+	50.3410i	−0.820214	+	0.572057i
$89$		−	69.0839i		−	0.776223i	−0.921612	−	0.388112i	$-0.873128\pi$
$89$		−	69.0839i		−	0.776223i	0.921612	−	0.388112i	$-0.126872\pi$
$90$	−107.916	−	43.0674i	−1.19906	−	0.478527i
$91$	157.149	+	51.0608i	1.72691	+	0.561107i
$92$	36.1842	+	112.103i	0.393306	+	1.21851i
$93$	10.6423	−	67.1931i	0.114434	−	0.722506i
$94$	8.30087	+	34.7240i	0.0883071	+	0.369404i
$95$	−9.65079	−	55.8753i	−0.101587	−	0.588161i
$96$	−110.033	−	94.9041i	−1.14618	−	0.988584i
$97$	22.7249	+	143.479i	0.234277	+	1.47917i	0.771771	+	0.635901i	$0.219371\pi$
$97$	22.7249	+	143.479i	0.234277	+	1.47917i	−0.537494	+	0.843268i	$0.680629\pi$
$98$	−3.38724	−	8.20000i	−0.0345636	−	0.0836735i
$99$	−81.4022	−	98.5364i	−0.822244	−	0.995317i
$100$	−87.8919	+	47.6970i	−0.878919	+	0.476970i
$101$	−73.0522	+	100.548i	−0.723289	+	0.995522i	0.276119	+	0.961123i	$0.410952\pi$
$101$	−73.0522	+	100.548i	−0.723289	+	0.995522i	−0.999408	+	0.0343985i	$0.989048\pi$
$102$	12.8371	+	165.159i	0.125854	+	1.61921i
$103$	−3.22225	+	6.32402i	−0.0312840	+	0.0613982i	−0.906119	−	0.423022i	$-0.860969\pi$
$103$	−3.22225	+	6.32402i	−0.0312840	+	0.0613982i	0.874836	+	0.484420i	$0.160969\pi$
$104$	103.955	−	168.536i	0.999564	−	1.62053i
$105$	134.072	−	70.6864i	1.27688	−	0.673204i
$106$	140.834	+	11.2213i	1.32862	+	0.105862i
$107$	0.785785	−	0.400378i	0.00734379	−	0.00374185i	−0.450315	−	0.892870i	$-0.648688\pi$
$107$	0.785785	−	0.400378i	0.00734379	−	0.00374185i	0.457659	+	0.889128i	$0.348688\pi$
$108$	28.0377	−	38.4336i	0.259608	−	0.355866i
$109$	187.495			1.72014			0.860068	−	0.510179i	$-0.170421\pi$
$109$	187.495			1.72014			0.860068	+	0.510179i	$0.170421\pi$
$110$	−109.999	−	0.375532i	−0.999994	−	0.00341392i
$111$		−	69.4279i		−	0.625477i
$112$	105.559	−	16.2993i	0.942491	−	0.145529i
$113$	−19.4858	−	38.2431i	−0.172441	−	0.338434i	0.788570	−	0.614945i	$-0.210822\pi$
$113$	−19.4858	−	38.2431i	−0.172441	−	0.338434i	−0.961011	+	0.276511i	$0.910822\pi$
$114$	102.666	+	8.18019i	0.900576	+	0.0717560i
$115$	−43.5437	+	140.662i	−0.378641	+	1.22315i
$116$	20.2576	−	126.315i	0.174635	−	1.08892i
$117$	256.254	+	130.568i	2.19020	+	1.11597i
$118$	12.4222	+	159.821i	0.105273	+	1.35442i
$119$	−98.5132	−	71.5740i	−0.827842	−	0.601462i
$120$	−44.3491	−	176.136i	−0.369576	−	1.46780i
$121$	−105.953	−	58.4382i	−0.875642	−	0.482960i
$122$	29.0770	+	70.3913i	0.238336	+	0.576978i
$123$	46.4651	−	7.35934i	0.377765	−	0.0598321i
$124$	53.4488	−	27.1030i	0.431038	−	0.218573i
$125$	−124.171	−	14.3708i	−0.993369	−	0.114966i
$126$	36.0682	+	150.880i	0.286256	+	1.19746i
$127$	8.30422	+	1.31526i	0.0653876	+	0.0103564i	0.189043	−	0.981969i	$-0.439462\pi$
$127$	8.30422	+	1.31526i	0.0653876	+	0.0103564i	−0.123655	+	0.992325i	$0.539462\pi$
$128$	10.9091	−	127.534i	0.0852274	−	0.996362i
$129$	−28.2164	+	86.8411i	−0.218732	+	0.673187i
$130$	227.431	−	97.6832i	1.74947	−	0.751410i
$131$	−160.641			−1.22627			−0.613134	−	0.789979i	$-0.710091\pi$
$131$	−160.641			−1.22627			−0.613134	+	0.789979i	$0.710091\pi$
$132$	50.1961	−	193.389i	0.380273	−	1.46507i
$133$	−53.5316	+	53.5316i	−0.402493	+	0.402493i
$134$	36.9246	−	22.5782i	0.275557	−	0.168494i
$135$	56.2946	−	19.1636i	0.416997	−	0.141953i
$136$	−111.239	+	94.4484i	−0.817933	+	0.694474i
$137$	−77.5066	−	12.2758i	−0.565741	−	0.0896046i	−0.132989	−	0.991118i	$-0.542458\pi$
$137$	−77.5066	−	12.2758i	−0.565741	−	0.0896046i	−0.432752	+	0.901513i	$0.642458\pi$
$138$	−227.904	−	139.964i	−1.65148	−	1.01423i
$139$	−49.9473	+	16.2289i	−0.359333	+	0.116754i	−0.483119	−	0.875554i	$-0.660496\pi$
$139$	−49.9473	+	16.2289i	−0.359333	+	0.116754i	0.123786	+	0.992309i	$0.460496\pi$
$140$	119.680	+	59.1800i	0.854857	+	0.422715i
$141$	−65.5784	−	47.6455i	−0.465095	−	0.337911i
$142$	−15.9443	−	38.5988i	−0.112284	−	0.271822i
$143$	271.048	+	25.8099i	1.89544	+	0.180489i
$144$	185.906	+	0.721436i	1.29101	+	0.00500998i
$145$	111.486	−	114.641i	0.768866	−	0.790627i
$146$	103.812	−	121.310i	0.711042	−	0.830889i
$147$	17.9478	+	9.14486i	0.122094	+	0.0622100i
$148$	49.5481	−	35.8521i	0.334784	−	0.242244i
$149$	−14.8092	+	10.7595i	−0.0993907	+	0.0722115i	−0.636371	−	0.771383i	$-0.719565\pi$
$149$	−14.8092	+	10.7595i	−0.0993907	+	0.0722115i	0.536980	+	0.843595i	$0.319565\pi$
$150$	81.2043	−	212.023i	0.541362	−	1.41349i
$151$	63.1157	−	194.250i	0.417984	−	1.28642i	−0.491570	−	0.870838i	$-0.663577\pi$
$151$	63.1157	−	194.250i	0.417984	−	1.28642i	0.909554	−	0.415586i	$-0.136423\pi$
$152$	47.1779	+	77.4928i	0.310381	+	0.509821i
$153$	−149.867	−	149.867i	−0.979524	−	0.979524i
$154$	84.2480	+	120.296i	0.547065	+	0.781146i
$155$	74.1438	+	10.6850i	0.478347	+	0.0689356i
$156$	69.4684	+	444.183i	0.445310	+	2.84732i
$157$	17.1413	−	8.73395i	0.109181	−	0.0556303i	−0.398547	−	0.917148i	$-0.630486\pi$
$157$	17.1413	−	8.73395i	0.109181	−	0.0556303i	0.507728	+	0.861518i	$0.330486\pi$
$158$	150.838	−	128.575i	0.954668	−	0.813763i
$159$	−259.504	+	188.541i	−1.63210	+	1.18579i
$160$	102.800	−	122.606i	0.642500	−	0.766286i
$161$	186.972	−	60.7509i	1.16132	−	0.377335i
$162$	−7.83704	−	100.830i	−0.0483768	−	0.622405i
$163$	−30.4629	−	192.335i	−0.186889	−	1.17997i	−0.885560	−	0.464526i	$-0.846225\pi$
$163$	−30.4629	−	192.335i	−0.186889	−	1.17997i	0.698671	−	0.715443i	$-0.253775\pi$
$164$	29.2463	+	29.3600i	0.178331	+	0.179025i
$165$	190.304	−	161.733i	1.15336	−	0.980197i
$166$	80.6669	−	194.214i	0.485945	−	1.16996i
$167$	35.5489	+	224.447i	0.212868	+	1.34400i	0.830276	+	0.557352i	$0.188183\pi$
$167$	35.5489	+	224.447i	0.212868	+	1.34400i	−0.617408	+	0.786643i	$0.711817\pi$
$168$	−158.029	+	183.942i	−0.940651	+	1.09489i
$169$	−421.955	+	137.101i	−2.49677	+	0.811251i
$170$	−181.645	+	16.6712i	−1.06850	+	0.0980658i
$171$	−106.603	+	77.4513i	−0.623407	+	0.452932i
$172$	−76.5459	+	24.7072i	−0.445034	+	0.143646i
$173$	69.3717	−	35.3466i	0.400992	−	0.204316i	−0.241851	−	0.970313i	$-0.577755\pi$
$173$	69.3717	−	35.3466i	0.400992	−	0.204316i	0.642844	+	0.765998i	$0.277755\pi$
$174$	151.521	+	247.798i	0.870807	+	1.42413i
$175$	79.8863	+	146.529i	0.456493	+	0.837307i
