LMFDB - Embedded newform 31.3.f.a.15.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,3,Mod(15,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.15"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	31.f (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.844688819517$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 20 x^{18} - 33 x^{17} + 250 x^{16} - 510 x^{15} + 2908 x^{14} - 6447 x^{13} + \cdots + 731025 $ x^20 - 2x^19 + 20x^18 - 33x^17 + 250x^16 - 510x^15 + 2908x^14 - 6447x^13 + 39842x^12 - 79034x^11 + 199542x^10 - 173039x^9 + 688988x^8 - 636120x^7 + 3401146x^6 - 2156427x^5 + 7116556x^4 - 6139950x^3 + 6454710x^2 - 3116475*x + 731025
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			15.5
Root			$-1.12738 - 3.46973i$ of defining polynomial
Character	$\chi$	$=$	31.15
Dual form			31.3.f.a.29.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.95153 - 2.14441i) q^{2} +(-2.80836 + 3.86537i) q^{3} +(2.87696 - 8.85438i) q^{4} -3.94423 q^{5} +17.4310i q^{6} +(-0.932951 + 2.87133i) q^{7} +(-5.98647 - 18.4245i) q^{8} +(-4.27307 - 13.1512i) q^{9} +(-11.6415 + 8.45807i) q^{10} +(10.9110 + 3.54519i) q^{11} +(26.1459 + 35.9868i) q^{12} +(4.53298 - 6.23912i) q^{13} +(3.40368 + 10.4755i) q^{14} +(11.0768 - 15.2459i) q^{15} +(-27.0510 - 19.6537i) q^{16} +(-15.6245 + 5.07671i) q^{17} +(-40.8136 - 29.6528i) q^{18} +(15.7996 - 11.4790i) q^{19} +(-11.3474 + 34.9238i) q^{20} +(-8.47869 - 11.6699i) q^{21} +(39.8064 - 12.9339i) q^{22} +(-23.9267 + 7.77425i) q^{23} +(88.0295 + 28.6025i) q^{24} -9.44302 q^{25} -28.1355i q^{26} +(21.9382 + 7.12816i) q^{27} +(22.7398 + 16.5214i) q^{28} +(9.12892 + 12.5649i) q^{29} -68.7521i q^{30} +(18.2893 + 25.0300i) q^{31} -44.4969 q^{32} +(-44.3454 + 32.2188i) q^{33} +(-35.2297 + 48.4895i) q^{34} +(3.67978 - 11.3252i) q^{35} -128.739 q^{36} -48.5373i q^{37} +(22.0171 - 67.7615i) q^{38} +(11.3863 + 35.0433i) q^{39} +(23.6120 + 72.6704i) q^{40} +(-1.26683 + 0.920402i) q^{41} +(-50.0502 - 16.2623i) q^{42} +(33.5466 + 46.1730i) q^{43} +(62.7810 - 86.4106i) q^{44} +(16.8540 + 51.8712i) q^{45} +(-53.9492 + 74.2547i) q^{46} +(-24.4619 - 17.7726i) q^{47} +(151.937 - 49.3674i) q^{48} +(32.2677 + 23.4439i) q^{49} +(-27.8714 + 20.2497i) q^{50} +(24.2558 - 74.6517i) q^{51} +(-42.2023 - 58.0865i) q^{52} +(-51.0737 + 16.5949i) q^{53} +(80.0371 - 26.0056i) q^{54} +(-43.0354 - 13.9831i) q^{55} +58.4878 q^{56} +93.3083i q^{57} +(53.8886 + 17.5095i) q^{58} +(-54.4113 - 39.5321i) q^{59} +(-103.126 - 141.940i) q^{60} -56.2711i q^{61} +(107.656 + 34.6571i) q^{62} +41.7479 q^{63} +(-23.1301 + 16.8050i) q^{64} +(-17.8791 + 24.6085i) q^{65} +(-61.7963 + 190.190i) q^{66} +87.2989 q^{67} +152.951i q^{68} +(37.1443 - 114.318i) q^{69} +(-13.4249 - 41.3176i) q^{70} +(-19.9102 - 61.2774i) q^{71} +(-216.722 + 157.458i) q^{72} +(-14.3964 - 4.67769i) q^{73} +(-104.084 - 143.259i) q^{74} +(26.5193 - 36.5007i) q^{75} +(-56.1851 - 172.920i) q^{76} +(-20.3588 + 28.0215i) q^{77} +(108.754 + 79.0146i) q^{78} +(-67.5006 + 21.9323i) q^{79} +(106.695 + 77.5187i) q^{80} +(11.5200 - 8.36981i) q^{81} +(-1.76535 + 5.43319i) q^{82} +(42.2812 + 58.1951i) q^{83} +(-127.723 + 41.4996i) q^{84} +(61.6267 - 20.0237i) q^{85} +(198.028 + 64.3432i) q^{86} -74.2052 q^{87} -222.252i q^{88} +(28.3122 + 9.19918i) q^{89} +(160.978 + 116.958i) q^{90} +(13.6855 + 18.8365i) q^{91} +234.222i q^{92} +(-148.113 + 0.401655i) q^{93} -110.312 q^{94} +(-62.3171 + 45.2760i) q^{95} +(124.963 - 171.997i) q^{96} +(35.5472 - 109.403i) q^{97} +145.512 q^{98} -158.641i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{2} - 5 q^{3} - 11 q^{4} - 14 q^{5} - q^{7} - 19 q^{8} + 2 q^{9} + 12 q^{10} - 10 q^{11} + 90 q^{12} + 10 q^{13} - 85 q^{15} - 103 q^{16} + 35 q^{17} + 6 q^{18} + 47 q^{19} - 125 q^{20} - 125 q^{21}+ \cdots - 1000 q^{98}+O(q^{100}) $ 20 * q - 3 * q^2 - 5 * q^3 - 11 * q^4 - 14 * q^5 - q^7 - 19 * q^8 + 2 * q^9 + 12 * q^10 - 10 * q^11 + 90 * q^12 + 10 * q^13 - 85 * q^15 - 103 * q^16 + 35 * q^17 + 6 * q^18 + 47 * q^19 - 125 * q^20 - 125 * q^21 + 150 * q^22 + 75 * q^23 + 195 * q^24 + 82 * q^25 + 25 * q^27 + 88 * q^28 + 5 * q^29 + 73 * q^31 + 226 * q^32 - 206 * q^33 - 265 * q^34 - 50 * q^35 - 520 * q^36 + 8 * q^38 + 91 * q^39 - 466 * q^40 - 98 * q^41 + 245 * q^43 + 380 * q^44 - 162 * q^45 - 445 * q^46 - 187 * q^47 + 570 * q^48 + 328 * q^49 - 44 * q^50 + 185 * q^51 - 15 * q^52 + 25 * q^53 + 920 * q^54 + 190 * q^55 + 64 * q^56 - 85 * q^58 - 173 * q^59 + 275 * q^60 - 40 * q^62 + 252 * q^63 - 469 * q^64 - 345 * q^65 - 564 * q^66 + 76 * q^67 - 197 * q^69 - 11 * q^70 - 467 * q^71 - 982 * q^72 - 15 * q^73 + 45 * q^74 - 175 * q^75 + 55 * q^76 - 320 * q^77 - 91 * q^78 + 500 * q^79 + 1030 * q^80 + 117 * q^81 + 178 * q^82 - 50 * q^83 + 65 * q^84 + 20 * q^85 + 1125 * q^86 - 366 * q^87 + 55 * q^89 + 444 * q^90 + 300 * q^91 + 502 * q^93 + 62 * q^94 - 559 * q^95 - 10 * q^96 - 405 * q^97 - 1000 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	2.95153	−	2.14441i	1.47577	−	1.07221i	0.496875	−	0.867822i	$-0.334481\pi$
$2$	2.95153	−	2.14441i	1.47577	−	1.07221i	0.978891	−	0.204385i	$-0.0655194\pi$
$3$	−2.80836	+	3.86537i	−0.936118	+	1.28846i	0.0213062	+	0.999773i	$0.493218\pi$
$3$	−2.80836	+	3.86537i	−0.936118	+	1.28846i	−0.957425	+	0.288683i	$0.906782\pi$
$4$	2.87696	−	8.85438i	0.719241	−	2.21360i
$5$	−3.94423			−0.788847			−0.394423	−	0.918929i	$-0.629056\pi$
$5$	−3.94423			−0.788847			−0.394423	+	0.918929i	$0.629056\pi$
$6$			17.4310i			2.90517i
$7$	−0.932951	+	2.87133i	−0.133279	+	0.410190i	−0.995318	−	0.0966511i	$-0.969187\pi$
$7$	−0.932951	+	2.87133i	−0.133279	+	0.410190i	0.862040	+	0.506841i	$0.169187\pi$
$8$	−5.98647	−	18.4245i	−0.748309	−	2.30306i
$9$	−4.27307	−	13.1512i	−0.474785	−	1.46124i
$10$	−11.6415	+	8.45807i	−1.16415	+	0.845807i
$11$	10.9110	+	3.54519i	0.991907	+	0.322290i	0.759627	−	0.650359i	$-0.225382\pi$
$11$	10.9110	+	3.54519i	0.991907	+	0.322290i	0.232280	+	0.972649i	$0.425382\pi$
$12$	26.1459	+	35.9868i	2.17883	+	2.99890i
$13$	4.53298	−	6.23912i	0.348691	−	0.479932i	−0.598264	−	0.801299i	$-0.704142\pi$
$13$	4.53298	−	6.23912i	0.348691	−	0.479932i	0.946955	+	0.321367i	$0.104142\pi$
$14$	3.40368	+	10.4755i	0.243120	+	0.748247i
$15$	11.0768	−	15.2459i	0.738454	−	1.01639i
$16$	−27.0510	−	19.6537i	−1.69068	−	1.22835i
$17$	−15.6245	+	5.07671i	−0.919089	+	0.298630i	−0.730093	−	0.683348i	$-0.760523\pi$
$17$	−15.6245	+	5.07671i	−0.919089	+	0.298630i	−0.188996	+	0.981978i	$0.560523\pi$
$18$	−40.8136	−	29.6528i	−2.26742	−	1.64738i
$19$	15.7996	−	11.4790i	0.831555	−	0.604160i	−0.0884436	−	0.996081i	$-0.528189\pi$
$19$	15.7996	−	11.4790i	0.831555	−	0.604160i	0.919999	+	0.391921i	$0.128189\pi$
$20$	−11.3474	+	34.9238i	−0.567371	+	1.74619i
$21$	−8.47869	−	11.6699i	−0.403747	−	0.555710i
$22$	39.8064	−	12.9339i	1.80938	−	0.587904i
$23$	−23.9267	+	7.77425i	−1.04029	+	0.338011i	−0.778851	−	0.627209i	$-0.784197\pi$
$23$	−23.9267	+	7.77425i	−1.04029	+	0.338011i	−0.261440	+	0.965220i	$0.584197\pi$
$24$	88.0295	+	28.6025i	3.66789	+	1.19177i
$25$	−9.44302			−0.377721
$26$		−	28.1355i		−	1.08214i
$27$	21.9382	+	7.12816i	0.812527	+	0.264006i
$28$	22.7398	+	16.5214i	0.812135	+	0.590051i
$29$	9.12892	+	12.5649i	0.314790	+	0.433272i	0.936868	−	0.349684i	$-0.113711\pi$
$29$	9.12892	+	12.5649i	0.314790	+	0.433272i	−0.622077	+	0.782956i	$0.713711\pi$
$30$		−	68.7521i		−	2.29174i
$31$	18.2893	+	25.0300i	0.589977	+	0.807420i
$31$	18.2893	+	25.0300i	0.589977	+	0.807420i
$32$	−44.4969			−1.39053
$33$	−44.3454	+	32.2188i	−1.34380	+	0.976327i
$34$	−35.2297	+	48.4895i	−1.03617	+	1.42616i
$35$	3.67978	−	11.3252i	0.105137	−	0.323577i
$36$	−128.739			−3.57608
$37$		−	48.5373i		−	1.31182i	−0.754840	−	0.655909i	$-0.772285\pi$
$37$		−	48.5373i		−	1.31182i	0.754840	−	0.655909i	$-0.227715\pi$
$38$	22.0171	−	67.7615i	0.579396	−	1.78320i
$39$	11.3863	+	35.0433i	0.291955	+	0.898546i
$40$	23.6120	+	72.6704i	0.590301	+	1.81676i
$41$	−1.26683	+	0.920402i	−0.0308982	+	0.0224488i	−0.603127	−	0.797645i	$-0.706079\pi$
$41$	−1.26683	+	0.920402i	−0.0308982	+	0.0224488i	0.572229	+	0.820094i	$0.306079\pi$
$42$	−50.0502	−	16.2623i	−1.19167	−	0.387198i
$43$	33.5466	+	46.1730i	0.780155	+	1.07379i	0.995265	+	0.0972010i	$0.0309890\pi$
$43$	33.5466	+	46.1730i	0.780155	+	1.07379i	−0.215110	+	0.976590i	$0.569011\pi$
$44$	62.7810	−	86.4106i	1.42684	−	1.96388i
$45$	16.8540	+	51.8712i	0.374533	+	1.15269i
$46$	−53.9492	+	74.2547i	−1.17281	+	1.61423i
$47$	−24.4619	−	17.7726i	−0.520466	−	0.378141i	0.296313	−	0.955091i	$-0.404243\pi$
$47$	−24.4619	−	17.7726i	−0.520466	−	0.378141i	−0.816779	+	0.576950i	$0.804243\pi$
$48$	151.937	−	49.3674i	3.16536	−	1.02849i
$49$	32.2677	+	23.4439i	0.658524	+	0.478446i
$50$	−27.8714	+	20.2497i	−0.557427	+	0.404995i
$51$	24.2558	−	74.6517i	0.475604	−	1.46376i
$52$	−42.2023	−	58.0865i	−0.811583	−	1.11705i
$53$	−51.0737	+	16.5949i	−0.963655	+	0.313111i	−0.748252	−	0.663415i	$-0.769107\pi$
$53$	−51.0737	+	16.5949i	−0.963655	+	0.313111i	−0.215403	+	0.976525i	$0.569107\pi$
$54$	80.0371	−	26.0056i	1.48217	−	0.481586i
