LMFDB - Embedded newform 220.3.s.a.31.8

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			31.8
Character	$\chi$	$=$	220.31
Dual form			220.3.s.a.71.8

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.874978 + 1.79845i) q^{2} +(0.667552 + 0.918806i) q^{3} +(-2.46883 - 3.14721i) q^{4} +(0.690983 + 2.12663i) q^{5} +(-2.23652 + 0.396621i) q^{6} +(4.67079 - 6.42880i) q^{7} +(7.82025 - 1.68632i) q^{8} +(2.38257 - 7.33281i) q^{9} +(-4.42922 - 0.618056i) q^{10} +(10.9722 - 0.781521i) q^{11} +(1.24360 - 4.36929i) q^{12} +(-1.80740 + 5.56259i) q^{13} +(7.47501 + 14.0252i) q^{14} +(-1.49269 + 2.05451i) q^{15} +(-3.80980 + 15.5398i) q^{16} +(-7.64225 - 23.5204i) q^{17} +(11.1030 + 10.7010i) q^{18} +(21.0474 + 28.9693i) q^{19} +(4.98702 - 7.42494i) q^{20} +9.02481 q^{21} +(-8.19492 + 20.4167i) q^{22} -0.700934i q^{23} +(6.76982 + 6.05959i) q^{24} +(-4.04508 + 2.93893i) q^{25} +(-8.42260 - 8.11765i) q^{26} +(18.0490 - 5.86448i) q^{27} +(-31.7641 + 1.17163i) q^{28} +(-4.33244 - 3.14770i) q^{29} +(-2.38886 - 4.48218i) q^{30} +(14.3708 + 4.66937i) q^{31} +(-24.6140 - 20.4487i) q^{32} +(8.04258 + 9.55962i) q^{33} +(48.9871 + 6.83568i) q^{34} +(16.8991 + 5.49085i) q^{35} +(-28.9600 + 10.6050i) q^{36} +(19.8276 + 14.4056i) q^{37} +(-70.5157 + 12.5052i) q^{38} +(-6.31747 + 2.05267i) q^{39} +(8.98983 + 15.4655i) q^{40} +(-4.56575 + 3.31721i) q^{41} +(-7.89652 + 16.2307i) q^{42} +32.1162i q^{43} +(-29.5481 - 32.6023i) q^{44} +17.2405 q^{45} +(1.26059 + 0.613302i) q^{46} +(-16.5912 - 22.8359i) q^{47} +(-16.8213 + 6.87315i) q^{48} +(-4.37127 - 13.4534i) q^{49} +(-1.74614 - 9.84637i) q^{50} +(16.5091 - 22.7229i) q^{51} +(21.9688 - 8.04482i) q^{52} +(-17.1581 + 52.8071i) q^{53} +(-5.24554 + 37.5915i) q^{54} +(9.24361 + 22.7938i) q^{55} +(25.6858 - 58.1512i) q^{56} +(-12.5669 + 38.6770i) q^{57} +(9.45176 - 5.03749i) q^{58} +(64.5303 - 88.8183i) q^{59} +(10.1512 - 0.374429i) q^{60} +(-17.6349 - 54.2745i) q^{61} +(-20.9718 + 21.7596i) q^{62} +(-36.0126 - 49.5671i) q^{63} +(58.3127 - 26.3748i) q^{64} -13.0784 q^{65} +(-24.2296 + 6.09969i) q^{66} -69.6011i q^{67} +(-55.1562 + 82.1196i) q^{68} +(0.644022 - 0.467910i) q^{69} +(-24.6613 + 25.5878i) q^{70} +(60.6265 - 19.6987i) q^{71} +(6.26689 - 61.3622i) q^{72} +(-62.6736 - 45.5351i) q^{73} +(-43.2565 + 23.0543i) q^{74} +(-5.40061 - 1.75476i) q^{75} +(39.2099 - 137.761i) q^{76} +(46.2247 - 74.1884i) q^{77} +(1.83603 - 13.1577i) q^{78} +(37.5999 + 12.2170i) q^{79} +(-35.6799 + 2.63571i) q^{80} +(-38.7020 - 28.1186i) q^{81} +(-1.97090 - 11.1138i) q^{82} +(-128.649 + 41.8007i) q^{83} +(-22.2807 - 28.4029i) q^{84} +(44.7385 - 32.5044i) q^{85} +(-57.7593 - 28.1010i) q^{86} -6.08192i q^{87} +(84.4875 - 24.6143i) q^{88} +22.8405 q^{89} +(-15.0850 + 31.0061i) q^{90} +(27.3188 + 37.6011i) q^{91} +(-2.20598 + 1.73048i) q^{92} +(5.30303 + 16.3211i) q^{93} +(55.5861 - 9.85756i) q^{94} +(-47.0634 + 64.7773i) q^{95} +(2.35727 - 36.2661i) q^{96} +(-35.1693 + 108.240i) q^{97} +(28.0200 + 3.90993i) q^{98} +(20.4113 - 82.3191i) 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

)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$\alpha_n$			$\theta_n$
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$\alpha_p$			$\theta_p$

$2$	−0.874978	+	1.79845i	−0.437489	+	0.899224i
$2$	−0.874978	+	1.79845i	−0.437489	+	0.899224i
$3$	0.667552	+	0.918806i	0.222517	+	0.306269i	0.905650	−	0.424025i	$-0.139383\pi$
$3$	0.667552	+	0.918806i	0.222517	+	0.306269i	−0.683133	+	0.730294i	$0.739383\pi$
$4$	−2.46883	−	3.14721i	−0.617206	−	0.786801i
$5$	0.690983	+	2.12663i	0.138197	+	0.425325i
$5$	0.690983	+	2.12663i	0.138197	+	0.425325i
$6$	−2.23652	+	0.396621i	−0.372753	+	0.0661035i
$7$	4.67079	−	6.42880i	0.667256	−	0.918399i	−0.332438	−	0.943125i	$-0.607871\pi$
$7$	4.67079	−	6.42880i	0.667256	−	0.918399i	0.999694	+	0.0247257i	$0.00787122\pi$
$8$	7.82025	−	1.68632i	0.977531	−	0.210790i
$9$	2.38257	−	7.33281i	0.264730	−	0.814756i
$10$	−4.42922	−	0.618056i	−0.442922	−	0.0618056i
$11$	10.9722	−	0.781521i	0.997473	−	0.0710474i
$11$	10.9722	−	0.781521i	0.997473	−	0.0710474i
$12$	1.24360	−	4.36929i	0.103634	−	0.364108i
$13$	−1.80740	+	5.56259i	−0.139030	+	0.427892i	−0.996195	−	0.0871507i	$-0.972224\pi$
$13$	−1.80740	+	5.56259i	−0.139030	+	0.427892i	0.857165	+	0.515042i	$0.172224\pi$
$14$	7.47501	+	14.0252i	0.533929	+	1.00180i
$15$	−1.49269	+	2.05451i	−0.0995127	+	0.136968i
$16$	−3.80980	+	15.5398i	−0.238113	+	0.971238i
$17$	−7.64225	−	23.5204i	−0.449544	−	1.38355i	−0.877423	−	0.479718i	$-0.840739\pi$
$17$	−7.64225	−	23.5204i	−0.449544	−	1.38355i	0.427878	−	0.903836i	$-0.359261\pi$
$18$	11.1030	+	10.7010i	0.616832	+	0.594499i
$19$	21.0474	+	28.9693i	1.10776	+	1.52470i	0.824678	+	0.565602i	$0.191356\pi$
$19$	21.0474	+	28.9693i	1.10776	+	1.52470i	0.283080	+	0.959096i	$0.408644\pi$
$20$	4.98702	−	7.42494i	0.249351	−	0.371247i
$21$	9.02481			0.429753
$22$	−8.19492	+	20.4167i	−0.372496	+	0.928034i
$23$		−	0.700934i		−	0.0304754i	−0.999884	−	0.0152377i	$-0.995150\pi$
$23$		−	0.700934i		−	0.0304754i	0.999884	−	0.0152377i	$-0.00485050\pi$
$24$	6.76982	+	6.05959i	0.282076	+	0.252483i
$25$	−4.04508	+	2.93893i	−0.161803	+	0.117557i
$26$	−8.42260	−	8.11765i	−0.323946	−	0.312217i
$27$	18.0490	−	5.86448i	0.668482	−	0.217203i
$28$	−31.7641	+	1.17163i	−1.13443	+	0.0418439i
$29$	−4.33244	−	3.14770i	−0.149394	−	0.108541i	0.510577	−	0.859832i	$-0.329432\pi$
$29$	−4.33244	−	3.14770i	−0.149394	−	0.108541i	−0.659972	+	0.751290i	$0.729432\pi$
$30$	−2.38886	−	4.48218i	−0.0796287	−	0.149406i
$31$	14.3708	+	4.66937i	0.463575	+	0.150625i	0.531487	−	0.847067i	$-0.321634\pi$
$31$	14.3708	+	4.66937i	0.463575	+	0.150625i	−0.0679115	+	0.997691i	$0.521634\pi$
$32$	−24.6140	−	20.4487i	−0.769188	−	0.639022i
$33$	8.04258	+	9.55962i	0.243715	+	0.289685i
$34$	48.9871	+	6.83568i	1.44080	+	0.201049i
$35$	16.8991	+	5.49085i	0.482831	+	0.156881i
$36$	−28.9600	+	10.6050i	−0.804445	+	0.294583i
$37$	19.8276	+	14.4056i	0.535882	+	0.389341i	0.822553	−	0.568688i	$-0.192549\pi$
$37$	19.8276	+	14.4056i	0.535882	+	0.389341i	−0.286671	+	0.958029i	$0.592549\pi$
$38$	−70.5157	+	12.5052i	−1.85568	+	0.329083i
$39$	−6.31747	+	2.05267i	−0.161986	+	0.0526326i
$40$	8.98983	+	15.4655i	0.224746	+	0.386639i
$41$	−4.56575	+	3.31721i	−0.111360	+	0.0809076i	−0.642071	−	0.766645i	$-0.721925\pi$
$41$	−4.56575	+	3.31721i	−0.111360	+	0.0809076i	0.530712	+	0.847552i	$0.321925\pi$
$42$	−7.89652	+	16.2307i	−0.188012	+	0.386444i
$43$			32.1162i			0.746888i	0.927653	+	0.373444i	$0.121823\pi$
$43$			32.1162i			0.746888i	−0.927653	+	0.373444i	$0.878177\pi$
$44$	−29.5481	−	32.6023i	−0.671547	−	0.740962i
$45$	17.2405			0.383121
$46$	1.26059	+	0.613302i	0.0274042	+	0.0133327i
$47$	−16.5912	−	22.8359i	−0.353005	−	0.485869i	0.595178	−	0.803594i	$-0.297081\pi$
$47$	−16.5912	−	22.8359i	−0.353005	−	0.485869i	−0.948183	+	0.317724i	$0.897081\pi$
$48$	−16.8213	+	6.87315i	−0.350444	+	0.143191i
$49$	−4.37127	−	13.4534i	−0.0892096	−	0.274559i
$50$	−1.74614	−	9.84637i	−0.0349228	−	0.196927i
$51$	16.5091	−	22.7229i	0.323708	−	0.445546i
$52$	21.9688	−	8.04482i	0.422476	−	0.154708i
$53$	−17.1581	+	52.8071i	−0.323737	+	0.996361i	0.648270	+	0.761411i	$0.275493\pi$
$53$	−17.1581	+	52.8071i	−0.323737	+	0.996361i	−0.972007	+	0.234951i	$0.924507\pi$
$54$	−5.24554	+	37.5915i	−0.0971396	+	0.696139i
$55$	9.24361	+	22.7938i	0.168066	+	0.414432i
$56$	25.6858	−	58.1512i	0.458675	−	1.03841i
$57$	−12.5669	+	38.6770i	−0.220472	+	0.678543i
$58$	9.45176	−	5.03749i	0.162961	−	0.0868533i
$59$	64.5303	−	88.8183i	1.09373	−	1.50540i	0.250296	−	0.968169i	$-0.419472\pi$
$59$	64.5303	−	88.8183i	1.09373	−	1.50540i	0.843438	−	0.537226i	$-0.180528\pi$
$60$	10.1512	−	0.374429i	0.169186	−	0.00624048i
$61$	−17.6349	−	54.2745i	−0.289096	−	0.889747i	−0.985141	−	0.171748i	$-0.945058\pi$
$61$	−17.6349	−	54.2745i	−0.289096	−	0.889747i	0.696045	−	0.717999i	$-0.254942\pi$
$62$	−20.9718	+	21.7596i	−0.338255	+	0.350961i
$63$	−36.0126	−	49.5671i	−0.571629	−	0.786780i
$64$	58.3127	−	26.3748i	0.911136	−	0.412107i
$65$	−13.0784			−0.201207
$66$	−24.2296	+	6.09969i	−0.367115	+	0.0924196i
$67$		−	69.6011i		−	1.03882i	−0.854524	−	0.519411i	$-0.826151\pi$
$67$		−	69.6011i		−	1.03882i	0.854524	−	0.519411i	$-0.173849\pi$
$68$	−55.1562	+	82.1196i	−0.811121	+	1.20764i
$69$	0.644022	−	0.467910i	0.00933366	−	0.00678130i
$70$	−24.6613	+	25.5878i	−0.352305	+	0.365539i
$71$	60.6265	−	19.6987i	0.853894	−	0.277447i	0.150818	−	0.988562i	$-0.451809\pi$
$71$	60.6265	−	19.6987i	0.853894	−	0.277447i	0.703076	+	0.711115i	$0.251809\pi$
$72$	6.26689	−	61.3622i	0.0870402	−	0.852252i
$73$	−62.6736	−	45.5351i	−0.858543	−	0.623768i	0.0689453	−	0.997620i	$-0.478037\pi$