$176$	163.935	−	64.0415i	0.931449	−	0.363872i
$177$	−257.356	−	257.356i	−1.45399	−	1.45399i
$178$	−32.3849	+	134.319i	−0.181938	+	0.754600i
$179$	51.6714	−	159.028i	0.288667	−	0.888426i	−0.696608	−	0.717452i	$-0.745308\pi$
$179$	51.6714	−	159.028i	0.288667	−	0.888426i	0.985275	−	0.170975i	$-0.0546916\pi$
$180$	189.630	+	134.324i	1.05350	+	0.746243i
$181$	−244.342	+	177.525i	−1.34996	+	0.980802i	−0.350945	+	0.936396i	$0.614139\pi$
$181$	−244.342	+	177.525i	−1.34996	+	0.980802i	−0.999014	+	0.0444058i	$0.985861\pi$
$182$	−281.606	−	172.945i	−1.54729	−	0.950245i
$183$	−154.069	−	78.5022i	−0.841909	−	0.428974i
$184$	−17.8010	−	234.923i	−0.0967447	−	1.27676i
$185$	76.4409	−	1.06664i	0.413194	−	0.00576564i
$186$	−52.1903	+	125.654i	−0.280593	+	0.675557i
$187$	−184.092	−	79.8142i	−0.984448	−	0.426814i
$188$	0.138548	−	71.4046i	0.000736956	−	0.379812i
$189$	−64.2327	−	46.6678i	−0.339855	−	0.246919i
$190$	−7.42919	+	113.162i	−0.0391010	+	0.595588i
$191$	123.363	−	40.0830i	0.645878	−	0.209859i	0.0322823	−	0.999479i	$-0.489722\pi$
$191$	123.363	−	40.0830i	0.645878	−	0.209859i	0.613596	+	0.789620i	$0.289722\pi$
$192$	169.447	+	236.102i	0.882536	+	1.22970i
$193$	67.9965	+	10.7696i	0.352314	+	0.0558010i	0.330083	−	0.943952i	$-0.392923\pi$
$193$	67.9965	+	10.7696i	0.352314	+	0.0558010i	0.0222305	+	0.999753i	$0.492923\pi$
$194$	23.0762	−	289.618i	0.118949	−	1.49288i
$195$	−248.121	+	504.237i	−1.27242	+	2.58583i
$196$	2.74178	+	17.5310i	0.0139887	+	0.0894439i
$197$	−67.2265	+	67.2265i	−0.341251	+	0.341251i	−0.856838	−	0.515586i	$-0.827574\pi$
$197$	−67.2265	+	67.2265i	−0.341251	+	0.341251i	0.515586	+	0.856838i	$0.327574\pi$
$198$	112.077	+	229.742i	0.566048	+	1.16032i
$199$	56.9753			0.286308			0.143154	−	0.989700i	$-0.454276\pi$
$199$	56.9753			0.286308			0.143154	+	0.989700i	$0.454276\pi$
$200$	193.246	−	51.5349i	0.966232	−	0.257675i
$201$	−30.3655	+	93.4554i	−0.151072	+	0.464952i
$202$	189.169	−	161.248i	0.936479	−	0.798259i
$203$	−210.873	−	33.3990i	−1.03878	−	0.164527i
$204$	52.4639	−	327.134i	0.257176	−	1.60360i
$205$	8.81658	+	51.0455i	0.0430077	+	0.249002i
$206$	9.22953	−	10.7852i	0.0448035	−	0.0523553i
$207$	337.968	−	53.5288i	1.63269	−	0.258593i
$208$	−281.123	+	278.950i	−1.35155	+	1.34111i
$209$	−66.9147	+	105.280i	−0.320166	+	0.503734i
$210$	−293.810	+	74.5848i	−1.39910	+	0.355166i
$211$	−225.181	−	163.604i	−1.06721	−	0.775373i	−0.0918009	−	0.995777i	$-0.529262\pi$
$211$	−225.181	−	163.604i	−1.06721	−	0.775373i	−0.975409	+	0.220404i	$0.929262\pi$
$212$	−268.561	−	87.8371i	−1.26680	−	0.414326i
$213$	84.4833	+	43.0464i	0.396635	+	0.202096i
$214$	−1.71548	+	0.410090i	−0.00801626	+	0.00191631i
$215$	−96.0465	−	29.7324i	−0.446728	−	0.138290i
$216$	−72.5301	+	61.5824i	−0.335788	+	0.285104i
$217$	−45.4054	−	89.1131i	−0.209241	−	0.410659i
$218$	−364.544	−	87.8933i	−1.67222	−	0.403180i
$219$			362.507i			1.65528i
$220$	213.694	+	52.2953i	0.971337	+	0.237706i
$221$	451.500			2.04299
$222$	−32.5462	+	134.988i	−0.146605	+	0.608053i
$223$	174.457	−	88.8904i	0.782319	−	0.398612i	−0.0167431	−	0.999860i	$-0.505330\pi$
$223$	174.457	−	88.8904i	0.782319	−	0.398612i	0.799062	+	0.601248i	$0.205330\pi$
$224$	−212.878	−	17.7933i	−0.950347	−	0.0794342i
$225$	97.4368	+	273.651i	0.433052	+	1.21623i
$226$	19.9585	+	83.4900i	0.0883121	+	0.369425i
$227$	51.4767	−	101.029i	0.226770	−	0.445061i	−0.749386	−	0.662134i	$-0.769651\pi$
$227$	51.4767	−	101.029i	0.226770	−	0.445061i	0.976155	+	0.217073i	$0.0696510\pi$
$228$	−195.777	−	64.0319i	−0.858670	−	0.280842i
$229$	69.2755	−	95.3495i	0.302513	−	0.416373i	−0.630515	−	0.776177i	$-0.717156\pi$
$229$	69.2755	−	95.3495i	0.302513	−	0.416373i	0.933028	+	0.359804i	$0.117156\pi$
$230$	150.601	−	253.075i	0.654785	−	1.10033i
$231$	−322.909	−	83.1461i	−1.39788	−	0.359940i
$232$	−98.6001	+	236.096i	−0.425000	+	1.01765i
$233$	46.3997	+	292.956i	0.199140	+	1.25732i	0.861353	+	0.508007i	$0.169618\pi$
$233$	46.3997	+	292.956i	0.199140	+	1.25732i	−0.662213	+	0.749316i	$0.730382\pi$
$234$	−437.024	−	373.987i	−1.86762	−	1.59824i
$235$	51.4507	−	72.9345i	0.218939	−	0.310360i
$236$	50.7683	−	316.562i	0.215120	−	1.34136i
$237$	−70.3952	+	444.458i	−0.297026	+	1.87535i
$238$	157.986	+	185.341i	0.663805	+	0.778744i
$239$	163.096	+	52.9932i	0.682412	+	0.221729i	0.629651	−	0.776878i	$-0.283198\pi$
$239$	163.096	+	52.9932i	0.682412	+	0.221729i	0.0527607	+	0.998607i	$0.483198\pi$
$240$	3.65887	+	363.249i	0.0152453	+	1.51354i
$241$		−	132.086i		−	0.548074i	−0.961719	−	0.274037i	$-0.911641\pi$
$241$		−	132.086i		−	0.548074i	0.961719	−	0.274037i	$-0.0883591\pi$
$242$	178.608	+	163.289i	0.738049	+	0.674747i
$243$	238.052	+	238.052i	0.979638	+	0.979638i
$244$	−23.5363	−	150.491i	−0.0964601	−	0.616768i
$245$	−9.79286	+	19.9012i	−0.0399709	+	0.0812295i
$246$	−93.7913	−	7.47310i	−0.381265	−	0.0303784i
$247$	43.9116	−	277.247i	0.177780	−	1.12246i
$248$	−116.625	+	27.6404i	−0.470262	+	0.111453i
$249$	147.546	+	454.101i	0.592555	+	1.82370i
$250$	234.688	+	86.1495i	0.938750	+	0.344598i
$251$	15.5316	−	21.3775i	0.0618791	−	0.0851692i	−0.776956	−	0.629555i	$-0.783237\pi$
$251$	15.5316	−	21.3775i	0.0618791	−	0.0851692i	0.838835	+	0.544386i	$0.183237\pi$
$252$	0.602006	−	310.261i	0.00238891	−	1.23120i
$253$	278.947	−	164.709i	1.10256	−	0.651025i
$254$	−15.5292	−	6.45007i	−0.0611387	−	0.0253940i
$255$	288.729	−	296.901i	1.13227	−	1.16432i
$256$	−80.9956	+	242.849i	−0.316389	+	0.948630i
$257$	177.337	−	348.044i	0.690029	−	1.35426i	−0.234114	−	0.972209i	$-0.575219\pi$
$257$	177.337	−	348.044i	0.690029	−	1.35426i	0.924142	−	0.382048i	$-0.124781\pi$
$258$	95.5698	−	155.617i	0.370426	−	0.603165i
$259$	−59.9941	−	82.5748i	−0.231638	−	0.318822i
$260$	−487.983	+	83.3096i	−1.87686	+	0.320422i
$261$	−353.420	−	114.833i	−1.35410	−	0.439974i
$262$	312.332	+	75.3048i	1.19211	+	0.287423i
$263$	236.266	−	236.266i	0.898349	−	0.898349i	−0.0969412	−	0.995290i	$-0.530906\pi$
$263$	236.266	−	236.266i	0.898349	−	0.898349i	0.995290	+	0.0969412i	$0.0309059\pi$
$264$	−188.252	+	352.472i	−0.713075	+	1.33512i
