LMFDB - Embedded newform 143.4.e.b.100.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [143,4,Mod(100,143)] 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("143.100"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(143, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 4])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	143.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [34,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$8.43727313082$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.14
Character	$\chi$	$=$	143.100
Dual form			143.4.e.b.133.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.58752 - 2.74967i) q^{2} +(0.300230 - 0.520013i) q^{3} +(-1.04047 - 1.80214i) q^{4} +12.4679 q^{5} +(-0.953244 - 1.65107i) q^{6} +(-5.31270 - 9.20186i) q^{7} +18.7933 q^{8} +(13.3197 + 23.0704i) q^{9} +(19.7931 - 34.2827i) q^{10} +(-5.50000 + 9.52628i) q^{11} -1.24952 q^{12} +(19.1701 - 42.7727i) q^{13} -33.7362 q^{14} +(3.74324 - 6.48348i) q^{15} +(38.1586 - 66.0926i) q^{16} +(31.4971 + 54.5545i) q^{17} +84.5816 q^{18} +(-70.2277 - 121.638i) q^{19} +(-12.9725 - 22.4690i) q^{20} -6.38012 q^{21} +(17.4628 + 30.2464i) q^{22} +(-34.6465 + 60.0095i) q^{23} +(5.64231 - 9.77277i) q^{24} +30.4490 q^{25} +(-87.1780 - 120.614i) q^{26} +32.2083 q^{27} +(-11.0554 + 19.1485i) q^{28} +(69.1320 - 119.740i) q^{29} +(-11.8850 - 20.5854i) q^{30} -168.325 q^{31} +(-45.9821 - 79.6434i) q^{32} +(3.30253 + 5.72014i) q^{33} +200.010 q^{34} +(-66.2383 - 114.728i) q^{35} +(27.7175 - 48.0081i) q^{36} +(-118.309 + 204.917i) q^{37} -445.953 q^{38} +(-16.4869 - 22.8103i) q^{39} +234.314 q^{40} +(-103.798 + 179.784i) q^{41} +(-10.1286 + 17.5432i) q^{42} +(150.904 + 261.373i) q^{43} +22.8903 q^{44} +(166.069 + 287.640i) q^{45} +(110.004 + 190.533i) q^{46} -343.732 q^{47} +(-22.9127 - 39.6859i) q^{48} +(115.050 - 199.273i) q^{49} +(48.3385 - 83.7248i) q^{50} +37.8254 q^{51} +(-97.0285 + 9.95637i) q^{52} +306.658 q^{53} +(51.1315 - 88.5623i) q^{54} +(-68.5736 + 118.773i) q^{55} +(-99.8432 - 172.934i) q^{56} -84.3378 q^{57} +(-219.498 - 380.181i) q^{58} +(133.191 + 230.693i) q^{59} -15.5789 q^{60} +(366.947 + 635.571i) q^{61} +(-267.220 + 462.839i) q^{62} +(141.527 - 245.133i) q^{63} +318.546 q^{64} +(239.011 - 533.287i) q^{65} +20.9714 q^{66} +(90.3342 - 156.463i) q^{67} +(65.5434 - 113.524i) q^{68} +(20.8038 + 36.0333i) q^{69} -420.620 q^{70} +(109.224 + 189.181i) q^{71} +(250.322 + 433.570i) q^{72} -817.244 q^{73} +(375.636 + 650.621i) q^{74} +(9.14169 - 15.8339i) q^{75} +(-146.139 + 253.121i) q^{76} +116.879 q^{77} +(-88.8944 + 9.12171i) q^{78} -289.899 q^{79} +(475.758 - 824.037i) q^{80} +(-349.963 + 606.153i) q^{81} +(329.564 + 570.822i) q^{82} -971.055 q^{83} +(6.63831 + 11.4979i) q^{84} +(392.703 + 680.182i) q^{85} +958.254 q^{86} +(-41.5109 - 71.8991i) q^{87} +(-103.363 + 179.030i) q^{88} +(-702.868 + 1217.40i) q^{89} +1054.56 q^{90} +(-495.434 + 50.8379i) q^{91} +144.194 q^{92} +(-50.5362 + 87.5313i) q^{93} +(-545.682 + 945.149i) q^{94} +(-875.594 - 1516.57i) q^{95} -55.2208 q^{96} +(-860.186 - 1489.89i) q^{97} +(-365.291 - 632.702i) q^{98} -293.034 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9} - 2 q^{10} - 187 q^{11} - 254 q^{12} + 76 q^{13} + 148 q^{15} - 126 q^{16} + 74 q^{17} + 180 q^{18} + 159 q^{19} + 222 q^{20}+ \cdots + 2970 q^{99}+O(q^{100}) $ 34 * q + 6 * q^3 - 50 * q^4 - 48 * q^5 - 16 * q^6 + 62 * q^7 - 42 * q^8 - 135 * q^9 - 2 * q^10 - 187 * q^11 - 254 * q^12 + 76 * q^13 + 148 * q^15 - 126 * q^16 + 74 * q^17 + 180 * q^18 + 159 * q^19 + 222 * q^20 - 368 * q^21 + 215 * q^23 - 214 * q^24 + 190 * q^25 + 123 * q^26 - 384 * q^27 + 358 * q^28 + 157 * q^29 - 829 * q^30 - 788 * q^31 + 553 * q^32 + 66 * q^33 - 1404 * q^34 - 58 * q^35 + 700 * q^36 - 88 * q^37 - 2636 * q^38 + 798 * q^39 + 1466 * q^40 + 512 * q^41 - 337 * q^42 - 927 * q^43 + 1100 * q^44 + 1482 * q^45 + 1361 * q^46 - 286 * q^47 + 178 * q^48 - 1835 * q^49 + 583 * q^50 - 1136 * q^51 + 2306 * q^52 + 212 * q^53 + 67 * q^54 + 264 * q^55 - 2059 * q^56 + 2596 * q^57 + 1690 * q^58 + 266 * q^59 + 74 * q^60 + 624 * q^61 - 643 * q^62 + 2360 * q^63 - 3178 * q^64 + 470 * q^65 + 352 * q^66 + 676 * q^67 + 413 * q^68 - 764 * q^69 - 2122 * q^70 + 763 * q^71 + 1366 * q^72 - 4748 * q^73 + 1649 * q^74 - 2420 * q^75 + 2101 * q^76 - 1364 * q^77 - 5848 * q^78 + 4328 * q^79 + 1013 * q^80 - 537 * q^81 - 3152 * q^82 + 1554 * q^83 + 3381 * q^84 + 1690 * q^85 + 5788 * q^86 + 4200 * q^87 + 231 * q^88 + 1687 * q^89 - 10798 * q^90 - 3380 * q^91 + 11084 * q^92 + 4310 * q^93 - 1777 * q^94 - 1124 * q^95 - 6930 * q^96 + 2047 * q^97 - 1553 * q^98 + 2970 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	1.58752	−	2.74967i	0.561275	−	0.972156i	−0.436111	−	0.899893i	$-0.643644\pi$
$2$	1.58752	−	2.74967i	0.561275	−	0.972156i	0.997386	−	0.0722633i	$-0.0230222\pi$
$3$	0.300230	−	0.520013i	0.0577792	−	0.100077i	−0.835689	−	0.549203i	$-0.814931\pi$
$3$	0.300230	−	0.520013i	0.0577792	−	0.100077i	0.893468	+	0.449126i	$0.148265\pi$
$4$	−1.04047	−	1.80214i	−0.130058	−	0.225268i
$5$	12.4679			1.11516			0.557582	−	0.830122i	$-0.311729\pi$
$5$	12.4679			1.11516			0.557582	+	0.830122i	$0.311729\pi$
$6$	−0.953244	−	1.65107i	−0.0648600	−	0.112341i
$7$	−5.31270	−	9.20186i	−0.286859	−	0.496854i	0.686200	−	0.727413i	$-0.259278\pi$
$7$	−5.31270	−	9.20186i	−0.286859	−	0.496854i	−0.973058	+	0.230560i	$0.925944\pi$
$8$	18.7933			0.830555
$9$	13.3197	+	23.0704i	0.493323	+	0.854461i
$10$	19.7931	−	34.2827i	0.625914	−	1.08411i
$11$	−5.50000	+	9.52628i	−0.150756	+	0.261116i
$11$	−5.50000	+	9.52628i	−0.150756	+	0.261116i
$12$	−1.24952			−0.0300587
$13$	19.1701	−	42.7727i	0.408987	−	0.912540i
$13$	19.1701	−	42.7727i	0.408987	−	0.912540i
$14$	−33.7362			−0.644026
$15$	3.74324	−	6.48348i	0.0644333	−	0.111602i
$16$	38.1586	−	66.0926i	0.596228	−	1.03270i
$17$	31.4971	+	54.5545i	0.449363	+	0.778319i	0.998345	−	0.0575153i	$-0.0183178\pi$
$17$	31.4971	+	54.5545i	0.449363	+	0.778319i	−0.548982	+	0.835834i	$0.684984\pi$
$18$	84.5816			1.10756
$19$	−70.2277	−	121.638i	−0.847966	−	1.46872i	−0.883021	−	0.469334i	$-0.844494\pi$
$19$	−70.2277	−	121.638i	−0.847966	−	1.46872i	0.0350548	−	0.999385i	$-0.488839\pi$
$20$	−12.9725	−	22.4690i	−0.145037	−	0.251211i
$21$	−6.38012			−0.0662979
$22$	17.4628	+	30.2464i	0.169231	+	0.293116i
$23$	−34.6465	+	60.0095i	−0.314100	+	0.544037i	−0.979246	−	0.202676i	$-0.935036\pi$
$23$	−34.6465	+	60.0095i	−0.314100	+	0.544037i	0.665146	+	0.746714i	$0.268369\pi$
$24$	5.64231	−	9.77277i	0.0479888	−	0.0831191i
$25$	30.4490			0.243592
$26$	−87.1780	−	120.614i	−0.657578	−	0.909785i
$27$	32.2083			0.229574
$28$	−11.0554	+	19.1485i	−0.0746168	+	0.129240i
$29$	69.1320	−	119.740i	0.442672	−	0.766731i	−0.555215	−	0.831707i	$-0.687364\pi$
$29$	69.1320	−	119.740i	0.442672	−	0.766731i	0.997887	+	0.0649765i	$0.0206972\pi$
$30$	−11.8850	−	20.5854i	−0.0723296	−	0.125279i
$31$	−168.325			−0.975229			−0.487614	−	0.873059i	$-0.662133\pi$
$31$	−168.325			−0.975229			−0.487614	+	0.873059i	$0.662133\pi$
$32$	−45.9821	−	79.6434i	−0.254018	−	0.439972i
$33$	3.30253	+	5.72014i	0.0174211	+	0.0301742i
$34$	200.010			1.00886
$35$	−66.2383	−	114.728i	−0.319895	−	0.554074i
$36$	27.7175	−	48.0081i	0.128322	−	0.222260i
$37$	−118.309	+	204.917i	−0.525672	+	0.910490i	0.473881	+	0.880589i	$0.342853\pi$
$37$	−118.309	+	204.917i	−0.525672	+	0.910490i	−0.999553	+	0.0299015i	$0.990481\pi$
$38$	−445.953			−1.90377
$39$	−16.4869	−	22.8103i	−0.0676929	−	0.0936559i
$40$	234.314			0.926206
$41$	−103.798	+	179.784i	−0.395379	+	0.684817i	−0.993149	−	0.116851i	$-0.962720\pi$
$41$	−103.798	+	179.784i	−0.395379	+	0.684817i	0.597770	+	0.801667i	$0.296053\pi$
$42$	−10.1286	+	17.5432i	−0.0372113	+	0.0644519i
$43$	150.904	+	261.373i	0.535177	+	0.926954i	0.999155	+	0.0411072i	$0.0130885\pi$
$43$	150.904	+	261.373i	0.535177	+	0.926954i	−0.463977	+	0.885847i	$0.653578\pi$
$44$	22.8903			0.0784282
$45$	166.069	+	287.640i	0.550136	+	0.952864i
$46$	110.004	+	190.533i	0.352593	+	0.610709i
$47$	−343.732			−1.06677			−0.533387	−	0.845871i	$-0.679081\pi$
$47$	−343.732			−1.06677			−0.533387	+	0.845871i	$0.679081\pi$
$48$	−22.9127	−	39.6859i	−0.0688992	−	0.119337i
$49$	115.050	−	199.273i	0.335424	−	0.580972i
$50$	48.3385	−	83.7248i	0.136722	−	0.236809i
$51$	37.8254			0.103855
$52$	−97.0285	+	9.95637i	−0.258758	+	0.0265519i
$53$	306.658			0.794769			0.397384	−	0.917652i	$-0.369918\pi$
$53$	306.658			0.794769			0.397384	+	0.917652i	$0.369918\pi$
$54$	51.1315	−	88.5623i	0.128854	−	0.223181i
$55$	−68.5736	+	118.773i	−0.168117	+	0.291188i
$56$	−99.8432	−	172.934i	−0.238252	−	0.412665i
$57$	−84.3378			−0.195979
$58$	−219.498	−	380.181i	−0.496921	−	0.860693i
