LMFDB - Embedded newform 19.4.e.a.17.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [19,4,Mod(4,19)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("19.4"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(19, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	19.e (of order $9$, degree $6$, 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:	$1.12103629011$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			17.1
Character	$\chi$	$=$	19.17
Dual form			19.4.e.a.9.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.851642 + 4.82990i) q^{2} +(0.458552 + 0.384771i) q^{3} +(-15.0851 - 5.49052i) q^{4} +(6.94640 - 2.52828i) q^{5} +(-2.24893 + 1.88707i) q^{6} +(14.5751 + 25.2448i) q^{7} +(19.7481 - 34.2048i) q^{8} +(-4.62628 - 26.2369i) q^{9} +(6.29551 + 35.7036i) q^{10} +(26.3895 - 45.7080i) q^{11} +(-4.80470 - 8.32199i) q^{12} +(-30.9868 + 26.0010i) q^{13} +(-134.343 + 48.8967i) q^{14} +(4.15809 + 1.51342i) q^{15} +(50.0074 + 41.9612i) q^{16} +(-0.0277382 + 0.157311i) q^{17} +130.662 q^{18} +(-13.4549 - 81.7188i) q^{19} -118.669 q^{20} +(-3.03002 + 17.1841i) q^{21} +(198.291 + 166.386i) q^{22} +(-39.4491 - 14.3583i) q^{23} +(22.2165 - 8.08616i) q^{24} +(-53.8953 + 45.2235i) q^{25} +(-99.1927 - 171.807i) q^{26} +(16.0549 - 27.8079i) q^{27} +(-81.2594 - 460.845i) q^{28} +(11.8095 + 66.9751i) q^{29} +(-10.8509 + 18.7943i) q^{30} +(108.113 + 187.257i) q^{31} +(-3.20963 + 2.69320i) q^{32} +(29.6881 - 10.8056i) q^{33} +(-0.736175 - 0.267946i) q^{34} +(165.071 + 138.511i) q^{35} +(-74.2667 + 421.187i) q^{36} -288.898 q^{37} +(406.152 + 4.60942i) q^{38} -24.2135 q^{39} +(50.6991 - 287.529i) q^{40} +(-24.4278 - 20.4974i) q^{41} +(-80.4171 - 29.2694i) q^{42} +(128.653 - 46.8260i) q^{43} +(-649.050 + 544.617i) q^{44} +(-98.4704 - 170.556i) q^{45} +(102.946 - 178.307i) q^{46} +(-32.7846 - 185.931i) q^{47} +(6.78555 + 38.4828i) q^{48} +(-253.367 + 438.844i) q^{49} +(-172.526 - 298.823i) q^{50} +(-0.0732482 + 0.0614625i) q^{51} +(610.199 - 222.094i) q^{52} +(-31.5953 - 11.4998i) q^{53} +(120.636 + 101.226i) q^{54} +(67.7495 - 384.227i) q^{55} +1151.32 q^{56} +(25.2732 - 42.6494i) q^{57} -333.540 q^{58} +(50.5342 - 286.594i) q^{59} +(-54.4157 - 45.6602i) q^{60} +(-10.9927 - 4.00101i) q^{61} +(-996.508 + 362.699i) q^{62} +(594.918 - 499.195i) q^{63} +(250.846 + 434.478i) q^{64} +(-149.509 + 258.957i) q^{65} +(26.9063 + 152.593i) q^{66} +(61.8269 + 350.638i) q^{67} +(1.28216 - 2.22076i) q^{68} +(-12.5648 - 21.7629i) q^{69} +(-809.573 + 679.313i) q^{70} +(-237.468 + 86.4315i) q^{71} +(-988.789 - 359.890i) q^{72} +(-619.706 - 519.995i) q^{73} +(246.037 - 1395.35i) q^{74} -42.1145 q^{75} +(-245.711 + 1306.61i) q^{76} +1538.52 q^{77} +(20.6212 - 116.949i) q^{78} +(540.834 + 453.814i) q^{79} +(453.461 + 165.046i) q^{80} +(-657.883 + 239.450i) q^{81} +(119.804 - 100.528i) q^{82} +(608.912 + 1054.67i) q^{83} +(140.058 - 242.588i) q^{84} +(0.205047 + 1.16288i) q^{85} +(116.598 + 661.261i) q^{86} +(-20.3548 + 35.2555i) q^{87} +(-1042.29 - 1805.30i) q^{88} +(895.877 - 751.730i) q^{89} +(907.628 - 330.350i) q^{90} +(-1108.03 - 403.289i) q^{91} +(516.259 + 433.193i) q^{92} +(-22.4757 + 127.466i) q^{93} +925.947 q^{94} +(-300.071 - 533.634i) q^{95} -2.50805 q^{96} +(-69.0328 + 391.505i) q^{97} +(-1903.80 - 1597.48i) q^{98} +(-1321.32 - 480.923i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 6 q^{2} - 3 q^{3} - 24 q^{4} - 6 q^{5} + 42 q^{6} + 3 q^{7} - 75 q^{8} - 51 q^{9} + 75 q^{10} + 39 q^{11} - 219 q^{12} - 156 q^{13} + 93 q^{14} - 192 q^{15} + 504 q^{16} + 12 q^{17} + 264 q^{18}+ \cdots + 492 q^{99}+O(q^{100}) $ 24 * q - 6 * q^2 - 3 * q^3 - 24 * q^4 - 6 * q^5 + 42 * q^6 + 3 * q^7 - 75 * q^8 - 51 * q^9 + 75 * q^10 + 39 * q^11 - 219 * q^12 - 156 * q^13 + 93 * q^14 - 192 * q^15 + 504 * q^16 + 12 * q^17 + 264 * q^18 + 546 * q^19 - 198 * q^20 + 453 * q^21 - 6 * q^22 + 6 * q^23 + 192 * q^24 - 498 * q^25 - 639 * q^26 - 870 * q^27 - 1368 * q^28 - 630 * q^29 - 522 * q^30 - 591 * q^31 + 147 * q^32 + 1506 * q^33 - 408 * q^34 + 2001 * q^35 + 1059 * q^36 - 72 * q^37 + 2934 * q^38 + 336 * q^39 + 2886 * q^40 - 477 * q^41 + 237 * q^42 + 588 * q^43 - 3423 * q^44 - 1569 * q^45 - 1728 * q^46 - 1242 * q^47 - 4599 * q^48 - 639 * q^49 - 1788 * q^50 + 9 * q^51 + 2733 * q^52 - 300 * q^53 + 3777 * q^54 + 315 * q^55 + 4638 * q^56 + 3342 * q^57 - 2820 * q^58 + 2097 * q^59 + 1116 * q^60 - 2316 * q^61 - 1320 * q^62 - 2979 * q^63 - 1785 * q^64 - 2433 * q^65 - 1590 * q^66 + 57 * q^67 - 438 * q^68 - 1767 * q^69 - 213 * q^70 - 792 * q^71 - 1686 * q^72 + 4068 * q^73 + 4287 * q^74 + 1332 * q^75 + 5538 * q^76 + 3786 * q^77 + 2121 * q^78 + 1824 * q^79 - 2739 * q^80 + 1536 * q^81 + 2205 * q^82 + 1071 * q^83 - 1437 * q^84 - 2394 * q^85 - 5256 * q^86 + 759 * q^87 + 1101 * q^88 - 3006 * q^89 - 3822 * q^90 - 3285 * q^91 - 1452 * q^92 - 135 * q^93 - 1086 * q^94 - 3078 * q^95 - 1590 * q^96 - 2535 * q^97 - 2403 * q^98 + 492 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.851642	+	4.82990i	−0.301101	+	1.70763i	0.340213	+	0.940348i	$0.389501\pi$
$2$	−0.851642	+	4.82990i	−0.301101	+	1.70763i	−0.641314	+	0.767279i	$0.721610\pi$
$3$	0.458552	+	0.384771i	0.0882483	+	0.0740492i	0.685845	−	0.727748i	$-0.259433\pi$
$3$	0.458552	+	0.384771i	0.0882483	+	0.0740492i	−0.597596	+	0.801797i	$0.703877\pi$
$4$	−15.0851	−	5.49052i	−1.88564	−	0.686315i
$5$	6.94640	−	2.52828i	0.621305	−	0.226137i	−0.0121374	−	0.999926i	$-0.503864\pi$
$5$	6.94640	−	2.52828i	0.621305	−	0.226137i	0.633442	+	0.773790i	$0.281641\pi$
$6$	−2.24893	+	1.88707i	−0.153020	+	0.128399i
$7$	14.5751	+	25.2448i	0.786981	+	1.36309i	0.927808	+	0.373057i	$0.121691\pi$
$7$	14.5751	+	25.2448i	0.786981	+	1.36309i	−0.140827	+	0.990034i	$0.544976\pi$
$8$	19.7481	−	34.2048i	0.872752	−	1.51165i
$9$	−4.62628	−	26.2369i	−0.171344	−	0.971738i
$10$	6.29551	+	35.7036i	0.199081	+	1.12905i
$11$	26.3895	−	45.7080i	0.723341	−	1.25286i	−0.236313	−	0.971677i	$-0.575939\pi$
$11$	26.3895	−	45.7080i	0.723341	−	1.25286i	0.959653	−	0.281186i	$-0.0907277\pi$
$12$	−4.80470	−	8.32199i	−0.115583	−	0.200196i
$13$	−30.9868	+	26.0010i	−0.661092	+	0.554722i	−0.910414	−	0.413698i	$-0.864237\pi$
$13$	−30.9868	+	26.0010i	−0.661092	+	0.554722i	0.249322	+	0.968421i	$0.419792\pi$
$14$	−134.343	+	48.8967i	−2.56461	+	0.933443i
$15$	4.15809	+	1.51342i	0.0715744	+	0.0260509i
$16$	50.0074	+	41.9612i	0.781366	+	0.655644i
$17$	−0.0277382	+	0.157311i	−0.000395736	+	0.00224433i	−0.985005	−	0.172526i	$-0.944807\pi$
$17$	−0.0277382	+	0.157311i	−0.000395736	+	0.00224433i	0.984609	+	0.174770i	$0.0559183\pi$
$18$	130.662			1.71096
$19$	−13.4549	−	81.7188i	−0.162461	−	0.986715i
$19$	−13.4549	−	81.7188i	−0.162461	−	0.986715i
$20$	−118.669			−1.32676
$21$	−3.03002	+	17.1841i	−0.0314860	+	0.178566i
$22$	198.291	+	166.386i	1.92162	+	1.61243i
$23$	−39.4491	−	14.3583i	−0.357640	−	0.130170i	0.156950	−	0.987606i	$-0.449834\pi$
$23$	−39.4491	−	14.3583i	−0.357640	−	0.130170i	−0.514590	+	0.857436i	$0.672056\pi$
$24$	22.2165	−	8.08616i	0.188955	−	0.0687742i
$25$	−53.8953	+	45.2235i	−0.431162	+	0.361788i
$26$	−99.1927	−	171.807i	−0.748204	−	1.29593i
$27$	16.0549	−	27.8079i	0.114436	−	0.198208i
$28$	−81.2594	−	460.845i	−0.548450	−	3.11041i
$29$	11.8095	+	66.9751i	0.0756197	+	0.428861i	0.998989	+	0.0449484i	$0.0143123\pi$
$29$	11.8095	+	66.9751i	0.0756197	+	0.428861i	−0.923370	+	0.383912i	$0.874577\pi$
$30$	−10.8509	+	18.7943i	−0.0660364	+	0.114378i
$31$	108.113	+	187.257i	0.626377	+	1.08492i	0.988273	+	0.152698i	$0.0487963\pi$
$31$	108.113	+	187.257i	0.626377	+	1.08492i	−0.361896	+	0.932219i	$0.617870\pi$
$32$	−3.20963	+	2.69320i	−0.0177309	+	0.0148780i
$33$	29.6881	−	10.8056i	0.156607	−	0.0570003i
$34$	−0.736175	−	0.267946i	−0.00371332	−	0.00135154i
$35$	165.071	+	138.511i	0.797200	+	0.668930i
$36$	−74.2667	+	421.187i	−0.343827	+	1.94994i
$37$	−288.898			−1.28363			−0.641817	−	0.766858i	$-0.721819\pi$
$37$	−288.898			−1.28363			−0.641817	+	0.766858i	$0.721819\pi$
$38$	406.152	+	4.60942i	1.73386	+	0.0196775i
$39$	−24.2135			−0.0994170
$40$	50.6991	−	287.529i	0.200406	−	1.13656i
$41$	−24.4278	−	20.4974i	−0.0930485	−	0.0780769i	0.595077	−	0.803669i	$-0.297122\pi$
$41$	−24.4278	−	20.4974i	−0.0930485	−	0.0780769i	−0.688125	+	0.725592i	$0.741566\pi$
$42$	−80.4171	−	29.2694i	−0.295444	−	0.107533i
$43$	128.653	−	46.8260i	0.456266	−	0.166067i	−0.103655	−	0.994613i	$-0.533054\pi$
$43$	128.653	−	46.8260i	0.456266	−	0.166067i	0.559921	+	0.828546i	$0.310831\pi$
$44$	−649.050	+	544.617i	−2.22382	+	1.86600i
$45$	−98.4704	−	170.556i	−0.326202	−	0.564999i
$46$	102.946	−	178.307i	0.329968	−	0.571521i
$47$	−32.7846	−	185.931i	−0.101747	−	0.577038i	−0.992470	−	0.122490i	$-0.960912\pi$
$47$	−32.7846	−	185.931i	−0.101747	−	0.577038i	0.890722	−	0.454548i	$-0.150199\pi$
$48$	6.78555	+	38.4828i	0.0204044	+	0.115719i
$49$	−253.367	+	438.844i	−0.738679	+	1.27943i
$50$	−172.526	−	298.823i	−0.487976	−	0.845199i
$51$	−0.0732482	+	0.0614625i	−0.000201114	+	0.000168754i
$52$	610.199	−	222.094i	1.62729	−	0.592287i
$53$	−31.5953	−	11.4998i	−0.0818859	−	0.0298040i	0.300752	−	0.953702i	$-0.402762\pi$
$53$	−31.5953	−	11.4998i	−0.0818859	−	0.0298040i	−0.382638	+	0.923898i	$0.624984\pi$
$54$	120.636	+	101.226i	0.304009	+	0.255094i
$55$	67.7495	−	384.227i	0.166097	−	0.941984i
$56$	1151.32			2.74736
$57$	25.2732	−	42.6494i	0.0587285	−	0.0991061i
$58$	−333.540			−0.755103
$59$	50.5342	−	286.594i	0.111508	−	0.632395i	−0.876912	−	0.480652i	$-0.840400\pi$