$265$	−211.572	−	282.820i	−0.798386	−	1.06725i
$266$	129.175	−	78.9864i	0.485621	−	0.296941i
$267$	−142.416	−	279.507i	−0.533394	−	1.04684i
$268$	−82.3761	+	26.5890i	−0.307374	+	0.0992128i
$269$	−88.3574	−	121.614i	−0.328466	−	0.452095i	0.612562	−	0.790422i	$-0.290139\pi$
$269$	−88.3574	−	121.614i	−0.328466	−	0.452095i	−0.941028	+	0.338327i	$0.890139\pi$
$270$	−118.436	+	10.8700i	−0.438653	+	0.0402591i
$271$	−10.1507	−	31.2405i	−0.0374563	−	0.115279i	0.930580	−	0.366088i	$-0.119303\pi$
$271$	−10.1507	−	31.2405i	−0.0374563	−	0.115279i	−0.968036	+	0.250810i	$0.919303\pi$
$272$	260.555	−	131.489i	0.957924	−	0.483414i
$273$	741.073	−	117.374i	2.71455	−	0.429943i
$274$	144.940	+	60.2010i	0.528979	+	0.219712i
$275$	180.993	+	207.042i	0.658156	+	0.752881i
$276$	377.499	+	378.966i	1.36775	+	1.37307i
$277$	−51.1198	+	8.09659i	−0.184548	+	0.0292296i	−0.248024	−	0.968754i	$-0.579781\pi$
$277$	−51.1198	+	8.09659i	−0.184548	+	0.0292296i	0.0634762	+	0.997983i	$0.479781\pi$
$278$	104.720	−	8.13939i	0.376689	−	0.0292784i
$279$	−53.7932	−	165.558i	−0.192807	−	0.593400i
$280$	−204.950	−	171.166i	−0.731964	−	0.611308i
$281$	−24.6258	−	33.8946i	−0.0876365	−	0.120621i	0.762948	−	0.646460i	$-0.223751\pi$
$281$	−24.6258	−	33.8946i	−0.0876365	−	0.120621i	−0.850584	+	0.525839i	$0.823751\pi$
$282$	105.168	+	123.378i	0.372936	+	0.437511i
$283$	5.92958	+	11.6374i	0.0209526	+	0.0411217i	0.901246	−	0.433309i	$-0.142654\pi$
$283$	5.92958	+	11.6374i	0.0209526	+	0.0411217i	−0.880293	+	0.474430i	$0.842654\pi$
$284$	12.9060	+	82.5214i	0.0454437	+	0.290568i
$285$	−154.233	−	206.172i	−0.541169	−	0.723410i
$286$	−514.895	−	177.243i	−1.80033	−	0.619730i
$287$	48.9044	−	48.9044i	0.170398	−	0.170398i
$288$	−361.116	−	88.5512i	−1.25388	−	0.307469i
$289$	−41.5878	−	13.5127i	−0.143903	−	0.0467568i
$290$	−270.501	+	170.633i	−0.932761	+	0.588389i
$291$	387.725	+	533.658i	1.33239	+	1.83388i
$292$	−258.708	+	187.196i	−0.885985	+	0.641083i
$293$	−31.5886	+	61.9962i	−0.107811	+	0.211591i	−0.938609	−	0.344983i	$-0.887885\pi$
$293$	−31.5886	+	61.9962i	−0.107811	+	0.211591i	0.830798	+	0.556574i	$0.187885\pi$
$294$	−30.6088	−	26.1938i	−0.104111	−	0.0890944i
$295$	279.398	−	287.305i	0.947111	−	0.973916i
$296$	−113.142	+	46.4797i	−0.382237	+	0.157026i
$297$	−120.032	−	52.0406i	−0.404147	−	0.175221i
$298$	33.8372	−	13.9774i	0.113548	−	0.0469039i
$299$	−428.460	+	589.725i	−1.43298	+	1.97232i
$300$	−257.276	+	374.167i	−0.857587	+	1.24722i
$301$	41.4818	+	127.668i	0.137813	+	0.424145i
$302$	−213.775	+	348.090i	−0.707864	+	1.15262i
$303$	−88.2842	+	557.405i	−0.291367	+	1.83962i
$304$	−55.4006	−	172.784i	−0.182239	−	0.568369i
$305$	84.0648	−	170.838i	0.275622	−	0.560125i
$306$	221.130	+	361.639i	0.722648	+	1.18183i
$307$	13.7530	+	13.7530i	0.0447979	+	0.0447979i	0.729151	−	0.684353i	$-0.239915\pi$
$307$	13.7530	+	13.7530i	0.0447979	+	0.0447979i	−0.684353	+	0.729151i	$0.739915\pi$
$308$	−107.410	−	273.384i	−0.348734	−	0.887611i
$309$			32.2291i			0.104301i
$310$	−139.148	−	55.5317i	−0.448864	−	0.179134i
$311$	−313.415	−	101.835i	−1.00776	−	0.327442i	−0.241800	−	0.970326i	$-0.577738\pi$
$311$	−313.415	−	101.835i	−1.00776	−	0.327442i	−0.765964	+	0.642884i	$0.777738\pi$
$312$	73.1562	−	896.183i	0.234475	−	2.87238i
$313$	6.96579	−	43.9802i	0.0222549	−	0.140512i	−0.974059	−	0.226294i	$-0.927339\pi$
$313$	6.96579	−	43.9802i	0.0222549	−	0.140512i	0.996314	+	0.0857822i	$0.0273389\pi$
$314$	−37.4220	+	8.94583i	−0.119178	+	0.0284899i
$315$	223.559	−	316.909i	0.709712	−	1.00606i
$316$	−353.544	+	179.277i	−1.11881	+	0.567331i
$317$	−1.82444	−	11.5191i	−0.00575534	−	0.0363378i	0.984644	−	0.174577i	$-0.0558558\pi$
$317$	−1.82444	−	11.5191i	−0.00575534	−	0.0363378i	−0.990399	+	0.138239i	$0.955856\pi$
$318$	592.934	−	244.928i	1.86457	−	0.770213i
$319$	−351.125	+	21.8482i	−1.10071	+	0.0684895i
$320$	−257.347	+	190.190i	−0.804210	+	0.594345i
$321$	2.35384	−	3.23979i	0.00733285	−	0.0100928i
$322$	−392.006	+	30.4689i	−1.21741	+	0.0946239i
$323$	−93.9128	+	184.314i	−0.290752	+	0.570632i
$324$	−32.0292	+	199.715i	−0.0988554	+	0.616405i
$325$	−558.982	−	265.438i	−1.71995	−	0.816731i
$326$	−30.9337	+	388.234i	−0.0948887	+	1.19090i
$327$	758.589	−	386.520i	2.31984	−	1.18202i
$328$	−43.0999	−	70.7943i	−0.131402	−	0.215836i
$329$	−119.168			−0.362212
$330$	−445.822	+	225.244i	−1.35098	+	0.682558i
$331$		−	389.384i		−	1.17639i	−0.808720	−	0.588194i	$-0.799839\pi$
$331$		−	389.384i		−	1.17639i	0.808720	−	0.588194i	$-0.200161\pi$
$332$	−247.882	+	339.793i	−0.746634	+	1.02347i
$333$	−80.6532	−	158.291i	−0.242202	−	0.475348i
$334$	36.0984	−	453.054i	0.108079	−	1.35645i
$335$	−103.362	−	31.9970i	−0.308543	−	0.0955134i
$336$	393.482	−	283.555i	1.17108	−	0.843914i
$337$	376.907	+	192.044i	1.11842	+	0.569863i	0.912652	−	0.408738i	$-0.134031\pi$
$337$	376.907	+	192.044i	1.11842	+	0.569863i	0.205768	+	0.978601i	$0.434031\pi$
$338$	884.670	−	68.7615i	2.61737	−	0.203437i
$339$	−157.676	−	114.558i	−0.465121	−	0.337930i
$340$	360.985	+	52.7374i	1.06172	+	0.155110i
$341$	−104.961	−	127.054i	−0.307803	−	0.372593i
$342$	243.573	−	100.615i	0.712203	−	0.294195i
$343$	352.327	−	55.8031i	1.02719	−	0.162691i
$344$	160.409	−	12.1548i	0.466306	−	0.0353338i
$345$	113.800	+	658.873i	0.329856	+	1.90978i
$346$	−151.448	+	36.2041i	−0.437711	+	0.104636i
$347$	−60.5584	−	9.59150i	−0.174520	−	0.0276412i	0.0685629	−	0.997647i	$-0.478159\pi$
$347$	−60.5584	−	9.59150i	−0.174520	−	0.0276412i	−0.243083	+	0.970006i	$0.578159\pi$
$348$	−178.437	−	552.820i	−0.512750	−	1.58856i
$349$	12.3427	−	37.9869i	0.0353658	−	0.108845i	−0.931815	−	0.362933i	$-0.881775\pi$
$349$	12.3427	−	37.9869i	0.0353658	−	0.108845i	0.967181	+	0.254088i	$0.0817754\pi$
$350$	−86.6326	−	322.343i	−0.247522	−	0.920979i
$351$	294.388			0.838711
$352$	−348.758	+	47.6660i	−0.990789	+	0.135415i
$353$	29.1128	−	29.1128i	0.0824725	−	0.0824725i	−0.664667	−	0.747140i	$-0.731427\pi$
$353$	29.1128	−	29.1128i	0.0824725	−	0.0824725i	0.747140	+	0.664667i	$0.231427\pi$
$354$	379.731	+	621.016i	1.07269	+	1.75428i
$355$	−46.0966	+	93.6784i	−0.129850	+	0.263883i
