LMFDB - Embedded newform 143.4.e.b.133.3

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			133.3
Character	$\chi$	$=$	143.133
Dual form			143.4.e.b.100.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.07785 - 3.59895i) q^{2} +(-3.58804 - 6.21467i) q^{3} +(-4.63495 + 8.02797i) q^{4} -11.1721 q^{5} +(-14.9108 + 25.8263i) q^{6} +(3.89211 - 6.74134i) q^{7} +5.27734 q^{8} +(-12.2481 + 21.2143i) q^{9} +(23.2141 + 40.2080i) q^{10} +(-5.50000 - 9.52628i) q^{11} +66.5216 q^{12} +(-28.1573 + 37.4722i) q^{13} -32.3490 q^{14} +(40.0861 + 69.4312i) q^{15} +(26.1141 + 45.2309i) q^{16} +(5.56783 - 9.64377i) q^{17} +101.799 q^{18} +(64.5583 - 111.818i) q^{19} +(51.7823 - 89.6897i) q^{20} -55.8602 q^{21} +(-22.8564 + 39.5884i) q^{22} +(-97.1550 - 168.277i) q^{23} +(-18.9353 - 32.7970i) q^{24} -0.183205 q^{25} +(193.367 + 23.4748i) q^{26} -17.9678 q^{27} +(36.0795 + 62.4915i) q^{28} +(65.2577 + 113.030i) q^{29} +(166.586 - 288.536i) q^{30} +160.453 q^{31} +(129.632 - 224.529i) q^{32} +(-39.4685 + 68.3614i) q^{33} -46.2766 q^{34} +(-43.4832 + 75.3152i) q^{35} +(-113.538 - 196.654i) q^{36} +(45.5731 + 78.9349i) q^{37} -536.571 q^{38} +(333.907 + 40.5363i) q^{39} -58.9593 q^{40} +(149.239 + 258.490i) q^{41} +(116.069 + 201.038i) q^{42} +(-55.9464 + 96.9021i) q^{43} +101.969 q^{44} +(136.837 - 237.009i) q^{45} +(-403.748 + 699.311i) q^{46} -247.250 q^{47} +(187.397 - 324.581i) q^{48} +(141.203 + 244.571i) q^{49} +(0.380672 + 0.659344i) q^{50} -79.9105 q^{51} +(-170.318 - 399.728i) q^{52} -353.642 q^{53} +(37.3344 + 64.6651i) q^{54} +(61.4468 + 106.429i) q^{55} +(20.5400 - 35.5764i) q^{56} -926.552 q^{57} +(271.192 - 469.718i) q^{58} +(-81.2938 + 140.805i) q^{59} -743.189 q^{60} +(-97.3380 + 168.594i) q^{61} +(-333.398 - 577.463i) q^{62} +(95.3418 + 165.137i) q^{63} -659.598 q^{64} +(314.577 - 418.645i) q^{65} +328.039 q^{66} +(478.153 + 828.186i) q^{67} +(51.6133 + 89.3968i) q^{68} +(-697.192 + 1207.57i) q^{69} +361.407 q^{70} +(210.272 - 364.202i) q^{71} +(-64.6373 + 111.955i) q^{72} -306.549 q^{73} +(189.388 - 328.030i) q^{74} +(0.657345 + 1.13856i) q^{75} +(598.449 + 1036.54i) q^{76} -85.6265 q^{77} +(-547.922 - 1285.94i) q^{78} -545.170 q^{79} +(-291.750 - 505.326i) q^{80} +(395.167 + 684.450i) q^{81} +(620.194 - 1074.21i) q^{82} -452.825 q^{83} +(258.910 - 448.444i) q^{84} +(-62.2047 + 107.742i) q^{85} +464.994 q^{86} +(468.295 - 811.111i) q^{87} +(-29.0254 - 50.2735i) q^{88} +(-141.479 - 245.048i) q^{89} -1137.31 q^{90} +(143.022 + 335.664i) q^{91} +1801.23 q^{92} +(-575.713 - 997.164i) q^{93} +(513.748 + 889.838i) q^{94} +(-721.255 + 1249.25i) q^{95} -1860.50 q^{96} +(-106.747 + 184.891i) q^{97} +(586.798 - 1016.36i) q^{98} +269.458 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 $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

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

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 $

$2$	−2.07785	−	3.59895i	−0.734632	−	1.27242i	−0.954885	−	0.296977i	$-0.904021\pi$
$2$	−2.07785	−	3.59895i	−0.734632	−	1.27242i	0.220252	−	0.975443i	$-0.429312\pi$
$3$	−3.58804	−	6.21467i	−0.690519	−	1.19601i	−0.971668	−	0.236350i	$-0.924049\pi$
$3$	−3.58804	−	6.21467i	−0.690519	−	1.19601i	0.281149	−	0.959664i	$-0.409284\pi$
$4$	−4.63495	+	8.02797i	−0.579369	+	1.00350i
$5$	−11.1721			−0.999267			−0.499633	−	0.866237i	$-0.666532\pi$
$5$	−11.1721			−0.999267			−0.499633	+	0.866237i	$0.666532\pi$
$6$	−14.9108	+	25.8263i	−1.01455	+	1.75726i
$7$	3.89211	−	6.74134i	0.210154	−	0.363998i	−0.741608	−	0.670833i	$-0.765937\pi$
$7$	3.89211	−	6.74134i	0.210154	−	0.363998i	0.951763	+	0.306835i	$0.0992700\pi$
$8$	5.27734			0.233228
$9$	−12.2481	+	21.2143i	−0.453633	+	0.785715i
$10$	23.2141	+	40.2080i	0.734094	+	1.27149i
$11$	−5.50000	−	9.52628i	−0.150756	−	0.261116i
$11$	−5.50000	−	9.52628i	−0.150756	−	0.261116i
$12$	66.5216			1.60026
$13$	−28.1573	+	37.4722i	−0.600725	+	0.799456i
$13$	−28.1573	+	37.4722i	−0.600725	+	0.799456i
$14$	−32.3490			−0.617545
$15$	40.0861	+	69.4312i	0.690013	+	1.19514i
$16$	26.1141	+	45.2309i	0.408032	+	0.706733i
$17$	5.56783	−	9.64377i	0.0794352	−	0.137586i	−0.823571	−	0.567213i	$-0.808022\pi$
$17$	5.56783	−	9.64377i	0.0794352	−	0.137586i	0.903006	+	0.429627i	$0.141355\pi$
$18$	101.799			1.33301
$19$	64.5583	−	111.818i	0.779510	−	1.35015i	−0.152714	−	0.988270i	$-0.548801\pi$
$19$	64.5583	−	111.818i	0.779510	−	1.35015i	0.932224	−	0.361881i	$-0.117865\pi$
$20$	51.7823	−	89.6897i	0.578944	−	1.00276i
$21$	−55.8602			−0.580462
$22$	−22.8564	+	39.5884i	−0.221500	+	0.383649i
$23$	−97.1550	−	168.277i	−0.880792	−	1.52558i	−0.850462	−	0.526036i	$-0.823678\pi$
$23$	−97.1550	−	168.277i	−0.880792	−	1.52558i	−0.0303294	−	0.999540i	$-0.509656\pi$
$24$	−18.9353	−	32.7970i	−0.161048	−	0.278944i
$25$	−0.183205			−0.00146564
$26$	193.367	+	23.4748i	1.45856	+	0.177069i
$27$	−17.9678			−0.128070
$28$	36.0795	+	62.4915i	0.243514	+	0.421778i
$29$	65.2577	+	113.030i	0.417864	+	0.723762i	0.995724	−	0.0923739i	$-0.0294455\pi$
$29$	65.2577	+	113.030i	0.417864	+	0.723762i	−0.577860	+	0.816136i	$0.696112\pi$
$30$	166.586	−	288.536i	1.01381	−	1.75597i
$31$	160.453			0.929621			0.464810	−	0.885410i	$-0.346122\pi$
$31$	160.453			0.929621			0.464810	+	0.885410i	$0.346122\pi$
$32$	129.632	−	224.529i	0.716121	−	1.24036i
$33$	−39.4685	+	68.3614i	−0.208199	+	0.360612i
$34$	−46.2766			−0.233423
$35$	−43.4832	+	75.3152i	−0.210000	+	0.363731i
$36$	−113.538	−	196.654i	−0.525641	−	0.910437i
$37$	45.5731	+	78.9349i	0.202491	+	0.350725i	0.949330	−	0.314280i	$-0.101763\pi$
$37$	45.5731	+	78.9349i	0.202491	+	0.350725i	−0.746839	+	0.665004i	$0.768430\pi$
$38$	−536.571			−2.29061
$39$	333.907	+	40.5363i	1.37097	+	0.166436i
$40$	−58.9593			−0.233057
$41$	149.239	+	258.490i	0.568469	+	0.984618i	0.996718	+	0.0809567i	$0.0257975\pi$
$41$	149.239	+	258.490i	0.568469	+	0.984618i	−0.428248	+	0.903661i	$0.640869\pi$
$42$	116.069	+	201.038i	0.426426	+	0.738592i
$43$	−55.9464	+	96.9021i	−0.198413	+	0.343661i	−0.948014	−	0.318229i	$-0.896912\pi$
$43$	−55.9464	+	96.9021i	−0.198413	+	0.343661i	0.749601	+	0.661890i	$0.230245\pi$
$44$	101.969			0.349373
$45$	136.837	−	237.009i	0.453300	−	0.785139i
$46$	−403.748	+	699.311i	−1.29412	+	2.24147i
$47$	−247.250			−0.767342			−0.383671	−	0.923470i	$-0.625340\pi$
$47$	−247.250			−0.767342			−0.383671	+	0.923470i	$0.625340\pi$
$48$	187.397	−	324.581i	0.563508	−	0.976024i
$49$	141.203	+	244.571i	0.411670	+	0.713034i
$50$	0.380672	+	0.659344i	0.00107670	+	0.00186491i
$51$	−79.9105			−0.219406
$52$	−170.318	−	399.728i	−0.454210	−	1.06601i
$53$	−353.642			−0.916536			−0.458268	−	0.888814i	$-0.651530\pi$
$53$	−353.642			−0.916536			−0.458268	+	0.888814i	$0.651530\pi$
$54$	37.3344	+	64.6651i	0.0940847	+	0.162959i
$55$	61.4468	+	106.429i	0.150645	+	0.260925i
$56$	20.5400	−	35.5764i	0.0490139	−	0.0848945i
$57$	−926.552			−2.15307
$58$	271.192	−	469.718i	0.613953	−	1.06340i
$59$	−81.2938	+	140.805i	−0.179382	+	0.310699i	−0.941669	−	0.336540i	$-0.890743\pi$
$59$	−81.2938	+	140.805i	−0.179382	+	0.310699i	0.762287	+	0.647239i	$0.224077\pi$
$60$	−743.189			−1.59909
$61$	−97.3380	+	168.594i	−0.204309	+	0.353874i	−0.949912	−	0.312516i	$-0.898828\pi$
$61$	−97.3380	+	168.594i	−0.204309	+	0.353874i	0.745603	+	0.666390i	$0.232161\pi$
$62$	−333.398	−	577.463i	−0.682929	−	1.18287i
$63$	95.3418	+	165.137i	0.190666	+	0.330243i
$64$	−659.598			−1.28828
$65$	314.577	−	418.645i	0.600285	−	0.798870i
$66$	328.039			0.611800
$67$	478.153	+	828.186i	0.871877	+	1.51013i	0.860053	+	0.510205i	$0.170430\pi$
$67$	478.153	+	828.186i	0.871877	+	1.51013i	0.0118239	+	0.999930i	$0.496236\pi$
$68$	51.6133	+	89.3968i	0.0920446	+	0.159426i
$69$	−697.192	+	1207.57i	−1.21641	+	2.10688i
$70$	361.407			0.617092
$71$	210.272	−	364.202i	0.351474	−	0.608772i	−0.635034	−	0.772485i	$-0.719014\pi$
$71$	210.272	−	364.202i	0.351474	−	0.608772i	0.986508	+	0.163713i	$0.0523471\pi$
$72$	−64.6373	+	111.955i	−0.105800	+	0.183251i
$73$	−306.549			−0.491491			−0.245746	−	0.969334i	$-0.579033\pi$
$73$	−306.549			−0.491491			−0.245746	+	0.969334i	$0.579033\pi$
$74$	189.388	−	328.030i	0.297513	−	0.515308i
$75$	0.657345	+	1.13856i	0.00101205	+	0.00175292i
$76$	598.449	+	1036.54i	0.903248	+	1.56447i
$77$	−85.6265			−0.126728