$59$	133.191	+	230.693i	0.293898	+	0.509046i	0.974728	−	0.223395i	$-0.0717141\pi$
$59$	133.191	+	230.693i	0.293898	+	0.509046i	−0.680830	+	0.732441i	$0.738381\pi$
$60$	−15.5789			−0.0335204
$61$	366.947	+	635.571i	0.770209	+	1.33404i	0.937448	+	0.348125i	$0.113181\pi$
$61$	366.947	+	635.571i	0.770209	+	1.33404i	−0.167239	+	0.985916i	$0.553485\pi$
$62$	−267.220	+	462.839i	−0.547371	+	0.948075i
$63$	141.527	−	245.133i	0.283028	−	0.490219i
$64$	318.546			0.622161
$65$	239.011	−	533.287i	0.456088	−	1.01763i
$66$	20.9714			0.0391121
$67$	90.3342	−	156.463i	0.164718	−	0.285299i	−0.771837	−	0.635820i	$-0.780662\pi$
$67$	90.3342	−	156.463i	0.164718	−	0.285299i	0.936555	+	0.350521i	$0.113995\pi$
$68$	65.5434	−	113.524i	0.116887	−	0.202454i
$69$	20.8038	+	36.0333i	0.0362969	+	0.0628681i
$70$	−420.620			−0.718195
$71$	109.224	+	189.181i	0.182570	+	0.316220i	0.942755	−	0.333486i	$-0.108225\pi$
$71$	109.224	+	189.181i	0.182570	+	0.316220i	−0.760185	+	0.649706i	$0.774892\pi$
$72$	250.322	+	433.570i	0.409732	+	0.709677i
$73$	−817.244			−1.31029			−0.655145	−	0.755503i	$-0.727393\pi$
$73$	−817.244			−1.31029			−0.655145	+	0.755503i	$0.727393\pi$
$74$	375.636	+	650.621i	0.590093	+	1.02207i
$75$	9.14169	−	15.8339i	0.0140745	−	0.0243778i
$76$	−146.139	+	253.121i	−0.220570	+	0.382039i
$77$	116.879			0.172982
$78$	−88.8944	+	9.12171i	−0.129042	+	0.0132414i
$79$	−289.899			−0.412863			−0.206432	−	0.978461i	$-0.566185\pi$
$79$	−289.899			−0.412863			−0.206432	+	0.978461i	$0.566185\pi$
$80$	475.758	−	824.037i	0.664892	−	1.15163i
$81$	−349.963	+	606.153i	−0.480059	+	0.831486i
$82$	329.564	+	570.822i	0.443832	+	0.768740i
$83$	−971.055			−1.28418			−0.642091	−	0.766628i	$-0.721933\pi$
$83$	−971.055			−1.28418			−0.642091	+	0.766628i	$0.721933\pi$
$84$	6.63831	+	11.4979i	0.00862260	+	0.0149348i
$85$	392.703	+	680.182i	0.501113	+	0.867954i
$86$	958.254			1.20153
$87$	−41.5109	−	71.8991i	−0.0511545	−	0.0886022i
$88$	−103.363	+	179.030i	−0.125211	+	0.216872i
$89$	−702.868	+	1217.40i	−0.837122	+	1.44994i	0.0551683	+	0.998477i	$0.482430\pi$
$89$	−702.868	+	1217.40i	−0.837122	+	1.44994i	−0.892291	+	0.451461i	$0.850903\pi$
$90$	1054.56			1.23511
$91$	−495.434	+	50.8379i	−0.570721	+	0.0585633i
$92$	144.194			0.163405
$93$	−50.5362	+	87.5313i	−0.0563479	+	0.0975975i
$94$	−545.682	+	945.149i	−0.598753	+	1.03707i
$95$	−875.594	−	1516.57i	−0.945621	−	1.63786i
$96$	−55.2208			−0.0587078
$97$	−860.186	−	1489.89i	−0.900399	−	1.55954i	−0.826977	−	0.562235i	$-0.809942\pi$
$97$	−860.186	−	1489.89i	−0.900399	−	1.55954i	−0.0734213	−	0.997301i	$-0.523392\pi$
$98$	−365.291	−	632.702i	−0.376530	−	0.652169i
$99$	−293.034			−0.297485
$100$	−31.6812	−	54.8734i	−0.0316812	−	0.0548734i
$101$	855.612	−	1481.96i	0.842936	−	1.46001i	−0.0444656	−	0.999011i	$-0.514158\pi$
$101$	855.612	−	1481.96i	0.842936	−	1.46001i	0.887402	−	0.460997i	$-0.152508\pi$
$102$	60.0488	−	104.008i	0.0582913	−	0.100964i
$103$	−755.128			−0.722378			−0.361189	−	0.932493i	$-0.617629\pi$
$103$	−755.128			−0.722378			−0.361189	+	0.932493i	$0.617629\pi$
$104$	360.270	−	803.842i	0.339686	−	0.757915i
$105$	−79.5468			−0.0739330
$106$	486.827	−	843.210i	0.446084	−	0.772639i
$107$	−125.054	+	216.601i	−0.112986	+	0.195697i	−0.916973	−	0.398950i	$-0.869375\pi$
$107$	−125.054	+	216.601i	−0.112986	+	0.195697i	0.803987	+	0.594647i	$0.202708\pi$
$108$	−33.5117	−	58.0440i	−0.0298580	−	0.0517156i
$109$	−290.883			−0.255611			−0.127805	−	0.991799i	$-0.540793\pi$
$109$	−290.883			−0.255611			−0.127805	+	0.991799i	$0.540793\pi$
$110$	217.724	+	377.110i	0.188720	+	0.326873i
$111$	71.0396	+	123.044i	0.0607458	+	0.105215i
$112$	−810.900			−0.684133
$113$	−180.849	−	313.240i	−0.150556	−	0.260771i	0.780876	−	0.624686i	$-0.214773\pi$
$113$	−180.849	−	313.240i	−0.150556	−	0.260771i	−0.931432	+	0.363915i	$0.881440\pi$
$114$	−133.888	+	231.901i	−0.109998	+	0.190522i
$115$	−431.970	+	748.194i	−0.350273	+	0.606691i
$116$	−287.719			−0.230293
$117$	1242.13	−	127.458i	0.981493	−	0.100714i
$118$	845.775			0.659830
$119$	334.669	−	579.664i	0.257807	−	0.446535i
$120$	70.3479	−	121.846i	0.0535154	−	0.0926914i
$121$	−60.5000	−	104.789i	−0.0454545	−	0.0787296i
$122$	2330.15			1.72919
$123$	62.3265	+	107.953i	0.0456894	+	0.0791363i
$124$	175.137	+	303.346i	0.126837	+	0.219688i
$125$	−1178.85			−0.843519
$126$	−449.356	−	778.308i	−0.317713	−	0.550295i
$127$	−276.652	+	479.176i	−0.193299	+	0.334803i	−0.946341	−	0.323168i	$-0.895252\pi$
$127$	−276.652	+	479.176i	−0.193299	+	0.334803i	0.753043	+	0.657972i	$0.228585\pi$
$128$	873.557	−	1513.05i	0.603221	−	1.04481i
$129$	181.223			0.123688
$130$	−1086.93	−	1503.81i	−0.733307	−	1.01456i
$131$	1473.00			0.982420			0.491210	−	0.871041i	$-0.336555\pi$
$131$	1473.00			0.982420			0.491210	+	0.871041i	$0.336555\pi$
$132$	6.87234	−	11.9032i	0.00453152	−	0.00784882i
$133$	−746.198	+	1292.45i	−0.486493	+	0.842630i
$134$	−286.816	−	496.779i	−0.184904	−	0.320263i
$135$	401.570			0.256012
$136$	591.935	+	1025.26i	0.373220	+	0.646437i
$137$	695.444	+	1204.55i	0.433692	+	0.751177i	0.997188	−	0.0749421i	$-0.0238772\pi$
$137$	695.444	+	1204.55i	0.433692	+	0.751177i	−0.563496	+	0.826119i	$0.690544\pi$
$138$	132.106			0.0814901
$139$	−943.452	−	1634.11i	−0.575702	−	0.997145i	−0.995965	−	0.0897429i	$-0.971395\pi$
$139$	−943.452	−	1634.11i	−0.575702	−	0.997145i	0.420263	−	0.907402i	$-0.361938\pi$
$140$	−137.838	+	238.742i	−0.0832100	+	0.144124i
$141$	−103.198	+	178.745i	−0.0616374	+	0.106759i
$142$	693.580			0.409887
$143$	302.029	+	417.870i	0.176622	+	0.244364i
$144$	2033.05			1.17653
$145$	861.932	−	1492.91i	0.493652	−	0.855031i
$146$	−1297.40	+	2247.15i	−0.735433	+	1.27381i
$147$	−69.0831	−	119.655i	−0.0387611	−	0.0671362i
$148$	492.386			0.273472
$149$	−1165.56	−	2018.81i	−0.640850	−	1.10998i	−0.985243	−	0.171159i	$-0.945249\pi$
$149$	−1165.56	−	2018.81i	−0.640850	−	1.10998i	0.344393	−	0.938825i	$-0.388085\pi$
$150$	−29.0253	−	50.2733i	−0.0157994	−	0.0273653i
$151$	2342.83			1.26263			0.631313	−	0.775528i	$-0.282516\pi$
$151$	2342.83			1.26263			0.631313	+	0.775528i	$0.282516\pi$
$152$	−1319.81	−	2285.98i	−0.704282	−	1.21985i
$153$	−839.065	+	1453.30i	−0.443362	+	0.767925i
$154$	185.549	−	321.380i	0.0970906	−	0.168166i
$155$	−2098.66			−1.08754
$156$	−23.9534	+	53.4453i	−0.0122936	+	0.0274298i
$157$	2276.13			1.15704			0.578518	−	0.815670i	$-0.303631\pi$
$157$	2276.13			1.15704			0.578518	+	0.815670i	$0.303631\pi$
$158$	−460.222	+	797.128i	−0.231730	+	0.401367i
$159$	92.0678	−	159.466i	0.0459211	−	0.0795377i
$160$	−573.302	−	992.987i	−0.283272	−	0.490641i
$161$	736.266			0.360409
$162$	1111.15	+	1924.57i	0.538889	+	0.933384i
$163$	−508.409	−	880.590i	−0.244305	−	0.423148i	0.717631	−	0.696423i	$-0.245226\pi$
$163$	−508.409	−	880.590i	−0.244305	−	0.423148i	−0.961936	+	0.273275i	$0.911893\pi$
$164$	431.994			0.205690
$165$	41.1756	+	71.3183i	0.0194274	+	0.0336492i
$166$	−1541.57	+	2670.09i	−0.720779	+	1.24843i
$167$	1035.52	−	1793.57i	0.479824	−	0.831079i	−0.519908	−	0.854222i	$-0.674034\pi$
$167$	1035.52	−	1793.57i	0.479824	−	0.831079i	0.999732	+	0.0231427i	$0.00736720\pi$
$168$	−119.904			−0.0550640
$169$	−1462.01	−	1639.92i	−0.665459	−	0.746434i
$170$	2493.70			1.12505
$171$	1870.83	−	3240.37i	0.836642	−	1.44911i
$172$	314.021	−	543.901i	0.139209	−	0.241117i
$173$	990.480	+	1715.56i	0.435288	+	0.753940i	0.997319	−	0.0731754i	$-0.0233133\pi$
$173$	990.480	+	1715.56i	0.435288	+	0.753940i	−0.562031	+	0.827116i	$0.689980\pi$
$174$	−263.599			−0.114847
$175$	−161.766	−	280.187i	−0.0698765	−	0.121030i
$176$	419.745	+	727.019i	0.179770	+	0.311370i
$177$	159.951			0.0679248
$178$	2231.64	+	3865.32i	0.939711	+	1.62763i
$179$	1720.42	−	2979.85i	0.718380	−	1.24427i	−0.243262	−	0.969961i	$-0.578217\pi$
$179$	1720.42	−	2979.85i	0.718380	−	1.24427i	0.961641	−	0.274310i	$-0.0884493\pi$
$180$	345.579	−	598.561i	0.143100	−	0.247856i
$181$	−2545.54			−1.04535			−0.522676	−	0.852532i	$-0.675066\pi$
$181$	−2545.54			−1.04535			−0.522676	+	0.852532i	$0.675066\pi$
$182$	−646.726	+	1442.99i	−0.263398	+	0.587700i
$183$	440.673			0.178008
$184$	−651.123	+	1127.78i	−0.260877	+	0.451853i
$185$	−1475.07	+	2554.89i	−0.586211	+	1.01535i
$186$	160.455	+	277.916i	0.0632533	+	0.109558i
$187$	−692.936			−0.270976
$188$	357.642	+	619.453i	0.138743	+	0.240310i
$189$	−171.113	−	296.376i	−0.0658552	−	0.114065i
$190$	−5560.11			−2.12301
$191$	850.227	+	1472.64i	0.322096	+	0.557886i	0.980920	−	0.194410i	$-0.0622794\pi$
$191$	850.227	+	1472.64i	0.322096	+	0.557886i	−0.658825	+	0.752297i	$0.728946\pi$
$192$	95.6371	−	165.648i	0.0359480	−	0.0622637i
$193$	−1769.17	+	3064.29i	−0.659832	+	1.14286i	0.320827	+	0.947138i	$0.396039\pi$
$193$	−1769.17	+	3064.29i	−0.659832	+	1.14286i	−0.980659	+	0.195725i	$0.937294\pi$
