LMFDB - Embedded newform 220.3.s.a.31.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(31,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 0, 6]))

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

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

chi := DirichletCharacter("220.31");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.s (of order $10$, degree $4$, 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:	$96$
Relative dimension:	$24$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			31.17
Character	$\chi$	$=$	220.31
Dual form			220.3.s.a.71.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.26877 - 1.54603i) q^{2} +(-2.91538 - 4.01268i) q^{3} +(-0.780445 - 3.92312i) q^{4} +(0.690983 + 2.12663i) q^{5} +(-9.90270 - 0.583887i) q^{6} +(-7.54604 + 10.3862i) q^{7} +(-7.05549 - 3.77095i) q^{8} +(-4.82100 + 14.8375i) q^{9} +(4.16454 + 1.62992i) q^{10} +(0.0160137 - 11.0000i) q^{11} +(-13.4670 + 14.5691i) q^{12} +(1.97936 - 6.09183i) q^{13} +(6.48328 + 24.8442i) q^{14} +(6.51900 - 8.97263i) q^{15} +(-14.7818 + 6.12356i) q^{16} +(4.43747 + 13.6571i) q^{17} +(16.8226 + 26.2788i) q^{18} +(-17.4187 - 23.9748i) q^{19} +(7.80375 - 4.37053i) q^{20} +63.6762 q^{21} +(-16.9860 - 13.9812i) q^{22} +8.75051i q^{23} +(5.43785 + 39.3052i) q^{24} +(-4.04508 + 2.93893i) q^{25} +(-6.90684 - 10.7893i) q^{26} +(31.1386 - 10.1175i) q^{27} +(46.6357 + 21.4982i) q^{28} +(-22.9890 - 16.7025i) q^{29} +(-5.60089 - 21.4628i) q^{30} +(-10.7951 - 3.50755i) q^{31} +(-9.28748 + 30.6226i) q^{32} +(-44.1861 + 32.0049i) q^{33} +(26.7445 + 10.4673i) q^{34} +(-27.3018 - 8.87090i) q^{35} +(61.9720 + 7.33352i) q^{36} +(-21.3051 - 15.4790i) q^{37} +(-59.1662 - 3.48858i) q^{38} +(-30.2152 + 9.81751i) q^{39} +(3.14418 - 17.6101i) q^{40} +(-19.9114 + 14.4665i) q^{41} +(80.7905 - 98.4456i) q^{42} +55.6364i q^{43} +(-43.1668 + 8.52206i) q^{44} -34.8851 q^{45} +(13.5286 + 11.1024i) q^{46} +(-2.75002 - 3.78508i) q^{47} +(67.6666 + 41.4622i) q^{48} +(-35.7892 - 110.148i) q^{49} +(-0.588602 + 9.98266i) q^{50} +(41.8648 - 57.6220i) q^{51} +(-25.4438 - 3.01092i) q^{52} +(13.8139 - 42.5149i) q^{53} +(23.8656 - 60.9782i) q^{54} +(23.4039 - 7.56675i) q^{55} +(92.4069 - 44.8242i) q^{56} +(-45.4210 + 139.792i) q^{57} +(-54.9904 + 14.3502i) q^{58} +(6.65811 - 9.16410i) q^{59} +(-40.2885 - 18.5722i) q^{60} +(-32.5142 - 100.068i) q^{61} +(-19.1193 + 12.2394i) q^{62} +(-117.726 - 162.036i) q^{63} +(35.5599 + 53.2118i) q^{64} +14.3228 q^{65} +(-6.58133 + 108.920i) q^{66} +8.87037i q^{67} +(50.1155 - 28.0674i) q^{68} +(35.1130 - 25.5111i) q^{69} +(-48.3544 + 30.9544i) q^{70} +(100.421 - 32.6289i) q^{71} +(89.9660 - 86.5062i) q^{72} +(10.5417 + 7.65898i) q^{73} +(-50.9623 + 13.2990i) q^{74} +(23.5860 + 7.66354i) q^{75} +(-80.4618 + 87.0468i) q^{76} +(114.128 + 83.1726i) q^{77} +(-23.1579 + 59.1699i) q^{78} +(11.0863 + 3.60215i) q^{79} +(-23.2365 - 27.2041i) q^{80} +(-17.7856 - 12.9220i) q^{81} +(-2.89732 + 49.1384i) q^{82} +(-106.995 + 34.7649i) q^{83} +(-49.6958 - 249.810i) q^{84} +(-25.9774 + 18.8737i) q^{85} +(86.0158 + 70.5898i) q^{86} +140.942i q^{87} +(-41.5934 + 77.5499i) q^{88} -41.7744 q^{89} +(-44.2612 + 53.9336i) q^{90} +(48.3349 + 66.5272i) q^{91} +(34.3293 - 6.82929i) q^{92} +(17.3973 + 53.5433i) q^{93} +(-9.34102 - 0.550769i) q^{94} +(38.9494 - 53.6093i) q^{95} +(149.955 - 52.0089i) q^{96} +(5.05260 - 15.5503i) q^{97} +(-215.701 - 84.4210i) q^{98} +(163.135 + 53.2686i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 2 q^{2} - 4 q^{4} + 120 q^{5} + 20 q^{6} - 10 q^{8} + 64 q^{9} + 10 q^{10} + 70 q^{12} - 20 q^{13} - 37 q^{14} - 4 q^{16} + 24 q^{17} + 45 q^{18} + 5 q^{20} - 15 q^{22} - 62 q^{24} - 120 q^{25} + 12 q^{26}+ \cdots + 158 q^{98}+O(q^{100}) $ 96 * q + 2 * q^2 - 4 * q^4 + 120 * q^5 + 20 * q^6 - 10 * q^8 + 64 * q^9 + 10 * q^10 + 70 * q^12 - 20 * q^13 - 37 * q^14 - 4 * q^16 + 24 * q^17 + 45 * q^18 + 5 * q^20 - 15 * q^22 - 62 * q^24 - 120 * q^25 + 12 * q^26 - 200 * q^28 + 72 * q^29 + 40 * q^30 - 348 * q^32 - 60 * q^33 - 246 * q^34 + 26 * q^36 + 144 * q^37 - 105 * q^38 + 132 * q^41 - 25 * q^42 - 67 * q^44 - 40 * q^45 - 85 * q^46 + 213 * q^48 - 28 * q^49 + 10 * q^50 + 312 * q^52 - 224 * q^53 + 752 * q^54 + 660 * q^56 - 204 * q^57 + 88 * q^58 + 105 * q^60 - 48 * q^61 + 88 * q^62 + 44 * q^64 - 40 * q^65 + 75 * q^66 - 117 * q^68 + 32 * q^69 - 75 * q^70 - 198 * q^72 - 64 * q^73 - 672 * q^74 - 1280 * q^76 + 80 * q^77 - 1132 * q^78 - 125 * q^80 - 44 * q^81 - 301 * q^82 - 348 * q^84 - 60 * q^85 + 470 * q^86 + 5 * q^88 + 176 * q^89 - 162 * q^92 + 280 * q^93 + 394 * q^94 + 1143 * q^96 + 204 * q^97 + 158 * q^98

Character values

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

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$-1$	$1$

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 $

$2$	1.26877	−	1.54603i	0.634385	−	0.773017i
$2$	1.26877	−	1.54603i	0.634385	−	0.773017i
$3$	−2.91538	−	4.01268i	−0.971795	−	1.33756i	−0.941135	−	0.338031i	$-0.890239\pi$
$3$	−2.91538	−	4.01268i	−0.971795	−	1.33756i	−0.0306599	−	0.999530i	$-0.509761\pi$
$4$	−0.780445	−	3.92312i	−0.195111	−	0.980781i
$5$	0.690983	+	2.12663i	0.138197	+	0.425325i
$5$	0.690983	+	2.12663i	0.138197	+	0.425325i
$6$	−9.90270	−	0.583887i	−1.65045	−	0.0973145i
$7$	−7.54604	+	10.3862i	−1.07801	+	1.48375i	−0.216307	+	0.976325i	$0.569401\pi$
$7$	−7.54604	+	10.3862i	−1.07801	+	1.48375i	−0.861698	+	0.507421i	$0.830599\pi$
$8$	−7.05549	−	3.77095i	−0.881936	−	0.471369i
$9$	−4.82100	+	14.8375i	−0.535667	+	1.64861i
$10$	4.16454	+	1.62992i	0.416454	+	0.162992i
$11$	0.0160137	−	11.0000i	0.00145579	−	0.999999i
$11$	0.0160137	−	11.0000i	0.00145579	−	0.999999i
$12$	−13.4670	+	14.5691i	−1.12225	+	1.21409i
$13$	1.97936	−	6.09183i	0.152258	−	0.468603i	−0.845615	−	0.533794i	$-0.820766\pi$
$13$	1.97936	−	6.09183i	0.152258	−	0.468603i	0.997873	+	0.0651914i	$0.0207658\pi$
$14$	6.48328	+	24.8442i	0.463091	+	1.77458i
$15$	6.51900	−	8.97263i	0.434600	−	0.598175i
$16$	−14.7818	+	6.12356i	−0.923863	+	0.382723i
$17$	4.43747	+	13.6571i	0.261028	+	0.803361i	0.992582	+	0.121578i	$0.0387954\pi$
$17$	4.43747	+	13.6571i	0.261028	+	0.803361i	−0.731554	+	0.681784i	$0.761205\pi$
$18$	16.8226	+	26.2788i	0.934587	+	1.45994i
$19$	−17.4187	−	23.9748i	−0.916775	−	1.26183i	−0.964800	−	0.262986i	$-0.915293\pi$
$19$	−17.4187	−	23.9748i	−0.916775	−	1.26183i	0.0480251	−	0.998846i	$-0.484707\pi$
$20$	7.80375	−	4.37053i	0.390187	−	0.218526i
$21$	63.6762			3.03220
$22$	−16.9860	−	13.9812i	−0.772093	−	0.635510i
$23$			8.75051i			0.380457i	0.981740	+	0.190228i	$0.0609229\pi$
$23$			8.75051i			0.380457i	−0.981740	+	0.190228i	$0.939077\pi$
$24$	5.43785	+	39.3052i	0.226577	+	1.63772i
$25$	−4.04508	+	2.93893i	−0.161803	+	0.117557i
$26$	−6.90684	−	10.7893i	−0.265648	−	0.414973i
$27$	31.1386	−	10.1175i	1.15328	−	0.374724i
$28$	46.6357	+	21.4982i	1.66556	+	0.767791i
$29$	−22.9890	−	16.7025i	−0.792724	−	0.575948i	0.116046	−	0.993244i	$-0.462978\pi$
$29$	−22.9890	−	16.7025i	−0.792724	−	0.575948i	−0.908771	+	0.417296i	$0.862978\pi$
$30$	−5.60089	−	21.4628i	−0.186696	−	0.715427i
$31$	−10.7951	−	3.50755i	−0.348230	−	0.113147i	0.129679	−	0.991556i	$-0.458605\pi$
$31$	−10.7951	−	3.50755i	−0.348230	−	0.113147i	−0.477909	+	0.878409i	$0.658605\pi$
$32$	−9.28748	+	30.6226i	−0.290234	+	0.956956i
$33$	−44.1861	+	32.0049i	−1.33897	+	0.969847i
$34$	26.7445	+	10.4673i	0.786604	+	0.307861i
$35$	−27.3018	−	8.87090i	−0.780052	−	0.253454i
$36$	61.9720	+	7.33352i	1.72144	+	0.203709i
$37$	−21.3051	−	15.4790i	−0.575812	−	0.418352i	0.261400	−	0.965231i	$-0.415816\pi$
$37$	−21.3051	−	15.4790i	−0.575812	−	0.418352i	−0.837212	+	0.546878i	$0.815816\pi$
$38$	−59.1662	−	3.48858i	−1.55701	−	0.0918048i
$39$	−30.2152	+	9.81751i	−0.774748	+	0.251731i
$40$	3.14418	−	17.6101i	0.0786044	−	0.440251i
$41$	−19.9114	+	14.4665i	−0.485644	+	0.352841i	−0.803507	−	0.595296i	$-0.797035\pi$
$41$	−19.9114	+	14.4665i	−0.485644	+	0.352841i	0.317863	+	0.948137i	$0.397035\pi$
$42$	80.7905	−	98.4456i	1.92358	−	2.34394i
$43$			55.6364i			1.29387i	0.762545	+	0.646935i	$0.223949\pi$
$43$			55.6364i			1.29387i	−0.762545	+	0.646935i	$0.776051\pi$
$44$	−43.1668	+	8.52206i	−0.981064	+	0.193683i
$45$	−34.8851			−0.775224
$46$	13.5286	+	11.1024i	0.294100	+	0.241356i
$47$	−2.75002	−	3.78508i	−0.0585112	−	0.0805337i	0.778759	−	0.627324i	$-0.215850\pi$
$47$	−2.75002	−	3.78508i	−0.0585112	−	0.0805337i	−0.837270	+	0.546790i	$0.815850\pi$
$48$	67.6666	+	41.4622i	1.40972	+	0.863795i
$49$	−35.7892	−	110.148i	−0.730392	−	2.24792i
$50$	−0.588602	+	9.98266i	−0.0117720	+	0.199653i
$51$	41.8648	−	57.6220i	0.820879	−	1.12984i
$52$	−25.4438	−	3.01092i	−0.489304	−	0.0579024i
$53$	13.8139	−	42.5149i	0.260640	−	0.802169i	−0.732025	−	0.681277i	$-0.761425\pi$
$53$	13.8139	−	42.5149i	0.260640	−	0.802169i	0.992666	−	0.120891i	$-0.0385752\pi$
$54$	23.8656	−	60.9782i	0.441956	−	1.12923i
$55$	23.4039	−	7.56675i	0.425526	−	0.137577i
$56$	92.4069	−	44.8242i	1.65012	−	0.800432i
$57$	−45.4210	+	139.792i	−0.796860	+	2.45248i
$58$	−54.9904	+	14.3502i	−0.948110	+	0.247417i
$59$	6.65811	−	9.16410i	0.112849	−	0.155324i	−0.748856	−	0.662733i	$-0.769397\pi$
$59$	6.65811	−	9.16410i	0.112849	−	0.155324i	0.861705	+	0.507409i	$0.169397\pi$
$60$	−40.2885	−	18.5722i	−0.671474	−	0.309537i