$55$	−43.0354	−	13.9831i	−0.782463	−	0.254238i
$56$	58.4878			1.04442
$57$			93.3083i			1.63699i
$58$	53.8886	+	17.5095i	0.929114	+	0.301887i
$59$	−54.4113	−	39.5321i	−0.922225	−	0.670035i	0.0218521	−	0.999761i	$-0.493044\pi$
$59$	−54.4113	−	39.5321i	−0.922225	−	0.670035i	−0.944077	+	0.329726i	$0.893044\pi$
$60$	−103.126	−	141.940i	−1.71876	−	2.36567i
$61$		−	56.2711i		−	0.922477i	−0.887276	−	0.461239i	$-0.847405\pi$
$61$		−	56.2711i		−	0.922477i	0.887276	−	0.461239i	$-0.152595\pi$
$62$	107.656	+	34.6571i	1.73639	+	0.558986i
$63$	41.7479			0.662664
$64$	−23.1301	+	16.8050i	−0.361408	+	0.262578i
$65$	−17.8791	+	24.6085i	−0.275064	+	0.378593i
$66$	−61.7963	+	190.190i	−0.936308	+	2.88166i
$67$	87.2989			1.30297			0.651484	−	0.758662i	$-0.274147\pi$
$67$	87.2989			1.30297			0.651484	+	0.758662i	$0.274147\pi$
$68$			152.951i			2.24928i
$69$	37.1443	−	114.318i	0.538323	−	1.65679i
$70$	−13.4249	−	41.3176i	−0.191785	−	0.590252i
$71$	−19.9102	−	61.2774i	−0.280426	−	0.863061i	−0.987733	−	0.156155i	$-0.950090\pi$
$71$	−19.9102	−	61.2774i	−0.280426	−	0.863061i	0.707307	−	0.706907i	$-0.249910\pi$
$72$	−216.722	+	157.458i	−3.01003	+	2.18692i
$73$	−14.3964	−	4.67769i	−0.197212	−	0.0640779i	0.208746	−	0.977970i	$-0.433062\pi$
$73$	−14.3964	−	4.67769i	−0.197212	−	0.0640779i	−0.405957	+	0.913892i	$0.633062\pi$
$74$	−104.084	−	143.259i	−1.40654	−	1.93594i
$75$	26.5193	−	36.5007i	0.353591	−	0.486677i
$76$	−56.1851	−	172.920i	−0.739278	−	2.27526i
$77$	−20.3588	+	28.0215i	−0.264400	+	0.363916i
$78$	108.754	+	79.0146i	1.39429	+	1.01301i
$79$	−67.5006	+	21.9323i	−0.854438	+	0.277624i	−0.703304	−	0.710890i	$-0.748293\pi$
$79$	−67.5006	+	21.9323i	−0.854438	+	0.277624i	−0.151134	+	0.988513i	$0.548293\pi$
$80$	106.695	+	77.5187i	1.33369	+	0.968984i
$81$	11.5200	−	8.36981i	0.142223	−	0.103331i
$82$	−1.76535	+	5.43319i	−0.0215287	+	0.0662585i
$83$	42.2812	+	58.1951i	0.509412	+	0.701145i	0.983820	−	0.179160i	$-0.0573379\pi$
$83$	42.2812	+	58.1951i	0.509412	+	0.701145i	−0.474408	+	0.880305i	$0.657338\pi$
$84$	−127.723	+	41.4996i	−1.52051	+	0.494043i
$85$	61.6267	−	20.0237i	0.725021	−	0.235573i
$86$	198.028	+	64.3432i	2.30265	+	0.748177i
$87$	−74.2052			−0.852933
$88$		−	222.252i		−	2.52559i
$89$	28.3122	+	9.19918i	0.318114	+	0.103362i	0.463722	−	0.885981i	$-0.346514\pi$
$89$	28.3122	+	9.19918i	0.318114	+	0.103362i	−0.145608	+	0.989342i	$0.546514\pi$
$90$	160.978	+	116.958i	1.78865	+	1.29953i
$91$	13.6855	+	18.8365i	0.150390	+	0.206994i
$92$			234.222i			2.54590i
$93$	−148.113	+	0.401655i	−1.59261	+	0.00431888i
$94$	−110.312			−1.17353
$95$	−62.3171	+	45.2760i	−0.655970	+	0.476590i
$96$	124.963	−	171.997i	1.30170	−	1.79163i
$97$	35.5472	−	109.403i	0.366466	−	1.12787i	−0.582592	−	0.812765i	$-0.697961\pi$
$97$	35.5472	−	109.403i	0.366466	−	1.12787i	0.949058	−	0.315102i	$-0.102039\pi$
$98$	145.512			1.48482
$99$		−	158.641i		−	1.60243i
$100$	−27.1672	+	83.6121i	−0.271672	+	0.836121i
$101$	−31.7093	−	97.5911i	−0.313953	−	0.966249i	−0.976183	−	0.216948i	$-0.930390\pi$
$101$	−31.7093	−	97.5911i	−0.313953	−	0.966249i	0.662230	−	0.749301i	$-0.269610\pi$
$102$	−88.4923	−	272.351i	−0.867572	−	2.67011i
$103$	−72.7309	+	52.8421i	−0.706125	+	0.513030i	−0.881921	−	0.471397i	$-0.843750\pi$
$103$	−72.7309	+	52.8421i	−0.706125	+	0.513030i	0.175796	+	0.984427i	$0.443750\pi$
$104$	−142.089	−	46.1675i	−1.36624	−	0.443918i
$105$	33.4419	+	46.0289i	0.318495	+	0.438370i
$106$	−115.159	+	158.503i	−1.08641	+	1.49532i
$107$	41.8782	+	128.888i	0.391385	+	1.20456i	0.931741	+	0.363122i	$0.118289\pi$
$107$	41.8782	+	128.888i	0.391385	+	1.20456i	−0.540357	+	0.841436i	$0.681711\pi$
$108$	126.231	−	173.742i	1.16880	−	1.60872i
$109$	48.9202	+	35.5426i	0.448809	+	0.326079i	0.789125	−	0.614232i	$-0.210534\pi$
$109$	48.9202	+	35.5426i	0.448809	+	0.326079i	−0.340316	+	0.940311i	$0.610534\pi$
$110$	−157.006	+	51.0143i	−1.42733	+	0.463767i
$111$	187.615	+	136.310i	1.69022	+	1.22802i
$112$	81.6694	−	59.3363i	0.729191	−	0.529788i
$113$	−4.24023	+	13.0501i	−0.0375242	+	0.115487i	−0.968064	−	0.250703i	$-0.919338\pi$
$113$	−4.24023	+	13.0501i	−0.0375242	+	0.115487i	0.930540	+	0.366191i	$0.119338\pi$
$114$	200.092	+	275.403i	1.75519	+	2.41581i
$115$	94.3725	−	30.6635i	0.820630	−	0.266639i
$116$	137.518	−	44.6823i	1.18550	−	0.385192i
$117$	−101.421	−	32.9538i	−0.866849	−	0.281656i
$118$	−245.370			−2.07940
$119$		−	49.5995i		−	0.416802i
$120$	−347.209	−	112.815i	−2.89341	−	0.940125i
$121$	8.58994	+	6.24096i	0.0709913	+	0.0515782i
$122$	−120.669	−	166.086i	−0.989086	−	1.36136i
$123$		−	7.48156i		−	0.0608257i
$124$	274.243	−	89.9299i	2.21164	−	0.725241i
$125$	135.851			1.08681
$126$	123.220	−	89.5247i	0.977937	−	0.710513i
$127$	15.7518	−	21.6805i	0.124030	−	0.170713i	−0.742487	−	0.669861i	$-0.766354\pi$
$127$	15.7518	−	21.6805i	0.124030	−	0.170713i	0.866517	+	0.499148i	$0.166354\pi$
$128$	22.7688	−	70.0752i	0.177881	−	0.547462i
$129$	−272.687			−2.11385
$130$			110.973i			0.853640i
$131$	−75.6209	+	232.737i	−0.577259	+	1.77662i	0.0510979	+	0.998694i	$0.483728\pi$
$131$	−75.6209	+	232.737i	−0.577259	+	1.77662i	−0.628356	+	0.777926i	$0.716272\pi$
$132$	157.698	+	485.343i	1.19468	+	3.67684i
$133$	18.2199	+	56.0751i	0.136992	+	0.421617i
$134$	257.665	−	187.205i	1.92288	−	1.39705i
$135$	−86.5295	−	28.1151i	−0.640959	−	0.208260i
$136$	187.071	+	257.482i	1.37552	+	1.89325i
$137$	−47.6994	+	65.6526i	−0.348171	+	0.479216i	−0.946806	−	0.321806i	$-0.895710\pi$
$137$	−47.6994	+	65.6526i	−0.348171	+	0.479216i	0.598635	+	0.801022i	$0.295710\pi$
$138$	−135.513	−	417.067i	−0.981980	−	3.02222i
$139$	−62.2830	+	85.7252i	−0.448079	+	0.616728i	−0.971984	−	0.235049i	$-0.924475\pi$
$139$	−62.2830	+	85.7252i	−0.448079	+	0.616728i	0.523904	+	0.851777i	$0.324475\pi$
$140$	−89.6910	−	65.1644i	−0.640650	−	0.465460i
$141$	137.395	−	44.6425i	0.974435	−	0.316613i
$142$	−190.170	−	138.166i	−1.33922	−	0.973002i
$143$	71.5781	−	52.0046i	0.500546	−	0.363668i
$144$	−142.878	+	439.733i	−0.992207	+	3.05370i
$145$	−36.0066	−	49.5588i	−0.248321	−	0.341785i
$146$	−52.5225	+	17.0656i	−0.359743	+	0.116888i
$147$	−181.238	+	58.8879i	−1.23291	+	0.400598i
$148$	−429.768	−	139.640i	−2.90384	−	0.943514i
$149$	241.145			1.61842			0.809210	−	0.587519i	$-0.199895\pi$
$149$	241.145			1.61842			0.809210	+	0.587519i	$0.199895\pi$
$150$		−	164.602i		−	1.09734i
$151$	−16.2020	−	5.26435i	−0.107298	−	0.0348633i	0.254876	−	0.966974i	$-0.417965\pi$
$151$	−16.2020	−	5.26435i	−0.107298	−	0.0348633i	−0.362174	+	0.932111i	$0.617965\pi$
$152$	−306.079	−	222.379i	−2.01368	−	1.46302i
$153$	133.529	+	183.787i	0.872740	+	1.20122i
$154$			126.364i			0.820546i
$155$	−72.1372	−	98.7243i	−0.465402	−	0.636931i
$156$	343.045			2.19900
$157$	−54.7192	+	39.7558i	−0.348530	+	0.253222i	−0.748252	−	0.663415i	$-0.769107\pi$
$157$	−54.7192	+	39.7558i	−0.348530	+	0.253222i	0.399722	+	0.916636i	$0.369107\pi$
$158$	−152.198	+	209.483i	−0.963280	+	1.32584i
$159$	79.2879	−	244.023i	0.498666	−	1.53474i
$160$	175.506			1.09691
$161$		−	75.9544i		−	0.471767i
$162$	16.0535	−	49.4075i	0.0990955	−	0.304985i
$163$	17.3607	+	53.4307i	0.106507	+	0.327795i	0.990081	−	0.140496i	$-0.0448697\pi$
$163$	17.3607	+	53.4307i	0.106507	+	0.327795i	−0.883574	+	0.468291i	$0.844870\pi$
$164$	4.50498	+	13.8649i	0.0274694	+	0.0845422i
$165$	174.909	−	127.078i	1.06005	−	0.770173i
$166$	249.589	+	81.0962i	1.50355	+	0.488531i
$167$	−42.0141	−	57.8274i	−0.251581	−	0.346272i	0.664483	−	0.747303i	$-0.268652\pi$
$167$	−42.0141	−	57.8274i	−0.251581	−	0.346272i	−0.916064	+	0.401031i	$0.868652\pi$
$168$	−164.254	+	226.077i	−0.977705	+	1.34570i
$169$	33.8452	+	104.165i	0.200268	+	0.616360i
$170$	138.954	−	191.254i	0.817377	−	1.12502i
$171$	−218.475	−	158.732i	−1.27763	−	0.928255i
$172$	505.346	−	164.197i	2.93806	−	0.954633i
$173$	155.826	+	113.214i	0.900726	+	0.654416i	0.938652	−	0.344865i	$-0.112075\pi$
$173$	155.826	+	113.214i	0.900726	+	0.654416i	−0.0379265	+	0.999281i	$0.512075\pi$
$174$	−219.019	+	159.127i	−1.25873	+	0.914520i
$175$	8.80988	−	27.1140i	0.0503421	−	0.154937i
$176$	−225.476	−	310.341i	−1.28112	−	1.76330i
$177$	305.612	−	99.2994i	1.72662	−	0.561014i
$178$	103.291	−	33.5613i	0.580287	−	0.188547i
$179$	−110.448	−	35.8868i	−0.617029	−	0.200485i	−0.0162084	−	0.999869i	$-0.505160\pi$
$179$	−110.448	−	35.8868i	−0.617029	−	0.200485i	−0.600821	+	0.799384i	$0.705160\pi$
$180$	507.776			2.82098
$181$		−	244.619i		−	1.35149i	−0.737137	−	0.675743i	$-0.763823\pi$
$181$		−	244.619i		−	1.35149i	0.737137	−	0.675743i	$-0.236177\pi$
$182$	80.7864	+	26.2491i	0.443881	+	0.144226i
$183$	217.509	+	158.029i	1.18857	+	0.863548i
$184$	286.473	+	394.296i	1.55692	+	2.14291i
$185$			191.442i			1.03482i
$186$	−436.299	+	318.801i	−2.34569	+	1.71398i
$187$	−188.477			−1.00790
$188$	−227.741	+	165.464i	−1.21139	+	0.880127i
$189$	−40.9346	+	56.3416i	−0.216585	+	0.298104i
$190$	−86.8404	+	267.267i	−0.457055	+	1.40667i
$191$	−131.778			−0.689939			−0.344969	−	0.938614i	$-0.612111\pi$
$191$	−131.778			−0.689939			−0.344969	+	0.938614i	$0.612111\pi$
$192$		−	136.601i		−	0.711462i