$73$	−62.6736	−	45.5351i	−0.858543	−	0.623768i	−0.927488	+	0.373853i	$0.878037\pi$
$74$	−43.2565	+	23.0543i	−0.584547	+	0.311545i
$75$	−5.40061	−	1.75476i	−0.0720081	−	0.0233968i
$76$	39.2099	−	137.761i	0.515919	−	1.81264i
$77$	46.2247	−	74.1884i	0.600320	−	0.963485i
$78$	1.83603	−	13.1577i	0.0235389	−	0.168688i
$79$	37.5999	+	12.2170i	0.475948	+	0.154645i	0.537161	−	0.843480i	$-0.319497\pi$
$79$	37.5999	+	12.2170i	0.475948	+	0.154645i	−0.0612126	+	0.998125i	$0.519497\pi$
$80$	−35.6799	+	2.63571i	−0.445998	+	0.0329464i
$81$	−38.7020	−	28.1186i	−0.477802	−	0.347143i
$82$	−1.97090	−	11.1138i	−0.0240353	−	0.135534i
$83$	−128.649	+	41.8007i	−1.54999	+	0.503623i	−0.954112	−	0.299450i	$-0.903197\pi$
$83$	−128.649	+	41.8007i	−1.54999	+	0.503623i	−0.595881	+	0.803073i	$0.703197\pi$
$84$	−22.2807	−	28.4029i	−0.265246	−	0.338130i
$85$	44.7385	−	32.5044i	0.526335	−	0.382405i
$86$	−57.7593	−	28.1010i	−0.671620	−	0.326756i
$87$		−	6.08192i		−	0.0699072i
$88$	84.4875	−	24.6143i	0.960085	−	0.279708i
$89$	22.8405			0.256635			0.128317	−	0.991733i	$-0.459042\pi$
$89$	22.8405			0.256635			0.128317	+	0.991733i	$0.459042\pi$
$90$	−15.0850	+	31.0061i	−0.167611	+	0.344512i
$91$	27.3188	+	37.6011i	0.300207	+	0.413199i
$92$	−2.20598	+	1.73048i	−0.0239781	+	0.0188096i
$93$	5.30303	+	16.3211i	0.0570219	+	0.175495i
$94$	55.5861	−	9.85756i	0.591341	−	0.104868i
$95$	−47.0634	+	64.7773i	−0.495405	+	0.681866i
$96$	2.35727	−	36.2661i	0.0245549	−	0.377772i
$97$	−35.1693	+	108.240i	−0.362570	+	1.11587i	0.588919	+	0.808192i	$0.299554\pi$
$97$	−35.1693	+	108.240i	−0.362570	+	1.11587i	−0.951489	+	0.307683i	$0.900446\pi$
$98$	28.0200	+	3.90993i	0.285918	+	0.0398972i
$99$	20.4113	−	82.3191i	0.206175	−	0.831506i
$100$	19.2360	+	5.47502i	0.192360	+	0.0547502i
$101$	−46.7472	+	143.873i	−0.462844	+	1.42449i	0.398830	+	0.917025i	$0.369416\pi$
$101$	−46.7472	+	143.873i	−0.462844	+	1.42449i	−0.861674	+	0.507462i	$0.830584\pi$
$102$	26.4207	+	49.5728i	0.259027	+	0.486008i
$103$	−65.1745	+	89.7050i	−0.632762	+	0.870922i	−0.998204	−	0.0599122i	$-0.980918\pi$
$103$	−65.1745	+	89.7050i	−0.632762	+	0.870922i	0.365442	+	0.930834i	$0.380918\pi$
$104$	−4.75400	+	46.5487i	−0.0457115	+	0.447584i
$105$	6.23599	+	19.1924i	0.0593904	+	0.182785i
$106$	−79.9579	−	77.0630i	−0.754320	−	0.727010i
$107$	−46.4231	−	63.8960i	−0.433861	−	0.597159i	0.534973	−	0.844869i	$-0.320322\pi$
$107$	−46.4231	−	63.8960i	−0.433861	−	0.597159i	−0.968834	+	0.247711i	$0.920322\pi$
$108$	−63.0166	−	42.3256i	−0.583487	−	0.391903i
$109$	−144.081			−1.32184			−0.660921	−	0.750455i	$-0.729834\pi$
$109$	−144.081			−1.32184			−0.660921	+	0.750455i	$0.729834\pi$
$110$	−49.0813	−	3.31991i	−0.446194	−	0.0301810i
$111$			27.8342i			0.250759i
$112$	82.1074	+	97.0756i	0.733102	+	0.866747i
$113$	136.692	−	99.3123i	1.20966	−	0.878870i	0.214461	−	0.976733i	$-0.431201\pi$
$113$	136.692	−	99.3123i	1.20966	−	0.878870i	0.995200	+	0.0978629i	$0.0312007\pi$
$114$	−58.5627	−	56.4424i	−0.513708	−	0.495109i
$115$	1.49062	−	0.484333i	0.0129620	−	0.00421159i
$116$	0.789575	+	21.4062i	0.00680668	+	0.184536i
$117$	36.4832	+	26.5066i	0.311822	+	0.226552i
$118$	103.272	+	193.768i	0.875191	+	1.64211i
$119$	−186.903	−	60.7286i	−1.57062	−	0.510324i
$120$	−8.20866	+	18.5840i	−0.0684055	+	0.154866i
$121$	119.778	−	17.1500i	0.989905	−	0.141736i
$122$	113.040	+	15.7737i	0.926558	+	0.129292i
$123$	−6.09575	−	1.98063i	−0.0495589	−	0.0161027i
$124$	−20.7836	−	56.7558i	−0.167610	−	0.457708i
$125$	−9.04508	−	6.57164i	−0.0723607	−	0.0525731i
$126$	120.654	−	21.3966i	0.957572	−	0.169815i
$127$	−8.35132	+	2.71351i	−0.0657585	+	0.0213662i	−0.341712	−	0.939805i	$-0.611007\pi$
$127$	−8.35132	+	2.71351i	−0.0657585	+	0.0213662i	0.275953	+	0.961171i	$0.411007\pi$
$128$	−3.58859	+	127.950i	−0.0280358	+	0.999607i
$129$	−29.5086	+	21.4392i	−0.228749	+	0.166196i
$130$	11.4433	−	23.5209i	0.0880258	−	0.180930i
$131$			114.044i			0.870562i	0.900295	+	0.435281i	$0.143351\pi$
$131$			114.044i			0.870562i	−0.900295	+	0.435281i	$0.856649\pi$
$132$	10.2304	−	48.9127i	0.0775028	−	0.370551i
$133$	284.546			2.13944
$134$	125.174	+	60.8995i	0.934134	+	0.454474i
$135$	24.9431	+	34.3313i	0.184764	+	0.254306i
$136$	−99.4272	−	171.048i	−0.731082	−	1.25771i
$137$	−39.6737	−	122.103i	−0.289589	−	0.891264i	−0.984985	−	0.172638i	$-0.944771\pi$
$137$	−39.6737	−	122.103i	−0.289589	−	0.891264i	0.695396	−	0.718627i	$-0.255229\pi$
$138$	0.278005	+	1.56765i	0.00201453	+	0.0113598i
$139$	−141.105	+	194.214i	−1.01514	+	1.39723i	−0.0995915	+	0.995028i	$0.531754\pi$
$139$	−141.105	+	194.214i	−1.01514	+	1.39723i	−0.915553	+	0.402198i	$0.868246\pi$
$140$	−24.4401	−	66.7409i	−0.174572	−	0.476720i
$141$	9.90623	−	30.4882i	0.0702569	−	0.216229i
$142$	−17.6197	+	126.269i	−0.124082	+	0.889222i
$143$	−15.4838	+	62.4464i	−0.108279	+	0.436688i
$144$	104.873	+	64.9613i	0.728286	+	0.451120i
$145$	3.70034	−	11.3885i	0.0255196	−	0.0785413i
$146$	136.730	−	72.8730i	0.936510	−	0.499130i
$147$	9.44301	−	12.9972i	0.0642382	−	0.0884163i
$148$	−3.61353	−	97.9666i	−0.0244157	−	0.661936i
$149$	10.6104	+	32.6553i	0.0712104	+	0.219163i	0.980328	−	0.197377i	$-0.0632424\pi$
$149$	10.6104	+	32.6553i	0.0712104	+	0.219163i	−0.909117	+	0.416540i	$0.863242\pi$
$150$	7.88126	−	8.17733i	0.0525418	−	0.0545155i
$151$	97.5167	+	134.220i	0.645806	+	0.888876i	0.998909	−	0.0467089i	$-0.0148733\pi$
$151$	97.5167	+	134.220i	0.645806	+	0.888876i	−0.353102	+	0.935585i	$0.614873\pi$
$152$	213.447	+	191.054i	1.40426	+	1.25694i
$153$	−190.679			−1.24627
$154$	92.9783	+	148.046i	0.603755	+	0.961337i
$155$			33.7879i			0.217986i
$156$	22.0569	+	14.8147i	0.141390	+	0.0949660i
$157$	−92.8633	+	67.4691i	−0.591486	+	0.429740i	−0.842847	−	0.538154i	$-0.819122\pi$
$157$	−92.8633	+	67.4691i	−0.591486	+	0.429740i	0.251361	+	0.967893i	$0.419122\pi$
$158$	−54.8707	+	56.9319i	−0.347283	+	0.360329i
$159$	−59.9734	+	19.4865i	−0.377191	+	0.122557i
$160$	26.4789	−	66.4746i	0.165493	−	0.415466i
$161$	−4.50616	−	3.27392i	−0.0279886	−	0.0203349i
$162$	84.4332	−	45.0002i	0.521193	−	0.277779i
$163$	125.257	+	40.6984i	0.768446	+	0.249683i	0.666900	−	0.745148i	$-0.267621\pi$
$163$	125.257	+	40.6984i	0.768446	+	0.249683i	0.101546	+	0.994831i	$0.467621\pi$
$164$	21.7120	+	6.17974i	0.132390	+	0.0376813i
$165$	−14.7725	+	23.7091i	−0.0895301	+	0.143692i
$166$	37.3890	−	267.944i	0.225235	−	1.61412i
$167$	−187.210	−	60.8283i	−1.12102	−	0.364241i	−0.310863	−	0.950455i	$-0.600618\pi$
$167$	−187.210	−	60.8283i	−1.12102	−	0.364241i	−0.810157	+	0.586214i	$0.800618\pi$
$168$	70.5763	−	15.2187i	0.420097	−	0.0905874i
$169$	109.048	+	79.2281i	0.645255	+	0.468805i
$170$	19.3123	+	108.901i	0.113602	+	0.640591i
$171$	262.573	−	85.3152i	1.53552	−	0.498919i
$172$	101.076	−	79.2893i	0.587653	−	0.460984i
$173$	−249.254	+	181.093i	−1.44077	+	1.04678i	−0.452892	+	0.891565i	$0.649608\pi$
$173$	−249.254	+	181.093i	−1.44077	+	1.04678i	−0.987880	+	0.155217i	$0.950392\pi$
$174$	10.9380	+	5.32155i	0.0628622	+	0.0305836i
$175$			39.7321i			0.227041i
$176$	−29.6572	+	173.483i	−0.168507	+	0.985700i
$177$	124.684			0.704430
$178$	−19.9849	+	41.0774i	−0.112275	+	0.230772i
$179$	−110.369	−	151.910i	−0.616586	−	0.848658i	0.380513	−	0.924776i	$-0.375747\pi$
$179$	−110.369	−	151.910i	−0.616586	−	0.848658i	−0.997099	+	0.0761179i	$0.975747\pi$
$180$	−42.5637	−	54.2593i	−0.236465	−	0.301440i
$181$	−60.1926	−	185.254i	−0.332556	−	1.02350i	−0.967914	−	0.251283i	$-0.919147\pi$
$181$	−60.1926	−	185.254i	−0.332556	−	1.02350i	0.635358	−	0.772218i	$-0.280853\pi$
$182$	−91.5269	+	16.2313i	−0.502895	+	0.0891828i
$183$	38.0956	−	52.4341i	0.208173	−	0.286525i
$184$	−1.18200	−	5.48148i	−0.00642389	−	0.0297906i
$185$	−16.9348	+	52.1200i	−0.0915396	+	0.281730i
$186$	−33.9926	−	4.74335i	−0.182756	−	0.0255019i
$187$	−102.234	−	252.098i	−0.546706	−	1.34812i
$188$	−30.9083	+	108.594i	−0.164406	+	0.577626i
$189$	46.6017	−	143.425i	0.246570	−	0.758863i
$190$	−75.3190	−	141.320i	−0.396416	−	0.743788i
$191$	−210.659	+	289.947i	−1.10293	+	1.51805i	−0.271478	+	0.962445i	$0.587513\pi$
$191$	−210.659	+	289.947i	−1.10293	+	1.51805i	−0.831448	+	0.555603i	$0.812487\pi$
$192$	63.1601	+	35.9715i	0.328959	+	0.187351i
$193$	−16.0488	−	49.3930i	−0.0831542	−	0.255922i	0.900832	−	0.434168i	$-0.142958\pi$
$193$	−16.0488	−	49.3930i	−0.0831542	−	0.255922i	−0.983986	+	0.178246i	$0.942958\pi$
$194$	−163.891	−	157.958i	−0.844801	−	0.814215i
$195$	−8.73053	−	12.0165i	−0.0447720	−	0.0616233i
$196$	−31.5487	+	46.9714i	−0.160963	+	0.239650i
$197$	−307.031			−1.55853			−0.779266	−	0.626694i	$-0.784408\pi$
$197$	−307.031			−1.55853			−0.779266	+	0.626694i	$0.784408\pi$
$198$	130.187	+	108.736i	0.657510	+	0.549172i