$78$	−547.922	−	1285.94i	−0.795384	−	1.86672i
$79$	−545.170			−0.776410			−0.388205	−	0.921573i	$-0.626905\pi$
$79$	−545.170			−0.776410			−0.388205	+	0.921573i	$0.626905\pi$
$80$	−291.750	−	505.326i	−0.407733	−	0.706214i
$81$	395.167	+	684.450i	0.542068	+	0.938889i
$82$	620.194	−	1074.21i	0.835232	−	1.44666i
$83$	−452.825			−0.598844			−0.299422	−	0.954121i	$-0.596794\pi$
$83$	−452.825			−0.598844			−0.299422	+	0.954121i	$0.596794\pi$
$84$	258.910	−	448.444i	0.336302	−	0.582492i
$85$	−62.2047	+	107.742i	−0.0793770	+	0.137485i
$86$	464.994			0.583042
$87$	468.295	−	811.111i	0.577086	−	0.999542i
$88$	−29.0254	−	50.2735i	−0.0351604	−	0.0608996i
$89$	−141.479	−	245.048i	−0.168502	−	0.291855i	0.769391	−	0.638778i	$-0.220560\pi$
$89$	−141.479	−	245.048i	−0.168502	−	0.291855i	−0.937893	+	0.346923i	$0.887226\pi$
$90$	−1137.31			−1.33204
$91$	143.022	+	335.664i	0.164755	+	0.386672i
$92$	1801.23			2.04121
$93$	−575.713	−	997.164i	−0.641921	−	1.11184i
$94$	513.748	+	889.838i	0.563714	+	0.976381i
$95$	−721.255	+	1249.25i	−0.778939	+	1.34916i
$96$	−1860.50			−1.97798
$97$	−106.747	+	184.891i	−0.111737	+	0.193535i	−0.916471	−	0.400102i	$-0.868975\pi$
$97$	−106.747	+	184.891i	−0.111737	+	0.193535i	0.804734	+	0.593636i	$0.202308\pi$
$98$	586.798	−	1016.36i	0.604853	−	1.04764i
$99$	269.458			0.273551
$100$	0.849144	−	1.47076i	0.000849144	−	0.00147076i
$101$	−862.574	−	1494.02i	−0.849795	−	1.47189i	−0.881391	−	0.472387i	$-0.843392\pi$
$101$	−862.574	−	1494.02i	−0.849795	−	1.47189i	0.0315962	−	0.999501i	$-0.489941\pi$
$102$	166.042	+	287.594i	0.161183	+	0.279177i
$103$	1416.79			1.35534			0.677672	−	0.735364i	$-0.262989\pi$
$103$	1416.79			1.35534			0.677672	+	0.735364i	$0.262989\pi$
$104$	−148.596	+	197.754i	−0.140106	+	0.186455i
$105$	624.079			0.580037
$106$	734.816	+	1272.74i	0.673317	+	1.16622i
$107$	146.497	+	253.741i	0.132359	+	0.229253i	0.924586	−	0.380974i	$-0.124411\pi$
$107$	146.497	+	253.741i	0.132359	+	0.229253i	−0.792226	+	0.610227i	$0.791078\pi$
$108$	83.2798	−	144.245i	0.0742001	−	0.128518i
$109$	−180.669			−0.158761			−0.0793806	−	0.996844i	$-0.525294\pi$
$109$	−180.669			−0.158761			−0.0793806	+	0.996844i	$0.525294\pi$
$110$	255.355	−	442.288i	0.221338	−	0.383368i
$111$	327.036	−	566.443i	0.279648	−	0.484364i
$112$	406.555			0.342999
$113$	−498.071	+	862.684i	−0.414642	+	0.718181i	−0.995391	−	0.0959018i	$-0.969427\pi$
$113$	−498.071	+	862.684i	−0.414642	+	0.718181i	0.580749	+	0.814083i	$0.302760\pi$
$114$	1925.24	+	3334.61i	1.58171	+	2.73960i
$115$	1085.43	+	1880.02i	0.880146	+	1.52446i
$116$	−1209.87			−0.968390
$117$	−450.074	−	1056.30i	−0.355636	−	0.834657i
$118$	675.666			0.527120
$119$	−43.3413	−	75.0693i	−0.0333873	−	0.0578285i
$120$	211.548	+	366.412i	0.160930	+	0.278739i
$121$	−60.5000	+	104.789i	−0.0454545	+	0.0787296i
$122$	809.017			0.600368
$123$	1070.95	−	1854.94i	0.785078	−	1.35979i
$124$	−743.693	+	1288.11i	−0.538593	+	0.932871i
$125$	1398.56			1.00073
$126$	396.213	−	686.260i	0.280138	−	0.485214i
$127$	−1135.59	−	1966.89i	−0.793440	−	1.37428i	−0.923825	−	0.382815i	$-0.874955\pi$
$127$	−1135.59	−	1966.89i	−0.793440	−	1.37428i	0.130384	−	0.991464i	$-0.458379\pi$
$128$	333.495	+	577.630i	0.230289	+	0.398873i
$129$	802.952			0.548031
$130$	−2160.33	−	262.264i	−1.45749	−	0.176939i
$131$	−1917.39			−1.27880			−0.639402	−	0.768872i	$-0.720818\pi$
$131$	−1917.39			−1.27880			−0.639402	+	0.768872i	$0.720818\pi$
$132$	−365.869	−	633.703i	−0.241248	−	0.417854i
$133$	−502.536	−	870.419i	−0.327635	−	0.567480i
$134$	1987.07	−	3441.70i	1.28102	−	2.21879i
$135$	200.739			0.127977
$136$	29.3834	−	50.8935i	0.0185265	−	0.0320888i
$137$	647.718	−	1121.88i	0.403929	−	0.699625i	−0.590267	−	0.807208i	$-0.700978\pi$
$137$	647.718	−	1121.88i	0.403929	−	0.699625i	0.994196	+	0.107582i	$0.0343110\pi$
$138$	5794.65			3.57445
$139$	−1427.71	+	2472.87i	−0.871200	+	1.50896i	−0.0104444	+	0.999945i	$0.503325\pi$
$139$	−1427.71	+	2472.87i	−0.871200	+	1.50896i	−0.860756	+	0.509018i	$0.830009\pi$
$140$	−403.085	−	698.164i	−0.243335	−	0.421469i
$141$	887.142	+	1536.57i	0.529864	+	0.917751i
$142$	−1747.66			−1.03282
$143$	511.836	+	62.1369i	0.299314	+	0.0363367i
$144$	−1279.39			−0.740387
$145$	−729.069	−	1262.78i	−0.417558	−	0.723231i
$146$	636.964	+	1103.25i	0.361065	+	0.625384i
$147$	1013.28	−	1755.06i	0.568532	−	0.984727i
$148$	−844.916			−0.469268
$149$	314.495	−	544.721i	0.172916	−	0.299499i	−0.766522	−	0.642218i	$-0.778015\pi$
$149$	314.495	−	544.721i	0.172916	−	0.299499i	0.939438	+	0.342719i	$0.111348\pi$
$150$	2.73173	−	4.73150i	0.00148697	−	0.00257550i
$151$	−13.3455			−0.00719233			−0.00359617	−	0.999994i	$-0.501145\pi$
$151$	−13.3455			−0.00719233			−0.00359617	+	0.999994i	$0.501145\pi$
$152$	340.697	−	590.104i	0.181804	−	0.314893i
$153$	136.391	+	236.235i	0.0720688	+	0.124827i
$154$	177.919	+	308.165i	0.0930983	+	0.161251i
$155$	−1792.61			−0.928939
$156$	−1873.07	+	2492.71i	−0.961316	+	1.27934i
$157$	−1586.13			−0.806288			−0.403144	−	0.915137i	$-0.632083\pi$
$157$	−1586.13			−0.806288			−0.403144	+	0.915137i	$0.632083\pi$
$158$	1132.78	+	1962.04i	0.570376	+	0.987920i
$159$	1268.88	+	2197.77i	0.632886	+	1.09619i
$160$	−1448.26	+	2508.47i	−0.715596	+	1.23945i
$161$	−1512.55			−0.740409
$162$	1642.20	−	2844.37i	0.796441	−	1.37948i
$163$	−304.037	+	526.608i	−0.146098	+	0.253050i	−0.929782	−	0.368110i	$-0.880005\pi$
$163$	−304.037	+	526.608i	−0.146098	+	0.253050i	0.783684	+	0.621160i	$0.213338\pi$
$164$	−2766.87			−1.31741
$165$	440.947	−	763.743i	0.208047	−	0.360347i
$166$	940.905	+	1629.69i	0.439930	+	0.761981i
$167$	527.397	+	913.479i	0.244379	+	0.423276i	0.961957	−	0.273202i	$-0.0880827\pi$
$167$	527.397	+	913.479i	0.244379	+	0.423276i	−0.717578	+	0.696478i	$0.754749\pi$
$168$	−294.794			−0.135380
$169$	−611.335	−	2110.23i	−0.278259	−	0.960506i
$170$	517.009			0.233251
$171$	1581.43	+	2739.12i	0.707222	+	1.22495i
$172$	−518.618	−	898.273i	−0.229908	−	0.398213i
$173$	−1654.39	+	2865.49i	−0.727057	+	1.25930i	0.231064	+	0.972938i	$0.425779\pi$
$173$	−1654.39	+	2865.49i	−0.727057	+	1.25930i	−0.958122	+	0.286362i	$0.907554\pi$
$174$	−3892.19			−1.69578
$175$	−0.713053	+	1.23504i	−0.000308010	+	0.000533489i
$176$	287.255	−	497.540i	0.123026	−	0.213088i
$177$	1166.74			0.495467
$178$	−587.944	+	1018.35i	−0.247574	+	0.428812i
$179$	1027.65	+	1779.95i	0.429108	+	0.743237i	0.996794	−	0.0800080i	$-0.0254946\pi$
$179$	1027.65	+	1779.95i	0.429108	+	0.743237i	−0.567686	+	0.823245i	$0.692161\pi$
$180$	1268.47	+	2197.05i	0.525256	+	0.909770i
$181$	−4694.21			−1.92772			−0.963862	−	0.266403i	$-0.914165\pi$
$181$	−4694.21			−1.92772			−0.963862	+	0.266403i	$0.914165\pi$
$182$	910.859	−	1212.19i	0.370974	−	0.493700i
$183$	1397.01			0.564317
$184$	−512.720	−	888.057i	−0.205425	−	0.355807i
$185$	−509.149	−	881.872i	−0.202343	−	0.350468i
$186$	−2392.49	+	4143.92i	−0.943151	+	1.63359i
$187$	−122.492			−0.0479012
$188$	1145.99	−	1984.91i	0.444574	−	0.770025i
$189$	−69.9327	+	121.127i	−0.0269146	+	0.0466174i
$190$	5994.65			2.28893
$191$	811.779	−	1406.04i	0.307530	−	0.532658i	−0.670291	−	0.742098i	$-0.733831\pi$
$191$	811.779	−	1406.04i	0.307530	−	0.532658i	0.977821	+	0.209440i	$0.0671642\pi$
$192$	2366.67	+	4099.19i	0.889580	+	1.54080i
$193$	−2583.20	−	4474.24i	−0.963435	−	1.66872i	−0.713763	−	0.700387i	$-0.753011\pi$
$193$	−2583.20	−	4474.24i	−0.963435	−	1.66872i	−0.249672	−	0.968331i	$-0.580323\pi$
$194$	887.219			0.328343
$195$	−3730.46	−	452.877i	−1.36997	−	0.166314i
$196$	−2617.87			−0.954036
$197$	−448.997	−	777.686i	−0.162384	−	0.281258i	0.773339	−	0.633993i	$-0.218585\pi$
$197$	−448.997	−	777.686i	−0.162384	−	0.281258i	−0.935723	+	0.352735i	$0.885252\pi$
$198$	−559.894	−	969.764i	−0.200959	−	0.348071i
$199$	16.8336	−	29.1566i	0.00599648	−	0.0103862i	−0.863012	−	0.505184i	$-0.831425\pi$
$199$	16.8336	−	29.1566i	0.00599648	−	0.0103862i	0.869008	+	0.494798i	$0.164758\pi$
$200$	−0.966833			−0.000341827
$201$	3431.27	−	5943.13i	1.20409	−	2.08555i
$202$	−3584.60	+	6208.72i	−1.24857	+	2.16259i
$203$	1015.96			0.351264
$204$	370.381	−	641.519i	0.127117	−	0.220173i
$205$	−1667.32	−	2887.89i	−0.568053	−	0.983896i
$206$	−2943.88	−	5098.95i	−0.995679	−	1.72457i
$207$	4759.85			1.59822
$208$	−2430.20	−	295.027i	−0.810117	−	0.0983481i
$209$	−1420.28			−0.470062