$59$	50.5342	−	286.594i	0.111508	−	0.632395i	0.988420	−	0.151743i	$-0.0484888\pi$
$60$	−54.4157	−	45.6602i	−0.117084	−	0.0982452i
$61$	−10.9927	−	4.00101i	−0.0230732	−	0.00839798i	0.330458	−	0.943821i	$-0.392797\pi$
$61$	−10.9927	−	4.00101i	−0.0230732	−	0.00839798i	−0.353531	+	0.935423i	$0.615019\pi$
$62$	−996.508	+	362.699i	−2.04124	+	0.742949i
$63$	594.918	−	499.195i	1.18972	−	0.998297i
$64$	250.846	+	434.478i	0.489933	+	0.848589i
$65$	−149.509	+	258.957i	−0.285297	+	0.494149i
$66$	26.9063	+	152.593i	0.0501808	+	0.284589i
$67$	61.8269	+	350.638i	0.112737	+	0.639362i	0.987846	+	0.155436i	$0.0496784\pi$
$67$	61.8269	+	350.638i	0.112737	+	0.639362i	−0.875109	+	0.483926i	$0.839211\pi$
$68$	1.28216	−	2.22076i	0.00228653	−	0.00396039i
$69$	−12.5648	−	21.7629i	−0.0219221	−	0.0379702i
$70$	−809.573	+	679.313i	−1.38232	+	1.15991i
$71$	−237.468	+	86.4315i	−0.396934	+	0.144472i	−0.532772	−	0.846259i	$-0.678850\pi$
$71$	−237.468	+	86.4315i	−0.396934	+	0.144472i	0.135838	+	0.990731i	$0.456627\pi$
$72$	−988.789	−	359.890i	−1.61847	−	0.589075i
$73$	−619.706	−	519.995i	−0.993577	−	0.833710i	−0.00749546	−	0.999972i	$-0.502386\pi$
$73$	−619.706	−	519.995i	−0.993577	−	0.833710i	−0.986082	+	0.166262i	$0.946830\pi$
$74$	246.037	−	1395.35i	0.386503	−	2.19197i
$75$	−42.1145			−0.0648395
$76$	−245.711	+	1306.61i	−0.370855	+	1.97209i
$77$	1538.52			2.27702
$78$	20.6212	−	116.949i	0.0299345	−	0.169767i
$79$	540.834	+	453.814i	0.770235	+	0.646304i	0.940769	−	0.339048i	$-0.110105\pi$
$79$	540.834	+	453.814i	0.770235	+	0.646304i	−0.170534	+	0.985352i	$0.554549\pi$
$80$	453.461	+	165.046i	0.633732	+	0.230659i
$81$	−657.883	+	239.450i	−0.902446	+	0.328463i
$82$	119.804	−	100.528i	0.161343	−	0.135383i
$83$	608.912	+	1054.67i	0.805263	+	1.39476i	0.916113	+	0.400919i	$0.131309\pi$
$83$	608.912	+	1054.67i	0.805263	+	1.39476i	−0.110851	+	0.993837i	$0.535358\pi$
$84$	140.058	−	242.588i	0.181924	−	0.315101i
$85$	0.205047	+	1.16288i	0.000261652	+	0.00148390i
$86$	116.598	+	661.261i	0.146199	+	0.829136i
$87$	−20.3548	+	35.2555i	−0.0250834	+	0.0434458i
$88$	−1042.29	−	1805.30i	−1.26259	−	2.18688i
$89$	895.877	−	751.730i	1.06700	−	0.895318i	0.0722208	−	0.997389i	$-0.476991\pi$
$89$	895.877	−	751.730i	1.06700	−	0.895318i	0.994777	+	0.102071i	$0.0325469\pi$
$90$	907.628	−	330.350i	1.06303	−	0.386910i
$91$	−1108.03	−	403.289i	−1.27640	−	0.464573i
$92$	516.259	+	433.193i	0.585041	+	0.490907i
$93$	−22.4757	+	127.466i	−0.0250604	+	0.142125i
$94$	925.947			1.01600
$95$	−300.071	−	533.634i	−0.324070	−	0.576313i
$96$	−2.50805			−0.00266642
$97$	−69.0328	+	391.505i	−0.0722600	+	0.409807i	0.927125	+	0.374751i	$0.122272\pi$
$97$	−69.0328	+	391.505i	−0.0722600	+	0.409807i	−0.999385	+	0.0350556i	$0.988839\pi$
$98$	−1903.80	−	1597.48i	−1.96237	−	1.64663i
$99$	−1321.32	−	480.923i	−1.34139	−	0.488228i
$100$	1061.32	−	386.287i	1.06132	−	0.386287i
$101$	−264.263	+	221.743i	−0.260348	+	0.218458i	−0.763613	−	0.645674i	$-0.776576\pi$
$101$	−264.263	+	221.743i	−0.260348	+	0.218458i	0.503265	+	0.864132i	$0.332132\pi$
$102$	−0.234477	−	0.406126i	−0.000227614	−	0.000394239i
$103$	−412.120	+	713.813i	−0.394247	+	0.682855i	−0.993005	−	0.118075i	$-0.962328\pi$
$103$	−412.120	+	713.813i	−0.394247	+	0.682855i	0.598758	+	0.800930i	$0.295661\pi$
$104$	277.427	+	1573.37i	0.261577	+	1.48348i
$105$	22.3986	+	127.029i	0.0208179	+	0.118064i
$106$	82.4506	−	142.809i	0.0755501	−	0.130857i
$107$	166.554	+	288.479i	0.150480	+	0.260639i	0.931404	−	0.363987i	$-0.118585\pi$
$107$	166.554	+	288.479i	0.150480	+	0.260639i	−0.780924	+	0.624626i	$0.785251\pi$
$108$	−394.869	+	331.334i	−0.351817	+	0.295210i
$109$	1381.61	−	502.866i	1.21408	−	0.441889i	0.345962	−	0.938248i	$-0.387553\pi$
$109$	1381.61	−	502.866i	1.21408	−	0.441889i	0.868117	+	0.496360i	$0.165330\pi$
$110$	1798.08	+	654.447i	1.55855	+	0.567264i
$111$	−132.475	−	111.159i	−0.113279	−	0.0950521i
$112$	−330.440	+	1874.02i	−0.278782	+	1.58105i
$113$	−2149.63			−1.78956			−0.894778	−	0.446511i	$-0.852666\pi$
$113$	−2149.63			−1.78956			−0.894778	+	0.446511i	$0.852666\pi$
$114$	184.468	+	158.389i	0.151553	+	0.130127i
$115$	−310.331			−0.251640
$116$	189.581	−	1075.17i	0.151742	−	0.860574i
$117$	825.541	+	692.711i	0.652319	+	0.547361i
$118$	1341.18	+	488.150i	1.04632	+	0.380829i
$119$	−4.37558	+	1.59258i	−0.00337066	+	0.00122682i
$120$	133.881	−	112.339i	0.101847	−	0.0854595i
$121$	−727.316	−	1259.75i	−0.546444	−	0.946468i
$122$	28.6863	−	49.6861i	0.0212880	−	0.0368719i
$123$	−3.31464	−	18.7982i	−0.00242984	−	0.0137803i
$124$	−602.755	−	3418.39i	−0.436524	−	2.47565i
$125$	−722.053	+	1250.63i	−0.516659	+	0.894880i
$126$	1904.41	+	3298.53i	1.34649	+	2.33219i
$127$	−581.035	+	487.547i	−0.405973	+	0.340652i	−0.822797	−	0.568336i	$-0.807588\pi$
$127$	−581.035	+	487.547i	−0.405973	+	0.340652i	0.416824	+	0.908987i	$0.363143\pi$
$128$	−2343.61	+	853.005i	−1.61834	+	0.589029i
$129$	77.0115	+	28.0299i	0.0525619	+	0.0191310i
$130$	−1123.41	−	942.652i	−0.757919	−	0.635970i
$131$	0.740327	−	4.19860i	0.000493761	−	0.00280026i	−0.984560	−	0.175048i	$-0.943992\pi$
$131$	0.740327	−	4.19860i	0.000493761	−	0.00280026i	0.985054	+	0.172248i	$0.0551030\pi$
$132$	−507.176			−0.334424
$133$	1866.87	−	1530.73i	1.21713	−	0.997976i
$134$	−1746.20			−1.12574
$135$	41.2175	−	233.756i	0.0262773	−	0.149026i
$136$	4.83302	+	4.05538i	0.00304726	+	0.00255696i
$137$	826.086	+	300.671i	0.515163	+	0.187504i	0.586501	−	0.809948i	$-0.300505\pi$
$137$	826.086	+	300.671i	0.515163	+	0.187504i	−0.0713386	+	0.997452i	$0.522727\pi$
$138$	115.813	−	42.1526i	0.0714397	−	0.0260019i
$139$	1508.17	−	1265.50i	0.920295	−	0.772219i	−0.0537547	−	0.998554i	$-0.517119\pi$
$139$	1508.17	−	1265.50i	0.920295	−	0.772219i	0.974049	+	0.226335i	$0.0726745\pi$
$140$	−1729.61	−	2995.77i	−1.04413	−	1.80849i
$141$	56.5072	−	97.8734i	0.0337501	−	0.0584569i
$142$	−215.217	−	1220.56i	−0.127188	−	0.721316i
$143$	370.728	+	2102.50i	0.216796	+	1.22951i
$144$	869.585	−	1506.17i	0.503232	−	0.871624i
$145$	251.365	+	435.378i	0.143964	+	0.249353i
$146$	3039.29	−	2550.27i	1.72283	−	1.44563i
$147$	−285.036	+	103.745i	−0.159928	+	0.0582090i
$148$	4358.05	+	1586.20i	2.42047	+	0.880978i
$149$	1153.19	+	967.640i	0.634046	+	0.532028i	0.902183	−	0.431353i	$-0.141964\pi$
$149$	1153.19	+	967.640i	0.634046	+	0.532028i	−0.268137	+	0.963381i	$0.586408\pi$
$150$	35.8664	−	203.409i	0.0195232	−	0.110722i
$151$	−2394.72			−1.29059			−0.645296	−	0.763933i	$-0.723266\pi$
$151$	−2394.72			−1.29059			−0.645296	+	0.763933i	$0.723266\pi$
$152$	−3060.88	−	1153.57i	−1.63336	−	0.615573i
$153$	4.25569			0.00224871
$154$	−1310.27	+	7430.90i	−0.685613	+	3.88831i
$155$	1224.44	+	1027.42i	0.634511	+	0.532418i
$156$	365.263	+	132.945i	0.187464	+	0.0682314i
$157$	2541.54	−	925.045i	1.29196	−	0.470233i	0.397587	−	0.917564i	$-0.369848\pi$
$157$	2541.54	−	925.045i	1.29196	−	0.470233i	0.894368	+	0.447331i	$0.147625\pi$
$158$	−2652.47	+	2225.69i	−1.33556	+	1.12067i
$159$	−10.0633	−	17.4302i	−0.00501933	−	0.00869374i
$160$	−15.4862	+	26.8229i	−0.00765183	+	0.0132534i
$161$	−212.502	−	1205.16i	−0.104022	−	0.589937i
$162$	−596.238	−	3381.43i	−0.289166	−	1.63994i
$163$	927.459	−	1606.41i	0.445670	−	0.771923i	−0.552429	−	0.833560i	$-0.686299\pi$
$163$	927.459	−	1606.41i	0.445670	−	0.771923i	0.998099	+	0.0616373i	$0.0196322\pi$
$164$	255.955	+	443.327i	0.121870	+	0.211085i
$165$	178.906	−	150.120i	0.0844109	−	0.0708292i
$166$	−5612.51	+	2042.79i	−2.62419	+	0.955127i
$167$	−835.550	−	304.115i	−0.387166	−	0.140917i	0.141101	−	0.989995i	$-0.454936\pi$
$167$	−835.550	−	304.115i	−0.387166	−	0.140917i	−0.528267	+	0.849078i	$0.677158\pi$
$168$	527.942	+	442.996i	0.242450	+	0.203440i
$169$	−97.3753	+	552.243i	−0.0443219	+	0.251362i
$170$	−5.79121			−0.00261274
$171$	−2081.81	+	731.069i	−0.930992	+	0.326937i
$172$	−2197.85			−0.974327
$173$	604.938	−	3430.77i	0.265853	−	1.50773i	−0.500743	−	0.865596i	$-0.666940\pi$
$173$	604.938	−	3430.77i	0.265853	−	1.50773i	0.766595	−	0.642130i	$-0.221949\pi$
$174$	−152.945	−	128.336i	−0.0666366	−	0.0559147i
$175$	−1927.19	−	701.439i	−0.832467	−	0.302993i
$176$	3237.64	−	1178.40i	1.38663	−	0.504690i
$177$	133.445	−	111.974i	0.0566688	−	0.0475507i
$178$	2867.82	+	4967.20i	1.20759	+	2.09162i
$179$	52.0088	−	90.0818i	0.0217169	−	0.0376147i	−0.854963	−	0.518689i	$-0.826420\pi$
$179$	52.0088	−	90.0818i	0.0217169	−	0.0376147i	0.876680	+	0.481075i	$0.159753\pi$
$180$	548.994	+	3113.50i	0.227331	+	1.28926i
$181$	191.556	+	1086.37i	0.0786642	+	0.446127i	0.998545	+	0.0539284i	$0.0171743\pi$
$181$	191.556	+	1086.37i	0.0786642	+	0.446127i	−0.919881	+	0.392199i	$0.871715\pi$
$182$	2891.49	−	5008.20i	1.17764	−	2.03974i
$183$	−3.50124	−	6.06433i	−0.00141431	−	0.00244966i
$184$	−1270.17	+	1065.80i	−0.508903	+	0.427020i
$185$	−2006.80	+	730.415i	−0.797529	+	0.290277i
$186$	−596.507	−	217.111i	−0.235150	−	0.0855878i
$187$	6.45839	+	5.41924i	0.00252559	+	0.00211922i
$188$	−526.298	+	2984.79i	−0.204172	+	1.15791i
$189$	936.005			0.360235
$190$	2832.95	−	994.849i	1.08170	−	0.379863i
$191$	2275.97			0.862216			0.431108	−	0.902300i	$-0.358123\pi$
$191$	2275.97			0.862216			0.431108	+	0.902300i	$0.358123\pi$
$192$	−52.1485	+	295.749i	−0.0196015	+	0.111166i
$193$	−444.200	−	372.728i	−0.165669	−	0.139013i	0.556184	−	0.831059i	$-0.312265\pi$
$193$	−444.200	−	372.728i	−0.165669	−	0.139013i	−0.721853	+	0.692046i	$0.756709\pi$
$194$	−1832.14	−	666.843i	−0.678040	−	0.246786i
$195$	−168.197	+	61.2186i	−0.0617683	+	0.0224818i