$199$		−	45.3984i		−	0.228133i	−0.993473	−	0.114066i	$-0.963612\pi$
$199$		−	45.3984i		−	0.228133i	0.993473	−	0.114066i	$-0.0363876\pi$
$200$	−26.6776	+	29.8044i	−0.133388	+	0.149022i
$201$	63.9499	−	46.4623i	0.318159	−	0.231156i
$202$	−217.846	−	209.958i	−1.07844	−	1.03940i
$203$	−40.4719	+	13.1501i	−0.199369	+	0.0647788i
$204$	−112.272	+	4.14117i	−0.550351	+	0.0202999i
$205$	−10.2093	−	7.41751i	−0.0498016	−	0.0361830i
$206$	−104.303	−	195.703i	−0.506327	−	0.950013i
$207$	−5.13981	−	1.67003i	−0.0248300	−	0.00806776i
$208$	−79.5557	−	49.2789i	−0.382480	−	0.236918i
$209$	253.577	+	301.408i	1.21328	+	1.44214i
$210$	−39.9729	−	5.57784i	−0.190347	−	0.0265612i
$211$	126.043	+	40.9540i	0.597362	+	0.194095i	0.592063	−	0.805891i	$-0.298314\pi$
$211$	126.043	+	40.9540i	0.597362	+	0.194095i	0.00529825	+	0.999986i	$0.498314\pi$
$212$	208.555	−	76.3716i	0.983751	−	0.360243i
$213$	58.5706	+	42.5540i	0.274979	+	0.199784i
$214$	155.533	−	27.5820i	0.726789	−	0.128888i
$215$	−68.2992	+	22.1917i	−0.317671	+	0.103217i
$216$	131.258	−	76.2980i	0.607678	−	0.353232i
$217$	97.1416	−	70.5775i	0.447657	−	0.325242i
$218$	126.068	−	259.122i	0.578292	−	1.18863i
$219$		−	87.9819i		−	0.401744i
$220$	48.9158	−	85.3654i	0.222345	−	0.388024i
$221$	144.647			0.654512
$222$	−50.0584	−	24.3544i	−0.225488	−	0.109704i
$223$	142.082	+	195.560i	0.637141	+	0.876950i	0.998459	−	0.0554930i	$-0.0176731\pi$
$223$	142.082	+	195.560i	0.637141	+	0.876950i	−0.361318	+	0.932443i	$0.617673\pi$
$224$	−246.428	+	62.7268i	−1.10012	+	0.280030i
$225$	11.9129	+	36.6640i	0.0529461	+	0.162951i
$226$	59.0057	+	332.729i	0.261087	+	1.47225i
$227$	208.039	−	286.342i	0.916473	−	1.26142i	−0.0484342	−	0.998826i	$-0.515423\pi$
$227$	208.039	−	286.342i	0.916473	−	1.26142i	0.964907	−	0.262591i	$-0.0845769\pi$
$228$	152.750	−	55.9361i	0.669956	−	0.245334i
$229$	15.0277	−	46.2506i	0.0656233	−	0.201968i	−0.912868	−	0.408254i	$-0.866138\pi$
$229$	15.0277	−	46.2506i	0.0656233	−	0.201968i	0.978492	+	0.206286i	$0.0661378\pi$
$230$	−0.433217	+	3.10459i	−0.00188355	+	0.0134982i
$231$	99.0221	−	7.05308i	0.428667	−	0.0305328i
$232$	−39.1888	−	17.3100i	−0.168917	−	0.0746119i
$233$	17.3327	−	53.3447i	0.0743894	−	0.228947i	−0.906947	−	0.421244i	$-0.861594\pi$
$233$	17.3327	−	53.3447i	0.0743894	−	0.228947i	0.981337	+	0.192297i	$0.0615936\pi$
$234$	−79.5926	+	42.4204i	−0.340139	+	0.181284i
$235$	37.0991	−	51.0625i	0.157869	−	0.217287i
$236$	−438.844	+	16.1869i	−1.85951	+	0.0685885i
$237$	13.8749	+	42.7025i	0.0585438	+	0.180179i
$238$	272.754	−	283.000i	1.14602	−	1.18907i
$239$	−59.0197	−	81.2336i	−0.246944	−	0.339890i	0.667494	−	0.744615i	$-0.267367\pi$
$239$	−59.0197	−	81.2336i	−0.246944	−	0.339890i	−0.914438	+	0.404726i	$0.867367\pi$
$240$	−26.2399	−	31.0234i	−0.109333	−	0.129264i
$241$	−48.2953			−0.200396			−0.100198	−	0.994968i	$-0.531948\pi$
$241$	−48.2953			−0.200396			−0.100198	+	0.994968i	$0.531948\pi$
$242$	−73.9602	+	230.421i	−0.305620	+	0.952153i
$243$		−	225.131i		−	0.926465i
$244$	−127.276	+	189.495i	−0.521622	+	0.776619i
$245$	25.5899	−	18.5921i	0.104448	−	0.0758863i
$246$	8.89571	−	9.22988i	0.0361614	−	0.0375198i
$247$	−199.185	+	64.7192i	−0.806418	+	0.262021i
$248$	120.258	+	12.2819i	0.484910	+	0.0495236i
$249$	−124.287	−	90.2997i	−0.499144	−	0.362649i
$250$	19.7330	−	10.5171i	0.0789320	−	0.0420683i
$251$	159.853	+	51.9394i	0.636864	+	0.206930i	0.609613	−	0.792699i	$-0.291325\pi$
$251$	159.853	+	51.9394i	0.636864	+	0.206930i	0.0272510	+	0.999629i	$0.491325\pi$
$252$	−67.0890	+	235.712i	−0.266226	+	0.935364i
$253$	−0.547795	−	7.69079i	−0.00216520	−	0.0303984i
$254$	2.42712	−	17.3937i	0.00955561	−	0.0684791i
$255$	59.7306	+	19.4076i	0.234237	+	0.0761084i
$256$	−226.971	−	118.407i	−0.886605	−	0.462528i
$257$	−104.736	−	76.0952i	−0.407533	−	0.296090i	0.365069	−	0.930980i	$-0.381045\pi$
$257$	−104.736	−	76.0952i	−0.407533	−	0.296090i	−0.772602	+	0.634890i	$0.781045\pi$
$258$	−12.7380	−	71.8284i	−0.0493719	−	0.278405i
$259$	185.222	−	60.1821i	0.715141	−	0.232363i
$260$	32.2884	+	41.1605i	0.124186	+	0.158310i
$261$	−33.4038	+	24.2693i	−0.127984	+	0.0929859i
$262$	−205.101	−	99.7857i	−0.782830	−	0.380862i
$263$		−	175.240i		−	0.666311i	−0.942872	−	0.333156i	$-0.891887\pi$
$263$		−	175.240i		−	0.666311i	0.942872	−	0.333156i	$-0.108113\pi$
$264$	79.0155	+	61.1963i	0.299301	+	0.231804i
$265$	−124.157			−0.468517
$266$	−248.971	+	511.740i	−0.935982	+	1.92384i
$267$	15.2472	+	20.9860i	0.0571057	+	0.0785992i
$268$	−219.049	+	171.833i	−0.817347	+	0.641168i
$269$	−92.0014	−	283.151i	−0.342013	−	1.05261i	−0.963164	−	0.268916i	$-0.913335\pi$
$269$	−92.0014	−	283.151i	−0.342013	−	1.05261i	0.621151	−	0.783691i	$-0.286665\pi$
$270$	−83.5677	+	14.8198i	−0.309510	+	0.0548881i
$271$	−176.110	+	242.395i	−0.649854	+	0.894447i	−0.999093	−	0.0425869i	$-0.986440\pi$
$271$	−176.110	+	242.395i	−0.649854	+	0.894447i	0.349239	+	0.937034i	$0.386440\pi$
$272$	394.618	−	29.1509i	1.45080	−	0.107172i
$273$	−16.3114	+	50.2014i	−0.0597487	+	0.183888i
$274$	254.310	+	35.4866i	0.928138	+	0.129513i
$275$	−42.0867	+	35.4078i	−0.153042	+	0.128756i
$276$	−3.06259	−	0.871683i	−0.0110963	−	0.00315827i
$277$	19.5246	−	60.0907i	0.0704861	−	0.216934i	−0.909608	−	0.415468i	$-0.863618\pi$
$277$	19.5246	−	60.0907i	0.0704861	−	0.216934i	0.980094	+	0.198534i	$0.0636180\pi$
$278$	−225.821	−	423.703i	−0.812304	−	1.52411i
$279$	68.4791	−	94.2534i	0.245445	−	0.337826i
$280$	141.414	+	14.4426i	0.505052	+	0.0515807i
$281$	−14.3794	−	44.2552i	−0.0511722	−	0.157492i	0.922205	−	0.386702i	$-0.126386\pi$
$281$	−14.3794	−	44.2552i	−0.0511722	−	0.157492i	−0.973377	+	0.229210i	$0.926386\pi$
$282$	46.1637	+	44.4924i	0.163701	+	0.157774i
$283$	−83.3873	−	114.773i	−0.294655	−	0.405558i	0.635864	−	0.771801i	$-0.280644\pi$
$283$	−83.3873	−	114.773i	−0.294655	−	0.405558i	−0.930519	+	0.366243i	$0.880644\pi$
$284$	−211.672	−	142.171i	−0.745324	−	0.500603i
$285$	−90.9350			−0.319070
$286$	−98.7585	−	82.4861i	−0.345310	−	0.288413i
$287$			44.8463i			0.156259i
$288$	−208.591	+	131.769i	−0.724275	+	0.457532i
$289$	−261.001	+	189.628i	−0.903117	+	0.656153i
$290$	17.2439	+	16.6196i	0.0594616	+	0.0573088i
$291$	−122.929	+	39.9420i	−0.422436	+	0.137258i
$292$	11.4221	+	309.665i	0.0391167	+	1.06050i
$293$	299.818	+	217.830i	1.02327	+	0.743448i	0.966950	−	0.254965i	$-0.0820640\pi$
$293$	299.818	+	217.830i	1.02327	+	0.743448i	0.0563179	+	0.998413i	$0.482064\pi$
$294$	15.1123	+	28.3550i	0.0514025	+	0.0964456i
$295$	233.473	+	75.8599i	0.791433	+	0.257152i
$296$	179.350	+	79.2199i	0.605910	+	0.267635i
$297$	193.454	−	78.4519i	0.651361	−	0.264148i
$298$	−68.0127	−	9.49053i	−0.228230	−	0.0318474i
$299$	3.89901	+	1.26686i	0.0130402	+	0.00423701i
$300$	7.81056	+	21.3290i	0.0260352	+	0.0710967i
$301$	206.468	+	150.008i	0.685942	+	0.498366i
$302$	−326.713	+	57.9389i	−1.08183	+	0.191851i
$303$	−163.398	+	53.0912i	−0.539267	+	0.175218i
$304$	−530.363	+	216.705i	−1.74462	+	0.712847i
$305$	103.236	−	75.0056i	0.338480	−	0.245920i
$306$	166.840	−	342.926i	0.545229	−	1.12067i
$307$			58.3107i			0.189937i	0.995480	+	0.0949685i	$0.0302750\pi$
$307$			58.3107i			0.189937i	−0.995480	+	0.0949685i	$0.969725\pi$
$308$	−347.607	+	37.6797i	−1.12859	+	0.122337i
$309$	−125.929			−0.407537
$310$	−60.7657	−	29.5636i	−0.196018	−	0.0953666i
$311$	−8.17984	−	11.2586i	−0.0263017	−	0.0362012i	0.795664	−	0.605739i	$-0.207122\pi$
$311$	−8.17984	−	11.2586i	−0.0263017	−	0.0362012i	−0.821965	+	0.569538i	$0.807122\pi$
$312$	−45.9428	+	26.7057i	−0.147252	+	0.0855951i
$313$	−117.541	−	361.754i	−0.375530	−	1.15576i	−0.943120	−	0.332451i	$-0.892124\pi$
$313$	−117.541	−	361.754i	−0.375530	−	1.15576i	0.567591	−	0.823311i	$-0.307876\pi$
$314$	−40.0863	−	226.044i	−0.127663	−	0.719885i
$315$	80.5267	−	110.835i	0.255640	−	0.351859i
$316$	−54.3784	−	148.496i	−0.172083	−	0.469925i
$317$	−126.672	+	389.857i	−0.399597	+	1.22983i	0.525726	+	0.850654i	$0.323794\pi$
$317$	−126.672	+	389.857i	−0.399597	+	1.22983i	−0.925323	+	0.379180i	$0.876206\pi$
$318$	17.4299	−	124.909i	0.0548111	−	0.392797i
$319$	−49.9964	−	31.1513i	−0.156728	−	0.0976530i
$320$	96.3825	+	105.785i	0.301195	+	0.330577i
$321$	27.7182	−	85.3078i	0.0863494	−	0.265756i
$322$	9.83076	−	5.23949i	0.0305303	−	0.0162717i
$323$	520.520	−	716.435i	1.61152	−	2.21806i
$324$	7.05332	+	191.223i	0.0217695	+	0.590194i
$325$	−9.03698	−	27.8130i	−0.0278061	−	0.0855783i
$326$	−182.791	+	189.657i	−0.560708	+	0.581771i
$327$	−96.1814	−	132.382i	−0.294133	−	0.404839i
$328$	−30.1115	+	33.6407i	−0.0918032	+	0.102563i
$329$	−224.301			−0.681767
$330$	−29.7140	−	47.3125i	−0.0900424	−	0.143371i
$331$			142.810i			0.431450i	0.976454	+	0.215725i	$0.0692114\pi$