$61$	−32.5142	−	100.068i	−0.533019	−	1.64046i	−0.747890	−	0.663822i	$-0.768933\pi$
$61$	−32.5142	−	100.068i	−0.533019	−	1.64046i	0.214871	−	0.976642i	$-0.431067\pi$
$62$	−19.1193	+	12.2394i	−0.308376	+	0.197409i
$63$	−117.726	−	162.036i	−1.86867	−	2.57201i
$64$	35.5599	+	53.2118i	0.555623	+	0.831434i
$65$	14.3228			0.220350
$66$	−6.58133	+	108.920i	−0.0997171	+	1.65031i
$67$			8.87037i			0.132394i	0.997807	+	0.0661968i	$0.0210865\pi$
$67$			8.87037i			0.132394i	−0.997807	+	0.0661968i	$0.978913\pi$
$68$	50.1155	−	28.0674i	0.736992	−	0.412756i
$69$	35.1130	−	25.5111i	0.508884	−	0.369726i
$70$	−48.3544	+	30.9544i	−0.690778	+	0.442206i
$71$	100.421	−	32.6289i	1.41439	−	0.459562i	0.500572	−	0.865695i	$-0.333123\pi$
$71$	100.421	−	32.6289i	1.41439	−	0.459562i	0.913814	+	0.406133i	$0.133123\pi$
$72$	89.9660	−	86.5062i	1.24953	−	1.20148i
$73$	10.5417	+	7.65898i	0.144407	+	0.104918i	0.657643	−	0.753330i	$-0.271554\pi$
$73$	10.5417	+	7.65898i	0.144407	+	0.104918i	−0.513236	+	0.858247i	$0.671554\pi$
$74$	−50.9623	+	13.2990i	−0.688680	+	0.179717i
$75$	23.5860	+	7.66354i	0.314479	+	0.102181i
$76$	−80.4618	+	87.0468i	−1.05871	+	1.14535i
$77$	114.128	+	83.1726i	1.48218	+	1.08016i
$78$	−23.1579	+	59.1699i	−0.296896	+	0.758588i
$79$	11.0863	+	3.60215i	0.140333	+	0.0455968i	0.378341	−	0.925666i	$-0.376495\pi$
$79$	11.0863	+	3.60215i	0.140333	+	0.0455968i	−0.238009	+	0.971263i	$0.576495\pi$
$80$	−23.2365	−	27.2041i	−0.290456	−	0.340052i
$81$	−17.7856	−	12.9220i	−0.219575	−	0.159530i
$82$	−2.89732	+	49.1384i	−0.0353331	+	0.599248i
$83$	−106.995	+	34.7649i	−1.28910	+	0.418854i	−0.871776	−	0.489905i	$-0.837032\pi$
$83$	−106.995	+	34.7649i	−1.28910	+	0.418854i	−0.417323	+	0.908758i	$0.637032\pi$
$84$	−49.6958	−	249.810i	−0.591617	−	2.97393i
$85$	−25.9774	+	18.8737i	−0.305617	+	0.222044i
$86$	86.0158	+	70.5898i	1.00018	+	0.820811i
$87$			140.942i			1.62002i
$88$	−41.5934	+	77.5499i	−0.472652	+	0.881249i
$89$	−41.7744			−0.469375			−0.234688	−	0.972071i	$-0.575407\pi$
$89$	−41.7744			−0.469375			−0.234688	+	0.972071i	$0.575407\pi$
$90$	−44.2612	+	53.9336i	−0.491791	+	0.599262i
$91$	48.3349	+	66.5272i	0.531152	+	0.731069i
$92$	34.3293	−	6.82929i	0.373145	−	0.0742314i
$93$	17.3973	+	53.5433i	0.187067	+	0.575734i
$94$	−9.34102	−	0.550769i	−0.0993725	−	0.00585924i
$95$	38.9494	−	53.6093i	0.409994	−	0.564308i
$96$	149.955	−	52.0089i	1.56203	−	0.541759i
$97$	5.05260	−	15.5503i	0.0520887	−	0.160312i	−0.921628	−	0.388074i	$-0.873141\pi$
$97$	5.05260	−	15.5503i	0.0520887	−	0.160312i	0.973717	+	0.227761i	$0.0731406\pi$
$98$	−215.701	−	84.4210i	−2.20103	−	0.861439i
$99$	163.135	+	53.2686i	1.64783	+	0.538066i
$100$	14.6867	+	13.5757i	0.146867	+	0.135757i
$101$	32.2532	−	99.2651i	0.319339	−	0.982823i	−0.654593	−	0.755981i	$-0.727160\pi$
$101$	32.2532	−	99.2651i	0.319339	−	0.982823i	0.973932	−	0.226842i	$-0.0728400\pi$
$102$	−35.9687	−	137.834i	−0.352635	−	1.35131i
$103$	71.6439	−	98.6093i	0.695571	−	0.957372i	−0.304417	−	0.952539i	$-0.598462\pi$
$103$	71.6439	−	98.6093i	0.695571	−	0.957372i	0.999988	−	0.00483308i	$-0.00153842\pi$
$104$	−36.9373	+	35.5168i	−0.355167	+	0.341508i
$105$	43.9992	+	135.416i	0.419040	+	1.28967i
$106$	−48.2028	−	75.2985i	−0.454744	−	0.710363i
$107$	−91.5535	−	126.013i	−0.855641	−	1.17769i	−0.982592	−	0.185779i	$-0.940519\pi$
$107$	−91.5535	−	126.013i	−0.855641	−	1.17769i	0.126951	−	0.991909i	$-0.459481\pi$
$108$	−63.9943	−	114.264i	−0.592540	−	1.05800i
$109$	14.2227			0.130483			0.0652417	−	0.997869i	$-0.479218\pi$
$109$	14.2227			0.130483			0.0652417	+	0.997869i	$0.479218\pi$
$110$	17.9958	−	45.7838i	0.163598	−	0.416216i
$111$			130.618i			1.17674i
$112$	47.9433	−	199.736i	0.428066	−	1.78336i
$113$	−53.6570	+	38.9841i	−0.474840	+	0.344992i	−0.799325	−	0.600899i	$-0.794809\pi$
$113$	−53.6570	+	38.9841i	−0.474840	+	0.344992i	0.324484	+	0.945891i	$0.394809\pi$
$114$	158.494	+	247.586i	1.39030	+	2.17181i
$115$	−18.6091	+	6.04645i	−0.161818	+	0.0525778i
$116$	−47.5843	+	103.224i	−0.410209	+	0.889863i
$117$	80.8452	+	58.7375i	0.690985	+	0.502030i
$118$	−5.72040	−	21.9208i	−0.0484780	−	0.185769i
$119$	−175.332	−	56.9687i	−1.47337	−	0.478728i
$120$	−79.8301	+	38.7235i	−0.665250	+	0.322696i
$121$	−120.999	−	0.352301i	−0.999996	−	0.00291158i
$122$	−195.962	−	76.6957i	−1.60625	−	0.628653i
$123$	116.099	+	37.7228i	0.943893	+	0.306689i
$124$	−5.33555	+	45.0881i	−0.0430286	+	0.363613i
$125$	−9.04508	−	6.57164i	−0.0723607	−	0.0525731i
$126$	−399.882	−	23.5780i	−3.17366	−	0.187127i
$127$	224.495	−	72.9427i	1.76767	−	0.574352i	0.769725	−	0.638376i	$-0.220393\pi$
$127$	224.495	−	72.9427i	1.76767	−	0.574352i	0.997948	+	0.0640238i	$0.0203934\pi$
$128$	127.385	+	12.5367i	0.995192	+	0.0979429i
$129$	223.251	−	162.201i	1.73063	−	1.25738i
$130$	18.1723	−	22.1435i	0.139787	−	0.170334i
$131$			109.549i			0.836253i	0.908389	+	0.418126i	$0.137313\pi$
$131$			109.549i			0.836253i	−0.908389	+	0.418126i	$0.862687\pi$
$132$	160.044	+	148.370i	1.21246	+	1.12401i
$133$	380.450			2.86053
$134$	13.7139	+	11.2545i	0.102343	+	0.0839885i
$135$	43.0325	+	59.2291i	0.318759	+	0.438734i
$136$	20.1918	−	113.091i	0.148469	−	0.831554i
$137$	−70.3609	−	216.548i	−0.513583	−	1.58065i	−0.785846	−	0.618423i	$-0.787772\pi$
$137$	−70.3609	−	216.548i	−0.513583	−	1.58065i	0.272263	−	0.962223i	$-0.412228\pi$
$138$	5.10931	−	86.6536i	0.0370240	−	0.627925i
$139$	−113.702	+	156.497i	−0.817998	+	1.12588i	0.172041	+	0.985090i	$0.444964\pi$
$139$	−113.702	+	156.497i	−0.817998	+	1.12588i	−0.990040	+	0.140788i	$0.955036\pi$
$140$	−13.4941	+	114.032i	−0.0963862	+	0.814512i
$141$	−7.17096	+	22.0700i	−0.0508579	+	0.156524i
$142$	76.9663	−	196.653i	0.542016	−	1.38488i
$143$	−66.9784	−	21.8705i	−0.468380	−	0.152940i
$144$	−19.5954	−	248.847i	−0.136079	−	1.72810i
$145$	19.6350	−	60.4302i	0.135413	−	0.416760i
$146$	25.2160	−	6.58032i	0.172712	−	0.0450707i
$147$	−337.649	+	464.734i	−2.29693	+	3.16146i
$148$	−44.0987	+	95.6629i	−0.297964	+	0.646371i
$149$	56.6213	+	174.262i	0.380009	+	1.16955i	0.940037	+	0.341073i	$0.110790\pi$
$149$	56.6213	+	174.262i	0.380009	+	1.16955i	−0.560028	+	0.828473i	$0.689210\pi$
$150$	41.7733	−	26.7414i	0.278488	−	0.178276i
$151$	17.6793	+	24.3334i	0.117081	+	0.161149i	0.863535	−	0.504288i	$-0.168245\pi$
$151$	17.6793	+	24.3334i	0.117081	+	0.161149i	−0.746454	+	0.665437i	$0.768245\pi$
$152$	32.4898	+	234.839i	0.213749	+	1.54499i
$153$	−224.031			−1.46426
$154$	273.389	−	70.9182i	1.77526	−	0.460508i
$155$		−	25.3809i		−	0.163747i
$156$	62.0966	+	110.876i	0.398055	+	0.710743i
$157$	105.878	−	76.9250i	0.674384	−	0.489968i	−0.197106	−	0.980382i	$-0.563154\pi$
$157$	105.878	−	76.9250i	0.674384	−	0.489968i	0.871490	+	0.490414i	$0.163154\pi$
$158$	19.6350	−	12.5695i	0.124272	−	0.0795536i
$159$	−210.872	+	68.5164i	−1.32624	+	0.430921i
$160$	−71.5403	+	1.40868i	−0.447127	+	0.00880427i
$161$	−90.8848	−	66.0316i	−0.564502	−	0.410134i
$162$	−42.5436	+	11.1021i	−0.262615	+	0.0685314i
$163$	43.0279	+	13.9806i	0.263975	+	0.0857706i	0.438014	−	0.898968i	$-0.355682\pi$
$163$	43.0279	+	13.9806i	0.263975	+	0.0857706i	−0.174039	+	0.984739i	$0.555682\pi$
$164$	72.2936	+	66.8246i	0.440814	+	0.407467i
$165$	−98.5944	−	71.8526i	−0.597542	−	0.435470i
$166$	−82.0047	+	209.527i	−0.494004	+	1.26221i
$167$	−212.979	−	69.2009i	−1.27532	−	0.414377i	−0.408391	−	0.912807i	$-0.633910\pi$
$167$	−212.979	−	69.2009i	−1.27532	−	0.414377i	−0.866930	+	0.498430i	$0.833910\pi$
$168$	−449.267	−	240.120i	−2.67421	−	1.42928i
$169$	103.531	+	75.2199i	0.612611	+	0.445088i
$170$	−3.77998	+	64.1084i	−0.0222352	+	0.377108i
$171$	439.702	−	142.868i	2.57136	−	0.835485i
$172$	218.268	−	43.4211i	1.26900	−	0.252448i
$173$	−247.563	+	179.865i	−1.43100	+	1.03968i	−0.441167	+	0.897425i	$0.645435\pi$
$173$	−247.563	+	179.865i	−1.43100	+	1.03968i	−0.989830	+	0.142255i	$0.954565\pi$
$174$	217.901	+	178.823i	1.25230	+	1.02772i
$175$		−	64.1904i		−	0.366802i
$176$	67.1224	+	162.698i	0.381377	+	0.924419i
$177$	−56.1836			−0.317421
$178$	−53.0021	+	64.5846i	−0.297765	+	0.362835i
$179$	70.6796	+	97.2821i	0.394858	+	0.543476i	0.959444	−	0.281899i	$-0.0909642\pi$
$179$	70.6796	+	97.2821i	0.394858	+	0.543476i	−0.564586	+	0.825374i	$0.690964\pi$
$180$	27.2259	+	136.859i	0.151255	+	0.760325i
$181$	22.4125	+	68.9785i	0.123826	+	0.381097i	0.993685	−	0.112203i	$-0.0357906\pi$
$181$	22.4125	+	68.9785i	0.123826	+	0.381097i	−0.869859	+	0.493300i	$0.835791\pi$
$182$	164.179	+	9.68040i	0.902084	+	0.0531890i
$183$	−306.751	+	422.207i	−1.67624	+	2.30714i
$184$	32.9977	−	61.7391i	0.179335	−	0.335539i
$185$	18.1967	−	56.0037i	0.0983605	−	0.302722i
$186$	104.853	+	41.0373i	0.563725	+	0.220631i
$187$	150.299	−	48.5935i	0.803741	−	0.259858i
$188$	−12.7031	+	13.7427i	−0.0675698	+	0.0730997i
$189$	−129.890	+	399.760i	−0.687248	+	2.11513i
$190$	−33.4639	−	128.235i	−0.176126	−	0.674921i
$191$	106.112	−	146.050i	0.555559	−	0.764661i	−0.435195	−	0.900336i	$-0.643320\pi$
$191$	106.112	−	146.050i	0.555559	−	0.764661i	0.990753	+	0.135675i	$0.0433204\pi$
$192$	109.851	−	297.823i	0.572142	−	1.55116i
$193$	−3.12541	−	9.61901i	−0.0161938	−	0.0498394i	0.942633	−	0.333831i	$-0.108341\pi$
$193$	−3.12541	−	9.61901i	−0.0161938	−	0.0498394i	−0.958827	+	0.283991i	$0.908341\pi$
$194$	−17.6307	−	27.5413i	−0.0908800	−	0.141965i
$195$	−41.7564	−	57.4727i	−0.214135	−	0.294732i
$196$	−404.193	+	226.370i	−2.06221	+	1.15495i