$194$	−5462.27			−2.02148
$195$	−205.558	−	284.398i	−0.0754887	−	0.104442i
$196$	−478.825			−0.174499
$197$	1295.23	−	2243.41i	0.468434	−	0.811351i	−0.530915	−	0.847425i	$-0.678152\pi$
$197$	1295.23	−	2243.41i	0.468434	−	0.811351i	0.999349	+	0.0360739i	$0.0114852\pi$
$198$	−465.199	+	805.748i	−0.166971	+	0.289202i
$199$	2340.64	+	4054.11i	0.833786	+	1.44416i	0.895015	+	0.446037i	$0.147165\pi$
$199$	2340.64	+	4054.11i	0.833786	+	1.44416i	−0.0612282	+	0.998124i	$0.519502\pi$
$200$	572.238			0.202317
$201$	−54.2420	−	93.9499i	−0.0190345	−	0.0329687i
$202$	−2716.61	−	4705.30i	−0.946237	−	1.63893i
$203$	−1469.11			−0.507937
$204$	−39.3561	−	68.1668i	−0.0135073	−	0.0233953i
$205$	−1294.15	+	2241.53i	−0.440913	+	0.763683i
$206$	−1198.78	+	2076.35i	−0.405453	+	0.702265i
$207$	−1845.93			−0.619811
$208$	−2095.46	−	2899.15i	−0.698528	−	0.966442i
$209$	1545.01			0.511343
$210$	−126.282	+	218.728i	−0.0414967	+	0.0718745i
$211$	−2474.29	+	4285.60i	−0.807286	+	1.39826i	0.107451	+	0.994210i	$0.465731\pi$
$211$	−2474.29	+	4285.60i	−0.807286	+	1.39826i	−0.914737	+	0.404050i	$0.867602\pi$
$212$	−319.068	−	552.642i	−0.103366	−	0.179036i
$213$	131.169			0.0421949
$214$	397.054	+	687.717i	0.126832	+	0.219679i
$215$	1881.46	+	3258.78i	0.596811	+	1.03371i
$216$	605.301			0.190674
$217$	894.261	+	1548.91i	0.279753	+	0.484546i
$218$	−461.784	+	799.834i	−0.143468	+	0.248493i
$219$	−245.361	+	424.978i	−0.0757076	+	0.131129i
$220$	285.394			0.0874604
$221$	2937.25	−	301.400i	0.894031	−	0.0917391i
$222$	451.109			0.136380
$223$	−70.5325	+	122.166i	−0.0211803	+	0.0366854i	−0.876421	−	0.481545i	$-0.840076\pi$
$223$	−70.5325	+	122.166i	−0.0211803	+	0.0366854i	0.855241	+	0.518231i	$0.173409\pi$
$224$	−488.578	+	846.243i	−0.145734	+	0.252419i
$225$	405.572	+	702.472i	0.120170	+	0.208140i
$226$	−1148.41			−0.338014
$227$	935.086	+	1619.62i	0.273409	+	0.473558i	0.969732	−	0.244170i	$-0.0785155\pi$
$227$	935.086	+	1619.62i	0.273409	+	0.473558i	−0.696324	+	0.717728i	$0.745182\pi$
$228$	87.7507	+	151.989i	0.0254888	+	0.0441478i
$229$	3641.42			1.05079			0.525397	−	0.850857i	$-0.323917\pi$
$229$	3641.42			1.05079			0.525397	+	0.850857i	$0.323917\pi$
$230$	1371.53	+	2375.55i	0.393199	+	0.681041i
$231$	35.0906	−	60.7788i	0.00999478	−	0.0173115i
$232$	1299.22	−	2250.31i	0.367664	−	0.636812i
$233$	520.689			0.146401			0.0732006	−	0.997317i	$-0.476679\pi$
$233$	520.689			0.146401			0.0732006	+	0.997317i	$0.476679\pi$
$234$	1621.44	−	3617.78i	0.452977	−	1.01069i
$235$	−4285.62			−1.18963
$236$	277.162	−	480.058i	0.0764478	−	0.132412i
$237$	−87.0363	+	150.751i	−0.0238549	+	0.0413179i
$238$	−1062.59	−	1840.46i	−0.289401	−	0.501258i
$239$	−1128.38			−0.305392			−0.152696	−	0.988273i	$-0.548796\pi$
$239$	−1128.38			−0.305392			−0.152696	+	0.988273i	$0.548796\pi$
$240$	−285.673	−	494.801i	−0.0768339	−	0.133080i
$241$	158.691	+	274.861i	0.0424157	+	0.0734662i	0.886454	−	0.462817i	$-0.153161\pi$
$241$	158.691	+	274.861i	0.0424157	+	0.0734662i	−0.844038	+	0.536283i	$0.819828\pi$
$242$	−384.181			−0.102050
$243$	644.950	+	1117.09i	0.170262	+	0.294902i
$244$	763.593	−	1322.58i	0.200344	−	0.347007i
$245$	1434.44	−	2484.52i	0.374053	−	0.647879i
$246$	395.779			0.102577
$247$	−6549.06	+	672.018i	−1.68707	+	0.173115i
$248$	−3163.39			−0.809981
$249$	−291.540	+	504.961i	−0.0741991	+	0.128517i
$250$	−1871.46	+	3241.46i	−0.473446	+	0.820033i
$251$	−1801.80	−	3120.81i	−0.453102	−	0.784796i	0.545475	−	0.838127i	$-0.316349\pi$
$251$	−1801.80	−	3120.81i	−0.453102	−	0.784796i	−0.998577	+	0.0533313i	$0.983016\pi$
$252$	−589.019			−0.147241
$253$	−381.112	−	660.105i	−0.0947047	−	0.164033i
$254$	878.385	+	1521.41i	0.216987	+	0.375833i
$255$	471.604			0.115816
$256$	−1499.40	−	2597.04i	−0.366065	−	0.634043i
$257$	2272.74	−	3936.50i	0.551632	−	0.955455i	−0.446525	−	0.894771i	$-0.647338\pi$
$257$	2272.74	−	3936.50i	0.551632	−	0.955455i	0.998157	−	0.0606840i	$-0.0193282\pi$
$258$	287.696	−	498.305i	0.0694232	−	0.120245i
$259$	2514.16			0.603174
$260$	−1209.74	+	124.135i	−0.288558	+	0.0296098i
$261$	3683.28			0.873522
$262$	2338.43	−	4050.28i	0.551407	−	0.955065i
$263$	−623.988	+	1080.78i	−0.146299	+	0.253398i	−0.929857	−	0.367921i	$-0.880070\pi$
$263$	−623.988	+	1080.78i	−0.146299	+	0.253398i	0.783558	+	0.621319i	$0.213403\pi$
$264$	62.0654	+	107.500i	0.0144692	+	0.0250613i
$265$	3823.39			0.886298
$266$	2369.21	+	4103.60i	0.546112	+	0.945894i
$267$	422.044	+	731.001i	0.0967365	+	0.167553i
$268$	−375.959			−0.0856917
$269$	2103.36	+	3643.12i	0.476743	+	0.825743i	0.999645	−	0.0266496i	$-0.00848382\pi$
$269$	2103.36	+	3643.12i	0.476743	+	0.825743i	−0.522902	+	0.852393i	$0.675150\pi$
$270$	637.503	−	1104.19i	0.143693	−	0.248884i
$271$	3370.70	−	5838.22i	0.755554	−	1.30866i	−0.189544	−	0.981872i	$-0.560701\pi$
$271$	3370.70	−	5838.22i	0.755554	−	1.30866i	0.945098	−	0.326786i	$-0.105966\pi$
$272$	4807.54			1.07169
$273$	−122.308	+	272.895i	−0.0271150	+	0.0604995i
$274$	4416.14			0.973682
$275$	−167.469	+	290.066i	−0.0367229	+	0.0636059i
$276$	43.2914	−	74.9829i	0.00944144	−	0.0163531i
$277$	−313.733	−	543.401i	−0.0680519	−	0.117869i	0.829992	−	0.557776i	$-0.188345\pi$
$277$	−313.733	−	543.401i	−0.0680519	−	0.117869i	−0.898044	+	0.439906i	$0.855012\pi$
$278$	−5991.02			−1.29251
$279$	−2242.04	−	3883.34i	−0.481103	−	0.833295i
$280$	−1244.84	−	2156.12i	−0.265690	−	0.460189i
$281$	8848.01			1.87839			0.939195	−	0.343383i	$-0.111573\pi$
$281$	8848.01			1.87839			0.939195	+	0.343383i	$0.111573\pi$
$282$	327.660	+	567.524i	0.0691910	+	0.119842i
$283$	4152.42	−	7192.21i	0.872212	−	1.51072i	0.0125088	−	0.999922i	$-0.496018\pi$
$283$	4152.42	−	7192.21i	0.872212	−	1.51072i	0.859703	−	0.510794i	$-0.170648\pi$
$284$	227.287	−	393.673i	0.0474895	−	0.0822542i
$285$	−1051.52			−0.218549
$286$	1628.48	−	167.104i	0.336693	−	0.0345491i
$287$	2205.79			0.453672
$288$	1224.94	−	2121.66i	0.250626	−	0.434096i
$289$	472.368	−	818.165i	0.0961466	−	0.166531i
$290$	−2736.68	−	4740.06i	−0.554149	−	0.959814i
$291$	−1033.01			−0.208097
$292$	850.317	+	1472.79i	0.170414	+	0.295166i
$293$	724.445	+	1254.78i	0.144446	+	0.250187i	0.929166	−	0.369663i	$-0.120527\pi$
$293$	724.445	+	1254.78i	0.144446	+	0.250187i	−0.784720	+	0.619850i	$0.787193\pi$
$294$	−438.685			−0.0870225
$295$	1660.61	+	2876.27i	0.327745	+	0.567670i
$296$	−2223.42	+	3851.07i	−0.436599	+	0.756213i
$297$	−177.146	+	306.825i	−0.0346095	+	0.0599455i
$298$	−7401.44			−1.43877
$299$	1902.59	+	2632.32i	0.367993	+	0.509133i
$300$	−38.0465			−0.00732206
$301$	1603.41	−	2777.19i	0.307041	−	0.531810i
$302$	3719.29	−	6442.00i	0.708680	−	1.22747i
$303$	−513.760	−	889.858i	−0.0974084	−	0.168716i
$304$	−10719.2			−2.02232
$305$	4575.06	+	7924.24i	0.858910	+	1.48768i
$306$	2664.07	+	4614.31i	0.497696	+	0.862034i
$307$	−3135.48			−0.582904			−0.291452	−	0.956585i	$-0.594138\pi$
$307$	−3135.48			−0.582904			−0.291452	+	0.956585i	$0.594138\pi$
$308$	−121.609	−	210.633i	−0.0224978	−	0.0389674i
$309$	−226.712	+	392.676i	−0.0417384	+	0.0722931i
$310$	−3331.68	+	5770.64i	−0.610409	+	1.05726i
$311$	−6381.54			−1.16355			−0.581775	−	0.813350i	$-0.697642\pi$
$311$	−6381.54			−1.16355			−0.581775	+	0.813350i	$0.697642\pi$
$312$	−309.844	−	428.682i	−0.0562227	−	0.0777864i
$313$	−895.167			−0.161654			−0.0808272	−	0.996728i	$-0.525756\pi$
$313$	−895.167			−0.161654			−0.0808272	+	0.996728i	$0.525756\pi$
$314$	3613.41	−	6258.60i	0.649415	−	1.12482i
$315$	1764.55	−	3056.29i	0.315623	−	0.546675i
$316$	301.631	+	522.440i	0.0536964	+	0.0930048i
$317$	1411.07			0.250011			0.125005	−	0.992156i	$-0.460105\pi$
$317$	1411.07			0.250011			0.125005	+	0.992156i	$0.460105\pi$
$318$	−292.320	−	506.313i	−0.0515487	−	0.0892850i
$319$	760.452	+	1317.14i	0.133471	+	0.231178i
$320$	3971.61			0.693812
$321$	75.0901	+	130.060i	0.0130564	+	0.0226144i
$322$	1168.84	−	2024.49i	0.202289	−	0.350374i
$323$	4423.94	−	7662.48i	0.762088	−	1.31998i
$324$	1456.50			0.249743
$325$	583.710	−	1302.39i	0.0996259	−	0.222287i
$326$	−3228.44			−0.548488
$327$	−87.3317	+	151.263i	−0.0147690	+	0.0255806i
$328$	−1950.71	+	3378.73i	−0.328384	+	0.568778i
$329$	1826.14	+	3162.97i	0.306014	+	0.530031i
$330$	261.469			0.0436164
$331$	179.145	+	310.289i	0.0297484	+	0.0515258i	0.880516	−	0.474016i	$-0.157196\pi$
$331$	179.145	+	310.289i	0.0297484	+	0.0515258i	−0.850768	+	0.525542i	$0.823863\pi$
$332$	1010.35	+	1749.98i	0.167019	+	0.289285i
$333$	−6303.37			−1.03730
$334$	−3287.81	−	5694.66i	−0.538626	−	0.932928i
$335$	1126.28	−	1950.77i	0.183687	−	0.318156i
$336$	−243.456	+	421.679i	−0.0395287	+	0.0684656i
$337$	583.989			0.0943973			0.0471986	−	0.998886i	$-0.484971\pi$
$337$	583.989			0.0943973			0.0471986	+	0.998886i	$0.484971\pi$
$338$	−6830.22	+	1416.65i	−1.09916	+	0.227976i