$196$	6231.55	−	5228.89i	2.27097	−	1.90557i
$197$	300.114	+	519.812i	0.108539	+	0.187995i	0.915179	−	0.403048i	$-0.132049\pi$
$197$	300.114	+	519.812i	0.108539	+	0.187995i	−0.806639	+	0.591044i	$0.798716\pi$
$198$	3448.10	−	5972.29i	1.23761	−	2.14360i
$199$	−193.396	−	1096.81i	−0.0688920	−	0.390706i	−0.999684	−	0.0251556i	$-0.991992\pi$
$199$	−193.396	−	1096.81i	−0.0688920	−	0.390706i	0.930792	−	0.365550i	$-0.119119\pi$
$200$	482.529	+	2736.56i	0.170600	+	0.967518i
$201$	−106.564	+	184.575i	−0.0373954	+	0.0647707i
$202$	−845.940	−	1465.21i	−0.294654	−	0.510356i
$203$	−1518.65	+	1274.30i	−0.525065	+	0.440582i
$204$	1.44242	−	0.524997i	0.000495046	−	0.000180182i
$205$	−221.509	−	80.6226i	−0.0754675	−	0.0274679i
$206$	−3096.67	−	2598.41i	−1.04735	−	0.878834i
$207$	−194.215	+	1101.45i	−0.0652121	+	0.369836i
$208$	−2640.61			−0.880255
$209$	−4090.28	−	1541.53i	−1.35373	−	0.510190i
$210$	−632.611			−0.207878
$211$	−151.430	+	858.804i	−0.0494071	+	0.280201i	−0.999495	−	0.0317813i	$-0.989882\pi$
$211$	−151.430	+	858.804i	−0.0494071	+	0.280201i	0.950088	+	0.311983i	$0.100993\pi$
$212$	413.479	+	346.950i	0.133952	+	0.112399i
$213$	−142.148	−	51.7376i	−0.0457268	−	0.0166432i
$214$	−1535.17	+	558.756i	−0.490384	+	0.178485i
$215$	775.288	−	650.544i	0.245927	−	0.206357i
$216$	−634.107	−	1098.31i	−0.199748	−	0.345974i
$217$	−3151.52	+	5458.59i	−0.985894	+	1.70762i
$218$	1252.15	+	7101.32i	0.389021	+	2.20625i
$219$	−84.0885	−	476.890i	−0.0259460	−	0.147147i
$220$	−3131.61	+	5424.11i	−0.959697	+	1.66224i
$221$	−3.23074	−	5.59580i	−0.000983362	−	0.00170323i
$222$	649.709	−	545.171i	0.196422	−	0.164817i
$223$	4308.68	−	1568.23i	1.29386	−	0.470926i	0.398867	−	0.917009i	$-0.369403\pi$
$223$	4308.68	−	1568.23i	1.29386	−	0.470926i	0.894992	+	0.446082i	$0.147181\pi$
$224$	−114.770	−	41.7729i	−0.0342339	−	0.0124601i
$225$	1435.86	+	1204.83i	0.425440	+	0.356987i
$226$	1830.71	−	10382.5i	0.538837	−	3.05589i
$227$	2444.50			0.714744			0.357372	−	0.933962i	$-0.383673\pi$
$227$	2444.50			0.714744			0.357372	+	0.933962i	$0.383673\pi$
$228$	−615.417	+	504.606i	−0.178759	+	0.146572i
$229$	225.313			0.0650178			0.0325089	−	0.999471i	$-0.489650\pi$
$229$	225.313			0.0650178			0.0325089	+	0.999471i	$0.489650\pi$
$230$	264.291	−	1498.87i	0.0757689	−	0.429707i
$231$	705.492	+	591.978i	0.200943	+	0.168612i
$232$	2524.08	+	918.691i	0.714285	+	0.259978i
$233$	1158.16	−	421.534i	0.325636	−	0.118522i	−0.174029	−	0.984741i	$-0.555679\pi$
$233$	1158.16	−	421.534i	0.325636	−	0.118522i	0.499665	+	0.866219i	$0.333456\pi$
$234$	−4048.79	+	3397.34i	−1.13110	+	0.949107i
$235$	−697.820	−	1208.66i	−0.193705	−	0.335508i
$236$	−2335.86	+	4045.83i	−0.644287	+	1.11594i
$237$	73.3862	+	416.194i	0.0201137	+	0.114071i
$238$	−3.96558	−	22.4899i	−0.00108004	−	0.00612523i
$239$	−1193.70	+	2067.54i	−0.323070	+	0.559574i	−0.981120	−	0.193400i	$-0.938048\pi$
$239$	−1193.70	+	2067.54i	−0.323070	+	0.559574i	0.658050	+	0.752975i	$0.271382\pi$
$240$	144.431	+	250.161i	0.0388456	+	0.0672826i
$241$	−1170.63	+	982.276i	−0.312892	+	0.262548i	−0.785686	−	0.618625i	$-0.787690\pi$
$241$	−1170.63	+	982.276i	−0.312892	+	0.262548i	0.472794	+	0.881173i	$0.343245\pi$
$242$	6703.87	−	2440.01i	1.78075	−	0.648140i
$243$	−1208.49	−	439.853i	−0.319030	−	0.116118i
$244$	143.858	+	120.711i	0.0377441	+	0.0316711i
$245$	−650.466	+	3688.97i	−0.169619	+	0.961959i
$246$	93.6164			0.0242633
$247$	2541.70	+	2182.37i	0.654755	+	0.562189i
$248$	8540.13			2.18669
$249$	−126.587	+	717.911i	−0.0322174	+	0.182714i
$250$	−5425.50	−	4552.54i	−1.37256	−	1.15171i
$251$	5132.44	+	1868.06i	1.29067	+	0.469764i	0.893945	−	0.448176i	$-0.147926\pi$
$251$	5132.44	+	1868.06i	1.29067	+	0.469764i	0.396720	+	0.917940i	$0.370148\pi$
$252$	−11715.2	+	4264.00i	−2.92853	+	1.06590i
$253$	−1697.33	+	1424.23i	−0.421781	+	0.353916i
$254$	−1859.97	−	3221.56i	−0.459467	−	0.795821i
$255$	−0.353417	+	0.612136i	−8.67914e−5	+	0.000150327i
$256$	−1427.07	−	8093.30i	−0.348405	−	1.97590i
$257$	−893.499	−	5067.29i	−0.216867	−	1.22992i	−0.877636	−	0.479327i	$-0.840881\pi$
$257$	−893.499	−	5067.29i	−0.216867	−	1.22992i	0.660769	−	0.750589i	$-0.270230\pi$
$258$	−200.968	+	348.086i	−0.0484950	+	0.0839957i
$259$	−4210.71	−	7293.17i	−1.01020	−	1.74971i
$260$	3677.17	−	3085.51i	0.877108	−	0.735981i
$261$	1702.59	−	619.691i	0.403783	−	0.146965i
$262$	19.6483	+	7.15141i	0.00463312	+	0.00168632i
$263$	−2709.39	−	2273.45i	−0.635241	−	0.533030i	0.267312	−	0.963610i	$-0.413865\pi$
$263$	−2709.39	−	2273.45i	−0.635241	−	0.533030i	−0.902553	+	0.430580i	$0.858309\pi$
$264$	216.682	−	1228.86i	0.0505146	−	0.286482i
$265$	−248.548			−0.0576159
$266$	5803.35	+	10320.4i	1.33769	+	2.37889i
$267$	700.050			0.160458
$268$	992.521	−	5628.87i	0.226223	−	1.28298i
$269$	−3470.12	−	2911.78i	−0.786532	−	0.659979i	0.158352	−	0.987383i	$-0.449382\pi$
$269$	−3470.12	−	2911.78i	−0.786532	−	0.659979i	−0.944884	+	0.327404i	$0.893826\pi$
$270$	1093.91	+	398.152i	0.246569	+	0.0897436i
$271$	2619.55	−	953.438i	0.587182	−	0.213717i	−0.0313075	−	0.999510i	$-0.509967\pi$
$271$	2619.55	−	953.438i	0.587182	−	0.213717i	0.618490	+	0.785793i	$0.287745\pi$
$272$	−7.98809	+	6.70280i	−0.00178070	+	0.00149418i
$273$	−352.914	−	611.265i	−0.0782394	−	0.135515i
$274$	−2155.74	+	3733.85i	−0.475303	+	0.823248i
$275$	644.806	+	3656.88i	0.141394	+	0.801883i
$276$	70.0517	+	397.283i	0.0152776	+	0.0866435i
$277$	−715.482	+	1239.25i	−0.155196	+	0.268807i	−0.933130	−	0.359539i	$-0.882934\pi$
$277$	−715.482	+	1239.25i	−0.155196	+	0.268807i	0.777935	+	0.628345i	$0.216267\pi$
$278$	4827.83	+	8362.04i	1.04156	+	1.80404i
$279$	4412.90	−	3702.86i	0.946930	−	0.794568i
$280$	7997.56	−	2910.87i	1.70695	−	0.621278i
$281$	−7973.14	−	2901.99i	−1.69266	−	0.616078i	−0.697704	−	0.716386i	$-0.745795\pi$
$281$	−7973.14	−	2901.99i	−1.69266	−	0.616078i	−0.994956	+	0.100308i	$0.968017\pi$
$282$	424.595	+	356.277i	0.0896605	+	0.0752341i
$283$	−1171.22	+	6642.33i	−0.246014	+	1.39521i	0.572112	+	0.820176i	$0.306124\pi$
$283$	−1171.22	+	6642.33i	−0.246014	+	1.39521i	−0.818126	+	0.575039i	$0.804987\pi$
$284$	4056.79			0.847627
$285$	67.7284	−	360.158i	0.0140768	−	0.0748558i
$286$	−10470.6			−2.16482
$287$	161.415	−	915.428i	0.0331986	−	0.188279i
$288$	85.5099	+	71.7514i	0.0174956	+	0.0146805i
$289$	4616.69	+	1680.34i	0.939688	+	0.342018i
$290$	−2316.90	+	843.284i	−0.469149	+	0.170756i
$291$	−182.295	+	152.963i	−0.0367227	+	0.0308140i
$292$	6493.28	+	11246.7i	1.30134	+	2.25398i
$293$	3990.52	−	6911.78i	0.795660	−	1.37812i	−0.126759	−	0.991934i	$-0.540458\pi$
$293$	3990.52	−	6911.78i	0.795660	−	1.37812i	0.922419	−	0.386190i	$-0.126209\pi$
$294$	−258.328	−	1465.05i	−0.0512449	−	0.290624i
$295$	−373.559	−	2118.56i	−0.0737270	−	0.418126i
$296$	−5705.19	+	9881.68i	−1.12030	+	1.94041i
$297$	−847.362	−	1467.67i	−0.165552	−	0.286744i
$298$	−5655.71	+	4745.70i	−1.09942	+	0.922521i
$299$	1595.73	−	580.800i	0.308641	−	0.112336i
$300$	635.300	+	231.230i	0.122264	+	0.0445003i
$301$	3057.25	+	2565.34i	0.585438	+	0.491241i
$302$	2039.44	−	11566.2i	0.388598	−	2.20385i
$303$	−206.499			−0.0391520
$304$	2756.18	−	4651.13i	0.519992	−	0.877502i
$305$	−86.4752			−0.0162346
$306$	−3.62432	+	20.5546i	−0.000677088	+	0.00383995i
$307$	3138.81	+	2633.77i	0.583522	+	0.489633i	0.886102	−	0.463491i	$-0.153403\pi$
$307$	3138.81	+	2633.77i	0.583522	+	0.489633i	−0.302580	+	0.953124i	$0.597848\pi$
$308$	−23208.7	−	8447.29i	−4.29364	−	1.56276i
$309$	−463.633	+	168.749i	−0.0853565	+	0.0310672i
$310$	−6005.14	+	5038.91i	−1.10022	+	0.923196i
$311$	−4343.64	−	7523.40i	−0.791978	−	1.37175i	−0.924741	−	0.380598i	$-0.875718\pi$
$311$	−4343.64	−	7523.40i	−0.791978	−	1.37175i	0.132763	−	0.991148i	$-0.457615\pi$
$312$	−478.172	+	828.217i	−0.0867665	+	0.150284i
$313$	1160.01	+	6578.73i	0.209481	+	1.18803i	0.890231	+	0.455510i	$0.150543\pi$
$313$	1160.01	+	6578.73i	0.209481	+	1.18803i	−0.680750	+	0.732516i	$0.738346\pi$
$314$	2303.39	+	13063.2i	0.413974	+	2.34777i
$315$	2870.43	−	4971.73i	0.513430	−	0.889287i
$316$	−5666.85	−	9815.28i	−1.00881	−	1.74732i
$317$	−7872.02	+	6605.41i	−1.39475	+	1.17034i	−0.431380	+	0.902170i	$0.641973\pi$
$317$	−7872.02	+	6605.41i	−1.39475	+	1.17034i	−0.963373	+	0.268166i	$0.913583\pi$
$318$	92.7564	−	33.7606i	0.0163570	−	0.00595346i
$319$	3372.95	+	1227.65i	0.592002	+	0.215471i
$320$	2840.96	+	2383.85i	0.496295	+	0.416441i
$321$	−34.6249	+	196.368i	−0.00602048	+	0.0341439i
$322$	6001.78			1.03871
$323$	13.2285	+	0.150130i	0.00227881	+	2.58621e-5i
$324$	11238.9			1.92711
$325$	494.186	−	2802.67i	0.0843461	−	0.478351i
$326$	6968.92	+	5847.61i	1.18396	+	0.993464i
$327$	827.030	+	301.014i	0.139862	+	0.0509056i
$328$	−1183.51	+	430.763i	−0.199233	+	0.0725150i
$329$	4215.95	−	3537.60i	0.706482	−	0.592809i
$330$	572.700	+	991.945i	0.0955336	+	0.165469i
$331$	867.289	−	1502.19i	0.144020	−	0.249449i	−0.784987	−	0.619512i	$-0.787330\pi$
$331$	867.289	−	1502.19i	0.144020	−	0.249449i	0.929007	+	0.370063i	$0.120664\pi$
$332$	−3394.82	−	19253.0i	−0.561190	−	3.18267i
$333$	1336.52	+	7579.79i	0.219943	+	1.24736i
$334$	2180.43	−	3776.62i	0.357210	−	0.618705i
$335$	1315.99	+	2279.36i	0.214627	+	0.371745i
$336$	−872.590	+	732.190i	−0.141678	+	0.118882i
$337$	−7972.22	+	2901.65i	−1.28865	+	0.469029i	−0.893283	−	0.449495i	$-0.851604\pi$
$337$	−7972.22	+	2901.65i	−1.28865	+	0.469029i	−0.395365	+	0.918524i	$0.629382\pi$
$338$	−2584.35	−	940.626i	−0.415888	−	0.151371i
$339$	−985.715	−	827.113i	−0.157925	−	0.132515i