$356$	125.931	−	245.973i	0.353739	−	0.690935i
$357$	−546.126	−	86.4978i	−1.52976	−	0.242291i
$358$	−175.013	+	284.974i	−0.488863	+	0.796017i
$359$	489.097	−	158.917i	1.36239	−	0.442667i	0.465548	−	0.885022i	$-0.345857\pi$
$359$	489.097	−	158.917i	1.36239	−	0.442667i	0.896840	+	0.442356i	$0.145857\pi$
$360$	−305.727	−	350.058i	−0.849242	−	0.972384i
$361$	−188.009	−	136.597i	−0.520802	−	0.378385i
$362$	558.291	−	230.618i	1.54224	−	0.637065i
$363$	−549.146	−	18.0148i	−1.51280	−	0.0496276i
$364$	466.451	+	468.264i	1.28146	+	1.28644i
$365$	−399.124	+	5.56932i	−1.09349	+	0.0152584i
$366$	262.755	+	224.855i	0.717909	+	0.614358i
$367$	615.620	+	313.674i	1.67744	+	0.854697i	0.991952	+	0.126611i	$0.0404100\pi$
$367$	615.620	+	313.674i	1.67744	+	0.854697i	0.685485	+	0.728086i	$0.259590\pi$
$368$	−75.5162	+	465.102i	−0.205207	+	1.26386i
$369$	97.3879	−	70.7564i	0.263924	−	0.191752i
$370$	−149.123	−	33.7599i	−0.403035	−	0.0912430i
$371$	−145.722	+	448.486i	−0.392782	+	1.20886i
$372$	160.376	−	219.841i	0.431120	−	0.590970i
$373$	196.331	+	196.331i	0.526355	+	0.526355i	0.919484	−	0.393128i	$-0.128607\pi$
$373$	196.331	+	196.331i	0.526355	+	0.526355i	−0.393128	+	0.919484i	$0.628607\pi$
$374$	320.512	+	241.480i	0.856984	+	0.645668i
$375$	−532.011	+	197.836i	−1.41870	+	0.527562i
$376$	−33.7422	+	138.766i	−0.0897400	+	0.369059i
$377$	705.347	−	359.392i	1.87095	−	0.953294i
$378$	103.010	+	120.846i	0.272513	+	0.319699i
$379$	520.868	−	378.433i	1.37432	−	0.998503i	0.376936	−	0.926239i	$-0.376978\pi$
$379$	520.868	−	378.433i	1.37432	−	0.998503i	0.997386	−	0.0722642i	$-0.0230225\pi$
$380$	67.4921	−	216.536i	0.177611	−	0.569832i
$381$	36.3096	−	11.7977i	0.0953008	−	0.0309651i
$382$	−258.642	+	20.1031i	−0.677074	+	0.0526260i
$383$	60.8799	+	384.380i	0.158955	+	1.00360i	0.930197	+	0.367061i	$0.119636\pi$
$383$	60.8799	+	384.380i	0.158955	+	1.00360i	−0.771241	+	0.636543i	$0.780364\pi$
$384$	−218.774	−	538.482i	−0.569725	−	1.40230i
$385$	86.5839	−	356.804i	0.224893	−	0.926764i
$386$	−127.156	−	52.8144i	−0.329420	−	0.136825i
$387$	36.5504	+	230.770i	0.0944454	+	0.596305i
$388$	−180.633	+	552.282i	−0.465549	+	1.42341i
$389$	−458.686	+	149.036i	−1.17914	+	0.383126i	−0.832047	−	0.554704i	$-0.812831\pi$
$389$	−458.686	+	149.036i	−1.17914	+	0.383126i	−0.347093	+	0.937831i	$0.612831\pi$
$390$	718.794	−	864.067i	1.84306	−	2.21556i
$391$	434.591	−	315.749i	1.11149	−	0.807542i
$392$	2.88733	−	35.3706i	0.00736564	−	0.0902311i
$393$	−649.940	+	331.161i	−1.65379	+	0.842649i
$394$	162.222	−	99.1933i	0.411730	−	0.251760i
$395$	−490.435	−	70.6776i	−1.24161	−	0.178931i
$396$	−110.213	−	499.224i	−0.278315	−	1.26067i
$397$	−248.934	−	248.934i	−0.627037	−	0.627037i	0.320285	−	0.947321i	$-0.396221\pi$
$397$	−248.934	−	248.934i	−0.627037	−	0.627037i	−0.947321	+	0.320285i	$0.896221\pi$
$398$	−110.776	−	26.7087i	−0.278333	−	0.0671074i
$399$	−106.229	+	326.940i	−0.266238	+	0.819398i
$400$	−399.885	+	9.60917i	−0.999711	+	0.0240229i
$401$	295.201	−	214.476i	0.736163	−	0.534854i	−0.155344	−	0.987860i	$-0.549649\pi$
$401$	295.201	−	214.476i	0.736163	−	0.534854i	0.891507	+	0.453007i	$0.149649\pi$
$402$	102.849	−	167.469i	0.255843	−	0.416591i
$403$	330.417	+	168.356i	0.819893	+	0.417757i
$404$	−443.388	+	224.835i	−1.09749	+	0.556522i
$405$	−176.269	+	181.258i	−0.435232	+	0.447550i
$406$	394.340	+	163.789i	0.971281	+	0.403422i
$407$	−126.082	−	111.311i	−0.309783	−	0.273490i
$408$	−255.358	+	611.449i	−0.625877	+	1.49865i
$409$	316.613	+	230.033i	0.774115	+	0.562427i	0.903207	−	0.429205i	$-0.141206\pi$
$409$	316.613	+	230.033i	0.774115	+	0.562427i	−0.129092	+	0.991633i	$0.541206\pi$
$410$	6.78702	−	103.380i	0.0165537	−	0.252146i
$411$	−338.892	+	110.113i	−0.824554	+	0.267914i
$412$	−23.0007	+	16.6429i	−0.0558269	+	0.0403954i
$413$	−528.475	−	83.7023i	−1.27960	−	0.202669i
$414$	−682.199	−	54.3562i	−1.64782	−	0.131295i
$415$	−497.703	+	169.427i	−1.19928	+	0.408257i
$416$	677.349	−	410.574i	1.62824	−	0.986957i
$417$	−168.627	+	168.627i	−0.404381	+	0.404381i
$418$	179.454	−	173.327i	0.429317	−	0.414658i
$419$	312.635			0.746145			0.373072	−	0.927802i	$-0.378304\pi$
$419$	312.635			0.746145			0.373072	+	0.927802i	$0.378304\pi$
$420$	606.215	−	7.28258i	1.44337	−	0.0173395i
$421$	32.3036	−	99.4203i	0.0767307	−	0.236153i	−0.905333	−	0.424703i	$-0.860379\pi$
$421$	32.3036	−	99.4203i	0.0767307	−	0.236153i	0.982064	+	0.188550i	$0.0603787\pi$
$422$	361.123	+	423.652i	0.855742	+	1.00392i
$423$	−204.863	−	32.4471i	−0.484310	−	0.0767071i
$424$	480.983	+	296.676i	1.13439	+	0.699707i
$425$	331.327	+	313.333i	0.779593	+	0.737253i
$426$	−144.081	−	123.298i	−0.338217	−	0.289433i
$427$	−251.079	+	39.7671i	−0.588008	+	0.0931313i
$428$	3.52762	+	0.00684471i	0.00824211	+	1.59923e-5i
$429$	1149.84	−	454.339i	2.68029	−	1.05907i
$430$	172.804	+	102.833i	0.401870	+	0.239146i
$431$	47.3487	+	34.4008i	0.109858	+	0.0798164i	0.641358	−	0.767242i	$-0.278371\pi$
$431$	47.3487	+	34.4008i	0.109858	+	0.0798164i	−0.531500	+	0.847058i	$0.678371\pi$
$432$	169.888	−	85.7333i	0.393259	−	0.198457i
$433$	236.902	+	120.708i	0.547118	+	0.278770i	0.705623	−	0.708588i	$-0.250667\pi$
$433$	236.902	+	120.708i	0.547118	+	0.278770i	−0.158505	+	0.987358i	$0.550667\pi$
$434$	46.5069	+	194.546i	0.107159	+	0.448263i
$435$	214.729	−	693.655i	0.493631	−	1.59461i
$436$	667.575	+	341.780i	1.53114	+	0.783898i
$437$	−151.621	−	297.573i	−0.346958	−	0.680944i
$438$	169.935	−	704.818i	0.387980	−	1.60917i
$439$			132.823i			0.302557i	0.988491	+	0.151279i	$0.0483391\pi$
$439$			132.823i			0.302557i	−0.988491	+	0.151279i	$0.951661\pi$
$440$	−390.968	−	201.852i	−0.888563	−	0.458755i
$441$	51.5432			0.116878
$442$	−877.845	−	211.653i	−1.98607	−	0.478853i
$443$	−4.03740	+	2.05716i	−0.00911378	+	0.00464370i	−0.458541	−	0.888673i	$-0.651628\pi$
$443$	−4.03740	+	2.05716i	−0.00911378	+	0.00464370i	0.449428	+	0.893317i	$0.351628\pi$
$444$	126.558	−	247.198i	0.285041	−	0.556752i
$445$	305.553	−	161.096i	0.686636	−	0.362013i
$446$	−380.864	+	91.0467i	−0.853956	+	0.204141i