$193$	12.7631	−	39.2808i	0.0661301	−	0.203527i	−0.912531	−	0.409007i	$-0.865875\pi$
$193$	12.7631	−	39.2808i	0.0661301	−	0.203527i	0.978661	+	0.205479i	$0.0658753\pi$
$194$	−129.687	−	399.135i	−0.668488	−	2.05740i
$195$	−44.9101	−	138.219i	−0.230308	−	0.708816i
$196$	300.414	−	218.263i	1.53272	−	1.11359i
$197$	−248.751	−	80.8240i	−1.26269	−	0.410274i	−0.400240	−	0.916410i	$-0.631073\pi$
$197$	−248.751	−	80.8240i	−1.26269	−	0.410274i	−0.862453	+	0.506136i	$0.831073\pi$
$198$	−340.191	−	468.233i	−1.71814	−	2.36481i
$199$	9.07689	−	12.4933i	0.0456125	−	0.0627802i	−0.785602	−	0.618733i	$-0.787646\pi$
$199$	9.07689	−	12.4933i	0.0456125	−	0.0627802i	0.831214	+	0.555953i	$0.187646\pi$
$200$	56.5303	+	173.982i	0.282652	+	0.869912i
$201$	−245.166	+	337.442i	−1.21973	+	1.67882i
$202$	−302.867	−	220.045i	−1.49934	−	1.08933i
$203$	−44.5948	+	14.4897i	−0.219679	+	0.0713779i
$204$	−591.212	−	429.541i	−2.89810	−	2.10559i
$205$	4.99665	−	3.63028i	0.0243739	−	0.0177087i
$206$	−101.352	+	311.930i	−0.492001	+	1.51422i
$207$	204.481	+	281.444i	0.987830	+	1.35963i
$208$	−245.243	+	79.6843i	−1.17905	+	0.383098i
$209$	213.084	−	69.2352i	1.01954	−	0.331269i
$210$	197.410	+	64.1424i	0.940047	+	0.305440i
$211$	−406.514			−1.92661			−0.963304	−	0.268413i	$-0.913501\pi$
$211$	−406.514			−1.92661			−0.963304	+	0.268413i	$0.913501\pi$
$212$			499.969i			2.35835i
$213$	292.775	+	95.1282i	1.37453	+	0.446611i
$214$	399.993	+	290.612i	1.86913	+	1.35800i
$215$	−132.316	−	182.117i	−0.615423	−	0.847056i
$216$		−	446.872i		−	2.06885i
$217$	−88.9325	+	29.1628i	−0.409827	+	0.134391i
$218$	220.608			1.01196
$219$	58.5113	−	42.5110i	0.267175	−	0.194114i
$220$	−247.623	+	340.824i	−1.12556	+	1.54920i
$221$	−39.1515	+	120.496i	−0.177156	+	0.545230i
$222$	846.055			3.81106
$223$			53.9778i			0.242053i	0.992649	+	0.121027i	$0.0386186\pi$
$223$			53.9778i			0.242053i	−0.992649	+	0.121027i	$0.961381\pi$
$224$	41.5134	−	127.765i	0.185328	−	0.570380i
$225$	40.3506	+	124.187i	0.179336	+	0.551940i
$226$	15.4696	+	47.6105i	0.0684496	+	0.210666i
$227$	138.386	−	100.544i	0.609631	−	0.442923i	−0.239653	−	0.970859i	$-0.577034\pi$
$227$	138.386	−	100.544i	0.609631	−	0.442923i	0.849284	+	0.527936i	$0.177034\pi$
$228$	826.188	+	268.445i	3.62363	+	1.17739i
$229$	−48.0594	−	66.1481i	−0.209867	−	0.288857i	0.691087	−	0.722771i	$-0.257132\pi$
$229$	−48.0594	−	66.1481i	−0.209867	−	0.288857i	−0.900954	+	0.433915i	$0.857132\pi$
$230$	212.788	−	292.878i	0.925166	−	1.27338i
$231$	−51.1387	−	157.389i	−0.221380	−	0.681336i
$232$	176.851	−	243.415i	0.762289	−	1.04920i
$233$	−87.8907	−	63.8563i	−0.377213	−	0.274061i	0.382983	−	0.923756i	$-0.374897\pi$
$233$	−87.8907	−	63.8563i	−0.377213	−	0.274061i	−0.760196	+	0.649694i	$0.774897\pi$
$234$	−370.015	+	120.225i	−1.58126	+	0.513782i
$235$	96.4835	+	70.0993i	0.410568	+	0.298295i
$236$	−506.571	+	368.046i	−2.14649	+	1.55952i
$237$	104.789	−	322.508i	0.442149	−	1.36079i
$238$	−106.362	−	146.394i	−0.446898	−	0.615102i
$239$	206.536	−	67.1078i	0.864169	−	0.280786i	0.156800	−	0.987630i	$-0.449882\pi$
$239$	206.536	−	67.1078i	0.864169	−	0.280786i	0.707369	+	0.706845i	$0.249882\pi$
$240$	−599.277	+	194.717i	−2.49699	+	0.811320i
$241$	−50.6814	−	16.4674i	−0.210296	−	0.0683294i	0.201974	−	0.979391i	$-0.435264\pi$
$241$	−50.6814	−	16.4674i	−0.210296	−	0.0683294i	−0.412271	+	0.911061i	$0.635264\pi$
$242$	38.7367			0.160069
$243$			275.640i			1.13432i
$244$	−498.246	−	161.890i	−2.04199	−	0.663483i
$245$	−127.271	−	92.4681i	−0.519475	−	0.377421i
$246$	−16.0436	−	22.0821i	−0.0652177	−	0.0897645i
$247$		−	150.610i		−	0.609755i
$248$	351.676	−	486.812i	1.41805	−	1.96295i
$249$	−343.686			−1.38026
$250$	400.970	−	291.321i	1.60388	−	1.16529i
$251$	247.733	−	340.976i	0.986985	−	1.35847i	0.0540055	−	0.998541i	$-0.482801\pi$
$251$	247.733	−	340.976i	0.986985	−	1.35847i	0.932980	−	0.359928i	$-0.117199\pi$
$252$	120.107	−	369.651i	0.476615	−	1.46687i
$253$	−288.625			−1.14081
$254$		−	97.7692i		−	0.384918i
$255$	−95.6706	+	294.444i	−0.375179	+	1.15468i
$256$	−118.407	−	364.419i	−0.462527	−	1.42351i
$257$	90.0443	+	277.128i	0.350367	+	1.07832i	0.958648	+	0.284596i	$0.0918595\pi$
$257$	90.0443	+	277.128i	0.350367	+	1.07832i	−0.608281	+	0.793722i	$0.708141\pi$
$258$	−804.843	+	584.753i	−3.11955	+	2.26648i
$259$	139.367	+	45.2829i	0.538095	+	0.174838i
$260$	166.456	+	229.107i	0.640214	+	0.881180i
$261$	126.234	−	173.746i	0.483656	−	0.665695i
$262$	275.887	+	849.093i	1.05300	+	3.24081i
$263$	18.2574	−	25.1291i	0.0694197	−	0.0955480i	−0.772895	−	0.634534i	$-0.781192\pi$
$263$	18.2574	−	25.1291i	0.0694197	−	0.0955480i	0.842315	+	0.538986i	$0.181192\pi$
$264$	859.086	+	624.162i	3.25411	+	2.36425i
$265$	201.447	−	65.4540i	0.760176	−	0.246996i
$266$	174.025	+	126.436i	0.654229	+	0.475325i
$267$	−115.069	+	83.6024i	−0.430969	+	0.313118i
$268$	251.156	−	772.978i	0.937148	−	2.88425i
$269$	71.6026	+	98.5525i	0.266181	+	0.366366i	0.921096	−	0.389336i	$-0.127296\pi$
$269$	71.6026	+	98.5525i	0.266181	+	0.366366i	−0.654915	+	0.755703i	$0.727296\pi$
$270$	−315.685	+	102.572i	−1.16920	+	0.379897i
$271$	−94.4952	+	30.7034i	−0.348691	+	0.113297i	−0.478126	−	0.878291i	$-0.658684\pi$
$271$	−94.4952	+	30.7034i	−0.348691	+	0.113297i	0.129435	+	0.991588i	$0.458684\pi$
$272$	522.434	+	169.749i	1.92071	+	0.624078i
$273$	−111.244			−0.407486
$274$			296.063i			1.08052i
$275$	−103.033	−	33.4773i	−0.374664	−	0.121736i
$276$	−905.356	−	657.780i	−3.28027	−	2.38326i
$277$	−245.522	−	337.932i	−0.886360	−	1.21997i	−0.974618	−	0.223872i	$-0.928130\pi$
$277$	−245.522	−	337.932i	−0.886360	−	1.21997i	0.0882585	−	0.996098i	$-0.471870\pi$
$278$			386.581i			1.39058i
$279$	251.022	−	347.480i	0.899721	−	1.24545i
$280$	−230.689			−0.823891
$281$	41.6719	−	30.2764i	0.148298	−	0.107745i	−0.511162	−	0.859484i	$-0.670785\pi$
$281$	41.6719	−	30.2764i	0.148298	−	0.107745i	0.659460	+	0.751739i	$0.270785\pi$
$282$	309.795	−	426.396i	1.09856	−	1.51204i
$283$	54.0307	−	166.290i	0.190921	−	0.587596i	−0.809079	−	0.587700i	$-0.800033\pi$
$283$	54.0307	−	166.290i	0.190921	−	0.587596i	1.00000		0.000104866i	$3.33797e-5\pi$
$284$	−599.854			−2.11216
$285$		−	368.030i		−	1.29133i
$286$	99.7459	−	306.986i	0.348762	−	1.07338i
$287$	−1.46089	−	4.49616i	−0.00509022	−	0.0156661i
$288$	190.138	+	585.185i	0.660202	+	2.03189i
$289$	−15.4535	+	11.2276i	−0.0534723	+	0.0388499i
$290$	−212.549	−	69.0614i	−0.732929	−	0.238143i
$291$	323.054	+	444.646i	1.11015	+	1.52799i
$292$	−82.8361	+	114.014i	−0.283685	+	0.390459i
$293$	−11.1393	−	34.2833i	−0.0380181	−	0.117008i	0.930246	−	0.366936i	$-0.119593\pi$
$293$	−11.1393	−	34.2833i	−0.0380181	−	0.117008i	−0.968264	+	0.249928i	$0.919593\pi$
$294$	−408.651	+	562.459i	−1.38997	+	1.91313i
$295$	214.611	+	155.924i	0.727494	+	0.528555i
$296$	−894.273	+	290.567i	−3.02119	+	0.981645i
$297$	214.097	+	155.550i	0.720864	+	0.523739i
$298$	711.746	−	517.114i	2.38841	−	1.73528i
$299$	−59.9548	+	184.522i	−0.200518	+	0.617130i
$300$	−246.896	−	339.824i	−0.822988	−	1.13275i
$301$	−163.875	+	53.2463i	−0.544436	+	0.176898i
$302$	−59.1097	+	19.2059i	−0.195727	+	0.0635957i
$303$	466.277	+	151.502i	1.53887	+	0.500008i
$304$	−652.998			−2.14802
$305$			221.946i			0.727693i
$306$	788.231	+	256.112i	2.57592	+	0.836967i
$307$	80.2732	+	58.3219i	0.261476	+	0.189974i	0.710798	−	0.703397i	$-0.248334\pi$
$307$	80.2732	+	58.3219i	0.261476	+	0.189974i	−0.449321	+	0.893370i	$0.648334\pi$
$308$	189.542	+	260.882i	0.615395	+	0.847018i
$309$		−	429.531i		−	1.39007i
$310$	−424.621	−	136.696i	−1.36975	−	0.440954i
$311$	428.987			1.37938			0.689689	−	0.724106i	$-0.257747\pi$
$311$	428.987			1.37938			0.689689	+	0.724106i	$0.257747\pi$
$312$	577.490	−	419.571i	1.85093	−	1.34478i
$313$	−124.931	+	171.952i	−0.399139	+	0.549368i	−0.960528	−	0.278185i	$-0.910267\pi$
$313$	−124.931	+	171.952i	−0.399139	+	0.549368i	0.561389	+	0.827552i	$0.310267\pi$
$314$	−76.2525	+	234.681i	−0.242842	+	0.747392i
$315$	−164.663			−0.522741
$316$			660.774i			2.09106i
$317$	49.1333	−	151.217i	0.154995	−	0.477025i	−0.843166	−	0.537654i	$-0.819311\pi$
$317$	49.1333	−	151.217i	0.154995	−	0.477025i	0.998160	+	0.0606293i	$0.0193107\pi$
$318$	−289.266	−	890.268i	−0.909640	−	2.79958i
$319$	55.0605	+	169.459i	0.172604	+	0.531219i
$320$	91.2305	−	66.2829i	0.285095	−	0.207134i
$321$	−615.807	−	200.088i	−1.91840	−	0.623327i
$322$	−162.878	−	224.182i	−0.505831	−	0.696217i
$323$	−188.584	+	259.564i	−0.583853	+	0.803605i
$324$	−40.9667	−	126.083i	−0.126440	−	0.389144i
$325$	−42.8050	+	58.9161i	−0.131708	+	0.181280i
$326$	165.818	+	120.474i	0.508644	+	0.369552i
$327$	−274.771	+	89.2783i	−0.840277	+	0.273022i
$328$	24.5417	+	17.8306i	0.0748223	+	0.0543616i
$329$	73.8528	−	53.6572i	0.224477	−	0.163092i
$330$	243.739	−	750.152i	0.738604	−	2.27319i
$331$	277.937	+	382.548i	0.839689	+	1.15573i	0.986041	+	0.166501i	$0.0532467\pi$
$331$	277.937	+	382.548i	0.839689	+	1.15573i	−0.146352	+	0.989233i	$0.546753\pi$
$332$	636.923	−	206.949i	1.91844	−	0.623340i
$333$	−638.321	+	207.403i	−1.91688	+	0.622832i
$334$	−248.012	−	80.5839i	−0.742550	−	0.241269i