$340$	3.29166	−	18.6679i	0.000525045	−	0.00297768i
$341$	11412.2			1.81234
$342$	−1758.04	−	10677.5i	−0.277964	−	1.68823i
$343$	−4772.88			−0.751344
$344$	938.991	−	5325.28i	0.147171	−	0.834651i
$345$	−142.303	−	119.406i	−0.0222068	−	0.0186337i
$346$	16055.1	+	5843.57i	2.49459	+	0.907955i
$347$	1475.13	−	536.902i	0.228210	−	0.0830618i	−0.225384	−	0.974270i	$-0.572364\pi$
$347$	1475.13	−	536.902i	0.228210	−	0.0830618i	0.453594	+	0.891208i	$0.350141\pi$
$348$	500.625	−	420.074i	0.0771158	−	0.0647078i
$349$	3113.45	+	5392.65i	0.477533	+	0.827112i	0.999668	−	0.0257507i	$-0.00819762\pi$
$349$	3113.45	+	5392.65i	0.477533	+	0.827112i	−0.522135	+	0.852863i	$0.674864\pi$
$350$	5029.15	−	8710.75i	0.768056	−	1.33031i
$351$	225.544	+	1279.12i	0.0342981	+	0.194514i
$352$	38.4002	+	217.778i	0.00581459	+	0.0329762i
$353$	3022.18	−	5234.56i	0.455678	−	0.789257i	−0.543049	−	0.839701i	$-0.682730\pi$
$353$	3022.18	−	5234.56i	0.455678	−	0.789257i	0.998727	+	0.0504440i	$0.0160636\pi$
$354$	427.175	+	739.889i	0.0641359	+	0.111087i
$355$	−1431.03	+	1200.78i	−0.213947	+	0.179523i
$356$	−17641.8	+	6421.08i	−2.62644	+	0.955946i
$357$	−2.61921	−	0.953315i	−0.000388301	−	0.000141330i
$358$	390.793	+	327.914i	0.0576929	+	0.0484101i
$359$	−1718.83	+	9747.95i	−0.252691	+	1.43308i	0.549239	+	0.835665i	$0.314918\pi$
$359$	−1718.83	+	9747.95i	−0.252691	+	1.43308i	−0.801930	+	0.597418i	$0.796193\pi$
$360$	−7778.43			−1.13878
$361$	−6496.93	+	2199.03i	−0.947213	+	0.320606i
$362$	−5410.18			−0.785505
$363$	151.202	−	857.510i	0.0218624	−	0.123988i
$364$	14500.4	+	12167.3i	2.08799	+	1.75203i
$365$	−5619.42	−	2045.30i	−0.805847	−	0.293304i
$366$	32.2719	−	11.7460i	0.00460896	−	0.00167752i
$367$	−6820.82	+	5723.35i	−0.970147	+	0.814050i	−0.982574	−	0.185873i	$-0.940489\pi$
$367$	−6820.82	+	5723.35i	−0.970147	+	0.814050i	0.0124266	+	0.999923i	$0.496044\pi$
$368$	−1370.26	−	2373.36i	−0.194102	−	0.336195i
$369$	−424.779	+	735.738i	−0.0599271	+	0.103797i
$370$	−1818.76	−	10314.7i	−0.255548	−	1.44928i
$371$	−170.196	−	965.228i	−0.0238170	−	0.135073i
$372$	1038.90	−	1799.43i	0.144797	−	0.250796i
$373$	−3961.67	−	6861.81i	−0.549939	−	0.952523i	−0.998278	−	0.0586591i	$-0.981318\pi$
$373$	−3961.67	−	6861.81i	−0.549939	−	0.952523i	0.448339	−	0.893864i	$-0.352016\pi$
$374$	−31.6746	+	26.5781i	−0.00437929	+	0.00367466i
$375$	−812.306	+	295.655i	−0.111859	+	0.0407135i
$376$	−7007.15	−	2550.39i	−0.961080	−	0.349805i
$377$	−2107.36	−	1768.29i	−0.287890	−	0.241569i
$378$	−797.141	+	4520.81i	−0.108467	+	0.615147i
$379$	566.318			0.0767541			0.0383771	−	0.999263i	$-0.487781\pi$
$379$	566.318			0.0767541			0.0383771	+	0.999263i	$0.487781\pi$
$380$	1596.67	+	9697.47i	0.215546	+	1.30913i
$381$	−454.028			−0.0610514
$382$	−1938.31	+	10992.7i	−0.259614	+	1.47234i
$383$	−1836.22	−	1540.78i	−0.244978	−	0.205561i	0.512028	−	0.858969i	$-0.328894\pi$
$383$	−1836.22	−	1540.78i	−0.244978	−	0.205561i	−0.757006	+	0.653408i	$0.773339\pi$
$384$	−1402.88	−	510.606i	−0.186433	−	0.0678561i
$385$	10687.2	−	3889.82i	1.41473	−	0.514918i
$386$	2178.54	−	1828.01i	0.287266	−	0.241045i
$387$	−1823.76	−	3158.84i	−0.239552	−	0.414917i
$388$	3190.93	−	5526.86i	0.417513	−	0.723154i
$389$	−1961.56	−	11124.5i	−0.255668	−	1.44997i	−0.794352	−	0.607458i	$-0.792189\pi$
$389$	−1961.56	−	11124.5i	−0.255668	−	1.44997i	0.538684	−	0.842508i	$-0.318922\pi$
$390$	−152.436	−	864.510i	−0.0197921	−	0.112247i
$391$	3.35297	−	5.80752i	0.000433676	−	0.000751148i
$392$	10007.0	+	17332.7i	1.28937	+	2.23325i
$393$	1.95498	−	1.64042i	0.000250930	−	0.000210556i
$394$	−2766.23	+	1006.83i	−0.353707	+	0.128739i
$395$	4904.22	+	1784.99i	0.624704	+	0.227374i
$396$	17291.8	+	14509.5i	2.19430	+	1.84124i
$397$	297.045	−	1684.63i	0.0375523	−	0.212970i	−0.960258	−	0.279115i	$-0.909959\pi$
$397$	297.045	−	1684.63i	0.0375523	−	0.212970i	0.997810	+	0.0661451i	$0.0210700\pi$
$398$	5462.16			0.687924
$399$	1445.04	+	16.3997i	0.181309	+	0.00205767i
$400$	−4592.80			−0.574100
$401$	−1599.12	+	9069.07i	−0.199143	+	1.12940i	0.707251	+	0.706963i	$0.249935\pi$
$401$	−1599.12	+	9069.07i	−0.199143	+	1.12940i	−0.906394	+	0.422434i	$0.861176\pi$
$402$	−800.723	−	671.887i	−0.0993444	−	0.0833599i
$403$	−8218.97	−	2991.46i	−1.01592	−	0.369765i
$404$	5203.92	−	1894.07i	0.640854	−	0.233252i
$405$	−3964.52	+	3326.63i	−0.486417	+	0.408152i
$406$	−4861.38	−	8420.16i	−0.594252	−	1.02927i
$407$	−7623.88	+	13204.9i	−0.928505	+	1.60822i
$408$	0.655797	+	3.71921i	7.95754e−5	+	0.000451295i
$409$	−1876.27	−	10640.9i	−0.226835	−	1.28645i	−0.859146	−	0.511731i	$-0.829004\pi$
$409$	−1876.27	−	10640.9i	−0.226835	−	1.28645i	0.632310	−	0.774715i	$-0.282107\pi$
$410$	578.045	−	1001.20i	0.0696283	−	0.120600i
$411$	263.114	+	455.727i	0.0315778	+	0.0546943i
$412$	10136.1	−	8505.18i	1.21206	−	1.01704i
$413$	7971.54	−	2901.40i	0.949768	−	0.345687i
$414$	−5154.49	−	1876.08i	−0.611907	−	0.222716i
$415$	6896.25	+	5786.64i	0.815719	+	0.684470i
$416$	29.4303	−	166.907i	0.00346860	−	0.0196714i
$417$	1178.50			0.138397
$418$	10928.9	−	18442.8i	1.27882	−	2.15805i
$419$	−15330.6			−1.78747			−0.893735	−	0.448596i	$-0.851924\pi$
$419$	−15330.6			−1.78747			−0.893735	+	0.448596i	$0.851924\pi$
$420$	359.569	−	2039.22i	0.0417742	−	0.236913i
$421$	−126.027	−	105.750i	−0.0145896	−	0.0122421i	0.635464	−	0.772131i	$-0.280809\pi$
$421$	−126.027	−	105.750i	−0.0145896	−	0.0122421i	−0.650053	+	0.759889i	$0.725253\pi$
$422$	−4018.97	−	1462.79i	−0.463603	−	0.168738i
$423$	−4726.58	+	1720.33i	−0.543296	+	0.197744i
$424$	−1017.30	+	853.612i	−0.116519	+	0.0977714i
$425$	−5.61921	−	9.73276i	−0.000641345	−	0.00111084i
$426$	370.946	−	642.498i	0.0421888	−	0.0730731i
$427$	−59.2147	−	335.823i	−0.00671101	−	0.0380600i
$428$	−928.574	−	5266.20i	−0.104870	−	0.594747i
$429$	−638.984	+	1106.75i	−0.0719124	+	0.124556i
$430$	2481.79	+	4298.59i	0.278332	+	0.482085i
$431$	9869.95	−	8281.87i	1.10306	−	0.925577i	0.105433	−	0.994426i	$-0.466377\pi$
$431$	9869.95	−	8281.87i	1.10306	−	0.925577i	0.997627	+	0.0688493i	$0.0219328\pi$
$432$	1969.71	−	716.917i	0.219370	−	0.0798442i
$433$	9951.14	+	3621.92i	1.10444	+	0.401982i	0.828950	−	0.559323i	$-0.188939\pi$
$433$	9951.14	+	3621.92i	1.10444	+	0.401982i	0.275487	+	0.961305i	$0.411161\pi$
$434$	−23680.5	−	19870.3i	−2.61912	−	2.19771i
$435$	−52.2565	+	296.361i	−0.00575979	+	0.0326654i
$436$	−23602.8			−2.59259
$437$	−642.561	+	3416.93i	−0.0703383	+	0.374036i
$438$	2374.94			0.259085
$439$	2617.95	−	14847.1i	0.284619	−	1.61415i	−0.422024	−	0.906584i	$-0.638680\pi$
$439$	2617.95	−	14847.1i	0.284619	−	1.61415i	0.706643	−	0.707570i	$-0.250209\pi$
$440$	−11804.5	−	9905.11i	−1.27899	−	1.07320i
$441$	12686.1	+	4617.36i	1.36984	+	0.498581i
$442$	29.7786	−	10.8385i	0.00320458	−	0.00116637i
$443$	−277.823	+	233.122i	−0.0297964	+	0.0250021i	−0.657564	−	0.753398i	$-0.728413\pi$
$443$	−277.823	+	233.122i	−0.0297964	+	0.0250021i	0.627768	+	0.778401i	$0.283969\pi$
$444$	1388.07	+	2404.20i	0.148367	+	0.256979i
$445$	4322.54	−	7486.85i	0.460467	−	0.797552i
$446$	3904.95	+	22146.1i	0.414584	+	2.35123i
$447$	156.477	+	887.426i	0.0165573	+	0.0939012i
$448$	−7312.20	+	12665.1i	−0.771136	+	1.33565i
$449$	6292.87	+	10899.6i	0.661423	+	1.14562i	0.980242	+	0.197802i	$0.0633805\pi$
$449$	6292.87	+	10899.6i	0.661423	+	1.14562i	−0.318819	+	0.947816i	$0.603286\pi$
$450$	−7042.05	+	5908.98i	−0.737701	+	0.619004i
$451$	−1581.53	+	575.632i	−0.165125	+	0.0601007i
$452$	32427.3	+	11802.6i	3.37445	+	1.22820i
$453$	−1098.10	−	921.417i	−0.113893	−	0.0955672i
$454$	−2081.83	+	11806.7i	−0.215210	+	1.22052i
$455$	−8716.43			−0.898094
$456$	−959.712	−	1706.71i	−0.0985584	−	0.175272i
$457$	19220.1			1.96735			0.983673	−	0.179965i	$-0.0575984\pi$
$457$	19220.1			1.96735			0.983673	+	0.179965i	$0.0575984\pi$
$458$	−191.886	+	1088.24i	−0.0195769	+	0.111026i
$459$	3.92916	+	3.29695i	0.000399559	+	0.000335269i
$460$	4681.38	+	1703.88i	0.474501	+	0.172704i
$461$	−5961.69	+	2169.88i	−0.602307	+	0.219222i	−0.625134	−	0.780518i	$-0.714956\pi$
$461$	−5961.69	+	2169.88i	−0.602307	+	0.219222i	0.0228268	+	0.999739i	$0.492733\pi$
$462$	−3460.02	+	2903.30i	−0.348430	+	0.292367i
$463$	−2665.67	−	4617.07i	−0.267568	−	0.463442i	0.700665	−	0.713490i	$-0.252887\pi$
$463$	−2665.67	−	4617.07i	−0.267568	−	0.463442i	−0.968233	+	0.250049i	$0.919553\pi$
$464$	−2219.79	+	3844.79i	−0.222093	+	0.384677i
$465$	166.145	+	942.255i	0.0165694	+	0.0939699i
$466$	1049.63	+	5952.77i	0.104342	+	0.591752i
$467$	2903.91	−	5029.71i	0.287745	−	0.498388i	−0.685526	−	0.728048i	$-0.740428\pi$
$467$	2903.91	−	5029.71i	0.287745	−	0.498388i	0.973271	+	0.229659i	$0.0737612\pi$
$468$	−8650.02	−	14982.3i	−0.854374	−	1.47982i
$469$	−7950.66	+	6671.39i	−0.782787	+	0.656836i
$470$	6432.00	−	2341.06i	0.631247	−	0.229755i
$471$	1521.36	+	553.729i	0.148833	+	0.0541709i
$472$	−8804.91	−	7388.20i	−0.858642	−	0.720486i
$473$	1254.78	−	7116.21i	0.121976	−	0.691762i
$474$	−2072.67			−0.200846
$475$	4420.77	+	3795.78i	0.427029	+	0.366658i
$476$	74.7502			0.00719783
$477$	−155.550	+	882.166i	−0.0149311	+	0.0846784i
$478$	−8969.42	−	7526.24i	−0.858268	−	0.720172i
$479$	7365.10	+	2680.68i	0.702547	+	0.255706i	0.668498	−	0.743714i	$-0.266937\pi$
$479$	7365.10	+	2680.68i	0.702547	+	0.255706i	0.0340492	+	0.999420i	$0.489160\pi$
$480$	−17.4219	+	6.34105i	−0.00165666	+	0.000602975i
$481$	8952.02	−	7511.64i	0.848601	−	0.712061i
$482$	−3747.34	−	6490.58i	−0.354121	−	0.613356i
$483$	366.267	−	634.393i	0.0345046	−	0.0597637i