$447$	−37.7361	+	74.0613i	−0.0844208	+	0.165685i
$448$	405.554	+	134.387i	0.905254	+	0.299972i
$449$	132.107	−	181.830i	0.294225	−	0.404967i	−0.636155	−	0.771561i	$-0.719476\pi$
$449$	132.107	−	181.830i	0.294225	−	0.404967i	0.930381	+	0.366594i	$0.119476\pi$
$450$	−61.1636	−	577.732i	−0.135919	−	1.28385i
$451$	61.1306	−	96.1800i	0.135545	−	0.213259i
$452$	0.333123	−	171.685i	0.000736998	−	0.379833i
$453$	−145.085	−	916.032i	−0.320276	−	2.02215i
$454$	−147.445	+	172.298i	−0.324770	+	0.379510i
$455$	140.616	+	814.126i	0.309046	+	1.78929i
$456$	350.629	+	216.272i	0.768924	+	0.474281i
$457$	58.7670	−	371.040i	0.128593	−	0.811904i	−0.836110	−	0.548562i	$-0.815175\pi$
$457$	58.7670	−	371.040i	0.128593	−	0.811904i	0.964703	−	0.263342i	$-0.0848246\pi$
$458$	−179.389	+	152.912i	−0.391679	+	0.333869i
$459$	−206.328	−	67.0399i	−0.449516	−	0.146056i
$460$	−411.447	+	421.452i	−0.894449	+	0.916201i
$461$			886.126i			1.92218i	0.276232	+	0.961091i	$0.410914\pi$
$461$			886.126i			1.92218i	−0.276232	+	0.961091i	$0.589086\pi$
$462$	588.851	+	313.032i	1.27457	+	0.677559i
$463$	−425.628	−	425.628i	−0.919284	−	0.919284i	0.0776934	−	0.996977i	$-0.475244\pi$
$463$	−425.628	−	425.628i	−0.919284	−	0.919284i	−0.996977	+	0.0776934i	$0.975244\pi$
$464$	302.383	−	412.816i	0.651688	−	0.889690i
$465$	322.007	−	109.617i	0.692488	−	0.235735i
$466$	47.1169	−	591.342i	0.101109	−	1.26897i
$467$	34.3556	−	216.913i	0.0735666	−	0.464481i	−0.923213	−	0.384289i	$-0.874447\pi$
$467$	34.3556	−	216.913i	0.0735666	−	0.464481i	0.996779	−	0.0801922i	$-0.0255534\pi$
$468$	674.382	+	932.005i	1.44099	+	1.99146i
$469$	44.6413	+	137.392i	0.0951839	+	0.292946i
$470$	−134.225	+	117.687i	−0.285585	+	0.250397i
$471$	51.3474	−	70.6737i	0.109018	−	0.150050i
$472$	−247.105	+	591.687i	−0.523528	+	1.25358i
$473$	112.466	+	190.469i	0.237772	+	0.402684i
$474$	345.220	−	831.153i	0.728313	−	1.75349i
$475$	224.628	−	172.980i	0.472901	−	0.364168i
$476$	−220.285	−	434.416i	−0.462784	−	0.912639i
$477$	−372.627	+	731.321i	−0.781188	+	1.53317i
$478$	−292.264	−	179.490i	−0.611431	−	0.375502i
$479$	−414.922	−	571.091i	−0.866226	−	1.19226i	−0.980049	−	0.198756i	$-0.936310\pi$
$479$	−414.922	−	571.091i	−0.866226	−	1.19226i	0.113823	−	0.993501i	$-0.463690\pi$
$480$	163.169	−	707.974i	0.339935	−	1.47495i
$481$	359.930	+	116.948i	0.748294	+	0.243136i
$482$	−61.9188	+	256.813i	−0.128462	+	0.532806i
$483$	631.236	−	631.236i	1.30691	−	1.30691i
$484$	−270.719	−	401.207i	−0.559336	−	0.828941i
$485$	−581.607	+	435.089i	−1.19919	+	0.897090i
$486$	−351.248	−	574.435i	−0.722732	−	1.18196i
$487$	157.422	+	308.957i	0.323248	+	0.634410i	0.994255	−	0.107042i	$-0.0341378\pi$
$487$	157.422	+	308.957i	0.323248	+	0.634410i	−0.671007	+	0.741451i	$0.734138\pi$
$488$	−24.7857	+	303.632i	−0.0507904	+	0.622196i
$489$	−519.748	−	715.372i	−1.06288	−	1.46293i
$490$	28.3694	−	34.1030i	0.0578967	−	0.0695980i
$491$	125.437	+	386.055i	0.255472	+	0.786263i	0.993736	+	0.111751i	$0.0356459\pi$
$491$	125.437	+	386.055i	0.255472	+	0.786263i	−0.738264	+	0.674512i	$0.764354\pi$
$492$	178.854	+	58.4971i	0.363524	+	0.118896i
$493$	−576.200	+	91.2611i	−1.16876	+	0.185114i
$494$	−215.344	+	518.462i	−0.435918	+	1.04952i
$495$	245.998	−	589.812i	0.496967	−	1.19154i
$496$	239.709	+	0.930229i	0.483285	+	0.00187546i
$497$	137.678	−	21.8061i	0.277019	−	0.0438755i
$498$	−74.0000	−	952.068i	−0.148594	−	1.91178i
$499$	−232.643	−	716.002i	−0.466219	−	1.43487i	−0.857443	−	0.514578i	$-0.827948\pi$
$499$	−232.643	−	716.002i	−0.466219	−	1.43487i	0.391225	−	0.920295i	$-0.372052\pi$
$500$	−415.915	−	277.515i	−0.831830	−	0.555031i
$501$	606.525	+	834.811i	1.21063	+	1.66629i
$502$	−40.2192	+	34.2830i	−0.0801180	+	0.0682929i
$503$	−394.361	−	773.978i	−0.784019	−	1.53872i	−0.841426	−	0.540372i	$-0.818283\pi$
$503$	−394.361	−	773.978i	−0.784019	−	1.53872i	0.0574073	−	0.998351i	$-0.481717\pi$
$504$	−146.614	+	602.955i	−0.290901	+	1.19634i
$505$	−615.065	−	88.6383i	−1.21795	−	0.175521i
$506$	−619.564	+	189.478i	−1.22443	+	0.374463i
$507$	−1424.56	+	1424.56i	−2.80978	+	2.80978i
$508$	27.1696	+	19.8205i	0.0534835	+	0.0390168i
$509$	820.967	+	266.748i	1.61290	+	0.524063i	0.970252	−	0.242097i	$-0.0778353\pi$
$509$	820.967	+	266.748i	1.61290	+	0.524063i	0.642649	+	0.766161i	$0.277835\pi$
$510$	−700.553	+	441.911i	−1.37363	+	0.866492i
$511$	313.250	+	431.152i	0.613014	+	0.843741i
$512$	271.321	−	434.199i	0.529923	−	0.848046i
$513$	−61.2331	+	120.177i	−0.119363	+	0.234263i
$514$	−507.950	+	593.566i	−0.988229	+	1.15480i
$515$	−35.4846	+	0.495146i	−0.0689021	+	0.000961449i
$516$	−258.765	+	257.762i	−0.501482	+	0.499539i
$517$	−191.663	+	42.7033i	−0.370722	+	0.0825982i
$518$	77.9365	+	188.673i	0.150457	+	0.364234i
$519$	207.805	−	286.019i	0.400395	−	0.551097i
$520$	987.832	+	66.7775i	1.89968	+	0.128418i
$521$	−200.511	−	617.108i	−0.384857	−	1.18447i	−0.936584	−	0.350444i	$-0.886031\pi$
$521$	−200.511	−	617.108i	−0.384857	−	1.18447i	0.551727	−	0.834025i	$-0.313969\pi$
$522$	633.319	+	388.944i	1.21325	+	0.745104i
$523$	−45.6928	+	288.493i	−0.0873667	+	0.551612i	0.904715	+	0.426017i	$0.140084\pi$
$523$	−45.6928	+	288.493i	−0.0873667	+	0.551612i	−0.992082	+	0.125594i	$0.959916\pi$
$524$	−571.962	−	292.828i	−1.09153	−	0.558833i
$525$	625.282	+	428.157i	1.19101	+	0.815538i
$526$	−570.124	+	348.612i	−1.08389	+	0.662761i
$527$	−193.241	−	193.241i	−0.366680	−	0.366680i
$528$	531.246	−	597.058i	1.00615	−	1.13079i
$529$			338.276i			0.639463i
$530$	278.778	+	649.064i	0.525995	+	1.22465i
$531$	−885.719	−	287.787i	−1.66802	−	0.541973i
$532$	−288.180	+	93.0177i	−0.541693	+	0.174845i
$533$	−40.1159	+	253.282i	−0.0752643	+	0.475200i
$534$	145.871	+	610.204i	0.273167	+	1.14270i
$535$	3.60321	+	2.54183i	0.00673496	+	0.00475109i
$536$	172.627	−	13.0806i	0.322065	−	0.0244041i
$537$	−118.778	−	749.936i	−0.221188	−	1.39653i
$538$	114.782	+	277.872i	0.213350	+	0.516490i
$539$	45.3820	−	17.9319i	0.0841967	−	0.0332688i
$540$	235.370	+	34.3859i	0.435870	+	0.0636777i
$541$	258.288	−	355.504i	0.477428	−	0.657123i	−0.500580	−	0.865690i	$-0.666880\pi$