$331$			142.810i			0.431450i	−0.976454	+	0.215725i	$0.930789\pi$
$332$	449.168	+	301.687i	1.35292	+	0.908697i
$333$	152.874	−	111.070i	0.459082	−	0.333543i
$334$	273.201	−	283.464i	0.817968	−	0.848695i
$335$	148.016	−	48.0932i	0.441838	−	0.143562i
$336$	−34.3827	+	140.244i	−0.102330	+	0.417392i
$337$	44.7585	+	32.5189i	0.132814	+	0.0964954i	0.652209	−	0.758039i	$-0.273842\pi$
$337$	44.7585	+	32.5189i	0.132814	+	0.0964954i	−0.519395	+	0.854535i	$0.673842\pi$
$338$	−237.902	+	126.794i	−0.703853	+	0.375131i
$339$	182.497	+	59.2970i	0.538341	+	0.174917i
$340$	−212.750	−	60.5535i	−0.625734	−	0.178099i
$341$	161.329	+	40.0021i	0.473105	+	0.117308i
$342$	−76.3109	+	546.873i	−0.223131	+	1.59904i
$343$	263.411	+	85.5875i	0.767963	+	0.249526i
$344$	54.1581	+	251.157i	0.157436	+	0.730107i
$345$	1.44008	+	1.04628i	0.00417414	+	0.00303269i
$346$	−107.595	−	606.722i	−0.310969	−	1.75353i
$347$	149.059	−	48.4321i	0.429564	−	0.139574i	−0.0862518	−	0.996273i	$-0.527489\pi$
$347$	149.059	−	48.4321i	0.429564	−	0.139574i	0.515816	+	0.856700i	$0.327489\pi$
$348$	−19.1411	+	15.0152i	−0.0550031	+	0.0431472i
$349$	414.734	−	301.322i	1.18835	−	0.863387i	0.195261	−	0.980751i	$-0.437445\pi$
$349$	414.734	−	301.322i	1.18835	−	0.863387i	0.993089	+	0.117364i	$0.0374445\pi$
$350$	−71.4562	−	34.7648i	−0.204160	−	0.0993279i
$351$			110.999i			0.316236i
$352$	−286.051	−	205.131i	−0.812645	−	0.582759i
$353$	−143.806			−0.407384			−0.203692	−	0.979035i	$-0.565294\pi$
$353$	−143.806			−0.407384			−0.203692	+	0.979035i	$0.565294\pi$
$354$	−109.096	+	224.238i	−0.308181	+	0.633440i
$355$	83.7837	+	115.318i	0.236010	+	0.324840i
$356$	−56.3892	−	71.8837i	−0.158397	−	0.201921i
$357$	−68.9699	−	212.268i	−0.193193	−	0.594587i
$358$	369.772	−	65.5749i	1.03288	−	0.183170i
$359$	136.807	−	188.298i	0.381077	−	0.524508i	−0.574792	−	0.818299i	$-0.694917\pi$
$359$	136.807	−	188.298i	0.381077	−	0.524508i	0.955870	+	0.293791i	$0.0949171\pi$
$360$	134.825	−	29.0729i	0.374513	−	0.0807580i
$361$	−284.670	+	876.125i	−0.788560	+	2.42694i
$362$	385.836	+	53.8398i	1.06585	+	0.148729i
$363$	95.7159	+	98.6047i	0.263680	+	0.271638i
$364$	50.8930	−	178.808i	0.139816	−	0.491232i
$365$	53.5297	−	164.747i	0.146657	−	0.451363i
$366$	60.9671	+	114.392i	0.166577	+	0.312545i
$367$	−326.330	+	449.154i	−0.889182	+	1.22385i	0.0846107	+	0.996414i	$0.473035\pi$
$367$	−326.330	+	449.154i	−0.889182	+	1.22385i	−0.973792	+	0.227439i	$0.926965\pi$
$368$	10.8924	+	2.67042i	0.0295988	+	0.00725657i
$369$	13.4462	+	41.3833i	0.0364397	+	0.112150i
$370$	−78.9175	−	76.0603i	−0.213291	−	0.205568i
$371$	259.344	+	356.957i	0.699042	+	0.962148i
$372$	38.2734	−	56.9836i	0.102886	−	0.153182i
$373$	−416.777			−1.11736			−0.558682	−	0.829382i	$-0.688693\pi$
$373$	−416.777			−1.11736			−0.558682	+	0.829382i	$0.688693\pi$
$374$	542.838	+	36.7181i	1.45144	+	0.0981767i
$375$		−	12.6976i		−	0.0338602i
$376$	−168.256	−	150.604i	−0.447489	−	0.400543i
$377$	25.3398	−	18.4104i	0.0672143	−	0.0488341i
$378$	217.167	+	209.305i	0.574516	+	0.553716i
$379$	307.650	−	99.9616i	0.811742	−	0.263751i	0.126407	−	0.991979i	$-0.459656\pi$
$379$	307.650	−	99.9616i	0.811742	−	0.263751i	0.685335	+	0.728228i	$0.259656\pi$
$380$	320.059	−	11.8055i	0.842260	−	0.0310670i
$381$	−8.06813	−	5.86184i	−0.0211762	−	0.0153854i
$382$	−337.133	−	632.556i	−0.882546	−	1.65591i
$383$	6.92719	+	2.25078i	0.0180866	+	0.00587671i	0.318046	−	0.948075i	$-0.396973\pi$
$383$	6.92719	+	2.25078i	0.0180866	+	0.00587671i	−0.299960	+	0.953952i	$0.596973\pi$
$384$	−119.957	+	82.1158i	−0.312387	+	0.213843i
$385$	189.711	+	47.0397i	0.492757	+	0.122181i
$386$	102.873	+	14.3550i	0.266510	+	0.0371890i
$387$	235.502	+	76.5192i	0.608532	+	0.197724i
$388$	427.480	−	156.540i	1.10175	−	0.403455i
$389$	580.800	+	421.976i	1.49306	+	1.08477i	0.973046	+	0.230611i	$0.0740726\pi$
$389$	580.800	+	421.976i	1.49306	+	1.08477i	0.520012	+	0.854159i	$0.325927\pi$
$390$	29.2502	−	5.18718i	0.0750004	−	0.0133005i
$391$	−16.4863	+	5.35671i	−0.0421644	+	0.0137000i
$392$	−56.8711	−	97.8376i	−0.145079	−	0.249586i
$393$	−104.784	+	76.1300i	−0.266626	+	0.193715i
$394$	268.645	−	552.179i	0.681841	−	1.40147i
$395$			88.4027i			0.223804i
$396$	−309.467	+	138.993i	−0.781482	+	0.350992i
$397$	122.158			0.307703			0.153851	−	0.988094i	$-0.450832\pi$
$397$	122.158			0.307703			0.153851	+	0.988094i	$0.450832\pi$
$398$	81.6466	+	39.7226i	0.205142	+	0.0998055i
$399$	189.949	+	261.442i	0.476063	+	0.655244i
$400$	−30.2594	−	74.0565i	−0.0756484	−	0.185141i
$401$	−205.692	−	633.054i	−0.512947	−	1.57869i	−0.786986	−	0.616971i	$-0.788360\pi$
$401$	−205.692	−	633.054i	−0.512947	−	1.57869i	0.274039	−	0.961719i	$-0.411640\pi$
$402$	27.6053	+	155.664i	0.0686698	+	0.387224i
$403$	−51.9476	+	71.4997i	−0.128902	+	0.177419i
$404$	568.209	−	208.075i	1.40646	−	0.515036i
$405$	33.0554	−	101.734i	0.0816183	−	0.251195i
$406$	11.7622	−	84.2926i	0.0289710	−	0.207617i
$407$	228.811	+	142.566i	0.562189	+	0.350284i
$408$	90.7876	−	205.538i	0.222519	−	0.503770i
$409$	43.6965	−	134.484i	0.106837	−	0.328812i	−0.883320	−	0.468771i	$-0.844697\pi$
$409$	43.6965	−	134.484i	0.106837	−	0.328812i	0.990157	+	0.139959i	$0.0446971\pi$
$410$	22.2730	−	11.8708i	0.0543243	−	0.0289531i
$411$	85.7049	−	117.963i	0.208528	−	0.287014i
$412$	443.224	−	16.3485i	1.07579	−	0.0396808i
$413$	−269.587	−	829.704i	−0.652754	−	2.00897i
$414$	7.50068	−	7.78245i	0.0181176	−	0.0187982i
$415$	−177.789	−	244.706i	−0.428407	−	0.589652i
$416$	158.235	−	99.9588i	0.380373	−	0.240286i
$417$	−272.640			−0.653814
$418$	−763.940	+	192.319i	−1.82761	+	0.460093i
$419$			408.435i			0.974785i	0.873183	+	0.487392i	$0.162052\pi$
$419$			408.435i			0.974785i	−0.873183	+	0.487392i	$0.837948\pi$
$420$	45.0069	−	67.0087i	0.107159	−	0.159544i
$421$	−165.361	+	120.142i	−0.392782	+	0.285373i	−0.766595	−	0.642131i	$-0.778050\pi$
$421$	−165.361	+	120.142i	−0.392782	+	0.285373i	0.373812	+	0.927504i	$0.378050\pi$
$422$	−183.939	+	190.848i	−0.435874	+	0.452247i
$423$	−206.981	+	67.2521i	−0.489316	+	0.158988i
$424$	−45.1310	+	441.899i	−0.106441	+	1.04221i
$425$	100.038	+	72.6821i	0.235384	+	0.171017i
$426$	−127.779	+	68.1023i	−0.299951	+	0.159865i
$427$	−431.289	−	140.134i	−1.01004	−	0.328183i
$428$	−86.4831	+	303.851i	−0.202063	+	0.709933i
$429$	−67.7124	+	27.4596i	−0.157838	+	0.0640083i
$430$	19.8496	−	142.250i	0.0461619	−	0.330813i
$431$	−687.780	−	223.473i	−1.59578	−	0.518499i	−0.629718	−	0.776824i	$-0.716830\pi$
$431$	−687.780	−	223.473i	−1.59578	−	0.518499i	−0.966058	+	0.258324i	$0.916830\pi$
$432$	22.3697	+	302.821i	0.0517817	+	0.700974i
$433$	350.457	+	254.622i	0.809369	+	0.588041i	0.913647	−	0.406507i	$-0.133253\pi$
$433$	350.457	+	254.622i	0.809369	+	0.588041i	−0.104279	+	0.994548i	$0.533253\pi$
$434$	41.9331	+	236.458i	0.0966201	+	0.544834i
$435$	12.9340	−	4.20251i	0.0297333	−	0.00966093i
$436$	355.710	+	453.452i	0.815850	+	1.04003i
$437$	20.3055	−	14.7528i	0.0464658	−	0.0337594i
$438$	158.231	+	76.9823i	0.361258	+	0.175759i
$439$			797.442i			1.81650i	0.418433	+	0.908248i	$0.362580\pi$
$439$			797.442i			1.81650i	−0.418433	+	0.908248i	$0.637420\pi$
$440$	110.725	+	162.665i	0.251647	+	0.369694i
$441$	−109.066			−0.247315
$442$	−126.563	+	260.140i	−0.286342	+	0.588552i
$443$	−368.349	−	506.989i	−0.831488	−	1.14445i	−0.987644	−	0.156713i	$-0.949910\pi$
$443$	−368.349	−	506.989i	−0.831488	−	1.14445i	0.156156	−	0.987732i	$-0.450090\pi$
$444$	87.6001	−	68.7179i	0.197297	−	0.154770i
$445$	15.7824	+	48.5732i	0.0354660	+	0.109153i
$446$	−476.023	+	84.4173i	−1.06732	+	0.189276i
$447$	−22.9209	+	31.5480i	−0.0512773	+	0.0705771i
$448$	102.808	−	498.072i	0.229482	−	1.11177i
$449$	101.267	−	311.666i	0.225538	−	0.694134i	−0.772699	−	0.634773i	$-0.781094\pi$
$449$	101.267	−	311.666i	0.225538	−	0.694134i	0.998237	−	0.0593613i	$-0.0189064\pi$
$450$	−76.3618	−	10.6556i	−0.169693	−	0.0236791i
$451$	−47.5039	+	39.9654i	−0.105330	+	0.0886150i
$452$	−650.024	−	185.012i	−1.43811	−	0.409318i
$453$	−58.2249	+	179.198i	−0.128532	+	0.395580i
$454$	332.940	+	624.691i	0.733349	+	1.37597i
$455$	−61.0867	+	84.0786i	−0.134256	+	0.184788i
$456$	−33.0548	+	323.655i	−0.0724886	+	0.709771i
$457$	224.985	+	692.434i	0.492309	+	1.51517i	0.821108	+	0.570772i	$0.193356\pi$
$457$	224.985	+	692.434i	0.492309	+	1.51517i	−0.328799	+	0.944400i	$0.606644\pi$
$458$	70.0304	+	67.4949i	0.152905	+	0.147369i
$459$	−275.870	−	379.703i	−0.601024	−	0.827239i
$460$	−5.20439	−	3.49557i	−0.0113139	−	0.00759906i
$461$	546.920			1.18638			0.593189	−	0.805064i	$-0.297869\pi$
$461$	546.920			1.18638			0.593189	+	0.805064i	$0.297869\pi$
$462$	−73.9576	+	184.257i	−0.160081	+	0.398825i
$463$		−	122.337i		−	0.264228i	−0.991235	−	0.132114i	$-0.957824\pi$