$484$	4054.95	+	22996.8i	0.380818	+	2.15973i
$485$	510.305	+	2894.08i	0.0477768	+	0.270956i
$486$	3153.64	−	5462.27i	0.294346	−	0.509822i
$487$	453.583	+	785.629i	0.0422049	+	0.0731011i	0.886356	−	0.463004i	$-0.153228\pi$
$487$	453.583	+	785.629i	0.0422049	+	0.0731011i	−0.844151	+	0.536105i	$0.819895\pi$
$488$	−353.938	+	296.990i	−0.0328320	+	0.0275494i
$489$	1043.39	−	379.761i	0.0964899	−	0.0351194i
$490$	−17263.4	−	6283.37i	−1.59159	−	0.579293i
$491$	9362.55	+	7856.11i	0.860542	+	0.722080i	0.962085	−	0.272751i	$-0.0879334\pi$
$491$	9362.55	+	7856.11i	0.860542	+	0.722080i	−0.101543	+	0.994831i	$0.532378\pi$
$492$	−53.2106	+	301.772i	−0.00487585	+	0.0276523i
$493$	−10.8635			−0.000992430
$494$	−12705.2	+	10417.6i	−1.15716	+	0.948801i
$495$	−10394.4			−0.943821
$496$	−2451.09	+	13900.8i	−0.221889	+	1.25840i
$497$	−5643.07	−	4735.10i	−0.509309	−	0.427361i
$498$	−3359.63	−	1222.81i	−0.302307	−	0.110031i
$499$	−16468.4	+	5994.00i	−1.47741	+	0.537732i	−0.950101	−	0.311943i	$-0.899020\pi$
$499$	−16468.4	+	5994.00i	−1.47741	+	0.537732i	−0.527307	+	0.849675i	$0.676798\pi$
$500$	17758.9	−	14901.5i	1.58840	−	1.33283i
$501$	−266.128	−	460.948i	−0.0237320	−	0.0411050i
$502$	−13393.5	+	23198.3i	−1.19080	+	2.06253i
$503$	1352.90	+	7672.65i	0.119926	+	0.680133i	0.984193	+	0.177100i	$0.0566715\pi$
$503$	1352.90	+	7672.65i	0.119926	+	0.680133i	−0.864267	+	0.503033i	$0.832217\pi$
$504$	−5326.35	−	30207.2i	−0.470743	−	2.66971i
$505$	−1275.05	+	2208.45i	−0.112354	+	0.194603i
$506$	−5433.38	−	9410.89i	−0.477358	−	0.826809i
$507$	−257.138	+	215.765i	−0.0225245	+	0.0189003i
$508$	11441.9	−	4164.49i	0.999311	−	0.363720i
$509$	−17576.7	−	6397.40i	−1.53060	−	0.557092i	−0.566830	−	0.823835i	$-0.691830\pi$
$509$	−17576.7	−	6397.40i	−1.53060	−	0.557092i	−0.963768	+	0.266743i	$0.914053\pi$
$510$	−2.65557	−	2.22829i	−0.000230570	−	0.000193471i
$511$	4094.90	−	23223.3i	0.354497	−	2.01045i
$512$	20353.0			1.75681
$513$	−2488.44	−	937.834i	−0.214166	−	0.0807142i
$514$	25235.4			2.16554
$515$	−1058.03	+	6000.39i	−0.0905289	+	0.513415i
$516$	−1007.83	−	845.667i	−0.0859827	−	0.0721481i
$517$	−9363.70	−	3408.11i	−0.796547	−	0.289920i
$518$	38811.3	−	14126.2i	3.29203	−	1.19820i
$519$	1597.46	−	1340.42i	0.135107	−	0.113368i
$520$	5905.05	+	10227.8i	0.497987	+	0.862539i
$521$	7347.85	−	12726.8i	0.617879	−	1.07020i	−0.371993	−	0.928236i	$-0.621325\pi$
$521$	7347.85	−	12726.8i	0.617879	−	1.07020i	0.989872	−	0.141963i	$-0.0453413\pi$
$522$	1543.05	+	8751.07i	0.129382	+	0.733763i
$523$	580.974	+	3294.87i	0.0485741	+	0.275477i	0.999415	−	0.0342028i	$-0.0108892\pi$
$523$	580.974	+	3294.87i	0.0485741	+	0.275477i	−0.950841	+	0.309680i	$0.899778\pi$
$524$	−34.2204	+	59.2715i	−0.00285291	+	0.00494139i
$525$	−613.822	−	1063.17i	−0.0510274	−	0.0883821i
$526$	13288.0	−	11149.9i	1.10149	−	0.924259i
$527$	−32.4566	+	11.8132i	−0.00268279	+	0.000976456i
$528$	1938.04	+	705.389i	0.159739	+	0.0581404i
$529$	−7970.39	−	6687.95i	−0.655083	−	0.549680i
$530$	211.674	−	1200.46i	0.0173482	−	0.0983865i
$531$	−7753.12			−0.633629
$532$	−36566.4	+	12841.0i	−2.97999	+	1.04648i
$533$	1289.89			0.104825
$534$	−596.192	+	3381.17i	−0.0483141	+	0.274003i
$535$	1886.31	+	1582.80i	0.152434	+	0.127907i
$536$	13214.5	+	4809.67i	1.06488	+	0.387586i
$537$	58.5096	−	21.2957i	0.00470181	−	0.00171132i
$538$	17018.9	−	14280.5i	1.36382	−	1.14438i
$539$	13372.5	+	23161.8i	1.06863	+	1.85093i
$540$	−1905.21	+	3299.92i	−0.151828	+	0.262974i
$541$	276.383	+	1567.44i	0.0219642	+	0.124565i	0.993818	−	0.111018i	$-0.0354111\pi$
$541$	276.383	+	1567.44i	0.0219642	+	0.124565i	−0.971854	+	0.235583i	$0.924300\pi$
$542$	2374.09	+	13464.2i	0.188148	+	1.06704i
$543$	−330.164	+	571.860i	−0.0260933	+	0.0451950i
$544$	−0.334641	−	0.579616i	−2.63743e−5	−	4.56817e-5i
$545$	8325.86	−	6986.22i	0.654386	−	0.549095i
$546$	3252.91	−	1183.96i	0.254966	−	0.0928001i
$547$	−3803.34	−	1384.30i	−0.297293	−	0.108206i	0.189068	−	0.981964i	$-0.439453\pi$
$547$	−3803.34	−	1384.30i	−0.297293	−	0.108206i	−0.486360	+	0.873758i	$0.661676\pi$
$548$	−10810.7	−	9071.29i	−0.842723	−	0.707128i
$549$	−54.1190	+	306.924i	−0.00420718	+	0.0238601i
$550$	−18211.5			−1.41189
$551$	5314.23	−	1866.20i	0.410878	−	0.144288i
$552$	−992.527			−0.0765303
$553$	−3573.73	+	20267.6i	−0.274811	+	1.55853i
$554$	−5376.13	−	4511.11i	−0.412292	−	0.345954i
$555$	−1201.26	−	437.224i	−0.0918753	−	0.0334399i
$556$	−29699.1	+	10809.6i	−2.26533	+	0.824512i
$557$	−6337.57	+	5317.86i	−0.482103	+	0.404533i	−0.851186	−	0.524864i	$-0.824116\pi$
$557$	−6337.57	+	5317.86i	−0.482103	+	0.404533i	0.369083	+	0.929397i	$0.379672\pi$
$558$	14126.2	+	24467.4i	1.07171	+	1.85625i
$559$	−2769.03	+	4796.11i	−0.209513	+	0.362887i
$560$	2442.68	+	13853.1i	0.184325	+	1.04536i
$561$	0.876345	+	4.97000i	6.59525e−5	+	0.000374035i
$562$	20806.6	−	36038.0i	1.56169	−	2.70493i
$563$	−6349.65	−	10997.9i	−0.475321	−	0.823281i	0.524279	−	0.851546i	$-0.324335\pi$
$563$	−6349.65	−	10997.9i	−0.475321	−	0.823281i	−0.999600	+	0.0282659i	$0.991002\pi$
$564$	−1389.79	+	1166.17i	−0.103760	+	0.0870653i
$565$	−14932.2	+	5434.86i	−1.11186	+	0.404684i
$566$	−31084.3	−	11313.8i	−2.30843	−	0.840200i
$567$	−15633.6	−	13118.1i	−1.15793	−	0.971622i
$568$	−1733.19	+	9829.41i	−0.128034	+	0.726114i
$569$	2775.56			0.204495			0.102247	−	0.994759i	$-0.467397\pi$
$569$	2775.56			0.204495			0.102247	+	0.994759i	$0.467397\pi$
$570$	1681.84	+	633.847i	0.123587	+	0.0465770i
$571$	12723.9			0.932537			0.466269	−	0.884643i	$-0.345598\pi$
$571$	12723.9			0.932537			0.466269	+	0.884643i	$0.345598\pi$
$572$	5951.38	−	33751.9i	0.435034	−	2.46720i
$573$	1043.65	+	875.725i	0.0760891	+	0.0638463i
$574$	4283.96	+	1559.23i	0.311514	+	0.113382i
$575$	2775.46	−	1010.18i	0.201295	−	0.0732653i
$576$	10238.9	−	8591.44i	0.740660	−	0.621487i
$577$	2815.52	+	4876.63i	0.203140	+	0.351849i	0.949538	−	0.313651i	$-0.101552\pi$
$577$	2815.52	+	4876.63i	0.203140	+	0.351849i	−0.746399	+	0.665499i	$0.768219\pi$
$578$	−12047.6	+	20867.1i	−0.866981	+	1.50165i
$579$	−60.2738	−	341.830i	−0.00432624	−	0.0245353i
$580$	−1401.42	−	7947.84i	−0.100329	−	0.568993i
$581$	−17749.9	+	30743.8i	−1.26745	+	2.19529i
$582$	−583.548	−	1010.73i	−0.0415616	−	0.0719868i
$583$	−1359.42	+	1140.69i	−0.0965718	+	0.0810333i
$584$	−30024.4	+	10928.0i	−2.12743	+	0.774320i
$585$	7485.91	+	2724.65i	0.529067	+	0.192565i
$586$	29984.7	+	25160.1i	2.11375	+	1.77364i
$587$	3296.82	−	18697.2i	0.231813	−	1.31468i	−0.617409	−	0.786642i	$-0.711818\pi$
$587$	3296.82	−	18697.2i	0.231813	−	1.31468i	0.849222	−	0.528036i	$-0.177071\pi$
$588$	4869.41			0.341516
$589$	13847.8	−	11354.4i	0.968742	−	0.794313i
$590$	10550.6			0.736203
$591$	−62.3908	+	353.836i	−0.00434250	+	0.0246275i
$592$	−14447.0	−	12122.5i	−1.00299	−	0.841607i
$593$	−2738.32	−	996.668i	−0.189628	−	0.0690190i	0.245461	−	0.969407i	$-0.421061\pi$
$593$	−2738.32	−	996.668i	−0.189628	−	0.0690190i	−0.435089	+	0.900388i	$0.643283\pi$
$594$	7810.36	−	2842.74i	0.539500	−	0.196362i
$595$	−26.3681	+	22.1254i	−0.00181678	+	0.00152446i
$596$	−12083.1	−	20928.5i	−0.830442	−	1.43837i
$597$	333.336	−	577.356i	0.0228518	−	0.0395806i
$598$	1446.21	+	8201.87i	0.0988963	+	0.560869i
$599$	3247.07	+	18415.0i	0.221488	+	1.25612i	0.869286	+	0.494310i	$0.164579\pi$
$599$	3247.07	+	18415.0i	0.221488	+	1.25612i	−0.647797	+	0.761813i	$0.724310\pi$
$600$	−831.682	+	1440.52i	−0.0565888	+	0.0980147i
$601$	12297.4	+	21299.7i	0.834645	+	1.44565i	0.894319	+	0.447429i	$0.147660\pi$
$601$	12297.4	+	21299.7i	0.834645	+	1.44565i	−0.0596744	+	0.998218i	$0.519006\pi$
$602$	−14994.0	+	12581.5i	−1.01513	+	0.851797i
$603$	8913.64	−	3244.30i	0.601976	−	0.219101i
$604$	36124.5	+	13148.3i	2.43359	+	0.885753i
$605$	−8237.23	−	6911.86i	−0.553539	−	0.464475i
$606$	175.863	−	997.368i	0.0117887	−	0.0668570i
$607$	8927.76			0.596980			0.298490	−	0.954413i	$-0.403517\pi$
$607$	8927.76			0.596980			0.298490	+	0.954413i	$0.403517\pi$
$608$	263.270	+	226.051i	0.0175609	+	0.0150782i
$609$	−1186.69			−0.0789608
$610$	73.6459	−	417.667i	0.00488825	−	0.0277227i
$611$	5850.28	+	4908.97i	0.387360	+	0.325034i
$612$	−64.1975	−	23.3660i	−0.00424025	−	0.00154332i
$613$	−6800.54	+	2475.19i	−0.448077	+	0.163087i	−0.556196	−	0.831051i	$-0.687740\pi$
$613$	−6800.54	+	2475.19i	−0.448077	+	0.163087i	0.108119	+	0.994138i	$0.465517\pi$
$614$	−15394.0	+	12917.1i	−1.01181	+	0.849009i
$615$	−70.5520	−	122.200i	−0.00462591	−	0.00801231i
$616$	30382.9	−	52624.8i	1.98728	−	3.44206i
$617$	−1209.90	−	6861.70i	−0.0789447	−	0.447718i	−0.998500	−	0.0547564i	$-0.982562\pi$
$617$	−1209.90	−	6861.70i	−0.0789447	−	0.447718i	0.919555	−	0.392961i	$-0.128549\pi$
$618$	−420.189	−	2383.01i	−0.0273503	−	0.155111i
$619$	10772.8	−	18659.0i	0.699508	−	1.21158i	−0.269130	−	0.963104i	$-0.586736\pi$
$619$	10772.8	−	18659.0i	0.699508	−	1.21158i	0.968637	−	0.248479i	$-0.0799307\pi$
$620$	−12829.6	−	22221.6i	−0.831050	−	1.43942i
$621$	−1032.62	+	866.475i	−0.0667275	+	0.0559911i
$622$	40036.5	−	14572.1i	2.58090	−	0.939369i
$623$	32034.8	+	11659.7i	2.06011	+	0.749818i
$624$	−1210.86	−	1016.03i	−0.0776811	−	0.0651822i
$625$	−326.584	+	1852.15i	−0.0209014	+	0.118537i
$626$	−32762.5			−2.09178
$627$	−1282.47	−	2280.69i	−0.0816856	−	0.145266i
$628$	−43418.3			−2.75889
$629$	8.01351	−	45.4469i	0.000507980	−	0.00288090i
$630$	21568.4	+	18098.0i	1.36398	+	1.14451i
$631$	−24103.4	−	8772.92i	−1.52067	−	0.553478i	−0.559353	−	0.828929i	$-0.688950\pi$