$197$	106.790			0.542079			0.271039	−	0.962568i	$-0.412633\pi$
$197$	106.790			0.542079			0.271039	+	0.962568i	$0.412633\pi$
$198$	289.336	−	184.627i	1.46129	−	0.932461i
$199$		−	31.8551i		−	0.160076i	−0.996792	−	0.0800380i	$-0.974496\pi$
$199$		−	31.8551i		−	0.160076i	0.996792	−	0.0800380i	$-0.0255042\pi$
$200$	39.6226	−	5.48176i	0.198113	−	0.0274088i
$201$	35.5940	−	25.8605i	0.177084	−	0.128659i
$202$	−112.545	−	175.809i	−0.557156	−	0.870343i
$203$	346.952	−	112.731i	1.70912	−	0.555327i
$204$	−258.731	−	119.270i	−1.26829	−	0.584658i
$205$	−44.5233	−	32.3480i	−0.217187	−	0.157795i
$206$	−61.5538	−	235.876i	−0.298805	−	1.14503i
$207$	−129.836	−	42.1862i	−0.627226	−	0.203798i
$208$	8.04526	+	102.169i	0.0386791	+	0.491197i
$209$	−264.002	+	191.222i	−1.26317	+	0.914937i
$210$	265.182	+	103.787i	1.26277	+	0.494224i
$211$	256.818	+	83.4454i	1.21715	+	0.395476i	0.846043	−	0.533115i	$-0.178979\pi$
$211$	256.818	+	83.4454i	1.21715	+	0.395476i	0.371106	+	0.928591i	$0.378979\pi$
$212$	−177.572	−	21.0132i	−0.837606	−	0.0991191i
$213$	−423.696	−	307.833i	−1.98918	−	1.44523i
$214$	−310.980	−	18.3361i	−1.45318	−	0.0856829i
$215$	−118.318	+	38.4438i	−0.550316	+	0.178808i
$216$	−257.851	−	46.0378i	−1.19375	−	0.213138i
$217$	117.891	−	85.6525i	0.543275	−	0.394712i
$218$	18.0453	−	21.9888i	0.0827767	−	0.100866i
$219$		−	64.6293i		−	0.295111i
$220$	−47.9508	−	85.9111i	−0.217958	−	0.390505i
$221$	91.9804			0.416201
$222$	201.940	+	165.724i	0.909638	+	0.746504i
$223$	55.5870	+	76.5089i	0.249269	+	0.343089i	0.915255	−	0.402875i	$-0.131989\pi$
$223$	55.5870	+	76.5089i	0.249269	+	0.343089i	−0.665986	+	0.745964i	$0.731989\pi$
$224$	−247.969	−	327.541i	−1.10701	−	1.46224i
$225$	−24.1050	−	74.1876i	−0.107133	−	0.329723i
$226$	−7.80764	+	132.417i	−0.0345471	+	0.585917i
$227$	−122.046	+	167.982i	−0.537649	+	0.740010i	−0.988272	−	0.152704i	$-0.951202\pi$
$227$	−122.046	+	167.982i	−0.537649	+	0.740010i	0.450623	+	0.892714i	$0.351202\pi$
$228$	583.868	+	69.0928i	2.56083	+	0.303038i
$229$	48.3835	−	148.909i	0.211282	−	0.650258i	−0.788115	−	0.615528i	$-0.788943\pi$
$229$	48.3835	−	148.909i	0.211282	−	0.650258i	0.999397	−	0.0347302i	$-0.0110572\pi$
$230$	−14.2626	+	36.4418i	−0.0620113	+	0.158443i
$231$	1.01969	−	700.438i	0.00441425	−	3.03220i
$232$	99.2145	+	204.535i	0.427649	+	0.881615i
$233$	−64.1333	+	197.382i	−0.275250	+	0.847133i	0.713903	+	0.700245i	$0.246926\pi$
$233$	−64.1333	+	197.382i	−0.275250	+	0.847133i	−0.989153	+	0.146888i	$0.953074\pi$
$234$	193.384	−	50.4651i	0.826428	−	0.215663i
$235$	6.14924	−	8.46371i	0.0261670	−	0.0360158i
$236$	−41.1482	−	18.9685i	−0.174357	−	0.0803750i
$237$	−17.8665	−	54.9874i	−0.0753860	−	0.232014i
$238$	−310.531	+	198.788i	−1.30475	+	0.835246i
$239$	71.6788	+	98.6575i	0.299911	+	0.412793i	0.932202	−	0.361939i	$-0.117885\pi$
$239$	71.6788	+	98.6575i	0.299911	+	0.412793i	−0.632290	+	0.774731i	$0.717885\pi$
$240$	−41.4181	+	172.551i	−0.172575	+	0.718964i
$241$	198.797			0.824883			0.412442	−	0.910984i	$-0.364676\pi$
$241$	198.797			0.824883			0.412442	+	0.910984i	$0.364676\pi$
$242$	−154.065	+	186.622i	−0.636633	+	0.771167i
$243$		−	185.629i		−	0.763906i
$244$	−367.205	+	205.655i	−1.50494	+	0.842848i
$245$	209.514	−	152.221i	0.855158	−	0.621309i
$246$	205.623	−	131.631i	0.835867	−	0.535086i
$247$	−180.528	+	58.6572i	−0.730884	+	0.237479i
$248$	62.9381	+	65.4553i	0.253783	+	0.263933i
$249$	451.432	+	327.985i	1.81298	+	1.31721i
$250$	−21.6361	+	5.64611i	−0.0865445	+	0.0225845i
$251$	−420.333	−	136.575i	−1.67463	−	0.544122i	−0.690775	−	0.723069i	$-0.742731\pi$
$251$	−420.333	−	136.575i	−1.67463	−	0.544122i	−0.983859	+	0.178948i	$0.942731\pi$
$252$	−543.810	+	588.316i	−2.15798	+	2.33459i
$253$	96.2555	+	0.140128i	0.380456	+	0.000553866i
$254$	172.060	−	439.624i	0.677402	−	1.73080i
$255$	151.468	+	49.2151i	0.593994	+	0.193000i
$256$	181.004	−	181.035i	0.707047	−	0.707167i
$257$	−183.515	−	133.331i	−0.714065	−	0.518799i	0.170417	−	0.985372i	$-0.445488\pi$
$257$	−183.515	−	133.331i	−0.714065	−	0.518799i	−0.884483	+	0.466573i	$0.845488\pi$
$258$	32.4854	−	550.950i	0.125912	−	2.13547i
$259$	321.537	−	104.474i	1.24146	−	0.403374i
$260$	−11.1781	−	56.1900i	−0.0429928	−	0.216115i
$261$	358.653	−	260.577i	1.37415	−	0.998379i
$262$	169.367	+	138.993i	0.646438	+	0.530506i
$263$		−	108.116i		−	0.411086i	−0.978648	−	0.205543i	$-0.934104\pi$
$263$		−	108.116i		−	0.411086i	0.978648	−	0.205543i	$-0.0658961\pi$
$264$	432.444	−	59.1869i	1.63805	−	0.224193i
$265$	99.9586			0.377202
$266$	482.704	−	588.189i	1.81468	−	2.21124i
$267$	121.788	+	167.627i	0.456136	+	0.627818i
$268$	34.7996	−	6.92283i	0.129849	−	0.0258315i
$269$	−36.1152	−	111.151i	−0.134257	−	0.413201i	0.861217	−	0.508238i	$-0.169703\pi$
$269$	−36.1152	−	111.151i	−0.134257	−	0.413201i	−0.995474	+	0.0950370i	$0.969703\pi$
$270$	146.169	+	8.61845i	0.541365	+	0.0319202i
$271$	23.6068	−	32.4920i	0.0871101	−	0.119897i	−0.763238	−	0.646118i	$-0.776392\pi$
$271$	23.6068	−	32.4920i	0.0871101	−	0.119897i	0.850348	+	0.526221i	$0.176392\pi$
$272$	−149.224	−	174.704i	−0.548619	−	0.642295i
$273$	126.038	−	387.905i	0.461678	−	1.42090i
$274$	−424.063	−	165.970i	−1.54768	−	0.605730i
$275$	32.2634	+	44.5430i	0.117321	+	0.161974i
$276$	−127.487	−	117.843i	−0.461909	−	0.426966i
$277$	−88.8937	+	273.587i	−0.320916	+	0.987677i	0.652335	+	0.757931i	$0.273790\pi$
$277$	−88.8937	+	273.587i	−0.320916	+	0.987677i	−0.973251	+	0.229746i	$0.926210\pi$
$278$	97.6884	+	374.346i	0.351397	+	1.34657i
$279$	104.087	−	143.263i	0.373070	−	0.513487i
$280$	159.176	+	165.542i	0.568486	+	0.591222i
$281$	35.0247	+	107.795i	0.124643	+	0.383612i	0.993836	−	0.110861i	$-0.0353610\pi$
$281$	35.0247	+	107.795i	0.124643	+	0.383612i	−0.869193	+	0.494473i	$0.835361\pi$
$282$	25.0226	+	39.0882i	0.0887326	+	0.138611i
$283$	−153.697	−	211.546i	−0.543099	−	0.747512i	0.445957	−	0.895055i	$-0.352864\pi$
$283$	−153.697	−	211.546i	−0.543099	−	0.747512i	−0.989056	+	0.147543i	$0.952864\pi$
$284$	−206.380	−	368.500i	−0.726692	−	1.29754i
$285$	−328.670			−1.15323
$286$	−118.793	+	75.8023i	−0.415359	+	0.265043i
$287$		−	315.969i		−	1.10094i
$288$	−409.588	−	285.435i	−1.42218	−	0.991093i
$289$	66.9795	−	48.6635i	0.231763	−	0.168386i
$290$	−68.5149	−	107.028i	−0.236258	−	0.369063i
$291$	−77.1287	+	25.0606i	−0.265047	+	0.0861191i
$292$	21.8199	−	47.3337i	0.0747258	−	0.162102i
$293$	277.747	+	201.795i	0.947942	+	0.688720i	0.950319	−	0.311277i	$-0.100757\pi$
$293$	277.747	+	201.795i	0.947942	+	0.688720i	−0.00237714	+	0.999997i	$0.500757\pi$
$294$	290.096	+	1111.66i	0.986721	+	3.78115i
$295$	24.0893	+	7.82707i	0.0816585	+	0.0265325i
$296$	91.9470	+	189.552i	0.310632	+	0.640380i
$297$	−110.794	−	342.686i	−0.373044	−	1.15383i
$298$	341.255	+	133.560i	1.14515	+	0.448189i
$299$	53.3066	+	17.3204i	0.178283	+	0.0579277i
$300$	11.6575	−	98.5116i	0.0388583	−	0.328372i
$301$	−577.852	−	419.834i	−1.91977	−	1.39480i
$302$	60.0513	+	3.54077i	0.198845	+	0.0117244i
$303$	−492.350	+	159.974i	−1.62492	+	0.527968i
$304$	404.291	+	247.726i	1.32991	+	0.814890i
$305$	190.341	−	138.291i	0.624070	−	0.453413i
$306$	−284.244	+	346.360i	−0.928902	+	1.13190i
$307$		−	273.763i		−	0.891735i	−0.895099	−	0.445867i	$-0.852895\pi$
$307$		−	273.763i		−	0.891735i	0.895099	−	0.445867i	$-0.147105\pi$
$308$	237.226	−	512.648i	0.770215	−	1.66444i
$309$	−604.557			−1.95650
$310$	−39.2397	−	32.2025i	−0.126580	−	0.103879i
$311$	−144.072	−	198.299i	−0.463255	−	0.637616i	0.511925	−	0.859030i	$-0.328933\pi$
$311$	−144.072	−	198.299i	−0.463255	−	0.637616i	−0.975180	+	0.221414i	$0.928933\pi$
$312$	250.204	+	44.6726i	0.801937	+	0.143181i
$313$	162.770	+	500.954i	0.520031	+	1.60049i	0.773938	+	0.633262i	$0.218284\pi$
$313$	162.770	+	500.954i	0.520031	+	1.60049i	−0.253907	+	0.967229i	$0.581716\pi$
$314$	15.4064	−	261.292i	0.0490649	−	0.832139i
$315$	263.244	−	362.325i	0.835696	−	1.15024i
$316$	5.47946	−	46.3041i	0.0173400	−	0.146532i
$317$	0.0582233	−	0.179193i	0.000183670	−	0.000565277i	−0.950965	−	0.309300i	$-0.899905\pi$
$317$	0.0582233	−	0.179193i	0.000183670	−	0.000565277i	0.951148	+	0.308734i	$0.0999054\pi$
$318$	−161.619	+	412.947i	−0.508236	+	1.29857i
$319$	−184.095	+	252.611i	−0.577101	+	0.791885i
$320$	−88.5903	+	112.391i	−0.276845	+	0.351222i
$321$	−238.735	+	734.751i	−0.743723	+	2.28894i
$322$	−217.399	+	56.7320i	−0.675152	+	0.176186i
$323$	250.132	−	344.278i	0.774403	−	1.06587i
$324$	−36.8138	+	79.8598i	−0.113623	+	0.246481i
$325$	9.89678	+	30.4592i	0.0304516	+	0.0937205i
$326$	76.2070	−	48.7844i	0.233764	−	0.149645i
$327$	−41.4646	−	57.0711i	−0.126803	−	0.174530i
$328$	195.037	−	26.9832i	0.594625	−	0.0822660i
$329$	60.0645			0.182567
$330$	−236.180	+	61.2660i	−0.715698	+	0.185655i
$331$		−	271.783i		−	0.821096i	−0.911839	−	0.410548i	$-0.865338\pi$
$331$		−	271.783i		−	0.821096i	0.911839	−	0.410548i	$-0.134662\pi$
$332$	219.891	+	392.623i	0.662321	+	1.18260i
$333$	332.382	−	241.490i	0.998144	−	0.725194i
$334$	−377.208	+	241.472i	−1.12936	+	0.722970i
$335$	−18.8640	+	6.12927i	−0.0563103	+	0.0182963i
$336$	−941.250	+	389.926i	−2.80134	+	1.16049i
$337$	−308.228	−	223.941i	−0.914623	−	0.664512i	0.0275571	−	0.999620i	$-0.491227\pi$
$337$	−308.228	−	223.941i	−0.914623	−	0.664512i	−0.942180	+	0.335108i	$0.891227\pi$
$338$	247.650	−	64.6262i	0.732692	−	0.191202i
$339$	312.861	+	101.655i	0.922895	+	0.299867i