$210$	−1296.74	−	2246.03i	−0.426114	−	0.738050i
$211$	−2314.08	−	4008.10i	−0.755012	−	1.30772i	−0.945368	−	0.326004i	$-0.894298\pi$
$211$	−2314.08	−	4008.10i	−0.755012	−	1.30772i	0.190356	−	0.981715i	$-0.439036\pi$
$212$	1639.11	−	2839.03i	0.531013	−	0.919741i
$213$	−3017.86			−0.970799
$214$	608.801	−	1054.47i	0.194471	−	0.336833i
$215$	625.042	−	1082.60i	0.198267	−	0.343409i
$216$	−94.8222			−0.0298696
$217$	624.502	−	1081.67i	0.195364	−	0.338380i
$218$	375.404	+	650.219i	0.116631	+	0.202011i
$219$	1099.91	+	1905.10i	0.339384	+	0.587830i
$220$	−1139.21			−0.349116
$221$	204.599	+	480.182i	0.0622751	+	0.146156i
$222$	−2718.13			−0.821753
$223$	964.972	+	1671.38i	0.289773	+	0.501901i	0.973755	−	0.227597i	$-0.0730869\pi$
$223$	964.972	+	1671.38i	0.289773	+	0.501901i	−0.683983	+	0.729498i	$0.739754\pi$
$224$	−1009.08	−	1747.78i	−0.300992	−	0.521333i
$225$	2.24390	−	3.88655i	0.000664860	−	0.00115157i
$226$	4139.67			1.21844
$227$	−825.853	+	1430.42i	−0.241470	+	0.418239i	−0.961133	−	0.276085i	$-0.910963\pi$
$227$	−825.853	+	1430.42i	−0.241470	+	0.418239i	0.719663	+	0.694324i	$0.244296\pi$
$228$	4294.52	−	7438.33i	1.24742	−	2.16059i
$229$	5935.63			1.71283			0.856414	−	0.516290i	$-0.172687\pi$
$229$	5935.63			1.71283			0.856414	+	0.516290i	$0.172687\pi$
$230$	4510.73	−	7812.81i	1.29317	−	2.23983i
$231$	307.231	+	532.140i	0.0875080	+	0.151568i
$232$	344.388	+	596.497i	0.0974576	+	0.168801i
$233$	−1019.92			−0.286770			−0.143385	−	0.989667i	$-0.545799\pi$
$233$	−1019.92			−0.286770			−0.143385	+	0.989667i	$0.545799\pi$
$234$	−2866.38	+	3814.63i	−0.800774	+	1.06568i
$235$	2762.31			0.766779
$236$	−753.585	−	1305.25i	−0.207857	−	0.360019i
$237$	1956.09	+	3388.05i	0.536126	+	0.928597i
$238$	−180.114	+	311.966i	−0.0490548	+	0.0849654i
$239$	3250.81			0.879821			0.439911	−	0.898042i	$-0.355010\pi$
$239$	3250.81			0.879821			0.439911	+	0.898042i	$0.355010\pi$
$240$	−2093.62	+	3626.26i	−0.563095	+	0.975309i
$241$	−1506.35	+	2609.08i	−0.402626	+	0.697369i	−0.994042	−	0.108998i	$-0.965236\pi$
$241$	−1506.35	+	2609.08i	−0.402626	+	0.697369i	0.591416	+	0.806367i	$0.298569\pi$
$242$	502.841			0.133569
$243$	2593.19	−	4491.53i	0.684581	−	1.18573i
$244$	−902.314	−	1562.85i	−0.236741	−	0.410047i
$245$	−1577.54	−	2732.38i	−0.411369	−	0.712511i
$246$	−8901.13			−2.30697
$247$	2372.29	+	5567.64i	0.611115	+	1.43425i
$248$	846.767			0.216814
$249$	1624.76	+	2814.16i	0.413513	+	0.716225i
$250$	−2906.01	−	5033.36i	−0.735170	−	1.27335i
$251$	−2888.54	+	5003.10i	−0.726387	+	1.25814i	0.232013	+	0.972713i	$0.425469\pi$
$251$	−2888.54	+	5003.10i	−0.726387	+	1.25814i	−0.958400	+	0.285427i	$0.907865\pi$
$252$	−1767.62			−0.441863
$253$	−1068.70	+	1851.05i	−0.265569	+	0.459978i
$254$	−4719.16	+	8173.83i	−1.16577	+	2.01918i
$255$	892.771			0.219245
$256$	−1252.49	+	2169.37i	−0.305783	+	0.529632i
$257$	3966.67	+	6870.48i	0.962779	+	1.66758i	0.715468	+	0.698646i	$0.246214\pi$
$257$	3966.67	+	6870.48i	0.962779	+	1.66758i	0.247311	+	0.968936i	$0.420453\pi$
$258$	−1668.42	−	2889.78i	−0.402601	−	0.697326i
$259$	709.502			0.170218
$260$	1902.82	+	4465.82i	0.453877	+	1.06522i
$261$	−3197.13			−0.758227
$262$	3984.06	+	6900.60i	0.939451	+	1.62718i
$263$	−1841.72	−	3189.96i	−0.431808	−	0.747914i	0.565221	−	0.824940i	$-0.308791\pi$
$263$	−1841.72	−	3189.96i	−0.431808	−	0.747914i	−0.997029	+	0.0770257i	$0.975458\pi$
$264$	−208.289	+	360.767i	−0.0485579	+	0.0841047i
$265$	3950.94			0.915864
$266$	−2088.39	+	3617.21i	−0.481382	+	0.833779i
$267$	−1015.26	+	1758.49i	−0.232708	+	0.403062i
$268$	−8864.87			−2.02055
$269$	1295.46	−	2243.80i	0.293626	−	0.508576i	−0.681038	−	0.732248i	$-0.738471\pi$
$269$	1295.46	−	2243.80i	0.293626	−	0.508576i	0.974664	+	0.223672i	$0.0718045\pi$
$270$	−417.106	−	722.448i	−0.0940157	−	0.162840i
$271$	3106.06	+	5379.85i	0.696235	+	1.20591i	0.969763	+	0.244050i	$0.0784761\pi$
$271$	3106.06	+	5379.85i	0.696235	+	1.20591i	−0.273528	+	0.961864i	$0.588191\pi$
$272$	581.595			0.129648
$273$	1572.87	−	2093.21i	0.348698	−	0.464054i
$274$	−5383.45			−1.18696
$275$	1.00762	+	1.74526i	0.000220953	+	0.000382702i
$276$	−6462.90	−	11194.1i	−1.40950	−	2.44132i
$277$	2214.06	−	3834.87i	0.480253	−	0.831822i	−0.519491	−	0.854476i	$-0.673878\pi$
$277$	2214.06	−	3834.87i	0.480253	−	0.831822i	0.999743	+	0.0226539i	$0.00721158\pi$
$278$	11866.3			2.56005
$279$	−1965.24	+	3403.90i	−0.421706	+	0.730417i
$280$	−229.476	+	397.464i	−0.0489779	+	0.0848322i
$281$	−3913.26			−0.830766			−0.415383	−	0.909647i	$-0.636352\pi$
$281$	−3913.26			−0.830766			−0.415383	+	0.909647i	$0.636352\pi$
$282$	3686.70	−	6385.55i	0.778510	−	1.34842i
$283$	−1565.11	−	2710.86i	−0.328751	−	0.569413i	0.653514	−	0.756915i	$-0.273294\pi$
$283$	−1565.11	−	2710.86i	−0.328751	−	0.569413i	−0.982264	+	0.187502i	$0.939961\pi$
$284$	1949.20	+	3376.11i	0.407267	+	0.705407i
$285$	10351.6			2.15149
$286$	−839.893	−	1971.18i	−0.173650	−	0.407547i
$287$	2323.42			0.477865
$288$	3175.48	+	5500.09i	0.649712	+	1.12533i
$289$	2394.50	+	4147.39i	0.487380	+	0.844167i
$290$	−3029.80	+	5247.76i	−0.613503	+	1.06262i
$291$	1532.05			0.308627
$292$	1420.84	−	2460.97i	0.284755	−	0.493210i
$293$	−274.804	+	475.974i	−0.0547926	+	0.0949035i	−0.892121	−	0.451797i	$-0.850783\pi$
$293$	−274.804	+	475.974i	−0.0547926	+	0.0949035i	0.837328	+	0.546701i	$0.184116\pi$
$294$	−8421.82			−1.67065
$295$	908.226	−	1573.09i	0.179251	−	0.310471i
$296$	240.505	+	416.567i	0.0472266	+	0.0817988i
$297$	98.8228	+	171.166i	0.0193073	+	0.0334413i
$298$	−2613.90			−0.508118
$299$	9041.35	+	1097.62i	1.74874	+	0.212298i
$300$	−12.1871			−0.00234540
$301$	435.500	+	754.307i	0.0833946	+	0.144444i
$302$	27.7300	+	48.0298i	0.00528372	+	0.00915167i
$303$	−6189.90	+	10721.2i	−1.17360	+	2.03273i
$304$	6743.52			1.27226
$305$	1087.47	−	1883.56i	0.204159	−	0.353614i
$306$	566.799	−	981.725i	0.105888	−	0.183404i
$307$	−9304.94			−1.72984			−0.864920	−	0.501909i	$-0.832631\pi$
$307$	−9304.94			−1.72984			−0.864920	+	0.501909i	$0.832631\pi$
$308$	396.875	−	687.407i	0.0734222	−	0.127171i
$309$	−5083.50	−	8804.88i	−0.935891	−	1.62101i
$310$	3724.77	+	6451.50i	0.682429	+	1.18200i
$311$	−10035.9			−1.82985			−0.914927	−	0.403620i	$-0.867752\pi$
$311$	−10035.9			−1.82985			−0.914927	+	0.403620i	$0.867752\pi$
$312$	1762.14	+	213.924i	0.319749	+	0.0388175i
$313$	3971.28			0.717156			0.358578	−	0.933500i	$-0.383262\pi$
$313$	3971.28			0.717156			0.358578	+	0.933500i	$0.383262\pi$
$314$	3295.75	+	5708.41i	0.592325	+	1.02594i
$315$	−1065.17	−	1844.93i	−0.190526	−	0.330001i
$316$	2526.83	−	4376.61i	0.449828	−	0.779125i
$317$	−1403.12			−0.248603			−0.124302	−	0.992244i	$-0.539669\pi$
$317$	−1403.12			−0.248603			−0.124302	+	0.992244i	$0.539669\pi$
$318$	5273.10	−	9133.27i	0.929876	−	1.61059i
$319$	717.835	−	1243.33i	0.125991	−	0.218222i
$320$	7369.13			1.28733
$321$	1051.28	−	1820.87i	0.182793	−	0.316607i
$322$	3142.86	+	5443.60i	0.543928	+	0.942111i
$323$	−718.900	−	1245.17i	−0.123841	−	0.214499i
$324$	−7326.32			−1.25623
$325$	5.15854	−	6.86508i	0.000880444	−	0.00117171i
$326$	2526.98			0.429314
$327$	648.248	+	1122.80i	0.109628	+	0.189880i
$328$	787.587	+	1364.14i	0.132583	+	0.229640i
$329$	−962.323	+	1666.79i	−0.161260	+	0.279311i
$330$	−3664.90			−0.611351
$331$	−1149.18	+	1990.44i	−0.190830	+	0.330527i	−0.945525	−	0.325548i	$-0.894451\pi$
$331$	−1149.18	+	1990.44i	−0.190830	+	0.330527i	0.754696	+	0.656075i	$0.227785\pi$
$332$	2098.82	−	3635.27i	0.346951	−	0.600938i
$333$	−2232.73			−0.367426
$334$	2191.71	−	3796.15i	0.359057	−	0.621905i
$335$	−5342.00	−	9252.61i	−0.871238	−	1.50903i
$336$	−1458.74	−	2526.61i	−0.236847	−	0.410231i
$337$	6515.63			1.05320			0.526601	−	0.850112i	$-0.323466\pi$
$337$	6515.63			1.05320			0.526601	+	0.850112i	$0.323466\pi$
$338$	−6324.35	+	6584.92i	−1.01775	+	1.05968i
$339$	7148.39			1.14527
$340$	−576.631	−	998.754i	−0.0919771	−	0.159309i
$341$	−882.493	−	1528.52i	−0.140146	−	0.242739i
$342$	6571.96	−	11383.0i	1.03910	−	1.79977i
$343$	4868.30			0.766366
$344$	−295.249	+	511.386i	−0.0462754	+	0.0801514i
$345$	7789.13	−	13491.2i	1.21551	−	2.10533i
$346$	13750.3			2.13648
$347$	−5180.99	+	8973.74i	−0.801528	+	1.38829i	0.117083	+	0.993122i	$0.462646\pi$
$347$	−5180.99	+	8973.74i	−0.801528	+	1.38829i	−0.918610	+	0.395165i	$0.870688\pi$