$339$	−217.185			−0.0347961
$340$	817.190	−	1415.41i	0.130348	−	0.225769i
$341$	925.788	−	1603.51i	0.147021	−	0.254648i
$342$	−5939.97	−	10288.3i	−0.939172	−	1.62669i
$343$	−6089.42			−0.958595
$344$	2835.98	+	4912.07i	0.444494	+	0.769887i
$345$	259.380	+	449.260i	0.0404770	+	0.0701082i
$346$	6289.64			0.977264
$347$	−1326.67	−	2297.86i	−0.205243	−	0.355491i	0.744967	−	0.667101i	$-0.232465\pi$
$347$	−1326.67	−	2297.86i	−0.205243	−	0.355491i	−0.950210	+	0.311610i	$0.899132\pi$
$348$	−86.3816	+	149.617i	−0.0133062	+	0.0230469i
$349$	1348.52	−	2335.70i	0.206833	−	0.358245i	−0.743882	−	0.668311i	$-0.767018\pi$
$349$	1348.52	−	2335.70i	0.206833	−	0.358245i	0.950715	+	0.310066i	$0.100351\pi$
$350$	−1027.23			−0.156880
$351$	617.437	−	1377.64i	0.0938927	−	0.209495i
$352$	1011.61			0.153179
$353$	219.773	−	380.658i	0.0331370	−	0.0573949i	−0.848981	−	0.528423i	$-0.822784\pi$
$353$	219.773	−	380.658i	0.0331370	−	0.0573949i	0.882118	+	0.471028i	$0.156117\pi$
$354$	253.927	−	439.814i	0.0381244	−	0.0660335i
$355$	1361.79	+	2358.69i	0.203595	+	0.352637i
$356$	2925.25			0.435499
$357$	−200.955	−	348.064i	−0.0297918	−	0.0516009i
$358$	−5462.41	−	9461.17i	−0.806417	−	1.39675i
$359$	4427.30			0.650874			0.325437	−	0.945564i	$-0.394489\pi$
$359$	4427.30			0.650874			0.325437	+	0.945564i	$0.394489\pi$
$360$	3120.99	+	5405.72i	0.456919	+	0.791406i
$361$	−6434.37	+	11144.7i	−0.938092	+	1.62482i
$362$	−4041.11	+	6999.41i	−0.586729	+	1.01624i
$363$	−72.6556			−0.0105053
$364$	607.100	+	839.947i	0.0874195	+	0.120948i
$365$	−10189.3			−1.46119
$366$	699.580	−	1211.71i	0.0999115	−	0.173052i
$367$	5149.68	−	8919.50i	0.732455	−	1.26865i	−0.223376	−	0.974732i	$-0.571708\pi$
$367$	5149.68	−	8919.50i	0.732455	−	1.26865i	0.955831	−	0.293916i	$-0.0949587\pi$
$368$	2644.13	+	4579.76i	0.374550	+	0.648740i
$369$	−5530.25			−0.780198
$370$	4683.40	+	8111.89i	0.658050	+	1.13978i
$371$	−1629.18	−	2821.83i	−0.227986	−	0.394884i
$372$	210.325			0.0293141
$373$	3589.45	+	6217.11i	0.498270	+	0.863029i	0.999998	−	0.00199616i	$-0.000635398\pi$
$373$	3589.45	+	6217.11i	0.498270	+	0.863029i	−0.501728	+	0.865026i	$0.667302\pi$
$374$	−1100.05	+	1905.35i	−0.152092	+	0.263431i
$375$	−353.927	+	613.019i	−0.0487379	+	0.0844165i
$376$	−6459.86			−0.886015
$377$	−3796.35	−	5252.40i	−0.518625	−	0.717539i
$378$	−1086.58			−0.147851
$379$	2107.12	−	3649.63i	0.285581	−	0.494642i	−0.687169	−	0.726498i	$-0.741147\pi$
$379$	2107.12	−	3649.63i	0.285581	−	0.494642i	0.972750	+	0.231856i	$0.0744800\pi$
$380$	−1822.05	+	3155.89i	−0.245972	+	0.426036i
$381$	166.118	+	287.726i	0.0223373	+	0.0386893i
$382$	5399.03			0.723137
$383$	−3253.14	−	5634.61i	−0.434015	−	0.751737i	0.563199	−	0.826321i	$-0.309570\pi$
$383$	−3253.14	−	5634.61i	−0.434015	−	0.751737i	−0.997215	+	0.0745844i	$0.976237\pi$
$384$	−524.536	−	908.522i	−0.0697073	−	0.120737i
$385$	1457.24			0.192904
$386$	5617.20	+	9729.28i	0.740694	+	1.28292i
$387$	−4020.00	+	6962.84i	−0.528031	+	0.914576i
$388$	−1789.99	+	3100.36i	−0.234209	+	0.405662i
$389$	−10872.8			−1.41715			−0.708577	−	0.705633i	$-0.750663\pi$
$389$	−10872.8			−1.41715			−0.708577	+	0.705633i	$0.750663\pi$
$390$	−1108.33	+	113.729i	−0.143904	+	0.0147664i
$391$	−4365.06			−0.564579
$392$	2162.18	−	3745.01i	0.278588	−	0.482529i
$393$	442.239	−	765.981i	0.0567634	−	0.0983171i
$394$	−4112.42	−	7122.93i	−0.525840	−	0.910781i
$395$	−3614.44			−0.460410
$396$	304.892	+	528.089i	0.0386905	+	0.0670138i
$397$	4510.24	+	7811.97i	0.570183	+	0.987585i	0.996547	+	0.0830336i	$0.0264609\pi$
$397$	4510.24	+	7811.97i	0.570183	+	0.987585i	−0.426364	+	0.904552i	$0.640206\pi$
$398$	14863.3			1.87193
$399$	448.061	+	776.065i	0.0562183	+	0.0973730i
$400$	1161.89	−	2012.45i	0.145236	−	0.251557i
$401$	303.624	−	525.891i	0.0378111	−	0.0654907i	−0.846501	−	0.532388i	$-0.821295\pi$
$401$	303.624	−	525.891i	0.0378111	−	0.0654907i	0.884312	+	0.466897i	$0.154628\pi$
$402$	−344.442			−0.0427344
$403$	−3226.81	+	7199.73i	−0.398856	+	0.889935i
$404$	−3560.95			−0.438524
$405$	−4363.31	+	7557.47i	−0.535344	+	0.927243i
$406$	−2332.25	+	4039.57i	−0.285092	+	0.493795i
$407$	−1301.40	−	2254.09i	−0.158496	−	0.274523i
$408$	710.865			0.0862575
$409$	7396.23	+	12810.6i	0.894181	+	1.54877i	0.834816	+	0.550530i	$0.185574\pi$
$409$	7396.23	+	12810.6i	0.894181	+	1.54877i	0.0593650	+	0.998236i	$0.481092\pi$
$410$	4108.98	+	7116.96i	0.494946	+	0.857272i
$411$	835.172			0.100234
$412$	785.686	+	1360.85i	0.0939514	+	0.162729i
$413$	1415.21	−	2451.21i	0.168614	−	0.292049i
$414$	−2930.46	+	5075.70i	−0.347884	+	0.602553i
$415$	−12107.0			−1.43208
$416$	−4288.05	+	440.009i	−0.505382	+	0.0518587i
$417$	−1133.01			−0.133054
$418$	2452.74	−	4248.27i	0.287004	−	0.497105i
$419$	4338.34	−	7514.23i	0.505828	−	0.876120i	−0.494149	−	0.869377i	$-0.664520\pi$
$419$	4338.34	−	7514.23i	0.505828	−	0.876120i	0.999977	−	0.00674292i	$-0.00214636\pi$
$420$	82.7658	+	143.355i	0.00961562	+	0.0166547i
$421$	9185.80			1.06339			0.531697	−	0.846935i	$-0.321555\pi$
$421$	9185.80			1.06339			0.531697	+	0.846935i	$0.321555\pi$
$422$	7856.00	+	13607.0i	0.906218	+	1.56962i
$423$	−4578.41	−	7930.04i	−0.526264	−	0.911517i
$424$	5763.12			0.660099
$425$	959.054	+	1661.13i	0.109461	+	0.189592i
$426$	208.233	−	360.671i	0.0236829	−	0.0410201i
$427$	3898.96	−	6753.19i	0.441882	−	0.765363i
$428$	520.460			0.0587790
$429$	307.976	−	31.6023i	0.0346602	−	0.00355658i
$430$	11947.4			1.33990
$431$	−6340.09	+	10981.4i	−0.708565	+	1.22727i	0.256825	+	0.966458i	$0.417324\pi$
$431$	−6340.09	+	10981.4i	−0.708565	+	1.22727i	−0.965390	+	0.260812i	$0.916010\pi$
$432$	1229.02	−	2128.73i	0.136878	−	0.237080i
$433$	356.672	+	617.774i	0.0395856	+	0.0685642i	0.885139	−	0.465326i	$-0.154063\pi$
$433$	356.672	+	617.774i	0.0395856	+	0.0685642i	−0.845554	+	0.533890i	$0.820730\pi$
$434$	5678.64			0.628073
$435$	−517.555	−	896.432i	−0.0570457	−	0.0988060i
$436$	302.655	+	524.213i	0.0332443	+	0.0575809i
$437$	9732.59			1.06538
$438$	779.033	+	1349.32i	0.0849855	+	0.147199i
$439$	7404.06	−	12824.2i	0.804958	−	1.39423i	−0.111362	−	0.993780i	$-0.535521\pi$
$439$	7404.06	−	12824.2i	0.804958	−	1.39423i	0.916320	−	0.400447i	$-0.131145\pi$
$440$	−1288.72	+	2232.14i	−0.139631	+	0.241848i
$441$	6129.76			0.661890
$442$	3834.20	−	8554.95i	0.412612	−	0.920628i
$443$	2373.33			0.254538			0.127269	−	0.991868i	$-0.459379\pi$
$443$	2373.33			0.254538			0.127269	+	0.991868i	$0.459379\pi$
$444$	147.829	−	256.047i	0.0158010	−	0.0273682i
$445$	−8763.30	+	15178.5i	−0.933529	+	1.61692i
$446$	223.944	+	387.883i	0.0237759	+	0.0411811i
$447$	−1399.75			−0.148111
$448$	−1692.34	−	2931.22i	−0.178472	−	0.309123i
$449$	−3446.57	−	5969.63i	−0.362257	−	0.627448i	0.626075	−	0.779763i	$-0.284661\pi$
$449$	−3446.57	−	5969.63i	−0.362257	−	0.627448i	−0.988332	+	0.152315i	$0.951327\pi$
$450$	2575.42			0.269792
$451$	−1141.78	−	1977.62i	−0.119211	−	0.206480i
$452$	−376.336	+	651.832i	−0.0391622	+	0.0678310i
$453$	703.386	−	1218.30i	0.0729535	−	0.126359i
$454$	5937.89			0.613830
$455$	−6177.03	+	633.843i	−0.636447	+	0.0653077i
$456$	−1584.99			−0.162772
$457$	247.265	−	428.276i	0.0253098	−	0.0438378i	−0.853093	−	0.521759i	$-0.825276\pi$
$457$	247.265	−	428.276i	0.0253098	−	0.0438378i	0.878403	+	0.477921i	$0.158609\pi$
$458$	5780.85	−	10012.7i	0.589784	−	1.02154i
$459$	1014.47	+	1757.11i	0.103162	+	0.178682i
$460$	1797.80			0.182224
$461$	−4413.53	−	7644.45i	−0.445897	−	0.772316i	0.552217	−	0.833700i	$-0.313782\pi$
$461$	−4413.53	−	7644.45i	−0.445897	−	0.772316i	−0.998114	+	0.0613841i	$0.980449\pi$
$462$	−111.414	−	192.976i	−0.0112196	−	0.0194330i
$463$	−16787.9			−1.68510			−0.842551	−	0.538617i	$-0.818947\pi$
$463$	−16787.9			−1.68510			−0.842551	+	0.538617i	$0.818947\pi$
$464$	−5275.96	−	9138.23i	−0.527867	−	0.914293i
$465$	−630.081	+	1091.33i	−0.0628372	+	0.108837i
$466$	826.607	−	1431.73i	0.0821713	−	0.142325i
$467$	−7114.94			−0.705011			−0.352506	−	0.935810i	$-0.614670\pi$
$467$	−7114.94			−0.705011			−0.352506	+	0.935810i	$0.614670\pi$
$468$	−1522.09	−	2105.87i	−0.150339	−	0.208000i
$469$	−1919.67			−0.189003
$470$	−6803.52	+	11784.0i	−0.667709	+	1.15651i
$471$	683.360	−	1183.62i	0.0668526	−	0.115792i
$472$	2503.10	+	4335.49i	0.244098	+	0.422791i
$473$	−3319.88			−0.322724
$474$	276.344	+	478.643i	0.0267783	+	0.0463814i
$475$	−2138.36	−	3703.75i	−0.206558	−	0.357768i
$476$	−1392.85			−0.134120
$477$	4084.60	+	7074.74i	0.392078	+	0.679099i
$478$	−1791.33	+	3102.67i	−0.171409	+	0.296889i
$479$	9044.84	−	15666.1i	0.862775	−	1.49437i	−0.00646448	−	0.999979i	$-0.502058\pi$
$479$	9044.84	−	15666.1i	0.862775	−	1.49437i	0.869240	−	0.494391i	$-0.164609\pi$
$480$	−688.488			−0.0654688
$481$	6496.87	+	8988.68i	0.615866	+	0.852075i