$340$	94.3179	+	87.1828i	0.277405	+	0.256420i
$341$	−38.7559	+	118.690i	−0.113654	+	0.348065i
$342$	337.002	−	861.061i	0.985387	−	2.51772i
$343$	815.811	+	265.073i	2.37846	+	0.772808i
$344$	209.802	−	392.542i	0.609889	−	1.14111i
$345$	78.5151	+	57.0445i	0.227580	+	0.165346i
$346$	−36.0229	+	610.947i	−0.104112	+	1.76574i
$347$	−503.089	+	163.463i	−1.44982	+	0.471076i	−0.924945	−	0.380101i	$-0.875889\pi$
$347$	−503.089	+	163.463i	−1.44982	+	0.471076i	−0.524878	+	0.851177i	$0.675889\pi$
$348$	552.932	−	109.997i	1.58889	−	0.316084i
$349$	−191.374	+	139.042i	−0.548351	+	0.398400i	−0.827177	−	0.561941i	$-0.810055\pi$
$349$	−191.374	+	139.042i	−0.548351	+	0.398400i	0.278826	+	0.960342i	$0.410055\pi$
$350$	−99.2406	−	81.4429i	−0.283545	−	0.232694i
$351$		−	209.717i		−	0.597485i
$352$	336.699	+	102.653i	0.956532	+	0.291627i
$353$	−224.328			−0.635491			−0.317745	−	0.948176i	$-0.602926\pi$
$353$	−224.328			−0.635491			−0.317745	+	0.948176i	$0.602926\pi$
$354$	−71.2840	+	86.8617i	−0.201367	+	0.245372i
$355$	138.779	+	191.013i	0.390927	+	0.538064i
$356$	32.6026	+	163.886i	0.0915804	+	0.460354i
$357$	282.562	+	869.635i	0.791489	+	2.43595i
$358$	240.078	+	14.1556i	0.670608	+	0.0395407i
$359$	−130.744	+	179.953i	−0.364189	+	0.501263i	−0.951310	−	0.308236i	$-0.900261\pi$
$359$	−130.744	+	179.953i	−0.364189	+	0.501263i	0.587121	+	0.809499i	$0.300261\pi$
$360$	246.131	+	131.550i	0.683698	+	0.365416i
$361$	−159.825	+	491.889i	−0.442727	+	1.36257i
$362$	135.079	+	52.8674i	0.373148	+	0.146043i
$363$	351.346	+	486.560i	0.967896	+	1.34038i
$364$	223.272	−	241.545i	0.613385	−	0.663584i
$365$	−9.00367	+	27.7104i	−0.0246676	+	0.0759190i
$366$	263.549	+	1009.93i	0.720080	+	2.75937i
$367$	−212.459	+	292.424i	−0.578906	+	0.796796i	−0.993575	−	0.113176i	$-0.963897\pi$
$367$	−212.459	+	292.424i	−0.578906	+	0.796796i	0.414669	+	0.909972i	$0.363897\pi$
$368$	−53.5843	−	129.348i	−0.145610	−	0.351490i
$369$	−118.654	−	365.179i	−0.321555	−	0.989644i
$370$	−63.4962	−	99.1885i	−0.171611	−	0.268077i
$371$	337.329	+	464.294i	0.909243	+	1.25147i
$372$	196.479	−	110.039i	0.528170	−	0.295804i
$373$	417.447			1.11916			0.559580	−	0.828776i	$-0.310962\pi$
$373$	417.447			1.11916			0.559580	+	0.828776i	$0.310962\pi$
$374$	115.568	−	294.022i	0.309006	−	0.786155i
$375$			55.4539i			0.147877i
$376$	5.12942	+	37.0758i	0.0136421	+	0.0986059i
$377$	−147.252	+	106.985i	−0.390589	+	0.283780i
$378$	453.242	+	708.018i	1.19905	+	1.87306i
$379$	−311.436	+	101.192i	−0.821731	+	0.266997i	−0.689558	−	0.724230i	$-0.742195\pi$
$379$	−311.436	+	101.192i	−0.821731	+	0.266997i	−0.132173	+	0.991227i	$0.542195\pi$
$380$	−240.714	−	110.964i	−0.633457	−	0.292012i
$381$	−947.184	−	688.169i	−2.48605	−	1.80622i
$382$	−91.1674	−	349.357i	−0.238658	−	0.914546i
$383$	−465.729	−	151.325i	−1.21600	−	0.395103i	−0.370378	−	0.928881i	$-0.620772\pi$
$383$	−465.729	−	151.325i	−1.21600	−	0.395103i	−0.845625	+	0.533777i	$0.820772\pi$
$384$	−321.069	−	547.703i	−0.836118	−	1.42631i
$385$	−98.0170	+	300.178i	−0.254590	+	0.779682i
$386$	−18.8367	−	7.37233i	−0.0487998	−	0.0190993i
$387$	−825.506	−	268.223i	−2.13309	−	0.693083i
$388$	−64.9491	−	7.68583i	−0.167395	−	0.0198088i
$389$	−276.285	−	200.733i	−0.710244	−	0.516022i	0.173009	−	0.984920i	$-0.444651\pi$
$389$	−276.285	−	200.733i	−0.710244	−	0.516022i	−0.883252	+	0.468898i	$0.844651\pi$
$390$	−141.834	−	8.36287i	−0.363677	−	0.0214433i
$391$	−119.507	+	38.8302i	−0.305644	+	0.0993099i
$392$	−162.852	+	912.107i	−0.415438	+	2.32680i
$393$	439.586	−	319.378i	1.11854	−	0.812666i
$394$	135.491	−	165.100i	0.343887	−	0.419036i
$395$			26.0654i			0.0659884i
$396$	81.6611	−	681.573i	0.206215	−	1.72114i
$397$	−598.007			−1.50632			−0.753158	−	0.657840i	$-0.771470\pi$
$397$	−598.007			−1.50632			−0.753158	+	0.657840i	$0.771470\pi$
$398$	−49.2491	−	40.4168i	−0.123741	−	0.101550i
$399$	−1109.16	−	1526.63i	−2.77985	−	3.82613i
$400$	41.7970	−	68.2130i	0.104492	−	0.170532i
$401$	−22.5191	−	69.3067i	−0.0561574	−	0.172835i	0.919044	−	0.394156i	$-0.128963\pi$
$401$	−22.5191	−	69.3067i	−0.0561574	−	0.172835i	−0.975201	+	0.221321i	$0.928963\pi$
$402$	5.17929	−	87.8406i	0.0128838	−	0.218509i
$403$	−42.7348	+	58.8194i	−0.106042	+	0.145954i
$404$	−414.601	−	49.0623i	−1.02624	−	0.121441i
$405$	15.1907	−	46.7521i	0.0375078	−	0.115437i
$406$	265.915	−	679.430i	0.654964	−	1.67347i
$407$	−170.610	+	234.108i	−0.419190	+	0.575203i
$408$	−512.667	+	248.681i	−1.25654	+	0.609513i
$409$	166.810	−	513.388i	0.407848	−	1.25523i	−0.510646	−	0.859791i	$-0.670594\pi$
$409$	166.810	−	513.388i	0.407848	−	1.25523i	0.918494	−	0.395435i	$-0.129406\pi$
$410$	−106.501	+	27.7923i	−0.259758	+	0.0677860i
$411$	−663.811	+	913.658i	−1.61511	+	2.22301i
$412$	−442.771	−	204.109i	−1.07469	−	0.495409i
$413$	44.9381	+	138.305i	0.108809	+	0.334880i
$414$	−229.953	+	147.206i	−0.555442	+	0.355570i
$415$	−147.864	−	203.517i	−0.356298	−	0.490402i
$416$	168.164	+	117.191i	0.404241	+	0.281709i
$417$	959.457			2.30086
$418$	−39.3218	+	650.772i	−0.0940714	+	1.55687i
$419$			56.9312i			0.135874i	0.997690	+	0.0679370i	$0.0216417\pi$
$419$			56.9312i			0.135874i	−0.997690	+	0.0679370i	$0.978358\pi$
$420$	496.913	−	278.299i	1.18313	−	0.662616i
$421$	−271.366	+	197.159i	−0.644574	+	0.468310i	−0.861418	−	0.507896i	$-0.830423\pi$
$421$	−271.366	+	197.159i	−0.644574	+	0.468310i	0.216845	+	0.976206i	$0.430423\pi$
$422$	454.853	−	291.177i	1.07785	−	0.689993i
$423$	69.4191	−	22.5556i	0.164111	−	0.0533230i
$424$	−257.786	+	247.872i	−0.607985	+	0.584604i
$425$	−58.0873	−	42.2029i	−0.136676	−	0.0993009i
$426$	−1013.49	+	264.479i	−2.37909	+	0.620843i
$427$	1284.69	+	417.420i	3.00863	+	0.977564i
$428$	−422.911	+	457.522i	−0.988109	+	1.06898i
$429$	107.509	+	332.524i	0.250603	+	0.775114i
$430$	−90.6827	+	231.700i	−0.210890	+	0.538837i
$431$	479.247	+	155.717i	1.11194	+	0.361292i	0.806687	−	0.590979i	$-0.201258\pi$
$431$	479.247	+	155.717i	1.11194	+	0.361292i	0.305255	+	0.952271i	$0.401258\pi$
$432$	−398.329	+	340.235i	−0.922059	+	0.787581i
$433$	−147.085	−	106.863i	−0.339688	−	0.246798i	0.404842	−	0.914386i	$-0.367326\pi$
$433$	−147.085	−	106.863i	−0.339688	−	0.246798i	−0.744530	+	0.667589i	$0.767326\pi$
$434$	17.1543	−	290.936i	0.0395260	−	0.670360i
$435$	−299.731	+	97.3884i	−0.689036	+	0.223881i
$436$	−11.1000	−	55.7974i	−0.0254588	−	0.127976i
$437$	209.792	−	152.423i	0.480073	−	0.348793i
$438$	−99.9191	−	81.9997i	−0.228126	−	0.187214i
$439$		−	50.4397i		−	0.114897i	−0.998348	−	0.0574484i	$-0.981704\pi$
$439$		−	50.4397i		−	0.114897i	0.998348	−	0.0574484i	$-0.0182965\pi$
$440$	−193.660	−	34.8679i	−0.440137	−	0.0792452i
$441$	1806.86			4.09719
$442$	116.702	−	142.205i	0.264032	−	0.321730i
$443$	112.476	+	154.810i	0.253896	+	0.349459i	0.916871	−	0.399183i	$-0.130706\pi$
$443$	112.476	+	154.810i	0.253896	+	0.349459i	−0.662975	+	0.748642i	$0.730706\pi$
$444$	512.430	−	101.940i	1.15412	−	0.229595i
$445$	−28.8654	−	88.8385i	−0.0648660	−	0.199637i
$446$	188.813	+	11.1328i	0.423346	+	0.0249615i
$447$	534.187	−	735.245i	1.19505	−	1.64484i
$448$	−821.006	−	32.2049i	−1.83260	−	0.0718858i
$449$	57.2614	−	176.232i	0.127531	−	0.392500i	−0.866823	−	0.498616i	$-0.833842\pi$
$449$	57.2614	−	176.232i	0.127531	−	0.392500i	0.994354	+	0.106117i	$0.0338417\pi$
$450$	−145.280	−	56.8598i	−0.322845	−	0.126355i
$451$	158.812	+	219.257i	0.352134	+	0.486157i
$452$	194.816	+	180.078i	0.431008	+	0.398403i
$453$	46.1005	−	141.883i	0.101767	−	0.313207i
$454$	104.858	+	401.819i	0.230964	+	0.885063i
$455$	−108.080	+	148.759i	−0.237539	+	0.326944i
$456$	847.614	−	815.018i	1.85880	−	1.78732i
$457$	−113.033	−	347.879i	−0.247337	−	0.761224i	−0.995243	−	0.0974200i	$-0.968941\pi$
$457$	−113.033	−	347.879i	−0.247337	−	0.761224i	0.747907	−	0.663804i	$-0.231059\pi$
$458$	−168.831	−	263.734i	−0.368627	−	0.575839i
$459$	276.353	+	380.368i	0.602077	+	0.828688i
$460$	38.2443	+	68.2868i	0.0831399	+	0.148449i
$461$	−698.303			−1.51476			−0.757379	−	0.652976i	$-0.773520\pi$
$461$	−698.303			−1.51476			−0.757379	+	0.652976i	$0.773520\pi$
$462$	−1081.61	−	890.271i	−2.34114	−	1.92699i
$463$			120.489i			0.260236i	0.991499	+	0.130118i	$0.0415356\pi$
$463$			120.489i			0.260236i	−0.991499	+	0.130118i	$0.958464\pi$
$464$	442.098	+	106.118i	0.952797	+	0.228703i
$465$	−101.845	+	73.9950i	−0.219022	+	0.159129i
$466$	223.789	+	349.584i	0.480234	+	0.750181i
$467$	598.212	−	194.371i	1.28097	−	0.416212i	0.412047	−	0.911163i	$-0.364814\pi$
$467$	598.212	−	194.371i	1.28097	−	0.416212i	0.868921	+	0.494951i	$0.164814\pi$
$468$	167.339	−	363.007i	0.357562	−	0.775656i
$469$	−92.1297	−	66.9361i	−0.196439	−	0.142721i
$470$	−5.28321	−	20.2454i	−0.0112409	−	0.0430754i
$471$	−617.351	−	200.590i	−1.31073	−	0.425880i
$472$	−81.5336	+	39.5498i	−0.172741	+	0.0837920i
$473$	612.000	+	0.890944i	1.29387	+	0.00188360i
$474$	−107.681	−	42.1441i	−0.227175	−	0.0889117i
$475$	140.920	+	45.7878i	0.296674	+	0.0963954i
$476$	−86.6586	+	732.308i	−0.182056	+	1.53846i
$477$	564.219	+	409.929i	1.18285	+	0.859390i
$478$	243.472	+	14.3557i	0.509355	+	0.0300328i
$479$	203.416	−	66.0938i	0.424667	−	0.137983i	−0.0888833	−	0.996042i	$-0.528330\pi$
$479$	203.416	−	66.0938i	0.424667	−	0.137983i	0.513551	+	0.858059i	$0.328330\pi$
$480$	214.220	+	282.962i	0.446292	+	0.589504i
$481$	−136.466	+	99.1483i	−0.283713	+	0.206130i