$348$	4341.05	+	7518.92i	0.668691	+	1.15821i
$349$	−77.6264	−	134.453i	−0.0119061	−	0.0206221i	0.860011	−	0.510276i	$-0.170457\pi$
$349$	−77.6264	−	134.453i	−0.0119061	−	0.0206221i	−0.871917	+	0.489654i	$0.837123\pi$
$350$	5.92648			0.000905096
$351$	505.924	−	673.293i	0.0769351	−	0.102387i
$352$	−2851.90			−0.431837
$353$	2578.33	+	4465.79i	0.388755	+	0.673343i	0.992282	−	0.123999i	$-0.0395720\pi$
$353$	2578.33	+	4465.79i	0.388755	+	0.673343i	−0.603528	+	0.797342i	$0.706239\pi$
$354$	−2424.32	−	4199.04i	−0.363986	−	0.630442i
$355$	−2349.19	+	4068.91i	−0.351217	+	0.608325i
$356$	2622.99			0.390500
$357$	−311.021	+	538.703i	−0.0461091	+	0.0798633i
$358$	4270.62	−	7396.94i	0.630473	−	1.09201i
$359$	−48.8381			−0.00717987			−0.00358994	−	0.999994i	$-0.501143\pi$
$359$	−48.8381			−0.00717987			−0.00358994	+	0.999994i	$0.501143\pi$
$360$	722.138	−	1250.78i	0.105722	−	0.183116i
$361$	−4906.05	−	8497.53i	−0.715272	−	1.23889i
$362$	9753.88	+	16894.2i	1.41617	+	2.45287i
$363$	868.306			0.125549
$364$	−3357.60	−	407.612i	−0.483478	−	0.0586942i
$365$	3424.81			0.491131
$366$	−2902.79	−	5027.77i	−0.414566	−	0.718049i
$367$	−4717.45	−	8170.87i	−0.670978	−	1.16217i	−0.977627	−	0.210346i	$-0.932541\pi$
$367$	−4717.45	−	8170.87i	−0.670978	−	1.16217i	0.306649	−	0.951823i	$-0.400792\pi$
$368$	5074.22	−	8788.81i	0.718783	−	1.24497i
$369$	−7311.57			−1.03150
$370$	−2115.87	+	3664.80i	−0.297295	+	0.514930i
$371$	−1376.41	+	2384.02i	−0.192614	+	0.333617i
$372$	10673.6			1.48764
$373$	2277.36	−	3944.51i	0.316132	−	0.547557i	−0.663545	−	0.748136i	$-0.730949\pi$
$373$	2277.36	−	3944.51i	0.316132	−	0.547557i	0.979678	+	0.200579i	$0.0642823\pi$
$374$	254.521	+	440.844i	0.0351898	+	0.0609505i
$375$	−5018.11	−	8691.62i	−0.691024	−	1.19689i
$376$	−1304.82			−0.178965
$377$	−6072.96	−	737.257i	−0.829637	−	0.100718i
$378$	581.239			0.0790892
$379$	−4175.46	−	7232.11i	−0.565908	−	0.980181i	−0.996965	−	0.0778562i	$-0.975193\pi$
$379$	−4175.46	−	7232.11i	−0.565908	−	0.980181i	0.431057	−	0.902325i	$-0.358141\pi$
$380$	−6685.96	−	11580.4i	−0.902586	−	1.56332i
$381$	−8149.06	+	14114.6i	−1.09577	+	1.89793i
$382$	−6747.03			−0.903686
$383$	5305.01	−	9188.55i	0.707764	−	1.22588i	−0.257921	−	0.966166i	$-0.583037\pi$
$383$	5305.01	−	9188.55i	0.707764	−	1.22588i	0.965685	−	0.259717i	$-0.0836293\pi$
$384$	2393.19	−	4145.12i	0.318038	−	0.550859i
$385$	956.631			0.126635
$386$	−10735.0	+	18593.6i	−1.41554	+	2.45179i
$387$	−1370.47	−	2373.73i	−0.180013	−	0.311792i
$388$	−989.534	−	1713.92i	−0.129474	−	0.224256i
$389$	197.769			0.0257771			0.0128886	−	0.999917i	$-0.495897\pi$
$389$	197.769			0.0257771			0.0128886	+	0.999917i	$0.495897\pi$
$390$	6121.46	+	14366.7i	0.794801	+	1.86535i
$391$	−2163.77			−0.279863
$392$	745.177	+	1290.68i	0.0960130	+	0.166299i
$393$	6879.68	+	11916.0i	0.883039	+	1.52947i
$394$	−1865.90	+	3231.84i	−0.238586	+	0.413242i
$395$	6090.71			0.775841
$396$	−1248.92	+	2163.20i	−0.158487	+	0.274507i
$397$	3394.37	−	5879.23i	0.429115	−	0.743249i	−0.567680	−	0.823249i	$-0.692159\pi$
$397$	3394.37	−	5879.23i	0.429115	−	0.743249i	0.996795	+	0.0800003i	$0.0254921\pi$
$398$	−139.911			−0.0176208
$399$	−3606.24	+	6246.20i	−0.452476	+	0.783712i
$400$	−4.78421	−	8.28650i	−0.000598027	−	0.00103581i
$401$	−5201.99	−	9010.11i	−0.647818	−	1.12205i	−0.983643	−	0.180129i	$-0.942348\pi$
$401$	−5201.99	−	9010.11i	−0.647818	−	1.12205i	0.335825	−	0.941924i	$-0.390985\pi$
$402$	−28518.7			−3.53827
$403$	−4517.93	+	6012.54i	−0.558446	+	0.743191i
$404$	15991.9			1.96938
$405$	−4414.87	−	7646.77i	−0.541670	−	0.938200i
$406$	−2111.02	−	3656.39i	−0.258050	−	0.446955i
$407$	501.304	−	868.284i	0.0610534	−	0.105748i
$408$	−421.715			−0.0511716
$409$	3944.95	−	6832.85i	0.476932	−	0.826071i	−0.522718	−	0.852505i	$-0.675082\pi$
$409$	3944.95	−	6832.85i	0.476932	−	0.826071i	0.999651	+	0.0264348i	$0.00841544\pi$
$410$	−6928.90	+	12001.2i	−0.834620	+	1.44560i
$411$	−9296.15			−1.11568
$412$	−6566.75	+	11373.9i	−0.785244	+	1.36008i
$413$	632.809	+	1096.06i	0.0753959	+	0.130589i
$414$	−9890.26	−	17130.4i	−1.17411	−	2.03361i
$415$	5059.03			0.598405
$416$	4763.52	+	11179.7i	0.561420	+	1.31762i
$417$	20490.7			2.40632
$418$	2951.14	+	5111.52i	0.345323	+	0.598117i
$419$	3661.14	+	6341.27i	0.426869	+	0.739359i	0.996593	−	0.0824772i	$-0.0262832\pi$
$419$	3661.14	+	6341.27i	0.426869	+	0.739359i	−0.569724	+	0.821836i	$0.692950\pi$
$420$	−2892.57	+	5010.09i	−0.336055	+	0.582065i
$421$	−12052.1			−1.39521			−0.697605	−	0.716482i	$-0.745751\pi$
$421$	−12052.1			−1.39521			−0.697605	+	0.716482i	$0.745751\pi$
$422$	−9616.62	+	16656.5i	−1.10931	+	1.92139i
$423$	3028.33	−	5245.22i	0.348091	−	0.602911i
$424$	−1866.29			−0.213762
$425$	−1.02005	+	1.76678i	−0.000116423	+	0.000201651i
$426$	6270.67	+	10861.1i	0.713180	+	1.23526i
$427$	757.701	+	1312.38i	0.0858729	+	0.148736i
$428$	−2716.03			−0.306739
$429$	−1450.33	−	3403.84i	−0.163223	−	0.383075i
$430$	−5194.98			−0.582614
$431$	1778.53	+	3080.50i	0.198767	+	0.344275i	0.948129	−	0.317886i	$-0.102973\pi$
$431$	1778.53	+	3080.50i	0.198767	+	0.344275i	−0.749362	+	0.662161i	$0.769640\pi$
$432$	−469.212	−	812.699i	−0.0522569	−	0.0905116i
$433$	−2718.58	+	4708.72i	−0.301724	+	0.522602i	−0.976527	−	0.215397i	$-0.930896\pi$
$433$	−2718.58	+	4708.72i	−0.301724	+	0.522602i	0.674802	+	0.737999i	$0.264229\pi$
$434$	−5190.49			−0.574082
$435$	−5231.86	+	9061.84i	−0.576663	+	0.998810i
$436$	837.393	−	1450.41i	0.0919813	−	0.159316i
$437$	−25088.6			−2.74634
$438$	4570.91	−	7917.05i	0.498645	−	0.863678i
$439$	1101.59	+	1908.01i	0.119763	+	0.207436i	0.919674	−	0.392683i	$-0.128453\pi$
$439$	1101.59	+	1908.01i	0.119763	+	0.207436i	−0.799911	+	0.600119i	$0.795120\pi$
$440$	324.276	+	561.662i	0.0351347	+	0.0608550i
$441$	−6917.86			−0.746988
$442$	1303.02	−	1734.09i	0.140223	−	0.186611i
$443$	14546.1			1.56006			0.780028	−	0.625744i	$-0.215205\pi$
$443$	14546.1			1.56006			0.780028	+	0.625744i	$0.215205\pi$
$444$	3031.59	+	5250.88i	0.324039	+	0.561251i
$445$	1580.62	+	2737.71i	0.168379	+	0.291641i
$446$	4010.14	−	6945.77i	0.425753	−	0.737426i
$447$	−4513.68			−0.477606
$448$	−2567.23	+	4446.58i	−0.270737	+	0.468931i
$449$	2187.01	−	3788.01i	0.229870	−	0.398146i	−0.727900	−	0.685684i	$-0.759503\pi$
$449$	2187.01	−	3788.01i	0.229870	−	0.398146i	0.957769	+	0.287538i	$0.0928367\pi$
$450$	−18.6500			−0.00195371
$451$	1641.63	−	2843.39i	0.171400	−	0.296873i
$452$	−4617.07	−	7996.99i	−0.480461	−	0.832183i
$453$	47.8842	+	82.9379i	0.00496644	+	0.00860213i
$454$	6864.01			0.709568
$455$	−1597.86	−	3750.08i	−0.164635	−	0.386388i
$456$	−4889.73			−0.502155
$457$	−4484.45	−	7767.30i	−0.459024	−	0.795053i	0.539886	−	0.841738i	$-0.318467\pi$
$457$	−4484.45	−	7767.30i	−0.459024	−	0.795053i	−0.998910	+	0.0466856i	$0.985134\pi$
$458$	−12333.4	−	21362.0i	−1.25830	−	2.17944i
$459$	−100.042	+	173.277i	−0.0101733	+	0.0176207i
$460$	−20123.6			−2.03972
$461$	−4674.74	+	8096.89i	−0.472287	+	0.818026i	−0.999497	−	0.0317094i	$-0.989905\pi$
$461$	−4674.74	+	8096.89i	−0.472287	+	0.818026i	0.527210	+	0.849735i	$0.323238\pi$
$462$	1276.76	−	2211.42i	0.128572	−	0.222694i
$463$	−12529.4			−1.25764			−0.628821	−	0.777550i	$-0.716462\pi$
$463$	−12529.4			−1.25764			−0.628821	+	0.777550i	$0.716462\pi$
$464$	−3408.29	+	5903.33i	−0.341004	+	0.590636i
$465$	6431.94	+	11140.5i	0.641450	+	1.11102i
$466$	2119.25	+	3670.65i	0.210670	+	0.364892i
$467$	−14842.5			−1.47073			−0.735363	−	0.677673i	$-0.762988\pi$
$467$	−14842.5			−1.47073			−0.735363	+	0.677673i	$0.762988\pi$
$468$	10566.0	+	1282.71i	1.04362	+	0.126695i
$469$	7444.11			0.732915
$470$	−5739.67	−	9941.40i	−0.563301	−	0.975665i
$471$	5691.11	+	9857.29i	0.556757	+	0.964332i
$472$	−429.015	+	743.076i	−0.0418369	+	0.0724637i
$473$	1230.82			0.119647
$474$	8128.94	−	14079.7i	0.787710	−	1.36435i
$475$	−11.8274	+	20.4856i	−0.00114248	+	0.00197883i
$476$	803.539			0.0773743
$477$	4331.43	−	7502.26i	0.415771	−	0.720136i
$478$	−6754.70	−	11699.5i	−0.646345	−	1.11950i
$479$	−5237.46	−	9071.55i	−0.499595	−	0.865323i	0.500405	−	0.865791i	$-0.333184\pi$
$479$	−5237.46	−	9071.55i	−0.499595	−	0.865323i	−1.00000		0.000468014i	$0.999851\pi$
$480$	20785.7			1.97653
$481$	−4241.08	−	514.867i	−0.402030	−	0.0488065i
$482$	12519.9			1.18313