$541$	258.288	−	355.504i	0.477428	−	0.657123i	0.978008	+	0.208567i	$0.0668799\pi$
$542$	5.09094	+	65.4989i	0.00939289	+	0.120847i
$543$	−622.621	+	1221.96i	−1.14663	+	2.25039i
$544$	−568.233	+	133.509i	−1.04455	+	0.245421i
$545$	437.218	+	829.276i	0.802234	+	1.52161i
$546$	−1495.88	−	119.189i	−2.73971	−	0.218294i
$547$	−397.803	+	202.691i	−0.727244	+	0.370549i	−0.778086	−	0.628157i	$-0.783809\pi$
$547$	−397.803	+	202.691i	−0.727244	+	0.370549i	0.0508421	+	0.998707i	$0.483809\pi$
$548$	−253.585	−	184.993i	−0.462745	−	0.337578i
$549$	−442.462			−0.805942
$550$	−254.845	−	487.395i	−0.463355	−	0.886173i
$551$			362.695i			0.658249i
$552$	−556.314	−	913.782i	−1.00782	−	1.65540i
$553$	300.340	+	589.451i	0.543111	+	1.06591i
$554$	103.187	+	8.22174i	0.186258	+	0.0148407i
$555$	307.075	−	161.898i	0.553288	−	0.291709i
$556$	−207.420	−	33.2648i	−0.373058	−	0.0598289i
$557$	386.971	+	197.171i	0.694741	+	0.353988i	0.765438	−	0.643510i	$-0.222522\pi$
$557$	386.971	+	197.171i	0.694741	+	0.353988i	−0.0706972	+	0.997498i	$0.522522\pi$
$558$	26.9793	+	347.110i	0.0483501	+	0.622061i
$559$	−402.674	−	292.560i	−0.720347	−	0.523363i
$560$	318.243	+	428.872i	0.568290	+	0.765843i
$561$	−909.357	+	56.5831i	−1.62096	+	0.100861i
$562$	31.9907	+	77.4448i	0.0569229	+	0.137802i
$563$	265.894	−	42.1135i	0.472280	−	0.0748019i	0.0842425	−	0.996445i	$-0.473153\pi$
$563$	265.894	−	42.1135i	0.472280	−	0.0748019i	0.388038	+	0.921643i	$0.373153\pi$
$564$	−146.640	−	289.183i	−0.260000	−	0.512735i
$565$	123.708	−	175.363i	0.218952	−	0.310377i
$566$	−6.07342	−	25.4062i	−0.0107304	−	0.0448872i
$567$	333.409	+	52.8068i	0.588023	+	0.0931338i
$568$	13.5912	−	166.495i	0.0239281	−	0.293125i
$569$	−9.37853	+	28.8642i	−0.0164825	+	0.0507279i	−0.958959	−	0.283543i	$-0.908490\pi$
$569$	−9.37853	+	28.8642i	−0.0164825	+	0.0507279i	0.942477	+	0.334271i	$0.108490\pi$
$570$	203.225	+	473.158i	0.356534	+	0.830102i
$571$	9.82448			0.0172057			0.00860287	−	0.999963i	$-0.497262\pi$
$571$	9.82448			0.0172057			0.00860287	+	0.999963i	$0.497262\pi$
$572$	918.016	+	585.982i	1.60492	+	1.02444i
$573$	416.484	−	416.484i	0.726849	−	0.726849i
$574$	−118.009	+	72.1588i	−0.205591	+	0.125712i
$575$	−723.678	+	135.418i	−1.25857	+	0.235510i
$576$	660.602	+	341.452i	1.14688	+	0.592798i
$577$	161.102	+	25.5160i	0.279206	+	0.0442219i	0.294467	−	0.955662i	$-0.404858\pi$
$577$	161.102	+	25.5160i	0.279206	+	0.0442219i	−0.0152610	+	0.999884i	$0.504858\pi$
$578$	74.5242	+	45.7680i	0.128935	+	0.0791834i
$579$	297.310	−	96.6018i	0.513488	−	0.166842i
$580$	605.920	−	204.954i	1.04469	−	0.353369i
$581$	567.883	+	412.591i	0.977424	+	0.710140i
$582$	−503.682	−	1219.34i	−0.865433	−	2.09509i
$583$	−73.6587	+	773.541i	−0.126344	+	1.32683i
$584$	590.755	−	242.687i	1.01157	−	0.415560i
$585$	20.0637	+	1437.86i	0.0342969	+	2.45788i
$586$	90.4797	−	105.730i	0.154402	−	0.180427i
$587$	−494.198	−	251.807i	−0.841905	−	0.428972i	−0.0208237	−	0.999783i	$-0.506629\pi$
$587$	−494.198	−	251.807i	−0.841905	−	0.428972i	−0.821081	+	0.570811i	$0.806629\pi$
$588$	47.2332	+	65.2768i	0.0803285	+	0.111015i
$589$	−137.455	+	99.8667i	−0.233370	+	0.169553i
$590$	−677.911	+	427.628i	−1.14900	+	0.724794i
$591$	−133.406	+	410.580i	−0.225729	+	0.694721i
$592$	241.770	−	37.3314i	0.408395	−	0.0630597i
$593$	86.9546	+	86.9546i	0.146635	+	0.146635i	0.776613	−	0.629978i	$-0.216936\pi$
$593$	86.9546	+	86.9546i	0.146635	+	0.146635i	−0.629978	+	0.776613i	$0.716936\pi$
$594$	208.981	+	157.450i	0.351819	+	0.265067i
$595$	86.8447	−	602.619i	0.145958	−	1.01281i
$596$	−72.3414	+	11.3139i	−0.121378	+	0.0189831i
$597$	230.517	−	117.455i	0.386126	−	0.196741i
$598$	1109.50	−	945.741i	1.85535	−	1.58151i
$599$	−2.16024	+	1.56951i	−0.00360641	+	0.00262021i	−0.589587	−	0.807705i	$-0.700709\pi$
$599$	−2.16024	+	1.56951i	−0.00360641	+	0.00262021i	0.585981	+	0.810325i	$0.300709\pi$
$600$	675.619	−	606.883i	1.12603	−	1.01147i
$601$	274.011	−	89.0315i	0.455925	−	0.148139i	−0.0720463	−	0.997401i	$-0.522953\pi$
$601$	274.011	−	89.0315i	0.455925	−	0.148139i	0.527971	+	0.849262i	$0.322953\pi$
$602$	−20.8047	−	267.668i	−0.0345593	−	0.444632i
$603$	39.3343	+	248.347i	0.0652310	+	0.411852i
$604$	578.816	−	576.575i	0.958305	−	0.954594i
$605$	11.3978	−	604.893i	0.0188394	−	0.999823i
$606$	432.948	−	1042.37i	0.714436	−	1.72008i
$607$	−138.995	−	877.578i	−0.228986	−	1.44576i	−0.787524	−	0.616284i	$-0.788637\pi$
$607$	−138.995	−	877.578i	−0.228986	−	1.44576i	0.558538	−	0.829479i	$-0.311363\pi$
$608$	26.7173	+	361.912i	0.0439430	+	0.595250i
$609$	−922.025	+	299.584i	−1.51400	+	0.491928i
$610$	−243.531	+	292.750i	−0.399231	+	0.479919i
$611$	357.468	−	259.716i	0.585055	−	0.425067i
$612$	−260.412	−	806.790i	−0.425510	−	1.31828i
$613$	−150.698	+	76.7845i	−0.245837	+	0.125260i	−0.572568	−	0.819857i	$-0.694053\pi$
$613$	−150.698	+	76.7845i	−0.245837	+	0.125260i	0.326731	+	0.945117i	$0.394053\pi$
$614$	−20.2926	−	33.1868i	−0.0330499	−	0.0540501i
$615$	140.901	+	188.350i	0.229108	+	0.306261i
$616$	80.6793	+	581.889i	0.130973	+	0.944624i
$617$	246.729	+	246.729i	0.399884	+	0.399884i	0.878192	−	0.478308i	$-0.158750\pi$
$617$	246.729	+	246.729i	0.399884	+	0.399884i	−0.478308	+	0.878192i	$0.658750\pi$
$618$	15.1083	−	62.6626i	0.0244470	−	0.101396i
$619$	−146.025	+	449.420i	−0.235905	+	0.726041i	0.761095	+	0.648641i	$0.224662\pi$
$619$	−146.025	+	449.420i	−0.235905	+	0.726041i	−0.997000	+	0.0774008i	$0.975338\pi$
$620$	244.511	+	173.199i	0.394373	+	0.279353i
$621$	283.363	−	205.875i	0.456301	−	0.331522i
$622$	561.630	+	344.917i	0.902942	+	0.554529i
$623$	−410.913	−	209.370i	−0.659571	−	0.336068i
$624$	−562.347	+	1708.14i	−0.901197	+	2.73741i
$625$	−225.993	−	582.711i	−0.361588	−	0.932338i
$626$	−34.1604	+	82.2448i	−0.0545694	+	0.131381i
$627$	−53.6961	+	563.900i	−0.0856397	+	0.899362i
$628$	76.9526	+	0.149313i	0.122536	+	0.000237759i
$629$	−225.632	−	163.931i	−0.358715	−	0.260622i
$630$	−583.223	+	511.362i	−0.925751	+	0.811686i
$631$	868.165	−	282.084i	1.37586	−	0.447042i	0.474550	−	0.880228i	$-0.342611\pi$
