LMFDB - Embedded newform 143.4.e.a.100.6

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,-4] 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			100.6
Character	$\chi$	$=$	143.100
Dual form			143.4.e.a.133.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.37242 + 2.37710i) q^{2} +(2.09604 - 3.63045i) q^{3} +(0.232916 + 0.403423i) q^{4} +5.57379 q^{5} +(5.75330 + 9.96502i) q^{6} +(3.44074 + 5.95954i) q^{7} -23.2374 q^{8} +(4.71323 + 8.16355i) q^{9} +(-7.64959 + 13.2495i) q^{10} +(5.50000 - 9.52628i) q^{11} +1.95281 q^{12} +(40.5553 - 23.5003i) q^{13} -18.8886 q^{14} +(11.6829 - 20.2354i) q^{15} +(30.0282 - 52.0103i) q^{16} +(48.4786 + 83.9674i) q^{17} -25.8741 q^{18} +(45.6604 + 79.0861i) q^{19} +(1.29823 + 2.24859i) q^{20} +28.8477 q^{21} +(15.0966 + 26.1481i) q^{22} +(-2.46326 + 4.26649i) q^{23} +(-48.7065 + 84.3621i) q^{24} -93.9329 q^{25} +(0.203750 + 128.657i) q^{26} +152.703 q^{27} +(-1.60281 + 2.77615i) q^{28} +(-60.3491 + 104.528i) q^{29} +(32.0677 + 55.5429i) q^{30} +62.6271 q^{31} +(-10.5269 - 18.2331i) q^{32} +(-23.0564 - 39.9349i) q^{33} -266.132 q^{34} +(19.1780 + 33.2172i) q^{35} +(-2.19557 + 3.80284i) q^{36} +(-29.9707 + 51.9107i) q^{37} -250.661 q^{38} +(-0.311179 - 196.492i) q^{39} -129.520 q^{40} +(27.4478 - 47.5409i) q^{41} +(-39.5913 + 68.5741i) q^{42} +(209.483 + 362.835i) q^{43} +5.12415 q^{44} +(26.2705 + 45.5019i) q^{45} +(-6.76126 - 11.7108i) q^{46} -158.651 q^{47} +(-125.881 - 218.031i) q^{48} +(147.823 - 256.036i) q^{49} +(128.916 - 223.288i) q^{50} +406.453 q^{51} +(18.9266 + 10.8873i) q^{52} +89.8532 q^{53} +(-209.572 + 362.990i) q^{54} +(30.6558 - 53.0975i) q^{55} +(-79.9539 - 138.484i) q^{56} +382.824 q^{57} +(-165.649 - 286.912i) q^{58} +(-329.022 - 569.883i) q^{59} +10.8845 q^{60} +(-219.842 - 380.777i) q^{61} +(-85.9507 + 148.871i) q^{62} +(-32.4340 + 56.1773i) q^{63} +538.240 q^{64} +(226.047 - 130.986i) q^{65} +126.573 q^{66} +(525.901 - 910.888i) q^{67} +(-22.5829 + 39.1147i) q^{68} +(10.3262 + 17.8855i) q^{69} -105.281 q^{70} +(-538.772 - 933.181i) q^{71} +(-109.523 - 189.700i) q^{72} -338.912 q^{73} +(-82.2648 - 142.487i) q^{74} +(-196.887 + 341.019i) q^{75} +(-21.2701 + 36.8409i) q^{76} +75.6963 q^{77} +(467.508 + 268.930i) q^{78} +664.285 q^{79} +(167.371 - 289.895i) q^{80} +(192.814 - 333.963i) q^{81} +(75.3398 + 130.492i) q^{82} -1011.19 q^{83} +(6.71910 + 11.6378i) q^{84} +(270.210 + 468.017i) q^{85} -1150.00 q^{86} +(252.988 + 438.189i) q^{87} +(-127.806 + 221.366i) q^{88} +(118.901 - 205.942i) q^{89} -144.217 q^{90} +(279.592 + 160.832i) q^{91} -2.29493 q^{92} +(131.269 - 227.364i) q^{93} +(217.736 - 377.130i) q^{94} +(254.501 + 440.809i) q^{95} -88.2593 q^{96} +(75.0273 + 129.951i) q^{97} +(405.750 + 702.779i) q^{98} +103.691 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 4 q^{2} + 6 q^{3} - 78 q^{4} + 32 q^{5} - 14 q^{6} + 6 q^{7} + 126 q^{8} - 135 q^{9} - 2 q^{10} + 187 q^{11} - 190 q^{12} - 60 q^{13} - 120 q^{14} + 28 q^{15} - 350 q^{16} - 118 q^{17} + 956 q^{18}+ \cdots - 2970 q^{99}+O(q^{100}) $ 34 * q - 4 * q^2 + 6 * q^3 - 78 * q^4 + 32 * q^5 - 14 * q^6 + 6 * q^7 + 126 * q^8 - 135 * q^9 - 2 * q^10 + 187 * q^11 - 190 * q^12 - 60 * q^13 - 120 * q^14 + 28 * q^15 - 350 * q^16 - 118 * q^17 + 956 * q^18 - 403 * q^19 - 98 * q^20 + 440 * q^21 + 44 * q^22 + 215 * q^23 - 26 * q^24 + 638 * q^25 - 989 * q^26 - 768 * q^27 + 396 * q^28 + 7 * q^29 + 1269 * q^30 + 1364 * q^31 - 813 * q^32 - 66 * q^33 + 1476 * q^34 - 10 * q^35 - 560 * q^36 - 1084 * q^37 + 820 * q^38 - 370 * q^39 + 190 * q^40 - 240 * q^41 - 393 * q^42 + 435 * q^43 - 1716 * q^44 - 1242 * q^45 - 1671 * q^46 + 1098 * q^47 - 894 * q^48 - 403 * q^49 + 651 * q^50 + 3104 * q^51 - 876 * q^52 - 1132 * q^53 - 311 * q^54 + 176 * q^55 + 1925 * q^56 - 1068 * q^57 - 618 * q^58 - 2010 * q^59 - 822 * q^60 - 460 * q^61 + 823 * q^62 - 820 * q^63 + 6342 * q^64 + 3070 * q^65 - 308 * q^66 + 232 * q^67 - 1795 * q^68 + 1608 * q^69 + 414 * q^70 - 489 * q^71 - 2556 * q^72 + 580 * q^73 - 2653 * q^74 + 2852 * q^75 - 2421 * q^76 + 132 * q^77 - 4760 * q^78 - 1464 * q^79 - 4915 * q^80 - 2393 * q^81 + 1772 * q^82 - 234 * q^83 - 4161 * q^84 - 4858 * q^85 + 2068 * q^86 - 3032 * q^87 + 693 * q^88 - 4113 * q^89 + 30290 * q^90 + 1096 * q^91 - 7108 * q^92 - 802 * q^93 - 2325 * q^94 + 3924 * q^95 + 5202 * q^96 - 2793 * q^97 - 533 * 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 $

$2$	−1.37242	+	2.37710i	−0.485224	+	0.840433i	−0.999856	−	0.0169781i	$-0.994595\pi$
$2$	−1.37242	+	2.37710i	−0.485224	+	0.840433i	0.514631	+	0.857412i	$0.327929\pi$
$3$	2.09604	−	3.63045i	0.403383	−	0.698680i	−0.590749	−	0.806856i	$-0.701167\pi$
$3$	2.09604	−	3.63045i	0.403383	−	0.698680i	0.994132	+	0.108175i	$0.0345008\pi$
$4$	0.232916	+	0.403423i	0.0291145	+	0.0504278i
$5$	5.57379			0.498535			0.249267	−	0.968435i	$-0.419810\pi$
$5$	5.57379			0.498535			0.249267	+	0.968435i	$0.419810\pi$
$6$	5.75330	+	9.96502i	0.391463	+	0.678033i
$7$	3.44074	+	5.95954i	0.185783	+	0.321785i	0.943840	−	0.330403i	$-0.107185\pi$
$7$	3.44074	+	5.95954i	0.185783	+	0.321785i	−0.758057	+	0.652188i	$0.773851\pi$
$8$	−23.2374			−1.02696
$9$	4.71323	+	8.16355i	0.174564	+	0.302354i
$10$	−7.64959	+	13.2495i	−0.241901	+	0.418985i
$11$	5.50000	−	9.52628i	0.150756	−	0.261116i
$11$	5.50000	−	9.52628i	0.150756	−	0.261116i
$12$	1.95281			0.0469772
$13$	40.5553	−	23.5003i	0.865232	−	0.501371i
$13$	40.5553	−	23.5003i	0.865232	−	0.501371i
$14$	−18.8886			−0.360585
$15$	11.6829	−	20.2354i	0.201101	−	0.348316i
$16$	30.0282	−	52.0103i	0.469190	−	0.812661i
$17$	48.4786	+	83.9674i	0.691635	+	1.19795i	0.971302	+	0.237850i	$0.0764426\pi$
$17$	48.4786	+	83.9674i	0.691635	+	1.19795i	−0.279667	+	0.960097i	$0.590224\pi$
$18$	−25.8741			−0.338811
$19$	45.6604	+	79.0861i	0.551327	+	0.954927i	0.998179	+	0.0603187i	$0.0192117\pi$
$19$	45.6604	+	79.0861i	0.551327	+	0.954927i	−0.446852	+	0.894608i	$0.647455\pi$
$20$	1.29823	+	2.24859i	0.0145146	+	0.0251400i
$21$	28.8477			0.299766
$22$	15.0966	+	26.1481i	0.146301	+	0.253400i
$23$	−2.46326	+	4.26649i	−0.0223315	+	0.0386793i	−0.876975	−	0.480536i	$-0.840442\pi$
$23$	−2.46326	+	4.26649i	−0.0223315	+	0.0386793i	0.854644	+	0.519215i	$0.173776\pi$
$24$	−48.7065	+	84.3621i	−0.414257	+	0.717515i
$25$	−93.9329			−0.751463
$26$	0.203750	+	128.657i	0.00153687	+	0.970448i
$27$	152.703			1.08843
$28$	−1.60281	+	2.77615i	−0.0108179	+	0.0187372i
$29$	−60.3491	+	104.528i	−0.386433	+	0.669321i	−0.991967	−	0.126498i	$-0.959626\pi$
$29$	−60.3491	+	104.528i	−0.386433	+	0.669321i	0.605534	+	0.795819i	$0.292959\pi$
$30$	32.0677	+	55.5429i	0.195158	+	0.338023i
$31$	62.6271			0.362844			0.181422	−	0.983405i	$-0.441930\pi$
$31$	62.6271			0.362844			0.181422	+	0.983405i	$0.441930\pi$
$32$	−10.5269	−	18.2331i	−0.0581535	−	0.100725i
$33$	−23.0564	−	39.9349i	−0.121625	−	0.210660i
$34$	−266.132			−1.34239
$35$	19.1780	+	33.2172i	0.0926191	+	0.160421i
$36$	−2.19557	+	3.80284i	−0.0101647	+	0.0176058i
$37$	−29.9707	+	51.9107i	−0.133166	+	0.230651i	−0.924895	−	0.380222i	$-0.875848\pi$
$37$	−29.9707	+	51.9107i	−0.133166	+	0.230651i	0.791729	+	0.610872i	$0.209181\pi$
$38$	−250.661			−1.07007
$39$	−0.311179	−	196.492i	−0.00127765	−	0.806765i
$40$	−129.520			−0.511974
$41$	27.4478	−	47.5409i	0.104552	−	0.181089i	−0.809003	−	0.587804i	$-0.799993\pi$
$41$	27.4478	−	47.5409i	0.104552	−	0.181089i	0.913555	+	0.406715i	$0.133326\pi$
$42$	−39.5913	+	68.5741i	−0.145454	+	0.251934i
$43$	209.483	+	362.835i	0.742927	+	1.28679i	0.951157	+	0.308707i	$0.0998963\pi$
$43$	209.483	+	362.835i	0.742927	+	1.28679i	−0.208230	+	0.978080i	$0.566770\pi$
$44$	5.12415			0.0175567
$45$	26.2705	+	45.5019i	0.0870262	+	0.150734i
$46$	−6.76126	−	11.7108i	−0.0216716	−	0.0375363i
$47$	−158.651			−0.492375			−0.246187	−	0.969222i	$-0.579178\pi$
$47$	−158.651			−0.492375			−0.246187	+	0.969222i	$0.579178\pi$
$48$	−125.881	−	218.031i	−0.378527	−	0.655628i
$49$	147.823	−	256.036i	0.430970	−	0.746461i
$50$	128.916	−	223.288i	0.364628	−	0.631555i
$51$	406.453			1.11598
$52$	18.9266	+	10.8873i	0.0504739	+	0.0290346i
$53$	89.8532			0.232873			0.116437	−	0.993198i	$-0.462853\pi$
$53$	89.8532			0.232873			0.116437	+	0.993198i	$0.462853\pi$
$54$	−209.572	+	362.990i	−0.528133	+	0.914754i
$55$	30.6558	−	53.0975i	0.0751570	−	0.130176i
$56$	−79.9539	−	138.484i	−0.190791	−	0.330459i
$57$	382.824			0.889584
$58$	−165.649	−	286.912i	−0.375013	−	0.649542i
$59$	−329.022	−	569.883i	−0.726018	−	1.25750i	−0.958554	−	0.284912i	$-0.908036\pi$
$59$	−329.022	−	569.883i	−0.726018	−	1.25750i	0.232536	−	0.972588i	$-0.425298\pi$
$60$	10.8845			0.0234198
$61$	−219.842	−	380.777i	−0.461441	−	0.799239i	0.537592	−	0.843205i	$-0.319334\pi$