$463$		−	122.337i		−	0.264228i	0.991235	−	0.132114i	$-0.0421764\pi$
$464$	65.4204	−	55.3331i	0.140992	−	0.119252i
$465$	−31.0445	+	22.5551i	−0.0667623	+	0.0485057i
$466$	80.7718	+	77.8474i	0.173330	+	0.167055i
$467$	118.380	−	38.4640i	0.253490	−	0.0823640i	−0.179515	−	0.983755i	$-0.557453\pi$
$467$	118.380	−	38.4640i	0.253490	−	0.0823640i	0.433006	+	0.901391i	$0.357453\pi$
$468$	−6.64895	−	180.260i	−0.0142072	−	0.385171i
$469$	−447.451	−	325.092i	−0.954054	−	0.693161i
$470$	59.3724	+	111.399i	0.126324	+	0.237020i
$471$	−123.982	−	40.2842i	−0.263232	−	0.0855291i
$472$	354.867	−	803.400i	0.751838	−	1.70212i
$473$	25.0995	+	352.385i	0.0530645	+	0.745001i
$474$	−88.9384	−	12.4105i	−0.187634	−	0.0261825i
$475$	−170.277	−	55.3264i	−0.358478	−	0.116477i
$476$	270.307	+	738.152i	0.567871	+	1.55074i
$477$	346.344	+	251.634i	0.726088	+	0.527534i
$478$	197.735	−	35.0661i	0.413672	−	0.0733601i
$479$	−277.196	+	90.0663i	−0.578696	+	0.188030i	−0.583717	−	0.811958i	$-0.698402\pi$
$479$	−277.196	+	90.0663i	−0.578696	+	0.188030i	0.00502006	+	0.999987i	$0.498402\pi$
$480$	78.7533	−	20.0462i	0.164069	−	0.0417629i
$481$	−115.969	+	84.2564i	−0.241100	+	0.175169i
$482$	42.2574	−	86.8566i	0.0876709	−	0.180200i
$483$		−	6.32580i		−	0.0130969i
$484$	−349.687	−	334.627i	−0.722493	−	0.691378i
$485$	−254.487			−0.524716
$486$	404.886	+	196.985i	0.833099	+	0.405318i
$487$	−94.4089	−	129.943i	−0.193858	−	0.266823i	0.701012	−	0.713149i	$-0.252732\pi$
$487$	−94.4089	−	129.943i	−0.193858	−	0.266823i	−0.894870	+	0.446327i	$0.852732\pi$
$488$	−229.433	−	394.703i	−0.470150	−	0.808817i
$489$	46.2214	+	142.255i	0.0945223	+	0.290910i
$490$	11.0464	+	62.2898i	0.0225436	+	0.127122i
$491$	−25.5004	+	35.0982i	−0.0519355	+	0.0714831i	−0.834195	−	0.551470i	$-0.814067\pi$
$491$	−25.5004	+	35.0982i	−0.0519355	+	0.0714831i	0.782259	+	0.622953i	$0.214067\pi$
$492$	8.81590	+	24.0744i	0.0179185	+	0.0489317i
$493$	−40.9257	+	125.956i	−0.0830136	+	0.255490i
$494$	57.8887	−	414.852i	0.117184	−	0.839781i
$495$	189.166	−	13.4738i	0.382153	−	0.0272198i
$496$	−127.311	+	205.531i	−0.256676	+	0.414376i
$497$	156.535	−	481.764i	0.314959	−	0.969344i
$498$	271.148	−	144.513i	0.544473	−	0.290187i
$499$	−165.040	+	227.159i	−0.330742	+	0.455228i	−0.941709	−	0.336428i	$-0.890781\pi$
$499$	−165.040	+	227.159i	−0.330742	+	0.455228i	0.610967	+	0.791656i	$0.290781\pi$
$500$	1.64844	+	44.6910i	0.00329688	+	0.0893819i
$501$	−69.0831	−	212.616i	−0.137890	−	0.424383i
$502$	−233.278	+	242.041i	−0.464698	+	0.482154i
$503$	302.462	+	416.304i	0.601317	+	0.827642i	0.995828	−	0.0912495i	$-0.0290861\pi$
$503$	302.462	+	416.304i	0.601317	+	0.827642i	−0.394511	+	0.918891i	$0.629086\pi$
$504$	−365.214	−	326.899i	−0.724630	−	0.648608i
$505$	−338.266			−0.669834
$506$	14.3108	+	5.74409i	0.0282822	+	0.0113520i
$507$			153.083i			0.301939i
$508$	29.1579	+	19.5841i	0.0573975	+	0.0385515i
$509$	−609.125	+	442.555i	−1.19671	+	0.869460i	−0.993957	−	0.109770i	$-0.964989\pi$
$509$	−609.125	+	442.555i	−1.19671	+	0.869460i	−0.202752	+	0.979230i	$0.564989\pi$
$510$	−87.1665	+	90.4410i	−0.170915	+	0.177335i
$511$	−585.471	+	190.231i	−1.14574	+	0.372272i
$512$	411.544	−	304.591i	0.803796	−	0.594905i
$513$	549.775	+	399.435i	1.07169	+	0.778625i
$514$	228.495	−	121.781i	0.444543	−	0.236927i
$515$	−235.803	−	76.6172i	−0.457871	−	0.148771i
$516$	140.325	+	39.9398i	0.271948	+	0.0774027i
$517$	−199.889	−	237.593i	−0.386632	−	0.459561i
$518$	−53.8305	+	385.769i	−0.103920	+	0.744728i
$519$	−332.779	−	108.127i	−0.641194	−	0.208336i
$520$	−102.277	+	22.0544i	−0.196686	+	0.0424123i
$521$	219.026	+	159.131i	0.420395	+	0.305435i	0.777797	−	0.628516i	$-0.216337\pi$
$521$	219.026	+	159.131i	0.420395	+	0.305435i	−0.357402	+	0.933951i	$0.616337\pi$
$522$	−14.4194	−	81.3102i	−0.0276234	−	0.155767i
$523$	−499.616	+	162.335i	−0.955288	+	0.310392i	−0.744863	−	0.667218i	$-0.767485\pi$
$523$	−499.616	+	162.335i	−0.955288	+	0.310392i	−0.210426	+	0.977610i	$0.567485\pi$
$524$	358.919	−	281.554i	0.684959	−	0.537316i
$525$	−36.5061	+	26.5233i	−0.0695355	+	0.0505205i
$526$	315.160	+	153.331i	0.599163	+	0.291504i
$527$		−	373.693i		−	0.709094i
$528$	−179.195	+	88.5598i	−0.339385	+	0.167727i
$529$	528.509			0.999071
$530$	108.635	−	223.290i	0.204971	−	0.421302i
$531$	−497.540	−	684.804i	−0.936986	−	1.28965i
$532$	−702.494	−	895.524i	−1.32048	−	1.68331i
$533$	−10.2002	−	31.3929i	−0.0191373	−	0.0588985i
$534$	−51.0832	+	9.05902i	−0.0956614	+	0.0169645i
$535$	103.805	−	142.876i	0.194029	−	0.267057i
$536$	−117.369	−	544.298i	−0.218973	−	1.01548i
$537$	65.8987	−	202.815i	0.122716	−	0.377682i
$538$	589.732	+	82.2915i	1.09616	+	0.152958i
$539$	−58.4766	−	144.197i	−0.108491	−	0.267527i
$540$	46.4673	−	163.259i	0.0860506	−	0.302332i
$541$	308.191	−	948.515i	0.569670	−	1.75326i	−0.0839821	−	0.996467i	$-0.526764\pi$
$541$	308.191	−	948.515i	0.569670	−	1.75326i	0.653652	−	0.756796i	$-0.273236\pi$
$542$	−281.842	−	528.816i	−0.520004	−	0.975675i
$543$	130.031	−	178.972i	0.239467	−	0.329598i
$544$	−292.856	+	735.207i	−0.538338	+	1.35148i
$545$	−99.5574	−	306.406i	−0.182674	−	0.562213i
$546$	−76.0124	−	73.2603i	−0.139217	−	0.134176i
$547$	392.845	+	540.705i	0.718181	+	0.988492i	0.999582	+	0.0289017i	$0.00920097\pi$
$547$	392.845	+	540.705i	0.718181	+	0.988492i	−0.281401	+	0.959590i	$0.590799\pi$
$548$	−286.336	+	426.313i	−0.522512	+	0.777943i
$549$	−440.001			−0.801459
$550$	−26.8542	−	106.672i	−0.0488258	−	0.193949i
$551$		−	191.759i		−	0.348019i
$552$	4.24737	−	4.74520i	0.00769452	−	0.00859637i
$553$	254.162	−	184.659i	0.459605	−	0.333923i
$554$	90.9863	+	87.6921i	0.164235	+	0.158289i
$555$	−59.1931	+	19.2330i	−0.106654	+	0.0346540i
$556$	959.596	−	35.3950i	1.72589	−	0.0636601i
$557$	133.827	+	97.2310i	0.240264	+	0.174562i	0.701401	−	0.712767i	$-0.252558\pi$
$557$	133.827	+	97.2310i	0.240264	+	0.174562i	−0.461137	+	0.887329i	$0.652558\pi$
$558$	109.592	+	205.626i	0.196402	+	0.368505i
$559$	−178.649	−	58.0467i	−0.319587	−	0.103840i
$560$	−149.709	+	241.689i	−0.267337	+	0.431588i
$561$	163.383	−	262.222i	0.291235	−	0.467419i
$562$	92.1723	+	12.8618i	0.164008	+	0.0228857i
$563$	519.437	+	168.775i	0.922623	+	0.299779i	0.731543	−	0.681796i	$-0.238801\pi$
$563$	519.437	+	168.775i	0.922623	+	0.299779i	0.191081	+	0.981574i	$0.438801\pi$
$564$	−120.409	+	44.0932i	−0.213492	+	0.0781794i
$565$	305.652	+	222.069i	0.540977	+	0.393042i
$566$	279.375	−	49.5440i	0.493595	−	0.0875335i
$567$	−361.538	+	117.471i	−0.637633	+	0.207179i
$568$	440.896	−	256.284i	0.776225	−	0.451205i
$569$	−329.627	+	239.488i	−0.579309	+	0.420893i	−0.838475	−	0.544940i	$-0.816552\pi$
$569$	−329.627	+	239.488i	−0.579309	+	0.420893i	0.259166	+	0.965833i	$0.416552\pi$
$570$	79.5662	−	163.542i	0.139590	−	0.286916i
$571$		−	402.301i		−	0.704554i	−0.935896	−	0.352277i	$-0.885407\pi$
$571$		−	402.301i		−	0.704554i	0.935896	−	0.352277i	$-0.114593\pi$
$572$	234.758	−	105.438i	0.410417	−	0.184333i
$573$	−407.031			−0.710351
$574$	−80.6537	−	39.2395i	−0.140512	−	0.0683616i
$575$	2.05999	+	2.83534i	0.00358260	+	0.00493102i
$576$	−54.4673	−	490.436i	−0.0945613	−	0.851451i
$577$	−54.0829	−	166.450i	−0.0937312	−	0.288475i	0.893190	−	0.449680i	$-0.148462\pi$
$577$	−54.0829	−	166.450i	−0.0937312	−	0.288475i	−0.986921	+	0.161205i	$0.948462\pi$
$578$	−112.666	−	635.317i	−0.194924	−	1.09916i
$579$	34.6692	−	47.7181i	0.0598777	−	0.0824146i
$580$	−44.9774	+	16.4704i	−0.0775473	+	0.0283973i
$581$	−332.166	+	1022.30i	−0.571715	+	1.75956i
$582$	35.7265	−	256.029i	0.0613857	−	0.439913i
$583$	−146.992	+	592.820i	−0.252130	+	1.01684i
$584$	−566.910	−	250.408i	−0.970736	−	0.428781i
$585$	−31.1603	+	95.9017i	−0.0532655	+	0.163934i
$586$	−654.090	+	348.609i	−1.11619	+	0.594897i
$587$	61.3484	−	84.4388i	0.104512	−	0.143848i	−0.753558	−	0.657382i	$-0.771664\pi$
$587$	61.3484	−	84.4388i	0.104512	−	0.143848i	0.858069	+	0.513534i	$0.171664\pi$
$588$	−64.2180	+	2.36870i	−0.109214	+	0.00402840i
$589$	167.201	+	514.591i	0.283872	+	0.873668i
$590$	−340.714	+	353.513i	−0.577481	+	0.599174i
$591$	−204.959	−	282.102i	−0.346800	−	0.477329i
$592$	−299.400	+	253.235i	−0.505743	+	0.427762i
$593$	−276.352			−0.466023			−0.233012	−	0.972474i	$-0.574858\pi$
$593$	−276.352			−0.466023			−0.233012	+	0.972474i	$0.574858\pi$
$594$	−28.1766	+	416.561i	−0.0474353	+	0.701281i
$595$		−	439.436i		−	0.738548i
$596$	76.5778	−	114.013i	0.128486	−	0.191297i
$597$	41.7123	−	30.3058i	0.0698699	−	0.0507634i
$598$	−5.68994	+	5.90368i	−0.00951495	+	0.00987238i
$599$	−256.468	+	83.3315i	−0.428160	+	0.139118i	−0.515167	−	0.857090i	$-0.672270\pi$
$599$	−256.468	+	83.3315i	−0.428160	+	0.139118i	0.0870064	+	0.996208i	$0.472270\pi$
$600$	−45.1932	−	4.61556i	−0.0753220	−	0.00769260i