$482$	252.227	−	307.347i	0.523294	−	0.637649i
$483$			557.199i			1.15362i
$484$	93.0513	+	474.971i	0.192255	+	0.981345i
$485$	36.5610			0.0753834
$486$	−286.989	−	235.521i	−0.590513	−	0.484611i
$487$	110.450	+	152.021i	0.226796	+	0.312158i	0.907217	−	0.420664i	$-0.138203\pi$
$487$	110.450	+	152.021i	0.226796	+	0.312158i	−0.680420	+	0.732822i	$0.738203\pi$
$488$	−147.949	+	828.640i	−0.303174	+	1.69803i
$489$	−69.3431	−	213.416i	−0.141806	−	0.436434i
$490$	30.4864	−	517.049i	0.0622172	−	1.05520i
$491$	206.404	−	284.091i	0.420375	−	0.578597i	−0.545335	−	0.838218i	$-0.683598\pi$
$491$	206.404	−	284.091i	0.420375	−	0.578597i	0.965711	+	0.259621i	$0.0835977\pi$
$492$	57.3825	−	484.911i	0.116631	−	0.985591i
$493$	126.095	−	388.081i	0.255771	−	0.787183i
$494$	−138.363	+	353.526i	−0.280087	+	0.715639i
$495$	−0.558639	+	383.736i	−0.00112856	+	0.775223i
$496$	181.050	−	14.2567i	0.365021	−	0.0287434i
$497$	−418.892	+	1289.22i	−0.842842	+	2.59400i
$498$	1079.84	−	281.793i	2.16835	−	0.565849i
$499$	63.5297	−	87.4412i	0.127314	−	0.175233i	−0.740602	−	0.671944i	$-0.765459\pi$
$499$	63.5297	−	87.4412i	0.127314	−	0.175233i	0.867916	+	0.496712i	$0.165459\pi$
$500$	−18.7222	+	40.6138i	−0.0374443	+	0.0812276i
$501$	343.233	+	1056.36i	0.685096	+	2.10851i
$502$	−744.455	+	476.568i	−1.48298	+	0.949338i
$503$	229.591	+	316.005i	0.456444	+	0.628241i	0.973767	−	0.227549i	$-0.0730713\pi$
$503$	229.591	+	316.005i	0.456444	+	0.628241i	−0.517323	+	0.855790i	$0.673071\pi$
$504$	219.586	+	1587.19i	0.435687	+	3.14918i
$505$	233.386			0.462151
$506$	122.343	−	148.636i	0.241784	−	0.293748i
$507$		−	634.733i		−	1.25194i
$508$	−461.369	−	823.792i	−0.908206	−	1.62164i
$509$	−200.073	+	145.361i	−0.393070	+	0.285582i	−0.766712	−	0.641991i	$-0.778109\pi$
$509$	−200.073	+	145.361i	−0.393070	+	0.285582i	0.373642	+	0.927573i	$0.378109\pi$
$510$	268.267	−	171.733i	0.526013	−	0.336731i
$511$	−159.096	+	51.6934i	−0.311342	+	0.101161i
$512$	−50.2336	−	509.530i	−0.0981126	−	0.995175i
$513$	−784.961	−	570.307i	−1.53014	−	1.11171i
$514$	−438.973	+	114.553i	−0.854033	+	0.222867i
$515$	259.210	+	84.2224i	0.503320	+	0.163539i
$516$	−810.572	−	749.253i	−1.57088	−	1.45204i
$517$	−41.6799	+	30.1896i	−0.0806188	+	0.0583939i
$518$	246.437	−	629.661i	0.475747	−	1.21556i
$519$	1443.48	+	469.015i	2.78127	+	0.903690i
$520$	−101.054	−	54.0104i	−0.194335	−	0.103866i
$521$	326.256	+	237.039i	0.626212	+	0.454970i	0.855086	−	0.518486i	$-0.173504\pi$
$521$	326.256	+	237.039i	0.626212	+	0.454970i	−0.228874	+	0.973456i	$0.573504\pi$
$522$	52.1878	−	885.103i	0.0999766	−	1.69560i
$523$	−266.727	+	86.6649i	−0.509994	+	0.165707i	−0.552700	−	0.833381i	$-0.686402\pi$
$523$	−266.727	+	86.6649i	−0.509994	+	0.165707i	0.0427054	+	0.999088i	$0.486402\pi$
$524$	429.775	−	85.4971i	0.820181	−	0.163162i
$525$	−257.576	+	187.140i	−0.490621	+	0.356457i
$526$	−167.151	−	137.174i	−0.317777	−	0.260787i
$527$		−	162.995i		−	0.309289i
$528$	457.167	−	743.668i	0.865847	−	1.40846i
$529$	452.429			0.855253
$530$	126.824	−	154.539i	0.239291	−	0.291584i
$531$	103.874	+	142.970i	0.195619	+	0.269247i
$532$	−296.920	−	1492.55i	−0.558121	−	2.80555i
$533$	48.7156	+	149.931i	0.0913989	+	0.281297i
$534$	413.679	+	24.3915i	0.774680	+	0.0456770i
$535$	204.720	−	281.773i	0.382654	−	0.526678i
$536$	33.4497	−	62.5848i	0.0624062	−	0.116763i
$537$	184.304	−	567.230i	0.343211	−	1.05629i
$538$	−217.665	−	85.1899i	−0.404582	−	0.158346i
$539$	−1212.20	+	391.917i	−2.24898	+	0.727119i
$540$	198.779	−	215.047i	0.368109	−	0.398235i
$541$	259.554	−	798.825i	0.479767	−	1.47657i	−0.359652	−	0.933087i	$-0.617104\pi$
$541$	259.554	−	798.825i	0.479767	−	1.47657i	0.839419	−	0.543485i	$-0.182896\pi$
$542$	−20.2821	−	77.7219i	−0.0374209	−	0.143398i
$543$	211.448	−	291.033i	0.389407	−	0.535973i
$544$	−459.430	+	9.04653i	−0.844540	+	0.0166296i
$545$	9.82764	+	30.2464i	0.0180324	+	0.0554979i
$546$	−439.801	−	687.021i	−0.805497	−	1.25828i
$547$	230.711	+	317.546i	0.421775	+	0.580523i	0.966041	−	0.258390i	$-0.0831919\pi$
$547$	230.711	+	317.546i	0.421775	+	0.580523i	−0.544266	+	0.838913i	$0.683192\pi$
$548$	−794.634	+	445.039i	−1.45006	+	0.812114i
$549$	1641.52			2.99001
$550$	109.800	+	6.63447i	0.199636	+	0.0120627i
$551$			842.093i			1.52830i
$552$	−343.941	+	47.5839i	−0.623081	+	0.0862028i
$553$	−121.070	+	87.9627i	−0.218934	+	0.159065i
$554$	310.189	+	484.551i	0.559907	+	0.874641i
$555$	−277.775	+	90.2547i	−0.500496	+	0.162621i
$556$	702.695	+	323.929i	1.26384	+	0.582606i
$557$	357.844	+	259.989i	0.642449	+	0.466766i	0.860691	−	0.509128i	$-0.170032\pi$
$557$	357.844	+	259.989i	0.642449	+	0.466766i	−0.218242	+	0.975895i	$0.570032\pi$
$558$	−89.4274	−	342.689i	−0.160264	−	0.614138i
$559$	338.928	+	110.124i	0.606311	+	0.197002i
$560$	457.892	−	36.0565i	0.817664	−	0.0643866i
$561$	−633.171	−	461.435i	−1.12865	−	0.822523i
$562$	211.093	+	82.6176i	0.375610	+	0.147006i
$563$	−683.142	−	221.966i	−1.21340	−	0.394256i	−0.368724	−	0.929539i	$-0.620205\pi$
$563$	−683.142	−	221.966i	−1.21340	−	0.394256i	−0.844673	+	0.535283i	$0.820205\pi$
$564$	92.1797	+	10.9082i	0.163439	+	0.0193408i
$565$	−119.981	−	87.1710i	−0.212355	−	0.154285i
$566$	−522.063	−	30.7821i	−0.922373	−	0.0543853i
$567$	268.421	−	87.2152i	0.473405	−	0.153819i
$568$	−831.564	−	148.471i	−1.46402	−	0.261393i
$569$	−107.380	+	78.0160i	−0.188717	+	0.137111i	−0.678132	−	0.734940i	$-0.737210\pi$
$569$	−107.380	+	78.0160i	−0.188717	+	0.137111i	0.489415	+	0.872051i	$0.337210\pi$
$570$	−417.006	+	508.135i	−0.731590	+	0.891464i
$571$		−	520.179i		−	0.910997i	−0.890237	−	0.455499i	$-0.849461\pi$
$571$		−	520.179i		−	0.910997i	0.890237	−	0.455499i	$-0.150539\pi$
$572$	−33.5276	+	279.833i	−0.0586146	+	0.489219i
$573$	−895.410			−1.56267
$574$	−488.499	−	400.892i	−0.851043	−	0.698418i
$575$	−25.7171	−	35.3965i	−0.0447254	−	0.0615592i
$576$	−960.965	+	271.086i	−1.66834	+	0.470636i
$577$	−185.268	−	570.197i	−0.321089	−	0.988209i	−0.973175	−	0.230065i	$-0.926106\pi$
$577$	−185.268	−	570.197i	−0.321089	−	0.988209i	0.652087	−	0.758144i	$-0.273894\pi$
$578$	9.74622	−	165.295i	0.0168620	−	0.285978i
$579$	−29.4863	+	40.5844i	−0.0509262	+	0.0700939i
$580$	−252.399	−	29.8679i	−0.435171	−	0.0514965i
$581$	446.314	−	1373.61i	0.768183	−	2.36422i
$582$	−59.1140	+	151.040i	−0.101570	+	0.259519i
$583$	−467.443	−	152.634i	−0.801788	−	0.261808i
$584$	−45.4951	−	93.7900i	−0.0779026	−	0.160599i
$585$	−69.0500	+	212.514i	−0.118034	+	0.363272i
$586$	664.379	−	173.375i	1.13375	−	0.295862i
$587$	−321.642	+	442.702i	−0.547941	+	0.754176i	−0.989731	−	0.142942i	$-0.954344\pi$
$587$	−321.642	+	442.702i	−0.547941	+	0.754176i	0.441790	+	0.897119i	$0.354344\pi$
$588$	2086.73	+	961.941i	3.54886	+	1.63595i
$589$	103.944	+	319.908i	0.176476	+	0.543138i
$590$	42.6647	−	27.3121i	0.0723130	−	0.0462916i
$591$	−311.333	−	428.512i	−0.526789	−	0.725063i
$592$	409.714	+	98.3452i	0.692085	+	0.166124i
$593$	−413.219			−0.696828			−0.348414	−	0.937341i	$-0.613280\pi$
$593$	−413.219			−0.696828			−0.348414	+	0.937341i	$0.613280\pi$
$594$	−670.377	−	263.498i	−1.12858	−	0.443600i
$595$		−	412.229i		−	0.692822i
$596$	639.463	−	358.135i	1.07292	−	0.600897i
$597$	−127.824	+	92.8699i	−0.214111	+	0.155561i
$598$	94.4118	−	60.4383i	0.157879	−	0.101067i
$599$	527.925	−	171.533i	0.881344	−	0.286366i	0.166829	−	0.985986i	$-0.446647\pi$
$599$	527.925	−	171.533i	0.881344	−	0.286366i	0.714515	+	0.699620i	$0.246647\pi$
$600$	−137.512	−	143.011i	−0.229186	−	0.238352i
$601$	805.551	+	585.267i	1.34035	+	0.973822i	0.999431	+	0.0337291i	$0.0107384\pi$
$601$	805.551	+	585.267i	1.34035	+	0.973822i	0.340919	+	0.940093i	$0.389262\pi$
$602$	−1382.24	+	360.706i	−2.29608	+	0.599180i
$603$	−131.614	−	42.7641i	−0.218266	−	0.0709188i
$604$	81.6654	−	88.3489i	0.135208	−	0.146273i
$605$	−82.8594	−	257.564i	−0.136958	−	0.425726i
$606$	−377.353	+	964.160i	−0.622695	+	1.59102i
$607$	−172.602	−	56.0817i	−0.284352	−	0.0923917i	0.163368	−	0.986565i	$-0.447764\pi$
$607$	−172.602	−	56.0817i	−0.284352	−	0.0923917i	−0.447721	+	0.894173i	$0.647764\pi$
$608$	895.947	−	310.741i	1.47360	−	0.511087i
$609$	−1463.85	−	1063.55i	−2.40370	−	1.74639i
$610$	27.6966	−	469.734i	0.0454043	−	0.770055i
$611$	−28.5014	+	9.26066i	−0.0466471	+	0.0151566i
$612$	174.844	+	878.902i	0.285693	+	1.43611i
$613$	−339.424	+	246.606i	−0.553710	+	0.402294i	−0.829151	−	0.559024i	$-0.811176\pi$
$613$	−339.424	+	246.606i	−0.553710	+	0.402294i	0.275442	+	0.961318i	$0.411176\pi$
$614$	−423.246	−	347.342i	−0.689326	−	0.565703i
$615$			272.965i			0.443845i
$616$	−491.586	−	1017.19i	−0.798029	−	1.65129i
$617$	−542.517			−0.879282			−0.439641	−	0.898174i	$-0.644894\pi$
$617$	−542.517			−0.879282			−0.439641	+	0.898174i	$0.644894\pi$
$618$	−767.044	+	934.666i	−1.24117	+	1.51241i
$619$	−650.368	−	895.155i	−1.05068	−	1.44613i	−0.888222	−	0.459415i	$-0.848059\pi$
$619$	−650.368	−	895.155i	−1.05068	−	1.44613i	−0.162454	−	0.986716i	$-0.551941\pi$
$620$	−99.5723	+	19.8084i	−0.160600	+	0.0319490i
$621$	88.5336	+	272.479i	0.142566	+	0.438774i
$622$	−489.371	−	28.8545i	−0.786771	−	0.0463899i
$623$	315.231	−	433.878i	0.505989	−	0.696434i
$624$	386.517	−	330.145i	0.619418	−	0.529079i
$625$	7.72542	−	23.7764i	0.0123607	−	0.0380423i
$626$	981.009	+	383.947i	1.56711	+	0.613334i
$627$	1536.98	+	501.869i	2.45132	+	0.800430i
$628$	−384.419	−	355.338i	−0.612132	−	0.565824i