$61$	−219.842	−	380.777i	−0.461441	−	0.799239i	−0.999033	+	0.0439663i	$0.986001\pi$
$62$	−85.9507	+	148.871i	−0.176061	+	0.304946i
$63$	−32.4340	+	56.1773i	−0.0648619	+	0.112344i
$64$	538.240			1.05125
$65$	226.047	−	130.986i	0.431349	−	0.249951i
$66$	126.573			0.236061
$67$	525.901	−	910.888i	0.958941	−	1.66093i	0.233862	−	0.972270i	$-0.424864\pi$
$67$	525.901	−	910.888i	0.958941	−	1.66093i	0.725080	−	0.688665i	$-0.241803\pi$
$68$	−22.5829	+	39.1147i	−0.0402732	+	0.0697553i
$69$	10.3262	+	17.8855i	0.0180163	+	0.0312052i
$70$	−105.281			−0.179764
$71$	−538.772	−	933.181i	−0.900570	−	1.55983i	−0.826755	−	0.562562i	$-0.809816\pi$
$71$	−538.772	−	933.181i	−0.900570	−	1.55983i	−0.0738149	−	0.997272i	$-0.523517\pi$
$72$	−109.523	−	189.700i	−0.179270	−	0.310504i
$73$	−338.912			−0.543379			−0.271689	−	0.962385i	$-0.587582\pi$
$73$	−338.912			−0.543379			−0.271689	+	0.962385i	$0.587582\pi$
$74$	−82.2648	−	142.487i	−0.129231	−	0.223835i
$75$	−196.887	+	341.019i	−0.303128	+	0.525032i
$76$	−21.2701	+	36.8409i	−0.0321032	+	0.0556044i
$77$	75.6963			0.112031
$78$	467.508	+	268.930i	0.678653	+	0.390389i
$79$	664.285			0.946049			0.473024	−	0.881049i	$-0.343162\pi$
$79$	664.285			0.946049			0.473024	+	0.881049i	$0.343162\pi$
$80$	167.371	−	289.895i	0.233908	−	0.405140i
$81$	192.814	−	333.963i	0.264491	−	0.458112i
$82$	75.3398	+	130.492i	0.101462	+	0.175738i
$83$	−1011.19			−1.33726			−0.668628	−	0.743597i	$-0.733118\pi$
$83$	−1011.19			−1.33726			−0.668628	+	0.743597i	$0.733118\pi$
$84$	6.71910	+	11.6378i	0.00872755	+	0.0151166i
$85$	270.210	+	468.017i	0.344804	+	0.597218i
$86$	−1150.00			−1.44194
$87$	252.988	+	438.189i	0.311761	+	0.539986i
$88$	−127.806	+	221.366i	−0.154820	+	0.268155i
$89$	118.901	−	205.942i	0.141612	−	0.245279i	−0.786492	−	0.617601i	$-0.788105\pi$
$89$	118.901	−	205.942i	0.141612	−	0.245279i	0.928104	+	0.372321i	$0.121438\pi$
$90$	−144.217			−0.168909
$91$	279.592	+	160.832i	0.322079	+	0.185273i
$92$	−2.29493			−0.00260068
$93$	131.269	−	227.364i	0.146365	−	0.253512i
$94$	217.736	−	377.130i	0.238912	−	0.413808i
$95$	254.501	+	440.809i	0.274856	+	0.476064i
$96$	−88.2593			−0.0938326
$97$	75.0273	+	129.951i	0.0785347	+	0.136026i	0.902618	−	0.430443i	$-0.141643\pi$
$97$	75.0273	+	129.951i	0.0785347	+	0.136026i	−0.824083	+	0.566469i	$0.808309\pi$
$98$	405.750	+	702.779i	0.418234	+	0.724403i
$99$	103.691			0.105266
$100$	−21.8785	−	37.8946i	−0.0218785	−	0.0378946i
$101$	−816.348	+	1413.96i	−0.804254	+	1.39301i	0.112540	+	0.993647i	$0.464101\pi$
$101$	−816.348	+	1413.96i	−0.804254	+	1.39301i	−0.916794	+	0.399361i	$0.869232\pi$
$102$	−557.825	+	966.180i	−0.541499	+	0.937903i
$103$	−38.9576			−0.0372681			−0.0186340	−	0.999826i	$-0.505932\pi$
$103$	−38.9576			−0.0372681			−0.0186340	+	0.999826i	$0.505932\pi$
$104$	−942.400	+	546.086i	−0.888557	+	0.514886i
$105$	160.791			0.149444
$106$	−123.317	+	213.591i	−0.112996	+	0.195715i
$107$	−148.310	+	256.880i	−0.133996	+	0.232089i	−0.925214	−	0.379447i	$-0.876114\pi$
$107$	−148.310	+	256.880i	−0.133996	+	0.232089i	0.791217	+	0.611535i	$0.209448\pi$
$108$	35.5669	+	61.6037i	0.0316891	+	0.0548872i
$109$	−1405.78			−1.23532			−0.617658	−	0.786447i	$-0.711918\pi$
$109$	−1405.78			−1.23532			−0.617658	+	0.786447i	$0.711918\pi$
$110$	84.1455	+	145.744i	0.0729360	+	0.126329i
$111$	125.640	+	217.614i	0.107434	+	0.186081i
$112$	413.277			0.348670
$113$	−729.861	−	1264.16i	−0.607607	−	1.05241i	−0.991634	−	0.129084i	$-0.958796\pi$
$113$	−729.861	−	1264.16i	−0.607607	−	1.05241i	0.384027	−	0.923322i	$-0.374537\pi$
$114$	−525.396	+	910.013i	−0.431648	+	0.747636i
$115$	−13.7297	+	23.7805i	−0.0111330	+	0.0192830i
$116$	−56.2251			−0.0450032
$117$	382.993	+	220.313i	0.302630	+	0.174085i
$118$	1806.23			1.40913
$119$	−333.605	+	577.821i	−0.256987	+	0.445115i
$120$	−271.480	+	470.217i	−0.206522	+	0.357706i
$121$	−60.5000	−	104.789i	−0.0454545	−	0.0787296i
$122$	1206.86			0.895609
$123$	−115.063	−	199.295i	−0.0843488	−	0.146096i
$124$	14.5868	+	25.2652i	0.0105640	+	0.0182974i
$125$	−1220.29			−0.873165
$126$	−89.0263	−	154.198i	−0.0629452	−	0.109024i
$127$	1114.63	−	1930.60i	0.778801	−	1.34892i	−0.153833	−	0.988097i	$-0.549162\pi$
$127$	1114.63	−	1930.60i	0.778801	−	1.34892i	0.932633	−	0.360825i	$-0.117505\pi$
$128$	−654.477	+	1133.59i	−0.451939	+	0.782781i
$129$	1756.34			1.19874
$130$	1.13566	+	717.105i	0.000766184	+	0.483802i
$131$	804.754			0.536730			0.268365	−	0.963317i	$-0.413517\pi$
$131$	804.754			0.536730			0.268365	+	0.963317i	$0.413517\pi$
$132$	10.7404	−	18.6030i	0.00708208	−	0.0122665i
$133$	−314.211	+	544.230i	−0.204854	+	0.354818i
$134$	1443.52	+	2500.24i	0.930603	+	1.61185i
$135$	851.132			0.542621
$136$	−1126.52	−	1951.18i	−0.710279	−	1.23024i
$137$	1024.47	+	1774.44i	0.638881	+	1.10657i	0.985679	+	0.168634i	$0.0539355\pi$
$137$	1024.47	+	1774.44i	0.638881	+	1.10657i	−0.346798	+	0.937940i	$0.612731\pi$
$138$	−56.6875			−0.0349678
$139$	−421.591	−	730.217i	−0.257258	−	0.445584i	0.708248	−	0.705963i	$-0.249486\pi$
$139$	−421.591	−	730.217i	−0.257258	−	0.445584i	−0.965506	+	0.260379i	$0.916152\pi$
$140$	−8.93372	+	15.4737i	−0.00539312	+	0.00934116i
$141$	−332.539	+	575.974i	−0.198616	+	0.344012i
$142$	2957.69			1.74791
$143$	−0.816531	−	515.593i	−0.000477495	−	0.301511i
$144$	566.118			0.327615
$145$	−336.373	+	582.615i	−0.192650	+	0.333680i
$146$	465.130	−	805.629i	0.263661	−	0.456674i
$147$	−619.684	−	1073.32i	−0.347692	−	0.602220i
$148$	−27.9226			−0.0155083
$149$	−1579.92	−	2736.51i	−0.868674	−	1.50459i	−0.863353	−	0.504601i	$-0.831640\pi$
$149$	−1579.92	−	2736.51i	−0.868674	−	1.50459i	−0.00532111	−	0.999986i	$-0.501694\pi$
$150$	−540.424	−	936.043i	−0.294170	−	0.509517i
$151$	2493.03			1.34357			0.671787	−	0.740745i	$-0.265527\pi$
$151$	2493.03			1.34357			0.671787	+	0.740745i	$0.265527\pi$
$152$	−1061.03	−	1837.76i	−0.566189	−	0.980669i
$153$	−456.982	+	791.515i	−0.241469	+	0.418237i
$154$	−103.887	+	179.938i	−0.0543602	+	0.0941547i
$155$	349.070			0.180890
$156$	79.1967	−	45.8916i	0.0406462	−	0.0235530i
$157$	176.934			0.0899421			0.0449710	−	0.998988i	$-0.485680\pi$
$157$	176.934			0.0899421			0.0449710	+	0.998988i	$0.485680\pi$
$158$	−911.679	+	1579.07i	−0.459046	+	0.795091i
$159$	188.336	−	326.208i	0.0939372	−	0.162704i
$160$	−58.6748	−	101.628i	−0.0289915	−	0.0502148i
$161$	−33.9017			−0.0165952
$162$	529.244	+	916.677i	0.256675	+	0.444574i
$163$	510.057	+	883.445i	0.245097	+	0.424520i	0.962159	−	0.272489i	$-0.0878470\pi$
$163$	510.057	+	883.445i	0.245097	+	0.424520i	−0.717062	+	0.697009i	$0.754514\pi$
$164$	25.5721			0.0121759
$165$	−128.512	−	222.589i	−0.0606341	−	0.105021i
$166$	1387.78	−	2403.70i	0.648869	−	1.12387i
$167$	122.756	−	212.620i	0.0568812	−	0.0985211i	−0.836183	−	0.548451i	$-0.815218\pi$
$167$	122.756	−	212.620i	0.0568812	−	0.0985211i	0.893064	+	0.449930i	$0.148551\pi$
$168$	−670.346			−0.307847
$169$	1092.47	−	1906.13i	0.497254	−	0.867605i
$170$	−1483.37			−0.669229
$171$	−430.416	+	745.502i	−0.192484	+	0.333392i
$172$	−97.5839	+	169.020i	−0.0432599	+	0.0749283i
$173$	545.371	+	944.610i	0.239675	+	0.415129i	0.960621	−	0.277862i	$-0.0896258\pi$
$173$	545.371	+	944.610i	0.239675	+	0.415129i	−0.720946	+	0.692991i	$0.756292\pi$
$174$	−1388.83			−0.605096
$175$	−323.199	−	559.797i	−0.139609	−	0.241809i
$176$	−330.310	−	572.114i	−0.141466	−	0.245027i
$177$	−2758.58			−1.17145
$178$	326.364	+	565.280i	0.137427	+	0.238031i
$179$	−1688.92	+	2925.30i	−0.705229	+	1.22149i	0.261379	+	0.965236i	$0.415823\pi$
$179$	−1688.92	+	2925.30i	−0.705229	+	1.22149i	−0.966609	+	0.256257i	$0.917511\pi$
$180$	−12.2377	+	21.1962i	−0.00506745	+	0.00877708i
$181$	3464.79			1.42285			0.711424	−	0.702763i	$-0.248051\pi$
$181$	3464.79			1.42285			0.711424	+	0.702763i	$0.248051\pi$
$182$	−766.033	+	443.889i	−0.311990	+	0.180787i
$183$	−1843.19			−0.744550
$184$	57.2397	−	99.1420i	0.0229335	−	0.0397220i
$185$	−167.050	+	289.339i	−0.0663880	+	0.114987i
$186$	360.312	+	624.080i	0.142040	+	0.246020i
$187$	1066.53			0.417072
$188$	−36.9523	−	64.0033i	−0.0143352	−	0.0248294i
$189$	525.411	+	910.038i	0.202212	+	0.350241i
$190$	−1397.13			−0.533467
$191$	−1451.70	−	2514.41i	−0.549953	−	0.952547i	−0.998277	−	0.0586756i	$-0.981312\pi$
$191$	−1451.70	−	2514.41i	−0.549953	−	0.952547i	0.448324	−	0.893871i	$-0.352021\pi$
$192$	1128.17	−	1954.05i	0.424057	−	0.734488i
$193$	−2302.86	+	3988.67i	−0.858878	+	1.48762i	0.0141216	+	0.999900i	$0.495505\pi$
$193$	−2302.86	+	3988.67i	−0.858878	+	1.48762i	−0.873000	+	0.487721i	$0.837829\pi$
$194$	−411.877			−0.152428
$195$	−1.73444	−	1095.20i	−0.000636954	−	0.402201i
$196$	137.721			0.0501899
$197$	−12.7399	+	22.0661i	−0.00460750	+	0.00798042i	−0.868320	−	0.496004i	$-0.834800\pi$