$601$	−526.839	−	382.771i	−0.876604	−	0.636890i	0.0557467	−	0.998445i	$-0.482246\pi$
$601$	−526.839	−	382.771i	−0.876604	−	0.636890i	−0.932351	+	0.361555i	$0.882246\pi$
$602$	−450.437	+	240.069i	−0.748234	+	0.398785i
$603$	−510.371	−	165.830i	−0.846387	−	0.275008i
$604$	181.667	−	638.271i	0.300773	−	1.05674i
$605$	119.237	+	242.874i	0.197085	+	0.401444i
$606$	47.4879	−	340.316i	0.0783629	−	0.561578i
$607$	−488.244	−	158.640i	−0.804356	−	0.261351i	−0.122151	−	0.992512i	$-0.538979\pi$
$607$	−488.244	−	158.640i	−0.804356	−	0.261351i	−0.682206	+	0.731160i	$0.738979\pi$
$608$	74.3231	−	1143.44i	0.122242	−	1.88066i
$609$	−39.0995	−	28.4074i	−0.0642027	−	0.0466460i
$610$	44.5640	+	251.293i	0.0730558	+	0.411956i
$611$	157.013	−	51.0168i	0.256978	−	0.0834972i
$612$	470.753	+	600.106i	0.769205	+	0.980565i
$613$	−490.321	+	356.239i	−0.799871	+	0.581140i	−0.910876	−	0.412679i	$-0.864593\pi$
$613$	−490.321	+	356.239i	−0.799871	+	0.581140i	0.111005	+	0.993820i	$0.464593\pi$
$614$	−104.869	−	51.0206i	−0.170796	−	0.0830954i
$615$		−	14.3320i		−	0.0233040i
$616$	236.383	−	658.121i	0.383739	−	1.06838i
$617$	134.684			0.218288			0.109144	−	0.994026i	$-0.465189\pi$
$617$	134.684			0.218288			0.109144	+	0.994026i	$0.465189\pi$
$618$	110.185	−	226.476i	0.178293	−	0.366467i
$619$	123.147	+	169.498i	0.198946	+	0.273825i	0.896821	−	0.442394i	$-0.145871\pi$
$619$	123.147	+	169.498i	0.198946	+	0.273825i	−0.697875	+	0.716220i	$0.745871\pi$
$620$	106.337	−	83.4163i	0.171512	−	0.134542i
$621$	−4.11061	−	12.6512i	−0.00661934	−	0.0203722i
$622$	27.4051	−	4.85999i	0.0440597	−	0.00781349i
$623$	106.683	−	146.837i	0.171241	−	0.235693i
$624$	−7.82979	−	105.993i	−0.0125477	−	0.169860i
$625$	7.72542	−	23.7764i	0.0123607	−	0.0380423i
$626$	753.440	+	105.136i	1.20358	+	0.167948i
$627$	−107.660	+	434.193i	−0.171706	+	0.692493i
$628$	441.602	+	125.690i	0.703189	+	0.200144i
$629$	187.299	−	576.446i	0.297772	−	0.916448i
$630$	128.873	+	241.802i	0.204560	+	0.383812i
$631$	461.826	−	635.649i	0.731895	−	1.00737i	−0.267149	−	0.963655i	$-0.586082\pi$
$631$	461.826	−	635.649i	0.731895	−	1.00737i	0.999044	−	0.0437123i	$-0.0139185\pi$
$632$	314.643	+	32.1343i	0.497852	+	0.0508454i
$633$	46.5117	+	143.148i	0.0734782	+	0.226143i
$634$	−590.302	−	568.930i	−0.931076	−	0.897366i
$635$	−11.5412	−	15.8852i	−0.0181752	−	0.0250160i
$636$	209.392	+	140.640i	0.329233	+	0.221132i
$637$	82.7363			0.129884
$638$	99.7698	−	62.6591i	0.156379	−	0.0982118i
$639$		−	491.496i		−	0.769164i
$640$	−274.581	+	80.7795i	−0.429033	+	0.126218i
$641$	−122.258	+	88.8254i	−0.190730	+	0.138573i	−0.679052	−	0.734090i	$-0.737609\pi$
$641$	−122.258	+	88.8254i	−0.190730	+	0.138573i	0.488323	+	0.872663i	$0.337609\pi$
$642$	129.169	+	124.492i	0.201197	+	0.193913i
$643$	−186.012	+	60.4390i	−0.289288	+	0.0939954i	−0.450066	−	0.892995i	$-0.648600\pi$
$643$	−186.012	+	60.4390i	−0.289288	+	0.0939954i	0.160778	+	0.986991i	$0.448600\pi$
$644$	0.821235	+	22.2645i	0.00127521	+	0.0345723i
$645$	−65.9831	−	47.9396i	−0.102299	−	0.0743249i
$646$	833.026	+	1562.99i	1.28951	+	2.41949i
$647$	1224.63	+	397.907i	1.89278	+	0.615003i	0.976960	+	0.213423i	$0.0684613\pi$
$647$	1224.63	+	397.907i	1.89278	+	0.615003i	0.915824	+	0.401580i	$0.131539\pi$
$648$	−350.076	−	154.631i	−0.540241	−	0.238628i
$649$	638.626	−	1024.96i	0.984016	−	1.57930i
$650$	57.9273	+	8.08321i	0.0891189	+	0.0124357i
$651$	129.694	+	42.1402i	0.199223	+	0.0647314i
$652$	−181.151	−	494.686i	−0.277839	−	0.758720i
$653$	161.840	+	117.583i	0.247840	+	0.180066i	0.704769	−	0.709437i	$-0.251051\pi$
$653$	161.840	+	117.583i	0.247840	+	0.180066i	−0.456929	+	0.889503i	$0.651051\pi$
$654$	322.239	−	57.1455i	0.492721	−	0.0873784i
$655$	−242.528	+	78.8022i	−0.370272	+	0.120309i
$656$	−34.1542	−	83.5888i	−0.0520644	−	0.127422i
$657$	−483.224	+	351.083i	−0.735501	+	0.534373i
$658$	196.259	−	403.394i	0.298266	−	0.613061i
$659$		−	1094.71i		−	1.66116i	−0.556897	−	0.830582i	$-0.688008\pi$
$659$		−	1094.71i		−	1.66116i	0.556897	−	0.830582i	$-0.311992\pi$
$660$	111.088	−	12.0417i	0.168315	−	0.0182449i
$661$	−487.565			−0.737617			−0.368808	−	0.929505i	$-0.620234\pi$
$661$	−487.565			−0.737617			−0.368808	+	0.929505i	$0.620234\pi$
$662$	−256.836	−	124.956i	−0.387970	−	0.188755i
$663$	96.5594	+	132.903i	0.145640	+	0.200456i
$664$	−935.581	+	543.836i	−1.40901	+	0.819030i
$665$	196.616	+	605.122i	0.295663	+	0.909959i
$666$	65.9913	+	372.120i	0.0990860	+	0.558739i
$667$	−2.20633	+	3.03675i	−0.00330784	+	0.00455285i
$668$	270.750	+	739.363i	0.405315	+	1.10683i
$669$	−84.8341	+	261.093i	−0.126807	+	0.390273i
$670$	−43.0174	+	308.279i	−0.0642051	+	0.460117i
$671$	−235.910	−	581.729i	−0.351580	−	0.866959i
$672$	−222.137	−	184.546i	−0.330561	−	0.274622i
$673$	260.349	−	801.273i	0.386849	−	1.19060i	−0.548281	−	0.836294i	$-0.684718\pi$
$673$	260.349	−	801.273i	0.386849	−	1.19060i	0.935130	−	0.354304i	$-0.115282\pi$
$674$	−97.6463	+	52.0424i	−0.144876	+	0.0772142i
$675$	−55.7745	+	76.7670i	−0.0826289	+	0.113729i
$676$	−19.8737	−	538.797i	−0.0293990	−	0.797037i
$677$	−42.3896	−	130.462i	−0.0626139	−	0.192706i	0.914856	−	0.403780i	$-0.132304\pi$
$677$	−42.3896	−	130.462i	−0.0626139	−	0.192706i	−0.977470	+	0.211074i	$0.932304\pi$
$678$	−266.324	+	276.328i	−0.392808	+	0.407564i
$679$	531.584	+	731.662i	0.782892	+	1.07756i
$680$	295.054	−	329.636i	0.433903	−	0.484759i
$681$	401.970			0.590264
$682$	−213.101	+	255.141i	−0.312465	+	0.374106i
$683$			788.659i			1.15470i	0.816497	+	0.577349i	$0.195913\pi$
$683$			788.659i			1.15470i	−0.816497	+	0.577349i	$0.804087\pi$
$684$	−916.751	−	615.743i	−1.34028	−	0.900209i
$685$	232.254	−	168.743i	0.339057	−	0.246339i
$686$	−384.404	+	398.844i	−0.560355	+	0.581405i
$687$	52.5272	−	17.0671i	0.0764588	−	0.0248430i
$688$	−499.079	−	122.356i	−0.725406	−	0.177843i
$689$	−262.733	−	190.887i	−0.381325	−	0.277049i
$690$	−3.14171	+	1.67443i	−0.00455321	+	0.00242672i
$691$	703.717	+	228.652i	1.01840	+	0.330899i	0.770196	−	0.637807i	$-0.220158\pi$
$691$	703.717	+	228.652i	1.01840	+	0.330899i	0.248208	+	0.968707i	$0.420158\pi$
$692$	1185.30	+	337.364i	1.71286	+	0.487521i
$693$	−433.875	−	515.716i	−0.626083	−	0.744179i
$694$	−43.3205	+	310.451i	−0.0624215	+	0.447336i
$695$	−510.523	−	165.879i	−0.734565	−	0.238675i
$696$	−10.2560	−	47.5622i	−0.0147357	−	0.0683365i
$697$	112.915	+	82.0375i	0.162001	+	0.117701i
$698$	179.028	+	1009.53i	0.256488	+	1.44632i
$699$	60.5839	−	19.6849i	0.0866723	−	0.0281615i
$700$	125.045	−	98.0917i	0.178636	−	0.140131i
$701$	−112.491	+	81.7296i	−0.160472	+	0.116590i	−0.665124	−	0.746733i	$-0.731621\pi$
$701$	−112.491	+	81.7296i	−0.160472	+	0.116590i	0.504651	+	0.863323i	$0.331621\pi$
$702$	−199.625	−	97.1215i	−0.284367	−	0.138350i
$703$			877.593i			1.24835i
$704$	619.206	−	334.963i	0.879554	−	0.475799i
$705$	71.6821			0.101677
$706$	125.828	−	258.628i	0.178226	−	0.366329i
$707$	706.585	+	972.531i	0.999413	+	1.37557i
$708$	−307.823	−	392.407i	−0.434779	−	0.554247i
$709$	411.565	+	1266.67i	0.580487	+	1.78656i	0.616684	+	0.787211i	$0.288476\pi$
$709$	411.565	+	1266.67i	0.580487	+	1.78656i	−0.0361971	+	0.999345i	$0.511524\pi$
$710$	−280.703	+	49.7795i	−0.395356	+	0.0701120i
$711$	179.169	−	246.605i	0.251996	−	0.346843i
$712$	178.618	−	38.5163i	0.250869	−	0.0540959i
$713$	3.27292	−	10.0730i	0.00459035	−	0.0141276i
$714$	442.099	+	61.6908i	0.619186	+	0.0864016i
$715$	−143.499	+	10.2211i	−0.200698	+	0.0142952i
$716$	−205.610	+	722.392i	−0.287164	+	1.00893i
$717$	35.2393	−	108.455i	0.0491482	−	0.151263i
$718$	218.942	+	410.797i	0.304933	+	0.572140i
$719$	1.18250	−	1.62757i	0.00164465	−	0.00226366i	−0.808194	−	0.588917i	$-0.799555\pi$
$719$	1.18250	−	1.62757i	0.00164465	−	0.00226366i	0.809839	+	0.586653i	$0.199555\pi$
$720$	−65.6827	+	267.913i	−0.0912260	+	0.372102i
$721$	272.278	+	837.987i	0.377640	+	1.16226i
$722$	−1326.58	−	1278.55i	−1.83737	−	1.77085i
$723$	−32.2396	−	44.3740i	−0.0445915	−	0.0613749i
$724$	−434.426	+	646.797i	−0.600036	+	0.893366i
$725$	26.7759			0.0369323
$726$	−261.085	+	85.8630i	−0.359621	+	0.118269i
$727$		−	31.7313i		−	0.0436469i	−0.999762	−	0.0218235i	$-0.993053\pi$
$727$		−	31.7313i		−	0.0436469i	0.999762	−	0.0218235i	$-0.00694718\pi$
$728$	277.047	+	247.982i	0.380559	+	0.340634i
$729$	−141.466	+	102.781i	−0.194055	+	0.140989i
$730$	249.452	+	240.421i	0.341715	+	0.329343i
$731$	755.387	−	245.440i	1.03336	−	0.335759i
$732$	−259.072	+	9.55596i	−0.353924	+	0.0130546i
$733$	740.641	+	538.107i	1.01042	+	0.734116i	0.964298	−	0.264820i	$-0.0853125\pi$
$733$	740.641	+	538.107i	1.01042	+	0.734116i	0.0461259	+	0.998936i	$0.485312\pi$
$734$	−522.249	−	979.887i	−0.711511	−	1.33500i