$335$	−344.327			−1.02784
$336$			482.320i			1.43548i
$337$	271.877	+	88.3383i	0.806758	+	0.262132i	0.683224	−	0.730209i	$-0.260577\pi$
$337$	271.877	+	88.3383i	0.806758	+	0.262132i	0.123534	+	0.992340i	$0.460577\pi$
$338$	323.268	+	234.868i	0.956414	+	0.694875i
$339$	−38.5353	−	53.0393i	−0.113674	−	0.156458i
$340$		−	603.274i		−	1.77434i
$341$	110.818	+	337.941i	0.324979	+	0.991029i
$342$	−985.223			−2.88077
$343$	−217.102	+	157.734i	−0.632949	+	0.459865i
$344$	649.887	−	894.492i	1.88921	−	2.60027i
$345$	−146.506	+	450.898i	−0.424654	+	1.30695i
$346$	702.702			2.03093
$347$		−	226.797i		−	0.653593i	−0.945095	−	0.326797i	$-0.894031\pi$
$347$		−	226.797i		−	0.653593i	0.945095	−	0.326797i	$-0.105969\pi$
$348$	−213.486	+	657.041i	−0.613464	+	1.88805i
$349$	198.443	+	610.746i	0.568605	+	1.74999i	0.656989	+	0.753901i	$0.271830\pi$
$349$	198.443	+	610.746i	0.568605	+	1.74999i	−0.0883832	+	0.996087i	$0.528170\pi$
$350$	−32.1410	−	98.9199i	−0.0918315	−	0.282628i
$351$	143.919	−	104.563i	0.410026	−	0.297901i
$352$	−485.504	−	157.750i	−1.37927	−	0.448153i
$353$	−349.013	−	480.375i	−0.988706	−	1.36084i	−0.932005	−	0.362445i	$-0.881942\pi$
$353$	−349.013	−	480.375i	−0.988706	−	1.36084i	−0.0567007	−	0.998391i	$-0.518058\pi$
$354$	689.085	−	948.445i	1.94657	−	2.67922i
$355$	78.5306	+	241.692i	0.221213	+	0.680823i
$356$	162.906	−	224.221i	0.457601	−	0.629834i
$357$	191.720	+	139.293i	0.537031	+	0.390176i
$358$	−402.948	+	130.926i	−1.12555	+	0.365714i
$359$	−255.375	−	185.541i	−0.711350	−	0.516826i	0.172259	−	0.985052i	$-0.444893\pi$
$359$	−255.375	−	185.541i	−0.711350	−	0.516826i	−0.883609	+	0.468225i	$0.844893\pi$
$360$	854.803	−	621.051i	2.37445	−	1.72514i
$361$	6.30218	−	19.3961i	0.0174576	−	0.0537289i
$362$	−524.564	−	722.001i	−1.44907	−	1.99448i
$363$	−48.2472	+	15.6765i	−0.132912	+	0.0431859i
$364$	206.158	−	66.9848i	0.566368	−	0.184024i
$365$	56.7830	+	18.4499i	0.155570	+	0.0505477i
$366$	980.864			2.67996
$367$		−	442.468i		−	1.20564i	−0.797879	−	0.602818i	$-0.794044\pi$
$367$		−	442.468i		−	1.20564i	0.797879	−	0.602818i	$-0.205956\pi$
$368$	800.033	+	259.946i	2.17400	+	0.706376i
$369$	17.5176	+	12.7273i	0.0474731	+	0.0344912i
$370$	410.532	+	565.049i	1.10955	+	1.52716i
$371$		−	162.132i		−	0.437013i
$372$	−422.560	+	1312.61i	−1.13591	+	3.52851i
$373$	462.727			1.24056			0.620278	−	0.784382i	$-0.287020\pi$
$373$	462.727			1.24056			0.620278	+	0.784382i	$0.287020\pi$
$374$	−556.295	+	404.172i	−1.48742	+	1.08067i
$375$	−381.519	+	525.116i	−1.01738	+	1.40031i
$376$	−181.010	+	557.092i	−0.481410	+	1.48163i
$377$	119.775			0.317706
$378$			254.075i			0.672156i
$379$	120.173	−	369.854i	0.317079	−	0.975868i	−0.657812	−	0.753182i	$-0.728518\pi$
$379$	120.173	−	369.854i	0.317079	−	0.975868i	0.974890	−	0.222685i	$-0.0714823\pi$
$380$	221.607	+	682.037i	0.583177	+	1.79483i
$381$	39.5665	+	121.773i	0.103849	+	0.319615i
$382$	−388.948	+	282.587i	−1.01819	+	0.739757i
$383$	263.127	+	85.4952i	0.687016	+	0.223225i	0.631665	−	0.775242i	$-0.282372\pi$
$383$	263.127	+	85.4952i	0.687016	+	0.223225i	0.0553517	+	0.998467i	$0.482372\pi$
$384$	206.923	+	284.806i	0.538863	+	0.741682i
$385$	80.3000	−	110.523i	0.208571	−	0.287074i
$386$	−46.5636	−	143.308i	−0.120631	−	0.371264i
$387$	463.881	−	638.477i	1.19866	−	1.64981i
$388$	−866.429	−	629.497i	−2.23306	−	1.62242i
$389$	−142.990	+	46.4603i	−0.367584	+	0.119435i	−0.486984	−	0.873411i	$-0.661903\pi$
$389$	−142.990	+	46.4603i	−0.367584	+	0.119435i	0.119400	+	0.992846i	$0.461903\pi$
$390$	−428.952	−	311.652i	−1.09988	−	0.799108i
$391$	334.375	−	242.938i	0.855180	−	0.621324i
$392$	238.771	−	734.861i	0.609109	−	1.87464i
$393$	−687.245	−	945.911i	−1.74871	−	2.40690i
$394$	−907.515	+	294.870i	−2.30334	+	0.748400i
$395$	266.238	−	86.5060i	0.674020	−	0.219003i
$396$	−1404.67	−	456.404i	−3.54714	−	1.15253i
$397$	324.296			0.816868			0.408434	−	0.912788i	$-0.366075\pi$
$397$	324.296			0.816868			0.408434	+	0.912788i	$0.366075\pi$
$398$		−	56.3389i		−	0.141555i
$399$	−267.919	−	87.0522i	−0.671476	−	0.218176i
$400$	255.443	+	185.590i	0.638606	+	0.463975i
$401$	195.364	+	268.895i	0.487191	+	0.670561i	0.979867	−	0.199652i	$-0.0639811\pi$
$401$	195.364	+	268.895i	0.487191	+	0.670561i	−0.492676	+	0.870213i	$0.663981\pi$
$402$			1521.71i			3.78535i
$403$	239.070	−	0.648314i	0.593226	−	0.00160872i
$404$	−955.335			−2.36469
$405$	−45.4378	+	33.0125i	−0.112192	+	0.0815123i
$406$	−100.551	+	138.396i	−0.247662	+	0.340878i
$407$	172.074	−	529.589i	0.422786	−	1.30120i
$408$	−1520.62			−3.72702
$409$			589.034i			1.44018i	0.693881	+	0.720090i	$0.255899\pi$
$409$			589.034i			1.44018i	−0.693881	+	0.720090i	$0.744101\pi$
$410$	6.96296	−	21.4298i	0.0169828	−	0.0522678i
$411$	−119.815	−	368.751i	−0.291520	−	0.897205i
$412$	258.640	+	796.012i	0.627767	+	1.93207i
$413$	164.273	−	119.351i	0.397755	−	0.288986i
$414$	1207.06	+	392.199i	2.91561	+	0.947339i
$415$	−166.767	−	229.535i	−0.401848	−	0.553096i
$416$	−201.704	+	277.621i	−0.484864	+	0.667359i
$417$	−156.447	−	481.494i	−0.375172	−	1.15466i
$418$	480.455	−	661.290i	1.14941	−	1.58203i
$419$	210.846	+	153.189i	0.503213	+	0.365606i	0.810243	−	0.586094i	$-0.199335\pi$
$419$	210.846	+	153.189i	0.503213	+	0.365606i	−0.307030	+	0.951700i	$0.599335\pi$
$420$	503.769	−	163.684i	1.19945	−	0.389725i
$421$	−535.789	−	389.274i	−1.27266	−	0.924640i	−0.273353	−	0.961914i	$-0.588133\pi$
$421$	−535.789	−	389.274i	−1.27266	−	0.924640i	−0.999305	+	0.0372732i	$0.988133\pi$
$422$	−1199.84	+	871.735i	−2.84322	+	2.06572i
$423$	−129.203	+	397.646i	−0.305444	+	0.940061i
$424$	611.503	+	841.661i	1.44222	+	1.98505i
$425$	147.543	−	47.9395i	0.347159	−	0.112799i
$426$	1068.13	−	347.056i	2.50734	−	0.814685i
$427$	161.573	+	52.4982i	0.378391	+	0.122947i
$428$	1261.70			2.94791
$429$			422.723i			0.985369i
$430$	−781.069	−	253.785i	−1.81644	−	0.590197i
$431$	−428.333	−	311.202i	−0.993811	−	0.722046i	−0.0330589	−	0.999453i	$-0.510525\pi$
$431$	−428.333	−	311.202i	−0.993811	−	0.722046i	−0.960752	+	0.277407i	$0.910525\pi$
$432$	−453.355	−	623.990i	−1.04943	−	1.44442i
$433$		−	665.728i		−	1.53748i	−0.639562	−	0.768739i	$-0.720884\pi$
$433$		−	665.728i		−	1.53748i	0.639562	−	0.768739i	$-0.279116\pi$
$434$	−199.950	+	276.783i	−0.460714	+	0.637748i
$435$	292.683			0.672833
$436$	455.449	−	330.903i	1.04461	−	0.758953i
$437$	−288.790	+	397.485i	−0.660847	+	0.909577i
$438$	81.5370	−	250.945i	0.186157	−	0.572934i
$439$	−239.143			−0.544744			−0.272372	−	0.962192i	$-0.587808\pi$
$439$	−239.143			−0.544744			−0.272372	+	0.962192i	$0.587808\pi$
$440$			876.614i			1.99230i
$441$	170.432	−	524.535i	0.386466	−	1.18942i
$442$	142.836	+	439.604i	0.323158	+	0.994580i
$443$	−106.758	−	328.568i	−0.240989	−	0.741689i	−0.996270	−	0.0862880i	$-0.972499\pi$
$443$	−106.758	−	328.568i	−0.240989	−	0.741689i	0.755281	−	0.655401i	$-0.227501\pi$
$444$	1746.70	−	1269.05i	3.93401	−	2.85823i
$445$	−111.670	−	36.2837i	−0.250943	−	0.0815364i
$446$	115.751	+	159.317i	0.259531	+	0.357214i
$447$	−677.220	+	932.113i	−1.51503	+	2.08526i
$448$	−26.6734	−	82.0924i	−0.0595389	−	0.183242i
$449$	−201.847	+	277.818i	−0.449548	+	0.618749i	−0.972300	−	0.233735i	$-0.924905\pi$
$449$	−201.847	+	277.818i	−0.449548	+	0.618749i	0.522753	+	0.852484i	$0.324905\pi$
$450$	385.403	+	280.012i	0.856452	+	0.622249i
$451$	−17.0853	+	5.55135i	−0.0378831	+	0.0123090i
$452$	103.351	+	75.0892i	0.228654	+	0.166127i
$453$	65.8497	−	47.8426i	0.145363	−	0.105613i
$454$	192.845	−	593.515i	0.424768	−	1.30730i
$455$	−53.9788	−	74.2955i	−0.118635	−	0.163287i
$456$	1719.16	−	558.587i	3.77008	−	1.22497i
$457$	297.115	−	96.5385i	0.650142	−	0.211244i	0.0346651	−	0.999399i	$-0.488964\pi$
$457$	297.115	−	96.5385i	0.650142	−	0.211244i	0.615477	+	0.788155i	$0.288964\pi$
$458$	−283.698	−	92.1790i	−0.619428	−	0.201264i
$459$	−378.962			−0.825624
$460$		−	923.828i		−	2.00832i
$461$	−85.2734	−	27.7070i	−0.184975	−	0.0601020i	0.215065	−	0.976600i	$-0.431004\pi$
$461$	−85.2734	−	27.7070i	−0.184975	−	0.0601020i	−0.400040	+	0.916498i	$0.631004\pi$
$462$	−488.444	−	354.875i	−1.05724	−	0.768128i
$463$	414.277	+	570.203i	0.894766	+	1.23154i	0.972108	+	0.234535i	$0.0753568\pi$
$463$	414.277	+	570.203i	0.894766	+	1.23154i	−0.0773416	+	0.997005i	$0.524643\pi$
$464$		−	519.309i		−	1.11920i
$465$	584.193	−	1.58422i	1.25633	−	0.00340693i
$466$	−396.346			−0.850529
$467$	231.578	−	168.251i	0.495883	−	0.360280i	−0.311559	−	0.950227i	$-0.600851\pi$
$467$	231.578	−	168.251i	0.495883	−	0.360280i	0.807442	+	0.589946i	$0.200851\pi$
$468$	−583.571	+	803.216i	−1.24695	+	1.71627i
$469$	−81.4456	+	250.664i	−0.173658	+	0.534464i
$470$	435.096			0.925736
$471$		−	323.158i		−	0.686111i
$472$	−402.626	+	1239.16i	−0.853021	+	2.62533i
$473$	202.335	+	622.722i	0.427769	+	1.31654i
$474$	−382.302	−	1176.60i	−0.806545	−	2.48229i
$475$	−149.195	+	108.397i	−0.314096	+	0.228204i
$476$	−439.173	−	142.696i	−0.922631	−	0.299781i
$477$	436.483	+	600.767i	0.915059	+	1.25947i
$478$	465.692	−	640.970i	0.974251	−	1.34094i
$479$	−85.8720	−	264.287i	−0.179274	−	0.551747i	0.820529	−	0.571604i	$-0.193679\pi$