$197$	−12.7399	+	22.0661i	−0.00460750	+	0.00798042i	0.863712	+	0.503985i	$0.168133\pi$
$198$	−142.308	+	246.484i	−0.0510777	+	0.0884691i
$199$	1348.53	+	2335.71i	0.480374	+	0.832032i	0.999746	−	0.0225158i	$-0.00716761\pi$
$199$	1348.53	+	2335.71i	0.480374	+	0.832032i	−0.519373	+	0.854548i	$0.673834\pi$
$200$	2182.75			0.771720
$201$	−2204.62	−	3818.52i	−0.773642	−	1.33999i
$202$	−2240.75	−	3881.09i	−0.780487	−	1.35184i
$203$	−830.583			−0.287170
$204$	94.6694	+	163.972i	0.0324911	+	0.0562762i
$205$	152.988	−	264.983i	0.0521227	−	0.0902791i
$206$	53.4663	−	92.6064i	0.0180834	−	0.0313213i
$207$	−46.4396			−0.0155931
$208$	−4.45799	−	2814.97i	−0.00148609	−	0.938379i
$209$	1004.53			0.332463
$210$	−220.673	+	382.218i	−0.0725139	+	0.125598i
$211$	1690.89	−	2928.71i	0.551687	−	0.955550i	−0.446466	−	0.894801i	$-0.647318\pi$
$211$	1690.89	−	2928.71i	0.551687	−	0.955550i	0.998153	−	0.0607494i	$-0.0193491\pi$
$212$	20.9283	+	36.2488i	0.00678000	+	0.0117433i
$213$	−4517.15			−1.45310
$214$	−407.087	−	705.095i	−0.130037	−	0.225230i
$215$	1167.61	+	2022.37i	0.370375	+	0.641508i
$216$	−3548.41			−1.11777
$217$	215.484	+	373.228i	0.0674100	+	0.116758i
$218$	1929.32	−	3341.69i	0.599405	−	1.03820i
$219$	−710.373	+	1230.40i	−0.219190	+	0.379648i
$220$	28.5610			0.00875263
$221$	3939.33	+	2266.06i	1.19904	+	0.689737i
$222$	−689.722			−0.208518
$223$	−1990.28	+	3447.26i	−0.597663	+	1.03518i	0.395502	+	0.918465i	$0.370571\pi$
$223$	−1990.28	+	3447.26i	−0.597663	+	1.03518i	−0.993165	+	0.116718i	$0.962763\pi$
$224$	72.4408	−	125.471i	0.0216078	−	0.0374258i
$225$	−442.727	−	766.826i	−0.131178	−	0.227208i
$226$	4006.71			1.17930
$227$	−653.859	−	1132.52i	−0.191181	−	0.331136i	0.754461	−	0.656345i	$-0.227899\pi$
$227$	−653.859	−	1132.52i	−0.191181	−	0.331136i	−0.945642	+	0.325210i	$0.894565\pi$
$228$	89.1659	+	154.440i	0.0258998	+	0.0448598i
$229$	−3204.14			−0.924611			−0.462305	−	0.886721i	$-0.652978\pi$
$229$	−3204.14			−0.924611			−0.462305	+	0.886721i	$0.652978\pi$
$230$	−37.6858	−	65.2738i	−0.0108040	−	0.0187132i
$231$	158.663	−	274.812i	0.0451915	−	0.0782739i
$232$	1402.36	−	2428.95i	0.396850	−	0.687364i
$233$	308.568			0.0867596			0.0433798	−	0.999059i	$-0.486187\pi$
$233$	308.568			0.0867596			0.0433798	+	0.999059i	$0.486187\pi$
$234$	−1049.33	+	608.051i	−0.293150	+	0.169870i
$235$	−884.286			−0.245466
$236$	153.269	−	265.470i	0.0422753	−	0.0732230i
$237$	1392.37	−	2411.65i	0.381620	−	0.660986i
$238$	−915.693	−	1586.03i	−0.249393	−	0.431962i
$239$	3295.42			0.891895			0.445948	−	0.895059i	$-0.352867\pi$
$239$	3295.42			0.891895			0.445948	+	0.895059i	$0.352867\pi$
$240$	−701.632	−	1215.26i	−0.188709	−	0.326853i
$241$	−2572.35	−	4455.43i	−0.687549	−	1.19087i	−0.972628	−	0.232366i	$-0.925353\pi$
$241$	−2572.35	−	4455.43i	−0.687549	−	1.19087i	0.285079	−	0.958504i	$-0.407980\pi$
$242$	332.126			0.0882226
$243$	1253.19	+	2170.60i	0.330833	+	0.573020i
$244$	102.409	−	177.378i	0.0268692	−	0.0465389i
$245$	823.932	−	1427.09i	0.214853	−	0.372137i
$246$	631.661			0.163712
$247$	3710.32	+	2134.33i	0.955798	+	0.549814i
$248$	−1455.29			−0.372625
$249$	−2119.49	+	3671.06i	−0.539426	+	0.934314i
$250$	1674.75	−	2900.75i	0.423681	−	0.733837i
$251$	339.071	+	587.288i	0.0852668	+	0.147687i	0.905505	−	0.424336i	$-0.139492\pi$
$251$	339.071	+	587.288i	0.0852668	+	0.147687i	−0.820238	+	0.572022i	$0.806159\pi$
$252$	−30.2176			−0.00755369
$253$	27.0958	+	46.9314i	0.00673321	+	0.0116623i
$254$	3059.49	+	5299.20i	0.755786	+	1.30906i
$255$	2265.48			0.556353
$256$	356.523	+	617.515i	0.0870416	+	0.150761i
$257$	−463.722	+	803.190i	−0.112553	+	0.194948i	−0.916799	−	0.399349i	$-0.869236\pi$
$257$	−463.722	+	803.190i	−0.112553	+	0.194948i	0.804246	+	0.594297i	$0.202570\pi$
$258$	−2410.44	+	4175.00i	−0.581656	+	1.00746i
$259$	−412.485			−0.0989599
$260$	105.493	+	60.6836i	0.0251630	+	0.0144748i
$261$	−1137.76			−0.269829
$262$	−1104.46	+	1912.98i	−0.260435	+	0.451086i
$263$	1234.21	−	2137.71i	0.289371	−	0.501205i	−0.684289	−	0.729211i	$-0.739887\pi$
$263$	1234.21	−	2137.71i	0.289371	−	0.501205i	0.973660	+	0.228006i	$0.0732205\pi$
$264$	535.772	+	927.984i	0.124903	+	0.216339i
$265$	500.823			0.116096
$266$	−862.461	−	1493.83i	−0.198800	−	0.344332i
$267$	−498.442	−	863.328i	−0.114248	−	0.197883i
$268$	489.963			0.111676
$269$	580.920	+	1006.18i	0.131670	+	0.228060i	0.924321	−	0.381617i	$-0.124633\pi$
$269$	580.920	+	1006.18i	0.131670	+	0.228060i	−0.792650	+	0.609677i	$0.791299\pi$
$270$	−1168.11	+	2023.23i	−0.263293	+	0.456037i
$271$	2267.52	−	3927.46i	0.508273	−	0.880354i	−0.491681	−	0.870775i	$-0.663617\pi$
$271$	2267.52	−	3927.46i	0.508273	−	0.880354i	0.999954	−	0.00957916i	$-0.00304919\pi$
$272$	5822.90			1.29803
$273$	1169.93	−	677.932i	0.259368	−	0.150294i
$274$	−5624.04			−1.24000
$275$	−516.631	+	894.831i	−0.113287	+	0.196219i
$276$	−4.81027	+	8.33163i	−0.00104907	+	0.00181705i
$277$	−1107.43	−	1918.12i	−0.240213	−	0.416061i	0.720562	−	0.693391i	$-0.243884\pi$
$277$	−1107.43	−	1918.12i	−0.240213	−	0.416061i	−0.960775	+	0.277330i	$0.910551\pi$
$278$	2314.40			0.499311
$279$	295.176	+	511.259i	0.0633394	+	0.109707i
$280$	−445.646	−	771.881i	−0.0951159	−	0.164745i
$281$	−1806.53			−0.383518			−0.191759	−	0.981442i	$-0.561419\pi$
$281$	−1806.53			−0.383518			−0.191759	+	0.981442i	$0.561419\pi$
$282$	−912.767	−	1580.96i	−0.192746	−	0.333846i
$283$	−3440.80	+	5959.64i	−0.722736	+	1.25181i	0.237164	+	0.971470i	$0.423782\pi$
$283$	−3440.80	+	5959.64i	−0.722736	+	1.25181i	−0.959899	+	0.280345i	$0.909551\pi$
$284$	250.977	−	434.706i	0.0524393	−	0.0908276i
$285$	2133.78			0.443489
$286$	1226.74	+	705.670i	0.253632	+	0.145899i
$287$	377.763			0.0776956
$288$	99.2314	−	171.874i	0.0203030	−	0.0351658i
$289$	−2243.85	+	3886.47i	−0.456718	+	0.791058i
$290$	−923.292	−	1599.19i	−0.186957	−	0.323819i
$291$	629.041			0.126718
$292$	−78.9381	−	136.725i	−0.0158202	−	0.0274014i
$293$	−422.727	−	732.185i	−0.0842866	−	0.145989i	0.820800	−	0.571215i	$-0.193528\pi$
$293$	−422.727	−	732.185i	−0.0842866	−	0.145989i	−0.905087	+	0.425226i	$0.860194\pi$
$294$	3401.87			0.674834
$295$	−1833.90	−	3176.41i	−0.361945	−	0.626907i
$296$	696.440	−	1206.27i	0.136756	−	0.236868i
$297$	839.865	−	1454.69i	0.164087	−	0.284207i
$298$	8673.29			1.68601
$299$	0.365696	+	230.916i	7.07315e−5	+	0.0446630i
$300$	−183.433			−0.0353016
$301$	−1441.55	+	2496.84i	−0.276046	+	0.478125i
$302$	−3421.48	+	5926.18i	−0.651935	+	1.12918i
$303$	3422.20	+	5927.42i	0.648845	+	1.12383i
$304$	5484.39			1.03471
$305$	−1225.35	−	2122.37i	−0.230044	−	0.398448i
$306$	−1254.34	−	2172.59i	−0.234333	−	0.405877i
$307$	3457.05			0.642685			0.321342	−	0.946963i	$-0.395866\pi$
$307$	3457.05			0.642685			0.321342	+	0.946963i	$0.395866\pi$
$308$	17.6309	+	30.5376i	0.00326173	+	0.00564949i
$309$	−81.6568	+	141.434i	−0.0150333	+	0.0260385i
$310$	−479.071	+	829.776i	−0.0877723	+	0.152026i
$311$	−1756.56			−0.320275			−0.160137	−	0.987095i	$-0.551194\pi$
$311$	−1756.56			−0.320275			−0.160137	+	0.987095i	$0.551194\pi$
$312$	7.23098	+	4565.95i	0.00131209	+	0.828513i
$313$	−4815.76			−0.869659			−0.434829	−	0.900513i	$-0.643191\pi$
$313$	−4815.76			−0.869659			−0.434829	+	0.900513i	$0.643191\pi$
$314$	−242.829	+	420.592i	−0.0436421	+	0.0755903i
$315$	−180.780	+	313.121i	−0.0323359	+	0.0560075i
$316$	154.723	+	267.987i	0.0275438	+	0.0477072i
$317$	−1278.25			−0.226479			−0.113239	−	0.993568i	$-0.536123\pi$
$317$	−1278.25			−0.226479			−0.113239	+	0.993568i	$0.536123\pi$
$318$	516.953	+	895.389i	0.0911613	+	0.157896i
$319$	663.840	+	1149.80i	0.116514	+	0.201808i
$320$	3000.04			0.524085
$321$	621.726	+	1076.86i	0.108104	+	0.187241i
$322$	46.5275	−	80.5880i	0.00805241	−	0.0139472i
$323$	−4427.11	+	7667.97i	−0.762634	+	1.32092i
$324$	179.638			0.0308021
$325$	−3809.48	+	2207.45i	−0.650190	+	0.376762i
$326$	−2800.05			−0.475707
$327$	−2946.57	+	5103.62i	−0.498306	+	0.863091i
$328$	−637.814	+	1104.73i	−0.107370	+	0.185971i
$329$	−545.877	−	945.486i	−0.0914747	−	0.158439i
$330$	705.489			0.117685
$331$	2970.48	+	5145.02i	0.493270	+	0.854368i	0.999970	−	0.00775420i	$-0.00246826\pi$
$331$	2970.48	+	5145.02i	0.493270	+	0.854368i	−0.506700	+	0.862122i	$0.669135\pi$
$332$	−235.522	−	407.936i	−0.0389335	−	0.0674349i
$333$	−565.034			−0.0929841
$334$	336.947	+	583.609i	0.0552003	+	0.0956097i
$335$	2931.26	−	5077.10i	0.478066	−	0.828034i
$336$	866.245	−	1500.38i	0.140647	−	0.243609i
$337$	−4606.79			−0.744652			−0.372326	−	0.928102i	$-0.621440\pi$
$337$	−4606.79			−0.744652			−0.372326	+	0.928102i	$0.621440\pi$
$338$	3031.74	+	5212.92i	0.487884	+	0.838892i
$339$	−6119.28			−0.980394
$340$	−125.872	+	218.017i	−0.0200776	+	0.0347754i
$341$	344.449	−	596.603i	0.0547007	−	0.0947444i