$482$	1007.70			0.0952275
$483$	221.049	−	382.868i	0.0208242	−	0.0360685i
$484$	−125.897	+	218.059i	−0.0118235	+	0.0204789i
$485$	−10724.7	−	18575.8i	−1.00409	−	1.73914i
$486$	4095.50			0.382254
$487$	4414.59	+	7646.29i	0.410768	+	0.711471i	0.994974	−	0.100135i	$-0.0319273\pi$
$487$	4414.59	+	7646.29i	0.410768	+	0.711471i	−0.584206	+	0.811605i	$0.698594\pi$
$488$	6896.15	+	11944.5i	0.639701	+	1.10799i
$489$	−610.557			−0.0564629
$490$	−4554.42	−	7888.48i	−0.419893	−	0.727276i
$491$	−7630.26	+	13216.0i	−0.701321	+	1.21472i	0.266681	+	0.963785i	$0.414073\pi$
$491$	−7630.26	+	13216.0i	−0.701321	+	1.21472i	−0.968003	+	0.250939i	$0.919260\pi$
$492$	129.697	−	224.643i	0.0118846	−	0.0205847i
$493$	8709.83			0.795681
$494$	−8548.97	+	19074.6i	−0.778616	+	1.73726i
$495$	−3653.52			−0.331745
$496$	−6423.05	+	11125.1i	−0.581459	+	1.00712i
$497$	1160.54	−	2010.12i	0.104743	−	0.181421i
$498$	925.652	+	1603.28i	0.0832921	+	0.144266i
$499$	6698.24			0.600911			0.300455	−	0.953796i	$-0.402861\pi$
$499$	6698.24			0.600911			0.300455	+	0.953796i	$0.402861\pi$
$500$	1226.56	+	2124.46i	0.109707	+	0.190018i
$501$	−621.785	−	1076.96i	−0.0554477	−	0.0960382i
$502$	−11441.6			−1.01726
$503$	−970.637	−	1681.19i	−0.0860409	−	0.149027i	0.819793	−	0.572659i	$-0.194088\pi$
$503$	−970.637	−	1681.19i	−0.0860409	−	0.149027i	−0.905834	+	0.423632i	$0.860755\pi$
$504$	2659.77	−	4606.85i	0.235070	−	0.407154i
$505$	10667.7	−	18477.0i	0.940012	−	1.62815i
$506$	−2420.10			−0.212621
$507$	−1291.72	+	267.915i	−0.113150	+	0.0234685i
$508$	1151.39			0.100561
$509$	−3799.87	+	6581.56i	−0.330896	+	0.573129i	−0.982688	−	0.185269i	$-0.940684\pi$
$509$	−3799.87	+	6581.56i	−0.330896	+	0.573129i	0.651792	+	0.758398i	$0.274018\pi$
$510$	748.683	−	1296.76i	0.0650044	−	0.112591i
$511$	4341.77	+	7520.17i	0.375868	+	0.651023i
$512$	4455.57			0.384590
$513$	−2261.92	−	3917.75i	−0.194671	−	0.337179i
$514$	−7216.06	−	12498.6i	−0.619235	−	1.07255i
$515$	−9414.87			−0.805571
$516$	−188.557	−	326.590i	−0.0160867	−	0.0278630i
$517$	1890.52	−	3274.48i	0.160822	−	0.278552i
$518$	3991.29	−	6913.11i	0.338546	−	0.586380i
$519$	1189.49			0.100602
$520$	4491.82	−	10022.2i	0.378806	−	0.845200i
$521$	−7464.85			−0.627718			−0.313859	−	0.949470i	$-0.601622\pi$
$521$	−7464.85			−0.627718			−0.313859	+	0.949470i	$0.601622\pi$
$522$	5847.29	−	10127.8i	0.490286	−	0.849199i
$523$	−8510.46	+	14740.6i	−0.711542	+	1.23243i	0.252736	+	0.967535i	$0.418670\pi$
$523$	−8510.46	+	14740.6i	−0.711542	+	1.23243i	−0.964278	+	0.264892i	$0.914664\pi$
$524$	−1532.61	−	2654.56i	−0.127772	−	0.221308i
$525$	−194.268			−0.0161496
$526$	1981.19	+	3431.52i	0.164228	+	0.284452i
$527$	−5301.75	−	9182.90i	−0.438231	−	0.759039i
$528$	504.079			0.0415478
$529$	3682.74	+	6378.69i	0.302682	+	0.524261i
$530$	6069.72	−	10513.1i	0.497456	−	0.861620i
$531$	−3548.13	+	6145.55i	−0.289973	+	0.502248i
$532$	3105.58			0.253090
$533$	5700.01	+	7886.20i	0.463218	+	0.640880i
$534$	2680.02			0.217183
$535$	−1559.17	+	2700.56i	−0.125998	+	0.218234i
$536$	1697.68	−	2940.47i	0.136807	−	0.236957i
$537$	−1033.04	−	1789.28i	−0.0830148	−	0.143786i
$538$	13356.5			1.07034
$539$	1265.56	+	2192.01i	0.101134	+	0.175170i
$540$	−417.821	−	723.687i	−0.0332966	−	0.0576714i
$541$	−9247.23			−0.734879			−0.367440	−	0.930047i	$-0.619766\pi$
$541$	−9247.23			−0.734879			−0.367440	+	0.930047i	$0.619766\pi$
$542$	−10702.1	−	18536.6i	−0.848147	−	1.46903i
$543$	−764.247	+	1323.71i	−0.0603996	+	0.104615i
$544$	2896.61	−	5017.07i	0.228292	−	0.395414i
$545$	−3626.71			−0.285048
$546$	556.206	+	769.533i	0.0435960	+	0.0603168i
$547$	3661.21			0.286183			0.143092	−	0.989709i	$-0.454296\pi$
$547$	3661.21			0.286183			0.143092	+	0.989709i	$0.454296\pi$
$548$	1447.18	−	2506.58i	0.112811	−	0.195394i
$549$	−9775.26	+	16931.3i	−0.759924	+	1.31623i
$550$	531.724	+	920.972i	0.0412232	+	0.0714007i
$551$	−19419.9			−1.50148
$552$	390.973	+	677.185i	0.0301466	+	0.0522154i
$553$	1540.15	+	2667.61i	0.118433	+	0.205133i
$554$	−1992.24			−0.152783
$555$	885.716	+	1534.11i	0.0677416	+	0.117332i
$556$	−1963.26	+	3400.47i	−0.149750	+	0.259374i
$557$	8401.95	−	14552.6i	0.639142	−	1.10703i	−0.346479	−	0.938058i	$-0.612623\pi$
$557$	8401.95	−	14552.6i	0.639142	−	1.10703i	0.985621	−	0.168969i	$-0.0540438\pi$
$558$	−14237.2			−1.08012
$559$	14072.5	−	1444.02i	1.06476	−	0.109258i
$560$	−10110.2			−0.762921
$561$	−208.040	+	360.336i	−0.0156568	+	0.0271183i
$562$	14046.4	−	24329.1i	1.05429	−	1.82609i
$563$	−6542.87	−	11332.6i	−0.489785	−	0.848333i	0.510145	−	0.860088i	$-0.329592\pi$
$563$	−6542.87	−	11332.6i	−0.489785	−	0.848333i	−0.999931	+	0.0117548i	$0.996258\pi$
$564$	429.498			0.0320659
$565$	−2254.81	−	3905.45i	−0.167895	−	0.290803i
$566$	−13184.2	−	22835.6i	−0.979101	−	1.69585i
$567$	7436.98			0.550836
$568$	2052.67	+	3555.33i	0.151634	+	0.262638i
$569$	10076.0	−	17452.1i	0.742368	−	1.28582i	−0.209046	−	0.977906i	$-0.567036\pi$
$569$	10076.0	−	17452.1i	0.742368	−	1.28582i	0.951414	−	0.307914i	$-0.0996309\pi$
$570$	−1669.31	+	2891.33i	−0.122666	+	0.212464i
$571$	8555.61			0.627042			0.313521	−	0.949581i	$-0.398491\pi$
$571$	8555.61			0.627042			0.313521	+	0.949581i	$0.398491\pi$
$572$	438.809	−	979.080i	0.0320761	−	0.0715689i
$573$	1021.05			0.0744417
$574$	3501.75	−	6065.21i	0.254634	−	0.441040i
$575$	−1054.95	+	1827.23i	−0.0765122	+	0.132523i
$576$	4242.95	+	7349.01i	0.306926	+	0.531612i
$577$	−13753.6			−0.992323			−0.496161	−	0.868230i	$-0.665258\pi$
$577$	−13753.6			−0.992323			−0.496161	+	0.868230i	$0.665258\pi$
$578$	−1499.79	−	2597.72i	−0.107929	−	0.186939i
$579$	1062.31	+	1839.98i	0.0762492	+	0.132067i
$580$	−3587.25			−0.256815
$581$	5158.92	+	8935.52i	0.368379	+	0.638051i
$582$	−1639.93	+	2840.45i	−0.116800	+	0.202303i
$583$	−1686.62	+	2921.31i	−0.119816	+	0.207527i
$584$	−15358.7			−1.08827
$585$	15486.7	−	1589.14i	1.09453	−	0.112312i
$586$	4600.30			0.324295
$587$	4091.41	−	7086.53i	0.287684	−	0.498283i	−0.685572	−	0.728004i	$-0.740448\pi$
$587$	4091.41	−	7086.53i	0.287684	−	0.498283i	0.973257	+	0.229721i	$0.0737814\pi$
$588$	−143.758	+	248.995i	−0.0100824	+	0.0174633i
$589$	11821.1	+	20474.7i	0.826961	+	1.43234i
$590$	10545.1			0.735819
$591$	−777.734	−	1347.07i	−0.0541314	−	0.0937584i
$592$	9029.00	+	15638.7i	0.626841	+	1.08572i
$593$	3774.00			0.261349			0.130674	−	0.991425i	$-0.458286\pi$
$593$	3774.00			0.261349			0.130674	+	0.991425i	$0.458286\pi$
$594$	562.446	+	974.185i	0.0388509	+	0.0672918i
$595$	4172.62	−	7227.20i	0.287497	−	0.497960i
$596$	−2425.46	+	4201.02i	−0.166696	+	0.288726i
$597$	2810.92			0.192702
$598$	10258.4	−	1052.65i	0.701502	−	0.0719831i
$599$	−3293.48			−0.224654			−0.112327	−	0.993671i	$-0.535830\pi$
$599$	−3293.48			−0.224654			−0.112327	+	0.993671i	$0.535830\pi$
$600$	171.803	−	297.571i	0.0116897	−	0.0202471i
$601$	6097.83	−	10561.8i	0.413870	−	0.716844i	−0.581439	−	0.813590i	$-0.697510\pi$
$601$	6097.83	−	10561.8i	0.413870	−	0.716844i	0.995309	+	0.0967462i	$0.0308435\pi$
$602$	−5090.92	−	8817.72i	−0.344668	−	0.596983i
$603$	4812.91			0.325036
$604$	−2437.63	−	4222.11i	−0.164215	−	0.284429i
$605$	−754.309	−	1306.50i	−0.0506893	−	0.0877964i
$606$	−3262.43			−0.218691
$607$	76.5610	+	132.608i	0.00511947	+	0.00886717i	0.868574	−	0.495560i	$-0.165037\pi$
$607$	76.5610	+	132.608i	0.00511947	+	0.00886717i	−0.863454	+	0.504427i	$0.831704\pi$
$608$	−6458.44	+	11186.4i	−0.430797	+	0.746162i
$609$	−441.070	+	763.956i	−0.0293482	+	0.0508326i
$610$	29052.1			1.92834
$611$	−6589.37	+	14702.3i	−0.436297	+	0.973474i
$612$	3492.08			0.230652
$613$	8841.87	−	15314.6i	0.582577	−	1.00905i	−0.412596	−	0.910914i	$-0.635378\pi$
$613$	8841.87	−	15314.6i	0.582577	−	1.00905i	0.995173	−	0.0981390i	$-0.0312890\pi$
$614$	−4977.66	+	8621.55i	−0.327169	+	0.566674i
$615$	777.082	+	1345.95i	0.0509512	+	0.0882500i
$616$	2196.55			0.143671
$617$	−2465.46	−	4270.31i	−0.160868	−	0.278632i	0.774312	−	0.632804i	$-0.218096\pi$
$617$	−2465.46	−	4270.31i	−0.160868	−	0.278632i	−0.935180	+	0.354172i	$0.884763\pi$
$618$	719.821	+	1246.77i	0.0468535	+	0.0811526i
$619$	22061.4			1.43251			0.716254	−	0.697839i	$-0.245855\pi$
$619$	22061.4			1.43251			0.716254	+	0.697839i	$0.245855\pi$
$620$	2183.59	+	3782.09i	0.141444	+	0.244988i
$621$	−1115.91	+	1932.81i	−0.0721091	+	0.124897i
$622$	−10130.9	+	17547.2i	−0.653071	+	1.13115i
$623$	14936.5			0.960543
$624$	−2136.71	+	219.254i	−0.137079	+	0.0140660i
$625$	−18504.0			−1.18425
$626$	−1421.10	+	2461.42i	−0.0907325	+	0.157153i
$627$	463.858	−	803.425i	0.0295450	−	0.0511734i
$628$	−2368.24	−	4101.91i	−0.150482	−	0.260643i
$629$	−14905.5			−0.944869
$630$	−5602.54	−	9703.88i	−0.354302	−	0.613669i
$631$	15273.9	+	26455.1i	0.963618	+	1.66904i	0.713283	+	0.700877i	$0.247208\pi$