$631$	−24103.4	−	8772.92i	−1.52067	−	0.553478i	−0.961315	+	0.275451i	$0.911173\pi$
$632$	26203.0	−	9537.13i	1.64921	−	0.600264i
$633$	−399.881	+	335.540i	−0.0251088	+	0.0210688i
$634$	−25199.3	−	43646.5i	−1.57854	−	2.73411i
$635$	−2803.45	+	4855.72i	−0.175199	+	0.303454i
$636$	56.1053	+	318.189i	0.00349799	+	0.0198381i
$637$	−3559.37	−	20186.2i	−0.221393	−	1.25558i
$638$	−8801.98	+	15245.5i	−0.546197	+	0.946041i
$639$	3366.29	+	5830.59i	0.208401	+	0.360962i
$640$	−14123.0	+	11850.6i	−0.872284	+	0.731933i
$641$	−3534.42	+	1286.42i	−0.217786	+	0.0792678i	−0.448609	−	0.893728i	$-0.648080\pi$
$641$	−3534.42	+	1286.42i	−0.217786	+	0.0792678i	0.230823	+	0.972996i	$0.425858\pi$
$642$	−918.948	−	334.470i	−0.0564922	−	0.0205615i
$643$	−4012.59	−	3366.96i	−0.246098	−	0.206501i	0.511392	−	0.859348i	$-0.329130\pi$
$643$	−4012.59	−	3366.96i	−0.246098	−	0.206501i	−0.757490	+	0.652847i	$0.773574\pi$
$644$	−3411.34	+	19346.7i	−0.208736	+	1.18380i
$645$	605.820			0.0369832
$646$	−11.9911	+	63.7645i	−0.000730313	+	0.00388356i
$647$	1791.60			0.108864			0.0544320	−	0.998517i	$-0.482665\pi$
$647$	1791.60			0.108864			0.0544320	+	0.998517i	$0.482665\pi$
$648$	−4801.64	+	27231.4i	−0.291090	+	1.65085i
$649$	−11766.1	−	9872.90i	−0.711646	−	0.597142i
$650$	13115.7	+	4773.73i	0.791448	+	0.288064i
$651$	−3545.44	+	1290.43i	−0.213451	+	0.0776899i
$652$	−22810.8	+	19140.5i	−1.37015	+	1.14970i
$653$	−3041.86	−	5268.66i	−0.182293	−	0.315741i	0.760368	−	0.649492i	$-0.225019\pi$
$653$	−3041.86	−	5268.66i	−0.182293	−	0.315741i	−0.942661	+	0.333752i	$0.891685\pi$
$654$	−2158.20	+	3738.11i	−0.129040	+	0.223504i
$655$	−5.47265	−	31.0369i	−0.000326464	−	0.00185147i
$656$	−361.478	−	2050.04i	−0.0215142	−	0.122013i
$657$	−10776.1	+	18664.8i	−0.639905	+	1.10835i
$658$	13495.8	+	23375.4i	0.799574	+	1.38490i
$659$	23608.8	−	19810.1i	1.39555	−	1.17101i	0.432515	−	0.901627i	$-0.357626\pi$
$659$	23608.8	−	19810.1i	1.39555	−	1.17101i	0.963034	−	0.269379i	$-0.0868184\pi$
$660$	−3523.05	+	1282.28i	−0.207779	+	0.0756255i
$661$	−7588.81	−	2762.10i	−0.446551	−	0.162531i	0.108950	−	0.994047i	$-0.465251\pi$
$661$	−7588.81	−	2762.10i	−0.446551	−	0.162531i	−0.555501	+	0.831516i	$0.687474\pi$
$662$	6516.80	+	5468.24i	0.382602	+	0.321041i
$663$	0.671640	−	3.80906i	3.93429e−5	−	0.000223125i
$664$	48099.5			2.81118
$665$	9097.92	−	15353.0i	0.530530	−	0.895285i
$666$	−37747.9			−2.19625
$667$	495.774	−	2811.67i	0.0287803	−	0.163221i
$668$	10934.6	+	9175.21i	0.633341	+	0.531436i
$669$	2579.16	+	938.739i	0.149053	+	0.0542507i
$670$	−12129.8	+	4414.89i	−0.699426	+	0.254570i
$671$	−472.970	+	396.869i	−0.0272113	+	0.0228330i
$672$	−36.5550	−	63.3152i	−0.00209842	−	0.00363458i
$673$	4863.53	−	8423.89i	0.278567	−	0.482492i	−0.692462	−	0.721454i	$-0.743474\pi$
$673$	4863.53	−	8423.89i	0.278567	−	0.482492i	0.971029	+	0.238963i	$0.0768073\pi$
$674$	−7225.20	−	40976.2i	−0.412915	−	2.34175i
$675$	392.287	+	2224.77i	0.0223691	+	0.126861i
$676$	4501.02	−	7795.99i	0.256089	−	0.443559i
$677$	13853.0	+	23994.0i	0.786429	+	1.36214i	0.928142	+	0.372227i	$0.121406\pi$
$677$	13853.0	+	23994.0i	0.786429	+	1.36214i	−0.141712	+	0.989908i	$0.545261\pi$
$678$	4834.35	−	4056.50i	0.273838	−	0.229777i
$679$	−10889.6	+	3963.50i	−0.615472	+	0.224013i
$680$	43.8253	+	15.9511i	0.00247150	+	0.000899553i
$681$	1120.93	+	940.570i	0.0630750	+	0.0529262i
$682$	−9719.13	+	55119.9i	−0.545696	+	3.09479i
$683$	−18109.8			−1.01457			−0.507285	−	0.861778i	$-0.669351\pi$
$683$	−18109.8			−1.01457			−0.507285	+	0.861778i	$0.669351\pi$
$684$	35418.2	+	401.961i	1.97989	+	0.0224698i
$685$	6498.51			0.362475
$686$	4064.78	−	23052.5i	0.226230	−	1.28302i
$687$	103.318	+	86.6937i	0.00573771	+	0.00481451i
$688$	8398.49	+	3056.80i	0.465392	+	0.169389i
$689$	1278.04	−	465.170i	0.0706671	−	0.0257207i
$690$	697.912	−	585.618i	0.0385059	−	0.0323103i
$691$	−1319.21	−	2284.94i	−0.0726267	−	0.125793i	0.827425	−	0.561576i	$-0.189805\pi$
$691$	−1319.21	−	2284.94i	−0.0726267	−	0.125793i	−0.900052	+	0.435783i	$0.856471\pi$
$692$	−27962.3	+	48432.1i	−1.53608	+	2.66057i
$693$	−7117.63	−	40366.1i	−0.390153	−	2.21267i
$694$	1336.90	+	7581.96i	0.0731242	+	0.414708i
$695$	7276.78	−	12603.8i	0.397157	−	0.687896i
$696$	803.937	+	1392.46i	0.0437833	+	0.0758349i
$697$	3.90206	−	3.27421i	0.000212053	−	0.000177934i
$698$	−28697.5	+	10445.0i	−1.55618	+	0.566405i
$699$	693.268	+	252.329i	0.0375133	+	0.0136537i
$700$	25220.5	+	21162.5i	1.36178	+	1.14267i
$701$	1096.82	−	6220.39i	0.0590962	−	0.335151i	−0.940898	−	0.338691i	$-0.890016\pi$
$701$	1096.82	−	6220.39i	0.0590962	−	0.335151i	0.999994	+	0.00354027i	$0.00112690\pi$
$702$	−6370.11			−0.342485
$703$	3887.08	+	23608.4i	0.208541	+	1.26658i
$704$	26478.8			1.41755
$705$	145.070	−	822.734i	0.00774988	−	0.0439517i
$706$	22708.6	+	19054.8i	1.21055	+	1.01577i
$707$	−9449.53	−	3439.35i	−0.502668	−	0.182956i
$708$	−2627.83	+	956.452i	−0.139491	+	0.0507707i
$709$	−16129.5	+	13534.3i	−0.854382	+	0.716911i	−0.960750	−	0.277416i	$-0.910522\pi$
$709$	−16129.5	+	13534.3i	−0.854382	+	0.716911i	0.106368	+	0.994327i	$0.466078\pi$
$710$	−4580.90	−	7934.35i	−0.242138	−	0.419396i
$711$	9404.63	−	16289.3i	0.496063	−	0.859207i
$712$	−8020.86	−	45488.5i	−0.422183	−	2.39432i
$713$	−1576.27	−	8939.47i	−0.0827935	−	0.469545i
$714$	6.83504	−	11.8386i	0.000358256	−	0.000620518i
$715$	7890.95	+	13667.5i	0.412734	+	0.714876i
$716$	−1279.15	+	1073.34i	−0.0667656	+	0.0560230i
$717$	−1342.90	+	488.776i	−0.0699464	+	0.0254584i
$718$	−45617.8	−	16603.5i	−2.37109	−	0.863005i
$719$	10752.4	+	9022.34i	0.557715	+	0.467978i	0.877543	−	0.479497i	$-0.159181\pi$
$719$	10752.4	+	9022.34i	0.557715	+	0.467978i	−0.319829	+	0.947475i	$0.603625\pi$
$720$	2232.47	−	12661.0i	0.115555	−	0.655343i
$721$	−24026.8			−1.24106
$722$	−5088.06	−	33252.3i	−0.262268	−	1.71402i
$723$	−914.746			−0.0470536
$724$	3075.09	−	17439.7i	0.157852	−	0.895222i
$725$	−3665.32	−	3075.57i	−0.187761	−	0.157550i
$726$	4012.92	+	1460.58i	0.205142	+	0.0746657i
$727$	−3622.30	+	1318.41i	−0.184792	+	0.0672587i	−0.432759	−	0.901510i	$-0.642460\pi$
$727$	−3622.30	+	1318.41i	−0.184792	+	0.0672587i	0.247967	+	0.968769i	$0.420238\pi$
$728$	−35675.9	+	29935.6i	−1.81626	+	1.52402i
$729$	9066.50	+	15703.6i	0.460626	+	0.797828i
$730$	14664.3	−	25399.4i	0.743495	−	1.28777i
$731$	3.79764	+	21.5375i	0.000192149	+	0.00108973i
$732$	19.5202	+	110.705i	0.000985639	+	0.00558984i
$733$	−6023.55	+	10433.1i	−0.303526	+	0.525723i	−0.976932	−	0.213550i	$-0.931497\pi$
$733$	−6023.55	+	10433.1i	−0.303526	+	0.525723i	0.673406	+	0.739273i	$0.264831\pi$
$734$	−21834.3	−	37818.1i	−1.09798	−	1.90176i
$735$	−1717.68	+	1441.31i	−0.0862008	+	0.0723311i
$736$	165.287	−	60.1595i	0.00827793	−	0.00301292i
$737$	17658.6	+	6427.19i	0.882580	+	0.321233i
$738$	−3191.78	−	2678.22i	−0.159202	−	0.133586i
$739$	4354.89	−	24697.8i	0.216776	−	1.22940i	−0.661023	−	0.750366i	$-0.729877\pi$
$739$	4354.89	−	24697.8i	0.216776	−	1.22940i	0.877798	−	0.479030i	$-0.159012\pi$
$740$	34283.1			1.70307
$741$	325.790	+	1978.70i	0.0161514	+	0.0980963i
$742$	4806.90			0.237826
$743$	−34.8023	+	197.374i	−0.00171840	+	0.00974554i	−0.985655	−	0.168773i	$-0.946019\pi$
$743$	−34.8023	+	197.374i	−0.00171840	+	0.00974554i	0.983936	+	0.178519i	$0.0571305\pi$
$744$	3916.09	+	3285.99i	0.192972	+	0.161922i
$745$	10457.0	+	3806.03i	0.514247	+	0.187171i
$746$	36515.8	−	13290.7i	1.79214	−	0.652286i
$747$	24854.2	−	20855.2i	1.21736	−	1.02149i
$748$	−67.6710	−	117.210i	−0.00330788	−	0.00572942i
$749$	−4855.07	+	8409.23i	−0.236850	+	0.410236i
$750$	−736.191	−	4175.15i	−0.0358425	−	0.203273i
$751$	3146.09	+	17842.4i	0.152866	+	0.866947i	0.960711	+	0.277552i	$0.0895229\pi$
$751$	3146.09	+	17842.4i	0.152866	+	0.866947i	−0.807845	+	0.589396i	$0.799366\pi$
$752$	6162.40	−	10673.6i	0.298829	−	0.517588i
$753$	1634.72	+	2831.42i	0.0791135	+	0.137029i
$754$	10335.4	−	8672.39i	0.499193	−	0.418873i
$755$	−16634.7	+	6054.52i	−0.801851	+	0.291850i
$756$	−14119.7	−	5139.16i	−0.679272	−	0.247235i
$757$	15248.9	+	12795.4i	0.732143	+	0.614341i	0.930715	−	0.365745i	$-0.119186\pi$
$757$	15248.9	+	12795.4i	0.732143	+	0.614341i	−0.198572	+	0.980086i	$0.563630\pi$
$758$	−482.300	+	2735.26i	−0.0231107	+	0.131067i
$759$	−1326.32			−0.0634286
$760$	−24178.7	−	274.404i	−1.15402	−	0.0130969i
$761$	−34118.1			−1.62520			−0.812602	−	0.582819i	$-0.801950\pi$
$761$	−34118.1			−1.62520			−0.812602	+	0.582819i	$0.801950\pi$
$762$	386.669	−	2192.91i	0.0183826	−	0.104253i
$763$	32831.9	+	27549.3i	1.55779	+	1.30714i
$764$	−34333.2	−	12496.2i	−1.62582	−	0.591752i
$765$	29.5617	−	10.7596i	0.00139713	−	0.000508515i
$766$	9005.60	−	7556.59i	0.424785	−	0.356437i
$767$	5885.84	+	10194.6i	0.277086	+	0.479928i
$768$	2459.68	−	4260.29i	0.115568	−	0.200169i
$769$	4352.49	+	24684.2i	0.204103	+	1.15752i	0.898846	+	0.438265i	$0.144407\pi$
$769$	4352.49	+	24684.2i	0.204103	+	1.15752i	−0.694743	+	0.719258i	$0.744482\pi$
$770$	9685.77	+	54930.7i	0.453313	+	2.57087i
$771$	1540.03	−	2667.41i	0.0719361	−	0.124597i
$772$	4654.32	+	8061.52i	0.216985	+	0.375830i
$773$	−5471.15	+	4590.84i	−0.254571	+	0.213611i	−0.761138	−	0.648590i	$-0.775359\pi$
$773$	−5471.15	+	4590.84i	−0.254571	+	0.213611i	0.506566	+	0.862201i	$0.330915\pi$
$774$	16810.1	−	6118.36i	0.780652	−	0.284134i
$775$	−14295.2	−	5203.04i	−0.662580	−	0.241159i
$776$	12028.1	+	10092.7i	0.556420	+	0.466892i
$777$	875.367	−	4964.45i	0.0404165	−	0.229213i
$778$	55401.0			2.55298
$779$	−1346.35	+	2272.00i	−0.0619229	+	0.104497i