$342$	−1181.42	−	2046.29i	−0.186796	−	0.323539i
$343$	4394.83			0.691832
$344$	−4867.84	−	8431.34i	−0.762954	−	1.32147i
$345$	57.5559	+	99.6898i	0.00898176	+	0.0155569i
$346$	−2993.91			−0.465184
$347$	5228.82	+	9056.58i	0.808928	+	1.40110i	0.913607	+	0.406598i	$0.133285\pi$
$347$	5228.82	+	9056.58i	0.808928	+	1.40110i	−0.104680	+	0.994506i	$0.533382\pi$
$348$	−117.850	+	204.122i	−0.0181535	+	0.0314428i
$349$	2933.92	−	5081.70i	0.449998	−	0.779419i	−0.548387	−	0.836224i	$-0.684758\pi$
$349$	2933.92	−	5081.70i	0.449998	−	0.779419i	0.998385	+	0.0568052i	$0.0180914\pi$
$350$	1774.26			0.270966
$351$	6192.91	−	3588.56i	0.941746	−	0.545708i
$352$	−231.592			−0.0350679
$353$	−2438.00	+	4222.74i	−0.367597	+	0.636697i	−0.989189	−	0.146644i	$-0.953153\pi$
$353$	−2438.00	+	4222.74i	−0.367597	+	0.636697i	0.621592	+	0.783341i	$0.286486\pi$
$354$	3785.93	−	6557.42i	0.568418	−	0.984529i
$355$	−3003.00	−	5201.35i	−0.448966	−	0.777631i
$356$	110.776			0.0164919
$357$	1398.50	+	2422.27i	0.207329	+	0.359104i
$358$	−4635.83	−	8029.49i	−0.684389	−	1.18540i
$359$	5199.25			0.764362			0.382181	−	0.924087i	$-0.375173\pi$
$359$	5199.25			0.764362			0.382181	+	0.924087i	$0.375173\pi$
$360$	−610.459	−	1057.35i	−0.0893722	−	0.154797i
$361$	−740.244	+	1282.14i	−0.107923	+	0.186928i
$362$	−4755.15	+	8236.16i	−0.690400	+	1.19581i
$363$	−507.242			−0.0733424
$364$	0.237953	+	150.254i	3.42641e−5	+	0.0216359i
$365$	−1889.02			−0.270893
$366$	2529.64	−	4381.46i	0.361274	−	0.625744i
$367$	3077.32	−	5330.08i	0.437697	−	0.758114i	−0.559814	−	0.828618i	$-0.689128\pi$
$367$	3077.32	−	5330.08i	0.437697	−	0.758114i	0.997511	+	0.0705043i	$0.0224609\pi$
$368$	147.934	+	256.230i	0.0209555	+	0.0362959i
$369$	517.470			0.0730039
$370$	−458.527	−	794.192i	−0.0644261	−	0.111589i
$371$	309.162	+	535.484i	0.0432638	+	0.0749352i
$372$	122.299			0.0170454
$373$	−5475.99	−	9484.70i	−0.760151	−	1.31662i	−0.942773	−	0.333437i	$-0.891792\pi$
$373$	−5475.99	−	9484.70i	−0.760151	−	1.31662i	0.182622	−	0.983183i	$-0.441542\pi$
$374$	−1463.73	+	2535.25i	−0.202373	+	0.350521i
$375$	−2557.77	+	4430.18i	−0.352220	+	0.610063i
$376$	3686.63			0.505648
$377$	8.95944	+	5657.38i	0.00122396	+	0.772864i
$378$	−2884.34			−0.392472
$379$	−1069.72	+	1852.82i	−0.144982	+	0.251115i	−0.929366	−	0.369159i	$-0.879646\pi$
$379$	−1069.72	+	1852.82i	−0.144982	+	0.251115i	0.784385	+	0.620275i	$0.212979\pi$
$380$	−118.555	+	205.343i	−0.0160046	+	0.0277207i
$381$	−4672.63	−	8093.24i	−0.628310	−	1.08827i
$382$	7969.36			1.06740
$383$	1347.76	+	2334.39i	0.179810	+	0.311440i	0.941815	−	0.336131i	$-0.109118\pi$
$383$	1347.76	+	2334.39i	0.179810	+	0.311440i	−0.762005	+	0.647571i	$0.775785\pi$
$384$	2743.62	+	4752.09i	0.364609	+	0.631521i
$385$	421.915			0.0558514
$386$	−6320.99	−	10948.3i	−0.833497	−	1.44366i
$387$	−1974.68	+	3420.25i	−0.259376	+	0.449253i
$388$	−34.9501	+	60.5354i	−0.00457300	+	0.00792067i
$389$	−9522.84			−1.24120			−0.620600	−	0.784127i	$-0.713111\pi$
$389$	−9522.84			−1.24120			−0.620600	+	0.784127i	$0.713111\pi$
$390$	2605.79	+	1498.96i	0.338332	+	0.194622i
$391$	−477.661			−0.0617810
$392$	−3435.01	+	5949.61i	−0.442587	+	0.766584i
$393$	1686.80	−	2921.62i	0.216508	−	0.375003i
$394$	−34.9689	−	60.5679i	−0.00447134	−	0.00774459i
$395$	3702.58			0.471638
$396$	24.1513	+	41.8313i	0.00306477	+	0.00530834i
$397$	2156.55	+	3735.26i	0.272630	+	0.472210i	0.969535	−	0.244954i	$-0.0787730\pi$
$397$	2156.55	+	3735.26i	0.272630	+	0.472210i	−0.696904	+	0.717164i	$0.745440\pi$
$398$	−7402.98			−0.932357
$399$	1317.20	+	2281.46i	0.165269	+	0.286255i
$400$	−2820.63	+	4885.48i	−0.352579	+	0.610685i
$401$	7265.98	−	12585.1i	0.904853	−	1.56725i	0.0837381	−	0.996488i	$-0.473314\pi$
$401$	7265.98	−	12585.1i	0.904853	−	1.56725i	0.821115	−	0.570763i	$-0.193353\pi$
$402$	12102.7			1.50156
$403$	2539.86	−	1471.76i	0.313944	−	0.181919i
$404$	−760.562			−0.0936618
$405$	1074.70	−	1861.44i	0.131858	−	0.228385i
$406$	1139.91	−	1974.38i	0.139342	−	0.241347i
$407$	329.677	+	571.018i	0.0401511	+	0.0695438i
$408$	−9444.90			−1.14606
$409$	−5273.12	−	9133.32i	−0.637504	−	1.10419i	−0.985979	−	0.166871i	$-0.946634\pi$
$409$	−5273.12	−	9133.32i	−0.637504	−	1.10419i	0.348475	−	0.937318i	$-0.386700\pi$
$410$	419.928	+	727.337i	0.0505824	+	0.0876113i
$411$	8589.35			1.03085
$412$	−9.07386	−	15.7164i	−0.00108504	−	0.00187935i
$413$	2264.16	−	3921.64i	0.269763	−	0.467243i
$414$	63.7347	−	110.392i	0.00756616	−	0.0131050i
$415$	−5636.14			−0.666668
$416$	−855.407	−	492.065i	−0.100817	−	0.0579939i
$417$	−3534.69			−0.415094
$418$	−1378.64	+	2387.87i	−0.161319	+	0.279413i
$419$	6231.86	−	10793.9i	0.726602	−	1.25851i	−0.231709	−	0.972785i	$-0.574432\pi$
$419$	6231.86	−	10793.9i	0.726602	−	1.25851i	0.958311	−	0.285727i	$-0.0922351\pi$
$420$	37.4509	+	64.8668i	0.00435099	+	0.00753613i
$421$	−5963.21			−0.690330			−0.345165	−	0.938542i	$-0.612177\pi$
$421$	−5963.21			−0.690330			−0.345165	+	0.938542i	$0.612177\pi$
$422$	4641.24	+	8038.87i	0.535384	+	0.927312i
$423$	−747.758	−	1295.15i	−0.0859509	−	0.148871i
$424$	−2087.95			−0.239151
$425$	−4553.74	−	7887.30i	−0.519738	−	0.900213i
$426$	6199.44	−	10737.7i	0.705079	−	1.22123i
$427$	1512.84	−	2620.31i	0.171455	−	0.296969i
$428$	−138.175			−0.0156050
$429$	−1873.55	−	1077.74i	−0.210852	−	0.121291i
$430$	−6409.83			−0.718860
$431$	64.8441	−	112.313i	0.00724694	−	0.0125521i	−0.862379	−	0.506263i	$-0.831027\pi$
$431$	64.8441	−	112.313i	0.00724694	−	0.0125521i	0.869626	+	0.493711i	$0.164360\pi$
$432$	4585.38	−	7942.11i	0.510681	−	0.884526i
$433$	3495.52	+	6054.42i	0.387954	+	0.671956i	0.992174	−	0.124861i	$-0.0398485\pi$
$433$	3495.52	+	6054.42i	0.387954	+	0.671956i	−0.604220	+	0.796817i	$0.706515\pi$
$434$	−1182.94			−0.130836
$435$	1410.10	+	2442.37i	0.155424	+	0.269202i
$436$	−327.429	−	567.124i	−0.0359656	−	0.0622943i
$437$	−449.893			−0.0492479
$438$	−1949.86	−	3377.26i	−0.212713	−	0.368429i
$439$	2036.54	−	3527.39i	0.221410	−	0.383493i	−0.733827	−	0.679337i	$-0.762268\pi$
$439$	2036.54	−	3527.39i	0.221410	−	0.383493i	0.955236	+	0.295844i	$0.0956009\pi$
$440$	−712.362	+	1233.85i	−0.0771830	+	0.133685i
$441$	2786.89			0.300927
$442$	−10793.1	+	6254.20i	−1.16148	+	0.673037i
$443$	9000.98			0.965348			0.482674	−	0.875800i	$-0.339666\pi$
$443$	9000.98			0.965348			0.482674	+	0.875800i	$0.339666\pi$
$444$	−58.5269	+	101.372i	−0.00625578	+	0.0108353i
$445$	662.729	−	1147.88i	0.0705985	−	0.122280i
$446$	−5463.00	−	9462.19i	−0.580001	−	1.00459i
$447$	−13246.3			−1.40163
$448$	1851.95	+	3207.66i	0.195304	+	0.338277i
$449$	−7454.81	−	12912.1i	−0.783551	−	1.35715i	−0.929861	−	0.367911i	$-0.880073\pi$
$449$	−7454.81	−	12912.1i	−0.783551	−	1.35715i	0.146311	−	0.989239i	$-0.453260\pi$
$450$	2430.43			0.254604
$451$	−301.925	−	522.950i	−0.0315235	−	0.0546004i
$452$	339.993	−	588.885i	0.0353804	−	0.0612806i
$453$	5225.48	−	9050.81i	0.541975	−	0.938728i
$454$	3589.48			0.371063
$455$	1558.38	+	896.446i	0.160567	+	0.0923649i
$456$	−8895.83			−0.913565
$457$	−6179.26	+	10702.8i	−0.632502	+	1.09553i	0.354536	+	0.935042i	$0.384639\pi$
$457$	−6179.26	+	10702.8i	−0.632502	+	1.09553i	−0.987038	+	0.160484i	$0.948695\pi$
$458$	4397.44	−	7616.59i	0.448644	−	0.777074i
$459$	7402.81	+	12822.1i	0.752797	+	1.30388i
$460$	−12.7915			−0.00129653
$461$	383.761	+	664.693i	0.0387712	+	0.0671537i	0.884760	−	0.466047i	$-0.154322\pi$
$461$	383.761	+	664.693i	0.0387712	+	0.0671537i	−0.845989	+	0.533201i	$0.820989\pi$
$462$	435.504	+	754.315i	0.0438560	+	0.0759609i
$463$	−2323.66			−0.233239			−0.116620	−	0.993177i	$-0.537206\pi$
$463$	−2323.66			−0.233239			−0.116620	+	0.993177i	$0.537206\pi$
$464$	3624.35	+	6277.55i	0.362621	+	0.628078i
$465$	731.665	−	1267.28i	0.0729680	−	0.126384i
$466$	−423.486	+	733.499i	−0.0420979	+	0.0729157i
$467$	5615.29			0.556413			0.278206	−	0.960521i	$-0.410260\pi$
$467$	5615.29			0.556413			0.278206	+	0.960521i	$0.410260\pi$
$468$	0.325955	+	205.822i	3.21950e−5	+	0.0203294i
$469$	7237.96			0.712619
$470$	1213.61	−	2102.04i	0.119106	−	0.206298i
$471$	370.862	−	642.351i	0.0362811	−	0.0628407i
$472$	7645.62	+	13242.6i	0.745589	+	1.29140i
$473$	4608.62			0.448002
$474$	3821.83	+	6619.61i	0.370343	+	0.641453i
$475$	−4289.01	−	7428.79i	−0.414302	−	0.717592i
$476$	−310.808			−0.0299283
$477$	423.499	+	733.521i	0.0406513	+	0.0704101i
$478$	−4522.71	+	7833.56i	−0.432769	+	0.749578i
$479$	5535.99	−	9588.61i	0.528070	−	0.914645i	−0.471394	−	0.881923i	$-0.656249\pi$
$479$	5535.99	−	9588.61i	0.528070	−	0.914645i	0.999464	−	0.0327220i	$-0.0104176\pi$
$480$	−491.939			−0.0467788
$481$	4.44945	+	2809.58i	0.000421783	+	0.266332i
$482$	14121.4			1.33446
$483$	−71.0594	+	123.079i	−0.00669424	+	0.0115948i
$484$	28.1828	−	48.8141i	0.00264677	−	0.00458435i