$631$	15273.9	+	26455.1i	0.963618	+	1.66904i	0.250336	+	0.968159i	$0.419459\pi$
$632$	−5448.16			−0.342906
$633$	1485.71	+	2573.33i	0.0932887	+	0.161581i
$634$	2240.10	−	3879.97i	0.140325	−	0.243049i
$635$	−3449.28	+	5974.33i	−0.215560	+	0.373361i
$636$	−383.175			−0.0238897
$637$	−6317.93	−	8741.11i	−0.392976	−	0.543698i
$638$	4828.95			0.299655
$639$	−2909.65	+	5039.67i	−0.180132	+	0.311997i
$640$	10891.4	−	18864.5i	0.672691	−	1.16513i
$641$	6770.02	+	11726.0i	0.417160	+	0.722543i	0.995653	−	0.0931451i	$-0.0296920\pi$
$641$	6770.02	+	11726.0i	0.417160	+	0.722543i	−0.578492	+	0.815688i	$0.696359\pi$
$642$	476.829			0.0293130
$643$	−1612.32	−	2792.62i	−0.0988861	−	0.171276i	0.812338	−	0.583187i	$-0.198195\pi$
$643$	−1612.32	−	2792.62i	−0.0988861	−	0.171276i	−0.911224	+	0.411911i	$0.864861\pi$
$644$	−766.061	−	1326.86i	−0.0468743	−	0.0811886i
$645$	2259.48			0.137933
$646$	−14046.2	−	24328.8i	−0.855482	−	1.48174i
$647$	2967.41	−	5139.70i	0.180310	−	0.312307i	−0.761676	−	0.647958i	$-0.775623\pi$
$647$	2967.41	−	5139.70i	0.180310	−	0.312307i	0.941986	+	0.335651i	$0.108956\pi$
$648$	−6576.96	+	11391.6i	−0.398715	+	0.690595i
$649$	−2930.20			−0.177227
$650$	−2654.48	−	3672.58i	−0.160181	−	0.221616i
$651$	1073.93			0.0646556
$652$	−1057.97	+	1832.45i	−0.0635477	+	0.110068i
$653$	−6691.82	+	11590.6i	−0.401028	+	0.694600i	−0.993850	−	0.110733i	$-0.964680\pi$
$653$	−6691.82	+	11590.6i	−0.401028	+	0.694600i	0.592823	+	0.805333i	$0.298014\pi$
$654$	277.282	+	480.267i	0.0165789	+	0.0287155i
$655$	18365.3			1.09556
$656$	7921.58	+	13720.6i	0.471472	+	0.816614i
$657$	−10885.5	−	18854.2i	−0.646397	−	1.11959i
$658$	11596.2			0.687031
$659$	−11060.9	−	19158.1i	−0.653829	−	1.13247i	−0.982186	−	0.187911i	$-0.939828\pi$
$659$	−11060.9	−	19158.1i	−0.653829	−	1.13247i	0.328357	−	0.944554i	$-0.393505\pi$
$660$	85.6838	−	148.409i	0.00505339	−	0.00875273i
$661$	−12335.5	+	21365.7i	−0.725861	+	1.25723i	0.232757	+	0.972535i	$0.425225\pi$
$661$	−12335.5	+	21365.7i	−0.725861	+	1.25723i	−0.958619	+	0.284694i	$0.908108\pi$
$662$	1137.59			0.0667881
$663$	725.117	−	1617.90i	0.0424755	−	0.0947721i
$664$	−18249.4			−1.06658
$665$	−9303.53	+	16114.2i	−0.542519	+	0.939671i
$666$	−10006.7	+	17332.2i	−0.582213	+	1.00842i
$667$	4790.37	+	8297.16i	0.278087	+	0.481660i
$668$	−4309.68			−0.249621
$669$	42.3519	+	73.3556i	0.00244756	+	0.00423930i
$670$	−3575.99	−	6193.80i	−0.206198	−	0.357145i
$671$	−8072.83			−0.464453
$672$	293.371	+	508.134i	0.0168408	+	0.0291692i
$673$	3354.89	−	5810.85i	0.192157	−	0.332826i	−0.753808	−	0.657095i	$-0.771785\pi$
$673$	3354.89	−	5810.85i	0.192157	−	0.332826i	0.945965	+	0.324269i	$0.105118\pi$
$674$	927.096	−	1605.78i	0.0529828	−	0.0917689i
$675$	980.710			0.0559223
$676$	−1434.19	+	4341.04i	−0.0815991	+	0.246987i
$677$	−3713.77			−0.210830			−0.105415	−	0.994428i	$-0.533617\pi$
$677$	−3713.77			−0.210830			−0.105415	+	0.994428i	$0.533617\pi$
$678$	−344.787	+	597.188i	−0.0195302	+	0.0338272i
$679$	−9139.82	+	15830.6i	−0.516574	+	0.894733i
$680$	7380.19	+	12782.9i	0.416202	+	0.720883i
$681$	1122.96			0.0631894
$682$	−2939.42	−	5091.23i	−0.165039	−	0.285855i
$683$	6010.78	+	10411.0i	0.336744	+	0.583258i	0.983818	−	0.179169i	$-0.0573410\pi$
$683$	6010.78	+	10411.0i	0.336744	+	0.583258i	−0.647074	+	0.762427i	$0.724008\pi$
$684$	−7786.15			−0.435250
$685$	8670.74	+	15018.2i	0.483638	+	0.837686i
$686$	−9667.11	+	16743.9i	−0.538035	+	0.931904i
$687$	1093.26	−	1893.59i	0.0607141	−	0.105160i
$688$	23033.1			1.27635
$689$	5878.67	−	13116.6i	0.325050	−	0.725258i
$690$	1647.09			0.0908749
$691$	5105.25	−	8842.55i	0.281060	−	0.486811i	−0.690586	−	0.723250i	$-0.742647\pi$
$691$	5105.25	−	8842.55i	0.281060	−	0.486811i	0.971646	+	0.236440i	$0.0759805\pi$
$692$	2061.12	−	3569.97i	0.113226	−	0.196113i
$693$	1556.80	+	2696.46i	0.0853362	+	0.147807i
$694$	−8424.47			−0.460790
$695$	−11762.9	−	20373.9i	−0.642003	−	1.11198i
$696$	−780.128	−	1351.22i	−0.0424866	−	0.0735890i
$697$	−13077.3			−0.710674
$698$	−4281.62	−	7415.98i	−0.232180	−	0.402147i
$699$	156.326	−	270.765i	0.00845895	−	0.0146513i
$700$	−336.625	+	583.052i	−0.0181761	+	0.0314818i
$701$	19676.4			1.06015			0.530076	−	0.847950i	$-0.322163\pi$
$701$	19676.4			1.06015			0.530076	+	0.847950i	$0.322163\pi$
$702$	−2807.86	−	3884.78i	−0.150963	−	0.208863i
$703$	33234.3			1.78301
$704$	−1752.01	+	3034.56i	−0.0937943	+	0.162457i
$705$	−1286.67	+	2228.58i	−0.0687358	+	0.119054i
$706$	−697.791	−	1208.61i	−0.0371979	−	0.0644286i
$707$	−18182.4			−0.967214
$708$	−166.424	−	288.255i	−0.00883419	−	0.0153013i
$709$	−2236.34	−	3873.45i	−0.118459	−	0.205177i	0.800698	−	0.599068i	$-0.204462\pi$
$709$	−2236.34	−	3873.45i	−0.118459	−	0.205177i	−0.919157	+	0.393891i	$0.871129\pi$
$710$	8647.50			0.457091
$711$	−3861.38	−	6688.10i	−0.203675	−	0.352775i
$712$	−13209.2	+	22879.1i	−0.695276	+	1.20425i
$713$	5831.88	−	10101.1i	0.306319	−	0.530561i
$714$	−1276.08			−0.0668855
$715$	3765.68	+	5209.97i	0.196963	+	0.272506i
$716$	−7160.15			−0.373726
$717$	−338.772	+	586.771i	−0.0176453	+	0.0305626i
$718$	7028.45	−	12173.6i	0.365319	−	0.632752i
$719$	6170.58	+	10687.8i	0.320061	+	0.554361i	0.980500	−	0.196518i	$-0.0629633\pi$
$719$	6170.58	+	10687.8i	0.320061	+	0.554361i	−0.660440	+	0.750879i	$0.729630\pi$
$720$	25347.9			1.31203
$721$	4011.77	+	6948.58i	0.207221	+	0.358916i
$722$	20429.4	+	35384.8i	1.05305	+	1.82394i
$723$	190.575			0.00980299
$724$	2648.55	+	4587.43i	0.135957	+	0.235484i
$725$	2105.00	−	3645.97i	0.107831	−	0.186769i
$726$	−115.342	+	199.779i	−0.00589636	+	0.0102128i
$727$	−11805.3			−0.602248			−0.301124	−	0.953585i	$-0.597362\pi$
$727$	−11805.3			−0.602248			−0.301124	+	0.953585i	$0.597362\pi$
$728$	−9310.85	+	955.413i	−0.474015	+	0.0486400i
$729$	−18123.5			−0.920767
$730$	−16175.8	+	28017.3i	−0.820129	+	1.42050i
$731$	−9506.06	+	16465.0i	−0.480977	+	0.833077i
$732$	−458.506	−	794.156i	−0.0231515	−	0.0400995i
$733$	−14972.2			−0.754448			−0.377224	−	0.926122i	$-0.623121\pi$
$733$	−14972.2			−0.754448			−0.377224	+	0.926122i	$0.623121\pi$
$734$	−16350.5	−	28319.8i	−0.822216	−	1.42412i
$735$	−861.323	−	1491.85i	−0.0432250	−	0.0748679i
$736$	6372.49			0.319148
$737$	993.677	+	1721.10i	0.0496642	+	0.0860210i
$738$	−8779.40	+	15206.4i	−0.437906	+	0.758475i
$739$	−9665.82	+	16741.7i	−0.481141	+	0.833360i	−0.999766	−	0.0216418i	$-0.993111\pi$
$739$	−9665.82	+	16741.7i	−0.481141	+	0.833360i	0.518625	+	0.855002i	$0.326444\pi$
$740$	6139.03			0.304967
$741$	−1616.76	+	3607.36i	−0.0801529	+	0.178839i
$742$	−10345.5			−0.511852
$743$	−17887.4	+	30981.9i	−0.883211	+	1.52977i	−0.0354597	+	0.999371i	$0.511290\pi$
$743$	−17887.4	+	30981.9i	−0.883211	+	1.52977i	−0.847751	+	0.530395i	$0.822044\pi$
$744$	−949.743	+	1645.00i	−0.0468001	+	0.0810601i
$745$	−14532.1	−	25170.4i	−0.714653	−	1.23782i
$746$	22793.4			1.11867
$747$	−12934.2	−	22402.7i	−0.633517	−	1.09728i
$748$	720.977	+	1248.77i	0.0352427	+	0.0610422i
$749$	2657.50			0.129644
$750$	1123.74	+	1946.37i	0.0547107	+	0.0947617i
$751$	−7227.40	+	12518.2i	−0.351174	+	0.608251i	−0.986455	−	0.164030i	$-0.947551\pi$
$751$	−7227.40	+	12518.2i	−0.351174	+	0.608251i	0.635282	+	0.772281i	$0.280884\pi$
$752$	−13116.3	+	22718.1i	−0.636041	+	1.10166i
$753$	−2163.82			−0.104720
$754$	−20469.2	+	2100.40i	−0.988651	+	0.101448i
$755$	29210.2			1.40804
$756$	−356.075	+	616.740i	−0.0171301	+	0.0296701i
$757$	12501.2	−	21652.7i	0.600215	−	1.03960i	−0.392573	−	0.919721i	$-0.628415\pi$
$757$	12501.2	−	21652.7i	0.600215	−	1.03960i	0.992788	−	0.119882i	$-0.0382517\pi$
$758$	−6690.20	−	11587.8i	−0.320579	−	0.555259i
$759$	−457.684			−0.0218879
$760$	−16455.3	−	28501.4i	−0.785391	−	1.36034i
$761$	−18009.9	−	31194.1i	−0.857897	−	1.48592i	−0.873931	−	0.486049i	$-0.838438\pi$
$761$	−18009.9	−	31194.1i	−0.857897	−	1.48592i	0.0160348	−	0.999871i	$-0.494896\pi$
$762$	1054.87			0.0501494
$763$	1545.37	+	2676.67i	0.0733241	+	0.127001i
$764$	1769.27	−	3064.46i	0.0837826	−	0.145116i
$765$	−10461.4	+	18119.7i	−0.494421	+	0.856363i
$766$	−20657.8			−0.974407
$767$	12420.7	−	1274.52i	0.584726	−	0.0600004i
$768$	−1800.66			−0.0846037
$769$	5981.52	−	10360.3i	0.280493	−	0.485828i	−0.691013	−	0.722842i	$-0.742835\pi$
$769$	5981.52	−	10360.3i	0.280493	−	0.485828i	0.971506	+	0.237014i	$0.0761688\pi$
$770$	2313.41	−	4006.94i	0.108272	−	0.187533i
$771$	−1364.69	−	2363.71i	−0.0637458	−	0.110411i
$772$	7363.06			0.343267
$773$	4501.78	+	7797.31i	0.209467	+	0.362807i	0.951547	−	0.307504i	$-0.0994939\pi$
$773$	4501.78	+	7797.31i	0.209467	+	0.362807i	−0.742080	+	0.670311i	$0.766161\pi$
$774$	12763.7	+	22107.3i	0.592740	+	1.02666i
$775$	−5125.33			−0.237558
$776$	−16165.8	−	27999.9i	−0.747831	−	1.29528i
$777$	754.824	−	1307.39i	0.0348509	−	0.0603636i