$483$	5427.10	+	9400.01i	0.511266	+	0.885539i
$484$	−560.829	−	971.385i	−0.0526699	−	0.0912269i
$485$	1192.59	−	2065.63i	0.111655	−	0.193393i
$486$	−21553.1			−2.01166
$487$	7254.77	−	12565.6i	0.675041	−	1.16920i	−0.301416	−	0.953493i	$-0.597459\pi$
$487$	7254.77	−	12565.6i	0.675041	−	1.16920i	0.976457	−	0.215712i	$-0.0692073\pi$
$488$	−513.686	+	889.731i	−0.0476506	+	0.0825333i
$489$	4363.59			0.403535
$490$	−6555.79	+	11355.0i	−0.604409	+	1.04687i
$491$	3056.67	+	5294.31i	0.280948	+	0.486617i	0.971619	−	0.236553i	$-0.0760178\pi$
$491$	3056.67	+	5294.31i	0.280948	+	0.486617i	−0.690670	+	0.723170i	$0.742684\pi$
$492$	9927.63	+	17195.2i	0.909699	+	1.57565i
$493$	1453.38			0.132772
$494$	15108.4	−	20106.5i	1.37603	−	1.83124i
$495$	−3010.42			−0.273350
$496$	4190.08	+	7257.44i	0.379315	+	0.656993i
$497$	−1636.80	−	2835.03i	−0.147728	−	0.255872i
$498$	6752.01	−	11694.8i	0.607560	−	1.05232i
$499$	6673.94			0.598731			0.299365	−	0.954139i	$-0.403225\pi$
$499$	6673.94			0.598731			0.299365	+	0.954139i	$0.403225\pi$
$500$	−6482.28	+	11227.6i	−0.579793	+	1.00423i
$501$	3784.65	−	6555.20i	0.337496	−	0.584560i
$502$	24007.9			2.13451
$503$	10753.3	−	18625.2i	0.953211	−	1.65101i	0.214802	−	0.976658i	$-0.431089\pi$
$503$	10753.3	−	18625.2i	0.953211	−	1.65101i	0.738409	−	0.674353i	$-0.235577\pi$
$504$	503.152	+	871.484i	0.0444686	+	0.0770218i
$505$	9636.80	+	16691.4i	0.849172	+	1.47081i
$506$	8882.45			0.780381
$507$	−10920.9	+	11370.8i	−0.956635	+	0.996049i
$508$	21053.5			1.83878
$509$	−82.4766	−	142.854i	−0.00718214	−	0.0124398i	0.862412	−	0.506207i	$-0.168953\pi$
$509$	−82.4766	−	142.854i	−0.00718214	−	0.0124398i	−0.869594	+	0.493767i	$0.835620\pi$
$510$	−1855.05	−	3213.04i	−0.161065	−	0.278972i
$511$	−1193.12	+	2066.55i	−0.103289	+	0.178902i
$512$	15745.9			1.35913
$513$	−1159.97	+	2009.13i	−0.0998322	+	0.172915i
$514$	16484.3	−	28551.7i	1.41458	−	2.45012i
$515$	−15828.6			−1.35435
$516$	−3721.65	+	6446.08i	−0.317512	+	0.549947i
$517$	1359.87	+	2355.37i	0.115681	+	0.200366i
$518$	−1474.24	−	2553.46i	−0.125047	−	0.216588i
$519$	23744.1			2.00819
$520$	1660.13	−	2209.33i	0.140003	−	0.186319i
$521$	6259.09			0.526325			0.263163	−	0.964751i	$-0.415234\pi$
$521$	6259.09			0.526325			0.263163	+	0.964751i	$0.415234\pi$
$522$	6643.16	+	11506.3i	0.557018	+	0.964783i
$523$	5974.24	+	10347.7i	0.499494	+	0.865149i	1.00000		0.000584389i	$-0.000186017\pi$
$523$	5974.24	+	10347.7i	0.499494	+	0.865149i	−0.500506	+	0.865733i	$0.666853\pi$
$524$	8887.02	−	15392.8i	0.740900	−	1.28328i
$525$	10.2338			0.000850746
$526$	−7653.67	+	13256.5i	−0.634441	+	1.09888i
$527$	893.377	−	1547.37i	0.0738446	−	0.127903i
$528$	−4122.73			−0.339808
$529$	−12794.7	+	22161.0i	−1.05159	+	1.82140i
$530$	−8209.47	−	14219.2i	−0.672823	−	1.16536i
$531$	−1991.39	−	3449.18i	−0.162747	−	0.281886i
$532$	9316.93			0.759286
$533$	−13888.4	−	1686.05i	−1.12865	−	0.137018i
$534$	8438.27			0.683819
$535$	−1636.69	−	2834.83i	−0.132262	−	0.229085i
$536$	2523.38	+	4370.62i	0.203346	+	0.352206i
$537$	7374.52	−	12773.0i	0.592615	−	1.02644i
$538$	−10767.1			−0.862830
$539$	1553.23	−	2690.28i	0.124123	−	0.214988i
$540$	−930.414	+	1611.52i	−0.0741457	+	0.128424i
$541$	−6559.40			−0.521277			−0.260638	−	0.965436i	$-0.583933\pi$
$541$	−6559.40			−0.521277			−0.260638	+	0.965436i	$0.583933\pi$
$542$	12907.9	−	22357.1i	1.02295	−	1.77181i
$543$	16843.0	+	29173.0i	1.33113	+	2.30558i
$544$	−1443.54	−	2500.28i	−0.113770	−	0.197056i
$545$	2018.46			0.158645
$546$	−10801.5	−	1311.31i	−0.846636	−	0.102782i
$547$	−7968.14			−0.622839			−0.311420	−	0.950273i	$-0.600804\pi$
$547$	−7968.14			−0.622839			−0.311420	+	0.950273i	$0.600804\pi$
$548$	6004.28	+	10399.7i	0.468048	+	0.810683i
$549$	−2384.41	−	4129.92i	−0.185363	−	0.321057i
$550$	4.18739	−	7.25278i	0.000324638	−	0.000562290i
$551$	16851.7			1.30292
$552$	−3679.32	+	6372.77i	−0.283700	+	0.491383i
$553$	−2121.86	+	3675.17i	−0.163166	+	0.282612i
$554$	−18402.0			−1.41124
$555$	−3653.70	+	6328.39i	−0.279443	+	0.484009i
$556$	−13234.7	−	22923.2i	−1.00949	−	1.74849i
$557$	−6076.79	−	10525.3i	−0.462265	−	0.800667i	0.536808	−	0.843704i	$-0.319630\pi$
$557$	−6076.79	−	10525.3i	−0.462265	−	0.800667i	−0.999073	+	0.0430374i	$0.986297\pi$
$558$	16334.0			1.23920
$559$	−2055.84	−	4824.94i	−0.155550	−	0.365068i
$560$	−4542.10			−0.342747
$561$	439.508	+	761.250i	0.0330767	+	0.0572905i
$562$	8131.17	+	14083.6i	0.610308	+	1.05708i
$563$	−11977.7	+	20745.9i	−0.896623	+	1.55300i	−0.0648403	+	0.997896i	$0.520654\pi$
$563$	−11977.7	+	20745.9i	−0.896623	+	1.55300i	−0.831783	+	0.555101i	$0.812680\pi$
$564$	−16447.4			−1.22795
$565$	5564.52	−	9638.03i	0.414338	−	0.717654i
$566$	−6504.16	+	11265.5i	−0.483022	+	0.836618i
$567$	6152.14			0.455671
$568$	1109.68	−	1922.02i	0.0819736	−	0.141983i
$569$	1136.23	+	1968.02i	0.0837143	+	0.144997i	0.904843	−	0.425746i	$-0.139988\pi$
$569$	1136.23	+	1968.02i	0.0837143	+	0.144997i	−0.821128	+	0.570744i	$0.806655\pi$
$570$	−21509.0	−	37254.8i	−1.58055	−	2.73760i
$571$	5926.97			0.434389			0.217195	−	0.976128i	$-0.430309\pi$
$571$	5926.97			0.434389			0.217195	+	0.976128i	$0.430309\pi$
$572$	−2871.17	+	3821.00i	−0.209877	+	0.279308i
$573$	−11650.8			−0.849421
$574$	−4827.73	−	8361.88i	−0.351055	−	0.608045i
$575$	17.7992	+	30.8292i	0.00129092	+	0.00223594i
$576$	8078.81	−	13992.9i	0.584405	−	1.01222i
$577$	23464.6			1.69297			0.846487	−	0.532410i	$-0.178713\pi$
$577$	23464.6			1.69297			0.846487	+	0.532410i	$0.178713\pi$
$578$	9950.83	−	17235.4i	0.716090	−	1.24030i
$579$	−18537.3	+	32107.5i	−1.33054	+	2.30456i
$580$	13516.8			0.967680
$581$	−1762.45	+	3052.65i	−0.125850	+	0.217978i
$582$	−3183.38	−	5513.77i	−0.226727	−	0.392703i
$583$	1945.03	+	3368.89i	0.138173	+	0.239323i
$584$	−1617.77			−0.114629
$585$	5028.29	+	11801.1i	0.355375	+	0.834046i
$586$	2284.01			0.161010
$587$	9780.49	+	16940.3i	0.687707	+	1.19114i	0.972578	+	0.232578i	$0.0747161\pi$
$587$	9780.49	+	16940.3i	0.687707	+	1.19114i	−0.284870	+	0.958566i	$0.591951\pi$
$588$	9393.04	+	16269.2i	0.658780	+	1.14104i
$589$	10358.6	−	17941.6i	0.724649	−	1.25513i
$590$	−7548.64			−0.526733
$591$	−3222.04	+	5580.74i	−0.224259	+	0.388428i
$592$	−2380.20	+	4122.62i	−0.165246	+	0.286214i
$593$	−26822.1			−1.85742			−0.928710	−	0.370807i	$-0.879081\pi$
$593$	−26822.1			−1.85742			−0.928710	+	0.370807i	$0.879081\pi$
$594$	410.679	−	711.317i	0.0283676	−	0.0491341i
$595$	484.215	+	838.685i	0.0333628	+	0.0577861i
$596$	2915.34	+	5049.51i	0.200364	+	0.347041i
$597$	−241.598			−0.0165627
$598$	−14836.3	−	34820.0i	−1.01455	−	2.38110i
$599$	−13911.1			−0.948902			−0.474451	−	0.880282i	$-0.657353\pi$
$599$	−13911.1			−0.948902			−0.474451	+	0.880282i	$0.657353\pi$
$600$	3.46904	+	6.00855i	0.000236038	+	0.000408830i
$601$	−5991.17	−	10377.0i	−0.406630	−	0.704305i	0.587879	−	0.808949i	$-0.299963\pi$
$601$	−5991.17	−	10377.0i	−0.406630	−	0.704305i	−0.994510	+	0.104644i	$0.966630\pi$
$602$	1809.81	−	3134.68i	0.122529	−	0.212226i
$603$	−23425.8			−1.58205
$604$	61.8558	−	107.137i	0.00416701	−	0.00721748i
$605$	675.915	−	1170.72i	0.0454212	−	0.0786719i
$606$	51446.8			3.44865
$607$	10917.0	−	18908.9i	0.729999	−	1.26440i	−0.226884	−	0.973922i	$-0.572854\pi$
$607$	10917.0	−	18908.9i	0.729999	−	1.26440i	0.956883	−	0.290473i	$-0.0938128\pi$
$608$	−16737.6	−	28990.4i	−1.11645	−	1.93374i
$609$	−3645.31	−	6313.87i	−0.242554	−	0.420116i
$610$	−9038.45			−0.599928
$611$	6961.87	−	9264.99i	0.460961	−	0.613456i
$612$	−2528.65			−0.167018
$613$	14020.1	+	24283.6i	0.923765	+	1.60001i	0.793536	+	0.608523i	$0.208238\pi$
$613$	14020.1	+	24283.6i	0.923765	+	1.60001i	0.130228	+	0.991484i	$0.458429\pi$
$614$	19334.3	+	33488.0i	1.27080	+	2.20108i
$615$	−11964.8	+	20723.7i	−0.784502	+	1.35880i
$616$	−451.880			−0.0295565
$617$	−13432.8	+	23266.4i	−0.876476	+	1.51810i	−0.0212946	+	0.999773i	$0.506779\pi$
$617$	−13432.8	+	23266.4i	−0.876476	+	1.51810i	−0.855182	+	0.518328i	$0.826555\pi$
$618$	−21125.5	+	36590.5i	−1.37507	+	2.38169i
$619$	−3647.24			−0.236826			−0.118413	−	0.992964i	$-0.537781\pi$
$619$	−3647.24			−0.236826			−0.118413	+	0.992964i	$0.537781\pi$
$620$	8308.64	−	14391.0i	0.538199	−	0.932187i
$621$	1745.66	+	3023.57i	0.112803	+	0.195381i
$622$	20853.2	+	36118.7i	1.34427	+	2.32834i