$485$	418.186	+	724.320i	0.0391523	+	0.0678138i
$486$	−6879.65			−0.642113
$487$	4298.59	+	7445.37i	0.399974	+	0.692776i	0.993722	−	0.111875i	$-0.0356857\pi$
$487$	4298.59	+	7445.37i	0.399974	+	0.692776i	−0.593748	+	0.804651i	$0.702352\pi$
$488$	5108.55	+	8848.27i	0.473880	+	0.820784i
$489$	4276.40			0.395471
$490$	2261.56	+	3917.14i	0.208504	+	0.361140i
$491$	4104.02	−	7108.36i	0.377213	−	0.653352i	−0.613443	−	0.789739i	$-0.710216\pi$
$491$	4104.02	−	7108.36i	0.377213	−	0.653352i	0.990656	+	0.136387i	$0.0435491\pi$
$492$	53.6002	−	92.8382i	0.00491155	−	0.00850705i
$493$	−11702.6			−1.06908
$494$	−10165.7	+	5890.63i	−0.925859	+	0.536502i
$495$	577.952			0.0524788
$496$	1880.58	−	3257.25i	0.170243	−	0.294869i
$497$	3707.55	−	6421.67i	0.334621	−	0.579580i
$498$	−5817.67	−	10076.5i	−0.523486	−	0.906704i
$499$	9787.67			0.878069			0.439034	−	0.898470i	$-0.355321\pi$
$499$	9787.67			0.878069			0.439034	+	0.898470i	$0.355321\pi$
$500$	−284.224	−	492.291i	−0.0254218	−	0.0440318i
$501$	−514.604	−	891.320i	−0.0458898	−	0.0794835i
$502$	−1861.39			−0.165494
$503$	−8838.84	−	15309.3i	−0.783508	−	1.35708i	−0.929886	−	0.367847i	$-0.880095\pi$
$503$	−8838.84	−	15309.3i	−0.783508	−	1.35708i	0.146378	−	0.989229i	$-0.453238\pi$
$504$	753.681	−	1305.41i	0.0666104	−	0.115373i
$505$	−4550.15	+	7881.09i	−0.400949	+	0.694463i
$506$	−148.748			−0.0130685
$507$	−4630.24	−	7961.47i	−0.405594	−	0.697399i
$508$	1038.46			0.0906976
$509$	−4805.82	+	8323.92i	−0.418495	+	0.724855i	−0.995788	−	0.0916821i	$-0.970776\pi$
$509$	−4805.82	+	8323.92i	−0.418495	+	0.724855i	0.577293	+	0.816537i	$0.304109\pi$
$510$	−3109.20	+	5385.29i	−0.269956	+	0.467577i
$511$	−1166.11	−	2019.76i	−0.100950	−	0.174851i
$512$	−12428.8			−1.07282
$513$	6972.46	+	12076.7i	0.600082	+	1.03937i
$514$	−1272.84	−	2204.63i	−0.109227	−	0.189187i
$515$	−217.142			−0.0185794
$516$	409.080	+	708.547i	0.0349006	+	0.0604497i
$517$	−872.580	+	1511.35i	−0.0742283	+	0.128567i
$518$	566.104	−	980.521i	0.0480177	−	0.0831692i
$519$	4572.48			0.386723
$520$	−5252.74	+	3043.77i	−0.442976	+	0.256689i
$521$	3095.56			0.260305			0.130152	−	0.991494i	$-0.458453\pi$
$521$	3095.56			0.260305			0.130152	+	0.991494i	$0.458453\pi$
$522$	1561.48	−	2704.56i	0.130928	−	0.226773i
$523$	−4978.83	+	8623.58i	−0.416270	+	0.721000i	−0.995561	−	0.0941206i	$-0.969996\pi$
$523$	−4978.83	+	8623.58i	−0.416270	+	0.721000i	0.579291	+	0.815121i	$0.303329\pi$
$524$	187.440	+	324.656i	0.0156266	+	0.0270661i
$525$	−2709.75			−0.225263
$526$	3387.71	+	5867.69i	0.280820	+	0.486394i
$527$	3036.07	+	5258.63i	0.250955	+	0.434667i
$528$	−2769.37			−0.228260
$529$	6071.36	+	10515.9i	0.499003	+	0.864298i
$530$	−687.340	+	1190.51i	−0.0563324	+	0.0975705i
$531$	3101.51	−	5371.98i	0.253473	−	0.439028i
$532$	−292.740			−0.0238569
$533$	−4.07490	−	2573.07i	−0.000331151	−	0.209103i
$534$	2736.29			0.221743
$535$	−826.646	+	1431.79i	−0.0668019	+	0.115704i
$536$	−12220.6	+	21166.7i	−0.984792	+	1.70571i
$537$	7080.10	+	12263.1i	0.568955	+	0.985460i
$538$	−3189.07			−0.255558
$539$	−1626.05	−	2816.40i	−0.129942	−	0.225067i
$540$	198.242	+	343.366i	0.0157981	+	0.0273632i
$541$	2425.98			0.192793			0.0963965	−	0.995343i	$-0.469268\pi$
$541$	2425.98			0.192793			0.0963965	+	0.995343i	$0.469268\pi$
$542$	6223.98	+	10780.3i	0.493253	+	0.854339i
$543$	7262.33	−	12578.7i	0.573953	−	0.994116i
$544$	1020.66	−	1767.83i	0.0804420	−	0.139330i
$545$	−7835.53			−0.615848
$546$	5.87773	+	3711.45i	0.000460702	+	0.290908i
$547$	−20777.9			−1.62413			−0.812064	−	0.583568i	$-0.801656\pi$
$547$	−20777.9			−1.62413			−0.812064	+	0.583568i	$0.801656\pi$
$548$	−477.232	+	826.591i	−0.0372014	+	0.0644347i
$549$	2072.33	−	3589.38i	0.161102	−	0.279037i
$550$	−1418.07	−	2456.17i	−0.109940	−	0.190421i
$551$	−11022.3			−0.852203
$552$	−239.953	−	415.612i	−0.0185020	−	0.0320464i
$553$	2285.63	+	3958.83i	0.175759	+	0.304424i
$554$	6079.44			0.466229
$555$	700.288	+	1212.93i	0.0535596	+	0.0927679i
$556$	196.391	−	340.158i	0.0149799	−	0.0259459i
$557$	−9890.18	+	17130.3i	−0.752352	+	1.30311i	0.194328	+	0.980937i	$0.437748\pi$
$557$	−9890.18	+	17130.3i	−0.752352	+	1.30311i	−0.946680	+	0.322176i	$0.895586\pi$
$558$	−1620.42			−0.122935
$559$	17022.4	+	9791.97i	1.28796	+	0.740888i
$560$	2303.52			0.173824
$561$	2235.49	−	3871.98i	0.168240	−	0.291400i
$562$	2479.32	−	4294.31i	0.186092	−	0.322322i
$563$	4220.58	+	7310.26i	0.315943	+	0.547230i	0.979638	−	0.200774i	$-0.0643457\pi$
$563$	4220.58	+	7310.26i	0.315943	+	0.547230i	−0.663694	+	0.748004i	$0.731012\pi$
$564$	−309.814			−0.0231304
$565$	−4068.09	−	7046.14i	−0.302913	−	0.524661i
$566$	−9444.45	−	16358.3i	−0.701378	−	1.21482i
$567$	2653.69			0.196551
$568$	12519.7	+	21684.7i	0.924847	+	1.60188i
$569$	−11838.9	+	20505.6i	−0.872254	+	1.51079i	−0.0125946	+	0.999921i	$0.504009\pi$
$569$	−11838.9	+	20505.6i	−0.872254	+	1.51079i	−0.859659	+	0.510868i	$0.829324\pi$
$570$	−2928.45	+	5072.22i	−0.215192	+	0.372723i
$571$	−22123.9			−1.62147			−0.810734	−	0.585415i	$-0.800932\pi$
$571$	−22123.9			−1.62147			−0.810734	+	0.585415i	$0.800932\pi$
$572$	207.812	−	120.419i	0.0151906	−	0.00880242i
$573$	−12171.3			−0.887367
$574$	−518.450	+	897.981i	−0.0376998	+	0.0652980i
$575$	231.381	−	400.764i	0.0167813	−	0.0290661i
$576$	2536.85	+	4393.95i	0.183510	+	0.317849i
$577$	3030.42			0.218645			0.109323	−	0.994006i	$-0.465132\pi$
$577$	3030.42			0.218645			0.109323	+	0.994006i	$0.465132\pi$
$578$	−6159.03	−	10667.7i	−0.443221	−	0.767681i
$579$	9653.78	+	16720.8i	0.692914	+	1.20016i
$580$	−313.387			−0.0224357
$581$	−3479.23	−	6026.21i	−0.248439	−	0.430309i
$582$	−863.310	+	1495.30i	−0.0614869	+	0.106498i
$583$	494.193	−	855.967i	0.0351070	−	0.0608071i
$584$	7875.43			0.558027
$585$	2134.72	+	1227.98i	0.150871	+	0.0867874i
$586$	2320.64			0.163592
$587$	6876.33	−	11910.1i	0.483503	−	0.837452i	−0.516317	−	0.856397i	$-0.672697\pi$
$587$	6876.33	−	11910.1i	0.483503	−	0.837452i	0.999821	+	0.0189452i	$0.00603081\pi$
$588$	288.669	−	499.989i	0.0202458	−	0.0350667i
$589$	2859.58	+	4952.93i	0.200045	+	0.346489i
$590$	10067.5			0.702498
$591$	53.4065	+	92.5028i	0.00371718	+	0.00643834i
$592$	1799.93	+	3117.57i	0.124961	+	0.216438i
$593$	25257.1			1.74905			0.874524	−	0.484983i	$-0.161174\pi$
$593$	25257.1			1.74905			0.874524	+	0.484983i	$0.161174\pi$
$594$	2305.30	+	3992.89i	0.159238	+	0.275809i
$595$	−1859.44	+	3220.65i	−0.128117	+	0.221906i
$596$	735.979	−	1274.75i	0.0505820	−	0.0876106i
$597$	11306.3			0.775099
$598$	−549.414	−	316.045i	−0.0375706	−	0.0216121i
$599$	13380.9			0.912735			0.456367	−	0.889791i	$-0.349150\pi$
$599$	13380.9			0.912735			0.456367	+	0.889791i	$0.349150\pi$
$600$	4575.14	−	7924.38i	0.311299	−	0.539186i
$601$	6749.47	−	11690.4i	0.458098	−	0.793449i	−0.540763	−	0.841175i	$-0.681864\pi$
$601$	6749.47	−	11690.4i	0.458098	−	0.793449i	0.998860	+	0.0477267i	$0.0151976\pi$
$602$	−3956.84	−	6853.45i	−0.267888	−	0.463996i
$603$	9914.77			0.669586
$604$	580.666	+	1005.74i	0.0391175	+	0.0677535i
$605$	−337.214	−	584.072i	−0.0226607	−	0.0392494i
$606$	−18786.8			−1.25934
$607$	13342.5	+	23109.9i	0.892182	+	1.54530i	0.837254	+	0.546814i	$0.184160\pi$
$607$	13342.5	+	23109.9i	0.892182	+	1.54530i	0.0549282	+	0.998490i	$0.482507\pi$
$608$	961.326	−	1665.06i	0.0641232	−	0.111065i
$609$	−1740.94	+	3015.39i	−0.115839	+	0.200640i
$610$	6726.80			0.446492
$611$	−6434.14	+	3728.35i	−0.426019	+	0.246862i
$612$	−425.753			−0.0281210
$613$	5967.85	−	10336.6i	0.393212	−	0.681064i	−0.599659	−	0.800256i	$-0.704697\pi$
$613$	5967.85	−	10336.6i	0.393212	−	0.681064i	0.992871	+	0.119192i	$0.0380304\pi$
$614$	−4744.53	+	8217.77i	−0.311846	+	0.540134i
$615$	−641.338	−	1110.83i	−0.0420508	−	0.0728342i
$616$	−1758.99			−0.115051
$617$	−5500.49	−	9527.14i	−0.358900	−	0.621634i	0.628877	−	0.777505i	$-0.283515\pi$
$617$	−5500.49	−	9527.14i	−0.358900	−	0.621634i	−0.987777	+	0.155871i	$0.950182\pi$
$618$	−224.135	−	388.213i	−0.0145891	−	0.0252690i
$619$	−16473.1			−1.06964			−0.534821	−	0.844965i	$-0.679621\pi$
$619$	−16473.1			−1.06964			−0.534821	+	0.844965i	$0.679621\pi$
$620$	81.3040	+	140.823i	0.00526653	+	0.00912189i
$621$	−376.146	+	651.504i	−0.0243063	+	0.0420998i
$622$	2410.74	−	4175.53i	0.155405	−	0.269170i
$623$	1636.43			0.105236
$624$	−10228.9	−	5884.10i	−0.656226	−	0.377488i
$625$	4940.00			0.316160
$626$	6609.26	−	11447.6i	0.421980	−	0.730890i
$627$	2105.53	−	3646.89i	0.134110	−	0.232285i
$628$	41.2109	+	71.3793i	0.00261862	+	0.00453558i
$629$	−5811.75			−0.368409
$630$	−496.214	−	859.467i	−0.0313804	−	0.0543524i
$631$	−9310.52	−	16126.3i	−0.587394	−	1.01740i	−0.994572	−	0.104048i	$-0.966820\pi$
$631$	−9310.52	−	16126.3i	−0.587394	−	1.01740i	0.407178	−	0.913349i	$-0.366513\pi$