$778$	−17260.8	+	29896.7i	−0.795413	+	1.37770i
$779$	29158.0			1.34107
$780$	−298.649	+	666.351i	−0.0137094	+	0.0305887i
$781$	−2402.92			−0.110094
$782$	−6929.64	+	12002.5i	−0.316884	+	0.548859i
$783$	2226.62	−	3856.63i	0.101626	−	0.176021i
$784$	−8780.33	−	15208.0i	−0.399979	−	0.692783i
$785$	28378.6			1.29029
$786$	−1404.13	−	2432.03i	−0.0637197	−	0.110366i
$787$	−1161.12	−	2011.11i	−0.0525912	−	0.0910907i	0.838531	−	0.544853i	$-0.183415\pi$
$787$	−1161.12	−	2011.11i	−0.0525912	−	0.0910907i	−0.891123	+	0.453763i	$0.850081\pi$
$788$	−5390.59			−0.243695
$789$	374.679	+	648.963i	0.0169061	+	0.0292823i
$790$	−5738.01	+	9938.52i	−0.258417	+	0.447591i
$791$	−1921.59	+	3328.30i	−0.0863768	+	0.149609i
$792$	−5507.08			−0.247078
$793$	34219.5	−	3511.36i	1.53237	−	0.157241i
$794$	28640.5			1.28012
$795$	1147.89	−	1988.21i	0.0512096	−	0.0886976i
$796$	4870.72	−	8436.33i	0.216882	−	0.375651i
$797$	4554.25	+	7888.19i	0.202409	+	0.350582i	0.949304	−	0.314359i	$-0.101790\pi$
$797$	4554.25	+	7888.19i	0.202409	+	0.350582i	−0.746895	+	0.664942i	$0.768456\pi$
$798$	2845.23			0.126216
$799$	−10826.5	−	18752.1i	−0.479368	−	0.830291i
$800$	−1400.11	−	2425.06i	−0.0618767	−	0.107174i
$801$	−37448.0			−1.65189
$802$	−964.019	−	1669.73i	−0.0424448	−	0.0735165i
$803$	4494.84	−	7785.30i	0.197534	−	0.342138i
$804$	−112.874	+	195.504i	−0.00495120	+	0.00857573i
$805$	9179.71			0.401916
$806$	14674.3	+	20302.4i	0.641289	+	0.887249i
$807$	2525.96			0.110183
$808$	16079.8	−	27851.0i	0.700105	−	1.21262i
$809$	10293.9	−	17829.5i	0.447359	−	0.774849i	−0.550854	−	0.834602i	$-0.685698\pi$
$809$	10293.9	−	17829.5i	0.447359	−	0.774849i	0.998213	+	0.0597525i	$0.0190312\pi$
$810$	13853.7	+	23995.3i	0.600950	+	1.04088i
$811$	−36898.8			−1.59765			−0.798823	−	0.601566i	$-0.794544\pi$
$811$	−36898.8			−1.59765			−0.798823	+	0.601566i	$0.794544\pi$
$812$	1528.56	+	2647.55i	0.0660616	+	0.114422i
$813$	−2023.97	−	3505.61i	−0.0873107	−	0.151227i
$814$	−8264.00			−0.355839
$815$	−6338.80	−	10979.1i	−0.272440	−	0.471879i
$816$	1443.36	−	2499.98i	0.0619214	−	0.107251i
$817$	21195.3	−	36711.3i	0.907624	−	1.57205i
$818$	46966.8			2.00752
$819$	−7771.89	−	10752.7i	−0.331590	−	0.458768i
$820$	5386.07			0.229378
$821$	−13008.7	+	22531.7i	−0.552991	+	0.957808i	0.445066	+	0.895498i	$0.353180\pi$
$821$	−13008.7	+	22531.7i	−0.552991	+	0.957808i	−0.998057	+	0.0623105i	$0.980153\pi$
$822$	1325.86	−	2296.45i	0.0562586	−	0.0974427i
$823$	21391.8	+	37051.7i	0.906041	+	1.56931i	0.819514	+	0.573060i	$0.194244\pi$
$823$	21391.8	+	37051.7i	0.906041	+	1.56931i	0.0865274	+	0.996249i	$0.472423\pi$
$824$	−14191.4			−0.599975
$825$	100.559	+	174.173i	0.00424364	+	0.00735019i
$826$	−4493.35	−	7782.71i	−0.189278	−	0.327839i
$827$	8366.69			0.351800			0.175900	−	0.984408i	$-0.443716\pi$
$827$	8366.69			0.351800			0.175900	+	0.984408i	$0.443716\pi$
$828$	1920.63	+	3326.63i	0.0806117	+	0.139624i
$829$	−15259.1	+	26429.5i	−0.639289	+	1.10728i	0.346300	+	0.938124i	$0.387438\pi$
$829$	−15259.1	+	26429.5i	−0.639289	+	1.10728i	−0.985589	+	0.169157i	$0.945895\pi$
$830$	−19220.2	+	33290.4i	−0.803788	+	1.39220i
$831$	−376.768			−0.0157279
$832$	6106.57	−	13625.1i	0.254456	−	0.567747i
$833$	14495.0			0.602908
$834$	−1798.68	+	3115.41i	−0.0746801	+	0.129350i
$835$	12910.7	−	22362.0i	0.535083	−	0.926790i
$836$	−1607.53	−	2784.33i	−0.0665044	−	0.115189i
$837$	−5421.47			−0.223887
$838$	−13774.5	−	23858.1i	−0.567817	−	0.983488i
$839$	20456.8	+	35432.1i	0.841771	+	1.45799i	0.888396	+	0.459078i	$0.151820\pi$
$839$	20456.8	+	35432.1i	0.841771	+	1.45799i	−0.0466253	+	0.998912i	$0.514847\pi$
$840$	−1494.95			−0.0614055
$841$	2636.03	+	4565.74i	0.108083	+	0.187205i
$842$	14582.7	−	25258.0i	0.596856	−	1.03378i
$843$	2656.43	−	4601.08i	0.108532	−	0.187983i
$844$	10297.7			0.419978
$845$	−18228.3	−	20446.3i	−0.742096	−	0.832397i
$846$	−29073.3			−1.18152
$847$	−642.836	+	1113.43i	−0.0260781	+	0.0451685i
$848$	11701.6	−	20267.8i	0.473863	−	0.820755i
$849$	−2493.36	−	4318.63i	−0.100791	−	0.174576i
$850$	6090.09			0.245751
$851$	−8197.98	−	14199.3i	−0.330227	−	0.571970i
$852$	−136.477	−	236.384i	−0.00548781	−	0.00950516i
$853$	−42770.2			−1.71679			−0.858396	−	0.512988i	$-0.828539\pi$
$853$	−42770.2			−1.71679			−0.858396	+	0.512988i	$0.828539\pi$
$854$	−12379.4	−	21441.7i	−0.496035	−	0.859157i
$855$	23325.3	−	40400.7i	0.932994	−	1.61599i
$856$	−2350.19	+	4070.64i	−0.0938408	+	0.162537i
$857$	36034.8			1.43632			0.718160	−	0.695878i	$-0.244984\pi$
$857$	36034.8			1.43632			0.718160	+	0.695878i	$0.244984\pi$
$858$	402.023	−	897.002i	0.0159963	−	0.0356913i
$859$	35219.1			1.39890			0.699452	−	0.714679i	$-0.253427\pi$
$859$	35219.1			1.39890			0.699452	+	0.714679i	$0.253427\pi$
$860$	3915.19	−	6781.31i	0.155241	−	0.268885i
$861$	662.244	−	1147.04i	0.0262128	−	0.0454019i
$862$	20130.1	+	34866.4i	0.795399	+	1.37767i
$863$	9065.72			0.357591			0.178795	−	0.983886i	$-0.442780\pi$
$863$	9065.72			0.357591			0.178795	+	0.983886i	$0.442780\pi$
$864$	−1481.01	−	2565.18i	−0.0583158	−	0.101006i
$865$	12349.2	+	21389.5i	0.485417	+	0.840768i
$866$	2264.90			0.0888735
$867$	−283.638	−	491.275i	−0.0111105	−	0.0192440i
$868$	1860.90	−	3223.17i	0.0727685	−	0.126039i
$869$	1594.44	−	2761.66i	0.0622415	−	0.107805i
$870$	−3286.53			−0.128073
$871$	−4960.65	−	6863.26i	−0.192980	−	0.266995i
$872$	−5466.66			−0.212299
$873$	22914.9	−	39689.7i	0.888375	−	1.53871i
$874$	15450.7	−	26761.4i	0.597973	−	1.03572i
$875$	6262.90	+	10847.7i	0.241971	+	0.419106i
$876$	1021.16			0.0393856
$877$	−21900.1	−	37932.1i	−0.843232	−	1.46052i	−0.887148	−	0.461486i	$-0.847317\pi$
$877$	−21900.1	−	37932.1i	−0.843232	−	1.46052i	0.0439154	−	0.999035i	$-0.486017\pi$
$878$	−23508.2	−	40717.5i	−0.903605	−	1.56509i
$879$	870.000			0.0333838
$880$	5233.34	+	9064.41i	0.200473	+	0.347229i
$881$	14432.1	−	24997.0i	0.551905	−	0.955927i	−0.446232	−	0.894917i	$-0.647234\pi$
$881$	14432.1	−	24997.0i	0.551905	−	0.955927i	0.998137	−	0.0610101i	$-0.0194322\pi$
$882$	9731.15	−	16854.8i	0.371502	−	0.643460i
$883$	35808.9			1.36474			0.682369	−	0.731008i	$-0.260950\pi$
$883$	35808.9			1.36474			0.682369	+	0.731008i	$0.260950\pi$
$884$	−3599.28	−	4979.75i	−0.136942	−	0.189465i
$885$	1994.26			0.0757473
$886$	3767.72	−	6525.88i	0.142866	−	0.247451i
$887$	5113.25	−	8856.41i	0.193558	−	0.335253i	−0.752869	−	0.658171i	$-0.771330\pi$
$887$	5113.25	−	8856.41i	0.193558	−	0.335253i	0.946427	+	0.322918i	$0.104664\pi$
$888$	1335.07	+	2312.41i	0.0504527	+	0.0873867i
$889$	5879.08			0.221798
$890$	27823.9	+	48192.4i	1.04793	+	1.81507i
$891$	−3849.59	−	6667.68i	−0.144743	−	0.250702i
$892$	293.547			0.0110187
$893$	24139.5	+	41810.8i	0.904588	+	1.56679i
$894$	−2222.13	+	3848.84i	−0.0831311	+	0.143987i
$895$	21450.0	−	37152.5i	0.801112	−	1.38757i
$896$	−18563.8			−0.692157
$897$	1940.05	−	199.074i	0.0722146	−	0.00741015i
$898$	−21886.0			−0.813303
$899$	−11636.7	+	20155.3i	−0.431707	+	0.747738i
$900$	843.970	−	1461.80i	0.0312581	−	0.0541407i
$901$	9658.84	+	16729.6i	0.357139	+	0.618583i
$902$	−7250.41			−0.267641
$903$	−962.784	−	1667.59i	−0.0354811	−	0.0614551i
$904$	−3398.76	−	5886.82i	−0.125045	−	0.216585i
$905$	−31737.6			−1.16574
$906$	−2233.28	−	3868.16i	−0.0818939	−	0.141844i
$907$	−12236.3	+	21193.9i	−0.447961	+	0.775891i	−0.998253	−	0.0590813i	$-0.981183\pi$
$907$	−12236.3	+	21193.9i	−0.447961	+	0.775891i	0.550292	+	0.834972i	$0.314516\pi$
$908$	1945.85	−	3370.32i	0.0711183	−	0.123181i
$909$	45586.0			1.66336
$910$	−8063.32	+	17991.0i	−0.293732	+	0.655382i
$911$	16334.0			0.594038			0.297019	−	0.954872i	$-0.404007\pi$
$911$	16334.0			0.594038			0.297019	+	0.954872i	$0.404007\pi$
$912$	−3218.21	+	5574.11i	−0.116848	+	0.202387i
$913$	5340.81	−	9250.55i	0.193598	−	0.335321i
$914$	−785.079	−	1359.80i	−0.0284115	−	0.0492101i
$915$	5494.28			0.198508
$916$	−3788.78	−	6562.36i	−0.136665	−	0.236710i
$917$	−7825.63	−	13554.4i	−0.281816	−	0.488119i
$918$	6441.97			0.231608
$919$	8181.48	+	14170.7i	0.293669	+	0.508650i	0.974674	−	0.223629i	$-0.0717902\pi$
$919$	8181.48	+	14170.7i	0.293669	+	0.508650i	−0.681005	+	0.732279i	$0.738457\pi$
$920$	−8118.15	+	14061.1i	−0.290921	+	0.503890i
$921$	−941.365	+	1630.49i	−0.0336797	+	0.0583350i
$922$	−28026.3			−1.00108
$923$	10185.6	−	1045.17i	0.363232	−	0.0372723i
$924$	−146.043			−0.00519962
$925$	−3602.39	+	6239.51i	−0.128049	+	0.221788i
$926$	−26651.3	+	46161.4i	−0.945805	+	1.63818i
$927$	−10058.1	−	17421.1i	−0.356366	−	0.617244i
$928$	−12715.3			−0.449786
$929$	−15218.0	−	26358.3i	−0.537444	−	0.930880i	−0.999041	−	0.0437901i	$-0.986057\pi$
$929$	−15218.0	−	26358.3i	−0.537444	−	0.930880i	0.461597	−	0.887090i	$-0.347277\pi$
$930$	2000.54	+	3465.03i	0.0705379	+	0.122175i