$629$	116.859	−	359.654i	0.185785	−	0.571787i
$630$	−226.170	−	866.691i	−0.359000	−	1.37570i
$631$	−7.09810	+	9.76970i	−0.0112490	+	0.0154829i	−0.814604	−	0.580017i	$-0.803046\pi$
$631$	−7.09810	+	9.76970i	−0.0112490	+	0.0154829i	0.803355	+	0.595500i	$0.203046\pi$
$632$	−64.6356	−	67.2207i	−0.102272	−	0.106362i
$633$	−413.885	−	1273.81i	−0.653846	−	2.01233i
$634$	−0.203166	−	0.317370i	−0.000320452	−	0.000500583i
$635$	310.244	+	427.014i	0.488573	+	0.672463i
$636$	433.372	+	773.803i	0.681403	+	1.21667i
$637$	−741.842			−1.16459
$638$	156.971	+	605.123i	0.246036	+	0.948469i
$639$			1647.31i			2.57795i
$640$	61.3597	+	279.562i	0.0958745	+	0.436816i
$641$	−545.081	+	396.024i	−0.850360	+	0.617822i	−0.925245	−	0.379370i	$-0.876141\pi$
$641$	−545.081	+	396.024i	−0.850360	+	0.617822i	0.0748856	+	0.997192i	$0.476141\pi$
$642$	833.050	+	1301.32i	1.29759	+	2.02698i
$643$	836.845	−	271.907i	1.30147	−	0.422873i	0.425377	−	0.905016i	$-0.360141\pi$
$643$	836.845	−	271.907i	1.30147	−	0.422873i	0.876093	+	0.482143i	$0.160141\pi$
$644$	−188.120	+	408.086i	−0.292112	+	0.633674i
$645$	499.205	+	362.693i	0.773961	+	0.562315i
$646$	−214.905	−	823.522i	−0.332670	−	1.27480i
$647$	−130.892	−	42.5294i	−0.202306	−	0.0657333i	0.206111	−	0.978529i	$-0.433919\pi$
$647$	−130.892	−	42.5294i	−0.202306	−	0.0657333i	−0.408417	+	0.912795i	$0.633919\pi$
$648$	76.7578	+	158.239i	0.118453	+	0.244196i
$649$	−100.698	−	73.3859i	−0.155159	−	0.113075i
$650$	59.6477	+	23.3449i	0.0917656	+	0.0359153i
$651$	−687.393	−	223.347i	−1.05590	−	0.343084i
$652$	21.2668	−	179.715i	0.0326178	−	0.275636i
$653$	338.944	+	246.257i	0.519057	+	0.377117i	0.816249	−	0.577701i	$-0.196050\pi$
$653$	338.944	+	246.257i	0.519057	+	0.377117i	−0.297191	+	0.954818i	$0.596050\pi$
$654$	−140.843	−	8.30444i	−0.215356	−	0.0126979i
$655$	−232.970	+	75.6966i	−0.355680	+	0.115567i
$656$	205.740	−	335.770i	0.313628	−	0.511844i
$657$	−164.462	+	119.488i	−0.250322	+	0.181870i
$658$	76.2081	−	92.8618i	0.115818	−	0.141127i
$659$			66.4070i			0.100769i	0.998730	+	0.0503847i	$0.0160447\pi$
$659$			66.4070i			0.100769i	−0.998730	+	0.0503847i	$0.983955\pi$
$660$	−204.939	+	442.875i	−0.310514	+	0.671023i
$661$	−968.455			−1.46514			−0.732568	−	0.680694i	$-0.761678\pi$
$661$	−968.455			−1.46514			−0.732568	+	0.680694i	$0.761678\pi$
$662$	−420.185	−	344.830i	−0.634721	−	0.520891i
$663$	−268.158	−	369.088i	−0.404462	−	0.556694i
$664$	886.000	+	158.190i	1.33434	+	0.238238i
$665$	262.885	+	809.075i	0.395315	+	1.21665i
$666$	48.3650	−	820.269i	0.0726202	−	1.23164i
$667$	146.155	−	201.165i	0.219123	−	0.301597i
$668$	−105.266	+	889.549i	−0.157584	+	1.33166i
$669$	144.949	−	446.106i	0.216665	−	0.666825i
$670$	−14.4580	+	36.9410i	−0.0215791	+	0.0551358i
$671$	−1101.27	+	356.053i	−1.64124	+	0.530630i
$672$	−591.392	+	1949.93i	−0.880047	+	2.90168i
$673$	−19.5557	+	60.1861i	−0.0290574	+	0.0894296i	−0.964533	−	0.263960i	$-0.914971\pi$
$673$	−19.5557	+	60.1861i	−0.0290574	+	0.0894296i	0.935476	+	0.353390i	$0.114971\pi$
$674$	−737.290	+	192.402i	−1.09390	+	0.285462i
$675$	−96.2236	+	132.440i	−0.142553	+	0.196208i
$676$	214.297	−	464.871i	0.317007	−	0.687679i
$677$	141.380	+	435.122i	0.208832	+	0.642720i	0.999534	+	0.0305186i	$0.00971589\pi$
$677$	141.380	+	435.122i	0.208832	+	0.642720i	−0.790702	+	0.612202i	$0.790284\pi$
$678$	554.111	−	354.718i	0.817273	−	0.523183i
$679$	123.382	+	169.821i	0.181711	+	0.250104i
$680$	254.455	−	35.2037i	0.374199	−	0.0517702i
$681$	1029.87			1.51229
$682$	134.327	+	210.508i	0.196960	+	0.308663i
$683$		−	783.361i		−	1.14694i	−0.819226	−	0.573471i	$-0.805597\pi$
$683$		−	783.361i		−	1.14694i	0.819226	−	0.573471i	$-0.194403\pi$
$684$	−903.652	−	1613.51i	−1.32113	−	2.35893i
$685$	411.900	−	299.263i	0.601313	−	0.436880i
$686$	1444.89	−	924.955i	2.10625	−	1.34833i
$687$	−738.582	+	239.980i	−1.07508	+	0.349315i
$688$	−340.693	−	822.407i	−0.495193	−	1.19536i
$689$	−231.651	−	168.304i	−0.336214	−	0.244273i
$690$	187.810	−	49.0106i	0.272189	−	0.0710299i
$691$	303.968	+	98.7653i	0.439896	+	0.142931i	0.520588	−	0.853808i	$-0.325713\pi$
$691$	303.968	+	98.7653i	0.439896	+	0.142931i	−0.0806914	+	0.996739i	$0.525713\pi$
$692$	898.840	+	830.844i	1.29890	+	1.20064i
$693$	−1784.28	+	1292.39i	−2.57472	+	1.86493i
$694$	−385.584	+	985.190i	−0.555596	+	1.41958i
$695$	−411.377	−	133.664i	−0.591909	−	0.192323i
$696$	531.484	−	994.413i	0.763627	−	1.42875i
$697$	−285.927	−	207.738i	−0.410225	−	0.298046i
$698$	−27.8470	+	472.284i	−0.0398954	+	0.676624i
$699$	979.004	−	318.098i	1.40058	−	0.455075i
$700$	−251.827	+	50.0971i	−0.359753	+	0.0715673i
$701$	302.326	−	219.652i	0.431278	−	0.313342i	−0.350882	−	0.936420i	$-0.614118\pi$
$701$	302.326	−	219.652i	0.431278	−	0.313342i	0.782160	+	0.623078i	$0.214118\pi$
$702$	−324.230	−	266.083i	−0.461866	−	0.379036i
$703$			780.410i			1.11011i
$704$	585.898	−	390.306i	0.832242	−	0.554412i
$705$	−51.8896			−0.0736022
$706$	−284.621	+	346.819i	−0.403146	+	0.491245i
$707$	787.607	+	1084.05i	1.11401	+	1.53331i
$708$	43.8482	+	220.415i	0.0619324	+	0.311321i
$709$	169.529	+	521.756i	0.239110	+	0.735904i	0.996550	+	0.0829989i	$0.0264498\pi$
$709$	169.529	+	521.756i	0.239110	+	0.735904i	−0.757440	+	0.652905i	$0.773550\pi$
$710$	471.391	+	27.7943i	0.663931	+	0.0391470i
$711$	−106.894	+	147.127i	−0.150343	+	0.206930i
$712$	294.739	+	157.529i	0.413959	+	0.221249i
$713$	30.6928	−	94.4628i	0.0430474	−	0.132486i
$714$	1702.99	+	666.517i	2.38514	+	0.933498i
$715$	0.229360	−	157.550i	0.000320784	−	0.220350i
$716$	326.488	−	353.208i	0.455989	−	0.493308i
$717$	186.910	−	575.249i	0.260683	−	0.802300i
$718$	112.330	+	430.454i	0.156449	+	0.599518i
$719$	416.516	−	573.285i	0.579299	−	0.797337i	−0.414319	−	0.910132i	$-0.635980\pi$
$719$	416.516	−	573.285i	0.579299	−	0.797337i	0.993618	+	0.112795i	$0.0359803\pi$
$720$	515.665	−	213.621i	0.716201	−	0.296696i
$721$	483.552	+	1488.22i	0.670668	+	2.06410i
$722$	557.697	+	871.189i	0.772434	+	1.20663i
$723$	−579.569	−	797.709i	−0.801617	−	1.10333i
$724$	253.120	−	141.761i	0.349613	−	0.195802i
$725$	142.080			0.195972
$726$	1198.02	+	74.1387i	1.65016	+	0.102119i
$727$		−	662.434i		−	0.911188i	−0.890188	−	0.455594i	$-0.849427\pi$
$727$		−	662.434i		−	0.911188i	0.890188	−	0.455594i	$-0.150573\pi$
$728$	−90.1554	−	651.651i	−0.123840	−	0.895125i
$729$	−904.941	+	657.478i	−1.24135	+	0.901891i
$730$	31.4177	+	49.0782i	0.0430380	+	0.0672304i
$731$	−759.834	+	246.885i	−1.03944	+	0.337736i
$732$	1895.77	+	873.914i	2.58985	+	1.19387i
$733$	886.186	+	643.852i	1.20898	+	0.878379i	0.995138	−	0.0984885i	$-0.0314008\pi$
$733$	886.186	+	643.852i	1.20898	+	0.878379i	0.213846	+	0.976867i	$0.431401\pi$
$734$	182.537	+	699.487i	0.248688	+	0.952980i
$735$	−1221.63	−	396.931i	−1.66208	−	0.540042i
$736$	−267.963	−	81.2702i	−0.364080	−	0.110421i
$737$	97.5740	+	0.142047i	0.132393	+	0.000192737i
$738$	−715.123	−	279.885i	−0.969002	−	0.379248i
$739$	−464.138	−	150.807i	−0.628062	−	0.204070i	−0.0223454	−	0.999750i	$-0.507113\pi$
$739$	−464.138	−	150.807i	−0.628062	−	0.204070i	−0.605716	+	0.795681i	$0.707113\pi$
$740$	−233.911	−	27.6801i	−0.316096	−	0.0374056i
$741$	761.683	+	553.395i	1.02791	+	0.746822i
$742$	1145.81	+	67.5596i	1.54422	+	0.0910506i
$743$	347.199	−	112.812i	0.467293	−	0.151833i	−0.0659002	−	0.997826i	$-0.520992\pi$
$743$	347.199	−	112.812i	0.467293	−	0.151833i	0.533193	+	0.845994i	$0.320992\pi$
$744$	79.1627	−	443.378i	0.106401	−	0.595938i
$745$	−331.467	+	240.825i	−0.444922	+	0.323255i
$746$	529.644	−	645.387i	0.709979	−	0.865130i
$747$		−	1755.14i		−	2.34959i
$748$	−307.939	−	551.719i	−0.411683	−	0.737592i
$749$	1999.66			2.66978
$750$	85.7337	+	70.3583i	0.114312	+	0.0938110i
$751$	666.869	+	917.867i	0.887975	+	1.22219i	0.974148	+	0.225912i	$0.0725363\pi$
$751$	666.869	+	917.867i	0.887975	+	1.22219i	−0.0861729	+	0.996280i	$0.527464\pi$
$752$	63.8286	+	39.1104i	0.0848784	+	0.0520086i
$753$	677.402	+	2084.83i	0.899605	+	2.76870i
$754$	−21.4267	+	363.396i	−0.0284174	+	0.481958i
$755$	−39.5321	+	54.4112i	−0.0523604	+	0.0720679i
$756$	1669.68	+	197.584i	2.20857	+	0.261354i
$757$	54.9631	−	169.159i	0.0726065	−	0.223460i	−0.908167	−	0.418607i	$-0.862518\pi$
$757$	54.9631	−	169.159i	0.0726065	−	0.223460i	0.980774	+	0.195147i	$0.0625185\pi$
$758$	−238.695	+	609.880i	−0.314901	+	0.804591i
$759$	−280.059	−	386.651i	−0.368985	−	0.509422i
$760$	−476.965	+	231.364i	−0.627586	+	0.304426i
$761$	260.576	−	801.972i	0.342413	−	1.05384i	−0.620541	−	0.784174i	$-0.713087\pi$
$761$	260.576	−	801.972i	0.342413	−	1.05384i	0.962954	−	0.269665i	$-0.0869130\pi$
$762$	−2265.69	+	591.250i	−2.97335	+	0.775919i
$763$	−107.325	+	147.720i	−0.140662	+	0.193604i
$764$	−655.788	−	302.305i	−0.858361	−	0.395688i
$765$	−154.802	−	476.431i	−0.202355	−	0.622785i
$766$	−824.857	+	528.037i	−1.07684	+	0.689344i
$767$	−42.6474	−	58.6991i	−0.0556029	−	0.0765308i
$768$	−1254.13	−	198.525i	−1.63298	−	0.258496i
$769$	−130.424			−0.169602			−0.0848008	−	0.996398i	$-0.527025\pi$
$769$	−130.424			−0.169602			−0.0848008	+	0.996398i	$0.527025\pi$
$770$	339.724	+	532.394i	0.441200	+	0.691421i
$771$			1125.10i			1.45927i
$772$	−35.2974	+	19.7685i	−0.0457220	+	0.0256068i
$773$	1033.97	−	751.222i	1.33761	−	0.971827i	0.338077	−	0.941118i	$-0.390224\pi$
$773$	1033.97	−	751.222i	1.33761	−	0.971827i	0.999528	−	0.0307086i	$-0.00977640\pi$