$623$	−2202.60			−0.141646
$624$	6886.17	+	16161.5i	0.441775	+	1.03682i
$625$	−15602.1			−0.998532
$626$	−8251.73	−	14292.4i	−0.526846	−	0.912524i
$627$	5096.03	+	8826.59i	0.324587	+	0.562201i
$628$	7351.65	−	12733.4i	0.467138	−	0.809107i
$629$	1014.97			0.0643397
$630$	−4426.54	+	7667.00i	−0.279933	+	0.484858i
$631$	14544.3	−	25191.5i	0.917590	−	1.58931i	0.114525	−	0.993420i	$-0.463465\pi$
$631$	14544.3	−	25191.5i	0.917590	−	1.58931i	0.803065	−	0.595892i	$-0.203201\pi$
$632$	−2877.05			−0.181080
$633$	−16606.0	+	28762.4i	−1.04270	+	1.80601i
$634$	2915.49	+	5049.77i	0.182632	+	0.316328i
$635$	12686.9	+	21974.4i	0.792859	+	1.37327i
$636$	−23524.8			−1.46670
$637$	−13140.5	−	1595.26i	−0.817340	−	0.0992250i
$638$	−5966.23			−0.370227
$639$	5150.85	+	8921.54i	0.318880	+	0.552317i
$640$	−3725.85	−	6453.36i	−0.230121	−	0.398581i
$641$	6153.40	−	10658.0i	0.379165	−	0.656733i	−0.611776	−	0.791031i	$-0.709545\pi$
$641$	6153.40	−	10658.0i	0.379165	−	0.656733i	0.990941	+	0.134298i	$0.0428780\pi$
$642$	−8737.61			−0.537143
$643$	7938.65	−	13750.1i	0.486889	−	0.843317i	−0.512997	−	0.858390i	$-0.671465\pi$
$643$	7938.65	−	13750.1i	0.486889	−	0.843317i	0.999886	+	0.0150734i	$0.00479821\pi$
$644$	7010.61	−	12142.7i	0.428970	−	0.742998i
$645$	−8970.70			−0.547629
$646$	−2987.54	+	5174.57i	−0.181955	+	0.315156i
$647$	7601.02	+	13165.4i	0.461866	+	0.799975i	0.999054	−	0.0434877i	$-0.0138469\pi$
$647$	7601.02	+	13165.4i	0.461866	+	0.799975i	−0.537188	+	0.843462i	$0.680514\pi$
$648$	2085.43	+	3612.08i	0.126425	+	0.218975i
$649$	1788.46			0.108172
$650$	−35.4258	−	4.30069i	−0.00213771	−	0.000259518i
$651$	−8962.95			−0.539610
$652$	−2818.40	−	4881.60i	−0.169290	−	0.293218i
$653$	5580.50	+	9665.72i	0.334429	+	0.579248i	0.983375	−	0.181587i	$-0.0581233\pi$
$653$	5580.50	+	9665.72i	0.334429	+	0.579248i	−0.648946	+	0.760834i	$0.724790\pi$
$654$	2693.93	−	4666.02i	0.161072	−	0.278985i
$655$	21421.4			1.27787
$656$	−7794.48	+	13500.4i	−0.463908	+	0.803512i
$657$	3754.64	−	6503.22i	0.222956	−	0.386172i
$658$	7998.27			0.473868
$659$	12689.6	−	21979.0i	0.750101	−	1.29921i	−0.197672	−	0.980268i	$-0.563338\pi$
$659$	12689.6	−	21979.0i	0.750101	−	1.29921i	0.947773	−	0.318945i	$-0.103328\pi$
$660$	4087.54	+	7079.82i	0.241072	+	0.417548i
$661$	7976.75	+	13816.1i	0.469379	+	0.812989i	0.999387	−	0.0350041i	$-0.0111444\pi$
$661$	7976.75	+	13816.1i	0.469379	+	0.812989i	−0.530008	+	0.847993i	$0.677811\pi$
$662$	9551.31			0.560759
$663$	2250.06	−	2994.42i	0.131803	−	0.175405i
$664$	−2389.72			−0.139667
$665$	5614.41	+	9724.44i	0.327395	+	0.567064i
$666$	4639.29	+	8035.48i	0.269923	+	0.467520i
$667$	12680.2	−	21962.8i	0.736102	−	1.27497i
$668$	−9777.84			−0.566342
$669$	6924.72	−	11994.0i	0.400187	−	0.693144i
$670$	−22199.8	+	38451.2i	−1.28008	+	2.21716i
$671$	2141.44			0.123203
$672$	−7241.26	+	12542.2i	−0.415681	+	0.719981i
$673$	−6119.12	−	10598.6i	−0.350483	−	0.607054i	0.635852	−	0.771811i	$-0.280649\pi$
$673$	−6119.12	−	10598.6i	−0.350483	−	0.607054i	−0.986334	+	0.164758i	$0.947316\pi$
$674$	−13538.5	−	23449.4i	−0.773716	−	1.34012i
$675$	3.29178			0.000187705
$676$	19774.4	+	4873.04i	1.12508	+	0.277255i
$677$	−11536.2			−0.654905			−0.327453	−	0.944868i	$-0.606190\pi$
$677$	−11536.2			−0.654905			−0.327453	+	0.944868i	$0.606190\pi$
$678$	−14853.3	−	25726.7i	−0.841354	−	1.45727i
$679$	830.943	+	1439.24i	0.0469641	+	0.0813443i
$680$	−328.275	+	568.590i	−0.0185129	+	0.0320653i
$681$	11852.8			0.666959
$682$	−3667.38	+	6352.09i	−0.205911	+	0.356648i
$683$	165.832	−	287.230i	0.00929048	−	0.0160916i	−0.861343	−	0.508024i	$-0.830376\pi$
$683$	165.832	−	287.230i	0.00929048	−	0.0160916i	0.870633	+	0.491933i	$0.163709\pi$
$684$	−29319.4			−1.63897
$685$	−7236.40	+	12533.8i	−0.403633	+	0.699113i
$686$	−10115.6	−	17520.8i	−0.562997	−	0.975139i
$687$	−21297.3	−	36888.0i	−1.18274	−	2.04857i
$688$	−5843.95			−0.323835
$689$	9957.59	−	13251.7i	0.550586	−	0.732730i
$690$	−64738.7			−3.57183
$691$	−3398.26	−	5885.95i	−0.187085	−	0.324041i	0.757192	−	0.653192i	$-0.226571\pi$
$691$	−3398.26	−	5885.95i	−0.187085	−	0.324041i	−0.944277	+	0.329152i	$0.893237\pi$
$692$	−15336.0	−	26562.8i	−0.842469	−	1.45920i
$693$	1048.76	−	1816.51i	0.0574879	−	0.0995719i
$694$	43061.4			2.35531
$695$	15950.6	−	27627.2i	0.870562	−	1.50786i
$696$	2471.35	−	4280.51i	0.134593	−	0.233121i
$697$	3323.76			0.180626
$698$	−322.593	+	558.747i	−0.0174933	+	0.0302992i
$699$	3659.52	+	6338.48i	0.198020	+	0.342981i
$700$	−6.60993	−	11.4487i	−0.000356903	−	0.000618173i
$701$	−8381.34			−0.451582			−0.225791	−	0.974176i	$-0.572497\pi$
$701$	−8381.34			−0.451582			−0.225791	+	0.974176i	$0.572497\pi$
$702$	−3474.38	−	421.790i	−0.186798	−	0.0226773i
$703$	11768.5			0.631375
$704$	3627.79	+	6283.52i	0.194215	+	0.336391i
$705$	−9911.27	−	17166.8i	−0.529475	−	0.917078i
$706$	10714.8	−	18558.5i	0.571183	−	0.989319i
$707$	−13428.9			−0.714352
$708$	−5407.79	+	9366.57i	−0.287058	+	0.497199i
$709$	810.952	−	1404.61i	0.0429562	−	0.0744023i	−0.843748	−	0.536740i	$-0.819656\pi$
$709$	810.952	−	1404.61i	0.0429562	−	0.0744023i	0.886704	+	0.462337i	$0.152989\pi$
$710$	19525.1			1.03206
$711$	6677.28	−	11565.4i	0.352205	−	0.610037i
$712$	−746.632	−	1293.20i	−0.0392994	−	0.0680686i
$713$	−15588.8	−	27000.6i	−0.818802	−	1.41821i
$714$	2585.02			0.135493
$715$	−5718.30	−	694.202i	−0.299094	−	0.0363101i
$716$	−19052.5			−0.994448
$717$	−11664.0	−	20202.7i	−0.607533	−	1.05228i
$718$	101.478	+	175.766i	0.00527457	+	0.00913582i
$719$	−8069.56	+	13976.9i	−0.418559	+	0.724965i	−0.995795	−	0.0916122i	$-0.970798\pi$
$719$	−8069.56	+	13976.9i	−0.418559	+	0.724965i	0.577236	+	0.816577i	$0.304131\pi$
$720$	14293.5			0.739844
$721$	5514.31	−	9551.06i	0.284831	−	0.493343i
$722$	−20388.1	+	35313.3i	−1.05092	+	1.82025i
$723$	21619.5			1.11208
$724$	21757.4	−	37685.0i	1.11686	−	1.93446i
$725$	−11.9555	−	20.7076i	−0.000612437	−	0.00106077i
$726$	−1804.21	−	3124.99i	−0.0922322	−	0.159751i
$727$	−4250.84			−0.216857			−0.108428	−	0.994104i	$-0.534582\pi$
$727$	−4250.84			−0.216857			−0.108428	+	0.994104i	$0.534582\pi$
$728$	754.774	+	1771.41i	0.0384255	+	0.0901826i
$729$	−15878.8			−0.806728
$730$	−7116.26	−	12325.7i	−0.360801	−	0.624925i
$731$	623.001	+	1079.07i	0.0315219	+	0.0545976i
$732$	−6475.08	+	11215.2i	−0.326948	+	0.566290i
$733$	−25348.0			−1.27729			−0.638643	−	0.769503i	$-0.720504\pi$
$733$	−25348.0			−1.27729			−0.638643	+	0.769503i	$0.720504\pi$
$734$	−19604.3	+	33955.7i	−0.985844	+	1.70753i
$735$	−11320.6	+	19607.8i	−0.568115	+	0.984005i
$736$	−50377.5			−2.52301
$737$	5259.69	−	9110.05i	0.262881	−	0.455323i
$738$	15192.4	+	26314.0i	0.757777	+	1.31251i
$739$	738.344	+	1278.85i	0.0367530	+	0.0636580i	0.883817	−	0.467833i	$-0.154965\pi$
$739$	738.344	+	1278.85i	0.0367530	+	0.0636580i	−0.847064	+	0.531491i	$0.821632\pi$
$740$	9439.53			0.468924
$741$	26089.2	−	34719.9i	1.29340	−	1.72128i
$742$	11439.9			0.566002
$743$	5611.77	+	9719.86i	0.277087	+	0.479929i	0.970660	−	0.240458i	$-0.0772976\pi$
$743$	5611.77	+	9719.86i	0.277087	+	0.479929i	−0.693572	+	0.720387i	$0.743964\pi$
$744$	−3038.23	−	5262.38i	−0.149714	−	0.259312i
$745$	−3513.58	+	6085.71i	−0.172789	+	0.299279i
$746$	−18928.1			−0.928964
$747$	5546.24	−	9606.37i	0.271655	−	0.470520i
$748$	567.746	−	983.365i	0.0277525	−	0.0480687i
$749$	2280.74			0.111264
$750$	−20853.8	+	36119.8i	−1.01530	+	1.75855i
$751$	1911.88	+	3311.47i	0.0928967	+	0.160902i	0.908729	−	0.417387i	$-0.137054\pi$
$751$	1911.88	+	3311.47i	0.0928967	+	0.160902i	−0.815832	+	0.578289i	$0.803721\pi$
$752$	−6456.69	−	11183.3i	−0.313100	−	0.542305i
$753$	41456.8			2.00634
$754$	9965.36	+	23388.2i	0.481322	+	1.12964i
$755$	149.098			0.00718706
$756$	−648.269	−	1122.83i	−0.0311869	−	0.0540173i
$757$	−605.493	−	1048.74i	−0.0290714	−	0.0503531i	0.851124	−	0.524965i	$-0.175922\pi$
$757$	−605.493	−	1048.74i	−0.0290714	−	0.0503531i	−0.880195	+	0.474612i	$0.842588\pi$
$758$	−17352.0	+	30054.5i	−0.831468	+	1.44014i
$759$	15338.2			0.733521
$760$	−3806.31	+	6592.72i	−0.181670	+	0.314662i
$761$	−17678.3	+	30619.8i	−0.842101	+	1.45856i	0.0460140	+	0.998941i	$0.485348\pi$
$761$	−17678.3	+	30619.8i	−0.842101	+	1.45856i	−0.888115	+	0.459621i	$0.847985\pi$
$762$	67730.2			3.21995
$763$	−703.184	+	1217.95i	−0.0333643	+	0.0577887i