$631$	868.165	−	282.084i	1.37586	−	0.447042i	0.901305	+	0.433186i	$0.142611\pi$
$632$	771.432	−	182.831i	1.22062	−	0.289290i
$633$	−1248.33	−	197.717i	−1.97209	−	0.312348i
$634$	−1.85264	+	23.2516i	−0.00292215	+	0.0366745i
$635$	13.5472	+	39.7960i	0.0213342	+	0.0626709i
$636$	−1267.65	+	198.255i	−1.99316	+	0.311722i
$637$	−77.6412	+	77.6412i	−0.121886	+	0.121886i
$638$	692.930	+	122.120i	1.08610	+	0.191411i
$639$	242.622			0.379691
$640$	589.514	−	249.146i	0.921115	−	0.389290i
$641$	−127.066	+	391.068i	−0.198230	+	0.610090i	0.801693	+	0.597735i	$0.203933\pi$
$641$	−127.066	+	391.068i	−0.198230	+	0.610090i	−0.999924	+	0.0123545i	$0.996067\pi$
$642$	−6.09529	+	5.19565i	−0.00949421	+	0.00809291i
$643$	−973.141	−	154.130i	−1.51344	−	0.239705i	−0.656186	−	0.754600i	$-0.727831\pi$
$643$	−973.141	−	154.130i	−1.51344	−	0.239705i	−0.857254	+	0.514894i	$0.827831\pi$
$644$	776.455	+	124.523i	1.20568	+	0.193359i
$645$	−449.889	+	77.7049i	−0.697503	+	0.120473i
$646$	268.996	−	314.335i	0.416402	−	0.486587i
$647$	−887.815	+	140.616i	−1.37220	+	0.217336i	−0.798632	−	0.601820i	$-0.794442\pi$
$647$	−887.815	+	140.616i	−1.37220	+	0.217336i	−0.573571	+	0.819156i	$0.694442\pi$
$648$	155.896	−	373.289i	0.240580	−	0.576064i
$649$	−879.967	+	54.7544i	−1.35588	+	0.0843673i
$650$	962.390	+	778.125i	1.48060	+	1.19711i
$651$	−367.413	−	266.941i	−0.564382	−	0.410048i
$652$	242.139	−	740.338i	0.371380	−	1.13549i
$653$	−46.9707	−	23.9328i	−0.0719306	−	0.0366505i	0.417655	−	0.908606i	$-0.362852\pi$
$653$	−46.9707	−	23.9328i	−0.0719306	−	0.0366505i	−0.489586	+	0.871955i	$0.662852\pi$
$654$	−1656.11	+	395.897i	−2.53227	+	0.605347i
$655$	−374.597	−	710.503i	−0.571904	−	1.08474i
$656$	50.6118	+	157.849i	0.0771521	+	0.240623i
$657$	421.118	+	826.491i	0.640971	+	1.25798i
$658$	231.696	+	55.8632i	0.352122	+	0.0848984i
$659$			741.252i			1.12481i	0.826861	+	0.562407i	$0.190125\pi$
$659$			741.252i			1.12481i	−0.826861	+	0.562407i	$0.809875\pi$
$660$	972.395	−	228.947i	1.47333	−	0.346890i
$661$	−747.326			−1.13060			−0.565299	−	0.824886i	$-0.691239\pi$
$661$	−747.326			−1.13060			−0.565299	+	0.824886i	$0.691239\pi$
$662$	−182.534	+	757.074i	−0.275732	+	1.14362i
$663$	1826.73	−	930.766i	2.75525	−	1.40387i
$664$	641.241	−	544.452i	0.965725	−	0.819958i
$665$	−361.596	−	111.937i	−0.543754	−	0.168326i
$666$	82.6097	+	345.571i	0.124039	+	0.518875i
$667$	427.596	−	839.205i	0.641074	−	1.25818i
$668$	−282.567	+	863.945i	−0.423005	+	1.29333i
$669$	522.592	−	719.286i	0.781154	−	1.07517i
$670$	185.966	+	110.665i	0.277561	+	0.165172i
$671$	−389.573	+	153.933i	−0.580586	+	0.229408i
$672$	−897.966	+	366.857i	−1.33626	+	0.545918i
$673$	−168.295	−	1062.58i	−0.250068	−	1.57886i	−0.718604	−	0.695420i	$-0.755218\pi$
$673$	−168.295	−	1062.58i	−0.250068	−	1.57886i	0.468536	−	0.883444i	$-0.344782\pi$
$674$	−642.790	−	550.074i	−0.953694	−	0.816133i
$675$	216.032	+	204.300i	0.320048	+	0.302666i
$676$	−1752.29	−	281.021i	−2.59214	−	0.415712i
$677$	61.9243	−	390.975i	0.0914688	−	0.577511i	−0.898802	−	0.438355i	$-0.855561\pi$
$677$	61.9243	−	390.975i	0.0914688	−	0.577511i	0.990271	−	0.139156i	$-0.0444388\pi$
$678$	252.865	+	296.649i	0.372957	+	0.437536i
$679$	922.291	+	299.670i	1.35831	+	0.441341i
$680$	−677.135	−	271.758i	−0.995787	−	0.399644i
$681$		−	514.873i		−	0.756054i
$682$	144.514	+	296.233i	0.211897	+	0.434359i
$683$	−544.013	−	544.013i	−0.796506	−	0.796506i	0.186037	−	0.982543i	$-0.440436\pi$
$683$	−544.013	−	544.013i	−0.796506	−	0.796506i	−0.982543	+	0.186037i	$0.940436\pi$
$684$	−520.742	+	81.4420i	−0.761319	+	0.119067i
$685$	−126.442	−	371.432i	−0.184586	−	0.542236i
$686$	−711.184	−	56.6657i	−1.03671	−	0.0826030i
$687$	83.7200	−	528.587i	0.121863	−	0.769414i
$688$	−317.579	−	51.5638i	−0.461598	−	0.0749473i
$689$	−540.314	−	1662.92i	−0.784200	−	2.41352i
$690$	87.6038	−	1334.38i	0.126962	−	1.93389i
$691$	−152.782	+	210.287i	−0.221103	+	0.304323i	−0.905130	−	0.425134i	$-0.860227\pi$
$691$	−152.782	+	210.287i	−0.221103	+	0.304323i	0.684027	+	0.729457i	$0.260227\pi$
$692$	311.430	+	0.604274i	0.450043	+	0.000873228i
$693$	−832.800	+	185.551i	−1.20173	+	0.267750i
$694$	113.247	+	47.0370i	0.163179	+	0.0677767i
$695$	−188.251	−	183.069i	−0.270864	−	0.263409i
$696$	87.7831	+	1158.49i	0.126125	+	1.66449i
$697$	85.7950	−	168.382i	0.123092	−	0.241581i
$698$	−41.8051	+	68.0713i	−0.0598926	+	0.0975234i
$699$	791.658	+	1089.62i	1.13256	+	1.55883i
$700$	17.3317	+	667.337i	0.0247595	+	0.953339i
$701$	626.487	+	203.558i	0.893705	+	0.290382i	0.719636	−	0.694351i	$-0.244308\pi$
$701$	626.487	+	203.558i	0.893705	+	0.290382i	0.174069	+	0.984733i	$0.444308\pi$
$702$	−572.374	−	138.002i	−0.815347	−	0.196584i
$703$	−122.607	+	122.607i	−0.174406	+	0.174406i
$704$	700.429	+	70.8133i	0.994928	+	0.100587i
$705$	57.8109	−	401.153i	0.0820013	−	0.569011i
$706$	−70.2510	+	42.9562i	−0.0995056	+	0.0608444i
$707$	376.663	+	739.243i	0.532763	+	1.04561i
$708$	−447.187	−	1385.44i	−0.631620	−	1.95684i
$709$	305.162	+	420.020i	0.430412	+	0.592411i	0.968048	−	0.250766i	$-0.0806824\pi$
$709$	305.162	+	420.020i	0.430412	+	0.592411i	−0.537636	+	0.843177i	$0.680682\pi$
$710$	133.539	−	160.529i	0.188084	−	0.226097i
$711$	355.823	+	1095.11i	0.500454	+	1.54024i
$712$	−360.153	+	419.208i	−0.505832	+	0.588775i
$713$	435.780	−	69.0207i	0.611192	−	0.0968033i
$714$	1021.28	+	424.188i	1.43036	+	0.594100i
$715$	517.898	+	1259.01i	0.724333	+	1.76085i
$716$	473.864	−	472.029i	0.661822	−	0.659259i
$717$	769.120	−	121.817i	1.07269	−	0.169898i
$718$	−1025.44	+	79.7031i	−1.42819	+	0.111007i
$719$	363.969	+	1120.18i	0.506216	+	1.55797i	0.798717	+	0.601706i	$0.205512\pi$
$719$	363.969	+	1120.18i	0.506216	+	1.55797i	−0.292502	+	0.956265i	$0.594488\pi$
$720$	430.321	+	823.931i	0.597669	+	1.14435i
$721$	27.8498	+	38.3320i	0.0386267	+	0.0531651i
$722$	301.511	+	353.718i	0.417605	+	0.489914i
$723$	−272.295	−	534.408i	−0.376618	−	0.739154i
$724$	−1193.59	+	186.672i	−1.64860	+	0.257834i
$725$	767.020	+	225.763i	1.05796	+	0.311397i
$726$	1059.25	+	292.453i	1.45902	+	0.402828i
$727$	−616.533	+	616.533i	−0.848051	+	0.848051i	−0.989890	−	0.141839i	$-0.954698\pi$