$780$	2873.39			0.131902
$781$	−2316.07	+	13135.1i	−0.106115	+	0.601807i
$782$	25.1942	+	21.1405i	0.00115210	+	0.000966728i
$783$	2052.03	+	746.879i	0.0936573	+	0.0340885i
$784$	−31084.7	+	11313.9i	−1.41603	+	0.515392i
$785$	15315.8	−	12851.5i	0.696361	−	0.584317i
$786$	6.25813	+	10.8394i	0.000283995	+	0.000491894i
$787$	2634.37	−	4562.86i	0.119320	−	0.206669i	−0.800178	−	0.599762i	$-0.795262\pi$
$787$	2634.37	−	4562.86i	0.119320	−	0.206669i	0.919499	+	0.393093i	$0.128595\pi$
$788$	−1673.20	−	9489.20i	−0.0756413	−	0.428983i
$789$	−367.640	−	2084.99i	−0.0165885	−	0.0940781i
$790$	−12798.0	+	22166.7i	−0.576368	+	0.998299i
$791$	−31331.0	−	54266.9i	−1.40835	−	2.43933i
$792$	−42543.5	+	35698.3i	−1.90874	+	1.60162i
$793$	444.659	−	161.843i	0.0199121	−	0.00724741i
$794$	7883.61	+	2869.40i	0.352366	+	0.128251i
$795$	−113.972	−	95.6342i	−0.00508451	−	0.00426641i
$796$	−3104.63	+	17607.3i	−0.138242	+	0.784011i
$797$	25762.7			1.14500			0.572498	−	0.819906i	$-0.305974\pi$
$797$	25762.7			1.14500			0.572498	+	0.819906i	$0.305974\pi$
$798$	−1309.86	+	6965.41i	−0.0581060	+	0.308988i
$799$	30.1584			0.00133533
$800$	51.1880	−	290.302i	0.00226221	−	0.0128296i
$801$	−23867.7	−	20027.4i	−1.05284	−	0.883436i
$802$	−42440.8	−	15447.2i	−1.86863	−	0.680124i
$803$	−40121.7	+	14603.1i	−1.76322	+	0.641759i
$804$	2620.95	−	2199.23i	0.114967	−	0.0964689i
$805$	−4523.11	−	7834.26i	−0.198036	−	0.343008i
$806$	21448.1	−	37149.1i	0.937315	−	1.62348i
$807$	−470.864	−	2670.40i	−0.0205393	−	0.116484i
$808$	2365.97	+	13418.1i	0.103013	+	0.584216i
$809$	−740.433	+	1282.47i	−0.0321783	+	0.0557344i	−0.881666	−	0.471874i	$-0.843578\pi$
$809$	−740.433	+	1282.47i	−0.0321783	+	0.0557344i	0.849488	+	0.527608i	$0.176911\pi$
$810$	−12690.9	−	21981.3i	−0.550511	−	0.953513i
$811$	−27059.9	+	22705.9i	−1.17164	+	0.983124i	−0.999998	−	0.00203518i	$-0.999352\pi$
$811$	−27059.9	+	22705.9i	−1.17164	+	0.983124i	−0.171644	+	0.985159i	$0.554908\pi$
$812$	29905.5	−	10884.7i	1.29246	−	0.470417i
$813$	1568.05	+	570.725i	0.0676434	+	0.0246202i
$814$	−57285.7	−	48068.4i	−2.46666	−	2.06978i
$815$	2381.05	−	13503.6i	0.102337	−	0.580382i
$816$	−6.24200			−0.000267786
$817$	−5557.58	−	9883.36i	−0.237987	−	0.423225i
$818$	52992.2			2.26507
$819$	−5455.02	+	30937.0i	−0.232740	+	1.31993i
$820$	2898.82	+	2432.40i	0.123453	+	0.103589i
$821$	25174.3	+	9162.69i	1.07014	+	0.389501i	0.816230	−	0.577726i	$-0.196060\pi$
$821$	25174.3	+	9162.69i	1.07014	+	0.389501i	0.253913	+	0.967227i	$0.418282\pi$
$822$	−2425.19	+	882.698i	−0.102906	+	0.0374545i
$823$	−18047.9	+	15144.0i	−0.764413	+	0.641418i	−0.939271	−	0.343175i	$-0.888498\pi$
$823$	−18047.9	+	15144.0i	−0.764413	+	0.641418i	0.174859	+	0.984594i	$0.444053\pi$
$824$	16277.2	+	28192.9i	0.688159	+	1.19193i
$825$	−1111.38	+	1924.97i	−0.0469010	+	0.0812349i
$826$	7224.59	+	40972.7i	0.304329	+	1.72594i
$827$	2209.39	+	12530.1i	0.0928997	+	0.526860i	0.995371	+	0.0961097i	$0.0306400\pi$
$827$	2209.39	+	12530.1i	0.0928997	+	0.526860i	−0.902471	+	0.430750i	$0.858249\pi$
$828$	8977.29	−	15549.1i	0.376790	−	0.652620i
$829$	11425.4	+	19789.4i	0.478675	+	0.829089i	0.999701	−	0.0244514i	$-0.00778390\pi$
$829$	11425.4	+	19789.4i	0.478675	+	0.829089i	−0.521026	+	0.853541i	$0.674451\pi$
$830$	−33822.0	+	28380.0i	−1.41443	+	1.18685i
$831$	−804.914	+	292.965i	−0.0336007	+	0.0122296i
$832$	−19069.8	−	6940.83i	−0.794622	−	0.289219i
$833$	−62.0073	−	52.0303i	−0.00257914	−	0.00216416i
$834$	−1003.66	+	5692.04i	−0.0416713	+	0.236330i
$835$	−6572.95			−0.272415
$836$	53238.4	+	45711.8i	2.20250	+	1.89112i
$837$	6942.97			0.286719
$838$	13056.2	−	74045.3i	0.538208	−	3.05233i
$839$	5552.00	+	4658.68i	0.228458	+	0.191699i	0.749830	−	0.661630i	$-0.230135\pi$
$839$	5552.00	+	4658.68i	0.228458	+	0.191699i	−0.521372	+	0.853329i	$0.674580\pi$
$840$	4787.31	+	1742.44i	0.196640	+	0.0715713i
$841$	18572.0	−	6759.64i	0.761490	−	0.277160i
$842$	618.090	−	518.639i	0.0252979	−	0.0212274i
$843$	−2539.50	−	4398.54i	−0.103754	−	0.179708i
$844$	6999.62	−	12123.7i	0.285470	−	0.494449i
$845$	719.818	+	4082.29i	0.0293047	+	0.166195i
$846$	−4283.69	−	24294.0i	−0.174085	−	0.987288i
$847$	21201.4	−	36721.9i	0.860082	−	1.48971i
$848$	−1097.46	−	1900.85i	−0.0444420	−	0.0769758i
$849$	−3092.84	+	2595.20i	−0.125025	+	0.104908i
$850$	51.7938	−	18.8514i	0.00209001	−	0.000760703i
$851$	11396.8	+	4148.08i	0.459079	+	0.167091i
$852$	1860.25	+	1560.93i	0.0748017	+	0.0627661i
$853$	6179.49	−	35045.6i	0.248044	−	1.40673i	−0.565271	−	0.824905i	$-0.691229\pi$
$853$	6179.49	−	35045.6i	0.248044	−	1.40673i	0.813315	−	0.581823i	$-0.197660\pi$
$854$	1672.42			0.0670130
$855$	−12612.7	+	10341.7i	−0.504498	+	0.413659i
$856$	13156.5			0.525327
$857$	6165.17	−	34964.4i	0.245739	−	1.39365i	−0.573032	−	0.819533i	$-0.694233\pi$
$857$	6165.17	−	34964.4i	0.245739	−	1.39365i	0.818771	−	0.574121i	$-0.194656\pi$
$858$	−4801.32	−	4028.78i	−0.191042	−	0.160303i
$859$	−25869.5	−	9415.74i	−1.02754	−	0.373994i	−0.227397	−	0.973802i	$-0.573021\pi$
$859$	−25869.5	−	9415.74i	−1.02754	−	0.373994i	−0.800144	+	0.599808i	$0.795244\pi$
$860$	−15267.1	+	5556.78i	−0.605354	+	0.220331i
$861$	426.247	−	357.663i	0.0168716	−	0.0141570i
$862$	31594.9	+	54724.0i	1.24841	+	2.16231i
$863$	−13821.9	+	23940.2i	−0.545195	+	0.944305i	0.453400	+	0.891307i	$0.350211\pi$
$863$	−13821.9	+	23940.2i	−0.545195	+	0.944305i	−0.998595	+	0.0529979i	$0.983122\pi$
$864$	23.3619	+	132.492i	0.000919893	+	0.00521697i
$865$	−4471.82	−	25361.0i	−0.175776	−	0.996877i
$866$	−25968.3	+	44978.4i	−1.01898	+	1.76493i
$867$	1470.45	+	2546.89i	0.0575997	+	0.0997656i
$868$	77511.5	−	65039.8i	3.03100	−	2.54331i
$869$	35015.3	−	12744.5i	1.36687	−	0.497501i
$870$	−1386.89	−	504.787i	−0.0540460	−	0.0196711i
$871$	−11032.8	−	9257.60i	−0.429198	−	0.360140i
$872$	10083.9	−	57188.5i	0.391609	−	2.22092i
$873$	10591.2			0.410607
$874$	−15956.2	−	6013.50i	−0.617535	−	0.232734i
$875$	−42096.0			−1.62640
$876$	−1349.89	+	7655.61i	−0.0520646	+	0.295273i
$877$	−23394.5	−	19630.3i	−0.900770	−	0.755836i	0.0695706	−	0.997577i	$-0.477837\pi$
$877$	−23394.5	−	19630.3i	−0.900770	−	0.755836i	−0.970341	+	0.241741i	$0.922282\pi$
$878$	69480.5	+	25288.8i	2.67067	+	0.972046i
$879$	4489.31	−	1633.97i	0.172265	−	0.0626992i
$880$	19510.6	−	16371.3i	0.747388	−	0.627133i
$881$	4483.15	+	7765.04i	0.171443	+	0.296948i	0.938925	−	0.344123i	$-0.111824\pi$
$881$	4483.15	+	7765.04i	0.171443	+	0.296948i	−0.767482	+	0.641071i	$0.778490\pi$
$882$	−33105.4	+	57340.2i	−1.26385	+	2.18905i
$883$	2935.50	+	16648.0i	0.111877	+	0.634486i	0.988249	+	0.152851i	$0.0488456\pi$
$883$	2935.50	+	16648.0i	0.111877	+	0.634486i	−0.876372	+	0.481635i	$0.840043\pi$
$884$	18.0121	+	102.152i	0.000685308	+	0.00388657i
$885$	643.863	−	1115.20i	0.0244556	−	0.0423584i
$886$	−889.348	−	1540.40i	−0.0337226	−	0.0584093i
$887$	25811.5	−	21658.4i	0.977075	−	0.819863i	−0.00657087	−	0.999978i	$-0.502092\pi$
$887$	25811.5	−	21658.4i	0.977075	−	0.819863i	0.983645	+	0.180115i	$0.0576471\pi$
$888$	−6418.31	+	2336.07i	−0.242550	+	0.0882809i
$889$	−20776.7	−	7562.09i	−0.783832	−	0.285292i
$890$	32479.5	+	27253.5i	1.22328	+	1.02645i
$891$	−6416.45	+	36389.5i	−0.241256	+	1.36823i
$892$	−73607.2			−2.76295
$893$	−14752.9	+	5180.79i	−0.552842	+	0.194142i
$894$	−4419.44			−0.165334
$895$	133.521	−	757.237i	0.00498673	−	0.0282812i
$896$	−55692.3	−	46731.4i	−2.07651	−	1.74240i
$897$	955.202	+	347.665i	0.0355555	+	0.0129411i
$898$	−58003.1	+	21111.4i	−2.15544	+	0.784517i
$899$	−11264.8	+	9452.30i	−0.417912	+	0.350669i
$900$	−15044.9	−	26058.6i	−0.557220	−	0.965133i
$901$	2.68544	−	4.65132i	9.92953e−5	−	0.000171984i
$902$	−1433.34	−	8128.89i	−0.0529103	−	0.300069i
$903$	414.841	+	2352.68i	0.0152880	+	0.0867024i
$904$	−42451.1	+	73527.5i	−1.56184	+	2.70518i
$905$	4077.27	+	7062.03i	0.149760	+	0.259392i
$906$	5385.54	−	4519.01i	0.197486	−	0.165711i
$907$	40322.1	−	14676.1i	1.47616	−	0.537277i	0.526392	−	0.850242i	$-0.323544\pi$
$907$	40322.1	−	14676.1i	1.47616	−	0.537277i	0.949765	+	0.312965i	$0.101322\pi$
$908$	−36875.4	−	13421.6i	−1.34775	−	0.490540i
$909$	7040.42	+	5907.61i	0.256893	+	0.215559i
$910$	7423.28	−	42099.5i	0.270417	−	1.53361i
$911$	11606.2			0.422097			0.211048	−	0.977476i	$-0.432312\pi$
$911$	11606.2			0.422097			0.211048	+	0.977476i	$0.432312\pi$
$912$	3053.47	−	1072.29i	0.110867	−	0.0389331i
$913$	64275.7			2.32992
$914$	−16368.6	+	92831.0i	−0.592369	+	3.35949i
$915$	−39.6534	−	33.2731i	−0.00143268	−	0.00120216i
$916$	−3398.86	−	1237.08i	−0.122600	−	0.0446227i
$917$	116.783	−	42.5056i	0.00420559	−	0.00153071i
$918$	−19.2702	+	16.1696i	−0.000692822	+	0.000581347i
$919$	−11281.4	−	19539.9i	−0.404938	−	0.701373i	0.589376	−	0.807859i	$-0.299374\pi$
$919$	−11281.4	−	19539.9i	−0.404938	−	0.701373i	−0.994314	+	0.106485i	$0.966040\pi$
$920$	−6128.46	+	10614.8i	−0.219619	+	0.380391i
$921$	425.908	+	2415.44i	0.0152379	+	0.0864186i
$922$	−5403.07	−	30642.3i	−0.192994	−	1.09452i
$923$	5111.09	−	8852.66i	0.182268	−	0.315698i
$924$	−7392.14	−	12803.6i	−0.263186	−	0.455851i
$925$	15570.2	−	13065.0i	0.553455	−	0.464404i
$926$	24570.2	−	8942.81i	0.871951	−	0.317364i
$927$	20634.8	+	7510.47i	0.731108	+	0.266102i
$928$	−218.281	−	183.160i	−0.00772138	−	0.00647900i
$929$	−7163.93	+	40628.7i	−0.253004	+	1.43486i	0.548139	+	0.836387i	$0.315336\pi$
$929$	−7163.93	+	40628.7i	−0.253004	+	1.43486i	−0.801144	+	0.598472i	$0.795775\pi$
$930$	−4692.49			−0.165455
$931$	39270.9	+	14800.3i	1.38244	+	0.521008i