$931$	−32318.9			−1.13771
$932$	−541.760	−	938.357i	−0.0190407	−	0.0329795i
$933$	−1915.93	+	3318.48i	−0.0672290	+	0.116444i
$934$	−11295.1	+	19563.8i	−0.395705	+	0.685381i
$935$	−8639.47			−0.302183
$936$	23343.7	−	2395.36i	0.815184	−	0.0836484i
$937$	−6898.43			−0.240514			−0.120257	−	0.992743i	$-0.538372\pi$
$937$	−6898.43			−0.240514			−0.120257	+	0.992743i	$0.538372\pi$
$938$	−3047.53	+	5278.48i	−0.106082	+	0.183740i
$939$	−268.756	+	465.498i	−0.00934026	+	0.0161778i
$940$	4459.05	+	7723.29i	0.154721	+	0.267985i
$941$	−2825.01			−0.0978668			−0.0489334	−	0.998802i	$-0.515582\pi$
$941$	−2825.01			−0.0978668			−0.0489334	+	0.998802i	$0.515582\pi$
$942$	−2169.70	−	3758.04i	−0.0750454	−	0.129982i
$943$	−7192.49	−	12457.8i	−0.248377	−	0.430202i
$944$	20329.5			0.700921
$945$	−2133.42	−	3695.20i	−0.0734394	−	0.127201i
$946$	−5270.40	+	9128.60i	−0.181137	+	0.313738i
$947$	−18702.6	+	32393.8i	−0.641766	+	1.11157i	0.343272	+	0.939236i	$0.388465\pi$
$947$	−18702.6	+	32393.8i	−0.641766	+	1.11157i	−0.985038	+	0.172336i	$0.944869\pi$
$948$	362.234			0.0124101
$949$	−15666.7	+	34955.8i	−0.535892	+	1.19569i
$950$	−13578.8			−0.463742
$951$	423.644	−	733.773i	0.0144454	−	0.0250202i
$952$	6289.54	−	10893.8i	0.214123	−	0.370872i
$953$	−21915.8	−	37959.4i	−0.744936	−	1.29027i	−0.950225	−	0.311565i	$-0.899147\pi$
$953$	−21915.8	−	37959.4i	−0.744936	−	1.29027i	0.205289	−	0.978701i	$-0.434187\pi$
$954$	25937.6			0.880253
$955$	10600.6	+	18360.7i	0.359190	+	0.622135i
$956$	1174.04	+	2033.50i	0.0397188	+	0.0687950i
$957$	913.241			0.0308473
$958$	−28717.8	−	49740.7i	−0.968508	−	1.67750i
$959$	7389.37	−	12798.8i	0.248817	−	0.430963i
$960$	1192.40	−	2065.29i	0.0400879	−	0.0694343i
$961$	−1457.64			−0.0489288
$962$	35029.9	−	3594.51i	1.17402	−	0.120470i
$963$	−6662.76			−0.222954
$964$	330.226	−	571.968i	0.0110330	−	0.0191098i
$965$	−22057.9	+	38205.3i	−0.735821	+	1.27448i
$966$	−701.841	−	1215.62i	−0.0233762	−	0.0404887i
$967$	−28908.3			−0.961352			−0.480676	−	0.876898i	$-0.659609\pi$
$967$	−28908.3			−0.961352			−0.480676	+	0.876898i	$0.659609\pi$
$968$	−1137.00	−	1969.33i	−0.0377525	−	0.0653893i
$969$	−2656.39	−	4601.01i	−0.0880657	−	0.152534i
$970$	−68103.1			−2.25429
$971$	2010.52	+	3482.32i	0.0664477	+	0.115091i	0.897335	−	0.441350i	$-0.145500\pi$
$971$	2010.52	+	3482.32i	0.0664477	+	0.115091i	−0.830888	+	0.556440i	$0.812167\pi$
$972$	1342.10	−	2324.59i	0.0442879	−	0.0767090i
$973$	−10024.6	+	17363.0i	−0.330290	+	0.572080i
$974$	28033.0			0.922214
$975$	−502.011	−	694.552i	−0.0164894	−	0.0228138i
$976$	56008.7			1.83688
$977$	−16483.2	+	28549.8i	−0.539760	+	0.934892i	0.459156	+	0.888356i	$0.348152\pi$
$977$	−16483.2	+	28549.8i	−0.539760	+	0.934892i	−0.998917	+	0.0465368i	$0.985182\pi$
$978$	−969.274	+	1678.83i	−0.0316912	+	0.0548907i
$979$	−7731.55	−	13391.4i	−0.252402	−	0.437173i
$980$	−5969.96			−0.194595
$981$	−3874.48	−	6710.80i	−0.126099	−	0.218409i
$982$	24226.4	+	41961.4i	0.787268	+	1.36359i
$983$	20732.5			0.672699			0.336350	−	0.941737i	$-0.390808\pi$
$983$	20732.5			0.672699			0.336350	+	0.941737i	$0.390808\pi$
$984$	1171.32	+	2028.79i	0.0379475	+	0.0657271i
$985$	16148.8	−	27970.6i	0.522381	−	0.904790i
$986$	13827.1	−	23949.2i	0.446596	−	0.773526i
$987$	2193.05			0.0707249
$988$	8025.16	+	11103.1i	0.258415	+	0.357528i
$989$	−20913.2			−0.672397
$990$	−5800.06	+	10046.0i	−0.186200	+	0.322508i
$991$	−17169.4	+	29738.3i	−0.550357	+	0.953246i	0.447892	+	0.894088i	$0.352175\pi$
$991$	−17169.4	+	29738.3i	−0.550357	+	0.953246i	−0.998249	+	0.0591582i	$0.981158\pi$
$992$	7739.95	+	13406.0i	0.247725	+	0.429073i
$993$	215.139			0.00687536
$994$	−3684.78	−	6382.23i	−0.117580	−	0.203654i
$995$	29182.9	+	50546.3i	0.929809	+	1.61048i
$996$	1213.35			0.0386009
$997$	896.020	+	1551.95i	0.0284626	+	0.0492987i	0.879906	−	0.475148i	$-0.157606\pi$
$997$	896.020	+	1551.95i	0.0284626	+	0.0492987i	−0.851443	+	0.524447i	$0.824272\pi$
$998$	10633.6	−	18418.0i	0.337276	−	0.584179i
$999$	−3810.53	+	6600.03i	−0.120680	+	0.209025i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.e.b.100.14	✓	34
13.3	even	3	inner	143.4.e.b.133.14	yes	34
13.4	even	6		1859.4.a.h.1.14		17
13.9	even	3		1859.4.a.g.1.4		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.b.100.14	✓	34	1.1	even	1	trivial
143.4.e.b.133.14	yes	34	13.3	even	3	inner
1859.4.a.g.1.4		17	13.9	even	3
1859.4.a.h.1.14		17	13.4	even	6

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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	143.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.58752 - 2.74967i) q^{2} +(0.300230 - 0.520013i) q^{3} +(-1.04047 - 1.80214i) q^{4} +12.4679 q^{5} +(-0.953244 - 1.65107i) q^{6} +(-5.31270 - 9.20186i) q^{7} +18.7933 q^{8} +(13.3197 + 23.0704i) q^{9} +(19.7931 - 34.2827i) q^{10} +(-5.50000 + 9.52628i) q^{11} -1.24952 q^{12} +(19.1701 - 42.7727i) q^{13} -33.7362 q^{14} +(3.74324 - 6.48348i) q^{15} +(38.1586 - 66.0926i) q^{16} +(31.4971 + 54.5545i) q^{17} +84.5816 q^{18} +(-70.2277 - 121.638i) q^{19} +(-12.9725 - 22.4690i) q^{20} -6.38012 q^{21} +(17.4628 + 30.2464i) q^{22} +(-34.6465 + 60.0095i) q^{23} +(5.64231 - 9.77277i) q^{24} +30.4490 q^{25} +(-87.1780 - 120.614i) q^{26} +32.2083 q^{27} +(-11.0554 + 19.1485i) q^{28} +(69.1320 - 119.740i) q^{29} +(-11.8850 - 20.5854i) q^{30} -168.325 q^{31} +(-45.9821 - 79.6434i) q^{32} +(3.30253 + 5.72014i) q^{33} +200.010 q^{34} +(-66.2383 - 114.728i) q^{35} +(27.7175 - 48.0081i) q^{36} +(-118.309 + 204.917i) q^{37} -445.953 q^{38} +(-16.4869 - 22.8103i) q^{39} +234.314 q^{40} +(-103.798 + 179.784i) q^{41} +(-10.1286 + 17.5432i) q^{42} +(150.904 + 261.373i) q^{43} +22.8903 q^{44} +(166.069 + 287.640i) q^{45} +(110.004 + 190.533i) q^{46} -343.732 q^{47} +(-22.9127 - 39.6859i) q^{48} +(115.050 - 199.273i) q^{49} +(48.3385 - 83.7248i) q^{50} +37.8254 q^{51} +(-97.0285 + 9.95637i) q^{52} +306.658 q^{53} +(51.1315 - 88.5623i) q^{54} +(-68.5736 + 118.773i) q^{55} +(-99.8432 - 172.934i) q^{56} -84.3378 q^{57} +(-219.498 - 380.181i) q^{58} +(133.191 + 230.693i) q^{59} -15.5789 q^{60} +(366.947 + 635.571i) q^{61} +(-267.220 + 462.839i) q^{62} +(141.527 - 245.133i) q^{63} +318.546 q^{64} +(239.011 - 533.287i) q^{65} +20.9714 q^{66} +(90.3342 - 156.463i) q^{67} +(65.5434 - 113.524i) q^{68} +(20.8038 + 36.0333i) q^{69} -420.620 q^{70} +(109.224 + 189.181i) q^{71} +(250.322 + 433.570i) q^{72} -817.244 q^{73} +(375.636 + 650.621i) q^{74} +(9.14169 - 15.8339i) q^{75} +(-146.139 + 253.121i) q^{76} +116.879 q^{77} +(-88.8944 + 9.12171i) q^{78} -289.899 q^{79} +(475.758 - 824.037i) q^{80} +(-349.963 + 606.153i) q^{81} +(329.564 + 570.822i) q^{82} -971.055 q^{83} +(6.63831 + 11.4979i) q^{84} +(392.703 + 680.182i) q^{85} +958.254 q^{86} +(-41.5109 - 71.8991i) q^{87} +(-103.363 + 179.030i) q^{88} +(-702.868 + 1217.40i) q^{89} +1054.56 q^{90} +(-495.434 + 50.8379i) q^{91} +144.194 q^{92} +(-50.5362 + 87.5313i) q^{93} +(-545.682 + 945.149i) q^{94} +(-875.594 - 1516.57i) q^{95} -55.2208 q^{96} +(-860.186 - 1489.89i) q^{97} +(-365.291 - 632.702i) q^{98} -293.034 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 6 q^{3} - 50 q^{4} - 48 q^{5} - 16 q^{6} + 62 q^{7} - 42 q^{8} - 135 q^{9} - 2 q^{10} - 187 q^{11} - 254 q^{12} + 76 q^{13} + 148 q^{15} - 126 q^{16} + 74 q^{17} + 180 q^{18} + 159 q^{19} + 222 q^{20}+ \cdots + 2970 q^{99}+O(q^{100}) \) 34 * q + 6 * q^3 - 50 * q^4 - 48 * q^5 - 16 * q^6 + 62 * q^7 - 42 * q^8 - 135 * q^9 - 2 * q^10 - 187 * q^11 - 254 * q^12 + 76 * q^13 + 148 * q^15 - 126 * q^16 + 74 * q^17 + 180 * q^18 + 159 * q^19 + 222 * q^20 - 368 * q^21 + 215 * q^23 - 214 * q^24 + 190 * q^25 + 123 * q^26 - 384 * q^27 + 358 * q^28 + 157 * q^29 - 829 * q^30 - 788 * q^31 + 553 * q^32 + 66 * q^33 - 1404 * q^34 - 58 * q^35 + 700 * q^36 - 88 * q^37 - 2636 * q^38 + 798 * q^39 + 1466 * q^40 + 512 * q^41 - 337 * q^42 - 927 * q^43 + 1100 * q^44 + 1482 * q^45 + 1361 * q^46 - 286 * q^47 + 178 * q^48 - 1835 * q^49 + 583 * q^50 - 1136 * q^51 + 2306 * q^52 + 212 * q^53 + 67 * q^54 + 264 * q^55 - 2059 * q^56 + 2596 * q^57 + 1690 * q^58 + 266 * q^59 + 74 * q^60 + 624 * q^61 - 643 * q^62 + 2360 * q^63 - 3178 * q^64 + 470 * q^65 + 352 * q^66 + 676 * q^67 + 413 * q^68 - 764 * q^69 - 2122 * q^70 + 763 * q^71 + 1366 * q^72 - 4748 * q^73 + 1649 * q^74 - 2420 * q^75 + 2101 * q^76 - 1364 * q^77 - 5848 * q^78 + 4328 * q^79 + 1013 * q^80 - 537 * q^81 - 3152 * q^82 + 1554 * q^83 + 3381 * q^84 + 1690 * q^85 + 5788 * q^86 + 4200 * q^87 + 231 * q^88 + 1687 * q^89 - 10798 * q^90 - 3380 * q^91 + 11084 * q^92 + 4310 * q^93 - 1777 * q^94 - 1124 * q^95 - 6930 * q^96 + 2047 * q^97 - 1553 * q^98 + 2970 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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