$764$	7525.11	+	13033.9i	0.356347	+	0.617211i
$765$	−1523.77	−	2639.26i	−0.0720159	−	0.124735i
$766$	−44092.2			−2.07978
$767$	−2987.26	−	7010.94i	−0.140631	−	0.330053i
$768$	17975.9			0.844596
$769$	−9340.06	−	16177.5i	−0.437986	−	0.758614i	0.559548	−	0.828798i	$-0.310975\pi$
$769$	−9340.06	−	16177.5i	−0.437986	−	0.758614i	−0.997534	+	0.0701841i	$0.977641\pi$
$770$	−1987.74	−	3442.87i	−0.0930301	−	0.161133i
$771$	28465.2	−	49303.1i	1.32963	−	2.30299i
$772$	47892.0			2.23274
$773$	−13449.6	+	23295.4i	−0.625807	+	1.08393i	0.362578	+	0.931954i	$0.381897\pi$
$773$	−13449.6	+	23295.4i	−0.625807	+	1.08393i	−0.988384	+	0.151975i	$0.951437\pi$
$774$	−5695.28	+	9864.52i	−0.264487	+	0.458104i
$775$	−29.3958			−0.00136249
$776$	−563.341	+	975.735i	−0.0260603	+	0.0451377i
$777$	−2545.72	−	4409.32i	−0.117538	−	0.203582i
$778$	−410.936	−	711.762i	−0.0189367	−	0.0327993i
$779$	38538.5			1.77251
$780$	20926.2	−	27848.9i	0.960612	−	1.27840i
$781$	−4625.98			−0.211947
$782$	4496.00	+	7787.30i	0.205597	+	0.356104i
$783$	−1172.54	−	2030.89i	−0.0535160	−	0.0926925i
$784$	−7374.76	+	12773.5i	−0.335949	+	0.581882i
$785$	17720.5			0.805697
$786$	28590.0	−	49519.3i	1.29742	−	2.24719i
$787$	−6306.76	+	10923.6i	−0.285657	+	0.494772i	−0.972768	−	0.231780i	$-0.925545\pi$
$787$	−6306.76	+	10923.6i	−0.285657	+	0.494772i	0.687112	+	0.726552i	$0.258878\pi$
$788$	8324.32			0.376322
$789$	−13216.4	+	22891.4i	−0.596344	+	1.03290i
$790$	−12655.6	−	21920.2i	−0.569958	−	0.987195i
$791$	3877.09	+	6715.32i	0.174278	+	0.301858i
$792$	1422.02			0.0637997
$793$	−3576.83	−	8394.63i	−0.160173	−	0.375917i
$794$	−28212.0			−1.26097
$795$	−14176.1	−	24553.8i	−0.632422	−	1.09539i
$796$	156.046	+	270.279i	0.00694835	+	0.0120349i
$797$	−3499.01	+	6060.47i	−0.155510	+	0.269351i	−0.933245	−	0.359242i	$-0.883035\pi$
$797$	−3499.01	+	6060.47i	−0.155510	+	0.269351i	0.777735	+	0.628593i	$0.216369\pi$
$798$	29973.0			1.32961
$799$	−1376.64	+	2384.42i	−0.0609539	+	0.105575i
$800$	−23.7491	+	41.1347i	−0.00104957	+	0.00181791i
$801$	6931.37			0.305753
$802$	−21618.0	+	37443.4i	−0.951816	+	1.64859i
$803$	1686.02	+	2920.27i	0.0740951	+	0.128336i
$804$	31807.5	+	55092.3i	1.39523	+	2.41661i
$805$	16898.5			0.739866
$806$	31026.4	+	3766.60i	1.35590	+	0.164607i
$807$	−18592.6			−0.811018
$808$	−4552.10	−	7884.47i	−0.198196	−	0.343285i
$809$	5998.06	+	10388.9i	0.260668	+	0.451490i	0.966420	−	0.256969i	$-0.0827238\pi$
$809$	5998.06	+	10388.9i	0.260668	+	0.451490i	−0.705752	+	0.708459i	$0.749391\pi$
$810$	−18346.9	+	31777.7i	−0.795857	+	1.37846i
$811$	−33568.2			−1.45344			−0.726719	−	0.686935i	$-0.758956\pi$
$811$	−33568.2			−1.45344			−0.726719	+	0.686935i	$0.758956\pi$
$812$	−4708.93	+	8156.11i	−0.203511	+	0.352492i
$813$	22289.3	−	38606.3i	0.961527	−	1.66541i
$814$	−4166.55			−0.179407
$815$	3396.75	−	5883.34i	0.145991	−	0.252864i
$816$	−2086.79	−	3614.42i	−0.0895247	−	0.155061i
$817$	7223.62	+	12511.7i	0.309330	+	0.535775i
$818$	−32788.1			−1.40148
$819$	−8872.61	−	1077.13i	−0.378552	−	0.0459562i
$820$	30911.8			1.31645
$821$	−18624.1	−	32257.9i	−0.791701	−	1.37127i	−0.924913	−	0.380179i	$-0.875863\pi$
$821$	−18624.1	−	32257.9i	−0.791701	−	1.37127i	0.133212	−	0.991088i	$-0.457471\pi$
$822$	19316.0	+	33456.4i	0.819616	+	1.41962i
$823$	−22067.6	+	38222.3i	−0.934665	+	1.61889i	−0.159436	+	0.987208i	$0.550967\pi$
$823$	−22067.6	+	38222.3i	−0.934665	+	1.61889i	−0.775230	+	0.631679i	$0.782366\pi$
$824$	7476.89			0.316104
$825$	7.23080	−	12.5241i	0.000305144	−	0.000528526i
$826$	2629.77	−	4554.89i	0.110776	−	0.191871i
$827$	6716.66			0.282420			0.141210	−	0.989980i	$-0.454901\pi$
$827$	6716.66			0.282420			0.141210	+	0.989980i	$0.454901\pi$
$828$	−22061.7	+	38211.9i	−0.925961	+	1.60381i
$829$	17012.0	+	29465.7i	0.712728	+	1.23448i	0.963829	+	0.266520i	$0.0858738\pi$
$829$	17012.0	+	29465.7i	0.712728	+	1.23448i	−0.251102	+	0.967961i	$0.580793\pi$
$830$	−10511.9	−	18207.2i	−0.439607	−	0.761422i
$831$	−31776.6			−1.32649
$832$	18572.5	−	24716.6i	0.773901	−	1.02992i
$833$	3144.78			0.130804
$834$	−42576.8	−	73745.1i	−1.76776	−	3.06185i
$835$	−5892.16	−	10205.5i	−0.244199	−	0.422966i
$836$	6582.94	−	11402.0i	0.272340	−	0.471706i
$837$	−2882.99			−0.119057
$838$	15214.6	−	26352.5i	0.627184	−	1.08631i
$839$	−4620.63	+	8003.17i	−0.190133	+	0.329321i	−0.945294	−	0.326219i	$-0.894225\pi$
$839$	−4620.63	+	8003.17i	−0.190133	+	0.329321i	0.755161	+	0.655539i	$0.227559\pi$
$840$	3293.48			0.135281
$841$	3677.35	−	6369.37i	0.150779	−	0.261157i
$842$	25042.5	+	43374.9i	1.02497	+	1.77529i
$843$	14040.9	+	24319.6i	0.573660	+	0.993608i
$844$	42902.5			1.74972
$845$	6829.93	+	23575.8i	0.278055	+	0.959802i
$846$	−25169.7			−1.02288
$847$	470.946	+	815.702i	0.0191049	+	0.0330907i
$848$	−9235.02	−	15995.5i	−0.373976	−	0.647746i
$849$	−11231.4	+	19453.3i	−0.454017	+	0.786380i
$850$	8.47808			0.000342113
$851$	8855.30	−	15337.8i	0.356705	−	0.617831i
$852$	13987.6	−	24227.3i	0.562451	−	0.974193i
$853$	−47127.6			−1.89170			−0.945849	−	0.324607i	$-0.894768\pi$
$853$	−47127.6			−1.89170			−0.945849	+	0.324607i	$0.894768\pi$
$854$	3148.78	−	5453.86i	0.126170	−	0.218533i
$855$	−17668.0	−	30601.8i	−0.706704	−	1.22405i
$856$	773.118	+	1339.08i	0.0308699	+	0.0534682i
$857$	24176.7			0.963665			0.481833	−	0.876263i	$-0.339971\pi$
$857$	24176.7			0.963665			0.481833	+	0.876263i	$0.339971\pi$
$858$	−9236.68	+	12292.3i	−0.367523	+	0.489107i
$859$	−797.373			−0.0316717			−0.0158359	−	0.999875i	$-0.505041\pi$
$859$	−797.373			−0.0316717			−0.0158359	+	0.999875i	$0.505041\pi$
$860$	5794.07	+	10035.6i	0.229740	+	0.397921i
$861$	−8336.54	−	14439.3i	−0.329975	−	0.571533i
$862$	7391.04	−	12801.7i	0.292041	−	0.505831i
$863$	27776.1			1.09561			0.547805	−	0.836606i	$-0.315464\pi$
$863$	27776.1			1.09561			0.547805	+	0.836606i	$0.315464\pi$
$864$	−2329.20	+	4034.29i	−0.0917140	+	0.158853i
$865$	18483.1	−	32013.6i	0.726524	−	1.25838i
$866$	22595.3			0.886626
$867$	17183.1	−	29762.0i	0.673090	−	1.16583i
$868$	5789.07	+	10027.0i	0.226375	+	0.392094i
$869$	2998.43	+	5193.44i	0.117048	+	0.202733i
$870$	43484.1			1.69454
$871$	−44497.5	−	5401.99i	−1.73104	−	0.210149i
$872$	−953.453			−0.0370275
$873$	−2614.89	−	4529.12i	−0.101375	−	0.175587i
$874$	52130.5	+	90292.7i	2.01755	+	3.49450i
$875$	5443.37	−	9428.20i	0.210308	−	0.364264i
$876$	−20392.1			−0.786514
$877$	5363.71	−	9290.21i	0.206522	−	0.357706i	−0.744095	−	0.668074i	$-0.767119\pi$
$877$	5363.71	−	9290.21i	0.206522	−	0.357706i	0.950616	+	0.310368i	$0.100452\pi$
$878$	4577.88	−	7929.12i	0.175964	−	0.304778i
$879$	3944.03			0.151341
$880$	−3209.25	+	5558.58i	−0.122936	+	0.212932i
$881$	−5077.57	−	8794.61i	−0.194174	−	0.336320i	0.752455	−	0.658643i	$-0.228869\pi$
$881$	−5077.57	−	8794.61i	−0.194174	−	0.336320i	−0.946630	+	0.322324i	$0.895536\pi$
$882$	14374.3	+	24897.0i	0.548762	+	0.950483i
$883$	−40449.8			−1.54161			−0.770806	−	0.637070i	$-0.780146\pi$
$883$	−40449.8			−1.54161			−0.770806	+	0.637070i	$0.780146\pi$
$884$	−4803.19	−	583.107i	−0.182747	−	0.0221855i
$885$	−13035.0			−0.495104
$886$	−30224.6	−	52350.6i	−1.14607	−	1.98505i
$887$	7859.83	+	13613.6i	0.297528	+	0.515333i	0.975570	−	0.219690i	$-0.0705046\pi$
$887$	7859.83	+	13613.6i	0.297528	+	0.515333i	−0.678042	+	0.735023i	$0.737171\pi$
$888$	1725.88	−	2989.32i	0.0652217	−	0.112967i
$889$	−17679.3			−0.666980
$890$	6568.59	−	11377.1i	0.247393	−	0.428497i
$891$	4346.84	−	7528.95i	0.163440	−	0.283086i
$892$	−17890.4			−0.671541
$893$	−15962.0	+	27647.0i	−0.598151	+	1.03603i
$894$	9378.78	+	16244.5i	0.350865	+	0.607716i
$895$	−11481.1	−	19885.8i	−0.428794	−	0.742692i
$896$	5192.00			0.193585
$897$	−25619.4	−	60127.3i	−0.953630	−	2.23812i
$898$	−18177.2			−0.675478
$899$	10470.8	+	18136.0i	0.388455	+	0.672824i
$900$	20.8008	+	36.0280i	0.000770399	+	0.00133437i
$901$	−1969.02	+	3410.44i	−0.0728052	+	0.126102i
$902$	−13644.3			−0.503664
$903$	3125.18	−	5412.97i	0.115171	−	0.199482i
$904$	−2628.49	+	4552.68i	−0.0967061	+	0.167500i
$905$	52444.4			1.92631
$906$	198.993	−	344.666i	0.00729701	−	0.0126388i
$907$	−25899.7	−	44859.6i	−0.948166	−	1.64227i	−0.749285	−	0.662248i	$-0.769603\pi$
$907$	−25899.7	−	44859.6i	−0.948166	−	1.64227i	−0.198881	−	0.980024i	$-0.563731\pi$
$908$	−7655.58	−	13259.8i	−0.279801	−	0.484629i