$727$	−616.533	+	616.533i	−0.848051	+	0.848051i	0.141839	+	0.989890i	$0.454698\pi$
$728$	−687.402	−	1129.10i	−0.944233	−	1.55096i
$729$	1021.06	+	331.761i	1.40062	+	0.455091i
$730$	778.623	+	176.272i	1.06661	+	0.241469i
$731$	215.599	+	296.746i	0.294937	+	0.405946i
$732$	−405.463	−	560.356i	−0.553912	−	0.765513i
$733$	−351.727	+	690.302i	−0.479845	+	0.941749i	0.516496	+	0.856289i	$0.327236\pi$
$733$	−351.727	+	690.302i	−0.479845	+	0.941749i	−0.996342	+	0.0854600i	$0.972764\pi$
$734$	−1049.90	−	898.460i	−1.43038	−	1.22406i
$735$	1.40524	+	100.707i	0.00191190	+	0.137016i
$736$	364.854	−	868.891i	0.495726	−	1.18056i
$737$	121.032	+	204.977i	0.164223	+	0.278123i
$738$	−222.519	+	91.9175i	−0.301516	+	0.124550i
$739$	401.252	−	552.275i	0.542966	−	0.747328i	−0.446071	−	0.894997i	$-0.647177\pi$
$739$	401.252	−	552.275i	0.542966	−	0.747328i	0.989037	+	0.147669i	$0.0471772\pi$
$740$	274.112	+	135.544i	0.370421	+	0.183168i
$741$	−393.881	−	1212.24i	−0.531553	−	1.63595i
$742$	493.565	−	803.674i	0.665182	−	1.08312i
$743$	158.762	−	1002.39i	0.213677	−	1.34911i	−0.614622	−	0.788822i	$-0.710692\pi$
$743$	158.762	−	1002.39i	0.213677	−	1.34911i	0.828300	−	0.560285i	$-0.189308\pi$
$744$	−414.874	+	352.253i	−0.557627	+	0.473458i
$745$	−82.1220	−	40.4100i	−0.110231	−	0.0542417i
$746$	−289.687	−	473.758i	−0.388321	−	0.635064i
$747$	863.916	+	863.916i	1.15651	+	1.15651i
$748$	−509.967	−	619.754i	−0.681774	−	0.828548i
$749$		−	5.88728i		−	0.00786019i
$750$	1127.12	−	135.254i	1.50283	−	0.180339i
$751$	486.255	+	157.994i	0.647477	+	0.210378i	0.614301	−	0.789071i	$-0.289438\pi$
$751$	486.255	+	157.994i	0.647477	+	0.210378i	0.0331758	+	0.999450i	$0.489438\pi$
$752$	130.655	−	253.983i	0.173743	−	0.337744i
$753$	18.7701	−	118.510i	0.0249271	−	0.157384i
$754$	−1539.87	+	368.110i	−2.04227	+	0.488210i
$755$	1006.33	−	173.814i	1.33289	−	0.230217i
$756$	−143.631	−	283.248i	−0.189988	−	0.374667i
$757$	175.399	+	1107.43i	0.231703	+	1.46292i	0.779551	+	0.626339i	$0.215448\pi$
$757$	175.399	+	1107.43i	0.231703	+	1.46292i	−0.547847	+	0.836578i	$0.684552\pi$
$758$	−1190.12	+	491.610i	−1.57008	+	0.648563i
$759$	789.047	−	1241.45i	1.03959	−	1.63564i
$760$	−232.731	+	389.369i	−0.306225	+	0.512328i
$761$	−69.5768	+	95.7643i	−0.0914282	+	0.125840i	−0.852281	−	0.523085i	$-0.824781\pi$
$761$	−69.5768	+	95.7643i	−0.0914282	+	0.125840i	0.760852	+	0.648925i	$0.224781\pi$
$762$	−76.1267	+	5.91700i	−0.0999039	+	0.00776509i
$763$	568.235	−	1115.22i	0.744738	−	1.46163i
$764$	512.299	+	82.1594i	0.670548	+	0.107538i
$765$	313.378	−	1012.33i	0.409644	−	1.32330i
$766$	61.8209	−	775.884i	0.0807061	−	1.01290i
$767$	1767.69	−	900.684i	2.30468	−	1.17430i
$768$	172.932	+	1149.52i	0.225171	+	1.49677i
$769$	−904.162			−1.17576			−0.587882	−	0.808947i	$-0.700038\pi$
$769$	−904.162			−1.17576			−0.587882	+	0.808947i	$0.700038\pi$

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.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.94429 - 0.468777i) q^{2} +(4.04592 - 2.06150i) q^{3} +(3.56050 + 1.82287i) q^{4} +(2.33189 + 4.42293i) q^{5} +(-8.83280 + 2.11151i) q^{6} +(3.03067 - 5.94803i) q^{7} +(-6.06810 - 5.21327i) q^{8} +(6.82960 - 9.40014i) q^{9} +(-2.46049 - 9.69257i) q^{10} +(2.74293 - 10.6525i) q^{11} +(18.1633 + 0.0352426i) q^{12} +(3.87209 + 24.4474i) q^{13} +(-8.68079 + 10.1440i) q^{14} +(18.5525 + 13.0876i) q^{15} +(9.35426 + 12.9807i) q^{16} +(2.85350 - 18.0163i) q^{17} +(-17.6853 + 15.0750i) q^{18} +(-10.7855 - 3.50442i) q^{19} +(0.240247 + 19.9986i) q^{20} -30.3129i q^{21} +(-10.3267 + 19.4257i) q^{22} +(20.8240 + 20.8240i) q^{23} +(-35.2982 - 8.58307i) q^{24} +(-14.1246 + 20.6276i) q^{25} +(3.93194 - 49.3479i) q^{26} +(1.86054 - 11.7470i) q^{27} +(21.6332 - 15.6534i) q^{28} +(-9.88305 - 30.4169i) q^{29} +(-29.9362 - 34.1430i) q^{30} +(8.80617 - 12.1207i) q^{31} +(-12.1023 - 29.6232i) q^{32} +(-10.8625 - 48.7538i) q^{33} +(-13.9936 + 33.6911i) q^{34} +(33.3749 - 0.465708i) q^{35} +(41.4520 - 21.0197i) q^{36} +(6.94136 - 13.6232i) q^{37} +(19.3273 + 11.8696i) q^{38} +(66.0644 + 90.9299i) q^{39} +(8.90776 - 38.9955i) q^{40} +(9.85319 + 3.20150i) q^{41} +(-14.2100 + 58.9370i) q^{42} +(-14.2190 + 14.2190i) q^{43} +(29.1844 - 32.9283i) q^{44} +(57.5020 + 8.28674i) q^{45} +(-30.7260 - 50.2496i) q^{46} +(-8.10427 - 15.9055i) q^{47} +(64.6062 + 33.2349i) q^{48} +(2.60743 + 3.58882i) q^{49} +(37.1319 - 33.4846i) q^{50} +(-25.5955 - 78.7748i) q^{51} +(-30.7780 + 94.1033i) q^{52} +(-69.7703 + 11.0505i) q^{53} +(-9.12414 + 21.9673i) q^{54} +(53.5116 - 12.7088i) q^{55} +(-49.3991 + 20.2935i) q^{56} +(-50.8615 + 8.05567i) q^{57} +(4.95673 + 63.7721i) q^{58} +(-24.7682 - 76.2288i) q^{59} +(42.1990 + 80.4172i) q^{60} +(-22.3830 - 30.8075i) q^{61} +(-22.8036 + 19.4379i) q^{62} +(-35.2140 - 69.1114i) q^{63} +(9.64368 + 63.2693i) q^{64} +(-99.0999 + 74.1347i) q^{65} +(-1.73484 + 99.8834i) q^{66} +(-15.3020 + 15.3020i) q^{67} +(43.0012 - 58.9453i) q^{68} +(127.181 + 41.3235i) q^{69} +(-65.1086 - 14.7399i) q^{70} +(12.2736 + 16.8932i) q^{71} +(-90.4481 + 21.4365i) q^{72} +(-36.2433 + 71.1314i) q^{73} +(-19.8822 + 23.2334i) q^{74} +(-14.6232 + 112.575i) q^{75} +(-32.0136 - 32.1380i) q^{76} +(-55.0486 - 48.5993i) q^{77} +(-85.8223 - 207.763i) q^{78} +(-58.2496 + 80.1738i) q^{79} +(-35.5995 + 71.6427i) q^{80} +(15.6260 + 48.0919i) q^{81} +(-17.6566 - 10.8436i) q^{82} +(-16.4491 + 103.856i) q^{83} +(55.2567 - 107.929i) q^{84} +(86.3386 - 29.3911i) q^{85} +(34.3112 - 20.9802i) q^{86} +(-102.690 - 102.690i) q^{87} +(-72.1788 + 50.3410i) q^{88} -69.0839i q^{89} +(-107.916 - 43.0674i) q^{90} +(157.149 + 51.0608i) q^{91} +(36.1842 + 112.103i) q^{92} +(10.6423 - 67.1931i) q^{93} +(8.30087 + 34.7240i) q^{94} +(-9.65079 - 55.8753i) q^{95} +(-110.033 - 94.9041i) q^{96} +(22.7249 + 143.479i) q^{97} +(-3.38724 - 8.20000i) q^{98} +(-81.4022 - 98.5364i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) \) 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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