$774$	−1462.06	+	935.947i	−1.88897	+	1.20923i
$775$	53.9756	−	17.5377i	0.0696460	−	0.0226293i
$776$	−94.2880	+	90.6620i	−0.121505	+	0.116832i
$777$	−1356.63	−	985.646i	−1.74598	−	1.26853i
$778$	−660.881	+	172.462i	−0.849462	+	0.221674i
$779$	693.662	+	225.385i	0.890452	+	0.289325i
$780$	−192.884	+	208.670i	−0.247287	+	0.267525i
$781$	−357.309	−	1105.16i	−0.457502	−	1.41505i
$782$	−91.5941	+	234.028i	−0.117128	+	0.299269i
$783$	−884.833	−	287.500i	−1.13006	−	0.367177i
$784$	1203.53	+	1409.03i	1.53511	+	1.79723i
$785$	236.751	+	172.010i	0.301594	+	0.219121i
$786$	63.9643	−	1084.83i	0.0813795	−	1.38019i
$787$	390.910	−	127.014i	0.496709	−	0.161390i	−0.0499404	−	0.998752i	$-0.515903\pi$
$787$	390.910	−	127.014i	0.496709	−	0.161390i	0.546649	+	0.837362i	$0.315903\pi$
$788$	−83.3433	−	418.949i	−0.105766	−	0.531661i
$789$	−433.834	+	315.199i	−0.549853	+	0.399492i
$790$	40.2980	+	33.0710i	0.0510102	+	0.0418620i
$791$		−	851.468i		−	1.07645i
$792$	−950.127	−	991.011i	−1.19965	−	1.25128i
$793$	−673.957			−0.849882
$794$	−758.734	+	924.540i	−0.955584	+	1.16441i
$795$	−291.418	−	401.102i	−0.366563	−	0.504531i
$796$	−124.972	+	24.8612i	−0.156999	+	0.0312326i
$797$	−27.2170	−	83.7653i	−0.0341493	−	0.105101i	0.932529	−	0.361095i	$-0.117597\pi$
$797$	−27.2170	−	83.7653i	−0.0341493	−	0.105101i	−0.966678	+	0.255995i	$0.917597\pi$
$798$	−3767.48	−	222.140i	−4.72116	−	0.278371i
$799$	39.4903	−	54.3537i	0.0494246	−	0.0680271i
$800$	−52.4289	−	151.166i	−0.0655361	−	0.188958i
$801$	201.394	−	619.828i	0.251429	−	0.773818i
$802$	−135.722	−	53.1189i	−0.169230	−	0.0662331i
$803$	84.4175	−	115.836i	0.105128	−	0.144254i
$804$	−129.233	−	119.457i	−0.160738	−	0.148578i
$805$	77.6249	−	238.905i	0.0964284	−	0.296776i
$806$	36.7162	+	140.698i	0.0455536	+	0.174563i
$807$	−340.725	+	468.967i	−0.422211	+	0.581124i
$808$	−601.886	+	578.739i	−0.744908	+	0.716261i
$809$	−32.7929	−	100.926i	−0.0405351	−	0.124754i	0.928741	−	0.370729i	$-0.120892\pi$
$809$	−32.7929	−	100.926i	−0.0405351	−	0.124754i	−0.969276	+	0.245975i	$0.920892\pi$
$810$	−53.0069	−	82.8030i	−0.0654406	−	0.102226i
$811$	−217.150	−	298.882i	−0.267756	−	0.368535i	0.653874	−	0.756603i	$-0.273143\pi$
$811$	−217.150	−	298.882i	−0.267756	−	0.368535i	−0.921631	+	0.388068i	$0.873143\pi$
$812$	−713.036	−	1273.15i	−0.878123	−	1.56792i
$813$	−199.203			−0.245022
$814$	145.473	+	560.798i	0.178714	+	0.688941i
$815$			101.165i			0.124128i
$816$	−265.986	+	1108.12i	−0.325963	+	1.35799i
$817$	1333.87	−	969.114i	1.63265	−	1.18619i
$818$	−582.072	−	909.265i	−0.711579	−	1.11157i
$819$	−1220.12	+	396.442i	−1.48977	+	0.484056i
$820$	−92.1574	+	199.916i	−0.112387	+	0.243800i
$821$	−106.514	−	77.3871i	−0.129737	−	0.0942596i	0.521024	−	0.853542i	$-0.325550\pi$
$821$	−106.514	−	77.3871i	−0.129737	−	0.0942596i	−0.650761	+	0.759282i	$0.725550\pi$
$822$	570.323	+	2185.50i	0.693823	+	2.65876i
$823$	1.78894	+	0.581260i	0.00217368	+	0.000706270i	0.310104	−	0.950703i	$-0.399636\pi$
$823$	1.78894	+	0.581260i	0.00217368	+	0.000706270i	−0.307930	+	0.951409i	$0.599636\pi$
$824$	−877.333	+	425.572i	−1.06472	+	0.516471i
$825$	84.6766	−	259.323i	0.102638	−	0.314330i
$826$	270.841	+	106.002i	0.327894	+	0.128331i
$827$	−992.058	−	322.339i	−1.19959	−	0.389769i	−0.359977	−	0.932961i	$-0.617216\pi$
$827$	−992.058	−	322.339i	−1.19959	−	0.389769i	−0.839609	+	0.543192i	$0.817216\pi$
$828$	−64.1721	+	542.286i	−0.0775025	+	0.654935i
$829$	−45.1811	−	32.8260i	−0.0545008	−	0.0395971i	0.560201	−	0.828356i	$-0.310724\pi$
$829$	−45.1811	−	32.8260i	−0.0545008	−	0.0395971i	−0.614702	+	0.788759i	$0.710724\pi$
$830$	−502.249	−	29.6138i	−0.605120	−	0.0356793i
$831$	1356.98	−	440.908i	1.63294	−	0.530575i
$832$	394.543	−	111.300i	0.474210	−	0.133774i
$833$	1345.49	−	977.557i	1.61524	−	1.17354i
$834$	1217.33	−	1483.35i	1.45963	−	1.77860i
$835$		−	500.743i		−	0.599692i
$836$	956.225	+	886.473i	1.14381	+	1.06037i
$837$	−371.633			−0.444006
$838$	88.0176	+	72.2326i	0.105033	+	0.0861964i
$839$	147.667	+	203.246i	0.176003	+	0.242247i	0.887900	−	0.460037i	$-0.152164\pi$
$839$	147.667	+	203.246i	0.176003	+	0.242247i	−0.711897	+	0.702284i	$0.752164\pi$
$840$	200.209	−	1121.34i	0.238344	−	1.33493i
$841$	−10.3621	−	31.8914i	−0.0123212	−	0.0379208i
$842$	−39.4865	+	669.689i	−0.0468961	+	0.795356i
$843$	330.436	−	454.807i	0.391977	−	0.539510i
$844$	126.934	−	1072.65i	0.150396	−	1.27092i
$845$	−88.4263	+	272.148i	−0.104646	+	0.322069i
$846$	53.2051	−	135.942i	0.0628902	−	0.160688i
$847$	916.726	−	1254.07i	1.08232	−	1.48060i
$848$	56.1479	+	713.038i	0.0662122	+	0.840847i
$849$	−400.780	+	1233.47i	−0.472061	+	1.45286i
$850$	−138.947	+	36.2592i	−0.163467	+	0.0426579i
$851$	135.449	−	186.430i	0.159165	−	0.219072i
$852$	−876.997	+	1902.46i	−1.02934	+	2.23293i
$853$	−25.8911	−	79.6848i	−0.0303530	−	0.0934171i	0.934732	−	0.355353i	$-0.115639\pi$
$853$	−25.8911	−	79.6848i	−0.0303530	−	0.0934171i	−0.965085	+	0.261936i	$0.915639\pi$
$854$	2275.32	−	1456.56i	2.66430	−	1.70557i
$855$	607.654	+	836.363i	0.710706	+	0.978203i
$856$	170.768	+	1234.32i	0.199495	+	1.44197i
$857$	334.148			0.389905			0.194952	−	0.980813i	$-0.437545\pi$
$857$	334.148			0.389905			0.194952	+	0.980813i	$0.437545\pi$
$858$	650.497	+	255.684i	0.758155	+	0.298000i
$859$		−	1505.52i		−	1.75264i	−0.481726	−	0.876322i	$-0.659990\pi$
$859$		−	1505.52i		−	1.75264i	0.481726	−	0.876322i	$-0.340010\pi$
$860$	243.160	+	434.172i	0.282745	+	0.504852i
$861$	−1267.88	+	921.171i	−1.47257	+	1.06989i
$862$	848.798	−	543.364i	0.984684	−	0.630352i
$863$	29.4644	−	9.57357i	0.0341419	−	0.0110934i	−0.291896	−	0.956450i	$-0.594286\pi$
$863$	29.4644	−	9.57357i	0.0341419	−	0.0110934i	0.326038	+	0.945357i	$0.394286\pi$
$864$	20.6263	+	1047.51i	0.0238730	+	1.21240i
$865$	−553.567	−	402.190i	−0.639961	−	0.464959i
$866$	−351.831	+	91.8131i	−0.406271	+	0.106020i
$867$	−390.542	−	126.895i	−0.450452	−	0.146361i
$868$	−428.033	−	395.652i	−0.493125	−	0.455821i
$869$	39.8012	−	121.891i	0.0458011	−	0.140266i
$870$	−229.723	+	586.957i	−0.264050	+	0.674663i
$871$	54.0368	+	17.5576i	0.0620400	+	0.0201580i
$872$	−100.348	−	53.6330i	−0.115078	−	0.0615058i
$873$	206.369	+	149.936i	0.236391	+	0.171748i
$874$	30.5269	−	517.735i	0.0349278	−	0.592374i
$875$	136.509	−	44.3545i	0.156010	−	0.0506908i
$876$	−253.549	+	50.4396i	−0.289439	+	0.0575794i
$877$	1265.25	−	919.257i	1.44270	−	1.04818i	0.455232	−	0.890373i	$-0.349556\pi$
$877$	1265.25	−	919.257i	1.44270	−	1.04818i	0.987469	−	0.157811i	$-0.0504437\pi$
$878$	−77.9815	−	63.9963i	−0.0888172	−	0.0728888i
$879$		−	1702.82i		−	1.93723i
$880$	−299.617	+	255.166i	−0.340474	+	0.289961i
$881$	−1423.89			−1.61621			−0.808107	−	0.589035i	$-0.799508\pi$
$881$	−1423.89			−1.61621			−0.808107	+	0.589035i	$0.799508\pi$
$882$	2292.49	−	2793.47i	2.59920	−	3.16720i
$883$	−936.823	−	1289.43i	−1.06096	−	1.46028i	−0.878909	−	0.476990i	$-0.841728\pi$
$883$	−936.823	−	1289.43i	−1.06096	−	1.46028i	−0.182046	−	0.983290i	$-0.558272\pi$
$884$	−71.7856	−	360.851i	−0.0812055	−	0.408202i
$885$	−38.8219	−	119.481i	−0.0438665	−	0.135007i
$886$	382.048	+	22.5265i	0.431206	+	0.0254249i
$887$	548.126	−	754.430i	0.617955	−	0.850542i	−0.379247	−	0.925295i	$-0.623817\pi$
$887$	548.126	−	754.430i	0.617955	−	0.850542i	0.997202	+	0.0747537i	$0.0238171\pi$
$888$	492.553	−	921.572i	0.554677	−	1.03781i
$889$	−936.444	+	2882.08i	−1.05337	+	3.24193i
$890$	−173.971	−	68.0888i	−0.195473	−	0.0765043i
$891$	−142.426	+	195.434i	−0.159850	+	0.219342i
$892$	256.771	−	277.786i	0.287860	−	0.311419i
$893$	−42.8448	+	131.863i	−0.0479785	+	0.147663i
$894$	−458.954	−	1758.73i	−0.513371	−	1.96726i
$895$	−158.044	+	217.529i	−0.176586	+	0.243050i
$896$	−1091.46	+	1228.44i	−1.21814	+	1.37103i
$897$	−85.9082	−	264.398i	−0.0957728	−	0.294758i
$898$	−199.810	−	312.127i	−0.222505	−	0.347580i
$899$	189.584	+	260.940i	0.210884	+	0.290256i
$900$	−272.234	+	152.466i	−0.302483	+	0.169407i
$901$	641.932			0.712466
$902$	540.475	+	32.6573i	0.599196	+	0.0362055i
$903$			3542.72i			3.92327i
$904$	525.583	−	72.7141i	0.581397	−	0.0804359i
$905$	−131.205	+	95.3260i	−0.144978	+	0.105333i
$906$	−160.865	−	251.289i	−0.177555	−	0.277361i
$907$	−543.325	+	176.537i	−0.599035	+	0.194638i	−0.592810	−	0.805342i	$-0.701982\pi$
$907$	−543.325	+	176.537i	−0.599035	+	0.194638i	−0.00622503	+	0.999981i	$0.501982\pi$
$908$	754.266	+	347.702i	0.830690	+	0.382932i
$909$	1317.36	+	957.115i	1.44924	+	1.05293i
$910$	92.8585	+	355.837i	0.102042	+	0.391030i
$911$	388.377	+	126.191i	0.426319	+	0.138520i	0.514315	−	0.857601i	$-0.328046\pi$
$911$	388.377	+	126.191i	0.426319	+	0.138520i	−0.0879957	+	0.996121i	$0.528046\pi$
$912$	−184.618	−	2344.51i	−0.202432	−	2.57074i
$913$	380.700	+	1177.50i	0.416977	+	1.28971i
$914$	−681.246	−	266.626i	−0.745346	−	0.291714i
$915$	−1109.84	−	360.608i	−1.21294	−	0.394107i
$916$	−621.950	−	73.5992i	−0.678984	−	0.0803484i
$917$	−1137.80	−	826.662i	−1.24079	−	0.901485i
$918$	938.691	+	55.3475i	1.02254	+	0.0602914i
$919$	−1321.25	+	429.300i	−1.43770	+	0.467138i	−0.921181	−	0.389135i	$-0.872774\pi$
$919$	−1321.25	+	429.300i	−1.43770	+	0.467138i	−0.516523	+	0.856273i	$0.672774\pi$
$920$	154.097	+	27.5131i	0.167497	+	0.0299056i
$921$	−1098.52	+	798.123i	−1.19275	+	0.866583i
$922$	−885.986	+	1079.60i	−0.960939	+	1.17093i
$923$		−	676.334i		−	0.732757i