$479$	−85.8720	−	264.287i	−0.179274	−	0.551747i	−0.999803	+	0.0198573i	$0.993679\pi$
$480$	−492.883	+	678.396i	−1.02684	+	1.41332i
$481$	−302.830	−	220.019i	−0.629584	−	0.457420i
$482$	−184.901	+	60.0779i	−0.383611	+	0.124643i
$483$	293.592	+	213.307i	0.607851	+	0.441629i
$484$	79.9728	−	58.1036i	0.165233	−	0.120049i
$485$	−140.207	+	431.511i	−0.289086	+	0.889714i
$486$	591.085	+	813.559i	1.21622	+	1.67399i
$487$	−414.210	+	134.585i	−0.850534	+	0.276355i	−0.701670	−	0.712502i	$-0.747562\pi$
$487$	−414.210	+	134.585i	−0.850534	+	0.276355i	−0.148864	+	0.988858i	$0.547562\pi$
$488$	−1036.76	+	336.865i	−2.12452	+	0.690298i
$489$	−255.284	−	82.9468i	−0.522053	−	0.169625i
$490$	−573.935			−1.17130
$491$			132.740i			0.270345i	0.990822	+	0.135173i	$0.0431589\pi$
$491$			132.740i			0.270345i	−0.990822	+	0.135173i	$0.956841\pi$
$492$	−66.2446	−	21.5242i	−0.134644	−	0.0437483i
$493$	−206.423	−	149.975i	−0.418708	−	0.304209i
$494$	−322.969	−	444.529i	−0.653784	−	0.899856i
$495$			625.716i			1.26407i
$496$	−2.81090	−	1036.54i	−0.00566713	−	2.08979i
$497$	194.523			0.391394
$498$	−1014.40	+	737.005i	−2.03695	+	1.47993i
$499$	568.136	−	781.972i	1.13855	−	1.56708i	0.367841	−	0.929889i	$-0.380097\pi$
$499$	568.136	−	781.972i	1.13855	−	1.56708i	0.770707	−	0.637189i	$-0.219903\pi$
$500$	390.839	−	1202.88i	0.781679	−	2.40576i
$501$	341.515			0.681666
$502$		−	1537.64i		−	3.06303i
$503$	8.40933	−	25.8813i	0.0167184	−	0.0514538i	−0.942349	−	0.334631i	$-0.891388\pi$
$503$	8.40933	−	25.8813i	0.0167184	−	0.0514538i	0.959068	+	0.283177i	$0.0913884\pi$
$504$	−249.922	−	769.182i	−0.495877	−	1.52615i
$505$	125.069	+	384.922i	0.247661	+	0.762222i
$506$	−851.885	+	618.931i	−1.68357	+	1.22318i
$507$	−497.685	−	161.708i	−0.981628	−	0.318950i
$508$	−146.650	−	201.847i	−0.288682	−	0.397336i
$509$	−186.528	+	256.733i	−0.366459	+	0.504387i	−0.951934	−	0.306303i	$-0.900908\pi$
$509$	−186.528	+	256.733i	−0.366459	+	0.504387i	0.585475	+	0.810690i	$0.300908\pi$
$510$	349.035	+	1074.22i	0.684381	+	2.10631i
$511$	26.8624	−	36.9729i	0.0525682	−	0.0723540i
$512$	−892.509	−	648.446i	−1.74318	−	1.26650i
$513$	428.439	−	139.208i	0.835163	−	0.271361i
$514$	860.045	+	624.859i	1.67324	+	1.21568i
$515$	286.868	−	208.422i	0.557025	−	0.404702i
$516$	−784.509	+	2414.47i	−1.52037	+	4.67921i
$517$	−203.896	−	280.639i	−0.394383	−	0.542821i
$518$	508.450	−	165.206i	0.981564	−	0.318930i
$519$	−875.227	+	284.379i	−1.68637	+	0.547935i
$520$	560.432	+	182.095i	1.07775	+	0.350183i
$521$	265.075			0.508782			0.254391	−	0.967102i	$-0.418125\pi$
$521$	265.075			0.508782			0.254391	+	0.967102i	$0.418125\pi$
$522$		−	783.516i		−	1.50099i
$523$	−176.234	−	57.2620i	−0.336968	−	0.109488i	0.135645	−	0.990757i	$-0.456689\pi$
$523$	−176.234	−	57.2620i	−0.336968	−	0.109488i	−0.472613	+	0.881270i	$0.656689\pi$
$524$	1843.19	+	1339.15i	3.51753	+	2.55563i
$525$	80.0644	+	110.199i	0.152504	+	0.209903i
$526$		−	113.321i		−	0.215439i
$527$	−412.831	−	298.232i	−0.783361	−	0.565906i
$528$	1832.80			3.47122
$529$	84.0776	−	61.0860i	0.158937	−	0.115474i
$530$	454.216	−	625.175i	0.857011	−	1.17958i
$531$	−287.390	+	884.494i	−0.541223	+	1.66571i
$532$	548.928			1.03182
$533$			12.0760i			0.0226567i
$534$	−160.351	+	493.510i	−0.300283	+	0.924176i
$535$	−165.177	−	508.363i	−0.308743	−	0.950212i
$536$	−522.612	−	1608.43i	−0.975022	−	3.00081i
$537$	448.894	−	326.140i	0.835929	−	0.607338i
$538$	422.675	+	137.335i	0.785641	+	0.255270i
$539$	268.959	+	370.190i	0.498996	+	0.686810i
$540$	−497.884	+	685.279i	−0.922008	+	1.26904i
$541$	118.173	+	363.700i	0.218435	+	0.672274i	0.998892	+	0.0470645i	$0.0149866\pi$
$541$	118.173	+	363.700i	0.218435	+	0.672274i	−0.780457	+	0.625210i	$0.785013\pi$
$542$	−213.065	+	293.259i	−0.393109	+	0.541068i
$543$	945.543	+	686.977i	1.74133	+	1.26515i
$544$	695.242	−	225.898i	1.27802	−	0.415253i
$545$	−192.953	−	140.188i	−0.354042	−	0.257226i
$546$	−328.339	+	238.553i	−0.601354	+	0.436909i
$547$	−263.137	+	809.851i	−0.481054	+	1.48053i	0.356561	+	0.934272i	$0.383949\pi$
$547$	−263.137	+	809.851i	−0.481054	+	1.48053i	−0.837616	+	0.546260i	$0.816051\pi$
$548$	444.084	+	611.229i	0.810371	+	1.11538i
$549$	−740.030	+	240.450i	−1.34796	+	0.437979i
$550$	−375.893	+	122.135i	−0.683442	+	0.222064i
$551$	288.466	+	93.7282i	0.523531	+	0.170106i
$552$	−2328.62			−4.21851
$553$		−	214.278i		−	0.387483i
$554$	−1449.33	−	470.916i	−2.61612	−	0.850029i
$555$	−739.996	−	537.639i	−1.33333	−	0.968718i
$556$	579.858	+	798.106i	1.04291	+	1.43544i
$557$		−	1012.43i		−	1.81766i	−0.417172	−	0.908828i	$-0.636979\pi$
$557$		−	1012.43i		−	1.81766i	0.417172	−	0.908828i	$-0.363021\pi$
$558$	−4.24099	−	1563.89i	−0.00760035	−	2.80268i
$559$	440.145			0.787380
$560$	−322.123	+	234.036i	−0.575220	+	0.417922i
$561$	529.309	−	728.532i	0.943510	−	1.29863i
$562$	58.0708	−	178.723i	0.103329	−	0.318013i
$563$	991.819			1.76167			0.880834	−	0.473426i	$-0.156983\pi$
$563$	991.819			1.76167			0.880834	+	0.473426i	$0.156983\pi$
$564$		−	1344.99i		−	2.38473i
$565$	16.7245	−	51.4726i	0.0296008	−	0.0911019i
$566$	−197.120	−	606.673i	−0.348269	−	1.07186i
$567$	13.2848	+	40.8865i	0.0234300	+	0.0721102i
$568$	−1009.81	+	733.670i	−1.77783	+	1.29167i
$569$	361.074	+	117.320i	0.634576	+	0.206186i	0.608601	−	0.793476i	$-0.291731\pi$
$569$	361.074	+	117.320i	0.634576	+	0.206186i	0.0259749	+	0.999663i	$0.491731\pi$
$570$	−789.208	−	1086.25i	−1.38458	−	1.90571i
$571$	−651.710	+	897.002i	−1.14135	+	1.57093i	−0.376890	+	0.926258i	$0.623007\pi$
$571$	−651.710	+	897.002i	−1.14135	+	1.57093i	−0.764458	+	0.644673i	$0.776993\pi$
$572$	−254.541	−	783.395i	−0.445001	−	1.36957i
$573$	370.080	−	509.372i	0.645864	−	0.888956i
$574$	−13.9535	−	10.1378i	−0.0243092	−	0.0176617i
$575$	225.940	−	73.4124i	0.392939	−	0.127674i
$576$	319.842	+	232.379i	0.555281	+	0.403435i
$577$	−602.456	+	437.710i	−1.04412	+	0.758596i	−0.971085	−	0.238734i	$-0.923268\pi$
$577$	−602.456	+	437.710i	−1.04412	+	0.758596i	−0.0730327	+	0.997330i	$0.523268\pi$
$578$	−21.5348	+	66.2774i	−0.0372575	+	0.114667i
$579$	115.991	+	159.649i	0.200331	+	0.275731i
$580$	−542.403	+	176.237i	−0.935177	+	0.303857i
$581$	−206.543	+	67.1100i	−0.355497	+	0.115508i
$582$	1907.01	+	619.625i	3.27665	+	1.06465i
$583$	−616.096			−1.05677
$584$			293.250i			0.502140i
$585$	400.029	+	129.977i	0.683811	+	0.222184i
$586$	−106.396	−	77.3009i	−0.181562	−	0.131913i
$587$	−412.213	−	567.363i	−0.702238	−	0.966547i	−0.999929	−	0.0118850i	$-0.996217\pi$
$587$	−412.213	−	567.363i	−0.702238	−	0.966547i	0.297692	−	0.954662i	$-0.403783\pi$
$588$			1774.17i			3.01730i
$589$	576.283	+	185.520i	0.978410	+	0.314974i
$590$	967.796			1.64033
$591$	1010.99	−	734.531i	1.71065	−	1.24286i
$592$	−953.936	+	1312.98i	−1.61138	+	2.21787i
$593$	−107.958	+	332.260i	−0.182054	+	0.560304i	−0.999885	−	0.0151540i	$-0.995176\pi$
$593$	−107.958	+	332.260i	−0.182054	+	0.560304i	0.817831	+	0.575458i	$0.195176\pi$
$594$	965.477			1.62538
$595$			195.632i			0.328793i
$596$	693.764	−	2135.19i	1.16403	−	3.58253i
$597$	22.8000	+	70.1710i	0.0381909	+	0.117539i
$598$	218.733	+	673.190i	0.365774	+	1.12574i
$599$	−229.413	+	166.678i	−0.382993	+	0.278261i	−0.762578	−	0.646896i	$-0.776067\pi$
$599$	−229.413	+	166.678i	−0.382993	+	0.278261i	0.379585	+	0.925157i	$0.376067\pi$
$600$	−831.264	−	270.094i	−1.38544	−	0.450157i
$601$	−369.717	−	508.871i	−0.615169	−	0.846708i	0.381821	−	0.924236i	$-0.375297\pi$
$601$	−369.717	−	508.871i	−0.615169	−	0.846708i	−0.996990	+	0.0775285i	$0.975297\pi$
$602$	−369.501	+	508.575i	−0.613789	+	0.844808i
$603$	−373.034	−	1148.08i	−0.618630	−	1.90395i
$604$	−93.2252	+	128.313i	−0.154346	+	0.212439i
$605$	−33.8807	−	24.6158i	−0.0560012	−	0.0406873i
$606$	1701.11	−	552.725i	2.80712	−	0.912088i
$607$	311.798	+	226.535i	0.513671	+	0.373204i	0.814214	−	0.580564i	$-0.197168\pi$
$607$	311.798	+	226.535i	0.513671	+	0.373204i	−0.300544	+	0.953768i	$0.597168\pi$
$608$	−703.031	+	510.782i	−1.15630	+	0.840101i
$609$	69.2298	−	213.067i	0.113678	−	0.349864i
$610$	475.945	+	655.082i	0.780238	+	1.07391i
$611$	−221.771	+	72.0577i	−0.362964	+	0.117934i
$612$	2011.48	−	653.570i	3.28673	−	1.06792i
$613$	−412.130	−	133.909i	−0.672317	−	0.218449i	−0.0470884	−	0.998891i	$-0.514994\pi$
$613$	−412.130	−	133.909i	−0.672317	−	0.218449i	−0.625229	+	0.780442i	$0.714994\pi$
$614$	361.995			0.589569
$615$			29.5090i			0.0479822i
$616$	638.159	+	207.350i	1.03597	+	0.336608i
$617$	349.000	+	253.563i	0.565640	+	0.410961i	0.833519	−	0.552491i	$-0.186323\pi$
$617$	349.000	+	253.563i	0.565640	+	0.410961i	−0.267879	+	0.963453i	$0.586323\pi$
$618$	−921.092	−	1267.77i	−1.49044	−	2.05142i
$619$			635.703i			1.02698i	0.858094	+	0.513492i	$0.171649\pi$
$619$			635.703i			1.02698i	−0.858094	+	0.513492i	$0.828351\pi$
$620$	−1081.68	+	354.705i	−1.74464	+	0.572104i
$621$	−580.325			−0.934501
$622$	1266.17	−	919.925i	2.03564	−	1.47898i
$623$	−52.8277	+	72.7111i	−0.0847957	+	0.116711i
$624$	380.720	−	1171.74i	0.610129	−	1.87778i
$625$	−299.754			−0.479607
$626$			775.425i			1.23870i
$627$	−330.796	+	1018.08i	−0.527585	+	1.62374i