$632$	−15436.2			−0.971552
$633$	−7088.37	−	12277.4i	−0.445083	−	0.770906i
$634$	1754.30	−	3038.54i	0.109893	−	0.190340i
$635$	6212.73	−	10760.8i	0.388259	−	0.672485i
$636$	175.466			0.0109397
$637$	−21.9458	−	13857.5i	−0.00136503	−	0.861938i
$638$	−3644.27			−0.226141
$639$	5078.71	−	8796.59i	0.314414	−	0.544581i
$640$	−3647.92	+	6318.38i	−0.225307	+	0.390244i
$641$	8819.43	+	15275.7i	0.543442	+	0.941269i	0.998703	+	0.0509114i	$0.0162126\pi$
$641$	8819.43	+	15275.7i	0.543442	+	0.941269i	−0.455261	+	0.890358i	$0.650454\pi$
$642$	−3413.08			−0.209819
$643$	1558.43	+	2699.27i	0.0955805	+	0.165550i	0.909851	−	0.414936i	$-0.136196\pi$
$643$	1558.43	+	2699.27i	0.0955805	+	0.165550i	−0.814270	+	0.580486i	$0.802863\pi$
$644$	−7.89626	−	13.6767i	−0.000483162	−	0.000836861i
$645$	9789.46			0.597612
$646$	−12151.7	−	21047.4i	−0.740097	−	1.28189i
$647$	2305.89	−	3993.91i	0.140114	−	0.242685i	−0.787425	−	0.616410i	$-0.788586\pi$
$647$	2305.89	−	3993.91i	0.140114	−	0.242685i	0.927539	+	0.373725i	$0.121920\pi$
$648$	−4480.49	+	7760.44i	−0.271621	+	0.470461i
$649$	−7238.49			−0.437805
$650$	−19.1388	−	12085.1i	−0.00115490	−	0.729256i
$651$	1806.65			0.108768
$652$	−237.601	+	411.537i	−0.0142717	+	0.0247194i
$653$	11594.6	−	20082.4i	0.694841	−	1.20350i	−0.275394	−	0.961332i	$-0.588808\pi$
$653$	11594.6	−	20082.4i	0.694841	−	1.20350i	0.970234	−	0.242168i	$-0.0778585\pi$
$654$	−8087.89	−	14008.6i	−0.483580	−	0.837585i
$655$	4485.53			0.267579
$656$	−1648.41	−	2855.13i	−0.0981093	−	0.169930i
$657$	−1597.37	−	2766.72i	−0.0948544	−	0.164293i
$658$	2996.69			0.177543
$659$	−10316.3	−	17868.4i	−0.609812	−	1.05623i	−0.991271	−	0.131840i	$-0.957911\pi$
$659$	−10316.3	−	17868.4i	−0.609812	−	1.05623i	0.381459	−	0.924386i	$-0.375422\pi$
$660$	59.8649	−	103.689i	0.00353066	−	0.00611529i
$661$	7557.00	−	13089.1i	0.444679	−	0.770207i	−0.553350	−	0.832949i	$-0.686651\pi$
$661$	7557.00	−	13089.1i	0.444679	−	0.770207i	0.998030	+	0.0627413i	$0.0199843\pi$
$662$	−16307.0			−0.957386
$663$	16483.8	−	9551.77i	0.965578	−	0.559518i
$664$	23497.3			1.37330
$665$	−1751.35	+	3033.42i	−0.102127	+	0.176889i
$666$	775.466	−	1343.15i	0.0451181	−	0.0781469i
$667$	−297.311	−	514.957i	−0.0172592	−	0.0298939i
$668$	114.368			0.00662427
$669$	8343.40	+	14451.2i	0.482174	+	0.835150i
$670$	8045.86	+	13935.8i	0.463938	+	0.803565i
$671$	−4836.52			−0.278259
$672$	−303.678	−	525.985i	−0.0174325	−	0.0301939i
$673$	−8576.79	+	14855.4i	−0.491249	+	0.850869i	−0.999949	−	0.0100750i	$-0.996793\pi$
$673$	−8576.79	+	14855.4i	−0.491249	+	0.850869i	0.508700	+	0.860944i	$0.330126\pi$
$674$	6322.46	−	10950.8i	0.361323	−	0.625830i
$675$	−14343.8			−0.817916
$676$	1023.43	−	3.24156i	0.0582287	−	0.000184431i
$677$	9987.36			0.566980			0.283490	−	0.958975i	$-0.408508\pi$
$677$	9987.36			0.566980			0.283490	+	0.958975i	$0.408508\pi$
$678$	8398.23	−	14546.2i	0.475711	−	0.823955i
$679$	−516.299	+	894.257i	−0.0291808	+	0.0505426i
$680$	−6278.97	−	10875.5i	−0.354099	−	0.613317i
$681$	−5482.06			−0.308477
$682$	945.458	+	1637.58i	0.0530843	+	0.0919446i
$683$	7795.01	+	13501.4i	0.436702	+	0.756391i	0.997433	−	0.0716076i	$-0.0228129\pi$
$683$	7795.01	+	13501.4i	0.436702	+	0.756391i	−0.560730	+	0.827998i	$0.689480\pi$
$684$	−401.003			−0.0224163
$685$	5710.20	+	9890.35i	0.318504	+	0.551665i
$686$	−6031.56	+	10447.0i	−0.335694	+	0.581439i
$687$	−6716.02	+	11632.5i	−0.372972	+	0.646007i
$688$	25161.6			1.39430
$689$	3644.03	−	2111.58i	0.201490	−	0.116756i
$690$	−315.964			−0.0174327
$691$	7259.37	−	12573.6i	0.399652	−	0.692218i	−0.594031	−	0.804442i	$-0.702464\pi$
$691$	7259.37	−	12573.6i	0.399652	−	0.692218i	0.993683	+	0.112225i	$0.0357976\pi$
$692$	−254.051	+	440.030i	−0.0139560	+	0.0241726i
$693$	356.774	+	617.951i	0.0195566	+	0.0338730i
$694$	−28704.6			−1.57005
$695$	−2349.86	−	4070.07i	−0.128252	−	0.222139i
$696$	−5878.79	−	10182.4i	−0.320165	−	0.554542i
$697$	5322.52			0.289246
$698$	8053.16	+	13948.5i	0.436700	+	0.756387i
$699$	646.772	−	1120.24i	0.0349974	−	0.0606172i
$700$	150.556	−	260.771i	0.00812928	−	0.0140803i
$701$	−17959.6			−0.967650			−0.483825	−	0.875165i	$-0.660753\pi$
$701$	−17959.6			−0.967650			−0.483825	+	0.875165i	$0.660753\pi$
$702$	31.1132	+	19646.2i	0.00167278	+	1.05627i
$703$	−5473.89			−0.293672
$704$	2960.32	−	5127.43i	0.158482	−	0.274499i
$705$	−1853.50	+	3210.36i	−0.0990168	+	0.171502i
$706$	−6691.94	−	11590.8i	−0.356734	−	0.617882i
$707$	−11235.4			−0.597666
$708$	−642.517	−	1112.87i	−0.0341063	−	0.0590738i
$709$	−33.7892	−	58.5246i	−0.00178982	−	0.00310005i	0.865129	−	0.501549i	$-0.167236\pi$
$709$	−33.7892	−	58.5246i	−0.00178982	−	0.00310005i	−0.866919	+	0.498449i	$0.833903\pi$
$710$	16485.5			0.871396
$711$	3130.92	+	5422.92i	0.165146	+	0.286041i
$712$	−2762.95	+	4785.56i	−0.145430	+	0.251891i
$713$	−154.267	+	267.198i	−0.00810285	+	0.0140345i
$714$	−7677.32			−0.402404
$715$	−4.55117	−	2873.81i	−0.000238048	−	0.150314i
$716$	−1573.51			−0.0821296
$717$	6907.33	−	11963.9i	0.359776	−	0.623150i
$718$	−7135.57	+	12359.2i	−0.370887	+	0.642396i
$719$	−3462.30	−	5996.88i	−0.179586	−	0.311051i	0.762153	−	0.647397i	$-0.224142\pi$
$719$	−3462.30	−	5996.88i	−0.179586	−	0.311051i	−0.941739	+	0.336346i	$0.890809\pi$
$720$	3155.42			0.163327
$721$	−134.043	−	232.170i	−0.00692376	−	0.0119923i
$722$	−2031.86	−	3519.28i	−0.104734	−	0.181404i
$723$	−21567.0			−1.10938
$724$	807.004	+	1397.77i	0.0414255	+	0.0717511i
$725$	5668.76	−	9818.59i	0.290390	−	0.502970i
$726$	696.150	−	1205.77i	0.0355875	−	0.0616394i
$727$	−31335.3			−1.59857			−0.799287	−	0.600950i	$-0.794789\pi$
$727$	−31335.3			−1.59857			−0.799287	+	0.600950i	$0.794789\pi$
$728$	−6496.98	−	3737.33i	−0.330761	−	0.190267i
$729$	20918.9			1.06279
$730$	2592.54	−	4490.41i	0.131444	−	0.227668i
$731$	−20310.9	+	35179.5i	−1.02767	+	1.77997i
$732$	−429.309	−	743.585i	−0.0216772	−	0.0375460i
$733$	165.612			0.00834517			0.00417258	−	0.999991i	$-0.498672\pi$
$733$	165.612			0.00834517			0.00417258	+	0.999991i	$0.498672\pi$
$734$	8446.77	+	14630.2i	0.424763	+	0.735711i
$735$	−3453.99	−	5982.48i	−0.173336	−	0.300228i
$736$	103.722			0.00519462
$737$	−5784.91	−	10019.8i	−0.289132	−	0.500791i
$738$	−710.187	+	1230.08i	−0.0354233	+	0.0613549i
$739$	−10551.8	+	18276.3i	−0.525242	+	0.909747i	0.474325	+	0.880350i	$0.342692\pi$
$739$	−10551.8	+	18276.3i	−0.525242	+	0.909747i	−0.999568	+	0.0293970i	$0.990641\pi$
$740$	−155.635			−0.00773141
$741$	15525.6	−	8996.50i	0.769697	−	0.446012i
$742$	−1697.20			−0.0839707
$743$	9534.87	−	16514.9i	0.470795	−	0.815440i	−0.528647	−	0.848842i	$-0.677301\pi$
$743$	9534.87	−	16514.9i	0.470795	−	0.815440i	0.999442	+	0.0334012i	$0.0106339\pi$
$744$	−3050.35	+	5283.35i	−0.150311	+	0.260346i
$745$	−8806.16	−	15252.7i	−0.433064	−	0.750089i
$746$	30061.5			1.47537
$747$	−4765.95	−	8254.87i	−0.233437	−	0.404324i
$748$	248.412	+	430.262i	0.0121428	+	0.0210320i
$749$	−2041.18			−0.0995769
$750$	−7020.67	−	12160.2i	−0.341812	−	0.592035i
$751$	−4483.21	+	7765.15i	−0.217836	+	0.377303i	−0.954146	−	0.299341i	$-0.903233\pi$
$751$	−4483.21	+	7765.15i	−0.217836	+	0.377303i	0.736310	+	0.676644i	$0.236566\pi$
$752$	−4764.00	+	8251.48i	−0.231017	+	0.400134i
$753$	2842.83			0.137581
$754$	−13460.5	−	7743.01i	−0.650135	−	0.373984i
$755$	13895.6			0.669818
$756$	−244.753	+	423.925i	−0.0117746	+	0.0203942i
$757$	−19184.2	+	33228.0i	−0.921085	+	1.59537i	−0.123346	+	0.992364i	$0.539362\pi$
$757$	−19184.2	+	33228.0i	−0.921085	+	1.59537i	−0.797739	+	0.603002i	$0.793971\pi$
$758$	−2936.22	−	5085.69i	−0.140697	−	0.243695i
$759$	227.176			0.0108642
$760$	−5913.95	−	10243.3i	−0.282265	−	0.488897i
$761$	10479.8	+	18151.6i	0.499203	+	0.864645i	1.00000		0.000919857i	$-0.000292800\pi$
$761$	10479.8	+	18151.6i	0.499203	+	0.864645i	−0.500796	+	0.865565i	$0.666959\pi$
$762$	25651.3			1.21949
$763$	−4836.93	−	8377.81i	−0.229500	−	0.397506i
$764$	676.247	−	1171.29i	0.0320232	−	0.0554659i
$765$	−2547.12	+	4411.74i	−0.120381	+	0.208506i
$766$	−7398.78			−0.348993
$767$	−26736.1	−	15379.7i	−1.25865	−	0.724025i
$768$	2989.14			0.140445
$769$	−12198.4	+	21128.2i	−0.572021	+	0.990770i	0.424337	+	0.905504i	$0.360507\pi$
$769$	−12198.4	+	21128.2i	−0.572021	+	0.990770i	−0.996358	+	0.0852653i	$0.972826\pi$
$770$	−579.046	+	1002.94i	−0.0271005	+	0.0469394i
$771$	1943.96	+	3367.04i	0.0908041	+	0.157277i
$772$	−2145.49			−0.100023
$773$	5650.74	+	9787.36i	0.262927	+	0.455403i	0.967019	−	0.254706i	$-0.0819787\pi$
$773$	5650.74	+	9787.36i	0.262927	+	0.455403i	−0.704091	+	0.710110i	$0.748645\pi$
$774$	−5420.19	−	9388.05i	−0.251712	−	0.435977i
$775$	−5882.74			−0.272664
$776$	−1743.44	−	3019.72i	−0.0806518	−	0.139693i
$777$	−864.586	+	1497.51i	−0.0399187	+	0.0691413i