$924$	−2748.70	+	542.653i	−2.97478	+	0.587286i
$925$	131.673			0.142349
$926$	186.280	+	152.873i	0.201167	+	0.165090i
$927$	1117.72	+	1538.41i	1.20574	+	1.65956i
$928$	724.983	−	548.859i	0.781232	−	0.591443i
$929$	−223.547	−	688.008i	−0.240632	−	0.740590i	−0.996324	−	0.0856625i	$-0.972699\pi$
$929$	−223.547	−	688.008i	−0.240632	−	0.740590i	0.755692	−	0.654927i	$-0.227301\pi$
$930$	−14.8195	+	251.339i	−0.0159350	+	0.270257i
$931$	−2017.37	+	2776.68i	−2.16689	+	2.98247i
$932$	824.406	+	97.5571i	0.884556	+	0.104675i
$933$	−375.683	+	1156.23i	−0.402661	+	1.23926i
$934$	458.490	−	1171.47i	0.490888	−	1.25425i
$935$	207.195	+	286.054i	0.221598	+	0.305940i
$936$	−348.907	−	719.285i	−0.372763	−	0.768467i
$937$	301.503	−	927.932i	0.321775	−	0.990323i	−0.651100	−	0.758992i	$-0.725692\pi$
$937$	301.503	−	927.932i	0.321775	−	0.990323i	0.972875	−	0.231330i	$-0.0743079\pi$
$938$	−220.377	+	57.5091i	−0.234943	+	0.0613103i
$939$	1535.63	−	2113.62i	1.63539	−	2.25092i
$940$	−38.0033	−	17.5188i	−0.0404291	−	0.0186370i
$941$	−2.14266	−	6.59444i	−0.00227701	−	0.00700790i	0.949912	−	0.312519i	$-0.101173\pi$
$941$	−2.14266	−	6.59444i	−0.00227701	−	0.00700790i	−0.952189	+	0.305511i	$0.901173\pi$
$942$	−1093.40	+	699.944i	−1.16072	+	0.743041i
$943$	−126.589	−	174.235i	−0.134241	−	0.184767i
$944$	−42.3019	+	176.233i	−0.0448114	+	0.186688i
$945$	−939.892			−0.994595
$946$	777.864	−	945.042i	0.822267	−	0.998987i
$947$			485.205i			0.512360i	0.966629	+	0.256180i	$0.0824639\pi$
$947$			485.205i			0.512360i	−0.966629	+	0.256180i	$0.917536\pi$
$948$	−201.779	+	113.007i	−0.212847	+	0.119206i
$949$	67.5230	−	49.0583i	0.0711517	−	0.0516947i
$950$	249.585	−	159.774i	0.262721	−	0.168183i
$951$	−0.888787	+	0.288784i	−0.000934582	+	0.000303664i
$952$	1022.22	+	1063.11i	1.07376	+	1.11671i
$953$	398.769	+	289.723i	0.418435	+	0.304011i	0.777008	−	0.629491i	$-0.216736\pi$
$953$	398.769	+	289.723i	0.418435	+	0.304011i	−0.358573	+	0.933502i	$0.616736\pi$
$954$	1349.63	−	352.196i	1.41471	−	0.369178i
$955$	383.916	+	124.742i	0.402006	+	0.130620i
$956$	331.104	−	358.202i	0.346343	−	0.374688i
$957$	1550.36	+	2.25700i	1.62002	+	0.00235841i
$958$	155.905	−	398.345i	0.162740	−	0.415809i
$959$	2780.07	+	903.299i	2.89892	+	0.941917i
$960$	709.265	+	27.8217i	0.738817	+	0.0289809i
$961$	−673.234	−	489.133i	−0.700555	−	0.508983i
$962$	−19.8572	+	336.778i	−0.0206416	+	0.350081i
$963$	2311.09	−	750.920i	2.39989	−	0.779772i
$964$	−155.150	−	779.905i	−0.160944	−	0.809030i
$965$	18.2964	−	13.2931i	0.0189600	−	0.0137753i
$966$	861.449	+	706.958i	0.891770	+	0.731840i
$967$		−	1386.40i		−	1.43371i	−0.697220	−	0.716857i	$-0.745580\pi$
$967$		−	1386.40i		−	1.43371i	0.697220	−	0.716857i	$-0.254420\pi$
$968$	852.382	+	458.768i	0.880560	+	0.473934i
$969$	−2110.71			−2.17823
$970$	46.3875	−	56.5245i	0.0478221	−	0.0582727i
$971$	334.906	+	460.959i	0.344908	+	0.474726i	0.945867	−	0.324554i	$-0.105214\pi$
$971$	334.906	+	460.959i	0.344908	+	0.474726i	−0.600959	+	0.799280i	$0.705214\pi$
$972$	−728.247	+	144.873i	−0.749225	+	0.149047i
$973$	−767.416	−	2361.86i	−0.788712	−	2.42740i
$974$	375.165	+	22.1206i	0.385180	+	0.0227111i
$975$	93.3700	−	128.513i	0.0957641	−	0.131808i
$976$	1093.39	+	1280.09i	1.12028	+	1.31157i
$977$	−223.427	+	687.636i	−0.228686	+	0.703824i	0.769210	+	0.638996i	$0.220650\pi$
$977$	−223.427	+	687.636i	−0.228686	+	0.703824i	−0.997896	+	0.0648284i	$0.979350\pi$
$978$	−417.929	−	163.569i	−0.427330	−	0.167249i
$979$	−0.668962	+	459.518i	−0.000683312	+	0.469375i
$980$	−760.695	−	703.149i	−0.776219	−	0.717499i
$981$	−68.5676	+	211.029i	−0.0698956	+	0.215117i
$982$	−177.335	−	679.554i	−0.180585	−	0.692010i
$983$	160.847	−	221.387i	0.163629	−	0.225215i	−0.719327	−	0.694671i	$-0.755550\pi$
$983$	160.847	−	221.387i	0.163629	−	0.225215i	0.882956	+	0.469456i	$0.155550\pi$
$984$	−676.883	−	703.955i	−0.687889	−	0.715402i
$985$	73.7898	+	227.102i	0.0749135	+	0.230560i
$986$	−440.001	−	687.333i	−0.446248	−	0.697092i
$987$	−175.111	−	241.020i	−0.177418	−	0.244194i
$988$	371.012	+	662.457i	0.375518	+	0.670503i
$989$	−486.847			−0.492261
$990$	592.560	+	487.736i	0.598545	+	0.492663i
$991$		−	1077.12i		−	1.08690i	−0.839441	−	0.543452i	$-0.817117\pi$
$991$		−	1077.12i		−	1.08690i	0.839441	−	0.543452i	$-0.182883\pi$
$992$	207.670	−	297.998i	0.209344	−	0.300402i
$993$	−1090.58	+	792.351i	−1.09827	+	0.797936i
$994$	1461.70	+	2283.34i	1.47052	+	2.29713i
$995$	67.7440	−	22.0113i	0.0680844	−	0.0221220i
$996$	934.407	−	2027.00i	0.938160	−	2.03514i
$997$	−575.438	−	418.081i	−0.577170	−	0.419339i	0.260533	−	0.965465i	$-0.416102\pi$
$997$	−575.438	−	418.081i	−0.577170	−	0.419339i	−0.837703	+	0.546126i	$0.816102\pi$
$998$	−54.5824	−	209.162i	−0.0546918	−	0.209581i
$999$	−820.019	−	266.440i	−0.820840	−	0.266707i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.s.a.31.17	yes	96
4.3	odd	2	inner	220.3.s.a.31.12	✓	96
11.5	even	5	inner	220.3.s.a.71.12	yes	96
44.27	odd	10	inner	220.3.s.a.71.17	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.s.a.31.12	✓	96	4.3	odd	2	inner
220.3.s.a.31.17	yes	96	1.1	even	1	trivial
220.3.s.a.71.12	yes	96	11.5	even	5	inner
220.3.s.a.71.17	yes	96	44.27	odd	10	inner

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.s (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26877 - 1.54603i) q^{2} +(-2.91538 - 4.01268i) q^{3} +(-0.780445 - 3.92312i) q^{4} +(0.690983 + 2.12663i) q^{5} +(-9.90270 - 0.583887i) q^{6} +(-7.54604 + 10.3862i) q^{7} +(-7.05549 - 3.77095i) q^{8} +(-4.82100 + 14.8375i) q^{9} +(4.16454 + 1.62992i) q^{10} +(0.0160137 - 11.0000i) q^{11} +(-13.4670 + 14.5691i) q^{12} +(1.97936 - 6.09183i) q^{13} +(6.48328 + 24.8442i) q^{14} +(6.51900 - 8.97263i) q^{15} +(-14.7818 + 6.12356i) q^{16} +(4.43747 + 13.6571i) q^{17} +(16.8226 + 26.2788i) q^{18} +(-17.4187 - 23.9748i) q^{19} +(7.80375 - 4.37053i) q^{20} +63.6762 q^{21} +(-16.9860 - 13.9812i) q^{22} +8.75051i q^{23} +(5.43785 + 39.3052i) q^{24} +(-4.04508 + 2.93893i) q^{25} +(-6.90684 - 10.7893i) q^{26} +(31.1386 - 10.1175i) q^{27} +(46.6357 + 21.4982i) q^{28} +(-22.9890 - 16.7025i) q^{29} +(-5.60089 - 21.4628i) q^{30} +(-10.7951 - 3.50755i) q^{31} +(-9.28748 + 30.6226i) q^{32} +(-44.1861 + 32.0049i) q^{33} +(26.7445 + 10.4673i) q^{34} +(-27.3018 - 8.87090i) q^{35} +(61.9720 + 7.33352i) q^{36} +(-21.3051 - 15.4790i) q^{37} +(-59.1662 - 3.48858i) q^{38} +(-30.2152 + 9.81751i) q^{39} +(3.14418 - 17.6101i) q^{40} +(-19.9114 + 14.4665i) q^{41} +(80.7905 - 98.4456i) q^{42} +55.6364i q^{43} +(-43.1668 + 8.52206i) q^{44} -34.8851 q^{45} +(13.5286 + 11.1024i) q^{46} +(-2.75002 - 3.78508i) q^{47} +(67.6666 + 41.4622i) q^{48} +(-35.7892 - 110.148i) q^{49} +(-0.588602 + 9.98266i) q^{50} +(41.8648 - 57.6220i) q^{51} +(-25.4438 - 3.01092i) q^{52} +(13.8139 - 42.5149i) q^{53} +(23.8656 - 60.9782i) q^{54} +(23.4039 - 7.56675i) q^{55} +(92.4069 - 44.8242i) q^{56} +(-45.4210 + 139.792i) q^{57} +(-54.9904 + 14.3502i) q^{58} +(6.65811 - 9.16410i) q^{59} +(-40.2885 - 18.5722i) q^{60} +(-32.5142 - 100.068i) q^{61} +(-19.1193 + 12.2394i) q^{62} +(-117.726 - 162.036i) q^{63} +(35.5599 + 53.2118i) q^{64} +14.3228 q^{65} +(-6.58133 + 108.920i) q^{66} +8.87037i q^{67} +(50.1155 - 28.0674i) q^{68} +(35.1130 - 25.5111i) q^{69} +(-48.3544 + 30.9544i) q^{70} +(100.421 - 32.6289i) q^{71} +(89.9660 - 86.5062i) q^{72} +(10.5417 + 7.65898i) q^{73} +(-50.9623 + 13.2990i) q^{74} +(23.5860 + 7.66354i) q^{75} +(-80.4618 + 87.0468i) q^{76} +(114.128 + 83.1726i) q^{77} +(-23.1579 + 59.1699i) q^{78} +(11.0863 + 3.60215i) q^{79} +(-23.2365 - 27.2041i) q^{80} +(-17.7856 - 12.9220i) q^{81} +(-2.89732 + 49.1384i) q^{82} +(-106.995 + 34.7649i) q^{83} +(-49.6958 - 249.810i) q^{84} +(-25.9774 + 18.8737i) q^{85} +(86.0158 + 70.5898i) q^{86} +140.942i q^{87} +(-41.5934 + 77.5499i) q^{88} -41.7744 q^{89} +(-44.2612 + 53.9336i) q^{90} +(48.3349 + 66.5272i) q^{91} +(34.3293 - 6.82929i) q^{92} +(17.3973 + 53.5433i) q^{93} +(-9.34102 - 0.550769i) q^{94} +(38.9494 - 53.6093i) q^{95} +(149.955 - 52.0089i) q^{96} +(5.05260 - 15.5503i) q^{97} +(-215.701 - 84.4210i) q^{98} +(163.135 + 53.2686i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 2 q^{2} - 4 q^{4} + 120 q^{5} + 20 q^{6} - 10 q^{8} + 64 q^{9} + 10 q^{10} + 70 q^{12} - 20 q^{13} - 37 q^{14} - 4 q^{16} + 24 q^{17} + 45 q^{18} + 5 q^{20} - 15 q^{22} - 62 q^{24} - 120 q^{25} + 12 q^{26}+ \cdots + 158 q^{98}+O(q^{100}) \) 96 * q + 2 * q^2 - 4 * q^4 + 120 * q^5 + 20 * q^6 - 10 * q^8 + 64 * q^9 + 10 * q^10 + 70 * q^12 - 20 * q^13 - 37 * q^14 - 4 * q^16 + 24 * q^17 + 45 * q^18 + 5 * q^20 - 15 * q^22 - 62 * q^24 - 120 * q^25 + 12 * q^26 - 200 * q^28 + 72 * q^29 + 40 * q^30 - 348 * q^32 - 60 * q^33 - 246 * q^34 + 26 * q^36 + 144 * q^37 - 105 * q^38 + 132 * q^41 - 25 * q^42 - 67 * q^44 - 40 * q^45 - 85 * q^46 + 213 * q^48 - 28 * q^49 + 10 * q^50 + 312 * q^52 - 224 * q^53 + 752 * q^54 + 660 * q^56 - 204 * q^57 + 88 * q^58 + 105 * q^60 - 48 * q^61 + 88 * q^62 + 44 * q^64 - 40 * q^65 + 75 * q^66 - 117 * q^68 + 32 * q^69 - 75 * q^70 - 198 * q^72 - 64 * q^73 - 672 * q^74 - 1280 * q^76 + 80 * q^77 - 1132 * q^78 - 125 * q^80 - 44 * q^81 - 301 * q^82 - 348 * q^84 - 60 * q^85 + 470 * q^86 + 5 * q^88 + 176 * q^89 - 162 * q^92 + 280 * q^93 + 394 * q^94 + 1143 * q^96 + 204 * q^97 + 158 * q^98

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