$909$	42259.5			1.54198
$910$	−10176.2	+	13542.7i	−0.370702	+	0.493338i
$911$	−13518.0			−0.491628			−0.245814	−	0.969317i	$-0.579055\pi$
$911$	−13518.0			−0.491628			−0.245814	+	0.969317i	$0.579055\pi$
$912$	−24196.0	−	41908.7i	−0.878520	−	1.52164i
$913$	2490.54	+	4313.74i	0.0902791	+	0.156368i
$914$	−18636.1	+	32278.6i	−0.674427	+	1.16814i
$915$	−15607.6			−0.563904
$916$	−27511.4	+	47651.1i	−0.992359	+	1.71882i
$917$	−7462.71	+	12925.8i	−0.268746	+	0.465482i
$918$	831.488			0.0298945
$919$	1863.60	−	3227.84i	0.0668926	−	0.115861i	−0.830639	−	0.556811i	$-0.812025\pi$
$919$	1863.60	−	3227.84i	0.0668926	−	0.115861i	0.897532	+	0.440949i	$0.145358\pi$
$920$	5728.18	+	9921.51i	0.205275	+	0.355546i
$921$	33386.5	+	57827.1i	1.19449	+	2.06891i
$922$	38853.7			1.38783
$923$	7726.76	+	18134.3i	0.275547	+	0.646693i
$924$	−5696.01			−0.202798
$925$	−8.34920	−	14.4612i	−0.000296778	−	0.000514035i
$926$	26034.2	+	45092.5i	0.923905	+	1.60025i
$927$	−17353.0	+	30056.2i	−0.614828	+	1.06491i
$928$	33837.9			1.19697
$929$	−13929.9	+	24127.3i	−0.491955	+	0.852090i	−0.999957	−	0.00926520i	$-0.997051\pi$
$929$	−13929.9	+	24127.3i	−0.491955	+	0.852090i	0.508002	+	0.861356i	$0.330384\pi$
$930$	26729.3	−	46296.5i	0.942460	−	1.63239i
$931$	36463.3			1.28360
$932$	4727.29	−	8187.91i	0.166145	−	0.287772i
$933$	36009.3	+	62369.9i	1.26355	+	2.18853i
$934$	30840.5	+	53417.4i	1.08044	+	1.87138i
$935$	1368.50			0.0478661
$936$	−2375.20	−	5574.46i	−0.0829442	−	0.194665i
$937$	−6058.26			−0.211222			−0.105611	−	0.994408i	$-0.533680\pi$
$937$	−6058.26			−0.211222			−0.105611	+	0.994408i	$0.533680\pi$
$938$	−15467.8	−	26791.0i	−0.538423	−	0.932576i
$939$	−14249.1	−	24680.2i	−0.495210	−	0.857728i
$940$	−12803.2	+	22175.7i	−0.444248	+	0.769460i
$941$	50684.6			1.75587			0.877934	−	0.478781i	$-0.158921\pi$
$941$	50684.6			1.75587			0.877934	+	0.478781i	$0.158921\pi$
$942$	23650.6	−	40964.0i	0.818023	−	1.41686i
$943$	28998.7	−	50227.1i	1.00141	−	1.73449i
$944$	−8491.64			−0.292775
$945$	781.298	−	1353.25i	0.0268948	−	0.0465832i
$946$	−2557.47	−	4429.66i	−0.0878969	−	0.152242i
$947$	13005.2	+	22525.7i	0.446265	+	0.772953i	0.998139	−	0.0609741i	$-0.0194207\pi$
$947$	13005.2	+	22525.7i	0.446265	+	0.772953i	−0.551875	+	0.833927i	$0.686087\pi$
$948$	−36265.5			−1.24246
$949$	8631.59	−	11487.1i	0.295251	−	0.392926i
$950$	98.3022			0.00335721
$951$	5034.47	+	8719.95i	0.171665	+	0.297333i
$952$	−228.727	−	396.167i	−0.00778685	−	0.0134872i
$953$	−8317.38	+	14406.1i	−0.282714	+	0.489675i	−0.972052	−	0.234765i	$-0.924568\pi$
$953$	−8317.38	+	14406.1i	−0.282714	+	0.489675i	0.689338	+	0.724440i	$0.257901\pi$
$954$	−36000.3			−1.22175
$955$	−9069.31	+	15708.5i	−0.307305	+	0.532267i
$956$	−15067.3	+	26097.4i	−0.509741	+	0.882898i
$957$	−10302.5			−0.347996
$958$	−21765.4	+	37698.7i	−0.734037	+	1.27139i
$959$	−5041.98	−	8732.97i	−0.169775	−	0.294059i
$960$	−26440.7	−	45796.7i	−0.888928	−	1.53967i
$961$	−4045.77			−0.135805
$962$	6959.37	+	16333.2i	0.233242	+	0.547407i
$963$	−7177.25			−0.240170
$964$	−13963.8	−	24185.9i	−0.466538	−	0.808067i
$965$	28859.9	+	49986.8i	0.962728	+	1.66749i
$966$	22553.4	−	39063.7i	0.751185	−	1.30109i
$967$	26428.0			0.878870			0.439435	−	0.898274i	$-0.355179\pi$
$967$	26428.0			0.878870			0.439435	+	0.898274i	$0.355179\pi$
$968$	−319.279	+	553.008i	−0.0106013	+	0.0183619i
$969$	−5158.89	+	8935.45i	−0.171029	+	0.296231i
$970$	−9912.13			−0.328103
$971$	24946.5	−	43208.6i	0.824481	−	1.42804i	−0.0778337	−	0.996966i	$-0.524800\pi$
$971$	24946.5	−	43208.6i	0.824481	−	1.42804i	0.902315	−	0.431077i	$-0.141866\pi$
$972$	24038.6	+	41636.1i	0.793249	+	1.37395i
$973$	11113.6	+	19249.4i	0.366173	+	0.634230i
$974$	−60297.4			−1.98363
$975$	−61.1733	−	7.42643i	−0.00200935	−	0.000243935i
$976$	−10167.6			−0.333459
$977$	515.146	+	892.259i	0.0168690	+	0.0292179i	0.874337	−	0.485320i	$-0.161297\pi$
$977$	515.146	+	892.259i	0.0168690	+	0.0292179i	−0.857468	+	0.514538i	$0.827964\pi$
$978$	−9066.91	−	15704.3i	−0.296450	−	0.513466i
$979$	−1556.27	+	2695.53i	−0.0508054	+	0.0879975i
$980$	29247.3			0.953337
$981$	2212.85	−	3832.77i	0.0720192	−	0.124741i
$982$	12702.6	−	22001.6i	0.412787	−	0.714968i
$983$	−1300.89			−0.0422095			−0.0211047	−	0.999777i	$-0.506718\pi$
$983$	−1300.89			−0.0422095			−0.0211047	+	0.999777i	$0.506718\pi$
$984$	5651.79	−	9789.18i	0.183102	−	0.317142i
$985$	5016.26	+	8688.42i	0.162265	+	0.281052i
$986$	−3019.91	−	5230.63i	−0.0975389	−	0.168942i
$987$	13811.4			0.445413
$988$	−55692.3	−	6761.05i	−1.79333	−	0.217710i
$989$	21741.9			0.699041
$990$	6255.21	+	10834.3i	0.200812	+	0.347816i
$991$	−22001.8	−	38108.2i	−0.705258	−	1.22154i	−0.966598	−	0.256296i	$-0.917498\pi$
$991$	−22001.8	−	38108.2i	−0.705258	−	1.22154i	0.261341	−	0.965247i	$-0.415835\pi$
$992$	20799.8	−	36026.4i	0.665721	−	1.15306i
$993$	16493.2			0.527086
$994$	−6802.08	+	11781.5i	−0.217051	+	0.375944i
$995$	−188.067	+	325.742i	−0.00599209	+	0.0103786i
$996$	−30122.7			−0.958306
$997$	26686.8	−	46222.9i	0.847723	−	1.46830i	−0.0355124	−	0.999369i	$-0.511306\pi$
$997$	26686.8	−	46222.9i	0.847723	−	1.46830i	0.883235	−	0.468930i	$-0.155360\pi$
$998$	−13867.5	−	24019.2i	−0.439847	−	0.761837i
$999$	−818.848	−	1418.29i	−0.0259331	−	0.0449175i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.e.b.133.3	yes	34
13.3	even	3		1859.4.a.g.1.15		17
13.9	even	3	inner	143.4.e.b.100.3	✓	34
13.10	even	6		1859.4.a.h.1.3		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.b.100.3	✓	34	13.9	even	3	inner
143.4.e.b.133.3	yes	34	1.1	even	1	trivial
1859.4.a.g.1.15		17	13.3	even	3
1859.4.a.h.1.3		17	13.10	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+(-2.07785 - 3.59895i) q^{2} +(-3.58804 - 6.21467i) q^{3} +(-4.63495 + 8.02797i) q^{4} -11.1721 q^{5} +(-14.9108 + 25.8263i) q^{6} +(3.89211 - 6.74134i) q^{7} +5.27734 q^{8} +(-12.2481 + 21.2143i) q^{9} +(23.2141 + 40.2080i) q^{10} +(-5.50000 - 9.52628i) q^{11} +66.5216 q^{12} +(-28.1573 + 37.4722i) q^{13} -32.3490 q^{14} +(40.0861 + 69.4312i) q^{15} +(26.1141 + 45.2309i) q^{16} +(5.56783 - 9.64377i) q^{17} +101.799 q^{18} +(64.5583 - 111.818i) q^{19} +(51.7823 - 89.6897i) q^{20} -55.8602 q^{21} +(-22.8564 + 39.5884i) q^{22} +(-97.1550 - 168.277i) q^{23} +(-18.9353 - 32.7970i) q^{24} -0.183205 q^{25} +(193.367 + 23.4748i) q^{26} -17.9678 q^{27} +(36.0795 + 62.4915i) q^{28} +(65.2577 + 113.030i) q^{29} +(166.586 - 288.536i) q^{30} +160.453 q^{31} +(129.632 - 224.529i) q^{32} +(-39.4685 + 68.3614i) q^{33} -46.2766 q^{34} +(-43.4832 + 75.3152i) q^{35} +(-113.538 - 196.654i) q^{36} +(45.5731 + 78.9349i) q^{37} -536.571 q^{38} +(333.907 + 40.5363i) q^{39} -58.9593 q^{40} +(149.239 + 258.490i) q^{41} +(116.069 + 201.038i) q^{42} +(-55.9464 + 96.9021i) q^{43} +101.969 q^{44} +(136.837 - 237.009i) q^{45} +(-403.748 + 699.311i) q^{46} -247.250 q^{47} +(187.397 - 324.581i) q^{48} +(141.203 + 244.571i) q^{49} +(0.380672 + 0.659344i) q^{50} -79.9105 q^{51} +(-170.318 - 399.728i) q^{52} -353.642 q^{53} +(37.3344 + 64.6651i) q^{54} +(61.4468 + 106.429i) q^{55} +(20.5400 - 35.5764i) q^{56} -926.552 q^{57} +(271.192 - 469.718i) q^{58} +(-81.2938 + 140.805i) q^{59} -743.189 q^{60} +(-97.3380 + 168.594i) q^{61} +(-333.398 - 577.463i) q^{62} +(95.3418 + 165.137i) q^{63} -659.598 q^{64} +(314.577 - 418.645i) q^{65} +328.039 q^{66} +(478.153 + 828.186i) q^{67} +(51.6133 + 89.3968i) q^{68} +(-697.192 + 1207.57i) q^{69} +361.407 q^{70} +(210.272 - 364.202i) q^{71} +(-64.6373 + 111.955i) q^{72} -306.549 q^{73} +(189.388 - 328.030i) q^{74} +(0.657345 + 1.13856i) q^{75} +(598.449 + 1036.54i) q^{76} -85.6265 q^{77} +(-547.922 - 1285.94i) q^{78} -545.170 q^{79} +(-291.750 - 505.326i) q^{80} +(395.167 + 684.450i) q^{81} +(620.194 - 1074.21i) q^{82} -452.825 q^{83} +(258.910 - 448.444i) q^{84} +(-62.2047 + 107.742i) q^{85} +464.994 q^{86} +(468.295 - 811.111i) q^{87} +(-29.0254 - 50.2735i) q^{88} +(-141.479 - 245.048i) q^{89} -1137.31 q^{90} +(143.022 + 335.664i) q^{91} +1801.23 q^{92} +(-575.713 - 997.164i) q^{93} +(513.748 + 889.838i) q^{94} +(-721.255 + 1249.25i) q^{95} -1860.50 q^{96} +(-106.747 + 184.891i) q^{97} +(586.798 - 1016.36i) q^{98} +269.458 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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