$628$	194.588	+	598.881i	0.309854	+	0.953632i
$629$	246.410	+	758.372i	0.391749	+	1.20568i
$630$	−486.009	+	353.106i	−0.771443	+	0.560486i
$631$	−111.160	−	36.1181i	−0.176165	−	0.0572395i	0.219606	−	0.975589i	$-0.429523\pi$
$631$	−111.160	−	36.1181i	−0.176165	−	0.0572395i	−0.395771	+	0.918349i	$0.629523\pi$
$632$	808.180	+	1112.36i	1.27877	+	1.76007i
$633$	1141.64	−	1571.33i	1.80353	−	2.48235i
$634$	−179.253	−	551.683i	−0.282733	−	0.870163i
$635$	−62.1289	+	85.5131i	−0.0978408	+	0.134666i
$636$	−1932.57	−	1404.09i	−3.03863	−	2.20769i
$637$	292.538	−	95.0513i	0.459243	−	0.149217i
$638$	525.903	+	382.091i	0.824299	+	0.598888i
$639$	−720.790	+	523.685i	−1.12800	+	0.819538i
$640$	−89.8055	+	276.393i	−0.140321	+	0.431864i
$641$	104.210	+	143.433i	0.162574	+	0.223764i	0.882530	−	0.470255i	$-0.155838\pi$
$641$	104.210	+	143.433i	0.162574	+	0.223764i	−0.719956	+	0.694019i	$0.755838\pi$
$642$	−2246.65	+	729.980i	−3.49945	+	1.13704i
$643$	634.179	−	206.057i	0.986281	−	0.320462i	0.228910	−	0.973447i	$-0.426484\pi$
$643$	634.179	−	206.057i	0.986281	−	0.320462i	0.757371	+	0.652985i	$0.226484\pi$
$644$	−672.530	−	218.518i	−1.04430	−	0.339314i
$645$	1075.54			1.66750
$646$			1170.52i			1.81194i
$647$	−1116.24	−	362.688i	−1.72525	−	0.560568i	−0.732502	−	0.680765i	$-0.761647\pi$
$647$	−1116.24	−	362.688i	−1.72525	−	0.560568i	−0.992750	+	0.120197i	$0.961647\pi$
$648$	−223.174	−	162.145i	−0.344404	−	0.250224i
$649$	−453.531	−	624.232i	−0.698815	−	0.961837i
$650$			265.684i			0.408745i
$651$	137.029	−	425.656i	0.210490	−	0.653850i
$652$	523.041			0.802211
$653$	−819.930	+	595.714i	−1.25563	+	0.912272i	−0.998535	−	0.0541126i	$-0.982767\pi$
$653$	−819.930	+	595.714i	−1.25563	+	0.912272i	−0.257100	+	0.966385i	$0.582767\pi$
$654$	−619.544	+	852.729i	−0.947315	+	1.30387i
$655$	298.266	−	917.970i	0.455369	−	1.40148i
$656$	52.3581			0.0798142
$657$			209.318i			0.318597i
$658$	102.916	−	316.742i	0.156407	−	0.481370i
$659$	87.1754	+	268.298i	0.132284	+	0.407130i	0.995158	−	0.0982906i	$-0.0313375\pi$
$659$	87.1754	+	268.298i	0.132284	+	0.407130i	−0.862873	+	0.505420i	$0.831337\pi$
$660$	−621.996	−	1914.31i	−0.942418	−	2.90047i
$661$	−737.874	+	536.097i	−1.11630	+	0.811039i	−0.983644	−	0.180124i	$-0.942350\pi$
$661$	−737.874	+	536.097i	−1.11630	+	0.811039i	−0.132655	+	0.991162i	$0.542350\pi$
$662$	1640.68	+	533.089i	2.47837	+	0.805271i
$663$	−355.810	−	489.730i	−0.536666	−	0.738657i
$664$	819.097	−	1127.39i	1.23358	−	1.69788i
$665$	−71.8636	−	221.173i	−0.108066	−	0.332592i
$666$	−1439.27	+	1980.98i	−2.16106	+	2.97445i
$667$	−316.107	−	229.666i	−0.473924	−	0.344326i
$668$	−632.899	+	205.641i	−0.947454	+	0.307846i
$669$	−208.644	−	151.589i	−0.311875	−	0.226590i
$670$	−1016.29	+	738.380i	−1.51685	+	1.10206i
$671$	199.492	−	613.973i	0.297305	−	0.915012i
$672$	377.275	+	519.275i	0.561421	+	0.772730i
$673$	639.966	−	207.937i	0.950915	−	0.308971i	0.207827	−	0.978166i	$-0.433361\pi$
$673$	639.966	−	207.937i	0.950915	−	0.308971i	0.743087	+	0.669195i	$0.233361\pi$
$674$	991.889	−	322.284i	1.47165	−	0.478166i
$675$	−207.163	−	67.3113i	−0.306908	−	0.0997205i
$676$	1019.69			1.50841
$677$			617.906i			0.912712i	0.889797	+	0.456356i	$0.150846\pi$
$677$			617.906i			0.912712i	−0.889797	+	0.456356i	$0.849154\pi$
$678$	−227.476	−	73.9116i	−0.335511	−	0.109014i
$679$	280.968	+	204.136i	0.413797	+	0.300641i
$680$	−737.853	−	1015.57i	−1.08508	−	1.49348i
$681$			817.276i			1.20011i
$682$	1051.77	+	759.804i	1.54218	+	1.11408i
$683$	−878.402			−1.28609			−0.643047	−	0.765827i	$-0.722330\pi$
$683$	−878.402			−1.28609			−0.643047	+	0.765827i	$0.722330\pi$
$684$	−2034.02	+	1477.80i	−2.97371	+	2.16052i
$685$	188.138	−	258.949i	0.274653	−	0.378028i
$686$	−302.536	+	931.111i	−0.441015	+	1.35731i
$687$	390.655			0.568639
$688$		−	1908.34i		−	2.77375i
$689$	−127.979	+	393.879i	−0.185746	+	0.571668i
$690$	534.496	+	1645.01i	0.774632	+	2.38407i
$691$	−28.7096	−	88.3592i	−0.0415480	−	0.127871i	0.928131	−	0.372254i	$-0.121415\pi$
$691$	−28.7096	−	88.3592i	−0.0415480	−	0.127871i	−0.969679	+	0.244382i	$0.921415\pi$
$692$	1450.74	−	1054.03i	2.09645	−	1.52316i
$693$	455.510	+	148.004i	0.657301	+	0.213570i
$694$	−486.346	−	669.398i	−0.700787	−	0.964550i
$695$	245.659	−	338.120i	0.353466	−	0.486504i
$696$	444.227	+	1367.19i	0.638257	+	1.96435i
$697$	15.1209	−	20.8121i	0.0216943	−	0.0298596i
$698$	1895.40	+	1377.09i	2.71548	+	1.97291i
$699$	493.656	−	160.399i	0.706232	−	0.229469i
$700$	−214.732	−	156.012i	−0.306760	−	0.222874i
$701$	728.748	−	529.466i	1.03958	−	0.755302i	0.0693793	−	0.997590i	$-0.477898\pi$
$701$	728.748	−	529.466i	1.03958	−	0.755302i	0.970204	+	0.242289i	$0.0778981\pi$
$702$	200.555	−	617.244i	0.285690	−	0.879265i
$703$	−557.162	−	766.868i	−0.792549	−	1.09085i
$704$	−311.949	+	101.358i	−0.443109	+	0.143975i
$705$	−541.920	+	176.080i	−0.768680	+	0.249759i
$706$	−2060.25	−	669.415i	−2.91820	−	0.948179i
$707$	309.799			0.438189
$708$		−	2991.69i		−	4.22555i
$709$	991.195	+	322.059i	1.39802	+	0.454244i	0.908550	−	0.417777i	$-0.137191\pi$
$709$	991.195	+	322.059i	1.39802	+	0.454244i	0.489469	+	0.872021i	$0.337191\pi$
$710$	750.074	+	544.960i	1.05644	+	0.767550i
$711$	576.869	+	793.992i	0.811349	+	1.11673i
$712$		−	576.707i		−	0.809981i
$713$	−632.192	−	456.700i	−0.886665	−	0.640533i
$714$	864.570			1.21088
$715$	−282.321	+	205.118i	−0.394854	+	0.286879i
$716$	−635.511	+	874.706i	−0.887586	+	1.22166i
$717$	−320.631	+	986.802i	−0.447185	+	1.37629i
$718$	−1151.62			−1.60393
$719$			583.949i			0.812169i	0.913836	+	0.406084i	$0.133106\pi$
$719$			583.949i			0.812169i	−0.913836	+	0.406084i	$0.866894\pi$
$720$	563.544	−	1734.41i	0.782699	−	2.40890i
$721$	−83.8726	−	258.133i	−0.116328	−	0.358021i
$722$	−22.9922	−	70.7628i	−0.0318452	−	0.0980094i
$723$	205.984	−	149.656i	0.284902	−	0.206993i
$724$	−2165.95	−	703.760i	−2.99164	−	0.972044i
$725$	−86.2045	−	118.650i	−0.118903	−	0.163656i
$726$	−108.786	+	149.732i	−0.149843	+	0.206242i
$727$	50.2526	+	154.661i	0.0691232	+	0.212739i	0.979651	−	0.200709i	$-0.0643244\pi$
$727$	50.2526	+	154.661i	0.0691232	+	0.212739i	−0.910528	+	0.413448i	$0.864324\pi$
$728$	265.124	−	364.912i	0.364181	−	0.501253i
$729$	−961.768	−	698.765i	−1.31930	−	0.958526i
$730$	207.161	−	67.3107i	0.283782	−	0.0922064i
$731$	−758.557	−	551.124i	−1.03770	−	0.753932i
$732$	2025.02	−	1471.26i	2.76642	−	2.00992i
$733$	−92.0371	+	283.261i	−0.125562	+	0.386441i	−0.994003	−	0.109352i	$-0.965122\pi$
$733$	−92.0371	+	283.261i	−0.125562	+	0.386441i	0.868441	+	0.495793i	$0.165122\pi$
$734$	−948.835	−	1305.96i	−1.29269	−	1.77924i
$735$	714.846	−	232.268i	0.972580	−	0.316010i
$736$	1064.66	−	345.930i	1.44655	−	0.470014i
$737$	952.516	+	309.491i	1.29242	+	0.419934i
$738$	78.9962			0.107041
$739$		−	736.678i		−	0.996858i	−0.866930	−	0.498429i	$-0.833910\pi$
$739$		−	736.678i		−	0.996858i	0.866930	−	0.498429i	$-0.166090\pi$
$740$	1695.11	+	550.773i	2.29068	+	0.744288i
$741$	582.162	+	422.965i	0.785643	+	0.570803i
$742$	−347.677	−	478.537i	−0.468568	−	0.644928i
$743$			554.954i			0.746910i	0.927648	+	0.373455i	$0.121827\pi$
$743$			554.954i			0.746910i	−0.927648	+	0.373455i	$0.878173\pi$
$744$	894.075	+	2726.50i	1.20171	+	3.66465i
$745$	−951.131			−1.27669
$746$	1365.75	−	992.279i	1.83077	−	1.33013i
$747$	584.662	−	804.718i	0.782680	−	1.07727i
$748$	−542.240	+	1668.84i	−0.724920	+	2.23107i
$749$	−409.149			−0.546261
$750$			2368.03i			3.15737i
$751$	−243.760	+	750.217i	−0.324581	+	0.998958i	0.647048	+	0.762449i	$0.276003\pi$
$751$	−243.760	+	750.217i	−0.324581	+	0.998958i	−0.971629	+	0.236509i	$0.923997\pi$
$752$	312.421	+	961.532i	0.415453	+	1.27863i
$753$	622.274	+	1915.16i	0.826393	+	2.54338i
$754$	353.520	−	256.847i	0.468859	−	0.340646i
$755$	63.9045	+	20.7638i	0.0846417	+	0.0275018i
$756$	381.103	+	524.543i	0.504105	+	0.693840i
$757$	31.4163	−	43.2408i	0.0415010	−	0.0571213i	−0.787762	−	0.615979i	$-0.788760\pi$
$757$	31.4163	−	43.2408i	0.0415010	−	0.0571213i	0.829263	+	0.558858i	$0.188760\pi$
$758$	−438.426	−	1349.34i	−0.578398	−	1.78013i
$759$	810.561	−	1115.64i	1.06793	−	1.46988i
$760$	1207.25	+	877.116i	1.58848	+	1.15410i
$761$	589.377	−	191.500i	0.774477	−	0.251643i	0.104996	−	0.994473i	$-0.466517\pi$
$761$	589.377	−	191.500i	0.774477	−	0.251643i	0.669480	+	0.742830i	$0.266517\pi$
$762$	377.914	+	274.571i	0.495950	+	0.360329i
$763$	−147.695	+	107.306i	−0.193571	+	0.140638i
$764$	−379.121	+	1166.82i	−0.496232	+	1.52725i
$765$	−526.671	−	724.900i	−0.688458	−	0.947581i
$766$	959.966	−	311.912i	1.25322	−	0.407195i
$767$	−493.291	+	160.280i	−0.643143	+	0.208970i
$768$	1741.14	+	565.732i	2.26711	+	0.736630i
$769$	−846.263			−1.10047			−0.550236	−	0.835009i	$-0.685462\pi$
$769$	−846.263			−1.10047			−0.550236	+	0.835009i	$0.685462\pi$
$770$		−	498.410i		−	0.647285i
$771$	−1324.08	−	430.219i	−1.71735	−	0.558001i
$772$	−311.088	−	226.019i	−0.402964	−	0.292770i
$773$	57.1648	+	78.6806i	0.0739519	+	0.101786i	0.844391	−	0.535728i	$-0.179963\pi$
$773$	57.1648	+	78.6806i	0.0739519	+	0.101786i	−0.770439	+	0.637514i	$0.779963\pi$