$778$	13069.4	−	22636.8i	0.602261	−	1.04315i
$779$	5013.10			0.230569
$780$	441.426	−	255.790i	0.0202636	−	0.0117420i
$781$	−11853.0			−0.543064
$782$	655.553	−	1135.45i	0.0299777	−	0.0519228i
$783$	−9215.47	+	15961.7i	−0.420605	+	0.728510i
$784$	−8877.68	−	15376.6i	−0.404413	−	0.700465i
$785$	986.195			0.0448392
$786$	4629.99	+	8019.38i	0.210110	+	0.363921i
$787$	10271.1	+	17790.0i	0.465215	+	0.805776i	0.999211	−	0.0397106i	$-0.0126436\pi$
$787$	10271.1	+	17790.0i	0.465215	+	0.805776i	−0.533996	+	0.845487i	$0.679310\pi$
$788$	−11.8693			−0.000536580
$789$	−5173.90	−	8961.46i	−0.233455	−	0.404356i
$790$	−5081.51	+	8801.43i	−0.228850	+	0.396381i
$791$	5022.53	−	8699.28i	0.225766	−	0.391037i
$792$	−2409.51			−0.108104
$793$	−17864.2	−	10276.2i	−0.799968	−	0.460174i
$794$	−11838.8			−0.529148
$795$	1049.75	−	1818.21i	0.0468310	−	0.0811136i
$796$	−628.186	+	1088.05i	−0.0279717	+	0.0484484i
$797$	12022.2	+	20823.0i	0.534313	+	0.925457i	0.999196	+	0.0400851i	$0.0127629\pi$
$797$	12022.2	+	20823.0i	0.534313	+	0.925457i	−0.464883	+	0.885372i	$0.653904\pi$
$798$	−7231.01			−0.320771
$799$	−7691.18	−	13321.5i	−0.340543	−	0.589839i
$800$	988.823	+	1712.69i	0.0437002	+	0.0756910i
$801$	2241.63			0.0988815
$802$	19944.0	+	34544.0i	0.878113	+	1.52094i
$803$	−1864.02	+	3228.57i	−0.0819174	+	0.141885i
$804$	1026.98	−	1778.79i	0.0450484	−	0.0780261i
$805$	−188.961			−0.00827330
$806$	12.7603	+	8057.38i	0.000557644	+	0.352121i
$807$	4870.52			0.212454
$808$	18969.8	−	32856.6i	0.825934	−	1.43056i
$809$	−10076.7	+	17453.3i	−0.437919	+	0.758499i	−0.997529	−	0.0702578i	$-0.977618\pi$
$809$	−10076.7	+	17453.3i	−0.437919	+	0.758499i	0.559609	+	0.828756i	$0.310951\pi$
$810$	2949.89	+	5109.37i	0.127961	+	0.221636i
$811$	22525.4			0.975305			0.487653	−	0.873038i	$-0.337853\pi$
$811$	22525.4			0.975305			0.487653	+	0.873038i	$0.337853\pi$
$812$	−193.456	−	335.076i	−0.00836081	−	0.0144813i
$813$	−9505.62	−	16464.2i	−0.410057	−	0.710240i
$814$	−1809.83			−0.0779292
$815$	2842.95	+	4924.13i	0.122189	+	0.211638i
$816$	12205.0	−	21139.7i	0.523605	−	0.906910i
$817$	−19130.1	+	33134.4i	−0.819191	+	1.41888i
$818$	28947.8			1.23733
$819$	4.81516	+	3040.50i	0.000205440	+	0.129724i
$820$	142.533			0.00607010
$821$	−12021.5	+	20821.9i	−0.511029	+	0.885128i	0.488890	+	0.872346i	$0.337402\pi$
$821$	−12021.5	+	20821.9i	−0.511029	+	0.885128i	−0.999918	+	0.0127821i	$0.995931\pi$
$822$	−11788.2	+	20417.8i	−0.500196	+	0.866365i
$823$	−10855.0	−	18801.4i	−0.459758	−	0.796324i	0.539190	−	0.842184i	$-0.318730\pi$
$823$	−10855.0	−	18801.4i	−0.459758	−	0.796324i	−0.998948	+	0.0458603i	$0.985397\pi$
$824$	905.274			0.0382727
$825$	2165.76	+	3751.20i	0.0913964	+	0.158303i
$826$	6214.77	+	10764.3i	0.261791	+	0.453436i
$827$	−4842.01			−0.203595			−0.101797	−	0.994805i	$-0.532459\pi$
$827$	−4842.01			−0.203595			−0.101797	+	0.994805i	$0.532459\pi$
$828$	−10.8165	−	18.7348i	−0.000453986	−	0.000786327i
$829$	18386.3	−	31846.0i	0.770304	−	1.33421i	−0.167093	−	0.985941i	$-0.553438\pi$
$829$	18386.3	−	31846.0i	0.770304	−	1.33421i	0.937396	−	0.348264i	$-0.113229\pi$
$830$	7735.17	−	13397.7i	0.323484	−	0.560290i
$831$	−9284.86			−0.387591
$832$	21828.5	−	12648.8i	0.909576	−	0.527066i
$833$	28664.9			1.19229
$834$	4851.08	−	8402.32i	0.201414	−	0.348859i
$835$	684.217	−	1185.10i	0.0283573	−	0.0491162i
$836$	233.971	+	405.250i	0.00967949	+	0.0167654i
$837$	9563.32			0.394930
$838$	17105.5	+	29627.6i	0.705130	+	1.22132i
$839$	1630.97	+	2824.93i	0.0671126	+	0.116242i	0.897629	−	0.440751i	$-0.145288\pi$
$839$	1630.97	+	2824.93i	0.0671126	+	0.116242i	−0.830517	+	0.556994i	$0.811955\pi$
$840$	−3736.37			−0.153473
$841$	4910.48	+	8505.19i	0.201340	+	0.348731i
$842$	8184.04	−	14175.2i	0.334965	−	0.580177i
$843$	−3786.56	+	6558.52i	−0.154705	+	0.267957i
$844$	1575.35			0.0642484
$845$	6089.19	−	10624.4i	0.247899	−	0.432531i
$846$	4104.96			0.166822
$847$	416.330	−	721.104i	0.0168893	−	0.0292532i
$848$	2698.13	−	4673.30i	0.109262	−	0.189247i
$849$	14424.1	+	24983.3i	0.583079	+	1.00992i
$850$	24998.6			1.00876
$851$	−147.651	−	255.739i	−0.00594760	−	0.0103016i
$852$	−1052.12	−	1822.32i	−0.0423063	−	0.0732766i
$853$	7398.89			0.296991			0.148495	−	0.988913i	$-0.452557\pi$
$853$	7398.89			0.296991			0.148495	+	0.988913i	$0.452557\pi$
$854$	4152.51	+	7192.35i	0.166389	+	0.288193i
$855$	−2399.05	+	4155.27i	−0.0959598	+	0.166207i
$856$	3446.33	−	5969.21i	0.137609	−	0.238345i
$857$	21584.3			0.860332			0.430166	−	0.902750i	$-0.358455\pi$
$857$	21584.3			0.860332			0.430166	+	0.902750i	$0.358455\pi$
$858$	5133.20	−	2974.50i	0.204248	−	0.118354i
$859$	−11879.3			−0.471848			−0.235924	−	0.971771i	$-0.575812\pi$
$859$	−11879.3			−0.471848			−0.235924	+	0.971771i	$0.575812\pi$
$860$	−543.912	+	942.083i	−0.0215666	+	0.0373544i
$861$	791.806	−	1371.45i	0.0313411	−	0.0542844i
$862$	177.987	+	308.283i	0.00703279	+	0.0121811i
$863$	6366.72			0.251131			0.125565	−	0.992085i	$-0.459926\pi$
$863$	6366.72			0.251131			0.125565	+	0.992085i	$0.459926\pi$
$864$	−1607.49	−	2784.25i	−0.0632961	−	0.109632i
$865$	3039.78	+	5265.05i	0.119486	+	0.206956i
$866$	−19189.3			−0.752979
$867$	9406.42	+	16292.4i	0.368464	+	0.638199i
$868$	−100.379	+	173.862i	−0.00392522	+	0.00679868i
$869$	3653.57	−	6328.16i	0.142622	−	0.247029i
$870$	−7741.03			−0.301661
$871$	−78.0754	−	49300.2i	−0.00303730	−	1.91788i
$872$	32666.7			1.26862
$873$	−707.242	+	1224.98i	−0.0274187	+	0.0474905i
$874$	617.444	−	1069.44i	0.0238963	−	0.0413896i
$875$	−4198.69	−	7272.34i	−0.162219	−	0.280971i
$876$	−661.830			−0.0255264
$877$	−8668.58	−	15014.4i	−0.333771	−	0.578108i	0.649477	−	0.760381i	$-0.274988\pi$
$877$	−8668.58	−	15014.4i	−0.333771	−	0.578108i	−0.983248	+	0.182273i	$0.941654\pi$
$878$	5589.99	+	9682.14i	0.214867	+	0.372160i
$879$	−3544.21			−0.135999
$880$	−1841.08	−	3188.84i	−0.0705258	−	0.122154i
$881$	−18583.2	+	32187.0i	−0.710651	+	1.23088i	0.253962	+	0.967214i	$0.418266\pi$
$881$	−18583.2	+	32187.0i	−0.710651	+	1.23088i	−0.964613	+	0.263670i	$0.915067\pi$
$882$	−3824.78	+	6624.72i	−0.146017	+	0.252909i
$883$	−30523.4			−1.16330			−0.581651	−	0.813438i	$-0.697593\pi$
$883$	−30523.4			−1.16330			−0.581651	+	0.813438i	$0.697593\pi$
$884$	3.35266	+	2117.02i	0.000127559	+	0.0805463i
$885$	−15375.7			−0.584010
$886$	−12353.1	+	21396.3i	−0.468411	+	0.811311i
$887$	−20615.5	+	35707.2i	−0.780386	+	1.35167i	0.151332	+	0.988483i	$0.451644\pi$
$887$	−20615.5	+	35707.2i	−0.780386	+	1.35167i	−0.931717	+	0.363184i	$0.881689\pi$
$888$	−2919.53	−	5056.78i	−0.110330	−	0.191097i
$889$	15340.7			0.578751
$890$	1819.09	+	3150.75i	0.0685123	+	0.118667i
$891$	−2120.95	−	3673.60i	−0.0797470	−	0.138126i
$892$	−1854.27			−0.0696027
$893$	−7244.06	−	12547.1i	−0.271459	−	0.470182i
$894$	18179.6	−	31487.9i	0.680107	−	1.17798i
$895$	−9413.70	+	16305.0i	−0.351581	+	0.608957i
$896$	−9007.55			−0.335850
$897$	839.096	+	482.682i	0.0312337	+	0.0179669i
$898$	40924.6			1.52079
$899$	−3779.49	+	6546.26i	−0.140215	+	0.242859i
$900$	206.236	−	357.212i	0.00763839	−	0.0132301i
$901$	4355.96	+	7544.75i	0.161063	+	0.278970i
$902$	1657.48			0.0611839
$903$	6043.11	+	10467.0i	0.222704	+	0.385735i
$904$	16960.1	+	29375.7i	0.623986	+	1.08078i
$905$	19312.0			0.709339
$906$	14343.1	+	24843.0i	0.525959	+	0.910988i
$907$	8314.40	−	14401.0i	0.304383	−	0.527206i	−0.672741	−	0.739878i	$-0.734883\pi$
$907$	8314.40	−	14401.0i	0.304383	−	0.527206i	0.977124	+	0.212672i	$0.0682165\pi$
$908$	304.589	−	527.563i	0.0111323	−	0.0192817i
$909$	−15390.5			−0.561575
$910$	−4269.71	+	2474.14i	−0.155538	+	0.0901285i
$911$	46330.1			1.68495			0.842473	−	0.538739i	$-0.181099\pi$
$911$	46330.1			1.68495			0.842473	+	0.538739i	$0.181099\pi$
$912$	11495.5	−	19910.8i	0.417384	−	0.722931i
$913$	−5561.53	+	9632.85i	−0.201599	+	0.349179i
$914$	−16961.1	−	29377.5i	−0.613811	−	1.06315i
$915$	−10273.6			−0.371184
$916$	−746.297	−	1292.62i	−0.0269196	−	0.0466261i
$917$	2768.95	+	4795.96i	0.0997151	+	0.172712i
$918$	−40639.1			−1.46110
$919$	9244.04	+	16011.1i	0.331809	+	0.574710i	0.982867	−	0.184318i	$-0.0590076\pi$
$919$	9244.04	+	16011.1i	0.331809	+	0.574710i	−0.651057	+	0.759028i	$0.725674\pi$
$920$	319.042	−	552.597i	0.0114332	−	0.0198028i
$921$	7246.12	−	12550.6i	0.259248	−	0.449031i
$922$	−2106.73			−0.0752509
$923$	−43780.1	−	25184.1i	−1.56126	−	0.898099i
$924$	147.820			0.00526291
$925$	2815.23	−	4876.12i	0.100069	−	0.173325i
$926$	3189.04	−	5523.59i	0.113173	−	0.196022i
$927$	−183.616	−	318.033i	−0.00650566	−	0.0112681i
$928$	2541.16			0.0898896
$929$	8600.46	+	14896.4i	0.303737	+	0.526088i	0.976979	−	0.213334i	$-0.0684322\pi$
$929$	8600.46	+	14896.4i	0.303737	+	0.526088i	−0.673242	+	0.739422i	$0.735099\pi$