$932$	−19785.3			−0.695375
$933$	903.001	−	5121.17i	0.0316859	−	0.179700i
$934$	21819.9	+	18309.1i	0.764421	+	0.641426i
$935$	58.5640	+	21.3155i	0.00204839	+	0.000745554i
$936$	39996.9	−	14557.7i	1.39673	−	0.508369i
$937$	−37364.5	+	31352.5i	−1.30271	+	1.09311i	−0.313045	+	0.949738i	$0.601349\pi$
$937$	−37364.5	+	31352.5i	−1.30271	+	1.09311i	−0.989669	+	0.143369i	$0.954206\pi$
$938$	−25451.0	−	44082.5i	−0.885934	−	1.53448i
$939$	−1999.38	+	3463.03i	−0.0694859	+	0.120353i
$940$	3890.51	+	22064.2i	0.134994	+	0.765589i
$941$	592.705	+	3361.39i	0.0205331	+	0.116449i	0.993352	−	0.115120i	$-0.0367253\pi$
$941$	592.705	+	3361.39i	0.0205331	+	0.116449i	−0.972819	+	0.231569i	$0.925614\pi$
$942$	−3970.11	+	6876.43i	−0.137318	+	0.237841i
$943$	669.349	+	1159.35i	0.0231145	+	0.0400355i
$944$	14552.9	−	12211.3i	0.501755	−	0.421022i
$945$	6501.87	−	2366.49i	0.223816	−	0.0814622i
$946$	33301.9	+	12120.9i	1.14454	+	0.416580i
$947$	−36827.9	−	30902.3i	−1.26372	−	1.06039i	−0.995275	−	0.0970969i	$-0.969044\pi$
$947$	−36827.9	−	30902.3i	−1.26372	−	1.06039i	−0.268449	−	0.963294i	$-0.586511\pi$
$948$	1178.09	−	6681.25i	0.0403612	−	0.228900i
$949$	32723.2			1.11932
$950$	−22098.2	+	18119.2i	−0.754693	+	0.618805i
$951$	−6151.29			−0.209747
$952$	−31.9357	+	181.116i	−0.00108723	+	0.00616598i
$953$	−16480.5	−	13828.8i	−0.560184	−	0.470050i	0.318188	−	0.948028i	$-0.396926\pi$
$953$	−16480.5	−	13828.8i	−0.560184	−	0.470050i	−0.878372	+	0.477978i	$0.841370\pi$
$954$	−4128.30	−	1502.58i	−0.140103	−	0.0509935i
$955$	15809.8	−	5754.29i	0.535699	−	0.194978i
$956$	29358.9	−	24635.1i	0.993238	−	0.833425i
$957$	1074.31	+	1860.75i	0.0362878	+	0.0628522i
$958$	−19219.8	+	33289.7i	−0.648189	+	1.12270i
$959$	4449.91	+	25236.7i	0.149838	+	0.849776i
$960$	385.492	+	2186.23i	0.0129601	+	0.0735004i
$961$	−8481.40	+	14690.2i	−0.284697	+	0.493109i
$962$	28656.5	+	49634.6i	0.960420	+	1.66350i
$963$	6798.29	−	5704.44i	0.227489	−	0.190886i
$964$	23052.3	−	8390.35i	0.770191	−	0.280327i
$965$	−4027.95	−	1466.05i	−0.134367	−	0.0489056i
$966$	2752.13	+	2309.31i	0.0916648	+	0.0769159i
$967$	−7269.67	+	41228.4i	−0.241755	+	1.37106i	0.586155	+	0.810199i	$0.300641\pi$
$967$	−7269.67	+	41228.4i	−0.241755	+	1.37106i	−0.827910	+	0.560861i	$0.810470\pi$
$968$	−57452.6			−1.90764
$969$	6.00819	+	5.15879i	0.000199186	+	0.000171026i
$970$	−14412.7			−0.477077
$971$	6597.37	−	37415.5i	0.218043	−	1.23658i	−0.657505	−	0.753450i	$-0.728388\pi$
$971$	6597.37	−	37415.5i	0.218043	−	1.23658i	0.875548	−	0.483132i	$-0.160501\pi$
$972$	15815.1	+	13270.4i	0.521882	+	0.437911i
$973$	53929.0	+	19628.6i	1.77686	+	0.646724i
$974$	−4180.80	+	1521.69i	−0.137537	+	0.0500595i
$975$	1304.99	−	1095.02i	0.0428649	−	0.0359679i
$976$	−381.828	−	661.346i	−0.0125226	−	0.0216897i
$977$	17478.5	−	30273.6i	0.572350	−	0.991339i	−0.423974	−	0.905674i	$-0.639365\pi$
$977$	17478.5	−	30273.6i	0.572350	−	0.991339i	0.996324	−	0.0856649i	$-0.0273015\pi$
$978$	945.618	+	5362.87i	0.0309177	+	0.175343i
$979$	−10718.3	−	60786.6i	−0.349907	−	1.98442i
$980$	30066.7	−	52077.1i	0.980047	−	1.69749i
$981$	−19585.4	−	33922.9i	−0.637425	−	1.10405i
$982$	−45917.8	+	38529.6i	−1.49215	+	1.25207i
$983$	−43607.8	+	15871.9i	−1.41493	+	0.514991i	−0.932571	−	0.360986i	$-0.882440\pi$
$983$	−43607.8	+	15871.9i	−1.41493	+	0.514991i	−0.482354	+	0.875976i	$0.660218\pi$
$984$	−708.447	−	257.854i	−0.0229517	−	0.00835373i
$985$	3398.94	+	2852.05i	0.109949	+	0.0922578i
$986$	9.25182	−	52.4697i	0.000298821	−	0.00169470i
$987$	3294.39			0.106243
$988$	−26359.4	−	46876.5i	−0.848790	−	1.50945i
$989$	−5747.60			−0.184796
$990$	8852.27	−	50203.7i	0.284185	−	1.61170i
$991$	8935.82	+	7498.04i	0.286434	+	0.240346i	0.774671	−	0.632365i	$-0.217916\pi$
$991$	8935.82	+	7498.04i	0.286434	+	0.240346i	−0.488237	+	0.872711i	$0.662360\pi$
$992$	−851.325	−	309.857i	−0.0272476	−	0.00991730i
$993$	975.695	−	355.124i	0.0311810	−	0.0113490i
$994$	27675.9	−	23222.9i	0.883126	−	0.741031i
$995$	−4116.44	−	7129.89i	−0.131156	−	0.227169i
$996$	5851.29	−	10134.7i	0.186150	−	0.322421i
$997$	−877.467	−	4976.36i	−0.0278733	−	0.158077i	0.967694	−	0.252127i	$-0.0811299\pi$
$997$	−877.467	−	4976.36i	−0.0278733	−	0.158077i	−0.995568	+	0.0940494i	$0.970019\pi$
$998$	−14925.3	−	84645.4i	−0.473398	−	2.68477i
$999$	−4638.22	+	8033.63i	−0.146894	+	0.254427i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.4.e.a.17.1	yes	24
3.2	odd	2		171.4.u.b.55.4		24
19.3	odd	18		361.4.a.m.1.12		12
19.9	even	9	inner	19.4.e.a.9.1	✓	24
19.16	even	9		361.4.a.n.1.1		12
57.47	odd	18		171.4.u.b.28.4		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.4.e.a.9.1	✓	24	19.9	even	9	inner
19.4.e.a.17.1	yes	24	1.1	even	1	trivial
171.4.u.b.28.4		24	57.47	odd	18
171.4.u.b.55.4		24	3.2	odd	2
361.4.a.m.1.12		12	19.3	odd	18
361.4.a.n.1.1		12	19.16	even	9

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:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	19.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.851642 + 4.82990i) q^{2} +(0.458552 + 0.384771i) q^{3} +(-15.0851 - 5.49052i) q^{4} +(6.94640 - 2.52828i) q^{5} +(-2.24893 + 1.88707i) q^{6} +(14.5751 + 25.2448i) q^{7} +(19.7481 - 34.2048i) q^{8} +(-4.62628 - 26.2369i) q^{9} +(6.29551 + 35.7036i) q^{10} +(26.3895 - 45.7080i) q^{11} +(-4.80470 - 8.32199i) q^{12} +(-30.9868 + 26.0010i) q^{13} +(-134.343 + 48.8967i) q^{14} +(4.15809 + 1.51342i) q^{15} +(50.0074 + 41.9612i) q^{16} +(-0.0277382 + 0.157311i) q^{17} +130.662 q^{18} +(-13.4549 - 81.7188i) q^{19} -118.669 q^{20} +(-3.03002 + 17.1841i) q^{21} +(198.291 + 166.386i) q^{22} +(-39.4491 - 14.3583i) q^{23} +(22.2165 - 8.08616i) q^{24} +(-53.8953 + 45.2235i) q^{25} +(-99.1927 - 171.807i) q^{26} +(16.0549 - 27.8079i) q^{27} +(-81.2594 - 460.845i) q^{28} +(11.8095 + 66.9751i) q^{29} +(-10.8509 + 18.7943i) q^{30} +(108.113 + 187.257i) q^{31} +(-3.20963 + 2.69320i) q^{32} +(29.6881 - 10.8056i) q^{33} +(-0.736175 - 0.267946i) q^{34} +(165.071 + 138.511i) q^{35} +(-74.2667 + 421.187i) q^{36} -288.898 q^{37} +(406.152 + 4.60942i) q^{38} -24.2135 q^{39} +(50.6991 - 287.529i) q^{40} +(-24.4278 - 20.4974i) q^{41} +(-80.4171 - 29.2694i) q^{42} +(128.653 - 46.8260i) q^{43} +(-649.050 + 544.617i) q^{44} +(-98.4704 - 170.556i) q^{45} +(102.946 - 178.307i) q^{46} +(-32.7846 - 185.931i) q^{47} +(6.78555 + 38.4828i) q^{48} +(-253.367 + 438.844i) q^{49} +(-172.526 - 298.823i) q^{50} +(-0.0732482 + 0.0614625i) q^{51} +(610.199 - 222.094i) q^{52} +(-31.5953 - 11.4998i) q^{53} +(120.636 + 101.226i) q^{54} +(67.7495 - 384.227i) q^{55} +1151.32 q^{56} +(25.2732 - 42.6494i) q^{57} -333.540 q^{58} +(50.5342 - 286.594i) q^{59} +(-54.4157 - 45.6602i) q^{60} +(-10.9927 - 4.00101i) q^{61} +(-996.508 + 362.699i) q^{62} +(594.918 - 499.195i) q^{63} +(250.846 + 434.478i) q^{64} +(-149.509 + 258.957i) q^{65} +(26.9063 + 152.593i) q^{66} +(61.8269 + 350.638i) q^{67} +(1.28216 - 2.22076i) q^{68} +(-12.5648 - 21.7629i) q^{69} +(-809.573 + 679.313i) q^{70} +(-237.468 + 86.4315i) q^{71} +(-988.789 - 359.890i) q^{72} +(-619.706 - 519.995i) q^{73} +(246.037 - 1395.35i) q^{74} -42.1145 q^{75} +(-245.711 + 1306.61i) q^{76} +1538.52 q^{77} +(20.6212 - 116.949i) q^{78} +(540.834 + 453.814i) q^{79} +(453.461 + 165.046i) q^{80} +(-657.883 + 239.450i) q^{81} +(119.804 - 100.528i) q^{82} +(608.912 + 1054.67i) q^{83} +(140.058 - 242.588i) q^{84} +(0.205047 + 1.16288i) q^{85} +(116.598 + 661.261i) q^{86} +(-20.3548 + 35.2555i) q^{87} +(-1042.29 - 1805.30i) q^{88} +(895.877 - 751.730i) q^{89} +(907.628 - 330.350i) q^{90} +(-1108.03 - 403.289i) q^{91} +(516.259 + 433.193i) q^{92} +(-22.4757 + 127.466i) q^{93} +925.947 q^{94} +(-300.071 - 533.634i) q^{95} -2.50805 q^{96} +(-69.0328 + 391.505i) q^{97} +(-1903.80 - 1597.48i) q^{98} +(-1321.32 - 480.923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{2} - 3 q^{3} - 24 q^{4} - 6 q^{5} + 42 q^{6} + 3 q^{7} - 75 q^{8} - 51 q^{9} + 75 q^{10} + 39 q^{11} - 219 q^{12} - 156 q^{13} + 93 q^{14} - 192 q^{15} + 504 q^{16} + 12 q^{17} + 264 q^{18}+ \cdots + 492 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 - 3 * q^3 - 24 * q^4 - 6 * q^5 + 42 * q^6 + 3 * q^7 - 75 * q^8 - 51 * q^9 + 75 * q^10 + 39 * q^11 - 219 * q^12 - 156 * q^13 + 93 * q^14 - 192 * q^15 + 504 * q^16 + 12 * q^17 + 264 * q^18 + 546 * q^19 - 198 * q^20 + 453 * q^21 - 6 * q^22 + 6 * q^23 + 192 * q^24 - 498 * q^25 - 639 * q^26 - 870 * q^27 - 1368 * q^28 - 630 * q^29 - 522 * q^30 - 591 * q^31 + 147 * q^32 + 1506 * q^33 - 408 * q^34 + 2001 * q^35 + 1059 * q^36 - 72 * q^37 + 2934 * q^38 + 336 * q^39 + 2886 * q^40 - 477 * q^41 + 237 * q^42 + 588 * q^43 - 3423 * q^44 - 1569 * q^45 - 1728 * q^46 - 1242 * q^47 - 4599 * q^48 - 639 * q^49 - 1788 * q^50 + 9 * q^51 + 2733 * q^52 - 300 * q^53 + 3777 * q^54 + 315 * q^55 + 4638 * q^56 + 3342 * q^57 - 2820 * q^58 + 2097 * q^59 + 1116 * q^60 - 2316 * q^61 - 1320 * q^62 - 2979 * q^63 - 1785 * q^64 - 2433 * q^65 - 1590 * q^66 + 57 * q^67 - 438 * q^68 - 1767 * q^69 - 213 * q^70 - 792 * q^71 - 1686 * q^72 + 4068 * q^73 + 4287 * q^74 + 1332 * q^75 + 5538 * q^76 + 3786 * q^77 + 2121 * q^78 + 1824 * q^79 - 2739 * q^80 + 1536 * q^81 + 2205 * q^82 + 1071 * q^83 - 1437 * q^84 - 2394 * q^85 - 5256 * q^86 + 759 * q^87 + 1101 * q^88 - 3006 * q^89 - 3822 * q^90 - 3285 * q^91 - 1452 * q^92 - 135 * q^93 - 1086 * q^94 - 3078 * q^95 - 1590 * q^96 - 2535 * q^97 - 2403 * q^98 + 492 * q^99

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