$735$	34.1651	+	11.1009i	0.0464832	+	0.0151033i
$736$	−14.3332	+	17.2528i	−0.0194745	+	0.0234413i
$737$	−54.3947	−	763.677i	−0.0738056	−	1.03620i
$738$	−86.1908	−	12.0271i	−0.116790	−	0.0162969i
$739$	1020.76	+	331.664i	1.38127	+	0.448801i	0.903085	−	0.429461i	$-0.141296\pi$
$739$	1020.76	+	331.664i	1.38127	+	0.448801i	0.478181	+	0.878261i	$0.341296\pi$
$740$	205.841	−	75.3779i	0.278164	−	0.101862i
$741$	−192.431	−	139.809i	−0.259691	−	0.188676i
$742$	−868.889	+	154.088i	−1.17101	+	0.207665i
$743$	1068.27	−	347.102i	1.43778	−	0.467163i	0.516574	−	0.856242i	$-0.327207\pi$
$743$	1068.27	−	347.102i	1.43778	−	0.467163i	0.921204	+	0.389080i	$0.127207\pi$
$744$	68.9935	+	118.692i	0.0927332	+	0.159532i
$745$	−62.1141	+	45.1285i	−0.0833746	+	0.0605752i
$746$	364.671	−	749.551i	0.488835	−	1.00476i
$747$			1042.95i			1.39619i
$748$	−541.007	+	944.138i	−0.723272	+	1.26222i
$749$	−627.607			−0.837927
$750$	22.8359	+	11.1101i	0.0304479	+	0.0148135i
$751$	−124.028	−	170.709i	−0.165150	−	0.227309i	0.718419	−	0.695611i	$-0.244866\pi$
$751$	−124.028	−	170.709i	−0.165150	−	0.227309i	−0.883569	+	0.468301i	$0.844866\pi$
$752$	418.074	−	170.824i	0.555949	−	0.227160i
$753$	58.9879	+	181.546i	0.0783372	+	0.241097i
$754$	10.9384	+	61.6810i	0.0145072	+	0.0818051i
$755$	−218.054	+	300.126i	−0.288813	+	0.397517i
$756$	−566.440	+	207.427i	−0.749259	+	0.274374i
$757$	347.466	−	1069.39i	0.459004	−	1.41267i	−0.407365	−	0.913265i	$-0.633552\pi$
$757$	347.466	−	1069.39i	0.459004	−	1.41267i	0.866369	−	0.499404i	$-0.166448\pi$
$758$	−89.4116	+	640.757i	−0.117957	+	0.845326i
$759$	6.70066	−	5.63732i	0.00882828	−	0.00742729i
$760$	−258.813	+	585.938i	−0.340543	+	0.770971i
$761$	−238.745	+	734.781i	−0.313725	+	0.965547i	0.662551	+	0.749017i	$0.269474\pi$
$761$	−238.745	+	734.781i	−0.313725	+	0.965547i	−0.976276	+	0.216530i	$0.930526\pi$
$762$	17.6017	−	9.38112i	0.0230993	−	0.0123112i
$763$	−672.972	+	926.266i	−0.882008	+	1.21398i
$764$	1432.60	−	52.8420i	1.87513	−	0.0691649i
$765$	−131.756	−	405.503i	−0.172230	−	0.530069i
$766$	−10.1090	+	10.4888i	−0.0131972	+	0.0136929i
$767$	377.428	+	519.486i	0.492084	+	0.677295i
$768$	−42.7216	−	287.585i	−0.0556271	−	0.374460i
$769$	178.398			0.231987			0.115993	−	0.993250i	$-0.462995\pi$
$769$	178.398			0.231987			0.115993	+	0.993250i	$0.462995\pi$
$770$	−250.592	+	300.027i	−0.325444	+	0.389646i
$771$		−	147.030i		−	0.190700i
$772$	−115.828	+	172.451i	−0.150037	+	0.223383i
$773$	1059.37	−	769.675i	1.37046	−	0.995699i	0.372761	−	0.927927i	$-0.378411\pi$
$773$	1059.37	−	769.675i	1.37046	−	0.995699i	0.997701	−	0.0677719i	$-0.0215890\pi$
$774$	−343.675	+	356.585i	−0.444024	+	0.460704i
$775$	−71.8542	+	23.3468i	−0.0927151	+	0.0301249i
$776$	−92.5059	+	905.770i	−0.119209	+	1.16723i
$777$	178.941	+	130.008i	0.230297	+	0.167320i
$778$	−1267.09	+	675.318i	−1.62865	+	0.868018i
$779$	−192.194	−	62.4478i	−0.246719	−	0.0801640i
$780$	−16.2644	+	57.1435i	−0.0208518	+	0.0732609i
$781$	649.811	−	263.519i	0.832024	−	0.337413i
$782$	4.79136	−	34.3367i	0.00612706	−	0.0439088i
$783$	−96.6559	−	31.4054i	−0.123443	−	0.0401091i
$784$	225.717	−	16.6740i	0.287904	−	0.0212678i
$785$	−207.649	−	150.866i	−0.264521	−	0.192185i
$786$	−45.2321	−	255.061i	−0.0575472	−	0.324505i
$787$	1049.27	−	340.929i	1.33326	−	0.433201i	0.446229	−	0.894919i	$-0.352767\pi$
$787$	1049.27	−	340.929i	1.33326	−	0.433201i	0.887027	+	0.461718i	$0.152767\pi$
$788$	758.005	+	966.289i	0.961936	+	1.22625i
$789$	161.011	−	116.982i	0.204070	−	0.148266i
$790$	−158.988	−	77.3505i	−0.201250	−	0.0979120i
$791$		−	1342.63i		−	1.69738i
$792$	20.8058	−	678.176i	0.0262699	−	0.856283i
$793$	333.780			0.420908
$794$	−106.886	+	219.695i	−0.134617	+	0.276693i
$795$	−82.8812	−	114.076i	−0.104253	−	0.143492i
$796$	−142.878	+	112.081i	−0.179495	+	0.140805i
$797$	108.630	+	334.330i	0.136299	+	0.419485i	0.995790	−	0.0916659i	$-0.0292192\pi$
$797$	108.630	+	334.330i	0.136299	+	0.419485i	−0.859491	+	0.511151i	$0.829219\pi$
$798$	−636.391	+	112.857i	−0.797483	+	0.141425i
$799$	−410.315	+	564.750i	−0.513536	+	0.706821i
$800$	159.663	+	10.3780i	0.199579	+	0.0129725i
$801$	54.4192	−	167.485i	0.0679390	−	0.209095i
$802$	1318.49	+	183.983i	1.64400	+	0.229405i
$803$	−723.254	−	450.639i	−0.900690	−	0.561194i
$804$	−304.108	−	86.5561i	−0.378243	−	0.107657i
$805$	3.84872	−	11.8451i	0.00478102	−	0.0147145i
$806$	−83.1354	−	155.986i	−0.103146	−	0.193531i
$807$	198.745	−	273.550i	0.246277	−	0.338971i
$808$	−122.960	+	1203.96i	−0.152178	+	1.49004i
$809$	−266.478	−	820.134i	−0.329391	−	1.01376i	−0.969419	−	0.245411i	$-0.921077\pi$
$809$	−266.478	−	820.134i	−0.329391	−	1.01376i	0.640028	−	0.768352i	$-0.278923\pi$
$810$	154.041	+	148.464i	0.190174	+	0.183288i
$811$	−513.011	−	706.099i	−0.632566	−	0.870652i	0.365626	−	0.930762i	$-0.380855\pi$
$811$	−513.011	−	706.099i	−0.632566	−	0.870652i	−0.998192	+	0.0601095i	$0.980855\pi$
$812$	141.304	+	94.9079i	0.174020	+	0.116882i
$813$	−340.277			−0.418545
$814$	−456.602	+	286.763i	−0.560936	+	0.352288i
$815$			294.496i			0.361345i
$816$	290.212	+	343.118i	0.355652	+	0.420488i
$817$	−930.383	+	675.963i	−1.13878	+	0.827372i
$818$	203.629	+	196.256i	0.248935	+	0.239922i
$819$	340.811	−	110.736i	0.416130	−	0.135209i
$820$	1.86062	+	50.4434i	0.00226905	+	0.0615163i
$821$	−286.807	−	208.378i	−0.349339	−	0.253810i	0.399253	−	0.916841i	$-0.369270\pi$
$821$	−286.807	−	208.378i	−0.349339	−	0.253810i	−0.748592	+	0.663031i	$0.769270\pi$
$822$	137.160	+	257.351i	0.166861	+	0.313079i
$823$	583.595	+	189.621i	0.709107	+	0.230403i	0.641294	−	0.767295i	$-0.278398\pi$
$823$	583.595	+	189.621i	0.709107	+	0.230403i	0.0678128	+	0.997698i	$0.478398\pi$
$824$	−358.410	+	811.420i	−0.434963	+	0.984733i
$825$	−60.6279	−	15.0329i	−0.0734884	−	0.0182217i
$826$	1728.06	+	241.135i	2.09209	+	0.291931i
$827$	322.996	+	104.948i	0.390563	+	0.126902i	0.497714	−	0.867341i	$-0.334173\pi$
$827$	322.996	+	104.948i	0.390563	+	0.126902i	−0.107151	+	0.994243i	$0.534173\pi$
$828$	7.43339	+	20.2990i	0.00897752	+	0.0245158i
$829$	−402.377	−	292.344i	−0.485376	−	0.352647i	0.318027	−	0.948082i	$-0.396980\pi$
$829$	−402.377	−	292.344i	−0.485376	−	0.352647i	−0.803403	+	0.595435i	$0.796980\pi$
$830$	595.652	−	105.632i	0.717653	−	0.127268i
$831$	68.2454	−	22.1743i	0.0821244	−	0.0266838i
$832$	41.3183	+	372.039i	0.0496615	+	0.447163i
$833$	−283.023	+	205.628i	−0.339764	+	0.246853i
$834$	238.554	−	490.329i	0.286036	−	0.587925i
$835$		−	440.158i		−	0.527135i
$836$	322.556	−	1542.18i	0.385832	−	1.84471i
$837$	286.763			0.342608
$838$	−734.548	−	357.372i	−0.876549	−	0.426458i
$839$	171.752	+	236.396i	0.204710	+	0.281759i	0.899011	−	0.437925i	$-0.144287\pi$
$839$	171.752	+	236.396i	0.204710	+	0.281759i	−0.694301	+	0.719684i	$0.744287\pi$
$840$	81.1315	+	139.574i	0.0965851	+	0.166159i
$841$	−251.021	−	772.564i	−0.298480	−	0.918626i
$842$	−71.3815	−	402.515i	−0.0847762	−	0.478047i
$843$	31.0630	−	42.7545i	0.0368481	−	0.0507171i
$844$	−182.288	−	497.792i	−0.215982	−	0.589801i
$845$	−93.1382	+	286.650i	−0.110223	+	0.339231i
$846$	60.1543	−	431.088i	0.0711044	−	0.509560i
$847$	449.206	−	850.135i	0.530350	−	1.00370i
$848$	−755.244	−	467.818i	−0.890617	−	0.551672i
$849$	49.7886	−	153.234i	0.0586438	−	0.180487i
$850$	−218.246	+	116.318i	−0.256760	+	0.136845i
$851$	10.0974	−	13.8979i	0.0118653	−	0.0163312i
$852$	−10.6743	−	289.392i	−0.0125286	−	0.339662i
$853$	−143.038	−	440.226i	−0.167688	−	0.516092i	0.831536	−	0.555471i	$-0.187462\pi$
$853$	−143.038	−	440.226i	−0.167688	−	0.516092i	−0.999224	+	0.0393793i	$0.987462\pi$
$854$	629.393	−	653.036i	0.736994	−	0.764679i
$855$	362.867	+	499.444i	0.424406	+	0.584145i
$856$	−470.790	−	421.399i	−0.549988	−	0.492288i
$857$	391.292			0.456583			0.228291	−	0.973593i	$-0.426686\pi$
$857$	391.292			0.456583			0.228291	+	0.973593i	$0.426686\pi$
$858$	9.86229	−	145.804i	0.0114945	−	0.169934i
$859$			962.258i			1.12021i	0.828422	+	0.560104i	$0.189239\pi$
$859$			962.258i			1.12021i	−0.828422	+	0.560104i	$0.810761\pi$
$860$	238.461	+	160.164i	0.277280	+	0.186237i
$861$	−41.2051	+	29.9372i	−0.0478572	+	0.0347703i
$862$	1003.70	−	1041.40i	1.16438	−	1.20812i
$863$	1268.64	−	412.206i	1.47003	−	0.477643i	0.538915	−	0.842360i	$-0.318834\pi$
$863$	1268.64	−	412.206i	1.47003	−	0.477643i	0.931118	+	0.364718i	$0.118834\pi$
$864$	−564.180	−	224.731i	−0.652986	−	0.260105i
$865$	−557.348	−	404.937i	−0.644333	−	0.468135i
$866$	−764.566	+	407.489i	−0.882870	+	0.470542i
$867$	−348.463	−	113.222i	−0.401918	−	0.130591i
$868$	−461.948	−	131.481i	−0.532198	−	0.151476i
$869$	422.102	+	104.662i	0.485733	+	0.120439i
$870$	−3.75897	+	26.9382i	−0.00432066	+	0.0309634i
$871$	387.162	+	125.797i	0.444503	+	0.144428i