$930$	2008.31	+	3478.49i	0.0708118	+	0.122650i
$931$	26998.6			0.950421
$932$	71.8705	+	124.483i	0.00252596	+	0.00437510i
$933$	−3681.83	+	6377.11i	−0.129194	+	0.223770i
$934$	−7706.55	+	13348.1i	−0.269985	+	0.467628i
$935$	5944.61			0.207925
$936$	−8899.75	−	5119.50i	−0.310788	−	0.178778i
$937$	−34989.5			−1.21991			−0.609955	−	0.792436i	$-0.708813\pi$
$937$	−34989.5			−1.21991			−0.609955	+	0.792436i	$0.708813\pi$
$938$	−9933.54	+	17205.4i	−0.345780	+	0.598908i
$939$	−10094.0	+	17483.4i	−0.350806	+	0.607613i
$940$	−205.965	−	356.741i	−0.00714662	−	0.0123783i
$941$	−31179.6			−1.08015			−0.540077	−	0.841616i	$-0.681605\pi$
$941$	−31179.6			−1.08015			−0.540077	+	0.841616i	$0.681605\pi$
$942$	1017.96	+	1763.15i	0.0352090	+	0.0609837i
$943$	135.222	+	234.211i	0.00466960	+	0.00808798i
$944$	−39519.7			−1.36256
$945$	2928.53	+	5072.36i	0.100810	+	0.174607i
$946$	−6324.98	+	10955.2i	−0.217381	+	0.376516i
$947$	16636.8	−	28815.7i	0.570879	−	0.988791i	−0.425597	−	0.904913i	$-0.639936\pi$
$947$	16636.8	−	28815.7i	0.570879	−	0.988791i	0.996476	−	0.0838786i	$-0.0267308\pi$
$948$	1297.22			0.0444428
$949$	−13744.7	+	7964.55i	−0.470149	+	0.272434i
$950$	23545.3			0.804118
$951$	−2679.27	+	4640.63i	−0.0913578	+	0.158236i
$952$	7752.11	−	13427.0i	0.263915	−	0.457114i
$953$	−8421.28	−	14586.1i	−0.286246	−	0.495792i	0.686665	−	0.726974i	$-0.259074\pi$
$953$	−8421.28	−	14586.1i	−0.286246	−	0.495792i	−0.972910	+	0.231182i	$0.925741\pi$
$954$	−2324.88			−0.0789000
$955$	−8091.45	−	14014.8i	−0.274171	−	0.474878i
$956$	767.556	+	1329.45i	0.0259671	+	0.0449763i
$957$	5565.74			0.187999
$958$	15195.4	+	26319.2i	0.512465	+	0.887616i
$959$	−7049.90	+	12210.8i	−0.237386	+	0.411164i
$960$	6288.20	−	10891.5i	0.211407	−	0.366168i
$961$	−25868.9			−0.868345
$962$	−6684.77	−	3845.35i	−0.224039	−	0.128876i
$963$	−2796.07			−0.0935638
$964$	1198.28	−	2075.48i	0.0400353	−	0.0693432i
$965$	−12835.7	+	22232.0i	−0.428181	+	0.741631i
$966$	−195.047	−	337.831i	−0.00649641	−	0.0112521i
$967$	−44144.9			−1.46805			−0.734025	−	0.679122i	$-0.762361\pi$
$967$	−44144.9			−1.46805			−0.734025	+	0.679122i	$0.762361\pi$
$968$	1405.86	+	2435.02i	0.0466799	+	0.0808519i
$969$	18558.8	+	32144.8i	0.615268	+	1.06567i
$970$	−2295.71			−0.0759906
$971$	−9096.88	−	15756.3i	−0.300652	−	0.520744i	0.675632	−	0.737239i	$-0.263871\pi$
$971$	−9096.88	−	15756.3i	−0.300652	−	0.520744i	−0.976284	+	0.216495i	$0.930538\pi$
$972$	−583.778	+	1011.13i	−0.0192641	+	0.0333664i
$973$	2901.17	−	5024.97i	0.0955881	−	0.165564i
$974$	−23597.9			−0.776309
$975$	29.2299	+	18457.0i	0.000960109	+	0.606254i
$976$	−26405.8			−0.866014
$977$	−8792.43	+	15228.9i	−0.287917	+	0.498686i	−0.973312	−	0.229485i	$-0.926296\pi$
$977$	−8792.43	+	15228.9i	−0.287917	+	0.498686i	0.685396	+	0.728171i	$0.259629\pi$
$978$	−5869.03	+	10165.5i	−0.191892	+	0.332367i
$979$	−1307.91	−	2265.37i	−0.0426976	−	0.0739545i
$980$	767.628			0.0250214
$981$	−6625.77	−	11476.2i	−0.215642	−	0.373502i
$982$	11264.9	+	19511.3i	0.366066	+	0.634045i
$983$	16945.0			0.549808			0.274904	−	0.961472i	$-0.411354\pi$
$983$	16945.0			0.549808			0.274904	+	0.961472i	$0.411354\pi$
$984$	2673.77	+	4631.10i	0.0866226	+	0.150035i
$985$	−71.0093	+	122.992i	−0.00229700	+	0.00397852i
$986$	16060.9	−	27818.2i	0.518744	−	0.898491i
$987$	−4576.72			−0.147597
$988$	3.15776	+	1993.95i	0.000101682	+	0.0642064i
$989$	−2064.04			−0.0663627
$990$	−793.194	+	1373.85i	−0.0254640	+	0.0441049i
$991$	−54.9338	+	95.1482i	−0.00176088	+	0.00304993i	−0.866905	−	0.498474i	$-0.833894\pi$
$991$	−54.9338	+	95.1482i	−0.00176088	+	0.00304993i	0.865144	+	0.501524i	$0.167227\pi$
$992$	−659.269	−	1141.89i	−0.0211006	−	0.0365474i
$993$	24905.0			0.795907
$994$	10176.7	+	17626.5i	0.324732	+	0.562453i
$995$	7516.39	+	13018.8i	0.239483	+	0.414797i
$996$	−1974.65			−0.0628205
$997$	−24158.9	−	41844.4i	−0.767421	−	1.32921i	−0.938957	−	0.344035i	$-0.888206\pi$
$997$	−24158.9	−	41844.4i	−0.767421	−	1.32921i	0.171536	−	0.985178i	$-0.445127\pi$
$998$	−13432.8	+	23266.3i	−0.426060	+	0.737958i
$999$	−4576.60	+	7926.91i	−0.144942	+	0.251047i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.4.e.a.100.6	✓	34
13.3	even	3	inner	143.4.e.a.133.6	yes	34
13.4	even	6		1859.4.a.f.1.6		17
13.9	even	3		1859.4.a.i.1.12		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.a.100.6	✓	34	1.1	even	1	trivial
143.4.e.a.133.6	yes	34	13.3	even	3	inner
1859.4.a.f.1.6		17	13.4	even	6
1859.4.a.i.1.12		17	13.9	even	3

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+(-1.37242 + 2.37710i) q^{2} +(2.09604 - 3.63045i) q^{3} +(0.232916 + 0.403423i) q^{4} +5.57379 q^{5} +(5.75330 + 9.96502i) q^{6} +(3.44074 + 5.95954i) q^{7} -23.2374 q^{8} +(4.71323 + 8.16355i) q^{9} +(-7.64959 + 13.2495i) q^{10} +(5.50000 - 9.52628i) q^{11} +1.95281 q^{12} +(40.5553 - 23.5003i) q^{13} -18.8886 q^{14} +(11.6829 - 20.2354i) q^{15} +(30.0282 - 52.0103i) q^{16} +(48.4786 + 83.9674i) q^{17} -25.8741 q^{18} +(45.6604 + 79.0861i) q^{19} +(1.29823 + 2.24859i) q^{20} +28.8477 q^{21} +(15.0966 + 26.1481i) q^{22} +(-2.46326 + 4.26649i) q^{23} +(-48.7065 + 84.3621i) q^{24} -93.9329 q^{25} +(0.203750 + 128.657i) q^{26} +152.703 q^{27} +(-1.60281 + 2.77615i) q^{28} +(-60.3491 + 104.528i) q^{29} +(32.0677 + 55.5429i) q^{30} +62.6271 q^{31} +(-10.5269 - 18.2331i) q^{32} +(-23.0564 - 39.9349i) q^{33} -266.132 q^{34} +(19.1780 + 33.2172i) q^{35} +(-2.19557 + 3.80284i) q^{36} +(-29.9707 + 51.9107i) q^{37} -250.661 q^{38} +(-0.311179 - 196.492i) q^{39} -129.520 q^{40} +(27.4478 - 47.5409i) q^{41} +(-39.5913 + 68.5741i) q^{42} +(209.483 + 362.835i) q^{43} +5.12415 q^{44} +(26.2705 + 45.5019i) q^{45} +(-6.76126 - 11.7108i) q^{46} -158.651 q^{47} +(-125.881 - 218.031i) q^{48} +(147.823 - 256.036i) q^{49} +(128.916 - 223.288i) q^{50} +406.453 q^{51} +(18.9266 + 10.8873i) q^{52} +89.8532 q^{53} +(-209.572 + 362.990i) q^{54} +(30.6558 - 53.0975i) q^{55} +(-79.9539 - 138.484i) q^{56} +382.824 q^{57} +(-165.649 - 286.912i) q^{58} +(-329.022 - 569.883i) q^{59} +10.8845 q^{60} +(-219.842 - 380.777i) q^{61} +(-85.9507 + 148.871i) q^{62} +(-32.4340 + 56.1773i) q^{63} +538.240 q^{64} +(226.047 - 130.986i) q^{65} +126.573 q^{66} +(525.901 - 910.888i) q^{67} +(-22.5829 + 39.1147i) q^{68} +(10.3262 + 17.8855i) q^{69} -105.281 q^{70} +(-538.772 - 933.181i) q^{71} +(-109.523 - 189.700i) q^{72} -338.912 q^{73} +(-82.2648 - 142.487i) q^{74} +(-196.887 + 341.019i) q^{75} +(-21.2701 + 36.8409i) q^{76} +75.6963 q^{77} +(467.508 + 268.930i) q^{78} +664.285 q^{79} +(167.371 - 289.895i) q^{80} +(192.814 - 333.963i) q^{81} +(75.3398 + 130.492i) q^{82} -1011.19 q^{83} +(6.71910 + 11.6378i) q^{84} +(270.210 + 468.017i) q^{85} -1150.00 q^{86} +(252.988 + 438.189i) q^{87} +(-127.806 + 221.366i) q^{88} +(118.901 - 205.942i) q^{89} -144.217 q^{90} +(279.592 + 160.832i) q^{91} -2.29493 q^{92} +(131.269 - 227.364i) q^{93} +(217.736 - 377.130i) q^{94} +(254.501 + 440.809i) q^{95} -88.2593 q^{96} +(75.0273 + 129.951i) q^{97} +(405.750 + 702.779i) q^{98} +103.691 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 4 q^{2} + 6 q^{3} - 78 q^{4} + 32 q^{5} - 14 q^{6} + 6 q^{7} + 126 q^{8} - 135 q^{9} - 2 q^{10} + 187 q^{11} - 190 q^{12} - 60 q^{13} - 120 q^{14} + 28 q^{15} - 350 q^{16} - 118 q^{17} + 956 q^{18}+ \cdots - 2970 q^{99}+O(q^{100}) \) 34 * q - 4 * q^2 + 6 * q^3 - 78 * q^4 + 32 * q^5 - 14 * q^6 + 6 * q^7 + 126 * q^8 - 135 * q^9 - 2 * q^10 + 187 * q^11 - 190 * q^12 - 60 * q^13 - 120 * q^14 + 28 * q^15 - 350 * q^16 - 118 * q^17 + 956 * q^18 - 403 * q^19 - 98 * q^20 + 440 * q^21 + 44 * q^22 + 215 * q^23 - 26 * q^24 + 638 * q^25 - 989 * q^26 - 768 * q^27 + 396 * q^28 + 7 * q^29 + 1269 * q^30 + 1364 * q^31 - 813 * q^32 - 66 * q^33 + 1476 * q^34 - 10 * q^35 - 560 * q^36 - 1084 * q^37 + 820 * q^38 - 370 * q^39 + 190 * q^40 - 240 * q^41 - 393 * q^42 + 435 * q^43 - 1716 * q^44 - 1242 * q^45 - 1671 * q^46 + 1098 * q^47 - 894 * q^48 - 403 * q^49 + 651 * q^50 + 3104 * q^51 - 876 * q^52 - 1132 * q^53 - 311 * q^54 + 176 * q^55 + 1925 * q^56 - 1068 * q^57 - 618 * q^58 - 2010 * q^59 - 822 * q^60 - 460 * q^61 + 823 * q^62 - 820 * q^63 + 6342 * q^64 + 3070 * q^65 - 308 * q^66 + 232 * q^67 - 1795 * q^68 + 1608 * q^69 + 414 * q^70 - 489 * q^71 - 2556 * q^72 + 580 * q^73 - 2653 * q^74 + 2852 * q^75 - 2421 * q^76 + 132 * q^77 - 4760 * q^78 - 1464 * q^79 - 4915 * q^80 - 2393 * q^81 + 1772 * q^82 - 234 * q^83 - 4161 * q^84 - 4858 * q^85 + 2068 * q^86 - 3032 * q^87 + 693 * q^88 - 4113 * q^89 + 30290 * q^90 + 1096 * q^91 - 7108 * q^92 - 802 * q^93 - 2325 * q^94 + 3924 * q^95 + 5202 * q^96 - 2793 * q^97 - 533 * q^98 - 2970 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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