$774$		−	2879.24i		−	3.71995i
$775$	−172.706	−	236.359i	−0.222846	−	0.304979i
$776$	−2228.49			−2.87177
$777$	−566.426	+	411.533i	−0.728991	+	0.529643i
$778$	−322.410	+	443.759i	−0.414409	+	0.570385i
$779$	−9.44993	+	29.0839i	−0.0121308	+	0.0373349i
$780$	−1353.05			−1.73468
$781$		−	739.181i		−	0.946455i
$782$	465.960	−	1434.08i	0.595857	−	1.83386i
$783$	110.708	+	340.724i	0.141389	+	0.435151i
$784$	−412.114	−	1268.36i	−0.525656	−	1.61780i
$785$	215.825	−	156.806i	0.274937	−	0.199753i
$786$	−4056.85	−	1318.15i	−5.16139	−	1.67704i
$787$	199.429	+	274.491i	0.253404	+	0.348781i	0.916700	−	0.399576i	$-0.130843\pi$
$787$	199.429	+	274.491i	0.253404	+	0.348781i	−0.663295	+	0.748358i	$0.730843\pi$
$788$	−1431.29	+	1970.01i	−1.81636	+	2.50001i
$789$	45.8601	+	141.143i	0.0581244	+	0.178888i
$790$	600.306	−	826.250i	0.759880	−	1.04589i
$791$	−33.5152	−	24.3502i	−0.0423706	−	0.0307841i
$792$	−2922.87	+	949.698i	−3.69049	+	1.19911i
$793$	−351.082	−	255.076i	−0.442726	−	0.321660i
$794$	957.171	−	695.426i	1.20551	−	0.875851i
$795$	−312.730	+	962.484i	−0.393371	+	1.21067i
$796$	−84.5063	−	116.313i	−0.106164	−	0.146122i
$797$	−363.890	+	118.235i	−0.456574	+	0.148350i	−0.528270	−	0.849077i	$-0.677159\pi$
$797$	−363.890	+	118.235i	−0.456574	+	0.148350i	0.0716955	+	0.997427i	$0.477159\pi$
$798$	−977.447	+	317.592i	−1.22487	+	0.397985i
$799$	472.432	+	153.502i	0.591279	+	0.192118i
$800$	420.185			0.525231
$801$		−	411.646i		−	0.513915i
$802$	1153.24	+	374.712i	1.43796	+	0.467222i
$803$	−140.496	−	102.076i	−0.174964	−	0.127119i
$804$	2282.51	+	3141.61i	2.83894	+	3.90747i
$805$			299.582i			0.372152i
$806$	704.233	−	514.579i	0.873739	−	0.638435i
$807$	−582.027			−0.721224
$808$	−1608.24	+	1168.45i	−1.99039	+	1.44610i
$809$	689.865	−	949.517i	0.852738	−	1.17369i	−0.130515	−	0.991446i	$-0.541663\pi$
$809$	689.865	−	949.517i	0.852738	−	1.17369i	0.983253	−	0.182246i	$-0.0583368\pi$
$810$	−63.3186	+	194.875i	−0.0781712	+	0.240586i
$811$	−284.392			−0.350668			−0.175334	−	0.984509i	$-0.556100\pi$
$811$	−284.392			−0.350668			−0.175334	+	0.984509i	$0.556100\pi$
$812$			436.545i			0.537617i
$813$	146.696	−	451.485i	0.180438	−	0.555332i
$814$	−627.776	−	1932.10i	−0.771224	−	2.37358i
$815$	−68.4746	−	210.743i	−0.0840179	−	0.258580i
$816$	−2123.32	+	1542.68i	−2.60211	+	1.89055i
$817$	1060.04	+	344.429i	1.29748	+	0.421578i
$818$	1263.13	+	1738.55i	1.54417	+	2.12537i
$819$	189.242	−	260.470i	0.231065	−	0.318034i
$820$	−17.7687	−	54.6865i	−0.0216692	−	0.0666908i
$821$	−451.777	+	621.818i	−0.550276	+	0.757390i	−0.990050	−	0.140718i	$-0.955059\pi$
$821$	−451.777	+	621.818i	−0.550276	+	0.757390i	0.439773	+	0.898109i	$0.355059\pi$
$822$	−1144.39	−	831.449i	−1.39220	−	1.01150i
$823$	393.697	−	127.920i	0.478368	−	0.155431i	−0.0599009	−	0.998204i	$-0.519078\pi$
$823$	393.697	−	127.920i	0.478368	−	0.155431i	0.538269	+	0.842773i	$0.319078\pi$
$824$	1408.99	+	1023.69i	1.70994	+	1.24234i
$825$	418.754	−	304.243i	0.507581	−	0.368779i
$826$	228.918	−	704.537i	0.277140	−	0.852951i
$827$	583.811	+	803.546i	0.705938	+	0.971640i	0.999875	+	0.0158154i	$0.00503439\pi$
$827$	583.811	+	803.546i	0.705938	+	0.971640i	−0.293937	+	0.955825i	$0.594966\pi$
$828$	3080.29	−	1000.85i	3.72016	−	1.20875i
$829$	772.657	−	251.051i	0.932035	−	0.302837i	0.196640	−	0.980476i	$-0.436997\pi$
$829$	772.657	−	251.051i	0.932035	−	0.302837i	0.735395	+	0.677639i	$0.236997\pi$
$830$	−984.436	−	319.863i	−1.18607	−	0.385377i
$831$	1995.74			2.40162
$832$			220.488i			0.265010i
$833$	−623.185	−	202.485i	−0.748121	−	0.243079i
$834$	−1494.28	−	1085.66i	−1.79170	−	1.30175i
$835$	165.713	+	228.085i	0.198459	+	0.273156i
$836$		−	2085.91i		−	2.49511i
$837$	222.816	+	679.483i	0.266208	+	0.811808i
$838$	950.820			1.13463
$839$	−429.214	+	311.842i	−0.511578	+	0.371683i	−0.813422	−	0.581674i	$-0.802398\pi$
$839$	−429.214	+	311.842i	−0.511578	+	0.371683i	0.301844	+	0.953357i	$0.402398\pi$
$840$	647.858	−	891.700i	0.771260	−	1.06155i
$841$	185.344	−	570.431i	0.220386	−	0.678277i
$842$	−2416.16			−2.86955
$843$			246.104i			0.291938i
$844$	−1169.53	+	3599.43i	−1.38569	+	4.26473i
$845$	−133.494	−	410.851i	−0.157981	−	0.486214i
$846$	471.370	+	1450.73i	0.557175	+	1.71481i
$847$	−25.9338	+	18.8420i	−0.0306185	+	0.0222456i
$848$	1707.74	+	554.879i	2.01385	+	0.654339i
$849$	491.033	+	675.849i	0.578366	+	0.796053i
$850$	332.674	−	457.887i	0.391382	−	0.538691i
$851$	377.341	+	1161.34i	0.443409	+	1.36467i
$852$	1684.60	−	2318.66i	1.97723	−	2.72143i
$853$	334.092	+	242.732i	0.391667	+	0.284563i	0.766138	−	0.642676i	$-0.222176\pi$
$853$	334.092	+	242.732i	0.391667	+	0.284563i	−0.374471	+	0.927239i	$0.622176\pi$
$854$	589.465	−	191.529i	0.690241	−	0.224273i
$855$	861.717	+	626.074i	1.00786	+	0.732251i
$856$	2123.98	−	1543.16i	2.48129	−	1.80276i
$857$	437.452	−	1346.34i	0.510446	−	1.57099i	−0.280973	−	0.959716i	$-0.590657\pi$
$857$	437.452	−	1346.34i	0.510446	−	1.57099i	0.791419	−	0.611274i	$-0.209343\pi$
$858$	906.493	+	1247.68i	1.05652	+	1.45417i
$859$	343.366	−	111.566i	0.399728	−	0.129879i	−0.102253	−	0.994758i	$-0.532605\pi$
$859$	343.366	−	111.566i	0.399728	−	0.129879i	0.501980	+	0.864879i	$0.332605\pi$
$860$	−1993.20	+	647.631i	−2.31768	+	0.753059i
$861$	21.4820	+	6.97994i	0.0249501	+	0.00810678i
$862$	−1931.58			−2.24082
$863$		−	613.078i		−	0.710403i	−0.934790	−	0.355201i	$-0.884412\pi$
$863$		−	613.078i		−	0.710403i	0.934790	−	0.355201i	$-0.115588\pi$
$864$	−976.182	−	317.181i	−1.12984	−	0.367107i
$865$	−614.613	−	446.542i	−0.710535	−	0.516234i
$866$	−1427.60	−	1964.92i	−1.64850	−	2.26896i
$867$		−	91.2646i		−	0.105265i
$868$	2.36292	+	871.342i	0.00272226	+	1.00385i
$869$	−814.251			−0.936998
$870$	863.862	−	627.632i	0.992945	−	0.721416i
$871$	395.724	−	544.668i	0.454333	−	0.625336i
$872$	361.994	−	1114.10i	0.415131	−	1.27764i
$873$	−1590.67			−1.82208
$874$			1792.48i			2.05089i
$875$	−126.743	+	390.074i	−0.144849	+	0.445799i
$876$	−208.073	−	640.384i	−0.237527	−	0.731032i
$877$	−242.369	−	745.934i	−0.276361	−	0.850552i	−0.988856	−	0.148875i	$-0.952435\pi$
$877$	−242.369	−	745.934i	−0.276361	−	0.850552i	0.712495	−	0.701677i	$-0.247565\pi$
$878$	−705.837	+	512.821i	−0.803915	+	0.584078i
$879$	163.801	+	53.2221i	0.186349	+	0.0605484i
$880$	889.331	+	1224.06i	1.01060	+	1.39098i
$881$	−355.021	+	488.644i	−0.402975	+	0.554647i	−0.961487	−	0.274849i	$-0.911372\pi$
$881$	−355.021	+	488.644i	−0.402975	+	0.554647i	0.558513	+	0.829496i	$0.311372\pi$
$882$	−621.785	−	1913.66i	−0.704971	−	2.16968i
$883$	−578.476	+	796.203i	−0.655125	+	0.901702i	−0.999308	−	0.0372003i	$-0.988156\pi$
$883$	−578.476	+	796.203i	−0.655125	+	0.901702i	0.344183	+	0.938903i	$0.388156\pi$
$884$	954.279	+	693.324i	1.07950	+	0.784303i
$885$	−1205.41	+	391.660i	−1.36204	+	0.442554i
$886$	−1019.69	−	740.846i	−1.15089	−	0.836169i
$887$	102.375	−	74.3799i	0.115417	−	0.0838556i	−0.528579	−	0.848884i	$-0.677275\pi$
$887$	102.375	−	74.3799i	0.115417	−	0.0838556i	0.643997	+	0.765028i	$0.277275\pi$
$888$	1388.29	−	4272.71i	1.56339	−	4.81161i
$889$	47.5562	+	65.4555i	0.0534941	+	0.0736283i
$890$	−407.404	+	132.374i	−0.457758	+	0.148734i
$891$	155.368	−	50.4820i	0.174374	−	0.0566576i
$892$	477.940	+	155.292i	0.535808	+	0.174094i
$893$	−590.500			−0.661254
$894$			4203.40i			4.70179i
$895$	435.634	+	141.546i	0.486742	+	0.158152i
$896$	179.967	+	130.753i	0.200856	+	0.145930i
$897$	−544.871	−	749.951i	−0.607437	−	0.836066i
$898$			1252.83i			1.39514i
$899$	−147.538	+	458.300i	−0.164113	+	0.509788i
$900$	1215.68			1.35076
$901$	713.755	−	518.573i	0.792181	−	0.575553i
$902$	−38.5234	+	53.0229i	−0.0427089	+	0.0587837i
$903$	254.403	−	782.973i	0.281731	−	0.867080i
$904$	265.825			0.294054
$905$			964.835i			1.06612i
$906$	91.7631	−	282.418i	0.101284	−	0.311719i
$907$	0.540555	+	1.66366i	0.000595981	+	0.00183424i	0.951354	−	0.308100i	$-0.0996930\pi$
$907$	0.540555	+	1.66366i	0.000595981	+	0.00183424i	−0.950758	+	0.309934i	$0.899693\pi$
$908$	−492.119	−	1514.59i	−0.541981	−	1.66805i
$909$	−1147.94	+	834.027i	−1.26286	+	0.917521i
$910$	−318.641	−	103.533i	−0.350154	−	0.113772i
$911$	613.900	+	844.961i	0.673875	+	0.927509i	0.999840	−	0.0178723i	$-0.00568924\pi$
$911$	613.900	+	844.961i	0.673875	+	0.927509i	−0.325965	+	0.945382i	$0.605689\pi$
$912$	1833.85	−	2524.08i	2.01080	−	2.76763i
$913$	255.016	+	784.860i	0.279317	+	0.859649i
$914$	669.925	−	922.073i	0.732960	−	1.00883i
$915$	−857.905	−	623.305i	−0.937601	−	0.681207i
$916$	−723.966	+	235.231i	−0.790356	+	0.256802i
$917$	−597.714	−	434.265i	−0.651815	−	0.473571i
$918$	−1118.52	+	812.650i	−1.21843	+	0.885240i
$919$	−139.538	+	429.454i	−0.151837	+	0.467305i	−0.997827	−	0.0658934i	$-0.979010\pi$
$919$	−139.538	+	429.454i	−0.151837	+	0.467305i	0.845990	+	0.533199i	$0.179010\pi$
$920$	−1129.92	−	1555.20i	−1.22817	−	1.69043i
$921$	−450.871	+	146.497i	−0.489546	+	0.159063i
$922$	−311.103	+	101.083i	−0.337421	+	0.109635i
$923$	−472.569	−	153.547i	−0.511993	−	0.166357i
$924$	−1540.70			−1.66743
$925$			458.338i			0.495501i
$926$	2445.50	+	794.592i	2.64093	+	0.858090i