$872$	−1126.75	+	242.966i	−1.29214	+	0.278631i
$873$	709.909	+	515.779i	0.813183	+	0.590812i
$874$	8.76529	+	49.4269i	0.0100289	+	0.0565525i
$875$	−84.4955	+	27.4542i	−0.0965662	+	0.0313763i
$876$	−276.897	+	217.212i	−0.316093	+	0.247959i
$877$	−1288.43	+	936.097i	−1.46913	+	1.06738i	−0.488264	+	0.872696i	$0.662370\pi$
$877$	−1288.43	+	936.097i	−1.46913	+	1.06738i	−0.980865	+	0.194689i	$0.937630\pi$
$878$	−1434.16	−	697.744i	−1.63344	−	0.794697i
$879$			420.887i			0.478825i
$880$	−389.427	+	56.8041i	−0.442531	+	0.0645502i
$881$	−1317.14			−1.49505			−0.747525	−	0.664234i	$-0.768758\pi$
$881$	−1317.14			−1.49505			−0.747525	+	0.664234i	$0.768758\pi$
$882$	95.4304	−	196.149i	0.108198	−	0.222392i
$883$	−698.780	−	961.787i	−0.791370	−	1.08923i	−0.993936	−	0.109959i	$-0.964928\pi$
$883$	−698.780	−	961.787i	−0.791370	−	1.08923i	0.202566	−	0.979269i	$-0.435072\pi$
$884$	−357.108	−	455.234i	−0.403969	−	0.514971i
$885$	86.1546	+	265.157i	0.0973499	+	0.299612i
$886$	1234.09	−	218.852i	1.39288	−	0.247011i
$887$	62.6807	−	86.2726i	0.0706660	−	0.0972634i	−0.772221	−	0.635354i	$-0.780854\pi$
$887$	62.6807	−	86.2726i	0.0706660	−	0.0972634i	0.842887	+	0.538091i	$0.180854\pi$
$888$	46.9373	+	217.671i	0.0528574	+	0.245125i
$889$	−21.5627	+	66.3632i	−0.0242550	+	0.0746493i
$890$	−101.166	−	14.1167i	−0.113669	−	0.0158615i
$891$	−446.621	−	278.277i	−0.501258	−	0.312320i
$892$	264.690	−	929.966i	0.296738	−	1.04256i
$893$	312.336	−	961.271i	0.349760	−	1.07645i
$894$	−36.6820	−	68.8259i	−0.0410313	−	0.0769864i
$895$	246.792	−	339.681i	0.275746	−	0.379531i
$896$	805.801	+	620.697i	0.899331	+	0.692742i
$897$	1.43879	+	4.42813i	0.00160400	+	0.00493660i
$898$	471.909	+	454.824i	0.525512	+	0.506485i
$899$	−47.5630	−	65.4648i	−0.0529065	−	0.0728196i
$900$	85.9785	−	128.009i	0.0955316	−	0.142233i
$901$	1373.17			1.52405
$902$	−30.3107	−	120.402i	−0.0336039	−	0.133483i
$903$			289.843i			0.320977i
$904$	901.491	−	1007.15i	0.997225	−	1.11411i
$905$	352.373	−	256.014i	0.389363	−	0.282889i
$906$	−271.332	−	261.509i	−0.299484	−	0.288641i
$907$	−524.704	+	170.487i	−0.578505	+	0.187968i	−0.583631	−	0.812019i	$-0.698368\pi$
$907$	−524.704	+	170.487i	−0.578505	+	0.187968i	0.00512563	+	0.999987i	$0.498368\pi$
$908$	−1414.79	+	52.1849i	−1.55814	+	0.0574724i
$909$	943.616	+	685.577i	1.03808	+	0.754210i
$910$	−97.7614	−	183.428i	−0.107430	−	0.201569i
$911$	−475.308	−	154.437i	−0.521743	−	0.169525i	0.0362932	−	0.999341i	$-0.488445\pi$
$911$	−475.308	−	154.437i	−0.521743	−	0.169525i	−0.558036	+	0.829817i	$0.688445\pi$
$912$	−553.155	−	342.639i	−0.606530	−	0.375701i
$913$	−1378.90	+	559.188i	−1.51029	+	0.612473i
$914$	−1442.16	−	201.240i	−1.57786	−	0.220175i
$915$	137.831	+	44.7841i	0.150635	+	0.0489443i
$916$	−182.661	+	66.8894i	−0.199412	+	0.0730233i
$917$	733.163	+	532.674i	0.799524	+	0.580888i
$918$	924.256	−	163.906i	1.00681	−	0.178547i
$919$	1163.90	−	378.174i	1.26648	−	0.411506i	0.402683	−	0.915339i	$-0.368078\pi$
$919$	1163.90	−	378.174i	1.26648	−	0.411506i	0.863801	+	0.503834i	$0.168078\pi$
$920$	10.8403	−	6.30127i	0.0117830	−	0.00684921i
$921$	−53.5762	+	38.9254i	−0.0581718	+	0.0422643i
$922$	−478.543	+	983.607i	−0.519027	+	1.06682i
$923$			372.844i			0.403948i
$924$	−266.666	−	294.230i	−0.288599	−	0.318431i
$925$	−122.542			−0.132477
$926$	220.017	+	107.043i	0.237600	+	0.115597i
$927$	502.506	+	691.641i	0.542078	+	0.746106i
$928$	42.2723	+	166.070i	0.0455520	+	0.178955i
$929$	157.031	+	483.292i	0.169033	+	0.520229i	0.999311	−	0.0371204i	$-0.0118185\pi$
$929$	157.031	+	483.292i	0.169033	+	0.520229i	−0.830278	+	0.557349i	$0.811819\pi$
$930$	−13.4010	−	75.5671i	−0.0144097	−	0.0812550i
$931$	297.731	−	409.792i	0.319797	−	0.440163i
$932$	−210.678	+	77.1490i	−0.226049	+	0.0827779i
$933$	4.88399	−	15.0314i	0.00523471	−	0.0161108i
$934$	−34.4045	+	246.555i	−0.0368356	+	0.263978i
$935$	465.477	−	391.609i	0.497837	−	0.418834i
$936$	330.006	+	145.766i	0.352570	+	0.155733i
$937$	−28.5669	+	87.9199i	−0.0304876	+	0.0938312i	−0.965142	−	0.261725i	$-0.915709\pi$
$937$	−28.5669	+	87.9199i	−0.0304876	+	0.0938312i	0.934655	+	0.355556i	$0.115709\pi$
$938$	976.172	−	520.269i	1.04069	−	0.554657i
$939$	253.917	−	349.486i	0.270412	−	0.372190i
$940$	−252.295	+	9.30600i	−0.268399	+	0.00990000i
$941$	−510.919	−	1572.45i	−0.542953	−	1.67104i	−0.725808	−	0.687898i	$-0.758534\pi$
$941$	−510.919	−	1572.45i	−0.542953	−	1.67104i	0.182855	−	0.983140i	$-0.441466\pi$
$942$	180.931	−	187.727i	0.192071	−	0.199286i
$943$	2.32515	+	3.20029i	0.00246569	+	0.00339373i
$944$	1134.37	+	1341.17i	1.20166	+	1.42073i
$945$	337.213			0.356839
$946$	−655.708	−	263.189i	−0.693137	−	0.278213i
$947$		−	741.454i		−	0.782950i	−0.920189	−	0.391475i	$-0.871965\pi$
$947$		−	741.454i		−	0.782950i	0.920189	−	0.391475i	$-0.128035\pi$
$948$	100.139	−	149.092i	0.105632	−	0.157270i
$949$	366.569	−	266.328i	0.386269	−	0.280641i
$950$	248.490	−	257.825i	0.261569	−	0.271395i
$951$	−442.764	+	143.863i	−0.465577	+	0.151275i
$952$	−1564.04	−	159.735i	−1.64290	−	0.167789i
$953$	152.590	+	110.863i	0.160116	+	0.116331i	0.664958	−	0.746881i	$-0.268449\pi$
$953$	152.590	+	110.863i	0.160116	+	0.116331i	−0.504842	+	0.863212i	$0.668449\pi$
$954$	−755.594	+	402.708i	−0.792027	+	0.422125i
$955$	−762.171	−	247.644i	−0.798085	−	0.259313i
$956$	−109.950	+	386.299i	−0.115010	+	0.404078i
$957$	−4.75315	−	66.7321i	−0.00496672	−	0.0697305i
$958$	80.5607	−	577.328i	0.0840925	−	0.602639i
$959$	−970.285	−	315.265i	−1.01177	−	0.328743i
$960$	−32.8554	+	159.174i	−0.0342244	+	0.165806i
$961$	−592.747	−	430.656i	−0.616803	−	0.448133i
$962$	−50.0603	−	282.287i	−0.0520378	−	0.293437i
$963$	−579.143	+	188.175i	−0.601395	+	0.195405i
$964$	119.233	+	151.995i	0.123685	+	0.157671i
$965$	93.9511	−	68.2594i	0.0973586	−	0.0707352i
$966$	11.3766	+	5.53494i	0.0117770	+	0.00572975i
$967$		−	1697.82i		−	1.75576i	−0.478884	−	0.877878i	$-0.658958\pi$
$967$		−	1697.82i		−	1.75576i	0.478884	−	0.877878i	$-0.341042\pi$
$968$	907.777	−	336.102i	0.937786	−	0.347213i
$969$	1005.74			1.03791
$970$	222.671	−	457.682i	0.229558	−	0.471837i
$971$	734.998	+	1011.64i	0.756950	+	1.04185i	0.997462	+	0.0712061i	$0.0226848\pi$
$971$	734.998	+	1011.64i	0.756950	+	1.04185i	−0.240512	+	0.970646i	$0.577315\pi$
$972$	−708.533	+	555.809i	−0.728944	+	0.571820i
$973$	589.492	+	1814.27i	0.605850	+	1.86462i
$974$	316.301	−	56.0924i	0.324744	−	0.0575897i
$975$	19.5221	−	26.8698i	0.0200226	−	0.0275588i
$976$	910.601	−	67.2671i	0.932993	−	0.0689213i
$977$	−52.7111	+	162.228i	−0.0539520	+	0.166047i	−0.974402	−	0.224814i	$-0.927823\pi$
$977$	−52.7111	+	162.228i	−0.0539520	+	0.166047i	0.920450	+	0.390861i	$0.127823\pi$
$978$	−296.281	−	41.3432i	−0.302945	−	0.0422732i
$979$	250.610	−	17.8503i	0.255986	−	0.0182332i
$980$	−121.690	−	34.6359i	−0.124174	−	0.0353427i
$981$	−343.283	+	1056.52i	−0.349932	+	1.07698i
$982$	−40.8100	−	76.5712i	−0.0415581	−	0.0779748i
$983$	−519.470	+	714.989i	−0.528453	+	0.727354i	−0.986894	−	0.161371i	$-0.948408\pi$
$983$	−519.470	+	714.989i	−0.528453	+	0.727354i	0.458440	+	0.888725i	$0.348408\pi$
$984$	−51.0103	−	5.20966i	−0.0518397	−	0.00529437i
$985$	−212.153	−	652.940i	−0.215384	−	0.662883i
$986$	−190.717	−	183.812i	−0.193425	−	0.186422i
$987$	−149.733	−	206.089i	−0.151705	−	0.208804i
$988$	695.438	+	467.096i	0.703885	+	0.472770i
$989$	22.5113			0.0227617
$990$	−141.284	+	351.994i	−0.142711	+	0.355550i
$991$		−	1304.58i		−	1.31643i	−0.752831	−	0.658214i	$-0.771312\pi$
$991$		−	1304.58i		−	1.31643i	0.752831	−	0.658214i	$-0.228688\pi$
$992$	−258.241	−	408.797i	−0.260324	−	0.412094i
$993$	−131.215	+	95.3329i	−0.132140	+	0.0960050i
$994$	729.463	+	703.052i	0.733866	+	0.707296i
$995$	96.5454	−	31.3695i	0.0970306	−	0.0315271i
$996$	22.6509	+	614.091i	0.0227419	+	0.616557i
$997$	−1223.26	−	888.752i	−1.22694	−	0.891427i	−0.230286	−	0.973123i	$-0.573966\pi$
$997$	−1223.26	−	888.752i	−1.22694	−	0.891427i	−0.996657	+	0.0816961i	$0.973966\pi$
$998$	−264.126	−	495.576i	−0.264655	−	0.496569i
$999$	442.351	+	143.728i	0.442793	+	0.143872i

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	220.3.s.a.31.8	✓	96
4.3	odd	2	inner	220.3.s.a.31.11	yes	96
11.5	even	5	inner	220.3.s.a.71.11	yes	96
44.27	odd	10	inner	220.3.s.a.71.8	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
220.3.s.a.31.8	✓	96	1.1	even	1	trivial
220.3.s.a.31.11	yes	96	4.3	odd	2	inner
220.3.s.a.71.8	yes	96	44.27	odd	10	inner
220.3.s.a.71.11	yes	96	11.5	even	5	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 $\F_{q}$
Belyi maps

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	220.3.s.a.31.8

Level	$220$
Weight	$3$
Character	220.31
Analytic conductor	$5.995$
Analytic rank	$0$
Dimension	$96$
Inner twists	$4$