$927$	1005.72	+	730.697i	1.08492	+	0.788238i
$928$	−406.208	−	559.098i	−0.437725	−	0.602476i
$929$		−	297.507i		−	0.320244i	−0.987097	−	0.160122i	$-0.948811\pi$
$929$		−	297.507i		−	0.320244i	0.987097	−	0.160122i	$-0.0511888\pi$
$930$	1720.87	−	1257.43i	1.85039	−	1.35207i
$931$	778.928			0.836658
$932$	−818.266	+	594.505i	−0.877968	+	0.637881i
$933$	−1204.75	+	1658.19i	−1.29126	+	1.77727i
$934$	322.709	−	993.196i	0.345513	−	1.06338i
$935$	743.396			0.795076
$936$			2065.91i			2.20717i
$937$	115.639	−	355.901i	0.123414	−	0.379830i	−0.870195	−	0.492708i	$-0.836007\pi$
$937$	115.639	−	355.901i	0.123414	−	0.379830i	0.993609	+	0.112878i	$0.0360069\pi$
$938$	297.138	+	914.495i	0.316778	+	0.974942i
$939$	−313.809	−	965.805i	−0.334195	−	1.02855i
$940$	898.266	−	652.628i	0.955602	−	0.694285i
$941$	91.4712	+	29.7208i	0.0972064	+	0.0315843i	0.357216	−	0.934022i	$-0.383726\pi$
$941$	91.4712	+	29.7208i	0.0972064	+	0.0315843i	−0.260010	+	0.965606i	$0.583726\pi$
$942$	−692.985	−	953.812i	−0.735653	−	1.01254i
$943$	23.1555	−	31.8708i	0.0245551	−	0.0337972i
$944$	694.926	+	2138.76i	0.736150	+	2.26564i
$945$	161.456	−	222.225i	0.170853	−	0.235158i
$946$	1932.57	+	1404.09i	2.04289	+	1.48424i
$947$	−354.052	+	115.039i	−0.373867	+	0.121477i	−0.489923	−	0.871766i	$-0.662975\pi$
$947$	−354.052	+	115.039i	−0.373867	+	0.121477i	0.116055	+	0.993243i	$0.462975\pi$
$948$	−2554.14	−	1855.69i	−2.69424	−	1.95748i
$949$	−94.4435	+	68.6172i	−0.0995190	+	0.0723048i
$950$	−207.907	+	639.873i	−0.218850	+	0.673551i
$951$	446.525	+	614.589i	0.469532	+	0.646255i
$952$	−913.843	+	296.926i	−0.959919	+	0.311897i
$953$	1152.04	−	374.322i	1.20886	−	0.392783i	0.365847	−	0.930675i	$-0.380779\pi$
$953$	1152.04	−	374.322i	1.20886	−	0.392783i	0.843014	+	0.537892i	$0.180779\pi$
$954$	2576.59	+	837.184i	2.70083	+	0.877551i
$955$	519.764			0.544256
$956$		−	2021.82i		−	2.11487i
$957$	−809.651	−	263.071i	−0.846030	−	0.274892i
$958$	−820.194	−	595.906i	−0.856153	−	0.622031i
$959$	−144.009	−	198.211i	−0.150166	−	0.206685i
$960$			538.786i			0.561235i
$961$	−292.004	+	915.562i	−0.303854	+	0.952719i
$962$	−1365.62			−1.41957
$963$	1516.07	−	1101.49i	1.57432	−	1.14381i
$964$	−291.617	+	401.377i	−0.302507	+	0.416366i
$965$	−50.3407	+	154.933i	−0.0521665	+	0.160552i
$966$	1323.96			1.37056
$967$		−	596.845i		−	0.617213i	−0.951190	−	0.308606i	$-0.900137\pi$
$967$		−	596.845i		−	0.617213i	0.951190	−	0.308606i	$-0.0998626\pi$
$968$	63.5628	−	195.626i	0.0656641	−	0.202093i
$969$	−473.700	−	1457.90i	−0.488854	−	1.50454i
$970$	511.515	+	1574.28i	0.527335	+	1.62297i
$971$	37.4885	−	27.2370i	0.0386081	−	0.0280504i	−0.568314	−	0.822812i	$-0.692404\pi$
$971$	37.4885	−	27.2370i	0.0386081	−	0.0280504i	0.606922	+	0.794761i	$0.292404\pi$
$972$	2440.62	+	793.005i	2.51092	+	0.815849i
$973$	−188.038	−	258.812i	−0.193256	−	0.265994i
$974$	−933.948	+	1285.47i	−0.958879	+	1.31978i
$975$	−107.521	−	330.915i	−0.110278	−	0.339400i
$976$	−1105.93	+	1522.19i	−1.13313	+	1.55962i
$977$	710.732	+	516.377i	0.727464	+	0.528533i	0.888760	−	0.458373i	$-0.151567\pi$
$977$	710.732	+	516.377i	0.727464	+	0.528533i	−0.161296	+	0.986906i	$0.551567\pi$
$978$	−931.352	+	302.614i	−0.952302	+	0.309422i
$979$	276.300	+	200.744i	0.282227	+	0.205050i
$980$	−1184.90	+	860.882i	−1.20908	+	0.878451i
$981$	258.387	−	795.233i	0.263391	−	0.810635i
$982$	284.649	+	391.785i	0.289866	+	0.398966i
$983$	−600.777	+	195.204i	−0.611167	+	0.198580i	−0.598215	−	0.801336i	$-0.704123\pi$
$983$	−600.777	+	195.204i	−0.611167	+	0.198580i	−0.0129523	+	0.999916i	$0.504123\pi$
$984$	−137.844	+	44.7881i	−0.140085	+	0.0455164i
$985$	981.131	+	318.789i	0.996072	+	0.323643i
$986$	−930.874			−0.944091
$987$			436.157i			0.441901i
$988$	−1333.55	−	433.298i	−1.34975	−	0.438561i
$989$	−1161.62	−	843.967i	−1.17454	−	0.853354i
$990$	1341.79	+	1846.82i	1.35535	+	1.86548i
$991$			485.456i			0.489865i	0.969540	+	0.244932i	$0.0787658\pi$
$991$			485.456i			0.489865i	−0.969540	+	0.244932i	$0.921234\pi$
$992$	−813.816	−	1113.76i	−0.820379	−	1.12274i
$993$	−2259.23			−2.27516
$994$	574.140	−	417.137i	0.577606	−	0.419655i
$995$	−35.8014	+	49.2764i	−0.0359813	+	0.0495240i
$996$	−988.772	+	3043.13i	−0.992743	+	3.05535i
$997$	822.008			0.824481			0.412241	−	0.911075i	$-0.364746\pi$
$997$	822.008			0.824481			0.412241	+	0.911075i	$0.364746\pi$
$998$		−	3526.33i		−	3.53340i
$999$	345.982	−	1064.82i	0.346328	−	1.06589i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.3.f.a.15.5	✓	20
3.2	odd	2		279.3.v.a.46.1		20
31.29	odd	10	inner	31.3.f.a.29.5	yes	20
93.29	even	10		279.3.v.a.91.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.3.f.a.15.5	✓	20	1.1	even	1	trivial
31.3.f.a.29.5	yes	20	31.29	odd	10	inner
279.3.v.a.46.1		20	3.2	odd	2
279.3.v.a.91.1		20	93.29	even	10

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

Level:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	31.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.95153 - 2.14441i) q^{2} +(-2.80836 + 3.86537i) q^{3} +(2.87696 - 8.85438i) q^{4} -3.94423 q^{5} +17.4310i q^{6} +(-0.932951 + 2.87133i) q^{7} +(-5.98647 - 18.4245i) q^{8} +(-4.27307 - 13.1512i) q^{9} +(-11.6415 + 8.45807i) q^{10} +(10.9110 + 3.54519i) q^{11} +(26.1459 + 35.9868i) q^{12} +(4.53298 - 6.23912i) q^{13} +(3.40368 + 10.4755i) q^{14} +(11.0768 - 15.2459i) q^{15} +(-27.0510 - 19.6537i) q^{16} +(-15.6245 + 5.07671i) q^{17} +(-40.8136 - 29.6528i) q^{18} +(15.7996 - 11.4790i) q^{19} +(-11.3474 + 34.9238i) q^{20} +(-8.47869 - 11.6699i) q^{21} +(39.8064 - 12.9339i) q^{22} +(-23.9267 + 7.77425i) q^{23} +(88.0295 + 28.6025i) q^{24} -9.44302 q^{25} -28.1355i q^{26} +(21.9382 + 7.12816i) q^{27} +(22.7398 + 16.5214i) q^{28} +(9.12892 + 12.5649i) q^{29} -68.7521i q^{30} +(18.2893 + 25.0300i) q^{31} -44.4969 q^{32} +(-44.3454 + 32.2188i) q^{33} +(-35.2297 + 48.4895i) q^{34} +(3.67978 - 11.3252i) q^{35} -128.739 q^{36} -48.5373i q^{37} +(22.0171 - 67.7615i) q^{38} +(11.3863 + 35.0433i) q^{39} +(23.6120 + 72.6704i) q^{40} +(-1.26683 + 0.920402i) q^{41} +(-50.0502 - 16.2623i) q^{42} +(33.5466 + 46.1730i) q^{43} +(62.7810 - 86.4106i) q^{44} +(16.8540 + 51.8712i) q^{45} +(-53.9492 + 74.2547i) q^{46} +(-24.4619 - 17.7726i) q^{47} +(151.937 - 49.3674i) q^{48} +(32.2677 + 23.4439i) q^{49} +(-27.8714 + 20.2497i) q^{50} +(24.2558 - 74.6517i) q^{51} +(-42.2023 - 58.0865i) q^{52} +(-51.0737 + 16.5949i) q^{53} +(80.0371 - 26.0056i) q^{54} +(-43.0354 - 13.9831i) q^{55} +58.4878 q^{56} +93.3083i q^{57} +(53.8886 + 17.5095i) q^{58} +(-54.4113 - 39.5321i) q^{59} +(-103.126 - 141.940i) q^{60} -56.2711i q^{61} +(107.656 + 34.6571i) q^{62} +41.7479 q^{63} +(-23.1301 + 16.8050i) q^{64} +(-17.8791 + 24.6085i) q^{65} +(-61.7963 + 190.190i) q^{66} +87.2989 q^{67} +152.951i q^{68} +(37.1443 - 114.318i) q^{69} +(-13.4249 - 41.3176i) q^{70} +(-19.9102 - 61.2774i) q^{71} +(-216.722 + 157.458i) q^{72} +(-14.3964 - 4.67769i) q^{73} +(-104.084 - 143.259i) q^{74} +(26.5193 - 36.5007i) q^{75} +(-56.1851 - 172.920i) q^{76} +(-20.3588 + 28.0215i) q^{77} +(108.754 + 79.0146i) q^{78} +(-67.5006 + 21.9323i) q^{79} +(106.695 + 77.5187i) q^{80} +(11.5200 - 8.36981i) q^{81} +(-1.76535 + 5.43319i) q^{82} +(42.2812 + 58.1951i) q^{83} +(-127.723 + 41.4996i) q^{84} +(61.6267 - 20.0237i) q^{85} +(198.028 + 64.3432i) q^{86} -74.2052 q^{87} -222.252i q^{88} +(28.3122 + 9.19918i) q^{89} +(160.978 + 116.958i) q^{90} +(13.6855 + 18.8365i) q^{91} +234.222i q^{92} +(-148.113 + 0.401655i) q^{93} -110.312 q^{94} +(-62.3171 + 45.2760i) q^{95} +(124.963 - 171.997i) q^{96} +(35.5472 - 109.403i) q^{97} +145.512 q^{98} -158.641i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{2} - 5 q^{3} - 11 q^{4} - 14 q^{5} - q^{7} - 19 q^{8} + 2 q^{9} + 12 q^{10} - 10 q^{11} + 90 q^{12} + 10 q^{13} - 85 q^{15} - 103 q^{16} + 35 q^{17} + 6 q^{18} + 47 q^{19} - 125 q^{20} - 125 q^{21}+ \cdots - 1000 q^{98}+O(q^{100}) \) 20 * q - 3 * q^2 - 5 * q^3 - 11 * q^4 - 14 * q^5 - q^7 - 19 * q^8 + 2 * q^9 + 12 * q^10 - 10 * q^11 + 90 * q^12 + 10 * q^13 - 85 * q^15 - 103 * q^16 + 35 * q^17 + 6 * q^18 + 47 * q^19 - 125 * q^20 - 125 * q^21 + 150 * q^22 + 75 * q^23 + 195 * q^24 + 82 * q^25 + 25 * q^27 + 88 * q^28 + 5 * q^29 + 73 * q^31 + 226 * q^32 - 206 * q^33 - 265 * q^34 - 50 * q^35 - 520 * q^36 + 8 * q^38 + 91 * q^39 - 466 * q^40 - 98 * q^41 + 245 * q^43 + 380 * q^44 - 162 * q^45 - 445 * q^46 - 187 * q^47 + 570 * q^48 + 328 * q^49 - 44 * q^50 + 185 * q^51 - 15 * q^52 + 25 * q^53 + 920 * q^54 + 190 * q^55 + 64 * q^56 - 85 * q^58 - 173 * q^59 + 275 * q^60 - 40 * q^62 + 252 * q^63 - 469 * q^64 - 345 * q^65 - 564 * q^66 + 76 * q^67 - 197 * q^69 - 11 * q^70 - 467 * q^71 - 982 * q^72 - 15 * q^73 + 45 * q^74 - 175 * q^75 + 55 * q^76 - 320 * q^77 - 91 * q^78 + 500 * q^79 + 1030 * q^80 + 117 * q^81 + 178 * q^82 - 50 * q^83 + 65 * q^84 + 20 * q^85 + 1125 * q^86 - 366 * q^87 + 55 * q^89 + 444 * q^90 + 300 * q^91 + 502 * q^93 + 62 * q^94 - 559 * q^95 - 10 * q^96 - 405 * q^97 - 1000 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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